LMFDB - Embedded newform 495.2.u.a.34.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(34,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("495.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.u (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			34.7
Character	$\chi$	$=$	495.34
Dual form			495.2.u.a.364.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18072 - 0.681687i) q^{2} +(1.20439 - 1.24477i) q^{3} +(-0.0706068 - 0.122295i) q^{4} +(-2.20536 - 0.369286i) q^{5} +(-2.27058 + 0.648705i) q^{6} +(-1.74985 - 1.01028i) q^{7} +2.91927i q^{8} +(-0.0989033 - 2.99837i) q^{9} +O(q^{10})$	\(q+(-1.18072 - 0.681687i) q^{2} +(1.20439 - 1.24477i) q^{3} +(-0.0706068 - 0.122295i) q^{4} +(-2.20536 - 0.369286i) q^{5} +(-2.27058 + 0.648705i) q^{6} +(-1.74985 - 1.01028i) q^{7} +2.91927i q^{8} +(-0.0989033 - 2.99837i) q^{9} +(2.35217 + 1.93939i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.237266 - 0.0594008i) q^{12} +(-2.54563 + 1.46972i) q^{13} +(1.37739 + 2.38570i) q^{14} +(-3.11579 + 2.30041i) q^{15} +(1.84882 - 3.20224i) q^{16} +0.804365i q^{17} +(-1.92717 + 3.60764i) q^{18} +3.27174 q^{19} +(0.110552 + 0.295778i) q^{20} +(-3.36507 + 0.961399i) q^{21} +(1.18072 - 0.681687i) q^{22} +(-6.06960 + 3.50429i) q^{23} +(3.63382 + 3.51593i) q^{24} +(4.72726 + 1.62882i) q^{25} +4.00755 q^{26} +(-3.85140 - 3.48809i) q^{27} +0.285330i q^{28} +(-3.30277 + 5.72056i) q^{29} +(5.24702 - 0.592136i) q^{30} +(0.0957062 + 0.165768i) q^{31} +(0.690477 - 0.398647i) q^{32} +(0.475809 + 1.66541i) q^{33} +(0.548325 - 0.949727i) q^{34} +(3.48598 + 2.87423i) q^{35} +(-0.359701 + 0.223801i) q^{36} -9.84307i q^{37} +(-3.86299 - 2.23030i) q^{38} +(-1.23646 + 4.93883i) q^{39} +(1.07805 - 6.43806i) q^{40} +(-0.767232 - 1.32889i) q^{41} +(4.62856 + 1.15878i) q^{42} +(-1.03925 - 0.600009i) q^{43} +0.141214 q^{44} +(-0.889138 + 6.64902i) q^{45} +9.55530 q^{46} +(0.461305 + 0.266335i) q^{47} +(-1.75937 - 6.15809i) q^{48} +(-1.45867 - 2.52650i) q^{49} +(-4.47120 - 5.14568i) q^{50} +(1.00125 + 0.968767i) q^{51} +(0.359477 + 0.207544i) q^{52} +10.9505i q^{53} +(2.16962 + 6.74388i) q^{54} +(1.42249 - 1.72526i) q^{55} +(2.94928 - 5.10830i) q^{56} +(3.94044 - 4.07256i) q^{57} +(7.79926 - 4.50291i) q^{58} +(-3.70974 - 6.42546i) q^{59} +(0.501323 + 0.218619i) q^{60} +(-5.88834 + 10.1989i) q^{61} -0.260966i q^{62} +(-2.85612 + 5.34663i) q^{63} -8.48227 q^{64} +(6.15678 - 2.30120i) q^{65} +(0.573496 - 2.29073i) q^{66} +(-6.40730 + 3.69925i) q^{67} +(0.0983695 - 0.0567937i) q^{68} +(-2.94812 + 11.7758i) q^{69} +(-2.15663 - 5.76999i) q^{70} -2.20600 q^{71} +(8.75306 - 0.288726i) q^{72} -1.09498i q^{73} +(-6.70989 + 11.6219i) q^{74} +(7.72095 - 3.92262i) q^{75} +(-0.231007 - 0.400115i) q^{76} +(1.74985 - 1.01028i) q^{77} +(4.82664 - 4.98848i) q^{78} +(-1.63615 + 2.83389i) q^{79} +(-5.25985 + 6.37937i) q^{80} +(-8.98044 + 0.593097i) q^{81} +2.09205i q^{82} +(-6.67498 - 3.85380i) q^{83} +(0.355170 + 0.343648i) q^{84} +(0.297041 - 1.77392i) q^{85} +(0.818037 + 1.41688i) q^{86} +(3.14297 + 11.0010i) q^{87} +(-2.52816 - 1.45964i) q^{88} -12.5659 q^{89} +(5.58237 - 7.24449i) q^{90} +5.93930 q^{91} +(0.857110 + 0.494853i) q^{92} +(0.321610 + 0.0805166i) q^{93} +(-0.363114 - 0.628931i) q^{94} +(-7.21537 - 1.20821i) q^{95} +(0.335378 - 1.33961i) q^{96} +(-6.79856 - 3.92515i) q^{97} +3.97743i q^{98} +(2.64612 + 1.41353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) $ 52 * q + 20 * q^4 + q^5 + 4 * q^6 + 6 * q^9	$ 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9} - 26 q^{11} - 10 q^{14} - 8 q^{16} + 40 q^{19} - 11 q^{20} - 26 q^{21} - 36 q^{24} + q^{25} - 24 q^{26} - 6 q^{29} + 4 q^{30} + 30 q^{31} - 22 q^{34} + 64 q^{36} + 4 q^{39} - 15 q^{40} + 6 q^{41} - 40 q^{44} - 25 q^{45} - 84 q^{46} - 12 q^{49} - 55 q^{50} + 12 q^{51} + 2 q^{54} - 2 q^{55} + 30 q^{56} - 30 q^{59} + 39 q^{60} + 74 q^{61} + 20 q^{64} + 7 q^{65} - 2 q^{66} - 30 q^{69} - 28 q^{70} - 48 q^{71} + 14 q^{74} + 94 q^{75} + 74 q^{76} - 32 q^{79} - 10 q^{80} - 30 q^{81} + 132 q^{84} - 25 q^{85} + 14 q^{86} + 92 q^{89} - 73 q^{90} - 104 q^{91} - 50 q^{94} + 6 q^{95} + 60 q^{96} + 6 q^{99}+O(q^{100}) $ 52 * q + 20 * q^4 + q^5 + 4 * q^6 + 6 * q^9 - 26 * q^11 - 10 * q^14 - 8 * q^16 + 40 * q^19 - 11 * q^20 - 26 * q^21 - 36 * q^24 + q^25 - 24 * q^26 - 6 * q^29 + 4 * q^30 + 30 * q^31 - 22 * q^34 + 64 * q^36 + 4 * q^39 - 15 * q^40 + 6 * q^41 - 40 * q^44 - 25 * q^45 - 84 * q^46 - 12 * q^49 - 55 * q^50 + 12 * q^51 + 2 * q^54 - 2 * q^55 + 30 * q^56 - 30 * q^59 + 39 * q^60 + 74 * q^61 + 20 * q^64 + 7 * q^65 - 2 * q^66 - 30 * q^69 - 28 * q^70 - 48 * q^71 + 14 * q^74 + 94 * q^75 + 74 * q^76 - 32 * q^79 - 10 * q^80 - 30 * q^81 + 132 * q^84 - 25 * q^85 + 14 * q^86 + 92 * q^89 - 73 * q^90 - 104 * q^91 - 50 * q^94 + 6 * q^95 + 60 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.18072	−	0.681687i	−0.834892	−	0.482025i	0.0206326	−	0.999787i	$-0.493432\pi$
$2$	−1.18072	−	0.681687i	−0.834892	−	0.482025i	−0.855525	+	0.517762i	$0.826765\pi$
$3$	1.20439	−	1.24477i	0.695353	−	0.718668i
$3$	1.20439	−	1.24477i	0.695353	−	0.718668i
$4$	−0.0706068	−	0.122295i	−0.0353034	−	0.0611473i
$5$	−2.20536	−	0.369286i	−0.986269	−	0.165150i
$5$	−2.20536	−	0.369286i	−0.986269	−	0.165150i
$6$	−2.27058	+	0.648705i	−0.926961	+	0.264833i
$7$	−1.74985	−	1.01028i	−0.661383	−	0.381849i	0.131421	−	0.991327i	$-0.458046\pi$
$7$	−1.74985	−	1.01028i	−0.661383	−	0.381849i	−0.792804	+	0.609477i	$0.791379\pi$
$8$			2.91927i			1.03212i
$9$	−0.0989033	−	2.99837i	−0.0329678	−	0.999456i
$10$	2.35217	+	1.93939i	0.743822	+	0.613289i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.237266	−	0.0594008i	−0.0684929	−	0.0171475i
$13$	−2.54563	+	1.46972i	−0.706030	+	0.407627i	−0.809589	−	0.586997i	$-0.800310\pi$
$13$	−2.54563	+	1.46972i	−0.706030	+	0.407627i	0.103559	+	0.994623i	$0.466977\pi$
$14$	1.37739	+	2.38570i	0.368122	+	0.637606i
$15$	−3.11579	+	2.30041i	−0.804493	+	0.593962i
$16$	1.84882	−	3.20224i	0.462204	−	0.800561i
$17$			0.804365i			0.195087i	0.995231	+	0.0975436i	$0.0310986\pi$
$17$			0.804365i			0.195087i	−0.995231	+	0.0975436i	$0.968901\pi$
$18$	−1.92717	+	3.60764i	−0.454239	+	0.850330i
$19$	3.27174			0.750588			0.375294	−	0.926906i	$-0.377542\pi$
$19$	3.27174			0.750588			0.375294	+	0.926906i	$0.377542\pi$
$20$	0.110552	+	0.295778i	0.0247202	+	0.0661380i
$21$	−3.36507	+	0.961399i	−0.734318	+	0.209794i
$22$	1.18072	−	0.681687i	0.251729	−	0.145336i
$23$	−6.06960	+	3.50429i	−1.26560	+	0.730694i	−0.974152	−	0.225892i	$-0.927470\pi$
$23$	−6.06960	+	3.50429i	−1.26560	+	0.730694i	−0.291448	+	0.956587i	$0.594137\pi$
$24$	3.63382	+	3.51593i	0.741751	+	0.717687i
$25$	4.72726	+	1.62882i	0.945451	+	0.325764i
$26$	4.00755			0.785945
$27$	−3.85140	−	3.48809i	−0.741202	−	0.671282i
$28$			0.285330i			0.0539223i
$29$	−3.30277	+	5.72056i	−0.613309	+	1.06228i	0.377370	+	0.926063i	$0.376829\pi$
$29$	−3.30277	+	5.72056i	−0.613309	+	1.06228i	−0.990679	+	0.136219i	$0.956505\pi$
$30$	5.24702	−	0.592136i	0.957970	−	0.108109i
$31$	0.0957062	+	0.165768i	0.0171893	+	0.0297728i	0.874492	−	0.485040i	$-0.161195\pi$
$31$	0.0957062	+	0.165768i	0.0171893	+	0.0297728i	−0.857303	+	0.514813i	$0.827862\pi$
$32$	0.690477	−	0.398647i	0.122060	−	0.0704715i
$33$	0.475809	+	1.66541i	0.0828277	+	0.289911i
$34$	0.548325	−	0.949727i	0.0940370	−	0.162877i
$35$	3.48598	+	2.87423i	0.589239	+	0.485833i
$36$	−0.359701	+	0.223801i	−0.0599502	+	0.0373001i
$37$		−	9.84307i		−	1.61819i	−0.587677	−	0.809096i	$-0.699957\pi$
$37$		−	9.84307i		−	1.61819i	0.587677	−	0.809096i	$-0.300043\pi$
$38$	−3.86299	−	2.23030i	−0.626660	−	0.361802i
$39$	−1.23646	+	4.93883i	−0.197992	+	0.790846i
$40$	1.07805	−	6.43806i	0.170454	−	1.01795i
$41$	−0.767232	−	1.32889i	−0.119822	−	0.207537i	0.799875	−	0.600166i	$-0.204899\pi$
$41$	−0.767232	−	1.32889i	−0.119822	−	0.207537i	−0.919697	+	0.392629i	$0.871566\pi$
$42$	4.62856	+	1.15878i	0.714202	+	0.178804i
$43$	−1.03925	−	0.600009i	−0.158484	−	0.0915006i	0.418661	−	0.908143i	$-0.362500\pi$
$43$	−1.03925	−	0.600009i	−0.158484	−	0.0915006i	−0.577144	+	0.816642i	$0.695833\pi$
$44$	0.141214			0.0212887
$45$	−0.889138	+	6.64902i	−0.132545	+	0.991177i
$46$	9.55530			1.40885
$47$	0.461305	+	0.266335i	0.0672883	+	0.0388489i	0.533267	−	0.845947i	$-0.320964\pi$
$47$	0.461305	+	0.266335i	0.0672883	+	0.0388489i	−0.465978	+	0.884796i	$0.654298\pi$
$48$	−1.75937	−	6.15809i	−0.253942	−	0.888844i
$49$	−1.45867	−	2.52650i	−0.208382	−	0.360928i
$50$	−4.47120	−	5.14568i	−0.632323	−	0.727709i
$51$	1.00125	+	0.968767i	0.140203	+	0.135655i
$52$	0.359477	+	0.207544i	0.0498505	+	0.0287812i
$53$			10.9505i			1.50417i	0.659068	+	0.752084i	$0.270951\pi$
$53$			10.9505i			1.50417i	−0.659068	+	0.752084i	$0.729049\pi$
$54$	2.16962	+	6.74388i	0.295248	+	0.917726i
$55$	1.42249	−	1.72526i	0.191809	−	0.232634i
$56$	2.94928	−	5.10830i	0.394114	−	0.682626i
$57$	3.94044	−	4.07256i	0.521924	−	0.539424i
$58$	7.79926	−	4.50291i	1.02409	−	0.591261i
$59$	−3.70974	−	6.42546i	−0.482967	−	0.836524i	0.516842	−	0.856081i	$-0.327108\pi$
$59$	−3.70974	−	6.42546i	−0.482967	−	0.836524i	−0.999809	+	0.0195574i	$0.993774\pi$
$60$	0.501323	+	0.218619i	0.0647205	+	0.0282237i
$61$	−5.88834	+	10.1989i	−0.753925	+	1.30584i	0.191983	+	0.981398i	$0.438508\pi$
$61$	−5.88834	+	10.1989i	−0.753925	+	1.30584i	−0.945907	+	0.324437i	$0.894825\pi$
$62$		−	0.260966i		−	0.0331428i
$63$	−2.85612	+	5.34663i	−0.359838	+	0.673612i
$64$	−8.48227			−1.06028
$65$	6.15678	−	2.30120i	0.763654	−	0.285429i
$66$	0.573496	−	2.29073i	0.0705925	−	0.281970i
$67$	−6.40730	+	3.69925i	−0.782776	+	0.451936i	−0.837413	−	0.546571i	$-0.815933\pi$
$67$	−6.40730	+	3.69925i	−0.782776	+	0.451936i	0.0546374	+	0.998506i	$0.482600\pi$
$68$	0.0983695	−	0.0567937i	0.0119291	−	0.00688724i
$69$	−2.94812	+	11.7758i	−0.354912	+	1.41764i
$70$	−2.15663	−	5.76999i	−0.257767	−	0.689646i
$71$	−2.20600			−0.261804			−0.130902	−	0.991395i	$-0.541787\pi$
$71$	−2.20600			−0.261804			−0.130902	+	0.991395i	$0.541787\pi$
$72$	8.75306	−	0.288726i	1.03156	−	0.0340267i
$73$		−	1.09498i		−	0.128158i	−0.997945	−	0.0640790i	$-0.979589\pi$
$73$		−	1.09498i		−	0.128158i	0.997945	−	0.0640790i	$-0.0204110\pi$
$74$	−6.70989	+	11.6219i	−0.780009	+	1.35102i
$75$	7.72095	−	3.92262i	0.891539	−	0.452945i
$76$	−0.231007	−	0.400115i	−0.0264983	−	0.0458964i
$77$	1.74985	−	1.01028i	0.199414	−	0.115132i
$78$	4.82664	−	4.98848i	0.546509	−	0.564834i
$79$	−1.63615	+	2.83389i	−0.184081	+	0.318838i	−0.943267	−	0.332037i	$-0.892264\pi$
$79$	−1.63615	+	2.83389i	−0.184081	+	0.318838i	0.759185	+	0.650874i	$0.225598\pi$
$80$	−5.25985	+	6.37937i	−0.588070	+	0.713235i
$81$	−8.98044	+	0.593097i	−0.997826	+	0.0658997i
$82$			2.09205i			0.231028i
$83$	−6.67498	−	3.85380i	−0.732675	−	0.423010i	0.0867252	−	0.996232i	$-0.472360\pi$
$83$	−6.67498	−	3.85380i	−0.732675	−	0.423010i	−0.819400	+	0.573222i	$0.805693\pi$
$84$	0.355170	+	0.343648i	0.0387523	+	0.0374951i
$85$	0.297041	−	1.77392i	0.0322186	−	0.192408i
$86$	0.818037	+	1.41688i	0.0882112	+	0.152786i
$87$	3.14297	+	11.0010i	0.336962	+	1.17943i
$88$	−2.52816	−	1.45964i	−0.269503	−	0.155598i
$89$	−12.5659			−1.33198			−0.665991	−	0.745960i	$-0.731991\pi$
$89$	−12.5659			−1.33198			−0.665991	+	0.745960i	$0.731991\pi$
$90$	5.58237	−	7.24449i	0.588433	−	0.763636i
$91$	5.93930			0.622608
$92$	0.857110	+	0.494853i	0.0893599	+	0.0515920i
$93$	0.321610	+	0.0805166i	0.0333494	+	0.00834919i
$94$	−0.363114	−	0.628931i	−0.0374523	−	0.0648693i
$95$	−7.21537	−	1.20821i	−0.740281	−	0.123959i
$96$	0.335378	−	1.33961i	0.0342294	−	0.136723i
$97$	−6.79856	−	3.92515i	−0.690289	−	0.398539i	0.113431	−	0.993546i	$-0.463816\pi$
$97$	−6.79856	−	3.92515i	−0.690289	−	0.398539i	−0.803720	+	0.595007i	$0.797149\pi$
$98$			3.97743i			0.401781i
$99$	2.64612	+	1.41353i	0.265945	+	0.142065i
$100$	−0.134581	−	0.693123i	−0.0134581	−	0.0693123i
$101$	5.11621	−	8.86154i	0.509082	−	0.881756i	−0.490863	−	0.871237i	$-0.663318\pi$
$101$	5.11621	−	8.86154i	0.509082	−	0.881756i	0.999945	−	0.0105188i	$-0.00334831\pi$
$102$	−0.521796	−	1.82638i	−0.0516655	−	0.180838i
$103$	3.94388	−	2.27700i	0.388602	−	0.224360i	−0.292952	−	0.956127i	$-0.594638\pi$
$103$	3.94388	−	2.27700i	0.388602	−	0.224360i	0.681554	+	0.731767i	$0.261304\pi$
$104$	−4.29051	−	7.43138i	−0.420719	−	0.728707i
$105$	7.77622	−	0.877562i	0.758882	−	0.0856412i
$106$	7.46481	−	12.9294i	0.725047	−	1.25582i
$107$		−	10.9755i		−	1.06104i	−0.847671	−	0.530522i	$-0.821996\pi$
$107$		−	10.9755i		−	1.06104i	0.847671	−	0.530522i	$-0.178004\pi$
$108$	−0.154639	+	0.717287i	−0.0148801	+	0.0690210i
$109$	5.97664			0.572458			0.286229	−	0.958161i	$-0.407598\pi$
$109$	5.97664			0.572458			0.286229	+	0.958161i	$0.407598\pi$
$110$	−2.85564	+	1.06734i	−0.272275	+	0.101767i
$111$	−12.2524	−	11.8549i	−1.16294	−	1.12521i
$112$	−6.47032	+	3.73564i	−0.611387	+	0.352985i
$113$	12.8972	−	7.44620i	1.21327	−	0.700480i	0.249797	−	0.968298i	$-0.419636\pi$
$113$	12.8972	−	7.44620i	1.21327	−	0.700480i	0.963469	+	0.267818i	$0.0863027\pi$
$114$	−7.42874	+	2.12239i	−0.695766	+	0.198780i
$115$	14.6798	−	5.48681i	1.36890	−	0.511647i
$116$	0.932792			0.0866075
$117$	4.65853	+	7.48737i	0.430681	+	0.692208i
$118$			10.1155i			0.931209i
$119$	0.812633	−	1.40752i	0.0744940	−	0.129027i
$120$	−6.71551	−	9.09583i	−0.613040	−	0.830332i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	13.9049	−	8.02800i	1.25889	−	0.726821i
$123$	−2.57820	−	0.645465i	−0.232469	−	0.0581996i
$124$	0.0135150	−	0.0234087i	0.00121368	−	0.00210216i
$125$	−9.82382	−	5.33785i	−0.878669	−	0.477432i
$126$	7.01699	−	4.36587i	0.625123	−	0.388942i
$127$		−	16.4110i		−	1.45624i	−0.685451	−	0.728119i	$-0.740395\pi$
$127$		−	16.4110i		−	1.45624i	0.685451	−	0.728119i	$-0.259605\pi$
$128$	8.63420	+	4.98496i	0.763163	+	0.440612i
$129$	−1.99853	+	0.570979i	−0.175961	+	0.0502719i
$130$	−8.83810	−	1.47993i	−0.775153	−	0.129799i
$131$	−9.04806	−	15.6717i	−0.790533	−	1.36924i	−0.925637	−	0.378412i	$-0.876470\pi$
$131$	−9.04806	−	15.6717i	−0.790533	−	1.36924i	0.135104	−	0.990831i	$-0.456863\pi$
$132$	0.170076	−	0.175778i	0.0148032	−	0.0152995i
$133$	−5.72506	−	3.30537i	−0.496426	−	0.286612i
$134$	10.0869			0.871378
$135$	7.20563	+	9.11476i	0.620162	+	0.784474i
$136$	−2.34816			−0.201353
$137$	−19.1855	−	11.0768i	−1.63913	−	0.946352i	−0.981134	−	0.193329i	$-0.938071\pi$
$137$	−19.1855	−	11.0768i	−1.63913	−	0.946352i	−0.657995	−	0.753022i	$-0.728595\pi$
$138$	11.5083	−	11.8942i	0.979650	−	1.01250i
$139$	8.24076	+	14.2734i	0.698972	+	1.21066i	0.968823	+	0.247754i	$0.0796923\pi$
$139$	8.24076	+	14.2734i	0.698972	+	1.21066i	−0.269851	+	0.962902i	$0.586974\pi$
$140$	0.105368	−	0.629257i	0.00890526	−	0.0531819i
$141$	0.887116	−	0.253449i	0.0747086	−	0.0213442i
$142$	2.60466	+	1.50380i	0.218578	+	0.126196i
$143$		−	2.93944i		−	0.245808i
$144$	−9.78436	−	5.22672i	−0.815363	−	0.435560i
$145$	9.39633	−	11.3963i	0.780323	−	0.946408i
$146$	−0.746435	+	1.29286i	−0.0617754	+	0.106998i
$147$	−4.90171	−	1.22717i	−0.404287	−	0.101215i
$148$	−1.20375	+	0.694988i	−0.0989480	+	0.0571276i
$149$	2.83630	+	4.91261i	0.232359	+	0.402457i	0.958502	−	0.285087i	$-0.0920224\pi$
$149$	2.83630	+	4.91261i	0.232359	+	0.402457i	−0.726143	+	0.687544i	$0.758689\pi$
$150$	−11.7902	−	0.631775i	−0.962669	−	0.0515842i
$151$	−8.63515	+	14.9565i	−0.702719	+	1.21714i	0.264790	+	0.964306i	$0.414697\pi$
$151$	−8.63515	+	14.9565i	−0.702719	+	1.21714i	−0.967509	+	0.252838i	$0.918636\pi$
$152$			9.55109i			0.774696i
$153$	2.41178	−	0.0795544i	0.194981	−	0.00643159i
$154$	−2.75477			−0.221986
$155$	−0.149851	−	0.400922i	−0.0120363	−	0.0322028i
$156$	0.691294	−	0.197503i	0.0553478	−	0.0158129i
$157$	−9.04817	+	5.22397i	−0.722123	+	0.416918i	−0.815534	−	0.578710i	$-0.803556\pi$
$157$	−9.04817	+	5.22397i	−0.722123	+	0.416918i	0.0934107	+	0.995628i	$0.470223\pi$
$158$	3.86365	−	2.23068i	0.307376	−	0.177463i
$159$	13.6309	+	13.1886i	1.08100	+	1.04593i
$160$	−1.66997	+	0.624178i	−0.132023	+	0.0493456i
$161$	14.1612			1.11606
$162$	11.0076	+	5.42156i	0.864843	+	0.425958i
$163$		−	16.8403i		−	1.31904i	−0.751688	−	0.659519i	$-0.770760\pi$
$163$		−	16.8403i		−	1.31904i	0.751688	−	0.659519i	$-0.229240\pi$
$164$	−0.108344	+	0.187657i	−0.00846021	+	0.0146535i
$165$	−0.434317	−	3.84855i	−0.0338115	−	0.299610i
$166$	5.25417	+	9.10049i	0.407803	+	0.706335i
$167$	12.4933	−	7.21301i	0.966760	−	0.558159i	0.0685131	−	0.997650i	$-0.478175\pi$
$167$	12.4933	−	7.21301i	0.966760	−	0.558159i	0.898247	+	0.439491i	$0.144841\pi$
$168$	−2.80659	−	9.82355i	−0.216533	−	0.757903i
$169$	−2.17986	+	3.77562i	−0.167681	+	0.290432i
$170$	−1.55998	+	1.89200i	−0.119645	+	0.145110i
$171$	−0.323586	−	9.80987i	−0.0247452	−	0.750180i
$172$			0.169459i			0.0129211i
$173$	−3.32210	−	1.91802i	−0.252575	−	0.145824i	0.368368	−	0.929680i	$-0.379917\pi$
$173$	−3.32210	−	1.91802i	−0.252575	−	0.145824i	−0.620943	+	0.783856i	$0.713250\pi$
$174$	3.78825	−	15.1315i	0.287187	−	1.14712i
$175$	−6.62645	−	7.62604i	−0.500912	−	0.576475i
$176$	1.84882	+	3.20224i	0.139360	+	0.241378i
$177$	−12.4662	−	3.12097i	−0.937016	−	0.234586i
$178$	14.8368	+	8.56600i	1.11206	+	0.642049i
$179$	1.64166			0.122703			0.0613517	−	0.998116i	$-0.480459\pi$
$179$	1.64166			0.122703			0.0613517	+	0.998116i	$0.480459\pi$
$180$	0.875918	−	0.360729i	0.0652870	−	0.0268872i
$181$	−15.7025			−1.16716			−0.583580	−	0.812056i	$-0.698348\pi$
$181$	−15.7025			−1.16716			−0.583580	+	0.812056i	$0.698348\pi$
$182$	−7.01263	−	4.04874i	−0.519810	−	0.300113i
$183$	5.60345	+	19.6131i	0.414219	+	1.44984i
$184$	−10.2300	−	17.7188i	−0.754163	−	1.30625i
$185$	−3.63491	+	21.7076i	−0.267244	+	1.59597i
$186$	−0.324843	−	0.314305i	−0.0238187	−	0.0230459i
$187$	−0.696601	−	0.402183i	−0.0509405	−	0.0294105i
$188$		−	0.0752202i		−	0.00548599i
$189$	3.21544	+	9.99463i	0.233889	+	0.727002i
$190$	7.69568	+	6.34517i	0.558303	+	0.460327i
$191$	−0.188618	+	0.326695i	−0.0136479	+	0.0236389i	−0.872769	−	0.488134i	$-0.837678\pi$
$191$	−0.188618	+	0.326695i	−0.0136479	+	0.0236389i	0.859121	+	0.511773i	$0.171011\pi$
$192$	−10.2159	+	10.5585i	−0.737272	+	0.761992i
$193$	3.61397	−	2.08653i	0.260140	−	0.150192i	−0.364259	−	0.931298i	$-0.618678\pi$
$193$	3.61397	−	2.08653i	0.260140	−	0.150192i	0.624398	+	0.781106i	$0.285344\pi$
$194$	5.35145	+	9.26898i	0.384211	+	0.665474i
$195$	4.55068	−	10.4353i	0.325881	−	0.747288i
$196$	−0.205985	+	0.356776i	−0.0147132	+	0.0254840i
$197$		−	0.989352i		−	0.0704884i	−0.999379	−	0.0352442i	$-0.988779\pi$
$197$		−	0.989352i		−	0.0704884i	0.999379	−	0.0352442i	$-0.0112209\pi$
$198$	−2.16072	−	3.47280i	−0.153556	−	0.246801i
$199$	16.6973			1.18364			0.591821	−	0.806069i	$-0.298409\pi$
$199$	16.6973			1.18364			0.591821	+	0.806069i	$0.298409\pi$
$200$	−4.75497	+	13.8002i	−0.336227	+	0.975818i
$201$	−3.11214	+	12.4309i	−0.219514	+	0.876811i
$202$	−12.0816	+	6.97530i	−0.850057	+	0.490781i
$203$	11.5587	−	6.67343i	0.811264	−	0.468383i
$204$	0.0477799	−	0.190849i	0.00334526	−	0.0133621i
$205$	1.20129	+	3.21400i	0.0839015	+	0.224476i
$206$	−6.20881			−0.432588
$207$	11.1075	+	17.8523i	0.772021	+	1.24082i
$208$			10.8690i			0.753626i
$209$	−1.63587	+	2.83341i	−0.113155	+	0.195991i
$210$	−9.77973	−	4.26480i	−0.674866	−	0.294299i
$211$	11.0698	+	19.1735i	0.762077	+	1.31996i	0.941778	+	0.336235i	$0.109154\pi$
$211$	11.0698	+	19.1735i	0.762077	+	1.31996i	−0.179701	+	0.983721i	$0.557513\pi$
$212$	1.33919	−	0.773180i	0.0919757	−	0.0531022i
$213$	−2.65688	+	2.74596i	−0.182046	+	0.188150i
$214$	−7.48187	+	12.9590i	−0.511450	+	0.885858i
$215$	2.07034	+	1.70702i	0.141196	+	0.116418i
$216$	10.1827	−	11.2433i	0.692843	−	0.765008i
$217$		−	0.386760i		−	0.0262550i
$218$	−7.05672	−	4.07420i	−0.477941	−	0.275939i
$219$	−1.36300	−	1.31878i	−0.0921030	−	0.0891151i
$220$	−0.311427	−	0.0521482i	−0.0209964	−	0.00351583i
$221$	−1.18219	−	2.04761i	−0.0795228	−	0.137737i
$222$	6.38525	+	22.3495i	0.428550	+	1.50000i
$223$	6.19407	+	3.57615i	0.414786	+	0.239477i	0.692844	−	0.721088i	$-0.256357\pi$
$223$	6.19407	+	3.57615i	0.414786	+	0.239477i	−0.278058	+	0.960564i	$0.589691\pi$
$224$	−1.61098			−0.107638
$225$	4.41626	−	14.3352i	0.294417	−	0.955677i
$226$	−20.3039			−1.35060
$227$	17.2118	+	9.93721i	1.14238	+	0.659556i	0.947020	−	0.321175i	$-0.104078\pi$
$227$	17.2118	+	9.93721i	1.14238	+	0.659556i	0.195365	+	0.980731i	$0.437411\pi$
$228$	−0.776273	−	0.194344i	−0.0514099	−	0.0128707i
$229$	−6.21091	−	10.7576i	−0.410429	−	0.710883i	0.584508	−	0.811388i	$-0.301288\pi$
$229$	−6.21091	−	10.7576i	−0.410429	−	0.710883i	−0.994937	+	0.100505i	$0.967954\pi$
$230$	−21.0729	−	3.52864i	−1.38951	−	0.232672i
$231$	0.849937	−	3.39493i	0.0559218	−	0.223370i
$232$	−16.6999	−	9.64168i	−1.09640	−	0.633008i
$233$			26.6495i			1.74587i	0.487837	+	0.872935i	$0.337786\pi$
$233$			26.6495i			1.74587i	−0.487837	+	0.872935i	$0.662214\pi$
$234$	−0.396360	−	12.0161i	−0.0259109	−	0.785518i
$235$	−0.918992	−	0.757719i	−0.0599484	−	0.0494281i
$236$	−0.523866	+	0.907362i	−0.0341008	+	0.0590642i
$237$	1.55699	+	5.44973i	0.101137	+	0.353998i
$238$	−1.91898	+	1.10792i	−0.124389	+	0.0718159i
$239$	−8.39860	−	14.5468i	−0.543260	−	0.940954i	−0.998714	−	0.0506950i	$-0.983856\pi$
$239$	−8.39860	−	14.5468i	−0.543260	−	0.940954i	0.455454	−	0.890259i	$-0.349477\pi$
$240$	1.60594	+	14.2305i	0.103663	+	0.918577i
$241$	−2.62803	+	4.55188i	−0.169286	+	0.293213i	−0.938169	−	0.346177i	$-0.887480\pi$
$241$	−2.62803	+	4.55188i	−0.169286	+	0.293213i	0.768883	+	0.639390i	$0.220813\pi$
$242$			1.36337i			0.0876409i
$243$	−10.0777	+	11.8929i	−0.646482	+	0.762929i
$244$	1.66303			0.106464
$245$	2.28391	+	6.11051i	0.145913	+	0.390386i
$246$	2.60412	+	2.51964i	0.166033	+	0.160646i
$247$	−8.32862	+	4.80853i	−0.529937	+	0.305959i
$248$	−0.483922	+	0.279392i	−0.0307291	+	0.0177414i
$249$	−12.8364	+	3.66735i	−0.813472	+	0.232409i
$250$	7.96040	+	12.9992i	0.503460	+	0.822145i
$251$	27.9525			1.76435			0.882173	−	0.470925i	$-0.156080\pi$
$251$	27.9525			1.76435			0.882173	+	0.470925i	$0.156080\pi$
$252$	0.855525	−	0.0282201i	0.0538930	−	0.00177770i
$253$		−	7.00857i		−	0.440625i
$254$	−11.1871	+	19.3767i	−0.701943	+	1.21580i
$255$	−1.85037	−	2.50623i	−0.115874	−	0.156946i
$256$	1.68592	+	2.92009i	0.105370	+	0.182506i
$257$	25.4407	−	14.6882i	1.58694	−	0.916223i	0.593138	−	0.805101i	$-0.297889\pi$
$257$	25.4407	−	14.6882i	1.58694	−	0.916223i	0.993807	−	0.111122i	$-0.0354444\pi$
$258$	2.74892	+	0.688206i	0.171141	+	0.0428458i
$259$	−9.94425	+	17.2239i	−0.617906	+	1.07024i
$260$	−0.716134	−	0.590460i	−0.0444128	−	0.0366188i
$261$	17.4790	+	9.33714i	1.08192	+	0.577954i
$262$			24.6718i			1.52423i
$263$	−21.4793	−	12.4011i	−1.32447	−	0.764682i	−0.340030	−	0.940415i	$-0.610437\pi$
$263$	−21.4793	−	12.4011i	−1.32447	−	0.764682i	−0.984438	+	0.175733i	$0.943770\pi$
$264$	−4.86180	+	1.38902i	−0.299223	+	0.0854880i
$265$	4.04387	−	24.1498i	0.248413	−	1.48351i
$266$	4.50645	+	7.80539i	0.276308	+	0.478579i
$267$	−15.1342	+	15.6416i	−0.926198	+	0.957253i
$268$	0.904797	+	0.522385i	0.0552693	+	0.0319097i
$269$	−6.43090			−0.392099			−0.196050	−	0.980594i	$-0.562811\pi$
$269$	−6.43090			−0.392099			−0.196050	+	0.980594i	$0.562811\pi$
$270$	−2.29439	−	15.6739i	−0.139632	−	0.953885i
$271$	−14.5188			−0.881955			−0.440977	−	0.897518i	$-0.645368\pi$
$271$	−14.5188			−0.881955			−0.440977	+	0.897518i	$0.645368\pi$
$272$	2.57577	+	1.48712i	0.156179	+	0.0901701i
$273$	7.15322	−	7.39306i	0.432932	−	0.447448i
$274$	15.1018	+	26.1570i	0.912331	+	1.58020i
$275$	−3.77423	+	3.27951i	−0.227594	+	0.197762i
$276$	1.64827	−	0.470911i	0.0992142	−	0.0283455i
$277$	0.897380	+	0.518103i	0.0539183	+	0.0311298i	0.526717	−	0.850041i	$-0.323423\pi$
$277$	0.897380	+	0.518103i	0.0539183	+	0.0311298i	−0.472799	+	0.881171i	$0.656756\pi$
$278$		−	22.4705i		−	1.34769i
$279$	0.487568	−	0.303357i	0.0291899	−	0.0181615i
$280$	−8.39066	+	10.1765i	−0.501438	+	0.608164i
$281$	2.18154	−	3.77854i	0.130140	−	0.225409i	−0.793590	−	0.608452i	$-0.791791\pi$
$281$	2.18154	−	3.77854i	0.130140	−	0.225409i	0.923730	+	0.383043i	$0.125124\pi$
$282$	−1.22020	−	0.305484i	−0.0726621	−	0.0181913i
$283$	−6.81102	+	3.93234i	−0.404873	+	0.233754i	−0.688584	−	0.725156i	$-0.741768\pi$
$283$	−6.81102	+	3.93234i	−0.404873	+	0.233754i	0.283711	+	0.958910i	$0.408434\pi$
$284$	0.155759	+	0.269782i	0.00924258	+	0.0160086i
$285$	−10.1940	+	7.52632i	−0.603842	+	0.445821i
$286$	−2.00377	+	3.47064i	−0.118486	+	0.205223i
$287$			3.10047i			0.183015i
$288$	−1.26358	−	2.03088i	−0.0744573	−	0.119671i
$289$	16.3530			0.961941
$290$	−18.8631	+	7.05039i	−1.10768	+	0.414013i
$291$	−13.0740	+	3.73524i	−0.766412	+	0.218964i
$292$	−0.133910	+	0.0773132i	−0.00783651	+	0.00452441i
$293$	−14.6767	+	8.47361i	−0.857423	+	0.495034i	−0.863149	−	0.504950i	$-0.831511\pi$
$293$	−14.6767	+	8.47361i	−0.857423	+	0.495034i	0.00572534	+	0.999984i	$0.498178\pi$
$294$	4.95099	+	4.79037i	0.288748	+	0.279380i
$295$	5.80850	+	15.5404i	0.338184	+	0.904799i
$296$	28.7346			1.67017
$297$	4.94647	−	1.59137i	0.287023	−	0.0923404i
$298$		−	7.73386i		−	0.448011i
$299$	10.3006	−	17.8412i	0.595701	−	1.03178i
$300$	−1.02487	−	0.667267i	−0.0591707	−	0.0385247i
$301$	1.21235	+	2.09986i	0.0698789	+	0.121034i
$302$	20.3913	−	11.7729i	1.17339	−	0.677456i
$303$	−4.86867	−	17.0412i	−0.279698	−	0.978993i
$304$	6.04884	−	10.4769i	0.346925	−	0.600891i
$305$	16.7522	−	20.3178i	0.959231	−	1.16339i
$306$	−2.90186	−	1.55015i	−0.165888	−	0.0886162i
$307$			30.7854i			1.75701i	0.477730	+	0.878507i	$0.341460\pi$
$307$			30.7854i			1.75701i	−0.477730	+	0.878507i	$0.658540\pi$
$308$	−0.247103	−	0.142665i	−0.0140800	−	0.00812910i
$309$	1.91562	−	7.65162i	0.108976	−	0.435285i
$310$	−0.0963713	+	0.575526i	−0.00547352	+	0.0326877i
$311$	0.464140	+	0.803913i	0.0263189	+	0.0455858i	0.878885	−	0.477034i	$-0.158288\pi$
$311$	0.464140	+	0.803913i	0.0263189	+	0.0455858i	−0.852566	+	0.522620i	$0.824955\pi$
$312$	−14.4178	−	3.60956i	−0.816247	−	0.204351i
$313$	5.11338	+	2.95221i	0.289025	+	0.166869i	0.637502	−	0.770449i	$-0.279968\pi$
$313$	5.11338	+	2.95221i	0.289025	+	0.166869i	−0.348477	+	0.937317i	$0.613301\pi$
$314$	14.2444			0.803860
$315$	8.27322	−	10.7365i	0.466143	−	0.604935i
$316$	0.462093			0.0259948
$317$	−7.67826	−	4.43304i	−0.431254	−	0.248984i	0.268627	−	0.963244i	$-0.413430\pi$
$317$	−7.67826	−	4.43304i	−0.431254	−	0.248984i	−0.699881	+	0.714260i	$0.746763\pi$
$318$	−7.10364	−	24.8640i	−0.398353	−	1.39430i
$319$	−3.30277	−	5.72056i	−0.184920	−	0.320290i
$320$	18.7065	+	3.13238i	1.04572	+	0.175106i
$321$	−13.6620	−	13.2188i	−0.762539	−	0.737801i
$322$	−16.7204	−	9.65352i	−0.931791	−	0.537970i
$323$			2.63167i			0.146430i
$324$	0.706612	+	1.05638i	0.0392562	+	0.0586879i
$325$	−14.4277	+	2.80137i	−0.800307	+	0.155392i
$326$	−11.4798	+	19.8837i	−0.635809	+	1.10125i
$327$	7.19819	−	7.43954i	0.398061	−	0.411408i
$328$	3.87938	−	2.23976i	0.214203	−	0.123670i
$329$	−0.538145	−	0.932094i	−0.0296689	−	0.0513880i
$330$	−2.11070	+	4.84012i	−0.116190	+	0.266440i
$331$	3.39787	−	5.88528i	0.186764	−	0.323484i	−0.757406	−	0.652945i	$-0.773533\pi$
$331$	3.39787	−	5.88528i	0.186764	−	0.323484i	0.944169	+	0.329460i	$0.106867\pi$
$332$			1.08842i			0.0597347i
$333$	−29.5132	+	0.973513i	−1.61731	+	0.0533482i
$334$	−19.6680			−1.07619
$335$	15.4965	−	5.79207i	0.846664	−	0.316455i
$336$	−3.14276	+	12.5532i	−0.171451	+	0.684834i
$337$	−8.02965	+	4.63592i	−0.437403	+	0.252535i	−0.702495	−	0.711688i	$-0.747931\pi$
$337$	−8.02965	+	4.63592i	−0.437403	+	0.252535i	0.265092	+	0.964223i	$0.414598\pi$
$338$	5.14758	−	2.97196i	0.279991	−	0.161653i
$339$	6.26442	−	25.0222i	0.340236	−	1.35902i
$340$	−0.237914	+	0.0889242i	−0.0129027	+	0.00482259i
$341$	−0.191412			−0.0103656
$342$	−6.30520	+	11.8033i	−0.340946	+	0.638247i
$343$			20.0386i			1.08198i
$344$	1.75159	−	3.03385i	0.0944395	−	0.163574i
$345$	10.8503	−	24.8812i	0.584161	−	1.33956i
$346$	2.61497	+	4.52926i	0.140582	+	0.243495i
$347$	−29.0227	+	16.7563i	−1.55802	+	0.899523i	−0.560573	+	0.828105i	$0.689419\pi$
$347$	−29.0227	+	16.7563i	−1.55802	+	0.899523i	−0.997446	+	0.0714180i	$0.977248\pi$
$348$	1.12344	−	1.16111i	0.0602228	−	0.0622421i
$349$	14.1536	−	24.5148i	0.757627	−	1.31225i	−0.186430	−	0.982468i	$-0.559692\pi$
$349$	14.1536	−	24.5148i	0.757627	−	1.31225i	0.944058	−	0.329781i	$-0.106975\pi$
$350$	2.62538	+	13.5213i	0.140332	+	0.722746i
$351$	14.9307	+	3.21890i	0.796943	+	0.171812i
$352$			0.797295i			0.0424959i
$353$	6.94342	+	4.00878i	0.369561	+	0.213366i	0.673267	−	0.739400i	$-0.264891\pi$
$353$	6.94342	+	4.00878i	0.369561	+	0.213366i	−0.303706	+	0.952766i	$0.598224\pi$
$354$	12.5915	+	12.1830i	0.669231	+	0.647519i
$355$	4.86504	+	0.814646i	0.258209	+	0.0432369i
$356$	0.887238	+	1.53674i	0.0470235	+	0.0814471i
$357$	−0.773316	−	2.70674i	−0.0409282	−	0.143256i
$358$	−1.93833	−	1.11910i	−0.102444	−	0.0591461i
$359$	23.3557			1.23267			0.616334	−	0.787485i	$-0.288617\pi$
$359$	23.3557			1.23267			0.616334	+	0.787485i	$0.288617\pi$
$360$	−19.4103	−	2.59564i	−1.02301	−	0.136802i
$361$	−8.29574			−0.436618
$362$	18.5402	+	10.7042i	0.974452	+	0.562600i
$363$	−1.68020	−	0.420645i	−0.0881874	−	0.0220781i
$364$	−0.419355	−	0.726344i	−0.0219802	−	0.0380708i
$365$	−0.404362	+	2.41483i	−0.0211653	+	0.126398i
$366$	6.75388	−	26.9772i	0.353031	−	1.41012i
$367$	28.5381	+	16.4765i	1.48967	+	0.860064i	0.999930	−	0.0118024i	$-0.00375691\pi$
$367$	28.5381	+	16.4765i	1.48967	+	0.860064i	0.489744	+	0.871866i	$0.337090\pi$
$368$			25.9151i			1.35092i
$369$	−3.90861	+	2.43188i	−0.203474	+	0.126598i
$370$	19.0895	−	23.1526i	0.992418	−	1.20365i
$371$	11.0631	−	19.1618i	0.574365	−	0.994830i
$372$	−0.0128611	−	0.0450162i	−0.000666818	−	0.00233398i
$373$	5.92643	−	3.42163i	0.306859	−	0.177165i	−0.338661	−	0.940908i	$-0.609974\pi$
$373$	5.92643	−	3.42163i	0.306859	−	0.177165i	0.645520	+	0.763743i	$0.276641\pi$
$374$	0.548325	+	0.949727i	0.0283532	+	0.0491092i
$375$	−18.4761	+	5.79955i	−0.954100	+	0.299488i
$376$	−0.777504	+	1.34668i	−0.0400967	+	0.0694495i
$377$		−	19.4166i		−	1.00000i
$378$	3.01668	−	13.9927i	0.155161	−	0.719709i
$379$	7.38372			0.379276			0.189638	−	0.981854i	$-0.439269\pi$
$379$	7.38372			0.379276			0.189638	+	0.981854i	$0.439269\pi$
$380$	0.361697	+	0.967708i	0.0185547	+	0.0496423i
$381$	−20.4279	−	19.7652i	−1.04655	−	1.01260i
$382$	0.445408	−	0.257156i	0.0227890	−	0.0131573i
$383$	5.13793	−	2.96638i	0.262536	−	0.151575i	−0.362955	−	0.931807i	$-0.618232\pi$
$383$	5.13793	−	2.96638i	0.262536	−	0.151575i	0.625491	+	0.780232i	$0.284899\pi$
$384$	16.6040	−	4.74377i	0.847322	−	0.242080i
$385$	−4.23215	+	1.58184i	−0.215690	+	0.0806178i
$386$	−5.68944			−0.289585
$387$	−1.69626	+	3.17539i	−0.0862260	+	0.161414i
$388$			1.10857i			0.0562791i
$389$	−4.33982	+	7.51679i	−0.220038	+	0.381116i	−0.954819	−	0.297188i	$-0.903951\pi$
$389$	−4.33982	+	7.51679i	−0.220038	+	0.381116i	0.734781	+	0.678304i	$0.237285\pi$
$390$	−12.4867	+	9.21899i	−0.632287	+	0.466822i
$391$	−2.81873	−	4.88218i	−0.142549	−	0.246902i
$392$	7.37553	−	4.25827i	0.372521	−	0.215075i
$393$	−30.4050	−	7.61204i	−1.53373	−	0.383977i
$394$	−0.674428	+	1.16814i	−0.0339772	+	0.0588502i
$395$	4.65482	−	5.64556i	0.234209	−	0.284059i
$396$	−0.0139665	−	0.423410i	−0.000701842	−	0.0212772i
$397$		−	24.1313i		−	1.21112i	−0.795801	−	0.605559i	$-0.792950\pi$
$397$		−	24.1313i		−	1.21112i	0.795801	−	0.605559i	$-0.207050\pi$
$398$	−19.7148	−	11.3823i	−0.988214	−	0.570545i
$399$	−11.0096	+	3.14544i	−0.551170	+	0.157469i
$400$	13.9557	−	12.1264i	0.697785	−	0.606322i
$401$	−0.595870	−	1.03208i	−0.0297563	−	0.0515395i	0.850764	−	0.525548i	$-0.176140\pi$
$401$	−0.595870	−	1.03208i	−0.0297563	−	0.0515395i	−0.880520	+	0.474009i	$0.842806\pi$
$402$	12.1486	−	12.5559i	0.605915	−	0.626231i
$403$	−0.487264	−	0.281322i	−0.0242724	−	0.0140137i
$404$	−1.44496			−0.0718893
$405$	20.0241	+	2.00835i	0.995008	+	0.0997959i
$406$	−18.1968			−0.903090
$407$	8.52435	+	4.92154i	0.422536	+	0.243952i
$408$	−2.82810	+	2.92292i	−0.140012	+	0.144706i
$409$	−20.1661	−	34.9287i	−0.997149	−	1.72711i	−0.563918	−	0.825831i	$-0.690707\pi$
$409$	−20.1661	−	34.9287i	−0.997149	−	1.72711i	−0.433231	−	0.901283i	$-0.642627\pi$
$410$	0.772564	−	4.61373i	0.0381542	−	0.227856i
$411$	−36.8948	+	10.5408i	−1.81989	+	0.519941i
$412$	−0.556930	−	0.321544i	−0.0274380	−	0.0158413i
$413$			14.9915i			0.737683i
$414$	−0.945051	−	28.6503i	−0.0464467	−	1.40809i
$415$	13.2976	+	10.9640i	0.652754	+	0.538202i
$416$	−1.17180	+	2.02961i	−0.0574521	+	0.0995100i
$417$	27.6922	+	6.93287i	1.35609	+	0.339504i
$418$	3.86299	−	2.23030i	0.188945	−	0.109087i
$419$	19.3504	+	33.5158i	0.945327	+	1.63736i	0.755094	+	0.655616i	$0.227591\pi$
$419$	19.3504	+	33.5158i	0.945327	+	1.63736i	0.190233	+	0.981739i	$0.439076\pi$
$420$	−0.656375	−	0.889028i	−0.0320278	−	0.0433801i
$421$	13.9936	−	24.2377i	0.682008	−	1.18127i	−0.292359	−	0.956309i	$-0.594440\pi$
$421$	13.9936	−	24.2377i	0.682008	−	1.18127i	0.974367	−	0.224964i	$-0.0722265\pi$
$422$		−	30.1846i		−	1.46936i
$423$	0.752945	−	1.40951i	0.0366095	−	0.0685325i
$424$	−31.9675			−1.55248
$425$	−1.31017	+	3.80244i	−0.0635524	+	0.184445i
$426$	5.00891	−	1.43104i	0.242682	−	0.0693343i
$427$	20.6075	−	11.8977i	0.997265	−	0.575771i
$428$	−1.34225	+	0.774947i	−0.0648800	+	0.0374585i
$429$	−3.65892	−	3.54022i	−0.176654	−	0.170923i
$430$	−1.28083	−	3.42683i	−0.0617673	−	0.165256i
$431$	−16.6895			−0.803903			−0.401951	−	0.915661i	$-0.631668\pi$
$431$	−16.6895			−0.803903			−0.401951	+	0.915661i	$0.631668\pi$
$432$	−18.2902	+	5.88428i	−0.879989	+	0.283108i
$433$		−	0.0124827i		−	0.000599880i	−1.00000		0.000299940i	$-0.999905\pi$
$433$		−	0.0124827i		−	0.000599880i	1.00000		0.000299940i	$-9.54739e-5\pi$
$434$	−0.263649	+	0.456653i	−0.0126556	+	0.0219201i
$435$	−2.86889	−	25.4218i	−0.137553	−	1.21888i
$436$	−0.421991	−	0.730911i	−0.0202097	−	0.0350043i
$437$	−19.8581	+	11.4651i	−0.949944	+	0.548450i
$438$	0.710320	+	2.48625i	0.0339404	+	0.118797i
$439$	−2.99411	+	5.18596i	−0.142901	+	0.247512i	−0.928588	−	0.371112i	$-0.878976\pi$
$439$	−2.99411	+	5.18596i	−0.142901	+	0.247512i	0.785687	+	0.618625i	$0.212310\pi$
$440$	5.03650	+	4.15265i	0.240106	+	0.197970i
$441$	−7.43110	+	4.62352i	−0.353862	+	0.220168i
$442$			3.22353i			0.153328i
$443$	11.5014	+	6.64034i	0.546448	+	0.315492i	0.747688	−	0.664050i	$-0.231164\pi$
$443$	11.5014	+	6.64034i	0.546448	+	0.315492i	−0.201240	+	0.979542i	$0.564497\pi$
$444$	−0.584686	+	2.33543i	−0.0277480	+	0.110835i
$445$	27.7124	+	4.64041i	1.31369	+	0.219977i
$446$	−4.87563	−	8.44483i	−0.230868	−	0.399874i
$447$	9.53107	+	2.38615i	0.450804	+	0.112861i
$448$	14.8427	+	8.56946i	0.701254	+	0.404869i
$449$	−36.0639			−1.70196			−0.850981	−	0.525197i	$-0.823992\pi$
$449$	−36.0639			−1.70196			−0.850981	+	0.525197i	$0.823992\pi$
$450$	−14.9864	+	13.9152i	−0.706467	+	0.655971i
$451$	1.53446			0.0722551
$452$	−1.82126	−	1.05150i	−0.0856648	−	0.0494586i
$453$	8.21736	+	28.7622i	0.386085	+	1.35137i
$454$	−13.5481	−	23.4660i	−0.635845	−	1.10132i
$455$	−13.0983	−	2.19330i	−0.614059	−	0.102824i
$456$	11.8889	+	11.5032i	0.556749	+	0.538687i
$457$	−28.2550	−	16.3130i	−1.32171	−	0.763092i	−0.337711	−	0.941250i	$-0.609653\pi$
$457$	−28.2550	−	16.3130i	−1.32171	−	0.763092i	−0.984002	+	0.178158i	$0.942986\pi$
$458$			16.9356i			0.791348i
$459$	2.80570	−	3.09793i	0.130959	−	0.144599i
$460$	−1.70750	−	1.40785i	−0.0796125	−	0.0656413i
$461$	−4.97377	+	8.61483i	−0.231652	+	0.401233i	−0.958294	−	0.285783i	$-0.907746\pi$
$461$	−4.97377	+	8.61483i	−0.231652	+	0.401233i	0.726643	+	0.687016i	$0.241080\pi$
$462$	−3.31781	+	3.42906i	−0.154359	+	0.159534i
$463$	19.6549	−	11.3478i	0.913440	−	0.527375i	0.0319038	−	0.999491i	$-0.489843\pi$
$463$	19.6549	−	11.3478i	0.913440	−	0.527375i	0.881536	+	0.472116i	$0.156510\pi$
$464$	12.2124	+	21.1525i	0.566948	+	0.981982i
$465$	−0.679534	−	0.296335i	−0.0315126	−	0.0137422i
$466$	18.1666	−	31.4655i	0.841553	−	1.45761i
$467$		−	22.3384i		−	1.03370i	−0.856077	−	0.516848i	$-0.827105\pi$
$467$		−	22.3384i		−	1.03370i	0.856077	−	0.516848i	$-0.172895\pi$
$468$	0.586741	−	1.09837i	0.0271221	−	0.0507722i
$469$	14.9491			0.690286
$470$	0.568542	+	1.52111i	0.0262249	+	0.0701638i
$471$	−4.39487	+	17.5546i	−0.202505	+	0.808872i
$472$	18.7577	−	10.8297i	0.863392	−	0.498480i
$473$	1.03925	−	0.600009i	0.0477846	−	0.0275885i
$474$	1.87665	−	7.49596i	0.0861974	−	0.344301i
$475$	15.4663	+	5.32907i	0.709644	+	0.244514i
$476$	−0.229510			−0.0105196
$477$	32.8337	−	1.08304i	1.50335	−	0.0495890i
$478$			22.9009i			1.04746i
$479$	11.7135	−	20.2883i	0.535202	−	0.926996i	−0.463952	−	0.885860i	$-0.653569\pi$
$479$	11.7135	−	20.2883i	0.535202	−	0.926996i	0.999154	−	0.0411359i	$-0.0130977\pi$
$480$	−1.23433	+	2.83048i	−0.0563392	+	0.129193i
$481$	14.4665	+	25.0568i	0.659618	+	1.14249i
$482$	6.20591	−	3.58299i	0.282672	−	0.163201i
$483$	17.0556	−	17.6275i	0.776057	−	0.802078i
$484$	−0.0706068	+	0.122295i	−0.00320940	+	0.00555884i
$485$	13.5438	+	11.1670i	0.614992	+	0.507067i
$486$	20.0061	−	7.17233i	0.907494	−	0.325343i
$487$			11.5926i			0.525311i	0.964890	+	0.262655i	$0.0845982\pi$
$487$			11.5926i			0.525311i	−0.964890	+	0.262655i	$0.915402\pi$
$488$	−29.7734	−	17.1897i	−1.34778	−	0.778140i
$489$	−20.9623	−	20.2823i	−0.947950	−	0.917197i
$490$	1.46881	−	8.77169i	0.0663541	−	0.396264i
$491$	20.6258	+	35.7249i	0.930829	+	1.61224i	0.781907	+	0.623395i	$0.214247\pi$
$491$	20.6258	+	35.7249i	0.930829	+	1.61224i	0.148922	+	0.988849i	$0.452420\pi$
$492$	0.103102	+	0.360874i	0.00464818	+	0.0162695i
$493$	−4.60142	−	2.65663i	−0.207238	−	0.119649i
$494$	13.1116			0.589921
$495$	−5.31365	−	4.09452i	−0.238831	−	0.184035i
$496$	0.707772			0.0317799
$497$	3.86018	+	2.22868i	0.173153	+	0.0999698i
$498$	17.6561	+	4.42028i	0.791188	+	0.198078i
$499$	11.9551	+	20.7068i	0.535184	+	0.926965i	0.999154	+	0.0411148i	$0.0130909\pi$
$499$	11.9551	+	20.7068i	0.535184	+	0.926965i	−0.463971	+	0.885851i	$0.653576\pi$
$500$	0.0408383	+	1.57829i	0.00182634	+	0.0705832i
$501$	6.06823	−	24.2385i	0.271109	−	1.08290i
$502$	−33.0040	−	19.0548i	−1.47304	−	0.850459i
$503$			5.13662i			0.229030i	0.993421	+	0.114515i	$0.0365315\pi$
$503$			5.13662i			0.229030i	−0.993421	+	0.114515i	$0.963469\pi$
$504$	−15.6083	−	8.33780i	−0.695248	−	0.371395i
$505$	−14.5555	+	17.6536i	−0.647713	+	0.785573i
$506$	−4.77765	+	8.27513i	−0.212392	+	0.367875i
$507$	2.07439	+	7.26073i	0.0921268	+	0.322460i
$508$	−2.00697	+	1.15873i	−0.0890450	+	0.0514101i
$509$	−10.5162	−	18.2146i	−0.466122	−	0.807347i	0.533129	−	0.846034i	$-0.321016\pi$
$509$	−10.5162	−	18.2146i	−0.466122	−	0.807347i	−0.999251	+	0.0386867i	$0.987683\pi$
$510$	0.476293	+	4.22052i	0.0210906	+	0.186888i
$511$	−1.10624	+	1.91606i	−0.0489371	+	0.0847615i
$512$		−	24.5369i		−	1.08439i
$513$	−12.6008	−	11.4121i	−0.556337	−	0.503856i
$514$	−40.0509			−1.76657
$515$	−9.53856	+	3.56520i	−0.420319	+	0.157101i
$516$	0.210937	+	0.204094i	0.00928600	+	0.00898474i
$517$	−0.461305	+	0.266335i	−0.0202882	+	0.0117134i
$518$	23.4827	−	13.5577i	1.03177	−	0.595692i
$519$	−6.38858	+	1.82522i	−0.280428	+	0.0801181i
$520$	6.71783	+	17.9733i	0.294596	+	0.788182i
$521$	−39.7411			−1.74109			−0.870544	−	0.492091i	$-0.836233\pi$
$521$	−39.7411			−1.74109			−0.870544	+	0.492091i	$0.836233\pi$
$522$	−14.2728	−	22.9397i	−0.624701	−	1.00404i
$523$			6.06604i			0.265249i	0.991166	+	0.132625i	$0.0423405\pi$
$523$			6.06604i			0.265249i	−0.991166	+	0.132625i	$0.957660\pi$
$524$	−1.27771	+	2.21306i	−0.0558170	+	0.0966779i
$525$	−17.4735	−	0.936309i	−0.762605	−	0.0408639i
$526$	16.9073	+	29.2842i	0.737192	+	1.27685i
$527$	−0.133338	+	0.0769827i	−0.00580830	+	0.00335342i
$528$	6.21274	+	1.55539i	0.270375	+	0.0676897i
$529$	13.0601	−	22.6207i	0.567829	−	0.983508i
$530$	−21.2373	+	25.7574i	−0.922489	+	1.11883i
$531$	−18.8990	+	11.7587i	−0.820147	+	0.510283i
$532$			0.933525i			0.0404734i
$533$	3.90617	+	2.25523i	0.169195	+	0.0976849i
$534$	28.5319	−	8.15156i	1.23470	−	0.352752i
$535$	−4.05311	+	24.2050i	−0.175231	+	1.04648i
$536$	−10.7991	−	18.7046i	−0.466451	−	0.807918i
$537$	1.97719	−	2.04349i	0.0853222	−	0.0881830i
$538$	7.59307	+	4.38386i	0.327360	+	0.189002i
$539$	2.91735			0.125659
$540$	0.605919	−	1.52477i	0.0260746	−	0.0656158i
$541$	−29.0577			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$541$	−29.0577			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$542$	17.1426	+	9.89728i	0.736337	+	0.425124i
$543$	−18.9119	+	19.5460i	−0.811588	+	0.838800i
$544$	0.320658	+	0.555396i	0.0137481	+	0.0238124i
$545$	−13.1807	−	2.20709i	−0.564598	−	0.0945414i
$546$	−13.4857	+	3.85285i	−0.577133	+	0.164887i
$547$	9.09531	+	5.25118i	0.388887	+	0.224524i	0.681678	−	0.731652i	$-0.261251\pi$
$547$	9.09531	+	5.25118i	0.388887	+	0.224524i	−0.292791	+	0.956177i	$0.594584\pi$
$548$			3.12838i			0.133638i
$549$	31.1625	+	16.6467i	1.32998	+	0.710464i
$550$	6.69189	−	1.29933i	0.285343	−	0.0554038i
$551$	−10.8058	+	18.7162i	−0.460342	+	0.797336i
$552$	−34.3767	−	8.60637i	−1.46317	−	0.366312i
$553$	5.72604	−	3.30593i	0.243496	−	0.140583i
$554$	−0.706367	−	1.22346i	−0.0300107	−	0.0519800i
$555$	22.6431	+	30.6689i	0.961145	+	1.30182i
$556$	1.16371	−	2.01560i	0.0493522	−	0.0854805i
$557$		−	10.5678i		−	0.447772i	−0.974615	−	0.223886i	$-0.928126\pi$
$557$		−	10.5678i		−	0.447772i	0.974615	−	0.223886i	$-0.0718743\pi$
$558$	−0.782474	+	0.0258104i	−0.0331248	+	0.00109264i
$559$	3.52738			0.149192
$560$	15.6489	−	5.84904i	0.661287	−	0.247167i
$561$	−1.33960	+	0.382724i	−0.0565580	+	0.0161586i
$562$	−5.15157	+	2.97426i	−0.217306	+	0.125461i
$563$	15.8668	−	9.16070i	0.668706	−	0.386077i	−0.126880	−	0.991918i	$-0.540496\pi$
$563$	15.8668	−	9.16070i	0.668706	−	0.386077i	0.795586	+	0.605841i	$0.207163\pi$
$564$	−0.0936318	−	0.0905942i	−0.00394261	−	0.00381470i
$565$	−31.1928	+	11.6588i	−1.31229	+	0.490490i
$566$	10.7225			0.450701
$567$	16.3136	+	8.03491i	0.685109	+	0.337435i
$568$		−	6.43992i		−	0.270213i
$569$	19.6001	−	33.9483i	0.821677	−	1.42319i	−0.0827553	−	0.996570i	$-0.526372\pi$
$569$	19.6001	−	33.9483i	0.821677	−	1.42319i	0.904432	−	0.426617i	$-0.140295\pi$
$570$	17.1669	−	1.93731i	0.719040	−	0.0811450i
$571$	−12.9526	−	22.4345i	−0.542049	−	0.938856i	−0.998786	−	0.0492542i	$-0.984316\pi$
$571$	−12.9526	−	22.4345i	−0.542049	−	0.938856i	0.456738	−	0.889601i	$-0.349018\pi$
$572$	−0.359477	+	0.207544i	−0.0150305	+	0.00867786i
$573$	0.179492	+	0.628253i	0.00749838	+	0.0262457i
$574$	2.11355	−	3.66078i	0.0882179	−	0.152798i
$575$	−34.4004	+	6.67937i	−1.43460	+	0.278549i
$576$	0.838925	+	25.4330i	0.0349552	+	1.05971i
$577$			16.5181i			0.687656i	0.939033	+	0.343828i	$0.111724\pi$
$577$			16.5181i			0.687656i	−0.939033	+	0.343828i	$0.888276\pi$
$578$	−19.3082	−	11.1476i	−0.803117	−	0.463680i
$579$	1.75538	−	7.01156i	0.0729509	−	0.291390i
$580$	−2.05714	−	0.344467i	−0.0854183	−	0.0143032i
$581$	7.78683	+	13.4872i	0.323052	+	0.559543i
$582$	17.9830	+	4.50212i	0.745417	+	0.186619i
$583$	−9.48341	−	5.47525i	−0.392763	−	0.226762i
$584$	3.19655			0.132274
$585$	−7.50877	−	18.2327i	−0.310449	−	0.753829i
$586$	23.1054			0.954475
$587$	9.05321	+	5.22687i	0.373666	+	0.215736i	0.675059	−	0.737764i	$-0.264118\pi$
$587$	9.05321	+	5.22687i	0.373666	+	0.215736i	−0.301393	+	0.953500i	$0.597452\pi$
$588$	0.196018	+	0.686099i	0.00808366	+	0.0282943i
$589$	0.313125	+	0.542349i	0.0129021	+	0.0223471i
$590$	3.73552	−	22.3084i	0.153789	−	0.918423i
$591$	−1.23151	−	1.19156i	−0.0506578	−	0.0490143i
$592$	−31.5199	−	18.1980i	−1.29546	−	0.747935i
$593$		−	13.3267i		−	0.547264i	−0.961834	−	0.273632i	$-0.911775\pi$
$593$		−	13.3267i		−	0.547264i	0.961834	−	0.273632i	$-0.0882250\pi$
$594$	−6.92519	−	1.49299i	−0.284144	−	0.0612582i
$595$	−2.31193	+	2.80400i	−0.0947799	+	0.114953i
$596$	0.400524	−	0.693727i	0.0164061	−	0.0284162i
$597$	20.1101	−	20.7843i	0.823050	−	0.850646i
$598$	−24.3242	+	14.0436i	−0.994692	+	0.574286i
$599$	−17.8823	−	30.9731i	−0.730651	−	1.26552i	−0.956605	−	0.291387i	$-0.905883\pi$
$599$	−17.8823	−	30.9731i	−0.730651	−	1.26552i	0.225954	−	0.974138i	$-0.427450\pi$
$600$	11.4512	+	22.5396i	0.467493	+	0.920174i
$601$	11.3497	−	19.6583i	0.462964	−	0.801878i	−0.536143	−	0.844127i	$-0.680119\pi$
$601$	11.3497	−	19.6583i	0.462964	−	0.801878i	0.999107	+	0.0422495i	$0.0134524\pi$
$602$		−	3.30578i		−	0.134734i
$603$	11.7254	+	18.8456i	0.477496	+	0.767451i
$604$	2.43880			0.0992334
$605$	0.782871	+	2.09454i	0.0318282	+	0.0851553i
$606$	−5.86825	+	23.4398i	−0.238381	+	0.952175i
$607$	−1.63835	+	0.945901i	−0.0664985	+	0.0383929i	−0.532881	−	0.846190i	$-0.678891\pi$
$607$	−1.63835	+	0.945901i	−0.0664985	+	0.0383929i	0.466382	+	0.884583i	$0.345557\pi$
$608$	2.25906	−	1.30427i	0.0916170	−	0.0528951i
$609$	5.61429	−	22.4254i	0.227503	−	0.908721i
$610$	−33.6300	+	12.5698i	−1.36164	+	0.508935i
$611$	−1.56575			−0.0633434
$612$	−0.180017	−	0.289331i	−0.00727677	−	0.0116955i
$613$			13.1839i			0.532494i	0.963905	+	0.266247i	$0.0857837\pi$
$613$			13.1839i			0.532494i	−0.963905	+	0.266247i	$0.914216\pi$
$614$	20.9860	−	36.3488i	0.846925	−	1.46692i
$615$	5.44751	+	2.37558i	0.219665	+	0.0957926i
$616$	2.94928	+	5.10830i	0.118830	+	0.205819i
$617$	19.1843	−	11.0761i	0.772330	−	0.445905i	−0.0613750	−	0.998115i	$-0.519549\pi$
$617$	19.1843	−	11.0761i	0.772330	−	0.445905i	0.833705	+	0.552210i	$0.186215\pi$
$618$	−7.47781	+	7.72854i	−0.300802	+	0.310887i
$619$	−0.708185	+	1.22661i	−0.0284644	+	0.0493017i	−0.879907	−	0.475147i	$-0.842395\pi$
$619$	−0.708185	+	1.22661i	−0.0284644	+	0.0493017i	0.851442	+	0.524448i	$0.175728\pi$
$620$	−0.0384500	+	0.0466337i	−0.00154419	+	0.00187286i
$621$	35.5997	+	7.67489i	1.42857	+	0.307983i
$622$		−	1.26559i		−	0.0507456i
$623$	21.9885	+	12.6951i	0.880950	+	0.508617i
$624$	13.5293	+	13.0904i	0.541607	+	0.524037i
$625$	19.6939	+	15.3997i	0.787756	+	0.615988i
$626$	−4.02496	−	6.97144i	−0.160870	−	0.278635i
$627$	1.55672	+	5.44880i	0.0621694	+	0.217604i
$628$	1.27772	+	0.737695i	0.0509868	+	0.0294372i
$629$	7.91743			0.315689
$630$	−17.0873	+	7.03705i	−0.680773	+	0.280363i
$631$	10.9115			0.434379			0.217190	−	0.976129i	$-0.430311\pi$
$631$	10.9115			0.434379			0.217190	+	0.976129i	$0.430311\pi$
$632$	−8.27291	−	4.77637i	−0.329079	−	0.189994i
$633$	37.1989	+	9.31292i	1.47852	+	0.370155i
$634$	6.04389	+	10.4683i	0.240034	+	0.415750i
$635$	−6.06034	+	36.1921i	−0.240497	+	1.43624i
$636$	0.650468	−	2.59819i	0.0257927	−	0.103025i
$637$	7.42648	+	4.28768i	0.294248	+	0.169884i
$638$			9.00581i			0.356544i
$639$	0.218181	+	6.61441i	0.00863110	+	0.261662i
$640$	−17.2007	−	14.1821i	−0.679916	−	0.560598i
$641$	−19.5717	+	33.8992i	−0.773036	+	1.33894i	0.162855	+	0.986650i	$0.447930\pi$
$641$	−19.5717	+	33.8992i	−0.773036	+	1.33894i	−0.935891	+	0.352288i	$0.885404\pi$
$642$	7.11988	+	24.9208i	0.280999	+	0.983547i
$643$	22.1146	−	12.7679i	0.872116	−	0.503516i	0.00406499	−	0.999992i	$-0.498706\pi$
$643$	22.1146	−	12.7679i	0.872116	−	0.503516i	0.868051	+	0.496475i	$0.165373\pi$
$644$	−0.999879	−	1.73184i	−0.0394007	−	0.0682441i
$645$	4.61834	−	0.521188i	0.181847	−	0.0205218i
$646$	1.79398	−	3.10726i	0.0705830	−	0.122253i
$647$		−	2.84469i		−	0.111836i	−0.998435	−	0.0559182i	$-0.982191\pi$
$647$		−	2.84469i		−	0.111836i	0.998435	−	0.0559182i	$-0.0178086\pi$
$648$	−1.73141	−	26.2163i	−0.0680163	−	1.02988i
$649$	7.41948			0.291240
$650$	18.9447	+	6.52758i	0.743073	+	0.256033i
$651$	−0.481427	−	0.465808i	−0.0188686	−	0.0182565i
$652$	−2.05948	+	1.18904i	−0.0806555	+	0.0465665i
$653$	13.2558	−	7.65324i	0.518739	−	0.299494i	−0.217679	−	0.976020i	$-0.569849\pi$
$653$	13.2558	−	7.65324i	0.518739	−	0.299494i	0.736419	+	0.676526i	$0.236515\pi$
$654$	−13.5705	+	3.87708i	−0.530647	+	0.151606i
$655$	14.1669	+	37.9031i	0.553548	+	1.48100i
$656$	−5.67389			−0.221528
$657$	−3.28316	+	0.108297i	−0.128088	+	0.00422508i
$658$			1.46738i			0.0572046i
$659$	−9.68204	+	16.7698i	−0.377159	+	0.653258i	−0.990648	−	0.136445i	$-0.956432\pi$
$659$	−9.68204	+	16.7698i	−0.377159	+	0.653258i	0.613489	+	0.789703i	$0.289766\pi$
$660$	−0.439991	+	0.324849i	−0.0171266	+	0.0126447i
$661$	14.2842	+	24.7410i	0.555592	+	0.962314i	0.997857	+	0.0654297i	$0.0208418\pi$
$661$	14.2842	+	24.7410i	0.555592	+	0.962314i	−0.442265	+	0.896885i	$0.645825\pi$
$662$	−8.02384	+	4.63257i	−0.311855	+	0.180050i
$663$	−3.97262	−	0.994565i	−0.154284	−	0.0386257i
$664$	11.2503	−	19.4861i	0.436597	−	0.756207i
$665$	11.4052	+	9.40372i	0.442275	+	0.364661i
$666$	35.5103	+	18.9693i	1.37600	+	0.735045i
$667$		−	46.2954i		−	1.79257i
$668$	−1.76422	−	1.01857i	−0.0682598	−	0.0394098i
$669$	11.9115	−	3.40313i	0.460527	−	0.131572i
$670$	−22.2453	−	3.72496i	−0.859412	−	0.143908i
$671$	−5.88834	−	10.1989i	−0.227317	−	0.393724i
$672$	−1.94024	+	2.00530i	−0.0748465	+	0.0773561i
$673$	−26.2425	−	15.1511i	−1.01157	−	0.584032i	−0.0999206	−	0.994995i	$-0.531859\pi$
$673$	−26.2425	−	15.1511i	−1.01157	−	0.584032i	−0.911652	+	0.410964i	$0.865192\pi$
$674$	12.6410			0.486913
$675$	−12.5251	−	22.7623i	−0.482090	−	0.876121i
$676$	0.615650			0.0236789
$677$	−15.6832	−	9.05472i	−0.602755	−	0.348001i	0.167369	−	0.985894i	$-0.446473\pi$
$677$	−15.6832	−	9.05472i	−0.602755	−	0.348001i	−0.770125	+	0.637893i	$0.779806\pi$
$678$	−24.4538	+	25.2737i	−0.939141	+	0.970630i
$679$	7.93099	+	13.7369i	0.304364	+	0.527173i
$680$	5.17855	+	0.867144i	0.198588	+	0.0332534i
$681$	33.0992	−	9.45642i	1.26836	−	0.362371i
$682$	0.226004	+	0.130483i	0.00865412	+	0.00499646i
$683$		−	4.83222i		−	0.184900i	−0.995717	−	0.0924499i	$-0.970530\pi$
$683$		−	4.83222i		−	0.184900i	0.995717	−	0.0924499i	$-0.0294698\pi$
$684$	−1.17685	+	0.732216i	−0.0449979	+	0.0279970i
$685$	38.2205	+	31.5132i	1.46033	+	1.20406i
$686$	13.6600	−	23.6599i	0.521542	−	0.903338i
$687$	−20.8711	−	5.22518i	−0.796282	−	0.199353i
$688$	−3.84275	+	2.21861i	−0.146504	+	0.0845839i
$689$	−16.0942	−	27.8759i	−0.613139	−	1.06199i
$690$	−29.7723	+	21.9811i	−1.13341	+	0.836805i
$691$	8.68378	−	15.0407i	0.330346	−	0.572177i	−0.652233	−	0.758018i	$-0.726168\pi$
$691$	8.68378	−	15.0407i	0.330346	−	0.572177i	0.982580	+	0.185841i	$0.0595011\pi$
$692$			0.541700i			0.0205923i
$693$	−3.20226	−	5.14679i	−0.121644	−	0.195510i
$694$	45.6901			1.73437
$695$	−12.9029	−	34.5213i	−0.489435	−	1.30947i
$696$	−32.1148	+	9.17519i	−1.21731	+	0.347785i
$697$	1.06891	−	0.617135i	0.0404878	−	0.0233757i
$698$	−33.4229	+	19.2967i	−1.26507	+	0.730391i
$699$	33.1725	+	32.0964i	1.25470	+	1.21400i
$700$	−0.464751	+	1.34883i	−0.0175659	+	0.0509809i
$701$	−30.9866			−1.17035			−0.585174	−	0.810908i	$-0.698974\pi$
$701$	−30.9866			−1.17035			−0.585174	+	0.810908i	$0.698974\pi$
$702$	−15.4347	−	13.9787i	−0.582544	−	0.527591i
$703$		−	32.2039i		−	1.21459i
$704$	4.24114	−	7.34586i	0.159844	−	0.276858i
$705$	−2.05001	+	0.231347i	−0.0772077	+	0.00871304i
$706$	−5.46547	−	9.46647i	−0.205696	−	0.356275i
$707$	−17.9052	+	10.3376i	−0.673396	+	0.388785i
$708$	0.498520	+	1.74491i	0.0187355	+	0.0655776i
$709$	2.12153	−	3.67459i	0.0796756	−	0.138002i	−0.823434	−	0.567411i	$-0.807945\pi$
$709$	2.12153	−	3.67459i	0.0796756	−	0.138002i	0.903110	+	0.429409i	$0.141278\pi$
$710$	−5.18889	−	4.27829i	−0.194736	−	0.160562i
$711$	8.65888	+	4.62550i	0.324733	+	0.173470i
$712$		−	36.6833i		−	1.37476i
$713$	−1.16180	−	0.670764i	−0.0435096	−	0.0251203i
$714$	−0.932084	+	3.72305i	−0.0348824	+	0.139332i
$715$	−1.08549	+	6.48253i	−0.0405951	+	0.242433i
$716$	−0.115912	−	0.200766i	−0.00433184	−	0.00750297i
$717$	−28.2226	−	7.06566i	−1.05399	−	0.263872i
$718$	−27.5765	−	15.9213i	−1.02914	−	0.594177i
$719$	−0.145953			−0.00544314			−0.00272157	−	0.999996i	$-0.500866\pi$
$719$	−0.145953			−0.00544314			−0.00272157	+	0.999996i	$0.500866\pi$
$720$	19.6479	+	15.1400i	0.732235	+	0.564236i
$721$	−9.20163			−0.342687
$722$	9.79491	+	5.65510i	0.364529	+	0.210461i
$723$	2.50088	+	8.75352i	0.0930087	+	0.325547i
$724$	1.10870	+	1.92033i	0.0412047	+	0.0713686i
$725$	−24.9308	+	21.6630i	−0.925907	+	0.804542i
$726$	1.69709	+	1.64203i	0.0629848	+	0.0609414i
$727$	−23.6668	−	13.6640i	−0.877753	−	0.506771i	−0.00783623	−	0.999969i	$-0.502494\pi$
$727$	−23.6668	−	13.6640i	−0.877753	−	0.506771i	−0.869917	+	0.493198i	$0.835828\pi$
$728$			17.3384i			0.642605i
$729$	2.66652	+	26.8680i	0.0987600	+	0.995111i
$730$	2.12360	−	2.57558i	0.0785978	−	0.0953267i
$731$	0.482627	−	0.835934i	0.0178506	−	0.0309181i
$732$	2.00293	−	2.07009i	0.0740304	−	0.0765126i
$733$	−32.5850	+	18.8130i	−1.20356	+	0.694873i	−0.961344	−	0.275350i	$-0.911206\pi$
$733$	−32.5850	+	18.8130i	−1.20356	+	0.694873i	−0.242212	+	0.970223i	$0.577873\pi$
$734$	−22.4636	−	38.9080i	−0.829145	−	1.43612i
$735$	10.3569	+	4.51649i	0.382020	+	0.166593i
$736$	−2.79395	+	4.83926i	−0.102986	+	0.178378i
$737$		−	7.39851i		−	0.272528i
$738$	6.27273	−	0.206910i	0.230902	−	0.00761648i
$739$	14.6094			0.537415			0.268707	−	0.963222i	$-0.413404\pi$
$739$	14.6094			0.537415			0.268707	+	0.963222i	$0.413404\pi$
$740$	2.91136	−	1.08817i	0.107024	−	0.0400020i
$741$	−4.04537	+	16.1585i	−0.148610	+	0.593599i
$742$	−26.1247	+	15.0831i	−0.959066	+	0.553717i
$743$	−31.8659	+	18.3978i	−1.16905	+	0.674950i	−0.953456	−	0.301533i	$-0.902501\pi$
$743$	−31.8659	+	18.3978i	−1.16905	+	0.674950i	−0.215592	+	0.976484i	$0.569168\pi$
$744$	−0.235050	+	0.938868i	−0.00861735	+	0.0344206i
$745$	−4.44091	−	11.8815i	−0.162702	−	0.435304i
$746$	−9.32991			−0.341592
$747$	−10.8949	+	20.3952i	−0.398625	+	0.746222i
$748$			0.113587i			0.00415316i
$749$	−11.0883	+	19.2056i	−0.405159	+	0.701757i
$750$	25.7685	+	5.74727i	0.940931	+	0.209860i
$751$	−7.79392	−	13.4995i	−0.284404	−	0.492602i	0.688060	−	0.725653i	$-0.258462\pi$
$751$	−7.79392	−	13.4995i	−0.284404	−	0.492602i	−0.972465	+	0.233051i	$0.925129\pi$
$752$	1.70574	−	0.984808i	0.0622018	−	0.0359122i
$753$	33.6656	−	34.7944i	1.22684	−	1.26798i
$754$	−13.2360	+	22.9254i	−0.482027	+	0.834895i
$755$	24.5669	−	29.7957i	0.894080	−	1.08438i
$756$	0.995256	−	1.09892i	0.0361971	−	0.0399673i
$757$			2.88405i			0.104823i	0.998626	+	0.0524113i	$0.0166907\pi$
$757$			2.88405i			0.104823i	−0.998626	+	0.0524113i	$0.983309\pi$
$758$	−8.71808	−	5.03338i	−0.316655	−	0.182821i
$759$	−8.72406	−	8.44104i	−0.316663	−	0.306390i
$760$	3.52708	−	21.0636i	0.127941	−	0.764058i
$761$	−20.5927	−	35.6676i	−0.746484	−	1.29295i	−0.949498	−	0.313773i	$-0.898407\pi$
$761$	−20.5927	−	35.6676i	−0.746484	−	1.29295i	0.203013	−	0.979176i	$-0.434926\pi$
$762$	10.6459	+	37.2624i	0.385659	+	1.34988i
$763$	−10.4583	−	6.03807i	−0.378614	−	0.218593i
$764$	0.0532708			0.00192727
$765$	−5.34824	−	0.715192i	−0.193366	−	0.0258578i
$766$	−8.08858			−0.292252
$767$	18.8872	+	10.9046i	0.681979	+	0.393740i
$768$	5.66534	+	1.41834i	0.204430	+	0.0511801i
$769$	−6.86546	−	11.8913i	−0.247575	−	0.428812i	0.715278	−	0.698840i	$-0.246300\pi$
$769$	−6.86546	−	11.8913i	−0.247575	−	0.428812i	−0.962852	+	0.270028i	$0.912967\pi$
$770$	6.07528	+	1.01730i	0.218938	+	0.0366609i
$771$	12.3570	−	49.3580i	0.445027	−	1.77759i
$772$	−0.510342	−	0.294646i	−0.0183676	−	0.0106046i
$773$			6.40444i			0.230352i	0.993345	+	0.115176i	$0.0367432\pi$
$773$			6.40444i			0.230352i	−0.993345	+	0.115176i	$0.963257\pi$
$774$	4.16743	−	2.59291i	0.149795	−	0.0932002i
$775$	0.182421	+	0.939516i	0.00655277	+	0.0337484i
$776$	11.4586	−	19.8469i	0.411339	−	0.712461i
$777$	9.46312	+	33.1226i	0.339488	+	1.18827i
$778$	10.2482	−	5.91680i	0.367415	−	0.212127i
$779$	−2.51018	−	4.34776i	−0.0899366	−	0.155775i
$780$	−1.59749	+	0.180280i	−0.0571993	+	0.00645505i
$781$	1.10300	−	1.91045i	0.0394685	−	0.0683614i
$782$			7.68595i			0.274849i
$783$	32.6741	−	10.5118i	1.16768	−	0.375662i
$784$	−10.7873			−0.385260
$785$	21.8836	−	8.17938i	0.781061	−	0.291935i
$786$	30.7107	+	29.7144i	1.09541	+	1.05988i
$787$	−28.0846	+	16.2146i	−1.00111	+	0.577990i	−0.908576	−	0.417720i	$-0.862829\pi$
$787$	−28.0846	+	16.2146i	−1.00111	+	0.577990i	−0.0925317	+	0.995710i	$0.529496\pi$
$788$	−0.120992	+	0.0698549i	−0.00431017	+	0.00248848i
$789$	−41.3058	+	11.8011i	−1.47053	+	0.420129i
$790$	−9.34452	+	3.49267i	−0.332463	+	0.124264i
$791$	−30.0910			−1.06991
$792$	−4.12649	+	7.72473i	−0.146628	+	0.274486i
$793$		−	34.6168i		−	1.22928i
$794$	−16.4500	+	28.4923i	−0.583789	+	1.01115i
$795$	−25.1906	−	34.1194i	−0.893419	−	1.21009i
$796$	−1.17894	−	2.04199i	−0.0417866	−	0.0723765i
$797$	−12.6518	+	7.30453i	−0.448151	+	0.258740i	−0.707049	−	0.707165i	$-0.749974\pi$
$797$	−12.6518	+	7.30453i	−0.448151	+	0.258740i	0.258898	+	0.965905i	$0.416641\pi$
$798$	15.1434	+	3.79123i	0.536071	+	0.134208i
$799$	−0.214230	+	0.371058i	−0.00757893	+	0.0131271i
$800$	3.91339	−	0.759844i	0.138359	−	0.0268646i
$801$	1.24281	+	37.6772i	0.0439125	+	1.33126i
$802$			1.62479i			0.0573732i
$803$	0.948282	+	0.547491i	0.0334642	+	0.0193205i
$804$	1.73997	−	0.497110i	0.0613642	−	0.0175317i
$805$	−31.2307	−	5.22954i	−1.10074	−	0.184317i
$806$	0.383547	+	0.664323i	0.0135099	+	0.0233998i
$807$	−7.74530	+	8.00499i	−0.272647	+	0.281789i
$808$	25.8692	+	14.9356i	0.910077	+	0.525433i
$809$	−2.42391			−0.0852200			−0.0426100	−	0.999092i	$-0.513567\pi$
$809$	−2.42391			−0.0852200			−0.0426100	+	0.999092i	$0.513567\pi$
$810$	−22.2738	−	16.0215i	−0.782620	−	0.562938i
$811$	−9.05830			−0.318080			−0.159040	−	0.987272i	$-0.550840\pi$
$811$	−9.05830			−0.318080			−0.159040	+	0.987272i	$0.550840\pi$
$812$	−1.63225	−	0.942379i	−0.0572807	−	0.0330710i
$813$	−17.4863	+	18.0726i	−0.613270	+	0.633833i
$814$	−6.70989	−	11.6219i	−0.235182	−	0.407346i
$815$	−6.21890	+	37.1391i	−0.217839	+	1.30093i
$816$	4.95335	−	1.41517i	0.173402	−	0.0495409i
$817$	−3.40014	−	1.96307i	−0.118956	−	0.0686792i
$818$			54.9878i			1.92260i
$819$	−0.587417	−	17.8082i	−0.0205260	−	0.622269i
$820$	0.308236	−	0.373841i	0.0107641	−	0.0130551i
$821$	−24.3533	+	42.1811i	−0.849934	+	1.47213i	0.0313317	+	0.999509i	$0.490025\pi$
$821$	−24.3533	+	42.1811i	−0.849934	+	1.47213i	−0.881266	+	0.472620i	$0.843308\pi$
$822$	50.7478	+	12.7050i	1.77003	+	0.443136i
$823$	−20.1548	+	11.6364i	−0.702551	+	0.405618i	−0.808297	−	0.588775i	$-0.799610\pi$
$823$	−20.1548	+	11.6364i	−0.702551	+	0.405618i	0.105746	+	0.994393i	$0.466277\pi$
$824$	6.64719	+	11.5133i	0.231566	+	0.401084i
$825$	−0.463391	+	8.64785i	−0.0161332	+	0.301079i
$826$	10.2195	−	17.7007i	0.355582	−	0.615886i
$827$		−	34.5142i		−	1.20018i	−0.799933	−	0.600089i	$-0.795132\pi$
$827$		−	34.5142i		−	1.20018i	0.799933	−	0.600089i	$-0.204868\pi$
$828$	1.39898	−	2.61888i	0.0486179	−	0.0910122i
$829$	44.0208			1.52891			0.764453	−	0.644680i	$-0.223009\pi$
$829$	44.0208			1.52891			0.764453	+	0.644680i	$0.223009\pi$
$830$	−8.22668	−	22.0102i	−0.285552	−	0.763985i
$831$	1.72571	−	0.493035i	0.0598643	−	0.0171032i
$832$	21.5927	−	12.4666i	0.748592	−	0.432200i
$833$	2.03223	−	1.17331i	0.0704125	−	0.0406527i
$834$	−27.9706	−	27.0631i	−0.968541	−	0.937120i
$835$	−30.2159	+	11.2937i	−1.04566	+	0.390835i
$836$	0.462014			0.0159791
$837$	0.209610	−	0.972270i	0.00724519	−	0.0336066i
$838$		−	52.7636i		−	1.82269i
$839$	11.2801	−	19.5376i	0.389431	−	0.674514i	−0.602942	−	0.797785i	$-0.706005\pi$
$839$	11.2801	−	19.5376i	0.389431	−	0.674514i	0.992373	+	0.123271i	$0.0393383\pi$
$840$	2.56184	+	22.7009i	0.0883919	+	0.783256i
$841$	−7.31657	−	12.6727i	−0.252295	−	0.436988i
$842$	−33.0450	+	19.0786i	−1.13881	+	0.657490i
$843$	−2.07599	−	7.26635i	−0.0715010	−	0.250266i
$844$	1.56321	−	2.70755i	0.0538078	−	0.0931979i
$845$	6.20166	−	7.52163i	0.213344	−	0.258752i
$846$	−1.84986	+	1.15095i	−0.0635993	+	0.0395706i
$847$			2.02056i			0.0694272i
$848$	35.0662	+	20.2455i	1.20418	+	0.695232i
$849$	−3.30824	+	13.2142i	−0.113539	+	0.453511i
$850$	4.13901	−	3.59648i	0.141967	−	0.123358i
$851$	34.4930	+	59.7436i	1.18240	+	2.04798i
$852$	0.523410	+	0.131038i	0.0179317	+	0.00448930i
$853$	35.4054	+	20.4413i	1.21226	+	0.699898i	0.963251	−	0.268604i	$-0.0865622\pi$
$853$	35.4054	+	20.4413i	1.21226	+	0.699898i	0.249008	+	0.968502i	$0.419896\pi$
$854$	−32.4421			−1.11015
$855$	−2.90903	+	21.7538i	−0.0994866	+	0.743965i
$856$	32.0406			1.09512
$857$	8.54571	+	4.93387i	0.291916	+	0.168538i	0.638806	−	0.769368i	$-0.279429\pi$
$857$	8.54571	+	4.93387i	0.291916	+	0.168538i	−0.346890	+	0.937906i	$0.612762\pi$
$858$	1.90683	+	6.67423i	0.0650980	+	0.227855i
$859$	12.8738	+	22.2981i	0.439248	+	0.760800i	0.997632	−	0.0687829i	$-0.0219116\pi$
$859$	12.8738	+	22.2981i	0.439248	+	0.760800i	−0.558384	+	0.829583i	$0.688578\pi$
$860$	0.0625788	−	0.373719i	0.00213392	−	0.0127437i
$861$	3.85938	+	3.73417i	0.131527	+	0.127260i
$862$	19.7055	+	11.3770i	0.671172	+	0.387501i
$863$		−	43.0167i		−	1.46431i	−0.681140	−	0.732153i	$-0.738516\pi$
$863$		−	43.0167i		−	1.46431i	0.681140	−	0.732153i	$-0.261484\pi$
$864$	−4.04982	−	0.873095i	−0.137778	−	0.0297033i
$865$	6.61814	+	5.45673i	0.225024	+	0.185534i
$866$	−0.00850929	+	0.0147385i	−0.000289157	+	0.000500835i
$867$	19.6953	−	20.3557i	0.668889	−	0.691316i
$868$	−0.0472986	+	0.0273079i	−0.00160542	+	0.000926889i
$869$	−1.63615	−	2.83389i	−0.0555025	−	0.0961332i
$870$	−13.9423	+	31.9716i	−0.472689	+	1.08394i
$871$	10.8737	−	18.8338i	0.368442	−	0.638160i
$872$			17.4474i			0.590845i
$873$	−11.0967	+	20.7728i	−0.375565	+	0.703053i
$874$	31.2624			1.05747
$875$	11.7975	+	19.2652i	0.398829	+	0.651284i
$876$	−0.0650428	+	0.259803i	−0.00219759	+	0.00877791i
$877$	−38.6963	+	22.3413i	−1.30668	+	0.754412i	−0.981540	−	0.191254i	$-0.938744\pi$
$877$	−38.6963	+	22.3413i	−1.30668	+	0.754412i	−0.325139	+	0.945666i	$0.605411\pi$
$878$	7.07039	−	4.08209i	0.238614	−	0.137764i
$879$	−7.12876	+	28.4746i	−0.240447	+	0.960426i
$880$	−2.89477	−	7.74485i	−0.0975826	−	0.261079i
$881$	−53.1295			−1.78998			−0.894988	−	0.446089i	$-0.852816\pi$
$881$	−53.1295			−1.78998			−0.894988	+	0.446089i	$0.852816\pi$
$882$	11.9258	−	0.393381i	0.401563	−	0.0132458i
$883$			26.2913i			0.884773i	0.896825	+	0.442386i	$0.145868\pi$
$883$			26.2913i			0.884773i	−0.896825	+	0.442386i	$0.854132\pi$
$884$	−0.166941	+	0.289151i	−0.00561485	+	0.00972520i
$885$	26.3399	+	11.4865i	0.885407	+	0.386113i
$886$	−9.05326	−	15.6807i	−0.304150	−	0.526804i
$887$	−30.4848	+	17.6004i	−1.02358	+	0.590965i	−0.915139	−	0.403138i	$-0.867919\pi$
$887$	−30.4848	+	17.6004i	−1.02358	+	0.590965i	−0.108442	+	0.994103i	$0.534586\pi$
$888$	34.6076	−	35.7680i	1.16136	−	1.20030i
$889$	−16.5796	+	28.7168i	−0.556064	+	0.963130i
$890$	−29.5571	−	24.3702i	−0.990757	−	0.816890i
$891$	3.97658	−	8.07383i	0.133220	−	0.270484i
$892$		−	1.01000i		−	0.0338173i
$893$	1.50927	+	0.871377i	0.0505058	+	0.0291595i
$894$	−9.62688	−	9.31457i	−0.321971	−	0.311526i
$895$	−3.62045	−	0.606242i	−0.121018	−	0.0202644i
$896$	−10.0724	−	17.4459i	−0.336495	−	0.582826i
$897$	−9.80226	−	34.3096i	−0.327288	−	1.14557i
$898$	42.5812	+	24.5843i	1.42095	+	0.820388i
$899$	−1.26438			−0.0421695
$900$	−2.06493	+	0.472074i	−0.0688310	+	0.0157358i
$901$	−8.80821			−0.293444
$902$	−1.81177	−	1.04602i	−0.0603252	−	0.0348288i
$903$	4.07398	+	1.01994i	0.135574	+	0.0339415i
$904$	21.7375	+	37.6505i	0.722978	+	1.25224i
$905$	34.6298	+	5.79872i	1.15113	+	0.192756i
$906$	9.90445	−	39.5617i	0.329053	−	1.31435i
$907$	38.5249	+	22.2423i	1.27920	+	0.738545i	0.976701	−	0.214605i	$-0.0688465\pi$
$907$	38.5249	+	22.2423i	1.27920	+	0.738545i	0.302497	+	0.953150i	$0.402180\pi$
$908$		−	2.80654i		−	0.0931382i
$909$	−27.0762	−	14.4639i	−0.898060	−	0.479736i
$910$	13.9702	+	11.5186i	0.463109	+	0.381838i
$911$	24.5464	−	42.5157i	0.813260	−	1.40861i	−0.0973106	−	0.995254i	$-0.531024\pi$
$911$	24.5464	−	42.5157i	0.813260	−	1.40861i	0.910571	−	0.413354i	$-0.135643\pi$
$912$	−5.75618	−	20.1476i	−0.190606	−	0.667155i
$913$	6.67498	−	3.85380i	0.220910	−	0.127542i
$914$	22.2408	+	38.5221i	0.735659	+	1.27420i
$915$	−5.11481	−	45.3232i	−0.169090	−	1.49834i
$916$	−0.877065	+	1.51912i	−0.0289790	+	0.0501932i
$917$			36.5643i			1.20746i
$918$	−5.42455	+	1.74517i	−0.179037	+	0.0575992i
$919$	7.16158			0.236239			0.118119	−	0.992999i	$-0.462313\pi$
$919$	7.16158			0.236239			0.118119	+	0.992999i	$0.462313\pi$
$920$	16.0175	+	42.8542i	0.528081	+	1.41286i
$921$	38.3207	+	37.0775i	1.26271	+	1.22175i
$922$	11.7452	−	6.78111i	0.386808	−	0.223324i
$923$	5.61566	−	3.24220i	0.184842	−	0.106718i
$924$	−0.475193	+	0.135763i	−0.0156327	+	0.00446626i
$925$	16.0326	−	46.5307i	0.527148	−	1.52992i
$926$	−30.9425			−1.01683
$927$	−7.21736	−	11.6000i	−0.237049	−	0.380995i
$928$			5.26656i			0.172883i
$929$	8.34690	−	14.4573i	0.273853	−	0.474327i	−0.695992	−	0.718049i	$-0.745035\pi$
$929$	8.34690	−	14.4573i	0.273853	−	0.474327i	0.969845	+	0.243722i	$0.0783685\pi$
$930$	0.600329	+	0.813116i	0.0196856	+	0.0266631i
$931$	−4.77240	−	8.26603i	−0.156409	−	0.270908i
$932$	3.25909	−	1.88164i	0.106755	−	0.0616351i
$933$	1.55969	+	0.390476i	0.0510620	+	0.0127836i
$934$	−15.2278	+	26.3753i	−0.498268	+	0.863025i
$935$	1.38774	+	1.14420i	0.0453839	+	0.0374195i
$936$	−21.8577	+	13.5995i	−0.714441	+	0.444514i
$937$			26.8522i			0.877222i	0.898677	+	0.438611i	$0.144529\pi$
$937$			26.8522i			0.877222i	−0.898677	+	0.438611i	$0.855471\pi$
$938$	−17.6506	−	10.1906i	−0.576314	−	0.332735i
$939$	9.83330	−	2.80937i	0.320898	−	0.0916804i
$940$	−0.0277778	+	0.165888i	−0.000906010	+	0.00541066i
$941$	4.86208	+	8.42137i	0.158499	+	0.274529i	0.934328	−	0.356415i	$-0.116001\pi$
$941$	4.86208	+	8.42137i	0.158499	+	0.274529i	−0.775828	+	0.630944i	$0.782668\pi$
$942$	17.1558	−	17.7310i	0.558966	−	0.577708i
$943$	9.31359	+	5.37720i	0.303292	+	0.175106i
$944$	−27.4345			−0.892917
$945$	−3.40035	−	23.2292i	−0.110613	−	0.755646i
$946$	−1.63607			−0.0531933
$947$	−21.2026	−	12.2413i	−0.688992	−	0.397790i	0.114242	−	0.993453i	$-0.463556\pi$
$947$	−21.2026	−	12.2413i	−0.688992	−	0.397790i	−0.803234	+	0.595663i	$0.796889\pi$
$948$	0.556539	−	0.575199i	0.0180755	−	0.0186816i
$949$	1.60932	+	2.78742i	0.0522406	+	0.0904834i
$950$	−14.6286	−	16.8353i	−0.474614	−	0.546210i
$951$	−14.7657	+	4.21856i	−0.478811	+	0.136796i
$952$	4.10894	+	2.37230i	0.133172	+	0.0768866i
$953$		−	26.7951i		−	0.867977i	−0.900918	−	0.433988i	$-0.857106\pi$
$953$		−	26.7951i		−	0.867977i	0.900918	−	0.433988i	$-0.142894\pi$
$954$	−39.5055	−	21.1035i	−1.27904	−	0.683251i
$955$	0.536615	−	0.650828i	0.0173644	−	0.0210603i
$956$	−1.18600	+	2.05421i	−0.0383579	+	0.0664378i
$957$	−11.0986	−	2.77859i	−0.358767	−	0.0898189i
$958$	−27.6605	+	15.9698i	−0.893671	+	0.515961i
$959$	22.3812	+	38.7654i	0.722728	+	1.25180i
$960$	26.4290	−	19.5127i	0.852991	−	0.629769i
$961$	15.4817	−	26.8151i	0.499409	−	0.865002i
$962$		−	39.4466i		−	1.27181i
$963$	−32.9087	+	1.08552i	−1.06047	+	0.0349803i
$964$	0.742227			0.0239055
$965$	−8.74065	+	3.26697i	−0.281372	+	0.105167i
$966$	−32.1542	+	9.18646i	−1.03455	+	0.295569i
$967$	16.4877	−	9.51920i	0.530210	−	0.306117i	−0.210892	−	0.977509i	$-0.567637\pi$
$967$	16.4877	−	9.51920i	0.530210	−	0.306117i	0.741102	+	0.671393i	$0.234304\pi$
$968$	2.52816	−	1.45964i	0.0812583	−	0.0469145i
$969$	3.27583	+	3.16955i	0.105235	+	0.101821i
$970$	−8.37898	−	22.4177i	−0.269033	−	0.719788i
$971$	14.0138			0.449723			0.224862	−	0.974391i	$-0.427807\pi$
$971$	14.0138			0.449723			0.224862	+	0.974391i	$0.427807\pi$
$972$	2.16599	+	0.392723i	0.0694740	+	0.0125966i
$973$		−	33.3019i		−	1.06761i
$974$	7.90252	−	13.6876i	0.253213	−	0.438578i
$975$	−13.8895	+	21.3331i	−0.444821	+	0.683207i
$976$	21.7729	+	37.7118i	0.696934	+	1.20712i
$977$	−1.17278	+	0.677102i	−0.0375204	+	0.0216624i	−0.518643	−	0.854991i	$-0.673563\pi$
$977$	−1.17278	+	0.677102i	−0.0375204	+	0.0216624i	0.481122	+	0.876653i	$0.340229\pi$
$978$	10.9244	+	38.2374i	0.349324	+	1.22270i
$979$	6.28295	−	10.8824i	0.200804	−	0.347803i
$980$	0.586023	−	0.710753i	0.0187198	−	0.0227042i
$981$	−0.591110	−	17.9202i	−0.0188727	−	0.572147i
$982$		−	56.2413i		−	1.79473i
$983$	13.8812	+	8.01429i	0.442740	+	0.255616i	0.704759	−	0.709447i	$-0.251055\pi$
$983$	13.8812	+	8.01429i	0.442740	+	0.255616i	−0.262019	+	0.965063i	$0.584388\pi$
$984$	1.88429	−	7.52647i	0.0600689	−	0.239935i
$985$	−0.365354	+	2.18188i	−0.0116411	+	0.0695205i
$986$	3.62198	+	6.27346i	0.115347	+	0.199788i
$987$	−1.80838	−	0.452736i	−0.0575613	−	0.0144107i
$988$	1.17611	+	0.679030i	0.0374172	+	0.0216028i
$989$	8.41042			0.267436
$990$	3.48273	+	8.45671i	0.110688	+	0.268772i
$991$	−24.8276			−0.788676			−0.394338	−	0.918965i	$-0.629026\pi$
$991$	−24.8276			−0.788676			−0.394338	+	0.918965i	$0.629026\pi$
$992$	0.132166	+	0.0763060i	0.00419627	+	0.00242272i
$993$	−3.23347	−	11.3177i	−0.102611	−	0.359157i
$994$	−3.03852	−	5.26287i	−0.0963759	−	0.166928i
$995$	−36.8237	−	6.16609i	−1.16739	−	0.195478i
$996$	1.35483	+	1.31088i	0.0429295	+	0.0415367i
$997$	10.5965	+	6.11792i	0.335596	+	0.193756i	0.658323	−	0.752736i	$-0.271266\pi$
$997$	10.5965	+	6.11792i	0.335596	+	0.193756i	−0.322727	+	0.946492i	$0.604600\pi$
$998$		−	32.5985i		−	1.03189i
$999$	−34.3335	+	37.9096i	−1.08626	+	1.19941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.u.a.34.7	✓	52
5.4	even	2	inner	495.2.u.a.34.20	yes	52
9.4	even	3	inner	495.2.u.a.364.20	yes	52
45.4	even	6	inner	495.2.u.a.364.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.u.a.34.7	✓	52	1.1	even	1	trivial
495.2.u.a.34.20	yes	52	5.4	even	2	inner
495.2.u.a.364.7	yes	52	45.4	even	6	inner
495.2.u.a.364.20	yes	52	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18072 - 0.681687i) q^{2} +(1.20439 - 1.24477i) q^{3} +(-0.0706068 - 0.122295i) q^{4} +(-2.20536 - 0.369286i) q^{5} +(-2.27058 + 0.648705i) q^{6} +(-1.74985 - 1.01028i) q^{7} +2.91927i q^{8} +(-0.0989033 - 2.99837i) q^{9} +O(q^{10})\)	\(q+(-1.18072 - 0.681687i) q^{2} +(1.20439 - 1.24477i) q^{3} +(-0.0706068 - 0.122295i) q^{4} +(-2.20536 - 0.369286i) q^{5} +(-2.27058 + 0.648705i) q^{6} +(-1.74985 - 1.01028i) q^{7} +2.91927i q^{8} +(-0.0989033 - 2.99837i) q^{9} +(2.35217 + 1.93939i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.237266 - 0.0594008i) q^{12} +(-2.54563 + 1.46972i) q^{13} +(1.37739 + 2.38570i) q^{14} +(-3.11579 + 2.30041i) q^{15} +(1.84882 - 3.20224i) q^{16} +0.804365i q^{17} +(-1.92717 + 3.60764i) q^{18} +3.27174 q^{19} +(0.110552 + 0.295778i) q^{20} +(-3.36507 + 0.961399i) q^{21} +(1.18072 - 0.681687i) q^{22} +(-6.06960 + 3.50429i) q^{23} +(3.63382 + 3.51593i) q^{24} +(4.72726 + 1.62882i) q^{25} +4.00755 q^{26} +(-3.85140 - 3.48809i) q^{27} +0.285330i q^{28} +(-3.30277 + 5.72056i) q^{29} +(5.24702 - 0.592136i) q^{30} +(0.0957062 + 0.165768i) q^{31} +(0.690477 - 0.398647i) q^{32} +(0.475809 + 1.66541i) q^{33} +(0.548325 - 0.949727i) q^{34} +(3.48598 + 2.87423i) q^{35} +(-0.359701 + 0.223801i) q^{36} -9.84307i q^{37} +(-3.86299 - 2.23030i) q^{38} +(-1.23646 + 4.93883i) q^{39} +(1.07805 - 6.43806i) q^{40} +(-0.767232 - 1.32889i) q^{41} +(4.62856 + 1.15878i) q^{42} +(-1.03925 - 0.600009i) q^{43} +0.141214 q^{44} +(-0.889138 + 6.64902i) q^{45} +9.55530 q^{46} +(0.461305 + 0.266335i) q^{47} +(-1.75937 - 6.15809i) q^{48} +(-1.45867 - 2.52650i) q^{49} +(-4.47120 - 5.14568i) q^{50} +(1.00125 + 0.968767i) q^{51} +(0.359477 + 0.207544i) q^{52} +10.9505i q^{53} +(2.16962 + 6.74388i) q^{54} +(1.42249 - 1.72526i) q^{55} +(2.94928 - 5.10830i) q^{56} +(3.94044 - 4.07256i) q^{57} +(7.79926 - 4.50291i) q^{58} +(-3.70974 - 6.42546i) q^{59} +(0.501323 + 0.218619i) q^{60} +(-5.88834 + 10.1989i) q^{61} -0.260966i q^{62} +(-2.85612 + 5.34663i) q^{63} -8.48227 q^{64} +(6.15678 - 2.30120i) q^{65} +(0.573496 - 2.29073i) q^{66} +(-6.40730 + 3.69925i) q^{67} +(0.0983695 - 0.0567937i) q^{68} +(-2.94812 + 11.7758i) q^{69} +(-2.15663 - 5.76999i) q^{70} -2.20600 q^{71} +(8.75306 - 0.288726i) q^{72} -1.09498i q^{73} +(-6.70989 + 11.6219i) q^{74} +(7.72095 - 3.92262i) q^{75} +(-0.231007 - 0.400115i) q^{76} +(1.74985 - 1.01028i) q^{77} +(4.82664 - 4.98848i) q^{78} +(-1.63615 + 2.83389i) q^{79} +(-5.25985 + 6.37937i) q^{80} +(-8.98044 + 0.593097i) q^{81} +2.09205i q^{82} +(-6.67498 - 3.85380i) q^{83} +(0.355170 + 0.343648i) q^{84} +(0.297041 - 1.77392i) q^{85} +(0.818037 + 1.41688i) q^{86} +(3.14297 + 11.0010i) q^{87} +(-2.52816 - 1.45964i) q^{88} -12.5659 q^{89} +(5.58237 - 7.24449i) q^{90} +5.93930 q^{91} +(0.857110 + 0.494853i) q^{92} +(0.321610 + 0.0805166i) q^{93} +(-0.363114 - 0.628931i) q^{94} +(-7.21537 - 1.20821i) q^{95} +(0.335378 - 1.33961i) q^{96} +(-6.79856 - 3.92515i) q^{97} +3.97743i q^{98} +(2.64612 + 1.41353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 52 * q + 20 * q^4 + q^5 + 4 * q^6 + 6 * q^9	\( 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9} - 26 q^{11} - 10 q^{14} - 8 q^{16} + 40 q^{19} - 11 q^{20} - 26 q^{21} - 36 q^{24} + q^{25} - 24 q^{26} - 6 q^{29} + 4 q^{30} + 30 q^{31} - 22 q^{34} + 64 q^{36} + 4 q^{39} - 15 q^{40} + 6 q^{41} - 40 q^{44} - 25 q^{45} - 84 q^{46} - 12 q^{49} - 55 q^{50} + 12 q^{51} + 2 q^{54} - 2 q^{55} + 30 q^{56} - 30 q^{59} + 39 q^{60} + 74 q^{61} + 20 q^{64} + 7 q^{65} - 2 q^{66} - 30 q^{69} - 28 q^{70} - 48 q^{71} + 14 q^{74} + 94 q^{75} + 74 q^{76} - 32 q^{79} - 10 q^{80} - 30 q^{81} + 132 q^{84} - 25 q^{85} + 14 q^{86} + 92 q^{89} - 73 q^{90} - 104 q^{91} - 50 q^{94} + 6 q^{95} + 60 q^{96} + 6 q^{99}+O(q^{100}) \) 52 * q + 20 * q^4 + q^5 + 4 * q^6 + 6 * q^9 - 26 * q^11 - 10 * q^14 - 8 * q^16 + 40 * q^19 - 11 * q^20 - 26 * q^21 - 36 * q^24 + q^25 - 24 * q^26 - 6 * q^29 + 4 * q^30 + 30 * q^31 - 22 * q^34 + 64 * q^36 + 4 * q^39 - 15 * q^40 + 6 * q^41 - 40 * q^44 - 25 * q^45 - 84 * q^46 - 12 * q^49 - 55 * q^50 + 12 * q^51 + 2 * q^54 - 2 * q^55 + 30 * q^56 - 30 * q^59 + 39 * q^60 + 74 * q^61 + 20 * q^64 + 7 * q^65 - 2 * q^66 - 30 * q^69 - 28 * q^70 - 48 * q^71 + 14 * q^74 + 94 * q^75 + 74 * q^76 - 32 * q^79 - 10 * q^80 - 30 * q^81 + 132 * q^84 - 25 * q^85 + 14 * q^86 + 92 * q^89 - 73 * q^90 - 104 * q^91 - 50 * q^94 + 6 * q^95 + 60 * q^96 + 6 * q^99

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