LMFDB - Embedded newform 605.2.g.e.81.1

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.e.366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} +O(q^{10})$	\(q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} -2.09529 q^{10} +4.57255 q^{12} +(2.46735 + 1.79264i) q^{13} +(1.98595 - 6.11211i) q^{14} +(-0.591149 - 1.81937i) q^{15} +(2.48141 - 1.80285i) q^{16} +(-0.375259 + 0.272641i) q^{17} +(0.427051 + 1.31433i) q^{18} +(2.43988 - 7.50919i) q^{19} +(1.93376 + 1.40496i) q^{20} +5.86752 q^{21} -1.39026 q^{23} +(-1.26552 - 0.919451i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.97470 - 6.07750i) q^{26} +(3.62218 - 2.63167i) q^{27} +(-5.93120 + 4.30927i) q^{28} +(-1.15004 - 3.53947i) q^{29} +(-1.23863 + 3.81211i) q^{30} +(8.47564 + 6.15791i) q^{31} -8.06206 q^{32} +0.971892 q^{34} +(2.48141 + 1.80285i) q^{35} +(0.487169 - 1.49935i) q^{36} +(0.569992 + 1.75425i) q^{37} +(-13.3841 + 9.72412i) q^{38} +(4.72004 - 3.42931i) q^{39} +(-0.252684 - 0.777682i) q^{40} +(1.36203 - 4.19190i) q^{41} +(-9.94619 - 7.22633i) q^{42} +1.31478 q^{43} -0.659557 q^{45} +(2.35666 + 1.71222i) q^{46} +(-0.920927 + 2.83432i) q^{47} +(-1.81316 - 5.58034i) q^{48} +(-1.94781 + 1.41517i) q^{49} +(-1.69513 + 1.23158i) q^{50} +(0.274201 + 0.843905i) q^{51} +(-2.25268 + 6.93305i) q^{52} +(-3.38828 - 2.46173i) q^{53} -9.38118 q^{54} +2.50805 q^{56} +(-12.2196 - 8.87809i) q^{57} +(-2.40968 + 7.41623i) q^{58} +(0.869890 + 2.67725i) q^{59} +(3.69927 - 2.68768i) q^{60} +(-1.63209 + 1.18578i) q^{61} +(-6.78332 - 20.8769i) q^{62} +(0.625136 - 1.92397i) q^{63} +(8.70342 + 6.32340i) q^{64} +3.04981 q^{65} -6.75753 q^{67} +(-0.896964 - 0.651683i) q^{68} +(-0.821848 + 2.52939i) q^{69} +(-1.98595 - 6.11211i) q^{70} +(5.27637 - 3.83351i) q^{71} +(-0.436320 + 0.317005i) q^{72} +(3.05179 + 9.39245i) q^{73} +(1.19430 - 3.67568i) q^{74} +(-1.54765 - 1.12443i) q^{75} +18.8726 q^{76} -12.2245 q^{78} +(-9.35051 - 6.79354i) q^{79} +(0.947813 - 2.91707i) q^{80} +(-3.25817 - 10.0276i) q^{81} +(-7.47150 + 5.42836i) q^{82} +(7.21531 - 5.24223i) q^{83} +(4.33392 + 13.3384i) q^{84} +(-0.143336 + 0.441143i) q^{85} +(-2.22872 - 1.61926i) q^{86} -7.11945 q^{87} -6.76978 q^{89} +(1.11803 + 0.812299i) q^{90} +(-2.89065 + 8.89651i) q^{91} +(-1.02689 - 3.16043i) q^{92} +(16.2139 - 11.7801i) q^{93} +(5.05179 - 3.67034i) q^{94} +(-2.43988 - 7.50919i) q^{95} +(-4.76588 + 14.6679i) q^{96} +(-12.4219 - 9.02506i) q^{97} +5.04469 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + q^8 + 5 * q^9	$ 8 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + q^{8} + 5 q^{9} - 2 q^{10} + 16 q^{12} - 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} - 12 q^{17} - 10 q^{18} - 5 q^{19} + 2 q^{20} + 20 q^{21} + 10 q^{23} + 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} - 19 q^{28} - 21 q^{29} - 7 q^{30} + 15 q^{31} - 16 q^{32} + 4 q^{34} - q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} + 14 q^{39} - q^{40} - 3 q^{41} - 21 q^{42} + 38 q^{43} + 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} - 3 q^{50} - 6 q^{51} - 17 q^{52} - 2 q^{53} - 16 q^{54} + 22 q^{56} - 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} + 5 q^{62} + 30 q^{63} + 29 q^{64} - 2 q^{65} - 38 q^{67} + 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} - 5 q^{72} + 2 q^{73} + 20 q^{74} - 5 q^{75} - 16 q^{78} + 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} + 38 q^{83} + 17 q^{84} - 13 q^{85} + 2 q^{86} - 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} + 18 q^{94} + 5 q^{95} + 17 q^{96} - 56 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + q^8 + 5 * q^9 - 2 * q^10 + 16 * q^12 - 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 - 12 * q^17 - 10 * q^18 - 5 * q^19 + 2 * q^20 + 20 * q^21 + 10 * q^23 + 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 - 19 * q^28 - 21 * q^29 - 7 * q^30 + 15 * q^31 - 16 * q^32 + 4 * q^34 - q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 + 14 * q^39 - q^40 - 3 * q^41 - 21 * q^42 + 38 * q^43 + 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 - 3 * q^50 - 6 * q^51 - 17 * q^52 - 2 * q^53 - 16 * q^54 + 22 * q^56 - 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 + 5 * q^62 + 30 * q^63 + 29 * q^64 - 2 * q^65 - 38 * q^67 + 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 - 5 * q^72 + 2 * q^73 + 20 * q^74 - 5 * q^75 - 16 * q^78 + 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 + 38 * q^83 + 17 * q^84 - 13 * q^85 + 2 * q^86 - 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 + 18 * q^94 + 5 * q^95 + 17 * q^96 - 56 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.69513	−	1.23158i	−1.19864	−	0.870861i	−0.204487	−	0.978869i	$-0.565553\pi$
$2$	−1.69513	−	1.23158i	−1.19864	−	0.870861i	−0.994150	+	0.108009i	$0.965553\pi$
$3$	0.591149	−	1.81937i	0.341300	−	1.05041i	−0.622235	−	0.782830i	$-0.713775\pi$
$3$	0.591149	−	1.81937i	0.341300	−	1.05041i	0.963535	−	0.267582i	$-0.0862247\pi$
$4$	0.738630	+	2.27327i	0.369315	+	1.13663i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−3.24278	+	2.35601i	−1.32386	+	0.961839i
$7$	0.947813	+	2.91707i	0.358239	+	1.10255i	0.954107	+	0.299465i	$0.0968082\pi$
$7$	0.947813	+	2.91707i	0.358239	+	1.10255i	−0.595868	+	0.803083i	$0.703192\pi$
$8$	0.252684	−	0.777682i	0.0893373	−	0.274952i
$9$	−0.533593	−	0.387678i	−0.177864	−	0.129226i
$10$	−2.09529			−0.662590
$11$		0			0
$11$		0			0
$12$	4.57255			1.31998
$13$	2.46735	+	1.79264i	0.684320	+	0.497188i	0.874788	−	0.484506i	$-0.161001\pi$
$13$	2.46735	+	1.79264i	0.684320	+	0.497188i	−0.190468	+	0.981693i	$0.561001\pi$
$14$	1.98595	−	6.11211i	0.530766	−	1.63353i
$15$	−0.591149	−	1.81937i	−0.152634	−	0.469759i
$16$	2.48141	−	1.80285i	0.620351	−	0.450712i
$17$	−0.375259	+	0.272641i	−0.0910136	+	0.0661252i	−0.632361	−	0.774674i	$-0.717914\pi$
$17$	−0.375259	+	0.272641i	−0.0910136	+	0.0661252i	0.541348	+	0.840799i	$0.317914\pi$
$18$	0.427051	+	1.31433i	0.100657	+	0.309790i
$19$	2.43988	−	7.50919i	0.559747	−	1.72273i	−0.123317	−	0.992367i	$-0.539353\pi$
$19$	2.43988	−	7.50919i	0.559747	−	1.72273i	0.683065	−	0.730358i	$-0.260647\pi$
$20$	1.93376	+	1.40496i	0.432402	+	0.314158i
$21$	5.86752			1.28040
$22$		0			0
$23$	−1.39026			−0.289889			−0.144944	−	0.989440i	$-0.546300\pi$
$23$	−1.39026			−0.289889			−0.144944	+	0.989440i	$0.546300\pi$
$24$	−1.26552	−	0.919451i	−0.258322	−	0.187682i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−1.97470	−	6.07750i	−0.387270	−	1.19189i
$27$	3.62218	−	2.63167i	0.697089	−	0.506465i
$28$	−5.93120	+	4.30927i	−1.12089	+	0.814375i
$29$	−1.15004	−	3.53947i	−0.213558	−	0.657263i	−0.999253	−	0.0386491i	$-0.987695\pi$
$29$	−1.15004	−	3.53947i	−0.213558	−	0.657263i	0.785695	−	0.618614i	$-0.212305\pi$
$30$	−1.23863	+	3.81211i	−0.226142	+	0.695993i
$31$	8.47564	+	6.15791i	1.52227	+	1.10599i	0.960348	+	0.278804i	$0.0899380\pi$
$31$	8.47564	+	6.15791i	1.52227	+	1.10599i	0.561922	+	0.827190i	$0.310062\pi$
$32$	−8.06206			−1.42518
$33$		0			0
$34$	0.971892			0.166678
$35$	2.48141	+	1.80285i	0.419434	+	0.304737i
$36$	0.487169	−	1.49935i	0.0811948	−	0.249892i
$37$	0.569992	+	1.75425i	0.0937061	+	0.288398i	0.986914	−	0.161246i	$-0.0515511\pi$
$37$	0.569992	+	1.75425i	0.0937061	+	0.288398i	−0.893208	+	0.449643i	$0.851551\pi$
$38$	−13.3841	+	9.72412i	−2.17119	+	1.57746i
$39$	4.72004	−	3.42931i	0.755811	−	0.549129i
$40$	−0.252684	−	0.777682i	−0.0399529	−	0.122962i
$41$	1.36203	−	4.19190i	0.212714	−	0.654665i	−0.786594	−	0.617470i	$-0.788158\pi$
$41$	1.36203	−	4.19190i	0.212714	−	0.654665i	0.999308	−	0.0371953i	$-0.0118424\pi$
$42$	−9.94619	−	7.22633i	−1.53473	−	1.11505i
$43$	1.31478			0.200502			0.100251	−	0.994962i	$-0.468035\pi$
$43$	1.31478			0.200502			0.100251	+	0.994962i	$0.468035\pi$
$44$		0			0
$45$	−0.659557			−0.0983210
$46$	2.35666	+	1.71222i	0.347471	+	0.252453i
$47$	−0.920927	+	2.83432i	−0.134331	+	0.413428i	−0.995485	−	0.0949152i	$-0.969742\pi$
$47$	−0.920927	+	2.83432i	−0.134331	+	0.413428i	0.861154	+	0.508344i	$0.169742\pi$
$48$	−1.81316	−	5.58034i	−0.261707	−	0.805453i
$49$	−1.94781	+	1.41517i	−0.278259	+	0.202167i
$50$	−1.69513	+	1.23158i	−0.239727	+	0.174172i
$51$	0.274201	+	0.843905i	0.0383959	+	0.118170i
$52$	−2.25268	+	6.93305i	−0.312391	+	0.961441i
$53$	−3.38828	−	2.46173i	−0.465416	−	0.338144i	0.330236	−	0.943898i	$-0.392872\pi$
$53$	−3.38828	−	2.46173i	−0.465416	−	0.338144i	−0.795652	+	0.605754i	$0.792872\pi$
$54$	−9.38118			−1.27662
$55$		0			0
$56$	2.50805			0.335152
$57$	−12.2196	−	8.87809i	−1.61853	−	1.17593i
$58$	−2.40968	+	7.41623i	−0.316406	+	0.973799i
$59$	0.869890	+	2.67725i	0.113250	+	0.348548i	0.991578	−	0.129511i	$-0.0413407\pi$
$59$	0.869890	+	2.67725i	0.113250	+	0.348548i	−0.878328	+	0.478059i	$0.841341\pi$
$60$	3.69927	−	2.68768i	0.477574	−	0.346978i
$61$	−1.63209	+	1.18578i	−0.208967	+	0.151824i	−0.687346	−	0.726330i	$-0.741225\pi$
$61$	−1.63209	+	1.18578i	−0.208967	+	0.151824i	0.478379	+	0.878154i	$0.341225\pi$
$62$	−6.78332	−	20.8769i	−0.861482	−	2.65137i
$63$	0.625136	−	1.92397i	0.0787598	−	0.242398i
$64$	8.70342	+	6.32340i	1.08793	+	0.790426i
$65$	3.04981			0.378283
$66$		0			0
$67$	−6.75753			−0.825564			−0.412782	−	0.910830i	$-0.635443\pi$
$67$	−6.75753			−0.825564			−0.412782	+	0.910830i	$0.635443\pi$
$68$	−0.896964	−	0.651683i	−0.108773	−	0.0790281i
$69$	−0.821848	+	2.52939i	−0.0989389	+	0.304503i
$70$	−1.98595	−	6.11211i	−0.237366	−	0.730537i
$71$	5.27637	−	3.83351i	0.626190	−	0.454953i	−0.228888	−	0.973453i	$-0.573509\pi$
$71$	5.27637	−	3.83351i	0.626190	−	0.454953i	0.855078	+	0.518499i	$0.173509\pi$
$72$	−0.436320	+	0.317005i	−0.0514209	+	0.0373594i
$73$	3.05179	+	9.39245i	0.357185	+	1.09930i	0.954732	+	0.297469i	$0.0961424\pi$
$73$	3.05179	+	9.39245i	0.357185	+	1.09930i	−0.597546	+	0.801834i	$0.703858\pi$
$74$	1.19430	−	3.67568i	0.138835	−	0.427289i
$75$	−1.54765	−	1.12443i	−0.178707	−	0.129838i
$76$	18.8726			2.16483
$77$		0			0
$78$	−12.2245			−1.38416
$79$	−9.35051	−	6.79354i	−1.05201	−	0.764333i	−0.0794197	−	0.996841i	$-0.525307\pi$
$79$	−9.35051	−	6.79354i	−1.05201	−	0.764333i	−0.972594	+	0.232508i	$0.925307\pi$
$80$	0.947813	−	2.91707i	0.105969	−	0.326138i
$81$	−3.25817	−	10.0276i	−0.362019	−	1.11418i
$82$	−7.47150	+	5.42836i	−0.825089	+	0.599462i
$83$	7.21531	−	5.24223i	0.791983	−	0.575409i	−0.116568	−	0.993183i	$-0.537189\pi$
$83$	7.21531	−	5.24223i	0.791983	−	0.575409i	0.908551	+	0.417773i	$0.137189\pi$
$84$	4.33392	+	13.3384i	0.472870	+	1.45534i
$85$	−0.143336	+	0.441143i	−0.0155470	+	0.0478487i
$86$	−2.22872	−	1.61926i	−0.240329	−	0.174609i
$87$	−7.11945			−0.763285
$88$		0			0
$89$	−6.76978			−0.717595			−0.358797	−	0.933415i	$-0.616813\pi$
$89$	−6.76978			−0.717595			−0.358797	+	0.933415i	$0.616813\pi$
$90$	1.11803	+	0.812299i	0.117851	+	0.0856239i
$91$	−2.89065	+	8.89651i	−0.303023	+	0.932608i
$92$	−1.02689	−	3.16043i	−0.107060	−	0.329497i
$93$	16.2139	−	11.7801i	1.68130	−	1.22154i
$94$	5.05179	−	3.67034i	0.521053	−	0.378567i
$95$	−2.43988	−	7.50919i	−0.250327	−	0.770426i
$96$	−4.76588	+	14.6679i	−0.486415	+	1.49703i
$97$	−12.4219	−	9.02506i	−1.26126	−	0.916356i	−0.262437	−	0.964949i	$-0.584526\pi$
$97$	−12.4219	−	9.02506i	−1.26126	−	0.916356i	−0.998819	+	0.0485933i	$0.984526\pi$
$98$	5.04469			0.509591
$99$		0			0
$100$	2.39026			0.239026
$101$	9.49186	+	6.89624i	0.944476	+	0.686202i	0.949494	−	0.313786i	$-0.101597\pi$
$101$	9.49186	+	6.89624i	0.944476	+	0.686202i	−0.00501815	+	0.999987i	$0.501597\pi$
$102$	0.574532	−	1.76823i	0.0568872	−	0.175081i
$103$	4.29165	+	13.2083i	0.422868	+	1.30146i	0.905021	+	0.425368i	$0.139855\pi$
$103$	4.29165	+	13.2083i	0.422868	+	1.30146i	−0.482152	+	0.876087i	$0.660145\pi$
$104$	2.01756	−	1.46584i	0.197838	−	0.143738i
$105$	4.74692	−	3.44884i	0.463252	−	0.336572i
$106$	2.71174	+	8.34589i	0.263388	+	0.810625i
$107$	2.26231	−	6.96269i	0.218706	−	0.673108i	−0.780164	−	0.625576i	$-0.784864\pi$
$107$	2.26231	−	6.96269i	0.218706	−	0.673108i	0.998870	−	0.0475327i	$-0.0151358\pi$
$108$	8.65794	+	6.29036i	0.833111	+	0.605290i
$109$	7.43306			0.711958			0.355979	−	0.934494i	$-0.384147\pi$
$109$	7.43306			0.711958			0.355979	+	0.934494i	$0.384147\pi$
$110$		0			0
$111$	3.52859			0.334919
$112$	7.61093	+	5.52967i	0.719165	+	0.522504i
$113$	−0.938299	+	2.88779i	−0.0882677	+	0.271660i	−0.985441	−	0.170019i	$-0.945617\pi$
$113$	−0.938299	+	2.88779i	−0.0882677	+	0.271660i	0.897173	+	0.441679i	$0.145617\pi$
$114$	9.77976	+	30.0990i	0.915958	+	2.81903i
$115$	−1.12474	+	0.817172i	−0.104883	+	0.0762017i
$116$	7.19671	−	5.22872i	0.668198	−	0.485474i
$117$	−0.621596	−	1.91308i	−0.0574666	−	0.176864i
$118$	1.82268	−	5.60962i	0.167791	−	0.516407i
$119$	−1.15099	−	0.836242i	−0.105511	−	0.0766581i
$120$	−1.56426			−0.142797
$121$		0			0
$122$	4.22699			0.382693
$123$	−6.82145	−	4.95608i	−0.615070	−	0.446874i
$124$	−7.73823	+	23.8158i	−0.694914	+	2.13873i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−3.42922	+	2.49147i	−0.305499	+	0.221958i
$127$	−0.365350	+	0.265442i	−0.0324196	+	0.0235542i	−0.603877	−	0.797077i	$-0.706378\pi$
$127$	−0.365350	+	0.265442i	−0.0324196	+	0.0235542i	0.571457	+	0.820632i	$0.306378\pi$
$128$	−1.98299	−	6.10301i	−0.175273	−	0.539435i
$129$	0.777230	−	2.39207i	0.0684313	−	0.210610i
$130$	−5.16983	−	3.75610i	−0.453424	−	0.329432i
$131$	−0.629003			−0.0549563			−0.0274781	−	0.999622i	$-0.508748\pi$
$131$	−0.629003			−0.0549563			−0.0274781	+	0.999622i	$0.508748\pi$
$132$		0			0
$133$	24.2173			2.09991
$134$	11.4549	+	8.32246i	0.989551	+	0.718951i
$135$	1.38355	−	4.25813i	0.119077	−	0.366481i
$136$	0.117206	+	0.360724i	0.0100504	+	0.0309318i
$137$	−9.04756	+	6.57343i	−0.772985	+	0.561606i	−0.902865	−	0.429923i	$-0.858541\pi$
$137$	−9.04756	+	6.57343i	−0.772985	+	0.561606i	0.129880	+	0.991530i	$0.458541\pi$
$138$	4.50829	−	3.27547i	0.383771	−	0.278826i
$139$	0.733901	+	2.25872i	0.0622487	+	0.191582i	0.977345	−	0.211655i	$-0.0678852\pi$
$139$	0.733901	+	2.25872i	0.0622487	+	0.191582i	−0.915096	+	0.403236i	$0.867885\pi$
$140$	−2.26552	+	6.97254i	−0.191471	+	0.589287i
$141$	4.61227	+	3.35101i	0.388423	+	0.282206i
$142$	−13.6654			−1.14678
$143$		0			0
$144$	−2.02298			−0.168582
$145$	−3.01085	−	2.18751i	−0.250038	−	0.181663i
$146$	6.39440	−	19.6799i	0.529205	−	1.62872i
$147$	1.42327	+	4.38036i	0.117389	+	0.361286i
$148$	−3.56688	+	2.59149i	−0.293196	+	0.213019i
$149$	−7.05490	+	5.12569i	−0.577960	+	0.419913i	−0.837988	−	0.545688i	$-0.816268\pi$
$149$	−7.05490	+	5.12569i	−0.577960	+	0.419913i	0.260028	+	0.965601i	$0.416268\pi$
$150$	1.23863	+	3.81211i	0.101134	+	0.311258i
$151$	−3.68825	+	11.3513i	−0.300145	+	0.923753i	0.681299	+	0.732005i	$0.261415\pi$
$151$	−3.68825	+	11.3513i	−0.300145	+	0.923753i	−0.981444	+	0.191747i	$0.938585\pi$
$152$	−5.22324	−	3.79490i	−0.423660	−	0.307807i
$153$	0.305932			0.0247332
$154$		0			0
$155$	10.4765			0.841490
$156$	11.2821	+	8.19692i	0.903291	+	0.656279i
$157$	1.19754	−	3.68565i	0.0955741	−	0.294147i	−0.891829	−	0.452373i	$-0.850578\pi$
$157$	1.19754	−	3.68565i	0.0955741	−	0.294147i	0.987403	+	0.158226i	$0.0505776\pi$
$158$	7.48350	+	23.0318i	0.595355	+	1.83232i
$159$	−6.48177	+	4.70928i	−0.514037	+	0.373470i
$160$	−6.52234	+	4.73876i	−0.515637	+	0.374632i
$161$	−1.31770	−	4.05547i	−0.103850	−	0.319616i
$162$	−6.82682	+	21.0108i	−0.536366	+	1.65076i
$163$	8.03857	+	5.84036i	0.629629	+	0.457452i	0.856272	−	0.516526i	$-0.172775\pi$
$163$	8.03857	+	5.84036i	0.629629	+	0.457452i	−0.226643	+	0.973978i	$0.572775\pi$
$164$	10.5354			0.822674
$165$		0			0
$166$	−18.6871			−1.45040
$167$	11.2615	+	8.18198i	0.871443	+	0.633140i	0.930974	−	0.365086i	$-0.118960\pi$
$167$	11.2615	+	8.18198i	0.871443	+	0.633140i	−0.0595308	+	0.998226i	$0.518960\pi$
$168$	1.48263	−	4.56306i	0.114387	−	0.352048i
$169$	−1.14294	−	3.51761i	−0.0879185	−	0.270585i
$170$	0.786277	−	0.571264i	0.0603047	−	0.0438139i
$171$	−4.21305	+	3.06096i	−0.322180	+	0.234077i
$172$	0.971136	+	2.98885i	0.0740484	+	0.227898i
$173$	−3.34700	+	10.3010i	−0.254468	+	0.783171i	0.739466	+	0.673193i	$0.235078\pi$
$173$	−3.34700	+	10.3010i	−0.254468	+	0.783171i	−0.993934	+	0.109977i	$0.964922\pi$
$174$	12.0684	+	8.76819i	0.914901	+	0.664715i
$175$	3.06719			0.231857
$176$		0			0
$177$	5.38513			0.404771
$178$	11.4756	+	8.33754i	0.860136	+	0.624925i
$179$	7.02502	−	21.6208i	0.525075	−	1.61601i	−0.239093	−	0.970997i	$-0.576850\pi$
$179$	7.02502	−	21.6208i	0.525075	−	1.61601i	0.764168	−	0.645018i	$-0.223150\pi$
$180$	−0.487169	−	1.49935i	−0.0363114	−	0.111755i
$181$	−1.94028	+	1.40969i	−0.144220	+	0.104782i	−0.657556	−	0.753406i	$-0.728410\pi$
$181$	−1.94028	+	1.40969i	−0.144220	+	0.104782i	0.513336	+	0.858188i	$0.328410\pi$
$182$	15.8568	−	11.5207i	1.17539	−	0.853968i
$183$	1.19257	+	3.67034i	0.0881570	+	0.271319i
$184$	−0.351296	+	1.08118i	−0.0258979	+	0.0797054i
$185$	1.49226	+	1.08419i	0.109713	+	0.0797112i
$186$	−41.9927			−3.07906
$187$		0			0
$188$	−7.12340			−0.519527
$189$	11.1099	+	8.07181i	0.808126	+	0.587138i
$190$	−5.11227	+	15.7340i	−0.370883	+	1.14146i
$191$	5.32938	+	16.4022i	0.385621	+	1.18682i	0.936029	+	0.351923i	$0.114472\pi$
$191$	5.32938	+	16.4022i	0.385621	+	1.18682i	−0.550408	+	0.834896i	$0.685528\pi$
$192$	16.6496	−	12.0967i	1.20158	−	0.873001i
$193$	−2.09190	+	1.51986i	−0.150579	+	0.109402i	−0.660524	−	0.750805i	$-0.729666\pi$
$193$	−2.09190	+	1.51986i	−0.150579	+	0.109402i	0.509945	+	0.860207i	$0.329666\pi$
$194$	9.94165	+	30.5973i	0.713769	+	2.19676i
$195$	1.80289	−	5.54873i	0.129108	−	0.397353i
$196$	−4.65577	−	3.38262i	−0.332555	−	0.241615i
$197$	−0.144731			−0.0103116			−0.00515582	−	0.999987i	$-0.501641\pi$
$197$	−0.144731			−0.0103116			−0.00515582	+	0.999987i	$0.501641\pi$
$198$		0			0
$199$	−7.54177			−0.534622			−0.267311	−	0.963610i	$-0.586135\pi$
$199$	−7.54177			−0.534622			−0.267311	+	0.963610i	$0.586135\pi$
$200$	−0.661536	−	0.480634i	−0.0467776	−	0.0339859i
$201$	−3.99470	+	12.2944i	−0.281765	+	0.867183i
$202$	−7.59663	−	23.3800i	−0.534497	−	1.64501i
$203$	9.23485	−	6.70951i	0.648159	−	0.470915i
$204$	−1.71589	+	1.24667i	−0.120136	+	0.0872842i
$205$	−1.36203	−	4.19190i	−0.0951285	−	0.292775i
$206$	8.99226	−	27.6753i	0.626520	−	1.92823i
$207$	0.741831	+	0.538972i	0.0515608	+	0.0374611i
$208$	9.35435			0.648607
$209$		0			0
$210$	−12.2942			−0.848379
$211$	−1.83551	−	1.33357i	−0.126362	−	0.0918070i	0.522809	−	0.852450i	$-0.324884\pi$
$211$	−1.83551	−	1.33357i	−0.126362	−	0.0918070i	−0.649171	+	0.760643i	$0.724884\pi$
$212$	3.09349	−	9.52078i	0.212462	−	0.653890i
$213$	−3.85544	−	11.8658i	−0.264170	−	0.813033i
$214$	−12.4100	+	9.01642i	−0.848333	+	0.616350i
$215$	1.06368	−	0.772808i	0.0725423	−	0.0527051i
$216$	−1.13133	−	3.48188i	−0.0769774	−	0.236912i
$217$	−9.92973	+	30.5606i	−0.674074	+	2.07459i
$218$	−12.6000	−	9.15443i	−0.853379	−	0.620016i
$219$	18.8924			1.27663
$220$		0			0
$221$	−1.41464			−0.0951591
$222$	−5.98141	−	4.34575i	−0.401446	−	0.291667i
$223$	2.65127	−	8.15976i	0.177542	−	0.546418i	−0.822199	−	0.569201i	$-0.807253\pi$
$223$	2.65127	−	8.15976i	0.177542	−	0.546418i	0.999740	+	0.0227830i	$0.00725268\pi$
$224$	−7.64132	−	23.5176i	−0.510557	−	1.57133i
$225$	−0.533593	+	0.387678i	−0.0355729	+	0.0258452i
$226$	5.14709	−	3.73958i	0.342379	−	0.248753i
$227$	−1.91603	−	5.89692i	−0.127171	−	0.391392i	0.867119	−	0.498101i	$-0.165969\pi$
$227$	−1.91603	−	5.89692i	−0.127171	−	0.391392i	−0.994290	+	0.106708i	$0.965969\pi$
$228$	11.1565	−	34.3362i	0.738857	−	2.27397i
$229$	−18.7416	−	13.6166i	−1.23848	−	0.899808i	−0.240983	−	0.970529i	$-0.577470\pi$
$229$	−18.7416	−	13.6166i	−1.23848	−	0.899808i	−0.997496	+	0.0707216i	$0.977470\pi$
$230$	2.91300			0.192077
$231$		0			0
$232$	−3.04318			−0.199794
$233$	−22.5414	−	16.3773i	−1.47674	−	1.07291i	−0.978590	−	0.205818i	$-0.934014\pi$
$233$	−22.5414	−	16.3773i	−1.47674	−	1.07291i	−0.498146	−	0.867093i	$-0.665986\pi$
$234$	−1.30243	+	4.00846i	−0.0851423	+	0.262041i
$235$	0.920927	+	2.83432i	0.0600747	+	0.184891i
$236$	−5.44358	+	3.95499i	−0.354347	+	0.257448i
$237$	−17.8875	+	12.9960i	−1.16192	+	0.844182i
$238$	0.921171	+	2.83507i	0.0597107	+	0.183771i
$239$	5.03272	−	15.4891i	0.325540	−	1.00191i	−0.645657	−	0.763628i	$-0.723416\pi$
$239$	5.03272	−	15.4891i	0.325540	−	1.00191i	0.971196	−	0.238280i	$-0.0765837\pi$
$240$	−4.74692	−	3.44884i	−0.306412	−	0.222622i
$241$	−4.39063			−0.282826			−0.141413	−	0.989951i	$-0.545164\pi$
$241$	−4.39063			−0.282826			−0.141413	+	0.989951i	$0.545164\pi$
$242$		0			0
$243$	−6.73820			−0.432256
$244$	−3.90111	−	2.83432i	−0.249743	−	0.181449i
$245$	−0.743998	+	2.28979i	−0.0475323	+	0.146289i
$246$	5.45942	+	16.8024i	0.348080	+	1.07128i
$247$	19.4813	−	14.1540i	1.23956	−	0.900596i
$248$	6.93056	−	5.03534i	0.440091	−	0.319745i
$249$	−5.27222	−	16.2262i	−0.334114	−	1.02830i
$250$	−0.647481	+	1.99274i	−0.0409503	+	0.126032i
$251$	2.15739	+	1.56744i	0.136173	+	0.0989357i	0.653787	−	0.756679i	$-0.273179\pi$
$251$	2.15739	+	1.56744i	0.136173	+	0.0989357i	−0.517613	+	0.855615i	$0.673179\pi$
$252$	4.83545			0.304605
$253$		0			0
$254$	0.946229			0.0593717
$255$	0.717868	+	0.521562i	0.0449547	+	0.0326615i
$256$	2.49388	−	7.67536i	0.155867	−	0.479710i
$257$	−6.68486	−	20.5739i	−0.416990	−	1.28336i	−0.910459	−	0.413600i	$-0.864271\pi$
$257$	−6.68486	−	20.5739i	−0.416990	−	1.28336i	0.493469	−	0.869764i	$-0.335729\pi$
$258$	−4.26354	+	3.09764i	−0.265436	+	0.192851i
$259$	−4.57703	+	3.32541i	−0.284403	+	0.206631i
$260$	2.25268	+	6.93305i	0.139706	+	0.429969i
$261$	−0.758519	+	2.33448i	−0.0469512	+	0.144501i
$262$	1.06624	+	0.774670i	0.0658726	+	0.0478593i
$263$	−22.1392			−1.36516			−0.682581	−	0.730810i	$-0.739142\pi$
$263$	−22.1392			−1.36516			−0.682581	+	0.730810i	$0.739142\pi$
$264$		0			0
$265$	−4.18814			−0.257276
$266$	−41.0515	−	29.8257i	−2.51703	−	1.82873i
$267$	−4.00194	+	12.3167i	−0.244915	+	0.753771i
$268$	−4.99131	−	15.3617i	−0.304893	−	0.938364i
$269$	−16.7615	+	12.1780i	−1.02197	+	0.742503i	−0.966685	−	0.255967i	$-0.917606\pi$
$269$	−16.7615	+	12.1780i	−1.02197	+	0.742503i	−0.0552828	+	0.998471i	$0.517606\pi$
$270$	−7.58953	+	5.51412i	−0.461884	+	0.335578i
$271$	0.130749	+	0.402403i	0.00794242	+	0.0244443i	0.954949	−	0.296769i	$-0.0959093\pi$
$271$	0.130749	+	0.402403i	0.00794242	+	0.0244443i	−0.947007	+	0.321214i	$0.895909\pi$
$272$	−0.439638	+	1.35307i	−0.0266570	+	0.0820417i
$273$	14.4772	+	10.5183i	0.876202	+	0.636598i
$274$	23.4325			1.41561
$275$		0			0
$276$	−6.35702			−0.382648
$277$	−6.93534	−	5.03882i	−0.416704	−	0.302753i	0.359606	−	0.933104i	$-0.382911\pi$
$277$	−6.93534	−	5.03882i	−0.416704	−	0.302753i	−0.776310	+	0.630351i	$0.782911\pi$
$278$	1.53774	−	4.73267i	0.0922274	−	0.283847i
$279$	−2.13525	−	6.57164i	−0.127834	−	0.393434i
$280$	2.02905	−	1.47419i	0.121259	−	0.0880999i
$281$	−5.67208	+	4.12101i	−0.338368	+	0.245839i	−0.743973	−	0.668210i	$-0.767061\pi$
$281$	−5.67208	+	4.12101i	−0.338368	+	0.245839i	0.405605	+	0.914049i	$0.367061\pi$
$282$	−3.69134	−	11.3608i	−0.219816	−	0.676525i
$283$	−3.07570	+	9.46603i	−0.182831	+	0.562697i	−0.999904	−	0.0138373i	$-0.995595\pi$
$283$	−3.07570	+	9.46603i	−0.182831	+	0.562697i	0.817073	+	0.576534i	$0.195595\pi$
$284$	12.6119	+	9.16306i	0.748377	+	0.543728i
$285$	−15.1043			−0.894702
$286$		0			0
$287$	13.5190			0.798002
$288$	4.30186	+	3.12548i	0.253489	+	0.184171i
$289$	−5.18680	+	15.9633i	−0.305106	+	0.939020i
$290$	2.40968	+	7.41623i	0.141501	+	0.435496i
$291$	−23.7631	+	17.2649i	−1.39302	+	1.01209i
$292$	−19.0974	+	13.8751i	−1.11759	+	0.811978i
$293$	−6.74302	−	20.7529i	−0.393931	−	1.21240i	−0.929791	−	0.368089i	$-0.880012\pi$
$293$	−6.74302	−	20.7529i	−0.393931	−	1.21240i	0.535859	−	0.844307i	$-0.319988\pi$
$294$	2.98216	−	9.17815i	0.173923	−	0.535280i
$295$	2.27740	+	1.65463i	0.132596	+	0.0963363i
$296$	1.50828			0.0876670
$297$		0			0
$298$	18.2717			1.05845
$299$	−3.43025	−	2.49222i	−0.198377	−	0.144129i
$300$	1.41300	−	4.34876i	0.0815794	−	0.251076i
$301$	1.24617	+	3.83530i	0.0718278	+	0.221063i
$302$	20.2321	−	14.6995i	1.16423	−	0.845859i
$303$	18.1579	−	13.1925i	1.04314	−	0.757889i
$304$	−7.48357	−	23.0321i	−0.429212	−	1.32098i
$305$	−0.623402	+	1.91863i	−0.0356959	+	0.109861i
$306$	−0.518595	−	0.376781i	−0.0296461	−	0.0215391i
$307$	30.8674			1.76170			0.880849	−	0.473397i	$-0.156972\pi$
$307$	30.8674			1.76170			0.880849	+	0.473397i	$0.156972\pi$
$308$		0			0
$309$	26.5678			1.51139
$310$	−17.7590	−	12.9026i	−1.00864	−	0.732821i
$311$	−5.99957	+	18.4648i	−0.340204	+	1.04704i	0.623897	+	0.781507i	$0.285549\pi$
$311$	−5.99957	+	18.4648i	−0.340204	+	1.04704i	−0.964101	+	0.265535i	$0.914451\pi$
$312$	−1.47423	−	4.53722i	−0.0834619	−	0.256869i
$313$	−0.850657	+	0.618038i	−0.0480820	+	0.0349336i	−0.611567	−	0.791193i	$-0.709460\pi$
$313$	−0.850657	+	0.618038i	−0.0480820	+	0.0349336i	0.563485	+	0.826127i	$0.309460\pi$
$314$	−6.56916	+	4.77278i	−0.370719	+	0.269343i
$315$	−0.625136	−	1.92397i	−0.0352225	−	0.108404i
$316$	8.53698	−	26.2741i	0.480243	−	1.47804i
$317$	19.2800	+	14.0078i	1.08287	+	0.786754i	0.978182	−	0.207750i	$-0.0666142\pi$
$317$	19.2800	+	14.0078i	1.08287	+	0.786754i	0.104692	+	0.994505i	$0.466614\pi$
$318$	16.7873			0.941385
$319$		0			0
$320$	10.7580			0.601391
$321$	−11.3303	−	8.23196i	−0.632397	−	0.459463i
$322$	−2.76097	+	8.49741i	−0.153863	+	0.473542i
$323$	1.13173	+	3.48310i	0.0629710	+	0.193805i
$324$	20.3889	−	14.8134i	1.13272	−	0.822966i
$325$	2.46735	−	1.79264i	0.136864	−	0.0994375i
$326$	−6.43351	−	19.8003i	−0.356319	−	1.09664i
$327$	4.39404	−	13.5235i	0.242991	−	0.747850i
$328$	−2.91580	−	2.11845i	−0.160998	−	0.116972i
$329$	−9.14077			−0.503947
$330$		0			0
$331$	25.6693			1.41091			0.705457	−	0.708753i	$-0.250742\pi$
$331$	25.6693			1.41091			0.705457	+	0.708753i	$0.250742\pi$
$332$	17.2464	+	12.5303i	0.946521	+	0.687688i
$333$	0.375942	−	1.15703i	0.0206015	−	0.0634049i
$334$	−9.01295	−	27.7390i	−0.493167	−	1.51781i
$335$	−5.46696	+	3.97198i	−0.298692	+	0.217012i
$336$	14.5597	−	10.5782i	0.794296	−	0.577090i
$337$	7.38308	+	22.7228i	0.402182	+	1.23779i	0.923225	+	0.384259i	$0.125543\pi$
$337$	7.38308	+	22.7228i	0.402182	+	1.23779i	−0.521043	+	0.853530i	$0.674457\pi$
$338$	−2.39480	+	7.37043i	−0.130260	+	0.400898i
$339$	4.69927	+	3.41422i	0.255230	+	0.185435i
$340$	−1.10871			−0.0601282
$341$		0			0
$342$	10.9115			0.590026
$343$	11.3955	+	8.27934i	0.615301	+	0.447042i
$344$	0.332224	−	1.02248i	0.0179123	−	0.0551285i
$345$	0.821848	+	2.52939i	0.0442468	+	0.136178i
$346$	18.3601	−	13.3394i	0.987047	−	0.717132i
$347$	−0.268717	+	0.195234i	−0.0144255	+	0.0104807i	−0.594975	−	0.803744i	$-0.702838\pi$
$347$	−0.268717	+	0.195234i	−0.0144255	+	0.0104807i	0.580549	+	0.814225i	$0.302838\pi$
$348$	−5.25864	−	16.1844i	−0.281892	−	0.867576i
$349$	−0.377460	+	1.16170i	−0.0202050	+	0.0621845i	−0.960651	−	0.277760i	$-0.910408\pi$
$349$	−0.377460	+	1.16170i	−0.0202050	+	0.0621845i	0.940446	+	0.339944i	$0.110408\pi$
$350$	−5.19927	−	3.77749i	−0.277913	−	0.201916i
$351$	13.6548			0.728840
$352$		0			0
$353$	−25.7038			−1.36808			−0.684039	−	0.729446i	$-0.739778\pi$
$353$	−25.7038			−1.36808			−0.684039	+	0.729446i	$0.739778\pi$
$354$	−9.12849	−	6.63224i	−0.485174	−	0.352499i
$355$	2.01539	−	6.20274i	0.106966	−	0.329207i
$356$	−5.00036	−	15.3895i	−0.265019	−	0.815643i
$357$	−2.20184	+	1.59973i	−0.116534	+	0.0846666i
$358$	−38.5361	+	27.9981i	−2.03670	+	1.47975i
$359$	5.54113	+	17.0538i	0.292450	+	0.900067i	0.984066	+	0.177802i	$0.0568988\pi$
$359$	5.54113	+	17.0538i	0.292450	+	0.900067i	−0.691617	+	0.722265i	$0.743101\pi$
$360$	−0.166660	+	0.512925i	−0.00878373	+	0.0270335i
$361$	−35.0635	−	25.4751i	−1.84545	−	1.34080i
$362$	5.02517			0.264117
$363$		0			0
$364$	−22.3593			−1.17195
$365$	7.98970	+	5.80485i	0.418200	+	0.303840i
$366$	2.49878	−	7.69045i	0.130613	−	0.401986i
$367$	−2.62383	−	8.07533i	−0.136963	−	0.421529i	0.858927	−	0.512098i	$-0.171131\pi$
$367$	−2.62383	−	8.07533i	−0.136963	−	0.421529i	−0.995890	+	0.0905689i	$0.971131\pi$
$368$	−3.44979	+	2.50642i	−0.179833	+	0.130656i
$369$	−2.35188	+	1.70874i	−0.122434	+	0.0889535i
$370$	−1.19430	−	3.67568i	−0.0620887	−	0.191089i
$371$	3.96957	−	12.2171i	0.206090	−	0.634280i
$372$	38.7553	+	28.1574i	2.00937	+	1.45989i
$373$	−35.8450			−1.85598			−0.927991	−	0.372604i	$-0.878465\pi$
$373$	−35.8450			−1.85598			−0.927991	+	0.372604i	$0.878465\pi$
$374$		0			0
$375$	−1.91300			−0.0987867
$376$	1.97150	+	1.43238i	0.101672	+	0.0738692i
$377$	3.50742	−	10.7947i	0.180641	−	0.555957i
$378$	−8.89160	−	27.3655i	−0.457334	−	1.40753i
$379$	−14.1995	+	10.3166i	−0.729380	+	0.529926i	−0.889367	−	0.457193i	$-0.848855\pi$
$379$	−14.1995	+	10.3166i	−0.729380	+	0.529926i	0.159987	+	0.987119i	$0.448855\pi$
$380$	15.2682	−	11.0930i	0.783244	−	0.569060i
$381$	0.266961	+	0.821622i	0.0136768	+	0.0420930i
$382$	11.1666	−	34.3673i	0.571334	−	1.75839i
$383$	17.4950	+	12.7109i	0.893954	+	0.649496i	0.936906	−	0.349581i	$-0.113676\pi$
$383$	17.4950	+	12.7109i	0.893954	+	0.649496i	−0.0429517	+	0.999077i	$0.513676\pi$
$384$	−12.2759			−0.626450
$385$		0			0
$386$	5.41788			0.275763
$387$	−0.701557	−	0.509711i	−0.0356622	−	0.0259101i
$388$	11.3412	−	34.9046i	0.575761	−	1.77201i
$389$	11.0448	+	33.9923i	0.559992	+	1.72348i	0.682381	+	0.730996i	$0.260944\pi$
$389$	11.0448	+	33.9923i	0.559992	+	1.72348i	−0.122389	+	0.992482i	$0.539056\pi$
$390$	−9.88986	+	7.18541i	−0.500793	+	0.363847i
$391$	0.521706	−	0.379041i	0.0263838	−	0.0191689i
$392$	0.608369	+	1.87237i	0.0307273	+	0.0945689i
$393$	−0.371834	+	1.14439i	−0.0187566	+	0.0577268i
$394$	0.245337	+	0.178248i	0.0123599	+	0.00898001i
$395$	−11.5579			−0.581539
$396$		0			0
$397$	−20.0447			−1.00601			−0.503007	−	0.864282i	$-0.667773\pi$
$397$	−20.0447			−1.00601			−0.503007	+	0.864282i	$0.667773\pi$
$398$	12.7843	+	9.28831i	0.640817	+	0.465581i
$399$	14.3161	−	44.0603i	0.716699	−	2.20577i
$400$	−0.947813	−	2.91707i	−0.0473906	−	0.145853i
$401$	16.9074	−	12.2839i	0.844315	−	0.613431i	−0.0792579	−	0.996854i	$-0.525255\pi$
$401$	16.9074	−	12.2839i	0.844315	−	0.613431i	0.923573	+	0.383424i	$0.125255\pi$
$402$	21.9132	−	15.9208i	1.09293	−	0.794059i
$403$	9.87349	+	30.3875i	0.491834	+	1.51371i
$404$	−8.66604	+	26.6713i	−0.431152	+	1.32695i
$405$	−8.53000	−	6.19741i	−0.423859	−	0.307952i
$406$	−23.9176			−1.18701
$407$		0			0
$408$	0.725576			0.0359214
$409$	19.0104	+	13.8119i	0.940005	+	0.682954i	0.948422	−	0.317011i	$-0.102679\pi$
$409$	19.0104	+	13.8119i	0.940005	+	0.682954i	−0.00841691	+	0.999965i	$0.502679\pi$
$410$	−2.85386	+	8.78327i	−0.140942	+	0.433775i
$411$	6.61105	+	20.3467i	0.326099	+	1.00363i
$412$	−26.8561	+	19.5121i	−1.32311	+	0.961294i
$413$	−6.98522	+	5.07506i	−0.343720	+	0.249727i
$414$	−0.593711	−	1.82725i	−0.0291793	−	0.0898046i
$415$	2.75600	−	8.48210i	0.135287	−	0.416370i
$416$	−19.8919	−	14.4523i	−0.975283	−	0.708584i
$417$	4.54328			0.222485
$418$		0			0
$419$	−10.1128			−0.494043			−0.247022	−	0.969010i	$-0.579452\pi$
$419$	−10.1128			−0.494043			−0.247022	+	0.969010i	$0.579452\pi$
$420$	11.3464	+	8.24361i	0.553646	+	0.402247i
$421$	2.75731	−	8.48612i	0.134383	−	0.413588i	−0.861111	−	0.508418i	$-0.830231\pi$
$421$	2.75731	−	8.48612i	0.134383	−	0.413588i	0.995494	+	0.0948296i	$0.0302306\pi$
$422$	1.46901	+	4.52116i	0.0715105	+	0.220087i
$423$	1.59020	−	1.15535i	0.0773184	−	0.0561751i
$424$	−2.77061	+	2.01296i	−0.134552	+	0.0977581i
$425$	0.143336	+	0.441143i	0.00695282	+	0.0213986i
$426$	−8.07828	+	24.8624i	−0.391394	+	1.20459i
$427$	−5.00592	−	3.63701i	−0.242253	−	0.176007i
$428$	17.4991			0.845850
$429$		0			0
$430$	−2.75485			−0.132851
$431$	−14.2486	−	10.3522i	−0.686331	−	0.498649i	0.189121	−	0.981954i	$-0.439436\pi$
$431$	−14.2486	−	10.3522i	−0.686331	−	0.498649i	−0.875452	+	0.483305i	$0.839436\pi$
$432$	4.24360	−	13.0605i	0.204170	−	0.628372i
$433$	2.82564	+	8.69644i	0.135792	+	0.417924i	0.995712	−	0.0925038i	$-0.0294870\pi$
$433$	2.82564	+	8.69644i	0.135792	+	0.417924i	−0.859921	+	0.510428i	$0.829487\pi$
$434$	54.4700	−	39.5748i	2.61465	−	1.89965i
$435$	−5.75975	+	4.18470i	−0.276159	+	0.200641i
$436$	5.49028	+	16.8973i	0.262937	+	0.809236i
$437$	−3.39206	+	10.4397i	−0.162264	+	0.499398i
$438$	−32.0250	−	23.2675i	−1.53021	−	1.11177i
$439$	−6.46946			−0.308770			−0.154385	−	0.988011i	$-0.549340\pi$
$439$	−6.46946			−0.308770			−0.154385	+	0.988011i	$0.549340\pi$
$440$		0			0
$441$	1.58797			0.0756176
$442$	2.39800	+	1.74225i	0.114061	+	0.0828703i
$443$	−12.6339	+	38.8832i	−0.600255	+	1.84739i	−0.0736507	+	0.997284i	$0.523465\pi$
$443$	−12.6339	+	38.8832i	−0.600255	+	1.84739i	−0.526604	+	0.850111i	$0.676535\pi$
$444$	2.60632	+	8.02143i	0.123690	+	0.380680i
$445$	−5.47686	+	3.97918i	−0.259628	+	0.188631i
$446$	−14.5437	+	10.5666i	−0.688662	+	0.500342i
$447$	5.15502	+	15.8655i	0.243824	+	0.750413i
$448$	−10.1966	+	31.3819i	−0.481743	+	1.48265i
$449$	9.83826	+	7.14791i	0.464296	+	0.337331i	0.795214	−	0.606329i	$-0.207358\pi$
$449$	9.83826	+	7.14791i	0.464296	+	0.337331i	−0.330918	+	0.943659i	$0.607358\pi$
$450$	1.38197			0.0651465
$451$		0			0
$452$	−7.25777			−0.341377
$453$	18.4718	+	13.4206i	0.867882	+	0.630553i
$454$	−4.01464	+	12.3558i	−0.188416	+	0.579886i
$455$	2.89065	+	8.89651i	0.135516	+	0.417075i
$456$	−9.99204	+	7.25964i	−0.467920	+	0.339964i
$457$	−8.01121	+	5.82049i	−0.374749	+	0.272271i	−0.759177	−	0.650884i	$-0.774398\pi$
$457$	−8.01121	+	5.82049i	−0.374749	+	0.272271i	0.384429	+	0.923155i	$0.374398\pi$
$458$	14.9995	+	46.1636i	0.700880	+	2.15709i
$459$	−0.641753	+	1.97511i	−0.0299544	+	0.0921903i
$460$	−2.68842	−	1.95325i	−0.125348	−	0.0910709i
$461$	3.12529			0.145559			0.0727796	−	0.997348i	$-0.476813\pi$
$461$	3.12529			0.145559			0.0727796	+	0.997348i	$0.476813\pi$
$462$		0			0
$463$	−24.3518			−1.13173			−0.565863	−	0.824499i	$-0.691457\pi$
$463$	−24.3518			−1.13173			−0.565863	+	0.824499i	$0.691457\pi$
$464$	−9.23485	−	6.70951i	−0.428717	−	0.311481i
$465$	6.19315	−	19.0606i	0.287200	−	0.883912i
$466$	18.0406	+	55.5232i	0.835714	+	2.57206i
$467$	−26.8381	+	19.4990i	−1.24192	+	0.902307i	−0.997725	−	0.0674196i	$-0.978523\pi$
$467$	−26.8381	+	19.4990i	−1.24192	+	0.902307i	−0.244194	+	0.969726i	$0.578523\pi$
$468$	3.88981	−	2.82611i	0.179806	−	0.130637i
$469$	−6.40487	−	19.7122i	−0.295749	−	0.910223i
$470$	1.92961	−	5.93874i	0.0890064	−	0.273934i
$471$	−5.99763	−	4.35753i	−0.276356	−	0.200784i
$472$	2.30185			0.105951
$473$		0			0
$474$	46.3273			2.12788
$475$	−6.38769	−	4.64093i	−0.293088	−	0.212941i
$476$	1.05085	−	3.23418i	0.0481655	−	0.148238i
$477$	0.853604	+	2.62712i	0.0390838	+	0.120288i
$478$	−27.6072	+	20.0578i	−1.26273	+	0.917424i
$479$	−13.9941	+	10.1673i	−0.639409	+	0.464558i	−0.859647	−	0.510888i	$-0.829317\pi$
$479$	−13.9941	+	10.1673i	−0.639409	+	0.464558i	0.220238	+	0.975446i	$0.429317\pi$
$480$	4.76588	+	14.6679i	0.217531	+	0.669493i
$481$	−1.73837	+	5.35015i	−0.0792628	+	0.243946i
$482$	7.44269	+	5.40743i	0.339005	+	0.246302i
$483$	−8.15736			−0.371173
$484$		0			0
$485$	−15.3543			−0.697205
$486$	11.4221	+	8.29865i	0.518118	+	0.376435i
$487$	2.36108	−	7.26665i	0.106991	−	0.329283i	−0.883202	−	0.468993i	$-0.844617\pi$
$487$	2.36108	−	7.26665i	0.106991	−	0.329283i	0.990192	+	0.139710i	$0.0446170\pi$
$488$	0.509758	+	1.56887i	0.0230756	+	0.0710195i
$489$	15.3778	−	11.1726i	0.695406	−	0.505242i
$490$	4.08124	−	2.96519i	0.184372	−	0.133954i
$491$	9.47332	+	29.1559i	0.427525	+	1.31579i	0.900556	+	0.434741i	$0.143160\pi$
$491$	9.47332	+	29.1559i	0.427525	+	1.31579i	−0.473030	+	0.881046i	$0.656840\pi$
$492$	6.22797	−	19.1677i	0.280778	−	0.864147i
$493$	1.39657	+	1.01467i	0.0628983	+	0.0456983i
$494$	−50.4551			−2.27008
$495$		0			0
$496$	32.1333			1.44283
$497$	16.1836	+	11.7581i	0.725934	+	0.527422i
$498$	−11.0469	+	33.9987i	−0.495021	+	1.52352i
$499$	−11.5814	−	35.6440i	−0.518456	−	1.59564i	−0.776905	−	0.629618i	$-0.783211\pi$
$499$	−11.5814	−	35.6440i	−0.518456	−	1.59564i	0.258449	−	0.966025i	$-0.416789\pi$
$500$	1.93376	−	1.40496i	0.0864803	−	0.0628316i
$501$	21.5433	−	15.6521i	0.962482	−	0.699284i
$502$	−1.72663	−	5.31401i	−0.0770631	−	0.237176i
$503$	−2.61952	+	8.06206i	−0.116799	+	0.359469i	−0.992318	−	0.123714i	$-0.960520\pi$
$503$	−2.61952	+	8.06206i	−0.116799	+	0.359469i	0.875519	+	0.483183i	$0.160520\pi$
$504$	−1.33828	−	0.972314i	−0.0596115	−	0.0433103i
$505$	11.7326			0.522093
$506$		0			0
$507$	−7.07548			−0.314233
$508$	−0.873280	−	0.634475i	−0.0387455	−	0.0281503i
$509$	−0.524474	+	1.61417i	−0.0232469	+	0.0715466i	−0.962007	−	0.273025i	$-0.911976\pi$
$509$	−0.524474	+	1.61417i	−0.0232469	+	0.0715466i	0.938760	+	0.344572i	$0.111976\pi$
$510$	−0.574532	−	1.76823i	−0.0254407	−	0.0782985i
$511$	−24.5059	+	17.8046i	−1.08408	+	0.787628i
$512$	−24.0633	+	17.4830i	−1.06346	+	0.772649i
$513$	−10.9240	−	33.6206i	−0.482306	−	1.48438i
$514$	−14.0067	+	43.1083i	−0.617811	+	1.90143i
$515$	11.2357	+	8.16319i	0.495103	+	0.359713i
$516$	6.01190			0.264659
$517$		0			0
$518$	11.8542			0.520843
$519$	16.7627	+	12.1788i	0.735803	+	0.534592i
$520$	0.770639	−	2.37178i	0.0337948	−	0.104010i
$521$	−11.4623	−	35.2775i	−0.502174	−	1.54553i	−0.805470	−	0.592637i	$-0.798087\pi$
$521$	−11.4623	−	35.2775i	−0.502174	−	1.54553i	0.303295	−	0.952897i	$-0.401913\pi$
$522$	4.16090	−	3.02307i	0.182117	−	0.132316i
$523$	−14.6285	+	10.6282i	−0.639659	+	0.464740i	−0.859733	−	0.510744i	$-0.829370\pi$
$523$	−14.6285	+	10.6282i	−0.639659	+	0.464740i	0.220074	+	0.975483i	$0.429370\pi$
$524$	−0.464601	−	1.42989i	−0.0202962	−	0.0624652i
$525$	1.81316	−	5.58034i	0.0791329	−	0.243546i
$526$	37.5288	+	27.2663i	1.63633	+	1.18887i
$527$	−4.85946			−0.211681
$528$		0			0
$529$	−21.0672			−0.915965
$530$	7.09944	+	5.15804i	0.308380	+	0.224051i
$531$	0.573742	−	1.76580i	0.0248983	−	0.0766291i
$532$	17.8877	+	55.0526i	0.775528	+	2.38683i
$533$	10.8752	−	7.90127i	0.471056	−	0.342242i
$534$	21.9529	−	15.9497i	0.949994	−	0.690211i
$535$	−2.26231	−	6.96269i	−0.0978084	−	0.301023i
$536$	−1.70752	+	5.25521i	−0.0737536	+	0.226990i
$537$	−35.1834	−	25.5622i	−1.51827	−	1.10309i
$538$	43.4111			1.87159
$539$		0			0
$540$	10.7018			0.460532
$541$	9.50790	+	6.90789i	0.408776	+	0.296993i	0.773106	−	0.634277i	$-0.218702\pi$
$541$	9.50790	+	6.90789i	0.408776	+	0.296993i	−0.364330	+	0.931270i	$0.618702\pi$
$542$	0.273957	−	0.843154i	0.0117675	−	0.0362165i
$543$	1.41776	+	4.36342i	0.0608419	+	0.187252i
$544$	3.02536	−	2.19805i	0.129711	−	0.0942407i
$545$	6.01347	−	4.36904i	0.257589	−	0.187149i
$546$	−11.5866	−	35.6598i	−0.495860	−	1.52610i
$547$	6.72324	−	20.6920i	0.287465	−	0.884726i	−0.698184	−	0.715918i	$-0.746008\pi$
$547$	6.72324	−	20.6920i	0.287465	−	0.884726i	0.985649	−	0.168808i	$-0.0539917\pi$
$548$	−21.6260	−	15.7122i	−0.923816	−	0.671192i
$549$	1.33057			0.0567874
$550$		0			0
$551$	−29.3845			−1.25182
$552$	1.75939	+	1.27827i	0.0748847	+	0.0544069i
$553$	10.9547	−	33.7151i	0.465841	−	1.43371i
$554$	5.55057	+	17.0829i	0.235821	+	0.725783i
$555$	2.85469	−	2.07405i	0.121175	−	0.0880385i
$556$	−4.59259	+	3.33671i	−0.194769	+	0.141508i
$557$	−1.49389	−	4.59771i	−0.0632980	−	0.194811i	0.914406	−	0.404798i	$-0.132658\pi$
$557$	−1.49389	−	4.59771i	−0.0632980	−	0.194811i	−0.977704	+	0.209986i	$0.932658\pi$
$558$	−4.47399	+	13.7695i	−0.189399	+	0.582910i
$559$	3.24402	+	2.35692i	0.137208	+	0.0996872i
$560$	9.40763			0.397545
$561$		0			0
$562$	14.6903			0.619672
$563$	3.86062	+	2.80491i	0.162706	+	0.118213i	0.666159	−	0.745810i	$-0.267937\pi$
$563$	3.86062	+	2.80491i	0.162706	+	0.118213i	−0.503453	+	0.864023i	$0.667937\pi$
$564$	−4.21099	+	12.9601i	−0.177315	+	0.545718i
$565$	0.938299	+	2.88779i	0.0394745	+	0.121490i
$566$	16.8719	−	12.2582i	0.709179	−	0.515249i
$567$	26.1631	−	19.0086i	1.09875	−	0.798286i
$568$	−1.64799	−	5.07200i	−0.0691483	−	0.212816i
$569$	−11.0377	+	33.9705i	−0.462724	+	1.42412i	0.399098	+	0.916908i	$0.369323\pi$
$569$	−11.0377	+	33.9705i	−0.462724	+	1.42412i	−0.861822	+	0.507210i	$0.830677\pi$
$570$	25.6037	+	18.6022i	1.07242	+	0.779161i
$571$	33.9838			1.42218			0.711090	−	0.703101i	$-0.248202\pi$
$571$	33.9838			1.42218			0.711090	+	0.703101i	$0.248202\pi$
$572$		0			0
$573$	32.9920			1.37826
$574$	−22.9165	−	16.6498i	−0.956515	−	0.694949i
$575$	−0.429613	+	1.32221i	−0.0179161	+	0.0551401i
$576$	−2.19264	−	6.74825i	−0.0913599	−	0.281177i
$577$	16.7126	−	12.1424i	0.695755	−	0.505495i	−0.182792	−	0.983152i	$-0.558514\pi$
$577$	16.7126	−	12.1424i	0.695755	−	0.505495i	0.878547	+	0.477656i	$0.158514\pi$
$578$	28.4525	−	20.6719i	1.18347	−	0.859839i
$579$	1.52855	+	4.70441i	0.0635245	+	0.195508i
$580$	2.74890	−	8.46024i	0.114142	−	0.351292i
$581$	22.1307	+	16.0789i	0.918136	+	0.667065i
$582$	61.5447			2.55111
$583$		0			0
$584$	8.07548			0.334166
$585$	−1.62736	−	1.18235i	−0.0672830	−	0.0488840i
$586$	−14.1286	+	43.4834i	−0.583647	+	1.79628i
$587$	4.12848	+	12.7062i	0.170401	+	0.524439i	0.999394	−	0.0348197i	$-0.0110857\pi$
$587$	4.12848	+	12.7062i	0.170401	+	0.524439i	−0.828993	+	0.559259i	$0.811086\pi$
$588$	−8.90648	+	6.47094i	−0.367297	+	0.266857i
$589$	66.9205	−	48.6206i	2.75741	−	2.00338i
$590$	−1.82268	−	5.60962i	−0.0750384	−	0.230944i
$591$	−0.0855575	+	0.263319i	−0.00351936	+	0.0108315i
$592$	4.57703	+	3.32541i	0.188115	+	0.136673i
$593$	−20.8062			−0.854410			−0.427205	−	0.904155i	$-0.640502\pi$
$593$	−20.8062			−0.854410			−0.427205	+	0.904155i	$0.640502\pi$
$594$		0			0
$595$	−1.42270			−0.0583250
$596$	−16.8630	−	12.2517i	−0.690737	−	0.501850i
$597$	−4.45830	+	13.7213i	−0.182466	+	0.561573i
$598$	2.74534	+	8.44928i	0.112265	+	0.345517i
$599$	11.5250	−	8.37338i	0.470897	−	0.342127i	−0.326894	−	0.945061i	$-0.606002\pi$
$599$	11.5250	−	8.37338i	0.470897	−	0.342127i	0.797791	+	0.602934i	$0.206002\pi$
$600$	−1.26552	+	0.919451i	−0.0516645	+	0.0375364i
$601$	6.41093	+	19.7308i	0.261507	+	0.804836i	0.992478	+	0.122427i	$0.0390677\pi$
$601$	6.41093	+	19.7308i	0.261507	+	0.804836i	−0.730970	+	0.682409i	$0.760932\pi$
$602$	2.61108	−	8.03609i	0.106420	−	0.327526i
$603$	3.60577	+	2.61975i	0.146838	+	0.106684i
$604$	−28.5287			−1.16082
$605$		0			0
$606$	−47.0276			−1.91037
$607$	14.4991	+	10.5342i	0.588502	+	0.427572i	0.841779	−	0.539822i	$-0.181508\pi$
$607$	14.4991	+	10.5342i	0.588502	+	0.427572i	−0.253277	+	0.967394i	$0.581508\pi$
$608$	−19.6705	+	60.5395i	−0.797743	+	2.45520i
$609$	−6.74790	−	20.7679i	−0.273439	−	0.841558i
$610$	3.41970	−	2.48456i	0.138460	−	0.100597i
$611$	−7.35316	+	5.34238i	−0.297477	+	0.216130i
$612$	0.225971	+	0.695467i	0.00913433	+	0.0281126i
$613$	8.71486	−	26.8216i	0.351990	−	1.08331i	−0.605745	−	0.795659i	$-0.707125\pi$
$613$	8.71486	−	26.8216i	0.351990	−	1.08331i	0.957734	−	0.287654i	$-0.0928753\pi$
$614$	−52.3243	−	38.0158i	−2.11164	−	1.53419i
$615$	−8.43178			−0.340002
$616$		0			0
$617$	−4.72930			−0.190394			−0.0951972	−	0.995458i	$-0.530348\pi$
$617$	−4.72930			−0.190394			−0.0951972	+	0.995458i	$0.530348\pi$
$618$	−45.0358	−	32.7205i	−1.81161	−	1.31621i
$619$	−9.28827	+	28.5864i	−0.373327	+	1.14898i	0.571273	+	0.820760i	$0.306450\pi$
$619$	−9.28827	+	28.5864i	−0.373327	+	1.14898i	−0.944600	+	0.328223i	$0.893550\pi$
$620$	7.73823	+	23.8158i	0.310775	+	0.956467i
$621$	−5.03576	+	3.65869i	−0.202078	+	0.146818i
$622$	32.9109	−	23.9112i	1.31961	−	0.958752i
$623$	−6.41648	−	19.7479i	−0.257071	−	0.791183i
$624$	5.52981	−	17.0190i	0.221369	−	0.681305i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	2.20314			0.0880551
$627$		0			0
$628$	9.26301			0.369634
$629$	−0.692177	−	0.502896i	−0.0275989	−	0.0200518i
$630$	−1.30984	+	4.03129i	−0.0521855	+	0.160610i
$631$	−9.79694	−	30.1519i	−0.390010	−	1.20033i	−0.932780	−	0.360446i	$-0.882624\pi$
$631$	−9.79694	−	30.1519i	−0.390010	−	1.20033i	0.542770	−	0.839882i	$-0.317376\pi$
$632$	−7.64594	+	5.55510i	−0.304139	+	0.220970i
$633$	−3.51132	+	2.55112i	−0.139562	+	0.101398i
$634$	−15.4304	−	47.4899i	−0.612820	−	1.88607i
$635$	−0.139551	+	0.429495i	−0.00553792	+	0.0170440i
$636$	−15.4931	−	11.2564i	−0.614341	−	0.446345i
$637$	−7.34282			−0.290933
$638$		0			0
$639$	−4.30160			−0.170169
$640$	−5.19153	−	3.77187i	−0.205213	−	0.149096i
$641$	−5.85814	+	18.0295i	−0.231383	+	0.712123i	0.766198	+	0.642605i	$0.222146\pi$
$641$	−5.85814	+	18.0295i	−0.231383	+	0.712123i	−0.997581	+	0.0695181i	$0.977854\pi$
$642$	9.06801	+	27.9085i	0.357886	+	1.10146i
$643$	29.3259	−	21.3065i	1.15650	−	0.840248i	0.167170	−	0.985928i	$-0.446537\pi$
$643$	29.3259	−	21.3065i	1.15650	−	0.840248i	0.989332	+	0.145680i	$0.0465370\pi$
$644$	8.24589	−	5.99099i	0.324933	−	0.236078i
$645$	−0.777230	−	2.39207i	−0.0306034	−	0.0941876i
$646$	2.37130	−	7.29812i	0.0932976	−	0.287141i
$647$	28.2767	+	20.5442i	1.11167	+	0.807676i	0.982926	−	0.184002i	$-0.0589052\pi$
$647$	28.2767	+	20.5442i	1.11167	+	0.807676i	0.128745	+	0.991678i	$0.458905\pi$
$648$	−8.62158			−0.338688
$649$		0			0
$650$	−6.39026			−0.250646
$651$	49.7310	+	36.1317i	1.94911	+	1.41611i
$652$	−7.33919	+	22.5877i	−0.287425	+	0.884602i
$653$	−9.20539	−	28.3313i	−0.360235	−	1.10869i	−0.952912	−	0.303248i	$-0.901929\pi$
$653$	−9.20539	−	28.3313i	−0.360235	−	1.10869i	0.592677	−	0.805440i	$-0.298071\pi$
$654$	−24.1037	+	17.5124i	−0.942531	+	0.684789i
$655$	−0.508874	+	0.369719i	−0.0198834	+	0.0144461i
$656$	−4.17761	−	12.8573i	−0.163108	−	0.501995i
$657$	2.01283	−	6.19486i	0.0785280	−	0.241684i
$658$	15.4948	+	11.2576i	0.604050	+	0.438868i
$659$	7.30532			0.284575			0.142287	−	0.989825i	$-0.454554\pi$
$659$	7.30532			0.284575			0.142287	+	0.989825i	$0.454554\pi$
$660$		0			0
$661$	−22.7352			−0.884296			−0.442148	−	0.896942i	$-0.645783\pi$
$661$	−22.7352			−0.884296			−0.442148	+	0.896942i	$0.645783\pi$
$662$	−43.5128	−	31.6139i	−1.69117	−	1.22871i
$663$	−0.836263	+	2.57375i	−0.0324778	+	0.0999563i
$664$	−2.25359	−	6.93584i	−0.0874563	−	0.269163i
$665$	19.5922	−	14.2346i	0.759755	−	0.551994i
$666$	−2.06225	+	1.49831i	−0.0799106	+	0.0580584i
$667$	1.59886	+	4.92077i	0.0619079	+	0.190533i
$668$	−10.2817	+	31.6439i	−0.397812	+	1.22434i
$669$	−13.2783	−	9.64726i	−0.513369	−	0.372985i
$670$	14.1590			0.547010
$671$		0			0
$672$	−47.3043			−1.82480
$673$	−14.3561	−	10.4303i	−0.553387	−	0.402059i	0.275646	−	0.961259i	$-0.411108\pi$
$673$	−14.3561	−	10.4303i	−0.553387	−	0.402059i	−0.829033	+	0.559200i	$0.811108\pi$
$674$	15.4697	−	47.6109i	0.595872	−	1.83390i
$675$	−1.38355	−	4.25813i	−0.0532528	−	0.163895i
$676$	7.15227	−	5.19643i	0.275087	−	0.199863i
$677$	6.60332	−	4.79759i	0.253786	−	0.184387i	−0.453617	−	0.891197i	$-0.649867\pi$
$677$	6.60332	−	4.79759i	0.253786	−	0.184387i	0.707403	+	0.706810i	$0.249867\pi$
$678$	−3.76097	−	11.5751i	−0.144439	−	0.444539i
$679$	14.5530	−	44.7897i	0.558494	−	1.71887i
$680$	0.306850	+	0.222940i	0.0117672	+	0.00854934i
$681$	−11.8613			−0.454527
$682$		0			0
$683$	−6.19100			−0.236892			−0.118446	−	0.992960i	$-0.537791\pi$
$683$	−6.19100			−0.236892			−0.118446	+	0.992960i	$0.537791\pi$
$684$	−10.0703	−	7.31648i	−0.385046	−	0.279753i
$685$	−3.45586	+	10.6360i	−0.132042	+	0.406382i
$686$	−9.12020	−	28.0691i	−0.348211	−	1.07168i
$687$	−35.8526	+	26.0484i	−1.36786	+	0.993810i
$688$	3.26250	−	2.37035i	0.124382	−	0.0903686i
$689$	−3.94709	−	12.1479i	−0.150372	−	0.462798i
$690$	1.72201	−	5.29981i	0.0655559	−	0.201760i
$691$	−19.0969	−	13.8747i	−0.726482	−	0.527820i	0.161967	−	0.986796i	$-0.448216\pi$
$691$	−19.0969	−	13.8747i	−0.726482	−	0.527820i	−0.888448	+	0.458976i	$0.848216\pi$
$692$	−25.8892			−0.984158
$693$		0			0
$694$	0.695956			0.0264181
$695$	1.92138	+	1.39596i	0.0728820	+	0.0529519i
$696$	−1.79897	+	5.53666i	−0.0681898	+	0.209867i
$697$	0.631772	+	1.94439i	0.0239301	+	0.0736492i
$698$	2.07058	−	1.50436i	0.0783724	−	0.0569409i
$699$	−43.1216	+	31.3297i	−1.63101	+	1.18500i
$700$	2.26552	+	6.97254i	0.0856284	+	0.263537i
$701$	−11.5042	+	35.4063i	−0.434508	+	1.33728i	0.459082	+	0.888394i	$0.348178\pi$
$701$	−11.5042	+	35.4063i	−0.434508	+	1.33728i	−0.893590	+	0.448884i	$0.851822\pi$
$702$	−23.1467	−	16.8170i	−0.873614	−	0.634718i
$703$	14.5637			0.549282
$704$		0			0
$705$	5.70108			0.214715
$706$	43.5713	+	31.6564i	1.63983	+	1.19140i
$707$	−11.1203	+	34.2247i	−0.418222	+	1.28715i
$708$	3.97762	+	12.2419i	0.149488	+	0.460077i
$709$	−14.7676	+	10.7293i	−0.554609	+	0.402947i	−0.829482	−	0.558534i	$-0.811364\pi$
$709$	−14.7676	+	10.7293i	−0.554609	+	0.402947i	0.274873	+	0.961480i	$0.411364\pi$
$710$	−11.0555	+	8.03232i	−0.414907	+	0.301448i
$711$	2.35566	+	7.24997i	0.0883441	+	0.271895i
$712$	−1.71062	+	5.26473i	−0.0641080	+	0.197304i
$713$	−11.7833	−	8.56108i	−0.441289	−	0.320615i
$714$	5.70259			0.213414
$715$		0			0
$716$	54.3388			2.03074
$717$	−25.2053	−	18.3127i	−0.941310	−	0.683902i
$718$	11.6103	−	35.7328i	0.433292	−	1.33354i
$719$	2.95849	+	9.10531i	0.110333	+	0.339571i	0.990945	−	0.134268i	$-0.0428682\pi$
$719$	2.95849	+	9.10531i	0.110333	+	0.339571i	−0.880612	+	0.473838i	$0.842868\pi$
$720$	−1.63663	+	1.18908i	−0.0609935	+	0.0443144i
$721$	−34.4619	+	25.0380i	−1.28343	+	0.932465i
$722$	28.0624	+	86.3673i	1.04438	+	3.21426i
$723$	−2.59552	+	7.98818i	−0.0965283	+	0.297084i
$724$	−4.63776	−	3.36953i	−0.172361	−	0.125228i
$725$	−3.72162			−0.138217
$726$		0			0
$727$	−14.0175			−0.519882			−0.259941	−	0.965625i	$-0.583703\pi$
$727$	−14.0175			−0.519882			−0.259941	+	0.965625i	$0.583703\pi$
$728$	6.18823	+	4.49601i	0.229351	+	0.166633i
$729$	5.79123	−	17.8236i	0.214490	−	0.660132i
$730$	−6.39440	−	19.6799i	−0.236667	−	0.728388i
$731$	−0.493383	+	0.358463i	−0.0182484	+	0.0132582i
$732$	−7.46281	+	5.42205i	−0.275833	+	0.200405i
$733$	−2.87006	−	8.83314i	−0.106008	−	0.326260i	0.883958	−	0.467567i	$-0.154869\pi$
$733$	−2.87006	−	8.83314i	−0.106008	−	0.326260i	−0.989966	+	0.141307i	$0.954869\pi$
$734$	−5.49771	+	16.9202i	−0.202924	+	0.624536i
$735$	3.72616	+	2.70721i	0.137441	+	0.0998571i
$736$	11.2083			0.413145
$737$		0			0
$738$	6.09119			0.224220
$739$	−31.5182	−	22.8993i	−1.15942	−	0.842365i	−0.169712	−	0.985494i	$-0.554284\pi$
$739$	−31.5182	−	22.8993i	−1.15942	−	0.842365i	−0.989704	+	0.143129i	$0.954284\pi$
$740$	−1.36243	+	4.19312i	−0.0500838	+	0.154142i
$741$	−14.2350	−	43.8107i	−0.522935	−	1.60943i
$742$	−21.7753	+	15.8207i	−0.799396	+	0.580795i
$743$	37.1578	−	26.9968i	1.36319	−	0.990415i	0.364954	−	0.931025i	$-0.381085\pi$
$743$	37.1578	−	26.9968i	1.36319	−	0.990415i	0.998235	−	0.0593894i	$-0.0189154\pi$
$744$	−5.06416	−	15.5859i	−0.185661	−	0.571406i
$745$	−2.69473	+	8.29354i	−0.0987274	+	0.303852i
$746$	60.7618	+	44.1460i	2.22465	+	1.61630i
$747$	−5.88233			−0.215223
$748$		0			0
$749$	22.4549			0.820483
$750$	3.24278	+	2.35601i	0.118409	+	0.0860295i
$751$	7.16698	−	22.0577i	0.261527	−	0.804896i	−0.730947	−	0.682435i	$-0.760921\pi$
$751$	7.16698	−	22.0577i	0.261527	−	0.804896i	0.992473	−	0.122462i	$-0.0390788\pi$
$752$	2.82465	+	8.69339i	0.103005	+	0.317015i
$753$	4.12708	−	2.99850i	0.150399	−	0.109271i
$754$	−19.2401	+	13.9788i	−0.700684	+	0.509077i
$755$	3.68825	+	11.3513i	0.134229	+	0.413115i
$756$	−10.1433	+	31.2179i	−0.368908	+	1.13538i
$757$	5.27642	+	3.83355i	0.191775	+	0.139333i	0.679530	−	0.733648i	$-0.262184\pi$
$757$	5.27642	+	3.83355i	0.191775	+	0.139333i	−0.487755	+	0.872981i	$0.662184\pi$
$758$	36.7757			1.33575
$759$		0			0
$760$	−6.45628			−0.234194
$761$	−5.31267	−	3.85988i	−0.192584	−	0.139921i	0.487315	−	0.873226i	$-0.337976\pi$
$761$	−5.31267	−	3.85988i	−0.192584	−	0.139921i	−0.679899	+	0.733306i	$0.737976\pi$
$762$	0.559362	−	1.72154i	0.0202635	−	0.0623648i
$763$	7.04515	+	21.6827i	0.255051	+	0.784968i
$764$	−33.3501	+	24.2302i	−1.20656	+	0.876620i
$765$	0.247504	−	0.179823i	0.00894854	−	0.00650150i
$766$	−14.0018	−	43.0932i	−0.505906	−	1.55702i
$767$	−2.65300	+	8.16511i	−0.0957944	+	0.294825i
$768$	−12.4901	−	9.07456i	−0.450696	−	0.327450i
$769$	−12.5950			−0.454188			−0.227094	−	0.973873i	$-0.572922\pi$
$769$	−12.5950			−0.454188			−0.227094	+	0.973873i	$0.572922\pi$
$770$		0			0
$771$	−41.3832			−1.49038
$772$	−5.00019	−	3.63285i	−0.179961	−	0.130749i
$773$	6.78131	−	20.8707i	0.243907	−	0.750668i	−0.751907	−	0.659269i	$-0.770866\pi$
$773$	6.78131	−	20.8707i	0.243907	−	0.750668i	0.995814	−	0.0913995i	$-0.0291340\pi$
$774$	0.561478	+	1.72805i	0.0201819	+	0.0621136i
$775$	8.47564	−	6.15791i	0.304454	−	0.221199i
$776$	−10.1574	+	7.37982i	−0.364631	+	0.264920i
$777$	3.34444	+	10.2931i	0.119981	+	0.369264i
$778$	23.1420	−	71.2239i	0.829682	−	2.55350i
$779$	−28.1546	−	20.4555i	−1.00874	−	0.732895i
$780$	13.9454			0.499327
$781$		0			0
$782$	−1.35118			−0.0483181
$783$	−13.4804	−	9.79406i	−0.481749	−	0.350011i
$784$	−2.28198	+	7.02321i	−0.0814993	+	0.250829i
$785$	−1.19754	−	3.68565i	−0.0427420	−	0.131546i
$786$	2.03972	−	1.48194i	0.0727543	−	0.0528591i
$787$	13.5347	−	9.83355i	0.482461	−	0.350528i	−0.319817	−	0.947479i	$-0.603621\pi$
$787$	13.5347	−	9.83355i	0.482461	−	0.350528i	0.802278	+	0.596951i	$0.203621\pi$
$788$	−0.106903	−	0.329012i	−0.00380825	−	0.0117206i
$789$	−13.0876	+	40.2793i	−0.465929	+	1.43398i
$790$	19.5921	+	14.2345i	0.697054	+	0.506439i
$791$	−9.31320			−0.331139
$792$		0			0
$793$	−6.15261			−0.218486
$794$	33.9783	+	24.6867i	1.20585	+	0.876098i
$795$	−2.47581	+	7.61977i	−0.0878081	+	0.270246i
$796$	−5.57058	−	17.1445i	−0.197444	−	0.607670i
$797$	9.52271	−	6.91865i	0.337312	−	0.245071i	−0.406215	−	0.913777i	$-0.633152\pi$
$797$	9.52271	−	6.91865i	0.337312	−	0.245071i	0.743527	+	0.668706i	$0.233152\pi$
$798$	−78.5314	+	57.0564i	−2.77998	+	2.01978i
$799$	−0.427168	−	1.31469i	−0.0151121	−	0.0465103i
$800$	−2.49131	+	7.66748i	−0.0880813	+	0.271086i
$801$	3.61231	+	2.62449i	0.127635	+	0.0927319i
$802$	−43.7889			−1.54624
$803$		0			0
$804$	−30.8992			−1.08973
$805$	−3.44979	−	2.50642i	−0.121589	−	0.0883397i
$806$	20.6879	−	63.6707i	0.728699	−	2.24270i
$807$	12.2476	+	37.6944i	0.431137	+	1.32690i
$808$	7.76152	−	5.63908i	0.273049	−	0.198382i
$809$	0.967540	−	0.702959i	0.0340169	−	0.0247147i	−0.570647	−	0.821196i	$-0.693307\pi$
$809$	0.967540	−	0.702959i	0.0340169	−	0.0247147i	0.604664	+	0.796481i	$0.293307\pi$
$810$	6.82682	+	21.0108i	0.239870	+	0.738244i
$811$	−11.0706	+	34.0719i	−0.388742	+	1.19643i	0.544987	+	0.838444i	$0.316535\pi$
$811$	−11.0706	+	34.0719i	−0.388742	+	1.19643i	−0.933729	+	0.357981i	$0.883465\pi$
$812$	22.0737	+	16.0374i	0.774633	+	0.562804i
$813$	0.809412			0.0283873
$814$		0			0
$815$	9.93621			0.348050
$816$	2.20184	+	1.59973i	0.0770797	+	0.0560017i
$817$	3.20791	−	9.87293i	0.112231	−	0.345410i
$818$	−15.2146	−	46.8258i	−0.531967	−	1.63723i
$819$	4.99141	−	3.62647i	0.174414	−	0.126719i
$820$	8.52329	−	6.19253i	0.297646	−	0.216253i
$821$	−1.69712	−	5.22320i	−0.0592299	−	0.182291i	0.917064	−	0.398740i	$-0.130552\pi$
$821$	−1.69712	−	5.22320i	−0.0592299	−	0.182291i	−0.976294	+	0.216449i	$0.930552\pi$
$822$	13.8521	−	42.6323i	0.483147	−	1.48697i
$823$	−34.5654	−	25.1133i	−1.20488	−	0.875393i	−0.210120	−	0.977676i	$-0.567386\pi$
$823$	−34.5654	−	25.1133i	−1.20488	−	0.875393i	−0.994755	+	0.102282i	$0.967386\pi$
$824$	11.3563			0.395616
$825$		0			0
$826$	18.0912			0.629473
$827$	26.2290	+	19.0565i	0.912070	+	0.662658i	0.941538	−	0.336908i	$-0.109381\pi$
$827$	26.2290	+	19.0565i	0.912070	+	0.662658i	−0.0294672	+	0.999566i	$0.509381\pi$
$828$	−0.677290	+	2.08448i	−0.0235374	+	0.0724408i
$829$	−0.899698	−	2.76899i	−0.0312478	−	0.0961709i	0.934216	−	0.356707i	$-0.116101\pi$
$829$	−0.899698	−	2.76899i	−0.0312478	−	0.0961709i	−0.965464	+	0.260536i	$0.916101\pi$
$830$	−15.1182	+	10.9840i	−0.524760	+	0.381260i
$831$	−13.2673	+	9.63925i	−0.460237	+	0.334382i
$832$	10.1388	+	31.2041i	0.351501	+	1.08181i
$833$	0.345100	−	1.06211i	0.0119570	−	0.0367999i
$834$	−7.70144	−	5.59542i	−0.266679	−	0.193754i
$835$	13.9200			0.481722
$836$		0			0
$837$	46.9059			1.62130
$838$	17.1425	+	12.4548i	0.592178	+	0.430243i
$839$	−6.44192	+	19.8262i	−0.222400	+	0.684476i	0.776145	+	0.630554i	$0.217172\pi$
$839$	−6.44192	+	19.8262i	−0.222400	+	0.684476i	−0.998545	+	0.0539222i	$0.982828\pi$
$840$	−1.48263	−	4.56306i	−0.0511555	−	0.157441i
$841$	12.2562	−	8.90468i	0.422629	−	0.307058i
$842$	−15.1253	+	10.9892i	−0.521254	+	0.378713i
$843$	4.14459	+	12.7557i	0.142747	+	0.439331i
$844$	1.67581	−	5.15762i	0.0576838	−	0.177533i
$845$	−2.99226	−	2.17400i	−0.102937	−	0.0747880i
$846$	−4.11851			−0.141597
$847$		0			0
$848$	−12.8458			−0.441127
$849$	15.4040	+	11.1917i	0.528664	+	0.384097i
$850$	0.300331	−	0.924324i	0.0103013	−	0.0317041i
$851$	−0.792435	−	2.43886i	−0.0271643	−	0.0836032i
$852$	24.1265	−	17.5289i	0.826560	−	0.600531i
$853$	27.9523	−	20.3085i	0.957067	−	0.695350i	0.00459957	−	0.999989i	$-0.498536\pi$
$853$	27.9523	−	20.3085i	0.957067	−	0.695350i	0.952468	+	0.304639i	$0.0985359\pi$
$854$	4.00639	+	12.3304i	0.137096	+	0.421938i
$855$	−1.60924	+	4.95274i	−0.0550349	+	0.169380i
$856$	−4.84310	−	3.51872i	−0.165534	−	0.120267i
$857$	−33.2969			−1.13740			−0.568699	−	0.822545i	$-0.692553\pi$
$857$	−33.2969			−1.13740			−0.568699	+	0.822545i	$0.692553\pi$
$858$		0			0
$859$	−16.7665			−0.572067			−0.286034	−	0.958220i	$-0.592337\pi$
$859$	−16.7665			−0.572067			−0.286034	+	0.958220i	$0.592337\pi$
$860$	2.54247	+	1.84721i	0.0866974	+	0.0629894i
$861$	7.99175	−	24.5961i	0.272358	−	0.838232i
$862$	11.4036	+	35.0967i	0.388408	+	1.19540i
$863$	1.20070	−	0.872362i	0.0408724	−	0.0296955i	−0.567161	−	0.823607i	$-0.691958\pi$
$863$	1.20070	−	0.872362i	0.0408724	−	0.0296955i	0.608034	+	0.793911i	$0.291958\pi$
$864$	−29.2022	+	21.2167i	−0.993480	+	0.721806i
$865$	3.34700	+	10.3010i	0.113801	+	0.350245i
$866$	5.92055	−	18.2216i	0.201189	−	0.619195i
$867$	25.9770	+	18.8734i	0.882226	+	0.640975i
$868$	−76.8068			−2.60699
$869$		0			0
$870$	14.9173			0.505745
$871$	−16.6732	−	12.1138i	−0.564950	−	0.410460i
$872$	1.87822	−	5.78055i	0.0636044	−	0.195754i
$873$	3.12944	+	9.63141i	0.105915	+	0.325974i
$874$	18.6073	−	13.5190i	0.629403	−	0.457288i
$875$	2.48141	−	1.80285i	0.0838868	−	0.0609473i
$876$	13.9545	+	42.9475i	0.471478	+	1.45106i
$877$	7.68262	−	23.6447i	0.259424	−	0.798424i	−0.733502	−	0.679687i	$-0.762115\pi$
$877$	7.68262	−	23.6447i	0.259424	−	0.798424i	0.992926	−	0.118737i	$-0.0378845\pi$
$878$	10.9666	+	7.96767i	0.370104	+	0.268896i
$879$	−41.7433			−1.40797
$880$		0			0
$881$	32.6968			1.10158			0.550792	−	0.834643i	$-0.314326\pi$
$881$	32.6968			1.10158			0.550792	+	0.834643i	$0.314326\pi$
$882$	−2.69181	−	1.95571i	−0.0906380	−	0.0658523i
$883$	14.7159	−	45.2910i	0.495231	−	1.52416i	−0.321366	−	0.946955i	$-0.604142\pi$
$883$	14.7159	−	45.2910i	0.495231	−	1.52416i	0.816597	−	0.577208i	$-0.195858\pi$
$884$	−1.04490	−	3.21586i	−0.0351437	−	0.108161i
$885$	4.35666	−	3.16530i	0.146448	−	0.106400i
$886$	69.3039	−	50.3522i	2.32831	−	1.69162i
$887$	−18.2617	−	56.2037i	−0.613167	−	1.88713i	−0.425704	−	0.904862i	$-0.639974\pi$
$887$	−18.2617	−	56.2037i	−0.613167	−	1.88713i	−0.187463	−	0.982272i	$-0.560026\pi$
$888$	0.891617	−	2.74412i	0.0299207	−	0.0920865i
$889$	−1.12060	−	0.814161i	−0.0375836	−	0.0273061i
$890$	14.1847			0.475471
$891$		0			0
$892$	20.5076			0.686646
$893$	19.0365	+	13.8308i	0.637032	+	0.462831i
$894$	10.8013	−	33.2429i	0.361249	−	1.11181i
$895$	−7.02502	−	21.6208i	−0.234821	−	0.722704i
$896$	15.9234	−	11.5690i	0.531963	−	0.386494i
$897$	−6.56206	+	4.76762i	−0.219101	+	0.159186i
$898$	−7.87386	−	24.2333i	−0.262754	−	0.808674i
$899$	12.0484	−	37.0811i	0.401836	−	1.23673i
$900$	−1.27542	−	0.926650i	−0.0425141	−	0.0308883i
$901$	1.94265			0.0647190
$902$		0			0
$903$	7.71450			0.256722
$904$	2.00869	+	1.45940i	0.0668079	+	0.0485388i
$905$	−0.741120	+	2.28093i	−0.0246357	+	0.0758208i
$906$	−14.7836	−	45.4992i	−0.491151	−	1.51161i
$907$	−28.0386	+	20.3712i	−0.931005	+	0.676415i	−0.946239	−	0.323469i	$-0.895151\pi$
$907$	−28.0386	+	20.3712i	−0.931005	+	0.676415i	0.0152337	+	0.999884i	$0.495151\pi$
$908$	11.9901	−	8.71129i	0.397904	−	0.289094i
$909$	−2.39127	−	7.35957i	−0.0793134	−	0.244102i
$910$	6.05677	−	18.6408i	0.200780	−	0.617937i
$911$	8.24247	+	5.98851i	0.273085	+	0.198408i	0.715896	−	0.698207i	$-0.246019\pi$
$911$	8.24247	+	5.98851i	0.273085	+	0.198408i	−0.442811	+	0.896615i	$0.646019\pi$
$912$	−46.3277			−1.53406
$913$		0			0
$914$	20.7484			0.686298
$915$	3.12218	+	2.26840i	0.103216	+	0.0749909i
$916$	17.1110	−	52.6623i	0.565364	−	1.74001i
$917$	−0.596177	−	1.83485i	−0.0196875	−	0.0605919i
$918$	3.52037	−	2.55770i	0.116189	−	0.0844165i
$919$	−29.2289	+	21.2360i	−0.964172	+	0.700512i	−0.954116	−	0.299438i	$-0.903201\pi$
$919$	−29.2289	+	21.2360i	−0.964172	+	0.700512i	−0.0100558	+	0.999949i	$0.503201\pi$
$920$	0.351296	+	1.08118i	0.0115819	+	0.0356454i
$921$	18.2472	−	56.1593i	0.601267	−	1.85051i
$922$	−5.29777	−	3.84905i	−0.174473	−	0.126762i
$923$	19.8907			0.654711
$924$		0			0
$925$	1.84453			0.0606479
$926$	41.2795	+	29.9913i	1.35653	+	0.985575i
$927$	2.83059	−	8.71164i	0.0929686	−	0.286128i
$928$	9.27172	+	28.5354i	0.304359	+	0.936721i
$929$	−22.7528	+	16.5309i	−0.746494	+	0.542360i	−0.894738	−	0.446591i	$-0.852638\pi$
$929$	−22.7528	+	16.5309i	−0.746494	+	0.542360i	0.148244	+	0.988951i	$0.452638\pi$
$930$	−33.9728	+	24.6827i	−1.11401	+	0.809378i
$931$	5.87433	+	18.0793i	0.192523	+	0.592526i
$932$	20.5802	−	63.3394i	0.674128	−	2.07475i
$933$	30.0476	+	21.8309i	0.983714	+	0.714710i
$934$	69.5087			2.27439
$935$		0			0
$936$	−1.64483			−0.0537630
$937$	0.0689021	+	0.0500603i	0.00225093	+	0.00163540i	0.588910	−	0.808199i	$-0.299557\pi$
$937$	0.0689021	+	0.0500603i	0.00225093	+	0.00163540i	−0.586659	+	0.809834i	$0.699557\pi$
$938$	−13.4201	+	41.3028i	−0.438181	+	1.34858i
$939$	0.621575	+	1.91301i	0.0202843	+	0.0624287i
$940$	−5.76295	+	4.18703i	−0.187967	+	0.136566i
$941$	−33.8294	+	24.5785i	−1.10281	+	0.801235i	−0.981516	−	0.191382i	$-0.938703\pi$
$941$	−33.8294	+	24.5785i	−1.10281	+	0.801235i	−0.121290	+	0.992617i	$0.538703\pi$
$942$	4.80009	+	14.7731i	0.156395	+	0.481335i
$943$	−1.89357	+	5.82782i	−0.0616633	+	0.189780i
$944$	6.98522	+	5.07506i	0.227349	+	0.165179i
$945$	13.7326			0.446721
$946$		0			0
$947$	8.92463			0.290012			0.145006	−	0.989431i	$-0.453680\pi$
$947$	8.92463			0.290012			0.145006	+	0.989431i	$0.453680\pi$
$948$	−42.7557	−	31.0638i	−1.38864	−	1.00891i
$949$	−9.30740	+	28.6452i	−0.302131	+	0.929863i
$950$	5.11227	+	15.7340i	0.165864	+	0.510477i
$951$	36.8826	−	26.7968i	1.19600	−	0.868946i
$952$	−0.941166	+	0.683797i	−0.0305034	+	0.0221620i
$953$	−1.62661	−	5.00620i	−0.0526912	−	0.162167i	0.921248	−	0.388975i	$-0.127171\pi$
$953$	−1.62661	−	5.00620i	−0.0526912	−	0.162167i	−0.973939	+	0.226808i	$0.927171\pi$
$954$	1.78855	−	5.50459i	0.0579065	−	0.178218i
$955$	13.9525	+	10.1371i	0.451493	+	0.328029i
$956$	38.9283			1.25903
$957$		0			0
$958$	36.2438			1.17098
$959$	−27.7505	−	20.1619i	−0.896112	−	0.651063i
$960$	6.35959	−	19.5728i	0.205255	−	0.631709i
$961$	24.3371	+	74.9018i	0.785067	+	2.41619i
$962$	9.53591	−	6.92825i	0.307450	−	0.223376i
$963$	−3.90644	+	2.83819i	−0.125883	+	0.0914594i
$964$	−3.24305	−	9.98109i	−0.104452	−	0.321469i
$965$	−0.799036	+	2.45918i	−0.0257219	+	0.0791638i
$966$	13.8278	+	10.0465i	0.444901	+	0.323240i
$967$	18.5421			0.596275			0.298138	−	0.954523i	$-0.403635\pi$
$967$	18.5421			0.596275			0.298138	+	0.954523i	$0.403635\pi$
$968$		0			0
$969$	7.00606			0.225067
$970$	26.0276	+	18.9102i	0.835696	+	0.607168i
$971$	−7.48533	+	23.0375i	−0.240216	+	0.739308i	0.756171	+	0.654374i	$0.227068\pi$
$971$	−7.48533	+	23.0375i	−0.240216	+	0.739308i	−0.996387	+	0.0849336i	$0.972932\pi$
$972$	−4.97704	−	15.3177i	−0.159639	−	0.491317i
$973$	−5.89322	+	4.28168i	−0.188928	+	0.137264i
$974$	−12.9518	+	9.41004i	−0.415003	+	0.301517i
$975$	−1.80289	−	5.54873i	−0.0577388	−	0.177702i
$976$	−1.91209	+	5.88481i	−0.0612045	+	0.188368i
$977$	−39.6918	−	28.8378i	−1.26985	−	0.922603i	−0.270658	−	0.962676i	$-0.587241\pi$
$977$	−39.6918	−	28.8378i	−1.26985	−	0.922603i	−0.999197	+	0.0400724i	$0.987241\pi$
$978$	−39.8272			−1.27353
$979$		0			0
$980$	−5.75485			−0.183832
$981$	−3.96623	−	2.88163i	−0.126632	−	0.0920035i
$982$	19.8494	−	61.0902i	0.633420	−	1.94947i
$983$	15.1849	+	46.7344i	0.484324	+	1.49060i	0.832958	+	0.553337i	$0.186646\pi$
$983$	15.1849	+	46.7344i	0.484324	+	1.49060i	−0.348634	+	0.937259i	$0.613354\pi$
$984$	−5.57792	+	4.05260i	−0.177818	+	0.129192i
$985$	−0.117090	+	0.0850707i	−0.00373079	+	0.00271058i
$986$	−1.11772	−	3.43998i	−0.0355954	−	0.109551i
$987$	−5.40356	+	16.6304i	−0.171997	+	0.529353i
$988$	46.5653	+	33.8316i	1.48144	+	1.07633i
$989$	−1.82788			−0.0581233
$990$		0			0
$991$	30.9620			0.983541			0.491771	−	0.870725i	$-0.336350\pi$
$991$	30.9620			0.983541			0.491771	+	0.870725i	$0.336350\pi$
$992$	−68.3312	−	49.6455i	−2.16952	−	1.57625i
$993$	15.1744	−	46.7019i	0.481544	−	1.48204i
$994$	−12.9522	−	39.8629i	−0.410820	−	1.26437i
$995$	−6.10142	+	4.43294i	−0.193428	+	0.140534i
$996$	32.9924	−	23.9704i	1.04540	−	0.759530i
$997$	−7.07461	−	21.7734i	−0.224055	−	0.689571i	−0.998386	−	0.0567903i	$-0.981913\pi$
$997$	−7.07461	−	21.7734i	−0.224055	−	0.689571i	0.774331	−	0.632781i	$-0.218087\pi$
$998$	−24.2665	+	74.6846i	−0.768143	+	2.36410i
$999$	6.68123	+	4.85420i	0.211385	+	0.153580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.e.81.1		8
11.2	odd	10		55.2.g.b.16.1	✓	8
11.3	even	5	inner	605.2.g.e.366.1		8
11.4	even	5		605.2.g.k.251.2		8
11.5	even	5		605.2.a.k.1.4		4
11.6	odd	10		605.2.a.j.1.1		4
11.7	odd	10		55.2.g.b.31.1	yes	8
11.8	odd	10		605.2.g.m.366.2		8
11.9	even	5		605.2.g.k.511.2		8
11.10	odd	2		605.2.g.m.81.2		8
33.2	even	10		495.2.n.e.181.2		8
33.5	odd	10		5445.2.a.bi.1.1		4
33.17	even	10		5445.2.a.bp.1.4		4
33.29	even	10		495.2.n.e.361.2		8
44.7	even	10		880.2.bo.h.801.2		8
44.27	odd	10		9680.2.a.cm.1.1		4
44.35	even	10		880.2.bo.h.401.2		8
44.39	even	10		9680.2.a.cn.1.1		4
55.2	even	20		275.2.z.a.49.4		16
55.7	even	20		275.2.z.a.174.1		16
55.13	even	20		275.2.z.a.49.1		16
55.18	even	20		275.2.z.a.174.4		16
55.24	odd	10		275.2.h.a.126.2		8
55.29	odd	10		275.2.h.a.251.2		8
55.39	odd	10		3025.2.a.bd.1.4		4
55.49	even	10		3025.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.1	✓	8	11.2	odd	10
55.2.g.b.31.1	yes	8	11.7	odd	10
275.2.h.a.126.2		8	55.24	odd	10
275.2.h.a.251.2		8	55.29	odd	10
275.2.z.a.49.1		16	55.13	even	20
275.2.z.a.49.4		16	55.2	even	20
275.2.z.a.174.1		16	55.7	even	20
275.2.z.a.174.4		16	55.18	even	20
495.2.n.e.181.2		8	33.2	even	10
495.2.n.e.361.2		8	33.29	even	10
605.2.a.j.1.1		4	11.6	odd	10
605.2.a.k.1.4		4	11.5	even	5
605.2.g.e.81.1		8	1.1	even	1	trivial
605.2.g.e.366.1		8	11.3	even	5	inner
605.2.g.k.251.2		8	11.4	even	5
605.2.g.k.511.2		8	11.9	even	5
605.2.g.m.81.2		8	11.10	odd	2
605.2.g.m.366.2		8	11.8	odd	10
880.2.bo.h.401.2		8	44.35	even	10
880.2.bo.h.801.2		8	44.7	even	10
3025.2.a.w.1.1		4	55.49	even	10
3025.2.a.bd.1.4		4	55.39	odd	10
5445.2.a.bi.1.1		4	33.5	odd	10
5445.2.a.bp.1.4		4	33.17	even	10
9680.2.a.cm.1.1		4	44.27	odd	10
9680.2.a.cn.1.1		4	44.39	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)

\(f(q)\)	\(=\)	\(q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} +O(q^{10})\)	\(q+(-1.69513 - 1.23158i) q^{2} +(0.591149 - 1.81937i) q^{3} +(0.738630 + 2.27327i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-3.24278 + 2.35601i) q^{6} +(0.947813 + 2.91707i) q^{7} +(0.252684 - 0.777682i) q^{8} +(-0.533593 - 0.387678i) q^{9} -2.09529 q^{10} +4.57255 q^{12} +(2.46735 + 1.79264i) q^{13} +(1.98595 - 6.11211i) q^{14} +(-0.591149 - 1.81937i) q^{15} +(2.48141 - 1.80285i) q^{16} +(-0.375259 + 0.272641i) q^{17} +(0.427051 + 1.31433i) q^{18} +(2.43988 - 7.50919i) q^{19} +(1.93376 + 1.40496i) q^{20} +5.86752 q^{21} -1.39026 q^{23} +(-1.26552 - 0.919451i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.97470 - 6.07750i) q^{26} +(3.62218 - 2.63167i) q^{27} +(-5.93120 + 4.30927i) q^{28} +(-1.15004 - 3.53947i) q^{29} +(-1.23863 + 3.81211i) q^{30} +(8.47564 + 6.15791i) q^{31} -8.06206 q^{32} +0.971892 q^{34} +(2.48141 + 1.80285i) q^{35} +(0.487169 - 1.49935i) q^{36} +(0.569992 + 1.75425i) q^{37} +(-13.3841 + 9.72412i) q^{38} +(4.72004 - 3.42931i) q^{39} +(-0.252684 - 0.777682i) q^{40} +(1.36203 - 4.19190i) q^{41} +(-9.94619 - 7.22633i) q^{42} +1.31478 q^{43} -0.659557 q^{45} +(2.35666 + 1.71222i) q^{46} +(-0.920927 + 2.83432i) q^{47} +(-1.81316 - 5.58034i) q^{48} +(-1.94781 + 1.41517i) q^{49} +(-1.69513 + 1.23158i) q^{50} +(0.274201 + 0.843905i) q^{51} +(-2.25268 + 6.93305i) q^{52} +(-3.38828 - 2.46173i) q^{53} -9.38118 q^{54} +2.50805 q^{56} +(-12.2196 - 8.87809i) q^{57} +(-2.40968 + 7.41623i) q^{58} +(0.869890 + 2.67725i) q^{59} +(3.69927 - 2.68768i) q^{60} +(-1.63209 + 1.18578i) q^{61} +(-6.78332 - 20.8769i) q^{62} +(0.625136 - 1.92397i) q^{63} +(8.70342 + 6.32340i) q^{64} +3.04981 q^{65} -6.75753 q^{67} +(-0.896964 - 0.651683i) q^{68} +(-0.821848 + 2.52939i) q^{69} +(-1.98595 - 6.11211i) q^{70} +(5.27637 - 3.83351i) q^{71} +(-0.436320 + 0.317005i) q^{72} +(3.05179 + 9.39245i) q^{73} +(1.19430 - 3.67568i) q^{74} +(-1.54765 - 1.12443i) q^{75} +18.8726 q^{76} -12.2245 q^{78} +(-9.35051 - 6.79354i) q^{79} +(0.947813 - 2.91707i) q^{80} +(-3.25817 - 10.0276i) q^{81} +(-7.47150 + 5.42836i) q^{82} +(7.21531 - 5.24223i) q^{83} +(4.33392 + 13.3384i) q^{84} +(-0.143336 + 0.441143i) q^{85} +(-2.22872 - 1.61926i) q^{86} -7.11945 q^{87} -6.76978 q^{89} +(1.11803 + 0.812299i) q^{90} +(-2.89065 + 8.89651i) q^{91} +(-1.02689 - 3.16043i) q^{92} +(16.2139 - 11.7801i) q^{93} +(5.05179 - 3.67034i) q^{94} +(-2.43988 - 7.50919i) q^{95} +(-4.76588 + 14.6679i) q^{96} +(-12.4219 - 9.02506i) q^{97} +5.04469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + q^8 + 5 * q^9	\( 8 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + q^{8} + 5 q^{9} - 2 q^{10} + 16 q^{12} - 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} - 12 q^{17} - 10 q^{18} - 5 q^{19} + 2 q^{20} + 20 q^{21} + 10 q^{23} + 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} - 19 q^{28} - 21 q^{29} - 7 q^{30} + 15 q^{31} - 16 q^{32} + 4 q^{34} - q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} + 14 q^{39} - q^{40} - 3 q^{41} - 21 q^{42} + 38 q^{43} + 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} - 3 q^{50} - 6 q^{51} - 17 q^{52} - 2 q^{53} - 16 q^{54} + 22 q^{56} - 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} + 5 q^{62} + 30 q^{63} + 29 q^{64} - 2 q^{65} - 38 q^{67} + 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} - 5 q^{72} + 2 q^{73} + 20 q^{74} - 5 q^{75} - 16 q^{78} + 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} + 38 q^{83} + 17 q^{84} - 13 q^{85} + 2 q^{86} - 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} + 18 q^{94} + 5 q^{95} + 17 q^{96} - 56 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + q^8 + 5 * q^9 - 2 * q^10 + 16 * q^12 - 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 - 12 * q^17 - 10 * q^18 - 5 * q^19 + 2 * q^20 + 20 * q^21 + 10 * q^23 + 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 - 19 * q^28 - 21 * q^29 - 7 * q^30 + 15 * q^31 - 16 * q^32 + 4 * q^34 - q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 + 14 * q^39 - q^40 - 3 * q^41 - 21 * q^42 + 38 * q^43 + 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 - 3 * q^50 - 6 * q^51 - 17 * q^52 - 2 * q^53 - 16 * q^54 + 22 * q^56 - 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 + 5 * q^62 + 30 * q^63 + 29 * q^64 - 2 * q^65 - 38 * q^67 + 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 - 5 * q^72 + 2 * q^73 + 20 * q^74 - 5 * q^75 - 16 * q^78 + 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 + 38 * q^83 + 17 * q^84 - 13 * q^85 + 2 * q^86 - 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 + 18 * q^94 + 5 * q^95 + 17 * q^96 - 56 * q^97 - 16 * q^98

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