LMFDB - Embedded newform 726.2.e.a.493.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,-1,-1,-5,-1,-3,-1,-1,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			493.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.493
Dual form			726.2.e.a.511.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.427051 + 1.31433i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.38197 q^{10} +1.00000 q^{12} +(0.381966 - 1.17557i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(-1.11803 - 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(6.23607 - 4.53077i) q^{19} +(0.427051 - 1.31433i) q^{20} +1.61803 q^{21} +7.70820 q^{23} +(0.309017 - 0.951057i) q^{24} +(2.50000 - 1.81636i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.500000 + 1.53884i) q^{28} +(0.118034 + 0.0857567i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(-1.73607 + 5.34307i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(0.690983 - 2.12663i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-7.23607 - 5.25731i) q^{37} +(-2.38197 - 7.33094i) q^{38} +(0.381966 + 1.17557i) q^{39} +(-1.11803 - 0.812299i) q^{40} +(6.23607 - 4.53077i) q^{41} +(0.500000 - 1.53884i) q^{42} +9.23607 q^{43} +1.38197 q^{45} +(2.38197 - 7.33094i) q^{46} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-1.35410 - 4.16750i) q^{49} +(-0.954915 - 2.93893i) q^{50} +(3.23607 + 2.35114i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(1.11803 - 3.44095i) q^{53} +1.00000 q^{54} +1.61803 q^{56} +(-2.38197 + 7.33094i) q^{57} +(0.118034 - 0.0857567i) q^{58} +(4.30902 + 3.13068i) q^{59} +(0.427051 + 1.31433i) q^{60} +(-3.00000 - 9.23305i) q^{61} +(4.54508 + 3.30220i) q^{62} +(-1.30902 + 0.951057i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.70820 q^{65} -12.9443 q^{67} +(-1.23607 + 3.80423i) q^{68} +(-6.23607 + 4.53077i) q^{69} +(-1.80902 - 1.31433i) q^{70} +(1.85410 + 5.70634i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-4.50000 - 3.26944i) q^{73} +(-7.23607 + 5.25731i) q^{74} +(-0.954915 + 2.93893i) q^{75} -7.70820 q^{76} +1.23607 q^{78} +(0.0450850 - 0.138757i) q^{79} +(-1.11803 + 0.812299i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.38197 - 7.33094i) q^{82} +(0.190983 + 0.587785i) q^{83} +(-1.30902 - 0.951057i) q^{84} +(4.47214 - 3.24920i) q^{85} +(2.85410 - 8.78402i) q^{86} -0.145898 q^{87} +11.2361 q^{89} +(0.427051 - 1.31433i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(-6.23607 - 4.53077i) q^{92} +(-1.73607 - 5.34307i) q^{93} +(1.23607 + 3.80423i) q^{94} +(8.61803 + 6.26137i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.28115 + 7.02067i) q^{97} -4.38197 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} - 5 q^{5} - q^{6} - 3 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} + 6 q^{13} - 3 q^{14} - q^{16} + 4 q^{17} - q^{18} + 16 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{23} - q^{24}+ \cdots - 22 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 - 5 * q^5 - q^6 - 3 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 + 6 * q^13 - 3 * q^14 - q^16 + 4 * q^17 - q^18 + 16 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^23 - q^24 + 10 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^31 + 4 * q^32 - 16 * q^34 + 5 * q^35 - q^36 - 20 * q^37 - 14 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^45 + 14 * q^46 - 4 * q^47 - q^48 + 8 * q^49 - 15 * q^50 + 4 * q^51 - 4 * q^52 + 4 * q^54 + 2 * q^56 - 14 * q^57 - 4 * q^58 + 15 * q^59 - 5 * q^60 - 12 * q^61 + 7 * q^62 - 3 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 - 16 * q^69 - 5 * q^70 - 6 * q^71 - q^72 - 18 * q^73 - 20 * q^74 - 15 * q^75 - 4 * q^76 - 4 * q^78 - 11 * q^79 - q^81 - 14 * q^82 + 3 * q^83 - 3 * q^84 - 2 * q^86 - 14 * q^87 + 36 * q^89 - 5 * q^90 - 2 * q^91 - 16 * q^92 + 2 * q^93 - 4 * q^94 + 30 * q^95 - q^96 + 11 * q^97 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.427051	+	1.31433i	0.190983	+	0.587785i	1.00000			$0$
$5$	0.427051	+	1.31433i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	0.312251	−	0.950000i	$-0.398917\pi$
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	−0.807013	+	0.590534i	$0.798917\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.38197			0.437016
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	−0.884011	−	0.467466i	$-0.845167\pi$
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	0.989950	+	0.141421i	$0.0451671\pi$
$14$	−1.30902	+	0.951057i	−0.349850	+	0.254181i
$15$	−1.11803	−	0.812299i	−0.288675	−	0.209735i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	−0.981570	−	0.191103i	$-0.938794\pi$
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	0.681780	−	0.731558i	$-0.261206\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	6.23607	−	4.53077i	1.43065	−	1.03943i	0.440757	−	0.897626i	$-0.354710\pi$
$19$	6.23607	−	4.53077i	1.43065	−	1.03943i	0.989895	−	0.141803i	$-0.0452900\pi$
$20$	0.427051	−	1.31433i	0.0954915	−	0.293893i
$21$	1.61803			0.353084
$22$		0			0
$23$	7.70820			1.60727			0.803636	−	0.595121i	$-0.202896\pi$
$23$	7.70820			1.60727			0.803636	+	0.595121i	$0.202896\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	2.50000	−	1.81636i	0.500000	−	0.363271i
$26$	−1.00000	−	0.726543i	−0.196116	−	0.142487i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.500000	+	1.53884i	0.0944911	+	0.290814i
$29$	0.118034	+	0.0857567i	0.0219184	+	0.0159246i	0.598691	−	0.800980i	$-0.295688\pi$
$29$	0.118034	+	0.0857567i	0.0219184	+	0.0159246i	−0.576772	+	0.816905i	$0.695688\pi$
$30$	−1.11803	+	0.812299i	−0.204124	+	0.148305i
$31$	−1.73607	+	5.34307i	−0.311807	+	0.959643i	0.665242	+	0.746628i	$0.268328\pi$
$31$	−1.73607	+	5.34307i	−0.311807	+	0.959643i	−0.977049	+	0.213015i	$0.931672\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.00000			−0.685994
$35$	0.690983	−	2.12663i	0.116797	−	0.359466i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−7.23607	−	5.25731i	−1.18960	−	0.864297i	−0.196380	−	0.980528i	$-0.562919\pi$
$37$	−7.23607	−	5.25731i	−1.18960	−	0.864297i	−0.993222	+	0.116231i	$0.962919\pi$
$38$	−2.38197	−	7.33094i	−0.386406	−	1.18924i
$39$	0.381966	+	1.17557i	0.0611635	+	0.188242i
$40$	−1.11803	−	0.812299i	−0.176777	−	0.128436i
$41$	6.23607	−	4.53077i	0.973910	−	0.707587i	0.0175708	−	0.999846i	$-0.494407\pi$
$41$	6.23607	−	4.53077i	0.973910	−	0.707587i	0.956339	+	0.292258i	$0.0944067\pi$
$42$	0.500000	−	1.53884i	0.0771517	−	0.237448i
$43$	9.23607			1.40849			0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607			1.40849			0.704244	+	0.709958i	$0.251286\pi$
$44$		0			0
$45$	1.38197			0.206011
$46$	2.38197	−	7.33094i	0.351202	−	1.08089i
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	−0.798232	−	0.602351i	$-0.794231\pi$
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	0.326202	+	0.945300i	$0.394231\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−1.35410	−	4.16750i	−0.193443	−	0.595357i
$50$	−0.954915	−	2.93893i	−0.135045	−	0.415627i
$51$	3.23607	+	2.35114i	0.453140	+	0.329226i
$52$	−1.00000	+	0.726543i	−0.138675	+	0.100753i
$53$	1.11803	−	3.44095i	0.153574	−	0.472651i	−0.844440	−	0.535650i	$-0.820066\pi$
$53$	1.11803	−	3.44095i	0.153574	−	0.472651i	0.998014	+	0.0629990i	$0.0200665\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	1.61803			0.216219
$57$	−2.38197	+	7.33094i	−0.315499	+	0.971006i
$58$	0.118034	−	0.0857567i	0.0154986	−	0.0112604i
$59$	4.30902	+	3.13068i	0.560986	+	0.407580i	0.831820	−	0.555046i	$-0.187299\pi$
$59$	4.30902	+	3.13068i	0.560986	+	0.407580i	−0.270834	+	0.962626i	$0.587299\pi$
$60$	0.427051	+	1.31433i	0.0551320	+	0.169679i
$61$	−3.00000	−	9.23305i	−0.384111	−	1.18217i	−0.937123	−	0.348998i	$-0.886522\pi$
$61$	−3.00000	−	9.23305i	−0.384111	−	1.18217i	0.553013	−	0.833173i	$-0.313478\pi$
$62$	4.54508	+	3.30220i	0.577226	+	0.419380i
$63$	−1.30902	+	0.951057i	−0.164921	+	0.119822i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.70820			0.211877
$66$		0			0
$67$	−12.9443			−1.58139			−0.790697	−	0.612207i	$-0.790282\pi$
$67$	−12.9443			−1.58139			−0.790697	+	0.612207i	$0.790282\pi$
$68$	−1.23607	+	3.80423i	−0.149895	+	0.461330i
$69$	−6.23607	+	4.53077i	−0.750734	+	0.545440i
$70$	−1.80902	−	1.31433i	−0.216219	−	0.157092i
$71$	1.85410	+	5.70634i	0.220041	+	0.677218i	0.998757	+	0.0498409i	$0.0158714\pi$
$71$	1.85410	+	5.70634i	0.220041	+	0.677218i	−0.778716	+	0.627377i	$0.784129\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−4.50000	−	3.26944i	−0.526685	−	0.382659i	0.292431	−	0.956287i	$-0.405536\pi$
$73$	−4.50000	−	3.26944i	−0.526685	−	0.382659i	−0.819116	+	0.573627i	$0.805536\pi$
$74$	−7.23607	+	5.25731i	−0.841176	+	0.611150i
$75$	−0.954915	+	2.93893i	−0.110264	+	0.339358i
$76$	−7.70820			−0.884192
$77$		0			0
$78$	1.23607			0.139957
$79$	0.0450850	−	0.138757i	0.00507246	−	0.0156114i	−0.948488	−	0.316812i	$-0.897387\pi$
$79$	0.0450850	−	0.138757i	0.00507246	−	0.0156114i	0.953561	+	0.301201i	$0.0973875\pi$
$80$	−1.11803	+	0.812299i	−0.125000	+	0.0908178i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.38197	−	7.33094i	−0.263044	−	0.809567i
$83$	0.190983	+	0.587785i	0.0209631	+	0.0645178i	0.960991	−	0.276580i	$-0.0892012\pi$
$83$	0.190983	+	0.587785i	0.0209631	+	0.0645178i	−0.940028	+	0.341098i	$0.889201\pi$
$84$	−1.30902	−	0.951057i	−0.142825	−	0.103769i
$85$	4.47214	−	3.24920i	0.485071	−	0.352425i
$86$	2.85410	−	8.78402i	0.307766	−	0.947206i
$87$	−0.145898			−0.0156419
$88$		0			0
$89$	11.2361			1.19102			0.595510	−	0.803348i	$-0.296950\pi$
$89$	11.2361			1.19102			0.595510	+	0.803348i	$0.296950\pi$
$90$	0.427051	−	1.31433i	0.0450151	−	0.138542i
$91$	−1.61803	+	1.17557i	−0.169616	+	0.123233i
$92$	−6.23607	−	4.53077i	−0.650155	−	0.472365i
$93$	−1.73607	−	5.34307i	−0.180022	−	0.554050i
$94$	1.23607	+	3.80423i	0.127491	+	0.392376i
$95$	8.61803	+	6.26137i	0.884192	+	0.642403i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−2.28115	+	7.02067i	−0.231616	+	0.712841i	0.765936	+	0.642916i	$0.222276\pi$
$97$	−2.28115	+	7.02067i	−0.231616	+	0.712841i	−0.997552	+	0.0699243i	$0.977724\pi$
$98$	−4.38197			−0.442645
$99$		0			0
$100$	−3.09017			−0.309017
$101$	−2.80902	+	8.64527i	−0.279508	+	0.860236i	0.708484	+	0.705727i	$0.249380\pi$
$101$	−2.80902	+	8.64527i	−0.279508	+	0.860236i	−0.987991	+	0.154509i	$0.950620\pi$
$102$	3.23607	−	2.35114i	0.320418	−	0.232798i
$103$	2.54508	+	1.84911i	0.250775	+	0.182198i	0.706070	−	0.708142i	$-0.250466\pi$
$103$	2.54508	+	1.84911i	0.250775	+	0.182198i	−0.455295	+	0.890340i	$0.650466\pi$
$104$	0.381966	+	1.17557i	0.0374548	+	0.115274i
$105$	0.690983	+	2.12663i	0.0674330	+	0.207538i
$106$	−2.92705	−	2.12663i	−0.284300	−	0.206556i
$107$	−8.16312	+	5.93085i	−0.789158	+	0.573357i	−0.907714	−	0.419590i	$-0.862174\pi$
$107$	−8.16312	+	5.93085i	−0.789158	+	0.573357i	0.118555	+	0.992947i	$0.462174\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−14.9443			−1.43140			−0.715701	−	0.698407i	$-0.753893\pi$
$109$	−14.9443			−1.43140			−0.715701	+	0.698407i	$0.753893\pi$
$110$		0			0
$111$	8.94427			0.848953
$112$	0.500000	−	1.53884i	0.0472456	−	0.145407i
$113$	8.85410	−	6.43288i	0.832924	−	0.605155i	−0.0874612	−	0.996168i	$-0.527875\pi$
$113$	8.85410	−	6.43288i	0.832924	−	0.605155i	0.920385	+	0.391013i	$0.127875\pi$
$114$	6.23607	+	4.53077i	0.584061	+	0.424345i
$115$	3.29180	+	10.1311i	0.306962	+	0.944731i
$116$	−0.0450850	−	0.138757i	−0.00418603	−	0.0128833i
$117$	−1.00000	−	0.726543i	−0.0924500	−	0.0671689i
$118$	4.30902	−	3.13068i	0.396677	−	0.288203i
$119$	−2.00000	+	6.15537i	−0.183340	+	0.564262i
$120$	1.38197			0.126156
$121$		0			0
$122$	−9.70820			−0.878939
$123$	−2.38197	+	7.33094i	−0.214775	+	0.661008i
$124$	4.54508	−	3.30220i	0.408161	−	0.296546i
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$	0.500000	+	1.53884i	0.0445435	+	0.137091i
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	0.881118	−	0.472897i	$-0.156792\pi$
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	−0.990801	+	0.135326i	$0.956792\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−7.47214	+	5.42882i	−0.657885	+	0.477981i
$130$	0.527864	−	1.62460i	0.0462967	−	0.142487i
$131$	2.85410			0.249364			0.124682	−	0.992197i	$-0.460209\pi$
$131$	2.85410			0.249364			0.124682	+	0.992197i	$0.460209\pi$
$132$		0			0
$133$	−12.4721			−1.08147
$134$	−4.00000	+	12.3107i	−0.345547	+	1.06349i
$135$	−1.11803	+	0.812299i	−0.0962250	+	0.0699116i
$136$	3.23607	+	2.35114i	0.277491	+	0.201609i
$137$	2.52786	+	7.77997i	0.215970	+	0.664687i	0.999083	+	0.0428083i	$0.0136305\pi$
$137$	2.52786	+	7.77997i	0.215970	+	0.664687i	−0.783113	+	0.621879i	$0.786370\pi$
$138$	2.38197	+	7.33094i	0.202766	+	0.624051i
$139$	−1.85410	−	1.34708i	−0.157263	−	0.114258i	0.506371	−	0.862316i	$-0.330987\pi$
$139$	−1.85410	−	1.34708i	−0.157263	−	0.114258i	−0.663634	+	0.748058i	$0.730987\pi$
$140$	−1.80902	+	1.31433i	−0.152890	+	0.111081i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	6.00000			0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$	−0.0623059	+	0.191758i	−0.00517422	+	0.0159246i
$146$	−4.50000	+	3.26944i	−0.372423	+	0.270581i
$147$	3.54508	+	2.57565i	0.292394	+	0.212436i
$148$	2.76393	+	8.50651i	0.227194	+	0.699231i
$149$	7.11803	+	21.9071i	0.583132	+	1.79470i	0.606646	+	0.794972i	$0.292515\pi$
$149$	7.11803	+	21.9071i	0.583132	+	1.79470i	−0.0235135	+	0.999724i	$0.507485\pi$
$150$	2.50000	+	1.81636i	0.204124	+	0.148305i
$151$	−3.88197	+	2.82041i	−0.315910	+	0.229522i	−0.734428	−	0.678686i	$-0.762550\pi$
$151$	−3.88197	+	2.82041i	−0.315910	+	0.229522i	0.418518	+	0.908208i	$0.362550\pi$
$152$	−2.38197	+	7.33094i	−0.193203	+	0.594618i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−7.76393			−0.623614
$156$	0.381966	−	1.17557i	0.0305818	−	0.0941210i
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.172144	−	0.985072i	$-0.444931\pi$
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.990054	+	0.140685i	$0.0449305\pi$
$158$	−0.118034	−	0.0857567i	−0.00939028	−	0.00682244i
$159$	1.11803	+	3.44095i	0.0886659	+	0.272885i
$160$	0.427051	+	1.31433i	0.0337613	+	0.103907i
$161$	−10.0902	−	7.33094i	−0.795217	−	0.577759i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−2.61803	+	8.05748i	−0.205060	+	0.631111i	0.794651	+	0.607067i	$0.207654\pi$
$163$	−2.61803	+	8.05748i	−0.205060	+	0.631111i	−0.999711	+	0.0240436i	$0.992346\pi$
$164$	−7.70820			−0.601910
$165$		0			0
$166$	0.618034			0.0479687
$167$	6.09017	−	18.7436i	0.471271	−	1.45042i	−0.379649	−	0.925130i	$-0.623955\pi$
$167$	6.09017	−	18.7436i	0.471271	−	1.45042i	0.850921	−	0.525294i	$-0.176045\pi$
$168$	−1.30902	+	0.951057i	−0.100993	+	0.0733756i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	−1.70820	−	5.25731i	−0.131013	−	0.403217i
$171$	−2.38197	−	7.33094i	−0.182153	−	0.560611i
$172$	−7.47214	−	5.42882i	−0.569745	−	0.413944i
$173$	1.07295	−	0.779543i	0.0815748	−	0.0592676i	−0.546250	−	0.837622i	$-0.683945\pi$
$173$	1.07295	−	0.779543i	0.0815748	−	0.0592676i	0.627825	+	0.778354i	$0.283945\pi$
$174$	−0.0450850	+	0.138757i	−0.00341788	+	0.0105192i
$175$	−5.00000			−0.377964
$176$		0			0
$177$	−5.32624			−0.400345
$178$	3.47214	−	10.6861i	0.260248	−	0.800960i
$179$	−1.26393	+	0.918300i	−0.0944707	+	0.0686370i	−0.634018	−	0.773318i	$-0.718595\pi$
$179$	−1.26393	+	0.918300i	−0.0944707	+	0.0686370i	0.539547	+	0.841955i	$0.318595\pi$
$180$	−1.11803	−	0.812299i	−0.0833333	−	0.0605452i
$181$	−1.67376	−	5.15131i	−0.124410	−	0.382894i	0.869383	−	0.494138i	$-0.164516\pi$
$181$	−1.67376	−	5.15131i	−0.124410	−	0.382894i	−0.993793	+	0.111244i	$0.964516\pi$
$182$	0.618034	+	1.90211i	0.0458117	+	0.140994i
$183$	7.85410	+	5.70634i	0.580592	+	0.421825i
$184$	−6.23607	+	4.53077i	−0.459729	+	0.334013i
$185$	3.81966	−	11.7557i	0.280827	−	0.864297i
$186$	−5.61803			−0.411934
$187$		0			0
$188$	4.00000			0.291730
$189$	0.500000	−	1.53884i	0.0363696	−	0.111934i
$190$	8.61803	−	6.26137i	0.625218	−	0.454247i
$191$	16.9443	+	12.3107i	1.22604	+	0.890773i	0.996587	−	0.0825453i	$-0.0263049\pi$
$191$	16.9443	+	12.3107i	1.22604	+	0.890773i	0.229457	+	0.973319i	$0.426305\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	0.736068	+	2.26538i	0.0529833	+	0.163066i	0.974047	−	0.226346i	$-0.0726781\pi$
$193$	0.736068	+	2.26538i	0.0529833	+	0.163066i	−0.921064	+	0.389412i	$0.872678\pi$
$194$	5.97214	+	4.33901i	0.428774	+	0.311523i
$195$	−1.38197	+	1.00406i	−0.0989646	+	0.0719020i
$196$	−1.35410	+	4.16750i	−0.0967216	+	0.297678i
$197$	−12.5066			−0.891057			−0.445528	−	0.895268i	$-0.646984\pi$
$197$	−12.5066			−0.891057			−0.445528	+	0.895268i	$0.646984\pi$
$198$		0			0
$199$	−2.61803			−0.185588			−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803			−0.185588			−0.0927938	+	0.995685i	$0.529580\pi$
$200$	−0.954915	+	2.93893i	−0.0675227	+	0.207813i
$201$	10.4721	−	7.60845i	0.738648	−	0.536659i
$202$	7.35410	+	5.34307i	0.517433	+	0.375937i
$203$	−0.0729490	−	0.224514i	−0.00512002	−	0.0157578i
$204$	−1.23607	−	3.80423i	−0.0865421	−	0.266349i
$205$	8.61803	+	6.26137i	0.601910	+	0.437313i
$206$	2.54508	−	1.84911i	0.177324	−	0.128834i
$207$	2.38197	−	7.33094i	0.165558	−	0.509535i
$208$	1.23607			0.0857059
$209$		0			0
$210$	2.23607			0.154303
$211$	1.47214	−	4.53077i	0.101346	−	0.311911i	−0.887509	−	0.460789i	$-0.847566\pi$
$211$	1.47214	−	4.53077i	0.101346	−	0.311911i	0.988855	+	0.148878i	$0.0475663\pi$
$212$	−2.92705	+	2.12663i	−0.201031	+	0.146057i
$213$	−4.85410	−	3.52671i	−0.332598	−	0.241646i
$214$	3.11803	+	9.59632i	0.213144	+	0.655991i
$215$	3.94427	+	12.1392i	0.268997	+	0.827888i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	7.35410	−	5.34307i	0.499229	−	0.362711i
$218$	−4.61803	+	14.2128i	−0.312773	+	0.962615i
$219$	5.56231			0.375866
$220$		0			0
$221$	−4.94427			−0.332588
$222$	2.76393	−	8.50651i	0.185503	−	0.570919i
$223$	−11.5902	+	8.42075i	−0.776135	+	0.563895i	−0.903817	−	0.427920i	$-0.859246\pi$
$223$	−11.5902	+	8.42075i	−0.776135	+	0.563895i	0.127681	+	0.991815i	$0.459246\pi$
$224$	−1.30902	−	0.951057i	−0.0874624	−	0.0635451i
$225$	−0.954915	−	2.93893i	−0.0636610	−	0.195928i
$226$	−3.38197	−	10.4086i	−0.224965	−	0.692371i
$227$	−19.4443	−	14.1271i	−1.29056	−	0.937648i	−0.290745	−	0.956801i	$-0.593903\pi$
$227$	−19.4443	−	14.1271i	−1.29056	−	0.937648i	−0.999817	+	0.0191526i	$0.993903\pi$
$228$	6.23607	−	4.53077i	0.412994	−	0.300057i
$229$	6.61803	−	20.3682i	0.437332	−	1.34597i	−0.453346	−	0.891335i	$-0.649770\pi$
$229$	6.61803	−	20.3682i	0.437332	−	1.34597i	0.890678	−	0.454635i	$-0.150230\pi$
$230$	10.6525			0.702403
$231$		0			0
$232$	−0.145898			−0.00957868
$233$	−0.291796	+	0.898056i	−0.0191162	+	0.0588336i	−0.960160	−	0.279452i	$-0.909847\pi$
$233$	−0.291796	+	0.898056i	−0.0191162	+	0.0588336i	0.941043	+	0.338286i	$0.109847\pi$
$234$	−1.00000	+	0.726543i	−0.0653720	+	0.0474956i
$235$	−4.47214	−	3.24920i	−0.291730	−	0.211954i
$236$	−1.64590	−	5.06555i	−0.107139	−	0.329739i
$237$	0.0450850	+	0.138757i	0.00292858	+	0.00901325i
$238$	5.23607	+	3.80423i	0.339404	+	0.246591i
$239$	−13.3262	+	9.68208i	−0.862003	+	0.626282i	−0.928429	−	0.371510i	$-0.878840\pi$
$239$	−13.3262	+	9.68208i	−0.862003	+	0.626282i	0.0664264	+	0.997791i	$0.478840\pi$
$240$	0.427051	−	1.31433i	0.0275660	−	0.0848395i
$241$	−6.38197			−0.411099			−0.205549	−	0.978647i	$-0.565898\pi$
$241$	−6.38197			−0.411099			−0.205549	+	0.978647i	$0.565898\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−3.00000	+	9.23305i	−0.192055	+	0.591085i
$245$	4.89919	−	3.55947i	0.312998	−	0.227406i
$246$	6.23607	+	4.53077i	0.397597	+	0.288871i
$247$	−2.94427	−	9.06154i	−0.187340	−	0.576572i
$248$	−1.73607	−	5.34307i	−0.110240	−	0.339285i
$249$	−0.500000	−	0.363271i	−0.0316862	−	0.0230214i
$250$	9.04508	−	6.57164i	0.572061	−	0.415627i
$251$	−0.100813	+	0.310271i	−0.00636326	+	0.0195841i	−0.954188	−	0.299209i	$-0.903277\pi$
$251$	−0.100813	+	0.310271i	−0.00636326	+	0.0195841i	0.947824	+	0.318793i	$0.103277\pi$
$252$	1.61803			0.101927
$253$		0			0
$254$	−4.00000			−0.250982
$255$	−1.70820	+	5.25731i	−0.106972	+	0.329226i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−17.5623	−	12.7598i	−1.09551	−	0.795932i	−0.115186	−	0.993344i	$-0.536746\pi$
$257$	−17.5623	−	12.7598i	−1.09551	−	0.795932i	−0.980321	+	0.197412i	$0.936746\pi$
$258$	2.85410	+	8.78402i	0.177689	+	0.546869i
$259$	4.47214	+	13.7638i	0.277885	+	0.855242i
$260$	−1.38197	−	1.00406i	−0.0857059	−	0.0622690i
$261$	0.118034	−	0.0857567i	0.00730612	−	0.00530821i
$262$	0.881966	−	2.71441i	0.0544880	−	0.167697i
$263$	12.7639			0.787058			0.393529	−	0.919312i	$-0.371254\pi$
$263$	12.7639			0.787058			0.393529	+	0.919312i	$0.371254\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$	−3.85410	+	11.8617i	−0.236310	+	0.727288i
$267$	−9.09017	+	6.60440i	−0.556309	+	0.404182i
$268$	10.4721	+	7.60845i	0.639688	+	0.464760i
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	0.991535	−	0.129843i	$-0.0414473\pi$
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	−0.878488	+	0.477764i	$0.841447\pi$
$270$	0.427051	+	1.31433i	0.0259895	+	0.0799874i
$271$	14.1803	+	10.3026i	0.861394	+	0.625840i	0.928264	−	0.371922i	$-0.121301\pi$
$271$	14.1803	+	10.3026i	0.861394	+	0.625840i	−0.0668696	+	0.997762i	$0.521301\pi$
$272$	3.23607	−	2.35114i	0.196215	−	0.142559i
$273$	0.618034	−	1.90211i	0.0374051	−	0.115121i
$274$	8.18034			0.494192
$275$		0			0
$276$	7.70820			0.463979
$277$	−0.708204	+	2.17963i	−0.0425519	+	0.130961i	−0.970076	−	0.242803i	$-0.921933\pi$
$277$	−0.708204	+	2.17963i	−0.0425519	+	0.130961i	0.927524	+	0.373764i	$0.121933\pi$
$278$	−1.85410	+	1.34708i	−0.111202	+	0.0807927i
$279$	4.54508	+	3.30220i	0.272107	+	0.197697i
$280$	0.690983	+	2.12663i	0.0412941	+	0.127090i
$281$	−5.18034	−	15.9434i	−0.309033	−	0.951106i	−0.978141	−	0.207941i	$-0.933324\pi$
$281$	−5.18034	−	15.9434i	−0.309033	−	0.951106i	0.669108	−	0.743165i	$-0.266676\pi$
$282$	−3.23607	−	2.35114i	−0.192705	−	0.140008i
$283$	−13.3262	+	9.68208i	−0.792163	+	0.575540i	−0.908604	−	0.417658i	$-0.862851\pi$
$283$	−13.3262	+	9.68208i	−0.792163	+	0.575540i	0.116442	+	0.993198i	$0.462851\pi$
$284$	1.85410	−	5.70634i	0.110021	−	0.338609i
$285$	−10.6525			−0.630998
$286$		0			0
$287$	−12.4721			−0.736207
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	0.163119	+	0.118513i	0.00957868	+	0.00695931i
$291$	−2.28115	−	7.02067i	−0.133724	−	0.411559i
$292$	1.71885	+	5.29007i	0.100588	+	0.309578i
$293$	6.16312	+	4.47777i	0.360053	+	0.261594i	0.753074	−	0.657935i	$-0.228570\pi$
$293$	6.16312	+	4.47777i	0.360053	+	0.261594i	−0.393021	+	0.919529i	$0.628570\pi$
$294$	3.54508	−	2.57565i	0.206754	−	0.150215i
$295$	−2.27458	+	7.00042i	−0.132431	+	0.407580i
$296$	8.94427			0.519875
$297$		0			0
$298$	23.0344			1.33435
$299$	2.94427	−	9.06154i	0.170272	−	0.524042i
$300$	2.50000	−	1.81636i	0.144338	−	0.104867i
$301$	−12.0902	−	8.78402i	−0.696866	−	0.506303i
$302$	1.48278	+	4.56352i	0.0853243	+	0.262601i
$303$	−2.80902	−	8.64527i	−0.161374	−	0.496658i
$304$	6.23607	+	4.53077i	0.357663	+	0.259857i
$305$	10.8541	−	7.88597i	0.621504	−	0.451549i
$306$	−1.23607	+	3.80423i	−0.0706613	+	0.217473i
$307$	12.7639			0.728476			0.364238	−	0.931306i	$-0.381329\pi$
$307$	12.7639			0.728476			0.364238	+	0.931306i	$0.381329\pi$
$308$		0			0
$309$	−3.14590			−0.178964
$310$	−2.39919	+	7.38394i	−0.136265	+	0.419380i
$311$	−6.09017	+	4.42477i	−0.345342	+	0.250906i	−0.746912	−	0.664923i	$-0.768465\pi$
$311$	−6.09017	+	4.42477i	−0.345342	+	0.250906i	0.401570	+	0.915828i	$0.368465\pi$
$312$	−1.00000	−	0.726543i	−0.0566139	−	0.0411324i
$313$	−7.71885	−	23.7562i	−0.436295	−	1.34278i	−0.891754	−	0.452521i	$-0.850525\pi$
$313$	−7.71885	−	23.7562i	−0.436295	−	1.34278i	0.455459	−	0.890257i	$-0.349475\pi$
$314$	−5.56231	−	17.1190i	−0.313899	−	0.966082i
$315$	−1.80902	−	1.31433i	−0.101927	−	0.0740540i
$316$	−0.118034	+	0.0857567i	−0.00663993	+	0.00482419i
$317$	−8.32624	+	25.6255i	−0.467648	+	1.43927i	0.387973	+	0.921671i	$0.373175\pi$
$317$	−8.32624	+	25.6255i	−0.467648	+	1.43927i	−0.855621	+	0.517602i	$0.826825\pi$
$318$	3.61803			0.202889
$319$		0			0
$320$	1.38197			0.0772542
$321$	3.11803	−	9.59632i	0.174032	−	0.535614i
$322$	−10.0902	+	7.33094i	−0.562303	+	0.408537i
$323$	−24.9443	−	18.1231i	−1.38794	−	1.00839i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−1.18034	−	3.63271i	−0.0654735	−	0.201507i
$326$	6.85410	+	4.97980i	0.379614	+	0.275805i
$327$	12.0902	−	8.78402i	0.668588	−	0.485758i
$328$	−2.38197	+	7.33094i	−0.131522	+	0.404783i
$329$	6.47214			0.356820
$330$		0			0
$331$	28.3607			1.55884			0.779422	−	0.626499i	$-0.215513\pi$
$331$	28.3607			1.55884			0.779422	+	0.626499i	$0.215513\pi$
$332$	0.190983	−	0.587785i	0.0104816	−	0.0322589i
$333$	−7.23607	+	5.25731i	−0.396534	+	0.288099i
$334$	−15.9443	−	11.5842i	−0.872432	−	0.633859i
$335$	−5.52786	−	17.0130i	−0.302019	−	0.929520i
$336$	0.500000	+	1.53884i	0.0272772	+	0.0839507i
$337$	−12.8541	−	9.33905i	−0.700208	−	0.508731i	0.179792	−	0.983705i	$-0.442457\pi$
$337$	−12.8541	−	9.33905i	−0.700208	−	0.508731i	−0.880000	+	0.474974i	$0.842457\pi$
$338$	9.28115	−	6.74315i	0.504828	−	0.366779i
$339$	−3.38197	+	10.4086i	−0.183683	+	0.565319i
$340$	−5.52786			−0.299791
$341$		0			0
$342$	−7.70820			−0.416812
$343$	−5.69098	+	17.5150i	−0.307284	+	0.945724i
$344$	−7.47214	+	5.42882i	−0.402871	+	0.292703i
$345$	−8.61803	−	6.26137i	−0.463979	−	0.337101i
$346$	−0.409830	−	1.26133i	−0.0220326	−	0.0678094i
$347$	5.77051	+	17.7598i	0.309777	+	0.953396i	0.977851	+	0.209301i	$0.0671190\pi$
$347$	5.77051	+	17.7598i	0.309777	+	0.953396i	−0.668074	+	0.744095i	$0.732881\pi$
$348$	0.118034	+	0.0857567i	0.00632729	+	0.00459704i
$349$	−20.7984	+	15.1109i	−1.11331	+	0.808868i	−0.983182	−	0.182629i	$-0.941539\pi$
$349$	−20.7984	+	15.1109i	−1.11331	+	0.808868i	−0.130130	+	0.991497i	$0.541539\pi$
$350$	−1.54508	+	4.75528i	−0.0825883	+	0.254181i
$351$	1.23607			0.0659764
$352$		0			0
$353$	11.2361			0.598036			0.299018	−	0.954248i	$-0.403341\pi$
$353$	11.2361			0.598036			0.299018	+	0.954248i	$0.403341\pi$
$354$	−1.64590	+	5.06555i	−0.0874785	+	0.269231i
$355$	−6.70820	+	4.87380i	−0.356034	+	0.258674i
$356$	−9.09017	−	6.60440i	−0.481778	−	0.350032i
$357$	−2.00000	−	6.15537i	−0.105851	−	0.325777i
$358$	0.482779	+	1.48584i	0.0255157	+	0.0785291i
$359$	−4.70820	−	3.42071i	−0.248489	−	0.180538i	0.456568	−	0.889689i	$-0.349079\pi$
$359$	−4.70820	−	3.42071i	−0.248489	−	0.180538i	−0.705057	+	0.709151i	$0.749079\pi$
$360$	−1.11803	+	0.812299i	−0.0589256	+	0.0428119i
$361$	12.4894	−	38.4383i	0.657335	−	2.02307i
$362$	−5.41641			−0.284680
$363$		0			0
$364$	2.00000			0.104828
$365$	2.37539	−	7.31069i	0.124334	−	0.382659i
$366$	7.85410	−	5.70634i	0.410540	−	0.298275i
$367$	−8.11803	−	5.89810i	−0.423758	−	0.307878i	0.355390	−	0.934718i	$-0.384348\pi$
$367$	−8.11803	−	5.89810i	−0.423758	−	0.307878i	−0.779148	+	0.626840i	$0.784348\pi$
$368$	2.38197	+	7.33094i	0.124169	+	0.382152i
$369$	−2.38197	−	7.33094i	−0.124000	−	0.381633i
$370$	−10.0000	−	7.26543i	−0.519875	−	0.377711i
$371$	−4.73607	+	3.44095i	−0.245884	+	0.178645i
$372$	−1.73607	+	5.34307i	−0.0900109	+	0.277025i
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$	−11.1803			−0.577350
$376$	1.23607	−	3.80423i	0.0637453	−	0.196188i
$377$	0.145898	−	0.106001i	0.00751413	−	0.00545934i
$378$	−1.30902	−	0.951057i	−0.0673286	−	0.0489171i
$379$	1.18034	+	3.63271i	0.0606300	+	0.186600i	0.976784	−	0.214226i	$-0.0687231\pi$
$379$	1.18034	+	3.63271i	0.0606300	+	0.186600i	−0.916154	+	0.400826i	$0.868723\pi$
$380$	−3.29180	−	10.1311i	−0.168866	−	0.519715i
$381$	3.23607	+	2.35114i	0.165789	+	0.120453i
$382$	16.9443	−	12.3107i	0.866944	−	0.629872i
$383$	11.6525	−	35.8626i	0.595414	−	1.83249i	0.0427577	−	0.999085i	$-0.486386\pi$
$383$	11.6525	−	35.8626i	0.595414	−	1.83249i	0.552656	−	0.833409i	$-0.313614\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	2.38197			0.121239
$387$	2.85410	−	8.78402i	0.145082	−	0.446517i
$388$	5.97214	−	4.33901i	0.303189	−	0.220280i
$389$	−0.854102	−	0.620541i	−0.0433047	−	0.0314627i	0.565922	−	0.824459i	$-0.308520\pi$
$389$	−0.854102	−	0.620541i	−0.0433047	−	0.0314627i	−0.609227	+	0.792996i	$0.708520\pi$
$390$	0.527864	+	1.62460i	0.0267294	+	0.0822647i
$391$	−9.52786	−	29.3238i	−0.481845	−	1.48297i
$392$	3.54508	+	2.57565i	0.179054	+	0.130090i
$393$	−2.30902	+	1.67760i	−0.116474	+	0.0846237i
$394$	−3.86475	+	11.8945i	−0.194703	+	0.599234i
$395$	0.201626			0.0101449
$396$		0			0
$397$	−12.9443			−0.649654			−0.324827	−	0.945773i	$-0.605306\pi$
$397$	−12.9443			−0.649654			−0.324827	+	0.945773i	$0.605306\pi$
$398$	−0.809017	+	2.48990i	−0.0405524	+	0.124807i
$399$	10.0902	−	7.33094i	0.505140	−	0.367006i
$400$	2.50000	+	1.81636i	0.125000	+	0.0908178i
$401$	3.61803	+	11.1352i	0.180676	+	0.556064i	0.999847	−	0.0174857i	$-0.00556614\pi$
$401$	3.61803	+	11.1352i	0.180676	+	0.556064i	−0.819171	+	0.573549i	$0.805566\pi$
$402$	−4.00000	−	12.3107i	−0.199502	−	0.614004i
$403$	5.61803	+	4.08174i	0.279854	+	0.203326i
$404$	7.35410	−	5.34307i	0.365880	−	0.265828i
$405$	0.427051	−	1.31433i	0.0212203	−	0.0653095i
$406$	−0.236068			−0.0117159
$407$		0			0
$408$	−4.00000			−0.198030
$409$	−5.24671	+	16.1477i	−0.259433	+	0.798453i	0.733491	+	0.679700i	$0.237890\pi$
$409$	−5.24671	+	16.1477i	−0.259433	+	0.798453i	−0.992924	+	0.118754i	$0.962110\pi$
$410$	8.61803	−	6.26137i	0.425614	−	0.309227i
$411$	−6.61803	−	4.80828i	−0.326444	−	0.237175i
$412$	−0.972136	−	2.99193i	−0.0478937	−	0.147402i
$413$	−2.66312	−	8.19624i	−0.131044	−	0.403310i
$414$	−6.23607	−	4.53077i	−0.306486	−	0.222675i
$415$	−0.690983	+	0.502029i	−0.0339190	+	0.0246436i
$416$	0.381966	−	1.17557i	0.0187274	−	0.0576371i
$417$	2.29180			0.112230
$418$		0			0
$419$	0.909830			0.0444481			0.0222241	−	0.999753i	$-0.492925\pi$
$419$	0.909830			0.0444481			0.0222241	+	0.999753i	$0.492925\pi$
$420$	0.690983	−	2.12663i	0.0337165	−	0.103769i
$421$	−32.0344	+	23.2744i	−1.56126	+	1.13432i	−0.626298	+	0.779583i	$0.715431\pi$
$421$	−32.0344	+	23.2744i	−1.56126	+	1.13432i	−0.934965	+	0.354741i	$0.884569\pi$
$422$	−3.85410	−	2.80017i	−0.187615	−	0.136310i
$423$	1.23607	+	3.80423i	0.0600997	+	0.184968i
$424$	1.11803	+	3.44095i	0.0542965	+	0.167108i
$425$	−10.0000	−	7.26543i	−0.485071	−	0.352425i
$426$	−4.85410	+	3.52671i	−0.235182	+	0.170870i
$427$	−4.85410	+	14.9394i	−0.234906	+	0.722968i
$428$	10.0902			0.487727
$429$		0			0
$430$	12.7639			0.615531
$431$	7.43769	−	22.8909i	0.358261	−	1.10261i	−0.595833	−	0.803108i	$-0.703178\pi$
$431$	7.43769	−	22.8909i	0.358261	−	1.10261i	0.954094	−	0.299506i	$-0.0968219\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−7.78115	−	5.65334i	−0.373938	−	0.271682i	0.384904	−	0.922957i	$-0.374235\pi$
$433$	−7.78115	−	5.65334i	−0.373938	−	0.271682i	−0.758842	+	0.651275i	$0.774235\pi$
$434$	−2.80902	−	8.64527i	−0.134837	−	0.414986i
$435$	−0.0623059	−	0.191758i	−0.00298734	−	0.00919408i
$436$	12.0902	+	8.78402i	0.579014	+	0.420678i
$437$	48.0689	−	34.9241i	2.29945	−	1.67065i
$438$	1.71885	−	5.29007i	0.0821297	−	0.252769i
$439$	34.9230			1.66678			0.833392	−	0.552683i	$-0.186396\pi$
$439$	34.9230			1.66678			0.833392	+	0.552683i	$0.186396\pi$
$440$		0			0
$441$	−4.38197			−0.208665
$442$	−1.52786	+	4.70228i	−0.0726731	+	0.223665i
$443$	−5.54508	+	4.02874i	−0.263455	+	0.191411i	−0.711669	−	0.702515i	$-0.752060\pi$
$443$	−5.54508	+	4.02874i	−0.263455	+	0.191411i	0.448214	+	0.893926i	$0.352060\pi$
$444$	−7.23607	−	5.25731i	−0.343409	−	0.249501i
$445$	4.79837	+	14.7679i	0.227465	+	0.700064i
$446$	4.42705	+	13.6251i	0.209627	+	0.645165i
$447$	−18.6353	−	13.5393i	−0.881417	−	0.640387i
$448$	−1.30902	+	0.951057i	−0.0618452	+	0.0449332i
$449$	−2.61803	+	8.05748i	−0.123553	+	0.380256i	−0.993635	−	0.112651i	$-0.964066\pi$
$449$	−2.61803	+	8.05748i	−0.123553	+	0.380256i	0.870082	+	0.492907i	$0.164066\pi$
$450$	−3.09017			−0.145672
$451$		0			0
$452$	−10.9443			−0.514775
$453$	1.48278	−	4.56352i	0.0696670	−	0.214413i
$454$	−19.4443	+	14.1271i	−0.912565	+	0.663017i
$455$	−2.23607	−	1.62460i	−0.104828	−	0.0761624i
$456$	−2.38197	−	7.33094i	−0.111546	−	0.343303i
$457$	5.22542	+	16.0822i	0.244435	+	0.752294i	0.995729	+	0.0923259i	$0.0294301\pi$
$457$	5.22542	+	16.0822i	0.244435	+	0.752294i	−0.751294	+	0.659968i	$0.770570\pi$
$458$	−17.3262	−	12.5882i	−0.809602	−	0.588210i
$459$	3.23607	−	2.35114i	0.151047	−	0.109742i
$460$	3.29180	−	10.1311i	0.153481	−	0.472365i
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	34.7426			1.61463			0.807314	−	0.590122i	$-0.200920\pi$
$463$	34.7426			1.61463			0.807314	+	0.590122i	$0.200920\pi$
$464$	−0.0450850	+	0.138757i	−0.00209302	+	0.00644164i
$465$	6.28115	−	4.56352i	0.291281	−	0.211628i
$466$	0.763932	+	0.555029i	0.0353885	+	0.0257112i
$467$	−3.64590	−	11.2209i	−0.168712	−	0.519242i	0.830579	−	0.556901i	$-0.188010\pi$
$467$	−3.64590	−	11.2209i	−0.168712	−	0.519242i	−0.999291	+	0.0376591i	$0.988010\pi$
$468$	0.381966	+	1.17557i	0.0176564	+	0.0543408i
$469$	16.9443	+	12.3107i	0.782414	+	0.568457i
$470$	−4.47214	+	3.24920i	−0.206284	+	0.149874i
$471$	−5.56231	+	17.1190i	−0.256298	+	0.788803i
$472$	−5.32624			−0.245160
$473$		0			0
$474$	0.145898			0.00670132
$475$	7.36068	−	22.6538i	0.337731	−	1.03943i
$476$	5.23607	−	3.80423i	0.239995	−	0.174366i
$477$	−2.92705	−	2.12663i	−0.134020	−	0.0973716i
$478$	5.09017	+	15.6659i	0.232819	+	0.716543i
$479$	−4.09017	−	12.5882i	−0.186885	−	0.575172i	0.813091	−	0.582136i	$-0.197783\pi$
$479$	−4.09017	−	12.5882i	−0.186885	−	0.575172i	−0.999976	+	0.00696468i	$0.997783\pi$
$480$	−1.11803	−	0.812299i	−0.0510310	−	0.0370762i
$481$	−8.94427	+	6.49839i	−0.407824	+	0.296301i
$482$	−1.97214	+	6.06961i	−0.0898283	+	0.276463i
$483$	12.4721			0.567502
$484$		0			0
$485$	−10.2016			−0.463232
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	6.54508	−	4.75528i	0.296586	−	0.215482i	−0.429533	−	0.903051i	$-0.641322\pi$
$487$	6.54508	−	4.75528i	0.296586	−	0.215482i	0.726119	+	0.687569i	$0.241322\pi$
$488$	7.85410	+	5.70634i	0.355538	+	0.258314i
$489$	−2.61803	−	8.05748i	−0.118392	−	0.364372i
$490$	−1.87132	−	5.75934i	−0.0845378	−	0.260180i
$491$	26.9443	+	19.5762i	1.21598	+	0.883460i	0.995760	−	0.0919909i	$-0.0293231\pi$
$491$	26.9443	+	19.5762i	1.21598	+	0.883460i	0.220218	+	0.975451i	$0.429323\pi$
$492$	6.23607	−	4.53077i	0.281144	−	0.204263i
$493$	0.180340	−	0.555029i	0.00812210	−	0.0249973i
$494$	−9.52786			−0.428679
$495$		0			0
$496$	−5.61803			−0.252257
$497$	3.00000	−	9.23305i	0.134568	−	0.414159i
$498$	−0.500000	+	0.363271i	−0.0224055	+	0.0162786i
$499$	20.4721	+	14.8739i	0.916459	+	0.665846i	0.942640	−	0.333811i	$-0.108335\pi$
$499$	20.4721	+	14.8739i	0.916459	+	0.665846i	−0.0261814	+	0.999657i	$0.508335\pi$
$500$	−3.45492	−	10.6331i	−0.154508	−	0.475528i
$501$	6.09017	+	18.7436i	0.272089	+	0.837403i
$502$	0.263932	+	0.191758i	0.0117799	+	0.00855857i
$503$	−25.4164	+	18.4661i	−1.13326	+	0.823363i	−0.986166	−	0.165760i	$-0.946992\pi$
$503$	−25.4164	+	18.4661i	−1.13326	+	0.823363i	−0.147095	+	0.989122i	$0.546992\pi$
$504$	0.500000	−	1.53884i	0.0222718	−	0.0685455i
$505$	−12.5623			−0.559015
$506$		0			0
$507$	−11.4721			−0.509495
$508$	−1.23607	+	3.80423i	−0.0548416	+	0.168785i
$509$	8.30902	−	6.03685i	0.368291	−	0.267579i	−0.388211	−	0.921570i	$-0.626907\pi$
$509$	8.30902	−	6.03685i	0.368291	−	0.267579i	0.756502	+	0.653992i	$0.226907\pi$
$510$	4.47214	+	3.24920i	0.198030	+	0.143877i
$511$	2.78115	+	8.55951i	0.123031	+	0.378650i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	6.23607	+	4.53077i	0.275329	+	0.200038i
$514$	−17.5623	+	12.7598i	−0.774640	+	0.562809i
$515$	−1.34346	+	4.13474i	−0.0591999	+	0.182198i
$516$	9.23607			0.406595
$517$		0			0
$518$	14.4721			0.635869
$519$	−0.409830	+	1.26133i	−0.0179895	+	0.0553661i
$520$	−1.38197	+	1.00406i	−0.0606032	+	0.0440308i
$521$	22.6525	+	16.4580i	0.992423	+	0.721038i	0.960450	−	0.278451i	$-0.0898211\pi$
$521$	22.6525	+	16.4580i	0.992423	+	0.721038i	0.0319726	+	0.999489i	$0.489821\pi$
$522$	−0.0450850	−	0.138757i	−0.00197332	−	0.00607324i
$523$	5.14590	+	15.8374i	0.225014	+	0.692523i	0.998290	+	0.0584532i	$0.0186169\pi$
$523$	5.14590	+	15.8374i	0.225014	+	0.692523i	−0.773276	+	0.634070i	$0.781383\pi$
$524$	−2.30902	−	1.67760i	−0.100870	−	0.0732863i
$525$	4.04508	−	2.93893i	0.176542	−	0.128265i
$526$	3.94427	−	12.1392i	0.171978	−	0.529295i
$527$	22.4721			0.978902
$528$		0			0
$529$	36.4164			1.58332
$530$	1.54508	−	4.75528i	0.0671142	−	0.206556i
$531$	4.30902	−	3.13068i	0.186995	−	0.135860i
$532$	10.0902	+	7.33094i	0.437464	+	0.317836i
$533$	−2.94427	−	9.06154i	−0.127531	−	0.392499i
$534$	3.47214	+	10.6861i	0.150254	+	0.462434i
$535$	−11.2812	−	8.19624i	−0.487727	−	0.354354i
$536$	10.4721	−	7.60845i	0.452327	−	0.328635i
$537$	0.482779	−	1.48584i	0.0208335	−	0.0641188i
$538$	6.00000			0.258678
$539$		0			0
$540$	1.38197			0.0594703
$541$	−1.38197	+	4.25325i	−0.0594154	+	0.182862i	−0.976359	−	0.216155i	$-0.930648\pi$
$541$	−1.38197	+	4.25325i	−0.0594154	+	0.182862i	0.916944	+	0.399017i	$0.130648\pi$
$542$	14.1803	−	10.3026i	0.609098	−	0.442535i
$543$	4.38197	+	3.18368i	0.188048	+	0.136625i
$544$	−1.23607	−	3.80423i	−0.0529960	−	0.163105i
$545$	−6.38197	−	19.6417i	−0.273373	−	0.841357i
$546$	−1.61803	−	1.17557i	−0.0692455	−	0.0503098i
$547$	−2.32624	+	1.69011i	−0.0994628	+	0.0722639i	−0.636405	−	0.771355i	$-0.719579\pi$
$547$	−2.32624	+	1.69011i	−0.0994628	+	0.0722639i	0.536942	+	0.843619i	$0.319579\pi$
$548$	2.52786	−	7.77997i	0.107985	−	0.332344i
$549$	−9.70820			−0.414336
$550$		0			0
$551$	1.12461			0.0479101
$552$	2.38197	−	7.33094i	0.101383	−	0.312025i
$553$	−0.190983	+	0.138757i	−0.00812142	+	0.00590056i
$554$	1.85410	+	1.34708i	0.0787732	+	0.0572321i
$555$	3.81966	+	11.7557i	0.162136	+	0.499002i
$556$	0.708204	+	2.17963i	0.0300345	+	0.0924368i
$557$	10.7812	+	7.83297i	0.456812	+	0.331893i	0.792279	−	0.610158i	$-0.208894\pi$
$557$	10.7812	+	7.83297i	0.456812	+	0.331893i	−0.335467	+	0.942052i	$0.608894\pi$
$558$	4.54508	−	3.30220i	0.192409	−	0.139793i
$559$	3.52786	−	10.8576i	0.149213	−	0.459230i
$560$	2.23607			0.0944911
$561$		0			0
$562$	−16.7639			−0.707144
$563$	−2.47214	+	7.60845i	−0.104188	+	0.320658i	−0.989539	−	0.144265i	$-0.953918\pi$
$563$	−2.47214	+	7.60845i	−0.104188	+	0.320658i	0.885351	+	0.464923i	$0.153918\pi$
$564$	−3.23607	+	2.35114i	−0.136263	+	0.0990009i
$565$	12.2361	+	8.89002i	0.514775	+	0.374006i
$566$	5.09017	+	15.6659i	0.213956	+	0.658488i
$567$	0.500000	+	1.53884i	0.0209980	+	0.0646253i
$568$	−4.85410	−	3.52671i	−0.203674	−	0.147978i
$569$	−13.3262	+	9.68208i	−0.558665	+	0.405894i	−0.830970	−	0.556317i	$-0.812214\pi$
$569$	−13.3262	+	9.68208i	−0.558665	+	0.405894i	0.272305	+	0.962211i	$0.412214\pi$
$570$	−3.29180	+	10.1311i	−0.137878	+	0.424345i
$571$	−1.34752			−0.0563921			−0.0281961	−	0.999602i	$-0.508976\pi$
$571$	−1.34752			−0.0563921			−0.0281961	+	0.999602i	$0.508976\pi$
$572$		0			0
$573$	−20.9443			−0.874960
$574$	−3.85410	+	11.8617i	−0.160867	+	0.495098i
$575$	19.2705	−	14.0008i	0.803636	−	0.583876i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−1.62461	−	5.00004i	−0.0676335	−	0.208154i	0.911528	−	0.411238i	$-0.134904\pi$
$577$	−1.62461	−	5.00004i	−0.0676335	−	0.208154i	−0.979161	+	0.203084i	$0.934904\pi$
$578$	−0.309017	−	0.951057i	−0.0128534	−	0.0395587i
$579$	−1.92705	−	1.40008i	−0.0800855	−	0.0581855i
$580$	0.163119	−	0.118513i	0.00677315	−	0.00492098i
$581$	0.309017	−	0.951057i	0.0128202	−	0.0394565i
$582$	−7.38197			−0.305992
$583$		0			0
$584$	5.56231			0.230170
$585$	0.527864	−	1.62460i	0.0218245	−	0.0671689i
$586$	6.16312	−	4.47777i	0.254596	−	0.184975i
$587$	17.1525	+	12.4620i	0.707958	+	0.514362i	0.882514	−	0.470285i	$-0.155849\pi$
$587$	17.1525	+	12.4620i	0.707958	+	0.514362i	−0.174556	+	0.984647i	$0.555849\pi$
$588$	−1.35410	−	4.16750i	−0.0558422	−	0.171865i
$589$	13.3820	+	41.1855i	0.551394	+	1.69702i
$590$	5.95492	+	4.32650i	0.245160	+	0.178119i
$591$	10.1180	−	7.35118i	0.416200	−	0.302387i
$592$	2.76393	−	8.50651i	0.113597	−	0.349615i
$593$	7.88854			0.323944			0.161972	−	0.986795i	$-0.448215\pi$
$593$	7.88854			0.323944			0.161972	+	0.986795i	$0.448215\pi$
$594$		0			0
$595$	−8.94427			−0.366679
$596$	7.11803	−	21.9071i	0.291566	−	0.897348i
$597$	2.11803	−	1.53884i	0.0866854	−	0.0629806i
$598$	−7.70820	−	5.60034i	−0.315212	−	0.229015i
$599$	10.0000	+	30.7768i	0.408589	+	1.25751i	0.917861	+	0.396902i	$0.129915\pi$
$599$	10.0000	+	30.7768i	0.408589	+	1.25751i	−0.509272	+	0.860606i	$0.670085\pi$
$600$	−0.954915	−	2.93893i	−0.0389842	−	0.119981i
$601$	−16.2533	−	11.8087i	−0.662985	−	0.481687i	0.204684	−	0.978828i	$-0.434383\pi$
$601$	−16.2533	−	11.8087i	−0.662985	−	0.481687i	−0.867670	+	0.497141i	$0.834383\pi$
$602$	−12.0902	+	8.78402i	−0.492759	+	0.358010i
$603$	−4.00000	+	12.3107i	−0.162893	+	0.501332i
$604$	4.79837			0.195243
$605$		0			0
$606$	−9.09017			−0.369263
$607$	−4.65248	+	14.3188i	−0.188838	+	0.581184i	−0.999993	−	0.00364685i	$-0.998839\pi$
$607$	−4.65248	+	14.3188i	−0.188838	+	0.581184i	0.811155	+	0.584831i	$0.198839\pi$
$608$	6.23607	−	4.53077i	0.252906	−	0.183747i
$609$	0.190983	+	0.138757i	0.00773902	+	0.00562273i
$610$	−4.14590	−	12.7598i	−0.167863	−	0.516628i
$611$	1.52786	+	4.70228i	0.0618108	+	0.190234i
$612$	3.23607	+	2.35114i	0.130810	+	0.0950392i
$613$	2.70820	−	1.96763i	0.109383	−	0.0794716i	−0.531749	−	0.846902i	$-0.678465\pi$
$613$	2.70820	−	1.96763i	0.109383	−	0.0794716i	0.641132	+	0.767430i	$0.278465\pi$
$614$	3.94427	−	12.1392i	0.159178	−	0.489899i
$615$	−10.6525			−0.429549
$616$		0			0
$617$	−15.1246			−0.608894			−0.304447	−	0.952529i	$-0.598472\pi$
$617$	−15.1246			−0.608894			−0.304447	+	0.952529i	$0.598472\pi$
$618$	−0.972136	+	2.99193i	−0.0391050	+	0.120353i
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	−0.650917	−	0.759149i	$-0.725616\pi$
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	0.520849	+	0.853649i	$0.325616\pi$
$620$	6.28115	+	4.56352i	0.252257	+	0.183276i
$621$	2.38197	+	7.33094i	0.0955850	+	0.294180i
$622$	2.32624	+	7.15942i	0.0932736	+	0.287067i
$623$	−14.7082	−	10.6861i	−0.589272	−	0.428131i
$624$	−1.00000	+	0.726543i	−0.0400320	+	0.0290850i
$625$		0			0
$626$	−24.9787			−0.998350
$627$		0			0
$628$	−18.0000			−0.718278
$629$	−11.0557	+	34.0260i	−0.440821	+	1.35671i
$630$	−1.80902	+	1.31433i	−0.0720730	+	0.0523641i
$631$	19.5902	+	14.2331i	0.779872	+	0.566610i	0.904941	−	0.425538i	$-0.139915\pi$
$631$	19.5902	+	14.2331i	0.779872	+	0.566610i	−0.125068	+	0.992148i	$0.539915\pi$
$632$	0.0450850	+	0.138757i	0.00179338	+	0.00551947i
$633$	1.47214	+	4.53077i	0.0585122	+	0.180082i
$634$	21.7984	+	15.8374i	0.865724	+	0.628985i
$635$	4.47214	−	3.24920i	0.177471	−	0.128940i
$636$	1.11803	−	3.44095i	0.0443329	−	0.136443i
$637$	−5.41641			−0.214606
$638$		0			0
$639$	6.00000			0.237356
$640$	0.427051	−	1.31433i	0.0168807	−	0.0519534i
$641$	16.3262	−	11.8617i	0.644848	−	0.468509i	−0.216665	−	0.976246i	$-0.569518\pi$
$641$	16.3262	−	11.8617i	0.644848	−	0.468509i	0.861512	+	0.507737i	$0.169518\pi$
$642$	−8.16312	−	5.93085i	−0.322173	−	0.234072i
$643$	1.85410	+	5.70634i	0.0731186	+	0.225036i	0.980936	−	0.194329i	$-0.0622528\pi$
$643$	1.85410	+	5.70634i	0.0731186	+	0.225036i	−0.907818	+	0.419365i	$0.862253\pi$
$644$	3.85410	+	11.8617i	0.151873	+	0.467417i
$645$	−10.3262	−	7.50245i	−0.406595	−	0.295409i
$646$	−24.9443	+	18.1231i	−0.981419	+	0.713043i
$647$	−6.56231	+	20.1967i	−0.257991	+	0.794014i	0.735235	+	0.677813i	$0.237072\pi$
$647$	−6.56231	+	20.1967i	−0.257991	+	0.794014i	−0.993226	+	0.116202i	$0.962928\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−3.81966			−0.149819
$651$	−2.80902	+	8.64527i	−0.110094	+	0.338835i
$652$	6.85410	−	4.97980i	0.268427	−	0.195024i
$653$	2.88197	+	2.09387i	0.112780	+	0.0819395i	0.642746	−	0.766080i	$-0.277795\pi$
$653$	2.88197	+	2.09387i	0.112780	+	0.0819395i	−0.529966	+	0.848019i	$0.677795\pi$
$654$	−4.61803	−	14.2128i	−0.180579	−	0.555766i
$655$	1.21885	+	3.75123i	0.0476243	+	0.146573i
$656$	6.23607	+	4.53077i	0.243478	+	0.176897i
$657$	−4.50000	+	3.26944i	−0.175562	+	0.127553i
$658$	2.00000	−	6.15537i	0.0779681	−	0.239961i
$659$	−45.9230			−1.78891			−0.894453	−	0.447162i	$-0.852435\pi$
$659$	−45.9230			−1.78891			−0.894453	+	0.447162i	$0.852435\pi$
$660$		0			0
$661$	−11.5967			−0.451061			−0.225531	−	0.974236i	$-0.572412\pi$
$661$	−11.5967			−0.451061			−0.225531	+	0.974236i	$0.572412\pi$
$662$	8.76393	−	26.9726i	0.340620	−	1.04832i
$663$	4.00000	−	2.90617i	0.155347	−	0.112866i
$664$	−0.500000	−	0.363271i	−0.0194038	−	0.0140977i
$665$	−5.32624	−	16.3925i	−0.206543	−	0.635673i
$666$	2.76393	+	8.50651i	0.107100	+	0.329620i
$667$	0.909830	+	0.661030i	0.0352288	+	0.0255952i
$668$	−15.9443	+	11.5842i	−0.616902	+	0.448206i
$669$	4.42705	−	13.6251i	0.171160	−	0.526775i
$670$	−17.8885			−0.691095
$671$		0			0
$672$	1.61803			0.0624170
$673$	−2.39261	+	7.36369i	−0.0922283	+	0.283850i	−0.986521	−	0.163632i	$-0.947679\pi$
$673$	−2.39261	+	7.36369i	−0.0922283	+	0.283850i	0.894293	+	0.447482i	$0.147679\pi$
$674$	−12.8541	+	9.33905i	−0.495122	+	0.359727i
$675$	2.50000	+	1.81636i	0.0962250	+	0.0699116i
$676$	−3.54508	−	10.9106i	−0.136349	−	0.419640i
$677$	−15.7148	−	48.3651i	−0.603968	−	1.85882i	−0.503734	−	0.863859i	$-0.668041\pi$
$677$	−15.7148	−	48.3651i	−0.603968	−	1.85882i	−0.100234	−	0.994964i	$-0.531959\pi$
$678$	8.85410	+	6.43288i	0.340040	+	0.247053i
$679$	9.66312	−	7.02067i	0.370836	−	0.269428i
$680$	−1.70820	+	5.25731i	−0.0655066	+	0.201609i
$681$	24.0344			0.921002
$682$		0			0
$683$	−14.4508			−0.552946			−0.276473	−	0.961022i	$-0.589166\pi$
$683$	−14.4508			−0.552946			−0.276473	+	0.961022i	$0.589166\pi$
$684$	−2.38197	+	7.33094i	−0.0910767	+	0.280305i
$685$	−9.14590	+	6.64488i	−0.349447	+	0.253888i
$686$	14.8992	+	10.8249i	0.568854	+	0.413296i
$687$	6.61803	+	20.3682i	0.252494	+	0.777096i
$688$	2.85410	+	8.78402i	0.108812	+	0.334888i
$689$	−3.61803	−	2.62866i	−0.137836	−	0.100144i
$690$	−8.61803	+	6.26137i	−0.328083	+	0.238366i
$691$	1.58359	−	4.87380i	0.0602427	−	0.185408i	−0.916406	−	0.400249i	$-0.868923\pi$
$691$	1.58359	−	4.87380i	0.0602427	−	0.185408i	0.976649	+	0.214841i	$0.0689235\pi$
$692$	−1.32624			−0.0504160
$693$		0			0
$694$	18.6738			0.708846
$695$	0.978714	−	3.01217i	0.0371247	−	0.114258i
$696$	0.118034	−	0.0857567i	0.00447407	−	0.00325060i
$697$	−24.9443	−	18.1231i	−0.944832	−	0.686460i
$698$	7.94427	+	24.4500i	0.300695	+	0.925444i
$699$	−0.291796	−	0.898056i	−0.0110367	−	0.0339676i
$700$	4.04508	+	2.93893i	0.152890	+	0.111081i
$701$	13.0344	−	9.47008i	0.492304	−	0.357680i	−0.313766	−	0.949500i	$-0.601591\pi$
$701$	13.0344	−	9.47008i	0.492304	−	0.357680i	0.806070	+	0.591821i	$0.201591\pi$
$702$	0.381966	−	1.17557i	0.0144164	−	0.0443690i
$703$	−68.9443			−2.60028
$704$		0			0
$705$	5.52786			0.208191
$706$	3.47214	−	10.6861i	0.130676	−	0.402178i
$707$	11.8992	−	8.64527i	0.447515	−	0.325139i
$708$	4.30902	+	3.13068i	0.161943	+	0.117658i
$709$	10.6738	+	32.8505i	0.400862	+	1.23372i	0.924302	+	0.381663i	$0.124648\pi$
$709$	10.6738	+	32.8505i	0.400862	+	1.23372i	−0.523440	+	0.852062i	$0.675352\pi$
$710$	2.56231	+	7.88597i	0.0961616	+	0.295955i
$711$	−0.118034	−	0.0857567i	−0.00442662	−	0.00321613i
$712$	−9.09017	+	6.60440i	−0.340669	+	0.247510i
$713$	−13.3820	+	41.1855i	−0.501159	+	1.54241i
$714$	−6.47214			−0.242214
$715$		0			0
$716$	1.56231			0.0583861
$717$	5.09017	−	15.6659i	0.190096	−	0.585055i
$718$	−4.70820	+	3.42071i	−0.175709	+	0.127660i
$719$	−0.854102	−	0.620541i	−0.0318526	−	0.0231423i	0.571745	−	0.820431i	$-0.306267\pi$
$719$	−0.854102	−	0.620541i	−0.0318526	−	0.0231423i	−0.603598	+	0.797289i	$0.706267\pi$
$720$	0.427051	+	1.31433i	0.0159153	+	0.0489821i
$721$	−1.57295	−	4.84104i	−0.0585797	−	0.180290i
$722$	−32.6976	−	23.7562i	−1.21688	−	0.884113i
$723$	5.16312	−	3.75123i	0.192018	−	0.139510i
$724$	−1.67376	+	5.15131i	−0.0622049	+	0.191447i
$725$	0.450850			0.0167441
$726$		0			0
$727$	−31.4164			−1.16517			−0.582585	−	0.812770i	$-0.697959\pi$
$727$	−31.4164			−1.16517			−0.582585	+	0.812770i	$0.697959\pi$
$728$	0.618034	−	1.90211i	0.0229059	−	0.0704970i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−6.21885	−	4.51826i	−0.230170	−	0.167228i
$731$	−11.4164	−	35.1361i	−0.422251	−	1.29956i
$732$	−3.00000	−	9.23305i	−0.110883	−	0.341263i
$733$	18.7984	+	13.6578i	0.694334	+	0.504463i	0.878082	−	0.478510i	$-0.158823\pi$
$733$	18.7984	+	13.6578i	0.694334	+	0.504463i	−0.183748	+	0.982973i	$0.558823\pi$
$734$	−8.11803	+	5.89810i	−0.299642	+	0.217703i
$735$	−1.87132	+	5.75934i	−0.0690248	+	0.212436i
$736$	7.70820			0.284128
$737$		0			0
$738$	−7.70820			−0.283743
$739$	−10.3607	+	31.8869i	−0.381124	+	1.17298i	0.558130	+	0.829754i	$0.311519\pi$
$739$	−10.3607	+	31.8869i	−0.381124	+	1.17298i	−0.939253	+	0.343225i	$0.888481\pi$
$740$	−10.0000	+	7.26543i	−0.367607	+	0.267082i
$741$	7.70820	+	5.60034i	0.283168	+	0.205734i
$742$	1.80902	+	5.56758i	0.0664111	+	0.204392i
$743$	7.74265	+	23.8294i	0.284050	+	0.874216i	0.986682	+	0.162663i	$0.0520082\pi$
$743$	7.74265	+	23.8294i	0.284050	+	0.874216i	−0.702632	+	0.711554i	$0.747992\pi$
$744$	4.54508	+	3.30220i	0.166631	+	0.121064i
$745$	−25.7533	+	18.7109i	−0.943528	+	0.685513i
$746$		0			0
$747$	0.618034			0.0226127
$748$		0			0
$749$	16.3262			0.596548
$750$	−3.45492	+	10.6331i	−0.126156	+	0.388267i
$751$	15.2361	−	11.0697i	0.555972	−	0.403937i	−0.274011	−	0.961727i	$-0.588350\pi$
$751$	15.2361	−	11.0697i	0.555972	−	0.403937i	0.829983	+	0.557789i	$0.188350\pi$
$752$	−3.23607	−	2.35114i	−0.118007	−	0.0857373i
$753$	−0.100813	−	0.310271i	−0.00367383	−	0.0113069i
$754$	−0.0557281	−	0.171513i	−0.00202950	−	0.00624615i
$755$	−5.36475	−	3.89772i	−0.195243	−	0.141852i
$756$	−1.30902	+	0.951057i	−0.0476085	+	0.0345896i
$757$	−16.8885	+	51.9776i	−0.613825	+	1.88916i	−0.196101	+	0.980584i	$0.562828\pi$
$757$	−16.8885	+	51.9776i	−0.613825	+	1.88916i	−0.417724	+	0.908574i	$0.637172\pi$
$758$	3.81966			0.138736
$759$		0			0
$760$	−10.6525			−0.386406
$761$	−16.7426	+	51.5286i	−0.606920	+	1.86791i	−0.123912	+	0.992293i	$0.539544\pi$
$761$	−16.7426	+	51.5286i	−0.606920	+	1.86791i	−0.483008	+	0.875616i	$0.660456\pi$
$762$	3.23607	−	2.35114i	0.117230	−	0.0851729i
$763$	19.5623	+	14.2128i	0.708203	+	0.514540i
$764$	−6.47214	−	19.9192i	−0.234154	−	0.720651i
$765$	−1.70820	−	5.25731i	−0.0617602	−	0.190078i
$766$	−30.5066	−	22.1643i	−1.10225	−	0.800830i
$767$	5.32624	−	3.86974i	0.192319	−	0.139728i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	41.5623			1.49878			0.749388	−	0.662132i	$-0.230348\pi$
$769$	41.5623			1.49878			0.749388	+	0.662132i	$0.230348\pi$
$770$		0			0
$771$	21.7082			0.781802
$772$	0.736068	−	2.26538i	0.0264917	−	0.0815330i
$773$	−34.0066	+	24.7072i	−1.22313	+	0.888657i	−0.996356	−	0.0852900i	$-0.972818\pi$
$773$	−34.0066	+	24.7072i	−1.22313	+	0.888657i	−0.226775	+	0.973947i	$0.572818\pi$
$774$	−7.47214	−	5.42882i	−0.268580	−	0.195135i
$775$	5.36475	+	16.5110i	0.192707	+	0.593092i
$776$	−2.28115	−	7.02067i	−0.0818886	−	0.252027i
$777$	−11.7082	−	8.50651i	−0.420029	−	0.305169i
$778$	−0.854102	+	0.620541i	−0.0306210	+	0.0222475i
$779$	18.3607	−	56.5084i	0.657840	−	2.02462i
$780$	1.70820			0.0611635
$781$		0			0
$782$	−30.8328			−1.10258
$783$	−0.0450850	+	0.138757i	−0.00161121	+	0.00495878i
$784$	3.54508	−	2.57565i	0.126610	−	0.0919877i
$785$	20.1246	+	14.6214i	0.718278	+	0.521860i
$786$	0.881966	+	2.71441i	0.0314587	+	0.0968199i
$787$	−6.27051	−	19.2986i	−0.223520	−	0.687922i	−0.998439	−	0.0558618i	$-0.982209\pi$
$787$	−6.27051	−	19.2986i	−0.223520	−	0.687922i	0.774919	−	0.632061i	$-0.217791\pi$
$788$	10.1180	+	7.35118i	0.360440	+	0.261875i
$789$	−10.3262	+	7.50245i	−0.367624	+	0.267094i
$790$	0.0623059	−	0.191758i	0.00221674	−	0.00682244i
$791$	−17.7082			−0.629631
$792$		0			0
$793$	−12.0000			−0.426132
$794$	−4.00000	+	12.3107i	−0.141955	+	0.436892i
$795$	−4.04508	+	2.93893i	−0.143464	+	0.104233i
$796$	2.11803	+	1.53884i	0.0750717	+	0.0545428i
$797$	14.4098	+	44.3489i	0.510422	+	1.57092i	0.791459	+	0.611222i	$0.209322\pi$
$797$	14.4098	+	44.3489i	0.510422	+	1.57092i	−0.281037	+	0.959697i	$0.590678\pi$
$798$	−3.85410	−	11.8617i	−0.136434	−	0.419900i
$799$	12.9443	+	9.40456i	0.457935	+	0.332710i
$800$	2.50000	−	1.81636i	0.0883883	−	0.0642179i
$801$	3.47214	−	10.6861i	0.122682	−	0.377576i
$802$	11.7082			0.413431
$803$		0			0
$804$	−12.9443			−0.456509
$805$	5.32624	−	16.3925i	0.187725	−	0.577759i
$806$	5.61803	−	4.08174i	0.197887	−	0.143773i
$807$	−4.85410	−	3.52671i	−0.170872	−	0.124146i
$808$	−2.80902	−	8.64527i	−0.0988209	−	0.304139i
$809$	0.944272	+	2.90617i	0.0331988	+	0.102175i	0.966283	−	0.257483i	$-0.0828932\pi$
$809$	0.944272	+	2.90617i	0.0331988	+	0.102175i	−0.933084	+	0.359659i	$0.882893\pi$
$810$	−1.11803	−	0.812299i	−0.0392837	−	0.0285413i
$811$	17.6525	−	12.8253i	0.619862	−	0.450356i	−0.233011	−	0.972474i	$-0.574858\pi$
$811$	17.6525	−	12.8253i	0.619862	−	0.450356i	0.852873	+	0.522118i	$0.174858\pi$
$812$	−0.0729490	+	0.224514i	−0.00256001	+	0.00787890i
$813$	−17.5279			−0.614729
$814$		0			0
$815$	−11.7082			−0.410120
$816$	−1.23607	+	3.80423i	−0.0432710	+	0.133175i
$817$	57.5967	−	41.8465i	2.01506	−	1.46402i
$818$	13.7361	+	9.97984i	0.480270	+	0.348937i
$819$	0.618034	+	1.90211i	0.0215959	+	0.0664652i
$820$	−3.29180	−	10.1311i	−0.114955	−	0.353794i
$821$	36.0517	+	26.1931i	1.25821	+	0.914144i	0.998668	−	0.0515872i	$-0.0164280\pi$
$821$	36.0517	+	26.1931i	1.25821	+	0.914144i	0.259543	+	0.965731i	$0.416428\pi$
$822$	−6.61803	+	4.80828i	−0.230830	+	0.167708i
$823$	7.37132	−	22.6866i	0.256948	−	0.790805i	−0.736491	−	0.676447i	$-0.763519\pi$
$823$	7.37132	−	22.6866i	0.256948	−	0.790805i	0.993440	−	0.114358i	$-0.0364812\pi$
$824$	−3.14590			−0.109593
$825$		0			0
$826$	−8.61803			−0.299860
$827$	−2.00658	+	6.17561i	−0.0697755	+	0.214747i	−0.979864	−	0.199668i	$-0.936014\pi$
$827$	−2.00658	+	6.17561i	−0.0697755	+	0.214747i	0.910088	+	0.414415i	$0.136014\pi$
$828$	−6.23607	+	4.53077i	−0.216718	+	0.157455i
$829$	17.6180	+	12.8003i	0.611900	+	0.444571i	0.850083	−	0.526649i	$-0.176552\pi$
$829$	17.6180	+	12.8003i	0.611900	+	0.444571i	−0.238183	+	0.971220i	$0.576552\pi$
$830$	0.263932	+	0.812299i	0.00916121	+	0.0281953i
$831$	−0.708204	−	2.17963i	−0.0245673	−	0.0756104i
$832$	−1.00000	−	0.726543i	−0.0346688	−	0.0251883i
$833$	−14.1803	+	10.3026i	−0.491320	+	0.356965i
$834$	0.708204	−	2.17963i	0.0245231	−	0.0754743i
$835$	27.2361			0.942543
$836$		0			0
$837$	−5.61803			−0.194188
$838$	0.281153	−	0.865300i	0.00971227	−	0.0298913i
$839$	−41.2705	+	29.9848i	−1.42482	+	1.03519i	−0.433863	+	0.900979i	$0.642850\pi$
$839$	−41.2705	+	29.9848i	−1.42482	+	1.03519i	−0.990953	+	0.134211i	$0.957150\pi$
$840$	−1.80902	−	1.31433i	−0.0624170	−	0.0453486i
$841$	−8.95492	−	27.5604i	−0.308790	−	0.950358i
$842$	12.2361	+	37.6587i	0.421683	+	1.29781i
$843$	13.5623	+	9.85359i	0.467111	+	0.339376i
$844$	−3.85410	+	2.80017i	−0.132664	+	0.0963858i
$845$	−4.89919	+	15.0781i	−0.168537	+	0.518704i
$846$	4.00000			0.137523
$847$		0			0
$848$	3.61803			0.124244
$849$	5.09017	−	15.6659i	0.174694	−	0.537653i
$850$	−10.0000	+	7.26543i	−0.342997	+	0.249202i
$851$	−55.7771	−	40.5244i	−1.91201	−	1.38916i
$852$	1.85410	+	5.70634i	0.0635205	+	0.195496i
$853$	−6.94427	−	21.3723i	−0.237767	−	0.731773i	−0.996742	−	0.0806528i	$-0.974300\pi$
$853$	−6.94427	−	21.3723i	−0.237767	−	0.731773i	0.758975	−	0.651120i	$-0.225700\pi$
$854$	12.7082	+	9.23305i	0.434866	+	0.315948i
$855$	8.61803	−	6.26137i	0.294731	−	0.214134i
$856$	3.11803	−	9.59632i	0.106572	−	0.327996i
$857$	2.18034			0.0744790			0.0372395	−	0.999306i	$-0.488144\pi$
$857$	2.18034			0.0744790			0.0372395	+	0.999306i	$0.488144\pi$
$858$		0			0
$859$	41.9574			1.43157			0.715784	−	0.698321i	$-0.246069\pi$
$859$	41.9574			1.43157			0.715784	+	0.698321i	$0.246069\pi$
$860$	3.94427	−	12.1392i	0.134499	−	0.413944i
$861$	10.0902	−	7.33094i	0.343872	−	0.249838i
$862$	−19.4721	−	14.1473i	−0.663224	−	0.481860i
$863$	−10.2361	−	31.5034i	−0.348440	−	1.07239i	−0.959716	−	0.280970i	$-0.909344\pi$
$863$	−10.2361	−	31.5034i	−0.348440	−	1.07239i	0.611277	−	0.791417i	$-0.290656\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	1.48278	+	1.07730i	0.0504160	+	0.0366294i
$866$	−7.78115	+	5.65334i	−0.264414	+	0.192108i
$867$	−0.309017	+	0.951057i	−0.0104948	+	0.0322996i
$868$	−9.09017			−0.308540
$869$		0			0
$870$	−0.201626			−0.00683577
$871$	−4.94427	+	15.2169i	−0.167530	+	0.515605i
$872$	12.0902	−	8.78402i	0.409425	−	0.297465i
$873$	5.97214	+	4.33901i	0.202126	+	0.146853i
$874$	−18.3607	−	56.5084i	−0.621059	−	1.91142i
$875$	−5.59017	−	17.2048i	−0.188982	−	0.581628i
$876$	−4.50000	−	3.26944i	−0.152041	−	0.110464i
$877$	20.0902	−	14.5964i	0.678397	−	0.492884i	−0.194429	−	0.980917i	$-0.562285\pi$
$877$	20.0902	−	14.5964i	0.678397	−	0.492884i	0.872825	+	0.488033i	$0.162285\pi$
$878$	10.7918	−	33.2137i	0.364205	−	1.12091i
$879$	−7.61803			−0.256950
$880$		0			0
$881$	34.0689			1.14781			0.573905	−	0.818922i	$-0.305428\pi$
$881$	34.0689			1.14781			0.573905	+	0.818922i	$0.305428\pi$
$882$	−1.35410	+	4.16750i	−0.0455950	+	0.140327i
$883$	−8.52786	+	6.19586i	−0.286985	+	0.208507i	−0.721959	−	0.691936i	$-0.756758\pi$
$883$	−8.52786	+	6.19586i	−0.286985	+	0.208507i	0.434973	+	0.900443i	$0.356758\pi$
$884$	4.00000	+	2.90617i	0.134535	+	0.0977451i
$885$	−2.27458	−	7.00042i	−0.0764590	−	0.235317i
$886$	2.11803	+	6.51864i	0.0711567	+	0.218998i
$887$	13.7639	+	10.0001i	0.462148	+	0.335770i	0.794373	−	0.607430i	$-0.207800\pi$
$887$	13.7639	+	10.0001i	0.462148	+	0.335770i	−0.332226	+	0.943200i	$0.607800\pi$
$888$	−7.23607	+	5.25731i	−0.242827	+	0.176424i
$889$	−2.00000	+	6.15537i	−0.0670778	+	0.206444i
$890$	15.5279			0.520495
$891$		0			0
$892$	14.3262			0.479678
$893$	−9.52786	+	29.3238i	−0.318838	+	0.981282i
$894$	−18.6353	+	13.5393i	−0.623256	+	0.452822i
$895$	−1.74671	−	1.26906i	−0.0583861	−	0.0424200i
$896$	0.500000	+	1.53884i	0.0167038	+	0.0514091i
$897$	2.94427	+	9.06154i	0.0983064	+	0.302556i
$898$	6.85410	+	4.97980i	0.228724	+	0.166178i
$899$	−0.663119	+	0.481784i	−0.0221163	+	0.0160684i
$900$	−0.954915	+	2.93893i	−0.0318305	+	0.0979642i
$901$	−14.4721			−0.482137
$902$		0			0
$903$	14.9443			0.497314
$904$	−3.38197	+	10.4086i	−0.112483	+	0.346186i
$905$	6.05573	−	4.39974i	0.201299	−	0.146252i
$906$	−3.88197	−	2.82041i	−0.128970	−	0.0937020i
$907$	3.61803	+	11.1352i	0.120135	+	0.369737i	0.992983	−	0.118254i	$-0.0377298\pi$
$907$	3.61803	+	11.1352i	0.120135	+	0.369737i	−0.872849	+	0.487991i	$0.837730\pi$
$908$	7.42705	+	22.8581i	0.246475	+	0.758573i
$909$	7.35410	+	5.34307i	0.243920	+	0.177218i
$910$	−2.23607	+	1.62460i	−0.0741249	+	0.0538549i
$911$	−12.5279	+	38.5568i	−0.415067	+	1.27744i	0.497125	+	0.867679i	$0.334389\pi$
$911$	−12.5279	+	38.5568i	−0.415067	+	1.27744i	−0.912191	+	0.409765i	$0.865611\pi$
$912$	−7.70820			−0.255244
$913$		0			0
$914$	16.9098			0.559327
$915$	−4.14590	+	12.7598i	−0.137059	+	0.421825i
$916$	−17.3262	+	12.5882i	−0.572475	+	0.415927i
$917$	−3.73607	−	2.71441i	−0.123376	−	0.0896378i
$918$	−1.23607	−	3.80423i	−0.0407963	−	0.125558i
$919$	3.30244	+	10.1639i	0.108937	+	0.335275i	0.990634	−	0.136541i	$-0.0435986\pi$
$919$	3.30244	+	10.1639i	0.108937	+	0.335275i	−0.881697	+	0.471816i	$0.843599\pi$
$920$	−8.61803	−	6.26137i	−0.284128	−	0.206431i
$921$	−10.3262	+	7.50245i	−0.340261	+	0.247214i
$922$	−6.79837	+	20.9232i	−0.223893	+	0.689070i
$923$	7.41641			0.244114
$924$		0			0
$925$	−27.6393			−0.908775
$926$	10.7361	−	33.0422i	0.352809	−	1.08583i
$927$	2.54508	−	1.84911i	0.0835916	−	0.0607328i
$928$	0.118034	+	0.0857567i	0.00387466	+	0.00281510i
$929$	1.18034	+	3.63271i	0.0387257	+	0.119185i	0.968551	−	0.248817i	$-0.0800418\pi$
$929$	1.18034	+	3.63271i	0.0387257	+	0.119185i	−0.929825	+	0.368002i	$0.880042\pi$
$930$	−2.39919	−	7.38394i	−0.0786724	−	0.242129i
$931$	−27.3262	−	19.8537i	−0.895581	−	0.650678i
$932$	0.763932	−	0.555029i	0.0250234	−	0.0181806i
$933$	2.32624	−	7.15942i	0.0761576	−	0.234389i
$934$	−11.7984			−0.386055
$935$		0			0
$936$	1.23607			0.0404021
$937$	16.2082	−	49.8837i	0.529499	−	1.62963i	−0.225745	−	0.974186i	$-0.572482\pi$
$937$	16.2082	−	49.8837i	0.529499	−	1.62963i	0.755244	−	0.655444i	$-0.227518\pi$
$938$	16.9443	−	12.3107i	0.553250	−	0.401960i
$939$	20.2082	+	14.6821i	0.659470	+	0.479133i
$940$	1.70820	+	5.25731i	0.0557155	+	0.171475i
$941$	10.4377	+	32.1239i	0.340259	+	1.04721i	0.964073	+	0.265637i	$0.0855823\pi$
$941$	10.4377	+	32.1239i	0.340259	+	1.04721i	−0.623814	+	0.781573i	$0.714418\pi$
$942$	14.5623	+	10.5801i	0.474466	+	0.344719i
$943$	48.0689	−	34.9241i	1.56534	−	1.13728i
$944$	−1.64590	+	5.06555i	−0.0535694	+	0.164870i
$945$	2.23607			0.0727393
$946$		0			0
$947$	−32.9230			−1.06985			−0.534927	−	0.844899i	$-0.679661\pi$
$947$	−32.9230			−1.06985			−0.534927	+	0.844899i	$0.679661\pi$
$948$	0.0450850	−	0.138757i	0.00146429	−	0.00450663i
$949$	−5.56231	+	4.04125i	−0.180560	+	0.131185i
$950$	−19.2705	−	14.0008i	−0.625218	−	0.454247i
$951$	−8.32624	−	25.6255i	−0.269997	−	0.830965i
$952$	−2.00000	−	6.15537i	−0.0648204	−	0.199497i
$953$	−21.4164	−	15.5599i	−0.693745	−	0.504036i	0.184144	−	0.982899i	$-0.441049\pi$
$953$	−21.4164	−	15.5599i	−0.693745	−	0.504036i	−0.877889	+	0.478864i	$0.841049\pi$
$954$	−2.92705	+	2.12663i	−0.0947668	+	0.0688521i
$955$	−8.94427	+	27.5276i	−0.289430	+	0.890773i
$956$	16.4721			0.532747
$957$		0			0
$958$	−13.2361			−0.427638
$959$	4.09017	−	12.5882i	0.132078	−	0.406496i
$960$	−1.11803	+	0.812299i	−0.0360844	+	0.0262168i
$961$	−0.454915	−	0.330515i	−0.0146747	−	0.0106618i
$962$	3.41641	+	10.5146i	0.110149	+	0.339005i
$963$	3.11803	+	9.59632i	0.100477	+	0.309237i
$964$	5.16312	+	3.75123i	0.166293	+	0.120819i
$965$	−2.66312	+	1.93487i	−0.0857288	+	0.0622856i
$966$	3.85410	−	11.8617i	0.124004	−	0.381644i
$967$	17.3820			0.558966			0.279483	−	0.960151i	$-0.409837\pi$
$967$	17.3820			0.558966			0.279483	+	0.960151i	$0.409837\pi$
$968$		0			0
$969$	30.8328			0.990493
$970$	−3.15248	+	9.70232i	−0.101220	+	0.311523i
$971$	11.7082	−	8.50651i	0.375734	−	0.272987i	−0.383851	−	0.923395i	$-0.625402\pi$
$971$	11.7082	−	8.50651i	0.375734	−	0.272987i	0.759585	+	0.650408i	$0.225402\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	1.14590	+	3.52671i	0.0367358	+	0.113061i
$974$	−2.50000	−	7.69421i	−0.0801052	−	0.246538i
$975$	3.09017	+	2.24514i	0.0989646	+	0.0719020i
$976$	7.85410	−	5.70634i	0.251404	−	0.182655i
$977$	17.6180	−	54.2227i	0.563651	−	1.73474i	−0.108275	−	0.994121i	$-0.534533\pi$
$977$	17.6180	−	54.2227i	0.563651	−	1.73474i	0.671926	−	0.740618i	$-0.265467\pi$
$978$	−8.47214			−0.270909
$979$		0			0
$980$	−6.05573			−0.193443
$981$	−4.61803	+	14.2128i	−0.147442	+	0.453781i
$982$	26.9443	−	19.5762i	0.859826	−	0.624700i
$983$	−23.9443	−	17.3965i	−0.763704	−	0.554863i	0.136340	−	0.990662i	$-0.456466\pi$
$983$	−23.9443	−	17.3965i	−0.763704	−	0.554863i	−0.900044	+	0.435799i	$0.856466\pi$
$984$	−2.38197	−	7.33094i	−0.0759343	−	0.233702i
$985$	−5.34095	−	16.4377i	−0.170177	−	0.523750i
$986$	−0.472136	−	0.343027i	−0.0150359	−	0.0109242i
$987$	−5.23607	+	3.80423i	−0.166666	+	0.121090i
$988$	−2.94427	+	9.06154i	−0.0936698	+	0.288286i
$989$	71.1935			2.26382
$990$		0			0
$991$	−18.3951			−0.584340			−0.292170	−	0.956366i	$-0.594377\pi$
$991$	−18.3951			−0.584340			−0.292170	+	0.956366i	$0.594377\pi$
$992$	−1.73607	+	5.34307i	−0.0551202	+	0.169643i
$993$	−22.9443	+	16.6700i	−0.728114	+	0.529006i
$994$	−7.85410	−	5.70634i	−0.249117	−	0.180994i
$995$	−1.11803	−	3.44095i	−0.0354441	−	0.109086i
$996$	0.190983	+	0.587785i	0.00605153	+	0.0186247i
$997$	−5.38197	−	3.91023i	−0.170449	−	0.123838i	0.499290	−	0.866435i	$-0.333594\pi$
$997$	−5.38197	−	3.91023i	−0.170449	−	0.123838i	−0.669739	+	0.742597i	$0.733594\pi$
$998$	20.4721	−	14.8739i	0.648034	−	0.470824i
$999$	2.76393	−	8.50651i	0.0874469	−	0.269134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.a.493.1		4
11.2	odd	10		66.2.e.b.25.1	✓	4
11.3	even	5		726.2.e.c.565.1		4
11.4	even	5		726.2.a.m.1.1		2
11.5	even	5	inner	726.2.e.a.511.1		4
11.6	odd	10		726.2.e.j.511.1		4
11.7	odd	10		726.2.a.k.1.1		2
11.8	odd	10		66.2.e.b.37.1	yes	4
11.9	even	5		726.2.e.c.487.1		4
11.10	odd	2		726.2.e.j.493.1		4
33.2	even	10		198.2.f.a.91.1		4
33.8	even	10		198.2.f.a.37.1		4
33.26	odd	10		2178.2.a.o.1.2		2
33.29	even	10		2178.2.a.v.1.2		2
44.7	even	10		5808.2.a.bz.1.1		2
44.15	odd	10		5808.2.a.by.1.1		2
44.19	even	10		528.2.y.g.433.1		4
44.35	even	10		528.2.y.g.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.25.1	✓	4	11.2	odd	10
66.2.e.b.37.1	yes	4	11.8	odd	10
198.2.f.a.37.1		4	33.8	even	10
198.2.f.a.91.1		4	33.2	even	10
528.2.y.g.289.1		4	44.35	even	10
528.2.y.g.433.1		4	44.19	even	10
726.2.a.k.1.1		2	11.7	odd	10
726.2.a.m.1.1		2	11.4	even	5
726.2.e.a.493.1		4	1.1	even	1	trivial
726.2.e.a.511.1		4	11.5	even	5	inner
726.2.e.c.487.1		4	11.9	even	5
726.2.e.c.565.1		4	11.3	even	5
726.2.e.j.493.1		4	11.10	odd	2
726.2.e.j.511.1		4	11.6	odd	10
2178.2.a.o.1.2		2	33.26	odd	10
2178.2.a.v.1.2		2	33.29	even	10
5808.2.a.by.1.1		2	44.15	odd	10
5808.2.a.bz.1.1		2	44.7	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.427051 + 1.31433i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.38197 q^{10} +1.00000 q^{12} +(0.381966 - 1.17557i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(-1.11803 - 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(6.23607 - 4.53077i) q^{19} +(0.427051 - 1.31433i) q^{20} +1.61803 q^{21} +7.70820 q^{23} +(0.309017 - 0.951057i) q^{24} +(2.50000 - 1.81636i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.500000 + 1.53884i) q^{28} +(0.118034 + 0.0857567i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(-1.73607 + 5.34307i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(0.690983 - 2.12663i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-7.23607 - 5.25731i) q^{37} +(-2.38197 - 7.33094i) q^{38} +(0.381966 + 1.17557i) q^{39} +(-1.11803 - 0.812299i) q^{40} +(6.23607 - 4.53077i) q^{41} +(0.500000 - 1.53884i) q^{42} +9.23607 q^{43} +1.38197 q^{45} +(2.38197 - 7.33094i) q^{46} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-1.35410 - 4.16750i) q^{49} +(-0.954915 - 2.93893i) q^{50} +(3.23607 + 2.35114i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(1.11803 - 3.44095i) q^{53} +1.00000 q^{54} +1.61803 q^{56} +(-2.38197 + 7.33094i) q^{57} +(0.118034 - 0.0857567i) q^{58} +(4.30902 + 3.13068i) q^{59} +(0.427051 + 1.31433i) q^{60} +(-3.00000 - 9.23305i) q^{61} +(4.54508 + 3.30220i) q^{62} +(-1.30902 + 0.951057i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.70820 q^{65} -12.9443 q^{67} +(-1.23607 + 3.80423i) q^{68} +(-6.23607 + 4.53077i) q^{69} +(-1.80902 - 1.31433i) q^{70} +(1.85410 + 5.70634i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-4.50000 - 3.26944i) q^{73} +(-7.23607 + 5.25731i) q^{74} +(-0.954915 + 2.93893i) q^{75} -7.70820 q^{76} +1.23607 q^{78} +(0.0450850 - 0.138757i) q^{79} +(-1.11803 + 0.812299i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.38197 - 7.33094i) q^{82} +(0.190983 + 0.587785i) q^{83} +(-1.30902 - 0.951057i) q^{84} +(4.47214 - 3.24920i) q^{85} +(2.85410 - 8.78402i) q^{86} -0.145898 q^{87} +11.2361 q^{89} +(0.427051 - 1.31433i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(-6.23607 - 4.53077i) q^{92} +(-1.73607 - 5.34307i) q^{93} +(1.23607 + 3.80423i) q^{94} +(8.61803 + 6.26137i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.28115 + 7.02067i) q^{97} -4.38197 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} - 5 q^{5} - q^{6} - 3 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} + 6 q^{13} - 3 q^{14} - q^{16} + 4 q^{17} - q^{18} + 16 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{23} - q^{24}+ \cdots - 22 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 - 5 * q^5 - q^6 - 3 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 + 6 * q^13 - 3 * q^14 - q^16 + 4 * q^17 - q^18 + 16 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^23 - q^24 + 10 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^31 + 4 * q^32 - 16 * q^34 + 5 * q^35 - q^36 - 20 * q^37 - 14 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^45 + 14 * q^46 - 4 * q^47 - q^48 + 8 * q^49 - 15 * q^50 + 4 * q^51 - 4 * q^52 + 4 * q^54 + 2 * q^56 - 14 * q^57 - 4 * q^58 + 15 * q^59 - 5 * q^60 - 12 * q^61 + 7 * q^62 - 3 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 - 16 * q^69 - 5 * q^70 - 6 * q^71 - q^72 - 18 * q^73 - 20 * q^74 - 15 * q^75 - 4 * q^76 - 4 * q^78 - 11 * q^79 - q^81 - 14 * q^82 + 3 * q^83 - 3 * q^84 - 2 * q^86 - 14 * q^87 + 36 * q^89 - 5 * q^90 - 2 * q^91 - 16 * q^92 + 2 * q^93 - 4 * q^94 + 30 * q^95 - q^96 + 11 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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