LMFDB - Embedded newform 930.2.z.d.109.13

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			109.13
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.13

$q$-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} +(-1.94182 + 1.10876i) 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} +(1.65455 + 1.50415i) 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} +(-2.03838 - 0.919253i) 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} +(4.69953 - 10.4209i) q^{35} +1.00000 q^{36} -9.25029i q^{37} +(-1.81597 - 0.590045i) q^{38} +(-1.75881 - 5.41305i) q^{39} +(-0.454435 - 2.18940i) 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} +(2.18940 - 0.454435i) 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} +(-1.98989 - 4.58698i) 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} +(-7.75795 - 3.49863i) q^{55} +5.11234 q^{56} +1.90943i q^{57} +(-0.204430 - 0.0664233i) q^{58} +(5.81044 + 4.22153i) q^{59} +(-1.94182 + 1.10876i) q^{60} +9.04256 q^{61} +(-1.18864 - 5.43941i) q^{62} +5.11234i q^{63} +(0.809017 - 0.587785i) q^{64} +(9.41704 + 8.56107i) q^{65} +(-1.17610 + 3.61967i) q^{66} +8.25869i q^{67} -2.99090i q^{68} +(-1.74506 + 5.37075i) q^{69} +(11.1930 - 2.32323i) 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} +(-3.74757 + 3.30995i) 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} +(1.50415 - 1.65455i) 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} +(-1.35917 - 6.54828i) q^{85} +(0.920671 - 2.83353i) q^{86} +0.214950i q^{87} -3.80595i q^{88} +(5.81210 - 17.8878i) q^{89} +(1.65455 + 1.50415i) q^{90} +(-23.5404 + 17.1031i) q^{91} -5.64714i q^{92} +(-4.80587 + 2.81134i) q^{93} -5.06770 q^{94} +(-2.11709 - 3.70776i) 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	$-0.983068\pi$
$7$	−4.86212	−	1.57980i	−1.83771	−	0.597108i	−0.839124	−	0.543941i	$-0.816932\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	−1.94182	+	1.10876i	−0.614057	+	0.350620i
$11$	−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	$-0.510451\pi$
$13$	3.34545	−	4.60462i	0.927861	−	1.27709i	0.960688	−	0.277630i	$-0.0895488\pi$
$14$	−1.57980	−	4.86212i	−0.422219	−	1.29946i
$15$	1.65455	+	1.50415i	0.427202	+	0.388371i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.84451	+	0.924238i	−0.689895	+	0.224161i	−0.632922	−	0.774215i	$-0.718145\pi$
$17$	−2.84451	+	0.924238i	−0.689895	+	0.224161i	−0.0569728	+	0.998376i	$0.518145\pi$
$18$	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	$0.370288\pi$
$20$	−2.03838	−	0.919253i	−0.455795	−	0.205551i
$21$	−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	−0.809721	−	0.586815i	$-0.800382\pi$
$23$	−5.37075	+	1.74506i	−1.11988	+	0.363871i	−0.310157	+	0.950685i	$0.600382\pi$
$24$	−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
$35$	4.69953	−	10.4209i	0.794366	−	1.76145i
$36$	1.00000			0.166667
$37$		−	9.25029i		−	1.52074i	−0.649491	−	0.760369i	$-0.725018\pi$
$37$		−	9.25029i		−	1.52074i	0.649491	−	0.760369i	$-0.274982\pi$
$38$	−1.81597	−	0.590045i	−0.294590	−	0.0957179i
$39$	−1.75881	−	5.41305i	−0.281635	−	0.866782i
$40$	−0.454435	−	2.18940i	−0.0718525	−	0.346175i
$41$	−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	0.654335	−	0.756205i	$-0.272949\pi$
$43$	−1.75122	−	2.41035i	−0.267059	−	0.367575i	−0.921394	+	0.388630i	$0.872949\pi$
$44$	−3.07908	−	2.23708i	−0.464188	−	0.337252i
$45$	2.18940	−	0.454435i	0.326377	−	0.0677432i
$46$	−4.56863	−	3.31930i	−0.673608	−	0.489405i
$47$	−2.97872	+	4.09986i	−0.434491	+	0.598026i	−0.968977	−	0.247152i	$-0.920505\pi$
$47$	−2.97872	+	4.09986i	−0.434491	+	0.598026i	0.534486	+	0.845178i	$0.320505\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	15.4813	+	11.2479i	2.21162	+	1.60684i
$50$	−1.98989	−	4.58698i	−0.281412	−	0.648696i
$51$	−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	−0.290953	−	0.956737i	$-0.593972\pi$
$53$	0.262206	−	0.0851960i	0.0360168	−	0.0117026i	0.326970	+	0.945035i	$0.393972\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−7.75795	−	3.49863i	−1.04608	−	0.471755i
$56$	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	$0.545150\pi$
$60$	−1.94182	+	1.10876i	−0.250688	+	0.143140i
$61$	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
$65$	9.41704	+	8.56107i	1.16804	+	1.06187i
$66$	−1.17610	+	3.61967i	−0.144768	+	0.445551i
$67$			8.25869i			1.00896i	0.863424	+	0.504480i	$0.168316\pi$
$67$			8.25869i			1.00896i	−0.863424	+	0.504480i	$0.831684\pi$
$68$		−	2.99090i		−	0.362699i
$69$	−1.74506	+	5.37075i	−0.210081	+	0.646562i
$70$	11.1930	−	2.32323i	1.33782	−	0.277679i
$71$	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	−0.436622	−	0.899645i	$-0.643825\pi$
$73$	−11.2666	−	3.66074i	−1.31866	−	0.428457i	−0.882033	+	0.471188i	$0.843825\pi$
$74$	7.48364	−	5.43718i	0.869955	−	0.632060i
$75$	−3.74757	+	3.30995i	−0.432732	+	0.382200i
$76$	−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	$0.543616\pi$
$80$	1.50415	−	1.65455i	0.168170	−	0.184984i
$81$	−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	0.628448	−	0.777851i	$-0.283690\pi$
$83$	−2.78354	−	3.83122i	−0.305533	−	0.420531i	−0.933982	+	0.357321i	$0.883690\pi$
$84$	−1.57980	−	4.86212i	−0.172370	−	0.530501i
$85$	−1.35917	−	6.54828i	−0.147423	−	0.710261i
$86$	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	$-0.374692\pi$
$90$	1.65455	+	1.50415i	0.174404	+	0.158552i
$91$	−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
$95$	−2.11709	−	3.70776i	−0.217209	−	0.380408i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−1.44984	−	0.471080i	−0.147209	−	0.0478310i	0.234486	−	0.972120i	$-0.424659\pi$
$97$	−1.44984	−	0.471080i	−0.147209	−	0.0478310i	−0.381694	+	0.924289i	$0.624659\pi$
$98$			19.1360i			1.93303i
$99$	3.80595			0.382512
$100$	2.54132	−	4.30601i	0.254132	−	0.430601i
$101$	−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	$0.00366077\pi$
$103$	7.12325	+	9.80431i	0.701875	+	0.966048i	−0.298059	+	0.954547i	$0.596339\pi$
$104$	−1.75881	+	5.41305i	−0.172465	+	0.530793i
$105$	−5.66834	−	9.92723i	−0.553173	−	0.968798i
$106$	0.223046	+	0.162052i	0.0216641	+	0.0157399i
$107$	0.613659	−	0.199390i	0.0593246	−	0.0192757i	−0.279204	−	0.960232i	$-0.590071\pi$
$107$	0.613659	−	0.199390i	0.0593246	−	0.0192757i	0.338529	+	0.940956i	$0.390071\pi$
$108$	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	$0.674219\pi$
$110$	−1.72956	−	8.33276i	−0.164907	−	0.794497i
$111$	−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	0.895138	−	0.445790i	$-0.147077\pi$
$113$	14.4282	+	4.68801i	1.35729	+	0.441010i	0.462153	+	0.886800i	$0.347077\pi$
$114$	−1.54476	+	1.12233i	−0.144680	+	0.105116i
$115$	−2.56626	−	12.3639i	−0.239305	−	1.15294i
$116$	−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
$120$	−2.03838	−	0.919253i	−0.186077	−	0.0839160i
$121$	−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	−0.754253	−	0.656584i	$-0.772001\pi$
$127$	1.16382	−	1.60186i	0.103273	−	0.142143i	0.857525	+	0.514442i	$0.172001\pi$
$128$	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
$135$	0.919253	−	2.03838i	0.0791167	−	0.175435i
$136$	2.41969	−	1.75800i	0.207486	−	0.150748i
$137$	−8.16142	+	11.2332i	−0.697278	+	0.959720i	0.302700	+	0.953086i	$0.402112\pi$
$137$	−8.16142	+	11.2332i	−0.697278	+	0.959720i	−0.999978	+	0.00663451i	$0.997888\pi$
$138$	−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	$0.885083\pi$
$140$	8.45859	+	7.68974i	0.714882	+	0.649902i
$141$	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
$145$	−0.238327	−	0.417394i	−0.0197920	−	0.0346627i
$146$	−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
$155$	6.21504	−	10.7876i	0.499204	−	0.866484i
$156$	5.69162			0.455694
$157$	1.34768	+	1.85493i	0.107557	+	0.148039i	0.859402	−	0.511300i	$-0.170836\pi$
$157$	1.34768	+	1.85493i	0.107557	+	0.148039i	−0.751845	+	0.659339i	$0.770836\pi$
$158$	−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	−0.800771	−	0.598970i	$-0.795577\pi$
$163$	−13.9997	+	4.54878i	−1.09654	+	0.356288i	−0.295771	+	0.955259i	$0.595577\pi$
$164$	−3.23563	−	9.95825i	−0.252660	−	0.777608i
$165$	−7.39046	+	4.21987i	−0.575346	+	0.328516i
$166$	1.46339	−	4.50387i	0.113581	−	0.349568i
$167$	−4.38299	−	6.03267i	−0.339166	−	0.466822i	0.605032	−	0.796202i	$-0.293161\pi$
$167$	−4.38299	−	6.03267i	−0.339166	−	0.466822i	−0.944198	+	0.329379i	$0.893161\pi$
$168$	3.00496	−	4.13597i	0.231837	−	0.319097i
$169$	−5.99324	−	18.4453i	−0.461018	−	1.41887i
$170$	4.49877	−	4.94857i	0.345040	−	0.379538i
$171$	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	−0.689445	−	0.724338i	$-0.742145\pi$
$173$	2.79490	−	3.84685i	0.212492	−	0.292470i	0.901937	+	0.431868i	$0.142145\pi$
$174$	−0.173898	+	0.126345i	−0.0131832	+	0.00957816i
$175$	22.0138	+	12.9921i	1.66408	+	0.982108i
$176$	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
$190$	1.75525	−	3.89213i	0.127339	−	0.282365i
$191$	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	−0.281601	−	0.959532i	$-0.590866\pi$
$193$	−14.9124	−	4.84534i	−1.07342	−	0.348775i	−0.791819	+	0.610756i	$0.790866\pi$
$194$	−0.471080	−	1.44984i	−0.0338216	−	0.104092i
$195$	12.4613	−	2.58647i	0.892369	−	0.185221i
$196$	−15.4813	+	11.2479i	−1.10581	+	0.803418i
$197$	6.20044	+	2.01465i	0.441763	+	0.143538i	0.521449	−	0.853282i	$-0.325392\pi$
$197$	6.20044	+	2.01465i	0.441763	+	0.143538i	−0.0796858	+	0.996820i	$0.525392\pi$
$198$	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	$0.821700\pi$
$200$	4.97738	−	0.475039i	0.351954	−	0.0335904i
$201$	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
$205$	−11.6095	−	20.3322i	−0.810841	−	1.42006i
$206$	−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
$210$	4.69953	−	10.4209i	0.324299	−	0.719108i
$211$	−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
$215$	5.78537	−	3.30338i	0.394559	−	0.225289i
$216$	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
$220$	5.72473	−	6.29711i	0.385961	−	0.424551i
$221$	−5.26041	+	16.1899i	−0.353853	+	1.08905i
$222$		−	9.25029i		−	0.620839i
$223$			18.4556i			1.23588i	0.786226	+	0.617939i	$0.212032\pi$
$223$			18.4556i			1.23588i	−0.786226	+	0.617939i	$0.787968\pi$
$224$	−1.57980	+	4.86212i	−0.105555	+	0.324864i
$225$	0.475039	+	4.97738i	0.0316693	+	0.331826i
$226$	4.68801	+	14.4282i	0.311841	+	0.959749i
$227$	11.1127	+	15.2953i	0.737577	+	1.01519i	0.998754	+	0.0498966i	$0.0158892\pi$
$227$	11.1127	+	15.2953i	0.737577	+	1.01519i	−0.261178	+	0.965291i	$0.584111\pi$
$228$	−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	$-0.0459274\pi$
$230$	8.49417	−	9.34345i	0.560089	−	0.616089i
$231$	−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	−0.906893	−	0.421361i	$-0.861552\pi$
$233$	−3.44835	+	4.74625i	−0.225909	+	0.310937i	0.680984	+	0.732298i	$0.261552\pi$
$234$	−1.75881	−	5.41305i	−0.114977	−	0.353862i
$235$	−8.38475	−	7.62261i	−0.546961	−	0.497244i
$236$	−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	$-0.383431\pi$
$240$	−0.454435	−	2.18940i	−0.0293337	−	0.141325i
$241$	−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
$245$	−28.7835	+	31.6614i	−1.83891	+	2.02277i
$246$	−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
$250$	10.6816	−	3.30195i	0.675565	−	0.208834i
$251$	−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
$255$	−6.09657	−	2.74939i	−0.381782	−	0.172174i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−27.2818	+	8.86440i	−1.70179	+	0.552946i	−0.988933	−	0.148361i	$-0.952600\pi$
$257$	−27.2818	+	8.86440i	−1.70179	+	0.552946i	−0.712859	+	0.701307i	$0.752600\pi$
$258$	−1.75122	−	2.41035i	−0.109026	−	0.150062i
$259$	−14.6136	+	44.9760i	−0.908045	+	2.79467i
$260$	−11.0521	+	6.31062i	−0.685422	+	0.391368i
$261$	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	−0.581748	−	0.813369i	$-0.697631\pi$
$263$	6.02605	−	8.29415i	0.371582	−	0.511439i	0.953330	+	0.301930i	$0.0976310\pi$
$264$	−3.07908	−	2.23708i	−0.189504	−	0.137683i
$265$	0.125288	+	0.603618i	0.00769637	+	0.0370800i
$266$	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	$0.286002\pi$
$270$	2.18940	−	0.454435i	0.133243	−	0.0276561i
$271$	−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
$275$	9.67212	−	16.3884i	0.583251	−	0.988260i
$276$	−4.56863	−	3.31930i	−0.274999	−	0.199799i
$277$	5.71485	+	7.86582i	0.343372	+	0.472611i	0.945423	−	0.325847i	$-0.105649\pi$
$277$	5.71485	+	7.86582i	0.343372	+	0.472611i	−0.602050	+	0.798458i	$0.705649\pi$
$278$		−	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	0.249274	−	0.968433i	$-0.419808\pi$
$283$	−1.98996	−	0.646576i	−0.118291	−	0.0384349i	−0.367564	+	0.929998i	$0.619808\pi$
$284$	−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
$290$	0.197594	−	0.438149i	0.0116031	−	0.0257290i
$291$	−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	0.333166	−	0.942868i	$-0.391883\pi$
$293$	19.8031	−	6.43441i	1.15691	−	0.375902i	0.823741	+	0.566966i	$0.191883\pi$
$294$	15.4813	+	11.2479i	0.902890	+	0.655988i
$295$	−10.8030	+	11.8831i	−0.628974	+	0.691861i
$296$	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
$300$	−1.98989	−	4.58698i	−0.114886	−	0.264829i
$301$	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	−0.514314	−	0.857602i	$-0.671953\pi$
$307$	8.06416	−	11.0994i	0.460246	−	0.633474i	0.974560	+	0.224128i	$0.0719534\pi$
$308$	11.4367	+	15.7413i	0.651667	+	0.896942i
$309$	12.1188			0.689414
$310$	12.3805	−	1.31274i	0.703165	−	0.0745589i
$311$	−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	−0.813970	−	0.580907i	$-0.802698\pi$
$313$	−0.176290	+	0.242642i	−0.00996449	+	0.0137149i	0.804006	+	0.594622i	$0.202698\pi$
$314$	−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	0.328672	−	0.944444i	$-0.393399\pi$
$317$	0.702265	+	0.228180i	0.0394431	+	0.0128159i	−0.289229	+	0.957260i	$0.593399\pi$
$318$	0.262206	−	0.0851960i	0.0147038	−	0.00477755i
$319$	−0.252803	−	0.778049i	−0.0141543	−	0.0435624i
$320$	1.10876	+	1.94182i	0.0619814	+	0.108551i
$321$	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
$325$	−21.3297	+	18.8390i	−1.18316	+	1.04500i
$326$	−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
$330$	−7.75795	−	3.49863i	−0.427061	−	0.192593i
$331$	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	0.240810	−	0.970572i	$-0.422587\pi$
$337$	−2.47567	−	0.804395i	−0.134858	−	0.0438182i	−0.375669	+	0.926754i	$0.622587\pi$
$338$	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
$345$	−11.5110	−	5.19115i	−0.619731	−	0.279482i
$346$	4.75496			0.255628
$347$		−	0.0333855i		−	0.00179223i	−1.00000		0.000896113i	$-0.999715\pi$
$347$		−	0.0333855i		−	0.00179223i	1.00000		0.000896113i	$-0.000285242\pi$
$348$	−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	$-0.257386\pi$
$350$	2.42856	+	25.4461i	0.129812	+	1.36015i
$351$	−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	$-0.909190\pi$
$353$	−17.4865	−	24.0681i	−0.930713	−	1.28102i	0.0288674	−	0.999583i	$-0.490810\pi$
$354$	5.81044	+	4.22153i	0.308821	+	0.224372i
$355$	−14.7859	+	3.06897i	−0.784752	+	0.162884i
$356$	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	$-0.636217\pi$
$360$	−1.94182	+	1.10876i	−0.102343	+	0.0584366i
$361$	−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
$365$	10.8898	−	24.1474i	0.570000	−	1.26393i
$366$	9.04256			0.472662
$367$			3.27226i			0.170811i	0.996346	+	0.0854053i	$0.0272185\pi$
$367$			3.27226i			0.170811i	−0.996346	+	0.0854053i	$0.972781\pi$
$368$	5.37075	+	1.74506i	0.279970	+	0.0909676i
$369$	8.47099	+	6.15453i	0.440982	+	0.320392i
$370$	10.2563	+	17.9624i	0.533201	+	0.933820i
$371$	−1.40947			−0.0731761
$372$	−1.18864	−	5.43941i	−0.0616283	−	0.282020i
$373$		−	20.0566i		−	1.03849i	−0.854625	−	0.519245i	$-0.826213\pi$
$373$		−	20.0566i		−	1.03849i	0.854625	−	0.519245i	$-0.173787\pi$
$374$	9.20920	−	6.69087i	0.476196	−	0.345977i
$375$	−6.44115	−	9.13847i	−0.332619	−	0.471909i
$376$	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	$-0.106570\pi$
$380$	4.18050	−	0.867711i	0.214455	−	0.0445126i
$381$	−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	0.123382	−	0.992359i	$-0.460626\pi$
$383$	−7.04716	−	2.28976i	−0.360093	−	0.117001i	−0.483476	+	0.875358i	$0.660626\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	32.1930	+	29.2668i	1.64071	+	1.49157i
$386$	−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	$0.624914\pi$
$390$	9.41704	+	8.56107i	0.476850	+	0.433507i
$391$	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
$395$	−35.0251	+	7.26985i	−1.76230	+	0.365786i
$396$	−1.17610	+	3.61967i	−0.0591014	+	0.181895i
$397$			21.1577i			1.06187i	0.847411	+	0.530937i	$0.178160\pi$
$397$			21.1577i			1.06187i	−0.847411	+	0.530937i	$0.821840\pi$
$398$		−	10.5260i		−	0.527620i
$399$	3.01651	−	9.28386i	0.151014	−	0.464774i
$400$	3.30995	+	3.74757i	0.165497	+	0.187378i
$401$	−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
$405$	−1.10876	−	1.94182i	−0.0550946	−	0.0964897i
$406$	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	$0.405286\pi$
$410$	9.62524	−	21.3433i	0.475357	−	1.05407i
$411$	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
$415$	9.19576	−	5.25068i	0.451402	−	0.257746i
$416$	−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	$0.588630\pi$
$420$	11.1930	−	2.32323i	0.546161	−	0.113362i
$421$	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
$425$	14.8868	−	1.42079i	0.722117	−	0.0689186i
$426$	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
$430$	6.07304	+	2.73878i	0.292868	+	0.132076i
$431$	−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	$0.108368\pi$
$433$			13.8965i			0.667821i	−0.942605	+	0.333911i	$0.891632\pi$
$434$	−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	−0.868405	−	0.495855i	$-0.834855\pi$
$443$	−26.9304	+	8.75023i	−1.27950	+	0.415736i	−0.411098	+	0.911591i	$0.634855\pi$
$444$	7.48364	−	5.43718i	0.355158	−	0.258037i
$445$	38.3385	+	17.2896i	1.81742	+	0.819608i
$446$	−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	$0.760172\pi$
$450$	−3.74757	+	3.30995i	−0.176662	+	0.156032i
$451$	−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
$455$	−32.2620	−	56.5020i	−1.51247	−	2.64886i
$456$	−0.590045	−	1.81597i	−0.0276314	−	0.0850407i
$457$	−1.48606	+	0.482851i	−0.0695151	+	0.0225868i	−0.343568	−	0.939128i	$-0.611636\pi$
$457$	−1.48606	+	0.482851i	−0.0695151	+	0.0225868i	0.274053	+	0.961715i	$0.411636\pi$
$458$	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	0.434538	−	0.900653i	$-0.356912\pi$
$463$	−11.9704	−	16.4759i	−0.556314	−	0.765700i	−0.990852	+	0.134953i	$0.956912\pi$
$464$	0.214950			0.00997881
$465$	−5.07428	−	11.3689i	−0.235314	−	0.527220i
$466$	−5.86668			−0.271769
$467$	−5.63759	−	7.75948i	−0.260877	−	0.359066i	0.658407	−	0.752662i	$-0.271231\pi$
$467$	−5.63759	−	7.75948i	−0.260877	−	0.359066i	−0.919283	+	0.393596i	$0.871231\pi$
$468$	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
$475$	8.75849	−	3.79954i	0.401867	−	0.174335i
$476$	−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	$0.993077\pi$
$480$	1.50415	−	1.65455i	0.0686549	−	0.0755193i
$481$	−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
$485$	1.40135	−	3.10740i	0.0636322	−	0.141100i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	5.70263	−	1.85290i	0.258411	−	0.0839627i	−0.176947	−	0.984220i	$-0.556622\pi$
$487$	5.70263	−	1.85290i	0.258411	−	0.0839627i	0.435357	+	0.900258i	$0.356622\pi$
$488$	−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	$0.812038\pi$
$500$	8.94984	+	6.70078i	0.400249	+	0.299668i
$501$	−7.45679			−0.333145
$502$		−	7.42704i		−	0.331485i
$503$	8.27037	+	2.68721i	0.368758	+	0.119817i	0.487533	−	0.873105i	$-0.337897\pi$
$503$	8.27037	+	2.68721i	0.368758	+	0.119817i	−0.118775	+	0.992921i	$0.537897\pi$
$504$	−1.57980	−	4.86212i	−0.0703698	−	0.216576i
$505$	0.409696	−	0.0850369i	0.0182312	−	0.00378409i
$506$	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	$0.865420\pi$
$510$	−1.35917	−	6.54828i	−0.0601850	−	0.289963i
$511$	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
$515$	−23.5325	+	13.4368i	−1.03697	+	0.592096i
$516$	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
$520$	−11.6017	−	5.23204i	−0.508766	−	0.229440i
$521$	−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	0.800844	−	0.598873i	$-0.204384\pi$
$523$	25.0814	+	8.14944i	1.09673	+	0.356350i	0.295888	+	0.955223i	$0.404384\pi$
$524$	−2.57264	−	1.86914i	−0.112386	−	0.0816536i
$525$	23.4502	−	10.1730i	1.02345	−	0.443985i
$526$	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
$530$	−0.414695	+	0.456158i	−0.0180132	+	0.0198142i
$531$	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
$535$	0.293220	+	1.41269i	0.0126770	+	0.0610759i
$536$	−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
$540$	1.65455	+	1.50415i	0.0712003	+	0.0647285i
$541$	−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
$545$	−2.54104	+	2.79510i	−0.108846	+	0.119729i
$546$	−23.5404	+	17.1031i	−1.00743	+	0.731944i
$547$	4.17535	+	1.35665i	0.178525	+	0.0580063i	0.396915	−	0.917855i	$-0.370081\pi$
$547$	4.17535	+	1.35665i	0.178525	+	0.0580063i	−0.218390	+	0.975861i	$0.570081\pi$
$548$	−8.16142	−	11.2332i	−0.348639	−	0.479860i
$549$	−2.79430	−	8.59998i	−0.119258	−	0.367038i
$550$	18.9437	−	1.80797i	0.807760	−	0.0770923i
$551$	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
$555$	13.9139	−	15.3050i	0.590610	−	0.649662i
$556$	10.4775	−	7.61234i	0.444344	−	0.322835i
$557$		−	9.06908i		−	0.384269i	−0.981369	−	0.192135i	$-0.938459\pi$
$557$		−	9.06908i		−	0.384269i	0.981369	−	0.192135i	$-0.0615411\pi$
$558$	−4.80587	+	2.81134i	−0.203449	+	0.119013i
$559$	−16.9574			−0.717220
$560$	−9.92723	+	5.66834i	−0.419502	+	0.239531i
$561$	−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	$0.0913700\pi$
$563$			13.4356i			0.566243i	−0.959084	+	0.283122i	$0.908630\pi$
$564$	−5.06770			−0.213389
$565$	−13.9457	+	30.9236i	−0.586701	+	1.30097i
$566$	−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	$-0.102962\pi$
$570$	−2.11709	−	3.70776i	−0.0886751	−	0.155301i
$571$	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
$575$	28.1080	−	2.68261i	1.17218	−	0.111873i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	18.1326	+	24.9574i	0.754870	+	1.03899i	0.997623	+	0.0689012i	$0.0219493\pi$
$577$	18.1326	+	24.9574i	0.754870	+	1.03899i	−0.242754	+	0.970088i	$0.578051\pi$
$578$	−7.66032	−	2.48899i	−0.318627	−	0.103528i
$579$	−12.6853	+	9.21639i	−0.527182	+	0.383020i
$580$	0.470613	−	0.0976810i	0.0195411	−	0.00405598i
$581$	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
$585$	5.23204	−	11.6017i	0.216318	−	0.479669i
$586$	16.8455	+	12.2390i	0.695881	+	0.505587i
$587$	−16.7381	−	23.0381i	−0.690857	−	0.950883i	0.309143	−	0.951016i	$-0.399958\pi$
$587$	−16.7381	−	23.0381i	−0.690857	−	0.950883i	−1.00000		0.000132644i	$0.999958\pi$
$588$			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	0.684634	−	0.728887i	$-0.259962\pi$
$593$	19.7269	+	6.40966i	0.810087	+	0.263213i	0.125452	+	0.992100i	$0.459962\pi$
$594$	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	$0.175372\pi$
$600$	2.54132	−	4.30601i	0.103749	−	0.175792i
$601$	−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
$605$	5.24233	−	5.76648i	0.213131	−	0.234441i
$606$	−0.0578253	−	0.177968i	−0.00234899	−	0.00722945i
$607$	−9.78049	+	13.4617i	−0.396978	+	0.546393i	−0.959982	−	0.280061i	$-0.909645\pi$
$607$	−9.78049	+	13.4617i	−0.396978	+	0.546393i	0.563005	+	0.826454i	$0.309645\pi$
$608$	1.12233	+	1.54476i	0.0455166	+	0.0626482i
$609$	0.339578	−	1.04511i	0.0137604	−	0.0423502i
$610$	−17.5590	+	10.0260i	−0.710943	+	0.405941i
$611$	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	−0.176857	−	0.984237i	$-0.556593\pi$
$613$	−22.2447	−	7.22776i	−0.898457	−	0.291926i	−0.721600	+	0.692310i	$0.756593\pi$
$614$	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	$0.402766\pi$
$617$	−17.3683	+	23.9054i	−0.699222	+	0.962396i	−0.999962	+	0.00869005i	$0.997234\pi$
$618$	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	$0.567607\pi$
$620$	8.33911	+	9.24442i	0.334907	+	0.371265i
$621$	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
$630$	−5.66834	−	9.92723i	−0.225832	−	0.395510i
$631$	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
$635$	3.27602	+	2.97825i	0.130005	+	0.118188i
$636$	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
$640$	−0.919253	+	2.03838i	−0.0363367	+	0.0805739i
$641$	−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	−0.282876	−	0.959157i	$-0.591288\pi$
$643$	1.31988	−	0.428855i	0.0520510	−	0.0169124i	0.334927	+	0.942244i	$0.391288\pi$
$644$	−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	0.587144	−	0.809483i	$-0.300252\pi$
$647$	14.9145	+	4.84603i	0.586351	+	0.190517i	−0.000792846		1.00000i	$0.500252\pi$
$648$	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	0.524798	−	0.851227i	$-0.324141\pi$
$653$	−11.4210	−	15.7197i	−0.446939	−	0.615158i	−0.971736	+	0.236069i	$0.924141\pi$
$654$	1.36671	+	0.992973i	0.0534426	+	0.0388283i
$655$	−6.48196	−	2.92319i	−0.253271	−	0.114219i
$656$	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	$0.821783\pi$
$660$	−1.72956	−	8.33276i	−0.0673229	−	0.324352i
$661$	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
$665$	4.43603	+	21.3721i	0.172022	+	0.828776i
$666$	−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
$670$	−9.15687	−	16.0369i	−0.353761	−	0.619558i
$671$	−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	−0.757979	−	0.652279i	$-0.773813\pi$
$673$	−25.6257	+	8.32628i	−0.987796	+	0.320955i	−0.229818	+	0.973234i	$0.573813\pi$
$674$	−0.804395	−	2.47567i	−0.0309841	−	0.0953593i
$675$	4.30601	+	2.54132i	0.165738	+	0.0978153i
$676$	19.3945			0.745943
$677$			41.1522i			1.58161i	0.612069	+	0.790804i	$0.290337\pi$
$677$			41.1522i			1.58161i	−0.612069	+	0.790804i	$0.709663\pi$
$678$	14.4282	+	4.68801i	0.554112	+	0.180042i
$679$	6.30507	+	4.58090i	0.241966	+	0.175799i
$680$	3.31618	+	5.80778i	0.127170	+	0.222718i
$681$	18.9061			0.724483
$682$	21.0868	+	2.09480i	0.807456	+	0.0802140i
$683$			39.0702i			1.49498i	0.664274	+	0.747489i	$0.268741\pi$
$683$			39.0702i			1.49498i	−0.664274	+	0.747489i	$0.731259\pi$
$684$	−1.54476	+	1.12233i	−0.0590653	+	0.0429135i
$685$	−22.9734	−	20.8853i	−0.877770	−	0.797984i
$686$	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
$690$	−2.56626	−	12.3639i	−0.0976958	−	0.470684i
$691$	−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
$695$	19.4801	−	21.4278i	0.738923	−	0.812804i
$696$	−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
$700$	−19.1588	+	16.9216i	−0.724135	+	0.639575i
$701$	−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
$705$	−11.0953	+	2.30294i	−0.417871	+	0.0867339i
$706$	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	$0.185482\pi$
$710$	−11.1738	−	10.1581i	−0.419344	−	0.381227i
$711$	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
$715$	−42.0637	+	24.0179i	−1.57309	+	0.898218i
$716$	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	$0.486457\pi$
$720$	−2.03838	−	0.919253i	−0.0759658	−	0.0342585i
$721$	−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
$725$	0.985972	−	0.427726i	0.0366181	−	0.0158854i
$726$	−2.81962	−	2.04857i	−0.104646	−	0.0760296i
$727$	−37.2104	+	12.0904i	−1.38006	+	0.448407i	−0.902688	−	0.430296i	$-0.858409\pi$
$727$	−37.2104	+	12.0904i	−1.38006	+	0.448407i	−0.477368	+	0.878703i	$0.658409\pi$
$728$	17.1031	−	23.5404i	0.633882	−	0.872463i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	25.9365	−	5.38342i	0.959955	−	0.199249i
$731$	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	0.272746	−	0.962086i	$-0.412068\pi$
$733$	−1.95195	−	0.634227i	−0.0720969	−	0.0234257i	−0.344843	+	0.938660i	$0.612068\pi$
$734$	−2.64731	+	1.92339i	−0.0977141	+	0.0709935i
$735$	8.69607	+	41.8964i	0.320759	+	1.54537i
$736$	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	$0.725834\pi$
$740$	−8.50336	+	18.8556i	−0.312590	+	0.693144i
$741$	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	$-0.873106\pi$
$743$		−	21.1617i		−	0.776346i	0.921587	−	0.388173i	$-0.126894\pi$
$744$	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
$755$	−10.9779	−	4.95075i	−0.399527	−	0.180176i
$756$	−4.13597	+	3.00496i	−0.150424	+	0.109289i
$757$	−6.36982	+	8.76730i	−0.231515	+	0.318653i	−0.908931	−	0.416947i	$-0.863100\pi$
$757$	−6.36982	+	8.76730i	−0.231515	+	0.318653i	0.677416	+	0.735601i	$0.263100\pi$
$758$	22.3795	−	7.27153i	0.812859	−	0.264114i
$759$	−17.3880	−	12.6331i	−0.631143	−	0.458552i
$760$	3.15923	+	2.87207i	0.114597	+	0.104181i
$761$	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
$765$	−5.80778	+	3.31618i	−0.209981	+	0.119897i
$766$	−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	0.994469	−	0.105029i	$-0.0334936\pi$
$773$	16.3279	+	22.4734i	0.587273	+	0.808312i	−0.407196	+	0.913341i	$0.633494\pi$
$774$	−2.97935			−0.107091
$775$	22.4587	+	16.4502i	0.806739	+	0.590908i
$776$	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
$785$	−4.45223	+	2.54217i	−0.158907	+	0.0907340i
$786$	−0.982663	+	3.02432i	−0.0350504	+	0.107874i
$787$	−10.5855	−	14.5697i	−0.377333	−	0.519355i	0.577542	−	0.816361i	$-0.304012\pi$
$787$	−10.5855	−	14.5697i	−0.377333	−	0.519355i	−0.954876	+	0.297006i	$0.904012\pi$
$788$	−3.83208	+	5.27441i	−0.136512	+	0.187893i
$789$	−3.16808	−	9.75035i	−0.112787	−	0.347122i
$790$	−26.4687	−	24.0628i	−0.941713	−	0.856115i
$791$	−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
$795$	0.561980	+	0.253438i	0.0199314	+	0.00898852i
$796$	8.51570	−	6.18702i	0.301831	−	0.219293i
$797$	−23.5794	+	7.66140i	−0.835224	+	0.271381i	−0.695244	−	0.718774i	$-0.744704\pi$
$797$	−23.5794	+	7.66140i	−0.835224	+	0.271381i	−0.139980	+	0.990154i	$0.544704\pi$
$798$	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	$0.710106\pi$
$810$	0.919253	−	2.03838i	0.0322993	−	0.0716212i
$811$	−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
$815$	−6.68937	−	32.2284i	−0.234318	−	1.12891i
$816$	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
$820$	22.9246	−	4.75827i	0.800563	−	0.166166i
$821$	−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	−0.565352	−	0.824850i	$-0.691260\pi$
$823$	−15.4312	+	5.01390i	−0.537897	+	0.174773i	0.0274549	+	0.999623i	$0.491260\pi$
$824$	−9.80431	−	7.12325i	−0.341549	−	0.248150i
$825$	−7.57340	−	17.4578i	−0.263672	−	0.607802i
$826$	11.3463	−	34.9202i	0.394787	−	1.21503i
$827$	5.50586	+	7.57817i	0.191458	+	0.263519i	0.893944	−	0.448178i	$-0.147927\pi$
$827$	5.50586	+	7.57817i	0.191458	+	0.263519i	−0.702487	+	0.711697i	$0.747927\pi$
$828$	−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	$0.600642\pi$
$830$	9.65302	+	4.35326i	0.335061	+	0.151104i
$831$	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
$835$	14.4797	−	8.26777i	0.501092	−	0.286118i
$836$	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	$0.272658\pi$
$840$	8.45859	+	7.68974i	0.291849	+	0.265321i
$841$	−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
$845$	42.4624	−	8.81356i	1.46075	−	0.303196i
$846$	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
$850$	9.89971	+	11.2086i	0.339557	+	0.384451i
$851$	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	−0.441616	−	0.897204i	$-0.645595\pi$
$853$	16.0091	−	22.0347i	0.548142	−	0.754453i	0.989759	+	0.142751i	$0.0455948\pi$
$854$	−14.2854	−	43.9660i	−0.488837	−	1.50449i
$855$	−2.87207	+	3.15923i	−0.0982228	+	0.108043i
$856$	−0.522009	+	0.379262i	−0.0178419	+	0.0129629i
$857$	11.1486	+	3.62242i	0.380831	+	0.123739i	0.493175	−	0.869930i	$-0.335836\pi$
$857$	11.1486	+	3.62242i	0.380831	+	0.123739i	−0.112345	+	0.993669i	$0.535836\pi$
$858$	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	$0.844021\pi$
$860$	1.35392	+	6.52301i	0.0461684	+	0.222433i
$861$	16.5416	−	50.9099i	0.563737	−	1.73500i
$862$		−	27.7908i		−	0.946557i
$863$			3.27852i			0.111602i	0.998442	+	0.0558011i	$0.0177713\pi$
$863$			3.27852i			0.111602i	−0.998442	+	0.0558011i	$0.982229\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	7.86730	+	7.15220i	0.267496	+	0.243182i
$866$	−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
$870$	−0.238327	−	0.417394i	−0.00808006	−	0.0141510i
$871$	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
$875$	−34.2566	+	45.7546i	−1.15809	+	1.54679i
$876$	−3.66074	−	11.2666i	−0.123685	−	0.380663i
$877$	−4.49276	+	1.45979i	−0.151710	+	0.0492935i	−0.383887	−	0.923380i	$-0.625415\pi$
$877$	−4.49276	+	1.45979i	−0.151710	+	0.0492935i	0.232178	+	0.972673i	$0.425415\pi$
$878$	11.6253	+	16.0008i	0.392335	+	0.540002i
$879$	6.43441	−	19.8031i	0.217027	−	0.667941i
$880$	4.21987	+	7.39046i	0.142252	+	0.249132i
$881$	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	−0.550604	−	0.834767i	$-0.685602\pi$
$883$	12.2859	−	16.9101i	0.413453	−	0.569069i	0.964056	+	0.265698i	$0.0856024\pi$
$884$	−13.7719	−	10.0059i	−0.463200	−	0.336535i
$885$	3.26380	+	15.7245i	0.109711	+	0.528574i
$886$	−22.9084	−	16.6439i	−0.769622	−	0.559163i
$887$	3.85924	+	5.31179i	0.129581	+	0.178353i	0.868877	−	0.495027i	$-0.164842\pi$
$887$	3.85924	+	5.31179i	0.129581	+	0.178353i	−0.739297	+	0.673380i	$0.764842\pi$
$888$	8.79755	+	2.85850i	0.295226	+	0.0959248i
$889$	−8.18927	+	5.94985i	−0.274659	+	0.199552i
$890$	8.54718	+	41.1791i	0.286502	+	1.38033i
$891$	−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
$895$	1.41156	+	0.636574i	0.0471831	+	0.0212783i
$896$	−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	−0.200040	−	0.979788i	$-0.564107\pi$
$907$	6.44578	−	2.09436i	0.214028	−	0.0695421i	0.414069	+	0.910246i	$0.364107\pi$
$908$	−17.9808	+	5.84230i	−0.596712	+	0.193884i
$909$	−0.151389	+	0.109990i	−0.00502124	+	0.00364815i
$910$	26.7479	−	59.3116i	0.886686	−	1.96616i
$911$	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
$915$	14.9613	+	13.6014i	0.494606	+	0.449648i
$916$	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	$-0.0219730\pi$
$920$	6.26130	+	10.9657i	0.206429	+	0.361529i
$921$	−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	$0.446338\pi$
$930$	6.21504	−	10.7876i	0.203799	−	0.353741i
$931$	−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	0.158360	−	0.987381i	$-0.449379\pi$
$937$	−8.99617	−	2.92303i	−0.293892	−	0.0954913i	−0.452252	+	0.891890i	$0.649379\pi$
$938$	40.1547	−	13.0471i	1.31110	−	0.426002i
$939$	0.0926810	+	0.285243i	0.00302453	+	0.00930855i
$940$	9.84056	−	5.61885i	0.320964	−	0.183267i
$941$	−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
$945$	−7.68974	+	8.45859i	−0.250147	+	0.275158i
$946$	9.17366	+	6.66505i	0.298261	+	0.216700i
$947$	−1.95029	+	0.633687i	−0.0633758	+	0.0205921i	−0.340533	−	0.940232i	$-0.610608\pi$
$947$	−1.95029	+	0.633687i	−0.0633758	+	0.0205921i	0.277157	+	0.960825i	$0.410608\pi$
$948$	−9.40312	+	12.9423i	−0.305399	+	0.420346i
$949$	−54.5481	+	39.6315i	−1.77071	+	1.28649i
$950$	8.22200	+	4.85246i	0.266757	+	0.157434i
$951$	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	−0.0920144	−	0.995758i	$-0.529331\pi$
$953$	12.9298	−	4.20113i	0.418836	−	0.136088i	0.510850	+	0.859670i	$0.329331\pi$
$954$	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
$965$	14.4138	−	31.9614i	0.463995	−	1.02887i
$966$	28.8701			0.928879
$967$			38.3601i			1.23358i	0.787129	+	0.616789i	$0.211567\pi$
$967$			38.3601i			1.23358i	−0.787129	+	0.616789i	$0.788433\pi$
$968$	3.31466	+	1.07700i	0.106537	+	0.0346160i
$969$	−1.76476	−	5.43138i	−0.0566924	−	0.174481i
$970$	3.33763	−	0.692763i	0.107165	−	0.0222433i
$971$	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
$975$	2.70374	+	28.3294i	0.0865891	+	0.907266i
$976$	−7.31558	−	5.31508i	−0.234166	−	0.170132i
$977$	−23.4011	+	32.2088i	−0.748667	+	1.03045i	0.249406	+	0.968399i	$0.419765\pi$
$977$	−23.4011	+	32.2088i	−0.748667	+	1.03045i	−0.998073	+	0.0620524i	$0.980235\pi$
$978$	−13.9997	+	4.54878i	−0.447662	+	0.145454i
$979$	57.9124	+	42.0758i	1.85089	+	1.34475i
$980$	−21.2172	−	37.1586i	−0.677757	−	1.18699i
$981$	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	−0.807402	−	0.590002i	$-0.799127\pi$
$983$	−34.9210	+	11.3465i	−1.11381	+	0.361898i	−0.306407	+	0.951901i	$0.599127\pi$
$984$	−3.23563	−	9.95825i	−0.103148	−	0.317457i
$985$	−5.99310	+	13.2892i	−0.190956	+	0.423431i
$986$	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
$990$	−7.39046	+	4.21987i	−0.234884	+	0.134116i
$991$	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
$995$	15.8327	−	17.4157i	0.501931	−	0.552115i
$996$	1.46339	−	4.50387i	0.0463694	−	0.142710i
$997$			32.4336i			1.02718i	0.858035	+	0.513591i	$0.171685\pi$
$997$			32.4336i			1.02718i	−0.858035	+	0.513591i	$0.828315\pi$
$998$		−	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.109.13	yes	72
5.4	even	2	inner	930.2.z.d.109.4	✓	72
31.2	even	5	inner	930.2.z.d.529.4	yes	72
155.64	even	10	inner	930.2.z.d.529.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.4	✓	72	5.4	even	2	inner
930.2.z.d.109.13	yes	72	1.1	even	1	trivial
930.2.z.d.529.4	yes	72	31.2	even	5	inner
930.2.z.d.529.13	yes	72	155.64	even	10	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} +(-1.94182 + 1.10876i) 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} +(1.65455 + 1.50415i) 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} +(-2.03838 - 0.919253i) 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} +(4.69953 - 10.4209i) q^{35} +1.00000 q^{36} -9.25029i q^{37} +(-1.81597 - 0.590045i) q^{38} +(-1.75881 - 5.41305i) q^{39} +(-0.454435 - 2.18940i) 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} +(2.18940 - 0.454435i) 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} +(-1.98989 - 4.58698i) 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} +(-7.75795 - 3.49863i) q^{55} +5.11234 q^{56} +1.90943i q^{57} +(-0.204430 - 0.0664233i) q^{58} +(5.81044 + 4.22153i) q^{59} +(-1.94182 + 1.10876i) q^{60} +9.04256 q^{61} +(-1.18864 - 5.43941i) q^{62} +5.11234i q^{63} +(0.809017 - 0.587785i) q^{64} +(9.41704 + 8.56107i) q^{65} +(-1.17610 + 3.61967i) q^{66} +8.25869i q^{67} -2.99090i q^{68} +(-1.74506 + 5.37075i) q^{69} +(11.1930 - 2.32323i) 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} +(-3.74757 + 3.30995i) 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} +(1.50415 - 1.65455i) 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} +(-1.35917 - 6.54828i) q^{85} +(0.920671 - 2.83353i) q^{86} +0.214950i q^{87} -3.80595i q^{88} +(5.81210 - 17.8878i) q^{89} +(1.65455 + 1.50415i) q^{90} +(-23.5404 + 17.1031i) q^{91} -5.64714i q^{92} +(-4.80587 + 2.81134i) q^{93} -5.06770 q^{94} +(-2.11709 - 3.70776i) 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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