LMFDB - Embedded newform 220.2.r.a.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	220.151
Dual form			220.2.r.a.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395472 + 1.35779i) q^{2} +(-0.639886 + 0.207912i) q^{3} +(-1.68720 + 1.07394i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.535358 - 0.786610i) q^{6} +(-0.513506 + 1.58041i) q^{7} +(-2.12543 - 1.86616i) q^{8} +(-2.06082 + 1.49728i) q^{9} +(-0.478148 + 1.33093i) q^{10} +(0.384301 + 3.29428i) q^{11} +(0.856335 - 1.03799i) q^{12} +(-0.182636 - 0.251377i) q^{13} +(-2.34894 - 0.0722281i) q^{14} +(-0.639886 - 0.207912i) q^{15} +(1.69332 - 3.62390i) q^{16} +(0.867017 - 1.19335i) q^{17} +(-2.84799 - 2.20604i) q^{18} +(0.342040 + 1.05269i) q^{19} +(-1.99622 - 0.122881i) q^{20} -1.11805i q^{21} +(-4.32098 + 1.82460i) q^{22} -1.98524i q^{23} +(1.74803 + 0.752232i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.269091 - 0.347395i) q^{26} +(2.19381 - 3.01952i) q^{27} +(-0.830869 - 3.21794i) q^{28} +(2.12543 + 0.690593i) q^{29} +(0.0292442 - 0.951057i) q^{30} +(6.00217 + 8.26128i) q^{31} +(5.59017 + 0.866025i) q^{32} +(-0.930829 - 2.02807i) q^{33} +(1.96320 + 0.705295i) q^{34} +(-1.34437 + 0.976746i) q^{35} +(1.86905 - 4.73941i) q^{36} +(1.52642 - 4.69784i) q^{37} +(-1.29407 + 0.880728i) q^{38} +(0.169131 + 0.122881i) q^{39} +(-0.622602 - 2.75905i) q^{40} +(4.42987 - 1.43935i) q^{41} +(1.51807 - 0.442155i) q^{42} +3.30211 q^{43} +(-4.18625 - 5.14542i) q^{44} -2.54732 q^{45} +(2.69555 - 0.785108i) q^{46} +(4.65701 - 1.51315i) q^{47} +(-0.330079 + 2.67095i) q^{48} +(3.42912 + 2.49140i) q^{49} +(-1.16913 + 0.795697i) q^{50} +(-0.306682 + 0.943869i) q^{51} +(0.578108 + 0.227985i) q^{52} +(-9.05609 + 6.57963i) q^{53} +(4.96747 + 1.78460i) q^{54} +(-1.62543 + 2.89102i) q^{55} +(4.04072 - 2.40075i) q^{56} +(-0.437733 - 0.602488i) q^{57} +(-0.0971366 + 3.15900i) q^{58} +(-3.61728 - 1.17533i) q^{59} +(1.30290 - 0.336408i) q^{60} +(3.54082 - 4.87352i) q^{61} +(-8.84342 + 11.4168i) q^{62} +(-1.30806 - 4.02580i) q^{63} +(1.03487 + 7.93278i) q^{64} -0.310719i q^{65} +(2.38558 - 2.06592i) q^{66} -8.88598i q^{67} +(-0.181256 + 2.94454i) q^{68} +(0.412756 + 1.27033i) q^{69} +(-1.85788 - 1.43911i) q^{70} +(-6.56322 + 9.03350i) q^{71} +(7.17429 + 0.663484i) q^{72} +(4.94844 + 1.60784i) q^{73} +(6.98235 + 0.214702i) q^{74} +(-0.395472 - 0.544320i) q^{75} +(-1.70761 - 1.40877i) q^{76} +(-5.40365 - 1.08428i) q^{77} +(-0.0999601 + 0.278240i) q^{78} +(9.33304 - 6.78085i) q^{79} +(3.50000 - 1.93649i) q^{80} +(1.58550 - 4.87967i) q^{81} +(3.70623 + 5.44563i) q^{82} +(-13.8102 - 10.0337i) q^{83} +(1.20071 + 1.88637i) q^{84} +(1.40286 - 0.455818i) q^{85} +(1.30589 + 4.48359i) q^{86} -1.50361 q^{87} +(5.33087 - 7.71893i) q^{88} -10.7378 q^{89} +(-1.00739 - 3.45873i) q^{90} +(0.491063 - 0.159556i) q^{91} +(2.13203 + 3.34951i) q^{92} +(-5.55832 - 4.03836i) q^{93} +(3.89626 + 5.72484i) q^{94} +(-0.342040 + 1.05269i) q^{95} +(-3.75713 + 0.608104i) q^{96} +(-8.32486 + 6.04836i) q^{97} +(-2.02669 + 5.64131i) q^{98} +(-5.72443 - 6.21354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.395472	+	1.35779i	0.279641	+	0.960105i
$2$	0.395472	+	1.35779i	0.279641	+	0.960105i
$3$	−0.639886	+	0.207912i	−0.369439	+	0.120038i	−0.487852	−	0.872927i	$-0.662219\pi$
$3$	−0.639886	+	0.207912i	−0.369439	+	0.120038i	0.118413	+	0.992964i	$0.462219\pi$
$4$	−1.68720	+	1.07394i	−0.843602	+	0.536969i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−0.535358	−	0.786610i	−0.218559	−	0.321132i
$7$	−0.513506	+	1.58041i	−0.194087	+	0.597338i	0.805899	+	0.592053i	$0.201682\pi$
$7$	−0.513506	+	1.58041i	−0.194087	+	0.597338i	−0.999986	+	0.00528511i	$0.998318\pi$
$8$	−2.12543	−	1.86616i	−0.751452	−	0.659788i
$9$	−2.06082	+	1.49728i	−0.686941	+	0.499092i
$10$	−0.478148	+	1.33093i	−0.151204	+	0.420877i
$11$	0.384301	+	3.29428i	0.115871	+	0.993264i
$11$	0.384301	+	3.29428i	0.115871	+	0.993264i
$12$	0.856335	−	1.03799i	0.247203	−	0.299641i
$13$	−0.182636	−	0.251377i	−0.0506541	−	0.0697195i	0.782939	−	0.622099i	$-0.213720\pi$
$13$	−0.182636	−	0.251377i	−0.0506541	−	0.0697195i	−0.833593	+	0.552380i	$0.813720\pi$
$14$	−2.34894	−	0.0722281i	−0.627782	−	0.0193038i
$15$	−0.639886	−	0.207912i	−0.165218	−	0.0536826i
$16$	1.69332	−	3.62390i	0.423330	−	0.905976i
$17$	0.867017	−	1.19335i	0.210283	−	0.289429i	−0.690827	−	0.723020i	$-0.742754\pi$
$17$	0.867017	−	1.19335i	0.210283	−	0.289429i	0.901110	+	0.433591i	$0.142754\pi$
$18$	−2.84799	−	2.20604i	−0.671277	−	0.519969i
$19$	0.342040	+	1.05269i	0.0784693	+	0.241504i	0.982594	−	0.185764i	$-0.0594761\pi$
$19$	0.342040	+	1.05269i	0.0784693	+	0.241504i	−0.904125	+	0.427268i	$0.859476\pi$
$20$	−1.99622	−	0.122881i	−0.446369	−	0.0274769i
$21$		−	1.11805i		−	0.243977i
$22$	−4.32098	+	1.82460i	−0.921235	+	0.389005i
$23$		−	1.98524i		−	0.413952i	−0.978346	−	0.206976i	$-0.933638\pi$
$23$		−	1.98524i		−	0.413952i	0.978346	−	0.206976i	$-0.0663622\pi$
$24$	1.74803	+	0.752232i	0.356815	+	0.153549i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.269091	−	0.347395i	0.0527730	−	0.0681297i
$27$	2.19381	−	3.01952i	0.422198	−	0.581106i
$28$	−0.830869	−	3.21794i	−0.157020	−	0.608134i
$29$	2.12543	+	0.690593i	0.394682	+	0.128240i	0.499632	−	0.866238i	$-0.333468\pi$
$29$	2.12543	+	0.690593i	0.394682	+	0.128240i	−0.104951	+	0.994477i	$0.533468\pi$
$30$	0.0292442	−	0.951057i	0.00533924	−	0.173638i
$31$	6.00217	+	8.26128i	1.07802	+	1.48377i	0.861680	+	0.507452i	$0.169412\pi$
$31$	6.00217	+	8.26128i	1.07802	+	1.48377i	0.216341	+	0.976318i	$0.430588\pi$
$32$	5.59017	+	0.866025i	0.988212	+	0.153093i
$33$	−0.930829	−	2.02807i	−0.162037	−	0.353041i
$34$	1.96320	+	0.705295i	0.336686	+	0.120957i
$35$	−1.34437	+	0.976746i	−0.227241	+	0.165100i
$36$	1.86905	−	4.73941i	0.311508	−	0.789901i
$37$	1.52642	−	4.69784i	0.250942	−	0.772320i	−0.743660	−	0.668558i	$-0.766912\pi$
$37$	1.52642	−	4.69784i	0.250942	−	0.772320i	0.994602	−	0.103762i	$-0.0330881\pi$
$38$	−1.29407	+	0.880728i	−0.209926	+	0.142873i
$39$	0.169131	+	0.122881i	0.0270826	+	0.0196766i
$40$	−0.622602	−	2.75905i	−0.0984421	−	0.436244i
$41$	4.42987	−	1.43935i	0.691830	−	0.224789i	0.0580628	−	0.998313i	$-0.481508\pi$
$41$	4.42987	−	1.43935i	0.691830	−	0.224789i	0.633767	+	0.773524i	$0.281508\pi$
$42$	1.51807	−	0.442155i	0.234244	−	0.0682260i
$43$	3.30211			0.503568			0.251784	−	0.967784i	$-0.418983\pi$
$43$	3.30211			0.503568			0.251784	+	0.967784i	$0.418983\pi$
$44$	−4.18625	−	5.14542i	−0.631101	−	0.775701i
$45$	−2.54732			−0.379732
$46$	2.69555	−	0.785108i	0.397437	−	0.115758i
$47$	4.65701	−	1.51315i	0.679294	−	0.220716i	0.0510078	−	0.998698i	$-0.483757\pi$
$47$	4.65701	−	1.51315i	0.679294	−	0.220716i	0.628286	+	0.777982i	$0.283757\pi$
$48$	−0.330079	+	2.67095i	−0.0476429	+	0.385518i
$49$	3.42912	+	2.49140i	0.489874	+	0.355914i
$50$	−1.16913	+	0.795697i	−0.165340	+	0.112529i
$51$	−0.306682	+	0.943869i	−0.0429440	+	0.132168i
$52$	0.578108	+	0.227985i	0.0801691	+	0.0316158i
$53$	−9.05609	+	6.57963i	−1.24395	+	0.903782i	−0.997855	−	0.0654635i	$-0.979147\pi$
$53$	−9.05609	+	6.57963i	−1.24395	+	0.903782i	−0.246095	+	0.969246i	$0.579147\pi$
$54$	4.96747	+	1.78460i	0.675986	+	0.242854i
$55$	−1.62543	+	2.89102i	−0.219172	+	0.389825i
$56$	4.04072	−	2.40075i	0.539963	−	0.320814i
$57$	−0.437733	−	0.602488i	−0.0579792	−	0.0798015i
$58$	−0.0971366	+	3.15900i	−0.0127547	+	0.414797i
$59$	−3.61728	−	1.17533i	−0.470930	−	0.153014i	0.0639315	−	0.997954i	$-0.479636\pi$
$59$	−3.61728	−	1.17533i	−0.470930	−	0.153014i	−0.534861	+	0.844940i	$0.679636\pi$
$60$	1.30290	−	0.336408i	0.168204	−	0.0434301i
$61$	3.54082	−	4.87352i	0.453355	−	0.623990i	−0.519759	−	0.854313i	$-0.673978\pi$
$61$	3.54082	−	4.87352i	0.453355	−	0.623990i	0.973114	+	0.230323i	$0.0739782\pi$
$62$	−8.84342	+	11.4168i	−1.12312	+	1.44994i
$63$	−1.30806	−	4.02580i	−0.164800	−	0.507203i
$64$	1.03487	+	7.93278i	0.129359	+	0.991598i
$65$		−	0.310719i		−	0.0385400i
$66$	2.38558	−	2.06592i	0.293645	−	0.254297i
$67$		−	8.88598i		−	1.08560i	−0.839863	−	0.542798i	$-0.817365\pi$
$67$		−	8.88598i		−	1.08560i	0.839863	−	0.542798i	$-0.182635\pi$
$68$	−0.181256	+	2.94454i	−0.0219805	+	0.357078i
$69$	0.412756	+	1.27033i	0.0496899	+	0.152930i
$70$	−1.85788	−	1.43911i	−0.222059	−	0.172006i
$71$	−6.56322	+	9.03350i	−0.778911	+	1.07208i	0.216490	+	0.976285i	$0.430539\pi$
$71$	−6.56322	+	9.03350i	−0.778911	+	1.07208i	−0.995401	+	0.0957944i	$0.969461\pi$
$72$	7.17429	+	0.663484i	0.845498	+	0.0781924i
$73$	4.94844	+	1.60784i	0.579171	+	0.188184i	0.583929	−	0.811805i	$-0.301515\pi$
$73$	4.94844	+	1.60784i	0.579171	+	0.188184i	−0.00475834	+	0.999989i	$0.501515\pi$
$74$	6.98235	+	0.214702i	0.811682	+	0.0249586i
$75$	−0.395472	−	0.544320i	−0.0456651	−	0.0628526i
$76$	−1.70761	−	1.40877i	−0.195877	−	0.161597i
$77$	−5.40365	−	1.08428i	−0.615803	−	0.123565i
$78$	−0.0999601	+	0.278240i	−0.0113182	+	0.0315045i
$79$	9.33304	−	6.78085i	1.05005	−	0.762905i	0.0778272	−	0.996967i	$-0.475202\pi$
$79$	9.33304	−	6.78085i	1.05005	−	0.762905i	0.972222	+	0.234062i	$0.0752018\pi$
$80$	3.50000	−	1.93649i	0.391312	−	0.216506i
$81$	1.58550	−	4.87967i	0.176167	−	0.542185i
$82$	3.70623	+	5.44563i	0.409285	+	0.601369i
$83$	−13.8102	−	10.0337i	−1.51587	−	1.10134i	−0.963488	−	0.267753i	$-0.913719\pi$
$83$	−13.8102	−	10.0337i	−1.51587	−	1.10134i	−0.552382	−	0.833591i	$-0.686281\pi$
$84$	1.20071	+	1.88637i	0.131008	+	0.205820i
$85$	1.40286	−	0.455818i	0.152162	−	0.0494404i
$86$	1.30589	+	4.48359i	0.140818	+	0.483478i
$87$	−1.50361			−0.161204
$88$	5.33087	−	7.71893i	0.568273	−	0.822840i
$89$	−10.7378			−1.13820			−0.569101	−	0.822268i	$-0.692709\pi$
$89$	−10.7378			−1.13820			−0.569101	+	0.822268i	$0.692709\pi$
$90$	−1.00739	−	3.45873i	−0.106188	−	0.364582i
$91$	0.491063	−	0.159556i	0.0514774	−	0.0167260i
$92$	2.13203	+	3.34951i	0.222279	+	0.349211i
$93$	−5.55832	−	4.03836i	−0.576371	−	0.418758i
$94$	3.89626	+	5.72484i	0.401869	+	0.590472i
$95$	−0.342040	+	1.05269i	−0.0350925	+	0.108004i
$96$	−3.75713	+	0.608104i	−0.383461	+	0.0620643i
$97$	−8.32486	+	6.04836i	−0.845261	+	0.614118i	−0.923835	−	0.382790i	$-0.874963\pi$
$97$	−8.32486	+	6.04836i	−0.845261	+	0.614118i	0.0785741	+	0.996908i	$0.474963\pi$
$98$	−2.02669	+	5.64131i	−0.204726	+	0.569859i
$99$	−5.72443	−	6.21354i	−0.575327	−	0.624484i
$100$	−1.54275	−	1.27276i	−0.154275	−	0.127276i
$101$	11.0887	+	15.2624i	1.10337	+	1.51866i	0.830838	+	0.556515i	$0.187862\pi$
$101$	11.0887	+	15.2624i	1.10337	+	1.51866i	0.272534	+	0.962146i	$0.412138\pi$
$102$	−1.40286	−	0.0431369i	−0.138904	−	0.00427119i
$103$	0.656415	+	0.213282i	0.0646785	+	0.0210153i	0.341178	−	0.939999i	$-0.389174\pi$
$103$	0.656415	+	0.213282i	0.0646785	+	0.0210153i	−0.276499	+	0.961014i	$0.589174\pi$
$104$	−0.0809311	+	0.875112i	−0.00793595	+	0.0858118i
$105$	0.657170	−	0.904517i	0.0641333	−	0.0882719i
$106$	−12.5152	−	9.69424i	−1.21558	−	0.941588i
$107$	−5.60309	−	17.2445i	−0.541671	−	1.66709i	−0.728777	−	0.684751i	$-0.759911\pi$
$107$	−5.60309	−	17.2445i	−0.541671	−	1.66709i	0.187106	−	0.982340i	$-0.440089\pi$
$108$	−0.458630	+	7.45055i	−0.0441317	+	0.716930i
$109$		−	16.5020i		−	1.58061i	−0.612715	−	0.790304i	$-0.709923\pi$
$109$		−	16.5020i		−	1.58061i	0.612715	−	0.790304i	$-0.290077\pi$
$110$	−4.56822	−	1.06368i	−0.435562	−	0.101418i
$111$			3.32344i			0.315447i
$112$	4.85772	+	4.53703i	0.459011	+	0.428709i
$113$	3.79088	+	11.6671i	0.356616	+	1.09755i	0.955067	+	0.296391i	$0.0957833\pi$
$113$	3.79088	+	11.6671i	0.356616	+	1.09755i	−0.598451	+	0.801160i	$0.704217\pi$
$114$	0.644943	−	0.832618i	0.0604044	−	0.0779818i
$115$	1.16690	−	1.60610i	0.108814	−	0.149769i
$116$	−4.32768	+	1.11740i	−0.401815	+	0.103748i
$117$	0.752762	+	0.244587i	0.0695928	+	0.0226121i
$118$	0.165318	−	5.37632i	0.0152187	−	0.494931i
$119$	1.44076	+	1.98303i	0.132074	+	0.181784i
$120$	0.972034	+	1.63603i	0.0887341	+	0.149349i
$121$	−10.7046	+	2.53200i	−0.973148	+	0.230181i
$122$	8.01752	+	2.88036i	0.725872	+	0.260776i
$123$	−2.53536	+	1.84205i	−0.228606	+	0.166092i
$124$	−18.9990	−	7.49251i	−1.70616	−	0.672848i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	4.94890	−	3.36817i	0.440883	−	0.300060i
$127$	4.39547	+	3.19350i	0.390035	+	0.283377i	0.765470	−	0.643472i	$-0.222507\pi$
$127$	4.39547	+	3.19350i	0.390035	+	0.283377i	−0.375435	+	0.926849i	$0.622507\pi$
$128$	−10.3618	+	4.54233i	−0.915864	+	0.401489i
$129$	−2.11298	+	0.686548i	−0.186037	+	0.0604472i
$130$	0.421892	−	0.122881i	0.0370024	−	0.0107773i
$131$	−15.8761			−1.38710			−0.693551	−	0.720407i	$-0.743955\pi$
$131$	−15.8761			−1.38710			−0.693551	+	0.720407i	$0.743955\pi$
$132$	3.74852	+	2.42211i	0.326266	+	0.210818i
$133$	−1.83932			−0.159489
$134$	12.0653	−	3.51415i	1.04229	−	0.303577i
$135$	3.54965	−	1.15335i	0.305506	−	0.0992648i
$136$	−4.06976	+	0.918375i	−0.348979	+	0.0787500i
$137$	1.97155	+	1.43241i	0.168441	+	0.122379i	0.668812	−	0.743432i	$-0.266803\pi$
$137$	1.97155	+	1.43241i	0.168441	+	0.122379i	−0.500371	+	0.865811i	$0.666803\pi$
$138$	−1.56161	+	1.06282i	−0.132933	+	0.0904729i
$139$	3.27240	−	10.0714i	0.277562	−	0.854247i	−0.710969	−	0.703224i	$-0.751743\pi$
$139$	3.27240	−	10.0714i	0.277562	−	0.854247i	0.988530	−	0.151023i	$-0.0482567\pi$
$140$	1.21927	−	3.09174i	0.103047	−	0.261300i
$141$	−2.66535	+	1.93649i	−0.224463	+	0.163082i
$142$	−14.8612	−	5.33901i	−1.24712	−	0.448039i
$143$	0.757920	−	0.698260i	0.0633805	−	0.0583914i
$144$	1.93635	+	10.0036i	0.161363	+	0.833632i
$145$	1.31359	+	1.80800i	0.109087	+	0.150146i
$146$	−0.226154	+	7.35481i	−0.0187167	+	0.608688i
$147$	−2.71224	−	0.881260i	−0.223702	−	0.0726851i
$148$	2.46980	+	9.56550i	0.203016	+	0.786279i
$149$	−1.22821	+	1.69049i	−0.100619	+	0.138490i	−0.856358	−	0.516383i	$-0.827278\pi$
$149$	−1.22821	+	1.69049i	−0.100619	+	0.138490i	0.755739	+	0.654873i	$0.227278\pi$
$150$	0.582676	−	0.752232i	0.0475753	−	0.0614195i
$151$	3.50536	+	10.7884i	0.285262	+	0.877946i	0.986320	+	0.164842i	$0.0527114\pi$
$151$	3.50536	+	10.7884i	0.285262	+	0.877946i	−0.701058	+	0.713104i	$0.747289\pi$
$152$	1.23751	−	2.87572i	0.100375	−	0.233251i
$153$			3.75744i			0.303771i
$154$	−0.664762	−	7.76585i	−0.0535680	−	0.625790i
$155$			10.2115i			0.820208i
$156$	−0.417324	−	0.0256890i	−0.0334127	−	0.00205677i
$157$	4.86517	+	14.9735i	0.388283	+	1.19501i	0.934071	+	0.357088i	$0.116230\pi$
$157$	4.86517	+	14.9735i	0.388283	+	1.19501i	−0.545788	+	0.837923i	$0.683770\pi$
$158$	12.8979	+	9.99070i	1.02611	+	0.794818i
$159$	4.42689	−	6.09309i	0.351075	−	0.483213i
$160$	4.01351	+	3.98645i	0.317295	+	0.315156i
$161$	3.13750	+	1.01943i	0.247269	+	0.0803427i
$162$	7.25260	+	0.223011i	0.569818	+	0.0175214i
$163$	9.01034	+	12.4017i	0.705744	+	0.971374i	0.999878	+	0.0156093i	$0.00496881\pi$
$163$	9.01034	+	12.4017i	0.705744	+	0.971374i	−0.294134	+	0.955764i	$0.595031\pi$
$164$	−5.92833	+	7.18589i	−0.462925	+	0.561124i
$165$	0.439011	−	2.18787i	0.0341770	−	0.170325i
$166$	8.16216	−	22.7195i	0.633507	−	1.76337i
$167$	0.114153	−	0.0829373i	0.00883346	−	0.00641788i	−0.583360	−	0.812214i	$-0.698262\pi$
$167$	0.114153	−	0.0829373i	0.00883346	−	0.00641788i	0.592193	+	0.805796i	$0.298262\pi$
$168$	−2.08645	+	2.37632i	−0.160973	+	0.183337i
$169$	3.98739	−	12.2719i	0.306722	−	0.943993i
$170$	1.17370	+	1.72454i	0.0900186	+	0.132266i
$171$	−2.28105	−	1.65728i	−0.174436	−	0.126735i
$172$	−5.57134	+	3.54626i	−0.424811	+	0.270400i
$173$	10.0174	−	3.25486i	0.761612	−	0.247463i	0.0976417	−	0.995222i	$-0.468870\pi$
$173$	10.0174	−	3.25486i	0.761612	−	0.247463i	0.663970	+	0.747759i	$0.268870\pi$
$174$	−0.594636	−	2.04160i	−0.0450793	−	0.154773i
$175$	−1.66174			−0.125616
$176$	12.5889	+	4.18560i	0.948925	+	0.315502i
$177$	2.55901			0.192347
$178$	−4.24648	−	14.5797i	−0.318287	−	1.09279i
$179$	−4.50894	+	1.46504i	−0.337014	+	0.109502i	−0.472635	−	0.881258i	$-0.656697\pi$
$179$	−4.50894	+	1.46504i	−0.337014	+	0.109502i	0.135621	+	0.990761i	$0.456697\pi$
$180$	4.29785	−	2.73566i	0.320343	−	0.203904i
$181$	−6.42626	−	4.66895i	−0.477660	−	0.347040i	0.322759	−	0.946481i	$-0.395390\pi$
$181$	−6.42626	−	4.66895i	−0.477660	−	0.347040i	−0.800419	+	0.599441i	$0.795390\pi$
$182$	0.410845	+	0.603662i	0.0304539	+	0.0447464i
$183$	−1.25246	+	3.85468i	−0.0925845	+	0.284946i
$184$	−3.70479	+	4.21949i	−0.273121	+	0.311065i
$185$	3.99622	−	2.90342i	0.293808	−	0.213464i
$186$	3.28510	−	9.14411i	0.240875	−	0.670479i
$187$	4.26442	+	2.39760i	0.311845	+	0.175330i
$188$	−6.23229	+	7.55433i	−0.454536	+	0.550956i
$189$	3.64553	+	5.01765i	0.265174	+	0.364980i
$190$	−1.56460	−	0.0481102i	−0.113508	−	0.00349028i
$191$	8.18799	+	2.66044i	0.592462	+	0.192503i	0.589876	−	0.807494i	$-0.299177\pi$
$191$	8.18799	+	2.66044i	0.592462	+	0.192503i	0.00258660	+	0.999997i	$0.499177\pi$
$192$	−2.31152	−	4.86092i	−0.166819	−	0.350807i
$193$	12.7024	−	17.4833i	0.914338	−	1.25848i	−0.0513252	−	0.998682i	$-0.516344\pi$
$193$	12.7024	−	17.4833i	0.914338	−	1.25848i	0.965663	−	0.259797i	$-0.0836555\pi$
$194$	−11.5047	−	8.91148i	−0.825987	−	0.639807i
$195$	0.0646021	+	0.198825i	0.00462626	+	0.0142382i
$196$	−8.46123	−	0.520845i	−0.604374	−	0.0372032i
$197$		−	18.9681i		−	1.35142i	−0.737168	−	0.675709i	$-0.763838\pi$
$197$		−	18.9681i		−	1.35142i	0.737168	−	0.675709i	$-0.236162\pi$
$198$	6.17285	−	10.2299i	0.438685	−	0.727005i
$199$			14.9984i			1.06321i	0.846994	+	0.531603i	$0.178410\pi$
$199$			14.9984i			1.06321i	−0.846994	+	0.531603i	$0.821590\pi$
$200$	1.11803	−	2.59808i	0.0790569	−	0.183712i
$201$	1.84750	+	5.68602i	0.130313	+	0.401061i
$202$	−16.3378	+	21.0921i	−1.14953	+	1.48403i
$203$	−2.18284	+	3.00442i	−0.153205	+	0.210869i
$204$	−0.496222	−	1.92186i	−0.0347425	−	0.134557i
$205$	4.42987	+	1.43935i	0.309396	+	0.100529i
$206$	−0.0299996	+	0.975623i	−0.00209017	+	0.0679749i
$207$	2.97246	+	4.09124i	0.206600	+	0.284361i
$208$	−1.22023	+	0.236194i	−0.0846075	+	0.0163771i
$209$	−3.33641	+	1.53133i	−0.230785	+	0.105924i
$210$	1.48804	+	0.534591i	0.102685	+	0.0368903i
$211$	5.86501	−	4.26118i	0.403764	−	0.293351i	−0.367309	−	0.930099i	$-0.619721\pi$
$211$	5.86501	−	4.26118i	0.403764	−	0.293351i	0.771072	+	0.636748i	$0.219721\pi$
$212$	8.21336	−	20.8269i	0.564096	−	1.43039i
$213$	2.32155	−	7.14498i	0.159070	−	0.489566i
$214$	21.1986	−	14.4275i	1.44911	−	0.986247i
$215$	2.67147	+	1.94093i	0.182192	+	0.132371i
$216$	−10.2977	+	2.32376i	−0.700668	+	0.158112i
$217$	−16.1383	+	5.24366i	−1.09554	+	0.355963i
$218$	22.4064	−	6.52609i	1.51755	−	0.442002i
$219$	−3.50073			−0.236557
$220$	−0.362347	−	6.62335i	−0.0244294	−	0.446546i
$221$	−0.458329			−0.0308305
$222$	−4.51255	+	1.31433i	−0.302863	+	0.0882119i
$223$	24.9409	−	8.10377i	1.67016	−	0.542669i	0.687199	−	0.726469i	$-0.258840\pi$
$223$	24.9409	−	8.10377i	1.67016	−	0.542669i	0.982964	+	0.183800i	$0.0588399\pi$
$224$	−4.23926	+	8.39004i	−0.283247	+	0.560583i
$225$	−2.06082	−	1.49728i	−0.137388	−	0.0998184i
$226$	−14.3424	+	9.76125i	−0.954040	+	0.649309i
$227$	0.464744	−	1.43034i	0.0308462	−	0.0949347i	−0.934448	−	0.356099i	$-0.884107\pi$
$227$	0.464744	−	1.43034i	0.0308462	−	0.0949347i	0.965294	+	0.261165i	$0.0841065\pi$
$228$	1.38558	+	0.546423i	0.0917622	+	0.0361877i
$229$	−5.33554	+	3.87650i	−0.352582	+	0.256166i	−0.749952	−	0.661493i	$-0.769923\pi$
$229$	−5.33554	+	3.87650i	−0.352582	+	0.256166i	0.397369	+	0.917659i	$0.369923\pi$
$230$	2.64222	+	0.949240i	0.174223	+	0.0625910i
$231$	3.68316	−	0.429666i	0.242334	−	0.0282700i
$232$	−3.22868	−	5.43420i	−0.211973	−	0.356772i
$233$	−10.8778	−	14.9720i	−0.712626	−	0.980845i	−0.999737	−	0.0229478i	$-0.992695\pi$
$233$	−10.8778	−	14.9720i	−0.712626	−	0.980845i	0.287111	−	0.957897i	$-0.407305\pi$
$234$	−0.0344029	+	1.11882i	−0.00224899	+	0.0731397i
$235$	4.65701	+	1.51315i	0.303790	+	0.0987072i
$236$	7.36531	−	1.90172i	0.479441	−	0.123791i
$237$	−4.56227	+	6.27942i	−0.296351	+	0.407892i
$238$	−2.12277	+	2.74048i	−0.137599	+	0.177639i
$239$	5.32504	+	16.3888i	0.344448	+	1.06010i	0.961878	+	0.273478i	$0.0881739\pi$
$239$	5.32504	+	16.3888i	0.344448	+	1.06010i	−0.617430	+	0.786626i	$0.711826\pi$
$240$	−1.83698	+	1.96683i	−0.118577	+	0.126958i
$241$		−	10.1759i		−	0.655490i	−0.944766	−	0.327745i	$-0.893711\pi$
$241$		−	10.1759i		−	0.655490i	0.944766	−	0.327745i	$-0.106289\pi$
$242$	−7.67130	−	13.5333i	−0.493130	−	0.869956i
$243$			14.6491i			0.939737i
$244$	−0.740233	+	12.0252i	−0.0473885	+	0.769837i
$245$	1.30981	+	4.03117i	0.0836805	+	0.257542i
$246$	−3.50378	−	2.71402i	−0.223393	−	0.173039i
$247$	0.202153	−	0.278240i	0.0128627	−	0.0177040i
$248$	2.65973	−	28.7598i	0.168893	−	1.82625i
$249$	10.9231	+	3.54913i	0.692224	+	0.224917i
$250$	−1.41355	−	0.0434654i	−0.0894005	−	0.00274899i
$251$	−9.19424	−	12.6548i	−0.580336	−	0.798763i	0.413397	−	0.910551i	$-0.364342\pi$
$251$	−9.19424	−	12.6548i	−0.580336	−	0.798763i	−0.993732	+	0.111788i	$0.964342\pi$
$252$	6.53042	+	5.38757i	0.411378	+	0.339385i
$253$	6.53996	−	0.762932i	0.411164	−	0.0479651i
$254$	−2.59782	+	7.23108i	−0.163002	+	0.453718i
$255$	−0.802903	+	0.583343i	−0.0502798	+	0.0365304i
$256$	−10.2653	−	12.2728i	−0.641584	−	0.767053i
$257$	4.47496	−	13.7725i	0.279140	−	0.859105i	−0.708954	−	0.705255i	$-0.750833\pi$
$257$	4.47496	−	13.7725i	0.279140	−	0.859105i	0.988094	−	0.153851i	$-0.0491674\pi$
$258$	−1.76781	−	2.59748i	−0.110059	−	0.161712i
$259$	6.64068	+	4.82473i	0.412632	+	0.299794i
$260$	0.333693	+	0.524247i	0.0206948	+	0.0325124i
$261$	−5.41414	+	1.75916i	−0.335127	+	0.108889i
$262$	−6.27855	−	21.5565i	−0.387890	−	1.33176i
$263$	16.8446			1.03868			0.519341	−	0.854567i	$-0.326177\pi$
$263$	16.8446			1.03868			0.519341	+	0.854567i	$0.326177\pi$
$264$	−1.80630	+	6.04759i	−0.111170	+	0.372203i
$265$	−11.1939			−0.687638
$266$	−0.727398	−	2.49741i	−0.0445996	−	0.153126i
$267$	6.87095	−	2.23251i	0.420496	−	0.136627i
$268$	9.54299	+	14.9925i	0.582931	+	0.915811i
$269$	11.8003	+	8.57345i	0.719479	+	0.522732i	0.886218	−	0.463269i	$-0.153324\pi$
$269$	11.8003	+	8.57345i	0.719479	+	0.522732i	−0.166738	+	0.986001i	$0.553324\pi$
$270$	2.96980	+	4.36358i	0.180736	+	0.265559i
$271$	−1.87439	+	5.76877i	−0.113861	+	0.350428i	−0.991708	−	0.128514i	$-0.958979\pi$
$271$	−1.87439	+	5.76877i	−0.113861	+	0.350428i	0.877847	+	0.478942i	$0.158979\pi$
$272$	−2.85644	−	5.16270i	−0.173197	−	0.313035i
$273$	−0.281051	+	0.204195i	−0.0170100	+	0.0123585i
$274$	−1.16523	+	3.24343i	−0.0703940	+	0.195943i
$275$	−3.01430	+	1.38348i	−0.181769	+	0.0834271i
$276$	−2.06066	−	1.70003i	−0.124037	−	0.102330i
$277$	−5.19309	−	7.14768i	−0.312023	−	0.429462i	0.623988	−	0.781434i	$-0.285511\pi$
$277$	−5.19309	−	7.14768i	−0.312023	−	0.429462i	−0.936011	+	0.351972i	$0.885511\pi$
$278$	14.9690	+	0.460286i	0.897784	+	0.0276061i
$279$	−24.7388	−	8.03813i	−1.48107	−	0.481230i
$280$	4.68014	+	0.432823i	0.279692	+	0.0258661i
$281$	5.03966	−	6.93650i	0.300641	−	0.413797i	−0.631793	−	0.775137i	$-0.717681\pi$
$281$	5.03966	−	6.93650i	0.300641	−	0.413797i	0.932434	+	0.361340i	$0.117681\pi$
$282$	−3.68343	−	2.85317i	−0.219345	−	0.169904i
$283$	5.97118	+	18.3774i	0.354950	+	1.09242i	0.956039	+	0.293241i	$0.0947338\pi$
$283$	5.97118	+	18.3774i	0.354950	+	1.09242i	−0.601089	+	0.799182i	$0.705266\pi$
$284$	1.37209	−	22.2898i	0.0814184	−	1.32266i
$285$		−	0.744716i		−	0.0441132i
$286$	1.24783	+	0.752957i	0.0737856	+	0.0445233i
$287$			7.74012i			0.456885i
$288$	−12.8170	+	6.58530i	−0.755251	+	0.388043i
$289$	4.58093	+	14.0987i	0.269467	+	0.829333i
$290$	−1.93540	+	2.49859i	−0.113650	+	0.146722i
$291$	4.06944	−	5.60110i	0.238555	−	0.328342i
$292$	−10.0757	+	2.60155i	−0.589639	+	0.152244i
$293$	10.5732	+	3.43543i	0.617691	+	0.200700i	0.601115	−	0.799162i	$-0.294723\pi$
$293$	10.5732	+	3.43543i	0.617691	+	0.200700i	0.0165764	+	0.999863i	$0.494723\pi$
$294$	0.123955	−	4.03117i	0.00722922	−	0.235103i
$295$	−2.23560	−	3.07704i	−0.130162	−	0.179152i
$296$	−12.0112	+	7.13636i	−0.698139	+	0.414793i
$297$	10.7902	+	6.06662i	0.626112	+	0.352021i
$298$	−2.78105	−	0.999115i	−0.161102	−	0.0578772i
$299$	−0.499045	+	0.362577i	−0.0288605	+	0.0209684i
$300$	1.25181	+	0.493667i	0.0722731	+	0.0285019i
$301$	−1.69565	+	5.21868i	−0.0977358	+	0.300800i
$302$	−13.2621	+	9.02605i	−0.763149	+	0.519391i
$303$	−10.2688	−	7.46069i	−0.589925	−	0.428606i
$304$	4.39403	+	0.543020i	0.252015	+	0.0311444i
$305$	5.72916	−	1.86152i	0.328051	−	0.106590i
$306$	−5.10183	+	1.48596i	−0.291652	+	0.0849467i
$307$	−29.1089			−1.66133			−0.830666	−	0.556771i	$-0.812040\pi$
$307$	−29.1089			−1.66133			−0.830666	+	0.556771i	$0.812040\pi$
$308$	10.2815	−	3.97378i	0.585844	−	0.226427i
$309$	−0.464375			−0.0264174
$310$	−13.8651	+	4.03836i	−0.787485	+	0.229363i
$311$	−10.8418	+	3.52272i	−0.614783	+	0.199755i	−0.599823	−	0.800133i	$-0.704762\pi$
$311$	−10.8418	+	3.52272i	−0.614783	+	0.199755i	−0.0149602	+	0.999888i	$0.504762\pi$
$312$	−0.130159	−	0.576799i	−0.00736882	−	0.0326548i
$313$	−2.55294	−	1.85482i	−0.144301	−	0.104841i	0.513293	−	0.858214i	$-0.328426\pi$
$313$	−2.55294	−	1.85482i	−0.144301	−	0.104841i	−0.657594	+	0.753373i	$0.728426\pi$
$314$	−18.4068	+	12.5275i	−1.03876	+	0.706966i
$315$	1.30806	−	4.02580i	0.0737009	−	0.226828i
$316$	−8.46454	+	21.4638i	−0.476168	+	1.20743i
$317$	−11.4737	+	8.33612i	−0.644426	+	0.468203i	−0.861368	−	0.507982i	$-0.830392\pi$
$317$	−11.4737	+	8.33612i	−0.644426	+	0.468203i	0.216942	+	0.976185i	$0.430392\pi$
$318$	10.0239	+	3.60115i	0.562110	+	0.201943i
$319$	−1.45821	+	7.26715i	−0.0816438	+	0.406882i
$320$	−3.82555	+	7.02604i	−0.213855	+	0.392767i
$321$	7.17068	+	9.86959i	0.400228	+	0.550867i
$322$	−0.143390	+	4.66323i	−0.00799084	+	0.259871i
$323$	1.55278	+	0.504528i	0.0863989	+	0.0280727i
$324$	2.56539	+	9.93572i	0.142522	+	0.551984i
$325$	0.182636	−	0.251377i	0.0101308	−	0.0139439i
$326$	−13.2756	+	17.1387i	−0.735266	+	0.949224i
$327$	3.43097	+	10.5594i	0.189733	+	0.583938i
$328$	−12.1014	−	5.20763i	−0.668190	−	0.287543i
$329$			8.13698i			0.448606i
$330$	3.14429	−	0.269153i	0.173087	−	0.0148164i
$331$		−	35.8167i		−	1.96866i	−0.176330	−	0.984331i	$-0.556422\pi$
$331$		−	35.8167i		−	1.96866i	0.176330	−	0.984331i	$-0.443578\pi$
$332$	34.0763	+	2.09762i	1.87018	+	0.115122i
$333$	3.88828	+	11.9669i	0.213076	+	0.655782i
$334$	0.157756	+	0.122197i	0.00863203	+	0.00668635i
$335$	5.22305	−	7.18891i	0.285366	−	0.392772i
$336$	−4.05169	−	1.89321i	−0.221038	−	0.103283i
$337$	17.6895	+	5.74766i	0.963607	+	0.313095i	0.748233	−	0.663437i	$-0.230903\pi$
$337$	17.6895	+	5.74766i	0.963607	+	0.313095i	0.215375	+	0.976531i	$0.430903\pi$
$338$	18.2396	+	0.560854i	0.992104	+	0.0305064i
$339$	−4.85147	−	6.67747i	−0.263495	−	0.362670i
$340$	−1.87740	+	2.27565i	−0.101816	+	0.123414i
$341$	−24.9084	+	22.9477i	−1.34886	+	1.24269i
$342$	1.34815	−	3.75260i	0.0728998	−	0.202918i
$343$	−15.1089	+	10.9773i	−0.815805	+	0.592717i
$344$	−7.01840	−	6.16228i	−0.378407	−	0.332248i
$345$	−0.412756	+	1.27033i	−0.0222220	+	0.0683923i
$346$	8.38105	+	12.3144i	0.450568	+	0.662027i
$347$	4.32788	+	3.14439i	0.232333	+	0.168800i	0.697861	−	0.716234i	$-0.254135\pi$
$347$	4.32788	+	3.14439i	0.232333	+	0.168800i	−0.465528	+	0.885033i	$0.654135\pi$
$348$	2.53690	−	1.61479i	0.135992	−	0.0865616i
$349$	−18.0694	+	5.87111i	−0.967234	+	0.314274i	−0.749699	−	0.661779i	$-0.769802\pi$
$349$	−18.0694	+	5.87111i	−0.967234	+	0.314274i	−0.217535	+	0.976052i	$0.569802\pi$
$350$	−0.657170	−	2.25630i	−0.0351272	−	0.120604i
$351$	−1.15971			−0.0619005
$352$	−0.704625	+	18.7484i	−0.0375566	+	0.999295i
$353$	−30.9248			−1.64596			−0.822979	−	0.568071i	$-0.807690\pi$
$353$	−30.9248			−1.64596			−0.822979	+	0.568071i	$0.807690\pi$
$354$	1.01202	+	3.47461i	0.0537880	+	0.184673i
$355$	−10.6195	+	3.45049i	−0.563625	+	0.183133i
$356$	18.1168	−	11.5317i	0.960189	−	0.611178i
$357$	−1.33422	−	0.969364i	−0.0706142	−	0.0513042i
$358$	−3.77238	−	5.54282i	−0.199377	−	0.292947i
$359$	2.53477	−	7.80121i	0.133780	−	0.411732i	−0.861618	−	0.507557i	$-0.830549\pi$
$359$	2.53477	−	7.80121i	0.133780	−	0.411732i	0.995398	+	0.0958245i	$0.0305488\pi$
$360$	5.41414	+	4.75371i	0.285350	+	0.250543i
$361$	14.3802	−	10.4478i	0.756850	−	0.549884i
$362$	3.79807	−	10.5720i	0.199622	−	0.555650i
$363$	6.32331	−	3.84581i	0.331888	−	0.201852i
$364$	−0.657170	+	0.796574i	−0.0344451	+	0.0417518i
$365$	3.05830	+	4.20939i	0.160079	+	0.220330i
$366$	−5.72916	−	0.176167i	−0.299468	−	0.00920841i
$367$	−11.3059	−	3.67351i	−0.590163	−	0.191756i	−0.00131453	−	0.999999i	$-0.500418\pi$
$367$	−11.3059	−	3.67351i	−0.590163	−	0.191756i	−0.588848	+	0.808244i	$0.700418\pi$
$368$	−7.19433	−	3.36165i	−0.375031	−	0.175238i
$369$	−6.97408	+	9.59900i	−0.363056	+	0.499704i
$370$	5.52264	+	4.27782i	0.287109	+	0.222393i
$371$	−5.74815	−	17.6910i	−0.298429	−	0.918471i
$372$	13.7150	+	0.844247i	0.711088	+	0.0437722i
$373$			0.743922i			0.0385188i	0.999815	+	0.0192594i	$0.00613084\pi$
$373$			0.743922i			0.0385188i	−0.999815	+	0.0192594i	$0.993869\pi$
$374$	−1.56898	+	6.73838i	−0.0811302	+	0.348433i
$375$		−	0.672816i		−	0.0347441i
$376$	−12.7219	−	5.47464i	−0.656082	−	0.282333i
$377$	−0.214580	−	0.660410i	−0.0110515	−	0.0340129i
$378$	−5.37122	+	6.93422i	−0.276266	+	0.356658i
$379$	8.25467	−	11.3616i	0.424014	−	0.583605i	−0.542552	−	0.840022i	$-0.682542\pi$
$379$	8.25467	−	11.3616i	0.424014	−	0.583605i	0.966566	+	0.256417i	$0.0825420\pi$
$380$	−0.553432	−	2.14343i	−0.0283905	−	0.109956i
$381$	−3.47657	−	1.12961i	−0.178110	−	0.0578714i
$382$	−0.374209	+	12.1697i	−0.0191462	+	0.622658i
$383$	−18.1676	−	25.0056i	−0.928322	−	1.27773i	−0.960510	−	0.278244i	$-0.910248\pi$
$383$	−18.1676	−	25.0056i	−0.928322	−	1.27773i	0.0321882	−	0.999482i	$-0.489752\pi$
$384$	5.68598	−	5.06092i	0.290162	−	0.258264i
$385$	−3.73432	−	4.05339i	−0.190319	−	0.206580i
$386$	28.7622	+	10.3331i	1.46396	+	0.525939i
$387$	−6.80507	+	4.94418i	−0.345921	+	0.251327i
$388$	7.55018	−	19.1452i	0.383302	−	0.971950i
$389$	4.72653	−	14.5468i	0.239644	−	0.737550i	−0.756827	−	0.653615i	$-0.773251\pi$
$389$	4.72653	−	14.5468i	0.239644	−	0.737550i	0.996471	−	0.0839343i	$-0.0267486\pi$
$390$	−0.244415	+	0.166346i	−0.0123764	+	0.00842325i
$391$	−2.36909	−	1.72124i	−0.119810	−	0.0870469i
$392$	−2.63898	−	11.6946i	−0.133288	−	0.590666i
$393$	10.1589	−	3.30083i	0.512449	−	0.166505i
$394$	25.7547	−	7.50133i	1.29750	−	0.377911i
$395$	11.5363			0.580453
$396$	16.3312	+	4.33583i	0.820675	+	0.217883i
$397$	30.1221			1.51178			0.755892	−	0.654696i	$-0.227203\pi$
$397$	30.1221			1.51178			0.755892	+	0.654696i	$0.227203\pi$
$398$	−20.3647	+	5.93143i	−1.02079	+	0.297316i
$399$	1.17695	−	0.382416i	0.0589214	−	0.0191447i
$400$	3.96980	+	0.490594i	0.198490	+	0.0245297i
$401$	−15.7563	−	11.4476i	−0.786834	−	0.571668i	0.120188	−	0.992751i	$-0.461650\pi$
$401$	−15.7563	−	11.4476i	−0.786834	−	0.571668i	−0.907022	+	0.421083i	$0.861650\pi$
$402$	−6.98981	+	4.75718i	−0.348620	+	0.237267i
$403$	0.980483	−	3.01762i	0.0488413	−	0.150318i
$404$	−35.0998	−	13.8421i	−1.74628	−	0.688670i
$405$	4.15089	−	3.01580i	0.206259	−	0.149856i
$406$	−4.94262	−	1.77568i	−0.245298	−	0.0881254i
$407$	16.0626	+	3.22308i	0.796195	+	0.159762i
$408$	2.41324	−	1.43381i	0.119473	−	0.0709840i
$409$	−13.4445	−	18.5047i	−0.664786	−	0.915000i	0.334842	−	0.942274i	$-0.391317\pi$
$409$	−13.4445	−	18.5047i	−0.664786	−	0.915000i	−0.999628	+	0.0272745i	$0.991317\pi$
$410$	−0.202455	+	6.58408i	−0.00999854	+	0.325164i
$411$	−1.55938	−	0.506673i	−0.0769186	−	0.0249924i
$412$	−1.33656	+	0.345098i	−0.0658475	+	0.0170017i
$413$	3.71499	−	5.11324i	0.182802	−	0.251606i
$414$	−4.37953	+	5.65395i	−0.215242	+	0.277877i
$415$	−5.27504	−	16.2349i	−0.258941	−	0.796940i
$416$	−0.803268	−	1.56341i	−0.0393835	−	0.0766524i
$417$			7.12493i			0.348910i
$418$	−3.39868	−	3.92456i	−0.166235	−	0.191957i
$419$			9.82290i			0.479880i	0.970788	+	0.239940i	$0.0771278\pi$
$419$			9.82290i			0.479880i	−0.970788	+	0.239940i	$0.922872\pi$
$420$	−0.137386	+	2.23187i	−0.00670375	+	0.108904i
$421$	−6.25831	−	19.2611i	−0.305011	−	0.938728i	−0.979673	−	0.200601i	$-0.935711\pi$
$421$	−6.25831	−	19.2611i	−0.305011	−	0.938728i	0.674662	−	0.738127i	$-0.264289\pi$
$422$	8.10524	+	6.27829i	0.394557	+	0.305622i
$423$	−7.33166	+	10.0912i	−0.356477	+	0.490649i
$424$	31.5267	+	2.91562i	1.53107	+	0.141595i
$425$	1.40286	+	0.455818i	0.0680489	+	0.0221104i
$426$	10.6195	+	0.326542i	0.514517	+	0.0158210i
$427$	5.88392	+	8.09851i	0.284743	+	0.391915i
$428$	27.9731	+	23.0777i	1.35213	+	1.11550i
$429$	−0.339807	+	0.604388i	−0.0164060	+	0.0291801i
$430$	−1.57890	+	4.39488i	−0.0761412	+	0.211940i
$431$	26.6495	−	19.3620i	1.28366	−	0.932636i	0.284006	−	0.958822i	$-0.408336\pi$
$431$	26.6495	−	19.3620i	1.28366	−	0.932636i	0.999657	+	0.0261864i	$0.00833635\pi$
$432$	−7.22762	−	13.0631i	−0.347739	−	0.628501i
$433$	−6.41735	+	19.7506i	−0.308398	+	0.949151i	0.669989	+	0.742371i	$0.266299\pi$
$433$	−6.41735	+	19.7506i	−0.308398	+	0.949151i	−0.978387	+	0.206781i	$0.933701\pi$
$434$	−13.5021	−	19.8388i	−0.648120	−	0.952293i
$435$	−1.21645	−	0.883802i	−0.0583243	−	0.0423751i
$436$	17.7221	+	27.8423i	0.848737	+	1.33340i
$437$	2.08985	−	0.679032i	0.0999709	−	0.0324825i
$438$	−1.38444	−	4.75326i	−0.0661510	−	0.227120i
$439$	−3.65495			−0.174441			−0.0872207	−	0.996189i	$-0.527799\pi$
$439$	−3.65495			−0.174441			−0.0872207	+	0.996189i	$0.527799\pi$
$440$	8.84984	−	3.11134i	0.421899	−	0.148327i
$441$	−10.7971			−0.514149
$442$	−0.181256	−	0.622316i	−0.00862147	−	0.0296005i
$443$	2.93134	−	0.952450i	0.139272	−	0.0452523i	−0.238551	−	0.971130i	$-0.576673\pi$
$443$	2.93134	−	0.952450i	0.139272	−	0.0452523i	0.377824	+	0.925878i	$0.376673\pi$
$444$	−3.56917	−	5.60733i	−0.169385	−	0.266112i
$445$	−8.68704	−	6.31150i	−0.411805	−	0.299194i
$446$	20.8666	+	30.6597i	0.988064	+	1.45178i
$447$	0.434443	−	1.33708i	0.0205484	−	0.0632416i
$448$	−13.0684	−	2.43801i	−0.617426	−	0.115185i
$449$	1.20449	−	0.875112i	0.0568433	−	0.0412991i	−0.559001	−	0.829167i	$-0.688815\pi$
$449$	1.20449	−	0.875112i	0.0568433	−	0.0412991i	0.615844	+	0.787868i	$0.288815\pi$
$450$	1.21799	−	3.39030i	0.0574168	−	0.159820i
$451$	6.44405	+	14.0401i	0.303438	+	0.661124i
$452$	−18.9258	−	15.6137i	−0.890193	−	0.734405i
$453$	−4.48606	−	6.17453i	−0.210774	−	0.290105i
$454$	2.12589	+	0.0653695i	0.0997731	+	0.00306794i
$455$	0.491063	+	0.159556i	0.0230214	+	0.00748010i
$456$	−0.193972	+	2.09742i	−0.00908355	+	0.0982209i
$457$	−5.86507	+	8.07258i	−0.274357	+	0.377619i	−0.923854	−	0.382744i	$-0.874979\pi$
$457$	−5.86507	+	8.07258i	−0.274357	+	0.377619i	0.649498	+	0.760363i	$0.274979\pi$
$458$	−7.37353	−	5.71152i	−0.344543	−	0.266882i
$459$	−1.70126	−	5.23594i	−0.0794081	−	0.244393i
$460$	−0.243948	+	3.96299i	−0.0113741	+	0.184775i
$461$		−	19.5207i		−	0.909168i	−0.890704	−	0.454584i	$-0.849788\pi$
$461$		−	19.5207i		−	0.909168i	0.890704	−	0.454584i	$-0.150212\pi$
$462$	2.03998	+	4.83105i	0.0949086	+	0.224761i
$463$		−	5.16101i		−	0.239852i	−0.992783	−	0.119926i	$-0.961734\pi$
$463$		−	5.16101i		−	0.239852i	0.992783	−	0.119926i	$-0.0382658\pi$
$464$	6.10166	−	6.53294i	0.283263	−	0.303284i
$465$	−2.12309	−	6.53420i	−0.0984560	−	0.303016i
$466$	16.0270	−	20.6907i	0.742435	−	0.958479i
$467$	−1.67953	+	2.31168i	−0.0777195	+	0.106972i	−0.846107	−	0.533013i	$-0.821060\pi$
$467$	−1.67953	+	2.31168i	−0.0777195	+	0.106972i	0.768387	+	0.639985i	$0.221060\pi$
$468$	−1.53273	+	0.395750i	−0.0708507	+	0.0182936i
$469$	14.0435	+	4.56300i	0.648467	+	0.210700i
$470$	−0.212835	+	6.92166i	−0.00981737	+	0.319272i
$471$	−6.22631	−	8.56978i	−0.286893	−	0.394875i
$472$	5.49491	+	9.24850i	0.252924	+	0.425697i
$473$	1.26901	+	10.8781i	0.0583490	+	0.500176i
$474$	−10.3304	−	3.71128i	−0.474491	−	0.170465i
$475$	−0.895472	+	0.650598i	−0.0410871	+	0.0298515i
$476$	−4.56050	−	1.79850i	−0.209030	−	0.0824340i
$477$	8.81148	−	27.1189i	0.403450	−	1.24169i
$478$	−20.1467	+	13.7116i	−0.921489	+	0.627155i
$479$	25.1392	+	18.2647i	1.14864	+	0.834536i	0.988300	−	0.152525i	$-0.0487406\pi$
$479$	25.1392	+	18.2647i	1.14864	+	0.834536i	0.160341	+	0.987062i	$0.448741\pi$
$480$	−3.39702	−	1.71642i	−0.155052	−	0.0783435i
$481$	−1.45971	+	0.474288i	−0.0665570	+	0.0216257i
$482$	13.8168	−	4.02430i	0.629340	−	0.183302i
$483$	−2.21959			−0.100995
$484$	15.3417	−	15.7681i	0.697349	−	0.716731i
$485$	−10.2901			−0.467249
$486$	−19.8904	+	5.79328i	−0.902246	+	0.262789i
$487$	−29.6282	+	9.62678i	−1.34258	+	0.436231i	−0.890190	−	0.455589i	$-0.849429\pi$
$487$	−29.6282	+	9.62678i	−1.34258	+	0.436231i	−0.452391	+	0.891820i	$0.649429\pi$
$488$	−16.6205	+	3.75056i	−0.752376	+	0.169780i
$489$	−8.34404	−	6.06230i	−0.377331	−	0.274147i
$490$	−4.95551	+	3.37266i	−0.223867	+	0.152361i
$491$	8.44831	−	26.0012i	0.381267	−	1.17342i	−0.557885	−	0.829918i	$-0.688387\pi$
$491$	8.44831	−	26.0012i	0.381267	−	1.17342i	0.939152	−	0.343501i	$-0.111613\pi$
$492$	2.29943	−	5.83072i	0.103666	−	0.262869i
$493$	2.66690	−	1.93761i	0.120111	−	0.0872658i
$494$	0.457738	+	0.164446i	0.0205946	+	0.00739879i
$495$	−0.978938	−	8.39159i	−0.0440000	−	0.377174i
$496$	40.1017	−	7.76231i	1.80062	−	0.348538i
$497$	−10.9064	−	15.0113i	−0.489217	−	0.673350i
$498$	−0.499210	+	16.2349i	−0.0223701	+	0.727503i
$499$	8.59428	+	2.79245i	0.384733	+	0.125007i	0.494996	−	0.868895i	$-0.335169\pi$
$499$	8.59428	+	2.79245i	0.384733	+	0.125007i	−0.110263	+	0.993902i	$0.535169\pi$
$500$	−0.500000	−	1.93649i	−0.0223607	−	0.0866025i
$501$	−0.0558016	+	0.0768043i	−0.00249303	+	0.00343136i
$502$	13.5465	−	17.4885i	0.604611	−	0.780550i
$503$	−12.6723	−	39.0014i	−0.565031	−	1.73899i	−0.667860	−	0.744287i	$-0.732790\pi$
$503$	−12.6723	−	39.0014i	−0.565031	−	1.73899i	0.102830	−	0.994699i	$-0.467210\pi$
$504$	−4.73261	+	10.9976i	−0.210807	+	0.489872i
$505$			18.8653i			0.839495i
$506$	3.62227	+	8.57820i	0.161030	+	0.381347i
$507$			8.68165i			0.385566i
$508$	−10.8457	−	0.667623i	−0.481199	−	0.0296210i
$509$	−9.13304	−	28.1086i	−0.404815	−	1.24589i	−0.921050	−	0.389445i	$-0.872667\pi$
$509$	−9.13304	−	28.1086i	−0.404815	−	1.24589i	0.516235	−	0.856447i	$-0.327333\pi$
$510$	−1.10959	−	0.859481i	−0.0491333	−	0.0380585i
$511$	−5.08210	+	6.99491i	−0.224819	+	0.309437i
$512$	12.6043	−	18.7918i	0.557038	−	0.830487i
$513$	3.92898	+	1.27660i	0.173469	+	0.0563634i
$514$	20.4699	+	0.629434i	0.902890	+	0.0277631i
$515$	0.405687	+	0.558380i	0.0178767	+	0.0246052i
$516$	2.82772	−	3.42755i	0.124483	−	0.150890i
$517$	6.77445	+	14.7600i	0.297940	+	0.649144i
$518$	−3.92479	+	10.9247i	−0.172445	+	0.480004i
$519$	−5.73330	+	4.16549i	−0.251664	+	0.182845i
$520$	−0.579853	+	0.660410i	−0.0254282	+	0.0289609i
$521$	−9.13149	+	28.1038i	−0.400058	+	1.23125i	0.524894	+	0.851167i	$0.324105\pi$
$521$	−9.13149	+	28.1038i	−0.400058	+	1.23125i	−0.924952	+	0.380084i	$0.875895\pi$
$522$	−4.52971	−	6.65558i	−0.198260	−	0.291307i
$523$	10.6513	+	7.73863i	0.465750	+	0.338387i	0.795782	−	0.605583i	$-0.207060\pi$
$523$	10.6513	+	7.73863i	0.465750	+	0.338387i	−0.330033	+	0.943969i	$0.607060\pi$
$524$	26.7862	−	17.0499i	1.17016	−	0.744830i
$525$	1.06332	−	0.345495i	0.0464073	−	0.0150786i
$526$	6.66156	+	22.8715i	0.290458	+	0.997244i
$527$	15.0626			0.656135
$528$	−8.92571	−	0.0609276i	−0.388442	−	0.00265153i
$529$	19.0588			0.828644
$530$	−4.42689	−	15.1991i	−0.192292	−	0.660205i
$531$	9.21436	−	2.99393i	0.399869	−	0.129925i
$532$	3.10331	−	1.97531i	0.134545	−	0.0856406i
$533$	−1.17088	−	0.850691i	−0.0507163	−	0.0368475i
$534$	5.74855	+	8.44644i	0.248764	+	0.365513i
$535$	5.60309	−	17.2445i	0.242242	−	0.745546i
$536$	−16.5827	+	18.8865i	−0.716263	+	0.815773i
$537$	2.58061	−	1.87492i	0.111361	−	0.0809088i
$538$	−6.97427	+	19.4130i	−0.300682	+	0.836953i
$539$	−6.88957	+	12.2539i	−0.296755	+	0.527815i
$540$	−4.75036	+	5.75805i	−0.204423	+	0.247787i
$541$	20.9681	+	28.8601i	0.901488	+	1.24079i	0.969991	+	0.243140i	$0.0781776\pi$
$541$	20.9681	+	28.8601i	0.901488	+	1.24079i	−0.0685034	+	0.997651i	$0.521822\pi$
$542$	−8.57407	−	0.263646i	−0.368288	−	0.0113245i
$543$	5.08281	+	1.65150i	0.218124	+	0.0708728i
$544$	5.88024	−	5.92015i	0.252113	−	0.253824i
$545$	9.69965	−	13.3504i	0.415487	−	0.571869i
$546$	−0.388403	−	0.300855i	−0.0166221	−	0.0128754i
$547$	10.1850	+	31.3463i	0.435481	+	1.34027i	0.892593	+	0.450864i	$0.148884\pi$
$547$	10.1850	+	31.3463i	0.435481	+	1.34027i	−0.457112	+	0.889409i	$0.651116\pi$
$548$	−4.86472	−	0.299456i	−0.207811	−	0.0127921i
$549$			15.3450i			0.654911i
$550$	−3.07055	−	3.54566i	−0.130929	−	0.151188i
$551$			2.47362i			0.105380i
$552$	1.49336	−	3.47026i	0.0635618	−	0.147704i
$553$	5.92394	+	18.2320i	0.251912	+	0.775304i
$554$	7.65135	−	9.87784i	0.325075	−	0.419669i
$555$	−1.95347	+	2.68872i	−0.0829203	+	0.114130i
$556$	5.29486	+	20.5069i	0.224552	+	0.869686i
$557$	−8.39704	−	2.72836i	−0.355794	−	0.115604i	0.125666	−	0.992073i	$-0.459893\pi$
$557$	−8.39704	−	2.72836i	−0.355794	−	0.115604i	−0.481460	+	0.876468i	$0.659893\pi$
$558$	1.13062	−	36.7691i	0.0478629	−	1.55656i
$559$	−0.603085	−	0.830076i	−0.0255078	−	0.0351085i
$560$	1.26318	+	6.52583i	0.0533790	+	0.275766i
$561$	−3.22723	−	0.647567i	−0.136254	−	0.0273403i
$562$	11.4114	+	4.09963i	0.481360	+	0.172932i
$563$	−19.9609	+	14.5024i	−0.841250	+	0.611204i	−0.922720	−	0.385472i	$-0.874039\pi$
$563$	−19.9609	+	14.5024i	−0.841250	+	0.611204i	0.0814697	+	0.996676i	$0.474039\pi$
$564$	2.41732	−	6.12968i	0.101788	−	0.258106i
$565$	−3.79088	+	11.6671i	−0.159484	+	0.490840i
$566$	−22.5913	+	15.3754i	−0.949582	+	0.646275i
$567$	6.89770	+	5.01147i	0.289676	+	0.210462i
$568$	30.8076	−	6.95199i	1.29266	−	0.291699i
$569$	35.4388	−	11.5147i	1.48567	−	0.482723i	0.549869	−	0.835251i	$-0.314678\pi$
$569$	35.4388	−	11.5147i	1.48567	−	0.482723i	0.935801	+	0.352528i	$0.114678\pi$
$570$	1.01117	−	0.294514i	0.0423533	−	0.0123358i
$571$	20.0777			0.840228			0.420114	−	0.907471i	$-0.361990\pi$
$571$	20.0777			0.840228			0.420114	+	0.907471i	$0.361990\pi$
$572$	−0.528879	+	1.99207i	−0.0221136	+	0.0832925i
$573$	−5.79252			−0.241986
$574$	−10.5095	+	3.06100i	−0.438657	+	0.127764i
$575$	1.88808	−	0.613474i	0.0787384	−	0.0255836i
$576$	−14.0102	−	14.7986i	−0.583760	−	0.616608i
$577$	10.5306	+	7.65092i	0.438394	+	0.318512i	0.784997	−	0.619500i	$-0.212665\pi$
$577$	10.5306	+	7.65092i	0.438394	+	0.318512i	−0.346602	+	0.938012i	$0.612665\pi$
$578$	−17.3314	+	11.7956i	−0.720892	+	0.490631i
$579$	−4.49310	+	13.8283i	−0.186727	+	0.574686i
$580$	−4.15796	−	1.63975i	−0.172650	−	0.0680869i
$581$	22.9490	−	16.6734i	0.952085	−	0.691730i
$582$	9.21448	+	3.31038i	0.381953	+	0.137220i
$583$	−25.1555	−	27.3048i	−1.04183	−	1.13085i
$584$	−7.51703	−	12.6519i	−0.311057	−	0.523541i
$585$	0.465232	+	0.640337i	0.0192350	+	0.0264747i
$586$	−0.483217	+	15.7148i	−0.0199615	+	0.649172i
$587$	7.89054	+	2.56379i	0.325677	+	0.105819i	0.467292	−	0.884103i	$-0.345230\pi$
$587$	7.89054	+	2.56379i	0.325677	+	0.105819i	−0.141615	+	0.989922i	$0.545230\pi$
$588$	5.52252	−	1.42591i	0.227745	−	0.0588034i
$589$	−6.64358	+	9.14411i	−0.273744	+	0.376776i
$590$	3.29387	−	4.25237i	0.135606	−	0.175067i
$591$	3.94368	+	12.1374i	0.162221	+	0.499266i
$592$	−14.4398	−	13.4865i	−0.593472	−	0.554293i
$593$			30.8668i			1.26755i	0.773519	+	0.633773i	$0.218495\pi$
$593$			30.8668i			1.26755i	−0.773519	+	0.633773i	$0.781505\pi$
$594$	−3.96999	+	17.0501i	−0.162891	+	0.699573i
$595$			2.45116i			0.100488i
$596$	0.256766	−	4.17121i	0.0105175	−	0.170860i
$597$	−3.11834	−	9.59725i	−0.127625	−	0.392789i
$598$	−0.689663	−	0.534211i	−0.0282024	−	0.0218455i
$599$	−22.6749	+	31.2093i	−0.926469	+	1.27518i	0.0347513	+	0.999396i	$0.488936\pi$
$599$	−22.6749	+	31.2093i	−0.926469	+	1.27518i	−0.961221	+	0.275780i	$0.911064\pi$
$600$	−0.175244	+	1.89493i	−0.00715432	+	0.0773600i
$601$	5.00956	+	1.62770i	0.204344	+	0.0663954i	0.409401	−	0.912355i	$-0.365738\pi$
$601$	5.00956	+	1.62770i	0.204344	+	0.0663954i	−0.205057	+	0.978750i	$0.565738\pi$
$602$	−7.75648	−	0.238505i	−0.316130	−	0.00972075i
$603$	13.3048	+	18.3124i	0.541812	+	0.745740i
$604$	−17.5003	−	14.4377i	−0.712077	−	0.587461i
$605$	−10.1485	−	4.24359i	−0.412595	−	0.172527i
$606$	6.06907	−	16.8933i	0.246539	−	0.686245i
$607$	−23.2323	+	16.8792i	−0.942969	+	0.685107i	−0.949134	−	0.314874i	$-0.898038\pi$
$607$	−23.2323	+	16.8792i	−0.942969	+	0.685107i	0.00616432	+	0.999981i	$0.498038\pi$
$608$	1.00040	+	6.18093i	0.0405717	+	0.250670i
$609$	0.772114	−	2.37632i	0.0312876	−	0.0962934i
$610$	4.79328	+	7.04284i	0.194074	+	0.285156i
$611$	−1.23091	−	0.894308i	−0.0497973	−	0.0361798i
$612$	−4.03526	−	6.33957i	−0.163116	−	0.256262i
$613$	−11.6976	+	3.80079i	−0.472462	+	0.153512i	−0.535564	−	0.844495i	$-0.679901\pi$
$613$	−11.6976	+	3.80079i	−0.472462	+	0.153512i	0.0631014	+	0.998007i	$0.479901\pi$
$614$	−11.5117	−	39.5239i	−0.464576	−	1.59505i
$615$	−3.13387			−0.126370
$616$	9.46162	+	12.3887i	0.381219	+	0.499153i
$617$	4.39688			0.177012			0.0885058	−	0.996076i	$-0.471791\pi$
$617$	4.39688			0.177012			0.0885058	+	0.996076i	$0.471791\pi$
$618$	−0.183647	−	0.630525i	−0.00738737	−	0.0253634i
$619$	3.59330	−	1.16753i	0.144427	−	0.0469271i	−0.235912	−	0.971775i	$-0.575808\pi$
$619$	3.59330	−	1.16753i	0.144427	−	0.0469271i	0.380338	+	0.924847i	$0.375808\pi$
$620$	−10.9665	−	17.2289i	−0.440426	−	0.691929i
$621$	−5.99448	−	4.35524i	−0.240550	−	0.174770i
$622$	−9.07075	−	13.3278i	−0.363704	−	0.534396i
$623$	5.51390	−	16.9701i	0.220910	−	0.679891i
$624$	0.731699	−	0.404837i	0.0292914	−	0.0162065i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	1.50885	−	4.19990i	0.0603057	−	0.167862i
$627$	1.81655	−	1.67355i	0.0725458	−	0.0668353i
$628$	−24.2891	−	20.0384i	−0.969240	−	0.799619i
$629$	−4.28272	−	5.89466i	−0.170763	−	0.235035i
$630$	5.98351	+	0.183988i	0.238389	+	0.00733026i
$631$	0.297436	+	0.0966427i	0.0118407	+	0.00384729i	0.314931	−	0.949114i	$-0.398018\pi$
$631$	0.297436	+	0.0966427i	0.0118407	+	0.00384729i	−0.303091	+	0.952962i	$0.598018\pi$
$632$	−32.4909	−	3.00478i	−1.29242	−	0.119524i
$633$	−2.86699	+	3.94607i	−0.113953	+	0.156842i
$634$	−15.8562	−	12.2822i	−0.629732	−	0.487788i
$635$	1.67892	+	5.16719i	0.0666259	+	0.205054i
$636$	−0.925471	+	15.0345i	−0.0366973	+	0.596156i
$637$		−	1.31702i		−	0.0521823i
$638$	−10.4440	+	0.894011i	−0.413481	+	0.0353942i
$639$		−	28.4434i		−	1.12520i
$640$	−11.0528	−	2.41570i	−0.436900	−	0.0954890i
$641$	−10.9010	−	33.5499i	−0.430564	−	1.32514i	−0.897564	−	0.440883i	$-0.854665\pi$
$641$	−10.9010	−	33.5499i	−0.430564	−	1.32514i	0.467000	−	0.884257i	$-0.345335\pi$
$642$	−10.5651	+	13.6394i	−0.416970	+	0.538306i
$643$	−19.3630	+	26.6509i	−0.763603	+	1.05101i	0.233303	+	0.972404i	$0.425047\pi$
$643$	−19.3630	+	26.6509i	−0.763603	+	1.05101i	−0.996906	+	0.0786050i	$0.974953\pi$
$644$	−6.38840	+	1.64948i	−0.251738	+	0.0649986i
$645$	−2.11298	−	0.686548i	−0.0831984	−	0.0270328i
$646$	−0.0709654	+	2.30788i	−0.00279210	+	0.0908023i
$647$	19.4162	+	26.7240i	0.763328	+	1.05063i	0.996930	+	0.0782983i	$0.0249487\pi$
$647$	19.4162	+	26.7240i	0.763328	+	1.05063i	−0.233602	+	0.972332i	$0.575051\pi$
$648$	−12.4761	+	7.41257i	−0.490108	+	0.291193i
$649$	2.48173	−	12.3680i	0.0974165	−	0.485487i
$650$	0.413545	+	0.148570i	0.0162206	+	0.00582738i
$651$	9.23648	−	6.71070i	0.362006	−	0.263013i
$652$	−28.5209	−	11.2476i	−1.11696	−	0.440490i
$653$	−5.59970	+	17.2341i	−0.219133	+	0.674422i	0.779701	+	0.626152i	$0.215371\pi$
$653$	−5.59970	+	17.2341i	−0.219133	+	0.674422i	−0.998834	+	0.0482705i	$0.984629\pi$
$654$	−12.9807	+	8.83450i	−0.507584	+	0.345456i
$655$	−12.8440	−	9.33174i	−0.501858	−	0.364621i
$656$	2.28511	−	18.4907i	0.0892185	−	0.721941i
$657$	−12.6052	+	4.09569i	−0.491777	+	0.159788i
$658$	−11.0483	+	3.21794i	−0.430709	+	0.125448i
$659$	24.5400			0.955944			0.477972	−	0.878375i	$-0.341372\pi$
$659$	24.5400			0.955944			0.477972	+	0.878375i	$0.341372\pi$
$660$	1.60893	+	4.16285i	0.0626276	+	0.162039i
$661$	30.6751			1.19312			0.596561	−	0.802567i	$-0.296533\pi$
$661$	30.6751			1.19312			0.596561	+	0.802567i	$0.296533\pi$
$662$	48.6316	−	14.1645i	1.89012	−	0.550518i
$663$	0.293278	−	0.0952919i	0.0113900	−	0.00370083i
$664$	10.6281	+	47.0981i	0.412449	+	1.82776i
$665$	−1.48804	−	1.08112i	−0.0577037	−	0.0419242i
$666$	−14.7109	+	10.0120i	−0.570034	+	0.387959i
$667$	1.37100	−	4.21949i	0.0530852	−	0.163379i
$668$	−0.103531	+	0.262526i	−0.00400572	+	0.0101574i
$669$	−14.2744	+	10.3710i	−0.551882	+	0.400966i
$670$	11.8266	+	4.24881i	0.456902	+	0.164146i
$671$	17.4155	+	9.79156i	0.672318	+	0.377999i
$672$	0.968255	−	6.25006i	0.0373513	−	0.241101i
$673$	−25.8084	−	35.5222i	−0.994840	−	1.36928i	−0.928438	−	0.371487i	$-0.878848\pi$
$673$	−25.8084	−	35.5222i	−0.994840	−	1.36928i	−0.0664020	−	0.997793i	$-0.521152\pi$
$674$	−0.808448	+	26.2917i	−0.0311403	+	1.01272i
$675$	3.54965	+	1.15335i	0.136626	+	0.0443926i
$676$	6.45173	+	24.9874i	0.248143	+	0.961055i
$677$	−18.9404	+	26.0693i	−0.727941	+	1.00192i	0.271282	+	0.962500i	$0.412552\pi$
$677$	−18.9404	+	26.0693i	−0.727941	+	1.00192i	−0.999223	+	0.0394243i	$0.987448\pi$
$678$	7.14801	−	9.22803i	0.274517	−	0.354401i
$679$	−5.28402	−	16.2625i	−0.202782	−	0.624099i
$680$	−3.83231	−	1.64916i	−0.146962	−	0.0632426i
$681$			1.01188i			0.0387752i
$682$	−41.0087	−	24.7453i	−1.57031	−	0.947545i
$683$			17.8326i			0.682344i	0.940001	+	0.341172i	$0.110824\pi$
$683$			17.8326i			0.682344i	−0.940001	+	0.341172i	$0.889176\pi$
$684$	5.62841	+	0.346466i	0.215208	+	0.0132475i
$685$	0.753063	+	2.31769i	0.0287731	+	0.0885544i
$686$	−20.8800	−	16.1736i	−0.797203	−	0.617511i
$687$	2.60817	−	3.58984i	0.0995079	−	0.136961i
$688$	5.59153	−	11.9665i	0.213175	−	0.456220i
$689$	3.30794	+	1.07481i	0.126022	+	0.0409472i
$690$	−1.88808	−	0.0580569i	−0.0718780	−	0.00221019i
$691$	−13.9772	−	19.2380i	−0.531718	−	0.731847i	0.455673	−	0.890147i	$-0.349399\pi$
$691$	−13.9772	−	19.2380i	−0.531718	−	0.731847i	−0.987391	+	0.158300i	$0.949399\pi$
$692$	−13.4060	+	16.2497i	−0.509618	+	0.617722i
$693$	12.7594	−	5.85625i	0.484691	−	0.222460i
$694$	−2.55788	+	7.11988i	−0.0970957	+	0.270267i
$695$	8.56726	−	6.22448i	0.324975	−	0.236108i
$696$	3.19582	+	2.80599i	0.121137	+	0.106361i
$697$	2.12313	−	6.53432i	0.0804193	−	0.247505i
$698$	−15.1177	−	22.2127i	−0.572214	−	0.840763i
$699$	10.0734	+	7.31873i	0.381010	+	0.276820i
$700$	2.80369	−	1.78460i	0.105970	−	0.0674517i
$701$	5.20485	−	1.69116i	0.196585	−	0.0638742i	−0.209070	−	0.977901i	$-0.567044\pi$
$701$	5.20485	−	1.69116i	0.196585	−	0.0638742i	0.405655	+	0.914026i	$0.367044\pi$
$702$	−0.458630	−	1.57464i	−0.0173099	−	0.0594310i
$703$	5.46747			0.206209
$704$	−25.7351	+	6.45773i	−0.969930	+	0.243385i
$705$	−3.29456			−0.124080
$706$	−12.2299	−	41.9894i	−0.460277	−	1.58029i
$707$	−29.8149	+	9.68744i	−1.12130	+	0.364334i
$708$	−4.31758	+	2.74822i	−0.162264	+	0.103284i
$709$	−3.56188	−	2.58786i	−0.133769	−	0.0971890i	0.518888	−	0.854842i	$-0.326346\pi$
$709$	−3.56188	−	2.58786i	−0.133769	−	0.0971890i	−0.652658	+	0.757653i	$0.726346\pi$
$710$	−8.88477	−	13.0545i	−0.333439	−	0.489928i
$711$	−9.08094	+	27.9483i	−0.340562	+	1.04814i
$712$	22.8223	+	20.0384i	0.855303	+	0.750972i
$713$	16.4007	−	11.9158i	0.614209	−	0.446249i
$714$	0.788552	−	2.19494i	0.0295108	−	0.0821437i
$715$	1.02360	−	0.119410i	0.0382804	−	0.00446567i
$716$	6.03414	−	7.31414i	0.225506	−	0.273342i
$717$	−6.81485	−	9.37983i	−0.254505	−	0.350296i
$718$	11.5949	+	0.356533i	0.432716	+	0.0133057i
$719$	5.62130	+	1.82647i	0.209639	+	0.0681159i	0.411954	−	0.911205i	$-0.364846\pi$
$719$	5.62130	+	1.82647i	0.209639	+	0.0681159i	−0.202315	+	0.979321i	$0.564846\pi$
$720$	−4.31342	+	9.23123i	−0.160752	+	0.344028i
$721$	−0.674145	+	0.927882i	−0.0251065	+	0.0345561i
$722$	19.8729	+	15.3935i	0.739592	+	0.572886i
$723$	2.11570	+	6.51145i	0.0786837	+	0.242163i
$724$	15.8566	+	0.976077i	0.589305	+	0.0362756i
$725$			2.23480i			0.0829986i
$726$	7.72250	+	7.06484i	0.286609	+	0.262201i
$727$		−	24.1614i		−	0.896096i	−0.894010	−	0.448048i	$-0.852119\pi$
$727$		−	24.1614i		−	0.896096i	0.894010	−	0.448048i	$-0.147881\pi$
$728$	−1.34148	−	0.577279i	−0.0497184	−	0.0213954i
$729$	1.71079	+	5.26527i	0.0633625	+	0.195010i
$730$	−4.50601	+	5.81724i	−0.166775	+	0.215306i
$731$	2.86299	−	3.94057i	0.105891	−	0.145747i
$732$	−2.02652	−	7.84869i	−0.0749024	−	0.290096i
$733$	−6.81624	−	2.21473i	−0.251764	−	0.0818030i	0.180416	−	0.983590i	$-0.442255\pi$
$733$	−6.81624	−	2.21473i	−0.251764	−	0.0818030i	−0.432180	+	0.901787i	$0.642255\pi$
$734$	0.516704	−	16.8038i	0.0190719	−	0.620241i
$735$	−1.67626	−	2.30717i	−0.0618296	−	0.0851012i
$736$	1.71927	−	11.0979i	0.0633732	−	0.409072i
$737$	29.2730	−	3.41489i	1.07828	−	0.125789i
$738$	−15.7915	−	5.67323i	−0.581293	−	0.208834i
$739$	−20.3029	+	14.7510i	−0.746856	+	0.542623i	−0.894851	−	0.446366i	$-0.852718\pi$
$739$	−20.3029	+	14.7510i	−0.746856	+	0.542623i	0.147995	+	0.988988i	$0.452718\pi$
$740$	−3.62435	+	9.19036i	−0.133234	+	0.337844i
$741$	−0.0715058	+	0.220072i	−0.00262683	+	0.00808455i
$742$	21.7475	−	14.8011i	0.798375	−	0.543365i
$743$	−15.7058	−	11.4109i	−0.576188	−	0.418625i	0.261160	−	0.965296i	$-0.415895\pi$
$743$	−15.7058	−	11.4109i	−0.576188	−	0.418625i	−0.837348	+	0.546670i	$0.815895\pi$
$744$	4.27757	+	18.9560i	0.156823	+	0.694960i
$745$	−1.98728	+	0.645708i	−0.0728085	+	0.0236569i
$746$	−1.01009	+	0.294200i	−0.0369821	+	0.0107714i
$747$	43.4837			1.59099
$748$	−9.76982	+	0.534482i	−0.357220	+	0.0195426i
$749$	30.1306			1.10095
$750$	0.913545	−	0.266080i	0.0333580	−	0.00971586i
$751$	−9.61376	+	3.12370i	−0.350811	+	0.113985i	−0.479121	−	0.877749i	$-0.659045\pi$
$751$	−9.61376	+	3.12370i	−0.350811	+	0.113985i	0.128310	+	0.991734i	$0.459045\pi$
$752$	2.40227	−	19.4388i	0.0876019	−	0.708860i
$753$	8.51435	+	6.18604i	0.310280	+	0.225432i
$754$	0.811840	−	0.552529i	0.0295655	−	0.0201219i
$755$	−3.50536	+	10.7884i	−0.127573	+	0.392629i
$756$	−11.5394	−	4.55072i	−0.419684	−	0.165508i
$757$	−0.177580	+	0.129019i	−0.00645424	+	0.00468928i	−0.591008	−	0.806666i	$-0.701270\pi$
$757$	−0.177580	+	0.129019i	−0.00645424	+	0.00468928i	0.584553	+	0.811355i	$0.301270\pi$
$758$	18.6912	+	6.71495i	0.678893	+	0.243898i
$759$	−4.02621	+	1.84792i	−0.146142	+	0.0670754i
$760$	2.69147	−	1.59911i	0.0976299	−	0.0580059i
$761$	20.0675	+	27.6206i	0.727448	+	1.00125i	0.999243	+	0.0388909i	$0.0123825\pi$
$761$	20.0675	+	27.6206i	0.727448	+	1.00125i	−0.271796	+	0.962355i	$0.587618\pi$
$762$	0.158887	−	5.16719i	0.00575586	−	0.187187i
$763$	26.0799	+	8.47389i	0.944157	+	0.306775i
$764$	−16.6720	+	4.30468i	−0.603171	+	0.155738i
$765$	−2.20857	+	3.03983i	−0.0798510	+	0.109905i
$766$	26.7676	−	34.5569i	0.967154	−	1.24859i
$767$	0.365196	+	1.12396i	0.0131865	+	0.0405838i
$768$	9.12032	+	5.71894i	0.329101	+	0.206364i
$769$			1.47479i			0.0531823i	0.999646	+	0.0265911i	$0.00846522\pi$
$769$			1.47479i			0.0531823i	−0.999646	+	0.0265911i	$0.991535\pi$
$770$	4.02685	−	6.67344i	0.145117	−	0.240494i
$771$			9.74324i			0.350894i
$772$	−2.65552	+	43.1395i	−0.0955744	+	1.55263i
$773$	−7.99255	−	24.5985i	−0.287472	−	0.884747i	−0.985647	−	0.168820i	$-0.946004\pi$
$773$	−7.99255	−	24.5985i	−0.287472	−	0.884747i	0.698175	−	0.715927i	$-0.253996\pi$
$774$	−9.40438	−	7.28460i	−0.338033	−	0.261840i
$775$	−6.00217	+	8.26128i	−0.215604	+	0.296754i
$776$	28.9811	+	2.68020i	1.04036	+	0.0962134i
$777$	−5.25240	−	1.70661i	−0.188429	−	0.0612242i
$778$	21.6207	+	0.664819i	0.775139	+	0.0238349i
$779$	3.03039	+	4.17097i	0.108575	+	0.149440i
$780$	−0.322523	−	0.266080i	−0.0115482	−	0.00952718i
$781$	−32.2812	−	18.1495i	−1.15511	−	0.649442i
$782$	1.40018	−	3.89743i	0.0500705	−	0.139372i
$783$	6.74803	−	4.90273i	0.241155	−	0.175209i
$784$	14.8352	−	8.20806i	0.529828	−	0.293145i
$785$	−4.86517	+	14.9735i	−0.173645	+	0.534425i
$786$	8.49940	+	12.4883i	0.303164	+	0.445443i
$787$	−13.1557	−	9.55817i	−0.468950	−	0.340712i	0.328082	−	0.944649i	$-0.393598\pi$
$787$	−13.1557	−	9.55817i	−0.468950	−	0.340712i	−0.797032	+	0.603937i	$0.793598\pi$
$788$	20.3705	+	32.0030i	0.725669	+	1.14006i
$789$	−10.7786	+	3.50219i	−0.383729	+	0.124681i
$790$	4.56227	+	15.6639i	0.162318	+	0.557295i
$791$	−20.3855			−0.724823
$792$	0.571382	+	23.8891i	0.0203032	+	0.848863i
$793$	−1.87177			−0.0664686
$794$	11.9124	+	40.8996i	0.422756	+	1.45147i
$795$	7.16285	−	2.32735i	0.254040	−	0.0825427i
$796$	−16.1073	−	25.3053i	−0.570908	−	0.896923i
$797$	33.9304	+	24.6519i	1.20188	+	0.873215i	0.994468	−	0.105039i	$-0.0334967\pi$
$797$	33.9304	+	24.6519i	1.20188	+	0.873215i	0.207410	+	0.978254i	$0.433497\pi$
$798$	0.984694	+	1.44683i	0.0348578	+	0.0512171i
$799$	2.23199	−	6.86935i	0.0789621	−	0.243020i
$800$	0.903818	+	5.58418i	0.0319548	+	0.197431i
$801$	22.1287	−	16.0774i	0.781878	−	0.568067i
$802$	9.31235	−	25.9211i	0.328831	−	0.915304i
$803$	−3.39501	+	16.9195i	−0.119807	+	0.597075i
$804$	−9.22354	−	7.60938i	−0.325289	−	0.268362i
$805$	1.93908	+	2.66891i	0.0683435	+	0.0940668i
$806$	4.48505	+	0.137912i	0.157979	+	0.00485773i
$807$	−9.33340	−	3.03260i	−0.328551	−	0.106753i
$808$	4.91373	−	53.1324i	0.172864	−	1.86919i
$809$	−16.5845	+	22.8266i	−0.583081	+	0.802541i	−0.994029	−	0.109117i	$-0.965198\pi$
$809$	−16.5845	+	22.8266i	−0.583081	+	0.802541i	0.410948	+	0.911659i	$0.365198\pi$
$810$	5.73639	+	4.44339i	0.201556	+	0.156125i
$811$	2.91542	+	8.97273i	0.102374	+	0.315075i	0.989105	−	0.147210i	$-0.0470295\pi$
$811$	2.91542	+	8.97273i	0.102374	+	0.315075i	−0.886731	+	0.462286i	$0.847029\pi$
$812$	0.456337	−	7.41329i	0.0160143	−	0.260156i
$813$		−	4.08107i		−	0.143129i
$814$	1.97604	+	23.0844i	0.0692601	+	0.809107i
$815$			15.3293i			0.536962i
$816$	2.90118	+	2.70966i	0.101562	+	0.0948569i
$817$	1.12945	+	3.47610i	0.0395146	+	0.121613i
$818$	19.8087	−	25.5729i	0.692594	−	0.894136i
$819$	−0.773095	+	1.06407i	−0.0270141	+	0.0371817i
$820$	−9.01988	+	2.32892i	−0.314988	+	0.0813295i
$821$	−31.8788	−	10.3580i	−1.11258	−	0.361498i	−0.305647	−	0.952145i	$-0.598873\pi$
$821$	−31.8788	−	10.3580i	−1.11258	−	0.361498i	−0.806930	+	0.590647i	$0.798873\pi$
$822$	0.0712671	−	2.31769i	0.00248573	−	0.0808388i
$823$	−4.95272	−	6.81684i	−0.172641	−	0.237620i	0.713925	−	0.700222i	$-0.246916\pi$
$823$	−4.95272	−	6.81684i	−0.172641	−	0.237620i	−0.886566	+	0.462602i	$0.846916\pi$
$824$	−0.997142	−	1.67829i	−0.0347371	−	0.0584661i
$825$	1.64116	−	1.51198i	0.0571380	−	0.0526403i
$826$	8.41189	+	3.02204i	0.292687	+	0.105150i
$827$	13.4987	−	9.80735i	0.469394	−	0.341035i	−0.327811	−	0.944743i	$-0.606311\pi$
$827$	13.4987	−	9.80735i	0.469394	−	0.341035i	0.797205	+	0.603708i	$0.206311\pi$
$828$	−9.40888	−	3.71052i	−0.326981	−	0.128950i
$829$	1.36850	−	4.21181i	0.0475300	−	0.146282i	−0.924475	−	0.381243i	$-0.875496\pi$
$829$	1.36850	−	4.21181i	0.0475300	−	0.146282i	0.972005	+	0.234961i	$0.0754962\pi$
$830$	19.9575	−	13.5829i	0.692735	−	0.471468i
$831$	4.80907	+	3.49400i	0.166825	+	0.121205i
$832$	1.80512	−	1.70896i	0.0625811	−	0.0592474i
$833$	5.94621	−	1.93204i	0.206024	−	0.0669413i
$834$	−9.67419	+	2.81771i	−0.334990	+	0.0975693i
$835$	0.141101			0.00488302
$836$	3.98467	−	6.16676i	0.137813	−	0.213282i
$837$	38.1127			1.31737
$838$	−13.3375	+	3.88468i	−0.460735	+	0.134194i
$839$	8.57706	−	2.78685i	0.296113	−	0.0962129i	−0.157193	−	0.987568i	$-0.550245\pi$
$839$	8.57706	−	2.78685i	0.296113	−	0.0962129i	0.453306	+	0.891355i	$0.350245\pi$
$840$	−3.08474	+	0.696098i	−0.106434	+	0.0240176i
$841$	−19.4210	−	14.1102i	−0.669689	−	0.486557i
$842$	23.6776	−	16.1147i	0.815984	−	0.555349i
$843$	−1.78263	+	5.48637i	−0.0613971	+	0.188961i
$844$	−5.31923	+	13.4881i	−0.183095	+	0.464280i
$845$	10.4391	−	7.58446i	0.359116	−	0.260913i
$846$	−16.6012	−	5.96411i	−0.570760	−	0.205050i
$847$	1.49530	−	18.2179i	0.0513791	−	0.625973i
$848$	8.50912	+	43.9598i	0.292204	+	1.50959i
$849$	−7.64175	−	10.5180i	−0.262264	−	0.360976i
$850$	−0.0641139	+	2.08506i	−0.00219909	+	0.0715170i
$851$	−9.32636	−	3.03032i	−0.319704	−	0.103878i
$852$	3.75634	+	14.5482i	0.128690	+	0.498415i
$853$	−7.20055	+	9.91071i	−0.246542	+	0.339336i	−0.914296	−	0.405046i	$-0.867256\pi$
$853$	−7.20055	+	9.91071i	−0.246542	+	0.339336i	0.667754	+	0.744382i	$0.267256\pi$
$854$	−8.66919	+	11.1919i	−0.296653	+	0.382978i
$855$	−0.871284	−	2.68154i	−0.0297973	−	0.0917066i
$856$	−20.2722	+	47.1082i	−0.692888	+	1.61013i
$857$			9.70429i			0.331492i	0.986168	+	0.165746i	$0.0530032\pi$
$857$			9.70429i			0.331492i	−0.986168	+	0.165746i	$0.946997\pi$
$858$	−0.955017	−	0.222369i	−0.0326037	−	0.00759155i
$859$		−	44.8501i		−	1.53027i	−0.643873	−	0.765133i	$-0.722673\pi$
$859$		−	44.8501i		−	1.53027i	0.643873	−	0.765133i	$-0.277327\pi$
$860$	−6.59175	−	0.405766i	−0.224777	−	0.0138365i
$861$	−1.60926	−	4.95280i	−0.0548435	−	0.168791i
$862$	36.8288	+	28.5274i	1.25439	+	0.971648i
$863$	29.6079	−	40.7518i	1.00787	−	1.38721i	0.0874923	−	0.996165i	$-0.472115\pi$
$863$	29.6079	−	40.7518i	1.00787	−	1.38721i	0.920373	−	0.391042i	$-0.127885\pi$
$864$	14.8787	−	14.9797i	0.506185	−	0.509620i
$865$	10.0174	+	3.25486i	0.340603	+	0.110669i
$866$	−29.3550	−	0.902644i	−0.997525	−	0.0306731i
$867$	−5.86255	−	8.06911i	−0.199103	−	0.274041i
$868$	21.5973	−	26.1787i	0.733060	−	0.888563i
$869$	25.9248	+	28.1398i	0.879437	+	0.954577i
$870$	0.718949	−	2.00120i	0.0243747	−	0.0678472i
$871$	−2.23373	+	1.62290i	−0.0756871	+	0.0549899i
$872$	−30.7955	+	35.0739i	−1.04287	+	1.18775i
$873$	8.09999	−	24.9292i	0.274143	−	0.843726i
$874$	1.74846	+	2.56904i	0.0591426	+	0.0868991i
$875$	−1.34437	−	0.976746i	−0.0454482	−	0.0330200i
$876$	5.90644	−	3.75956i	0.199560	−	0.127024i
$877$	−44.5072	+	14.4613i	−1.50290	+	0.488323i	−0.940863	−	0.338788i	$-0.889983\pi$
$877$	−44.5072	+	14.4613i	−1.50290	+	0.488323i	−0.562040	+	0.827110i	$0.689983\pi$
$878$	−1.44543	−	4.96267i	−0.0487809	−	0.167482i
$879$	−7.47990			−0.252291
$880$	7.72441	+	10.7858i	0.260390	+	0.363589i
$881$	−32.7098			−1.10202			−0.551010	−	0.834498i	$-0.685758\pi$
$881$	−32.7098			−1.10202			−0.551010	+	0.834498i	$0.685758\pi$
$882$	−4.26996	−	14.6603i	−0.143777	−	0.493637i
$883$	18.6039	−	6.04477i	0.626070	−	0.203423i	0.0212368	−	0.999774i	$-0.493240\pi$
$883$	18.6039	−	6.04477i	0.626070	−	0.203423i	0.604834	+	0.796352i	$0.293240\pi$
$884$	0.773294	−	0.492216i	0.0260087	−	0.0165550i
$885$	2.07028	+	1.50415i	0.0695918	+	0.0505614i
$886$	2.45249	+	3.60349i	0.0823930	+	0.121061i
$887$	−7.87392	+	24.2334i	−0.264380	+	0.813679i	0.727455	+	0.686155i	$0.240703\pi$
$887$	−7.87392	+	24.2334i	−0.264380	+	0.813679i	−0.991836	+	0.127524i	$0.959297\pi$
$888$	6.20209	−	7.06374i	0.208129	−	0.237043i
$889$	−7.30413	+	5.30676i	−0.244973	+	0.177983i
$890$	5.13424	−	14.2912i	0.172100	−	0.479043i
$891$	16.6843	+	3.34783i	0.558946	+	0.112156i
$892$	−33.3774	+	40.4576i	−1.11756	+	1.35462i
$893$	3.18576	+	4.38482i	0.106607	+	0.146733i
$894$	1.98728	+	0.0611074i	0.0664647	+	0.00204374i
$895$	−4.50894	−	1.46504i	−0.150717	−	0.0489710i
$896$	−1.85788	−	18.7084i	−0.0620674	−	0.625004i
$897$	0.243948	−	0.335766i	0.00814519	−	0.0112109i
$898$	1.66456	+	1.28936i	0.0555472	+	0.0430266i
$899$	7.05199	+	21.7038i	0.235197	+	0.723862i
$900$	5.08501	+	0.313016i	0.169500	+	0.0104339i
$901$			16.5117i			0.550085i
$902$	−16.5151	+	14.3022i	−0.549894	+	0.476210i
$903$		−	3.69191i		−	0.122859i
$904$	13.7155	−	31.8720i	0.456172	−	1.06005i
$905$	−2.45461	−	7.55452i	−0.0815941	−	0.251121i
$906$	6.60963	−	8.53300i	0.219590	−	0.283490i
$907$	24.5814	−	33.8333i	0.816211	−	1.12342i	−0.174124	−	0.984724i	$-0.555709\pi$
$907$	24.5814	−	33.8333i	0.816211	−	1.12342i	0.990335	−	0.138694i	$-0.0442905\pi$
$908$	0.751972	+	2.91237i	0.0249551	+	0.0966505i
$909$	−45.7039	−	14.8501i	−1.51590	−	0.492547i
$910$	−0.0224427	+	0.729862i	−0.000743967	+	0.0241947i
$911$	2.43152	+	3.34670i	0.0805599	+	0.110881i	0.847395	−	0.530963i	$-0.178170\pi$
$911$	2.43152	+	3.34670i	0.0805599	+	0.110881i	−0.766835	+	0.641844i	$0.778170\pi$
$912$	−2.92458	+	0.566099i	−0.0968425	+	0.0187454i
$913$	27.7466	−	49.3508i	0.918280	−	1.63327i
$914$	−13.2804	−	4.77108i	−0.439275	−	0.157813i
$915$	−3.27898	+	2.38232i	−0.108400	+	0.0787571i
$916$	4.83903	−	12.2705i	0.159886	−	0.405428i
$917$	8.15247	−	25.0907i	0.269218	−	0.828569i
$918$	6.43653	−	4.38063i	0.212437	−	0.144582i
$919$	−34.9694	−	25.4068i	−1.15354	−	0.838093i	−0.164588	−	0.986362i	$-0.552630\pi$
$919$	−34.9694	−	25.4068i	−1.15354	−	0.838093i	−0.988947	+	0.148270i	$0.952630\pi$
$920$	−5.47739	+	1.23602i	−0.180584	+	0.0407503i
$921$	18.6264	−	6.05208i	0.613760	−	0.199423i
$922$	26.5050	−	7.71986i	0.872896	−	0.254240i
$923$	3.46950			0.114200
$924$	−5.75281	+	4.68042i	−0.189253	+	0.153974i
$925$	4.93960			0.162413
$926$	7.00758	−	2.04103i	0.230283	−	0.0670724i
$927$	−1.67210	+	0.543298i	−0.0549189	+	0.0178442i
$928$	11.2834	+	5.70120i	0.370396	+	0.187151i
$929$	10.0809	+	7.32423i	0.330745	+	0.240300i	0.740747	−	0.671785i	$-0.234472\pi$
$929$	10.0809	+	7.32423i	0.330745	+	0.240300i	−0.410002	+	0.912085i	$0.634472\pi$
$930$	8.03247	−	5.46681i	0.263395	−	0.179264i
$931$	−1.44978	+	4.46196i	−0.0475145	+	0.146235i
$932$	34.4319	+	13.5787i	1.12786	+	0.444786i
$933$	6.20511	−	4.50828i	0.203146	−	0.147594i
$934$	−3.80299	−	1.36625i	−0.124438	−	0.0447052i
$935$	2.04072	+	4.44626i	0.0667386	+	0.145408i
$936$	−1.14350	−	1.92463i	−0.0373765	−	0.0629084i
$937$	−21.3671	−	29.4093i	−0.698034	−	0.960761i	−0.999972	−	0.00743374i	$-0.997634\pi$
$937$	−21.3671	−	29.4093i	−0.698034	−	0.960761i	0.301939	−	0.953327i	$-0.402366\pi$
$938$	−0.641818	+	20.8727i	−0.0209561	+	0.681517i
$939$	2.01923	+	0.656089i	0.0658952	+	0.0214106i
$940$	−9.48235	+	2.44833i	−0.309280	+	0.0798558i
$941$	6.15466	−	8.47116i	0.200636	−	0.276152i	−0.696829	−	0.717237i	$-0.745406\pi$
$941$	6.15466	−	8.47116i	0.200636	−	0.276152i	0.897465	+	0.441085i	$0.145406\pi$
$942$	9.17366	−	11.8431i	0.298894	−	0.385871i
$943$	−2.85747	−	8.79438i	−0.0930520	−	0.286385i
$944$	−10.3845	+	11.1185i	−0.337986	+	0.361875i
$945$			6.20215i			0.201756i
$946$	−14.2684	+	6.02503i	−0.463904	+	0.195891i
$947$		−	43.0287i		−	1.39825i	−0.715002	−	0.699123i	$-0.753574\pi$
$947$		−	43.0287i		−	1.39825i	0.715002	−	0.699123i	$-0.246426\pi$
$948$	0.953773	−	15.4943i	0.0309771	−	0.503230i
$949$	−0.499588	−	1.53757i	−0.0162173	−	0.0499118i
$950$	−1.23751	−	0.958572i	−0.0401502	−	0.0311002i
$951$	5.60868	−	7.71968i	0.181874	−	0.250328i
$952$	0.638439	−	6.90347i	0.0206919	−	0.223743i
$953$	−22.1136	−	7.18514i	−0.716330	−	0.232750i	−0.0718986	−	0.997412i	$-0.522906\pi$
$953$	−22.1136	−	7.18514i	−0.716330	−	0.232750i	−0.644431	+	0.764662i	$0.722906\pi$
$954$	40.3066	+	1.23940i	1.30497	+	0.0401269i
$955$	5.06046	+	6.96512i	0.163753	+	0.225386i
$956$	−26.5850	−	21.9325i	−0.859820	−	0.709348i
$957$	−0.577840	−	4.95333i	−0.0186789	−	0.160118i
$958$	−14.8579	+	41.3570i	−0.480036	+	1.33619i
$959$	−3.27619	+	2.38029i	−0.105794	+	0.0768637i
$960$	0.987119	−	5.29124i	0.0318591	−	0.170774i
$961$	−22.6431	+	69.6884i	−0.730424	+	2.24801i
$962$	−1.22126	−	1.79442i	−0.0393750	−	0.0578543i
$963$	37.3668	+	27.1486i	1.20413	+	0.874850i
$964$	10.9283	+	17.1689i	0.351978	+	0.552973i
$965$	20.5529	−	6.67804i	0.661621	−	0.214974i
$966$	−0.877786	−	3.01375i	−0.0282423	−	0.0969657i
$967$	−20.7581			−0.667535			−0.333767	−	0.942655i	$-0.608320\pi$
$967$	−20.7581			−0.667535			−0.333767	+	0.942655i	$0.608320\pi$
$968$	27.4770	+	14.5950i	0.883144	+	0.469101i
$969$	−1.09850			−0.0352889
$970$	−4.06944	−	13.9718i	−0.130662	−	0.448608i
$971$	−22.3620	+	7.26585i	−0.717631	+	0.233172i	−0.644996	−	0.764186i	$-0.723141\pi$
$971$	−22.3620	+	7.26585i	−0.717631	+	0.233172i	−0.0726350	+	0.997359i	$0.523141\pi$
$972$	−15.7322	−	24.7160i	−0.504609	−	0.792765i
$973$	14.2365	+	10.3435i	0.456403	+	0.331596i
$974$	−24.7883	−	36.4218i	−0.794268	−	1.16703i
$975$	−0.0646021	+	0.198825i	−0.00206892	+	0.00636749i
$976$	−11.6654	−	21.0840i	−0.373401	−	0.674882i
$977$	−46.4797	+	33.7695i	−1.48702	+	1.08038i	−0.511808	+	0.859100i	$0.671024\pi$
$977$	−46.4797	+	33.7695i	−1.48702	+	1.08038i	−0.975210	+	0.221282i	$0.928976\pi$
$978$	4.93152	−	13.7270i	0.157693	−	0.438940i
$979$	−4.12654	−	35.3733i	−0.131885	−	1.13053i
$980$	−6.53914	−	5.39476i	−0.208885	−	0.172329i
$981$	24.7081	+	34.0078i	0.788869	+	1.08579i
$982$	38.6454	+	1.18831i	1.23322	+	0.0379206i
$983$	−13.1791	−	4.28214i	−0.420347	−	0.136579i	0.0912032	−	0.995832i	$-0.470929\pi$
$983$	−13.1791	−	4.28214i	−0.420347	−	0.136579i	−0.511551	+	0.859253i	$0.670929\pi$
$984$	8.82627	+	0.816261i	0.281371	+	0.0260214i
$985$	11.1491	−	15.3455i	0.355241	−	0.488948i
$986$	3.68556	+	2.85482i	0.117372	+	0.0909161i
$987$	−1.69177	−	5.20674i	−0.0538497	−	0.165732i
$988$	−0.0422615	+	0.686548i	−0.00134452	+	0.0218420i
$989$		−	6.55550i		−	0.208453i
$990$	11.0069	−	4.64783i	0.349822	−	0.147718i
$991$			9.00177i			0.285951i	0.989726	+	0.142975i	$0.0456669\pi$
$991$			9.00177i			0.285951i	−0.989726	+	0.142975i	$0.954333\pi$
$992$	26.3987	+	51.3800i	0.838159	+	1.63132i
$993$	7.44670	+	22.9186i	0.236314	+	0.727300i
$994$	16.0691	−	20.7451i	0.509681	−	0.657996i
$995$	−8.81582	+	12.1339i	−0.279480	+	0.384672i
$996$	−22.2411	+	5.74262i	−0.704735	+	0.181962i
$997$	−38.8804	−	12.6330i	−1.23135	−	0.400091i	−0.380149	−	0.924925i	$-0.624127\pi$
$997$	−38.8804	−	12.6330i	−1.23135	−	0.400091i	−0.851204	+	0.524834i	$0.824127\pi$
$998$	−0.392777	+	12.7736i	−0.0124332	+	0.404341i
$999$	−10.8365	−	14.9152i	−0.342853	−	0.471896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.a.151.1	yes	8
4.3	odd	2		220.2.r.b.151.2	yes	8
11.7	odd	10		220.2.r.b.51.2	yes	8
44.7	even	10	inner	220.2.r.a.51.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.a.51.1	✓	8	44.7	even	10	inner
220.2.r.a.151.1	yes	8	1.1	even	1	trivial
220.2.r.b.51.2	yes	8	11.7	odd	10
220.2.r.b.151.2	yes	8	4.3	odd	2

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395472 + 1.35779i) q^{2} +(-0.639886 + 0.207912i) q^{3} +(-1.68720 + 1.07394i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.535358 - 0.786610i) q^{6} +(-0.513506 + 1.58041i) q^{7} +(-2.12543 - 1.86616i) q^{8} +(-2.06082 + 1.49728i) q^{9} +(-0.478148 + 1.33093i) q^{10} +(0.384301 + 3.29428i) q^{11} +(0.856335 - 1.03799i) q^{12} +(-0.182636 - 0.251377i) q^{13} +(-2.34894 - 0.0722281i) q^{14} +(-0.639886 - 0.207912i) q^{15} +(1.69332 - 3.62390i) q^{16} +(0.867017 - 1.19335i) q^{17} +(-2.84799 - 2.20604i) q^{18} +(0.342040 + 1.05269i) q^{19} +(-1.99622 - 0.122881i) q^{20} -1.11805i q^{21} +(-4.32098 + 1.82460i) q^{22} -1.98524i q^{23} +(1.74803 + 0.752232i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.269091 - 0.347395i) q^{26} +(2.19381 - 3.01952i) q^{27} +(-0.830869 - 3.21794i) q^{28} +(2.12543 + 0.690593i) q^{29} +(0.0292442 - 0.951057i) q^{30} +(6.00217 + 8.26128i) q^{31} +(5.59017 + 0.866025i) q^{32} +(-0.930829 - 2.02807i) q^{33} +(1.96320 + 0.705295i) q^{34} +(-1.34437 + 0.976746i) q^{35} +(1.86905 - 4.73941i) q^{36} +(1.52642 - 4.69784i) q^{37} +(-1.29407 + 0.880728i) q^{38} +(0.169131 + 0.122881i) q^{39} +(-0.622602 - 2.75905i) q^{40} +(4.42987 - 1.43935i) q^{41} +(1.51807 - 0.442155i) q^{42} +3.30211 q^{43} +(-4.18625 - 5.14542i) q^{44} -2.54732 q^{45} +(2.69555 - 0.785108i) q^{46} +(4.65701 - 1.51315i) q^{47} +(-0.330079 + 2.67095i) q^{48} +(3.42912 + 2.49140i) q^{49} +(-1.16913 + 0.795697i) q^{50} +(-0.306682 + 0.943869i) q^{51} +(0.578108 + 0.227985i) q^{52} +(-9.05609 + 6.57963i) q^{53} +(4.96747 + 1.78460i) q^{54} +(-1.62543 + 2.89102i) q^{55} +(4.04072 - 2.40075i) q^{56} +(-0.437733 - 0.602488i) q^{57} +(-0.0971366 + 3.15900i) q^{58} +(-3.61728 - 1.17533i) q^{59} +(1.30290 - 0.336408i) q^{60} +(3.54082 - 4.87352i) q^{61} +(-8.84342 + 11.4168i) q^{62} +(-1.30806 - 4.02580i) q^{63} +(1.03487 + 7.93278i) q^{64} -0.310719i q^{65} +(2.38558 - 2.06592i) q^{66} -8.88598i q^{67} +(-0.181256 + 2.94454i) q^{68} +(0.412756 + 1.27033i) q^{69} +(-1.85788 - 1.43911i) q^{70} +(-6.56322 + 9.03350i) q^{71} +(7.17429 + 0.663484i) q^{72} +(4.94844 + 1.60784i) q^{73} +(6.98235 + 0.214702i) q^{74} +(-0.395472 - 0.544320i) q^{75} +(-1.70761 - 1.40877i) q^{76} +(-5.40365 - 1.08428i) q^{77} +(-0.0999601 + 0.278240i) q^{78} +(9.33304 - 6.78085i) q^{79} +(3.50000 - 1.93649i) q^{80} +(1.58550 - 4.87967i) q^{81} +(3.70623 + 5.44563i) q^{82} +(-13.8102 - 10.0337i) q^{83} +(1.20071 + 1.88637i) q^{84} +(1.40286 - 0.455818i) q^{85} +(1.30589 + 4.48359i) q^{86} -1.50361 q^{87} +(5.33087 - 7.71893i) q^{88} -10.7378 q^{89} +(-1.00739 - 3.45873i) q^{90} +(0.491063 - 0.159556i) q^{91} +(2.13203 + 3.34951i) q^{92} +(-5.55832 - 4.03836i) q^{93} +(3.89626 + 5.72484i) q^{94} +(-0.342040 + 1.05269i) q^{95} +(-3.75713 + 0.608104i) q^{96} +(-8.32486 + 6.04836i) q^{97} +(-2.02669 + 5.64131i) q^{98} +(-5.72443 - 6.21354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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