LMFDB - Embedded newform 550.2.t.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(89,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("550.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.t (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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	550.529
Dual form			550.2.t.a.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.260074 + 0.357960i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.357960 - 0.260074i) q^{6} +0.273457i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.866554 + 2.66698i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.260074 + 0.357960i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.357960 - 0.260074i) q^{6} +0.273457i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.866554 + 2.66698i) q^{9} +(-0.530249 + 2.17229i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.420808 + 0.136729i) q^{12} +(2.50000 - 0.812299i) q^{13} +(0.0845030 - 0.260074i) q^{14} +(0.841616 + 0.520147i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.623345 + 0.857960i) q^{17} -2.80423i q^{18} +(6.55899 - 4.76538i) q^{19} +(1.17557 - 1.90211i) q^{20} +(-0.0978870 - 0.0711190i) q^{21} +(0.587785 - 0.809017i) q^{22} +(-4.09252 - 1.32974i) q^{23} +0.442463 q^{24} +(-4.94424 + 0.744661i) q^{25} -2.62866 q^{26} +(-2.44246 - 0.793604i) q^{27} +(-0.160734 + 0.221232i) q^{28} +(1.40211 + 1.01869i) q^{29} +(-0.639690 - 0.754763i) q^{30} +(5.78022 - 4.19958i) q^{31} -1.00000i q^{32} +(-0.260074 - 0.357960i) q^{33} +(-0.327712 - 1.00859i) q^{34} +(0.609762 - 0.0456612i) q^{35} +(-0.866554 + 2.66698i) q^{36} +(10.2743 - 3.33833i) q^{37} +(-7.71055 + 2.50531i) q^{38} +(-0.359413 + 1.10616i) q^{39} +(-1.70582 + 1.44575i) q^{40} +(2.55223 + 7.85494i) q^{41} +(0.0711190 + 0.0978870i) q^{42} -4.85004i q^{43} +(-0.809017 + 0.587785i) q^{44} +(5.80220 - 2.37759i) q^{45} +(3.48131 + 2.52932i) q^{46} +(2.81761 - 3.87811i) q^{47} +(-0.420808 - 0.136729i) q^{48} +6.92522 q^{49} +(4.93236 + 0.819639i) q^{50} -0.469231 q^{51} +(2.50000 + 0.812299i) q^{52} +(4.20196 - 5.78350i) q^{53} +(2.07768 + 1.50953i) q^{54} +(2.17229 + 0.530249i) q^{55} +(0.221232 - 0.160734i) q^{56} +3.58721i q^{57} +(-1.01869 - 1.40211i) q^{58} +(-0.546915 - 1.68323i) q^{59} +(0.375147 + 0.915497i) q^{60} +(-4.33099 + 13.3294i) q^{61} +(-6.79506 + 2.20785i) q^{62} +(-0.729305 + 0.236966i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.22873 - 5.43893i) q^{65} +(0.136729 + 0.420808i) q^{66} +(-8.21992 - 11.3138i) q^{67} +1.06050i q^{68} +(1.54035 - 1.11913i) q^{69} +(-0.594028 - 0.145000i) q^{70} +(-5.48552 - 3.98546i) q^{71} +(1.64828 - 2.26867i) q^{72} +(-2.51297 - 0.816514i) q^{73} -10.8031 q^{74} +(1.01931 - 1.96351i) q^{75} +8.10736 q^{76} +(-0.260074 - 0.0845030i) q^{77} +(0.683644 - 0.940955i) q^{78} +(13.5388 + 9.83650i) q^{79} +(2.06909 - 0.847859i) q^{80} +(-5.88670 + 4.27694i) q^{81} -8.25918i q^{82} +(5.49469 + 7.56279i) q^{83} +(-0.0373895 - 0.115073i) q^{84} +(1.80902 - 1.53321i) q^{85} +(-1.49875 + 4.61267i) q^{86} +(-0.729305 + 0.236966i) q^{87} +(0.951057 - 0.309017i) q^{88} +(4.44424 - 13.6780i) q^{89} +(-6.25293 + 0.468243i) q^{90} +(0.222129 + 0.683644i) q^{91} +(-2.52932 - 3.48131i) q^{92} +3.16129i q^{93} +(-3.87811 + 2.81761i) q^{94} +(-11.7212 - 13.8297i) q^{95} +(0.357960 + 0.260074i) q^{96} +(-2.88010 + 3.96412i) q^{97} +(-6.58628 - 2.14001i) q^{98} -2.80423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9	$ 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9} + 2 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} + 16 q^{19} - 16 q^{21} + 10 q^{23} + 4 q^{24} - 10 q^{25} - 20 q^{27} - 10 q^{28} - 4 q^{29} + 10 q^{31} + 10 q^{33} - 10 q^{34} + 10 q^{35} - 2 q^{36} + 20 q^{37} - 10 q^{38} + 30 q^{39} + 26 q^{41} - 20 q^{42} - 2 q^{44} + 20 q^{45} + 16 q^{46} + 10 q^{47} + 8 q^{49} + 20 q^{50} - 40 q^{51} + 20 q^{52} - 10 q^{53} - 8 q^{54} + 10 q^{55} + 2 q^{56} - 20 q^{58} - 16 q^{59} - 10 q^{60} - 40 q^{61} - 30 q^{63} + 2 q^{64} - 10 q^{65} + 4 q^{66} + 28 q^{69} + 10 q^{70} - 26 q^{71} - 10 q^{73} + 8 q^{74} + 10 q^{75} + 4 q^{76} + 10 q^{77} + 20 q^{78} + 32 q^{79} - 18 q^{81} + 50 q^{83} - 24 q^{84} + 10 q^{85} - 10 q^{86} - 30 q^{87} + 6 q^{89} - 10 q^{90} + 40 q^{91} - 20 q^{92} - 10 q^{94} - 30 q^{95} + 6 q^{96} - 40 q^{97} - 20 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9 + 2 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 + 16 * q^19 - 16 * q^21 + 10 * q^23 + 4 * q^24 - 10 * q^25 - 20 * q^27 - 10 * q^28 - 4 * q^29 + 10 * q^31 + 10 * q^33 - 10 * q^34 + 10 * q^35 - 2 * q^36 + 20 * q^37 - 10 * q^38 + 30 * q^39 + 26 * q^41 - 20 * q^42 - 2 * q^44 + 20 * q^45 + 16 * q^46 + 10 * q^47 + 8 * q^49 + 20 * q^50 - 40 * q^51 + 20 * q^52 - 10 * q^53 - 8 * q^54 + 10 * q^55 + 2 * q^56 - 20 * q^58 - 16 * q^59 - 10 * q^60 - 40 * q^61 - 30 * q^63 + 2 * q^64 - 10 * q^65 + 4 * q^66 + 28 * q^69 + 10 * q^70 - 26 * q^71 - 10 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 20 * q^78 + 32 * q^79 - 18 * q^81 + 50 * q^83 - 24 * q^84 + 10 * q^85 - 10 * q^86 - 30 * q^87 + 6 * q^89 - 10 * q^90 + 40 * q^91 - 20 * q^92 - 10 * q^94 - 30 * q^95 + 6 * q^96 - 40 * q^97 - 20 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.260074	+	0.357960i	−0.150154	+	0.206669i	−0.877467	−	0.479637i	$-0.840769\pi$
$3$	−0.260074	+	0.357960i	−0.150154	+	0.206669i	0.727314	+	0.686305i	$0.240769\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.166977	−	2.22982i	−0.0746746	−	0.997208i
$5$	−0.166977	−	2.22982i	−0.0746746	−	0.997208i
$6$	0.357960	−	0.260074i	0.146137	−	0.106175i
$7$			0.273457i			0.103357i	0.998664	+	0.0516786i	$0.0164571\pi$
$7$			0.273457i			0.103357i	−0.998664	+	0.0516786i	$0.983543\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.866554	+	2.66698i	0.288851	+	0.888992i
$10$	−0.530249	+	2.17229i	−0.167679	+	0.686938i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$	−0.420808	+	0.136729i	−0.121477	+	0.0394702i
$13$	2.50000	−	0.812299i	0.693375	−	0.225291i	0.0589335	−	0.998262i	$-0.481230\pi$
$13$	2.50000	−	0.812299i	0.693375	−	0.225291i	0.634442	+	0.772971i	$0.281230\pi$
$14$	0.0845030	−	0.260074i	0.0225844	−	0.0695076i
$15$	0.841616	+	0.520147i	0.217304	+	0.134301i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.623345	+	0.857960i	0.151183	+	0.208086i	0.877891	−	0.478861i	$-0.158950\pi$
$17$	0.623345	+	0.857960i	0.151183	+	0.208086i	−0.726707	+	0.686947i	$0.758950\pi$
$18$		−	2.80423i		−	0.660962i
$19$	6.55899	−	4.76538i	1.50474	−	1.09325i	0.536288	−	0.844035i	$-0.319826\pi$
$19$	6.55899	−	4.76538i	1.50474	−	1.09325i	0.968447	−	0.249219i	$-0.0801739\pi$
$20$	1.17557	−	1.90211i	0.262866	−	0.425325i
$21$	−0.0978870	−	0.0711190i	−0.0213607	−	0.0155194i
$22$	0.587785	−	0.809017i	0.125316	−	0.172483i
$23$	−4.09252	−	1.32974i	−0.853349	−	0.277270i	−0.150501	−	0.988610i	$-0.548089\pi$
$23$	−4.09252	−	1.32974i	−0.853349	−	0.277270i	−0.702848	+	0.711340i	$0.748089\pi$
$24$	0.442463			0.0903175
$25$	−4.94424	+	0.744661i	−0.988847	+	0.148932i
$26$	−2.62866			−0.515522
$27$	−2.44246	−	0.793604i	−0.470052	−	0.152729i
$28$	−0.160734	+	0.221232i	−0.0303759	+	0.0418089i
$29$	1.40211	+	1.01869i	0.260366	+	0.189167i	0.710308	−	0.703891i	$-0.248556\pi$
$29$	1.40211	+	1.01869i	0.260366	+	0.189167i	−0.449942	+	0.893058i	$0.648556\pi$
$30$	−0.639690	−	0.754763i	−0.116791	−	0.137800i
$31$	5.78022	−	4.19958i	1.03816	−	0.754266i	0.0682331	−	0.997669i	$-0.478264\pi$
$31$	5.78022	−	4.19958i	1.03816	−	0.754266i	0.969925	+	0.243403i	$0.0782638\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.260074	−	0.357960i	−0.0452730	−	0.0623129i
$34$	−0.327712	−	1.00859i	−0.0562021	−	0.172972i
$35$	0.609762	−	0.0456612i	0.103069	−	0.00771816i
$36$	−0.866554	+	2.66698i	−0.144426	+	0.444496i
$37$	10.2743	−	3.33833i	1.68909	−	0.548819i	0.702450	−	0.711733i	$-0.252090\pi$
$37$	10.2743	−	3.33833i	1.68909	−	0.548819i	0.986640	+	0.162915i	$0.0520895\pi$
$38$	−7.71055	+	2.50531i	−1.25082	+	0.406415i
$39$	−0.359413	+	1.10616i	−0.0575521	+	0.177127i
$40$	−1.70582	+	1.44575i	−0.269714	+	0.228592i
$41$	2.55223	+	7.85494i	0.398591	+	1.22674i	0.926130	+	0.377205i	$0.123115\pi$
$41$	2.55223	+	7.85494i	0.398591	+	1.22674i	−0.527539	+	0.849531i	$0.676885\pi$
$42$	0.0711190	+	0.0978870i	0.0109739	+	0.0151043i
$43$		−	4.85004i		−	0.739625i	−0.929106	−	0.369812i	$-0.879422\pi$
$43$		−	4.85004i		−	0.739625i	0.929106	−	0.369812i	$-0.120578\pi$
$44$	−0.809017	+	0.587785i	−0.121964	+	0.0886120i
$45$	5.80220	−	2.37759i	0.864941	−	0.354430i
$46$	3.48131	+	2.52932i	0.513290	+	0.372927i
$47$	2.81761	−	3.87811i	0.410991	−	0.565680i	−0.552469	−	0.833533i	$-0.686314\pi$
$47$	2.81761	−	3.87811i	0.410991	−	0.565680i	0.963460	+	0.267853i	$0.0863143\pi$
$48$	−0.420808	−	0.136729i	−0.0607384	−	0.0197351i
$49$	6.92522			0.989317
$50$	4.93236	+	0.819639i	0.697541	+	0.115914i
$51$	−0.469231			−0.0657055
$52$	2.50000	+	0.812299i	0.346688	+	0.112646i
$53$	4.20196	−	5.78350i	0.577184	−	0.794425i	−0.416199	−	0.909273i	$-0.636638\pi$
$53$	4.20196	−	5.78350i	0.577184	−	0.794425i	0.993383	+	0.114848i	$0.0366382\pi$
$54$	2.07768	+	1.50953i	0.282737	+	0.205420i
$55$	2.17229	+	0.530249i	0.292911	+	0.0714987i
$56$	0.221232	−	0.160734i	0.0295633	−	0.0214790i
$57$			3.58721i			0.475137i
$58$	−1.01869	−	1.40211i	−0.133761	−	0.184106i
$59$	−0.546915	−	1.68323i	−0.0712023	−	0.219138i	0.909123	−	0.416528i	$-0.136753\pi$
$59$	−0.546915	−	1.68323i	−0.0712023	−	0.219138i	−0.980325	+	0.197390i	$0.936753\pi$
$60$	0.375147	+	0.915497i	0.0484312	+	0.118190i
$61$	−4.33099	+	13.3294i	−0.554527	+	1.70666i	0.142662	+	0.989771i	$0.454434\pi$
$61$	−4.33099	+	13.3294i	−0.554527	+	1.70666i	−0.697189	+	0.716887i	$0.745566\pi$
$62$	−6.79506	+	2.20785i	−0.862973	+	0.280397i
$63$	−0.729305	+	0.236966i	−0.0918838	+	0.0298549i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.22873	−	5.43893i	−0.276440	−	0.674616i
$66$	0.136729	+	0.420808i	0.0168301	+	0.0517979i
$67$	−8.21992	−	11.3138i	−1.00422	−	1.38219i	−0.922698	−	0.385523i	$-0.874021\pi$
$67$	−8.21992	−	11.3138i	−1.00422	−	1.38219i	−0.0815252	−	0.996671i	$-0.525979\pi$
$68$			1.06050i			0.128604i
$69$	1.54035	−	1.11913i	0.185436	−	0.134727i
$70$	−0.594028	−	0.145000i	−0.0710000	−	0.0173309i
$71$	−5.48552	−	3.98546i	−0.651011	−	0.472987i	0.212604	−	0.977138i	$-0.431806\pi$
$71$	−5.48552	−	3.98546i	−0.651011	−	0.472987i	−0.863616	+	0.504151i	$0.831806\pi$
$72$	1.64828	−	2.26867i	0.194252	−	0.267365i
$73$	−2.51297	−	0.816514i	−0.294121	−	0.0955657i	0.158240	−	0.987401i	$-0.449418\pi$
$73$	−2.51297	−	0.816514i	−0.294121	−	0.0955657i	−0.452361	+	0.891835i	$0.649418\pi$
$74$	−10.8031			−1.25583
$75$	1.01931	−	1.96351i	0.117699	−	0.226726i
$76$	8.10736			0.929978
$77$	−0.260074	−	0.0845030i	−0.0296381	−	0.00963001i
$78$	0.683644	−	0.940955i	0.0774074	−	0.106542i
$79$	13.5388	+	9.83650i	1.52323	+	1.10669i	0.959856	+	0.280493i	$0.0904978\pi$
$79$	13.5388	+	9.83650i	1.52323	+	1.10669i	0.563376	+	0.826201i	$0.309502\pi$
$80$	2.06909	−	0.847859i	0.231331	−	0.0947935i
$81$	−5.88670	+	4.27694i	−0.654078	+	0.475215i
$82$		−	8.25918i		−	0.912073i
$83$	5.49469	+	7.56279i	0.603120	+	0.830124i	0.995989	−	0.0894703i	$-0.0285174\pi$
$83$	5.49469	+	7.56279i	0.603120	+	0.830124i	−0.392869	+	0.919594i	$0.628517\pi$
$84$	−0.0373895	−	0.115073i	−0.00407953	−	0.0125555i
$85$	1.80902	−	1.53321i	0.196215	−	0.166300i
$86$	−1.49875	+	4.61267i	−0.161614	+	0.497397i
$87$	−0.729305	+	0.236966i	−0.0781897	+	0.0254054i
$88$	0.951057	−	0.309017i	0.101383	−	0.0329413i
$89$	4.44424	−	13.6780i	0.471088	−	1.44986i	−0.380073	−	0.924956i	$-0.624101\pi$
$89$	4.44424	−	13.6780i	0.471088	−	1.44986i	0.851161	−	0.524904i	$-0.175899\pi$
$90$	−6.25293	+	0.468243i	−0.659117	+	0.0493571i
$91$	0.222129	+	0.683644i	0.0232855	+	0.0716653i
$92$	−2.52932	−	3.48131i	−0.263699	−	0.362951i
$93$			3.16129i			0.327810i
$94$	−3.87811	+	2.81761i	−0.399996	+	0.290614i
$95$	−11.7212	−	13.8297i	−1.20257	−	1.41890i
$96$	0.357960	+	0.260074i	0.0365342	+	0.0265436i
$97$	−2.88010	+	3.96412i	−0.292430	+	0.402495i	−0.929802	−	0.368061i	$-0.880022\pi$
$97$	−2.88010	+	3.96412i	−0.292430	+	0.402495i	0.637372	+	0.770557i	$0.280022\pi$
$98$	−6.58628	−	2.14001i	−0.665314	−	0.216174i
$99$	−2.80423			−0.281835
$100$	−4.43767	−	2.30371i	−0.443767	−	0.230371i
$101$	−0.0842480			−0.00838299			−0.00419150	−	0.999991i	$-0.501334\pi$
$101$	−0.0842480			−0.00838299			−0.00419150	+	0.999991i	$0.501334\pi$
$102$	0.446266	+	0.145000i	0.0441869	+	0.0143572i
$103$	−6.47684	+	8.91460i	−0.638182	+	0.878382i	−0.998517	−	0.0544412i	$-0.982662\pi$
$103$	−6.47684	+	8.91460i	−0.638182	+	0.878382i	0.360335	+	0.932823i	$0.382662\pi$
$104$	−2.12663	−	1.54508i	−0.208533	−	0.151508i
$105$	−0.142238	+	0.230146i	−0.0138810	+	0.0224600i
$106$	−5.78350	+	4.20196i	−0.561743	+	0.408131i
$107$			5.38010i			0.520114i	0.965593	+	0.260057i	$0.0837414\pi$
$107$			5.38010i			0.520114i	−0.965593	+	0.260057i	$0.916259\pi$
$108$	−1.50953	−	2.07768i	−0.145254	−	0.199925i
$109$	−0.669006	−	2.05899i	−0.0640792	−	0.197215i	0.913891	−	0.405959i	$-0.133063\pi$
$109$	−0.669006	−	2.05899i	−0.0640792	−	0.197215i	−0.977970	+	0.208744i	$0.933063\pi$
$110$	−1.90211	−	1.17557i	−0.181359	−	0.112086i
$111$	−1.47709	+	4.54602i	−0.140199	+	0.431489i
$112$	−0.260074	+	0.0845030i	−0.0245746	+	0.00798478i
$113$	−18.8310	+	6.11855i	−1.77147	+	0.575585i	−0.998282	−	0.0585931i	$-0.981339\pi$
$113$	−18.8310	+	6.11855i	−1.77147	+	0.575585i	−0.773187	+	0.634178i	$0.781339\pi$
$114$	1.10851	−	3.41164i	0.103821	−	0.319529i
$115$	−2.28173	+	9.34764i	−0.212772	+	0.871672i
$116$	0.535560	+	1.64828i	0.0497255	+	0.153039i
$117$	4.33277	+	5.96354i	0.400565	+	0.551330i
$118$			1.76985i			0.162928i
$119$	−0.234616	+	0.170458i	−0.0215072	+	0.0156259i
$120$	−0.0738814	−	0.986616i	−0.00674442	−	0.0900653i
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$	8.23804	−	11.3387i	0.745837	−	1.02656i
$123$	−3.47553	−	1.12927i	−0.313378	−	0.101823i
$124$	7.14475			0.641617
$125$	2.48604	+	10.9004i	0.222358	+	0.974965i
$126$	0.766837			0.0683152
$127$	0.632458	+	0.205498i	0.0561215	+	0.0182350i	0.336943	−	0.941525i	$-0.390607\pi$
$127$	0.632458	+	0.205498i	0.0561215	+	0.0182350i	−0.280822	+	0.959760i	$0.590607\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	1.73612	+	1.26137i	0.152857	+	0.111057i
$130$	0.438926	+	5.86144i	0.0384964	+	0.514082i
$131$	−14.5334	+	10.5591i	−1.26979	+	0.922557i	−0.999194	−	0.0401360i	$-0.987221\pi$
$131$	−14.5334	+	10.5591i	−1.26979	+	0.922557i	−0.270596	+	0.962693i	$0.587221\pi$
$132$		−	0.442463i		−	0.0385115i
$133$	1.30313	+	1.79360i	0.112996	+	0.155525i
$134$	4.32147	+	13.3001i	0.373318	+	1.14895i
$135$	−1.36176	+	5.57878i	−0.117202	+	0.480145i
$136$	0.327712	−	1.00859i	0.0281011	−	0.0864861i
$137$	−0.574136	+	0.186548i	−0.0490518	+	0.0159379i	−0.333440	−	0.942771i	$-0.608210\pi$
$137$	−0.574136	+	0.186548i	−0.0490518	+	0.0159379i	0.284388	+	0.958709i	$0.408210\pi$
$138$	−1.81079	+	0.588362i	−0.154145	+	0.0500847i
$139$	2.93690	−	9.03884i	0.249104	−	0.766665i	−0.745830	−	0.666137i	$-0.767947\pi$
$139$	2.93690	−	9.03884i	0.249104	−	0.766665i	0.994934	−	0.100528i	$-0.0320532\pi$
$140$	0.520147	+	0.321469i	0.0439604	+	0.0271691i
$141$	0.655423	+	2.01719i	0.0551966	+	0.169878i
$142$	3.98546	+	5.48552i	0.334453	+	0.460335i
$143$			2.62866i			0.219819i
$144$	−2.26867	+	1.64828i	−0.189056	+	0.137357i
$145$	2.03739	−	3.29657i	0.169196	−	0.273765i
$146$	2.13766	+	1.55310i	0.176914	+	0.128536i
$147$	−1.80107	+	2.47896i	−0.148549	+	0.204461i
$148$	10.2743	+	3.33833i	0.844545	+	0.274409i
$149$	11.2609			0.922525			0.461263	−	0.887264i	$-0.347397\pi$
$149$	11.2609			0.922525			0.461263	+	0.887264i	$0.347397\pi$
$150$	−1.57617	+	1.55242i	−0.128694	+	0.126755i
$151$	−15.0615			−1.22569			−0.612845	−	0.790203i	$-0.709975\pi$
$151$	−15.0615			−1.22569			−0.612845	+	0.790203i	$0.709975\pi$
$152$	−7.71055	−	2.50531i	−0.625408	−	0.203208i
$153$	−1.74800	+	2.40592i	−0.141317	+	0.194507i
$154$	0.221232	+	0.160734i	0.0178274	+	0.0129523i
$155$	−10.3295	−	12.1876i	−0.829684	−	0.978935i
$156$	−0.940955	+	0.683644i	−0.0753367	+	0.0547353i
$157$			20.9203i			1.66962i	0.550535	+	0.834812i	$0.314424\pi$
$157$			20.9203i			1.66962i	−0.550535	+	0.834812i	$0.685576\pi$
$158$	−9.83650	−	13.5388i	−0.782550	−	1.07709i
$159$	0.977447	+	3.00827i	0.0775166	+	0.238571i
$160$	−2.22982	+	0.166977i	−0.176283	+	0.0132007i
$161$	0.363627	−	1.11913i	0.0286579	−	0.0881998i
$162$	6.92023	−	2.24852i	0.543705	−	0.176660i
$163$	−12.0167	+	3.90446i	−0.941221	+	0.305821i	−0.739143	−	0.673548i	$-0.764769\pi$
$163$	−12.0167	+	3.90446i	−0.941221	+	0.305821i	−0.202078	+	0.979370i	$0.564769\pi$
$164$	−2.55223	+	7.85494i	−0.199295	+	0.613368i
$165$	−0.754763	+	0.639690i	−0.0587582	+	0.0497998i
$166$	−2.88873	−	8.89059i	−0.224209	−	0.690044i
$167$	−7.78273	−	10.7120i	−0.602246	−	0.828920i	0.393666	−	0.919254i	$-0.371207\pi$
$167$	−7.78273	−	10.7120i	−0.602246	−	0.828920i	−0.995912	+	0.0903336i	$0.971207\pi$
$168$			0.120995i			0.00933496i
$169$	−4.92705	+	3.57971i	−0.379004	+	0.275362i
$170$	−2.19427	+	0.899152i	−0.168292	+	0.0689618i
$171$	18.3929	+	13.3632i	1.40654	+	1.02191i
$172$	2.85078	−	3.92377i	0.217370	−	0.299185i
$173$	−0.459741	−	0.149379i	−0.0349534	−	0.0113571i	0.291488	−	0.956574i	$-0.405850\pi$
$173$	−0.459741	−	0.149379i	−0.0349534	−	0.0113571i	−0.326442	+	0.945217i	$0.605850\pi$
$174$	0.766837			0.0581337
$175$	−0.203633	−	1.35204i	−0.0153932	−	0.102205i
$176$	−1.00000			−0.0753778
$177$	0.744768	+	0.241990i	0.0559802	+	0.0181891i
$178$	−8.45344	+	11.6352i	−0.633612	+	0.872092i
$179$	3.71357	+	2.69807i	0.277565	+	0.201663i	0.717855	−	0.696193i	$-0.245124\pi$
$179$	3.71357	+	2.69807i	0.277565	+	0.201663i	−0.440289	+	0.897856i	$0.645124\pi$
$180$	6.09159	+	1.48694i	0.454040	+	0.110830i
$181$	4.69041	−	3.40778i	0.348635	−	0.253298i	−0.399661	−	0.916663i	$-0.630872\pi$
$181$	4.69041	−	3.40778i	0.348635	−	0.253298i	0.748296	+	0.663365i	$0.230872\pi$
$182$		−	0.718826i		−	0.0532829i
$183$	−3.64503	−	5.01696i	−0.269449	−	0.370864i
$184$	1.32974	+	4.09252i	0.0980298	+	0.301705i
$185$	−9.15948	−	22.3525i	−0.673418	−	1.64339i
$186$	0.976892	−	3.00656i	0.0716292	−	0.220452i
$187$	−1.00859	+	0.327712i	−0.0737556	+	0.0239647i
$188$	4.55899	−	1.48131i	0.332498	−	0.108035i
$189$	0.217017	−	0.667910i	0.0157857	−	0.0485833i
$190$	6.87389	+	16.7749i	0.498685	+	1.21698i
$191$	−5.51519	−	16.9740i	−0.399065	−	1.22820i	−0.925750	−	0.378136i	$-0.876565\pi$
$191$	−5.51519	−	16.9740i	−0.399065	−	1.22820i	0.526685	−	0.850061i	$-0.323435\pi$
$192$	−0.260074	−	0.357960i	−0.0187692	−	0.0258336i
$193$			4.88557i			0.351671i	0.984420	+	0.175835i	$0.0562627\pi$
$193$			4.88557i			0.351671i	−0.984420	+	0.175835i	$0.943737\pi$
$194$	3.96412	−	2.88010i	0.284607	−	0.206779i
$195$	2.52655	+	0.616724i	0.180930	+	0.0441645i
$196$	5.60262	+	4.07054i	0.400187	+	0.290753i
$197$	11.2194	−	15.4422i	0.799352	−	1.10021i	−0.193527	−	0.981095i	$-0.561993\pi$
$197$	11.2194	−	15.4422i	0.799352	−	1.10021i	0.992880	−	0.119119i	$-0.0380071\pi$
$198$	2.66698	+	0.866554i	0.189534	+	0.0615833i
$199$	−11.8024			−0.836652			−0.418326	−	0.908297i	$-0.637383\pi$
$199$	−11.8024			−0.836652			−0.418326	+	0.908297i	$0.637383\pi$
$200$	3.50859	+	3.56227i	0.248095	+	0.251891i
$201$	6.18766			0.436444
$202$	0.0801246	+	0.0260341i	0.00563755	+	0.00183175i
$203$	−0.278570	+	0.383418i	−0.0195518	+	0.0269107i
$204$	−0.379616	−	0.275807i	−0.0265784	−	0.0193104i
$205$	17.0890	−	7.00261i	1.19355	−	0.489084i
$206$	8.91460	−	6.47684i	0.621110	−	0.451263i
$207$		−	12.0669i		−	0.838711i
$208$	1.54508	+	2.12663i	0.107132	+	0.147455i
$209$	2.50531	+	7.71055i	0.173296	+	0.533350i
$210$	0.206396	−	0.174928i	0.0142426	−	0.0120712i
$211$	−4.66239	+	14.3493i	−0.320972	+	0.987850i	0.652254	+	0.758000i	$0.273823\pi$
$211$	−4.66239	+	14.3493i	−0.320972	+	0.987850i	−0.973226	+	0.229850i	$0.926177\pi$
$212$	6.79892	−	2.20910i	0.466951	−	0.151722i
$213$	2.85328	−	0.927086i	0.195503	−	0.0635229i
$214$	1.66254	−	5.11678i	0.113649	−	0.349776i
$215$	−10.8148	+	0.809848i	−0.737560	+	0.0552312i
$216$	0.793604	+	2.44246i	0.0539979	+	0.166189i
$217$	1.14841	+	1.58064i	0.0779588	+	0.107301i
$218$			2.16495i			0.146629i
$219$	0.945837	−	0.687191i	0.0639137	−	0.0464361i
$220$	1.44575	+	1.70582i	0.0974722	+	0.115006i
$221$	2.25528	+	1.63856i	0.151707	+	0.110221i
$222$	2.80959	−	3.86707i	0.188568	−	0.259541i
$223$	3.66816	+	1.19186i	0.245638	+	0.0798128i	0.429249	−	0.903186i	$-0.358778\pi$
$223$	3.66816	+	1.19186i	0.245638	+	0.0798128i	−0.183610	+	0.982999i	$0.558778\pi$
$224$	0.273457			0.0182711
$225$	−6.27044	−	12.5409i	−0.418029	−	0.836059i
$226$	19.8001			1.31708
$227$	−2.73523	−	0.888729i	−0.181543	−	0.0589870i	0.216835	−	0.976208i	$-0.430427\pi$
$227$	−2.73523	−	0.888729i	−0.181543	−	0.0589870i	−0.398378	+	0.917221i	$0.630427\pi$
$228$	−2.10851	+	2.90211i	−0.139639	+	0.192197i
$229$	5.33828	+	3.87849i	0.352763	+	0.256298i	0.750027	−	0.661407i	$-0.230040\pi$
$229$	5.33828	+	3.87849i	0.352763	+	0.256298i	−0.397264	+	0.917704i	$0.630040\pi$
$230$	5.05863	−	8.18504i	0.333556	−	0.539706i
$231$	0.0978870	−	0.0711190i	0.00644049	−	0.00467929i
$232$		−	1.73311i		−	0.113784i
$233$	15.8977	+	21.8813i	1.04149	+	1.43349i	0.895959	+	0.444137i	$0.146490\pi$
$233$	15.8977	+	21.8813i	1.04149	+	1.43349i	0.145532	+	0.989353i	$0.453510\pi$
$234$	−2.27787	−	7.01057i	−0.148909	−	0.458295i
$235$	−9.11798	−	5.63522i	−0.594791	−	0.367601i
$236$	0.546915	−	1.68323i	0.0356011	−	0.109569i
$237$	−7.04216	+	2.28814i	−0.457437	+	0.148630i
$238$	0.275807	−	0.0896152i	0.0178779	−	0.00580889i
$239$	−1.87405	+	5.76773i	−0.121222	+	0.373084i	−0.993194	−	0.116473i	$-0.962841\pi$
$239$	−1.87405	+	5.76773i	−0.121222	+	0.373084i	0.871972	+	0.489556i	$0.162841\pi$
$240$	−0.234616	+	0.961158i	−0.0151444	+	0.0620425i
$241$	−7.76075	−	23.8851i	−0.499914	−	1.53858i	−0.809156	−	0.587594i	$-0.800075\pi$
$241$	−7.76075	−	23.8851i	−0.499914	−	1.53858i	0.309242	−	0.950983i	$-0.399925\pi$
$242$	0.587785	+	0.809017i	0.0377843	+	0.0520056i
$243$		−	10.9240i		−	0.700775i
$244$	−11.3387	+	8.23804i	−0.725885	+	0.527386i
$245$	−1.15636	−	15.4420i	−0.0738769	−	0.986555i
$246$	2.95646	+	2.14799i	0.188497	+	0.136951i
$247$	12.5266	−	17.2413i	0.797046	−	1.09704i
$248$	−6.79506	−	2.20785i	−0.431487	−	0.140198i
$249$	−4.13620			−0.262121
$250$	1.00406	−	11.1352i	0.0635021	−	0.704250i
$251$	−23.5017			−1.48341			−0.741707	−	0.670724i	$-0.765983\pi$
$251$	−23.5017			−1.48341			−0.741707	+	0.670724i	$0.765983\pi$
$252$	−0.729305	−	0.236966i	−0.0459419	−	0.0149274i
$253$	2.52932	−	3.48131i	0.159017	−	0.218868i
$254$	−0.538001	−	0.390880i	−0.0337572	−	0.0245260i
$255$	0.0783511	+	1.04630i	0.00490653	+	0.0655221i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			11.6881i			0.729084i	0.931187	+	0.364542i	$0.118775\pi$
$257$			11.6881i			0.729084i	−0.931187	+	0.364542i	$0.881225\pi$
$258$	−1.26137	−	1.73612i	−0.0785294	−	0.108086i
$259$	0.912892	+	2.80959i	0.0567244	+	0.174580i
$260$	1.39384	−	5.71020i	0.0864424	−	0.354131i
$261$	−1.50183	+	4.62216i	−0.0929609	+	0.286104i
$262$	17.0851	−	5.55127i	1.05552	−	0.342959i
$263$	22.7266	−	7.38432i	1.40138	−	0.455336i	0.491744	−	0.870740i	$-0.336360\pi$
$263$	22.7266	−	7.38432i	1.40138	−	0.455336i	0.909637	+	0.415403i	$0.136360\pi$
$264$	−0.136729	+	0.420808i	−0.00841507	+	0.0258989i
$265$	−13.5978	−	8.40392i	−0.835308	−	0.516249i
$266$	−0.685096	−	2.10851i	−0.0420059	−	0.129281i
$267$	3.74034	+	5.14814i	0.228905	+	0.315061i
$268$		−	13.9846i		−	0.854243i
$269$	13.6818	−	9.94042i	0.834195	−	0.606078i	−0.0865481	−	0.996248i	$-0.527584\pi$
$269$	13.6818	−	9.94042i	0.834195	−	0.606078i	0.920743	+	0.390170i	$0.127584\pi$
$270$	3.01905	−	4.88493i	0.183734	−	0.297287i
$271$	−0.251802	−	0.182945i	−0.0152959	−	0.0111131i	0.580111	−	0.814537i	$-0.303009\pi$
$271$	−0.251802	−	0.182945i	−0.0152959	−	0.0111131i	−0.595407	+	0.803424i	$0.703009\pi$
$272$	−0.623345	+	0.857960i	−0.0377958	+	0.0520215i
$273$	−0.302487	−	0.0982841i	−0.0183074	−	0.00594842i
$274$	0.603683			0.0364698
$275$	0.819639	−	4.93236i	0.0494261	−	0.297433i
$276$	1.90398			0.114606
$277$	7.71956	+	2.50824i	0.463823	+	0.150705i	0.531601	−	0.846995i	$-0.321591\pi$
$277$	7.71956	+	2.50824i	0.463823	+	0.150705i	−0.0677773	+	0.997700i	$0.521591\pi$
$278$	−5.58631	+	7.68890i	−0.335045	+	0.461149i
$279$	16.2090	+	11.7766i	0.970410	+	0.705044i
$280$	−0.395350	−	0.466469i	−0.0236267	−	0.0278769i
$281$	−2.08097	+	1.51191i	−0.124140	+	0.0901930i	−0.648123	−	0.761536i	$-0.724446\pi$
$281$	−2.08097	+	1.51191i	−0.124140	+	0.0901930i	0.523983	+	0.851729i	$0.324446\pi$
$282$		−	2.12099i		−	0.126303i
$283$	−1.68599	−	2.32057i	−0.100222	−	0.137944i	0.755961	−	0.654617i	$-0.227170\pi$
$283$	−1.68599	−	2.32057i	−0.100222	−	0.137944i	−0.856183	+	0.516673i	$0.827170\pi$
$284$	−2.09528	−	6.44862i	−0.124332	−	0.382655i
$285$	7.99885	−	0.598983i	0.473811	−	0.0354807i
$286$	0.812299	−	2.50000i	0.0480323	−	0.147828i
$287$	−2.14799	+	0.697925i	−0.126792	+	0.0411972i
$288$	2.66698	−	0.866554i	0.157153	−	0.0510622i
$289$	4.90575	−	15.0984i	0.288574	−	0.888138i
$290$	−2.95637	+	2.50563i	−0.173604	+	0.147136i
$291$	−0.669960	−	2.06192i	−0.0392737	−	0.120872i
$292$	−1.55310	−	2.13766i	−0.0908884	−	0.125097i
$293$			14.9364i			0.872592i	0.899803	+	0.436296i	$0.143710\pi$
$293$			14.9364i			0.872592i	−0.899803	+	0.436296i	$0.856290\pi$
$294$	2.47896	−	1.80107i	0.144576	−	0.105040i
$295$	−3.66199	+	1.50059i	−0.213209	+	0.0873675i
$296$	−8.73987	−	6.34989i	−0.507995	−	0.369080i
$297$	1.50953	−	2.07768i	0.0875916	−	0.120559i
$298$	−10.7097	−	3.47980i	−0.620397	−	0.201579i
$299$	−11.3114			−0.654158
$300$	1.97876	−	0.989378i	0.114244	−	0.0571218i
$301$	1.32628			0.0764456
$302$	14.3244	+	4.65427i	0.824275	+	0.267823i
$303$	0.0219107	−	0.0301575i	0.00125874	−	0.00173250i
$304$	6.55899	+	4.76538i	0.376184	+	0.273314i
$305$	30.4455	+	7.43164i	1.74330	+	0.425535i
$306$	2.40592	−	1.74800i	0.137537	−	0.0999265i
$307$			22.9918i			1.31221i	0.754670	+	0.656105i	$0.227797\pi$
$307$			22.9918i			1.31221i	−0.754670	+	0.656105i	$0.772203\pi$
$308$	−0.160734	−	0.221232i	−0.00915868	−	0.0126058i
$309$	−1.50662	−	4.63690i	−0.0857087	−	0.263784i
$310$	6.05774	+	14.7831i	0.344056	+	0.839625i
$311$	0.189052	−	0.581842i	0.0107201	−	0.0329932i	−0.945553	−	0.325467i	$-0.894478\pi$
$311$	0.189052	−	0.581842i	0.0107201	−	0.0329932i	0.956274	+	0.292474i	$0.0944785\pi$
$312$	1.10616	−	0.359413i	0.0626239	−	0.0203477i
$313$	15.7899	−	5.13046i	0.892500	−	0.289991i	0.173362	−	0.984858i	$-0.444537\pi$
$313$	15.7899	−	5.13046i	0.892500	−	0.289991i	0.719138	+	0.694867i	$0.244537\pi$
$314$	6.46474	−	19.8964i	0.364826	−	1.12282i
$315$	0.650169	+	1.58665i	0.0366329	+	0.0893978i
$316$	5.17136	+	15.9158i	0.290911	+	0.895334i
$317$	−8.41164	−	11.5776i	−0.472445	−	0.650264i	0.504586	−	0.863361i	$-0.331645\pi$
$317$	−8.41164	−	11.5776i	−0.472445	−	0.650264i	−0.977031	+	0.213097i	$0.931645\pi$
$318$		−	3.16308i		−	0.177377i
$319$	−1.40211	+	1.01869i	−0.0785033	+	0.0570360i
$320$	2.17229	+	0.530249i	0.121435	+	0.0296418i
$321$	−1.92586	−	1.39922i	−0.107491	−	0.0780969i
$322$	−0.691660	+	0.951989i	−0.0385447	+	0.0530523i
$323$	8.17702	+	2.65688i	0.454982	+	0.147833i
$324$	−7.27636			−0.404242
$325$	−11.7557	+	5.87785i	−0.652089	+	0.326045i
$326$	12.6351			0.699794
$327$	0.911027	+	0.296011i	0.0503799	+	0.0163694i
$328$	4.85462	−	6.68181i	0.268052	−	0.368941i
$329$	1.06050	+	0.770497i	0.0584671	+	0.0424788i
$330$	0.915497	−	0.375147i	0.0503965	−	0.0206511i
$331$	11.4564	−	8.32356i	0.629701	−	0.457504i	−0.226596	−	0.973989i	$-0.572760\pi$
$331$	11.4564	−	8.32356i	0.629701	−	0.457504i	0.856297	+	0.516484i	$0.172760\pi$
$332$			9.34812i			0.513045i
$333$	17.8065	+	24.5086i	0.975791	+	1.34306i
$334$	4.09162	+	12.5927i	0.223884	+	0.689043i
$335$	−23.8551	+	20.2181i	−1.30335	+	1.10463i
$336$	0.0373895	−	0.115073i	0.00203976	−	0.00627775i
$337$	7.29251	−	2.36948i	0.397248	−	0.129074i	−0.103579	−	0.994621i	$-0.533029\pi$
$337$	7.29251	−	2.36948i	0.397248	−	0.129074i	0.500827	+	0.865547i	$0.333029\pi$
$338$	5.79210	−	1.88197i	0.315048	−	0.102365i
$339$	2.70724	−	8.33202i	0.147037	−	0.452533i
$340$	2.36472	−	0.177079i	0.128245	−	0.00960347i
$341$	2.20785	+	6.79506i	0.119562	+	0.367973i
$342$	−13.3632	−	18.3929i	−0.722600	−	0.994573i
$343$			3.80796i			0.205610i
$344$	−3.92377	+	2.85078i	−0.211555	+	0.153704i
$345$	−2.75267	−	3.24784i	−0.148199	−	0.174858i
$346$	0.391079	+	0.284135i	0.0210245	+	0.0152752i
$347$	−5.28505	+	7.27424i	−0.283716	+	0.390502i	−0.926960	−	0.375159i	$-0.877588\pi$
$347$	−5.28505	+	7.27424i	−0.283716	+	0.390502i	0.643244	+	0.765661i	$0.277588\pi$
$348$	−0.729305	−	0.236966i	−0.0390948	−	0.0127027i
$349$	−24.3225			−1.30195			−0.650977	−	0.759097i	$-0.725641\pi$
$349$	−24.3225			−1.30195			−0.650977	+	0.759097i	$0.725641\pi$
$350$	−0.224136	+	1.34879i	−0.0119806	+	0.0720959i
$351$	−6.75080			−0.360331
$352$	0.951057	+	0.309017i	0.0506915	+	0.0164707i
$353$	−7.77997	+	10.7082i	−0.414086	+	0.569940i	−0.964209	−	0.265143i	$-0.914581\pi$
$353$	−7.77997	+	10.7082i	−0.414086	+	0.569940i	0.550123	+	0.835083i	$0.314581\pi$
$354$	−0.633538	−	0.460292i	−0.0336722	−	0.0244643i
$355$	−7.97093	+	12.8972i	−0.423053	+	0.684514i
$356$	11.6352	−	8.45344i	0.616662	−	0.448031i
$357$		−	0.128315i		−	0.00679114i
$358$	−2.69807	−	3.71357i	−0.142597	−	0.196268i
$359$	−7.14459	−	21.9888i	−0.377077	−	1.16052i	−0.942067	−	0.335426i	$-0.891120\pi$
$359$	−7.14459	−	21.9888i	−0.377077	−	1.16052i	0.564990	−	0.825098i	$-0.308880\pi$
$360$	−5.33395	−	3.29657i	−0.281124	−	0.173744i
$361$	14.4401	−	44.4421i	0.760007	−	2.33906i
$362$	−5.51390	+	1.79158i	−0.289804	+	0.0941631i
$363$	0.420808	−	0.136729i	0.0220867	−	0.00717640i
$364$	−0.222129	+	0.683644i	−0.0116427	+	0.0358327i
$365$	−1.40107	+	5.73983i	−0.0733355	+	0.300436i
$366$	1.91631	+	5.89779i	0.100167	+	0.308282i
$367$	12.5830	+	17.3190i	0.656827	+	0.904045i	0.999371	−	0.0354569i	$-0.0112887\pi$
$367$	12.5830	+	17.3190i	0.656827	+	0.904045i	−0.342544	+	0.939502i	$0.611289\pi$
$368$		−	4.30313i		−	0.224316i
$369$	−18.7373	+	13.6135i	−0.975426	+	0.708688i
$370$	1.80387	+	24.0890i	0.0937787	+	1.25233i
$371$	1.58154	+	1.14906i	0.0821096	+	0.0596561i
$372$	−1.85816	+	2.55754i	−0.0963411	+	0.132602i
$373$	−15.1038	−	4.90752i	−0.782046	−	0.254102i	−0.109332	−	0.994005i	$-0.534871\pi$
$373$	−15.1038	−	4.90752i	−0.782046	−	0.254102i	−0.672713	+	0.739903i	$0.734871\pi$
$374$	1.06050			0.0548370
$375$	−4.54848	−	1.94501i	−0.234882	−	0.100440i
$376$	−4.79360			−0.247211
$377$	4.33277	+	1.40780i	0.223149	+	0.0725055i
$378$	−0.412791	+	0.568158i	−0.0212317	+	0.0292229i
$379$	12.6918	+	9.22113i	0.651934	+	0.473658i	0.863929	−	0.503613i	$-0.167996\pi$
$379$	12.6918	+	9.22113i	0.651934	+	0.473658i	−0.211995	+	0.977271i	$0.567996\pi$
$380$	−1.35375	−	18.0780i	−0.0694457	−	0.927381i
$381$	−0.238046	+	0.172950i	−0.0121954	+	0.00886051i
$382$			17.8475i			0.913159i
$383$	1.61241	+	2.21929i	0.0823904	+	0.113401i	0.848223	−	0.529640i	$-0.177673\pi$
$383$	1.61241	+	2.21929i	0.0823904	+	0.113401i	−0.765832	+	0.643040i	$0.777673\pi$
$384$	0.136729	+	0.420808i	0.00697741	+	0.0214743i
$385$	−0.145000	+	0.594028i	−0.00738991	+	0.0302745i
$386$	1.50972	−	4.64645i	0.0768429	−	0.236498i
$387$	12.9350	−	4.20282i	0.657521	−	0.213642i
$388$	−4.66010	+	1.51416i	−0.236581	+	0.0768698i
$389$	−8.30915	+	25.5729i	−0.421291	+	1.29660i	0.485211	+	0.874397i	$0.338743\pi$
$389$	−8.30915	+	25.5729i	−0.421291	+	1.29660i	−0.906502	+	0.422202i	$0.861257\pi$
$390$	−2.21232	−	1.36729i	−0.112025	−	0.0692353i
$391$	−1.41019	−	4.34011i	−0.0713162	−	0.219489i
$392$	−4.07054	−	5.60262i	−0.205593	−	0.282975i
$393$		−	7.94854i		−	0.400951i
$394$	−15.4422	+	11.2194i	−0.777969	+	0.565228i
$395$	19.6730	−	31.8316i	0.989856	−	1.60162i
$396$	−2.26867	−	1.64828i	−0.114005	−	0.0828293i
$397$	−4.33981	+	5.97323i	−0.217809	+	0.299788i	−0.903914	−	0.427714i	$-0.859319\pi$
$397$	−4.33981	+	5.97323i	−0.217809	+	0.299788i	0.686105	+	0.727502i	$0.259319\pi$
$398$	11.2248	+	3.64715i	0.562647	+	0.182815i
$399$	−0.980949			−0.0491089
$400$	−2.23607	−	4.47214i	−0.111803	−	0.223607i
$401$	−6.32262			−0.315737			−0.157868	−	0.987460i	$-0.550462\pi$
$401$	−6.32262			−0.315737			−0.157868	+	0.987460i	$0.550462\pi$
$402$	−5.88481	−	1.91209i	−0.293508	−	0.0953665i
$403$	11.0392	−	15.1942i	0.549904	−	0.756877i
$404$	−0.0681581	−	0.0495197i	−0.00339099	−	0.00246370i
$405$	10.5198	+	12.4122i	0.522732	+	0.616765i
$406$	0.383418	−	0.278570i	0.0190287	−	0.0138252i
$407$			10.8031i			0.535488i
$408$	0.275807	+	0.379616i	0.0136545	+	0.0187938i
$409$	−3.66036	−	11.2654i	−0.180993	−	0.557039i	0.818863	−	0.573988i	$-0.194605\pi$
$409$	−3.66036	−	11.2654i	−0.180993	−	0.557039i	−0.999856	+	0.0169494i	$0.994605\pi$
$410$	−18.4165	+	1.37910i	−0.909527	+	0.0681087i
$411$	0.0825408	−	0.254034i	0.00407144	−	0.0125306i
$412$	−10.4797	+	3.40507i	−0.516300	+	0.167756i
$413$	0.460292	−	0.149558i	0.0226495	−	0.00735927i
$414$	−3.72889	+	11.4764i	−0.183265	+	0.564032i
$415$	15.9462	−	13.5150i	0.782769	−	0.663426i
$416$	−0.812299	−	2.50000i	−0.0398262	−	0.122573i
$417$	2.47174	+	3.40206i	0.121042	+	0.166599i
$418$		−	8.10736i		−	0.396544i
$419$	2.04264	−	1.48407i	0.0997897	−	0.0725014i	−0.536771	−	0.843728i	$-0.680356\pi$
$419$	2.04264	−	1.48407i	0.0997897	−	0.0725014i	0.636561	+	0.771226i	$0.280356\pi$
$420$	−0.250349	+	0.102587i	−0.0122158	+	0.00500571i
$421$	18.8190	+	13.6728i	0.917182	+	0.666372i	0.942821	−	0.333299i	$-0.108162\pi$
$421$	18.8190	+	13.6728i	0.917182	+	0.666372i	−0.0256388	+	0.999671i	$0.508162\pi$
$422$	8.86838	−	12.2063i	0.431706	−	0.594193i
$423$	12.7844	+	4.15391i	0.621601	+	0.201970i
$424$	−7.14880			−0.347177
$425$	−3.72085	−	3.77778i	−0.180488	−	0.183249i
$426$	−3.00011			−0.145356
$427$	−3.64503	−	1.18434i	−0.176395	−	0.0573144i
$428$	−3.16234	+	4.35259i	−0.152858	+	0.210391i
$429$	−0.940955	−	0.683644i	−0.0454297	−	0.0330066i
$430$	10.5357	+	2.57173i	0.508076	+	0.124020i
$431$	−2.49808	+	1.81496i	−0.120328	+	0.0874236i	−0.646322	−	0.763065i	$-0.723694\pi$
$431$	−2.49808	+	1.81496i	−0.120328	+	0.0874236i	0.525994	+	0.850489i	$0.323694\pi$
$432$		−	2.56816i		−	0.123561i
$433$	−15.9428	−	21.9433i	−0.766161	−	1.05453i	−0.996677	−	0.0814610i	$-0.974041\pi$
$433$	−15.9428	−	21.9433i	−0.766161	−	1.05453i	0.230516	−	0.973069i	$-0.425959\pi$
$434$	−0.603752	−	1.85816i	−0.0289810	−	0.0891945i
$435$	0.650169	+	1.58665i	0.0311732	+	0.0760742i
$436$	0.669006	−	2.05899i	0.0320396	−	0.0986077i
$437$	−33.1795	+	10.7807i	−1.58719	+	0.515710i
$438$	−1.11190	+	0.361278i	−0.0531285	+	0.0172625i
$439$	4.85004	−	14.9269i	0.231480	−	0.712422i	−0.766089	−	0.642735i	$-0.777800\pi$
$439$	4.85004	−	14.9269i	0.231480	−	0.712422i	0.997569	−	0.0696875i	$-0.0222002\pi$
$440$	−0.847859	−	2.06909i	−0.0404201	−	0.0986400i
$441$	6.00107	+	18.4694i	0.285765	+	0.879496i
$442$	−1.63856	−	2.25528i	−0.0779383	−	0.107273i
$443$		−	4.86286i		−	0.231041i	−0.993305	−	0.115521i	$-0.963146\pi$
$443$		−	4.86286i		−	0.231041i	0.993305	−	0.115521i	$-0.0368537\pi$
$444$	−3.86707	+	2.80959i	−0.183523	+	0.133337i
$445$	−31.2415	−	7.62596i	−1.48099	−	0.361505i
$446$	−3.12033	−	2.26705i	−0.147752	−	0.107348i
$447$	−2.92865	+	4.03094i	−0.138520	+	0.190657i
$448$	−0.260074	−	0.0845030i	−0.0122873	−	0.00399239i
$449$	−12.3131			−0.581092			−0.290546	−	0.956861i	$-0.593837\pi$
$449$	−12.3131			−0.581092			−0.290546	+	0.956861i	$0.593837\pi$
$450$	2.08820	+	13.8648i	0.0984386	+	0.653591i
$451$	−8.25918			−0.388909
$452$	−18.8310	−	6.11855i	−0.885734	−	0.287793i
$453$	3.91711	−	5.39144i	0.184042	−	0.253312i
$454$	2.32672	+	1.69046i	0.109199	+	0.0793374i
$455$	1.48732	−	0.609463i	0.0697264	−	0.0285720i
$456$	2.90211	−	2.10851i	0.135904	−	0.0987400i
$457$			20.2680i			0.948098i	0.880498	+	0.474049i	$0.157208\pi$
$457$			20.2680i			0.948098i	−0.880498	+	0.474049i	$0.842792\pi$
$458$	−3.87849	−	5.33828i	−0.181230	−	0.249441i
$459$	−0.841616	−	2.59023i	−0.0392833	−	0.120901i
$460$	−7.34036	+	6.22123i	−0.342246	+	0.290066i
$461$	−4.19870	+	12.9223i	−0.195553	+	0.601850i	0.804417	+	0.594065i	$0.202478\pi$
$461$	−4.19870	+	12.9223i	−0.195553	+	0.601850i	−0.999970	+	0.00778471i	$0.997522\pi$
$462$	−0.115073	+	0.0373895i	−0.00535368	+	0.00173952i
$463$	3.29407	−	1.07031i	0.153089	−	0.0497415i	−0.231470	−	0.972842i	$-0.574354\pi$
$463$	3.29407	−	1.07031i	0.153089	−	0.0497415i	0.384559	+	0.923100i	$0.374354\pi$
$464$	−0.535560	+	1.64828i	−0.0248627	+	0.0765196i
$465$	7.04912	−	0.527864i	0.326895	−	0.0244791i
$466$	−8.35790	−	25.7230i	−0.387172	−	1.19159i
$467$	−24.2685	−	33.4028i	−1.12301	−	1.54570i	−0.800703	−	0.599062i	$-0.795540\pi$
$467$	−24.2685	−	33.4028i	−1.12301	−	1.54570i	−0.322311	−	0.946634i	$-0.604460\pi$
$468$			7.37134i			0.340741i
$469$	3.09383	−	2.24780i	0.142860	−	0.103794i
$470$	6.93033	+	8.17702i	0.319672	+	0.377178i
$471$	−7.48865	−	5.44083i	−0.345059	−	0.250700i
$472$	−1.04029	+	1.43184i	−0.0478834	+	0.0659059i
$473$	4.61267	+	1.49875i	0.212091	+	0.0689124i
$474$	7.40456			0.340103
$475$	−28.8806	+	28.4454i	−1.32513	+	1.30517i
$476$	−0.290001			−0.0132922
$477$	19.0657	+	6.19482i	0.872958	+	0.283641i
$478$	3.56466	−	4.90633i	0.163044	−	0.224410i
$479$	18.0319	+	13.1009i	0.823899	+	0.598598i	0.917827	−	0.396981i	$-0.129942\pi$
$479$	18.0319	+	13.1009i	0.823899	+	0.598598i	−0.0939277	+	0.995579i	$0.529942\pi$
$480$	0.520147	−	0.841616i	0.0237414	−	0.0384143i
$481$	22.9741	−	16.6917i	1.04753	−	0.761074i
$482$			25.1143i			1.14393i
$483$	0.306034	+	0.421220i	0.0139251	+	0.0191662i
$484$	−0.309017	−	0.951057i	−0.0140462	−	0.0432298i
$485$	9.32020	+	5.76020i	0.423209	+	0.261557i
$486$	−3.37570	+	10.3893i	−0.153125	+	0.471270i
$487$	−35.5373	+	11.5468i	−1.61035	+	0.523234i	−0.969637	−	0.244549i	$-0.921360\pi$
$487$	−35.5373	+	11.5468i	−1.61035	+	0.523234i	−0.640710	+	0.767783i	$0.721360\pi$
$488$	13.3294	−	4.33099i	0.603395	−	0.196055i
$489$	1.72758	−	5.31695i	0.0781240	−	0.240441i
$490$	−3.67209	+	15.0436i	−0.165888	+	0.679600i
$491$	−10.0183	−	30.8333i	−0.452121	−	1.39149i	−0.874482	−	0.485058i	$-0.838798\pi$
$491$	−10.0183	−	30.8333i	−0.452121	−	1.39149i	0.422361	−	0.906428i	$-0.361202\pi$
$492$	−2.14799	−	2.95646i	−0.0968390	−	0.133287i
$493$			1.83796i			0.0827774i
$494$	−17.2413	+	12.5266i	−0.775724	+	0.563596i
$495$	0.468243	+	6.25293i	0.0210459	+	0.281048i
$496$	5.78022	+	4.19958i	0.259540	+	0.188567i
$497$	1.08985	−	1.50006i	0.0488867	−	0.0672867i
$498$	3.93376	+	1.27816i	0.176276	+	0.0572756i
$499$	−8.10266			−0.362725			−0.181362	−	0.983416i	$-0.558051\pi$
$499$	−8.10266			−0.362725			−0.181362	+	0.983416i	$0.558051\pi$
$500$	−4.39587	+	10.2799i	−0.196589	+	0.459731i
$501$	5.85856			0.261741
$502$	22.3514	+	7.26242i	0.997594	+	0.324138i
$503$	−9.25737	+	12.7417i	−0.412766	+	0.568123i	−0.963890	−	0.266300i	$-0.914199\pi$
$503$	−9.25737	+	12.7417i	−0.412766	+	0.568123i	0.551125	+	0.834423i	$0.314199\pi$
$504$	0.620384	+	0.450735i	0.0276341	+	0.0200773i
$505$	0.0140675	+	0.187858i	0.000625997	+	0.00835959i
$506$	−3.48131	+	2.52932i	−0.154763	+	0.112442i
$507$		−	2.69468i		−	0.119675i
$508$	0.390880	+	0.538001i	0.0173425	+	0.0238699i
$509$	3.75419	+	11.5542i	0.166401	+	0.512131i	0.999137	−	0.0415403i	$-0.0132265\pi$
$509$	3.75419	+	11.5542i	0.166401	+	0.512131i	−0.832735	+	0.553671i	$0.813226\pi$
$510$	0.248809	−	1.01931i	0.0110175	−	0.0451356i
$511$	0.223282	−	0.687191i	0.00987741	−	0.0303995i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−19.8019	+	6.43403i	−0.874276	+	0.284070i
$514$	3.61183	−	11.1161i	0.159311	−	0.490308i
$515$	20.9595	+	12.9537i	0.923585	+	0.570807i
$516$	0.663141	+	2.04094i	0.0291931	+	0.0898472i
$517$	2.81761	+	3.87811i	0.123918	+	0.170559i
$518$		−	2.95418i		−	0.129799i
$519$	0.173038	−	0.125720i	0.00759553	−	0.00551848i
$520$	−3.09017	+	5.00000i	−0.135513	+	0.219265i
$521$	−9.47199	−	6.88180i	−0.414975	−	0.301497i	0.360638	−	0.932706i	$-0.382559\pi$
$521$	−9.47199	−	6.88180i	−0.414975	−	0.301497i	−0.775613	+	0.631209i	$0.782559\pi$
$522$	2.85665	−	3.93184i	0.125032	−	0.172092i
$523$	−5.27440	−	1.71376i	−0.230633	−	0.0749373i	0.191420	−	0.981508i	$-0.438691\pi$
$523$	−5.27440	−	1.71376i	−0.230633	−	0.0749373i	−0.422054	+	0.906571i	$0.638691\pi$
$524$	−17.9643			−0.784774
$525$	0.536936	+	0.278737i	0.0234338	+	0.0121651i
$526$	−23.8961			−1.04192
$527$	7.20614	+	2.34142i	0.313904	+	0.101994i
$528$	0.260074	−	0.357960i	0.0113182	−	0.0155782i
$529$	−3.62688	−	2.63508i	−0.157691	−	0.114569i
$530$	10.3354	+	12.1946i	0.448939	+	0.529698i
$531$	4.01521	−	2.91722i	0.174245	−	0.126597i
$532$			2.21702i			0.0961199i
$533$	12.7611	+	17.5642i	0.552746	+	0.760789i
$534$	−1.96641	−	6.05200i	−0.0850950	−	0.261895i
$535$	11.9967	−	0.898356i	0.518662	−	0.0388393i
$536$	−4.32147	+	13.3001i	−0.186659	+	0.574477i
$537$	−1.93160	+	0.627616i	−0.0833548	+	0.0270836i
$538$	−16.0839	+	5.22599i	−0.693428	+	0.225308i
$539$	−2.14001	+	6.58628i	−0.0921768	+	0.283691i
$540$	−4.38081	+	3.71290i	−0.188520	+	0.159778i
$541$	−2.30490	−	7.09376i	−0.0990955	−	0.304985i	0.889204	−	0.457511i	$-0.151259\pi$
$541$	−2.30490	−	7.09376i	−0.0990955	−	0.304985i	−0.988299	+	0.152527i	$0.951259\pi$
$542$	0.182945	+	0.251802i	0.00785815	+	0.0108158i
$543$			2.56525i			0.110086i
$544$	0.857960	−	0.623345i	0.0367848	−	0.0267257i
$545$	−4.47948	+	1.83557i	−0.191880	+	0.0786272i
$546$	0.257311	+	0.186947i	0.0110119	+	0.00800061i
$547$	1.88638	−	2.59638i	0.0806558	−	0.111013i	−0.766783	−	0.641907i	$-0.778144\pi$
$547$	1.88638	−	2.59638i	0.0806558	−	0.111013i	0.847438	+	0.530894i	$0.178144\pi$
$548$	−0.574136	−	0.186548i	−0.0245259	−	0.00796895i
$549$	−39.3023			−1.67738
$550$	−2.30371	+	4.43767i	−0.0982304	+	0.189223i
$551$	14.0509			0.598589
$552$	−1.81079	−	0.588362i	−0.0770724	−	0.0250423i
$553$	−2.68987	+	3.70228i	−0.114385	+	0.157437i
$554$	−6.56665	−	4.77095i	−0.278990	−	0.202698i
$555$	10.3835	+	2.53457i	0.440753	+	0.107587i
$556$	7.68890	−	5.58631i	0.326082	−	0.236912i
$557$			41.9400i			1.77705i	0.458824	+	0.888527i	$0.348271\pi$
$557$			41.9400i			1.77705i	−0.458824	+	0.888527i	$0.651729\pi$
$558$	−11.7766	−	16.2090i	−0.498542	−	0.686184i
$559$	−3.93969	−	12.1251i	−0.166631	−	0.512838i
$560$	0.231853	+	0.565808i	0.00979759	+	0.0239098i
$561$	0.145000	−	0.446266i	0.00612193	−	0.0188413i
$562$	2.44632	−	0.794858i	0.103192	−	0.0335291i
$563$	34.5855	−	11.2375i	1.45761	−	0.473605i	0.530268	−	0.847830i	$-0.322091\pi$
$563$	34.5855	−	11.2375i	1.45761	−	0.473605i	0.927338	+	0.374225i	$0.122091\pi$
$564$	−0.655423	+	2.01719i	−0.0275983	+	0.0849389i
$565$	16.7877	+	40.9681i	0.706262	+	1.72354i
$566$	0.886379	+	2.72799i	0.0372573	+	0.114666i
$567$	−1.16956	−	1.60976i	−0.0491169	−	0.0676037i
$568$			6.78048i			0.284502i
$569$	−21.8332	+	15.8627i	−0.915294	+	0.665000i	−0.942348	−	0.334634i	$-0.891387\pi$
$569$	−21.8332	+	15.8627i	−0.915294	+	0.665000i	0.0270540	+	0.999634i	$0.491387\pi$
$570$	−7.79245	−	1.90211i	−0.326390	−	0.0796707i
$571$	−20.6183	−	14.9801i	−0.862850	−	0.626898i	0.0658085	−	0.997832i	$-0.479037\pi$
$571$	−20.6183	−	14.9801i	−0.862850	−	0.626898i	−0.928659	+	0.370935i	$0.879037\pi$
$572$	−1.54508	+	2.12663i	−0.0646032	+	0.0889187i
$573$	7.51038	+	2.44027i	0.313751	+	0.101944i
$574$	2.25853			0.0942694
$575$	21.2246	+	3.52701i	0.885127	+	0.147087i
$576$	−2.80423			−0.116843
$577$	−21.2076	−	6.89078i	−0.882886	−	0.286867i	−0.167731	−	0.985833i	$-0.553644\pi$
$577$	−21.2076	−	6.89078i	−0.882886	−	0.286867i	−0.715155	+	0.698966i	$0.753644\pi$
$578$	−9.33129	+	12.8434i	−0.388131	+	0.534216i
$579$	−1.74884	−	1.27061i	−0.0726793	−	0.0528046i
$580$	3.58596	−	1.46943i	0.148899	−	0.0610148i
$581$	−2.06810	+	1.50256i	−0.0857993	+	0.0623369i
$582$			2.16804i			0.0898680i
$583$	4.20196	+	5.78350i	0.174027	+	0.239528i
$584$	0.816514	+	2.51297i	0.0337876	+	0.103987i
$585$	12.5742	−	10.6571i	0.519878	−	0.440616i
$586$	4.61559	−	14.2053i	0.190668	−	0.586817i
$587$	−25.3752	+	8.24489i	−1.04735	+	0.340303i	−0.781626	−	0.623747i	$-0.785609\pi$
$587$	−25.3752	+	8.24489i	−1.04735	+	0.340303i	−0.265719	+	0.964050i	$0.585609\pi$
$588$	−2.91419	+	0.946877i	−0.120179	+	0.0390485i
$589$	17.8998	−	55.0899i	0.737549	−	2.26994i
$590$	3.94646	−	0.295526i	0.162473	−	0.0121666i
$591$	2.60983	+	8.03224i	0.107354	+	0.330402i
$592$	6.34989	+	8.73987i	0.260979	+	0.359206i
$593$		−	40.9409i		−	1.68124i	−0.541624	−	0.840621i	$-0.682190\pi$
$593$		−	40.9409i		−	1.68124i	0.541624	−	0.840621i	$-0.317810\pi$
$594$	−2.07768	+	1.50953i	−0.0852484	+	0.0619366i
$595$	0.419268	+	0.494689i	0.0171883	+	0.0202803i
$596$	9.11023	+	6.61897i	0.373169	+	0.271123i
$597$	3.06950	−	4.22480i	0.125626	−	0.172910i
$598$	10.7578	+	3.49543i	0.439920	+	0.142939i
$599$	−14.7062			−0.600879			−0.300440	−	0.953801i	$-0.597133\pi$
$599$	−14.7062			−0.600879			−0.300440	+	0.953801i	$0.597133\pi$
$600$	−2.18764	+	0.329485i	−0.0893102	+	0.0134512i
$601$	−5.27823			−0.215303			−0.107652	−	0.994189i	$-0.534333\pi$
$601$	−5.27823			−0.215303			−0.107652	+	0.994189i	$0.534333\pi$
$602$	−1.26137	−	0.409843i	−0.0514095	−	0.0167040i
$603$	23.0505	−	31.7263i	0.938690	−	1.29200i
$604$	−12.1850	−	8.85295i	−0.495802	−	0.360221i
$605$	−1.17557	+	1.90211i	−0.0477937	+	0.0773319i
$606$	−0.0301575	+	0.0219107i	−0.00122506	+	0.000890061i
$607$		−	21.9268i		−	0.889981i	−0.895535	−	0.444990i	$-0.853207\pi$
$607$		−	21.9268i		−	0.889981i	0.895535	−	0.444990i	$-0.146793\pi$
$608$	−4.76538	−	6.55899i	−0.193262	−	0.266002i
$609$	−0.0648000	−	0.199434i	−0.00262583	−	0.00808147i
$610$	−26.6589	−	16.4761i	−1.07939	−	0.667097i
$611$	3.89384	−	11.9840i	0.157528	−	0.484821i
$612$	−2.82832	+	0.918978i	−0.114328	+	0.0371475i
$613$	−18.8345	+	6.11971i	−0.760719	+	0.247173i	−0.663587	−	0.748099i	$-0.730967\pi$
$613$	−18.8345	+	6.11971i	−0.760719	+	0.247173i	−0.0971318	+	0.995272i	$0.530967\pi$
$614$	7.10485	−	21.8665i	0.286728	−	0.882459i
$615$	−1.93773	+	7.93837i	−0.0781369	+	0.320106i
$616$	0.0845030	+	0.260074i	0.00340472	+	0.0104787i
$617$	10.0894	+	13.8869i	0.406185	+	0.559066i	0.962283	−	0.272051i	$-0.0877020\pi$
$617$	10.0894	+	13.8869i	0.406185	+	0.559066i	−0.556098	+	0.831117i	$0.687702\pi$
$618$			4.87553i			0.196122i
$619$	17.1043	−	12.4270i	0.687481	−	0.499484i	−0.188350	−	0.982102i	$-0.560314\pi$
$619$	17.1043	−	12.4270i	0.687481	−	0.499484i	0.875831	+	0.482618i	$0.160314\pi$
$620$	−1.19301	−	15.9315i	−0.0479125	−	0.639826i
$621$	8.94054	+	6.49568i	0.358772	+	0.260663i
$622$	−0.359598	+	0.494944i	−0.0144186	+	0.0198455i
$623$	3.74034	+	1.21531i	0.149854	+	0.0486904i
$624$	−1.16308			−0.0465606
$625$	23.8910	−	7.36356i	0.955638	−	0.294542i
$626$	−16.6025			−0.663571
$627$	−3.41164	−	1.10851i	−0.136248	−	0.0442696i
$628$	−12.2967	+	16.9249i	−0.490690	+	0.675377i
$629$	9.26861	+	6.73404i	0.369564	+	0.268504i
$630$	−0.128044	−	1.70991i	−0.00510141	−	0.0681245i
$631$	−32.2545	+	23.4343i	−1.28403	+	0.932904i	−0.999667	−	0.0258120i	$-0.991783\pi$
$631$	−32.2545	+	23.4343i	−1.28403	+	0.932904i	−0.284365	+	0.958716i	$0.591783\pi$
$632$		−	16.7349i		−	0.665677i
$633$	−3.92394	−	5.40083i	−0.155962	−	0.214664i
$634$	4.42226	+	13.6103i	0.175630	+	0.540535i
$635$	0.352618	−	1.44458i	0.0139932	−	0.0573265i
$636$	−0.977447	+	3.00827i	−0.0387583	+	0.119286i
$637$	17.3131	−	5.62535i	0.685968	−	0.222885i
$638$	1.64828	−	0.535560i	0.0652561	−	0.0212030i
$639$	5.87564	−	18.0834i	0.232437	−	0.715367i
$640$	−1.90211	−	1.17557i	−0.0751876	−	0.0464685i
$641$	3.60594	+	11.0980i	0.142426	+	0.438343i	0.996671	−	0.0815280i	$-0.0259800\pi$
$641$	3.60594	+	11.0980i	0.142426	+	0.438343i	−0.854245	+	0.519871i	$0.825980\pi$
$642$	1.39922	+	1.92586i	0.0552229	+	0.0760078i
$643$			30.8659i			1.21723i	0.793466	+	0.608615i	$0.208275\pi$
$643$			30.8659i			1.21723i	−0.793466	+	0.608615i	$0.791725\pi$
$644$	0.951989	−	0.691660i	0.0375136	−	0.0272552i
$645$	2.52274	−	4.08187i	0.0993326	−	0.160724i
$646$	−6.95579	−	5.05368i	−0.273672	−	0.198834i
$647$	17.1635	−	23.6236i	0.674768	−	0.928739i	−0.325088	−	0.945684i	$-0.605394\pi$
$647$	17.1635	−	23.6236i	0.674768	−	0.928739i	0.999856	+	0.0169447i	$0.00539392\pi$
$648$	6.92023	+	2.24852i	0.271852	+	0.0883302i
$649$	1.76985			0.0694728
$650$	12.9967	−	1.95746i	0.509772	−	0.0767778i
$651$	−0.864478			−0.0338816
$652$	−12.0167	−	3.90446i	−0.470610	−	0.152911i
$653$	27.3036	−	37.5802i	1.06847	−	1.47063i	0.196862	−	0.980431i	$-0.436925\pi$
$653$	27.3036	−	37.5802i	1.06847	−	1.47063i	0.871612	−	0.490196i	$-0.163075\pi$
$654$	−0.774966	−	0.563046i	−0.0303036	−	0.0220168i
$655$	25.9718	+	30.6438i	1.01480	+	1.19735i
$656$	−6.68181	+	4.85462i	−0.260881	+	0.189541i
$657$		−	7.40959i		−	0.289076i
$658$	−0.770497	−	1.06050i	−0.0300371	−	0.0413425i
$659$	7.69231	+	23.6745i	0.299650	+	0.922228i	0.981620	+	0.190847i	$0.0611236\pi$
$659$	7.69231	+	23.6745i	0.299650	+	0.922228i	−0.681970	+	0.731380i	$0.738876\pi$
$660$	−0.986616	+	0.0738814i	−0.0384040	+	0.00287583i
$661$	−0.568228	+	1.74883i	−0.0221015	+	0.0680214i	−0.961499	−	0.274809i	$-0.911386\pi$
$661$	−0.568228	+	1.74883i	−0.0221015	+	0.0680214i	0.939397	+	0.342830i	$0.111386\pi$
$662$	−13.4678	+	4.37596i	−0.523441	+	0.170076i
$663$	−1.17308	+	0.381156i	−0.0455586	+	0.0148029i
$664$	2.88873	−	8.89059i	0.112104	−	0.345022i
$665$	3.78183	−	3.20524i	0.146653	−	0.124294i
$666$	−9.36144	−	28.8116i	−0.362748	−	1.11643i
$667$	−4.38358	−	6.03347i	−0.169733	−	0.233617i
$668$		−	13.2408i		−	0.512301i
$669$	−1.38063	+	1.00309i	−0.0533783	+	0.0387816i
$670$	28.9353	−	11.8569i	1.11787	−	0.458073i
$671$	−11.3387	−	8.23804i	−0.437725	−	0.318026i
$672$	−0.0711190	+	0.0978870i	−0.00274348	+	0.00377607i
$673$	−8.61152	−	2.79805i	−0.331950	−	0.107857i	0.138300	−	0.990390i	$-0.455836\pi$
$673$	−8.61152	−	2.79805i	−0.331950	−	0.107857i	−0.470250	+	0.882533i	$0.655836\pi$
$674$	−7.66780			−0.295353
$675$	12.6671	+	2.10496i	0.487556	+	0.0810200i
$676$	−6.09017			−0.234237
$677$	−16.6268	−	5.40237i	−0.639019	−	0.207630i	−0.0284531	−	0.999595i	$-0.509058\pi$
$677$	−16.6268	−	5.40237i	−0.639019	−	0.207630i	−0.610566	+	0.791965i	$0.709058\pi$
$678$	−5.14947	+	7.08764i	−0.197764	+	0.272199i
$679$	−1.08402	−	0.787585i	−0.0416008	−	0.0302247i
$680$	−2.30371	−	0.562327i	−0.0883431	−	0.0215643i
$681$	1.02949	−	0.747968i	0.0394501	−	0.0286622i
$682$		−	7.14475i		−	0.273586i
$683$	27.6840	+	38.1037i	1.05930	+	1.45800i	0.880460	+	0.474121i	$0.157234\pi$
$683$	27.6840	+	38.1037i	1.05930	+	1.45800i	0.178838	+	0.983878i	$0.442766\pi$
$684$	7.02546	+	21.6221i	0.268625	+	0.826743i
$685$	0.511838	+	1.24907i	0.0195563	+	0.0477247i
$686$	1.17672	−	3.62158i	0.0449275	−	0.138273i
$687$	−2.77669	+	0.902201i	−0.105937	+	0.0344211i
$688$	4.61267	−	1.49875i	0.175856	−	0.0571392i
$689$	5.80697	−	17.8720i	0.221228	−	0.680869i
$690$	1.61430	+	3.93950i	0.0614555	+	0.149974i
$691$	6.00786	+	18.4903i	0.228550	+	0.703404i	0.997912	+	0.0645908i	$0.0205742\pi$
$691$	6.00786	+	18.4903i	0.228550	+	0.703404i	−0.769362	+	0.638813i	$0.779426\pi$
$692$	−0.284135	−	0.391079i	−0.0108012	−	0.0148666i
$693$		−	0.766837i		−	0.0291297i
$694$	7.27424	−	5.28505i	0.276126	−	0.200618i
$695$	−20.6454	−	5.03948i	−0.783126	−	0.191159i
$696$	0.620384	+	0.450735i	0.0235156	+	0.0170851i
$697$	−5.14831	+	7.08605i	−0.195006	+	0.268403i
$698$	23.1321	+	7.51607i	0.875562	+	0.284487i
$699$	−11.9672			−0.452641
$700$	0.629966	−	1.21351i	0.0238105	−	0.0458665i
$701$	−19.9002			−0.751620			−0.375810	−	0.926697i	$-0.622636\pi$
$701$	−19.9002			−0.751620			−0.375810	+	0.926697i	$0.622636\pi$
$702$	6.42040	+	2.08611i	0.242322	+	0.0787353i
$703$	51.4808	−	70.8572i	1.94164	−	2.67243i
$704$	−0.809017	−	0.587785i	−0.0304910	−	0.0221530i
$705$	4.38853	−	1.79830i	0.165282	−	0.0677281i
$706$	10.7082	−	7.77997i	0.403009	−	0.292803i
$707$		−	0.0230383i		−	0.000866443i
$708$	0.460292	+	0.633538i	0.0172988	+	0.0238098i
$709$	−8.28239	−	25.4906i	−0.311052	−	0.957318i	−0.977349	−	0.211632i	$-0.932122\pi$
$709$	−8.28239	−	25.4906i	−0.311052	−	0.957318i	0.666298	−	0.745686i	$-0.267878\pi$
$710$	11.5663	−	9.80284i	0.434074	−	0.367894i
$711$	−14.5017	+	44.6315i	−0.543854	+	1.67381i
$712$	−13.6780	+	4.44424i	−0.512603	+	0.166555i
$713$	−29.2400	+	9.50066i	−1.09505	+	0.355802i
$714$	−0.0396515	+	0.122035i	−0.00148392	+	0.00456703i
$715$	5.86144	−	0.438926i	0.219205	−	0.0164149i
$716$	1.41846	+	4.36556i	0.0530103	+	0.163149i
$717$	−1.57723	−	2.17087i	−0.0589027	−	0.0810727i
$718$			23.1204i			0.862845i
$719$	−7.82920	+	5.68825i	−0.291980	+	0.212136i	−0.724126	−	0.689668i	$-0.757757\pi$
$719$	−7.82920	+	5.68825i	−0.291980	+	0.212136i	0.432146	+	0.901804i	$0.357757\pi$
$720$	4.05420	+	4.78350i	0.151091	+	0.178271i
$721$	−2.43776	−	1.77114i	−0.0907871	−	0.0659607i
$722$	−27.4667	+	37.8047i	−1.02221	+	1.40695i
$723$	10.5683	+	3.43385i	0.393039	+	0.127706i
$724$	5.79766			0.215468
$725$	−7.69096	−	3.99257i	−0.285635	−	0.148280i
$726$	−0.442463			−0.0164214
$727$	−4.00120	−	1.30007i	−0.148396	−	0.0482168i	0.233877	−	0.972266i	$-0.424859\pi$
$727$	−4.00120	−	1.30007i	−0.148396	−	0.0482168i	−0.382273	+	0.924049i	$0.624859\pi$
$728$	0.422515	−	0.581542i	0.0156594	−	0.0215534i
$729$	−13.7497	−	9.98977i	−0.509250	−	0.369992i
$730$	3.10620	−	5.02594i	0.114966	−	0.186018i
$731$	4.16115	−	3.02325i	0.153906	−	0.111819i
$732$		−	6.20130i		−	0.229207i
$733$	−19.8312	−	27.2953i	−0.732482	−	1.00817i	−0.999016	−	0.0443494i	$-0.985879\pi$
$733$	−19.8312	−	27.2953i	−0.732482	−	1.00817i	0.266534	−	0.963825i	$-0.414121\pi$
$734$	−6.61527	−	20.3597i	−0.244174	−	0.751491i
$735$	5.82837	+	3.60213i	0.214983	+	0.132867i
$736$	−1.32974	+	4.09252i	−0.0490149	+	0.150852i
$737$	13.3001	−	4.32147i	0.489916	−	0.159183i
$738$	22.0270	−	7.15702i	0.810826	−	0.263453i
$739$	−1.82533	+	5.61778i	−0.0671457	+	0.206653i	−0.979000	−	0.203861i	$-0.934651\pi$
$739$	−1.82533	+	5.61778i	−0.0671457	+	0.206653i	0.911854	+	0.410515i	$0.134651\pi$
$740$	5.72832	−	23.4674i	0.210577	−	0.862678i
$741$	2.91389	+	8.96802i	0.107044	+	0.329449i
$742$	−1.14906	−	1.58154i	−0.0421832	−	0.0580602i
$743$			22.7514i			0.834668i	0.908753	+	0.417334i	$0.137035\pi$
$743$			22.7514i			0.834668i	−0.908753	+	0.417334i	$0.862965\pi$
$744$	2.55754	−	1.85816i	0.0937638	−	0.0681234i
$745$	−1.88031	−	25.1097i	−0.0688892	−	0.919950i
$746$	12.8481	+	9.33467i	0.470401	+	0.341766i
$747$	−15.4084	+	21.2078i	−0.563762	+	0.775952i
$748$	−1.00859	−	0.327712i	−0.0368778	−	0.0119823i
$749$	−1.47123			−0.0537575
$750$	3.72482	+	3.25537i	0.136011	+	0.118869i
$751$	46.9257			1.71234			0.856172	−	0.516691i	$-0.172837\pi$
$751$	46.9257			1.71234			0.856172	+	0.516691i	$0.172837\pi$
$752$	4.55899	+	1.48131i	0.166249	+	0.0540176i
$753$	6.11217	−	8.41268i	0.222740	−	0.306575i
$754$	−3.68567	−	2.67780i	−0.134224	−	0.0975196i
$755$	2.51494	+	33.5846i	0.0915279	+	1.22227i
$756$	0.568158	−	0.412791i	0.0206637	−	0.0150131i
$757$			11.8781i			0.431718i	0.976425	+	0.215859i	$0.0692552\pi$
$757$			11.8781i			0.431718i	−0.976425	+	0.215859i	$0.930745\pi$
$758$	−9.22113	−	12.6918i	−0.334927	−	0.460987i
$759$	0.588362	+	1.81079i	0.0213562	+	0.0657275i
$760$	−4.29892	+	17.6115i	−0.155938	+	0.638837i
$761$	14.5471	−	44.7714i	0.527332	−	1.62296i	−0.232326	−	0.972638i	$-0.574634\pi$
$761$	14.5471	−	44.7714i	0.527332	−	1.62296i	0.759658	−	0.650323i	$-0.225366\pi$
$762$	0.279839	−	0.0909253i	0.0101375	−	0.00329388i
$763$	0.563046	−	0.182945i	0.0203836	−	0.00662304i
$764$	5.51519	−	16.9740i	0.199533	−	0.614098i
$765$	5.65665	+	3.49600i	0.204516	+	0.126398i
$766$	−0.847695	−	2.60894i	−0.0306285	−	0.0942647i
$767$	−2.73457	−	3.76382i	−0.0987398	−	0.135904i
$768$		−	0.442463i		−	0.0159660i
$769$	−25.1790	+	18.2936i	−0.907978	+	0.659685i	−0.940503	−	0.339786i	$-0.889645\pi$
$769$	−25.1790	+	18.2936i	−0.907978	+	0.659685i	0.0325246	+	0.999471i	$0.489645\pi$
$770$	0.321469	−	0.520147i	0.0115849	−	0.0187448i
$771$	−4.18388	−	3.03977i	−0.150679	−	0.109475i
$772$	−2.87167	+	3.95251i	−0.103354	+	0.142254i
$773$	4.04051	+	1.31284i	0.145327	+	0.0472196i	0.380777	−	0.924667i	$-0.375656\pi$
$773$	4.04051	+	1.31284i	0.145327	+	0.0472196i	−0.235450	+	0.971886i	$0.575656\pi$
$774$	−13.6006			−0.488864
$775$	−25.4515	+	25.0680i	−0.914246	+	0.900469i
$776$	4.89992			0.175897
$777$	−1.24314	−	0.403921i	−0.0445975	−	0.0144906i
$778$	15.8049	−	21.7536i	0.566635	−	0.779906i
$779$	54.1718	+	39.3581i	1.94091	+	1.41015i
$780$	1.68152	+	1.98401i	0.0602082	+	0.0710390i
$781$	5.48552	−	3.98546i	0.196287	−	0.142611i
$782$			4.56346i			0.163189i
$783$	−2.61617	−	3.60085i	−0.0934943	−	0.128684i
$784$	2.14001	+	6.58628i	0.0764290	+	0.235224i
$785$	46.6487	−	3.49323i	1.66496	−	0.124679i
$786$	−2.45624	+	7.55951i	−0.0876110	+	0.269639i
$787$	5.23510	−	1.70099i	0.186611	−	0.0606336i	−0.214221	−	0.976785i	$-0.568721\pi$
$787$	5.23510	−	1.70099i	0.186611	−	0.0606336i	0.400832	+	0.916152i	$0.368721\pi$
$788$	18.1534	−	5.89841i	0.646690	−	0.210122i
$789$	−3.26729	+	10.0557i	−0.116319	+	0.357992i
$790$	−28.5466	+	24.1944i	−1.01564	+	0.860796i
$791$	−1.67316	−	5.14947i	−0.0594909	−	0.183094i
$792$	1.64828	+	2.26867i	0.0585692	+	0.0806136i
$793$			36.8416i			1.30828i
$794$	5.97323	−	4.33981i	0.211982	−	0.154014i
$795$	6.54471	−	2.68185i	0.232117	−	0.0951154i
$796$	−9.54837	−	6.93729i	−0.338433	−	0.245886i
$797$	8.16386	−	11.2366i	0.289179	−	0.398020i	−0.639568	−	0.768734i	$-0.720887\pi$
$797$	8.16386	−	11.2366i	0.289179	−	0.398020i	0.928747	+	0.370714i	$0.120887\pi$
$798$	0.932938	+	0.303130i	0.0330256	+	0.0107307i
$799$	5.08361			0.179845
$800$	0.744661	+	4.94424i	0.0263277	+	0.174805i
$801$	40.3300			1.42499
$802$	6.01317	+	1.95380i	0.212332	+	0.0689910i
$803$	1.55310	−	2.13766i	0.0548078	−	0.0754364i
$804$	5.00592	+	3.63702i	0.176545	+	0.128268i
$805$	−2.55618	−	0.623956i	−0.0900936	−	0.0219916i
$806$	−15.1942	+	11.0392i	−0.535193	+	0.388841i
$807$			7.48279i			0.263407i
$808$	0.0495197	+	0.0681581i	0.00174210	+	0.00239779i
$809$	−13.5810	−	41.7981i	−0.477483	−	1.46954i	−0.842580	−	0.538572i	$-0.818964\pi$
$809$	−13.5810	−	41.7981i	−0.477483	−	1.46954i	0.365097	−	0.930970i	$-0.381036\pi$
$810$	−6.16933	−	15.0555i	−0.216768	−	0.528995i
$811$	7.07005	−	21.7594i	0.248263	−	0.764076i	−0.746819	−	0.665027i	$-0.768420\pi$
$811$	7.07005	−	21.7594i	0.248263	−	0.764076i	0.995083	−	0.0990486i	$-0.0315799\pi$
$812$	−0.450735	+	0.146453i	−0.0158177	+	0.00513948i
$813$	0.130974	−	0.0425560i	0.00459346	−	0.00149250i
$814$	3.33833	−	10.2743i	0.117009	−	0.360115i
$815$	10.7128	+	26.1432i	0.375253	+	0.915756i
$816$	−0.145000	−	0.446266i	−0.00507603	−	0.0156224i
$817$	−23.1123	−	31.8114i	−0.808598	−	1.11294i
$818$			11.8452i			0.414156i
$819$	−1.63078	+	1.18483i	−0.0569839	+	0.0414012i
$820$	17.9413	+	4.37942i	0.626538	+	0.152936i
$821$	22.1477	+	16.0912i	0.772958	+	0.561587i	0.902857	−	0.429940i	$-0.141465\pi$
$821$	22.1477	+	16.0912i	0.772958	+	0.561587i	−0.129899	+	0.991527i	$0.541465\pi$
$822$	−0.157002	+	0.216095i	−0.00547607	+	0.00753716i
$823$	−24.0942	−	7.82869i	−0.839872	−	0.272891i	−0.142674	−	0.989770i	$-0.545570\pi$
$823$	−24.0942	−	7.82869i	−0.839872	−	0.272891i	−0.697198	+	0.716879i	$0.745570\pi$
$824$	11.0191			0.383867
$825$	1.55242	+	1.57617i	0.0540485	+	0.0548754i
$826$	−0.483980			−0.0168398
$827$	18.7152	+	6.08093i	0.650791	+	0.211455i	0.615763	−	0.787932i	$-0.288848\pi$
$827$	18.7152	+	6.08093i	0.650791	+	0.211455i	0.0350279	+	0.999386i	$0.488848\pi$
$828$	7.09277	−	9.76237i	0.246491	−	0.339266i
$829$	−14.6089	−	10.6140i	−0.507388	−	0.368639i	0.304444	−	0.952530i	$-0.401529\pi$
$829$	−14.6089	−	10.6140i	−0.507388	−	0.368639i	−0.811832	+	0.583891i	$0.801529\pi$
$830$	−19.3421	+	7.92589i	−0.671375	+	0.275112i
$831$	−2.90550	+	2.11097i	−0.100791	+	0.0732288i
$832$			2.62866i			0.0911322i
$833$	4.31680	+	5.94157i	0.149568	+	0.205863i
$834$	−1.29947	−	3.99936i	−0.0449970	−	0.138486i
$835$	−22.5864	+	19.1428i	−0.781633	+	0.662463i
$836$	−2.50531	+	7.71055i	−0.0866480	+	0.266675i
$837$	−17.4508	+	5.67010i	−0.603187	+	0.195987i
$838$	−2.40127	+	0.780221i	−0.0829506	+	0.0269523i
$839$	3.02085	−	9.29721i	0.104291	−	0.320975i	−0.885272	−	0.465073i	$-0.846028\pi$
$839$	3.02085	−	9.29721i	0.104291	−	0.320975i	0.989563	+	0.144098i	$0.0460280\pi$
$840$	0.269798	−	0.0202034i	0.00930890	−	0.000697085i
$841$	−8.03331	−	24.7240i	−0.277011	−	0.852551i
$842$	−13.6728	−	18.8190i	−0.471196	−	0.648546i
$843$		−	1.13811i		−	0.0391986i
$844$	−12.2063	+	8.86838i	−0.420158	+	0.305262i
$845$	8.80484	+	10.3887i	0.302896	+	0.357383i
$846$	−10.8751	−	7.90122i	−0.373893	−	0.271649i
$847$	0.160734	−	0.221232i	0.00552289	−	0.00760161i
$848$	6.79892	+	2.20910i	0.233476	+	0.0758609i
$849$	1.26915			0.0435573
$850$	2.37134	+	4.74269i	0.0813364	+	0.162673i
$851$	−46.4870			−1.59355
$852$	2.85328	+	0.927086i	0.0977517	+	0.0317614i
$853$	−31.5409	+	43.4123i	−1.07994	+	1.48641i	−0.220354	+	0.975420i	$0.570721\pi$
$853$	−31.5409	+	43.4123i	−1.07994	+	1.48641i	−0.859586	+	0.510990i	$0.829279\pi$
$854$	3.10065	+	2.25275i	0.106102	+	0.0770876i
$855$	26.7264	−	43.2443i	0.914025	−	1.47892i
$856$	4.35259	−	3.16234i	0.148769	−	0.108087i
$857$			38.5194i			1.31580i	0.753106	+	0.657899i	$0.228555\pi$
$857$			38.5194i			1.31580i	−0.753106	+	0.657899i	$0.771445\pi$
$858$	0.683644	+	0.940955i	0.0233392	+	0.0321237i
$859$	2.65275	+	8.16432i	0.0905106	+	0.278563i	0.986058	−	0.166404i	$-0.0532155\pi$
$859$	2.65275	+	8.16432i	0.0905106	+	0.278563i	−0.895547	+	0.444967i	$0.853215\pi$
$860$	−9.22533	−	5.70157i	−0.314581	−	0.194422i
$861$	0.308806	−	0.950408i	0.0105241	−	0.0323898i
$862$	2.93667	−	0.954181i	0.100023	−	0.0324995i
$863$	1.26887	−	0.412281i	0.0431929	−	0.0140342i	−0.287341	−	0.957828i	$-0.592771\pi$
$863$	1.26887	−	0.412281i	0.0431929	−	0.0140342i	0.330534	+	0.943794i	$0.392771\pi$
$864$	−0.793604	+	2.44246i	−0.0269990	+	0.0830943i
$865$	−0.256322	+	1.05008i	−0.00871522	+	0.0357039i
$866$	8.38161	+	25.7959i	0.284819	+	0.876582i
$867$	4.12876	+	5.68275i	0.140220	+	0.192996i
$868$			1.95378i			0.0663158i
$869$	−13.5388	+	9.83650i	−0.459272	+	0.333681i
$870$	−0.128044	−	1.70991i	−0.00434111	−	0.0579714i
$871$	−29.7400	−	21.6073i	−1.00770	−	0.732137i
$872$	−1.27253	+	1.75148i	−0.0430931	+	0.0593126i
$873$	−13.0680	−	4.24604i	−0.442284	−	0.143707i
$874$	34.8870			1.18007
$875$	−2.98081	+	0.679826i	−0.100770	+	0.0229823i
$876$	1.16912			0.0395009
$877$	41.7010	+	13.5495i	1.40814	+	0.457533i	0.911814	−	0.410603i	$-0.134682\pi$
$877$	41.7010	+	13.5495i	1.40814	+	0.457533i	0.496327	+	0.868136i	$0.334682\pi$
$878$	−9.22533	+	12.6976i	−0.311340	+	0.428523i
$879$	−5.34663	−	3.88455i	−0.180337	−	0.131023i
$880$	0.166977	+	2.22982i	0.00562881	+	0.0751674i
$881$	10.7812	−	7.83299i	0.363227	−	0.263900i	−0.391170	−	0.920319i	$-0.627929\pi$
$881$	10.7812	−	7.83299i	0.363227	−	0.263900i	0.754397	+	0.656418i	$0.227929\pi$
$882$		−	19.4199i		−	0.653902i
$883$	−25.6217	−	35.2652i	−0.862238	−	1.18677i	−0.981031	−	0.193850i	$-0.937903\pi$
$883$	−25.6217	−	35.2652i	−0.862238	−	1.18677i	0.118793	−	0.992919i	$-0.462097\pi$
$884$	0.861441	+	2.65124i	0.0289734	+	0.0891710i
$885$	0.415236	−	1.70111i	0.0139580	−	0.0571822i
$886$	−1.50271	+	4.62485i	−0.0504844	+	0.155375i
$887$	7.99530	−	2.59783i	0.268456	−	0.0872266i	−0.171696	−	0.985150i	$-0.554925\pi$
$887$	7.99530	−	2.59783i	0.268456	−	0.0872266i	0.440152	+	0.897923i	$0.354925\pi$
$888$	4.54602	−	1.47709i	0.152554	−	0.0495679i
$889$	−0.0561950	+	0.172950i	−0.00188472	+	0.00580057i
$890$	27.3559	+	16.9069i	0.916972	+	0.566720i
$891$	−2.24852	−	6.92023i	−0.0753282	−	0.231836i
$892$	2.26705	+	3.12033i	0.0759065	+	0.104476i
$893$		−	38.8635i		−	1.30052i
$894$	4.03094	−	2.92865i	0.134815	−	0.0979487i
$895$	5.39613	−	8.73113i	0.180373	−	0.291849i
$896$	0.221232	+	0.160734i	0.00739083	+	0.00536976i
$897$	2.94181	−	4.04905i	0.0982241	−	0.135194i
$898$	11.7105	+	3.80496i	0.390783	+	0.126973i
$899$	12.3826			0.412983
$900$	2.29845	−	13.8315i	0.0766151	−	0.461049i
$901$	7.58129			0.252569
$902$	7.85494	+	2.55223i	0.261541	+	0.0849798i
$903$	−0.344931	+	0.474756i	−0.0114786	+	0.0157989i
$904$	16.0186	+	11.6382i	0.532770	+	0.387080i
$905$	−8.38194	−	9.88976i	−0.278625	−	0.328747i
$906$	−5.39144	+	3.91711i	−0.179118	+	0.130137i
$907$			11.5429i			0.383277i	0.981466	+	0.191638i	$0.0613801\pi$
$907$			11.5429i			0.383277i	−0.981466	+	0.191638i	$0.938620\pi$
$908$	−1.69046	−	2.32672i	−0.0561000	−	0.0772150i
$909$	−0.0730054	−	0.224688i	−0.00242144	−	0.00745242i
$910$	−1.60285	+	0.120028i	−0.0531341	+	0.00397888i
$911$	3.27767	−	10.0876i	0.108594	−	0.334218i	−0.881963	−	0.471319i	$-0.843778\pi$
$911$	3.27767	−	10.0876i	0.108594	−	0.334218i	0.990557	+	0.137100i	$0.0437782\pi$
$912$	−3.41164	+	1.10851i	−0.112971	+	0.0367064i
$913$	−8.89059	+	2.88873i	−0.294236	+	0.0956030i
$914$	6.26316	−	19.2760i	0.207167	−	0.637595i
$915$	−10.5783	+	8.96550i	−0.349708	+	0.296390i
$916$	2.03904	+	6.27552i	0.0673718	+	0.207349i
$917$	−2.88748	−	3.97427i	−0.0953529	−	0.131242i
$918$			2.72353i			0.0898897i
$919$	33.0811	−	24.0349i	1.09125	−	0.792837i	0.111637	−	0.993749i	$-0.464391\pi$
$919$	33.0811	−	24.0349i	1.09125	−	0.792837i	0.979609	+	0.200912i	$0.0643906\pi$
$920$	8.90357	−	3.64845i	0.293542	−	0.120286i
$921$	−8.23015	−	5.97955i	−0.271193	−	0.197033i
$922$	7.98640	−	10.9923i	0.263018	−	0.362013i
$923$	−16.9512	−	5.50778i	−0.557955	−	0.181291i
$924$	0.120995			0.00398044
$925$	−48.3128	+	24.1564i	−1.58852	+	0.794258i
$926$	−3.46359			−0.113821
$927$	−29.3876	−	9.54860i	−0.965214	−	0.313617i
$928$	1.01869	−	1.40211i	0.0334403	−	0.0460266i
$929$	30.4442	+	22.1190i	0.998840	+	0.725700i	0.961839	−	0.273615i	$-0.0882195\pi$
$929$	30.4442	+	22.1190i	0.998840	+	0.725700i	0.0370012	+	0.999315i	$0.488219\pi$
$930$	−6.86723	−	1.67627i	−0.225185	−	0.0549670i
$931$	45.4224	−	33.0013i	1.48866	−	1.08158i
$932$			27.0467i			0.885946i
$933$	0.159109	+	0.218995i	0.00520899	+	0.00716957i
$934$	12.7587	+	39.2673i	0.417478	+	1.28487i
$935$	0.899152	+	2.19427i	0.0294054	+	0.0717601i
$936$	2.27787	−	7.01057i	0.0744545	−	0.229147i
$937$	−13.4511	+	4.37051i	−0.439427	+	0.142778i	−0.520371	−	0.853940i	$-0.674206\pi$
$937$	−13.4511	+	4.37051i	−0.439427	+	0.142778i	0.0809443	+	0.996719i	$0.474206\pi$
$938$	−3.63702	+	1.18174i	−0.118753	+	0.0385851i
$939$	−2.27004	+	6.98647i	−0.0740801	+	0.227995i
$940$	−4.06430	−	9.91840i	−0.132563	−	0.323503i
$941$	13.7434	+	42.2978i	0.448022	+	1.37887i	0.879136	+	0.476572i	$0.158121\pi$
$941$	13.7434	+	42.2978i	0.448022	+	1.37887i	−0.431114	+	0.902298i	$0.641879\pi$
$942$	5.44083	+	7.48865i	0.177272	+	0.243994i
$943$		−	35.5403i		−	1.15735i
$944$	1.43184	−	1.04029i	0.0466025	−	0.0338587i
$945$	−1.52556	−	0.372384i	−0.0496264	−	0.0121137i
$946$	−3.92377	−	2.85078i	−0.127573	−	0.0926870i
$947$	20.8327	−	28.6737i	0.676971	−	0.931771i	−0.322922	−	0.946426i	$-0.604665\pi$
$947$	20.8327	−	28.6737i	0.676971	−	0.931771i	0.999893	+	0.0146551i	$0.00466502\pi$
$948$	−7.04216	−	2.28814i	−0.228719	−	0.0743152i
$949$	−6.94568			−0.225466
$950$	36.2572	−	18.1286i	1.17634	−	0.588169i
$951$	6.33198			0.205328
$952$	0.275807	+	0.0896152i	0.00893897	+	0.00290445i
$953$	1.23043	−	1.69354i	0.0398575	−	0.0548592i	−0.788623	−	0.614877i	$-0.789206\pi$
$953$	1.23043	−	1.69354i	0.0398575	−	0.0548592i	0.828481	+	0.560018i	$0.189206\pi$
$954$	−16.2182	−	11.7832i	−0.525085	−	0.381497i
$955$	−36.9282	+	15.1322i	−1.19497	+	0.489666i
$956$	−4.90633	+	3.56466i	−0.158682	+	0.115289i
$957$		−	0.766837i		−	0.0247883i
$958$	−13.1009	−	18.0319i	−0.423272	−	0.582585i
$959$	−0.0510130	−	0.157002i	−0.00164730	−	0.00506986i
$960$	−0.754763	+	0.639690i	−0.0243599	+	0.0206459i
$961$	6.19498	−	19.0662i	0.199838	−	0.615039i
$962$	−27.0077	+	8.77533i	−0.870763	+	0.282928i
$963$	−14.3486	+	4.66215i	−0.462377	+	0.150236i
$964$	7.76075	−	23.8851i	0.249957	−	0.769288i
$965$	10.8940	−	0.815780i	0.350689	−	0.0262609i
$966$	−0.160892	−	0.495174i	−0.00517661	−	0.0159320i
$967$	26.1035	+	35.9284i	0.839433	+	1.15538i	0.986093	+	0.166193i	$0.0531476\pi$
$967$	26.1035	+	35.9284i	0.839433	+	1.15538i	−0.146660	+	0.989187i	$0.546852\pi$
$968$			1.00000i			0.0321412i
$969$	−3.07768	+	2.23607i	−0.0988694	+	0.0718329i
$970$	−7.08404	−	8.35838i	−0.227455	−	0.268371i
$971$	3.63414	+	2.64036i	0.116625	+	0.0847331i	0.644569	−	0.764546i	$-0.277037\pi$
$971$	3.63414	+	2.64036i	0.116625	+	0.0847331i	−0.527944	+	0.849279i	$0.677037\pi$
$972$	6.42097	−	8.83770i	0.205953	−	0.283469i
$973$	2.47174	+	0.803117i	0.0792403	+	0.0257467i
$974$	37.3661			1.19729
$975$	0.953309	−	5.73675i	0.0305303	−	0.183723i
$976$	−14.0154			−0.448622
$977$	−6.13407	−	1.99308i	−0.196246	−	0.0637643i	0.209245	−	0.977863i	$-0.432899\pi$
$977$	−6.13407	−	1.99308i	−0.196246	−	0.0637643i	−0.405491	+	0.914099i	$0.632899\pi$
$978$	−3.28606	+	4.52287i	−0.105077	+	0.144625i
$979$	11.6352	+	8.45344i	0.371861	+	0.270173i
$980$	8.14109	−	13.1726i	0.260057	−	0.420782i
$981$	4.91155	−	3.56845i	0.156814	−	0.113932i
$982$			32.4200i			1.03456i
$983$	16.3192	+	22.4614i	0.520500	+	0.716407i	0.985646	−	0.168827i	$-0.0539979\pi$
$983$	16.3192	+	22.4614i	0.520500	+	0.716407i	−0.465145	+	0.885234i	$0.653998\pi$
$984$	1.12927	+	3.47553i	0.0359997	+	0.110796i
$985$	−36.3069	−	22.4389i	−1.15683	−	0.714963i
$986$	0.567960	−	1.74800i	0.0180875	−	0.0556676i
$987$	−0.551615	+	0.179230i	−0.0175581	+	0.00570497i
$988$	20.2684	−	6.58560i	0.644823	−	0.209516i
$989$	−6.44930	+	19.8489i	−0.205076	+	0.631158i
$990$	1.48694	−	6.09159i	0.0472580	−	0.193603i
$991$	13.0420	+	40.1392i	0.414293	+	1.27506i	0.912882	+	0.408224i	$0.133852\pi$
$991$	13.0420	+	40.1392i	0.414293	+	1.27506i	−0.498589	+	0.866838i	$0.666148\pi$
$992$	−4.19958	−	5.78022i	−0.133337	−	0.183522i
$993$			6.26568i			0.198835i
$994$	−1.50006	+	1.08985i	−0.0475789	+	0.0345681i
$995$	1.97074	+	26.3174i	0.0624767	+	0.834316i
$996$	−3.34626	−	2.43120i	−0.106030	−	0.0770355i
$997$	−2.17267	+	2.99042i	−0.0688090	+	0.0947075i	−0.842034	−	0.539424i	$-0.818642\pi$
$997$	−2.17267	+	2.99042i	−0.0688090	+	0.0947075i	0.773225	+	0.634131i	$0.218642\pi$
$998$	7.70608	+	2.50386i	0.243932	+	0.0792583i
$999$	−27.7440			−0.877781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.t.a.529.1	yes	8
25.19	even	10	inner	550.2.t.a.419.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.t.a.419.1	✓	8	25.19	even	10	inner
550.2.t.a.529.1	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.260074 + 0.357960i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.357960 - 0.260074i) q^{6} +0.273457i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.866554 + 2.66698i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.260074 + 0.357960i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.357960 - 0.260074i) q^{6} +0.273457i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.866554 + 2.66698i) q^{9} +(-0.530249 + 2.17229i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.420808 + 0.136729i) q^{12} +(2.50000 - 0.812299i) q^{13} +(0.0845030 - 0.260074i) q^{14} +(0.841616 + 0.520147i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.623345 + 0.857960i) q^{17} -2.80423i q^{18} +(6.55899 - 4.76538i) q^{19} +(1.17557 - 1.90211i) q^{20} +(-0.0978870 - 0.0711190i) q^{21} +(0.587785 - 0.809017i) q^{22} +(-4.09252 - 1.32974i) q^{23} +0.442463 q^{24} +(-4.94424 + 0.744661i) q^{25} -2.62866 q^{26} +(-2.44246 - 0.793604i) q^{27} +(-0.160734 + 0.221232i) q^{28} +(1.40211 + 1.01869i) q^{29} +(-0.639690 - 0.754763i) q^{30} +(5.78022 - 4.19958i) q^{31} -1.00000i q^{32} +(-0.260074 - 0.357960i) q^{33} +(-0.327712 - 1.00859i) q^{34} +(0.609762 - 0.0456612i) q^{35} +(-0.866554 + 2.66698i) q^{36} +(10.2743 - 3.33833i) q^{37} +(-7.71055 + 2.50531i) q^{38} +(-0.359413 + 1.10616i) q^{39} +(-1.70582 + 1.44575i) q^{40} +(2.55223 + 7.85494i) q^{41} +(0.0711190 + 0.0978870i) q^{42} -4.85004i q^{43} +(-0.809017 + 0.587785i) q^{44} +(5.80220 - 2.37759i) q^{45} +(3.48131 + 2.52932i) q^{46} +(2.81761 - 3.87811i) q^{47} +(-0.420808 - 0.136729i) q^{48} +6.92522 q^{49} +(4.93236 + 0.819639i) q^{50} -0.469231 q^{51} +(2.50000 + 0.812299i) q^{52} +(4.20196 - 5.78350i) q^{53} +(2.07768 + 1.50953i) q^{54} +(2.17229 + 0.530249i) q^{55} +(0.221232 - 0.160734i) q^{56} +3.58721i q^{57} +(-1.01869 - 1.40211i) q^{58} +(-0.546915 - 1.68323i) q^{59} +(0.375147 + 0.915497i) q^{60} +(-4.33099 + 13.3294i) q^{61} +(-6.79506 + 2.20785i) q^{62} +(-0.729305 + 0.236966i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.22873 - 5.43893i) q^{65} +(0.136729 + 0.420808i) q^{66} +(-8.21992 - 11.3138i) q^{67} +1.06050i q^{68} +(1.54035 - 1.11913i) q^{69} +(-0.594028 - 0.145000i) q^{70} +(-5.48552 - 3.98546i) q^{71} +(1.64828 - 2.26867i) q^{72} +(-2.51297 - 0.816514i) q^{73} -10.8031 q^{74} +(1.01931 - 1.96351i) q^{75} +8.10736 q^{76} +(-0.260074 - 0.0845030i) q^{77} +(0.683644 - 0.940955i) q^{78} +(13.5388 + 9.83650i) q^{79} +(2.06909 - 0.847859i) q^{80} +(-5.88670 + 4.27694i) q^{81} -8.25918i q^{82} +(5.49469 + 7.56279i) q^{83} +(-0.0373895 - 0.115073i) q^{84} +(1.80902 - 1.53321i) q^{85} +(-1.49875 + 4.61267i) q^{86} +(-0.729305 + 0.236966i) q^{87} +(0.951057 - 0.309017i) q^{88} +(4.44424 - 13.6780i) q^{89} +(-6.25293 + 0.468243i) q^{90} +(0.222129 + 0.683644i) q^{91} +(-2.52932 - 3.48131i) q^{92} +3.16129i q^{93} +(-3.87811 + 2.81761i) q^{94} +(-11.7212 - 13.8297i) q^{95} +(0.357960 + 0.260074i) q^{96} +(-2.88010 + 3.96412i) q^{97} +(-6.58628 - 2.14001i) q^{98} -2.80423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9	\( 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9} + 2 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} + 16 q^{19} - 16 q^{21} + 10 q^{23} + 4 q^{24} - 10 q^{25} - 20 q^{27} - 10 q^{28} - 4 q^{29} + 10 q^{31} + 10 q^{33} - 10 q^{34} + 10 q^{35} - 2 q^{36} + 20 q^{37} - 10 q^{38} + 30 q^{39} + 26 q^{41} - 20 q^{42} - 2 q^{44} + 20 q^{45} + 16 q^{46} + 10 q^{47} + 8 q^{49} + 20 q^{50} - 40 q^{51} + 20 q^{52} - 10 q^{53} - 8 q^{54} + 10 q^{55} + 2 q^{56} - 20 q^{58} - 16 q^{59} - 10 q^{60} - 40 q^{61} - 30 q^{63} + 2 q^{64} - 10 q^{65} + 4 q^{66} + 28 q^{69} + 10 q^{70} - 26 q^{71} - 10 q^{73} + 8 q^{74} + 10 q^{75} + 4 q^{76} + 10 q^{77} + 20 q^{78} + 32 q^{79} - 18 q^{81} + 50 q^{83} - 24 q^{84} + 10 q^{85} - 10 q^{86} - 30 q^{87} + 6 q^{89} - 10 q^{90} + 40 q^{91} - 20 q^{92} - 10 q^{94} - 30 q^{95} + 6 q^{96} - 40 q^{97} - 20 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9 + 2 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 + 16 * q^19 - 16 * q^21 + 10 * q^23 + 4 * q^24 - 10 * q^25 - 20 * q^27 - 10 * q^28 - 4 * q^29 + 10 * q^31 + 10 * q^33 - 10 * q^34 + 10 * q^35 - 2 * q^36 + 20 * q^37 - 10 * q^38 + 30 * q^39 + 26 * q^41 - 20 * q^42 - 2 * q^44 + 20 * q^45 + 16 * q^46 + 10 * q^47 + 8 * q^49 + 20 * q^50 - 40 * q^51 + 20 * q^52 - 10 * q^53 - 8 * q^54 + 10 * q^55 + 2 * q^56 - 20 * q^58 - 16 * q^59 - 10 * q^60 - 40 * q^61 - 30 * q^63 + 2 * q^64 - 10 * q^65 + 4 * q^66 + 28 * q^69 + 10 * q^70 - 26 * q^71 - 10 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 20 * q^78 + 32 * q^79 - 18 * q^81 + 50 * q^83 - 24 * q^84 + 10 * q^85 - 10 * q^86 - 30 * q^87 + 6 * q^89 - 10 * q^90 + 40 * q^91 - 20 * q^92 - 10 * q^94 - 30 * q^95 + 6 * q^96 - 40 * q^97 - 20 * q^98 + 8 * q^99

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