LMFDB - Embedded newform 930.2.z.d.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.244369 - 2.22267i) q^{5} +1.00000 q^{6} +(4.86212 + 1.57980i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.244369 - 2.22267i) q^{5} +1.00000 q^{6} +(4.86212 + 1.57980i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.65455 + 1.50415i) q^{10} +(-1.17610 + 3.61967i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-3.34545 + 4.60462i) q^{13} +(-1.57980 - 4.86212i) q^{14} +(1.94182 + 1.10876i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.84451 - 0.924238i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-1.54476 + 1.12233i) q^{19} +(2.18940 + 0.454435i) q^{20} +(-4.13597 + 3.00496i) q^{21} +(3.61967 - 1.17610i) q^{22} +(5.37075 - 1.74506i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.88057 + 1.08631i) q^{25} +5.69162 q^{26} +(0.951057 + 0.309017i) q^{27} +(-3.00496 + 4.13597i) q^{28} +(-0.173898 + 0.126345i) q^{29} +(-0.244369 - 2.22267i) q^{30} +(-5.09924 - 2.23557i) q^{31} +1.00000i q^{32} +(-2.23708 - 3.07908i) q^{33} +(-2.41969 - 1.75800i) q^{34} +(2.32323 - 11.1930i) q^{35} +1.00000 q^{36} +9.25029i q^{37} +(1.81597 + 0.590045i) q^{38} +(-1.75881 - 5.41305i) q^{39} +(-0.919253 - 2.03838i) q^{40} +(-8.47099 + 6.15453i) q^{41} +(4.86212 + 1.57980i) q^{42} +(1.75122 + 2.41035i) q^{43} +(-3.07908 - 2.23708i) q^{44} +(-2.03838 + 0.919253i) q^{45} +(-4.56863 - 3.31930i) q^{46} +(2.97872 - 4.09986i) q^{47} +(0.951057 - 0.309017i) q^{48} +(15.4813 + 11.2479i) q^{49} +(3.74757 + 3.30995i) q^{50} +(-0.924238 + 2.84451i) q^{51} +(-3.34545 - 4.60462i) q^{52} +(-0.262206 + 0.0851960i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(8.33276 + 1.72956i) q^{55} +5.11234 q^{56} -1.90943i q^{57} +(0.204430 + 0.0664233i) q^{58} +(5.81044 + 4.22153i) q^{59} +(-1.65455 + 1.50415i) q^{60} +9.04256 q^{61} +(1.18864 + 5.43941i) q^{62} -5.11234i q^{63} +(0.809017 - 0.587785i) q^{64} +(11.0521 + 6.31062i) q^{65} +(-1.17610 + 3.61967i) q^{66} -8.25869i q^{67} +2.99090i q^{68} +(-1.74506 + 5.37075i) q^{69} +(-10.4209 + 4.69953i) q^{70} +(2.08691 + 6.42284i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(11.2666 + 3.66074i) q^{73} +(7.48364 - 5.43718i) q^{74} +(1.98989 - 4.58698i) q^{75} +(-0.590045 - 1.81597i) q^{76} +(-11.4367 + 15.7413i) q^{77} +(-3.34545 + 4.60462i) q^{78} +(4.94351 + 15.2146i) q^{79} +(-1.10876 + 1.94182i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(9.95825 + 3.23563i) q^{82} +(2.78354 + 3.83122i) q^{83} +(-1.57980 - 4.86212i) q^{84} +(-2.74939 - 6.09657i) q^{85} +(0.920671 - 2.83353i) q^{86} -0.214950i q^{87} +3.80595i q^{88} +(5.81210 - 17.8878i) q^{89} +(1.94182 + 1.10876i) q^{90} +(-23.5404 + 17.1031i) q^{91} +5.64714i q^{92} +(4.80587 - 2.81134i) q^{93} -5.06770 q^{94} +(2.87207 + 3.15923i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(1.44984 + 0.471080i) q^{97} -19.1360i q^{98} +3.80595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.244369	−	2.22267i	−0.109285	−	0.994010i
$5$	−0.244369	−	2.22267i	−0.109285	−	0.994010i
$6$	1.00000			0.408248
$7$	4.86212	+	1.57980i	1.83771	+	0.597108i	0.998586	+	0.0531670i	$0.0169316\pi$
$7$	4.86212	+	1.57980i	1.83771	+	0.597108i	0.839124	+	0.543941i	$0.183068\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	−1.65455	+	1.50415i	−0.523213	+	0.475655i
$11$	−1.17610	+	3.61967i	−0.354608	+	1.09137i	0.601628	+	0.798776i	$0.294519\pi$
$11$	−1.17610	+	3.61967i	−0.354608	+	1.09137i	−0.956236	+	0.292596i	$0.905481\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	−3.34545	+	4.60462i	−0.927861	+	1.27709i	0.0328274	+	0.999461i	$0.489549\pi$
$13$	−3.34545	+	4.60462i	−0.927861	+	1.27709i	−0.960688	+	0.277630i	$0.910451\pi$
$14$	−1.57980	−	4.86212i	−0.422219	−	1.29946i
$15$	1.94182	+	1.10876i	0.501375	+	0.286280i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.84451	−	0.924238i	0.689895	−	0.224161i	0.0569728	−	0.998376i	$-0.481855\pi$
$17$	2.84451	−	0.924238i	0.689895	−	0.224161i	0.632922	+	0.774215i	$0.281855\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−1.54476	+	1.12233i	−0.354392	+	0.257481i	−0.750709	−	0.660633i	$-0.770288\pi$
$19$	−1.54476	+	1.12233i	−0.354392	+	0.257481i	0.396317	+	0.918114i	$0.370288\pi$
$20$	2.18940	+	0.454435i	0.489566	+	0.101615i
$21$	−4.13597	+	3.00496i	−0.902542	+	0.655735i
$22$	3.61967	−	1.17610i	0.771716	−	0.250746i
$23$	5.37075	−	1.74506i	1.11988	−	0.363871i	0.310157	−	0.950685i	$-0.399618\pi$
$23$	5.37075	−	1.74506i	1.11988	−	0.363871i	0.809721	+	0.586815i	$0.199618\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.88057	+	1.08631i	−0.976113	+	0.217261i
$26$	5.69162			1.11622
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	−3.00496	+	4.13597i	−0.567883	+	0.781624i
$29$	−0.173898	+	0.126345i	−0.0322921	+	0.0234616i	−0.603814	−	0.797125i	$-0.706353\pi$
$29$	−0.173898	+	0.126345i	−0.0322921	+	0.0234616i	0.571522	+	0.820587i	$0.306353\pi$
$30$	−0.244369	−	2.22267i	−0.0446155	−	0.405803i
$31$	−5.09924	−	2.23557i	−0.915850	−	0.401520i
$31$	−5.09924	−	2.23557i	−0.915850	−	0.401520i
$32$			1.00000i			0.176777i
$33$	−2.23708	−	3.07908i	−0.389426	−	0.535998i
$34$	−2.41969	−	1.75800i	−0.414973	−	0.301495i
$35$	2.32323	−	11.1930i	0.392697	−	1.89196i
$36$	1.00000			0.166667
$37$			9.25029i			1.52074i	0.649491	+	0.760369i	$0.274982\pi$
$37$			9.25029i			1.52074i	−0.649491	+	0.760369i	$0.725018\pi$
$38$	1.81597	+	0.590045i	0.294590	+	0.0957179i
$39$	−1.75881	−	5.41305i	−0.281635	−	0.866782i
$40$	−0.919253	−	2.03838i	−0.145347	−	0.322295i
$41$	−8.47099	+	6.15453i	−1.32295	+	0.961177i	−0.323056	+	0.946380i	$0.604710\pi$
$41$	−8.47099	+	6.15453i	−1.32295	+	0.961177i	−0.999891	+	0.0147968i	$0.995290\pi$
$42$	4.86212	+	1.57980i	0.750242	+	0.243768i
$43$	1.75122	+	2.41035i	0.267059	+	0.367575i	0.921394	−	0.388630i	$-0.127051\pi$
$43$	1.75122	+	2.41035i	0.267059	+	0.367575i	−0.654335	+	0.756205i	$0.727051\pi$
$44$	−3.07908	−	2.23708i	−0.464188	−	0.337252i
$45$	−2.03838	+	0.919253i	−0.303863	+	0.137034i
$46$	−4.56863	−	3.31930i	−0.673608	−	0.489405i
$47$	2.97872	−	4.09986i	0.434491	−	0.598026i	−0.534486	−	0.845178i	$-0.679495\pi$
$47$	2.97872	−	4.09986i	0.434491	−	0.598026i	0.968977	+	0.247152i	$0.0794946\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	15.4813	+	11.2479i	2.21162	+	1.60684i
$50$	3.74757	+	3.30995i	0.529986	+	0.468097i
$51$	−0.924238	+	2.84451i	−0.129419	+	0.398311i
$52$	−3.34545	−	4.60462i	−0.463930	−	0.638545i
$53$	−0.262206	+	0.0851960i	−0.0360168	+	0.0117026i	−0.326970	−	0.945035i	$-0.606028\pi$
$53$	−0.262206	+	0.0851960i	−0.0360168	+	0.0117026i	0.290953	+	0.956737i	$0.406028\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	8.33276	+	1.72956i	1.12359	+	0.233213i
$56$	5.11234			0.683165
$57$		−	1.90943i		−	0.252910i
$58$	0.204430	+	0.0664233i	0.0268429	+	0.00872180i
$59$	5.81044	+	4.22153i	0.756455	+	0.549596i	0.897821	−	0.440361i	$-0.145150\pi$
$59$	5.81044	+	4.22153i	0.756455	+	0.549596i	−0.141366	+	0.989957i	$0.545150\pi$
$60$	−1.65455	+	1.50415i	−0.213601	+	0.194185i
$61$	9.04256			1.15778			0.578890	−	0.815405i	$-0.303486\pi$
$61$	9.04256			1.15778			0.578890	+	0.815405i	$0.303486\pi$
$62$	1.18864	+	5.43941i	0.150958	+	0.690805i
$63$		−	5.11234i		−	0.644094i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	11.0521	+	6.31062i	1.37084	+	0.782736i
$66$	−1.17610	+	3.61967i	−0.144768	+	0.445551i
$67$		−	8.25869i		−	1.00896i	−0.863424	−	0.504480i	$-0.831684\pi$
$67$		−	8.25869i		−	1.00896i	0.863424	−	0.504480i	$-0.168316\pi$
$68$			2.99090i			0.362699i
$69$	−1.74506	+	5.37075i	−0.210081	+	0.646562i
$70$	−10.4209	+	4.69953i	−1.24553	+	0.561702i
$71$	2.08691	+	6.42284i	0.247670	+	0.762251i	0.995186	+	0.0980066i	$0.0312466\pi$
$71$	2.08691	+	6.42284i	0.247670	+	0.762251i	−0.747515	+	0.664244i	$0.768753\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	11.2666	+	3.66074i	1.31866	+	0.428457i	0.882033	−	0.471188i	$-0.156175\pi$
$73$	11.2666	+	3.66074i	1.31866	+	0.428457i	0.436622	+	0.899645i	$0.356175\pi$
$74$	7.48364	−	5.43718i	0.869955	−	0.632060i
$75$	1.98989	−	4.58698i	0.229772	−	0.529658i
$76$	−0.590045	−	1.81597i	−0.0676828	−	0.208306i
$77$	−11.4367	+	15.7413i	−1.30333	+	1.79388i
$78$	−3.34545	+	4.60462i	−0.378798	+	0.521370i
$79$	4.94351	+	15.2146i	0.556189	+	1.71177i	0.692784	+	0.721146i	$0.256384\pi$
$79$	4.94351	+	15.2146i	0.556189	+	1.71177i	−0.136595	+	0.990627i	$0.543616\pi$
$80$	−1.10876	+	1.94182i	−0.123963	+	0.217102i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	9.95825	+	3.23563i	1.09970	+	0.357316i
$83$	2.78354	+	3.83122i	0.305533	+	0.420531i	0.933982	−	0.357321i	$-0.116310\pi$
$83$	2.78354	+	3.83122i	0.305533	+	0.420531i	−0.628448	+	0.777851i	$0.716310\pi$
$84$	−1.57980	−	4.86212i	−0.172370	−	0.530501i
$85$	−2.74939	−	6.09657i	−0.298213	−	0.661266i
$86$	0.920671	−	2.83353i	0.0992785	−	0.305548i
$87$		−	0.214950i		−	0.0230451i
$88$			3.80595i			0.405715i
$89$	5.81210	−	17.8878i	0.616082	−	1.89610i	0.232504	−	0.972595i	$-0.425308\pi$
$89$	5.81210	−	17.8878i	0.616082	−	1.89610i	0.383577	−	0.923509i	$-0.374692\pi$
$90$	1.94182	+	1.10876i	0.204686	+	0.116873i
$91$	−23.5404	+	17.1031i	−2.46770	+	1.79289i
$92$			5.64714i			0.588755i
$93$	4.80587	−	2.81134i	0.498346	−	0.291522i
$94$	−5.06770			−0.522694
$95$	2.87207	+	3.15923i	0.294668	+	0.324130i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	1.44984	+	0.471080i	0.147209	+	0.0478310i	0.381694	−	0.924289i	$-0.375341\pi$
$97$	1.44984	+	0.471080i	0.147209	+	0.0478310i	−0.234486	+	0.972120i	$0.575341\pi$
$98$		−	19.1360i		−	1.93303i
$99$	3.80595			0.382512
$100$	0.475039	−	4.97738i	0.0475039	−	0.497738i
$101$	−0.0578253	−	0.177968i	−0.00575383	−	0.0177085i	0.948138	−	0.317858i	$-0.102963\pi$
$101$	−0.0578253	−	0.177968i	−0.00575383	−	0.0177085i	−0.953892	+	0.300149i	$0.902963\pi$
$102$	2.84451	−	0.924238i	0.281649	−	0.0915132i
$103$	−7.12325	−	9.80431i	−0.701875	−	0.966048i	−0.999934	−	0.0115004i	$-0.996339\pi$
$103$	−7.12325	−	9.80431i	−0.701875	−	0.966048i	0.298059	−	0.954547i	$-0.403661\pi$
$104$	−1.75881	+	5.41305i	−0.172465	+	0.530793i
$105$	7.68974	+	8.45859i	0.750442	+	0.825474i
$106$	0.223046	+	0.162052i	0.0216641	+	0.0157399i
$107$	−0.613659	+	0.199390i	−0.0593246	+	0.0192757i	−0.338529	−	0.940956i	$-0.609929\pi$
$107$	−0.613659	+	0.199390i	−0.0593246	+	0.0192757i	0.279204	+	0.960232i	$0.409929\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	1.36671	+	0.992973i	0.130907	+	0.0951095i	0.651312	−	0.758810i	$-0.274219\pi$
$109$	1.36671	+	0.992973i	0.130907	+	0.0951095i	−0.520405	+	0.853920i	$0.674219\pi$
$110$	−3.49863	−	7.75795i	−0.333581	−	0.739691i
$111$	−7.48364	−	5.43718i	−0.710316	−	0.516075i
$112$	−3.00496	−	4.13597i	−0.283942	−	0.390812i
$113$	−14.4282	−	4.68801i	−1.35729	−	0.441010i	−0.462153	−	0.886800i	$-0.652923\pi$
$113$	−14.4282	−	4.68801i	−1.35729	−	0.441010i	−0.895138	+	0.445790i	$0.852923\pi$
$114$	−1.54476	+	1.12233i	−0.144680	+	0.105116i
$115$	−5.19115	−	11.5110i	−0.484077	−	1.07341i
$116$	−0.0664233	−	0.204430i	−0.00616725	−	0.0189808i
$117$	5.41305	+	1.75881i	0.500437	+	0.162602i
$118$		−	7.18210i		−	0.661166i
$119$	15.2905			1.40167
$120$	2.18940	+	0.454435i	0.199864	+	0.0414841i
$121$	−2.81962	−	2.04857i	−0.256329	−	0.186234i
$122$	−5.31508	−	7.31558i	−0.481205	−	0.662322i
$123$		−	10.4707i		−	0.944113i
$124$	3.70190	−	4.15883i	0.332441	−	0.373474i
$125$	3.60717	+	10.5825i	0.322635	+	0.946524i
$126$	−4.13597	+	3.00496i	−0.368461	+	0.267703i
$127$	−1.16382	+	1.60186i	−0.103273	+	0.142143i	−0.857525	−	0.514442i	$-0.827999\pi$
$127$	−1.16382	+	1.60186i	−0.103273	+	0.142143i	0.754253	+	0.656584i	$0.227999\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−2.97935			−0.262318
$130$	−1.39086	−	12.6506i	−0.121986	−	1.10953i
$131$	−0.982663	+	3.02432i	−0.0858556	+	0.264236i	−0.984763	−	0.173903i	$-0.944362\pi$
$131$	−0.982663	+	3.02432i	−0.0858556	+	0.264236i	0.898907	+	0.438139i	$0.144362\pi$
$132$	3.61967	−	1.17610i	0.315052	−	0.102367i
$133$	−9.28386	+	3.01651i	−0.805013	+	0.261565i
$134$	−6.68142	+	4.85433i	−0.577187	+	0.419351i
$135$	0.454435	−	2.18940i	0.0391116	−	0.188434i
$136$	2.41969	−	1.75800i	0.207486	−	0.150748i
$137$	8.16142	−	11.2332i	0.697278	−	0.959720i	−0.302700	−	0.953086i	$-0.597888\pi$
$137$	8.16142	−	11.2332i	0.697278	−	0.959720i	0.999978	−	0.00663451i	$-0.00211185\pi$
$138$	5.37075	−	1.74506i	0.457188	−	0.148550i
$139$	−10.4775	−	7.61234i	−0.888689	−	0.645670i	0.0468470	−	0.998902i	$-0.485083\pi$
$139$	−10.4775	−	7.61234i	−0.888689	−	0.645670i	−0.935536	+	0.353232i	$0.885083\pi$
$140$	9.92723	+	5.66834i	0.839004	+	0.479062i
$141$	1.56601	+	4.81967i	0.131882	+	0.405890i
$142$	3.96953	−	5.46360i	0.333116	−	0.458495i
$143$	−12.7326	−	17.5249i	−1.06475	−	1.46551i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	0.323318	+	0.355645i	0.0268501	+	0.0295347i
$146$	−3.66074	−	11.2666i	−0.302965	−	0.932430i
$147$	−18.1994	+	5.91335i	−1.50106	+	0.487725i
$148$	−8.79755	−	2.85850i	−0.723154	−	0.234967i
$149$	−20.6471			−1.69148			−0.845738	−	0.533598i	$-0.820839\pi$
$149$	−20.6471			−1.69148			−0.845738	+	0.533598i	$0.820839\pi$
$150$	−4.88057	+	1.08631i	−0.398497	+	0.0886966i
$151$	−1.66425	+	5.12203i	−0.135435	+	0.416825i	−0.995657	−	0.0930934i	$-0.970324\pi$
$151$	−1.66425	+	5.12203i	−0.135435	+	0.416825i	0.860223	+	0.509919i	$0.170324\pi$
$152$	−1.12233	+	1.54476i	−0.0910332	+	0.125296i
$153$	−1.75800	−	2.41969i	−0.142126	−	0.195620i
$154$	19.4573			1.56791
$155$	−3.72285	+	11.8803i	−0.299026	+	0.954245i
$156$	5.69162			0.455694
$157$	−1.34768	−	1.85493i	−0.107557	−	0.148039i	0.751845	−	0.659339i	$-0.229164\pi$
$157$	−1.34768	−	1.85493i	−0.107557	−	0.148039i	−0.859402	+	0.511300i	$0.829164\pi$
$158$	9.40312	−	12.9423i	0.748072	−	1.02963i
$159$	0.0851960	−	0.262206i	0.00675648	−	0.0207943i
$160$	2.22267	−	0.244369i	0.175718	−	0.0193191i
$161$	28.8701			2.27528
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	13.9997	−	4.54878i	1.09654	−	0.356288i	0.295771	−	0.955259i	$-0.404423\pi$
$163$	13.9997	−	4.54878i	1.09654	−	0.356288i	0.800771	+	0.598970i	$0.204423\pi$
$164$	−3.23563	−	9.95825i	−0.252660	−	0.777608i
$165$	−6.29711	+	5.72473i	−0.490230	+	0.445670i
$166$	1.46339	−	4.50387i	0.113581	−	0.349568i
$167$	4.38299	+	6.03267i	0.339166	+	0.466822i	0.944198	−	0.329379i	$-0.106839\pi$
$167$	4.38299	+	6.03267i	0.339166	+	0.466822i	−0.605032	+	0.796202i	$0.706839\pi$
$168$	−3.00496	+	4.13597i	−0.231837	+	0.319097i
$169$	−5.99324	−	18.4453i	−0.461018	−	1.41887i
$170$	−3.31618	+	5.80778i	−0.254339	+	0.445436i
$171$	1.54476	+	1.12233i	0.118131	+	0.0858269i
$172$	−2.83353	+	0.920671i	−0.216055	+	0.0702005i
$173$	−2.79490	+	3.84685i	−0.212492	+	0.292470i	−0.901937	−	0.431868i	$-0.857855\pi$
$173$	−2.79490	+	3.84685i	−0.212492	+	0.292470i	0.689445	+	0.724338i	$0.257855\pi$
$174$	−0.173898	+	0.126345i	−0.0131832	+	0.00957816i
$175$	−25.4461	−	2.42856i	−1.92354	−	0.183582i
$176$	3.07908	−	2.23708i	0.232094	−	0.168626i
$177$	−6.83058	+	2.21939i	−0.513418	+	0.166820i
$178$	−17.8878	+	5.81210i	−1.34075	+	0.435635i
$179$	0.213991	−	0.658598i	0.0159945	−	0.0492259i	−0.942741	−	0.333526i	$-0.891761\pi$
$179$	0.213991	−	0.658598i	0.0159945	−	0.0492259i	0.958735	+	0.284301i	$0.0917614\pi$
$180$	−0.244369	−	2.22267i	−0.0182142	−	0.165668i
$181$	0.649994			0.0483137			0.0241568	−	0.999708i	$-0.492310\pi$
$181$	0.649994			0.0483137			0.0241568	+	0.999708i	$0.492310\pi$
$182$	27.6733	+	8.99161i	2.05128	+	0.666503i
$183$	−5.31508	+	7.31558i	−0.392902	+	0.540783i
$184$	4.56863	−	3.31930i	0.336804	−	0.244702i
$185$	20.5604	−	2.26049i	1.51163	−	0.166194i
$186$	−5.09924	−	2.23557i	−0.373894	−	0.163920i
$187$			11.3832i			0.832422i
$188$	2.97872	+	4.09986i	0.217246	+	0.299013i
$189$	4.13597	+	3.00496i	0.300847	+	0.218578i
$190$	0.867711	−	4.18050i	0.0629504	−	0.303286i
$191$	10.7957			0.781147			0.390573	−	0.920572i	$-0.372277\pi$
$191$	10.7957			0.781147			0.390573	+	0.920572i	$0.372277\pi$
$192$			1.00000i			0.0721688i
$193$	14.9124	+	4.84534i	1.07342	+	0.348775i	0.791819	−	0.610756i	$-0.209134\pi$
$193$	14.9124	+	4.84534i	1.07342	+	0.348775i	0.281601	+	0.959532i	$0.409134\pi$
$194$	−0.471080	−	1.44984i	−0.0338216	−	0.104092i
$195$	−11.6017	+	5.23204i	−0.830812	+	0.374674i
$196$	−15.4813	+	11.2479i	−1.10581	+	0.803418i
$197$	−6.20044	−	2.01465i	−0.441763	−	0.143538i	0.0796858	−	0.996820i	$-0.474608\pi$
$197$	−6.20044	−	2.01465i	−0.441763	−	0.143538i	−0.521449	+	0.853282i	$0.674608\pi$
$198$	−2.23708	−	3.07908i	−0.158982	−	0.218820i
$199$	−8.51570	−	6.18702i	−0.603662	−	0.438586i	0.243515	−	0.969897i	$-0.421700\pi$
$199$	−8.51570	−	6.18702i	−0.603662	−	0.438586i	−0.847177	+	0.531311i	$0.821700\pi$
$200$	−4.30601	+	2.54132i	−0.304481	+	0.179698i
$201$	6.68142	+	4.85433i	0.471271	+	0.342398i
$202$	−0.109990	+	0.151389i	−0.00773888	+	0.0106517i
$203$	−1.04511	+	0.339578i	−0.0733526	+	0.0238337i
$204$	−2.41969	−	1.75800i	−0.169412	−	0.123085i
$205$	15.7496	+	17.3243i	1.10000	+	1.20998i
$206$	−3.74491	+	11.5257i	−0.260921	+	0.803031i
$207$	−3.31930	−	4.56863i	−0.230708	−	0.317542i
$208$	5.41305	−	1.75881i	0.375328	−	0.121951i
$209$	−2.24568	−	6.91149i	−0.155337	−	0.478078i
$210$	2.32323	−	11.1930i	0.160318	−	0.772388i
$211$	−3.40318			−0.234285			−0.117142	−	0.993115i	$-0.537373\pi$
$211$	−3.40318			−0.234285			−0.117142	+	0.993115i	$0.537373\pi$
$212$		−	0.275700i		−	0.0189351i
$213$	−6.42284	−	2.08691i	−0.440086	−	0.142993i
$214$	0.522009	+	0.379262i	0.0356838	+	0.0259258i
$215$	4.92948	−	4.48141i	0.336188	−	0.305630i
$216$	1.00000			0.0680414
$217$	−21.2614	−	18.9254i	−1.44332	−	1.28474i
$218$		−	1.68935i		−	0.114417i
$219$	−9.58394	+	6.96314i	−0.647622	+	0.470525i
$220$	−4.21987	+	7.39046i	−0.284504	+	0.498265i
$221$	−5.26041	+	16.1899i	−0.353853	+	1.08905i
$222$			9.25029i			0.620839i
$223$		−	18.4556i		−	1.23588i	−0.786226	−	0.617939i	$-0.787968\pi$
$223$		−	18.4556i		−	1.23588i	0.786226	−	0.617939i	$-0.212032\pi$
$224$	−1.57980	+	4.86212i	−0.105555	+	0.324864i
$225$	2.54132	+	4.30601i	0.169421	+	0.287067i
$226$	4.68801	+	14.4282i	0.311841	+	0.959749i
$227$	−11.1127	−	15.2953i	−0.737577	−	1.01519i	−0.998754	−	0.0498966i	$-0.984111\pi$
$227$	−11.1127	−	15.2953i	−0.737577	−	1.01519i	0.261178	−	0.965291i	$-0.415889\pi$
$228$	1.81597	+	0.590045i	0.120266	+	0.0390767i
$229$	21.6726	−	15.7460i	1.43216	−	1.04053i	0.442554	−	0.896742i	$-0.354073\pi$
$229$	21.6726	−	15.7460i	1.43216	−	1.04053i	0.989609	−	0.143785i	$-0.0459274\pi$
$230$	−6.26130	+	10.9657i	−0.412858	+	0.723058i
$231$	−6.01263	−	18.5050i	−0.395602	−	1.21754i
$232$	−0.126345	+	0.173898i	−0.00829493	+	0.0114170i
$233$	3.44835	−	4.74625i	0.225909	−	0.310937i	−0.680984	−	0.732298i	$-0.738448\pi$
$233$	3.44835	−	4.74625i	0.225909	−	0.310937i	0.906893	+	0.421361i	$0.138448\pi$
$234$	−1.75881	−	5.41305i	−0.114977	−	0.353862i
$235$	−9.84056	−	5.61885i	−0.641927	−	0.366533i
$236$	−5.81044	+	4.22153i	−0.378227	+	0.274798i
$237$	−15.2146	−	4.94351i	−0.988292	−	0.321116i
$238$	−8.98751	−	12.3702i	−0.582574	−	0.801844i
$239$	−7.42715	−	22.8584i	−0.480422	−	1.47859i	−0.838503	−	0.544897i	$-0.816569\pi$
$239$	−7.42715	−	22.8584i	−0.480422	−	1.47859i	0.358081	−	0.933691i	$-0.383431\pi$
$240$	−0.919253	−	2.03838i	−0.0593375	−	0.131577i
$241$	−6.53163	+	20.1023i	−0.420739	+	1.29490i	0.486276	+	0.873805i	$0.338355\pi$
$241$	−6.53163	+	20.1023i	−0.420739	+	1.29490i	−0.907016	+	0.421097i	$0.861645\pi$
$242$			3.48524i			0.224040i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.79430	+	8.59998i	−0.178887	+	0.550557i
$245$	21.2172	−	37.1586i	1.35551	−	2.37398i
$246$	−8.47099	+	6.15453i	−0.540091	+	0.392399i
$247$		−	10.8677i		−	0.691497i
$248$	−5.54049	−	0.550402i	−0.351822	−	0.0349505i
$249$	−4.73565			−0.300109
$250$	6.44115	−	9.13847i	0.407374	−	0.577968i
$251$	−6.00860	−	4.36550i	−0.379259	−	0.275548i	0.381781	−	0.924253i	$-0.375311\pi$
$251$	−6.00860	−	4.36550i	−0.379259	−	0.275548i	−0.761040	+	0.648705i	$0.775311\pi$
$252$	4.86212	+	1.57980i	0.306285	+	0.0995180i
$253$			21.4927i			1.35124i
$254$	1.98001			0.124237
$255$	6.54828	+	1.35917i	0.410069	+	0.0851145i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	27.2818	−	8.86440i	1.70179	−	0.552946i	0.712859	−	0.701307i	$-0.247400\pi$
$257$	27.2818	−	8.86440i	1.70179	−	0.552946i	0.988933	+	0.148361i	$0.0473998\pi$
$258$	1.75122	+	2.41035i	0.109026	+	0.150062i
$259$	−14.6136	+	44.9760i	−0.908045	+	2.79467i
$260$	−9.41704	+	8.56107i	−0.584020	+	0.530935i
$261$	0.173898	+	0.126345i	0.0107640	+	0.00782053i
$262$	3.02432	−	0.982663i	0.186843	−	0.0607091i
$263$	−6.02605	+	8.29415i	−0.371582	+	0.511439i	−0.953330	−	0.301930i	$-0.902369\pi$
$263$	−6.02605	+	8.29415i	−0.371582	+	0.511439i	0.581748	+	0.813369i	$0.302369\pi$
$264$	−3.07908	−	2.23708i	−0.189504	−	0.137683i
$265$	0.253438	+	0.561980i	0.0155686	+	0.0345222i
$266$	7.89732	+	5.73774i	0.484216	+	0.351803i
$267$	11.0553	+	15.2163i	0.676572	+	0.931221i
$268$	7.85448	+	2.55207i	0.479789	+	0.155893i
$269$	1.16667	−	0.847633i	0.0711329	−	0.0516811i	−0.551651	−	0.834075i	$-0.686002\pi$
$269$	1.16667	−	0.847633i	0.0711329	−	0.0516811i	0.622783	+	0.782394i	$0.286002\pi$
$270$	−2.03838	+	0.919253i	−0.124052	+	0.0559440i
$271$	−4.88687	−	15.0403i	−0.296856	−	0.913630i	−0.982592	−	0.185779i	$-0.940519\pi$
$271$	−4.88687	−	15.0403i	−0.296856	−	0.913630i	0.685735	−	0.727851i	$-0.259481\pi$
$272$	−2.84451	−	0.924238i	−0.172474	−	0.0560401i
$273$		−	29.0975i		−	1.76106i
$274$	−13.8850			−0.838826
$275$	1.80797	−	18.9437i	0.109025	−	1.14235i
$276$	−4.56863	−	3.31930i	−0.274999	−	0.199799i
$277$	−5.71485	−	7.86582i	−0.343372	−	0.472611i	0.602050	−	0.798458i	$-0.294351\pi$
$277$	−5.71485	−	7.86582i	−0.343372	−	0.472611i	−0.945423	+	0.325847i	$0.894351\pi$
$278$			12.9509i			0.776742i
$279$	−0.550402	+	5.54049i	−0.0329517	+	0.331701i
$280$	−1.24930	−	11.3631i	−0.0746598	−	0.679073i
$281$	−12.4403	+	9.03838i	−0.742124	+	0.539184i	−0.893375	−	0.449311i	$-0.851670\pi$
$281$	−12.4403	+	9.03838i	−0.742124	+	0.539184i	0.151252	+	0.988495i	$0.451670\pi$
$282$	2.97872	−	4.09986i	0.177380	−	0.244143i
$283$	1.98996	+	0.646576i	0.118291	+	0.0384349i	0.367564	−	0.929998i	$-0.380192\pi$
$283$	1.98996	+	0.646576i	0.118291	+	0.0384349i	−0.249274	+	0.968433i	$0.580192\pi$
$284$	−6.75338			−0.400739
$285$	−4.24403	+	0.466605i	−0.251395	+	0.0276393i
$286$	−6.69393	+	20.6018i	−0.395820	+	1.21821i
$287$	−50.9099	+	16.5416i	−3.00512	+	0.976422i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	−6.51626	+	4.73434i	−0.383309	+	0.278491i
$290$	0.0976810	−	0.470613i	0.00573602	−	0.0276353i
$291$	−1.23330	+	0.896048i	−0.0722976	+	0.0525273i
$292$	−6.96314	+	9.58394i	−0.407487	+	0.560857i
$293$	−19.8031	+	6.43441i	−1.15691	+	0.375902i	−0.823741	−	0.566966i	$-0.808117\pi$
$293$	−19.8031	+	6.43441i	−1.15691	+	0.375902i	−0.333166	+	0.942868i	$0.608117\pi$
$294$	15.4813	+	11.2479i	0.902890	+	0.655988i
$295$	7.96320	−	13.9463i	0.463635	−	0.811987i
$296$	2.85850	+	8.79755i	0.166147	+	0.511347i
$297$	−2.23708	+	3.07908i	−0.129809	+	0.178666i
$298$	12.1361	+	16.7039i	0.703023	+	0.967628i
$299$	−9.93223	+	30.5683i	−0.574396	+	1.76781i
$300$	3.74757	+	3.30995i	0.216366	+	0.191100i
$301$	4.70678	+	14.4860i	0.271294	+	0.834958i
$302$	5.12203	−	1.66425i	0.294740	−	0.0957668i
$303$	0.177968	+	0.0578253i	0.0102240	+	0.00332198i
$304$	1.90943			0.109513
$305$	−2.20972	−	20.0987i	−0.126528	−	1.15085i
$306$	−0.924238	+	2.84451i	−0.0528352	+	0.162610i
$307$	−8.06416	+	11.0994i	−0.460246	+	0.633474i	−0.974560	−	0.224128i	$-0.928047\pi$
$307$	−8.06416	+	11.0994i	−0.460246	+	0.633474i	0.514314	+	0.857602i	$0.328047\pi$
$308$	−11.4367	−	15.7413i	−0.651667	−	0.896942i
$309$	12.1188			0.689414
$310$	11.7996	−	3.97119i	0.670170	−	0.225548i
$311$	−11.0234			−0.625082			−0.312541	−	0.949904i	$-0.601180\pi$
$311$	−11.0234			−0.625082			−0.312541	+	0.949904i	$0.601180\pi$
$312$	−3.34545	−	4.60462i	−0.189399	−	0.260685i
$313$	0.176290	−	0.242642i	0.00996449	−	0.0137149i	−0.804006	−	0.594622i	$-0.797302\pi$
$313$	0.176290	−	0.242642i	0.00996449	−	0.0137149i	0.813970	+	0.580907i	$0.197302\pi$
$314$	−0.708518	+	2.18060i	−0.0399840	+	0.123058i
$315$	−11.3631	+	1.24930i	−0.640236	+	0.0703899i
$316$	−15.9975			−0.899932
$317$	−0.702265	−	0.228180i	−0.0394431	−	0.0128159i	0.289229	−	0.957260i	$-0.406601\pi$
$317$	−0.702265	−	0.228180i	−0.0394431	−	0.0128159i	−0.328672	+	0.944444i	$0.606601\pi$
$318$	−0.262206	+	0.0851960i	−0.0147038	+	0.00477755i
$319$	−0.252803	−	0.778049i	−0.0141543	−	0.0435624i
$320$	−1.50415	−	1.65455i	−0.0840848	−	0.0924919i
$321$	0.199390	−	0.613659i	0.0111289	−	0.0342511i
$322$	−16.9694	−	23.3564i	−0.945668	−	1.30160i
$323$	−3.35678	+	4.62021i	−0.186776	+	0.257075i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	11.3257	−	26.1073i	0.628235	−	1.44817i
$326$	−11.9089	−	8.65230i	−0.659571	−	0.479207i
$327$	−1.60666	+	0.522037i	−0.0888487	+	0.0288687i
$328$	−6.15453	+	8.47099i	−0.339827	+	0.467732i
$329$	20.9599	−	15.2282i	1.15555	−	0.839560i
$330$	8.33276	+	1.72956i	0.458703	+	0.0952090i
$331$	17.3178	−	12.5822i	0.951875	−	0.691578i	0.000625403	−	1.00000i	$-0.499801\pi$
$331$	17.3178	−	12.5822i	0.951875	−	0.691578i	0.951250	+	0.308422i	$0.0998009\pi$
$332$	−4.50387	+	1.46339i	−0.247182	+	0.0803142i
$333$	8.79755	−	2.85850i	0.482103	−	0.156645i
$334$	2.30428	−	7.09183i	0.126084	−	0.388048i
$335$	−18.3564	+	2.01817i	−1.00292	+	0.110264i
$336$	5.11234			0.278901
$337$	2.47567	+	0.804395i	0.134858	+	0.0438182i	0.375669	−	0.926754i	$-0.377413\pi$
$337$	2.47567	+	0.804395i	0.134858	+	0.0438182i	−0.240810	+	0.970572i	$0.577413\pi$
$338$	−11.3998	+	15.6905i	−0.620068	+	0.853451i
$339$	12.2734	−	8.91712i	0.666597	−	0.484311i
$340$	6.64779	−	0.730883i	0.360527	−	0.0396377i
$341$	14.0893	−	15.8283i	0.762976	−	0.857151i
$342$		−	1.90943i		−	0.103250i
$343$	36.4681	+	50.1941i	1.96909	+	2.71022i
$344$	2.41035	+	1.75122i	0.129957	+	0.0944195i
$345$	12.3639	+	2.56626i	0.665648	+	0.138163i
$346$	4.75496			0.255628
$347$			0.0333855i			0.00179223i	1.00000		0.000896113i	$0.000285242\pi$
$347$			0.0333855i			0.00179223i	−1.00000		0.000896113i	$0.999715\pi$
$348$	0.204430	+	0.0664233i	0.0109586	+	0.00356066i
$349$	−5.47898	−	16.8626i	−0.293283	−	0.902632i	−0.983793	−	0.179309i	$-0.942614\pi$
$349$	−5.47898	−	16.8626i	−0.293283	−	0.902632i	0.690510	−	0.723323i	$-0.257386\pi$
$350$	12.9921	+	22.0138i	0.694455	+	1.17669i
$351$	−4.60462	+	3.34545i	−0.245776	+	0.178567i
$352$	−3.61967	−	1.17610i	−0.192929	−	0.0626865i
$353$	17.4865	+	24.0681i	0.930713	+	1.28102i	0.959581	+	0.281434i	$0.0908099\pi$
$353$	17.4865	+	24.0681i	0.930713	+	1.28102i	−0.0288674	+	0.999583i	$0.509190\pi$
$354$	5.81044	+	4.22153i	0.308821	+	0.224372i
$355$	13.7659	−	6.20806i	0.730619	−	0.329490i
$356$	15.2163	+	11.0553i	0.806461	+	0.585928i
$357$	−8.98751	+	12.3702i	−0.475670	+	0.654703i
$358$	−0.658598	+	0.213991i	−0.0348080	+	0.0113098i
$359$	−26.6878	−	19.3899i	−1.40853	−	1.02336i	−0.993534	−	0.113534i	$-0.963783\pi$
$359$	−26.6878	−	19.3899i	−1.40853	−	1.02336i	−0.414996	−	0.909823i	$-0.636217\pi$
$360$	−1.65455	+	1.50415i	−0.0872022	+	0.0792759i
$361$	−4.74468	+	14.6026i	−0.249720	+	0.768558i
$362$	−0.382057	−	0.525856i	−0.0200805	−	0.0276384i
$363$	3.31466	−	1.07700i	0.173974	−	0.0565277i
$364$	−8.99161	−	27.6733i	−0.471289	−	1.45048i
$365$	5.38342	−	25.9365i	0.281781	−	1.35758i
$366$	9.04256			0.472662
$367$		−	3.27226i		−	0.170811i	−0.996346	−	0.0854053i	$-0.972781\pi$
$367$		−	3.27226i		−	0.170811i	0.996346	−	0.0854053i	$-0.0272185\pi$
$368$	−5.37075	−	1.74506i	−0.279970	−	0.0909676i
$369$	8.47099	+	6.15453i	0.440982	+	0.320392i
$370$	−13.9139	−	15.3050i	−0.723347	−	0.795670i
$371$	−1.40947			−0.0731761
$372$	1.18864	+	5.43941i	0.0616283	+	0.282020i
$373$			20.0566i			1.03849i	0.854625	+	0.519245i	$0.173787\pi$
$373$			20.0566i			1.03849i	−0.854625	+	0.519245i	$0.826213\pi$
$374$	9.20920	−	6.69087i	0.476196	−	0.345977i
$375$	−10.6816	−	3.30195i	−0.551597	−	0.170512i
$376$	1.56601	−	4.81967i	0.0807606	−	0.248556i
$377$		−	1.22341i		−	0.0630091i
$378$		−	5.11234i		−	0.262950i
$379$	7.27153	−	22.3795i	0.373513	−	1.14956i	−0.570963	−	0.820976i	$-0.693430\pi$
$379$	7.27153	−	22.3795i	0.373513	−	1.14956i	0.944476	−	0.328580i	$-0.106570\pi$
$380$	−3.89213	+	1.75525i	−0.199662	+	0.0900422i
$381$	−0.611858	−	1.88310i	−0.0313464	−	0.0964744i
$382$	−6.34553	−	8.73387i	−0.324666	−	0.446864i
$383$	7.04716	+	2.28976i	0.360093	+	0.117001i	0.483476	−	0.875358i	$-0.339374\pi$
$383$	7.04716	+	2.28976i	0.360093	+	0.117001i	−0.123382	+	0.992359i	$0.539374\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	37.7825	+	21.5734i	1.92558	+	1.09948i
$386$	−4.84534	−	14.9124i	−0.246621	−	0.759022i
$387$	1.75122	−	2.41035i	0.0890196	−	0.122525i
$388$	−0.896048	+	1.23330i	−0.0454900	+	0.0626115i
$389$	9.27114	+	28.5336i	0.470066	+	1.44671i	0.852498	+	0.522730i	$0.175086\pi$
$389$	9.27114	+	28.5336i	0.470066	+	1.44671i	−0.382433	+	0.923983i	$0.624914\pi$
$390$	11.0521	+	6.31062i	0.559644	+	0.319551i
$391$	13.6643	−	9.92770i	0.691033	−	0.502065i
$392$	18.1994	+	5.91335i	0.919209	+	0.298669i
$393$	−1.86914	−	2.57264i	−0.0942854	−	0.129773i
$394$	2.01465	+	6.20044i	0.101496	+	0.312374i
$395$	32.6090	−	14.7058i	1.64074	−	0.739929i
$396$	−1.17610	+	3.61967i	−0.0591014	+	0.181895i
$397$		−	21.1577i		−	1.06187i	−0.847411	−	0.530937i	$-0.821840\pi$
$397$		−	21.1577i		−	1.06187i	0.847411	−	0.530937i	$-0.178160\pi$
$398$			10.5260i			0.527620i
$399$	3.01651	−	9.28386i	0.151014	−	0.464774i
$400$	4.58698	+	1.98989i	0.229349	+	0.0994943i
$401$	−14.7795	+	10.7379i	−0.738053	+	0.536227i	−0.892101	−	0.451837i	$-0.850769\pi$
$401$	−14.7795	+	10.7379i	−0.738053	+	0.536227i	0.154048	+	0.988063i	$0.450769\pi$
$402$		−	8.25869i		−	0.411906i
$403$	27.3532	−	16.0011i	1.36256	−	0.797069i
$404$	0.187127			0.00930989
$405$	1.50415	+	1.65455i	0.0747420	+	0.0822150i
$406$	0.889027	+	0.645916i	0.0441217	+	0.0320563i
$407$	−33.4830	−	10.8793i	−1.65969	−	0.539266i
$408$			2.99090i			0.148071i
$409$	11.8585			0.586365			0.293183	−	0.956056i	$-0.405286\pi$
$409$	11.8585			0.586365			0.293183	+	0.956056i	$0.405286\pi$
$410$	4.75827	−	22.9246i	0.234994	−	1.13217i
$411$	4.29072	+	13.2055i	0.211645	+	0.651377i
$412$	11.5257	−	3.74491i	0.567829	−	0.184499i
$413$	21.5819	+	29.7049i	1.06198	+	1.46168i
$414$	−1.74506	+	5.37075i	−0.0857651	+	0.263958i
$415$	7.83534	−	7.12314i	0.384622	−	0.349661i
$416$	−4.60462	−	3.34545i	−0.225760	−	0.164024i
$417$	12.3170	−	4.00204i	0.603167	−	0.195981i
$418$	−4.27154	+	5.87927i	−0.208928	+	0.287564i
$419$	11.3531	+	8.24850i	0.554635	+	0.402966i	0.829491	−	0.558519i	$-0.188630\pi$
$419$	11.3531	+	8.24850i	0.554635	+	0.402966i	−0.274857	+	0.961485i	$0.588630\pi$
$420$	−10.4209	+	4.69953i	−0.508486	+	0.229314i
$421$	24.7558	+	17.9862i	1.20652	+	0.876592i	0.994911	−	0.100762i	$-0.0321279\pi$
$421$	24.7558	+	17.9862i	1.20652	+	0.876592i	0.211614	+	0.977353i	$0.432128\pi$
$422$	2.00034	+	2.75323i	0.0973750	+	0.134025i
$423$	−4.81967	−	1.56601i	−0.234341	−	0.0761419i
$424$	−0.223046	+	0.162052i	−0.0108321	+	0.00786996i
$425$	−12.8788	+	7.60082i	−0.624715	+	0.368694i
$426$	2.08691	+	6.42284i	0.101111	+	0.311188i
$427$	43.9660	+	14.2854i	2.12766	+	0.691320i
$428$		−	0.645239i		−	0.0311888i
$429$	21.6620			1.04585
$430$	−6.52301	−	1.35392i	−0.314567	−	0.0652920i
$431$	−22.4832	−	16.3350i	−1.08298	−	0.786829i	−0.104778	−	0.994496i	$-0.533413\pi$
$431$	−22.4832	−	16.3350i	−1.08298	−	0.786829i	−0.978200	+	0.207666i	$0.933413\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$		−	13.8965i		−	0.667821i	−0.942605	−	0.333911i	$-0.891632\pi$
$433$		−	13.8965i		−	0.667821i	0.942605	−	0.333911i	$-0.108368\pi$
$434$	−2.81384	+	28.3249i	−0.135069	+	1.35964i
$435$	−0.477764	+	0.0525272i	−0.0229070	+	0.00251849i
$436$	−1.36671	+	0.992973i	−0.0654535	+	0.0475548i
$437$	−6.33797	+	8.72346i	−0.303186	+	0.417300i
$438$	11.2666	+	3.66074i	0.538339	+	0.174917i
$439$	19.7781			0.943959			0.471979	−	0.881610i	$-0.343540\pi$
$439$	19.7781			0.943959			0.471979	+	0.881610i	$0.343540\pi$
$440$	8.45938	−	0.930056i	0.403285	−	0.0443387i
$441$	5.91335	−	18.1994i	0.281588	−	0.866638i
$442$	16.1899	−	5.26041i	0.770074	−	0.250212i
$443$	26.9304	−	8.75023i	1.27950	−	0.415736i	0.411098	−	0.911591i	$-0.365145\pi$
$443$	26.9304	−	8.75023i	1.27950	−	0.415736i	0.868405	+	0.495855i	$0.165145\pi$
$444$	7.48364	−	5.43718i	0.355158	−	0.258037i
$445$	−41.1791	−	8.54718i	−1.95208	−	0.405175i
$446$	−14.9309	+	10.8479i	−0.706999	+	0.513665i
$447$	12.1361	−	16.7039i	0.574016	−	0.790065i
$448$	4.86212	−	1.57980i	0.229714	−	0.0746385i
$449$	−6.44266	−	4.68087i	−0.304048	−	0.220904i	0.425290	−	0.905057i	$-0.360172\pi$
$449$	−6.44266	−	4.68087i	−0.304048	−	0.220904i	−0.729338	+	0.684153i	$0.760172\pi$
$450$	1.98989	−	4.58698i	0.0938041	−	0.216232i
$451$	−12.3146	−	37.9006i	−0.579874	−	1.78467i
$452$	8.91712	−	12.2734i	0.419426	−	0.577290i
$453$	−3.16559	−	4.35706i	−0.148732	−	0.204713i
$454$	−5.84230	+	17.9808i	−0.274193	+	0.843878i
$455$	43.7671	+	48.1431i	2.05183	+	2.25698i
$456$	−0.590045	−	1.81597i	−0.0276314	−	0.0850407i
$457$	1.48606	−	0.482851i	0.0695151	−	0.0225868i	−0.274053	−	0.961715i	$-0.588364\pi$
$457$	1.48606	−	0.482851i	0.0695151	−	0.0225868i	0.343568	+	0.939128i	$0.388364\pi$
$458$	−25.4776	−	8.27818i	−1.19049	−	0.386814i
$459$	2.99090			0.139603
$460$	12.5518	−	1.37999i	0.585229	−	0.0643422i
$461$	0.616321	−	1.89684i	0.0287049	−	0.0883447i	−0.935678	−	0.352856i	$-0.885211\pi$
$461$	0.616321	−	1.89684i	0.0287049	−	0.0883447i	0.964383	+	0.264511i	$0.0852106\pi$
$462$	−11.4367	+	15.7413i	−0.532084	+	0.732350i
$463$	11.9704	+	16.4759i	0.556314	+	0.765700i	0.990852	−	0.134953i	$-0.0430884\pi$
$463$	11.9704	+	16.4759i	0.556314	+	0.765700i	−0.434538	+	0.900653i	$0.643088\pi$
$464$	0.214950			0.00997881
$465$	−7.42309	−	9.99488i	−0.344238	−	0.463502i
$466$	−5.86668			−0.271769
$467$	5.63759	+	7.75948i	0.260877	+	0.359066i	0.919283	−	0.393596i	$-0.128769\pi$
$467$	5.63759	+	7.75948i	0.260877	+	0.359066i	−0.658407	+	0.752662i	$0.728769\pi$
$468$	−3.34545	+	4.60462i	−0.154643	+	0.212848i
$469$	13.0471	−	40.1547i	0.602457	−	1.85417i
$470$	1.23839	+	11.2639i	0.0571227	+	0.519563i
$471$	2.29281			0.105647
$472$	6.83058	+	2.21939i	0.314403	+	0.102156i
$473$	−10.7843	+	3.50403i	−0.495862	+	0.161115i
$474$	4.94351	+	15.2146i	0.227063	+	0.698828i
$475$	6.32010	−	7.15570i	0.289986	−	0.328326i
$476$	−4.72501	+	14.5421i	−0.216571	+	0.666536i
$477$	0.162052	+	0.223046i	0.00741987	+	0.0102126i
$478$	−14.1273	+	19.4445i	−0.646166	+	0.889372i
$479$	−3.89911	−	12.0002i	−0.178155	−	0.548305i	0.821608	−	0.570052i	$-0.193077\pi$
$479$	−3.89911	−	12.0002i	−0.178155	−	0.548305i	−0.999763	+	0.0217473i	$0.993077\pi$
$480$	−1.10876	+	1.94182i	−0.0506076	+	0.0886315i
$481$	−42.5940	−	30.9464i	−1.94212	−	1.41103i
$482$	20.1023	−	6.53163i	0.915634	−	0.297508i
$483$	−16.9694	+	23.3564i	−0.772135	+	1.06275i
$484$	2.81962	−	2.04857i	0.128164	−	0.0931169i
$485$	0.692763	−	3.33763i	0.0314568	−	0.151554i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−5.70263	+	1.85290i	−0.258411	+	0.0839627i	−0.435357	−	0.900258i	$-0.643378\pi$
$487$	−5.70263	+	1.85290i	−0.258411	+	0.0839627i	0.176947	+	0.984220i	$0.443378\pi$
$488$	8.59998	−	2.79430i	0.389303	−	0.126492i
$489$	−4.54878	+	13.9997i	−0.205703	+	0.633089i
$490$	−42.5331	+	4.67625i	−1.92145	+	0.211251i
$491$	−12.6851			−0.572469			−0.286235	−	0.958160i	$-0.592404\pi$
$491$	−12.6851			−0.572469			−0.286235	+	0.958160i	$0.592404\pi$
$492$	9.95825	+	3.23563i	0.448952	+	0.145873i
$493$	−0.377883	+	0.520112i	−0.0170190	+	0.0234247i
$494$	−8.79217	+	6.38789i	−0.395579	+	0.287405i
$495$	−0.930056	−	8.45938i	−0.0418029	−	0.380221i
$496$	2.81134	+	4.80587i	0.126233	+	0.215790i
$497$			34.5255i			1.54868i
$498$	2.78354	+	3.83122i	0.124734	+	0.171681i
$499$	−12.4609	−	9.05338i	−0.557827	−	0.405285i	0.272836	−	0.962061i	$-0.412038\pi$
$499$	−12.4609	−	9.05338i	−0.557827	−	0.405285i	−0.830663	+	0.556776i	$0.812038\pi$
$500$	−11.1792	+	0.160461i	−0.499949	+	0.00717603i
$501$	−7.45679			−0.333145
$502$			7.42704i			0.331485i
$503$	−8.27037	−	2.68721i	−0.368758	−	0.119817i	0.118775	−	0.992921i	$-0.462103\pi$
$503$	−8.27037	−	2.68721i	−0.368758	−	0.119817i	−0.487533	+	0.873105i	$0.662103\pi$
$504$	−1.57980	−	4.86212i	−0.0703698	−	0.216576i
$505$	−0.381434	+	0.172017i	−0.0169736	+	0.00765464i
$506$	17.3880	−	12.6331i	0.772990	−	0.561610i
$507$	18.4453	+	5.99324i	0.819184	+	0.266169i
$508$	−1.16382	−	1.60186i	−0.0516363	−	0.0710713i
$509$	−18.1283	−	13.1710i	−0.803522	−	0.583793i	0.108423	−	0.994105i	$-0.465420\pi$
$509$	−18.1283	−	13.1710i	−0.803522	−	0.583793i	−0.911945	+	0.410312i	$0.865420\pi$
$510$	−2.74939	−	6.09657i	−0.121745	−	0.269961i
$511$	48.9963	+	35.5979i	2.16747	+	1.57476i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−1.81597	+	0.590045i	−0.0801771	+	0.0260511i
$514$	−23.2073	−	16.8611i	−1.02363	−	0.743711i
$515$	−20.0511	+	18.2285i	−0.883557	+	0.803246i
$516$	0.920671	−	2.83353i	0.0405303	−	0.124739i
$517$	11.3369	+	15.6038i	0.498595	+	0.686256i
$518$	44.9760	−	14.6136i	1.97613	−	0.642084i
$519$	−1.46936	−	4.52224i	−0.0644979	−	0.198504i
$520$	12.4613	+	2.58647i	0.546462	+	0.113424i
$521$	−15.8119			−0.692730			−0.346365	−	0.938100i	$-0.612584\pi$
$521$	−15.8119			−0.692730			−0.346365	+	0.938100i	$0.612584\pi$
$522$		−	0.214950i		−	0.00940811i
$523$	−25.0814	−	8.14944i	−1.09673	−	0.356350i	−0.295888	−	0.955223i	$-0.595616\pi$
$523$	−25.0814	−	8.14944i	−1.09673	−	0.356350i	−0.800844	+	0.598873i	$0.795616\pi$
$524$	−2.57264	−	1.86914i	−0.112386	−	0.0816536i
$525$	16.9216	−	19.1588i	0.738518	−	0.836159i
$526$	10.2521			0.447014
$527$	−16.5710	−	1.64619i	−0.721846	−	0.0717093i
$528$			3.80595i			0.165633i
$529$	7.19230	−	5.22551i	0.312709	−	0.227196i
$530$	0.305684	−	0.535359i	0.0132781	−	0.0232545i
$531$	2.21939	−	6.83058i	0.0963133	−	0.296422i
$532$		−	9.76163i		−	0.423220i
$533$		−	59.5953i		−	2.58136i
$534$	5.81210	−	17.8878i	0.251514	−	0.774081i
$535$	0.593138	+	1.31524i	0.0256436	+	0.0568628i
$536$	−2.55207	−	7.85448i	−0.110233	−	0.339262i
$537$	0.407036	+	0.560237i	0.0175649	+	0.0241760i
$538$	−1.37150	−	0.445627i	−0.0591295	−	0.0192123i
$539$	−58.9212	+	42.8087i	−2.53791	+	1.84390i
$540$	1.94182	+	1.10876i	0.0835626	+	0.0477133i
$541$	−1.27295	−	3.91773i	−0.0547283	−	0.168436i	0.919956	−	0.392021i	$-0.128224\pi$
$541$	−1.27295	−	3.91773i	−0.0547283	−	0.168436i	−0.974684	+	0.223585i	$0.928224\pi$
$542$	−9.29539	+	12.7940i	−0.399271	+	0.549549i
$543$	−0.382057	+	0.525856i	−0.0163956	+	0.0225667i
$544$	0.924238	+	2.84451i	0.0396264	+	0.121957i
$545$	1.87307	−	3.28040i	0.0802337	−	0.140517i
$546$	−23.5404	+	17.1031i	−1.00743	+	0.731944i
$547$	−4.17535	−	1.35665i	−0.178525	−	0.0580063i	0.218390	−	0.975861i	$-0.429919\pi$
$547$	−4.17535	−	1.35665i	−0.178525	−	0.0580063i	−0.396915	+	0.917855i	$0.629919\pi$
$548$	8.16142	+	11.2332i	0.348639	+	0.479860i
$549$	−2.79430	−	8.59998i	−0.119258	−	0.367038i
$550$	−16.3884	+	9.67212i	−0.698805	+	0.412421i
$551$	0.126830	−	0.390344i	0.00540315	−	0.0166292i
$552$			5.64714i			0.240358i
$553$			81.7848i			3.47784i
$554$	−3.00448	+	9.24682i	−0.127648	+	0.392860i
$555$	−10.2563	+	17.9624i	−0.435356	+	0.762460i
$556$	10.4775	−	7.61234i	0.444344	−	0.322835i
$557$			9.06908i			0.384269i	0.981369	+	0.192135i	$0.0615411\pi$
$557$			9.06908i			0.384269i	−0.981369	+	0.192135i	$0.938459\pi$
$558$	4.80587	−	2.81134i	0.203449	−	0.119013i
$559$	−16.9574			−0.717220
$560$	−8.45859	+	7.68974i	−0.357441	+	0.324951i
$561$	−9.20920	−	6.69087i	−0.388813	−	0.282489i
$562$	14.6244	+	4.75176i	0.616893	+	0.200441i
$563$		−	13.4356i		−	0.566243i	−0.959084	−	0.283122i	$-0.908630\pi$
$563$		−	13.4356i		−	0.566243i	0.959084	−	0.283122i	$-0.0913700\pi$
$564$	−5.06770			−0.213389
$565$	−6.89410	+	33.2148i	−0.290037	+	1.39736i
$566$	−0.646576	−	1.98996i	−0.0271776	−	0.0836441i
$567$	−4.86212	+	1.57980i	−0.204190	+	0.0663453i
$568$	3.96953	+	5.46360i	0.166558	+	0.229247i
$569$	8.77598	−	27.0097i	0.367908	−	1.13231i	−0.580231	−	0.814452i	$-0.697038\pi$
$569$	8.77598	−	27.0097i	0.367908	−	1.13231i	0.948140	−	0.317854i	$-0.102962\pi$
$570$	2.87207	+	3.15923i	0.120298	+	0.132326i
$571$	21.7853	+	15.8279i	0.911685	+	0.662378i	0.941440	−	0.337180i	$-0.109473\pi$
$571$	21.7853	+	15.8279i	0.911685	+	0.662378i	−0.0297558	+	0.999557i	$0.509473\pi$
$572$	20.6018	−	6.69393i	0.861404	−	0.279887i
$573$	−6.34553	+	8.73387i	−0.265088	+	0.364863i
$574$	43.3066	+	31.4641i	1.80758	+	1.31328i
$575$	−24.3166	+	14.3512i	−1.01407	+	0.598485i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−18.1326	−	24.9574i	−0.754870	−	1.03899i	−0.997623	−	0.0689012i	$-0.978051\pi$
$577$	−18.1326	−	24.9574i	−0.754870	−	1.03899i	0.242754	−	0.970088i	$-0.421949\pi$
$578$	7.66032	+	2.48899i	0.318627	+	0.103528i
$579$	−12.6853	+	9.21639i	−0.527182	+	0.383020i
$580$	−0.438149	+	0.197594i	−0.0181932	+	0.00820463i
$581$	7.48137	+	23.0253i	0.310379	+	0.955250i
$582$	1.44984	+	0.471080i	0.0600976	+	0.0195269i
$583$		−	1.04930i		−	0.0434575i
$584$	11.8464			0.490207
$585$	2.58647	−	12.4613i	0.106938	−	0.515209i
$586$	16.8455	+	12.2390i	0.695881	+	0.505587i
$587$	16.7381	+	23.0381i	0.690857	+	0.950883i	1.00000		0.000132644i	$-4.22219e-5\pi$
$587$	16.7381	+	23.0381i	0.690857	+	0.950883i	−0.309143	+	0.951016i	$0.600042\pi$
$588$		−	19.1360i		−	0.789155i
$589$	10.3861	−	2.26963i	0.427953	−	0.0935183i
$590$	−15.9635	+	1.75508i	−0.657206	+	0.0722556i
$591$	5.27441	−	3.83208i	0.216960	−	0.157631i
$592$	5.43718	−	7.48364i	0.223467	−	0.307576i
$593$	−19.7269	−	6.40966i	−0.810087	−	0.263213i	−0.125452	−	0.992100i	$-0.540038\pi$
$593$	−19.7269	−	6.40966i	−0.810087	−	0.263213i	−0.684634	+	0.728887i	$0.740038\pi$
$594$	3.80595			0.156160
$595$	−3.73652	−	33.9857i	−0.153182	−	1.39328i
$596$	6.38030	−	19.6366i	0.261347	−	0.804345i
$597$	10.0108	−	3.25271i	0.409715	−	0.133124i
$598$	30.5683	−	9.93223i	1.25003	−	0.406159i
$599$	15.1117	−	10.9793i	0.617447	−	0.448601i	−0.234582	−	0.972096i	$-0.575372\pi$
$599$	15.1117	−	10.9793i	0.617447	−	0.448601i	0.852029	+	0.523495i	$0.175372\pi$
$600$	0.475039	−	4.97738i	0.0193934	−	0.203201i
$601$	−36.1252	+	26.2465i	−1.47358	+	1.07062i	−0.494020	+	0.869450i	$0.664473\pi$
$601$	−36.1252	+	26.2465i	−1.47358	+	1.07062i	−0.979557	+	0.201166i	$0.935527\pi$
$602$	8.95283	−	12.3225i	0.364890	−	0.502228i
$603$	−7.85448	+	2.55207i	−0.319859	+	0.103929i
$604$	−4.35706	−	3.16559i	−0.177286	−	0.128806i
$605$	−3.86428	+	6.76770i	−0.157105	+	0.275146i
$606$	−0.0578253	−	0.177968i	−0.00234899	−	0.00722945i
$607$	9.78049	−	13.4617i	0.396978	−	0.546393i	−0.563005	−	0.826454i	$-0.690355\pi$
$607$	9.78049	−	13.4617i	0.396978	−	0.546393i	0.959982	+	0.280061i	$0.0903547\pi$
$608$	−1.12233	−	1.54476i	−0.0455166	−	0.0626482i
$609$	0.339578	−	1.04511i	0.0137604	−	0.0423502i
$610$	−14.9613	+	13.6014i	−0.605766	+	0.550705i
$611$	8.91311	+	27.4317i	0.360586	+	1.10977i
$612$	2.84451	−	0.924238i	0.114983	−	0.0373601i
$613$	22.2447	+	7.22776i	0.898457	+	0.291926i	0.721600	−	0.692310i	$-0.243407\pi$
$613$	22.2447	+	7.22776i	0.898457	+	0.291926i	0.176857	+	0.984237i	$0.443407\pi$
$614$	13.7196			0.553676
$615$	−23.2730	+	2.55872i	−0.938458	+	0.103178i
$616$	−6.01263	+	18.5050i	−0.242256	+	0.745587i
$617$	17.3683	−	23.9054i	0.699222	−	0.962396i	−0.300741	−	0.953706i	$-0.597234\pi$
$617$	17.3683	−	23.9054i	0.699222	−	0.962396i	0.999962	−	0.00869005i	$-0.00276616\pi$
$618$	−7.12325	−	9.80431i	−0.286539	−	0.394387i
$619$	−10.4893			−0.421600			−0.210800	−	0.977529i	$-0.567607\pi$
$619$	−10.4893			−0.421600			−0.210800	+	0.977529i	$0.567607\pi$
$620$	−10.1484	−	7.21184i	−0.407568	−	0.289634i
$621$	5.64714			0.226612
$622$	6.47941	+	8.91815i	0.259801	+	0.357585i
$623$	56.5183	−	77.7908i	2.26436	−	3.11662i
$624$	−1.75881	+	5.41305i	−0.0704086	+	0.216695i
$625$	22.6399	−	10.6036i	0.905595	−	0.424143i
$626$	−0.299922			−0.0119873
$627$	6.91149	+	2.24568i	0.276018	+	0.0896838i
$628$	2.18060	−	0.708518i	0.0870152	−	0.0282730i
$629$	8.54946	+	26.3125i	0.340889	+	1.04915i
$630$	7.68974	+	8.45859i	0.306367	+	0.336998i
$631$	4.93312	−	15.1826i	0.196384	−	0.604409i	−0.803573	−	0.595206i	$-0.797071\pi$
$631$	4.93312	−	15.1826i	0.196384	−	0.604409i	0.999958	−	0.00920301i	$-0.00292945\pi$
$632$	9.40312	+	12.9423i	0.374036	+	0.514816i
$633$	2.00034	−	2.75323i	0.0795064	−	0.109431i
$634$	0.228180	+	0.702265i	0.00906218	+	0.0278905i
$635$	3.84483	+	2.19535i	0.152577	+	0.0871199i
$636$	0.223046	+	0.162052i	0.00884435	+	0.00642579i
$637$	−103.584	+	33.6565i	−4.10415	+	1.33352i
$638$	−0.480861	+	0.661848i	−0.0190375	+	0.0262028i
$639$	5.46360	−	3.96953i	0.216136	−	0.157032i
$640$	−0.454435	+	2.18940i	−0.0179631	+	0.0865438i
$641$	−4.40743	+	3.20219i	−0.174083	+	0.126479i	−0.671415	−	0.741082i	$-0.734313\pi$
$641$	−4.40743	+	3.20219i	−0.174083	+	0.126479i	0.497332	+	0.867560i	$0.334313\pi$
$642$	−0.613659	+	0.199390i	−0.0242192	+	0.00786929i
$643$	−1.31988	+	0.428855i	−0.0520510	+	0.0169124i	−0.334927	−	0.942244i	$-0.608712\pi$
$643$	−1.31988	+	0.428855i	−0.0520510	+	0.0169124i	0.282876	+	0.959157i	$0.408712\pi$
$644$	−8.92134	+	27.4571i	−0.351550	+	1.08196i
$645$	0.728063	+	6.62214i	0.0286674	+	0.260746i
$646$	5.71089			0.224692
$647$	−14.9145	−	4.84603i	−0.586351	−	0.190517i	0.000792846	−	1.00000i	$-0.499748\pi$
$647$	−14.9145	−	4.84603i	−0.586351	−	0.190517i	−0.587144	+	0.809483i	$0.699748\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	−22.1142	+	16.0669i	−0.868059	+	0.630682i
$650$	−27.7783	+	6.18284i	−1.08956	+	0.242511i
$651$	27.8081	−	6.07674i	1.08988	−	0.238166i
$652$			14.7202i			0.576487i
$653$	11.4210	+	15.7197i	0.446939	+	0.615158i	0.971736	−	0.236069i	$-0.0758591\pi$
$653$	11.4210	+	15.7197i	0.446939	+	0.615158i	−0.524798	+	0.851227i	$0.675859\pi$
$654$	1.36671	+	0.992973i	0.0534426	+	0.0388283i
$655$	6.96222	+	1.44509i	0.272037	+	0.0564643i
$656$	10.4707			0.408813
$657$		−	11.8464i		−	0.462172i
$658$	−24.6398	−	8.00595i	−0.960559	−	0.312105i
$659$	3.85945	+	11.8782i	0.150343	+	0.462708i	0.997659	−	0.0683807i	$-0.0217832\pi$
$659$	3.85945	+	11.8782i	0.150343	+	0.462708i	−0.847316	+	0.531088i	$0.821783\pi$
$660$	−3.49863	−	7.75795i	−0.136184	−	0.301978i
$661$	40.0583	−	29.1041i	1.55809	−	1.13202i	0.620535	−	0.784179i	$-0.286915\pi$
$661$	40.0583	−	29.1041i	1.55809	−	1.13202i	0.937554	−	0.347839i	$-0.113085\pi$
$662$	−20.3584	−	6.61483i	−0.791250	−	0.257093i
$663$	−10.0059	−	13.7719i	−0.388597	−	0.534857i
$664$	3.83122	+	2.78354i	0.148680	+	0.108022i
$665$	8.97341	+	19.8979i	0.347974	+	0.771606i
$666$	−7.48364	−	5.43718i	−0.289985	−	0.210687i
$667$	−0.713485	+	0.982028i	−0.0276263	+	0.0380243i
$668$	−7.09183	+	2.30428i	−0.274391	+	0.0891551i
$669$	14.9309	+	10.8479i	0.577262	+	0.419405i
$670$	12.4223	+	13.6644i	0.479917	+	0.527901i
$671$	−10.6350	+	32.7311i	−0.410559	+	1.26357i
$672$	−3.00496	−	4.13597i	−0.115919	−	0.159548i
$673$	25.6257	−	8.32628i	0.987796	−	0.320955i	0.229818	−	0.973234i	$-0.426187\pi$
$673$	25.6257	−	8.32628i	0.987796	−	0.320955i	0.757979	+	0.652279i	$0.226187\pi$
$674$	−0.804395	−	2.47567i	−0.0309841	−	0.0953593i
$675$	−4.97738	−	0.475039i	−0.191580	−	0.0182843i
$676$	19.3945			0.745943
$677$		−	41.1522i		−	1.58161i	−0.612069	−	0.790804i	$-0.709663\pi$
$677$		−	41.1522i		−	1.58161i	0.612069	−	0.790804i	$-0.290337\pi$
$678$	−14.4282	−	4.68801i	−0.554112	−	0.180042i
$679$	6.30507	+	4.58090i	0.241966	+	0.175799i
$680$	−4.49877	−	4.94857i	−0.172520	−	0.189769i
$681$	18.9061			0.724483
$682$	−21.0868	−	2.09480i	−0.807456	−	0.0802140i
$683$		−	39.0702i		−	1.49498i	−0.664274	−	0.747489i	$-0.731259\pi$
$683$		−	39.0702i		−	1.49498i	0.664274	−	0.747489i	$-0.268741\pi$
$684$	−1.54476	+	1.12233i	−0.0590653	+	0.0429135i
$685$	−26.9622	−	15.3951i	−1.03017	−	0.588218i
$686$	19.1724	−	59.0067i	0.732007	−	2.25288i
$687$			26.7887i			1.02205i
$688$		−	2.97935i		−	0.113587i
$689$	0.484903	−	1.49238i	0.0184733	−	0.0568551i
$690$	−5.19115	−	11.5110i	−0.197624	−	0.438216i
$691$	−11.8523	−	36.4778i	−0.450884	−	1.38768i	−0.875900	−	0.482493i	$-0.839731\pi$
$691$	−11.8523	−	36.4778i	−0.450884	−	1.38768i	0.425016	−	0.905186i	$-0.360269\pi$
$692$	−2.79490	−	3.84685i	−0.106246	−	0.146235i
$693$	18.5050	+	6.01263i	0.702946	+	0.228401i
$694$	0.0270094	−	0.0196235i	0.00102526	−	0.000744897i
$695$	−14.3594	+	25.1483i	−0.544682	+	0.953928i
$696$	−0.0664233	−	0.204430i	−0.00251777	−	0.00774889i
$697$	−18.4076	+	25.3358i	−0.697236	+	0.959664i
$698$	−10.4216	+	14.3441i	−0.394465	+	0.542934i
$699$	1.81290	+	5.57955i	0.0685704	+	0.211038i
$700$	10.1730	−	23.4502i	0.384502	−	0.886333i
$701$	−13.0905	+	9.51081i	−0.494422	+	0.359218i	−0.806882	−	0.590712i	$-0.798847\pi$
$701$	−13.0905	+	9.51081i	−0.494422	+	0.359218i	0.312461	+	0.949931i	$0.398847\pi$
$702$	5.41305	+	1.75881i	0.204302	+	0.0663819i
$703$	−10.3819	−	14.2895i	−0.391561	−	0.538937i
$704$	1.17610	+	3.61967i	0.0443260	+	0.136421i
$705$	10.3299	−	4.65850i	0.389046	−	0.175449i
$706$	9.19320	−	28.2938i	0.345991	−	1.06485i
$707$		−	0.956654i		−	0.0359787i
$708$		−	7.18210i		−	0.269920i
$709$	−4.36643	+	13.4385i	−0.163985	+	0.504693i	−0.998960	−	0.0455943i	$-0.985482\pi$
$709$	−4.36643	+	13.4385i	−0.163985	+	0.504693i	0.834975	+	0.550287i	$0.185482\pi$
$710$	−13.1138	−	7.48785i	−0.492153	−	0.281014i
$711$	12.9423	−	9.40312i	0.485374	−	0.352645i
$712$		−	18.8084i		−	0.704873i
$713$	−31.2879	−	3.10819i	−1.17174	−	0.116403i
$714$	15.2905			0.572231
$715$	−35.8408	+	32.5830i	−1.34037	+	1.21853i
$716$	0.560237	+	0.407036i	0.0209370	+	0.0152116i
$717$	22.8584	+	7.42715i	0.853663	+	0.277372i
$718$			32.9880i			1.23110i
$719$	2.28106			0.0850690			0.0425345	−	0.999095i	$-0.486457\pi$
$719$	2.28106			0.0850690			0.0425345	+	0.999095i	$0.486457\pi$
$720$	2.18940	+	0.454435i	0.0815943	+	0.0169358i
$721$	−19.1453	−	58.9231i	−0.713007	−	2.19441i
$722$	14.6026	−	4.74468i	0.543453	−	0.176579i
$723$	−12.4239	−	17.1000i	−0.462050	−	0.635957i
$724$	−0.200859	+	0.618181i	−0.00746487	+	0.0229745i
$725$	0.711474	−	0.805540i	0.0264235	−	0.0299170i
$726$	−2.81962	−	2.04857i	−0.104646	−	0.0760296i
$727$	37.2104	−	12.0904i	1.38006	−	0.448407i	0.477368	−	0.878703i	$-0.341591\pi$
$727$	37.2104	−	12.0904i	1.38006	−	0.448407i	0.902688	+	0.430296i	$0.141591\pi$
$728$	−17.1031	+	23.5404i	−0.633882	+	0.872463i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−24.1474	+	10.8898i	−0.893735	+	0.403051i
$731$	7.20910	+	5.23772i	0.266638	+	0.193724i
$732$	−5.31508	−	7.31558i	−0.196451	−	0.270392i
$733$	1.95195	+	0.634227i	0.0720969	+	0.0234257i	0.344843	−	0.938660i	$-0.387932\pi$
$733$	1.95195	+	0.634227i	0.0720969	+	0.0234257i	−0.272746	+	0.962086i	$0.587932\pi$
$734$	−2.64731	+	1.92339i	−0.0977141	+	0.0709935i
$735$	17.5908	+	39.0063i	0.648847	+	1.43877i
$736$	1.74506	+	5.37075i	0.0643238	+	0.197968i
$737$	29.8937	+	9.71306i	1.10115	+	0.357785i
$738$		−	10.4707i		−	0.385432i
$739$	−35.4181			−1.30288			−0.651438	−	0.758702i	$-0.725834\pi$
$739$	−35.4181			−1.30288			−0.651438	+	0.758702i	$0.725834\pi$
$740$	−4.20366	+	20.2526i	−0.154530	+	0.744501i
$741$	8.79217	+	6.38789i	0.322989	+	0.234665i
$742$	0.828466	+	1.14029i	0.0304140	+	0.0418612i
$743$			21.1617i			0.776346i	0.921587	+	0.388173i	$0.126894\pi$
$743$			21.1617i			0.776346i	−0.921587	+	0.388173i	$0.873106\pi$
$744$	3.70190	−	4.15883i	0.135718	−	0.152470i
$745$	5.04551	+	45.8918i	0.184853	+	1.68134i
$746$	16.2261	−	11.7890i	0.594080	−	0.431624i
$747$	2.78354	−	3.83122i	0.101844	−	0.140177i
$748$	−10.8261	−	3.51760i	−0.395840	−	0.128616i
$749$	−3.29868			−0.120531
$750$	3.60717	+	10.5825i	0.131715	+	0.386417i
$751$	11.9727	−	36.8483i	0.436892	−	1.34461i	−0.454244	−	0.890877i	$-0.650090\pi$
$751$	11.9727	−	36.8483i	0.436892	−	1.34461i	0.891135	−	0.453737i	$-0.149910\pi$
$752$	−4.81967	+	1.56601i	−0.175755	+	0.0571064i
$753$	7.06353	−	2.29508i	0.257409	−	0.0836374i
$754$	−0.989763	+	0.719105i	−0.0360450	+	0.0261883i
$755$	11.7913	+	2.44742i	0.429130	+	0.0890707i
$756$	−4.13597	+	3.00496i	−0.150424	+	0.109289i
$757$	6.36982	−	8.76730i	0.231515	−	0.318653i	−0.677416	−	0.735601i	$-0.736900\pi$
$757$	6.36982	−	8.76730i	0.231515	−	0.318653i	0.908931	+	0.416947i	$0.136900\pi$
$758$	−22.3795	+	7.27153i	−0.812859	+	0.264114i
$759$	−17.3880	−	12.6331i	−0.631143	−	0.458552i
$760$	3.70776	+	2.11709i	0.134495	+	0.0767949i
$761$	9.48535	+	29.1929i	0.343844	+	1.05824i	0.962200	+	0.272344i	$0.0877989\pi$
$761$	9.48535	+	29.1929i	0.343844	+	1.05824i	−0.618356	+	0.785898i	$0.712201\pi$
$762$	−1.16382	+	1.60186i	−0.0421609	+	0.0580294i
$763$	5.07641	+	6.98708i	0.183778	+	0.252949i
$764$	−3.33604	+	10.2673i	−0.120694	+	0.371457i
$765$	−4.94857	+	4.49877i	−0.178916	+	0.162653i
$766$	−2.28976	−	7.04716i	−0.0827325	−	0.254624i
$767$	−38.8771	+	12.6319i	−1.40377	+	0.456112i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	32.1996			1.16115			0.580573	−	0.814208i	$-0.302829\pi$
$769$	32.1996			1.16115			0.580573	+	0.814208i	$0.302829\pi$
$770$	−4.75476	−	43.2472i	−0.171350	−	1.55852i
$771$	−8.86440	+	27.2818i	−0.319243	+	0.982530i
$772$	−9.21639	+	12.6853i	−0.331705	+	0.456553i
$773$	−16.3279	−	22.4734i	−0.587273	−	0.808312i	0.407196	−	0.913341i	$-0.366506\pi$
$773$	−16.3279	−	22.4734i	−0.587273	−	0.808312i	−0.994469	+	0.105029i	$0.966506\pi$
$774$	−2.97935			−0.107091
$775$	27.3157	+	5.37151i	0.981209	+	0.192950i
$776$	1.52445			0.0547245
$777$	−27.7967	−	38.2589i	−0.997201	−	1.37253i
$778$	17.6348	−	24.2722i	0.632237	−	0.870199i
$779$	6.17820	−	19.0145i	0.221357	−	0.681266i
$780$	−1.39086	−	12.6506i	−0.0498006	−	0.452965i
$781$	−25.7030			−0.919725
$782$	−16.0633	−	5.21930i	−0.574424	−	0.186642i
$783$	−0.204430	+	0.0664233i	−0.00730572	+	0.00237377i
$784$	−5.91335	−	18.1994i	−0.211191	−	0.649979i
$785$	−3.79356	+	3.44875i	−0.135398	+	0.123091i
$786$	−0.982663	+	3.02432i	−0.0350504	+	0.107874i
$787$	10.5855	+	14.5697i	0.377333	+	0.519355i	0.954876	−	0.297006i	$-0.0959881\pi$
$787$	10.5855	+	14.5697i	0.377333	+	0.519355i	−0.577542	+	0.816361i	$0.695988\pi$
$788$	3.83208	−	5.27441i	0.136512	−	0.187893i
$789$	−3.16808	−	9.75035i	−0.112787	−	0.347122i
$790$	−31.0643	−	17.7374i	−1.10522	−	0.631068i
$791$	−62.7455	−	45.5873i	−2.23097	−	1.62090i
$792$	3.61967	−	1.17610i	0.128619	−	0.0417910i
$793$	−30.2514	+	41.6375i	−1.07426	+	1.47859i
$794$	−17.1169	+	12.4362i	−0.607457	+	0.441343i
$795$	−0.603618	−	0.125288i	−0.0214081	−	0.00444350i
$796$	8.51570	−	6.18702i	0.301831	−	0.219293i
$797$	23.5794	−	7.66140i	0.835224	−	0.271381i	0.139980	−	0.990154i	$-0.455296\pi$
$797$	23.5794	−	7.66140i	0.835224	−	0.271381i	0.695244	+	0.718774i	$0.255296\pi$
$798$	−9.28386	+	3.01651i	−0.328645	+	0.106783i
$799$	4.68376	−	14.4151i	0.165700	−	0.509971i
$800$	−1.08631	−	4.88057i	−0.0384067	−	0.172554i
$801$	−18.8084			−0.664561
$802$	17.3743	+	5.64527i	0.613509	+	0.199341i
$803$	−26.5013	+	36.4760i	−0.935212	+	1.28721i
$804$	−6.68142	+	4.85433i	−0.235635	+	0.171199i
$805$	−7.05496	−	64.1688i	−0.248655	−	2.26165i
$806$	−29.0229	−	12.7240i	−1.02229	−	0.448184i
$807$			1.44208i			0.0507636i
$808$	−0.109990	−	0.151389i	−0.00386944	−	0.00532583i
$809$	−1.46087	−	1.06138i	−0.0513614	−	0.0373163i	0.561808	−	0.827267i	$-0.310106\pi$
$809$	−1.46087	−	1.06138i	−0.0513614	−	0.0373163i	−0.613170	+	0.789951i	$0.710106\pi$
$810$	0.454435	−	2.18940i	0.0159672	−	0.0769278i
$811$	−28.7633			−1.01002			−0.505008	−	0.863115i	$-0.668510\pi$
$811$	−28.7633			−1.01002			−0.505008	+	0.863115i	$0.668510\pi$
$812$		−	1.09890i		−	0.0385638i
$813$	15.0403	+	4.88687i	0.527485	+	0.171390i
$814$	10.8793	+	33.4830i	0.381319	+	1.17358i
$815$	−13.5316	−	30.0052i	−0.473990	−	1.05104i
$816$	2.41969	−	1.75800i	0.0847059	−	0.0615425i
$817$	−5.41042	−	1.75795i	−0.189287	−	0.0615030i
$818$	−6.97026	−	9.59373i	−0.243709	−	0.335437i
$819$	23.5404	+	17.1031i	0.822566	+	0.597629i
$820$	−21.3433	+	9.62524i	−0.745339	+	0.336128i
$821$	−6.59061	−	4.78836i	−0.230014	−	0.167115i	0.466809	−	0.884358i	$-0.345404\pi$
$821$	−6.59061	−	4.78836i	−0.230014	−	0.167115i	−0.696823	+	0.717243i	$0.745404\pi$
$822$	8.16142	−	11.2332i	0.284662	−	0.391804i
$823$	15.4312	−	5.01390i	0.537897	−	0.174773i	−0.0274549	−	0.999623i	$-0.508740\pi$
$823$	15.4312	−	5.01390i	0.537897	−	0.174773i	0.565352	+	0.824850i	$0.308740\pi$
$824$	−9.80431	−	7.12325i	−0.341549	−	0.248150i
$825$	14.2630	+	12.5975i	0.496575	+	0.438588i
$826$	11.3463	−	34.9202i	0.394787	−	1.21503i
$827$	−5.50586	−	7.57817i	−0.191458	−	0.263519i	0.702487	−	0.711697i	$-0.252073\pi$
$827$	−5.50586	−	7.57817i	−0.191458	−	0.263519i	−0.893944	+	0.448178i	$0.852073\pi$
$828$	5.37075	−	1.74506i	0.186646	−	0.0606451i
$829$	14.3751	+	44.2419i	0.499266	+	1.53658i	0.810201	+	0.586152i	$0.199358\pi$
$829$	14.3751	+	44.2419i	0.499266	+	1.53658i	−0.310934	+	0.950431i	$0.600642\pi$
$830$	−10.3682	−	2.15204i	−0.359887	−	0.0746986i
$831$	9.72269			0.337276
$832$			5.69162i			0.197321i
$833$	54.4325	+	17.6862i	1.88598	+	0.612791i
$834$	−10.4775	−	7.61234i	−0.362806	−	0.263594i
$835$	12.3376	−	11.2162i	0.426960	−	0.388151i
$836$	7.26717			0.251340
$837$	−4.15883	−	3.70190i	−0.143750	−	0.127957i
$838$		−	14.0332i		−	0.484769i
$839$	4.02080	−	2.92128i	0.138813	−	0.100854i	−0.516212	−	0.856461i	$-0.672658\pi$
$839$	4.02080	−	2.92128i	0.138813	−	0.100854i	0.655025	+	0.755607i	$0.272658\pi$
$840$	9.92723	+	5.66834i	0.342522	+	0.195576i
$841$	−8.94722	+	27.5367i	−0.308525	+	0.949541i
$842$		−	30.5999i		−	1.05454i
$843$		−	15.3770i		−	0.529612i
$844$	1.05164	−	3.23662i	0.0361990	−	0.111409i
$845$	−39.5333	+	17.8285i	−1.35999	+	0.613318i
$846$	1.56601	+	4.81967i	0.0538404	+	0.165704i
$847$	−10.4730	−	14.4148i	−0.359856	−	0.495299i
$848$	0.262206	+	0.0851960i	0.00900420	+	0.00292564i
$849$	−1.69276	+	1.22986i	−0.0580953	+	0.0422087i
$850$	13.7192	+	5.95154i	0.470564	+	0.204136i
$851$	16.1423	+	49.6810i	0.553352	+	1.70304i
$852$	3.96953	−	5.46360i	0.135994	−	0.187180i
$853$	−16.0091	+	22.0347i	−0.548142	+	0.754453i	−0.989759	−	0.142751i	$-0.954405\pi$
$853$	−16.0091	+	22.0347i	−0.548142	+	0.754453i	0.441616	+	0.897204i	$0.354405\pi$
$854$	−14.2854	−	43.9660i	−0.488837	−	1.50449i
$855$	2.11709	−	3.70776i	0.0724029	−	0.126803i
$856$	−0.522009	+	0.379262i	−0.0178419	+	0.0129629i
$857$	−11.1486	−	3.62242i	−0.380831	−	0.123739i	0.112345	−	0.993669i	$-0.464164\pi$
$857$	−11.1486	−	3.62242i	−0.380831	−	0.123739i	−0.493175	+	0.869930i	$0.664164\pi$
$858$	−12.7326	−	17.5249i	−0.434684	−	0.598291i
$859$	3.16916	+	9.75366i	0.108130	+	0.332791i	0.990452	−	0.137855i	$-0.0440209\pi$
$859$	3.16916	+	9.75366i	0.108130	+	0.332791i	−0.882322	+	0.470646i	$0.844021\pi$
$860$	2.73878	+	6.07304i	0.0933917	+	0.207089i
$861$	16.5416	−	50.9099i	0.563737	−	1.73500i
$862$			27.7908i			0.946557i
$863$		−	3.27852i		−	0.111602i	−0.998442	−	0.0558011i	$-0.982229\pi$
$863$		−	3.27852i		−	0.111602i	0.998442	−	0.0558011i	$-0.0177713\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	9.23327	+	5.27210i	0.313941	+	0.179257i
$866$	−11.2425	+	8.16813i	−0.382035	+	0.277564i
$867$		−	8.05454i		−	0.273547i
$868$	24.5692	−	14.3725i	0.833934	−	0.487834i
$869$	−60.8858			−2.06541
$870$	0.323318	+	0.355645i	0.0109615	+	0.0120575i
$871$	38.0281	+	27.6290i	1.28853	+	0.936174i
$872$	1.60666	+	0.522037i	0.0544085	+	0.0176784i
$873$		−	1.52445i		−	0.0515948i
$874$	10.7828			0.364733
$875$	0.820331	+	57.1518i	0.0277322	+	1.93208i
$876$	−3.66074	−	11.2666i	−0.123685	−	0.380663i
$877$	4.49276	−	1.45979i	0.151710	−	0.0492935i	−0.232178	−	0.972673i	$-0.574585\pi$
$877$	4.49276	−	1.45979i	0.151710	−	0.0492935i	0.383887	+	0.923380i	$0.374585\pi$
$878$	−11.6253	−	16.0008i	−0.392335	−	0.540002i
$879$	6.43441	−	19.8031i	0.217027	−	0.667941i
$880$	−5.72473	−	6.29711i	−0.192981	−	0.212276i
$881$	29.6996	+	21.5780i	1.00060	+	0.726982i	0.962218	−	0.272281i	$-0.0877781\pi$
$881$	29.6996	+	21.5780i	1.00060	+	0.726982i	0.0383868	+	0.999263i	$0.487778\pi$
$882$	−18.1994	+	5.91335i	−0.612806	+	0.199113i
$883$	−12.2859	+	16.9101i	−0.413453	+	0.569069i	−0.964056	−	0.265698i	$-0.914398\pi$
$883$	−12.2859	+	16.9101i	−0.413453	+	0.569069i	0.550604	+	0.834767i	$0.314398\pi$
$884$	−13.7719	−	10.0059i	−0.463200	−	0.336535i
$885$	6.60217	+	14.6398i	0.221929	+	0.492112i
$886$	−22.9084	−	16.6439i	−0.769622	−	0.559163i
$887$	−3.85924	−	5.31179i	−0.129581	−	0.178353i	0.739297	−	0.673380i	$-0.235158\pi$
$887$	−3.85924	−	5.31179i	−0.129581	−	0.178353i	−0.868877	+	0.495027i	$0.835158\pi$
$888$	−8.79755	−	2.85850i	−0.295226	−	0.0959248i
$889$	−8.18927	+	5.94985i	−0.274659	+	0.199552i
$890$	17.2896	+	38.3385i	0.579550	+	1.28511i
$891$	−1.17610	−	3.61967i	−0.0394009	−	0.121264i
$892$	17.5523	+	5.70310i	0.587695	+	0.190954i
$893$			9.67641i			0.323809i
$894$	−20.6471			−0.690542
$895$	−1.51614	−	0.314692i	−0.0506790	−	0.0105190i
$896$	−4.13597	−	3.00496i	−0.138173	−	0.100389i
$897$	−18.8922	−	26.0029i	−0.630793	−	0.868212i
$898$			7.96357i			0.265748i
$899$	1.16920	−	0.255499i	0.0389950	−	0.00852137i
$900$	−4.88057	+	1.08631i	−0.162686	+	0.0362102i
$901$	−0.667107	+	0.484682i	−0.0222246	+	0.0161471i
$902$	−23.4238	+	32.2401i	−0.779928	+	1.07348i
$903$	−14.4860	−	4.70678i	−0.482063	−	0.156632i
$904$	−15.1707			−0.504570
$905$	−0.158839	−	1.44473i	−0.00527997	−	0.0480243i
$906$	−1.66425	+	5.12203i	−0.0552910	+	0.170168i
$907$	−6.44578	+	2.09436i	−0.214028	+	0.0695421i	−0.414069	−	0.910246i	$-0.635893\pi$
$907$	−6.44578	+	2.09436i	−0.214028	+	0.0695421i	0.200040	+	0.979788i	$0.435893\pi$
$908$	17.9808	−	5.84230i	0.596712	−	0.193884i
$909$	−0.151389	+	0.109990i	−0.00502124	+	0.00364815i
$910$	13.2229	−	63.7061i	0.438336	−	2.11184i
$911$	21.2063	−	15.4073i	0.702597	−	0.510467i	−0.178180	−	0.983998i	$-0.557021\pi$
$911$	21.2063	−	15.4073i	0.702597	−	0.510467i	0.880777	+	0.473531i	$0.157021\pi$
$912$	−1.12233	+	1.54476i	−0.0371641	+	0.0511520i
$913$	−17.1415	+	5.56960i	−0.567300	+	0.184327i
$914$	−1.26412	−	0.918438i	−0.0418134	−	0.0303792i
$915$	17.5590	+	10.0260i	0.580483	+	0.331449i
$916$	8.27818	+	25.4776i	0.273519	+	0.841804i
$917$	−9.55565	+	13.1522i	−0.315555	+	0.434325i
$918$	−1.75800	−	2.41969i	−0.0580228	−	0.0798615i
$919$	7.00492	−	21.5589i	0.231071	−	0.711163i	−0.766548	−	0.642188i	$-0.778027\pi$
$919$	7.00492	−	21.5589i	0.231071	−	0.711163i	0.997618	−	0.0689753i	$-0.0219730\pi$
$920$	−8.49417	−	9.34345i	−0.280044	−	0.308044i
$921$	−4.23958	−	13.0481i	−0.139699	−	0.429949i
$922$	−1.89684	+	0.616321i	−0.0624691	+	0.0202975i
$923$	−36.5564	−	11.8779i	−1.20327	−	0.390965i
$924$	19.4573			0.640098
$925$	−10.0486	−	45.1466i	−0.330397	−	1.48441i
$926$	6.29323	−	19.3686i	0.206809	−	0.636491i
$927$	−7.12325	+	9.80431i	−0.233958	+	0.322016i
$928$	−0.126345	−	0.173898i	−0.00414746	−	0.00570849i
$929$	10.2281			0.335572			0.167786	−	0.985823i	$-0.446338\pi$
$929$	10.2281			0.335572			0.167786	+	0.985823i	$0.446338\pi$
$930$	−3.72285	+	11.8803i	−0.122077	+	0.389569i
$931$	−36.5388			−1.19751
$932$	3.44835	+	4.74625i	0.112954	+	0.155468i
$933$	6.47941	−	8.91815i	0.212126	−	0.291967i
$934$	2.96386	−	9.12182i	0.0969804	−	0.298475i
$935$	25.3011	−	2.78170i	0.827436	−	0.0909714i
$936$	5.69162			0.186036
$937$	8.99617	+	2.92303i	0.293892	+	0.0954913i	0.452252	−	0.891890i	$-0.350621\pi$
$937$	8.99617	+	2.92303i	0.293892	+	0.0954913i	−0.158360	+	0.987381i	$0.550621\pi$
$938$	−40.1547	+	13.0471i	−1.31110	+	0.426002i
$939$	0.0926810	+	0.285243i	0.00302453	+	0.00930855i
$940$	8.38475	−	7.62261i	0.273480	−	0.248622i
$941$	−5.14092	+	15.8221i	−0.167589	+	0.515786i	−0.999218	−	0.0395459i	$-0.987409\pi$
$941$	−5.14092	+	15.8221i	−0.167589	+	0.515786i	0.831629	+	0.555332i	$0.187409\pi$
$942$	−1.34768	−	1.85493i	−0.0439099	−	0.0604367i
$943$	−34.7555	+	47.8369i	−1.13180	+	1.55778i
$944$	−2.21939	−	6.83058i	−0.0722350	−	0.222316i
$945$	5.66834	−	9.92723i	0.184391	−	0.322933i
$946$	9.17366	+	6.66505i	0.298261	+	0.216700i
$947$	1.95029	−	0.633687i	0.0633758	−	0.0205921i	−0.277157	−	0.960825i	$-0.589392\pi$
$947$	1.95029	−	0.633687i	0.0633758	−	0.0205921i	0.340533	+	0.940232i	$0.389392\pi$
$948$	9.40312	−	12.9423i	0.305399	−	0.420346i
$949$	−54.5481	+	39.6315i	−1.77071	+	1.28649i
$950$	−9.50394	−	0.907052i	−0.308349	−	0.0294287i
$951$	0.597382	−	0.434024i	0.0193715	−	0.0140742i
$952$	14.5421	−	4.72501i	0.471312	−	0.153139i
$953$	−12.9298	+	4.20113i	−0.418836	+	0.136088i	−0.510850	−	0.859670i	$-0.670669\pi$
$953$	−12.9298	+	4.20113i	−0.418836	+	0.136088i	0.0920144	+	0.995758i	$0.470669\pi$
$954$	0.0851960	−	0.262206i	0.00275832	−	0.00848924i
$955$	−2.63813	−	23.9952i	−0.0853678	−	0.776468i
$956$	24.0347			0.777339
$957$	0.778049	+	0.252803i	0.0251508	+	0.00817197i
$958$	−7.41656	+	10.2080i	−0.239618	+	0.329806i
$959$	57.4281	−	41.7240i	1.85445	−	1.34734i
$960$	2.22267	−	0.244369i	0.0717365	−	0.00788698i
$961$	21.0045	+	22.7994i	0.677563	+	0.735465i
$962$			52.6491i			1.69748i
$963$	0.379262	+	0.522009i	0.0122215	+	0.0168215i
$964$	−17.1000	−	12.4239i	−0.550755	−	0.400147i
$965$	7.12548	−	34.3295i	0.229377	−	1.10511i
$966$	28.8701			0.928879
$967$		−	38.3601i		−	1.23358i	−0.787129	−	0.616789i	$-0.788433\pi$
$967$		−	38.3601i		−	1.23358i	0.787129	−	0.616789i	$-0.211567\pi$
$968$	−3.31466	−	1.07700i	−0.106537	−	0.0346160i
$969$	−1.76476	−	5.43138i	−0.0566924	−	0.174481i
$970$	−3.10740	+	1.40135i	−0.0997725	+	0.0449948i
$971$	31.6361	−	22.9850i	1.01525	−	0.737623i	0.0499468	−	0.998752i	$-0.484095\pi$
$971$	31.6361	−	22.9850i	1.01525	−	0.737623i	0.965304	+	0.261129i	$0.0840948\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−38.9168	−	53.5644i	−1.24762	−	1.71720i
$974$	4.85094	+	3.52442i	0.155434	+	0.112930i
$975$	14.4642	+	24.5082i	0.463225	+	0.784889i
$976$	−7.31558	−	5.31508i	−0.234166	−	0.170132i
$977$	23.4011	−	32.2088i	0.748667	−	1.03045i	−0.249406	−	0.968399i	$-0.580235\pi$
$977$	23.4011	−	32.2088i	0.748667	−	1.03045i	0.998073	−	0.0620524i	$-0.0197646\pi$
$978$	13.9997	−	4.54878i	0.447662	−	0.145454i
$979$	57.9124	+	42.0758i	1.85089	+	1.34475i
$980$	28.7835	+	31.6614i	0.919455	+	1.01138i
$981$	0.522037	−	1.60666i	0.0166673	−	0.0512968i
$982$	7.45610	+	10.2624i	0.237934	+	0.327488i
$983$	34.9210	−	11.3465i	1.11381	−	0.361898i	0.306407	−	0.951901i	$-0.400873\pi$
$983$	34.9210	−	11.3465i	1.11381	−	0.361898i	0.807402	+	0.590002i	$0.200873\pi$
$984$	−3.23563	−	9.95825i	−0.103148	−	0.317457i
$985$	−2.96270	+	14.2739i	−0.0943996	+	0.454804i
$986$	0.642894			0.0204739
$987$			25.9078i			0.824655i
$988$	10.3358	+	3.35831i	0.328826	+	0.106842i
$989$	13.6116	+	9.88939i	0.432823	+	0.314464i
$990$	−6.29711	+	5.72473i	−0.200135	+	0.181944i
$991$	16.7163			0.531012			0.265506	−	0.964109i	$-0.414461\pi$
$991$	16.7163			0.531012			0.265506	+	0.964109i	$0.414461\pi$
$992$	2.23557	−	5.09924i	0.0709794	−	0.161901i
$993$			21.4060i			0.679300i
$994$	27.9317	−	20.2936i	0.885941	−	0.643674i
$995$	−11.6708	+	20.4396i	−0.369988	+	0.647977i
$996$	1.46339	−	4.50387i	0.0463694	−	0.142710i
$997$		−	32.4336i		−	1.02718i	−0.858035	−	0.513591i	$-0.828315\pi$
$997$		−	32.4336i		−	1.02718i	0.858035	−	0.513591i	$-0.171685\pi$
$998$			15.4025i			0.487559i
$999$	−2.85850	+	8.79755i	−0.0904388	+	0.278342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.4	✓	72
5.4	even	2	inner	930.2.z.d.109.13	yes	72
31.2	even	5	inner	930.2.z.d.529.13	yes	72
155.64	even	10	inner	930.2.z.d.529.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.4	✓	72	1.1	even	1	trivial
930.2.z.d.109.13	yes	72	5.4	even	2	inner
930.2.z.d.529.4	yes	72	155.64	even	10	inner
930.2.z.d.529.13	yes	72	31.2	even	5	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.244369 - 2.22267i) q^{5} +1.00000 q^{6} +(4.86212 + 1.57980i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.244369 - 2.22267i) q^{5} +1.00000 q^{6} +(4.86212 + 1.57980i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.65455 + 1.50415i) q^{10} +(-1.17610 + 3.61967i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-3.34545 + 4.60462i) q^{13} +(-1.57980 - 4.86212i) q^{14} +(1.94182 + 1.10876i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.84451 - 0.924238i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-1.54476 + 1.12233i) q^{19} +(2.18940 + 0.454435i) q^{20} +(-4.13597 + 3.00496i) q^{21} +(3.61967 - 1.17610i) q^{22} +(5.37075 - 1.74506i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.88057 + 1.08631i) q^{25} +5.69162 q^{26} +(0.951057 + 0.309017i) q^{27} +(-3.00496 + 4.13597i) q^{28} +(-0.173898 + 0.126345i) q^{29} +(-0.244369 - 2.22267i) q^{30} +(-5.09924 - 2.23557i) q^{31} +1.00000i q^{32} +(-2.23708 - 3.07908i) q^{33} +(-2.41969 - 1.75800i) q^{34} +(2.32323 - 11.1930i) q^{35} +1.00000 q^{36} +9.25029i q^{37} +(1.81597 + 0.590045i) q^{38} +(-1.75881 - 5.41305i) q^{39} +(-0.919253 - 2.03838i) q^{40} +(-8.47099 + 6.15453i) q^{41} +(4.86212 + 1.57980i) q^{42} +(1.75122 + 2.41035i) q^{43} +(-3.07908 - 2.23708i) q^{44} +(-2.03838 + 0.919253i) q^{45} +(-4.56863 - 3.31930i) q^{46} +(2.97872 - 4.09986i) q^{47} +(0.951057 - 0.309017i) q^{48} +(15.4813 + 11.2479i) q^{49} +(3.74757 + 3.30995i) q^{50} +(-0.924238 + 2.84451i) q^{51} +(-3.34545 - 4.60462i) q^{52} +(-0.262206 + 0.0851960i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(8.33276 + 1.72956i) q^{55} +5.11234 q^{56} -1.90943i q^{57} +(0.204430 + 0.0664233i) q^{58} +(5.81044 + 4.22153i) q^{59} +(-1.65455 + 1.50415i) q^{60} +9.04256 q^{61} +(1.18864 + 5.43941i) q^{62} -5.11234i q^{63} +(0.809017 - 0.587785i) q^{64} +(11.0521 + 6.31062i) q^{65} +(-1.17610 + 3.61967i) q^{66} -8.25869i q^{67} +2.99090i q^{68} +(-1.74506 + 5.37075i) q^{69} +(-10.4209 + 4.69953i) q^{70} +(2.08691 + 6.42284i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(11.2666 + 3.66074i) q^{73} +(7.48364 - 5.43718i) q^{74} +(1.98989 - 4.58698i) q^{75} +(-0.590045 - 1.81597i) q^{76} +(-11.4367 + 15.7413i) q^{77} +(-3.34545 + 4.60462i) q^{78} +(4.94351 + 15.2146i) q^{79} +(-1.10876 + 1.94182i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(9.95825 + 3.23563i) q^{82} +(2.78354 + 3.83122i) q^{83} +(-1.57980 - 4.86212i) q^{84} +(-2.74939 - 6.09657i) q^{85} +(0.920671 - 2.83353i) q^{86} -0.214950i q^{87} +3.80595i q^{88} +(5.81210 - 17.8878i) q^{89} +(1.94182 + 1.10876i) q^{90} +(-23.5404 + 17.1031i) q^{91} +5.64714i q^{92} +(4.80587 - 2.81134i) q^{93} -5.06770 q^{94} +(2.87207 + 3.15923i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(1.44984 + 0.471080i) q^{97} -19.1360i q^{98} +3.80595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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