LMFDB - Embedded newform 605.2.g.k.366.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.1
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.k.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.596764 + 0.433574i) q^{2} +(-0.868820 - 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.67784 + 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} +O(q^{10})$	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.868820 - 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.67784 + 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} -0.737640 q^{10} +4.09331 q^{12} +(2.79029 - 2.02726i) q^{13} +(-0.235096 - 0.723552i) q^{14} +(0.868820 - 2.67395i) q^{15} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(1.11803 - 3.44095i) q^{18} +(2.36979 + 7.29347i) q^{19} +(-1.17784 + 0.855749i) q^{20} +2.89979 q^{21} +2.45589 q^{23} +(-5.79842 + 4.21280i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.786174 + 2.41960i) q^{26} +(4.33283 + 3.14799i) q^{27} +(-1.21480 - 0.882602i) q^{28} +(1.83998 - 5.66289i) q^{29} +(0.640877 + 1.97242i) q^{30} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(-0.834404 + 0.606230i) q^{35} +(-2.20667 - 6.79144i) q^{36} +(1.84130 - 5.66694i) q^{37} +(-4.57646 - 3.32500i) q^{38} +(-7.84507 - 5.69978i) q^{39} +(0.787747 - 2.42443i) q^{40} +(-1.21637 - 3.74360i) q^{41} +(-1.73049 + 1.25727i) q^{42} +7.64941 q^{43} -4.90488 q^{45} +(-1.46558 + 1.06481i) q^{46} +(1.80557 + 5.55697i) q^{47} +(-0.896084 + 2.75786i) q^{48} +(4.80253 + 3.48924i) q^{49} +(-0.596764 - 0.433574i) q^{50} +(2.08362 - 6.41272i) q^{51} +(1.55168 + 4.77558i) q^{52} +(9.58526 - 6.96410i) q^{53} -3.95056 q^{54} +2.62920 q^{56} +(17.4435 - 12.6734i) q^{57} +(1.35725 + 4.17718i) q^{58} +(0.910456 - 2.80210i) q^{59} +(3.31156 + 2.40599i) q^{60} +(2.00666 + 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.56325 - 4.81120i) q^{63} +(-1.82774 + 1.32793i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(-2.13372 - 6.56693i) q^{69} +(0.235096 - 0.723552i) q^{70} +(-1.63676 - 1.18918i) q^{71} +(10.1156 + 7.34938i) q^{72} +(0.255207 - 0.785446i) q^{73} +(1.35822 + 4.18017i) q^{74} +(2.27460 - 1.65259i) q^{75} -11.1649 q^{76} +7.15293 q^{78} +(-9.77146 + 7.09938i) q^{79} +(-0.318714 - 0.980901i) q^{80} +(0.106048 - 0.326382i) q^{81} +(2.34901 + 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(-1.30460 + 4.01513i) q^{84} +(0.741089 + 2.28084i) q^{85} +(-4.56489 + 3.31659i) q^{86} -16.7409 q^{87} +8.16116 q^{89} +(2.92705 - 2.12663i) q^{90} +(1.09924 + 3.38312i) q^{91} +(-1.10489 + 3.40050i) q^{92} +(-8.38919 - 6.09510i) q^{93} +(-3.48685 - 2.53335i) q^{94} +(-2.36979 + 7.29347i) q^{95} +(-5.09058 - 15.6672i) q^{96} +(-1.97625 + 1.43583i) q^{97} -4.37882 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23} - 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} + 6 q^{28} + 9 q^{29} + 8 q^{30} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} - 15 q^{36} + 24 q^{37} - 21 q^{39} + 4 q^{40} - 8 q^{41} + 9 q^{42} + 38 q^{43} - 3 q^{46} + 5 q^{48} + q^{49} + 2 q^{50} - q^{51} + 28 q^{52} + 13 q^{53} - 16 q^{54} + 22 q^{56} + 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} - 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} + 30 q^{72} - 13 q^{73} - 20 q^{74} + 5 q^{75} - 16 q^{78} - 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} - 27 q^{83} - 28 q^{84} + 12 q^{85} - 3 q^{86} - 38 q^{87} - 16 q^{89} + 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} - 17 q^{94} + 15 q^{95} + 17 q^{96} + 24 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	−0.778432	−	0.627729i	$-0.783985\pi$
$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	0.356457	+	0.934312i	$0.383985\pi$
$3$	−0.868820	−	2.67395i	−0.501614	−	1.54381i	−0.806390	−	0.591384i	$-0.798582\pi$
$3$	−0.868820	−	2.67395i	−0.501614	−	1.54381i	0.304777	−	0.952424i	$-0.401418\pi$
$4$	−0.449894	+	1.38463i	−0.224947	+	0.692315i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	1.67784	+	1.21902i	0.684974	+	0.497663i
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	−0.993047	−	0.117717i	$-0.962442\pi$
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	0.872585	+	0.488463i	$0.162442\pi$
$8$	−0.787747	−	2.42443i	−0.278510	−	0.857167i
$9$	−3.96813	+	2.88301i	−1.32271	+	0.961005i
$10$	−0.737640			−0.233262
$11$		0			0
$11$		0			0
$12$	4.09331			1.18164
$13$	2.79029	−	2.02726i	0.773887	−	0.562262i	−0.129251	−	0.991612i	$-0.541257\pi$
$13$	2.79029	−	2.02726i	0.773887	−	0.562262i	0.903138	+	0.429350i	$0.141257\pi$
$14$	−0.235096	−	0.723552i	−0.0628321	−	0.193377i
$15$	0.868820	−	2.67395i	0.224328	−	0.690412i
$16$	−0.834404	−	0.606230i	−0.208601	−	0.151557i
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	0.797662	−	0.603105i	$-0.206070\pi$
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	−0.327095	+	0.944991i	$0.606070\pi$
$18$	1.11803	−	3.44095i	0.263523	−	0.811041i
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	0.724137	+	0.689656i	$0.242238\pi$
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	−0.180470	+	0.983581i	$0.557762\pi$
$20$	−1.17784	+	0.855749i	−0.263372	+	0.191351i
$21$	2.89979			0.632786
$22$		0			0
$23$	2.45589			0.512088			0.256044	−	0.966665i	$-0.417581\pi$
$23$	2.45589			0.512088			0.256044	+	0.966665i	$0.417581\pi$
$24$	−5.79842	+	4.21280i	−1.18360	+	0.859933i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.786174	+	2.41960i	−0.154181	+	0.474522i
$27$	4.33283	+	3.14799i	0.833854	+	0.605830i
$28$	−1.21480	−	0.882602i	−0.229575	−	0.166796i
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	−0.621663	−	0.783285i	$-0.713542\pi$
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	0.963339	−	0.268287i	$-0.0864575\pi$
$30$	0.640877	+	1.97242i	0.117008	+	0.360112i
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	−0.286654	−	0.958034i	$-0.592543\pi$
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	0.822564	+	0.568673i	$0.192543\pi$
$32$	5.85919			1.03577
$33$		0			0
$34$	−1.76902			−0.303384
$35$	−0.834404	+	0.606230i	−0.141040	+	0.102472i
$36$	−2.20667	−	6.79144i	−0.367779	−	1.13191i
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	−0.677814	−	0.735233i	$-0.737073\pi$
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	0.980523	−	0.196407i	$-0.0629273\pi$
$38$	−4.57646	−	3.32500i	−0.742401	−	0.539386i
$39$	−7.84507	−	5.69978i	−1.25622	−	0.912695i
$40$	0.787747	−	2.42443i	0.124554	−	0.383337i
$41$	−1.21637	−	3.74360i	−0.189965	−	0.584652i	0.810033	−	0.586384i	$-0.199449\pi$
$41$	−1.21637	−	3.74360i	−0.189965	−	0.584652i	−0.999999	+	0.00173135i	$0.999449\pi$
$42$	−1.73049	+	1.25727i	−0.267020	+	0.194001i
$43$	7.64941			1.16652			0.583262	−	0.812284i	$-0.301776\pi$
$43$	7.64941			1.16652			0.583262	+	0.812284i	$0.301776\pi$
$44$		0			0
$45$	−4.90488			−0.731176
$46$	−1.46558	+	1.06481i	−0.216089	+	0.156998i
$47$	1.80557	+	5.55697i	0.263369	+	0.810567i	0.992065	+	0.125729i	$0.0401270\pi$
$47$	1.80557	+	5.55697i	0.263369	+	0.810567i	−0.728695	+	0.684838i	$0.759873\pi$
$48$	−0.896084	+	2.75786i	−0.129339	+	0.398063i
$49$	4.80253	+	3.48924i	0.686076	+	0.498463i
$50$	−0.596764	−	0.433574i	−0.0843951	−	0.0613166i
$51$	2.08362	−	6.41272i	0.291765	−	0.897960i
$52$	1.55168	+	4.77558i	0.215179	+	0.662253i
$53$	9.58526	−	6.96410i	1.31664	−	0.956592i	0.316669	−	0.948536i	$-0.397436\pi$
$53$	9.58526	−	6.96410i	1.31664	−	0.956592i	0.999968	−	0.00805607i	$-0.00256435\pi$
$54$	−3.95056			−0.537603
$55$		0			0
$56$	2.62920			0.351341
$57$	17.4435	−	12.6734i	2.31044	−	1.67864i
$58$	1.35725	+	4.17718i	0.178215	+	0.548490i
$59$	0.910456	−	2.80210i	0.118531	−	0.364802i	−0.874136	−	0.485681i	$-0.838572\pi$
$59$	0.910456	−	2.80210i	0.118531	−	0.364802i	0.992667	+	0.120880i	$0.0385715\pi$
$60$	3.31156	+	2.40599i	0.427521	+	0.310612i
$61$	2.00666	+	1.45792i	0.256927	+	0.186668i	0.708791	−	0.705419i	$-0.249241\pi$
$61$	2.00666	+	1.45792i	0.256927	+	0.186668i	−0.451864	+	0.892087i	$0.649241\pi$
$62$	−0.840701	+	2.58741i	−0.106769	+	0.328602i
$63$	−1.56325	−	4.81120i	−0.196951	−	0.606154i
$64$	−1.82774	+	1.32793i	−0.228468	+	0.165992i
$65$	3.44899			0.427794
$66$		0			0
$67$	−6.14702			−0.750978			−0.375489	−	0.926827i	$-0.622525\pi$
$67$	−6.14702			−0.750978			−0.375489	+	0.926827i	$0.622525\pi$
$68$	−2.82471	+	2.05227i	−0.342546	+	0.248874i
$69$	−2.13372	−	6.56693i	−0.256870	−	0.790565i
$70$	0.235096	−	0.723552i	0.0280994	−	0.0864810i
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	0.486410	−	0.873731i	$-0.338306\pi$
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	−0.680658	+	0.732601i	$0.738306\pi$
$72$	10.1156	+	7.34938i	1.19213	+	0.866133i
$73$	0.255207	−	0.785446i	0.0298697	−	0.0919295i	−0.935010	−	0.354621i	$-0.884610\pi$
$73$	0.255207	−	0.785446i	0.0298697	−	0.0919295i	0.964880	+	0.262691i	$0.0846100\pi$
$74$	1.35822	+	4.18017i	0.157890	+	0.485934i
$75$	2.27460	−	1.65259i	0.262648	−	0.190825i
$76$	−11.1649			−1.28070
$77$		0			0
$78$	7.15293			0.809910
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.980958	−	0.194221i	$-0.937782\pi$
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.118417	+	0.992964i	$0.537782\pi$
$80$	−0.318714	−	0.980901i	−0.0356333	−	0.109668i
$81$	0.106048	−	0.326382i	0.0117831	−	0.0362647i
$82$	2.34901	+	1.70666i	0.259405	+	0.188469i
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	0.656972	−	0.753915i	$-0.271837\pi$
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	−0.514000	+	0.857790i	$0.671837\pi$
$84$	−1.30460	+	4.01513i	−0.142343	+	0.438087i
$85$	0.741089	+	2.28084i	0.0803824	+	0.247392i
$86$	−4.56489	+	3.31659i	−0.492245	+	0.357637i
$87$	−16.7409			−1.79481
$88$		0			0
$89$	8.16116			0.865081			0.432541	−	0.901614i	$-0.357617\pi$
$89$	8.16116			0.865081			0.432541	+	0.901614i	$0.357617\pi$
$90$	2.92705	−	2.12663i	0.308538	−	0.224166i
$91$	1.09924	+	3.38312i	0.115232	+	0.354647i
$92$	−1.10489	+	3.40050i	−0.115193	+	0.354526i
$93$	−8.38919	−	6.09510i	−0.869918	−	0.632032i
$94$	−3.48685	−	2.53335i	−0.359642	−	0.261295i
$95$	−2.36979	+	7.29347i	−0.243136	+	0.748294i
$96$	−5.09058	−	15.6672i	−0.519555	−	1.59903i
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	−0.683577	−	0.729879i	$-0.739577\pi$
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	0.482919	+	0.875665i	$0.339577\pi$
$98$	−4.37882			−0.442328
$99$		0			0
$100$	−1.45589			−0.145589
$101$	−6.08683	+	4.42234i	−0.605662	+	0.440039i	−0.847884	−	0.530182i	$-0.822124\pi$
$101$	−6.08683	+	4.42234i	−0.605662	+	0.440039i	0.242222	+	0.970221i	$0.422124\pi$
$102$	1.53696	+	4.73028i	0.152182	+	0.468367i
$103$	−2.93020	+	9.01821i	−0.288721	+	0.888591i	0.696538	+	0.717520i	$0.254723\pi$
$103$	−2.93020	+	9.01821i	−0.288721	+	0.888591i	−0.985259	+	0.171071i	$0.945277\pi$
$104$	−7.11301	−	5.16791i	−0.697488	−	0.506755i
$105$	2.34598	+	1.70445i	0.228944	+	0.166338i
$106$	−2.70068	+	8.31184i	−0.262313	+	0.807317i
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	0.996164	−	0.0875039i	$-0.0278890\pi$
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	−0.857347	+	0.514739i	$0.827889\pi$
$108$	−6.30811	+	4.58311i	−0.606998	+	0.441010i
$109$	5.32826			0.510355			0.255178	−	0.966894i	$-0.417866\pi$
$109$	5.32826			0.510355			0.255178	+	0.966894i	$0.417866\pi$
$110$		0			0
$111$	−16.7529			−1.59012
$112$	0.860587	−	0.625253i	0.0813179	−	0.0590809i
$113$	0.0942195	+	0.289978i	0.00886342	+	0.0272788i	0.955390	−	0.295346i	$-0.0954349\pi$
$113$	0.0942195	+	0.289978i	0.00886342	+	0.0272788i	−0.946527	+	0.322625i	$0.895435\pi$
$114$	−4.91476	+	15.1261i	−0.460310	+	1.41669i
$115$	1.98685	+	1.44353i	0.185275	+	0.134610i
$116$	7.01321	+	5.09540i	0.651160	+	0.473096i
$117$	−5.22760	+	16.0889i	−0.483292	+	1.48742i
$118$	0.671589	+	2.06694i	0.0618248	+	0.190277i
$119$	−2.00108	+	1.45387i	−0.183439	+	0.133276i
$120$	−7.16724			−0.654276
$121$		0			0
$122$	−1.82962			−0.165646
$123$	−8.95341	+	6.50503i	−0.807302	+	0.586539i
$124$	1.65930	+	5.10680i	0.149009	+	0.458604i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	3.01890	+	2.19336i	0.268945	+	0.195400i
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	0.0715199	−	0.997439i	$-0.477215\pi$
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	−0.926520	+	0.376245i	$0.877215\pi$
$128$	−3.10621	+	9.55992i	−0.274552	+	0.844985i
$129$	−6.64596	−	20.4542i	−0.585145	−	1.80089i
$130$	−2.05823	+	1.49539i	−0.180519	+	0.131155i
$131$	11.1875			0.977452			0.488726	−	0.872437i	$-0.337462\pi$
$131$	11.1875			0.977452			0.488726	+	0.872437i	$0.337462\pi$
$132$		0			0
$133$	−7.90945			−0.685837
$134$	3.66832	−	2.66519i	0.316894	−	0.230237i
$135$	1.65499	+	5.09355i	0.142439	+	0.438383i
$136$	1.88919	−	5.81432i	0.161996	−	0.498573i
$137$	3.46360	+	2.51645i	0.295915	+	0.214995i	0.725829	−	0.687875i	$-0.241456\pi$
$137$	3.46360	+	2.51645i	0.295915	+	0.214995i	−0.429914	+	0.902870i	$0.641456\pi$
$138$	4.12058	+	2.99378i	0.350767	+	0.254847i
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	−0.842228	−	0.539121i	$-0.818757\pi$
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	0.998264	+	0.0588913i	$0.0187565\pi$
$140$	−0.464011	−	1.42808i	−0.0392161	−	0.120695i
$141$	13.2904	−	9.65601i	1.11925	−	0.813183i
$142$	1.49235			0.125236
$143$		0			0
$144$	5.05879			0.421566
$145$	4.81714	−	3.49986i	0.400042	−	0.290647i
$146$	0.188251	+	0.579377i	0.0155798	+	0.0479495i
$147$	5.15754	−	15.8733i	0.425387	−	1.30921i
$148$	7.01823	+	5.09905i	0.576895	+	0.419139i
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	0.455269	−	0.890354i	$-0.349543\pi$
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	−0.706091	+	0.708121i	$0.749543\pi$
$150$	−0.640877	+	1.97242i	−0.0523274	+	0.161047i
$151$	7.52661	+	23.1645i	0.612507	+	1.88510i	0.433159	+	0.901317i	$0.357399\pi$
$151$	7.52661	+	23.1645i	0.612507	+	1.88510i	0.179348	+	0.983786i	$0.442601\pi$
$152$	15.8157	−	11.4908i	1.28283	−	0.932028i
$153$	−11.7629			−0.950978
$154$		0			0
$155$	3.68820			0.296243
$156$	11.4215	−	8.29823i	0.914455	−	0.664390i
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	0.999771	−	0.0214015i	$-0.00681284\pi$
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	−0.821411	+	0.570336i	$0.806813\pi$
$158$	2.75314	−	8.47330i	0.219028	−	0.674100i
$159$	−26.9495	−	19.5800i	−2.13724	−	1.55279i
$160$	4.74018	+	3.44395i	0.374744	+	0.272268i
$161$	−0.782725	+	2.40898i	−0.0616874	+	0.189854i
$162$	0.0782252	+	0.240753i	0.00614596	+	0.0189153i
$163$	−15.1198	+	10.9852i	−1.18428	+	0.860428i	−0.992648	−	0.121039i	$-0.961377\pi$
$163$	−15.1198	+	10.9852i	−1.18428	+	0.860428i	−0.191630	+	0.981467i	$0.561377\pi$
$164$	5.73074			0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	−0.314172	−	0.949366i	$-0.601727\pi$
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	0.805816	+	0.592166i	$0.201727\pi$
$168$	−2.28430	−	7.03035i	−0.176237	−	0.542403i
$169$	−0.341302	+	1.05042i	−0.0262540	+	0.0808014i
$170$	−1.43117	−	1.03980i	−0.109766	−	0.0797493i
$171$	−30.4308	−	22.1093i	−2.32710	−	1.69074i
$172$	−3.44142	+	10.5916i	−0.262406	+	0.807603i
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	−0.992093	−	0.125508i	$-0.959944\pi$
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	0.728848	−	0.684675i	$-0.240056\pi$
$174$	9.99037	−	7.25843i	0.757368	−	0.550260i
$175$	−1.03138			−0.0779650
$176$		0			0
$177$	−8.28370			−0.622641
$178$	−4.87028	+	3.53847i	−0.365043	+	0.265219i
$179$	0.452595	+	1.39295i	0.0338286	+	0.104114i	0.966545	−	0.256497i	$-0.0825684\pi$
$179$	0.452595	+	1.39295i	0.0338286	+	0.104114i	−0.932716	+	0.360611i	$0.882568\pi$
$180$	2.20667	−	6.79144i	0.164476	−	0.506204i
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	0.272357	−	0.962196i	$-0.412197\pi$
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	−0.830940	+	0.556362i	$0.812197\pi$
$182$	−2.12282	−	1.54232i	−0.157354	−	0.114324i
$183$	2.15499	−	6.63239i	0.159302	−	0.490280i
$184$	−1.93462	−	5.95414i	−0.142622	−	0.438945i
$185$	4.82059	−	3.50236i	0.354417	−	0.257499i
$186$	7.64904			0.560855
$187$		0			0
$188$	−8.50666			−0.620412
$189$	−4.46880	+	3.24677i	−0.325057	+	0.236168i
$190$	−1.74805	−	5.37996i	−0.126817	−	0.390303i
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	−0.988528	−	0.151038i	$-0.951738\pi$
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	0.888514	+	0.458850i	$0.151738\pi$
$192$	5.13881	+	3.73357i	0.370862	+	0.269447i
$193$	−18.3372	−	13.3227i	−1.31994	−	0.958992i	−0.999933	−	0.0115772i	$-0.996315\pi$
$193$	−18.3372	−	13.3227i	−1.31994	−	0.958992i	−0.320007	−	0.947415i	$-0.603685\pi$
$194$	0.556816	−	1.71370i	0.0399771	−	0.123037i
$195$	−2.99655	−	9.22244i	−0.214587	−	0.660432i
$196$	−6.99194	+	5.07994i	−0.499424	+	0.362853i
$197$	11.2080			0.798535			0.399267	−	0.916835i	$-0.369265\pi$
$197$	11.2080			0.798535			0.399267	+	0.916835i	$0.369265\pi$
$198$		0			0
$199$	−7.81979			−0.554330			−0.277165	−	0.960822i	$-0.589395\pi$
$199$	−7.81979			−0.554330			−0.277165	+	0.960822i	$0.589395\pi$
$200$	2.06235	−	1.49838i	0.145830	−	0.105952i
$201$	5.34065	+	16.4368i	0.376701	+	1.15937i
$202$	1.71499	−	5.27818i	0.120666	−	0.371372i
$203$	4.96830	+	3.60968i	0.348707	+	0.253350i
$204$	7.94184	+	5.77008i	0.556040	+	0.403987i
$205$	1.21637	−	3.74360i	0.0849550	−	0.261464i
$206$	−2.16143	−	6.65220i	−0.150594	−	0.463481i
$207$	−9.74527	+	7.08035i	−0.677343	+	0.492119i
$208$	−3.55722			−0.246649
$209$		0			0
$210$	−2.13900			−0.147605
$211$	−18.4189	+	13.3821i	−1.26801	+	0.921262i	−0.999121	−	0.0419098i	$-0.986656\pi$
$211$	−18.4189	+	13.3821i	−1.26801	+	0.921262i	−0.268887	+	0.963172i	$0.586656\pi$
$212$	5.33035	+	16.4051i	0.366090	+	1.12671i
$213$	−1.75775	+	5.40980i	−0.120439	+	0.370673i
$214$	−2.77303	−	2.01472i	−0.189560	−	0.137724i
$215$	6.18851	+	4.49621i	0.422053	+	0.306639i
$216$	4.21891	−	12.9845i	0.287061	−	0.883482i
$217$	1.17548	+	3.61776i	0.0797969	+	0.245589i
$218$	−3.17971	+	2.31020i	−0.215357	+	0.156466i
$219$	−2.32197			−0.156905
$220$		0			0
$221$	8.27142			0.556396
$222$	9.99752	−	7.26363i	0.670990	−	0.487503i
$223$	−4.95746	−	15.2575i	−0.331976	−	1.02172i	−0.968192	−	0.250207i	$-0.919501\pi$
$223$	−4.95746	−	15.2575i	−0.331976	−	1.02172i	0.636216	−	0.771511i	$-0.280499\pi$
$224$	−1.86741	+	5.74728i	−0.124771	+	0.384006i
$225$	−3.96813	−	2.88301i	−0.264542	−	0.192201i
$226$	−0.181954	−	0.132197i	−0.0121034	−	0.00879361i
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	−0.320809	−	0.947144i	$-0.603955\pi$
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	0.816257	−	0.577689i	$-0.196045\pi$
$228$	9.70030	+	29.8545i	0.642418	+	1.97716i
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	−0.109017	−	0.994040i	$-0.534770\pi$
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	0.911700	+	0.410856i	$0.134770\pi$
$230$	−1.81156			−0.119451
$231$		0			0
$232$	−15.1787			−0.996534
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	−0.242275	−	0.970208i	$-0.577894\pi$
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	0.847855	+	0.530228i	$0.177894\pi$
$234$	−3.85609	−	11.8678i	−0.252080	−	0.775823i
$235$	−1.80557	+	5.55697i	−0.117782	+	0.362497i
$236$	3.47026	+	2.52129i	0.225895	+	0.164122i
$237$	27.4730	+	19.9603i	1.78457	+	1.29656i
$238$	0.563811	−	1.73523i	0.0365465	−	0.112478i
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	−0.714181	−	0.699961i	$-0.753201\pi$
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	0.166358	−	0.986065i	$-0.446799\pi$
$240$	−2.34598	+	1.70445i	−0.151432	+	0.110022i
$241$	−10.9387			−0.704624			−0.352312	−	0.935883i	$-0.614604\pi$
$241$	−10.9387			−0.704624			−0.352312	+	0.935883i	$0.614604\pi$
$242$		0			0
$243$	15.1022			0.968804
$244$	−2.92147	+	2.12257i	−0.187028	+	0.135884i
$245$	1.83440	+	5.64571i	0.117196	+	0.360691i
$246$	2.52265	−	7.76393i	0.160839	−	0.495010i
$247$	21.3982	+	15.5467i	1.36154	+	0.989213i
$248$	−7.60635	−	5.52634i	−0.483004	−	0.350923i
$249$	1.39882	−	4.30511i	0.0886463	−	0.272825i
$250$	−0.227943	−	0.701538i	−0.0144164	−	0.0443691i
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	−0.933225	−	0.359291i	$-0.883018\pi$
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	0.0533238	+	0.998577i	$0.483018\pi$
$252$	7.36503			0.463953
$253$		0			0
$254$	8.78527			0.551237
$255$	5.45498	−	3.96328i	0.341604	−	0.248190i
$256$	−3.68753	−	11.3491i	−0.230471	−	0.709316i
$257$	5.71540	−	17.5902i	0.356517	−	1.09725i	−0.598608	−	0.801042i	$-0.704279\pi$
$257$	5.71540	−	17.5902i	0.356517	−	1.09725i	0.955125	−	0.296204i	$-0.0957207\pi$
$258$	12.8345	+	9.32479i	0.799039	+	0.580536i
$259$	4.97186	+	3.61227i	0.308936	+	0.224455i
$260$	−1.55168	+	4.77558i	−0.0962310	+	0.296169i
$261$	9.02489	+	27.7758i	0.558627	+	1.71928i
$262$	−6.67626	+	4.85059i	−0.412461	+	0.299670i
$263$	−3.69135			−0.227618			−0.113809	−	0.993503i	$-0.536305\pi$
$263$	−3.69135			−0.227618			−0.113809	+	0.993503i	$0.536305\pi$
$264$		0			0
$265$	11.8480			0.727819
$266$	4.72007	−	3.42933i	0.289406	−	0.210266i
$267$	−7.09058	−	21.8226i	−0.433937	−	1.33552i
$268$	2.76550	−	8.51135i	0.168930	−	0.519913i
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	0.805399	−	0.592733i	$-0.201951\pi$
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	−0.314841	+	0.949145i	$0.601951\pi$
$270$	−3.19607	−	2.32208i	−0.194507	−	0.141317i
$271$	−0.387400	+	1.19229i	−0.0235329	+	0.0724267i	−0.962133	−	0.272580i	$-0.912123\pi$
$271$	−0.387400	+	1.19229i	−0.0235329	+	0.0724267i	0.938600	+	0.345006i	$0.112123\pi$
$272$	−0.764345	−	2.35241i	−0.0463452	−	0.142636i
$273$	8.09125	−	5.87864i	0.489705	−	0.355791i
$274$	−3.15802			−0.190783
$275$		0			0
$276$	10.0527			0.605102
$277$	−6.54763	+	4.75713i	−0.393409	+	0.285828i	−0.766851	−	0.641825i	$-0.778177\pi$
$277$	−6.54763	+	4.75713i	−0.393409	+	0.285828i	0.373442	+	0.927654i	$0.378177\pi$
$278$	1.35699	+	4.17639i	0.0813870	+	0.250483i
$279$	−5.59017	+	17.2048i	−0.334675	+	1.03002i
$280$	2.12706	+	1.54540i	0.127116	+	0.0923554i
$281$	20.5250	+	14.9123i	1.22442	+	0.889591i	0.996459	−	0.0840804i	$-0.0267953\pi$
$281$	20.5250	+	14.9123i	1.22442	+	0.889591i	0.227958	+	0.973671i	$0.426795\pi$
$282$	−3.74461	+	11.5247i	−0.222988	+	0.686286i
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	0.943134	+	0.332412i	$0.107863\pi$
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	−0.567624	+	0.823288i	$0.692137\pi$
$284$	2.38294	−	1.73131i	0.141401	−	0.102734i
$285$	21.5613			1.27718
$286$		0			0
$287$	4.05977			0.239641
$288$	−23.2500	+	16.8921i	−1.37002	+	0.995378i
$289$	−3.47600	−	10.6980i	−0.204470	−	0.629295i
$290$	−1.35725	+	4.17718i	−0.0797003	+	0.245292i
$291$	5.55635	+	4.03693i	0.325719	+	0.236649i
$292$	0.972737	+	0.706734i	0.0569251	+	0.0413585i
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	−0.971426	−	0.237344i	$-0.923723\pi$
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	0.925407	+	0.378974i	$0.123723\pi$
$294$	3.80441	+	11.7088i	0.221878	+	0.682869i
$295$	2.38361	−	1.73179i	0.138779	−	0.100829i
$296$	−15.1896			−0.882878
$297$		0			0
$298$	2.79156			0.161711
$299$	6.85264	−	4.97873i	0.396298	−	0.287928i
$300$	1.26490	+	3.89297i	0.0730293	+	0.224761i
$301$	−2.43797	+	7.50331i	−0.140523	+	0.432484i
$302$	−14.5352	−	10.5604i	−0.836404	−	0.607683i
$303$	17.1135	+	12.4337i	0.983144	+	0.714296i
$304$	2.44416	−	7.52234i	0.140182	−	0.431436i
$305$	0.766476	+	2.35897i	0.0438883	+	0.135074i
$306$	7.01970	−	5.10011i	0.401289	−	0.291554i
$307$	−8.99273			−0.513242			−0.256621	−	0.966512i	$-0.582609\pi$
$307$	−8.99273			−0.513242			−0.256621	+	0.966512i	$0.582609\pi$
$308$		0			0
$309$	26.6601			1.51664
$310$	−2.20098	+	1.59911i	−0.125008	+	0.0908233i
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	−0.957380	−	0.288830i	$-0.906734\pi$
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	0.604767	−	0.796402i	$-0.293266\pi$
$312$	−7.63881	+	23.5098i	−0.432463	+	1.33098i
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	0.413368	−	0.910564i	$-0.364352\pi$
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	−0.738260	+	0.674516i	$0.764352\pi$
$314$	−4.31585	−	3.13565i	−0.243558	−	0.176955i
$315$	1.56325	−	4.81120i	0.0880793	−	0.271080i
$316$	−5.43390	−	16.7238i	−0.305681	−	0.940789i
$317$	−1.85526	+	1.34793i	−0.104202	+	0.0757071i	−0.638666	−	0.769484i	$-0.720513\pi$
$317$	−1.85526	+	1.34793i	−0.104202	+	0.0757071i	0.534464	+	0.845191i	$0.320513\pi$
$318$	24.5719			1.37792
$319$		0			0
$320$	−2.25922			−0.126294
$321$	10.5696	−	7.67924i	0.589936	−	0.428613i
$322$	−0.577370	−	1.77696i	−0.0321756	−	0.0990262i
$323$	−5.68327	+	17.4913i	−0.316226	+	0.973242i
$324$	0.404208	+	0.293674i	0.0224560	+	0.0163152i
$325$	2.79029	+	2.02726i	0.154777	+	0.112452i
$326$	4.26007	−	13.1111i	0.235943	−	0.726159i
$327$	−4.62930	−	14.2475i	−0.256001	−	0.787890i
$328$	−8.11793	+	5.89802i	−0.448237	+	0.325664i
$329$	−6.02629			−0.332240
$330$		0			0
$331$	15.3951			0.846192			0.423096	−	0.906085i	$-0.360943\pi$
$331$	15.3951			0.846192			0.423096	+	0.906085i	$0.360943\pi$
$332$	−1.89634	+	1.37777i	−0.104075	+	0.0756150i
$333$	9.03136	+	27.7957i	0.494915	+	1.52319i
$334$	−1.79010	+	5.50937i	−0.0979501	+	0.301459i
$335$	−4.97304	−	3.61313i	−0.271706	−	0.197406i
$336$	−2.41959	−	1.75794i	−0.132000	−	0.0959034i
$337$	6.02485	−	18.5426i	0.328195	−	1.01008i	−0.641783	−	0.766886i	$-0.721805\pi$
$337$	6.02485	−	18.5426i	0.328195	−	1.01008i	0.969978	−	0.243193i	$-0.0781949\pi$
$338$	−0.251758	−	0.774831i	−0.0136938	−	0.0421453i
$339$	0.693527	−	0.503877i	0.0376672	−	0.0273668i
$340$	−3.49153			−0.189355
$341$		0			0
$342$	27.7460			1.50033
$343$	−10.7941	+	7.84234i	−0.582825	+	0.423447i
$344$	−6.02580	−	18.5455i	−0.324889	−	0.999907i
$345$	2.13372	−	6.56693i	0.114876	−	0.353551i
$346$	6.68655	+	4.85806i	0.359471	+	0.261171i
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	0.539687	−	0.841866i	$-0.318543\pi$
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	−0.633889	+	0.773424i	$0.718543\pi$
$348$	7.53163	−	23.1800i	0.403738	−	1.24258i
$349$	7.74150	+	23.8259i	0.414393	+	1.27537i	0.912793	+	0.408423i	$0.133921\pi$
$349$	7.74150	+	23.8259i	0.414393	+	1.27537i	−0.498400	+	0.866947i	$0.666079\pi$
$350$	0.615490	−	0.447180i	0.0328993	−	0.0239028i
$351$	18.4717			0.985944
$352$		0			0
$353$	−23.2532			−1.23764			−0.618821	−	0.785532i	$-0.712389\pi$
$353$	−23.2532			−1.23764			−0.618821	+	0.785532i	$0.712389\pi$
$354$	4.94341	−	3.59160i	0.262739	−	0.190891i
$355$	−0.625187	−	1.92413i	−0.0331815	−	0.102122i
$356$	−3.67166	+	11.3002i	−0.194597	+	0.598909i
$357$	5.62616	+	4.08764i	0.297768	+	0.216341i
$358$	−0.874037	−	0.635025i	−0.0461943	−	0.0335621i
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	−0.999043	−	0.0437429i	$-0.986072\pi$
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	0.833954	+	0.551834i	$0.186072\pi$
$360$	3.86380	+	11.8916i	0.203640	+	0.626740i
$361$	−32.2075	+	23.4001i	−1.69513	+	1.23158i
$362$	6.85194			0.360130
$363$		0			0
$364$	−5.17891			−0.271448
$365$	0.668140	−	0.485432i	0.0349721	−	0.0254087i
$366$	1.58961	+	4.89232i	0.0830903	+	0.255726i
$367$	1.14622	−	3.52770i	0.0598322	−	0.184145i	−0.916673	−	0.399638i	$-0.869136\pi$
$367$	1.14622	−	3.52770i	0.0598322	−	0.184145i	0.976505	+	0.215493i	$0.0691359\pi$
$368$	−2.04920	−	1.48883i	−0.106822	−	0.0776107i
$369$	15.6196	+	11.3483i	0.813122	+	0.590768i
$370$	−1.35822	+	4.18017i	−0.0706104	+	0.217316i
$371$	3.77613	+	11.6217i	0.196047	+	0.603371i
$372$	12.2137	−	8.87378i	0.633251	−	0.460084i
$373$	9.34017			0.483616			0.241808	−	0.970324i	$-0.422260\pi$
$373$	9.34017			0.483616			0.241808	+	0.970324i	$0.422260\pi$
$374$		0			0
$375$	2.81156			0.145188
$376$	12.0502	−	8.75496i	0.621440	−	0.451503i
$377$	−6.34609	−	19.5312i	−0.326840	−	1.00591i
$378$	1.25910	−	3.87511i	0.0647611	−	0.199314i
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	0.772686	−	0.634789i	$-0.218913\pi$
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	−0.364947	+	0.931028i	$0.618913\pi$
$380$	−9.03261	−	6.56257i	−0.463363	−	0.336653i
$381$	−10.3476	+	31.8467i	−0.530124	+	1.63156i
$382$	−1.01958	−	3.13795i	−0.0521663	−	0.160552i
$383$	14.6002	−	10.6076i	0.746034	−	0.542025i	−0.148561	−	0.988903i	$-0.547464\pi$
$383$	14.6002	−	10.6076i	0.746034	−	0.542025i	0.894595	+	0.446878i	$0.147464\pi$
$384$	28.2615			1.44221
$385$		0			0
$386$	16.7194			0.850993
$387$	−30.3539	+	22.0534i	−1.54297	+	1.12104i
$388$	−1.09899	−	3.38235i	−0.0557929	−	0.171713i
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	−0.337844	−	0.941202i	$-0.609698\pi$
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	0.826546	−	0.562869i	$-0.190302\pi$
$390$	5.78684	+	4.20439i	0.293028	+	0.212897i
$391$	4.76490	+	3.46191i	0.240972	+	0.175076i
$392$	4.67626	−	14.3921i	0.236187	−	0.726909i
$393$	−9.71989	−	29.9147i	−0.490303	−	1.50900i
$394$	−6.68851	+	4.85948i	−0.336962	+	0.244817i
$395$	−12.0782			−0.607719
$396$		0			0
$397$	−10.6212			−0.533062			−0.266531	−	0.963826i	$-0.585877\pi$
$397$	−10.6212			−0.533062			−0.266531	+	0.963826i	$0.585877\pi$
$398$	4.66657	−	3.39046i	0.233914	−	0.169948i
$399$	6.87189	+	21.1495i	0.344025	+	1.05880i
$400$	0.318714	−	0.980901i	0.0159357	−	0.0490450i
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.983251	−	0.182258i	$-0.0583407\pi$
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.130503	+	0.991448i	$0.458341\pi$
$402$	−10.3137	−	7.49334i	−0.514400	−	0.373734i
$403$	3.93087	−	12.0980i	0.195811	−	0.602643i
$404$	−3.38488	−	10.4176i	−0.168404	−	0.518295i
$405$	0.277637	−	0.201715i	0.0137959	−	0.0100233i
$406$	−4.52997			−0.224818
$407$		0			0
$408$	−17.1886			−0.850961
$409$	11.6241	−	8.44540i	0.574774	−	0.417598i	−0.262062	−	0.965051i	$-0.584402\pi$
$409$	11.6241	−	8.44540i	0.574774	−	0.417598i	0.836836	+	0.547453i	$0.184402\pi$
$410$	0.897243	+	2.76143i	0.0443117	+	0.136377i
$411$	3.71963	−	11.4478i	0.183476	−	0.564681i
$412$	−11.1686	−	8.11448i	−0.550238	−	0.399772i
$413$	2.45840	+	1.78613i	0.120970	+	0.0878899i
$414$	2.74576	−	8.45060i	0.134947	−	0.415324i
$415$	0.497523	+	1.53122i	0.0244224	+	0.0751645i
$416$	16.3488	−	11.8781i	0.801568	−	0.582373i
$417$	−16.7378			−0.819652
$418$		0			0
$419$	−31.4707			−1.53744			−0.768722	−	0.639584i	$-0.779107\pi$
$419$	−31.4707			−1.53744			−0.768722	+	0.639584i	$0.779107\pi$
$420$	−3.41548	+	2.48149i	−0.166658	+	0.121084i
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	0.924856	+	0.380318i	$0.124185\pi$
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	−0.524679	+	0.851300i	$0.675815\pi$
$422$	5.18959	−	15.9719i	0.252625	−	0.777500i
$423$	−23.1855	−	16.8453i	−1.12732	−	0.819045i
$424$	−24.4348	−	17.7529i	−1.18666	−	0.862156i
$425$	−0.741089	+	2.28084i	−0.0359481	+	0.110637i
$426$	−1.29659	−	3.99049i	−0.0628199	−	0.193340i
$427$	−2.06963	+	1.50367i	−0.100156	+	0.0727679i
$428$	−6.76518			−0.327008
$429$		0			0
$430$	−5.64252			−0.272106
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	−0.660608	−	0.750731i	$-0.729701\pi$
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	0.509849	+	0.860264i	$0.329701\pi$
$432$	−1.70693	−	5.25338i	−0.0821246	−	0.252754i
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.0467895	−	0.998905i	$-0.485101\pi$
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.549288	−	0.835633i	$-0.314899\pi$
$434$	−2.27005	−	1.64929i	−0.108966	−	0.0791684i
$435$	−13.5437	−	9.84007i	−0.649370	−	0.471795i
$436$	−2.39715	+	7.37768i	−0.114803	+	0.353327i
$437$	5.81994	+	17.9119i	0.278406	+	0.856844i
$438$	1.38567	−	1.00675i	0.0662099	−	0.0481043i
$439$	−1.02336			−0.0488425			−0.0244212	−	0.999702i	$-0.507774\pi$
$439$	−1.02336			−0.0488425			−0.0244212	+	0.999702i	$0.507774\pi$
$440$		0			0
$441$	−29.1166			−1.38650
$442$	−4.93608	+	3.58627i	−0.234785	+	0.170582i
$443$	−4.96678	−	15.2862i	−0.235979	−	0.726268i	−0.996990	−	0.0775295i	$-0.975297\pi$
$443$	−4.96678	−	15.2862i	−0.235979	−	0.726268i	0.761011	−	0.648739i	$-0.224703\pi$
$444$	7.53703	−	23.1966i	0.357691	−	1.10086i
$445$	6.60252	+	4.79701i	0.312989	+	0.227400i
$446$	9.57368	+	6.95569i	0.453327	+	0.329361i
$447$	−3.28800	+	10.1194i	−0.155517	+	0.478633i
$448$	−0.720043	−	2.21607i	−0.0340188	−	0.104699i
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.370590	+	0.928797i	$0.620844\pi$
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.997857	+	0.0654379i	$0.979156\pi$
$450$	3.61803			0.170556
$451$		0			0
$452$	−0.443901			−0.0208793
$453$	55.4016	−	40.2516i	2.60299	−	1.89119i
$454$	5.50625	+	16.9465i	0.258421	+	0.795338i
$455$	−1.09924	+	3.38312i	−0.0515332	+	0.158603i
$456$	−44.4669	−	32.3071i	−2.08235	−	1.51292i
$457$	−20.3488	−	14.7842i	−0.951875	−	0.691578i	−0.000625413	−	1.00000i	$-0.500199\pi$
$457$	−20.3488	−	14.7842i	−0.951875	−	0.691578i	−0.951250	+	0.308422i	$0.900199\pi$
$458$	−3.42241	+	10.5331i	−0.159919	+	0.492179i
$459$	3.96903	+	12.2154i	0.185259	+	0.570167i
$460$	−2.89263	+	2.10162i	−0.134870	+	0.0979886i
$461$	−6.65631			−0.310015			−0.155008	−	0.987913i	$-0.549540\pi$
$461$	−6.65631			−0.310015			−0.155008	+	0.987913i	$0.549540\pi$
$462$		0			0
$463$	38.7730			1.80194			0.900968	−	0.433886i	$-0.142858\pi$
$463$	38.7730			1.80194			0.900968	+	0.433886i	$0.142858\pi$
$464$	−4.96830	+	3.60968i	−0.230648	+	0.167575i
$465$	−3.20438	−	9.86208i	−0.148600	−	0.457343i
$466$	−2.60447	+	8.01573i	−0.120650	+	0.371321i
$467$	−18.2429	−	13.2542i	−0.844179	−	0.613332i	0.0793559	−	0.996846i	$-0.474714\pi$
$467$	−18.2429	−	13.2542i	−0.844179	−	0.613332i	−0.923535	+	0.383514i	$0.874714\pi$
$468$	−19.9253	−	14.4766i	−0.921048	−	0.669180i
$469$	1.95914	−	6.02961i	0.0904647	−	0.278422i
$470$	−1.33186	−	4.09904i	−0.0614341	−	0.189075i
$471$	16.4501	−	11.9517i	0.757982	−	0.550706i
$472$	−7.51071			−0.345708
$473$		0			0
$474$	−25.0492			−1.15055
$475$	−6.20420	+	4.50761i	−0.284668	+	0.206823i
$476$	−1.11280	−	3.42484i	−0.0510051	−	0.156977i
$477$	−17.9579	+	55.2689i	−0.822238	+	2.53059i
$478$	16.3553	+	11.8828i	0.748075	+	0.543509i
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	0.557216	−	0.830368i	$-0.311870\pi$
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	−0.617538	+	0.786541i	$0.711870\pi$
$480$	5.09058	−	15.6672i	0.232352	−	0.715107i
$481$	−6.35063	−	19.5452i	−0.289564	−	0.891186i
$482$	6.52782	−	4.74274i	0.297334	−	0.216026i
$483$	7.12155			0.324042
$484$		0			0
$485$	−2.44278			−0.110921
$486$	−9.01242	+	6.54790i	−0.408811	+	0.297019i
$487$	0.324560	+	0.998894i	0.0147072	+	0.0452642i	0.958141	−	0.286297i	$-0.0924245\pi$
$487$	0.324560	+	0.998894i	0.0147072	+	0.0452642i	−0.943434	+	0.331562i	$0.892425\pi$
$488$	1.95390	−	6.01349i	0.0884490	−	0.272218i
$489$	42.5104	+	30.8856i	1.92239	+	1.39669i
$490$	−3.54254	−	2.57381i	−0.160036	−	0.116273i
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	−0.805944	−	0.591992i	$-0.798342\pi$
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	0.999986	−	0.00520928i	$-0.00165817\pi$
$492$	−4.97898	−	15.3237i	−0.224470	−	0.690847i
$493$	11.5525	−	8.39341i	0.520300	−	0.378020i
$494$	−19.5103			−0.877811
$495$		0			0
$496$	−3.80394			−0.170802
$497$	1.68812	−	1.22649i	0.0757226	−	0.0550157i
$498$	1.03182	+	3.17562i	0.0462371	+	0.142303i
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	−0.756131	−	0.654420i	$-0.772913\pi$
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	0.996381	−	0.0849943i	$-0.0270872\pi$
$500$	−1.17784	−	0.855749i	−0.0526745	−	0.0382702i
$501$	−17.8631	−	12.9783i	−0.798063	−	0.579827i
$502$	3.92772	−	12.0883i	0.175303	−	0.539526i
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	−0.818502	−	0.574503i	$-0.805195\pi$
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	0.324498	−	0.945887i	$-0.394805\pi$
$504$	−10.4330	+	7.58000i	−0.464722	+	0.337640i
$505$	−7.52373			−0.334802
$506$		0			0
$507$	3.10530			0.137911
$508$	14.0280	−	10.1919i	0.622392	−	0.452194i
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	0.964635	−	0.263590i	$-0.0849065\pi$
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	−0.935340	+	0.353750i	$0.884906\pi$
$510$	−1.53696	+	4.73028i	−0.0680577	+	0.209460i
$511$	0.689106	+	0.500665i	0.0304843	+	0.0221481i
$512$	−9.14306	−	6.64282i	−0.404070	−	0.293574i
$513$	−12.6918	+	39.0614i	−0.560358	+	1.72461i
$514$	4.21591	+	12.9752i	0.185956	+	0.572313i
$515$	−7.67135	+	5.57356i	−0.338040	+	0.245601i
$516$	31.3115			1.37841
$517$		0			0
$518$	−4.53321			−0.199178
$519$	−25.4862	+	18.5168i	−1.11872	+	0.812797i
$520$	−2.71693	−	8.36185i	−0.119145	−	0.366691i
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	−0.999506	−	0.0314326i	$-0.989993\pi$
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	0.827093	+	0.562065i	$0.189993\pi$
$522$	−17.4286	−	12.6626i	−0.762828	−	0.554227i
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	0.923983	−	0.382434i	$-0.124914\pi$
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	−0.0781901	+	0.996938i	$0.524914\pi$
$524$	−5.03317	+	15.4905i	−0.219875	+	0.676705i
$525$	0.896084	+	2.75786i	0.0391083	+	0.120363i
$526$	2.20286	−	1.60047i	0.0960493	−	0.0697839i
$527$	8.84510			0.385299
$528$		0			0
$529$	−16.9686			−0.737766
$530$	−7.07047	+	5.13700i	−0.307122	+	0.223137i
$531$	4.46567	+	13.7439i	0.193794	+	0.596436i
$532$	3.55841	−	10.9517i	0.154277	−	0.474815i
$533$	−10.9833	−	7.97983i	−0.475739	−	0.345645i
$534$	13.6931	+	9.94862i	0.592558	+	0.430519i
$535$	−1.43593	+	4.41935i	−0.0620808	+	0.191065i
$536$	4.84229	+	14.9030i	0.209155	+	0.643713i
$537$	3.33145	−	2.42044i	0.143763	−	0.104450i
$538$	−7.33590			−0.316273
$539$		0			0
$540$	−7.79726			−0.335540
$541$	1.06726	−	0.775410i	0.0458851	−	0.0333375i	−0.564606	−	0.825360i	$-0.690972\pi$
$541$	1.06726	−	0.775410i	0.0458851	−	0.0333375i	0.610491	+	0.792023i	$0.290972\pi$
$542$	−0.285762	−	0.879484i	−0.0122745	−	0.0377771i
$543$	−8.07047	+	24.8384i	−0.346337	+	1.06592i
$544$	11.3680	+	8.25932i	0.487398	+	0.354116i
$545$	4.31066	+	3.13188i	0.184648	+	0.134155i
$546$	−2.27974	+	7.01631i	−0.0975638	+	0.300270i
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	0.870403	−	0.492341i	$-0.163859\pi$
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	−0.993561	+	0.113298i	$0.963859\pi$
$548$	−5.04261	+	3.66367i	−0.215410	+	0.156504i
$549$	−12.1659			−0.519228
$550$		0			0
$551$	45.6625			1.94529
$552$	−14.2403	+	10.3461i	−0.606105	+	0.440361i
$553$	−3.84949	−	11.8475i	−0.163697	−	0.503807i
$554$	1.84482	−	5.67776i	0.0783788	−	0.241225i
$555$	−13.5534	−	9.84711i	−0.575309	−	0.417987i
$556$	7.01190	+	5.09444i	0.297371	+	0.216052i
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	0.268850	+	0.963182i	$0.413356\pi$
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	−0.783648	+	0.621205i	$0.786644\pi$
$558$	−4.12353	−	12.6909i	−0.174563	−	0.537250i
$559$	21.3441	−	15.5074i	0.902759	−	0.655893i
$560$	1.06374			0.0449514
$561$		0			0
$562$	−18.7141			−0.789407
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	−0.192508	−	0.981295i	$-0.561662\pi$
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	0.873779	+	0.486323i	$0.161662\pi$
$564$	7.39076	+	22.7464i	0.311207	+	0.957797i
$565$	−0.0942195	+	0.289978i	−0.00396384	+	0.0121995i
$566$	−12.1993	−	8.86330i	−0.512774	−	0.372552i
$567$	0.286349	+	0.208045i	0.0120255	+	0.00873707i
$568$	−1.59373	+	4.90499i	−0.0668713	+	0.205809i
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	0.879412	+	0.476061i	$0.157936\pi$
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	−0.431637	+	0.902047i	$0.642064\pi$
$570$	−12.8670	+	9.34843i	−0.538940	+	0.391563i
$571$	−3.15090			−0.131861			−0.0659306	−	0.997824i	$-0.521002\pi$
$571$	−3.15090			−0.131861			−0.0659306	+	0.997824i	$0.521002\pi$
$572$		0			0
$573$	12.5760			0.525370
$574$	−2.42273	+	1.76021i	−0.101123	+	0.0734699i
$575$	0.758911	+	2.33569i	0.0316488	+	0.0974049i
$576$	3.42427	−	10.5388i	0.142678	−	0.439117i
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	0.0233590	−	0.999727i	$-0.492564\pi$
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	−0.943579	+	0.331148i	$0.892564\pi$
$578$	6.71273	+	4.87709i	0.279213	+	0.202860i
$579$	−19.6927	+	60.6079i	−0.818400	+	2.51878i
$580$	2.67881	+	8.24453i	0.111231	+	0.342335i
$581$	−1.34340	+	0.976041i	−0.0557338	+	0.0404930i
$582$	−5.06614			−0.209998
$583$		0			0
$584$	−2.10530			−0.0871180
$585$	−13.6860	+	9.94348i	−0.565848	+	0.411112i
$586$	−0.581043	−	1.78827i	−0.0240027	−	0.0738726i
$587$	−14.2667	+	43.9082i	−0.588848	+	1.81229i	−0.00561158	+	0.999984i	$0.501786\pi$
$587$	−14.2667	+	43.9082i	−0.588848	+	1.81229i	−0.583236	+	0.812303i	$0.698214\pi$
$588$	19.6583	+	14.2826i	0.810694	+	0.589003i
$589$	22.8823	+	16.6250i	0.942850	+	0.685020i
$590$	−0.671589	+	2.06694i	−0.0276489	+	0.0850945i
$591$	−9.73771	−	29.9696i	−0.400556	−	1.23278i
$592$	−4.97186	+	3.61227i	−0.204342	+	0.148463i
$593$	−39.4265			−1.61905			−0.809525	−	0.587085i	$-0.800275\pi$
$593$	−39.4265			−1.61905			−0.809525	+	0.587085i	$0.800275\pi$
$594$		0			0
$595$	−2.47347			−0.101402
$596$	4.45746	−	3.23853i	0.182585	−	0.132656i
$597$	6.79399	+	20.9098i	0.278060	+	0.855780i
$598$	−1.93075	+	5.94225i	−0.0789544	+	0.242997i
$599$	−0.848455	−	0.616438i	−0.0346669	−	0.0251870i	0.570317	−	0.821425i	$-0.306820\pi$
$599$	−0.848455	−	0.616438i	−0.0346669	−	0.0251870i	−0.604984	+	0.796238i	$0.706820\pi$
$600$	−5.79842	−	4.21280i	−0.236719	−	0.171987i
$601$	−8.42065	+	25.9161i	−0.343485	+	1.05714i	0.618904	+	0.785466i	$0.287577\pi$
$601$	−8.42065	+	25.9161i	−0.343485	+	1.05714i	−0.962390	+	0.271673i	$0.912423\pi$
$602$	−1.79835	−	5.53475i	−0.0732952	−	0.225579i
$603$	24.3921	−	17.7219i	0.993325	−	0.721693i
$604$	−35.4605			−1.44287
$605$		0			0
$606$	−15.6036			−0.633854
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	−0.166492	−	0.986043i	$-0.553244\pi$
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	0.886334	+	0.463047i	$0.153244\pi$
$608$	13.8851	+	42.7338i	0.563114	+	1.73309i
$609$	5.33556	−	16.4212i	0.216208	−	0.665420i
$610$	−1.48019	−	1.07542i	−0.0599313	−	0.0435426i
$611$	16.3035	+	11.8452i	0.659569	+	0.479205i
$612$	5.29208	−	16.2873i	0.213920	−	0.658377i
$613$	−3.27313	−	10.0736i	−0.132200	−	0.406871i	0.862944	−	0.505300i	$-0.168618\pi$
$613$	−3.27313	−	10.0736i	−0.132200	−	0.406871i	−0.995144	+	0.0984293i	$0.968618\pi$
$614$	5.36653	−	3.89901i	0.216576	−	0.157351i
$615$	−11.0670			−0.446265
$616$		0			0
$617$	4.60402			0.185351			0.0926755	−	0.995696i	$-0.470458\pi$
$617$	4.60402			0.185351			0.0926755	+	0.995696i	$0.470458\pi$
$618$	−15.9098	+	11.5591i	−0.639985	+	0.464976i
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	0.865645	+	0.500657i	$0.166908\pi$
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	−0.406043	+	0.913854i	$0.633092\pi$
$620$	−1.65930	+	5.10680i	−0.0666390	+	0.205094i
$621$	10.6409	+	7.73110i	0.427006	+	0.310238i
$622$	12.0088	+	8.72489i	0.481508	+	0.349836i
$623$	−2.60108	+	8.00529i	−0.104210	+	0.320725i
$624$	3.09058	+	9.51183i	0.123722	+	0.380778i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	5.24081			0.209465
$627$		0			0
$628$	−10.5291			−0.420157
$629$	11.5608	−	8.39942i	0.460960	−	0.334907i
$630$	1.15312	+	3.54893i	0.0459413	+	0.141393i
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	0.673875	+	0.738845i	$0.264628\pi$
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	−0.979459	+	0.201644i	$0.935372\pi$
$632$	24.9094	+	18.0977i	0.990843	+	0.719890i
$633$	51.7858	+	37.6246i	2.05830	+	1.49544i
$634$	0.522727	−	1.60879i	0.0207601	−	0.0638931i
$635$	−3.68038	−	11.3270i	−0.146051	−	0.449500i
$636$	39.2355	−	28.5062i	1.55579	−	1.13035i
$637$	20.4741			0.811213
$638$		0			0
$639$	9.92328			0.392559
$640$	−8.13215	+	5.90835i	−0.321452	+	0.233548i
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	−0.727374	−	0.686241i	$-0.759260\pi$
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	0.185096	−	0.982720i	$-0.440740\pi$
$642$	−2.97801	+	9.16538i	−0.117533	+	0.361729i
$643$	−20.9220	−	15.2007i	−0.825082	−	0.599457i	0.0930818	−	0.995658i	$-0.470328\pi$
$643$	−20.9220	−	15.2007i	−0.825082	−	0.599457i	−0.918164	+	0.396201i	$0.870328\pi$
$644$	−2.98341	−	2.16757i	−0.117563	−	0.0854143i
$645$	6.64596	−	20.4542i	0.261685	−	0.805382i
$646$	−4.19221	−	12.9023i	−0.164940	−	0.507634i
$647$	−15.7649	+	11.4539i	−0.619782	+	0.450298i	−0.852845	−	0.522163i	$-0.825125\pi$
$647$	−15.7649	+	11.4539i	−0.619782	+	0.450298i	0.233063	+	0.972462i	$0.425125\pi$
$648$	−0.874831			−0.0343666
$649$		0			0
$650$	−2.54411			−0.0997883
$651$	8.65244	−	6.28636i	0.339116	−	0.246382i
$652$	−8.40814	−	25.8776i	−0.329288	−	1.01344i
$653$	−5.16979	+	15.9110i	−0.202310	+	0.622645i	0.797504	+	0.603314i	$0.206153\pi$
$653$	−5.16979	+	15.9110i	−0.202310	+	0.622645i	−0.999813	+	0.0193305i	$0.993847\pi$
$654$	8.93996	+	6.49526i	0.349580	+	0.253985i
$655$	9.05084	+	6.57582i	0.353646	+	0.256939i
$656$	−1.25454	+	3.86108i	−0.0489815	+	0.150750i
$657$	1.25176	+	3.85251i	0.0488357	+	0.150301i
$658$	3.59627	−	2.61284i	0.140197	−	0.101859i
$659$	1.66127			0.0647137			0.0323569	−	0.999476i	$-0.489699\pi$
$659$	1.66127			0.0647137			0.0323569	+	0.999476i	$0.489699\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$	−9.18724	+	6.67492i	−0.357072	+	0.259428i
$663$	−7.18637	−	22.1174i	−0.279096	−	0.858968i
$664$	1.26829	−	3.90338i	0.0492190	−	0.151481i
$665$	−6.39888	−	4.64906i	−0.248138	−	0.180283i
$666$	−17.4411	−	12.6717i	−0.675827	−	0.491017i
$667$	4.51879	−	13.9074i	0.174968	−	0.538497i
$668$	3.53314	+	10.8739i	0.136701	+	0.420723i
$669$	−36.4907	+	26.5120i	−1.41081	+	1.02501i
$670$	4.53429			0.175175
$671$		0			0
$672$	16.9904			0.655419
$673$	−31.2239	+	22.6855i	−1.20359	+	0.874462i	−0.994633	−	0.103462i	$-0.967008\pi$
$673$	−31.2239	+	22.6855i	−1.20359	+	0.874462i	−0.208961	+	0.977924i	$0.567008\pi$
$674$	4.44417	+	13.6778i	0.171183	+	0.526848i
$675$	−1.65499	+	5.09355i	−0.0637008	+	0.196051i
$676$	−1.30089	−	0.945154i	−0.0500343	−	0.0363521i
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.205855	−	0.978582i	$-0.565998\pi$
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.994300	+	0.106619i	$0.965998\pi$
$678$	−0.195404	+	0.601391i	−0.00750443	+	0.0230963i
$679$	−0.778549	−	2.39613i	−0.0298780	−	0.0919549i
$680$	4.94595	−	3.59344i	0.189669	−	0.137802i
$681$	−67.9167			−2.60257
$682$		0			0
$683$	−0.748158			−0.0286275			−0.0143137	−	0.999898i	$-0.504556\pi$
$683$	−0.748158			−0.0286275			−0.0143137	+	0.999898i	$0.504556\pi$
$684$	44.3038	−	32.1886i	1.69400	−	1.23076i
$685$	1.32298	+	4.07170i	0.0505484	+	0.155572i
$686$	3.04126	−	9.36005i	0.116116	−	0.357368i
$687$	−34.1515	−	24.8125i	−1.30296	−	0.946656i
$688$	−6.38270	−	4.63730i	−0.243338	−	0.176796i
$689$	12.6276	−	38.8637i	0.481073	−	1.48059i
$690$	1.57392	+	4.84403i	0.0599181	+	0.184409i
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	−0.665234	−	0.746635i	$-0.731668\pi$
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	0.504524	+	0.863398i	$0.331668\pi$
$692$	16.3128			0.620118
$693$		0			0
$694$	1.59998			0.0607342
$695$	4.81624	−	3.49920i	0.182690	−	0.132732i
$696$	13.1876	+	40.5873i	0.499875	+	1.53846i
$697$	2.91712	−	8.97796i	0.110494	−	0.340065i
$698$	−14.9501	−	10.8619i	−0.565871	−	0.411129i
$699$	−25.9895	−	18.8824i	−0.983011	−	0.714200i
$700$	0.464011	−	1.42808i	0.0175380	−	0.0539764i
$701$	4.37506	+	13.4650i	0.165244	+	0.508568i	0.999054	−	0.0434831i	$-0.0138455\pi$
$701$	4.37506	+	13.4650i	0.165244	+	0.508568i	−0.833811	+	0.552051i	$0.813845\pi$
$702$	−11.0232	+	8.00883i	−0.416044	+	0.302274i
$703$	45.6952			1.72343
$704$		0			0
$705$	16.4278			0.618706
$706$	13.8766	−	10.0820i	0.522255	−	0.379440i
$707$	−2.39792	−	7.38004i	−0.0901830	−	0.277555i
$708$	3.72678	−	11.4699i	0.140061	−	0.431064i
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	0.817744	−	0.575583i	$-0.195225\pi$
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	−0.294715	+	0.955585i	$0.595225\pi$
$710$	1.20734	+	0.877184i	0.0453107	+	0.0329201i
$711$	18.3068	−	56.3425i	0.686558	−	2.11301i
$712$	−6.42893	−	19.7862i	−0.240934	−	0.741519i
$713$	7.32792	−	5.32404i	0.274433	−	0.199387i
$714$	−5.12978			−0.191977
$715$		0			0
$716$	−2.13233			−0.0796891
$717$	−62.3393	+	45.2922i	−2.32811	+	1.69147i
$718$	−2.30733	−	7.10123i	−0.0861087	−	0.265015i
$719$	−8.20624	+	25.2562i	−0.306041	+	0.941897i	0.673246	+	0.739419i	$0.264900\pi$
$719$	−8.20624	+	25.2562i	−0.306041	+	0.941897i	−0.979287	+	0.202478i	$0.935100\pi$
$720$	4.09265	+	2.97348i	0.152524	+	0.110815i
$721$	−7.91208	−	5.74846i	−0.294661	−	0.214084i
$722$	9.07457	−	27.9286i	0.337720	−	1.03940i
$723$	9.50377	+	29.2496i	0.353449	+	1.08780i
$724$	10.9409	−	7.94905i	0.406617	−	0.295424i
$725$	5.95431			0.221138
$726$		0			0
$727$	44.1917			1.63898			0.819490	−	0.573094i	$-0.194257\pi$
$727$	44.1917			1.63898			0.819490	+	0.573094i	$0.194257\pi$
$728$	7.33622	−	5.33007i	0.271898	−	0.197546i
$729$	−13.4392	−	41.3616i	−0.497748	−	1.53191i
$730$	−0.188251	+	0.579377i	−0.00696748	+	0.0214437i
$731$	14.8414	+	10.7829i	0.548928	+	0.398819i
$732$	8.21389	+	5.96774i	0.303594	+	0.220574i
$733$	−7.71320	+	23.7388i	−0.284894	+	0.876812i	0.701537	+	0.712633i	$0.252498\pi$
$733$	−7.71320	+	23.7388i	−0.284894	+	0.876812i	−0.986431	+	0.164179i	$0.947502\pi$
$734$	0.845498	+	2.60218i	0.0312079	+	0.0960480i
$735$	13.5026	−	9.81022i	0.498051	−	0.361855i
$736$	14.3895			0.530404
$737$		0			0
$738$	−14.2415			−0.524237
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	−0.225135	−	0.974327i	$-0.572282\pi$
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	0.857070	+	0.515200i	$0.172282\pi$
$740$	2.68073	+	8.25043i	0.0985455	+	0.303292i
$741$	22.9800	−	70.7251i	0.844190	−	2.59815i
$742$	−7.29234	−	5.29820i	−0.267710	−	0.194503i
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	0.0311852	−	0.999514i	$-0.490072\pi$
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	−0.940957	+	0.338526i	$0.890072\pi$
$744$	−8.16862	+	25.1404i	−0.299476	+	0.921693i
$745$	−1.16946	−	3.59922i	−0.0428456	−	0.131865i
$746$	−5.57387	+	4.04965i	−0.204074	+	0.148268i
$747$	−7.89694			−0.288934
$748$		0			0
$749$	−4.79259			−0.175118
$750$	−1.67784	+	1.21902i	−0.0612660	+	0.0445123i
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	−0.963300	−	0.268427i	$-0.913496\pi$
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	0.621549	−	0.783375i	$-0.286504\pi$
$752$	1.86223	−	5.73134i	0.0679084	−	0.209001i
$753$	39.1939	+	28.4760i	1.42831	+	1.03772i
$754$	12.2554	+	8.90404i	0.446314	+	0.324266i
$755$	−7.52661	+	23.1645i	−0.273922	+	0.843044i
$756$	−2.48509	−	7.64833i	−0.0903820	−	0.278167i
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.0579427	−	0.998320i	$-0.481546\pi$
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.967364	+	0.253391i	$0.0815459\pi$
$758$	−7.23750			−0.262878
$759$		0			0
$760$	19.5493			0.709129
$761$	−2.17603	+	1.58098i	−0.0788809	+	0.0573104i	−0.626527	−	0.779400i	$-0.715524\pi$
$761$	−2.17603	+	1.58098i	−0.0788809	+	0.0573104i	0.547646	+	0.836710i	$0.315524\pi$
$762$	−7.63282	−	23.4914i	−0.276508	−	0.851004i
$763$	−1.69819	+	5.22650i	−0.0614787	+	0.189212i
$764$	−5.26842	−	3.82773i	−0.190605	−	0.138482i
$765$	−9.51642	−	6.91409i	−0.344067	−	0.249979i
$766$	−4.11365	+	12.6605i	−0.148632	+	0.457443i
$767$	−3.14015	−	9.66440i	−0.113384	−	0.348961i
$768$	−27.1431	+	19.7206i	−0.979441	+	0.711605i
$769$	32.5735			1.17463			0.587315	−	0.809359i	$-0.300185\pi$
$769$	32.5735			1.17463			0.587315	+	0.809359i	$0.300185\pi$
$770$		0			0
$771$	−52.0010			−1.87277
$772$	26.6969	−	19.3964i	0.960841	−	0.698092i
$773$	12.8748	+	39.6246i	0.463074	+	1.42520i	0.861388	+	0.507947i	$0.169595\pi$
$773$	12.8748	+	39.6246i	0.463074	+	1.42520i	−0.398314	+	0.917249i	$0.630405\pi$
$774$	8.55230	−	26.3213i	0.307406	−	0.946099i
$775$	2.98382	+	2.16787i	0.107182	+	0.0778722i
$776$	5.03787	+	3.66022i	0.180849	+	0.131394i
$777$	5.33938	−	16.4329i	0.191549	−	0.589528i
$778$	7.10990	+	21.8820i	0.254902	+	0.784509i
$779$	24.4213	−	17.7431i	0.874984	−	0.635713i
$780$	14.1178			0.505498
$781$		0			0
$782$	−4.34451			−0.155359
$783$	25.7990	−	18.7441i	0.921983	−	0.669860i
$784$	−1.89197	−	5.82288i	−0.0675703	−	0.207960i
$785$	−2.23484	+	6.87813i	−0.0797649	+	0.245491i
$786$	18.7707	+	13.6377i	0.669530	+	0.486442i
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.0664148	−	0.997792i	$-0.521156\pi$
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.969480	+	0.245170i	$0.921156\pi$
$788$	−5.04239	+	15.5189i	−0.179628	+	0.552838i
$789$	3.20712	+	9.87049i	0.114176	+	0.351399i
$790$	7.20782	−	5.23679i	0.256443	−	0.186317i
$791$	−0.314468			−0.0111812
$792$		0			0
$793$	8.55476			0.303789
$794$	6.33833	−	4.60507i	0.224939	−	0.163428i
$795$	−10.2938	−	31.6811i	−0.365084	−	1.12361i
$796$	3.51808	−	10.8275i	0.124695	−	0.383771i
$797$	25.6618	+	18.6444i	0.908987	+	0.660418i	0.940759	−	0.339077i	$-0.110115\pi$
$797$	25.6618	+	18.6444i	0.908987	+	0.660418i	−0.0317713	+	0.999495i	$0.510115\pi$
$798$	−13.2708	−	9.64178i	−0.469780	−	0.341315i
$799$	−4.33014	+	13.3268i	−0.153189	+	0.471468i
$800$	1.81059	+	5.57242i	0.0640140	+	0.197015i
$801$	−32.3845	+	23.5287i	−1.14425	+	0.831347i
$802$	−20.3352			−0.718061
$803$		0			0
$804$	−25.1617			−0.887384
$805$	−2.04920	+	1.48883i	−0.0722249	+	0.0524744i
$806$	2.89957	+	8.92396i	0.102133	+	0.314333i
$807$	8.64050	−	26.5927i	0.304160	−	0.936108i
$808$	15.5166	+	11.2734i	0.545870	+	0.396598i
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	0.460053	−	0.887891i	$-0.347830\pi$
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	−0.702270	+	0.711910i	$0.747830\pi$
$810$	−0.0782252	+	0.240753i	−0.00274855	+	0.00845918i
$811$	−2.79052	−	8.58832i	−0.0979882	−	0.301577i	0.890033	−	0.455897i	$-0.150681\pi$
$811$	−2.79052	−	8.58832i	−0.0979882	−	0.301577i	−0.988021	+	0.154320i	$0.950681\pi$
$812$	−7.23329	+	5.25529i	−0.253839	+	0.184425i
$813$	3.52472			0.123617
$814$		0			0
$815$	−18.6892			−0.654653
$816$	−5.62616	+	4.08764i	−0.196955	+	0.143096i
$817$	18.1275	+	55.7908i	0.634202	+	1.95187i
$818$	−3.27513	+	10.0798i	−0.114512	+	0.352432i
$819$	−14.1155	−	10.2555i	−0.493235	−	0.358356i
$820$	4.63627	+	3.36845i	0.161906	+	0.117631i
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	−0.00994979	−	0.999950i	$-0.503167\pi$
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	0.595806	−	0.803129i	$-0.296833\pi$
$822$	2.74375	+	8.44439i	0.0956993	+	0.294532i
$823$	−14.4486	+	10.4975i	−0.503646	+	0.365920i	−0.810408	−	0.585866i	$-0.800755\pi$
$823$	−14.4486	+	10.4975i	−0.503646	+	0.365920i	0.306762	+	0.951786i	$0.400755\pi$
$824$	24.1723			0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.478474	+	0.878102i	$0.658810\pi$
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.982981	+	0.183708i	$0.941190\pi$
$828$	−5.41934	−	16.6790i	−0.188335	−	0.579636i
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	0.787431	+	0.616402i	$0.211410\pi$
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	−0.999358	+	0.0358392i	$0.988590\pi$
$830$	−0.960800	−	0.698062i	−0.0333498	−	0.0242301i
$831$	18.4091	+	13.3750i	0.638603	+	0.463972i
$832$	−2.40786	+	7.41064i	−0.0834776	+	0.256918i
$833$	4.39930	+	13.5396i	0.152427	+	0.469121i
$834$	9.98849	−	7.25707i	0.345873	−	0.251292i
$835$	7.85328			0.271774
$836$		0			0
$837$	19.7528			0.682757
$838$	18.7806	−	13.6449i	0.648763	−	0.471354i
$839$	−1.27207	−	3.91502i	−0.0439166	−	0.135162i	0.926694	−	0.375817i	$-0.122638\pi$
$839$	−1.27207	−	3.91502i	−0.0439166	−	0.135162i	−0.970611	+	0.240655i	$0.922638\pi$
$840$	2.28430	−	7.03035i	0.0788158	−	0.242570i
$841$	−5.22128	−	3.79348i	−0.180044	−	0.130810i
$842$	−15.8567	−	11.5206i	−0.546458	−	0.397025i
$843$	22.0422	−	67.8389i	0.759173	−	2.33649i
$844$	−10.2427	−	31.5239i	−0.352569	−	1.08510i
$845$	−0.893540	+	0.649194i	−0.0307387	+	0.0223330i
$846$	21.1400			0.726807
$847$		0			0
$848$	−12.2198			−0.419630
$849$	46.4983	−	33.7830i	1.59582	−	1.15943i
$850$	−0.546657	−	1.68244i	−0.0187502	−	0.0577072i
$851$	4.52203	−	13.9174i	0.155013	−	0.477081i
$852$	−6.69978	−	4.86767i	−0.229531	−	0.166764i
$853$	4.45190	+	3.23449i	0.152430	+	0.110747i	0.661386	−	0.750046i	$-0.269968\pi$
$853$	4.45190	+	3.23449i	0.152430	+	0.110747i	−0.508956	+	0.860792i	$0.669968\pi$
$854$	0.583125	−	1.79468i	0.0199541	−	0.0614125i
$855$	−11.6235	−	35.7736i	−0.397516	−	1.22343i
$856$	9.58327	−	6.96265i	0.327549	−	0.237979i
$857$	26.9281			0.919847			0.459924	−	0.887959i	$-0.347877\pi$
$857$	26.9281			0.919847			0.459924	+	0.887959i	$0.347877\pi$
$858$		0			0
$859$	19.1519			0.653456			0.326728	−	0.945118i	$-0.394054\pi$
$859$	19.1519			0.653456			0.326728	+	0.945118i	$0.394054\pi$
$860$	−9.00976	+	6.54598i	−0.307230	+	0.223216i
$861$	−3.52721	−	10.8556i	−0.120207	−	0.369960i
$862$	0.881845	−	2.71404i	0.0300358	−	0.0924405i
$863$	−4.01394	−	2.91630i	−0.136636	−	0.0992720i	0.517368	−	0.855763i	$-0.326912\pi$
$863$	−4.01394	−	2.91630i	−0.136636	−	0.0992720i	−0.654004	+	0.756491i	$0.726912\pi$
$864$	25.3869	+	18.4447i	0.863679	+	0.627500i
$865$	3.46244	−	10.6563i	0.117726	−	0.362325i
$866$	9.14937	+	28.1589i	0.310908	+	0.956877i
$867$	−25.5860	+	18.5893i	−0.868946	+	0.631326i
$868$	−5.53810			−0.187975
$869$		0			0
$870$	12.3488			0.418663
$871$	−17.1520	+	12.4616i	−0.581172	+	0.422246i
$872$	−4.19732	−	12.9180i	−0.142139	−	0.437460i
$873$	3.70250	−	11.3951i	0.125311	−	0.385667i
$874$	−11.2393	−	8.16581i	−0.380174	−	0.276213i
$875$	−0.834404	−	0.606230i	−0.0282080	−	0.0204943i
$876$	1.04464	−	3.21508i	0.0352952	−	0.108627i
$877$	8.40691	+	25.8738i	0.283881	+	0.873696i	0.986732	+	0.162359i	$0.0519102\pi$
$877$	8.40691	+	25.8738i	0.283881	+	0.873696i	−0.702851	+	0.711338i	$0.748090\pi$
$878$	0.610706	−	0.443704i	0.0206103	−	0.0149743i
$879$	7.16686			0.241732
$880$		0			0
$881$	10.3570			0.348935			0.174467	−	0.984663i	$-0.444180\pi$
$881$	10.3570			0.348935			0.174467	+	0.984663i	$0.444180\pi$
$882$	17.3757	−	12.6242i	0.585071	−	0.425079i
$883$	2.28515	+	7.03296i	0.0769014	+	0.236678i	0.982116	−	0.188276i	$-0.0602901\pi$
$883$	2.28515	+	7.03296i	0.0769014	+	0.236678i	−0.905215	+	0.424954i	$0.860290\pi$
$884$	−3.72126	+	11.4529i	−0.125159	+	0.385201i
$885$	−6.70165	−	4.86903i	−0.225274	−	0.163671i
$886$	9.59168	+	6.96877i	0.322239	+	0.234120i
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	−0.812605	−	0.582815i	$-0.801951\pi$
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	0.999981	+	0.00612989i	$0.00195122\pi$
$888$	13.1970	+	40.6163i	0.442864	+	1.36299i
$889$	9.93772	−	7.22018i	0.333300	−	0.242157i
$890$	−6.02000			−0.201791
$891$		0			0
$892$	23.3563			0.782027
$893$	−36.2507	+	26.3377i	−1.21309	+	0.881358i
$894$	−2.42536	−	7.46450i	−0.0811163	−	0.249650i
$895$	−0.452595	+	1.39295i	−0.0151286	+	0.0465610i
$896$	−8.38734	−	6.09376i	−0.280201	−	0.203578i
$897$	−19.2666	−	13.9980i	−0.643293	−	0.467380i
$898$	8.16997	−	25.1446i	0.272635	−	0.839085i
$899$	−6.78623	−	20.8859i	−0.226334	−	0.696583i
$900$	5.77714	−	4.19734i	0.192571	−	0.139911i
$901$	28.4141			0.946612
$902$		0			0
$903$	22.1817			0.738160
$904$	0.628811	−	0.456858i	0.0209139	−	0.0151949i
$905$	−2.87046	−	8.83437i	−0.0954173	−	0.293664i
$906$	−15.6096	+	48.0414i	−0.518594	+	1.59607i
$907$	−21.2748	−	15.4570i	−0.706417	−	0.513242i	0.175599	−	0.984462i	$-0.443814\pi$
$907$	−21.2748	−	15.4570i	−0.706417	−	0.513242i	−0.882016	+	0.471220i	$0.843814\pi$
$908$	28.4521	+	20.6716i	0.944215	+	0.686013i
$909$	11.4036	−	35.0968i	0.378235	−	1.16409i
$910$	−0.810844	−	2.49552i	−0.0268792	−	0.0827258i
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	−0.901324	−	0.433146i	$-0.857403\pi$
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	0.133422	+	0.991059i	$0.457403\pi$
$912$	−22.2379			−0.736371
$913$		0			0
$914$	18.5535			0.613694
$915$	5.64185	−	4.09904i	0.186514	−	0.135510i
$916$	6.75483	+	20.7892i	0.223186	+	0.686896i
$917$	−3.56560	+	10.9738i	−0.117746	+	0.362386i
$918$	−7.66487	−	5.56885i	−0.252978	−	0.183799i
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.969692	−	0.244330i	$-0.0785681\pi$
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.0672794	+	0.997734i	$0.478568\pi$
$920$	1.93462	−	5.95414i	0.0637824	−	0.196302i
$921$	7.81306	+	24.0461i	0.257449	+	0.792347i
$922$	3.97224	−	2.88600i	0.130819	−	0.0950455i
$923$	−6.97781			−0.229677
$924$		0			0
$925$	5.95858			0.195917
$926$	−23.1383	+	16.8110i	−0.760373	+	0.552443i
$927$	−14.3722	−	44.2332i	−0.472046	−	1.45281i
$928$	10.7808	−	33.1799i	0.353898	−	1.08919i
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	0.484921	−	0.874558i	$-0.338848\pi$
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	−0.681905	+	0.731441i	$0.738848\pi$
$930$	6.18820	+	4.49599i	0.202919	+	0.147429i
$931$	−14.0677	+	43.2959i	−0.461050	+	1.41897i
$932$	5.14046	+	15.8207i	0.168381	+	0.518224i
$933$	−45.7722	+	33.2554i	−1.49851	+	1.08873i
$934$	16.6334			0.544260
$935$		0			0
$936$	43.1245			1.40957
$937$	−12.0834	+	8.77914i	−0.394749	+	0.286802i	−0.767399	−	0.641170i	$-0.778449\pi$
$937$	−12.0834	+	8.77914i	−0.394749	+	0.286802i	0.372650	+	0.927972i	$0.378449\pi$
$938$	1.44514	+	4.44768i	0.0471855	+	0.145222i
$939$	−6.17282	+	18.9980i	−0.201442	+	0.619975i
$940$	−6.88203	−	5.00009i	−0.224467	−	0.163085i
$941$	−42.3447	−	30.7652i	−1.38040	−	1.00292i	−0.996843	−	0.0793986i	$-0.974700\pi$
$941$	−42.3447	−	30.7652i	−1.38040	−	1.00292i	−0.383554	−	0.923518i	$-0.625300\pi$
$942$	−4.63488	+	14.2647i	−0.151013	+	0.464769i
$943$	−2.98727	−	9.19386i	−0.0972788	−	0.299393i
$944$	−2.45840	+	1.78613i	−0.0800142	+	0.0581337i
$945$	−5.52373			−0.179687
$946$		0			0
$947$	−3.69553			−0.120088			−0.0600442	−	0.998196i	$-0.519124\pi$
$947$	−3.69553			−0.120088			−0.0600442	+	0.998196i	$0.519124\pi$
$948$	−39.9976	+	29.0600i	−1.29906	+	0.943825i
$949$	−0.880206	−	2.70899i	−0.0285727	−	0.0879377i
$950$	1.74805	−	5.37996i	0.0567144	−	0.174549i
$951$	5.21618	+	3.78978i	0.169146	+	0.122892i
$952$	5.10116	+	3.70621i	0.165329	+	0.120119i
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	0.464211	+	0.885724i	$0.346338\pi$
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	−0.896171	+	0.443709i	$0.853662\pi$
$954$	−13.2465	−	40.7685i	−0.428871	−	1.31993i
$955$	−3.61870	+	2.62914i	−0.117098	+	0.0850770i
$956$	39.9011			1.29049
$957$		0			0
$958$	1.20373			0.0388907
$959$	−3.57229	+	2.59542i	−0.115355	+	0.0838104i
$960$	1.96285	+	6.04104i	0.0633508	+	0.194974i
$961$	−5.37602	+	16.5457i	−0.173420	+	0.533732i
$962$	12.2641	+	8.91041i	0.395411	+	0.287283i
$963$	−18.4390	−	13.3967i	−0.594189	−	0.431704i
$964$	4.92126	−	15.1461i	0.158503	−	0.487822i
$965$	−7.00418	−	21.5567i	−0.225473	−	0.693933i
$966$	−4.24988	+	3.08772i	−0.136738	+	0.0993457i
$967$	29.2144			0.939471			0.469736	−	0.882807i	$-0.344349\pi$
$967$	29.2144			0.939471			0.469736	+	0.882807i	$0.344349\pi$
$968$		0			0
$969$	51.7087			1.66112
$970$	1.45776	−	1.05913i	0.0468060	−	0.0340065i
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	−0.992402	−	0.123035i	$-0.960737\pi$
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	0.730552	−	0.682857i	$-0.239263\pi$
$972$	−6.79437	+	20.9109i	−0.217929	+	0.670718i
$973$	4.96737	+	3.60901i	0.159247	+	0.115699i
$974$	−0.626780	−	0.455382i	−0.0200833	−	0.0145914i
$975$	2.99655	−	9.22244i	0.0959664	−	0.295354i
$976$	−0.790528	−	2.43300i	−0.0253042	−	0.0778783i
$977$	12.8176	−	9.31251i	0.410070	−	0.297934i	−0.363560	−	0.931571i	$-0.618439\pi$
$977$	12.8176	−	9.31251i	0.410070	−	0.297934i	0.773630	+	0.633637i	$0.218439\pi$
$978$	−38.7598			−1.23940
$979$		0			0
$980$	−8.64252			−0.276075
$981$	−21.1432	+	15.3615i	−0.675051	+	0.490454i
$982$	3.17163	+	9.76126i	0.101211	+	0.311494i
$983$	10.8477	−	33.3858i	0.345988	−	1.06484i	−0.615064	−	0.788477i	$-0.710870\pi$
$983$	10.8477	−	33.3858i	0.345988	−	1.06484i	0.961053	−	0.276365i	$-0.0891300\pi$
$984$	22.8240	+	16.5826i	0.727604	+	0.528635i
$985$	9.06744	+	6.58788i	0.288913	+	0.209907i
$986$	−3.25497	+	10.0178i	−0.103659	+	0.319031i
$987$	5.23576	+	16.1140i	0.166656	+	0.512915i
$988$	−31.1534	+	22.6342i	−0.991120	+	0.720091i
$989$	18.7861			0.597363
$990$		0			0
$991$	18.9700			0.602600			0.301300	−	0.953529i	$-0.402579\pi$
$991$	18.9700			0.602600			0.301300	+	0.953529i	$0.402579\pi$
$992$	17.4828	−	12.7020i	0.555078	−	0.403288i
$993$	−13.3756	−	41.1658i	−0.424461	−	1.30636i
$994$	−0.475634	+	1.46385i	−0.0150862	+	0.0464306i
$995$	−6.32635	−	4.59636i	−0.200559	−	0.145714i
$996$	5.33167	+	3.87369i	0.168940	+	0.122742i
$997$	−9.31213	+	28.6598i	−0.294918	+	0.907665i	0.688331	+	0.725397i	$0.258344\pi$
$997$	−9.31213	+	28.6598i	−0.294918	+	0.907665i	−0.983249	+	0.182268i	$0.941656\pi$
$998$	3.95876	+	12.1838i	0.125312	+	0.385672i
$999$	25.8175	−	18.7575i	0.816830	−	0.593462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.k.366.1		8
11.2	odd	10		605.2.a.j.1.2		4
11.3	even	5		605.2.g.e.511.2		8
11.4	even	5	inner	605.2.g.k.81.1		8
11.5	even	5		605.2.g.e.251.2		8
11.6	odd	10		605.2.g.m.251.1		8
11.7	odd	10		55.2.g.b.26.2	✓	8
11.8	odd	10		605.2.g.m.511.1		8
11.9	even	5		605.2.a.k.1.3		4
11.10	odd	2		55.2.g.b.36.2	yes	8
33.2	even	10		5445.2.a.bp.1.3		4
33.20	odd	10		5445.2.a.bi.1.2		4
33.29	even	10		495.2.n.e.136.1		8
33.32	even	2		495.2.n.e.91.1		8
44.7	even	10		880.2.bo.h.81.2		8
44.31	odd	10		9680.2.a.cm.1.4		4
44.35	even	10		9680.2.a.cn.1.4		4
44.43	even	2		880.2.bo.h.641.2		8
55.7	even	20		275.2.z.a.224.2		16
55.9	even	10		3025.2.a.w.1.2		4
55.18	even	20		275.2.z.a.224.3		16
55.24	odd	10		3025.2.a.bd.1.3		4
55.29	odd	10		275.2.h.a.26.1		8
55.32	even	4		275.2.z.a.124.3		16
55.43	even	4		275.2.z.a.124.2		16
55.54	odd	2		275.2.h.a.201.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	11.7	odd	10
55.2.g.b.36.2	yes	8	11.10	odd	2
275.2.h.a.26.1		8	55.29	odd	10
275.2.h.a.201.1		8	55.54	odd	2
275.2.z.a.124.2		16	55.43	even	4
275.2.z.a.124.3		16	55.32	even	4
275.2.z.a.224.2		16	55.7	even	20
275.2.z.a.224.3		16	55.18	even	20
495.2.n.e.91.1		8	33.32	even	2
495.2.n.e.136.1		8	33.29	even	10
605.2.a.j.1.2		4	11.2	odd	10
605.2.a.k.1.3		4	11.9	even	5
605.2.g.e.251.2		8	11.5	even	5
605.2.g.e.511.2		8	11.3	even	5
605.2.g.k.81.1		8	11.4	even	5	inner
605.2.g.k.366.1		8	1.1	even	1	trivial
605.2.g.m.251.1		8	11.6	odd	10
605.2.g.m.511.1		8	11.8	odd	10
880.2.bo.h.81.2		8	44.7	even	10
880.2.bo.h.641.2		8	44.43	even	2
3025.2.a.w.1.2		4	55.9	even	10
3025.2.a.bd.1.3		4	55.24	odd	10
5445.2.a.bi.1.2		4	33.20	odd	10
5445.2.a.bp.1.3		4	33.2	even	10
9680.2.a.cm.1.4		4	44.31	odd	10
9680.2.a.cn.1.4		4	44.35	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.868820 - 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.67784 + 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} +O(q^{10})\)	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.868820 - 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.67784 + 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} -0.737640 q^{10} +4.09331 q^{12} +(2.79029 - 2.02726i) q^{13} +(-0.235096 - 0.723552i) q^{14} +(0.868820 - 2.67395i) q^{15} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(1.11803 - 3.44095i) q^{18} +(2.36979 + 7.29347i) q^{19} +(-1.17784 + 0.855749i) q^{20} +2.89979 q^{21} +2.45589 q^{23} +(-5.79842 + 4.21280i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.786174 + 2.41960i) q^{26} +(4.33283 + 3.14799i) q^{27} +(-1.21480 - 0.882602i) q^{28} +(1.83998 - 5.66289i) q^{29} +(0.640877 + 1.97242i) q^{30} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(-0.834404 + 0.606230i) q^{35} +(-2.20667 - 6.79144i) q^{36} +(1.84130 - 5.66694i) q^{37} +(-4.57646 - 3.32500i) q^{38} +(-7.84507 - 5.69978i) q^{39} +(0.787747 - 2.42443i) q^{40} +(-1.21637 - 3.74360i) q^{41} +(-1.73049 + 1.25727i) q^{42} +7.64941 q^{43} -4.90488 q^{45} +(-1.46558 + 1.06481i) q^{46} +(1.80557 + 5.55697i) q^{47} +(-0.896084 + 2.75786i) q^{48} +(4.80253 + 3.48924i) q^{49} +(-0.596764 - 0.433574i) q^{50} +(2.08362 - 6.41272i) q^{51} +(1.55168 + 4.77558i) q^{52} +(9.58526 - 6.96410i) q^{53} -3.95056 q^{54} +2.62920 q^{56} +(17.4435 - 12.6734i) q^{57} +(1.35725 + 4.17718i) q^{58} +(0.910456 - 2.80210i) q^{59} +(3.31156 + 2.40599i) q^{60} +(2.00666 + 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.56325 - 4.81120i) q^{63} +(-1.82774 + 1.32793i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(-2.13372 - 6.56693i) q^{69} +(0.235096 - 0.723552i) q^{70} +(-1.63676 - 1.18918i) q^{71} +(10.1156 + 7.34938i) q^{72} +(0.255207 - 0.785446i) q^{73} +(1.35822 + 4.18017i) q^{74} +(2.27460 - 1.65259i) q^{75} -11.1649 q^{76} +7.15293 q^{78} +(-9.77146 + 7.09938i) q^{79} +(-0.318714 - 0.980901i) q^{80} +(0.106048 - 0.326382i) q^{81} +(2.34901 + 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(-1.30460 + 4.01513i) q^{84} +(0.741089 + 2.28084i) q^{85} +(-4.56489 + 3.31659i) q^{86} -16.7409 q^{87} +8.16116 q^{89} +(2.92705 - 2.12663i) q^{90} +(1.09924 + 3.38312i) q^{91} +(-1.10489 + 3.40050i) q^{92} +(-8.38919 - 6.09510i) q^{93} +(-3.48685 - 2.53335i) q^{94} +(-2.36979 + 7.29347i) q^{95} +(-5.09058 - 15.6672i) q^{96} +(-1.97625 + 1.43583i) q^{97} -4.37882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23} - 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} + 6 q^{28} + 9 q^{29} + 8 q^{30} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} - 15 q^{36} + 24 q^{37} - 21 q^{39} + 4 q^{40} - 8 q^{41} + 9 q^{42} + 38 q^{43} - 3 q^{46} + 5 q^{48} + q^{49} + 2 q^{50} - q^{51} + 28 q^{52} + 13 q^{53} - 16 q^{54} + 22 q^{56} + 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} - 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} + 30 q^{72} - 13 q^{73} - 20 q^{74} + 5 q^{75} - 16 q^{78} - 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} - 27 q^{83} - 28 q^{84} + 12 q^{85} - 3 q^{86} - 38 q^{87} - 16 q^{89} + 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} - 17 q^{94} + 15 q^{95} + 17 q^{96} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * q^98

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