LMFDB - Embedded newform 520.2.by.c.61.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(61,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("520.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.by (of order $6$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.9
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17245 + 0.790798i) q^{2} +(-0.105918 - 0.0611516i) q^{3} +(0.749278 - 1.85434i) q^{4} +1.00000i q^{5} +(0.172542 - 0.0120623i) q^{6} +(-0.0953817 - 0.165206i) q^{7} +(0.587918 + 2.76665i) q^{8} +(-1.49252 - 2.58512i) q^{9} +O(q^{10})$	\(q+(-1.17245 + 0.790798i) q^{2} +(-0.105918 - 0.0611516i) q^{3} +(0.749278 - 1.85434i) q^{4} +1.00000i q^{5} +(0.172542 - 0.0120623i) q^{6} +(-0.0953817 - 0.165206i) q^{7} +(0.587918 + 2.76665i) q^{8} +(-1.49252 - 2.58512i) q^{9} +(-0.790798 - 1.17245i) q^{10} +(-2.12420 - 1.22641i) q^{11} +(-0.192758 + 0.150588i) q^{12} +(-2.18946 - 2.86466i) q^{13} +(0.242475 + 0.118268i) q^{14} +(0.0611516 - 0.105918i) q^{15} +(-2.87717 - 2.77883i) q^{16} +(2.49932 + 4.32896i) q^{17} +(3.79421 + 1.85064i) q^{18} +(-6.92772 + 3.99972i) q^{19} +(1.85434 + 0.749278i) q^{20} +0.0233310i q^{21} +(3.46036 - 0.241912i) q^{22} +(3.78448 - 6.55491i) q^{23} +(0.106914 - 0.328990i) q^{24} -1.00000 q^{25} +(4.83240 + 1.62725i) q^{26} +0.731990i q^{27} +(-0.377816 + 0.0530851i) q^{28} +(-4.47749 - 2.58508i) q^{29} +(0.0120623 + 0.172542i) q^{30} -7.61772 q^{31} +(5.57083 + 0.982788i) q^{32} +(0.149994 + 0.259797i) q^{33} +(-6.35366 - 3.09902i) q^{34} +(0.165206 - 0.0953817i) q^{35} +(-5.91201 + 0.830669i) q^{36} +(-3.17825 - 1.83496i) q^{37} +(4.95943 - 10.1679i) q^{38} +(0.0567241 + 0.437307i) q^{39} +(-2.76665 + 0.587918i) q^{40} +(3.35405 - 5.80938i) q^{41} +(-0.0184501 - 0.0273544i) q^{42} +(-1.68267 + 0.971488i) q^{43} +(-3.86580 + 3.02008i) q^{44} +(2.58512 - 1.49252i) q^{45} +(0.746495 + 10.6781i) q^{46} -8.35969 q^{47} +(0.134813 + 0.470271i) q^{48} +(3.48180 - 6.03066i) q^{49} +(1.17245 - 0.790798i) q^{50} -0.611351i q^{51} +(-6.95257 + 1.91358i) q^{52} -2.27807i q^{53} +(-0.578856 - 0.858222i) q^{54} +(1.22641 - 2.12420i) q^{55} +(0.400990 - 0.361015i) q^{56} +0.978358 q^{57} +(7.29391 - 0.509912i) q^{58} +(7.97682 - 4.60542i) q^{59} +(-0.150588 - 0.192758i) q^{60} +(4.08245 - 2.35700i) q^{61} +(8.93139 - 6.02407i) q^{62} +(-0.284718 + 0.493146i) q^{63} +(-7.30870 + 3.25313i) q^{64} +(2.86466 - 2.18946i) q^{65} +(-0.381307 - 0.185984i) q^{66} +(-9.32800 - 5.38552i) q^{67} +(9.90005 - 1.39101i) q^{68} +(-0.801687 + 0.462854i) q^{69} +(-0.118268 + 0.242475i) q^{70} +(-2.99802 - 5.19272i) q^{71} +(6.27465 - 5.64912i) q^{72} +16.6184 q^{73} +(5.17742 - 0.361950i) q^{74} +(0.105918 + 0.0611516i) q^{75} +(2.22606 + 15.8433i) q^{76} +0.467908i q^{77} +(-0.412328 - 0.467864i) q^{78} -11.2814 q^{79} +(2.77883 - 2.87717i) q^{80} +(-4.43280 + 7.67784i) q^{81} +(0.661592 + 9.46358i) q^{82} +13.0475i q^{83} +(0.0432636 + 0.0174814i) q^{84} +(-4.32896 + 2.49932i) q^{85} +(1.20459 - 2.46967i) q^{86} +(0.316164 + 0.547612i) q^{87} +(2.14419 - 6.59796i) q^{88} +(-7.78874 + 13.4905i) q^{89} +(-1.85064 + 3.79421i) q^{90} +(-0.264424 + 0.634948i) q^{91} +(-9.31941 - 11.9292i) q^{92} +(0.806852 + 0.465836i) q^{93} +(9.80132 - 6.61082i) q^{94} +(-3.99972 - 6.92772i) q^{95} +(-0.529951 - 0.444760i) q^{96} +(0.130150 + 0.225427i) q^{97} +(0.686793 + 9.82405i) q^{98} +7.32177i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.17245	+	0.790798i	−0.829047	+	0.559178i
$2$	−1.17245	+	0.790798i	−0.829047	+	0.559178i
$3$	−0.105918	−	0.0611516i	−0.0611516	−	0.0353059i	0.469112	−	0.883138i	$-0.344574\pi$
$3$	−0.105918	−	0.0611516i	−0.0611516	−	0.0353059i	−0.530264	+	0.847833i	$0.677907\pi$
$4$	0.749278	−	1.85434i	0.374639	−	0.927171i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.172542	−	0.0120623i	0.0704399	−	0.00492440i
$7$	−0.0953817	−	0.165206i	−0.0360509	−	0.0624420i	0.847437	−	0.530896i	$-0.178145\pi$
$7$	−0.0953817	−	0.165206i	−0.0360509	−	0.0624420i	−0.883488	+	0.468454i	$0.844811\pi$
$8$	0.587918	+	2.76665i	0.207861	+	0.978158i
$9$	−1.49252	−	2.58512i	−0.497507	−	0.861707i
$10$	−0.790798	−	1.17245i	−0.250072	−	0.370761i
$11$	−2.12420	−	1.22641i	−0.640472	−	0.369776i	0.144325	−	0.989530i	$-0.453899\pi$
$11$	−2.12420	−	1.22641i	−0.640472	−	0.369776i	−0.784796	+	0.619754i	$0.787232\pi$
$12$	−0.192758	+	0.150588i	−0.0556444	+	0.0434710i
$13$	−2.18946	−	2.86466i	−0.607247	−	0.794513i
$13$	−2.18946	−	2.86466i	−0.607247	−	0.794513i
$14$	0.242475	+	0.118268i	0.0648041	+	0.0316085i
$15$	0.0611516	−	0.105918i	0.0157893	−	0.0273478i
$16$	−2.87717	−	2.77883i	−0.719291	−	0.694709i
$17$	2.49932	+	4.32896i	0.606175	+	1.04993i	0.991865	+	0.127297i	$0.0406302\pi$
$17$	2.49932	+	4.32896i	0.606175	+	1.04993i	−0.385690	+	0.922629i	$0.626036\pi$
$18$	3.79421	+	1.85064i	0.894305	+	0.436201i
$19$	−6.92772	+	3.99972i	−1.58933	+	0.917599i	−0.595910	+	0.803051i	$0.703209\pi$
$19$	−6.92772	+	3.99972i	−1.58933	+	0.917599i	−0.993418	+	0.114548i	$0.963458\pi$
$20$	1.85434	+	0.749278i	0.414643	+	0.167544i
$21$			0.0233310i			0.00509124i
$22$	3.46036	−	0.241912i	0.737752	−	0.0515757i
$23$	3.78448	−	6.55491i	0.789118	−	1.36679i	−0.137390	−	0.990517i	$-0.543871\pi$
$23$	3.78448	−	6.55491i	0.789118	−	1.36679i	0.926508	−	0.376276i	$-0.122795\pi$
$24$	0.106914	−	0.328990i	0.0218238	−	0.0671547i
$25$	−1.00000			−0.200000
$26$	4.83240	+	1.62725i	0.947711	+	0.319130i
$27$			0.731990i			0.140872i
$28$	−0.377816	+	0.0530851i	−0.0714004	+	0.0100321i
$29$	−4.47749	−	2.58508i	−0.831449	−	0.480037i	0.0228995	−	0.999738i	$-0.492710\pi$
$29$	−4.47749	−	2.58508i	−0.831449	−	0.480037i	−0.854349	+	0.519700i	$0.826044\pi$
$30$	0.0120623	+	0.172542i	0.00220226	+	0.0315017i
$31$	−7.61772			−1.36818			−0.684091	−	0.729396i	$-0.739801\pi$
$31$	−7.61772			−1.36818			−0.684091	+	0.729396i	$0.739801\pi$
$32$	5.57083	+	0.982788i	0.984793	+	0.173734i
$33$	0.149994	+	0.259797i	0.0261106	+	0.0452249i
$34$	−6.35366	−	3.09902i	−1.08964	−	0.531478i
$35$	0.165206	−	0.0953817i	0.0279249	−	0.0161224i
$36$	−5.91201	+	0.830669i	−0.985335	+	0.138445i
$37$	−3.17825	−	1.83496i	−0.522501	−	0.301666i	0.215456	−	0.976513i	$-0.430876\pi$
$37$	−3.17825	−	1.83496i	−0.522501	−	0.301666i	−0.737957	+	0.674847i	$0.764209\pi$
$38$	4.95943	−	10.1679i	0.804527	−	1.64945i
$39$	0.0567241	+	0.437307i	0.00908313	+	0.0700252i
$40$	−2.76665	+	0.587918i	−0.437446	+	0.0929580i
$41$	3.35405	−	5.80938i	0.523814	−	0.907273i	−0.475801	−	0.879553i	$-0.657842\pi$
$41$	3.35405	−	5.80938i	0.523814	−	0.907273i	0.999616	−	0.0277202i	$-0.00882475\pi$
$42$	−0.0184501	−	0.0273544i	−0.00284691	−	0.00422088i
$43$	−1.68267	+	0.971488i	−0.256604	+	0.148151i	−0.622785	−	0.782393i	$-0.713999\pi$
$43$	−1.68267	+	0.971488i	−0.256604	+	0.148151i	0.366180	+	0.930544i	$0.380665\pi$
$44$	−3.86580	+	3.02008i	−0.582791	+	0.455294i
$45$	2.58512	−	1.49252i	0.385367	−	0.222492i
$46$	0.746495	+	10.6781i	0.110065	+	1.57439i
$47$	−8.35969			−1.21939			−0.609693	−	0.792638i	$-0.708707\pi$
$47$	−8.35969			−1.21939			−0.609693	+	0.792638i	$0.708707\pi$
$48$	0.134813	+	0.470271i	0.0194585	+	0.0678778i
$49$	3.48180	−	6.03066i	0.497401	−	0.861523i
$50$	1.17245	−	0.790798i	0.165809	−	0.111836i
$51$		−	0.611351i		−	0.0856063i
$52$	−6.95257	+	1.91358i	−0.964148	+	0.265366i
$53$		−	2.27807i		−	0.312917i	−0.987685	−	0.156459i	$-0.949992\pi$
$53$		−	2.27807i		−	0.312917i	0.987685	−	0.156459i	$-0.0500078\pi$
$54$	−0.578856	−	0.858222i	−0.0787724	−	0.116789i
$55$	1.22641	−	2.12420i	0.165369	−	0.286428i
$56$	0.400990	−	0.361015i	0.0535846	−	0.0482427i
$57$	0.978358			0.129587
$58$	7.29391	−	0.509912i	0.957737	−	0.0669547i
$59$	7.97682	−	4.60542i	1.03849	−	0.599575i	0.119088	−	0.992884i	$-0.462003\pi$
$59$	7.97682	−	4.60542i	1.03849	−	0.599575i	0.919406	+	0.393309i	$0.128670\pi$
$60$	−0.150588	−	0.192758i	−0.0194408	−	0.0248849i
$61$	4.08245	−	2.35700i	0.522704	−	0.301784i	−0.215336	−	0.976540i	$-0.569085\pi$
$61$	4.08245	−	2.35700i	0.522704	−	0.301784i	0.738040	+	0.674757i	$0.235751\pi$
$62$	8.93139	−	6.02407i	1.13429	−	0.765058i
$63$	−0.284718	+	0.493146i	−0.0358711	+	0.0621306i
$64$	−7.30870	+	3.25313i	−0.913588	+	0.406641i
$65$	2.86466	−	2.18946i	0.355317	−	0.271569i
$66$	−0.381307	−	0.185984i	−0.0469357	−	0.0228931i
$67$	−9.32800	−	5.38552i	−1.13960	−	0.657946i	−0.193266	−	0.981146i	$-0.561908\pi$
$67$	−9.32800	−	5.38552i	−1.13960	−	0.657946i	−0.946331	+	0.323200i	$0.895241\pi$
$68$	9.90005	−	1.39101i	1.20056	−	0.168685i
$69$	−0.801687	+	0.462854i	−0.0965118	+	0.0557211i
$70$	−0.118268	+	0.242475i	−0.0141357	+	0.0289813i
$71$	−2.99802	−	5.19272i	−0.355799	−	0.616263i	0.631455	−	0.775412i	$-0.282458\pi$
$71$	−2.99802	−	5.19272i	−0.355799	−	0.616263i	−0.987254	+	0.159150i	$0.949125\pi$
$72$	6.27465	−	5.64912i	0.739474	−	0.665756i
$73$	16.6184			1.94504			0.972519	−	0.232825i	$-0.0747969\pi$
$73$	16.6184			1.94504			0.972519	+	0.232825i	$0.0747969\pi$
$74$	5.17742	−	0.361950i	0.601863	−	0.0420758i
$75$	0.105918	+	0.0611516i	0.0122303	+	0.00706118i
$76$	2.22606	+	15.8433i	0.255347	+	1.81735i
$77$			0.467908i			0.0533231i
$78$	−0.412328	−	0.467864i	−0.0466869	−	0.0529751i
$79$	−11.2814			−1.26926			−0.634631	−	0.772815i	$-0.718848\pi$
$79$	−11.2814			−1.26926			−0.634631	+	0.772815i	$0.718848\pi$
$80$	2.77883	−	2.87717i	0.310683	−	0.321677i
$81$	−4.43280	+	7.67784i	−0.492533	+	0.853093i
$82$	0.661592	+	9.46358i	0.0730606	+	1.04508i
$83$			13.0475i			1.43215i	0.698021	+	0.716077i	$0.254064\pi$
$83$			13.0475i			1.43215i	−0.698021	+	0.716077i	$0.745936\pi$
$84$	0.0432636	+	0.0174814i	0.00472045	+	0.00190738i
$85$	−4.32896	+	2.49932i	−0.469541	+	0.271090i
$86$	1.20459	−	2.46967i	0.129895	−	0.266311i
$87$	0.316164	+	0.547612i	0.0338963	+	0.0587101i
$88$	2.14419	−	6.59796i	0.228571	−	0.703345i
$89$	−7.78874	+	13.4905i	−0.825604	+	1.42999i	0.0758520	+	0.997119i	$0.475832\pi$
$89$	−7.78874	+	13.4905i	−0.825604	+	1.42999i	−0.901456	+	0.432870i	$0.857501\pi$
$90$	−1.85064	+	3.79421i	−0.195075	+	0.399945i
$91$	−0.264424	+	0.634948i	−0.0277192	+	0.0665606i
$92$	−9.31941	−	11.9292i	−0.971616	−	1.24370i
$93$	0.806852	+	0.465836i	0.0836666	+	0.0483049i
$94$	9.80132	−	6.61082i	1.01093	−	0.681854i
$95$	−3.99972	−	6.92772i	−0.410363	−	0.710769i
$96$	−0.529951	−	0.444760i	−0.0540878	−	0.0453931i
$97$	0.130150	+	0.225427i	0.0132148	+	0.0228887i	0.872557	−	0.488512i	$-0.162460\pi$
$97$	0.130150	+	0.225427i	0.0132148	+	0.0228887i	−0.859342	+	0.511401i	$0.829127\pi$
$98$	0.686793	+	9.82405i	0.0693765	+	0.992379i
$99$			7.32177i			0.735865i
$100$	−0.749278	+	1.85434i	−0.0749278	+	0.185434i
$101$	4.79421	+	2.76794i	0.477041	+	0.275420i	0.719183	−	0.694821i	$-0.244516\pi$
$101$	4.79421	+	2.76794i	0.477041	+	0.275420i	−0.242141	+	0.970241i	$0.577850\pi$
$102$	0.483455	+	0.716778i	0.0478692	+	0.0709716i
$103$	2.98104			0.293730			0.146865	−	0.989157i	$-0.453082\pi$
$103$	2.98104			0.293730			0.146865	+	0.989157i	$0.453082\pi$
$104$	6.63828	−	7.74165i	0.650937	−	0.759132i
$105$	−0.0233310			−0.00227687
$106$	1.80149	+	2.67092i	0.174976	+	0.259423i
$107$	2.44243	+	1.41014i	0.236119	+	0.136323i	0.613392	−	0.789779i	$-0.289805\pi$
$107$	2.44243	+	1.41014i	0.236119	+	0.136323i	−0.377273	+	0.926102i	$0.623138\pi$
$108$	1.35736	+	0.548464i	0.130612	+	0.0527760i
$109$			0.491524i			0.0470795i	0.999723	+	0.0235398i	$0.00749363\pi$
$109$			0.491524i			0.0470795i	−0.999723	+	0.0235398i	$0.992506\pi$
$110$	0.241912	+	3.46036i	0.0230654	+	0.329933i
$111$	0.224422	+	0.388710i	0.0213012	+	0.0368947i
$112$	−0.184651	+	0.740374i	−0.0174479	+	0.0699588i
$113$	−0.375893	−	0.651066i	−0.0353610	−	0.0612471i	0.847803	−	0.530311i	$-0.177925\pi$
$113$	−0.375893	−	0.651066i	−0.0353610	−	0.0612471i	−0.883164	+	0.469064i	$0.844591\pi$
$114$	−1.14708	+	0.773683i	−0.107433	+	0.0724621i
$115$	6.55491	+	3.78448i	0.611248	+	0.352904i
$116$	−8.14851	+	6.36585i	−0.756570	+	0.591055i
$117$	−4.13768	+	9.93558i	−0.382528	+	0.918545i
$118$	−5.71047	+	11.7077i	−0.525691	+	1.07778i
$119$	0.476779	−	0.825806i	0.0437063	−	0.0757015i
$120$	0.328990	+	0.106914i	0.0300325	+	0.00975989i
$121$	−2.49184	−	4.31599i	−0.226531	−	0.392363i
$122$	−2.92256	+	5.99186i	−0.264596	+	0.542478i
$123$	−0.710506	+	0.410211i	−0.0640642	+	0.0369875i
$124$	−5.70779	+	14.1259i	−0.512574	+	1.26854i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.0561612	−	0.803344i	−0.00500324	−	0.0715676i
$127$	1.66941	−	2.89150i	0.148136	−	0.256579i	−0.782403	−	0.622773i	$-0.786006\pi$
$127$	1.66941	−	2.89150i	0.148136	−	0.256579i	0.930539	+	0.366194i	$0.119339\pi$
$128$	5.99652	−	9.59384i	0.530023	−	0.847983i
$129$	0.237632			0.0209224
$130$	−1.62725	+	4.83240i	−0.142719	+	0.423829i
$131$		−	2.05289i		−	0.179362i	−0.995971	−	0.0896810i	$-0.971415\pi$
$131$		−	2.05289i		−	0.179362i	0.995971	−	0.0896810i	$-0.0285848\pi$
$132$	0.594140	−	0.0834798i	0.0517132	−	0.00726598i
$133$	1.32155	+	0.763000i	0.114593	+	0.0661605i
$134$	15.1955	−	1.06230i	1.31269	−	0.0917691i
$135$	−0.731990			−0.0629997
$136$	−10.5073	+	9.45983i	−0.900994	+	0.811173i
$137$	10.5797	+	18.3246i	0.903886	+	1.56558i	0.822405	+	0.568902i	$0.192632\pi$
$137$	10.5797	+	18.3246i	0.903886	+	1.56558i	0.0814809	+	0.996675i	$0.474035\pi$
$138$	0.573914	−	1.17665i	0.0488548	−	0.100163i
$139$	−18.4629	+	10.6596i	−1.56601	+	0.904134i	−0.569378	+	0.822076i	$0.692816\pi$
$139$	−18.4629	+	10.6596i	−1.56601	+	0.904134i	−0.996628	+	0.0820581i	$0.973851\pi$
$140$	−0.0530851	−	0.377816i	−0.00448651	−	0.0319312i
$141$	0.885439	+	0.511209i	0.0745675	+	0.0430515i
$142$	7.62142	+	3.71738i	0.639575	+	0.311956i
$143$	1.13761	+	8.77029i	0.0951321	+	0.733409i
$144$	−2.88940	+	11.5853i	−0.240783	+	0.965441i
$145$	2.58508	−	4.47749i	0.214679	−	0.371835i
$146$	−19.4843	+	13.1418i	−1.61253	+	1.08762i
$147$	−0.737570	+	0.425836i	−0.0608337	+	0.0351224i
$148$	−5.78404	+	4.51866i	−0.475445	+	0.371432i
$149$	17.4362	−	10.0668i	1.42843	−	0.824703i	0.431431	−	0.902146i	$-0.358009\pi$
$149$	17.4362	−	10.0668i	1.42843	−	0.824703i	0.996997	+	0.0774433i	$0.0246757\pi$
$150$	−0.172542	+	0.0120623i	−0.0140880	+	0.000984881i
$151$	6.92545			0.563585			0.281793	−	0.959475i	$-0.409071\pi$
$151$	6.92545			0.563585			0.281793	+	0.959475i	$0.409071\pi$
$152$	−15.1388	−	16.8151i	−1.22792	−	1.36388i
$153$	7.46059	−	12.9221i	0.603153	−	1.04469i
$154$	−0.370021	−	0.548599i	−0.0298171	−	0.0442073i
$155$		−	7.61772i		−	0.611870i
$156$	0.853419	+	0.222479i	0.0683282	+	0.0178126i
$157$			21.3529i			1.70415i	0.523422	+	0.852074i	$0.324655\pi$
$157$			21.3529i			1.70415i	−0.523422	+	0.852074i	$0.675345\pi$
$158$	13.2269	−	8.92134i	1.05228	−	0.709744i
$159$	−0.139308	+	0.241288i	−0.0110478	+	0.0191354i
$160$	−0.982788	+	5.57083i	−0.0776962	+	0.440413i
$161$	−1.44388			−0.113794
$162$	−0.874378	−	12.5073i	−0.0686976	−	0.982668i
$163$	5.23053	−	3.01985i	0.409687	−	0.236533i	−0.280968	−	0.959717i	$-0.590656\pi$
$163$	5.23053	−	3.01985i	0.409687	−	0.236533i	0.690655	+	0.723184i	$0.257322\pi$
$164$	−8.25946	−	10.5724i	−0.644956	−	0.825565i
$165$	−0.259797	+	0.149994i	−0.0202252	+	0.0116770i
$166$	−10.3180	−	15.2976i	−0.800830	−	1.18732i
$167$	−10.3782	+	17.9756i	−0.803089	+	1.39099i	0.114485	+	0.993425i	$0.463478\pi$
$167$	−10.3782	+	17.9756i	−0.803089	+	1.39099i	−0.917574	+	0.397566i	$0.869855\pi$
$168$	−0.0645487	+	0.0137167i	−0.00498004	+	0.00105827i
$169$	−3.41253	+	12.5441i	−0.262502	+	0.964931i
$170$	3.09902	−	6.35366i	0.237684	−	0.487303i
$171$	20.6795	+	11.9393i	1.58140	+	0.913024i
$172$	0.540686	+	3.84815i	0.0412269	+	0.293419i
$173$	12.4869	−	7.20929i	0.949358	−	0.548112i	0.0564763	−	0.998404i	$-0.482013\pi$
$173$	12.4869	−	7.20929i	0.949358	−	0.548112i	0.892881	+	0.450292i	$0.148680\pi$
$174$	−0.803736	−	0.392026i	−0.0609311	−	0.0297194i
$175$	0.0953817	+	0.165206i	0.00721018	+	0.0124884i
$176$	2.70370	+	9.43139i	0.203799	+	0.710918i
$177$	−1.12652			−0.0846742
$178$	−1.53634	−	21.9762i	−0.115154	−	1.64719i
$179$	7.80552	+	4.50652i	0.583412	+	0.336833i	0.762488	−	0.647002i	$-0.223977\pi$
$179$	7.80552	+	4.50652i	0.583412	+	0.336833i	−0.179076	+	0.983835i	$0.557311\pi$
$180$	−0.830669	−	5.91201i	−0.0619144	−	0.440655i
$181$		−	14.3364i		−	1.06562i	−0.846235	−	0.532810i	$-0.821136\pi$
$181$		−	14.3364i		−	1.06562i	0.846235	−	0.532810i	$-0.178864\pi$
$182$	−0.192091	−	0.953550i	−0.0142387	−	0.0706818i
$183$	−0.576539			−0.0426190
$184$	20.3601	+	6.61658i	1.50097	+	0.487780i
$185$	1.83496	−	3.17825i	0.134909	−	0.233670i
$186$	−1.31438	+	0.0918870i	−0.0963747	+	0.00673748i
$187$		−	12.2608i		−	0.896597i
$188$	−6.26373	+	15.5017i	−0.456829	+	1.13058i
$189$	0.120929	−	0.0698185i	0.00879630	−	0.00507855i
$190$	10.1679	+	4.95943i	0.737657	+	0.359795i
$191$	−7.55155	−	13.0797i	−0.546411	−	0.946412i	−0.998517	−	0.0544473i	$-0.982660\pi$
$191$	−7.55155	−	13.0797i	−0.546411	−	0.946412i	0.452106	−	0.891964i	$-0.350673\pi$
$192$	0.973056	+	0.102375i	0.0702242	+	0.00738830i
$193$	−2.48640	+	4.30658i	−0.178975	+	0.309994i	−0.941530	−	0.336930i	$-0.890612\pi$
$193$	−2.48640	+	4.30658i	−0.178975	+	0.309994i	0.762555	+	0.646924i	$0.223945\pi$
$194$	−0.330862	−	0.161379i	−0.0237545	−	0.0115864i
$195$	−0.437307	+	0.0567241i	−0.0313162	+	0.00406210i
$196$	−8.57407	−	10.9751i	−0.612434	−	0.783936i
$197$	−16.7477	−	9.66932i	−1.19323	−	0.688910i	−0.234191	−	0.972191i	$-0.575244\pi$
$197$	−16.7477	−	9.66932i	−1.19323	−	0.688910i	−0.959037	+	0.283280i	$0.908577\pi$
$198$	−5.79004	−	8.58441i	−0.411480	−	0.610067i
$199$	0.304000	+	0.526544i	0.0215500	+	0.0373257i	0.876599	−	0.481221i	$-0.159807\pi$
$199$	0.304000	+	0.526544i	0.0215500	+	0.0373257i	−0.855049	+	0.518547i	$0.826473\pi$
$200$	−0.587918	−	2.76665i	−0.0415721	−	0.195632i
$201$	0.658667	+	1.14085i	0.0464588	+	0.0804690i
$202$	−7.80984	+	0.545981i	−0.549499	+	0.0384151i
$203$			0.986277i			0.0692231i
$204$	−1.13365	−	0.458072i	−0.0793716	−	0.0320714i
$205$	5.80938	+	3.35405i	0.405745	+	0.234257i
$206$	−3.49512	+	2.35740i	−0.243516	+	0.164248i
$207$	−22.5937			−1.57037
$208$	−1.66097	+	14.3262i	−0.115168	+	0.993346i
$209$	19.6212			1.35723
$210$	0.0273544	−	0.0184501i	0.00188763	−	0.00127318i
$211$	−0.338187	−	0.195252i	−0.0232818	−	0.0134417i	0.488314	−	0.872668i	$-0.337612\pi$
$211$	−0.338187	−	0.195252i	−0.0232818	−	0.0134417i	−0.511596	+	0.859226i	$0.670945\pi$
$212$	−4.22432	−	1.70691i	−0.290128	−	0.117231i
$213$			0.733335i			0.0502473i
$214$	−3.97877	+	0.278153i	−0.271983	+	0.0190141i
$215$	−0.971488	−	1.68267i	−0.0662550	−	0.114757i
$216$	−2.02516	+	0.430351i	−0.137795	+	0.0292816i
$217$	0.726591	+	1.25849i	0.0493242	+	0.0854320i
$218$	−0.388696	−	0.576288i	−0.0263258	−	0.0390311i
$219$	−1.76018	−	1.01624i	−0.118942	−	0.0686713i
$220$	−3.02008	−	3.86580i	−0.203614	−	0.260632i
$221$	6.92881	−	16.6378i	0.466082	−	1.11918i
$222$	−0.570515	−	0.278271i	−0.0382904	−	0.0186763i
$223$	1.69664	−	2.93867i	0.113616	−	0.196788i	−0.803610	−	0.595156i	$-0.797090\pi$
$223$	1.69664	−	2.93867i	0.113616	−	0.196788i	0.917225	+	0.398368i	$0.130423\pi$
$224$	−0.368992	−	1.01407i	−0.0246543	−	0.0677556i
$225$	1.49252	+	2.58512i	0.0995014	+	0.172341i
$226$	0.955577	+	0.466087i	0.0635640	+	0.0310036i
$227$	12.1843	−	7.03460i	0.808699	−	0.466903i	−0.0378047	−	0.999285i	$-0.512036\pi$
$227$	12.1843	−	7.03460i	0.808699	−	0.466903i	0.846504	+	0.532382i	$0.178703\pi$
$228$	0.733062	−	1.81421i	0.0485482	−	0.120149i
$229$		−	24.4844i		−	1.61798i	−0.587824	−	0.808989i	$-0.700015\pi$
$229$		−	24.4844i		−	1.61798i	0.587824	−	0.808989i	$-0.299985\pi$
$230$	−10.6781	+	0.746495i	−0.704090	+	0.0492225i
$231$	0.0286133	−	0.0495598i	0.00188262	−	0.00326079i
$232$	4.51961	−	13.9075i	0.296727	−	0.913070i
$233$	−15.7233			−1.03007			−0.515033	−	0.857170i	$-0.672220\pi$
$233$	−15.7233			−1.03007			−0.515033	+	0.857170i	$0.672220\pi$
$234$	−3.00582	−	14.9210i	−0.196497	−	0.975419i
$235$		−	8.35969i		−	0.545326i
$236$	−2.56317	−	18.2425i	−0.166848	−	1.18749i
$237$	1.19491	+	0.689879i	0.0776175	+	0.0448125i
$238$	0.0940456	+	1.34525i	0.00609607	+	0.0871997i
$239$	21.4788			1.38935			0.694674	−	0.719325i	$-0.255549\pi$
$239$	21.4788			1.38935			0.694674	+	0.719325i	$0.255549\pi$
$240$	−0.470271	+	0.134813i	−0.0303559	+	0.00870212i
$241$	−5.53926	−	9.59428i	−0.356815	−	0.618022i	0.630612	−	0.776098i	$-0.282804\pi$
$241$	−5.53926	−	9.59428i	−0.356815	−	0.618022i	−0.987427	+	0.158077i	$0.949471\pi$
$242$	6.33463	+	3.08974i	0.407206	+	0.198616i
$243$	2.84079	−	1.64013i	0.182237	−	0.105214i
$244$	−1.31180	−	9.33631i	−0.0839794	−	0.597696i
$245$	6.03066	+	3.48180i	0.385285	+	0.222444i
$246$	0.508639	−	1.04282i	0.0324297	−	0.0664877i
$247$	26.6258	+	11.0883i	1.69416	+	0.705533i
$248$	−4.47860	−	21.0756i	−0.284391	−	1.33830i
$249$	0.797879	−	1.38197i	0.0505635	−	0.0875786i
$250$	0.790798	+	1.17245i	0.0500144	+	0.0741522i
$251$	6.04032	−	3.48738i	0.381262	−	0.220122i	−0.297105	−	0.954845i	$-0.596021\pi$
$251$	6.04032	−	3.48738i	0.381262	−	0.220122i	0.678367	+	0.734723i	$0.262688\pi$
$252$	0.701129	+	0.897469i	0.0441670	+	0.0565352i
$253$	−16.0780	+	9.28264i	−1.01082	+	0.583595i
$254$	0.329294	+	4.71030i	0.0206617	+	0.295551i
$255$	0.611351			0.0382843
$256$	0.556161	+	15.9903i	0.0347601	+	0.999396i
$257$	−1.20729	+	2.09109i	−0.0753087	+	0.130438i	−0.901220	−	0.433361i	$-0.857328\pi$
$257$	−1.20729	+	2.09109i	−0.0753087	+	0.130438i	0.825912	+	0.563799i	$0.190661\pi$
$258$	−0.278612	+	0.187919i	−0.0173456	+	0.0116993i
$259$			0.700087i			0.0435013i
$260$	−1.91358	−	6.95257i	−0.118675	−	0.431180i
$261$			15.4331i			0.955288i
$262$	1.62342	+	2.40691i	0.100295	+	0.148700i
$263$	2.59243	−	4.49022i	0.159856	−	0.276879i	−0.774961	−	0.632010i	$-0.782230\pi$
$263$	2.59243	−	4.49022i	0.159856	−	0.276879i	0.934817	+	0.355131i	$0.115564\pi$
$264$	−0.630584	+	0.567720i	−0.0388097	+	0.0349408i
$265$	2.27807			0.139941
$266$	−2.15284	+	0.150503i	−0.131999	+	0.00922794i
$267$	1.64993	−	0.952588i	0.100974	−	0.0582974i
$268$	−16.9759	+	13.2620i	−1.03697	+	0.810108i
$269$	4.98614	−	2.87875i	0.304010	−	0.175520i	−0.340233	−	0.940341i	$-0.610506\pi$
$269$	4.98614	−	2.87875i	0.304010	−	0.175520i	0.644243	+	0.764821i	$0.277173\pi$
$270$	0.858222	−	0.578856i	0.0522297	−	0.0352281i
$271$	−2.54456	+	4.40731i	−0.154571	+	0.267725i	−0.932903	−	0.360128i	$-0.882733\pi$
$271$	−2.54456	+	4.40731i	−0.154571	+	0.267725i	0.778332	+	0.627853i	$0.216066\pi$
$272$	4.83848	−	19.4003i	0.293376	−	1.17632i
$273$	0.0668353	−	0.0510823i	0.00404506	−	0.00309164i
$274$	−26.8952	−	13.1183i	−1.62480	−	0.792504i
$275$	2.12420	+	1.22641i	0.128094	+	0.0739553i
$276$	0.257603	+	1.83341i	0.0155059	+	0.110358i
$277$	−7.57836	+	4.37537i	−0.455339	+	0.262890i	−0.710083	−	0.704118i	$-0.751342\pi$
$277$	−7.57836	+	4.37537i	−0.455339	+	0.262890i	0.254743	+	0.967009i	$0.418009\pi$
$278$	13.2173	−	27.0983i	0.792721	−	1.62525i
$279$	11.3696	+	19.6927i	0.680680	+	1.17897i
$280$	0.361015	+	0.400990i	0.0215748	+	0.0239638i
$281$	−17.9933			−1.07339			−0.536694	−	0.843777i	$-0.680327\pi$
$281$	−17.9933			−1.07339			−0.536694	+	0.843777i	$0.680327\pi$
$282$	−1.44240	+	0.100837i	−0.0858934	+	0.00600475i
$283$	−0.383437	−	0.221377i	−0.0227930	−	0.0131595i	0.488560	−	0.872530i	$-0.337522\pi$
$283$	−0.383437	−	0.221377i	−0.0227930	−	0.0131595i	−0.511353	+	0.859371i	$0.670856\pi$
$284$	−11.8754	+	1.66856i	−0.704677	+	0.0990108i
$285$			0.978358i			0.0579529i
$286$	−8.26932	−	9.38311i	−0.488975	−	0.554835i
$287$	−1.27966			−0.0755359
$288$	−5.77395	−	15.8681i	−0.340233	−	0.935037i
$289$	−3.99324	+	6.91649i	−0.234896	+	0.406852i
$290$	0.509912	+	7.29391i	0.0299431	+	0.428313i
$291$		−	0.0318357i		−	0.00186624i
$292$	12.4518	−	30.8162i	0.728687	−	1.80338i
$293$	10.7208	−	6.18968i	0.626318	−	0.361605i	−0.153006	−	0.988225i	$-0.548896\pi$
$293$	10.7208	−	6.18968i	0.626318	−	0.361605i	0.779325	+	0.626620i	$0.215562\pi$
$294$	0.528014	−	1.08254i	0.0307944	−	0.0631350i
$295$	4.60542	+	7.97682i	0.268138	+	0.464429i
$296$	3.20815	−	9.87191i	0.186470	−	0.573793i
$297$	0.897720	−	1.55490i	0.0520910	−	0.0902243i
$298$	−12.4823	+	25.5913i	−0.723078	+	1.48246i
$299$	−27.0635	+	3.51047i	−1.56512	+	0.203016i
$300$	0.192758	−	0.150588i	0.0111289	−	0.00869421i
$301$	0.320991	+	0.185324i	0.0185016	+	0.0106819i
$302$	−8.11975	+	5.47663i	−0.467239	+	0.315145i
$303$	−0.338528	−	0.586347i	−0.0194479	−	0.0336848i
$304$	31.0468	+	7.74313i	1.78065	+	0.444099i
$305$	2.35700	+	4.08245i	0.134962	+	0.233760i
$306$	1.47161	+	21.0503i	0.0841266	+	1.20337i
$307$		−	16.6286i		−	0.949044i	−0.880244	−	0.474522i	$-0.842621\pi$
$307$		−	16.6286i		−	0.949044i	0.880244	−	0.474522i	$-0.157379\pi$
$308$	0.867661	+	0.350593i	0.0494396	+	0.0199769i
$309$	−0.315745	−	0.182295i	−0.0179621	−	0.0103704i
$310$	6.02407	+	8.93139i	0.342144	+	0.507269i
$311$	−24.5663			−1.39303			−0.696514	−	0.717543i	$-0.745267\pi$
$311$	−24.5663			−1.39303			−0.696514	+	0.717543i	$0.745267\pi$
$312$	−1.17653	+	0.414037i	−0.0666077	+	0.0234402i
$313$	−13.4354			−0.759414			−0.379707	−	0.925107i	$-0.623975\pi$
$313$	−13.4354			−0.759414			−0.379707	+	0.925107i	$0.623975\pi$
$314$	−16.8858	−	25.0352i	−0.952922	−	1.41282i
$315$	−0.493146	−	0.284718i	−0.0277857	−	0.0160421i
$316$	−8.45294	+	20.9197i	−0.475515	+	1.17682i
$317$		−	13.0779i		−	0.734528i	−0.930117	−	0.367264i	$-0.880295\pi$
$317$		−	13.0779i		−	0.734528i	0.930117	−	0.367264i	$-0.119705\pi$
$318$	−0.0274787	−	0.393063i	−0.00154093	−	0.0220419i
$319$	6.34073	+	10.9825i	0.355013	+	0.614901i
$320$	−3.25313	−	7.30870i	−0.181855	−	0.408569i
$321$	−0.172465	−	0.298718i	−0.00962604	−	0.0166728i
$322$	1.69288	−	1.14182i	0.0943403	−	0.0636309i
$323$	−34.6292	−	19.9932i	−1.92682	−	1.11245i
$324$	10.9159	+	13.9728i	0.606441	+	0.776264i
$325$	2.18946	+	2.86466i	0.121449	+	0.158903i
$326$	−3.74445	+	7.67692i	−0.207386	+	0.425185i
$327$	0.0300575	−	0.0520612i	0.00166219	−	0.00287899i
$328$	18.0444	+	5.86403i	0.996337	+	0.323787i
$329$	0.797361	+	1.38107i	0.0439599	+	0.0761408i
$330$	0.185984	−	0.381307i	0.0102381	−	0.0209903i
$331$	11.2108	−	6.47255i	0.616200	−	0.355764i	−0.159188	−	0.987248i	$-0.550888\pi$
$331$	11.2108	−	6.47255i	0.616200	−	0.355764i	0.775388	+	0.631485i	$0.217554\pi$
$332$	24.1946	+	9.77624i	1.32785	+	0.536541i
$333$			10.9549i			0.600324i
$334$	−2.04712	−	29.2825i	−0.112013	−	1.60227i
$335$	5.38552	−	9.32800i	0.294243	−	0.509643i
$336$	0.0648329	−	0.0671271i	0.00353693	−	0.00366208i
$337$	6.42507			0.349996			0.174998	−	0.984569i	$-0.444008\pi$
$337$	6.42507			0.349996			0.174998	+	0.984569i	$0.444008\pi$
$338$	−5.91883	−	17.4060i	−0.321942	−	0.946759i
$339$			0.0919459i			0.00499382i
$340$	1.39101	+	9.90005i	0.0754381	+	0.536906i
$341$	16.1816	+	9.34244i	0.876282	+	0.505922i
$342$	−33.6873	+	2.35506i	−1.82160	+	0.127347i
$343$	−2.66374			−0.143829
$344$	−3.67704	−	4.08420i	−0.198253	−	0.220205i
$345$	−0.462854	−	0.801687i	−0.0249192	−	0.0431614i
$346$	−8.93912	+	18.3271i	−0.480570	+	0.985271i
$347$	−1.72311	+	0.994837i	−0.0925013	+	0.0534056i	−0.545537	−	0.838087i	$-0.683674\pi$
$347$	−1.72311	+	0.994837i	−0.0925013	+	0.0534056i	0.453036	+	0.891492i	$0.350341\pi$
$348$	1.25235	−	0.175962i	0.0671332	−	0.00943257i
$349$	−20.1722	−	11.6464i	−1.07979	−	0.623420i	−0.148954	−	0.988844i	$-0.547590\pi$
$349$	−20.1722	−	11.6464i	−1.07979	−	0.623420i	−0.930841	+	0.365425i	$0.880924\pi$
$350$	−0.242475	−	0.118268i	−0.0129608	−	0.00632169i
$351$	2.09690	−	1.60266i	0.111924	−	0.0855438i
$352$	−10.6283	−	8.91976i	−0.566489	−	0.475425i
$353$	−13.7810	+	23.8693i	−0.733487	+	1.27044i	0.221898	+	0.975070i	$0.428775\pi$
$353$	−13.7810	+	23.8693i	−0.733487	+	1.27044i	−0.955384	+	0.295366i	$0.904558\pi$
$354$	1.32078	−	0.890847i	0.0701989	−	0.0473480i
$355$	5.19272	−	2.99802i	0.275601	−	0.159118i
$356$	19.1800	+	24.5511i	1.01654	+	1.30121i
$357$	−0.100999	+	0.0583117i	−0.00534542	+	0.00308618i
$358$	−12.7153	+	0.888920i	−0.672026	+	0.0469809i
$359$	14.3123			0.755373			0.377687	−	0.925934i	$-0.376720\pi$
$359$	14.3123			0.755373			0.377687	+	0.925934i	$0.376720\pi$
$360$	5.64912	+	6.27465i	0.297735	+	0.330703i
$361$	22.4955	−	38.9634i	1.18398	−	2.05071i
$362$	11.3372	+	16.8088i	0.595871	+	0.883449i
$363$			0.609520i			0.0319915i
$364$	0.979282	+	0.966085i	0.0513283	+	0.0506366i
$365$			16.6184i			0.869847i
$366$	0.675963	−	0.455926i	0.0353331	−	0.0238316i
$367$	3.91594	−	6.78260i	0.204410	−	0.354049i	−0.745534	−	0.666467i	$-0.767806\pi$
$367$	3.91594	−	6.78260i	0.204410	−	0.354049i	0.949945	+	0.312418i	$0.101139\pi$
$368$	−29.1036	+	8.34312i	−1.51713	+	0.434915i
$369$	−20.0239			−1.04241
$370$	0.361950	+	5.17742i	0.0188169	+	0.269161i
$371$	−0.376351	+	0.217286i	−0.0195392	+	0.0112809i
$372$	1.46838	−	1.14714i	0.0761317	−	0.0594763i
$373$	14.7653	−	8.52475i	0.764519	−	0.441395i	−0.0663972	−	0.997793i	$-0.521150\pi$
$373$	14.7653	−	8.52475i	0.764519	−	0.441395i	0.830916	+	0.556398i	$0.187817\pi$
$374$	9.69580	+	14.3751i	0.501358	+	0.743321i
$375$	−0.0611516	+	0.105918i	−0.00315786	+	0.00546957i
$376$	−4.91481	−	23.1283i	−0.253462	−	1.19275i
$377$	2.39791	+	18.4864i	0.123499	+	0.952098i
$378$	−0.0865711	+	0.177489i	−0.00445273	+	0.00912905i
$379$	13.2568	+	7.65382i	0.680956	+	0.393150i	0.800215	−	0.599713i	$-0.204719\pi$
$379$	13.2568	+	7.65382i	0.680956	+	0.393150i	−0.119259	+	0.992863i	$0.538052\pi$
$380$	−15.8433	+	2.22606i	−0.812742	+	0.114195i
$381$	−0.353640	+	0.204174i	−0.0181175	+	0.0104602i
$382$	19.1972	+	9.36351i	0.982214	+	0.479079i
$383$	−5.49478	−	9.51724i	−0.280770	−	0.486308i	0.690804	−	0.723042i	$-0.257257\pi$
$383$	−5.49478	−	9.51724i	−0.280770	−	0.486308i	−0.971575	+	0.236733i	$0.923923\pi$
$384$	−1.22182	+	0.649460i	−0.0623506	+	0.0331426i
$385$	−0.467908			−0.0238468
$386$	−0.490448	−	7.01549i	−0.0249631	−	0.357079i
$387$	5.02283	+	2.89993i	0.255325	+	0.147412i
$388$	0.515538	−	0.0724358i	0.0261725	−	0.00367737i
$389$			27.0280i			1.37038i	0.728366	+	0.685188i	$0.240280\pi$
$389$			27.0280i			1.37038i	−0.728366	+	0.685188i	$0.759720\pi$
$390$	0.467864	−	0.412328i	0.0236912	−	0.0208790i
$391$	37.8345			1.91337
$392$	18.7317	+	6.08740i	0.946096	+	0.307460i
$393$	−0.125538	+	0.217438i	−0.00633254	+	0.0109683i
$394$	27.2824	−	1.90729i	1.37447	−	0.0960879i
$395$		−	11.2814i		−	0.567631i
$396$	13.5771	+	5.48604i	0.682273	+	0.275684i
$397$	−25.3865	+	14.6569i	−1.27411	+	0.735609i	−0.975759	−	0.218847i	$-0.929770\pi$
$397$	−25.3865	+	14.6569i	−1.27411	+	0.735609i	−0.298353	+	0.954456i	$0.596437\pi$
$398$	−0.772815	−	0.376944i	−0.0387377	−	0.0188945i
$399$	−0.0933174	−	0.161631i	−0.00467171	−	0.00809165i
$400$	2.87717	+	2.77883i	0.143858	+	0.138942i
$401$	1.74580	−	3.02381i	0.0871809	−	0.151002i	−0.819138	−	0.573597i	$-0.805548\pi$
$401$	1.74580	−	3.02381i	0.0871809	−	0.151002i	0.906318	+	0.422595i	$0.138881\pi$
$402$	−1.67443	−	0.816711i	−0.0835131	−	0.0407339i
$403$	16.6787	+	21.8222i	0.830825	+	1.08704i
$404$	8.72489	−	6.81614i	0.434080	−	0.339116i
$405$	−7.67784	−	4.43280i	−0.381515	−	0.220268i
$406$	−0.779946	−	1.15636i	−0.0387081	−	0.0573892i
$407$	4.50083	+	7.79567i	0.223098	+	0.386417i
$408$	1.69139	−	0.359424i	0.0837365	−	0.0177942i
$409$	−14.1378	−	24.4874i	−0.699069	−	1.21082i	−0.968789	−	0.247885i	$-0.920264\pi$
$409$	−14.1378	−	24.4874i	−0.699069	−	1.21082i	0.269720	−	0.962939i	$-0.413069\pi$
$410$	−9.46358	+	0.661592i	−0.467373	+	0.0326737i
$411$		−	2.58787i		−	0.127650i
$412$	2.23363	−	5.52786i	0.110043	−	0.272338i
$413$	−1.52169	−	0.878546i	−0.0748773	−	0.0432304i
$414$	26.4899	−	17.8670i	1.30191	−	0.878116i
$415$	−13.0475			−0.640479
$416$	−9.38175	−	18.1103i	−0.459978	−	0.887930i
$417$	2.60740			0.127685
$418$	−23.0049	+	15.5164i	−1.12520	+	0.758931i
$419$	21.2990	+	12.2970i	1.04053	+	0.600747i	0.919982	−	0.391961i	$-0.128203\pi$
$419$	21.2990	+	12.2970i	1.04053	+	0.600747i	0.120543	+	0.992708i	$0.461536\pi$
$420$	−0.0174814	+	0.0432636i	−0.000853004	+	0.00211105i
$421$		−	12.2189i		−	0.595514i	−0.954642	−	0.297757i	$-0.903762\pi$
$421$		−	12.2189i		−	0.595514i	0.954642	−	0.297757i	$-0.0962385\pi$
$422$	0.550912	−	0.0385139i	0.0268180	−	0.00187483i
$423$	12.4770	+	21.6108i	0.606653	+	1.05075i
$424$	6.30262	−	1.33932i	0.306082	−	0.0650431i
$425$	−2.49932	−	4.32896i	−0.121235	−	0.209985i
$426$	−0.579920	−	0.859799i	−0.0280972	−	0.0416574i
$427$	−0.778782	−	0.449630i	−0.0376879	−	0.0217591i
$428$	4.44494	−	3.47252i	0.214854	−	0.167851i
$429$	0.415824	−	0.998497i	0.0200762	−	0.0482079i
$430$	2.46967	+	1.20459i	0.119098	+	0.0580906i
$431$	13.9080	−	24.0894i	0.669925	−	1.16034i	−0.307999	−	0.951387i	$-0.599659\pi$
$431$	13.9080	−	24.0894i	0.669925	−	1.16034i	0.977925	−	0.208958i	$-0.0670072\pi$
$432$	2.03408	−	2.10606i	0.0978647	−	0.101328i
$433$	−15.4885	−	26.8269i	−0.744330	−	1.28922i	−0.950507	−	0.310703i	$-0.899435\pi$
$433$	−15.4885	−	26.8269i	−0.744330	−	1.28922i	0.206177	−	0.978515i	$-0.433898\pi$
$434$	−1.84710	−	0.900933i	−0.0886638	−	0.0432461i
$435$	−0.547612	+	0.316164i	−0.0262560	+	0.0151589i
$436$	0.911454	+	0.368288i	0.0436507	+	0.0176378i
$437$			60.5474i			2.89638i
$438$	2.86737	−	0.200456i	0.137008	−	0.00957815i
$439$	9.15679	−	15.8600i	0.437030	−	0.756958i	−0.560429	−	0.828202i	$-0.689364\pi$
$439$	9.15679	−	15.8600i	0.437030	−	0.756958i	0.997459	+	0.0712447i	$0.0226971\pi$
$440$	6.59796	+	2.14419i	0.314545	+	0.102220i
$441$	−20.7867			−0.989841
$442$	5.03344	+	24.9863i	0.239416	+	1.18847i
$443$			16.5053i			0.784191i	0.919925	+	0.392095i	$0.128250\pi$
$443$			16.5053i			0.784191i	−0.919925	+	0.392095i	$0.871750\pi$
$444$	0.888956	−	0.124903i	0.0421880	−	0.00592763i
$445$	−13.4905	−	7.78874i	−0.639510	−	0.369222i
$446$	0.334666	+	4.78714i	0.0158469	+	0.226678i
$447$	−2.46240			−0.116468
$448$	1.23455	+	0.897152i	0.0583271	+	0.0423865i
$449$	−5.56002	−	9.63023i	−0.262393	−	0.454479i	0.704484	−	0.709720i	$-0.251178\pi$
$449$	−5.56002	−	9.63023i	−0.262393	−	0.454479i	−0.966877	+	0.255241i	$0.917845\pi$
$450$	−3.79421	−	1.85064i	−0.178861	−	0.0872402i
$451$	−14.2494	+	8.22687i	−0.670976	+	0.387388i
$452$	−1.48895	+	0.209205i	−0.0700342	+	0.00984017i
$453$	−0.733528	−	0.423503i	−0.0344642	−	0.0198979i
$454$	−8.72252	+	17.8830i	−0.409368	+	0.839292i
$455$	−0.634948	−	0.264424i	−0.0297668	−	0.0123964i
$456$	0.575195	+	2.70677i	0.0269360	+	0.126756i
$457$	−2.74982	+	4.76283i	−0.128631	+	0.222796i	−0.923146	−	0.384448i	$-0.874392\pi$
$457$	−2.74982	+	4.76283i	−0.128631	+	0.222796i	0.794515	+	0.607244i	$0.207725\pi$
$458$	19.3622	+	28.7068i	0.904738	+	1.34138i
$459$	−3.16875	+	1.82948i	−0.147905	+	0.0853928i
$460$	11.9292	−	9.31941i	0.556200	−	0.434520i
$461$	−12.4987	+	7.21612i	−0.582122	+	0.336088i	−0.761976	−	0.647605i	$-0.775771\pi$
$461$	−12.4987	+	7.21612i	−0.582122	+	0.336088i	0.179854	+	0.983693i	$0.442437\pi$
$462$	0.00564404	+	0.0807337i	0.000262584	+	0.00375607i
$463$	−24.5545			−1.14115			−0.570573	−	0.821247i	$-0.693279\pi$
$463$	−24.5545			−1.14115			−0.570573	+	0.821247i	$0.693279\pi$
$464$	5.69897	+	19.8799i	0.264568	+	0.922901i
$465$	−0.465836	+	0.806852i	−0.0216026	+	0.0374168i
$466$	18.4348	−	12.4339i	0.853974	−	0.575991i
$467$		−	32.4362i		−	1.50097i	−0.660889	−	0.750483i	$-0.729821\pi$
$467$		−	32.4362i		−	1.50097i	0.660889	−	0.750483i	$-0.270179\pi$
$468$	15.3237	+	15.1172i	0.708338	+	0.698792i
$469$			2.05472i			0.0948782i
$470$	6.61082	+	9.80132i	0.304935	+	0.452101i
$471$	1.30577	−	2.26165i	0.0601665	−	0.104211i
$472$	17.4313	+	19.3615i	0.802341	+	0.891184i
$473$	4.76577			0.219130
$474$	−1.94652	+	0.136080i	−0.0894067	+	0.00625036i
$475$	6.92772	−	3.99972i	0.317866	−	0.183520i
$476$	−1.17409	−	1.50287i	−0.0538141	−	0.0688839i
$477$	−5.88909	+	3.40007i	−0.269643	+	0.155678i
$478$	−25.1828	+	16.9854i	−1.15183	+	0.776893i
$479$	−10.3433	+	17.9152i	−0.472599	+	0.818565i	−0.999508	−	0.0313565i	$-0.990017\pi$
$479$	−10.3433	+	17.9152i	−0.472599	+	0.818565i	0.526910	+	0.849921i	$0.323351\pi$
$480$	0.444760	−	0.529951i	0.0203004	−	0.0241888i
$481$	1.70211	+	13.1222i	0.0776094	+	0.598320i
$482$	14.0816	+	6.86838i	0.641401	+	0.312846i
$483$	0.152932	+	0.0882956i	0.00695867	+	0.00401759i
$484$	−9.87040	+	1.38684i	−0.448655	+	0.0630383i
$485$	−0.225427	+	0.130150i	−0.0102361	+	0.00590983i
$486$	−2.03367	+	4.16946i	−0.0922493	+	0.189131i
$487$	−2.26087	−	3.91593i	−0.102450	−	0.177448i	0.810244	−	0.586093i	$-0.199335\pi$
$487$	−2.26087	−	3.91593i	−0.102450	−	0.177448i	−0.912693	+	0.408645i	$0.866001\pi$
$488$	8.92115	+	9.90899i	0.403842	+	0.448559i
$489$	−0.738675			−0.0334040
$490$	−9.82405	+	0.686793i	−0.443805	+	0.0310261i
$491$	1.39069	+	0.802916i	0.0627611	+	0.0362351i	0.531052	−	0.847339i	$-0.321797\pi$
$491$	1.39069	+	0.802916i	0.0627611	+	0.0362351i	−0.468291	+	0.883574i	$0.655130\pi$
$492$	0.228305	+	1.62488i	0.0102928	+	0.0732554i
$493$		−	25.8438i		−	1.16395i
$494$	−39.9860	+	8.05512i	−1.79906	+	0.362417i
$495$	−7.32177			−0.329089
$496$	21.9174	+	21.1684i	0.984122	+	0.950488i
$497$	−0.571912	+	0.990581i	−0.0256538	+	0.0444336i
$498$	0.157383	+	2.25125i	0.00705251	+	0.100881i
$499$			15.4915i			0.693496i	0.937958	+	0.346748i	$0.112714\pi$
$499$			15.4915i			0.693496i	−0.937958	+	0.346748i	$0.887286\pi$
$500$	−1.85434	−	0.749278i	−0.0829287	−	0.0335087i
$501$	2.19847	−	1.26929i	0.0982204	−	0.0567076i
$502$	−4.32416	+	8.86545i	−0.192997	+	0.395684i
$503$	16.6416	+	28.8241i	0.742012	+	1.28520i	0.951578	+	0.307409i	$0.0994618\pi$
$503$	16.6416	+	28.8241i	0.742012	+	1.28520i	−0.209565	+	0.977795i	$0.567205\pi$
$504$	−1.53175	−	0.497786i	−0.0682298	−	0.0221731i
$505$	−2.76794	+	4.79421i	−0.123172	+	0.213339i
$506$	11.5100	−	23.5979i	0.511680	−	1.04905i
$507$	1.12854	−	1.11996i	0.0501202	−	0.0497393i
$508$	−4.11098	−	5.26219i	−0.182395	−	0.233472i
$509$	−5.59807	−	3.23205i	−0.248130	−	0.143258i	0.370778	−	0.928722i	$-0.379091\pi$
$509$	−5.59807	−	3.23205i	−0.248130	−	0.143258i	−0.618908	+	0.785464i	$0.712425\pi$
$510$	−0.716778	+	0.483455i	−0.0317395	+	0.0214077i
$511$	−1.58509	−	2.74546i	−0.0701203	−	0.121452i
$512$	−13.2972	−	18.3081i	−0.587658	−	0.809109i
$513$	−2.92776	−	5.07102i	−0.129264	−	0.223891i
$514$	−0.238140	−	3.40642i	−0.0105039	−	0.150251i
$515$			2.98104i			0.131360i
$516$	0.178053	−	0.440652i	0.00783833	−	0.0193986i
$517$	17.7577	+	10.2524i	0.780982	+	0.450900i
$518$	−0.553627	−	0.820817i	−0.0243250	−	0.0360646i
$519$	−1.76344			−0.0774064
$520$	7.74165	+	6.63828i	0.339494	+	0.291108i
$521$	9.79496			0.429125			0.214563	−	0.976710i	$-0.431167\pi$
$521$	9.79496			0.429125			0.214563	+	0.976710i	$0.431167\pi$
$522$	−12.2045	−	18.0946i	−0.534176	−	0.791979i
$523$	−9.23194	−	5.33006i	−0.403684	−	0.233067i	0.284388	−	0.958709i	$-0.408210\pi$
$523$	−9.23194	−	5.33006i	−0.403684	−	0.233067i	−0.688073	+	0.725642i	$0.741543\pi$
$524$	−3.80676	−	1.53819i	−0.166299	−	0.0671960i
$525$		−	0.0233310i		−	0.00101825i
$526$	0.511361	+	7.31464i	0.0222964	+	0.318934i
$527$	−19.0391	−	32.9768i	−0.829358	−	1.43649i
$528$	0.290376	−	1.16429i	0.0126370	−	0.0506691i
$529$	−17.1445	−	29.6952i	−0.745415	−	1.29110i
$530$	−2.67092	+	1.80149i	−0.116018	+	0.0782519i
$531$	−23.8112	−	13.7474i	−1.03332	−	0.596585i
$532$	2.40507	−	1.87892i	0.104273	−	0.0814613i
$533$	−23.9854	+	3.11121i	−1.03892	+	0.134761i
$534$	−1.18116	+	2.42162i	−0.0511137	+	0.104794i
$535$	−1.41014	+	2.44243i	−0.0609656	+	0.105596i
$536$	9.41576	−	28.9736i	0.406699	−	1.25147i
$537$	−0.551162	−	0.954641i	−0.0237844	−	0.0411958i
$538$	−3.56949	+	7.31822i	−0.153892	+	0.315511i
$539$	−14.7921	+	8.54024i	−0.637142	+	0.367854i
$540$	−0.548464	+	1.35736i	−0.0236021	+	0.0584115i
$541$			24.6223i			1.05860i	0.848436	+	0.529298i	$0.177544\pi$
$541$			24.6223i			1.05860i	−0.848436	+	0.529298i	$0.822456\pi$
$542$	−0.501920	−	7.17958i	−0.0215593	−	0.308390i
$543$	−0.876697	+	1.51848i	−0.0376227	+	0.0651644i
$544$	9.66886	+	26.5722i	0.414549	+	1.13927i
$545$	−0.491524			−0.0210546
$546$	−0.0379653	+	0.112745i	−0.00162476	+	0.00482502i
$547$		−	27.8393i		−	1.19032i	−0.803606	−	0.595162i	$-0.797088\pi$
$547$		−	27.8393i		−	1.19032i	0.803606	−	0.595162i	$-0.202912\pi$
$548$	41.9072	−	5.88819i	1.79019	−	0.251531i
$549$	−12.1863	−	7.03576i	−0.520098	−	0.300279i
$550$	−3.46036	+	0.241912i	−0.147550	+	0.0103151i
$551$	41.3584			1.76193
$552$	−1.75188	−	1.94587i	−0.0745650	−	0.0828216i
$553$	1.07604	+	1.86376i	0.0457580	+	0.0792552i
$554$	5.42522	−	11.1228i	0.230495	−	0.472565i
$555$	−0.388710	+	0.224422i	−0.0164998	+	0.00952618i
$556$	5.93263	+	42.2236i	0.251600	+	1.79068i
$557$	17.9635	+	10.3712i	0.761137	+	0.439443i	0.829704	−	0.558204i	$-0.188509\pi$
$557$	17.9635	+	10.3712i	0.761137	+	0.439443i	−0.0685667	+	0.997647i	$0.521843\pi$
$558$	−28.9033	−	14.0977i	−1.22357	−	0.596803i
$559$	6.46711	+	2.69323i	0.273530	+	0.113912i
$560$	−0.740374	−	0.184651i	−0.0312865	−	0.00780293i
$561$	−0.749767	+	1.29863i	−0.0316552	+	0.0548284i
$562$	21.0962	−	14.2290i	0.889889	−	0.600215i
$563$	3.12573	−	1.80464i	0.131734	−	0.0760564i	−0.432685	−	0.901545i	$-0.642434\pi$
$563$	3.12573	−	1.80464i	0.131734	−	0.0760564i	0.564419	+	0.825489i	$0.309100\pi$
$564$	1.61140	−	1.25887i	0.0678520	−	0.0530080i
$565$	0.651066	−	0.375893i	0.0273905	−	0.0158139i
$566$	0.624625	−	0.0436671i	0.0262550	−	0.00183547i
$567$	1.69123			0.0710250
$568$	12.6039	−	11.3474i	0.528846	−	0.476125i
$569$	−5.16327	+	8.94305i	−0.216456	+	0.374912i	−0.953722	−	0.300690i	$-0.902783\pi$
$569$	−5.16327	+	8.94305i	−0.216456	+	0.374912i	0.737266	+	0.675602i	$0.236116\pi$
$570$	−0.773683	−	1.14708i	−0.0324060	−	0.0480457i
$571$		−	0.394028i		−	0.0164896i	−0.999966	−	0.00824479i	$-0.997376\pi$
$571$		−	0.394028i		−	0.0164896i	0.999966	−	0.00824479i	$-0.00262443\pi$
$572$	17.1155	+	4.46186i	0.715635	+	0.186560i
$573$			1.84716i			0.0771662i
$574$	1.50034	−	1.01195i	0.0626228	−	0.0422380i
$575$	−3.78448	+	6.55491i	−0.157824	+	0.273359i
$576$	19.3181	+	14.0385i	0.804922	+	0.584939i
$577$	27.1274			1.12933			0.564663	−	0.825321i	$-0.309006\pi$
$577$	27.1274			1.12933			0.564663	+	0.825321i	$0.309006\pi$
$578$	−0.787673	−	11.2671i	−0.0327629	−	0.468649i
$579$	0.526709	−	0.304095i	0.0218893	−	0.0126378i
$580$	−6.36585	−	8.14851i	−0.264328	−	0.338348i
$581$	2.15553	−	1.24450i	0.0894265	−	0.0516304i
$582$	0.0251756	+	0.0373257i	0.00104356	+	0.00154720i
$583$	−2.79385	+	4.83909i	−0.115709	+	0.200414i
$584$	9.77027	+	45.9773i	0.404296	+	1.90255i
$585$	−9.93558	−	4.13768i	−0.410786	−	0.171072i
$586$	−7.67487	+	15.7351i	−0.317046	+	0.650012i
$587$	−3.29720	−	1.90364i	−0.136090	−	0.0785716i	0.430409	−	0.902634i	$-0.358369\pi$
$587$	−3.29720	−	1.90364i	−0.136090	−	0.0785716i	−0.566499	+	0.824062i	$0.691703\pi$
$588$	0.237001	+	1.68678i	0.00977375	+	0.0695615i
$589$	52.7734	−	30.4687i	2.17449	−	1.25544i
$590$	−11.7077	−	5.71047i	−0.481998	−	0.235096i
$591$	1.18259	+	2.04830i	0.0486452	+	0.0842560i
$592$	4.04529	+	14.1113i	0.166260	+	0.579972i
$593$	1.47064			0.0603918			0.0301959	−	0.999544i	$-0.490387\pi$
$593$	1.47064			0.0603918			0.0301959	+	0.999544i	$0.490387\pi$
$594$	0.177077	+	2.53295i	0.00726556	+	0.103928i
$595$	0.825806	+	0.476779i	0.0338547	+	0.0195460i
$596$	−5.60271	−	39.8754i	−0.229496	−	1.63336i
$597$		−	0.0743605i		−	0.00304337i
$598$	28.9546	−	25.5176i	1.18404	−	1.04349i
$599$	15.6421			0.639121			0.319560	−	0.947566i	$-0.396465\pi$
$599$	15.6421			0.639121			0.319560	+	0.947566i	$0.396465\pi$
$600$	−0.106914	+	0.328990i	−0.00436475	+	0.0134309i
$601$	2.50656	−	4.34149i	0.102245	−	0.177093i	−0.810364	−	0.585926i	$-0.800731\pi$
$601$	2.50656	−	4.34149i	0.102245	−	0.177093i	0.912609	+	0.408833i	$0.134064\pi$
$602$	−0.522900	+	0.0365556i	−0.0213118	+	0.00148989i
$603$			32.1520i			1.30933i
$604$	5.18909	−	12.8422i	0.211141	−	0.522540i
$605$	4.31599	−	2.49184i	0.175470	−	0.101308i
$606$	0.860589	+	0.419756i	0.0349590	+	0.0170514i
$607$	4.16413	+	7.21249i	0.169017	+	0.292746i	0.938075	−	0.346434i	$-0.112607\pi$
$607$	4.16413	+	7.21249i	0.169017	+	0.292746i	−0.769058	+	0.639180i	$0.779274\pi$
$608$	−42.5240	+	15.4733i	−1.72458	+	0.627524i
$609$	0.0603125	−	0.104464i	0.00244398	−	0.00423311i
$610$	−5.99186	−	2.92256i	−0.242603	−	0.118331i
$611$	18.3032	+	23.9476i	0.740468	+	0.968818i
$612$	−18.3720	−	23.5167i	−0.742642	−	0.950607i
$613$	−22.3703	−	12.9155i	−0.903528	−	0.521652i	−0.0251848	−	0.999683i	$-0.508017\pi$
$613$	−22.3703	−	12.9155i	−0.903528	−	0.521652i	−0.878343	+	0.478031i	$0.841351\pi$
$614$	13.1498	+	19.4962i	0.530685	+	0.786802i
$615$	−0.410211	−	0.710506i	−0.0165413	−	0.0286504i
$616$	−1.29454	+	0.275092i	−0.0521584	+	0.0110838i
$617$	−12.7719	−	22.1216i	−0.514177	−	0.890581i	−0.999865	−	0.0164483i	$-0.994764\pi$
$617$	−12.7719	−	22.1216i	−0.514177	−	0.890581i	0.485688	−	0.874132i	$-0.338569\pi$
$618$	0.514354	−	0.0359581i	0.0206903	−	0.00144645i
$619$		−	43.5109i		−	1.74885i	−0.485159	−	0.874426i	$-0.661238\pi$
$619$		−	43.5109i		−	1.74885i	0.485159	−	0.874426i	$-0.338762\pi$
$620$	−14.1259	−	5.70779i	−0.567308	−	0.229230i
$621$	4.79813	+	2.77020i	0.192542	+	0.111164i
$622$	28.8028	−	19.4270i	1.15489	−	0.778951i
$623$	2.97161			0.119055
$624$	1.05200	−	1.41583i	0.0421137	−	0.0566786i
$625$	1.00000			0.0400000
$626$	15.7523	−	10.6247i	0.629590	−	0.424648i
$627$	−2.07823	−	1.19987i	−0.0829966	−	0.0479181i
$628$	39.5956	+	15.9993i	1.58004	+	0.638440i
$629$		−	18.3447i		−	0.731450i
$630$	0.803344	−	0.0561612i	0.0320060	−	0.00223752i
$631$	−11.8128	−	20.4604i	−0.470261	−	0.814517i	0.529160	−	0.848522i	$-0.322507\pi$
$631$	−11.8128	−	20.4604i	−0.470261	−	0.814517i	−0.999422	+	0.0340053i	$0.989174\pi$
$632$	−6.63257	−	31.2118i	−0.263829	−	1.24154i
$633$	0.0238800	+	0.0413614i	0.000949145	+	0.00164397i
$634$	10.3420	+	15.3332i	0.410732	+	0.608958i
$635$	2.89150	+	1.66941i	0.114746	+	0.0662484i
$636$	0.343050	+	0.439116i	0.0136028	+	0.0174121i
$637$	−24.8991	+	3.22971i	−0.986537	+	0.127966i
$638$	−16.1191	−	7.86216i	−0.638162	−	0.311266i
$639$	−8.94921	+	15.5005i	−0.354025	+	0.613190i
$640$	9.59384	+	5.99652i	0.379230	+	0.237033i
$641$	−8.84590	−	15.3215i	−0.349392	−	0.605165i	0.636750	−	0.771071i	$-0.280278\pi$
$641$	−8.84590	−	15.3215i	−0.349392	−	0.605165i	−0.986142	+	0.165906i	$0.946945\pi$
$642$	0.438431	+	0.213847i	0.0173035	+	0.00843986i
$643$	2.52217	−	1.45617i	0.0994646	−	0.0574259i	−0.449443	−	0.893309i	$-0.648377\pi$
$643$	2.52217	−	1.45617i	0.0994646	−	0.0574259i	0.548907	+	0.835883i	$0.315044\pi$
$644$	−1.08187	+	2.67745i	−0.0426315	+	0.105506i
$645$			0.237632i			0.00935677i
$646$	56.4116	−	3.94370i	2.21948	−	0.155163i
$647$	12.3151	−	21.3303i	0.484155	−	0.838581i	−0.515679	−	0.856782i	$-0.672460\pi$
$647$	12.3151	−	21.3303i	0.484155	−	0.838581i	0.999834	+	0.0182003i	$0.00579366\pi$
$648$	−23.8480	−	7.75007i	−0.936838	−	0.304451i
$649$	−22.5925			−0.886835
$650$	−4.83240	−	1.62725i	−0.189542	−	0.0638259i
$651$		−	0.177729i		−	0.00696574i
$652$	−1.68071	−	11.9619i	−0.0658217	−	0.468464i
$653$	−3.50829	−	2.02551i	−0.137290	−	0.0792643i	0.429782	−	0.902933i	$-0.358590\pi$
$653$	−3.50829	−	2.02551i	−0.137290	−	0.0792643i	−0.567072	+	0.823668i	$0.691924\pi$
$654$	0.00592890	+	0.0848085i	0.000231839	+	0.00331628i
$655$	2.05289			0.0802132
$656$	−25.7935	+	7.39421i	−1.00707	+	0.288695i
$657$	−24.8033	−	42.9606i	−0.967670	−	1.67605i
$658$	−2.02701	−	0.988684i	−0.0790212	−	0.0385429i
$659$	−31.2189	+	18.0242i	−1.21611	+	0.702124i	−0.964085	−	0.265596i	$-0.914431\pi$
$659$	−31.2189	+	18.0242i	−1.21611	+	0.702124i	−0.252030	+	0.967719i	$0.581098\pi$
$660$	0.0834798	+	0.594140i	0.00324945	+	0.0231269i
$661$	−9.90299	−	5.71749i	−0.385182	−	0.222385i	0.294889	−	0.955532i	$-0.404717\pi$
$661$	−9.90299	−	5.71749i	−0.385182	−	0.222385i	−0.680070	+	0.733147i	$0.738051\pi$
$662$	−8.02561	+	16.4542i	−0.311924	+	0.639511i
$663$	−1.75131	+	1.33853i	−0.0680153	+	0.0519841i
$664$	−36.0980	+	7.67089i	−1.40087	+	0.297688i
$665$	−0.763000	+	1.32155i	−0.0295879	+	0.0512477i
$666$	−8.66310	−	12.8441i	−0.335688	−	0.497697i
$667$	−33.8899	+	19.5664i	−1.31222	+	0.757612i
$668$	25.5567	+	32.7134i	0.988817	+	1.26572i
$669$	−0.359409	+	0.207505i	−0.0138955	+	0.00802260i
$670$	1.06230	+	15.1955i	0.0410404	+	0.587052i
$671$	−11.5626			−0.446370
$672$	−0.0229294	+	0.129973i	−0.000884521	+	0.00501381i
$673$	−5.58336	+	9.67066i	−0.215223	+	0.372777i	−0.953341	−	0.301894i	$-0.902381\pi$
$673$	−5.58336	+	9.67066i	−0.215223	+	0.372777i	0.738119	+	0.674671i	$0.235714\pi$
$674$	−7.53307	+	5.08093i	−0.290163	+	0.195710i
$675$		−	0.731990i		−	0.0281743i
$676$	20.7041	+	15.7270i	0.796313	+	0.604885i
$677$		−	6.36889i		−	0.244776i	−0.992482	−	0.122388i	$-0.960945\pi$
$677$		−	6.36889i		−	0.244776i	0.992482	−	0.122388i	$-0.0390553\pi$
$678$	−0.0727106	−	0.107802i	−0.00279243	−	0.00414011i
$679$	0.0248279	−	0.0430032i	0.000952809	−	0.00165031i
$680$	−9.45983	−	10.5073i	−0.362768	−	0.402937i
$681$	−1.72071			−0.0659377
$682$	−26.3601	+	1.84281i	−1.00938	+	0.0705650i
$683$	25.2899	−	14.6011i	0.967690	−	0.558696i	0.0691585	−	0.997606i	$-0.477969\pi$
$683$	25.2899	−	14.6011i	0.967690	−	0.558696i	0.898531	+	0.438910i	$0.144635\pi$
$684$	37.6343	−	29.4010i	1.43898	−	1.12418i
$685$	−18.3246	+	10.5797i	−0.700147	+	0.404230i
$686$	3.12311	−	2.10648i	0.119241	−	0.0804259i
$687$	−1.49726	+	2.59334i	−0.0571242	+	0.0989420i
$688$	7.54092	+	1.88072i	0.287495	+	0.0717018i
$689$	−6.52589	+	4.98774i	−0.248617	+	0.190018i
$690$	1.17665	+	0.573914i	0.0447941	+	0.0218485i
$691$	2.87352	+	1.65903i	0.109314	+	0.0631125i	0.553660	−	0.832743i	$-0.313231\pi$
$691$	2.87352	+	1.65903i	0.109314	+	0.0631125i	−0.444346	+	0.895855i	$0.646564\pi$
$692$	−4.01236	−	28.5566i	−0.152527	−	1.08556i
$693$	1.20960	−	0.698362i	0.0459489	−	0.0265286i
$694$	1.23354	−	2.52903i	0.0468247	−	0.0960005i
$695$	−10.6596	−	18.4629i	−0.404341	−	0.700339i
$696$	−1.32917	+	1.19667i	−0.0503821	+	0.0453595i
$697$	33.5314			1.27009
$698$	32.8609	−	2.29728i	1.24380	−	0.0869534i
$699$	1.66537	+	0.961504i	0.0629902	+	0.0363674i
$700$	0.377816	−	0.0530851i	0.0142801	−	0.00200643i
$701$		−	4.22312i		−	0.159505i	−0.996815	−	0.0797524i	$-0.974587\pi$
$701$		−	4.22312i		−	0.159505i	0.996815	−	0.0797524i	$-0.0254130\pi$
$702$	−1.19113	+	3.53727i	−0.0449563	+	0.133506i
$703$	29.3574			1.10723
$704$	19.5148	+	2.05316i	0.735493	+	0.0773813i
$705$	−0.511209	+	0.885439i	−0.0192532	+	0.0333476i
$706$	−2.71832	−	38.8835i	−0.102305	−	1.46340i
$707$		−	1.05604i		−	0.0397165i
$708$	−0.844074	+	2.08895i	−0.0317222	+	0.0785074i
$709$	−19.7892	+	11.4253i	−0.743200	+	0.429087i	−0.823232	−	0.567706i	$-0.807831\pi$
$709$	−19.7892	+	11.4253i	−0.743200	+	0.429087i	0.0800317	+	0.996792i	$0.474498\pi$
$710$	−3.71738	+	7.62142i	−0.139511	+	0.286027i
$711$	16.8378	+	29.1639i	0.631467	+	1.09373i
$712$	−41.9026	−	13.6174i	−1.57037	−	0.510334i
$713$	−28.8291	+	49.9334i	−1.07966	+	1.87002i
$714$	0.0723033	−	0.148237i	0.00270588	−	0.00554764i
$715$	−8.77029	+	1.13761i	−0.327990	+	0.0425444i
$716$	14.2051	−	11.0975i	0.530871	−	0.414732i
$717$	−2.27498	−	1.31346i	−0.0849609	−	0.0490522i
$718$	−16.7804	+	11.3181i	−0.626240	+	0.422388i
$719$	−15.1035	−	26.1601i	−0.563266	−	0.975606i	−0.997209	−	0.0746654i	$-0.976211\pi$
$719$	−15.1035	−	26.1601i	−0.563266	−	0.975606i	0.433942	−	0.900941i	$-0.357122\pi$
$720$	−11.5853	−	2.88940i	−0.431758	−	0.107681i
$721$	−0.284336	−	0.492485i	−0.0105892	−	0.0183411i
$722$	4.43729	+	63.4721i	0.165139	+	2.36219i
$723$			1.35494i			0.0503907i
$724$	−26.5847	−	10.7420i	−0.988011	−	0.399223i
$725$	4.47749	+	2.58508i	0.166290	+	0.0960075i
$726$	−0.482007	−	0.714632i	−0.0178890	−	0.0265225i
$727$	20.7596			0.769930			0.384965	−	0.922931i	$-0.374214\pi$
$727$	20.7596			0.769930			0.384965	+	0.922931i	$0.374214\pi$
$728$	−1.91214	−	0.358271i	−0.0708685	−	0.0132784i
$729$	26.1956			0.970208
$730$	−13.1418	−	19.4843i	−0.486400	−	0.721144i
$731$	−8.41106	−	4.85613i	−0.311094	−	0.179610i
$732$	−0.431988	+	1.06910i	−0.0159667	+	0.0395151i
$733$			7.46000i			0.275541i	0.990464	+	0.137771i	$0.0439937\pi$
$733$			7.46000i			0.275541i	−0.990464	+	0.137771i	$0.956006\pi$
$734$	0.772426	+	11.0490i	0.0285108	+	0.407825i
$735$	−0.425836	−	0.737570i	−0.0157072	−	0.0272057i
$736$	27.5248	−	32.7969i	1.01458	−	1.20891i
$737$	13.2097	+	22.8799i	0.486586	+	0.842792i
$738$	23.4771	−	15.8349i	0.864203	−	0.582890i
$739$	−18.2194	−	10.5190i	−0.670211	−	0.386946i	0.125946	−	0.992037i	$-0.459803\pi$
$739$	−18.2194	−	10.5190i	−0.670211	−	0.386946i	−0.796157	+	0.605091i	$0.793137\pi$
$740$	−4.51866	−	5.78404i	−0.166109	−	0.212626i
$741$	−2.14208	−	2.80266i	−0.0786911	−	0.102958i
$742$	0.269423	−	0.552374i	0.00989083	−	0.0202783i
$743$	15.3515	−	26.5896i	0.563192	−	0.975477i	−0.434023	−	0.900902i	$-0.642906\pi$
$743$	15.3515	−	26.5896i	0.563192	−	0.975477i	0.997215	−	0.0745757i	$-0.0237602\pi$
$744$	−0.814442	+	2.50615i	−0.0298589	+	0.0918799i
$745$	10.0668	+	17.4362i	0.368818	+	0.638812i
$746$	−10.5702	+	21.6712i	−0.387003	+	0.793440i
$747$	33.7295	−	19.4737i	1.23410	−	0.712507i
$748$	−22.7357	−	9.18673i	−0.831298	−	0.335900i
$749$		−	0.538006i		−	0.0196583i
$750$	−0.0120623	−	0.172542i	−0.000440452	−	0.00630034i
$751$	−15.3774	+	26.6345i	−0.561131	+	0.971907i	0.436267	+	0.899817i	$0.356300\pi$
$751$	−15.3774	+	26.6345i	−0.561131	+	0.971907i	−0.997398	+	0.0720898i	$0.977033\pi$
$752$	24.0522	+	23.2302i	0.877094	+	0.847118i
$753$	−0.853036			−0.0310864
$754$	−17.4304	−	19.7781i	−0.634779	−	0.720277i
$755$			6.92545i			0.252043i
$756$	−0.0388578	−	0.276557i	−0.00141324	−	0.0100583i
$757$	−9.74843	−	5.62826i	−0.354313	−	0.204563i	0.312270	−	0.949993i	$-0.398911\pi$
$757$	−9.74843	−	5.62826i	−0.354313	−	0.204563i	−0.666583	+	0.745431i	$0.732244\pi$
$758$	−21.5956	+	1.50973i	−0.784386	+	0.0548358i
$759$	2.27060			0.0824174
$760$	16.8151	−	15.1388i	0.609947	−	0.549141i
$761$	16.6699	+	28.8731i	0.604284	+	1.04665i	0.992164	+	0.124941i	$0.0398741\pi$
$761$	16.6699	+	28.8731i	0.604284	+	1.04665i	−0.387880	+	0.921710i	$0.626793\pi$
$762$	0.253165	−	0.519042i	0.00917119	−	0.0188029i
$763$	0.0812027	−	0.0468824i	0.00293974	−	0.00169726i
$764$	−29.9124	+	4.20285i	−1.08219	+	0.152054i
$765$	12.9221	+	7.46059i	0.467200	+	0.269738i
$766$	13.9686	+	6.81323i	0.504705	+	0.246172i
$767$	−30.6579	−	12.7675i	−1.10699	−	0.461007i
$768$	0.918928	−	1.72767i	0.0331589	−	0.0623419i
$769$	−10.9095	+	18.8959i	−0.393408	+	0.681403i	−0.992897	−	0.118981i	$-0.962037\pi$
$769$	−10.9095	+	18.8959i	−0.393408	+	0.681403i	0.599488	+	0.800383i	$0.295371\pi$
$770$	0.548599	−	0.370021i	0.0197701	−	0.0133346i
$771$	0.255747	−	0.147655i	0.00921050	−	0.00531768i
$772$	6.12286	+	7.83746i	0.220366	+	0.282077i
$773$	6.56934	−	3.79281i	0.236283	−	0.136418i	−0.377184	−	0.926138i	$-0.623108\pi$
$773$	6.56934	−	3.79281i	0.236283	−	0.136418i	0.613467	+	0.789720i	$0.289774\pi$
$774$	−8.18228	+	0.572017i	−0.294106	+	0.0205607i
$775$	7.61772			0.273637
$776$	−0.547160	+	0.492614i	−0.0196419	+	0.0176838i
$777$	0.0428115	−	0.0741517i	0.00153585	−	0.00266018i
$778$	−21.3737	−	31.6890i	−0.766285	−	1.13611i
$779$			53.6610i			1.92261i
$780$	−0.222479	+	0.853419i	−0.00796602	+	0.0305573i
$781$			14.7072i			0.526265i
$782$	−44.3591	+	29.9195i	−1.58628	+	1.06992i
$783$	1.89225	−	3.27748i	0.0676236	−	0.117128i
$784$	−26.7759	+	7.67586i	−0.956284	+	0.274138i
$785$	−21.3529			−0.762118
$786$	−0.0247626	−	0.354210i	−0.000883251	−	0.0126342i
$787$	40.9178	−	23.6239i	1.45856	−	0.842101i	0.459622	−	0.888115i	$-0.347985\pi$
$787$	40.9178	−	23.6239i	1.45856	−	0.842101i	0.998941	+	0.0460134i	$0.0146517\pi$
$788$	−30.4789	+	23.8110i	−1.08577	+	0.848233i
$789$	−0.549168	+	0.317063i	−0.0195509	+	0.0112877i
$790$	8.92134	+	13.2269i	0.317407	+	0.470593i
$791$	−0.0717066	+	0.124199i	−0.00254959	+	0.00441602i
$792$	−20.2568	+	4.30460i	−0.719793	+	0.152957i
$793$	−15.6904	−	6.53426i	−0.557182	−	0.232038i
$794$	18.1738	−	37.2601i	0.644962	−	1.32231i
$795$	−0.241288	−	0.139308i	−0.00855761	−	0.00494074i
$796$	1.20417	−	0.169193i	0.0426808	−	0.00599688i
$797$	−13.5501	+	7.82317i	−0.479970	+	0.277111i	−0.720404	−	0.693555i	$-0.756044\pi$
$797$	−13.5501	+	7.82317i	−0.479970	+	0.277111i	0.240434	+	0.970666i	$0.422710\pi$
$798$	0.237227	+	0.115708i	0.00839775	+	0.00409604i
$799$	−20.8936	−	36.1887i	−0.739161	−	1.28026i
$800$	−5.57083	−	0.982788i	−0.196959	−	0.0347468i
$801$	46.4994			1.64298
$802$	0.344362	+	4.92584i	0.0121598	+	0.173937i
$803$	−35.3009	−	20.3810i	−1.24574	−	0.719229i
$804$	2.60904	−	0.366584i	0.0920138	−	0.0129284i
$805$		−	1.44388i		−	0.0508901i
$806$	−36.8118	−	12.3959i	−1.29664	−	0.436628i
$807$	−0.704161			−0.0247876
$808$	−4.83931	+	14.8912i	−0.170246	+	0.523871i
$809$	20.9306	−	36.2528i	0.735879	−	1.27458i	−0.218457	−	0.975847i	$-0.570102\pi$
$809$	20.9306	−	36.2528i	0.735879	−	1.27458i	0.954337	−	0.298734i	$-0.0965642\pi$
$810$	12.5073	−	0.874378i	0.439463	−	0.0307225i
$811$		−	46.6888i		−	1.63947i	−0.572746	−	0.819733i	$-0.694122\pi$
$811$		−	46.6888i		−	1.63947i	0.572746	−	0.819733i	$-0.305878\pi$
$812$	1.82889	+	0.738996i	0.0641816	+	0.0259337i
$813$	0.539028	−	0.311208i	0.0189046	−	0.0109145i
$814$	−11.4418	−	5.58079i	−0.401035	−	0.195606i
$815$	3.01985	+	5.23053i	0.105781	+	0.183218i
$816$	−1.69884	+	1.75896i	−0.0594714	+	0.0615758i
$817$	7.77136	−	13.4604i	0.271886	−	0.470920i
$818$	35.9404	+	17.5301i	1.25663	+	0.612926i
$819$	2.03608	−	0.264104i	0.0711462	−	0.00922854i
$820$	10.5724	−	8.25946i	0.369204	−	0.288433i
$821$	−29.8924	−	17.2584i	−1.04325	−	0.602321i	−0.122498	−	0.992469i	$-0.539091\pi$
$821$	−29.8924	−	17.2584i	−1.04325	−	0.602321i	−0.920752	+	0.390148i	$0.872424\pi$
$822$	2.04648	+	3.03415i	0.0713792	+	0.105828i
$823$	15.2971	+	26.4954i	0.533224	+	0.923572i	0.999247	+	0.0387989i	$0.0123532\pi$
$823$	15.2971	+	26.4954i	0.533224	+	0.923572i	−0.466023	+	0.884773i	$0.654314\pi$
$824$	1.75261	+	8.24749i	0.0610550	+	0.287315i
$825$	−0.149994	−	0.259797i	−0.00522212	−	0.00904497i
$826$	2.47885	−	0.173295i	0.0862503	−	0.00602970i
$827$			4.98675i			0.173406i	0.996234	+	0.0867031i	$0.0276332\pi$
$827$			4.98675i			0.173406i	−0.996234	+	0.0867031i	$0.972367\pi$
$828$	−16.9289	+	41.8963i	−0.588321	+	1.45600i
$829$	25.4425	+	14.6893i	0.883656	+	0.510179i	0.871862	−	0.489752i	$-0.162913\pi$
$829$	25.4425	+	14.6893i	0.883656	+	0.510179i	0.0117936	+	0.999930i	$0.496246\pi$
$830$	15.2976	−	10.3180i	0.530987	−	0.358142i
$831$	1.07024			0.0371263
$832$	25.3212	+	13.8143i	0.877855	+	0.478926i
$833$	34.8086			1.20605
$834$	−3.05705	+	2.06193i	−0.105857	+	0.0713988i
$835$	−17.9756	−	10.3782i	−0.622070	−	0.359152i
$836$	14.7017	−	36.3844i	0.508470	−	1.25838i
$837$		−	5.57610i		−	0.192738i
$838$	−34.6965	+	2.42561i	−1.19857	+	0.0837912i
$839$	−11.4005	−	19.7462i	−0.393589	−	0.681715i	0.599331	−	0.800501i	$-0.295433\pi$
$839$	−11.4005	−	19.7462i	−0.393589	−	0.681715i	−0.992920	+	0.118786i	$0.962100\pi$
$840$	−0.0137167	−	0.0645487i	−0.000473272	−	0.00222714i
$841$	−1.13472	−	1.96539i	−0.0391283	−	0.0677722i
$842$	9.66270	+	14.3261i	0.332999	+	0.493709i
$843$	1.90580	+	1.10032i	0.0656394	+	0.0378969i
$844$	−0.615461	+	0.480816i	−0.0211850	+	0.0165504i
$845$	−12.5441	−	3.41253i	−0.431530	−	0.117395i
$846$	−31.7185	−	15.4708i	−1.09050	−	0.531897i
$847$	−0.475351	+	0.823333i	−0.0163333	+	0.0282901i
$848$	−6.33038	+	6.55439i	−0.217386	+	0.225079i
$849$	0.0270752	+	0.0468956i	0.000929218	+	0.00160945i
$850$	6.35366	+	3.09902i	0.217929	+	0.106296i
$851$	−24.0560	+	13.8888i	−0.824630	+	0.476100i
$852$	1.35985	+	0.549472i	0.0465878	+	0.0188246i
$853$		−	4.95213i		−	0.169558i	−0.996400	−	0.0847789i	$-0.972982\pi$
$853$		−	4.95213i		−	0.169558i	0.996400	−	0.0847789i	$-0.0270184\pi$
$854$	1.26865	−	0.0886904i	0.0434123	−	0.00303492i
$855$	−11.9393	+	20.6795i	−0.408317	+	0.707225i
$856$	−2.46541	+	7.58640i	−0.0842660	+	0.259298i
$857$	−11.8991			−0.406464			−0.203232	−	0.979131i	$-0.565145\pi$
$857$	−11.8991			−0.406464			−0.203232	+	0.979131i	$0.565145\pi$
$858$	0.302076	+	1.49952i	0.0103127	+	0.0511928i
$859$			8.60447i			0.293581i	0.989168	+	0.146790i	$0.0468943\pi$
$859$			8.60447i			0.293581i	−0.989168	+	0.146790i	$0.953106\pi$
$860$	−3.84815	+	0.540686i	−0.131221	+	0.0184372i
$861$	0.135539	+	0.0782532i	0.00461914	+	0.00266686i
$862$	2.74338	+	39.2420i	0.0934399	+	1.33659i
$863$	−46.9541			−1.59834			−0.799169	−	0.601107i	$-0.794727\pi$
$863$	−46.9541			−1.59834			−0.799169	+	0.601107i	$0.794727\pi$
$864$	−0.719391	+	4.07779i	−0.0244742	+	0.138729i
$865$	7.20929	+	12.4869i	0.245123	+	0.424566i
$866$	39.3741	+	19.2049i	1.33799	+	0.652609i
$867$	0.845909	−	0.488386i	0.0287286	−	0.0165865i
$868$	2.87809	−	0.404387i	0.0976888	−	0.0137258i
$869$	23.9641	+	13.8357i	0.812926	+	0.469343i
$870$	0.392026	−	0.803736i	0.0132909	−	0.0272492i
$871$	4.99560	+	38.5129i	0.169269	+	1.30496i
$872$	−1.35988	+	0.288976i	−0.0460512	+	0.00978597i
$873$	0.388505	−	0.672910i	0.0131489	−	0.0227745i
$874$	−47.8808	−	70.9888i	−1.61959	−	2.40123i
$875$	−0.165206	+	0.0953817i	−0.00558498	+	0.00322449i
$876$	−3.20333	+	2.50253i	−0.108230	+	0.0845528i
$877$	17.6709	−	10.2023i	0.596704	−	0.344507i	−0.171040	−	0.985264i	$-0.554713\pi$
$877$	17.6709	−	10.2023i	0.596704	−	0.344507i	0.767744	+	0.640757i	$0.221379\pi$
$878$	1.80619	+	25.8363i	0.0609561	+	0.871931i
$879$	−1.51404			−0.0510672
$880$	−9.43139	+	2.70370i	−0.317932	+	0.0911416i
$881$	−5.70216	+	9.87644i	−0.192111	+	0.332746i	−0.945950	−	0.324314i	$-0.894867\pi$
$881$	−5.70216	+	9.87644i	−0.192111	+	0.332746i	0.753839	+	0.657059i	$0.228200\pi$
$882$	24.3713	−	16.4380i	0.820625	−	0.553498i
$883$		−	35.8007i		−	1.20479i	−0.798198	−	0.602395i	$-0.794213\pi$
$883$		−	35.8007i		−	1.20479i	0.798198	−	0.602395i	$-0.205787\pi$
$884$	−25.6605	−	25.3147i	−0.863057	−	0.851425i
$885$		−	1.12652i		−	0.0378674i
$886$	−13.0524	−	19.3516i	−0.438503	−	0.650131i
$887$	−12.9277	+	22.3915i	−0.434071	+	0.751833i	−0.997219	−	0.0745229i	$-0.976257\pi$
$887$	−12.9277	+	22.3915i	−0.434071	+	0.751833i	0.563148	+	0.826356i	$0.309590\pi$
$888$	−0.943484	+	0.849427i	−0.0316612	+	0.0285049i
$889$	−0.636924			−0.0213617
$890$	21.9762	−	1.53634i	0.736645	−	0.0514983i
$891$	18.8323	−	10.8729i	0.630907	−	0.364254i
$892$	−4.17804	−	5.34803i	−0.139891	−	0.179065i
$893$	57.9136	−	33.4364i	1.93800	−	1.11891i
$894$	2.88704	−	1.94726i	0.0965571	−	0.0651262i
$895$	−4.50652	+	7.80552i	−0.150636	+	0.260910i
$896$	−2.15692	−	0.0755848i	−0.0720575	−	0.00252511i
$897$	3.08118	+	1.28316i	0.102878	+	0.0428434i
$898$	14.1344	+	6.89412i	0.471671	+	0.230060i
$899$	34.1083	+	19.6924i	1.13757	+	0.656779i
$900$	5.91201	−	0.830669i	0.197067	−	0.0276890i
$901$	9.86167	−	5.69364i	0.328540	−	0.189683i
$902$	10.2009	−	20.9140i	0.339652	−	0.696359i
$903$	−0.0226658	−	0.0392583i	−0.000754270	−	0.00130643i
$904$	1.58028	−	1.42274i	0.0525592	−	0.0473196i
$905$	14.3364			0.476559
$906$	1.19493	−	0.0835367i	0.0396989	−	0.00277532i
$907$	20.7596	+	11.9855i	0.689310	+	0.397973i	0.803353	−	0.595503i	$-0.203047\pi$
$907$	20.7596	+	11.9855i	0.689310	+	0.397973i	−0.114044	+	0.993476i	$0.536380\pi$
$908$	−3.91514	−	27.8647i	−0.129928	−	0.924722i
$909$		−	16.5248i		−	0.548093i
$910$	0.953550	−	0.192091i	0.0316099	−	0.00636776i
$911$	−30.4715			−1.00957			−0.504784	−	0.863246i	$-0.668428\pi$
$911$	−30.4715			−1.00957			−0.504784	+	0.863246i	$0.668428\pi$
$912$	−2.81490	−	2.71869i	−0.0932106	−	0.0900250i
$913$	16.0016	−	27.7156i	0.529577	−	0.917254i
$914$	−0.542407	−	7.75872i	−0.0179412	−	0.256636i
$915$		−	0.576539i		−	0.0190598i
$916$	−45.4025	−	18.3456i	−1.50014	−	0.606157i
$917$	−0.339150	+	0.195808i	−0.0111997	+	0.00646616i
$918$	2.26846	−	4.65082i	0.0748702	−	0.153500i
$919$	18.6774	+	32.3502i	0.616111	+	1.06714i	0.990188	+	0.139739i	$0.0446262\pi$
$919$	18.6774	+	32.3502i	0.616111	+	1.06714i	−0.374077	+	0.927398i	$0.622040\pi$
$920$	−6.61658	+	20.3601i	−0.218142	+	0.671253i
$921$	−1.01687	+	1.76126i	−0.0335069	+	0.0580356i
$922$	8.94759	−	18.3445i	0.294673	−	0.604143i
$923$	−8.31133	+	19.9576i	−0.273571	+	0.656911i
$924$	−0.0704614	−	0.0901929i	−0.00231801	−	0.00296713i
$925$	3.17825	+	1.83496i	0.104500	+	0.0603332i
$926$	28.7889	−	19.4177i	0.946064	−	0.638104i
$927$	−4.44926	−	7.70635i	−0.146133	−	0.253110i
$928$	−22.4027	−	18.8015i	−0.735406	−	0.617188i
$929$	20.5072	+	35.5195i	0.672820	+	1.16536i	0.977101	+	0.212776i	$0.0682505\pi$
$929$	20.5072	+	35.5195i	0.672820	+	1.16536i	−0.304281	+	0.952582i	$0.598416\pi$
$930$	−0.0918870	−	1.31438i	−0.00301309	−	0.0431001i
$931$			55.7050i			1.82566i
$932$	−11.7811	+	29.1563i	−0.385903	+	0.955047i
$933$	2.60201	+	1.50227i	0.0851860	+	0.0491821i
$934$	25.6504	+	38.0298i	0.839308	+	1.24437i
$935$	12.2608			0.400970
$936$	−29.9209	−	5.60619i	−0.977995	−	0.183244i
$937$	27.2260			0.889435			0.444717	−	0.895671i	$-0.353304\pi$
$937$	27.2260			0.889435			0.444717	+	0.895671i	$0.353304\pi$
$938$	−1.62487	−	2.40906i	−0.0530538	−	0.0786585i
$939$	1.42305	+	0.821597i	0.0464394	+	0.0268118i
$940$	−15.5017	−	6.26373i	−0.505610	−	0.204300i
$941$		−	11.0021i		−	0.358658i	−0.983789	−	0.179329i	$-0.942607\pi$
$941$		−	11.0021i		−	0.358658i	0.983789	−	0.179329i	$-0.0573927\pi$
$942$	0.257565	+	3.68427i	0.00839191	+	0.120040i
$943$	−25.3866	−	43.9710i	−0.826703	−	1.43189i
$944$	−35.7483	−	8.91571i	−1.16351	−	0.290182i
$945$	0.0698185	+	0.120929i	0.00227119	+	0.00393382i
$946$	−5.58763	+	3.76876i	−0.181669	+	0.122533i
$947$	−0.440186	−	0.254141i	−0.0143041	−	0.00825848i	0.492831	−	0.870125i	$-0.335962\pi$
$947$	−0.440186	−	0.254141i	−0.0143041	−	0.00825848i	−0.507135	+	0.861867i	$0.669295\pi$
$948$	2.17459	−	1.69885i	0.0706273	−	0.0551762i
$949$	−36.3853	−	47.6061i	−1.18112	−	1.54536i
$950$	−4.95943	+	10.1679i	−0.160905	+	0.329890i
$951$	−0.799735	+	1.38518i	−0.0259332	+	0.0449176i
$952$	2.56502	+	0.833575i	0.0831329	+	0.0270163i
$953$	−0.887368	−	1.53697i	−0.0287447	−	0.0497873i	0.851295	−	0.524687i	$-0.175818\pi$
$953$	−0.887368	−	1.53697i	−0.0287447	−	0.0497873i	−0.880040	+	0.474900i	$0.842484\pi$
$954$	4.21590	−	8.64349i	0.136495	−	0.279843i
$955$	13.0797	−	7.55155i	0.423248	−	0.244362i
$956$	16.0936	−	39.8290i	0.520504	−	1.28816i
$957$		−	1.55099i		−	0.0501362i
$958$	−2.04024	−	29.1841i	−0.0659172	−	0.942896i
$959$	2.01822	−	3.49566i	0.0651718	−	0.112881i
$960$	−0.102375	+	0.973056i	−0.00330415	+	0.0314052i
$961$	27.0296			0.871924
$962$	−12.3726	−	14.0391i	−0.398909	−	0.452638i
$963$		−	8.41865i		−	0.271287i
$964$	−21.9415	+	3.08290i	−0.706688	+	0.0992934i
$965$	−4.30658	−	2.48640i	−0.138634	−	0.0800402i
$966$	−0.249130	+	0.0174165i	−0.00801561	+	0.000560366i
$967$	−22.4248			−0.721134			−0.360567	−	0.932733i	$-0.617417\pi$
$967$	−22.4248			−0.721134			−0.360567	+	0.932733i	$0.617417\pi$
$968$	10.4758	−	9.43150i	0.336706	−	0.303140i
$969$	2.44523	+	4.23527i	0.0785522	+	0.136056i
$970$	0.161379	−	0.330862i	0.00518158	−	0.0106233i
$971$	−25.5388	+	14.7448i	−0.819579	+	0.473184i	−0.850271	−	0.526345i	$-0.823562\pi$
$971$	−25.5388	+	14.7448i	−0.819579	+	0.473184i	0.0306923	+	0.999529i	$0.490229\pi$
$972$	−0.912822	−	6.49671i	−0.0292788	−	0.208382i
$973$	3.52205	+	2.03346i	0.112912	+	0.0651896i
$974$	5.74746	+	2.80335i	0.184161	+	0.0898251i
$975$	−0.0567241	−	0.437307i	−0.00181663	−	0.0140050i
$976$	−18.2956	−	4.56296i	−0.585628	−	0.146057i
$977$	−11.0271	+	19.0995i	−0.352788	+	0.611046i	−0.986737	−	0.162329i	$-0.948100\pi$
$977$	−11.0271	+	19.0995i	−0.352788	+	0.611046i	0.633949	+	0.773375i	$0.281433\pi$
$978$	0.866060	−	0.584143i	0.0276935	−	0.0186788i
$979$	33.0897	−	19.1044i	1.05755	−	0.610578i
$980$	10.9751	−	8.57407i	0.350587	−	0.273889i
$981$	1.27065	−	0.733611i	0.0405688	−	0.0234224i
$982$	−2.26546	+	0.158377i	−0.0722938	+	0.00505401i
$983$	1.61372			0.0514695			0.0257348	−	0.999669i	$-0.491807\pi$
$983$	1.61372			0.0514695			0.0257348	+	0.999669i	$0.491807\pi$
$984$	−1.55263	−	1.72455i	−0.0494960	−	0.0549767i
$985$	9.66932	−	16.7477i	0.308090	−	0.533628i
$986$	20.4372	+	30.3006i	0.650854	+	0.964967i
$987$		−	0.195040i		−	0.00620818i
$988$	40.5117	−	41.0651i	1.28885	−	1.30645i
$989$			14.7063i			0.467633i
$990$	8.58441	−	5.79004i	0.272830	−	0.184019i
$991$	−4.13793	+	7.16711i	−0.131446	+	0.227671i	−0.924234	−	0.381826i	$-0.875295\pi$
$991$	−4.13793	+	7.16711i	−0.131446	+	0.227671i	0.792788	+	0.609497i	$0.208629\pi$
$992$	−42.4370	−	7.48660i	−1.34738	−	0.237700i
$993$	−1.58323			−0.0502422
$994$	−0.112811	−	1.61367i	−0.00357814	−	0.0511826i
$995$	−0.526544	+	0.304000i	−0.0166926	+	0.00963746i
$996$	−1.96481	−	2.51502i	−0.0622572	−	0.0796914i
$997$	42.7112	−	24.6593i	1.35268	−	0.780968i	0.364053	−	0.931378i	$-0.381393\pi$
$997$	42.7112	−	24.6593i	1.35268	−	0.780968i	0.988624	+	0.150410i	$0.0480594\pi$
$998$	−12.2507	−	18.1630i	−0.387788	−	0.574941i
$999$	1.34318	−	2.32645i	0.0424962	−	0.0736055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.9	✓	104
8.5	even	2	inner	520.2.by.c.61.27	yes	104
13.3	even	3	inner	520.2.by.c.341.27	yes	104
104.29	even	6	inner	520.2.by.c.341.9	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.9	✓	104	1.1	even	1	trivial
520.2.by.c.61.27	yes	104	8.5	even	2	inner
520.2.by.c.341.9	yes	104	104.29	even	6	inner
520.2.by.c.341.27	yes	104	13.3	even	3	inner

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17245 + 0.790798i) q^{2} +(-0.105918 - 0.0611516i) q^{3} +(0.749278 - 1.85434i) q^{4} +1.00000i q^{5} +(0.172542 - 0.0120623i) q^{6} +(-0.0953817 - 0.165206i) q^{7} +(0.587918 + 2.76665i) q^{8} +(-1.49252 - 2.58512i) q^{9} +O(q^{10})\)	\(q+(-1.17245 + 0.790798i) q^{2} +(-0.105918 - 0.0611516i) q^{3} +(0.749278 - 1.85434i) q^{4} +1.00000i q^{5} +(0.172542 - 0.0120623i) q^{6} +(-0.0953817 - 0.165206i) q^{7} +(0.587918 + 2.76665i) q^{8} +(-1.49252 - 2.58512i) q^{9} +(-0.790798 - 1.17245i) q^{10} +(-2.12420 - 1.22641i) q^{11} +(-0.192758 + 0.150588i) q^{12} +(-2.18946 - 2.86466i) q^{13} +(0.242475 + 0.118268i) q^{14} +(0.0611516 - 0.105918i) q^{15} +(-2.87717 - 2.77883i) q^{16} +(2.49932 + 4.32896i) q^{17} +(3.79421 + 1.85064i) q^{18} +(-6.92772 + 3.99972i) q^{19} +(1.85434 + 0.749278i) q^{20} +0.0233310i q^{21} +(3.46036 - 0.241912i) q^{22} +(3.78448 - 6.55491i) q^{23} +(0.106914 - 0.328990i) q^{24} -1.00000 q^{25} +(4.83240 + 1.62725i) q^{26} +0.731990i q^{27} +(-0.377816 + 0.0530851i) q^{28} +(-4.47749 - 2.58508i) q^{29} +(0.0120623 + 0.172542i) q^{30} -7.61772 q^{31} +(5.57083 + 0.982788i) q^{32} +(0.149994 + 0.259797i) q^{33} +(-6.35366 - 3.09902i) q^{34} +(0.165206 - 0.0953817i) q^{35} +(-5.91201 + 0.830669i) q^{36} +(-3.17825 - 1.83496i) q^{37} +(4.95943 - 10.1679i) q^{38} +(0.0567241 + 0.437307i) q^{39} +(-2.76665 + 0.587918i) q^{40} +(3.35405 - 5.80938i) q^{41} +(-0.0184501 - 0.0273544i) q^{42} +(-1.68267 + 0.971488i) q^{43} +(-3.86580 + 3.02008i) q^{44} +(2.58512 - 1.49252i) q^{45} +(0.746495 + 10.6781i) q^{46} -8.35969 q^{47} +(0.134813 + 0.470271i) q^{48} +(3.48180 - 6.03066i) q^{49} +(1.17245 - 0.790798i) q^{50} -0.611351i q^{51} +(-6.95257 + 1.91358i) q^{52} -2.27807i q^{53} +(-0.578856 - 0.858222i) q^{54} +(1.22641 - 2.12420i) q^{55} +(0.400990 - 0.361015i) q^{56} +0.978358 q^{57} +(7.29391 - 0.509912i) q^{58} +(7.97682 - 4.60542i) q^{59} +(-0.150588 - 0.192758i) q^{60} +(4.08245 - 2.35700i) q^{61} +(8.93139 - 6.02407i) q^{62} +(-0.284718 + 0.493146i) q^{63} +(-7.30870 + 3.25313i) q^{64} +(2.86466 - 2.18946i) q^{65} +(-0.381307 - 0.185984i) q^{66} +(-9.32800 - 5.38552i) q^{67} +(9.90005 - 1.39101i) q^{68} +(-0.801687 + 0.462854i) q^{69} +(-0.118268 + 0.242475i) q^{70} +(-2.99802 - 5.19272i) q^{71} +(6.27465 - 5.64912i) q^{72} +16.6184 q^{73} +(5.17742 - 0.361950i) q^{74} +(0.105918 + 0.0611516i) q^{75} +(2.22606 + 15.8433i) q^{76} +0.467908i q^{77} +(-0.412328 - 0.467864i) q^{78} -11.2814 q^{79} +(2.77883 - 2.87717i) q^{80} +(-4.43280 + 7.67784i) q^{81} +(0.661592 + 9.46358i) q^{82} +13.0475i q^{83} +(0.0432636 + 0.0174814i) q^{84} +(-4.32896 + 2.49932i) q^{85} +(1.20459 - 2.46967i) q^{86} +(0.316164 + 0.547612i) q^{87} +(2.14419 - 6.59796i) q^{88} +(-7.78874 + 13.4905i) q^{89} +(-1.85064 + 3.79421i) q^{90} +(-0.264424 + 0.634948i) q^{91} +(-9.31941 - 11.9292i) q^{92} +(0.806852 + 0.465836i) q^{93} +(9.80132 - 6.61082i) q^{94} +(-3.99972 - 6.92772i) q^{95} +(-0.529951 - 0.444760i) q^{96} +(0.130150 + 0.225427i) q^{97} +(0.686793 + 9.82405i) q^{98} +7.32177i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

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