LMFDB - Embedded newform 546.2.bb.a.269.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.15
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.32763 + 1.11238i) q^{3} -1.00000 q^{4} +(-1.76347 - 3.05441i) q^{5} +(1.11238 - 1.32763i) q^{6} +(-2.64100 + 0.158422i) q^{7} +1.00000i q^{8} +(0.525225 + 2.95367i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.32763 + 1.11238i) q^{3} -1.00000 q^{4} +(-1.76347 - 3.05441i) q^{5} +(1.11238 - 1.32763i) q^{6} +(-2.64100 + 0.158422i) q^{7} +1.00000i q^{8} +(0.525225 + 2.95367i) q^{9} +(-3.05441 + 1.76347i) q^{10} +(4.83655 - 2.79238i) q^{11} +(-1.32763 - 1.11238i) q^{12} +(-1.38855 - 3.32745i) q^{13} +(0.158422 + 2.64100i) q^{14} +(1.05643 - 6.01678i) q^{15} +1.00000 q^{16} -2.75055 q^{17} +(2.95367 - 0.525225i) q^{18} +(-6.26098 - 3.61478i) q^{19} +(1.76347 + 3.05441i) q^{20} +(-3.68251 - 2.72747i) q^{21} +(-2.79238 - 4.83655i) q^{22} -4.52231i q^{23} +(-1.11238 + 1.32763i) q^{24} +(-3.71962 + 6.44257i) q^{25} +(-3.32745 + 1.38855i) q^{26} +(-2.58829 + 4.50564i) q^{27} +(2.64100 - 0.158422i) q^{28} +(-0.473303 - 0.273262i) q^{29} +(-6.01678 - 1.05643i) q^{30} +(-1.25106 - 0.722302i) q^{31} -1.00000i q^{32} +(9.52735 + 1.67281i) q^{33} +2.75055i q^{34} +(5.14121 + 7.78734i) q^{35} +(-0.525225 - 2.95367i) q^{36} -2.70444 q^{37} +(-3.61478 + 6.26098i) q^{38} +(1.85790 - 5.96223i) q^{39} +(3.05441 - 1.76347i) q^{40} +(3.63062 - 6.28842i) q^{41} +(-2.72747 + 3.68251i) q^{42} +(0.0709937 + 0.122965i) q^{43} +(-4.83655 + 2.79238i) q^{44} +(8.09550 - 6.81294i) q^{45} -4.52231 q^{46} +(-1.96371 - 3.40124i) q^{47} +(1.32763 + 1.11238i) q^{48} +(6.94980 - 0.836788i) q^{49} +(6.44257 + 3.71962i) q^{50} +(-3.65172 - 3.05965i) q^{51} +(1.38855 + 3.32745i) q^{52} +(9.33624 + 5.39028i) q^{53} +(4.50564 + 2.58829i) q^{54} +(-17.0582 - 9.84854i) q^{55} +(-0.158422 - 2.64100i) q^{56} +(-4.29128 - 11.7637i) q^{57} +(-0.273262 + 0.473303i) q^{58} +7.42880 q^{59} +(-1.05643 + 6.01678i) q^{60} +(10.8209 + 6.24747i) q^{61} +(-0.722302 + 1.25106i) q^{62} +(-1.85505 - 7.71743i) q^{63} -1.00000 q^{64} +(-7.71474 + 10.1091i) q^{65} +(1.67281 - 9.52735i) q^{66} +(5.25998 + 9.11054i) q^{67} +2.75055 q^{68} +(5.03052 - 6.00397i) q^{69} +(7.78734 - 5.14121i) q^{70} +(1.01248 - 0.584557i) q^{71} +(-2.95367 + 0.525225i) q^{72} +(11.2019 + 6.46743i) q^{73} +2.70444i q^{74} +(-12.1049 + 4.41575i) q^{75} +(6.26098 + 3.61478i) q^{76} +(-12.3310 + 8.14091i) q^{77} +(-5.96223 - 1.85790i) q^{78} +(-4.47939 - 7.75854i) q^{79} +(-1.76347 - 3.05441i) q^{80} +(-8.44828 + 3.10268i) q^{81} +(-6.28842 - 3.63062i) q^{82} -3.92570 q^{83} +(3.68251 + 2.72747i) q^{84} +(4.85050 + 8.40131i) q^{85} +(0.122965 - 0.0709937i) q^{86} +(-0.324403 - 0.889285i) q^{87} +(2.79238 + 4.83655i) q^{88} +1.35423 q^{89} +(-6.81294 - 8.09550i) q^{90} +(4.19431 + 8.56783i) q^{91} +4.52231i q^{92} +(-0.857481 - 2.35061i) q^{93} +(-3.40124 + 1.96371i) q^{94} +25.4981i q^{95} +(1.11238 - 1.32763i) q^{96} +(-11.1130 + 6.41610i) q^{97} +(-0.836788 - 6.94980i) q^{98} +(10.7880 + 12.8189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.32763	+	1.11238i	0.766510	+	0.642232i
$3$	1.32763	+	1.11238i	0.766510	+	0.642232i
$4$	−1.00000			−0.500000
$5$	−1.76347	−	3.05441i	−0.788646	−	1.36597i	−0.926797	−	0.375563i	$-0.877449\pi$
$5$	−1.76347	−	3.05441i	−0.788646	−	1.36597i	0.138151	−	0.990411i	$-0.455884\pi$
$6$	1.11238	−	1.32763i	0.454127	−	0.542004i
$7$	−2.64100	+	0.158422i	−0.998206	+	0.0598780i
$7$	−2.64100	+	0.158422i	−0.998206	+	0.0598780i
$8$			1.00000i			0.353553i
$9$	0.525225	+	2.95367i	0.175075	+	0.984555i
$10$	−3.05441	+	1.76347i	−0.965890	+	0.557657i
$11$	4.83655	−	2.79238i	1.45827	−	0.841935i	0.459347	−	0.888257i	$-0.348084\pi$
$11$	4.83655	−	2.79238i	1.45827	−	0.841935i	0.998927	+	0.0463224i	$0.0147502\pi$
$12$	−1.32763	−	1.11238i	−0.383255	−	0.321116i
$13$	−1.38855	−	3.32745i	−0.385115	−	0.922869i
$13$	−1.38855	−	3.32745i	−0.385115	−	0.922869i
$14$	0.158422	+	2.64100i	0.0423401	+	0.705838i
$15$	1.05643	−	6.01678i	0.272768	−	1.55353i
$16$	1.00000			0.250000
$17$	−2.75055			−0.667106			−0.333553	−	0.942731i	$-0.608248\pi$
$17$	−2.75055			−0.667106			−0.333553	+	0.942731i	$0.608248\pi$
$18$	2.95367	−	0.525225i	0.696186	−	0.123797i
$19$	−6.26098	−	3.61478i	−1.43637	−	0.829287i	−0.438772	−	0.898599i	$-0.644586\pi$
$19$	−6.26098	−	3.61478i	−1.43637	−	0.829287i	−0.997595	+	0.0693117i	$0.977920\pi$
$20$	1.76347	+	3.05441i	0.394323	+	0.682987i
$21$	−3.68251	−	2.72747i	−0.803590	−	0.595183i
$22$	−2.79238	−	4.83655i	−0.595338	−	1.03116i
$23$		−	4.52231i		−	0.942966i	−0.881875	−	0.471483i	$-0.843719\pi$
$23$		−	4.52231i		−	0.942966i	0.881875	−	0.471483i	$-0.156281\pi$
$24$	−1.11238	+	1.32763i	−0.227063	+	0.271002i
$25$	−3.71962	+	6.44257i	−0.743924	+	1.28851i
$26$	−3.32745	+	1.38855i	−0.652567	+	0.272317i
$27$	−2.58829	+	4.50564i	−0.498117	+	0.867110i
$28$	2.64100	−	0.158422i	0.499103	−	0.0299390i
$29$	−0.473303	−	0.273262i	−0.0878902	−	0.0507435i	0.455411	−	0.890281i	$-0.349492\pi$
$29$	−0.473303	−	0.273262i	−0.0878902	−	0.0507435i	−0.543301	+	0.839538i	$0.682826\pi$
$30$	−6.01678	−	1.05643i	−1.09851	−	0.192876i
$31$	−1.25106	−	0.722302i	−0.224698	−	0.129729i	0.383426	−	0.923572i	$-0.374744\pi$
$31$	−1.25106	−	0.722302i	−0.224698	−	0.129729i	−0.608124	+	0.793842i	$0.708077\pi$
$32$		−	1.00000i		−	0.176777i
$33$	9.52735	+	1.67281i	1.65850	+	0.291199i
$34$			2.75055i			0.471715i
$35$	5.14121	+	7.78734i	0.869023	+	1.31630i
$36$	−0.525225	−	2.95367i	−0.0875375	−	0.492278i
$37$	−2.70444			−0.444608			−0.222304	−	0.974977i	$-0.571358\pi$
$37$	−2.70444			−0.444608			−0.222304	+	0.974977i	$0.571358\pi$
$38$	−3.61478	+	6.26098i	−0.586394	+	1.01566i
$39$	1.85790	−	5.96223i	0.297502	−	0.954721i
$40$	3.05441	−	1.76347i	0.482945	−	0.278828i
$41$	3.63062	−	6.28842i	0.567008	−	0.982086i	−0.429852	−	0.902899i	$-0.641434\pi$
$41$	3.63062	−	6.28842i	0.567008	−	0.982086i	0.996860	−	0.0791869i	$-0.0252324\pi$
$42$	−2.72747	+	3.68251i	−0.420858	+	0.568224i
$43$	0.0709937	+	0.122965i	0.0108264	+	0.0187519i	0.871388	−	0.490595i	$-0.163220\pi$
$43$	0.0709937	+	0.122965i	0.0108264	+	0.0187519i	−0.860561	+	0.509347i	$0.829887\pi$
$44$	−4.83655	+	2.79238i	−0.729137	+	0.420967i
$45$	8.09550	−	6.81294i	1.20681	−	1.01561i
$46$	−4.52231			−0.666778
$47$	−1.96371	−	3.40124i	−0.286436	−	0.496122i	0.686520	−	0.727110i	$-0.259137\pi$
$47$	−1.96371	−	3.40124i	−0.286436	−	0.496122i	−0.972956	+	0.230989i	$0.925804\pi$
$48$	1.32763	+	1.11238i	0.191627	+	0.160558i
$49$	6.94980	−	0.836788i	0.992829	−	0.119541i
$50$	6.44257	+	3.71962i	0.911118	+	0.526034i
$51$	−3.65172	−	3.05965i	−0.511343	−	0.428437i
$52$	1.38855	+	3.32745i	0.192558	+	0.461434i
$53$	9.33624	+	5.39028i	1.28243	+	0.740412i	0.977292	−	0.211896i	$-0.0679639\pi$
$53$	9.33624	+	5.39028i	1.28243	+	0.740412i	0.305139	+	0.952308i	$0.401297\pi$
$54$	4.50564	+	2.58829i	0.613139	+	0.352222i
$55$	−17.0582	−	9.84854i	−2.30012	−	1.32798i
$56$	−0.158422	−	2.64100i	−0.0211701	−	0.352919i
$57$	−4.29128	−	11.7637i	−0.568395	−	1.55814i
$58$	−0.273262	+	0.473303i	−0.0358810	+	0.0621478i
$59$	7.42880			0.967147			0.483574	−	0.875304i	$-0.339339\pi$
$59$	7.42880			0.967147			0.483574	+	0.875304i	$0.339339\pi$
$60$	−1.05643	+	6.01678i	−0.136384	+	0.776763i
$61$	10.8209	+	6.24747i	1.38548	+	0.799907i	0.992802	−	0.119769i	$-0.0382155\pi$
$61$	10.8209	+	6.24747i	1.38548	+	0.799907i	0.392678	+	0.919676i	$0.371549\pi$
$62$	−0.722302	+	1.25106i	−0.0917324	+	0.158885i
$63$	−1.85505	−	7.71743i	−0.233714	−	0.972305i
$64$	−1.00000			−0.125000
$65$	−7.71474	+	10.1091i	−0.956896	+	1.25387i
$66$	1.67281	−	9.52735i	0.205909	−	1.17274i
$67$	5.25998	+	9.11054i	0.642608	+	1.11303i	0.984848	+	0.173418i	$0.0554810\pi$
$67$	5.25998	+	9.11054i	0.642608	+	1.11303i	−0.342240	+	0.939613i	$0.611186\pi$
$68$	2.75055			0.333553
$69$	5.03052	−	6.00397i	0.605603	−	0.722793i
$70$	7.78734	−	5.14121i	0.930765	−	0.614492i
$71$	1.01248	−	0.584557i	0.120159	−	0.0693741i	−0.438716	−	0.898626i	$-0.644566\pi$
$71$	1.01248	−	0.584557i	0.120159	−	0.0693741i	0.558875	+	0.829252i	$0.311233\pi$
$72$	−2.95367	+	0.525225i	−0.348093	+	0.0618983i
$73$	11.2019	+	6.46743i	1.31109	+	0.756956i	0.982276	−	0.187441i	$-0.0600192\pi$
$73$	11.2019	+	6.46743i	1.31109	+	0.756956i	0.328810	+	0.944396i	$0.393353\pi$
$74$			2.70444i			0.314385i
$75$	−12.1049	+	4.41575i	−1.39775	+	0.509887i
$76$	6.26098	+	3.61478i	0.718183	+	0.414643i
$77$	−12.3310	+	8.14091i	−1.40524	+	0.927742i
$78$	−5.96223	−	1.85790i	−0.675090	−	0.210365i
$79$	−4.47939	−	7.75854i	−0.503971	−	0.872904i	−0.999989	−	0.00459152i	$-0.998538\pi$
$79$	−4.47939	−	7.75854i	−0.503971	−	0.872904i	0.496018	−	0.868312i	$-0.334795\pi$
$80$	−1.76347	−	3.05441i	−0.197161	−	0.341494i
$81$	−8.44828	+	3.10268i	−0.938698	+	0.344742i
$82$	−6.28842	−	3.63062i	−0.694440	−	0.400935i
$83$	−3.92570			−0.430901			−0.215451	−	0.976515i	$-0.569122\pi$
$83$	−3.92570			−0.430901			−0.215451	+	0.976515i	$0.569122\pi$
$84$	3.68251	+	2.72747i	0.401795	+	0.297592i
$85$	4.85050	+	8.40131i	0.526110	+	0.911249i
$86$	0.122965	−	0.0709937i	0.0132596	−	0.00765544i
$87$	−0.324403	−	0.889285i	−0.0347797	−	0.0953413i
$88$	2.79238	+	4.83655i	0.297669	+	0.515578i
$89$	1.35423			0.143548			0.0717739	−	0.997421i	$-0.477134\pi$
$89$	1.35423			0.143548			0.0717739	+	0.997421i	$0.477134\pi$
$90$	−6.81294	−	8.09550i	−0.718147	−	0.853340i
$91$	4.19431	+	8.56783i	0.439684	+	0.898153i
$92$			4.52231i			0.471483i
$93$	−0.857481	−	2.35061i	−0.0889166	−	0.243747i
$94$	−3.40124	+	1.96371i	−0.350811	+	0.202541i
$95$			25.4981i			2.61605i
$96$	1.11238	−	1.32763i	0.113532	−	0.135501i
$97$	−11.1130	+	6.41610i	−1.12836	+	0.651456i	−0.943521	−	0.331313i	$-0.892508\pi$
$97$	−11.1130	+	6.41610i	−1.12836	+	0.651456i	−0.184835	+	0.982770i	$0.559175\pi$
$98$	−0.836788	−	6.94980i	−0.0845283	−	0.702036i
$99$	10.7880	+	12.8189i	1.08424	+	1.28835i
$100$	3.71962	−	6.44257i	0.371962	−	0.644257i
$101$	−3.86514	−	6.69463i	−0.384596	−	0.666140i	0.607117	−	0.794613i	$-0.292326\pi$
$101$	−3.86514	−	6.69463i	−0.384596	−	0.666140i	−0.991713	+	0.128472i	$0.958993\pi$
$102$	−3.05965	+	3.65172i	−0.302951	+	0.361574i
$103$	−2.85313	+	1.64725i	−0.281127	+	0.162309i	−0.633933	−	0.773388i	$-0.718561\pi$
$103$	−2.85313	+	1.64725i	−0.281127	+	0.162309i	0.352807	+	0.935696i	$0.385227\pi$
$104$	3.32745	−	1.38855i	0.326283	−	0.136159i
$105$	−1.83684	+	16.0577i	−0.179257	+	1.56707i
$106$	5.39028	−	9.33624i	0.523550	−	0.906815i
$107$			1.51172i			0.146144i	0.997327	+	0.0730719i	$0.0232803\pi$
$107$			1.51172i			0.146144i	−0.997327	+	0.0730719i	$0.976720\pi$
$108$	2.58829	−	4.50564i	0.249058	−	0.433555i
$109$	5.99142	−	10.3775i	0.573874	−	0.993979i	−0.422289	−	0.906461i	$-0.638773\pi$
$109$	5.99142	−	10.3775i	0.573874	−	0.993979i	0.996163	−	0.0875181i	$-0.0278935\pi$
$110$	−9.84854	+	17.0582i	−0.939021	+	1.62643i
$111$	−3.59051	−	3.00837i	−0.340796	−	0.285542i
$112$	−2.64100	+	0.158422i	−0.249551	+	0.0149695i
$113$	−3.57873	+	2.06618i	−0.336659	+	0.194370i	−0.658793	−	0.752324i	$-0.728933\pi$
$113$	−3.57873	+	2.06618i	−0.336659	+	0.194370i	0.322135	+	0.946694i	$0.395600\pi$
$114$	−11.7637	+	4.29128i	−1.10177	+	0.401916i
$115$	−13.8130	+	7.97493i	−1.28807	+	0.743666i
$116$	0.473303	+	0.273262i	0.0439451	+	0.0253717i
$117$	9.09887	−	5.84898i	0.841191	−	0.540738i
$118$		−	7.42880i		−	0.683877i
$119$	7.26421	−	0.435748i	0.665909	−	0.0399449i
$120$	6.01678	+	1.05643i	0.549255	+	0.0964382i
$121$	10.0948	−	17.4847i	0.917708	−	1.58952i
$122$	6.24747	−	10.8209i	0.565620	−	0.979682i
$123$	11.8152	−	4.31009i	1.06534	−	0.388628i
$124$	1.25106	+	0.722302i	0.112349	+	0.0648646i
$125$	8.60304			0.769480
$126$	−7.71743	+	1.85505i	−0.687524	+	0.165261i
$127$	2.29973	−	3.98324i	0.204068	−	0.353456i	−0.745768	−	0.666206i	$-0.767917\pi$
$127$	2.29973	−	3.98324i	0.204068	−	0.353456i	0.949835	+	0.312751i	$0.101250\pi$
$128$			1.00000i			0.0883883i
$129$	−0.0425297	+	0.242224i	−0.00374453	+	0.0213266i
$130$	10.1091	+	7.71474i	0.886623	+	0.676627i
$131$	−2.02661	−	3.51018i	−0.177065	−	0.306686i	0.763809	−	0.645443i	$-0.223327\pi$
$131$	−2.02661	−	3.51018i	−0.177065	−	0.306686i	−0.940874	+	0.338756i	$0.889994\pi$
$132$	−9.52735	−	1.67281i	−0.829249	−	0.145600i
$133$	17.1079	+	8.55476i	1.48345	+	0.741792i
$134$	9.11054	−	5.25998i	0.787031	−	0.454393i
$135$	18.3264	−	0.0398309i	1.57729	−	0.00342810i
$136$		−	2.75055i		−	0.235857i
$137$		−	2.66334i		−	0.227545i	−0.993507	−	0.113772i	$-0.963707\pi$
$137$		−	2.66334i		−	0.227545i	0.993507	−	0.113772i	$-0.0362935\pi$
$138$	−6.00397	−	5.03052i	−0.511092	−	0.428226i
$139$	12.6149	−	7.28322i	1.06998	−	0.617755i	0.141806	−	0.989894i	$-0.454709\pi$
$139$	12.6149	−	7.28322i	1.06998	−	0.617755i	0.928177	+	0.372139i	$0.121376\pi$
$140$	−5.14121	−	7.78734i	−0.434511	−	0.658151i
$141$	1.17638	−	6.69999i	0.0990694	−	0.564241i
$142$	−0.584557	−	1.01248i	−0.0490549	−	0.0849656i
$143$	−16.0073	−	12.2160i	−1.33860	−	1.02155i
$144$	0.525225	+	2.95367i	0.0437687	+	0.246139i
$145$			1.92755i			0.160074i
$146$	6.46743	−	11.2019i	0.535248	−	0.927077i
$147$	10.1576	+	6.61987i	0.837787	+	0.545998i
$148$	2.70444			0.222304
$149$	6.11590	+	3.53101i	0.501034	+	0.289272i	0.729140	−	0.684364i	$-0.239920\pi$
$149$	6.11590	+	3.53101i	0.501034	+	0.289272i	−0.228107	+	0.973636i	$0.573253\pi$
$150$	4.41575	+	12.1049i	0.360545	+	0.988360i
$151$	−0.381853	+	0.661388i	−0.0310747	+	0.0538230i	−0.881145	−	0.472847i	$-0.843226\pi$
$151$	−0.381853	+	0.661388i	−0.0310747	+	0.0538230i	0.850070	+	0.526670i	$0.176560\pi$
$152$	3.61478	−	6.26098i	0.293197	−	0.507832i
$153$	−1.44466	−	8.12420i	−0.116793	−	0.656802i
$154$	8.14091	+	12.3310i	0.656013	+	0.993657i
$155$			5.09502i			0.409242i
$156$	−1.85790	+	5.96223i	−0.148751	+	0.477361i
$157$	−13.9268	−	8.04062i	−1.11148	−	0.641711i	−0.172265	−	0.985051i	$-0.555108\pi$
$157$	−13.9268	−	8.04062i	−1.11148	−	0.641711i	−0.939211	+	0.343340i	$0.888442\pi$
$158$	−7.75854	+	4.47939i	−0.617236	+	0.356361i
$159$	6.39907	+	17.5418i	0.507479	+	1.39115i
$160$	−3.05441	+	1.76347i	−0.241472	+	0.139414i
$161$	0.716434	+	11.9434i	0.0564629	+	0.941274i
$162$	3.10268	+	8.44828i	0.243769	+	0.663759i
$163$	−3.59628	+	6.22894i	−0.281682	+	0.487888i	−0.971799	−	0.235810i	$-0.924226\pi$
$163$	−3.59628	+	6.22894i	−0.281682	+	0.487888i	0.690117	+	0.723698i	$0.257559\pi$
$164$	−3.63062	+	6.28842i	−0.283504	+	0.491043i
$165$	−11.6917	−	32.0504i	−0.910197	−	2.49512i
$166$			3.92570i			0.304693i
$167$	3.75042	−	6.49592i	0.290216	−	0.502669i	−0.683644	−	0.729815i	$-0.739606\pi$
$167$	3.75042	−	6.49592i	0.290216	−	0.502669i	0.973861	+	0.227146i	$0.0729394\pi$
$168$	2.72747	−	3.68251i	0.210429	−	0.284112i
$169$	−9.14385	+	9.24067i	−0.703373	+	0.710821i
$170$	8.40131	−	4.85050i	0.644351	−	0.372016i
$171$	7.38842	−	20.3914i	0.565007	−	1.55937i
$172$	−0.0709937	−	0.122965i	−0.00541322	−	0.00937596i
$173$	11.0331	−	19.1098i	0.838827	−	1.45289i	−0.0520486	−	0.998645i	$-0.516575\pi$
$173$	11.0331	−	19.1098i	0.838827	−	1.45289i	0.890876	−	0.454247i	$-0.150092\pi$
$174$	−0.889285	+	0.324403i	−0.0674165	+	0.0245929i
$175$	8.80289	−	17.6041i	0.665436	−	1.33075i
$176$	4.83655	−	2.79238i	0.364568	−	0.210484i
$177$	9.86273	+	8.26364i	0.741328	+	0.621133i
$178$		−	1.35423i		−	0.101504i
$179$	−9.63731	+	5.56410i	−0.720326	+	0.415881i	−0.814873	−	0.579640i	$-0.803193\pi$
$179$	−9.63731	+	5.56410i	−0.720326	+	0.415881i	0.0945465	+	0.995520i	$0.469860\pi$
$180$	−8.09550	+	6.81294i	−0.603403	+	0.507807i
$181$			3.28580i			0.244232i	0.992516	+	0.122116i	$0.0389680\pi$
$181$			3.28580i			0.244232i	−0.992516	+	0.122116i	$0.961032\pi$
$182$	8.56783	−	4.19431i	0.635090	−	0.310903i
$183$	7.41669	+	20.3313i	0.548257	+	1.50294i
$184$	4.52231			0.333389
$185$	4.76919	+	8.26048i	0.350638	+	0.607323i
$186$	−2.35061	+	0.857481i	−0.172355	+	0.0628735i
$187$	−13.3031	+	7.68058i	−0.972823	+	0.561659i
$188$	1.96371	+	3.40124i	0.143218	+	0.248061i
$189$	6.12189	−	12.3094i	0.445302	−	0.895380i
$190$	25.4981			1.84983
$191$	−1.96531	−	1.13467i	−0.142204	−	0.0821018i	0.427210	−	0.904153i	$-0.359497\pi$
$191$	−1.96531	−	1.13467i	−0.142204	−	0.0821018i	−0.569414	+	0.822051i	$0.692830\pi$
$192$	−1.32763	−	1.11238i	−0.0958137	−	0.0802791i
$193$	−8.00636	−	13.8674i	−0.576311	−	0.998199i	−0.995898	−	0.0904843i	$-0.971159\pi$
$193$	−8.00636	−	13.8674i	−0.576311	−	0.998199i	0.419587	−	0.907715i	$-0.362175\pi$
$194$	6.41610	+	11.1130i	0.460649	+	0.797868i
$195$	−21.4875	+	4.83941i	−1.53875	+	0.346557i
$196$	−6.94980	+	0.836788i	−0.496415	+	0.0597705i
$197$	20.3601	+	11.7549i	1.45060	+	0.837503i	0.998515	−	0.0544726i	$-0.0173478\pi$
$197$	20.3601	+	11.7549i	1.45060	+	0.837503i	0.452083	+	0.891976i	$0.350681\pi$
$198$	12.8189	−	10.7880i	0.911000	−	0.766672i
$199$			4.36567i			0.309474i	0.987956	+	0.154737i	$0.0494531\pi$
$199$			4.36567i			0.309474i	−0.987956	+	0.154737i	$0.950547\pi$
$200$	−6.44257	−	3.71962i	−0.455559	−	0.263017i
$201$	−3.15106	+	17.9466i	−0.222258	+	1.26585i
$202$	−6.69463	+	3.86514i	−0.471032	+	0.271951i
$203$	1.29329	+	0.646704i	0.0907710	+	0.0453897i
$204$	3.65172	+	3.05965i	0.255672	+	0.214218i
$205$	−25.6099			−1.78867
$206$	1.64725	+	2.85313i	0.114770	+	0.198787i
$207$	13.3574	−	2.37523i	0.928402	−	0.165090i
$208$	−1.38855	−	3.32745i	−0.0962788	−	0.230717i
$209$	−40.3753			−2.79282
$210$	16.0577	+	1.83684i	1.10809	+	0.126754i
$211$	2.97744	−	5.15707i	0.204975	−	0.355028i	−0.745150	−	0.666897i	$-0.767622\pi$
$211$	2.97744	−	5.15707i	0.204975	−	0.355028i	0.950125	+	0.311870i	$0.100955\pi$
$212$	−9.33624	−	5.39028i	−0.641215	−	0.370206i
$213$	1.99445	+	0.350186i	0.136658	+	0.0239944i
$214$	1.51172			0.103339
$215$	0.250390	−	0.433688i	0.0170764	−	0.0295773i
$216$	−4.50564	−	2.58829i	−0.306570	−	0.176111i
$217$	3.41849	+	1.70941i	0.232062	+	0.116042i
$218$	−10.3775	−	5.99142i	−0.702850	−	0.405790i
$219$	7.67781	+	21.0472i	0.518819	+	1.42224i
$220$	17.0582	+	9.84854i	1.15006	+	0.663988i
$221$	3.81928	+	9.15231i	0.256912	+	0.615651i
$222$	−3.00837	+	3.59051i	−0.201908	+	0.240979i
$223$	7.80461	+	4.50599i	0.522635	+	0.301744i	0.738012	−	0.674787i	$-0.235765\pi$
$223$	7.80461	+	4.50599i	0.522635	+	0.301744i	−0.215377	+	0.976531i	$0.569098\pi$
$224$	0.158422	+	2.64100i	0.0105850	+	0.176460i
$225$	−20.9828	−	7.60272i	−1.39886	−	0.506848i
$226$	2.06618	+	3.57873i	0.137440	+	0.238054i
$227$	−25.2066			−1.67302			−0.836511	−	0.547950i	$-0.815408\pi$
$227$	−25.2066			−1.67302			−0.836511	+	0.547950i	$0.815408\pi$
$228$	4.29128	+	11.7637i	0.284197	+	0.779069i
$229$	−6.18369	+	3.57015i	−0.408630	+	0.235922i	−0.690201	−	0.723618i	$-0.742478\pi$
$229$	−6.18369	+	3.57015i	−0.408630	+	0.235922i	0.281571	+	0.959540i	$0.409144\pi$
$230$	7.97493	+	13.8130i	0.525851	+	0.910801i
$231$	−25.4268	−	2.90856i	−1.67296	−	0.191369i
$232$	0.273262	−	0.473303i	0.0179405	−	0.0310739i
$233$	18.7499	−	10.8253i	1.22835	−	0.709187i	0.261664	−	0.965159i	$-0.415729\pi$
$233$	18.7499	−	10.8253i	1.22835	−	0.709187i	0.966684	+	0.255972i	$0.0823954\pi$
$234$	−5.84898	−	9.09887i	−0.382360	−	0.594812i
$235$	−6.92586	+	11.9959i	−0.451793	+	0.782528i
$236$	−7.42880			−0.483574
$237$	2.68344	−	15.2833i	0.174308	−	0.992756i
$238$	−0.435748	−	7.26421i	−0.0282453	−	0.470869i
$239$		−	23.2948i		−	1.50682i	−0.657552	−	0.753409i	$-0.728408\pi$
$239$		−	23.2948i		−	1.50682i	0.657552	−	0.753409i	$-0.271592\pi$
$240$	1.05643	−	6.01678i	0.0681921	−	0.388382i
$241$			0.935892i			0.0602861i	0.999546	+	0.0301431i	$0.00959629\pi$
$241$			0.935892i			0.0602861i	−0.999546	+	0.0301431i	$0.990404\pi$
$242$	−17.4847	−	10.0948i	−1.12396	−	0.648917i
$243$	−14.6676	−	5.27847i	−0.940925	−	0.338614i
$244$	−10.8209	−	6.24747i	−0.692740	−	0.399953i
$245$	−14.8116	−	19.7519i	−0.946281	−	1.26190i
$246$	−4.31009	−	11.8152i	−0.274802	−	0.753312i
$247$	−3.33430	+	25.8524i	−0.212156	+	1.64495i
$248$	0.722302	−	1.25106i	0.0458662	−	0.0794426i
$249$	−5.21189	−	4.36687i	−0.330290	−	0.276739i
$250$		−	8.60304i		−	0.544104i
$251$	12.4011	+	21.4793i	0.782748	+	1.35576i	0.930335	+	0.366711i	$0.119516\pi$
$251$	12.4011	+	21.4793i	0.782748	+	1.35576i	−0.147587	+	0.989049i	$0.547151\pi$
$252$	1.85505	+	7.71743i	0.116857	+	0.486153i
$253$	−12.6280	−	21.8723i	−0.793916	−	1.37510i
$254$	−3.98324	−	2.29973i	−0.249931	−	0.144298i
$255$	−2.90575	+	16.5495i	−0.181965	+	1.03637i
$256$	1.00000			0.0625000
$257$	28.4217			1.77290			0.886448	−	0.462828i	$-0.153165\pi$
$257$	28.4217			1.77290			0.886448	+	0.462828i	$0.153165\pi$
$258$	0.242224	+	0.0425297i	0.0150802	+	0.00264778i
$259$	7.14245	−	0.428444i	0.443810	−	0.0266222i
$260$	7.71474	−	10.1091i	0.478448	−	0.626937i
$261$	0.558533	−	1.54150i	0.0345724	−	0.0954167i
$262$	−3.51018	+	2.02661i	−0.216860	+	0.125204i
$263$	−11.0930	+	6.40456i	−0.684025	+	0.394922i	−0.801370	−	0.598169i	$-0.795895\pi$
$263$	−11.0930	+	6.40456i	−0.684025	+	0.394922i	0.117345	+	0.993091i	$0.462562\pi$
$264$	−1.67281	+	9.52735i	−0.102955	+	0.586368i
$265$		−	38.0223i		−	2.33569i
$266$	8.55476	−	17.1079i	0.524526	−	1.04895i
$267$	1.79792	+	1.50641i	0.110031	+	0.0921910i
$268$	−5.25998	−	9.11054i	−0.321304	−	0.556515i
$269$	−5.47053			−0.333544			−0.166772	−	0.985995i	$-0.553334\pi$
$269$	−5.47053			−0.333544			−0.166772	+	0.985995i	$0.553334\pi$
$270$	−0.0398309	−	18.3264i	−0.00242403	−	1.11531i
$271$		−	4.51379i		−	0.274193i	−0.990558	−	0.137097i	$-0.956223\pi$
$271$		−	4.51379i		−	0.274193i	0.990558	−	0.137097i	$-0.0437771\pi$
$272$	−2.75055			−0.166776
$273$	−3.96216	+	16.0406i	−0.239801	+	0.970822i
$274$	−2.66334			−0.160898
$275$			41.5464i			2.50534i
$276$	−5.03052	+	6.00397i	−0.302802	+	0.361396i
$277$	−2.76586			−0.166184			−0.0830922	−	0.996542i	$-0.526480\pi$
$277$	−2.76586			−0.166184			−0.0830922	+	0.996542i	$0.526480\pi$
$278$	−7.28322	−	12.6149i	−0.436819	−	0.756592i
$279$	1.47635	−	4.07459i	0.0883866	−	0.243939i
$280$	−7.78734	+	5.14121i	−0.465383	+	0.307246i
$281$		−	4.56102i		−	0.272088i	−0.990703	−	0.136044i	$-0.956561\pi$
$281$		−	4.56102i		−	0.272088i	0.990703	−	0.136044i	$-0.0434388\pi$
$282$	−6.69999	−	1.17638i	−0.398978	−	0.0700526i
$283$	−9.40723	+	5.43127i	−0.559202	+	0.322855i	−0.752825	−	0.658221i	$-0.771309\pi$
$283$	−9.40723	+	5.43127i	−0.559202	+	0.322855i	0.193623	+	0.981076i	$0.437976\pi$
$284$	−1.01248	+	0.584557i	−0.0600797	+	0.0346871i
$285$	−28.3636	+	33.8522i	−1.68011	+	2.00523i
$286$	−12.2160	+	16.0073i	−0.722347	+	0.946532i
$287$	−8.59226	+	17.1829i	−0.507185	+	1.01428i
$288$	2.95367	−	0.525225i	0.174046	−	0.0309492i
$289$	−9.43449			−0.554970
$290$	1.92755			0.113190
$291$	−21.8912	−	3.84365i	−1.28328	−	0.225319i
$292$	−11.2019	−	6.46743i	−0.655543	−	0.378478i
$293$	−2.27824	−	3.94604i	−0.133096	−	0.230530i	0.791772	−	0.610816i	$-0.209159\pi$
$293$	−2.27824	−	3.94604i	−0.133096	−	0.230530i	−0.924869	+	0.380287i	$0.875825\pi$
$294$	6.61987	−	10.1576i	0.386079	−	0.592405i
$295$	−13.1004	−	22.6906i	−0.762737	−	1.32110i
$296$		−	2.70444i		−	0.157193i
$297$	0.0630707	+	29.0192i	0.00365973	+	1.68387i
$298$	3.53101	−	6.11590i	0.204546	−	0.354284i
$299$	−15.0477	+	6.27946i	−0.870234	+	0.363150i
$300$	12.1049	−	4.41575i	0.698876	−	0.254943i
$301$	−0.206975	−	0.313503i	−0.0119298	−	0.0180700i
$302$	0.661388	+	0.381853i	0.0380586	+	0.0219731i
$303$	2.31547	−	13.1875i	0.133020	−	0.757603i
$304$	−6.26098	−	3.61478i	−0.359092	−	0.207322i
$305$		−	44.0688i		−	2.52337i
$306$	−8.12420	+	1.44466i	−0.464429	+	0.0825855i
$307$			14.2501i			0.813298i	0.913584	+	0.406649i	$0.133303\pi$
$307$			14.2501i			0.813298i	−0.913584	+	0.406649i	$0.866697\pi$
$308$	12.3310	−	8.14091i	0.702622	−	0.463871i
$309$	−5.62028	−	0.986809i	−0.319727	−	0.0561376i
$310$	5.09502			0.289377
$311$	9.01815	−	15.6199i	0.511372	−	0.885723i	−0.488541	−	0.872541i	$-0.662471\pi$
$311$	9.01815	−	15.6199i	0.511372	−	0.885723i	0.999913	−	0.0131816i	$-0.00419596\pi$
$312$	5.96223	+	1.85790i	0.337545	+	0.105183i
$313$	18.1151	−	10.4587i	1.02392	−	0.591163i	0.108686	−	0.994076i	$-0.465336\pi$
$313$	18.1151	−	10.4587i	1.02392	−	0.591163i	0.915238	+	0.402913i	$0.132002\pi$
$314$	−8.04062	+	13.9268i	−0.453758	+	0.785932i
$315$	−20.3009	+	19.2755i	−1.14383	+	1.08605i
$316$	4.47939	+	7.75854i	0.251986	+	0.436452i
$317$	12.2233	−	7.05711i	0.686528	−	0.396367i	−0.115782	−	0.993275i	$-0.536937\pi$
$317$	12.2233	−	7.05711i	0.686528	−	0.396367i	0.802310	+	0.596908i	$0.203604\pi$
$318$	17.5418	−	6.39907i	0.983693	−	0.358842i
$319$	−3.05221			−0.170891
$320$	1.76347	+	3.05441i	0.0985807	+	0.170747i
$321$	−1.68161	+	2.00702i	−0.0938583	+	0.112021i
$322$	11.9434	−	0.716434i	0.665581	−	0.0399253i
$323$	17.2211	+	9.94262i	0.958209	+	0.553222i
$324$	8.44828	−	3.10268i	0.469349	−	0.172371i
$325$	26.6022	+	3.43101i	1.47563	+	0.190318i
$326$	6.22894	+	3.59628i	0.344989	+	0.199180i
$327$	19.4981	−	7.11272i	1.07825	−	0.393334i
$328$	6.28842	+	3.63062i	0.347220	+	0.200468i
$329$	5.72499	+	8.67159i	0.315629	+	0.478080i
$330$	−32.0504	+	11.6917i	−1.76432	+	0.643607i
$331$	−1.16628	+	2.02005i	−0.0641043	+	0.111032i	−0.896296	−	0.443456i	$-0.853752\pi$
$331$	−1.16628	+	2.02005i	−0.0641043	+	0.111032i	0.832192	+	0.554488i	$0.187086\pi$
$332$	3.92570			0.215451
$333$	−1.42044	−	7.98802i	−0.0778397	−	0.437741i
$334$	−6.49592	−	3.75042i	−0.355441	−	0.205214i
$335$	18.5516	−	32.1323i	1.01358	−	1.75557i
$336$	−3.68251	−	2.72747i	−0.200898	−	0.148796i
$337$	33.7268			1.83722			0.918609	−	0.395168i	$-0.129313\pi$
$337$	33.7268			1.83722			0.918609	+	0.395168i	$0.129313\pi$
$338$	9.24067	+	9.14385i	0.502626	+	0.497360i
$339$	−7.04962	−	1.23777i	−0.382883	−	0.0672266i
$340$	−4.85050	−	8.40131i	−0.263055	−	0.455625i
$341$	−8.06777			−0.436894
$342$	−20.3914	−	7.38842i	−1.10264	−	0.399520i
$343$	−18.2219	+	3.31096i	−0.983890	+	0.178775i
$344$	−0.122965	+	0.0709937i	−0.00662981	+	0.00382772i
$345$	−27.2097	−	4.77749i	−1.46492	−	0.257211i
$346$	−19.1098	−	11.0331i	−1.02735	−	0.593140i
$347$		−	2.95977i		−	0.158889i	−0.996839	−	0.0794443i	$-0.974685\pi$
$347$		−	2.95977i		−	0.158889i	0.996839	−	0.0794443i	$-0.0253146\pi$
$348$	0.324403	+	0.889285i	0.0173898	+	0.0476707i
$349$	−7.78741	−	4.49606i	−0.416851	−	0.240669i	0.276878	−	0.960905i	$-0.410700\pi$
$349$	−7.78741	−	4.49606i	−0.416851	−	0.240669i	−0.693729	+	0.720236i	$0.744033\pi$
$350$	−17.6041	−	8.80289i	−0.940981	−	0.470534i
$351$	18.5863	+	2.35609i	0.992061	+	0.125759i
$352$	−2.79238	−	4.83655i	−0.148834	−	0.257789i
$353$	−7.81614	−	13.5379i	−0.416011	−	0.720552i	0.579523	−	0.814956i	$-0.303239\pi$
$353$	−7.81614	−	13.5379i	−0.416011	−	0.720552i	−0.995534	+	0.0944037i	$0.969906\pi$
$354$	8.26364	−	9.86273i	0.439208	−	0.524198i
$355$	−3.57095	−	2.06169i	−0.189527	−	0.109423i
$356$	−1.35423			−0.0717739
$357$	10.1289	+	7.50204i	0.536080	+	0.397050i
$358$	5.56410	+	9.63731i	0.294072	+	0.509348i
$359$	7.17996	−	4.14535i	0.378944	−	0.218783i	−0.298415	−	0.954436i	$-0.596458\pi$
$359$	7.17996	−	4.14535i	0.378944	−	0.218783i	0.677359	+	0.735653i	$0.263125\pi$
$360$	6.81294	+	8.09550i	0.359073	+	0.426670i
$361$	16.6332	+	28.8096i	0.875433	+	1.51629i
$362$	3.28580			0.172698
$363$	32.8518	−	11.9840i	1.72427	−	0.628998i
$364$	−4.19431	−	8.56783i	−0.219842	−	0.449076i
$365$		−	45.6204i		−	2.38788i
$366$	20.3313	−	7.41669i	1.06274	−	0.387677i
$367$	−23.7559	+	13.7155i	−1.24005	+	0.715943i	−0.969104	−	0.246652i	$-0.920670\pi$
$367$	−23.7559	+	13.7155i	−1.24005	+	0.715943i	−0.270945	+	0.962595i	$0.587336\pi$
$368$		−	4.52231i		−	0.235741i
$369$	20.4808	+	7.42081i	1.06619	+	0.386312i
$370$	8.26048	−	4.76919i	0.429442	−	0.247939i
$371$	−25.5110	−	12.7567i	−1.32446	−	0.662294i
$372$	0.857481	+	2.35061i	0.0444583	+	0.121873i
$373$	−16.5767	+	28.7117i	−0.858308	+	1.48663i	0.0152335	+	0.999884i	$0.495151\pi$
$373$	−16.5767	+	28.7117i	−0.858308	+	1.48663i	−0.873542	+	0.486749i	$0.838182\pi$
$374$	7.68058	+	13.3031i	0.397153	+	0.687889i
$375$	11.4217	+	9.56985i	0.589814	+	0.494185i
$376$	3.40124	−	1.96371i	0.175405	−	0.101270i
$377$	−0.252059	+	1.95433i	−0.0129817	+	0.100653i
$378$	−12.3094	−	6.12189i	−0.633130	−	0.314876i
$379$	8.65643	−	14.9934i	0.444651	−	0.770158i	−0.553377	−	0.832931i	$-0.686661\pi$
$379$	8.65643	−	14.9934i	0.444651	−	0.770158i	0.998028	+	0.0627730i	$0.0199944\pi$
$380$		−	25.4981i		−	1.30803i
$381$	7.48407	−	2.73012i	0.383421	−	0.139868i
$382$	−1.13467	+	1.96531i	−0.0580547	+	0.100554i
$383$	−5.99225	+	10.3789i	−0.306190	+	0.530336i	−0.977526	−	0.210817i	$-0.932388\pi$
$383$	−5.99225	+	10.3789i	−0.306190	+	0.530336i	0.671336	+	0.741153i	$0.265721\pi$
$384$	−1.11238	+	1.32763i	−0.0567659	+	0.0677505i
$385$	46.6109	+	23.3076i	2.37551	+	1.18787i
$386$	−13.8674	+	8.00636i	−0.705833	+	0.407513i
$387$	−0.325909	+	0.274276i	−0.0165669	+	0.0139422i
$388$	11.1130	−	6.41610i	0.564178	−	0.325728i
$389$	6.65966	+	3.84496i	0.337658	+	0.194947i	0.659236	−	0.751936i	$-0.270880\pi$
$389$	6.65966	+	3.84496i	0.337658	+	0.194947i	−0.321578	+	0.946883i	$0.604213\pi$
$390$	4.83941	+	21.4875i	0.245053	+	1.08806i
$391$			12.4388i			0.629058i
$392$	0.836788	+	6.94980i	0.0422642	+	0.351018i
$393$	1.21406	−	6.91459i	0.0612415	−	0.348795i
$394$	11.7549	−	20.3601i	0.592204	−	1.02573i
$395$	−15.7985	+	27.3638i	−0.794909	+	1.37682i
$396$	−10.7880	−	12.8189i	−0.542119	−	0.644174i
$397$	−1.74420	−	1.00702i	−0.0875391	−	0.0505407i	0.455591	−	0.890189i	$-0.349428\pi$
$397$	−1.74420	−	1.00702i	−0.0875391	−	0.0505407i	−0.543131	+	0.839648i	$0.682761\pi$
$398$	4.36567			0.218831
$399$	13.1969	+	30.3881i	0.660673	+	1.52131i
$400$	−3.71962	+	6.44257i	−0.185981	+	0.322129i
$401$		−	29.6383i		−	1.48007i	−0.672571	−	0.740033i	$-0.734810\pi$
$401$		−	29.6383i		−	1.48007i	0.672571	−	0.740033i	$-0.265190\pi$
$402$	17.9466	+	3.15106i	0.895093	+	0.157160i
$403$	−0.666256	+	5.16580i	−0.0331886	+	0.257327i
$404$	3.86514	+	6.69463i	0.192298	+	0.333070i
$405$	24.3751	+	20.3331i	1.21121	+	1.01036i
$406$	0.646704	−	1.29329i	0.0320954	−	0.0641848i
$407$	−13.0802	+	7.55184i	−0.648360	+	0.374331i
$408$	3.05965	−	3.65172i	0.151475	−	0.180787i
$409$		−	22.6776i		−	1.12134i	−0.828041	−	0.560668i	$-0.810544\pi$
$409$		−	22.6776i		−	1.12134i	0.828041	−	0.560668i	$-0.189456\pi$
$410$			25.6099i			1.26478i
$411$	2.96265	−	3.53595i	0.146137	−	0.174415i
$412$	2.85313	−	1.64725i	0.140563	−	0.0811544i
$413$	−19.6195	+	1.17689i	−0.965412	+	0.0579108i
$414$	−2.37523	−	13.3574i	−0.116736	−	0.656479i
$415$	6.92284	+	11.9907i	0.339829	+	0.588600i
$416$	−3.32745	+	1.38855i	−0.163142	+	0.0680794i
$417$	24.8497	+	4.36311i	1.21689	+	0.213663i
$418$			40.3753i			1.97482i
$419$	2.01719	−	3.49388i	0.0985463	−	0.170687i	−0.812537	−	0.582910i	$-0.801914\pi$
$419$	2.01719	−	3.49388i	0.0985463	−	0.170687i	0.911083	+	0.412223i	$0.135247\pi$
$420$	1.83684	−	16.0577i	0.0896285	−	0.783536i
$421$	−7.21848			−0.351807			−0.175904	−	0.984407i	$-0.556285\pi$
$421$	−7.21848			−0.351807			−0.175904	+	0.984407i	$0.556285\pi$
$422$	−5.15707	−	2.97744i	−0.251042	−	0.144939i
$423$	9.01473	−	7.58654i	0.438311	−	0.368870i
$424$	−5.39028	+	9.33624i	−0.261775	+	0.453408i
$425$	10.2310	−	17.7206i	0.496276	−	0.859576i
$426$	0.350186	−	1.99445i	0.0169666	−	0.0966316i
$427$	−29.5679	−	14.7853i	−1.43089	−	0.715512i
$428$		−	1.51172i		−	0.0730719i
$429$	−7.66302	−	34.0246i	−0.369974	−	1.64272i
$430$	−0.433688	−	0.250390i	−0.0209143	−	0.0120749i
$431$	−15.9374	+	9.20149i	−0.767680	+	0.443220i	−0.832046	−	0.554706i	$-0.812831\pi$
$431$	−15.9374	+	9.20149i	−0.767680	+	0.443220i	0.0643665	+	0.997926i	$0.479497\pi$
$432$	−2.58829	+	4.50564i	−0.124529	+	0.216778i
$433$	1.86816	−	1.07858i	0.0897781	−	0.0518334i	−0.454439	−	0.890778i	$-0.650160\pi$
$433$	1.86816	−	1.07858i	0.0897781	−	0.0518334i	0.544217	+	0.838945i	$0.316827\pi$
$434$	1.70941	−	3.41849i	0.0820541	−	0.164093i
$435$	−2.14417	+	2.55908i	−0.102805	+	0.122699i
$436$	−5.99142	+	10.3775i	−0.286937	+	0.496990i
$437$	−16.3471	+	28.3141i	−0.781989	+	1.35444i
$438$	21.0472	−	7.67781i	1.00567	−	0.366860i
$439$			35.9416i			1.71540i	0.514152	+	0.857699i	$0.328107\pi$
$439$			35.9416i			1.71540i	−0.514152	+	0.857699i	$0.671893\pi$
$440$	9.84854	−	17.0582i	0.469511	−	0.813216i
$441$	6.12180	+	20.0879i	0.291514	+	0.956566i
$442$	9.15231	−	3.81928i	0.435331	−	0.181665i
$443$	12.0373	−	6.94972i	0.571908	−	0.330191i	−0.186003	−	0.982549i	$-0.559553\pi$
$443$	12.0373	−	6.94972i	0.571908	−	0.330191i	0.757911	+	0.652358i	$0.226220\pi$
$444$	3.59051	+	3.00837i	0.170398	+	0.142771i
$445$	−2.38813	−	4.13637i	−0.113208	−	0.196083i
$446$	4.50599	−	7.80461i	0.213365	−	0.369559i
$447$	4.19185	+	11.4911i	0.198268	+	0.543510i
$448$	2.64100	−	0.158422i	0.124776	−	0.00748475i
$449$	7.01192	−	4.04833i	0.330913	−	0.191053i	−0.325333	−	0.945599i	$-0.605477\pi$
$449$	7.01192	−	4.04833i	0.330913	−	0.191053i	0.656246	+	0.754547i	$0.272143\pi$
$450$	−7.60272	+	20.9828i	−0.358396	+	0.989141i
$451$		−	40.5523i		−	1.90953i
$452$	3.57873	−	2.06618i	0.168329	−	0.0971849i
$453$	−1.24267	+	0.453316i	−0.0583860	+	0.0212987i
$454$			25.2066i			1.18301i
$455$	18.7732	−	27.9202i	0.880099	−	1.30892i
$456$	11.7637	−	4.29128i	0.550885	−	0.200958i
$457$	−14.9863			−0.701032			−0.350516	−	0.936557i	$-0.613994\pi$
$457$	−14.9863			−0.701032			−0.350516	+	0.936557i	$0.613994\pi$
$458$	3.57015	+	6.18369i	0.166822	+	0.288945i
$459$	7.11921	−	12.3930i	0.332296	−	0.578454i
$460$	13.8130	−	7.97493i	0.644034	−	0.371833i
$461$	19.1448	+	33.1598i	0.891662	+	1.54440i	0.837882	+	0.545851i	$0.183794\pi$
$461$	19.1448	+	33.1598i	0.891662	+	1.54440i	0.0537801	+	0.998553i	$0.482873\pi$
$462$	−2.90856	+	25.4268i	−0.135319	+	1.18296i
$463$	−33.6387			−1.56333			−0.781663	−	0.623702i	$-0.785628\pi$
$463$	−33.6387			−1.56333			−0.781663	+	0.623702i	$0.785628\pi$
$464$	−0.473303	−	0.273262i	−0.0219726	−	0.0126859i
$465$	−5.66759	+	6.76432i	−0.262828	+	0.313688i
$466$	−10.8253	−	18.7499i	−0.501471	−	0.868573i
$467$	−19.5650	−	33.8876i	−0.905362	−	1.56813i	−0.820431	−	0.571746i	$-0.806266\pi$
$467$	−19.5650	−	33.8876i	−0.905362	−	1.56813i	−0.0849307	−	0.996387i	$-0.527067\pi$
$468$	−9.09887	+	5.84898i	−0.420595	+	0.270369i
$469$	−15.3349	−	23.2277i	−0.708101	−	1.07255i
$470$	11.9959	+	6.92586i	0.553331	+	0.319466i
$471$	−9.54542	−	26.1668i	−0.439830	−	1.20570i
$472$			7.42880i			0.341938i
$473$	0.686728	+	0.396483i	0.0315758	+	0.0182303i
$474$	−15.2833	−	2.68344i	−0.701984	−	0.123254i
$475$	46.5769	−	26.8912i	2.13710	−	1.23385i
$476$	−7.26421	+	0.435748i	−0.332954	+	0.0199725i
$477$	−11.0175	+	30.4072i	−0.504455	+	1.39225i
$478$	−23.2948			−1.06548
$479$	−4.00505	−	6.93695i	−0.182996	−	0.316958i	0.759904	−	0.650036i	$-0.225246\pi$
$479$	−4.00505	−	6.93695i	−0.182996	−	0.316958i	−0.942899	+	0.333078i	$0.891913\pi$
$480$	−6.01678	−	1.05643i	−0.274627	−	0.0482191i
$481$	3.75526	+	8.99890i	0.171225	+	0.410314i
$482$	0.935892			0.0426287
$483$	−12.3345	+	16.6534i	−0.561237	+	0.757758i
$484$	−10.0948	+	17.4847i	−0.458854	+	0.794758i
$485$	39.1948	+	22.6292i	1.77975	+	1.02754i
$486$	−5.27847	+	14.6676i	−0.239436	+	0.665335i
$487$	15.3257			0.694473			0.347236	−	0.937778i	$-0.387120\pi$
$487$	15.3257			0.694473			0.347236	+	0.937778i	$0.387120\pi$
$488$	−6.24747	+	10.8209i	−0.282810	+	0.489841i
$489$	−11.7035	+	4.26933i	−0.529250	+	0.193066i
$490$	−19.7519	+	14.8116i	−0.892301	+	0.669121i
$491$	13.6930	+	7.90566i	0.617956	+	0.356777i	0.776073	−	0.630643i	$-0.217209\pi$
$491$	13.6930	+	7.90566i	0.617956	+	0.356777i	−0.158116	+	0.987420i	$0.550542\pi$
$492$	−11.8152	+	4.31009i	−0.532672	+	0.194314i
$493$	1.30184	+	0.751620i	0.0586321	+	0.0338513i
$494$	25.8524	+	3.33430i	1.16315	+	0.150017i
$495$	20.1299	−	55.5568i	0.904772	−	2.49709i
$496$	−1.25106	−	0.722302i	−0.0561744	−	0.0324323i
$497$	−2.58136	+	1.70422i	−0.115790	+	0.0764445i
$498$	−4.36687	+	5.21189i	−0.195684	+	0.233550i
$499$	9.63442	+	16.6873i	0.431296	+	0.747026i	0.996985	−	0.0775923i	$-0.0247232\pi$
$499$	9.63442	+	16.6873i	0.431296	+	0.747026i	−0.565689	+	0.824618i	$0.691390\pi$
$500$	−8.60304			−0.384740
$501$	12.2051	−	4.45231i	0.545284	−	0.198915i
$502$	21.4793	−	12.4011i	0.958667	−	0.553487i
$503$	−12.4057	−	21.4872i	−0.553141	−	0.958069i	−0.998046	−	0.0624908i	$-0.980096\pi$
$503$	−12.4057	−	21.4872i	−0.553141	−	0.958069i	0.444904	−	0.895578i	$-0.353238\pi$
$504$	7.71743	−	1.85505i	0.343762	−	0.0826304i
$505$	−13.6321	+	23.6115i	−0.606620	+	1.05070i
$506$	−21.8723	+	12.6280i	−0.972344	+	0.561383i
$507$	−22.4188	+	2.09681i	−0.995655	+	0.0931226i
$508$	−2.29973	+	3.98324i	−0.102034	+	0.176728i
$509$	10.1000			0.447677			0.223838	−	0.974626i	$-0.428141\pi$
$509$	10.1000			0.447677			0.223838	+	0.974626i	$0.428141\pi$
$510$	16.5495	+	2.90575i	0.732822	+	0.128669i
$511$	−30.6089	−	15.3059i	−1.35406	−	0.677092i
$512$		−	1.00000i		−	0.0441942i
$513$	32.4921	−	18.8536i	1.43456	−	0.832407i
$514$		−	28.4217i		−	1.25363i
$515$	10.0628	+	5.80975i	0.443419	+	0.256008i
$516$	0.0425297	−	0.242224i	0.00187227	−	0.0106633i
$517$	−18.9951	−	10.9668i	−0.835404	−	0.482321i
$518$	−0.428444	−	7.14245i	−0.0188247	−	0.313821i
$519$	35.9052	−	13.0979i	1.57606	−	0.574934i
$520$	−10.1091	−	7.71474i	−0.443311	−	0.338314i
$521$	7.92535	−	13.7271i	0.347216	−	0.601395i	−0.638538	−	0.769590i	$-0.720460\pi$
$521$	7.92535	−	13.7271i	0.347216	−	0.601395i	0.985754	+	0.168195i	$0.0537938\pi$
$522$	−1.54150	−	0.558533i	−0.0674698	−	0.0244463i
$523$		−	38.7502i		−	1.69443i	−0.531251	−	0.847215i	$-0.678278\pi$
$523$		−	38.7502i		−	1.69443i	0.531251	−	0.847215i	$-0.321722\pi$
$524$	2.02661	+	3.51018i	0.0885327	+	0.153343i
$525$	31.2695	−	13.5797i	1.36471	−	0.592667i
$526$	6.40456	+	11.0930i	0.279252	+	0.483679i
$527$	3.44111	+	1.98672i	0.149897	+	0.0865431i
$528$	9.52735	+	1.67281i	0.414625	+	0.0727998i
$529$	2.54875			0.110815
$530$	−38.0223			−1.65158
$531$	3.90179	+	21.9422i	0.169323	+	0.952210i
$532$	−17.1079	−	8.55476i	−0.741723	−	0.370896i
$533$	−25.9657	−	3.34891i	−1.12470	−	0.145057i
$534$	1.50641	−	1.79792i	0.0651889	−	0.0778035i
$535$	4.61743	−	2.66587i	0.199629	−	0.115256i
$536$	−9.11054	+	5.25998i	−0.393516	+	0.227196i
$537$	−18.9842	−	3.33325i	−0.819229	−	0.143840i
$538$			5.47053i			0.235851i
$539$	31.2764	−	23.4537i	1.34717	−	1.01022i
$540$	−18.3264	+	0.0398309i	−0.788644	+	0.00171405i
$541$	8.32547	+	14.4201i	0.357940	+	0.619970i	0.987617	−	0.156887i	$-0.0501459\pi$
$541$	8.32547	+	14.4201i	0.357940	+	0.619970i	−0.629676	+	0.776857i	$0.716813\pi$
$542$	−4.51379			−0.193884
$543$	−3.65506	+	4.36234i	−0.156854	+	0.187206i
$544$			2.75055i			0.117929i
$545$	−42.2627			−1.81033
$546$	16.0406	+	3.96216i	0.686475	+	0.169565i
$547$	−15.5709			−0.665762			−0.332881	−	0.942969i	$-0.608021\pi$
$547$	−15.5709			−0.665762			−0.332881	+	0.942969i	$0.608021\pi$
$548$			2.66334i			0.113772i
$549$	−12.7695	+	35.2428i	−0.544990	+	1.50412i
$550$	41.5464			1.77154
$551$	1.97556	+	3.42177i	0.0841618	+	0.145772i
$552$	6.00397	+	5.03052i	0.255546	+	0.214113i
$553$	13.0592	+	19.7807i	0.555335	+	0.841161i
$554$			2.76586i			0.117510i
$555$	−2.85705	+	16.2721i	−0.121275	+	0.690710i
$556$	−12.6149	+	7.28322i	−0.534992	+	0.308877i
$557$	−24.2770	+	14.0163i	−1.02865	+	0.593890i	−0.916597	−	0.399812i	$-0.869075\pi$
$557$	−24.2770	+	14.0163i	−1.02865	+	0.593890i	−0.112051	+	0.993702i	$0.535742\pi$
$558$	−4.07459	−	1.47635i	−0.172491	−	0.0624988i
$559$	0.310580	−	0.406971i	0.0131361	−	0.0172130i
$560$	5.14121	+	7.78734i	0.217256	+	0.329075i
$561$	−26.2054	−	4.60115i	−1.10639	−	0.194261i
$562$	−4.56102			−0.192395
$563$	29.0239			1.22321			0.611605	−	0.791163i	$-0.290524\pi$
$563$	29.0239			1.22321			0.611605	+	0.791163i	$0.290524\pi$
$564$	−1.17638	+	6.69999i	−0.0495347	+	0.282120i
$565$	12.6219	+	7.28728i	0.531009	+	0.306578i
$566$	5.43127	+	9.40723i	0.228293	+	0.395415i
$567$	21.8204	−	9.53258i	0.916371	−	0.400331i
$568$	0.584557	+	1.01248i	0.0245274	+	0.0424828i
$569$			20.9190i			0.876969i	0.898739	+	0.438484i	$0.144485\pi$
$569$			20.9190i			0.876969i	−0.898739	+	0.438484i	$0.855515\pi$
$570$	33.8522	+	28.3636i	1.41791	+	1.18802i
$571$	13.7259	−	23.7740i	0.574412	−	0.994910i	−0.421694	−	0.906738i	$-0.638564\pi$
$571$	13.7259	−	23.7740i	0.574412	−	0.994910i	0.996105	−	0.0881718i	$-0.0281025\pi$
$572$	16.0073	+	12.2160i	0.669299	+	0.510777i
$573$	−1.34702	−	3.69259i	−0.0562727	−	0.154260i
$574$	17.1829	+	8.59226i	0.717201	+	0.358634i
$575$	29.1353	+	16.8213i	1.21503	+	0.701495i
$576$	−0.525225	−	2.95367i	−0.0218844	−	0.123069i
$577$	12.3366	+	7.12257i	0.513581	+	0.296516i	0.734305	−	0.678820i	$-0.237508\pi$
$577$	12.3366	+	7.12257i	0.513581	+	0.296516i	−0.220723	+	0.975336i	$0.570842\pi$
$578$			9.43449i			0.392423i
$579$	4.79632	−	27.3170i	0.199328	−	1.13526i
$580$		−	1.92755i		−	0.0800372i
$581$	10.3678	−	0.621918i	0.430128	−	0.0258015i
$582$	−3.84365	+	21.8912i	−0.159324	+	0.907418i
$583$	60.2068			2.49351
$584$	−6.46743	+	11.2019i	−0.267624	+	0.463539i
$585$	−33.9107	−	17.4772i	−1.40204	−	0.722595i
$586$	−3.94604	+	2.27824i	−0.163009	+	0.0941134i
$587$	−14.8030	+	25.6395i	−0.610983	+	1.05825i	0.380092	+	0.924949i	$0.375892\pi$
$587$	−14.8030	+	25.6395i	−0.610983	+	1.05825i	−0.991075	+	0.133305i	$0.957441\pi$
$588$	−10.1576	−	6.61987i	−0.418893	−	0.272999i
$589$	5.22192	+	9.04463i	0.215165	+	0.372677i
$590$	−22.6906	+	13.1004i	−0.934158	+	0.539336i
$591$	13.9549	+	38.2544i	0.574026	+	1.57358i
$592$	−2.70444			−0.111152
$593$	11.0829	+	19.1962i	0.455121	+	0.788292i	0.998695	−	0.0510687i	$-0.0162627\pi$
$593$	11.0829	+	19.1962i	0.455121	+	0.788292i	−0.543574	+	0.839361i	$0.682929\pi$
$594$	29.0192	−	0.0630707i	1.19067	−	0.00258782i
$595$	−14.1411	−	21.4195i	−0.579730	−	0.878112i
$596$	−6.11590	−	3.53101i	−0.250517	−	0.144636i
$597$	−4.85628	+	5.79602i	−0.198754	+	0.237215i
$598$	6.27946	+	15.0477i	0.256786	+	0.615348i
$599$	6.69141	+	3.86329i	0.273404	+	0.157850i	0.630433	−	0.776243i	$-0.282877\pi$
$599$	6.69141	+	3.86329i	0.273404	+	0.157850i	−0.357030	+	0.934093i	$0.616211\pi$
$600$	−4.41575	−	12.1049i	−0.180272	−	0.494180i
$601$	30.6255	+	17.6816i	1.24924	+	0.721249i	0.970958	−	0.239251i	$-0.0769017\pi$
$601$	30.6255	+	17.6816i	1.24924	+	0.721249i	0.278282	+	0.960499i	$0.410235\pi$
$602$	−0.313503	+	0.206975i	−0.0127774	+	0.00843567i
$603$	−24.1468	+	20.3213i	−0.983335	+	0.827547i
$604$	0.381853	−	0.661388i	0.0155374	−	0.0269115i
$605$	−71.2072			−2.89498
$606$	−13.1875	−	2.31547i	−0.535706	−	0.0940594i
$607$	33.3856	+	19.2752i	1.35508	+	0.782356i	0.988956	−	0.148210i	$-0.0473512\pi$
$607$	33.3856	+	19.2752i	1.35508	+	0.782356i	0.366124	+	0.930566i	$0.380685\pi$
$608$	−3.61478	+	6.26098i	−0.146599	+	0.253916i
$609$	0.997632	+	2.29721i	0.0404261	+	0.0930877i
$610$	−44.0688			−1.78429
$611$	−8.59074	+	11.2569i	−0.347544	+	0.455407i
$612$	1.44466	+	8.12420i	0.0583967	+	0.328401i
$613$	6.69027	+	11.5879i	0.270218	+	0.468030i	0.968917	−	0.247384i	$-0.0795711\pi$
$613$	6.69027	+	11.5879i	0.270218	+	0.468030i	−0.698700	+	0.715415i	$0.746238\pi$
$614$	14.2501			0.575089
$615$	−34.0006	−	28.4879i	−1.37104	−	1.14874i
$616$	−8.14091	−	12.3310i	−0.328006	−	0.496829i
$617$	9.07671	−	5.24044i	0.365415	−	0.210972i	−0.306039	−	0.952019i	$-0.599004\pi$
$617$	9.07671	−	5.24044i	0.365415	−	0.210972i	0.671453	+	0.741047i	$0.265670\pi$
$618$	−0.986809	+	5.62028i	−0.0396953	+	0.226081i
$619$	3.18142	+	1.83679i	0.127872	+	0.0738269i	0.562571	−	0.826749i	$-0.309812\pi$
$619$	3.18142	+	1.83679i	0.127872	+	0.0738269i	−0.434700	+	0.900576i	$0.643145\pi$
$620$		−	5.09502i		−	0.204621i
$621$	20.3759	+	11.7050i	0.817655	+	0.469707i
$622$	−15.6199	−	9.01815i	−0.626300	−	0.361595i
$623$	−3.57652	+	0.214540i	−0.143290	+	0.00859535i
$624$	1.85790	−	5.96223i	0.0743754	−	0.238680i
$625$	3.42694	+	5.93563i	0.137077	+	0.237425i
$626$	−10.4587	−	18.1151i	−0.418015	−	0.724024i
$627$	−53.6037	−	44.9127i	−2.14072	−	1.79364i
$628$	13.9268	+	8.04062i	0.555738	+	0.320855i
$629$	7.43870			0.296600
$630$	19.2755	+	20.3009i	0.767955	+	0.808808i
$631$	−3.19085	−	5.52672i	−0.127026	−	0.220015i	0.795497	−	0.605957i	$-0.207210\pi$
$631$	−3.19085	−	5.52672i	−0.127026	−	0.220015i	−0.922523	+	0.385942i	$0.873876\pi$
$632$	7.75854	−	4.47939i	0.308618	−	0.178181i
$633$	9.68957	−	3.53467i	0.385126	−	0.140490i
$634$	−7.05711	−	12.2233i	−0.280274	−	0.485448i
$635$	−16.2220			−0.643749
$636$	−6.39907	−	17.5418i	−0.253740	−	0.695576i
$637$	−12.4345	−	21.9632i	−0.492674	−	0.870214i
$638$			3.05221i			0.120838i
$639$	2.25836	+	2.68351i	0.0893395	+	0.106158i
$640$	3.05441	−	1.76347i	0.120736	−	0.0697071i
$641$			13.9007i			0.549046i	0.961580	+	0.274523i	$0.0885200\pi$
$641$			13.9007i			0.549046i	−0.961580	+	0.274523i	$0.911480\pi$
$642$	2.00702	+	1.68161i	0.0792106	+	0.0663679i
$643$	−15.1084	+	8.72286i	−0.595818	+	0.343996i	−0.767395	−	0.641175i	$-0.778447\pi$
$643$	−15.1084	+	8.72286i	−0.595818	+	0.343996i	0.171576	+	0.985171i	$0.445114\pi$
$644$	−0.716434	−	11.9434i	−0.0282314	−	0.470637i
$645$	0.814851	−	0.297250i	0.0320847	−	0.0117042i
$646$	9.94262	−	17.2211i	0.391187	−	0.677556i
$647$	−17.6474	−	30.5663i	−0.693792	−	1.20168i	−0.970586	−	0.240754i	$-0.922605\pi$
$647$	−17.6474	−	30.5663i	−0.693792	−	1.20168i	0.276794	−	0.960929i	$-0.410728\pi$
$648$	−3.10268	−	8.44828i	−0.121885	−	0.331880i
$649$	35.9297	−	20.7440i	1.41037	−	0.814275i
$650$	3.43101	−	26.6022i	0.134575	−	1.04343i
$651$	2.63700	+	6.07212i	0.103352	+	0.237985i
$652$	3.59628	−	6.22894i	0.140841	−	0.243944i
$653$			35.9493i			1.40680i	0.710792	+	0.703402i	$0.248337\pi$
$653$			35.9493i			1.40680i	−0.710792	+	0.703402i	$0.751663\pi$
$654$	−7.11272	−	19.4981i	−0.278129	−	0.762435i
$655$	−7.14770	+	12.3802i	−0.279284	+	0.483733i
$656$	3.63062	−	6.28842i	0.141752	−	0.245522i
$657$	−13.2191	+	36.4836i	−0.515726	+	1.42336i
$658$	8.67159	−	5.72499i	0.338054	−	0.223183i
$659$	−8.28033	+	4.78065i	−0.322556	+	0.186228i	−0.652531	−	0.757762i	$-0.726293\pi$
$659$	−8.28033	+	4.78065i	−0.322556	+	0.186228i	0.329975	+	0.943990i	$0.392960\pi$
$660$	11.6917	+	32.0504i	0.455099	+	1.24756i
$661$	16.6757	−	9.62770i	0.648608	−	0.374474i	−0.139315	−	0.990248i	$-0.544490\pi$
$661$	16.6757	−	9.62770i	0.648608	−	0.374474i	0.787923	+	0.615774i	$0.211157\pi$
$662$	2.02005	+	1.16628i	0.0785114	+	0.0453286i
$663$	−5.11023	+	16.3994i	−0.198465	+	0.636900i
$664$		−	3.92570i		−	0.152347i
$665$	−4.03947	−	67.3407i	−0.156644	−	2.61136i
$666$	−7.98802	+	1.42044i	−0.309529	+	0.0550410i
$667$	−1.23577	+	2.14042i	−0.0478494	+	0.0828775i
$668$	−3.75042	+	6.49592i	−0.145108	+	0.251335i
$669$	5.34929	+	14.6640i	0.206816	+	0.566943i
$670$	−32.1323	−	18.5516i	−1.24138	−	0.716710i
$671$	69.7813			2.69388
$672$	−2.72747	+	3.68251i	−0.105214	+	0.142056i
$673$	−10.1725	+	17.6192i	−0.392120	+	0.679172i	−0.992729	−	0.120371i	$-0.961592\pi$
$673$	−10.1725	+	17.6192i	−0.392120	+	0.679172i	0.600609	+	0.799543i	$0.294925\pi$
$674$		−	33.7268i		−	1.29911i
$675$	−19.4004	−	33.4345i	−0.746723	−	1.28689i
$676$	9.14385	−	9.24067i	0.351686	−	0.355411i
$677$	−0.353311	−	0.611953i	−0.0135788	−	0.0235193i	0.859156	−	0.511714i	$-0.170989\pi$
$677$	−0.353311	−	0.611953i	−0.0135788	−	0.0235193i	−0.872735	+	0.488194i	$0.837656\pi$
$678$	−1.23777	+	7.04962i	−0.0475364	+	0.270739i
$679$	28.3331	−	18.7055i	1.08732	−	0.717851i
$680$	−8.40131	+	4.85050i	−0.322175	+	0.186008i
$681$	−33.4652	−	28.0393i	−1.28239	−	1.07447i
$682$			8.06777i			0.308931i
$683$			32.0947i			1.22807i	0.789279	+	0.614035i	$0.210455\pi$
$683$			32.0947i			1.22807i	−0.789279	+	0.614035i	$0.789545\pi$
$684$	−7.38842	+	20.3914i	−0.282503	+	0.779685i
$685$	−8.13495	+	4.69671i	−0.310820	+	0.179452i
$686$	3.31096	+	18.2219i	0.126413	+	0.695715i
$687$	−12.1810	−	2.13875i	−0.464736	−	0.0815983i
$688$	0.0709937	+	0.122965i	0.00270661	+	0.00468798i
$689$	4.97203	−	38.5505i	0.189419	−	1.46866i
$690$	−4.77749	+	27.2097i	−0.181876	+	1.03586i
$691$		−	39.1341i		−	1.48873i	−0.667772	−	0.744366i	$-0.732752\pi$
$691$		−	39.1341i		−	1.48873i	0.667772	−	0.744366i	$-0.267248\pi$
$692$	−11.0331	+	19.1098i	−0.419414	+	0.726446i
$693$	−30.5220	−	32.1457i	−1.15944	−	1.22112i
$694$	−2.95977			−0.112351
$695$	−44.4919	−	25.6874i	−1.68768	−	0.974380i
$696$	0.889285	−	0.324403i	0.0337083	−	0.0122965i
$697$	−9.98620	+	17.2966i	−0.378254	+	0.655155i
$698$	−4.49606	+	7.78741i	−0.170179	+	0.294758i
$699$	36.9348	+	6.48502i	1.39700	+	0.245286i
$700$	−8.80289	+	17.6041i	−0.332718	+	0.665374i
$701$			17.9693i			0.678690i	0.940662	+	0.339345i	$0.110205\pi$
$701$			17.9693i			0.678690i	−0.940662	+	0.339345i	$0.889795\pi$
$702$	2.35609	−	18.5863i	0.0889251	−	0.701493i
$703$	16.9325	+	9.77596i	0.638620	+	0.368707i
$704$	−4.83655	+	2.79238i	−0.182284	+	0.105242i
$705$	−22.5390	+	8.22203i	−0.848869	+	0.309660i
$706$	−13.5379	+	7.81614i	−0.509507	+	0.294164i
$707$	11.2684	+	17.0682i	0.423793	+	0.641916i
$708$	−9.86273	−	8.26364i	−0.370664	−	0.310567i
$709$	7.05408	−	12.2180i	0.264921	−	0.458857i	−0.702622	−	0.711564i	$-0.747987\pi$
$709$	7.05408	−	12.2180i	0.264921	−	0.458857i	0.967543	+	0.252706i	$0.0813207\pi$
$710$	−2.06169	+	3.57095i	−0.0773739	+	0.134015i
$711$	20.5634	−	17.3056i	0.771189	−	0.649011i
$712$			1.35423i			0.0507518i
$713$	−3.26647	+	5.65769i	−0.122330	+	0.211882i
$714$	7.50204	−	10.1289i	0.280757	−	0.379066i
$715$	−9.08436	+	70.4354i	−0.339736	+	2.63413i
$716$	9.63731	−	5.56410i	0.360163	−	0.207940i
$717$	25.9127	−	30.9270i	0.967727	−	1.15499i
$718$	−4.14535	−	7.17996i	−0.154703	−	0.267954i
$719$	−3.11135	+	5.38902i	−0.116034	+	0.200977i	−0.918193	−	0.396134i	$-0.870351\pi$
$719$	−3.11135	+	5.38902i	−0.116034	+	0.200977i	0.802159	+	0.597111i	$0.203685\pi$
$720$	8.09550	−	6.81294i	0.301701	−	0.253903i
$721$	7.27416	−	4.80240i	0.270904	−	0.178851i
$722$	28.8096	−	16.6332i	1.07218	−	0.619025i
$723$	−1.04107	+	1.24252i	−0.0387177	+	0.0462099i
$724$		−	3.28580i		−	0.122116i
$725$	3.52102	−	2.03286i	0.130767	−	0.0754986i
$726$	−11.9840	−	32.8518i	−0.444769	−	1.21924i
$727$			28.3604i			1.05183i	0.850537	+	0.525915i	$0.176277\pi$
$727$			28.3604i			1.05183i	−0.850537	+	0.525915i	$0.823723\pi$
$728$	−8.56783	+	4.19431i	−0.317545	+	0.155452i
$729$	−13.6015	−	23.3238i	−0.503760	−	0.863844i
$730$	−45.6204			−1.68849
$731$	−0.195271	−	0.338220i	−0.00722237	−	0.0125095i
$732$	−7.41669	−	20.3313i	−0.274129	−	0.751468i
$733$	−21.0117	+	12.1311i	−0.776086	+	0.448073i	−0.835041	−	0.550187i	$-0.814556\pi$
$733$	−21.0117	+	12.1311i	−0.776086	+	0.448073i	0.0589554	+	0.998261i	$0.481223\pi$
$734$	13.7155	+	23.7559i	0.506248	+	0.876847i
$735$	2.30719	−	42.6995i	0.0851021	−	1.57499i
$736$	−4.52231			−0.166694
$737$	50.8802	+	29.3757i	1.87420	+	1.08207i
$738$	7.42081	−	20.4808i	0.273164	−	0.753908i
$739$	5.46573	+	9.46691i	0.201060	+	0.348246i	0.948870	−	0.315666i	$-0.102228\pi$
$739$	5.46573	+	9.46691i	0.201060	+	0.348246i	−0.747810	+	0.663912i	$0.768895\pi$
$740$	−4.76919	−	8.26048i	−0.175319	−	0.303661i
$741$	−33.1844	+	30.6135i	−1.21906	+	1.12462i
$742$	−12.7567	+	25.5110i	−0.468312	+	0.936537i
$743$	32.1661	+	18.5711i	1.18006	+	0.681307i	0.956028	−	0.293275i	$-0.0947451\pi$
$743$	32.1661	+	18.5711i	1.18006	+	0.681307i	0.224031	+	0.974582i	$0.428078\pi$
$744$	2.35061	−	0.857481i	0.0861775	−	0.0314368i
$745$		−	24.9073i		−	0.912533i
$746$	28.7117	+	16.5767i	1.05121	+	0.606916i
$747$	−2.06187	−	11.5952i	−0.0754400	−	0.424246i
$748$	13.3031	−	7.68058i	0.486411	−	0.280830i
$749$	−0.239491	−	3.99247i	−0.00875080	−	0.145882i
$750$	9.56985	−	11.4217i	0.349441	−	0.417061i
$751$	−9.36563			−0.341757			−0.170878	−	0.985292i	$-0.554661\pi$
$751$	−9.36563			−0.341757			−0.170878	+	0.985292i	$0.554661\pi$
$752$	−1.96371	−	3.40124i	−0.0716090	−	0.124030i
$753$	−7.42902	+	42.3113i	−0.270729	+	1.54191i
$754$	1.95433	+	0.252059i	0.0711726	+	0.00917944i
$755$	2.69354			0.0980278
$756$	−6.12189	+	12.3094i	−0.222651	+	0.447690i
$757$	19.2229	−	33.2950i	0.698667	−	1.21013i	−0.270262	−	0.962787i	$-0.587110\pi$
$757$	19.2229	−	33.2950i	0.698667	−	1.21013i	0.968929	−	0.247340i	$-0.0795564\pi$
$758$	−14.9934	−	8.65643i	−0.544584	−	0.314416i
$759$	7.56497	−	43.0856i	0.274591	−	1.56391i
$760$	−25.4981			−0.924915
$761$	16.2193	−	28.0927i	0.587950	−	1.01836i	−0.406551	−	0.913628i	$-0.633269\pi$
$761$	16.2193	−	28.0927i	0.587950	−	1.01836i	0.994501	−	0.104730i	$-0.0333980\pi$
$762$	−2.73012	−	7.48407i	−0.0989019	−	0.271119i
$763$	−14.1794	+	28.3561i	−0.513327	+	1.02656i
$764$	1.96531	+	1.13467i	0.0711022	+	0.0410509i
$765$	−22.2670	+	18.7393i	−0.805067	+	0.677521i
$766$	10.3789	+	5.99225i	0.375004	+	0.216509i
$767$	−10.3153	−	24.7190i	−0.372463	−	0.892550i
$768$	1.32763	+	1.11238i	0.0479069	+	0.0401395i
$769$	24.3005	+	14.0299i	0.876299	+	0.505931i	0.869436	−	0.494045i	$-0.164482\pi$
$769$	24.3005	+	14.0299i	0.876299	+	0.505931i	0.00686245	+	0.999976i	$0.497816\pi$
$770$	23.3076	−	46.6109i	0.839949	−	1.67974i
$771$	37.7336	+	31.6157i	1.35894	+	1.13861i
$772$	8.00636	+	13.8674i	0.288155	+	0.499100i
$773$	−9.85283			−0.354382			−0.177191	−	0.984177i	$-0.556701\pi$
$773$	−9.85283			−0.354382			−0.177191	+	0.984177i	$0.556701\pi$
$774$	0.274276	+	0.325909i	0.00985863	+	0.0117145i
$775$	9.30696	−	5.37338i	0.334316	−	0.193017i
$776$	−6.41610	−	11.1130i	−0.230325	−	0.398934i
$777$	9.95915	+	7.37629i	0.357282	+	0.264623i
$778$	3.84496	−	6.65966i	0.137848	−	0.238760i
$779$	−45.4625	+	26.2478i	−1.62886	+	0.940424i
$780$	21.4875	−	4.83941i	0.769374	−	0.173279i
$781$	3.26461	−	5.65447i	0.116817	−	0.202333i
$782$	12.4388			0.444811
$783$	2.45627	−	1.42525i	0.0877798	−	0.0509344i
$784$	6.94980	−	0.836788i	0.248207	−	0.0298853i
$785$			56.7174i			2.02433i
$786$	−6.91459	−	1.21406i	−0.246635	−	0.0433043i
$787$			31.1625i			1.11082i	0.831575	+	0.555412i	$0.187439\pi$
$787$			31.1625i			1.11082i	−0.831575	+	0.555412i	$0.812561\pi$
$788$	−20.3601	−	11.7549i	−0.725299	−	0.418752i
$789$	−21.8518	−	3.83674i	−0.777944	−	0.136591i
$790$	27.3638	+	15.7985i	0.973561	+	0.562086i
$791$	9.12411	−	6.02374i	0.324416	−	0.214180i
$792$	−12.8189	+	10.7880i	−0.455500	+	0.383336i
$793$	5.76271	−	44.6811i	0.204640	−	1.58667i
$794$	−1.00702	+	1.74420i	−0.0357377	+	0.0618995i
$795$	42.2952	−	50.4797i	1.50006	−	1.79033i
$796$		−	4.36567i		−	0.154737i
$797$	−9.23872	−	16.0019i	−0.327252	−	0.566817i	0.654713	−	0.755877i	$-0.272789\pi$
$797$	−9.23872	−	16.0019i	−0.327252	−	0.566817i	−0.981966	+	0.189060i	$0.939456\pi$
$798$	30.3881	−	13.1969i	1.07573	−	0.467166i
$799$	5.40127	+	9.35527i	0.191083	+	0.330966i
$800$	6.44257	+	3.71962i	0.227779	+	0.131508i
$801$	0.711273	+	3.99993i	0.0251316	+	0.141331i
$802$	−29.6383			−1.04656
$803$	72.2381			2.54923
$804$	3.15106	−	17.9466i	0.111129	−	0.632926i
$805$	35.2167	−	23.2501i	1.24123	−	0.819459i
$806$	5.16580	+	0.666256i	0.181958	+	0.0234679i
$807$	−7.26286	−	6.08530i	−0.255665	−	0.214213i
$808$	6.69463	−	3.86514i	0.235516	−	0.135975i
$809$	−20.4038	+	11.7802i	−0.717361	+	0.414168i	−0.813780	−	0.581172i	$-0.802594\pi$
$809$	−20.4038	+	11.7802i	−0.717361	+	0.414168i	0.0964198	+	0.995341i	$0.469261\pi$
$810$	20.3331	−	24.3751i	0.714431	−	0.856454i
$811$		−	45.8210i		−	1.60899i	−0.593957	−	0.804497i	$-0.702435\pi$
$811$		−	45.8210i		−	1.60899i	0.593957	−	0.804497i	$-0.297565\pi$
$812$	−1.29329	−	0.646704i	−0.0453855	−	0.0226949i
$813$	5.02105	−	5.99266i	0.176096	−	0.210172i
$814$	7.55184	+	13.0802i	0.264692	+	0.458459i
$815$	25.3677			0.888591
$816$	−3.65172	−	3.05965i	−0.127836	−	0.107109i
$817$		−	1.02651i		−	0.0359129i
$818$	−22.6776			−0.792904
$819$	−23.1035	+	16.8886i	−0.807303	+	0.590137i
$820$	25.6099			0.894337
$821$		−	28.7210i		−	1.00237i	−0.865340	−	0.501185i	$-0.832898\pi$
$821$		−	28.7210i		−	1.00237i	0.865340	−	0.501185i	$-0.167102\pi$
$822$	−3.53595	−	2.96265i	−0.123330	−	0.103334i
$823$	−6.73314			−0.234703			−0.117351	−	0.993090i	$-0.537440\pi$
$823$	−6.73314			−0.234703			−0.117351	+	0.993090i	$0.537440\pi$
$824$	−1.64725	−	2.85313i	−0.0573848	−	0.0993934i
$825$	−46.2154	+	55.1584i	−1.60901	+	1.92037i
$826$	1.17689	+	19.6195i	0.0409491	+	0.682649i
$827$		−	31.0993i		−	1.08143i	−0.841207	−	0.540714i	$-0.818154\pi$
$827$		−	31.0993i		−	1.08143i	0.841207	−	0.540714i	$-0.181846\pi$
$828$	−13.3574	+	2.37523i	−0.464201	+	0.0825448i
$829$	32.5005	−	18.7642i	1.12879	−	0.651707i	0.185159	−	0.982709i	$-0.440720\pi$
$829$	32.5005	−	18.7642i	1.12879	−	0.651707i	0.943630	+	0.331002i	$0.107387\pi$
$830$	11.9907	−	6.92284i	0.416203	−	0.240295i
$831$	−3.67205	−	3.07668i	−0.127382	−	0.106729i
$832$	1.38855	+	3.32745i	0.0481394	+	0.115359i
$833$	−19.1158	+	2.30162i	−0.662322	+	0.0797465i
$834$	4.36311	−	24.8497i	0.151082	−	0.860475i
$835$	−26.4549			−0.915511
$836$	40.3753			1.39641
$837$	6.49254	−	3.76731i	0.224415	−	0.130217i
$838$	−3.49388	−	2.01719i	−0.120694	−	0.0696827i
$839$	−12.6736	−	21.9513i	−0.437540	−	0.757841i	0.559959	−	0.828520i	$-0.310817\pi$
$839$	−12.6736	−	21.9513i	−0.437540	−	0.757841i	−0.997499	+	0.0706787i	$0.977483\pi$
$840$	−16.0577	−	1.83684i	−0.554044	−	0.0633769i
$841$	−14.3507	−	24.8561i	−0.494850	−	0.857106i
$842$			7.21848i			0.248765i
$843$	5.07358	−	6.05536i	0.174743	−	0.208558i
$844$	−2.97744	+	5.15707i	−0.102488	+	0.177514i
$845$	44.3497	+	11.6335i	1.52568	+	0.400203i
$846$	−7.58654	−	9.01473i	−0.260831	−	0.309933i
$847$	−23.8904	+	47.7763i	−0.820884	+	1.64161i
$848$	9.33624	+	5.39028i	0.320608	+	0.185103i
$849$	−18.5310	−	3.25367i	−0.635982	−	0.111666i
$850$	−17.7206	−	10.2310i	−0.607812	−	0.350920i
$851$			12.2303i			0.419250i
$852$	−1.99445	−	0.350186i	−0.0683289	−	0.0119972i
$853$			9.89084i			0.338656i	0.985560	+	0.169328i	$0.0541597\pi$
$853$			9.89084i			0.338656i	−0.985560	+	0.169328i	$0.945840\pi$
$854$	−14.7853	+	29.5679i	−0.505943	+	1.01179i
$855$	−75.3130	+	13.3923i	−2.57565	+	0.458005i
$856$	−1.51172			−0.0516697
$857$	−0.210413	+	0.364446i	−0.00718757	+	0.0124492i	−0.869597	−	0.493762i	$-0.835621\pi$
$857$	−0.210413	+	0.364446i	−0.00718757	+	0.0124492i	0.862409	+	0.506212i	$0.168955\pi$
$858$	−34.0246	+	7.66302i	−1.16158	+	0.261611i
$859$	−7.74209	+	4.46990i	−0.264157	+	0.152511i	−0.626229	−	0.779639i	$-0.715403\pi$
$859$	−7.74209	+	4.46990i	−0.264157	+	0.152511i	0.362073	+	0.932150i	$0.382069\pi$
$860$	−0.250390	+	0.433688i	−0.00853822	+	0.0147886i
$861$	−30.5213	+	13.2548i	−1.04016	+	0.451721i
$862$	9.20149	+	15.9374i	0.313404	+	0.542832i
$863$	−12.6784	+	7.31989i	−0.431578	+	0.249172i	−0.700019	−	0.714124i	$-0.746825\pi$
$863$	−12.6784	+	7.31989i	−0.431578	+	0.249172i	0.268441	+	0.963296i	$0.413492\pi$
$864$	4.50564	+	2.58829i	0.153285	+	0.0880554i
$865$	−77.8256			−2.64615
$866$	−1.07858	−	1.86816i	−0.0366518	−	0.0634827i
$867$	−12.5255	−	10.4947i	−0.425390	−	0.356420i
$868$	−3.41849	−	1.70941i	−0.116031	−	0.0580210i
$869$	−43.3296	−	25.0163i	−1.46986	−	0.848621i
$870$	2.55908	+	2.14417i	0.0867611	+	0.0726941i
$871$	23.0111	−	30.1528i	0.779702	−	1.02169i
$872$	10.3775	+	5.99142i	0.351425	+	0.202895i
$873$	−24.7878	−	29.4542i	−0.838942	−	0.996875i
$874$	28.3141	+	16.3471i	0.957737	+	0.552950i
$875$	−22.7207	+	1.36291i	−0.768099	+	0.0460749i
$876$	−7.67781	−	21.0472i	−0.259409	−	0.711118i
$877$	12.6643	−	21.9352i	0.427644	−	0.740701i	−0.569020	−	0.822324i	$-0.692677\pi$
$877$	12.6643	−	21.9352i	0.427644	−	0.740701i	0.996663	+	0.0816235i	$0.0260105\pi$
$878$	35.9416			1.21297
$879$	1.36481	−	7.77316i	0.0460340	−	0.262182i
$880$	−17.0582	−	9.84854i	−0.575031	−	0.331994i
$881$	−8.55127	+	14.8112i	−0.288100	+	0.499003i	−0.973356	−	0.229299i	$-0.926357\pi$
$881$	−8.55127	+	14.8112i	−0.288100	+	0.499003i	0.685256	+	0.728302i	$0.259690\pi$
$882$	20.0879	−	6.12180i	0.676395	−	0.206132i
$883$	−22.9146			−0.771139			−0.385570	−	0.922679i	$-0.625995\pi$
$883$	−22.9146			−0.771139			−0.385570	+	0.922679i	$0.625995\pi$
$884$	−3.81928	−	9.15231i	−0.128456	−	0.307825i
$885$	7.84799	−	44.6975i	0.263807	−	1.50249i
$886$	−6.94972	−	12.0373i	−0.233480	−	0.404400i
$887$	−37.8691			−1.27152			−0.635759	−	0.771887i	$-0.719313\pi$
$887$	−37.8691			−1.27152			−0.635759	+	0.771887i	$0.719313\pi$
$888$	3.00837	−	3.59051i	0.100954	−	0.120490i
$889$	−5.44255	+	10.8841i	−0.182537	+	0.365041i
$890$	−4.13637	+	2.38813i	−0.138651	+	0.0800504i
$891$	−32.1966	+	38.5970i	−1.07863	+	1.29305i
$892$	−7.80461	−	4.50599i	−0.261318	−	0.150872i
$893$			28.3934i			0.950150i
$894$	11.4911	−	4.19185i	0.384320	−	0.140196i
$895$	33.9901	+	19.6242i	1.13616	+	0.655965i
$896$	−0.158422	−	2.64100i	−0.00529252	−	0.0882298i
$897$	−26.9630	−	8.40198i	−0.900270	−	0.280534i
$898$	−4.04833	−	7.01192i	−0.135095	−	0.233991i
$899$	0.394755	+	0.683736i	0.0131658	+	0.0228039i
$900$	20.9828	+	7.60272i	0.699428	+	0.253424i
$901$	−25.6798	−	14.8262i	−0.855517	−	0.493933i
$902$	−40.5523			−1.35024
$903$	0.0739474	−	0.646452i	0.00246082	−	0.0215126i
$904$	−2.06618	−	3.57873i	−0.0687201	−	0.119027i
$905$	10.0362	−	5.79440i	0.333614	−	0.192612i
$906$	0.453316	+	1.24267i	0.0150604	+	0.0412851i
$907$	−10.8920	−	18.8655i	−0.361664	−	0.626420i	0.626571	−	0.779364i	$-0.284458\pi$
$907$	−10.8920	−	18.8655i	−0.361664	−	0.626420i	−0.988235	+	0.152944i	$0.951125\pi$
$908$	25.2066			0.836511
$909$	17.7436	−	14.9325i	0.588519	−	0.495281i
$910$	−27.9202	−	18.7732i	−0.925547	−	0.622324i
$911$			18.1187i			0.600299i	0.953892	+	0.300149i	$0.0970365\pi$
$911$			18.1187i			0.600299i	−0.953892	+	0.300149i	$0.902963\pi$
$912$	−4.29128	−	11.7637i	−0.142099	−	0.389534i
$913$	−18.9868	+	10.9620i	−0.628372	+	0.362791i
$914$			14.9863i			0.495704i
$915$	49.0212	−	58.5073i	1.62059	−	1.93419i
$916$	6.18369	−	3.57015i	0.204315	−	0.117961i
$917$	5.90836	+	8.94935i	0.195111	+	0.295534i
$918$	−12.3930	−	7.11921i	−0.409029	−	0.234969i
$919$	24.2036	−	41.9219i	0.798403	−	1.38288i	−0.122252	−	0.992499i	$-0.539012\pi$
$919$	24.2036	−	41.9219i	0.798403	−	1.38288i	0.920655	−	0.390376i	$-0.127655\pi$
$920$	−7.97493	−	13.8130i	−0.262926	−	0.455401i
$921$	−15.8516	+	18.9190i	−0.522327	+	0.623401i
$922$	33.1598	−	19.1448i	1.09206	−	0.630500i
$923$	−3.35097	−	2.55729i	−0.110298	−	0.0841744i
$924$	25.4268	+	2.90856i	0.836480	+	0.0956846i
$925$	10.0595	−	17.4236i	0.330754	−	0.572884i
$926$			33.6387i			1.10544i
$927$	−6.36397	−	7.56200i	−0.209020	−	0.248369i
$928$	−0.273262	+	0.473303i	−0.00897026	+	0.0155369i
$929$	−7.05379	+	12.2175i	−0.231427	+	0.400844i	−0.958228	−	0.286004i	$-0.907673\pi$
$929$	−7.05379	+	12.2175i	−0.231427	+	0.400844i	0.726801	+	0.686848i	$0.241006\pi$
$930$	6.76432	+	5.66759i	0.221811	+	0.185848i
$931$	−46.5374	−	19.8829i	−1.52520	−	0.651635i
$932$	−18.7499	+	10.8253i	−0.614174	+	0.354594i
$933$	29.3480	−	10.7059i	0.960812	−	0.350495i
$934$	−33.8876	+	19.5650i	−1.10884	+	0.640187i
$935$	46.9193	+	27.0889i	1.53442	+	0.885901i
$936$	5.84898	+	9.09887i	0.191180	+	0.297406i
$937$			28.8937i			0.943916i	0.881621	+	0.471958i	$0.156453\pi$
$937$			28.8937i			0.943916i	−0.881621	+	0.471958i	$0.843547\pi$
$938$	−23.2277	+	15.3349i	−0.758411	+	0.500703i
$939$	35.6843	+	6.26545i	1.16451	+	0.204465i
$940$	6.92586	−	11.9959i	0.225896	−	0.391264i
$941$	−23.8512	+	41.3114i	−0.777525	+	1.34671i	0.155839	+	0.987782i	$0.450192\pi$
$941$	−23.8512	+	41.3114i	−0.777525	+	1.34671i	−0.933364	+	0.358931i	$0.883141\pi$
$942$	−26.1668	+	9.54542i	−0.852561	+	0.311007i
$943$	−28.4382	−	16.4188i	−0.926074	−	0.534669i
$944$	7.42880			0.241787
$945$	−48.3939	+	3.00851i	−1.57425	+	0.0978668i
$946$	0.396483	−	0.686728i	0.0128908	−	0.0223275i
$947$		−	52.6254i		−	1.71010i	−0.518549	−	0.855048i	$-0.673528\pi$
$947$		−	52.6254i		−	1.71010i	0.518549	−	0.855048i	$-0.326472\pi$
$948$	−2.68344	+	15.2833i	−0.0871541	+	0.496378i
$949$	5.96561	−	46.2542i	0.193652	−	1.50147i
$950$	−26.8912	−	46.5769i	−0.872466	−	1.51116i
$951$	24.0782	+	4.22766i	0.780790	+	0.137091i
$952$	0.435748	+	7.26421i	0.0141227	+	0.235434i
$953$	12.9345	−	7.46774i	0.418990	−	0.241904i	−0.275655	−	0.961257i	$-0.588895\pi$
$953$	12.9345	−	7.46774i	0.418990	−	0.241904i	0.694645	+	0.719353i	$0.255561\pi$
$954$	30.4072	+	11.0175i	0.984470	+	0.356703i
$955$			8.00380i			0.258997i
$956$			23.2948i			0.753409i
$957$	−4.05221	−	3.39521i	−0.130989	−	0.109752i
$958$	−6.93695	+	4.00505i	−0.224123	+	0.129397i
$959$	0.421933	+	7.03390i	0.0136249	+	0.227136i
$960$	−1.05643	+	6.01678i	−0.0340960	+	0.194191i
$961$	−14.4566	−	25.0395i	−0.466341	−	0.807726i
$962$	8.99890	−	3.75526i	0.290136	−	0.121074i
$963$	−4.46513	+	0.793995i	−0.143887	+	0.0255861i
$964$		−	0.935892i		−	0.0301431i
$965$	−28.2379	+	48.9095i	−0.909010	+	1.57445i
$966$	16.6534	+	12.3345i	0.535816	+	0.396855i
$967$	−34.0525			−1.09505			−0.547527	−	0.836788i	$-0.684430\pi$
$967$	−34.0525			−1.09505			−0.547527	+	0.836788i	$0.684430\pi$
$968$	17.4847	+	10.0948i	0.561979	+	0.324459i
$969$	11.8034	+	32.3566i	0.379179	+	1.03944i
$970$	22.6292	−	39.1948i	0.726578	−	1.25847i
$971$	−8.61134	+	14.9153i	−0.276351	+	0.478654i	−0.970475	−	0.241201i	$-0.922459\pi$
$971$	−8.61134	+	14.9153i	−0.276351	+	0.478654i	0.694124	+	0.719855i	$0.255792\pi$
$972$	14.6676	+	5.27847i	0.470463	+	0.169307i
$973$	−32.1622	+	21.2335i	−1.03107	+	0.680715i
$974$		−	15.3257i		−	0.491066i
$975$	31.5014	+	34.1469i	1.00885	+	1.09358i
$976$	10.8209	+	6.24747i	0.346370	+	0.199977i
$977$	−1.21765	+	0.703013i	−0.0389562	+	0.0224914i	−0.519352	−	0.854561i	$-0.673827\pi$
$977$	−1.21765	+	0.703013i	−0.0389562	+	0.0224914i	0.480395	+	0.877052i	$0.340493\pi$
$978$	4.26933	+	11.7035i	0.136518	+	0.374236i
$979$	6.54978	−	3.78152i	0.209332	−	0.120858i
$980$	14.8116	+	19.7519i	0.473140	+	0.630952i
$981$	33.7984	+	12.2462i	1.07910	+	0.390990i
$982$	7.90566	−	13.6930i	0.252280	−	0.436961i
$983$	−21.6028	+	37.4171i	−0.689022	+	1.19342i	0.283133	+	0.959081i	$0.408626\pi$
$983$	−21.6028	+	37.4171i	−0.689022	+	1.19342i	−0.972155	+	0.234340i	$0.924707\pi$
$984$	4.31009	+	11.8152i	0.137401	+	0.376656i
$985$		−	82.9176i		−	2.64197i
$986$	0.751620	−	1.30184i	0.0239364	−	0.0414591i
$987$	−2.04541	+	17.8811i	−0.0651061	+	0.569160i
$988$	3.33430	−	25.8524i	0.106078	−	0.822474i
$989$	0.556084	−	0.321055i	0.0176824	−	0.0102090i
$990$	−55.5568	−	20.1299i	−1.76571	−	0.639770i
$991$	24.2722	+	42.0407i	0.771031	+	1.33547i	0.936998	+	0.349334i	$0.113592\pi$
$991$	24.2722	+	42.0407i	0.771031	+	1.33547i	−0.165967	+	0.986131i	$0.553074\pi$
$992$	−0.722302	+	1.25106i	−0.0229331	+	0.0397213i
$993$	−3.79545	+	1.38454i	−0.120445	+	0.0439372i
$994$	1.70422	+	2.58136i	0.0540544	+	0.0818758i
$995$	13.3346	−	7.69871i	0.422734	−	0.244066i
$996$	5.21189	+	4.36687i	0.165145	+	0.138369i
$997$			54.0333i			1.71125i	0.517594	+	0.855627i	$0.326828\pi$
$997$			54.0333i			1.71125i	−0.517594	+	0.855627i	$0.673172\pi$
$998$	16.6873	−	9.63442i	0.528227	−	0.304972i
$999$	6.99988	−	12.1852i	0.221466	−	0.385524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.15	yes	76
3.2	odd	2	inner	546.2.bb.a.269.28	yes	76
7.5	odd	6		546.2.u.a.425.17	yes	76
13.3	even	3		546.2.u.a.185.22	yes	76
21.5	even	6		546.2.u.a.425.22	yes	76
39.29	odd	6		546.2.u.a.185.17	✓	76
91.68	odd	6	inner	546.2.bb.a.341.9	yes	76
273.68	even	6	inner	546.2.bb.a.341.34	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.17	✓	76	39.29	odd	6
546.2.u.a.185.22	yes	76	13.3	even	3
546.2.u.a.425.17	yes	76	7.5	odd	6
546.2.u.a.425.22	yes	76	21.5	even	6
546.2.bb.a.269.15	yes	76	1.1	even	1	trivial
546.2.bb.a.269.28	yes	76	3.2	odd	2	inner
546.2.bb.a.341.9	yes	76	91.68	odd	6	inner
546.2.bb.a.341.34	yes	76	273.68	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.32763 + 1.11238i) q^{3} -1.00000 q^{4} +(-1.76347 - 3.05441i) q^{5} +(1.11238 - 1.32763i) q^{6} +(-2.64100 + 0.158422i) q^{7} +1.00000i q^{8} +(0.525225 + 2.95367i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.32763 + 1.11238i) q^{3} -1.00000 q^{4} +(-1.76347 - 3.05441i) q^{5} +(1.11238 - 1.32763i) q^{6} +(-2.64100 + 0.158422i) q^{7} +1.00000i q^{8} +(0.525225 + 2.95367i) q^{9} +(-3.05441 + 1.76347i) q^{10} +(4.83655 - 2.79238i) q^{11} +(-1.32763 - 1.11238i) q^{12} +(-1.38855 - 3.32745i) q^{13} +(0.158422 + 2.64100i) q^{14} +(1.05643 - 6.01678i) q^{15} +1.00000 q^{16} -2.75055 q^{17} +(2.95367 - 0.525225i) q^{18} +(-6.26098 - 3.61478i) q^{19} +(1.76347 + 3.05441i) q^{20} +(-3.68251 - 2.72747i) q^{21} +(-2.79238 - 4.83655i) q^{22} -4.52231i q^{23} +(-1.11238 + 1.32763i) q^{24} +(-3.71962 + 6.44257i) q^{25} +(-3.32745 + 1.38855i) q^{26} +(-2.58829 + 4.50564i) q^{27} +(2.64100 - 0.158422i) q^{28} +(-0.473303 - 0.273262i) q^{29} +(-6.01678 - 1.05643i) q^{30} +(-1.25106 - 0.722302i) q^{31} -1.00000i q^{32} +(9.52735 + 1.67281i) q^{33} +2.75055i q^{34} +(5.14121 + 7.78734i) q^{35} +(-0.525225 - 2.95367i) q^{36} -2.70444 q^{37} +(-3.61478 + 6.26098i) q^{38} +(1.85790 - 5.96223i) q^{39} +(3.05441 - 1.76347i) q^{40} +(3.63062 - 6.28842i) q^{41} +(-2.72747 + 3.68251i) q^{42} +(0.0709937 + 0.122965i) q^{43} +(-4.83655 + 2.79238i) q^{44} +(8.09550 - 6.81294i) q^{45} -4.52231 q^{46} +(-1.96371 - 3.40124i) q^{47} +(1.32763 + 1.11238i) q^{48} +(6.94980 - 0.836788i) q^{49} +(6.44257 + 3.71962i) q^{50} +(-3.65172 - 3.05965i) q^{51} +(1.38855 + 3.32745i) q^{52} +(9.33624 + 5.39028i) q^{53} +(4.50564 + 2.58829i) q^{54} +(-17.0582 - 9.84854i) q^{55} +(-0.158422 - 2.64100i) q^{56} +(-4.29128 - 11.7637i) q^{57} +(-0.273262 + 0.473303i) q^{58} +7.42880 q^{59} +(-1.05643 + 6.01678i) q^{60} +(10.8209 + 6.24747i) q^{61} +(-0.722302 + 1.25106i) q^{62} +(-1.85505 - 7.71743i) q^{63} -1.00000 q^{64} +(-7.71474 + 10.1091i) q^{65} +(1.67281 - 9.52735i) q^{66} +(5.25998 + 9.11054i) q^{67} +2.75055 q^{68} +(5.03052 - 6.00397i) q^{69} +(7.78734 - 5.14121i) q^{70} +(1.01248 - 0.584557i) q^{71} +(-2.95367 + 0.525225i) q^{72} +(11.2019 + 6.46743i) q^{73} +2.70444i q^{74} +(-12.1049 + 4.41575i) q^{75} +(6.26098 + 3.61478i) q^{76} +(-12.3310 + 8.14091i) q^{77} +(-5.96223 - 1.85790i) q^{78} +(-4.47939 - 7.75854i) q^{79} +(-1.76347 - 3.05441i) q^{80} +(-8.44828 + 3.10268i) q^{81} +(-6.28842 - 3.63062i) q^{82} -3.92570 q^{83} +(3.68251 + 2.72747i) q^{84} +(4.85050 + 8.40131i) q^{85} +(0.122965 - 0.0709937i) q^{86} +(-0.324403 - 0.889285i) q^{87} +(2.79238 + 4.83655i) q^{88} +1.35423 q^{89} +(-6.81294 - 8.09550i) q^{90} +(4.19431 + 8.56783i) q^{91} +4.52231i q^{92} +(-0.857481 - 2.35061i) q^{93} +(-3.40124 + 1.96371i) q^{94} +25.4981i q^{95} +(1.11238 - 1.32763i) q^{96} +(-11.1130 + 6.41610i) q^{97} +(-0.836788 - 6.94980i) q^{98} +(10.7880 + 12.8189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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