LMFDB - Embedded newform 845.2.t.c.427.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.t (of order $12$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{13} - 14 x^{12} + 8 x^{11} + 8 x^{10} + 26 x^{9} + 179 x^{8} + 104 x^{7} + 40 x^{6} + \cdots + 1 $ x^16 - 4x^13 - 14x^12 + 8x^11 + 8x^10 + 26x^9 + 179x^8 + 104x^7 + 40x^6 + 74x^5 + 6x^4 - 20x^3 + 2x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.1
Root			$0.432841 - 1.61538i$ of defining polynomial
Character	$\chi$	$=$	845.427
Dual form			845.2.t.c.188.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00594 + 1.15813i) q^{2} +(0.328222 + 0.0879467i) q^{3} +(1.68254 - 2.91425i) q^{4} +(-1.55654 - 1.60536i) q^{5} +(-0.760248 + 0.203708i) q^{6} +(-1.97936 + 3.42835i) q^{7} +3.16190i q^{8} +(-2.49808 - 1.44227i) q^{9} +O(q^{10})$	\(q+(-2.00594 + 1.15813i) q^{2} +(0.328222 + 0.0879467i) q^{3} +(1.68254 - 2.91425i) q^{4} +(-1.55654 - 1.60536i) q^{5} +(-0.760248 + 0.203708i) q^{6} +(-1.97936 + 3.42835i) q^{7} +3.16190i q^{8} +(-2.49808 - 1.44227i) q^{9} +(4.98155 + 1.41758i) q^{10} +(0.760248 + 0.203708i) q^{11} +(0.808545 - 0.808545i) q^{12} -9.16944i q^{14} +(-0.369704 - 0.663806i) q^{15} +(-0.296815 - 0.514099i) q^{16} +(-0.425285 - 1.58719i) q^{17} +6.68135 q^{18} +(-0.453972 - 1.69425i) q^{19} +(-7.29737 + 1.83506i) q^{20} +(-0.951180 + 0.951180i) q^{21} +(-1.76094 + 0.471842i) q^{22} +(-1.02800 + 3.83654i) q^{23} +(-0.278079 + 1.03780i) q^{24} +(-0.154365 + 4.99762i) q^{25} +(-1.41391 - 1.41391i) q^{27} +(6.66071 + 11.5367i) q^{28} +(3.01218 - 1.73908i) q^{29} +(1.51038 + 0.903393i) q^{30} +(-2.07599 - 2.07599i) q^{31} +(-4.28578 - 2.47440i) q^{32} +(0.231614 + 0.133723i) q^{33} +(2.69127 + 2.69127i) q^{34} +(8.58469 - 2.15878i) q^{35} +(-8.40626 + 4.85336i) q^{36} +(3.42282 + 5.92849i) q^{37} +(2.87281 + 2.87281i) q^{38} +(5.07599 - 4.92163i) q^{40} +(2.75507 - 10.2821i) q^{41} +(0.806422 - 3.00961i) q^{42} +(9.60959 - 2.57488i) q^{43} +(1.87281 - 1.87281i) q^{44} +(1.57300 + 6.25527i) q^{45} +(-2.38112 - 8.88646i) q^{46} +9.09526 q^{47} +(-0.0522078 - 0.194842i) q^{48} +(-4.33572 - 7.50968i) q^{49} +(-5.47826 - 10.2037i) q^{50} -0.558351i q^{51} +(0.958716 - 0.958716i) q^{53} +(4.47371 + 1.19873i) q^{54} +(-0.856332 - 1.53755i) q^{55} +(-10.8401 - 6.25853i) q^{56} -0.596014i q^{57} +(-4.02818 + 6.97701i) q^{58} +(10.1993 - 2.73291i) q^{59} +(-2.55654 - 0.0394734i) q^{60} +(-1.84463 + 3.19499i) q^{61} +(6.56860 + 1.76005i) q^{62} +(9.88919 - 5.70953i) q^{63} +12.6500 q^{64} -0.619474 q^{66} +(-3.27955 + 1.89345i) q^{67} +(-5.34102 - 1.43112i) q^{68} +(-0.674823 + 1.16883i) q^{69} +(-14.7203 + 14.2726i) q^{70} +(5.02635 - 1.34681i) q^{71} +(4.56031 - 7.89869i) q^{72} -5.57581i q^{73} +(-13.7320 - 7.92815i) q^{74} +(-0.490190 + 1.62675i) q^{75} +(-5.70129 - 1.52765i) q^{76} +(-2.20318 + 2.20318i) q^{77} +9.03051i q^{79} +(-0.363309 + 1.27671i) q^{80} +(3.98708 + 6.90582i) q^{81} +(6.38147 + 23.8160i) q^{82} +6.16980 q^{83} +(1.17157 + 4.37238i) q^{84} +(-1.88603 + 3.15326i) q^{85} +(-16.2942 + 16.2942i) q^{86} +(1.14161 - 0.305893i) q^{87} +(-0.644104 + 2.40383i) q^{88} +(-1.28734 + 4.80440i) q^{89} +(-10.3998 - 10.7260i) q^{90} +(9.45100 + 9.45100i) q^{92} +(-0.498808 - 0.863961i) q^{93} +(-18.2446 + 10.5335i) q^{94} +(-2.01325 + 3.36595i) q^{95} +(-1.18907 - 1.18907i) q^{96} +(7.82065 + 4.51526i) q^{97} +(17.3944 + 10.0427i) q^{98} +(-1.60536 - 1.60536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} + 8 q^{4} - 4 q^{5} + 6 q^{6}+O(q^{10}) $ 16 * q + 6 * q^3 + 8 * q^4 - 4 * q^5 + 6 * q^6	$ 16 q + 6 q^{3} + 8 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{15} + 8 q^{16} - 16 q^{17} + 40 q^{18} + 14 q^{19} + 2 q^{20} - 24 q^{21} - 10 q^{22} + 14 q^{23} + 2 q^{24} - 24 q^{25} + 24 q^{27} + 8 q^{28} + 14 q^{30} + 4 q^{31} + 24 q^{35} + 44 q^{37} - 4 q^{38} + 44 q^{40} - 16 q^{41} - 24 q^{42} + 6 q^{43} - 20 q^{44} - 22 q^{45} - 2 q^{46} + 32 q^{47} + 14 q^{48} - 24 q^{49} - 44 q^{50} - 48 q^{53} - 20 q^{54} - 10 q^{55} - 24 q^{58} + 22 q^{59} - 20 q^{60} - 20 q^{61} + 30 q^{62} + 96 q^{64} - 72 q^{66} - 4 q^{68} - 4 q^{69} - 136 q^{70} + 10 q^{71} + 16 q^{72} - 30 q^{75} - 6 q^{76} - 48 q^{77} + 26 q^{80} + 20 q^{81} - 20 q^{82} + 96 q^{83} + 16 q^{84} - 32 q^{85} - 92 q^{86} - 16 q^{87} + 10 q^{88} - 28 q^{89} - 28 q^{90} + 100 q^{92} + 40 q^{93} - 2 q^{95} + 60 q^{96} + 4 q^{99}+O(q^{100}) $ 16 * q + 6 * q^3 + 8 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^15 + 8 * q^16 - 16 * q^17 + 40 * q^18 + 14 * q^19 + 2 * q^20 - 24 * q^21 - 10 * q^22 + 14 * q^23 + 2 * q^24 - 24 * q^25 + 24 * q^27 + 8 * q^28 + 14 * q^30 + 4 * q^31 + 24 * q^35 + 44 * q^37 - 4 * q^38 + 44 * q^40 - 16 * q^41 - 24 * q^42 + 6 * q^43 - 20 * q^44 - 22 * q^45 - 2 * q^46 + 32 * q^47 + 14 * q^48 - 24 * q^49 - 44 * q^50 - 48 * q^53 - 20 * q^54 - 10 * q^55 - 24 * q^58 + 22 * q^59 - 20 * q^60 - 20 * q^61 + 30 * q^62 + 96 * q^64 - 72 * q^66 - 4 * q^68 - 4 * q^69 - 136 * q^70 + 10 * q^71 + 16 * q^72 - 30 * q^75 - 6 * q^76 - 48 * q^77 + 26 * q^80 + 20 * q^81 - 20 * q^82 + 96 * q^83 + 16 * q^84 - 32 * q^85 - 92 * q^86 - 16 * q^87 + 10 * q^88 - 28 * q^89 - 28 * q^90 + 100 * q^92 + 40 * q^93 - 2 * q^95 + 60 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.00594	+	1.15813i	−1.41842	+	0.818924i	−0.996160	−	0.0875526i	$-0.972095\pi$
$2$	−2.00594	+	1.15813i	−1.41842	+	0.818924i	−0.422257	+	0.906476i	$0.638762\pi$
$3$	0.328222	+	0.0879467i	0.189499	+	0.0507760i	0.352320	−	0.935880i	$-0.385393\pi$
$3$	0.328222	+	0.0879467i	0.189499	+	0.0507760i	−0.162821	+	0.986656i	$0.552059\pi$
$4$	1.68254	−	2.91425i	0.841271	−	1.45712i
$5$	−1.55654	−	1.60536i	−0.696106	−	0.717939i
$5$	−1.55654	−	1.60536i	−0.696106	−	0.717939i
$6$	−0.760248	+	0.203708i	−0.310370	+	0.0831634i
$7$	−1.97936	+	3.42835i	−0.748127	+	1.29579i	0.200593	+	0.979675i	$0.435713\pi$
$7$	−1.97936	+	3.42835i	−0.748127	+	1.29579i	−0.948719	+	0.316119i	$0.897620\pi$
$8$			3.16190i			1.11790i
$9$	−2.49808	−	1.44227i	−0.832694	−	0.480756i
$10$	4.98155	+	1.41758i	1.57531	+	0.448279i
$11$	0.760248	+	0.203708i	0.229223	+	0.0614202i	0.371602	−	0.928392i	$-0.378808\pi$
$11$	0.760248	+	0.203708i	0.229223	+	0.0614202i	−0.142379	+	0.989812i	$0.545475\pi$
$12$	0.808545	−	0.808545i	0.233407	−	0.233407i
$13$		0			0
$13$		0			0
$14$		−	9.16944i		−	2.45064i
$15$	−0.369704	−	0.663806i	−0.0954571	−	0.171394i
$16$	−0.296815	−	0.514099i	−0.0742038	−	0.128525i
$17$	−0.425285	−	1.58719i	−0.103147	−	0.384949i	0.894982	−	0.446103i	$-0.147189\pi$
$17$	−0.425285	−	1.58719i	−0.103147	−	0.384949i	−0.998128	+	0.0611541i	$0.980522\pi$
$18$	6.68135			1.57481
$19$	−0.453972	−	1.69425i	−0.104148	−	0.388687i	0.894099	−	0.447870i	$-0.147817\pi$
$19$	−0.453972	−	1.69425i	−0.104148	−	0.388687i	−0.998247	+	0.0591828i	$0.981151\pi$
$20$	−7.29737	+	1.83506i	−1.63174	+	0.410332i
$21$	−0.951180	+	0.951180i	−0.207564	+	0.207564i
$22$	−1.76094	+	0.471842i	−0.375433	+	0.100597i
$23$	−1.02800	+	3.83654i	−0.214353	+	0.799975i	0.772041	+	0.635573i	$0.219236\pi$
$23$	−1.02800	+	3.83654i	−0.214353	+	0.799975i	−0.986393	+	0.164402i	$0.947431\pi$
$24$	−0.278079	+	1.03780i	−0.0567626	+	0.211841i
$25$	−0.154365	+	4.99762i	−0.0308729	+	0.999523i
$26$		0			0
$27$	−1.41391	−	1.41391i	−0.272106	−	0.272106i
$28$	6.66071	+	11.5367i	1.25876	+	2.18023i
$29$	3.01218	−	1.73908i	0.559348	−	0.322940i	−0.193536	−	0.981093i	$-0.561996\pi$
$29$	3.01218	−	1.73908i	0.559348	−	0.322940i	0.752884	+	0.658154i	$0.228662\pi$
$30$	1.51038	+	0.903393i	0.275757	+	0.164936i
$31$	−2.07599	−	2.07599i	−0.372859	−	0.372859i	0.495659	−	0.868517i	$-0.334927\pi$
$31$	−2.07599	−	2.07599i	−0.372859	−	0.372859i	−0.868517	+	0.495659i	$0.834927\pi$
$32$	−4.28578	−	2.47440i	−0.757627	−	0.437416i
$33$	0.231614	+	0.133723i	0.0403189	+	0.0232781i
$34$	2.69127	+	2.69127i	0.461549	+	0.461549i
$35$	8.58469	−	2.15878i	1.45108	−	0.364900i
$36$	−8.40626	+	4.85336i	−1.40104	+	0.808893i
$37$	3.42282	+	5.92849i	0.562708	+	0.974638i	0.997259	+	0.0739913i	$0.0235737\pi$
$37$	3.42282	+	5.92849i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$38$	2.87281	+	2.87281i	0.466031	+	0.466031i
$39$		0			0
$40$	5.07599	−	4.92163i	0.802585	−	0.778177i
$41$	2.75507	−	10.2821i	0.430269	−	1.60579i	−0.321871	−	0.946784i	$-0.604312\pi$
$41$	2.75507	−	10.2821i	0.430269	−	1.60579i	0.752140	−	0.659003i	$-0.229022\pi$
$42$	0.806422	−	3.00961i	0.124434	−	0.464392i
$43$	9.60959	−	2.57488i	1.46545	−	0.392666i	0.564080	−	0.825720i	$-0.309231\pi$
$43$	9.60959	−	2.57488i	1.46545	−	0.392666i	0.901368	+	0.433054i	$0.142564\pi$
$44$	1.87281	−	1.87281i	0.282336	−	0.282336i
$45$	1.57300	+	6.25527i	0.234490	+	0.932481i
$46$	−2.38112	−	8.88646i	−0.351077	−	1.31024i
$47$	9.09526			1.32668			0.663340	−	0.748318i	$-0.269138\pi$
$47$	9.09526			1.32668			0.663340	+	0.748318i	$0.269138\pi$
$48$	−0.0522078	−	0.194842i	−0.00753555	−	0.0281231i
$49$	−4.33572	−	7.50968i	−0.619388	−	1.07281i
$50$	−5.47826	−	10.2037i	−0.774742	−	1.44302i
$51$		−	0.558351i		−	0.0781848i
$52$		0			0
$53$	0.958716	−	0.958716i	0.131690	−	0.131690i	−0.638190	−	0.769879i	$-0.720316\pi$
$53$	0.958716	−	0.958716i	0.131690	−	0.131690i	0.769879	+	0.638190i	$0.220316\pi$
$54$	4.47371	+	1.19873i	0.608795	+	0.163126i
$55$	−0.856332	−	1.53755i	−0.115468	−	0.207323i
$56$	−10.8401	−	6.25853i	−1.44857	−	0.836332i
$57$		−	0.596014i		−	0.0789439i
$58$	−4.02818	+	6.97701i	−0.528926	+	0.916126i
$59$	10.1993	−	2.73291i	1.32784	−	0.355794i	0.475931	−	0.879482i	$-0.342111\pi$
$59$	10.1993	−	2.73291i	1.32784	−	0.355794i	0.851910	+	0.523689i	$0.175444\pi$
$60$	−2.55654	−	0.0394734i	−0.330048	−	0.00509599i
$61$	−1.84463	+	3.19499i	−0.236180	+	0.409076i	−0.959615	−	0.281316i	$-0.909229\pi$
$61$	−1.84463	+	3.19499i	−0.236180	+	0.409076i	0.723435	+	0.690393i	$0.242562\pi$
$62$	6.56860	+	1.76005i	0.834212	+	0.223527i
$63$	9.88919	−	5.70953i	1.24592	−	0.719333i
$64$	12.6500			1.58125
$65$		0			0
$66$	−0.619474			−0.0762520
$67$	−3.27955	+	1.89345i	−0.400661	+	0.231321i	−0.686769	−	0.726876i	$-0.740972\pi$
$67$	−3.27955	+	1.89345i	−0.400661	+	0.231321i	0.286108	+	0.958197i	$0.407638\pi$
$68$	−5.34102	−	1.43112i	−0.647693	−	0.173549i
$69$	−0.674823	+	1.16883i	−0.0812391	+	0.140710i
$70$	−14.7203	+	14.2726i	−1.75941	+	1.70590i
$71$	5.02635	−	1.34681i	0.596517	−	0.159836i	0.0520873	−	0.998643i	$-0.483413\pi$
$71$	5.02635	−	1.34681i	0.596517	−	0.159836i	0.544430	+	0.838806i	$0.316746\pi$
$72$	4.56031	−	7.89869i	0.537437	−	0.930869i
$73$		−	5.57581i		−	0.652599i	−0.945266	−	0.326299i	$-0.894198\pi$
$73$		−	5.57581i		−	0.652599i	0.945266	−	0.326299i	$-0.105802\pi$
$74$	−13.7320	−	7.92815i	−1.59631	−	0.921629i
$75$	−0.490190	+	1.62675i	−0.0566022	+	0.187841i
$76$	−5.70129	−	1.52765i	−0.653982	−	0.175234i
$77$	−2.20318	+	2.20318i	−0.251076	+	0.251076i
$78$		0			0
$79$			9.03051i			1.01601i	0.861354	+	0.508006i	$0.169617\pi$
$79$			9.03051i			1.01601i	−0.861354	+	0.508006i	$0.830383\pi$
$80$	−0.363309	+	1.27671i	−0.0406192	+	0.142741i
$81$	3.98708	+	6.90582i	0.443009	+	0.767314i
$82$	6.38147	+	23.8160i	0.704715	+	2.63003i
$83$	6.16980			0.677224			0.338612	−	0.940926i	$-0.390043\pi$
$83$	6.16980			0.677224			0.338612	+	0.940926i	$0.390043\pi$
$84$	1.17157	+	4.37238i	0.127829	+	0.477065i
$85$	−1.88603	+	3.15326i	−0.204569	+	0.342019i
$86$	−16.2942	+	16.2942i	−1.75705	+	1.75705i
$87$	1.14161	−	0.305893i	0.122393	−	0.0327952i
$88$	−0.644104	+	2.40383i	−0.0686617	+	0.256249i
$89$	−1.28734	+	4.80440i	−0.136457	+	0.509266i	0.863530	+	0.504297i	$0.168248\pi$
$89$	−1.28734	+	4.80440i	−0.136457	+	0.509266i	−0.999988	+	0.00496877i	$0.998418\pi$
$90$	−10.3998	−	10.7260i	−1.09623	−	1.13062i
$91$		0			0
$92$	9.45100	+	9.45100i	0.985334	+	0.985334i
$93$	−0.498808	−	0.863961i	−0.0517240	−	0.0895886i
$94$	−18.2446	+	10.5335i	−1.88179	+	1.08645i
$95$	−2.01325	+	3.36595i	−0.206555	+	0.345339i
$96$	−1.18907	−	1.18907i	−0.121359	−	0.121359i
$97$	7.82065	+	4.51526i	0.794067	+	0.458455i	0.841392	−	0.540425i	$-0.181736\pi$
$97$	7.82065	+	4.51526i	0.794067	+	0.458455i	−0.0473254	+	0.998880i	$0.515070\pi$
$98$	17.3944	+	10.0427i	1.75710	+	1.01446i
$99$	−1.60536	−	1.60536i	−0.161345	−	0.161345i
$100$	14.3046	+	8.85856i	1.43046	+	0.885856i
$101$	2.84481	−	1.64245i	0.283069	−	0.163430i	−0.351743	−	0.936097i	$-0.614411\pi$
$101$	2.84481	−	1.64245i	0.283069	−	0.163430i	0.634812	+	0.772667i	$0.281078\pi$
$102$	0.646645	+	1.12002i	0.0640274	+	0.110899i
$103$	3.64426	+	3.64426i	0.359080	+	0.359080i	0.863474	−	0.504394i	$-0.168284\pi$
$103$	3.64426	+	3.64426i	0.359080	+	0.359080i	−0.504394	+	0.863474i	$0.668284\pi$
$104$		0			0
$105$	3.00754	+	0.0464368i	0.293505	+	0.00453177i
$106$	−0.812811	+	3.03345i	−0.0789472	+	0.294635i
$107$	−1.71779	+	6.41087i	−0.166065	+	0.619762i	0.831837	+	0.555020i	$0.187289\pi$
$107$	−1.71779	+	6.41087i	−0.166065	+	0.619762i	−0.997902	+	0.0647424i	$0.979377\pi$
$108$	−6.49943	+	1.74152i	−0.625408	+	0.167578i
$109$	−4.12300	+	4.12300i	−0.394912	+	0.394912i	−0.876434	−	0.481522i	$-0.840084\pi$
$109$	−4.12300	+	4.12300i	−0.394912	+	0.394912i	0.481522	+	0.876434i	$0.340084\pi$
$110$	3.49844	+	2.09250i	0.333564	+	0.199512i
$111$	0.602051	+	2.24688i	0.0571441	+	0.213265i
$112$	2.35001			0.222055
$113$	−4.68221	−	17.4743i	−0.440466	−	1.64384i	−0.727638	−	0.685961i	$-0.759382\pi$
$113$	−4.68221	−	17.4743i	−0.440466	−	1.64384i	0.287172	−	0.957879i	$-0.407285\pi$
$114$	0.690263	+	1.19557i	0.0646490	+	0.111975i
$115$	7.75916	−	4.32143i	0.723545	−	0.402975i
$116$		−	11.7043i		−	1.08672i
$117$		0			0
$118$	−17.2942	+	17.2942i	−1.59206	+	1.59206i
$119$	6.28322	+	1.68358i	0.575982	+	0.154334i
$120$	2.09889	−	1.16897i	0.191602	−	0.106712i
$121$	−8.98980	−	5.19026i	−0.817254	−	0.471842i
$122$		−	8.54529i		−	0.773655i
$123$	1.80855	−	3.13249i	0.163071	−	0.282447i
$124$	−9.54290	+	2.55701i	−0.856978	+	0.229626i
$125$	8.26325	−	7.53118i	0.739088	−	0.673609i
$126$	−13.2248	+	22.9060i	−1.17816	+	2.04063i
$127$	7.44345	+	1.99447i	0.660499	+	0.176980i	0.573471	−	0.819226i	$-0.305596\pi$
$127$	7.44345	+	1.99447i	0.660499	+	0.176980i	0.0870278	+	0.996206i	$0.472263\pi$
$128$	−16.8036	+	9.70157i	−1.48524	+	0.857505i
$129$	3.38053			0.297639
$130$		0			0
$131$	2.42144			0.211562			0.105781	−	0.994389i	$-0.466266\pi$
$131$	2.42144			0.211562			0.105781	+	0.994389i	$0.466266\pi$
$132$	0.779402	−	0.449988i	0.0678383	−	0.0391664i
$133$	6.70704	+	1.79715i	0.581574	+	0.155832i
$134$	4.38573	−	7.59630i	0.378869	−	0.656221i
$135$	−0.0690272	+	4.47063i	−0.00594091	+	0.384771i
$136$	5.01852	−	1.34471i	0.430335	−	0.115308i
$137$	0.289095	−	0.500727i	0.0246991	−	0.0427800i	−0.853412	−	0.521237i	$-0.825471\pi$
$137$	0.289095	−	0.500727i	0.0246991	−	0.0427800i	0.878111	+	0.478457i	$0.158804\pi$
$138$		−	3.12614i		−	0.266114i
$139$	14.3969	+	8.31207i	1.22113	+	0.705021i	0.965159	−	0.261663i	$-0.0842710\pi$
$139$	14.3969	+	8.31207i	1.22113	+	0.705021i	0.255972	+	0.966684i	$0.417604\pi$
$140$	8.15288	−	28.6502i	0.689044	−	2.42138i
$141$	2.98526	+	0.799898i	0.251404	+	0.0673635i
$142$	−8.52279	+	8.52279i	−0.715217	+	0.715217i
$143$		0			0
$144$			1.71235i			0.142696i
$145$	−7.48044	−	2.12868i	−0.621216	−	0.176777i
$146$	6.45752	+	11.1848i	0.534429	+	0.925657i
$147$	−0.762624	−	2.84615i	−0.0629001	−	0.234747i
$148$	23.0361			1.89356
$149$	0.349028	+	1.30259i	0.0285935	+	0.106712i	0.978748	−	0.205068i	$-0.0657414\pi$
$149$	0.349028	+	1.30259i	0.0285935	+	0.106712i	−0.950154	+	0.311780i	$0.899075\pi$
$150$	−0.900698	−	3.83087i	−0.0735417	−	0.312790i
$151$	9.13988	−	9.13988i	0.743793	−	0.743793i	−0.229513	−	0.973306i	$-0.573713\pi$
$151$	9.13988	−	9.13988i	0.743793	−	0.743793i	0.973306	+	0.229513i	$0.0737132\pi$
$152$	5.35704	−	1.43541i	0.434513	−	0.116428i
$153$	−1.22675	+	4.57830i	−0.0991769	+	0.370133i
$154$	1.86789	−	6.97105i	0.150519	−	0.561743i
$155$	−0.101350	+	6.56408i	−0.00814065	+	0.527239i
$156$		0			0
$157$	2.45519	+	2.45519i	0.195945	+	0.195945i	0.798259	−	0.602314i	$-0.205754\pi$
$157$	2.45519	+	2.45519i	0.195945	+	0.195945i	−0.602314	+	0.798259i	$0.705754\pi$
$158$	−10.4585	−	18.1147i	−0.832036	−	1.44113i
$159$	0.398987	−	0.230355i	0.0316417	−	0.0182684i
$160$	2.69869	+	10.7317i	0.213350	+	0.848418i
$161$	−11.1182	−	11.1182i	−0.876240	−	0.876240i
$162$	−15.9957	−	9.23513i	−1.25674	−	0.725580i
$163$	−3.56410	−	2.05773i	−0.279162	−	0.161174i	0.353882	−	0.935290i	$-0.384861\pi$
$163$	−3.56410	−	2.05773i	−0.279162	−	0.161174i	−0.633044	+	0.774116i	$0.718195\pi$
$164$	−25.3290	−	25.3290i	−1.97786	−	1.97786i
$165$	−0.145844	−	0.579969i	−0.0113539	−	0.0451505i
$166$	−12.3763	+	7.14545i	−0.960586	+	0.554595i
$167$	−2.63773	−	4.56869i	−0.204114	−	0.353536i	0.745736	−	0.666241i	$-0.232098\pi$
$167$	−2.63773	−	4.56869i	−0.204114	−	0.353536i	−0.949850	+	0.312706i	$0.898765\pi$
$168$	−3.00754	−	3.00754i	−0.232036	−	0.232036i
$169$		0			0
$170$	0.131388	−	8.50953i	0.0100770	−	0.652651i
$171$	−1.30950	+	4.88712i	−0.100140	+	0.373727i
$172$	8.66470	−	32.3371i	0.660677	−	2.46568i
$173$	−4.67378	+	1.25233i	−0.355341	+	0.0952132i	−0.432073	−	0.901838i	$-0.642218\pi$
$173$	−4.67378	+	1.25233i	−0.355341	+	0.0952132i	0.0767327	+	0.997052i	$0.475551\pi$
$174$	−1.93574	+	1.93574i	−0.146748	+	0.146748i
$175$	−16.8280	−	10.4213i	−1.27208	−	0.787775i
$176$	−0.120927	−	0.451306i	−0.00911523	−	0.0340185i
$177$	3.58799			0.269690
$178$	−2.98181	−	11.1283i	−0.223496	−	0.834099i
$179$	−6.54243	−	11.3318i	−0.489004	−	0.846980i	0.510916	−	0.859631i	$-0.329306\pi$
$179$	−6.54243	−	11.3318i	−0.489004	−	0.846980i	−0.999920	+	0.0126510i	$0.995973\pi$
$180$	20.8761	+	5.94063i	1.55601	+	0.442789i
$181$		−	4.65035i		−	0.345658i	−0.984952	−	0.172829i	$-0.944709\pi$
$181$		−	4.65035i		−	0.345658i	0.984952	−	0.172829i	$-0.0552908\pi$
$182$		0			0
$183$	−0.886435	+	0.886435i	−0.0655272	+	0.0655272i
$184$	−12.1308	−	3.25043i	−0.894292	−	0.239625i
$185$	4.18962	−	14.7228i	0.308027	−	1.08244i
$186$	2.00116	+	1.15537i	0.146732	+	0.0847160i
$187$		−	1.29329i		−	0.0945747i
$188$	15.3032	−	26.5058i	1.11610	−	1.93314i
$189$	7.64599	−	2.04874i	0.556164	−	0.149024i
$190$	0.140251	−	9.08353i	0.0101749	−	0.658988i
$191$	2.00992	−	3.48128i	0.145433	−	0.251897i	−0.784102	−	0.620632i	$-0.786876\pi$
$191$	2.00992	−	3.48128i	0.145433	−	0.251897i	0.929534	+	0.368736i	$0.120209\pi$
$192$	4.15200	+	1.11252i	0.299645	+	0.0802895i
$193$	−19.9685	+	11.5288i	−1.43736	+	0.829861i	−0.997666	−	0.0682859i	$-0.978247\pi$
$193$	−19.9685	+	11.5288i	−1.43736	+	0.829861i	−0.439696	+	0.898147i	$0.644914\pi$
$194$	−20.9171			−1.50176
$195$		0			0
$196$	−29.1801			−2.08429
$197$	−0.216179	+	0.124811i	−0.0154021	+	0.00889240i	−0.507681	−	0.861545i	$-0.669497\pi$
$197$	−0.216179	+	0.124811i	−0.0154021	+	0.00889240i	0.492279	+	0.870437i	$0.336164\pi$
$198$	5.07948	+	1.36104i	0.360983	+	0.0967252i
$199$	8.84325	−	15.3170i	0.626882	−	1.08579i	−0.361292	−	0.932453i	$-0.617664\pi$
$199$	8.84325	−	15.3170i	0.626882	−	1.08579i	0.988174	−	0.153338i	$-0.0490023\pi$
$200$	−15.8020	−	0.488086i	−1.11737	−	0.0345129i
$201$	−1.24294	+	0.333045i	−0.0876703	+	0.0234912i
$202$	−3.80435	+	6.58933i	−0.267673	+	0.463624i
$203$			13.7691i			0.966399i
$204$	−1.62717	−	0.939450i	−0.113925	−	0.0657746i
$205$	−20.7948	+	11.5816i	−1.45237	+	0.808891i
$206$	−11.5307	−	3.08965i	−0.803384	−	0.215266i
$207$	8.10135	−	8.10135i	0.563083	−	0.563083i
$208$		0			0
$209$		−	1.38053i		−	0.0954930i
$210$	−6.08673	+	3.38998i	−0.420024	+	0.233931i
$211$	−4.55235	−	7.88489i	−0.313396	−	0.542819i	0.665699	−	0.746220i	$-0.268134\pi$
$211$	−4.55235	−	7.88489i	−0.313396	−	0.542819i	−0.979095	+	0.203402i	$0.934800\pi$
$212$	−1.18086	−	4.40702i	−0.0811016	−	0.302675i
$213$	1.76820			0.121155
$214$	−3.97885	−	14.8493i	−0.271989	−	1.01508i
$215$	−19.0913	−	11.4189i	−1.30202	−	0.778766i
$216$	4.47063	−	4.47063i	0.304188	−	0.304188i
$217$	11.2263	−	3.00809i	0.762094	−	0.204203i
$218$	3.49553	−	13.0455i	0.236747	−	0.883552i
$219$	0.490374	−	1.83010i	0.0331364	−	0.123667i
$220$	−5.92163	−	0.0914308i	−0.399236	−	0.00616426i
$221$		0			0
$222$	−3.80987	−	3.80987i	−0.255702	−	0.255702i
$223$	−7.13372	−	12.3560i	−0.477709	−	0.827417i	0.521964	−	0.852967i	$-0.325199\pi$
$223$	−7.13372	−	12.3560i	−0.477709	−	0.827417i	−0.999674	+	0.0255505i	$0.991866\pi$
$224$	16.9662	−	9.79544i	1.13360	−	0.654485i
$225$	7.59352	−	12.2618i	0.506235	−	0.817455i
$226$	29.6298	+	29.6298i	1.97094	+	1.97094i
$227$	10.7116	+	6.18435i	0.710955	+	0.410470i	0.811414	−	0.584471i	$-0.198698\pi$
$227$	10.7116	+	6.18435i	0.710955	+	0.410470i	−0.100460	+	0.994941i	$0.532031\pi$
$228$	−1.73693	−	1.00282i	−0.115031	−	0.0664133i
$229$	6.93888	+	6.93888i	0.458534	+	0.458534i	0.898174	−	0.439640i	$-0.144894\pi$
$229$	6.93888	+	6.93888i	0.458534	+	0.458534i	−0.439640	+	0.898174i	$0.644894\pi$
$230$	−10.5597	+	17.6547i	−0.696283	+	1.16412i
$231$	−0.916896	+	0.529370i	−0.0603273	+	0.0348300i
$232$	5.49881	+	9.52422i	0.361014	+	0.625295i
$233$	−3.17544	−	3.17544i	−0.208030	−	0.208030i	0.595400	−	0.803430i	$-0.296994\pi$
$233$	−3.17544	−	3.17544i	−0.208030	−	0.208030i	−0.803430	+	0.595400i	$0.796994\pi$
$234$		0			0
$235$	−14.1571	−	14.6012i	−0.923510	−	0.952475i
$236$	9.19646	−	34.3217i	0.598639	−	2.23415i
$237$	−0.794204	+	2.96401i	−0.0515891	+	0.192533i
$238$	−14.5536	+	3.89963i	−0.943370	+	0.252775i
$239$	12.3783	−	12.3783i	0.800689	−	0.800689i	−0.182514	−	0.983203i	$-0.558424\pi$
$239$	12.3783	−	12.3783i	0.800689	−	0.800689i	0.983203	+	0.182514i	$0.0584236\pi$
$240$	−0.231528	+	0.387092i	−0.0149451	+	0.0249867i
$241$	4.50632	+	16.8178i	0.290278	+	1.08333i	0.944896	+	0.327371i	$0.106163\pi$
$241$	4.50632	+	16.8178i	0.290278	+	1.08333i	−0.654618	+	0.755960i	$0.727171\pi$
$242$	24.0441			1.54561
$243$	2.25388	+	8.41158i	0.144586	+	0.539603i
$244$	6.20733	+	10.7514i	0.397384	+	0.688289i
$245$	−5.30703	+	18.6495i	−0.339054	+	1.19147i
$246$			8.37814i			0.534171i
$247$		0			0
$248$	6.56408	−	6.56408i	0.416819	−	0.416819i
$249$	2.02506	+	0.542614i	0.128333	+	0.0343868i
$250$	−7.85352	+	24.6771i	−0.496700	+	1.56072i
$251$	−17.1304	−	9.89026i	−1.08126	−	0.624268i	−0.150027	−	0.988682i	$-0.547936\pi$
$251$	−17.1304	−	9.89026i	−1.08126	−	0.624268i	−0.931237	+	0.364414i	$0.881269\pi$
$252$		−	38.4261i		−	2.42062i
$253$	−1.56307	+	2.70731i	−0.0982693	+	0.170207i
$254$	−17.2410	+	4.61971i	−1.08180	+	0.289866i
$255$	−0.896355	+	0.869096i	−0.0561319	+	0.0544249i
$256$	9.82142	−	17.0112i	0.613839	−	1.06320i
$257$	19.9109	+	5.33512i	1.24201	+	0.332795i	0.819245	−	0.573444i	$-0.194393\pi$
$257$	19.9109	+	5.33512i	1.24201	+	0.332795i	0.422765	+	0.906240i	$0.361060\pi$
$258$	−6.78115	+	3.91510i	−0.422176	+	0.243743i
$259$	−27.0999			−1.68391
$260$		0			0
$261$	−10.0329			−0.621021
$262$	−4.85728	+	2.80435i	−0.300084	+	0.173253i
$263$	−19.8884	−	5.32908i	−1.22637	−	0.328605i	−0.413205	−	0.910638i	$-0.635591\pi$
$263$	−19.8884	−	5.32908i	−1.22637	−	0.328605i	−0.813165	+	0.582033i	$0.802257\pi$
$264$	−0.422818	+	0.732342i	−0.0260226	+	0.0450725i
$265$	−3.03136	−	0.0468047i	−0.186215	−	0.00287519i
$266$	−15.5353	+	4.16267i	−0.952530	+	0.255230i
$267$	−0.845063	+	1.46369i	−0.0517170	+	0.0895765i
$268$			12.7432i			0.778417i
$269$	7.49944	+	4.32981i	0.457249	+	0.263993i	0.710887	−	0.703306i	$-0.248294\pi$
$269$	7.49944	+	4.32981i	0.457249	+	0.263993i	−0.253638	+	0.967299i	$0.581627\pi$
$270$	−5.03912	−	9.04778i	−0.306671	−	0.550630i
$271$	19.3415	+	5.18253i	1.17491	+	0.314816i	0.792906	−	0.609344i	$-0.208567\pi$
$271$	19.3415	+	5.18253i	1.17491	+	0.314816i	0.382005	+	0.924160i	$0.375234\pi$
$272$	−0.689739	+	0.689739i	−0.0418216	+	0.0418216i
$273$		0			0
$274$			1.33924i			0.0809066i
$275$	−1.13541	+	3.76798i	−0.0684678	+	0.227218i
$276$	2.27084	+	3.93320i	0.136688	+	0.236751i
$277$	0.310396	+	1.15842i	0.0186499	+	0.0696024i	0.974624	−	0.223850i	$-0.0718625\pi$
$277$	0.310396	+	1.15842i	0.0186499	+	0.0696024i	−0.955974	+	0.293452i	$0.905196\pi$
$278$	−38.5059			−2.30943
$279$	2.19186	+	8.18013i	0.131223	+	0.489731i
$280$	6.82585	+	27.1439i	0.407922	+	1.62216i
$281$	−13.1441	+	13.1441i	−0.784110	+	0.784110i	−0.980522	−	0.196412i	$-0.937071\pi$
$281$	−13.1441	+	13.1441i	−0.784110	+	0.784110i	0.196412	+	0.980522i	$0.437071\pi$
$282$	−6.91465	+	1.85278i	−0.411762	+	0.110331i
$283$	2.70925	−	10.1111i	0.161048	−	0.601040i	−0.837463	−	0.546494i	$-0.815962\pi$
$283$	2.70925	−	10.1111i	0.161048	−	0.601040i	0.998511	−	0.0545461i	$-0.0173712\pi$
$284$	4.53212	−	16.9141i	0.268932	−	1.00367i
$285$	−0.956817	+	0.927719i	−0.0566769	+	0.0549533i
$286$		0			0
$287$	29.7972	+	29.7972i	1.75887	+	1.75887i
$288$	7.13749	+	12.3625i	0.420581	+	0.728467i
$289$	12.3841	−	7.14999i	0.728479	−	0.420587i
$290$	17.4706	−	4.39332i	1.02591	−	0.257985i
$291$	2.16980	+	2.16980i	0.127196	+	0.127196i
$292$	−16.2493	−	9.38153i	−0.950918	−	0.549013i
$293$	−9.72321	−	5.61370i	−0.568036	−	0.327956i	0.188328	−	0.982106i	$-0.439693\pi$
$293$	−9.72321	−	5.61370i	−0.568036	−	0.327956i	−0.756365	+	0.654150i	$0.773026\pi$
$294$	4.82600	+	4.82600i	0.281458	+	0.281458i
$295$	−20.2630	−	12.1197i	−1.17976	−	0.705639i
$296$	−18.7453	+	10.8226i	−1.08955	+	0.629051i
$297$	−0.786896	−	1.36294i	−0.0456603	−	0.0790860i
$298$	−2.20871	−	2.20871i	−0.127947	−	0.127947i
$299$		0			0
$300$	3.91599	+	4.16561i	0.226090	+	0.240502i
$301$	−10.1932	+	38.0416i	−0.587528	+	2.19268i
$302$	−7.74890	+	28.9193i	−0.445899	+	1.66412i
$303$	1.07818	−	0.288896i	0.0619395	−	0.0165967i
$304$	−0.736265	+	0.736265i	−0.0422277	+	0.0422277i
$305$	8.00035	−	2.01184i	0.458098	−	0.115197i
$306$	−2.84148	−	10.6045i	−0.162437	−	0.606222i
$307$	−28.2579			−1.61276			−0.806382	−	0.591395i	$-0.798577\pi$
$307$	−28.2579			−1.61276			−0.806382	+	0.591395i	$0.798577\pi$
$308$	2.71368	+	10.1276i	0.154626	+	0.577073i
$309$	0.875624	+	1.51663i	0.0498125	+	0.0862778i
$310$	−7.39877	−	13.2846i	−0.420222	−	0.754512i
$311$		−	9.55436i		−	0.541778i	−0.962611	−	0.270889i	$-0.912682\pi$
$311$		−	9.55436i		−	0.541778i	0.962611	−	0.270889i	$-0.0873177\pi$
$312$		0			0
$313$	17.7119	−	17.7119i	1.00113	−	1.00113i	0.00113436	−	0.999999i	$-0.499639\pi$
$313$	17.7119	−	17.7119i	1.00113	−	1.00113i	0.999999	−	0.00113436i	$-0.000361078\pi$
$314$	−7.76841	−	2.08154i	−0.438397	−	0.117468i
$315$	−24.5588	−	6.98861i	−1.38373	−	0.393764i
$316$	26.3172	+	15.1942i	1.48046	+	0.854742i
$317$			0.912395i			0.0512452i	0.999672	+	0.0256226i	$0.00815683\pi$
$317$			0.912395i			0.0512452i	−0.999672	+	0.0256226i	$0.991843\pi$
$318$	−0.533564	+	0.924160i	−0.0299208	+	0.0518243i
$319$	2.64427	−	0.708530i	0.148051	−	0.0396701i
$320$	−19.6902	−	20.3078i	−1.10072	−	1.13524i
$321$	−1.12763	+	1.95311i	−0.0629381	+	0.109012i
$322$	35.1790	+	9.42617i	1.96045	+	0.525300i
$323$	−2.49602	+	1.44108i	−0.138882	+	0.0801836i
$324$	26.8337			1.49076
$325$		0			0
$326$	9.53251			0.527957
$327$	−1.71586	+	0.990653i	−0.0948874	+	0.0547832i
$328$	32.5108	+	8.71125i	1.79511	+	0.480998i
$329$	−18.0028	+	31.1817i	−0.992525	+	1.71910i
$330$	0.964237	+	0.994479i	0.0530795	+	0.0547443i
$331$	20.8435	−	5.58499i	1.14566	−	0.306979i	0.364436	−	0.931228i	$-0.381262\pi$
$331$	20.8435	−	5.58499i	1.14566	−	0.306979i	0.781225	+	0.624249i	$0.214595\pi$
$332$	10.3810	−	17.9804i	0.569729	−	0.986800i
$333$		−	19.7465i		−	1.08210i
$334$	10.5823	+	6.10969i	0.579037	+	0.334307i
$335$	8.14441	+	2.31763i	0.444977	+	0.126626i
$336$	0.771325	+	0.206676i	0.0420792	+	0.0112751i
$337$	8.33973	−	8.33973i	0.454294	−	0.454294i	−0.442483	−	0.896777i	$-0.645902\pi$
$337$	8.33973	−	8.33973i	0.454294	−	0.454294i	0.896777	+	0.442483i	$0.145902\pi$
$338$		0			0
$339$		−	6.14721i		−	0.333871i
$340$	6.01604	+	10.8019i	0.326266	+	0.585813i
$341$	−1.15537	−	2.00116i	−0.0625669	−	0.108369i
$342$	−3.03315	−	11.3199i	−0.164014	−	0.612108i
$343$	6.61672			0.357269
$344$	8.14152	+	30.3846i	0.438961	+	1.63823i
$345$	2.92678	−	0.735993i	0.157572	−	0.0396245i
$346$	7.92497	−	7.92497i	0.426049	−	0.426049i
$347$	−30.7153	+	8.23013i	−1.64888	+	0.441816i	−0.959299	−	0.282391i	$-0.908872\pi$
$347$	−30.7153	+	8.23013i	−1.64888	+	0.441816i	−0.689582	+	0.724208i	$0.742206\pi$
$348$	1.02936	−	3.84161i	0.0551793	−	0.205932i
$349$	7.03726	−	26.2634i	0.376696	−	1.40585i	−0.474155	−	0.880442i	$-0.657246\pi$
$349$	7.03726	−	26.2634i	0.376696	−	1.40585i	0.850851	−	0.525407i	$-0.176087\pi$
$350$	45.8253	+	1.41544i	2.44947	+	0.0756583i
$351$		0			0
$352$	−2.75420	−	2.75420i	−0.146800	−	0.146800i
$353$	2.22717	+	3.85757i	0.118540	+	0.205318i	0.919189	−	0.393816i	$-0.128845\pi$
$353$	2.22717	+	3.85757i	0.118540	+	0.205318i	−0.800649	+	0.599133i	$0.795512\pi$
$354$	−7.19732	+	4.15537i	−0.382533	+	0.220856i
$355$	−9.98582	−	5.97274i	−0.529992	−	0.317000i
$356$	11.8352	+	11.8352i	0.627266	+	0.627266i
$357$	1.91422	+	1.10518i	0.101311	+	0.0584921i
$358$	26.2475	+	15.1540i	1.38722	+	0.800914i
$359$	11.6335	+	11.6335i	0.613992	+	0.613992i	0.943984	−	0.329992i	$-0.107046\pi$
$359$	11.6335	+	11.6335i	0.613992	+	0.613992i	−0.329992	+	0.943984i	$0.607046\pi$
$360$	−19.7785	+	4.97368i	−1.04242	+	0.262136i
$361$	13.7901	−	7.96172i	0.725795	−	0.419038i
$362$	5.38573	+	9.32835i	0.283068	+	0.490287i
$363$	−2.49418	−	2.49418i	−0.130910	−	0.130910i
$364$		0			0
$365$	−8.95118	+	8.67897i	−0.468526	+	0.454278i
$366$	0.751530	−	2.80475i	0.0392831	−	0.146607i
$367$	0.322539	−	1.20373i	0.0168364	−	0.0628344i	−0.956997	−	0.290099i	$-0.906312\pi$
$367$	0.322539	−	1.20373i	0.0168364	−	0.0628344i	0.973833	+	0.227265i	$0.0729783\pi$
$368$	2.27749	−	0.610251i	0.118722	−	0.0318115i
$369$	−21.7119	+	21.7119i	−1.13027	+	1.13027i
$370$	8.64681	+	34.3852i	0.449526	+	1.78760i
$371$	1.38917	+	5.18445i	0.0721221	+	0.269163i
$372$	−3.35707			−0.174056
$373$	3.10612	+	11.5922i	0.160829	+	0.600221i	0.998535	+	0.0541005i	$0.0172291\pi$
$373$	3.10612	+	11.5922i	0.160829	+	0.600221i	−0.837707	+	0.546120i	$0.816104\pi$
$374$	1.49780	+	2.59427i	0.0774494	+	0.134146i
$375$	3.37452	−	1.74517i	0.174259	−	0.0901202i
$376$			28.7583i			1.48310i
$377$		0			0
$378$	−12.9647	+	12.9647i	−0.666833	+	0.666833i
$379$	29.9385	+	8.02199i	1.53784	+	0.412062i	0.925566	−	0.378586i	$-0.123590\pi$
$379$	29.9385	+	8.02199i	1.53784	+	0.412062i	0.612271	+	0.790648i	$0.290256\pi$
$380$	6.42184	+	11.5305i	0.329434	+	0.591501i
$381$	2.26769	+	1.30925i	0.116177	+	0.0670751i
$382$			9.31101i			0.476393i
$383$	5.92062	−	10.2548i	0.302529	−	0.523996i	−0.674179	−	0.738568i	$-0.735502\pi$
$383$	5.92062	−	10.2548i	0.302529	−	0.523996i	0.976708	+	0.214572i	$0.0688356\pi$
$384$	−6.36853	+	1.70644i	−0.324992	+	0.0870815i
$385$	6.96625	+	0.107560i	0.355033	+	0.00548176i
$386$	26.7038	−	46.2523i	1.35919	−	2.35418i
$387$	−27.7192	−	7.42734i	−1.40905	−	0.377553i
$388$	26.3172	−	15.1942i	1.33605	−	0.771370i
$389$	22.0771			1.11935			0.559676	−	0.828712i	$-0.310926\pi$
$389$	22.0771			1.11935			0.559676	+	0.828712i	$0.310926\pi$
$390$		0			0
$391$	6.52650			0.330059
$392$	23.7449	−	13.7091i	1.19930	−	0.692414i
$393$	0.794769	+	0.212958i	0.0400908	+	0.0107423i
$394$	0.289095	−	0.500727i	0.0145644	−	0.0252263i
$395$	14.4972	−	14.0564i	0.729435	−	0.707252i
$396$	−7.37951	+	1.97733i	−0.370834	+	0.0993647i
$397$	8.06527	−	13.9695i	0.404784	−	0.701107i	−0.589512	−	0.807760i	$-0.700680\pi$
$397$	8.06527	−	13.9695i	0.404784	−	0.701107i	0.994296	+	0.106653i	$0.0340133\pi$
$398$			40.9666i			2.05347i
$399$	2.04334	+	1.17972i	0.102295	+	0.0590601i
$400$	2.61509	−	1.40401i	0.130754	−	0.0702005i
$401$	−31.1481	−	8.34610i	−1.55546	−	0.416784i	−0.624237	−	0.781235i	$-0.714590\pi$
$401$	−31.1481	−	8.34610i	−1.55546	−	0.416784i	−0.931223	+	0.364450i	$0.881257\pi$
$402$	2.10756	−	2.10756i	0.105116	−	0.105116i
$403$		0			0
$404$		−	11.0540i		−	0.549956i
$405$	4.88029	−	17.1499i	0.242503	−	0.852185i
$406$	−15.9464	−	27.6200i	−0.791407	−	1.37076i
$407$	1.39451	+	5.20438i	0.0691233	+	0.257972i
$408$	1.76545			0.0874028
$409$	1.12960	+	4.21571i	0.0558550	+	0.208454i	0.988214	−	0.153081i	$-0.0489196\pi$
$409$	1.12960	+	4.21571i	0.0558550	+	0.208454i	−0.932359	+	0.361535i	$0.882253\pi$
$410$	28.3002	−	47.3151i	1.39765	−	2.33672i
$411$	0.138925	−	0.138925i	0.00685264	−	0.00685264i
$412$	16.7519	−	4.48866i	0.825307	−	0.221140i
$413$	−10.8188	+	40.3763i	−0.532358	+	1.98679i
$414$	−6.86842	+	25.6333i	−0.337565	+	1.25981i
$415$	−9.60355	−	9.90476i	−0.471420	−	0.486206i
$416$		0			0
$417$	3.99436	+	3.99436i	0.195605	+	0.195605i
$418$	1.59883	+	2.76926i	0.0782014	+	0.135449i
$419$	−8.24345	+	4.75936i	−0.402719	+	0.232510i	−0.687656	−	0.726036i	$-0.741360\pi$
$419$	−8.24345	+	4.75936i	−0.402719	+	0.232510i	0.284938	+	0.958546i	$0.408027\pi$
$420$	5.19564	−	8.68658i	0.253521	−	0.423862i
$421$	20.6718	+	20.6718i	1.00748	+	1.00748i	0.999972	+	0.00751095i	$0.00239083\pi$
$421$	20.6718	+	20.6718i	1.00748	+	1.00748i	0.00751095	+	0.999972i	$0.497609\pi$
$422$	18.2635	+	10.5444i	0.889054	+	0.513295i
$423$	−22.7207	−	13.1178i	−1.10472	−	0.637809i
$424$	3.03136	+	3.03136i	0.147216	+	0.147216i
$425$	7.99780	−	1.88041i	0.387950	−	0.0912131i
$426$	−3.54692	+	2.04781i	−0.171849	+	0.0992168i
$427$	−7.30236	−	12.6481i	−0.353386	−	0.612082i
$428$	15.7926	+	15.7926i	0.763365	+	0.763365i
$429$		0			0
$430$	51.5208	+	0.795489i	2.48455	+	0.0383619i
$431$	−6.16279	+	22.9998i	−0.296851	+	1.10786i	0.642885	+	0.765962i	$0.277737\pi$
$431$	−6.16279	+	22.9998i	−0.296851	+	1.10786i	−0.939736	+	0.341900i	$0.888929\pi$
$432$	−0.307219	+	1.14656i	−0.0147811	+	0.0551637i
$433$	−24.6723	+	6.61093i	−1.18568	+	0.317701i	−0.797176	−	0.603748i	$-0.793673\pi$
$433$	−24.6723	+	6.61093i	−1.18568	+	0.317701i	−0.388501	+	0.921449i	$0.627007\pi$
$434$	−19.0357	+	19.0357i	−0.913741	+	0.913741i
$435$	−2.26803	−	1.35656i	−0.108744	−	0.0650420i
$436$	5.07833	+	18.9526i	0.243208	+	0.907664i
$437$	6.96674			0.333264
$438$	1.13584	+	4.23900i	0.0542723	+	0.202547i
$439$	−16.3992	−	28.4043i	−0.782692	−	1.35566i	−0.930368	−	0.366627i	$-0.880513\pi$
$439$	−16.3992	−	28.4043i	−0.782692	−	1.35566i	0.147676	−	0.989036i	$-0.452821\pi$
$440$	4.86159	−	2.70764i	0.231767	−	0.129082i
$441$			25.0131i			1.19110i
$442$		0			0
$443$	−11.4661	+	11.4661i	−0.544769	+	0.544769i	−0.924923	−	0.380154i	$-0.875871\pi$
$443$	−11.4661	+	11.4661i	−0.544769	+	0.544769i	0.380154	+	0.924923i	$0.375871\pi$
$444$	7.56096	+	2.02595i	0.358827	+	0.0961475i
$445$	9.71659	−	5.41161i	0.460610	−	0.256535i
$446$	28.6197	+	16.5236i	1.35518	+	0.782415i
$447$			0.458234i			0.0216737i
$448$	−25.0389	+	43.3686i	−1.18297	+	2.04897i
$449$	27.3807	−	7.33663i	1.29217	−	0.346237i	0.453689	−	0.891160i	$-0.350108\pi$
$449$	27.3807	−	7.33663i	1.29217	−	0.346237i	0.838486	+	0.544923i	$0.183441\pi$
$450$	−1.03136	+	33.3908i	−0.0486190	+	1.57406i
$451$	4.18907	−	7.25568i	0.197256	−	0.341657i
$452$	−58.8024	−	15.7561i	−2.76583	−	0.741102i
$453$	3.80373	−	2.19608i	0.178715	−	0.103181i
$454$	−28.6492			−1.34457
$455$		0			0
$456$	1.88454			0.0882515
$457$	−2.73993	+	1.58190i	−0.128169	+	0.0739982i	−0.562713	−	0.826652i	$-0.690243\pi$
$457$	−2.73993	+	1.58190i	−0.128169	+	0.0739982i	0.434545	+	0.900650i	$0.356909\pi$
$458$	−21.9551	−	5.88286i	−1.02590	−	0.274888i
$459$	−1.64282	+	2.84544i	−0.0766802	+	0.132814i
$460$	0.461400	−	29.8831i	0.0215129	−	1.39331i
$461$	−27.3301	+	7.32309i	−1.27289	+	0.341070i	−0.831138	−	0.556066i	$-0.812310\pi$
$461$	−27.3301	+	7.32309i	−1.27289	+	0.341070i	−0.441754	+	0.897136i	$0.645643\pi$
$462$	1.22616	−	2.12377i	0.0570462	−	0.0988069i
$463$			4.68050i			0.217521i	0.994068	+	0.108761i	$0.0346882\pi$
$463$			4.68050i			0.217521i	−0.994068	+	0.108761i	$0.965312\pi$
$464$	−1.78812	−	1.03237i	−0.0830114	−	0.0479267i
$465$	−0.610554	+	2.14556i	−0.0283138	+	0.0994979i
$466$	10.0473	+	2.69218i	0.465434	+	0.124713i
$467$	−5.31207	+	5.31207i	−0.245813	+	0.245813i	−0.819250	−	0.573437i	$-0.805610\pi$
$467$	−5.31207	+	5.31207i	−0.245813	+	0.245813i	0.573437	+	0.819250i	$0.305610\pi$
$468$		0			0
$469$		−	14.9912i		−	0.692231i
$470$	45.3085	+	12.8933i	2.08993	+	0.594723i
$471$	0.589920	+	1.02177i	0.0271821	+	0.0470808i
$472$	8.64118	+	32.2493i	0.397742	+	1.48439i
$473$	7.83020			0.360033
$474$	−1.83959	−	6.86543i	−0.0844950	−	0.315340i
$475$	8.53727	−	2.00725i	0.391717	−	0.0920988i
$476$	15.4782	−	15.4782i	0.709441	−	0.709441i
$477$	−3.77768	+	1.01223i	−0.172968	+	0.0463466i
$478$	−10.4945	+	39.1660i	−0.480008	+	1.79141i
$479$	−6.60612	+	24.6544i	−0.301841	+	1.12649i	0.633789	+	0.773506i	$0.281499\pi$
$479$	−6.60612	+	24.6544i	−0.301841	+	1.12649i	−0.935631	+	0.352981i	$0.885168\pi$
$480$	−0.0580507	+	3.75973i	−0.00264964	+	0.171607i
$481$		0			0
$482$	−28.5167	−	28.5167i	−1.29890	−	1.29890i
$483$	−2.67143	−	4.62706i	−0.121554	−	0.210538i
$484$	−30.2514	+	17.4657i	−1.37507	+	0.793895i
$485$	−4.92455	−	19.5831i	−0.223612	−	0.889225i
$486$	−14.2629	−	14.2629i	−0.646978	−	0.646978i
$487$	−0.847135	−	0.489094i	−0.0383873	−	0.0221629i	0.480684	−	0.876894i	$-0.340389\pi$
$487$	−0.847135	−	0.489094i	−0.0383873	−	0.0221629i	−0.519071	+	0.854731i	$0.673722\pi$
$488$	−10.1022	−	5.83253i	−0.457307	−	0.264026i
$489$	−0.988842	−	0.988842i	−0.0447170	−	0.0447170i
$490$	−10.9530	−	43.5561i	−0.494806	−	1.96766i
$491$	16.6596	−	9.61842i	0.751837	−	0.434073i	−0.0745205	−	0.997219i	$-0.523743\pi$
$491$	16.6596	−	9.61842i	0.751837	−	0.434073i	0.826357	+	0.563146i	$0.190409\pi$
$492$	−6.08591	−	10.5411i	−0.274374	−	0.475230i
$493$	−4.04128	−	4.04128i	−0.182010	−	0.182010i
$494$		0			0
$495$	−0.0783740	+	5.07599i	−0.00352265	+	0.228149i
$496$	−0.451079	+	1.68345i	−0.0202540	+	0.0755891i
$497$	−5.33162	+	19.8979i	−0.239156	+	0.892542i
$498$	−4.69058	+	1.25684i	−0.210190	+	0.0563203i
$499$	−16.4546	+	16.4546i	−0.736610	+	0.736610i	−0.971920	−	0.235310i	$-0.924389\pi$
$499$	−16.4546	+	16.4546i	−0.736610	+	0.736610i	0.235310	+	0.971920i	$0.424389\pi$
$500$	−8.04447	−	36.7527i	−0.359759	−	1.64363i
$501$	−0.463960	−	1.73152i	−0.0207282	−	0.0773587i
$502$	45.8169			2.04491
$503$	4.70162	+	17.5467i	0.209635	+	0.782368i	0.987987	+	0.154539i	$0.0493894\pi$
$503$	4.70162	+	17.5467i	0.209635	+	0.782368i	−0.778352	+	0.627828i	$0.783944\pi$
$504$	18.0530	+	31.2687i	0.804143	+	1.39282i
$505$	−7.06478	−	2.01040i	−0.314379	−	0.0894617i
$506$		−	7.24096i		−	0.321900i
$507$		0			0
$508$	18.3363	−	18.3363i	0.813541	−	0.813541i
$509$	9.52362	+	2.55185i	0.422127	+	0.113109i	0.463628	−	0.886030i	$-0.346547\pi$
$509$	9.52362	+	2.55185i	0.422127	+	0.113109i	−0.0415012	+	0.999138i	$0.513214\pi$
$510$	0.791510	−	2.78146i	0.0350486	−	0.123165i
$511$	19.1158	+	11.0365i	0.845634	+	0.488227i
$512$			6.69175i			0.295737i
$513$	−1.75363	+	3.03738i	−0.0774247	+	0.134104i
$514$	−46.1190	+	12.3575i	−2.03422	+	0.545068i
$515$	0.177914	−	11.5228i	0.00783981	−	0.507755i
$516$	5.68788	−	9.85170i	0.250395	−	0.433697i
$517$	6.91465	+	1.85278i	0.304106	+	0.0814850i
$518$	54.3610	−	31.3853i	2.38848	−	1.37899i
$519$	−1.64417			−0.0721712
$520$		0			0
$521$	9.45108			0.414060			0.207030	−	0.978335i	$-0.433620\pi$
$521$	9.45108			0.414060			0.207030	+	0.978335i	$0.433620\pi$
$522$	20.1254	−	11.6194i	0.880866	−	0.508568i
$523$	20.7384	+	5.55683i	0.906825	+	0.242983i	0.681945	−	0.731403i	$-0.261134\pi$
$523$	20.7384	+	5.55683i	0.906825	+	0.242983i	0.224880	+	0.974386i	$0.427801\pi$
$524$	4.07418	−	7.05669i	0.177981	−	0.308273i
$525$	−4.60680	−	4.90046i	−0.201057	−	0.213874i
$526$	46.0668	−	12.3436i	2.00861	−	0.538205i
$527$	−2.41210	+	4.17787i	−0.105073	+	0.181991i
$528$		−	0.158764i		−	0.00690930i
$529$	6.25629	+	3.61207i	0.272013	+	0.157047i
$530$	6.13496	−	3.41683i	0.266485	−	0.148418i
$531$	−29.4204	−	7.88316i	−1.27674	−	0.342100i
$532$	16.5222	−	16.5222i	0.716329	−	0.716329i
$533$		0			0
$534$		−	3.91478i		−	0.169409i
$535$	12.9656	−	7.22111i	0.560550	−	0.312196i
$536$	−5.98689	−	10.3696i	−0.258594	−	0.447899i
$537$	−1.15077	−	4.29473i	−0.0496594	−	0.185331i
$538$	−20.0580			−0.864760
$539$	−1.76644	−	6.59244i	−0.0760859	−	0.283956i
$540$	12.9124	+	7.72319i	0.555661	+	0.332353i
$541$	−15.2507	+	15.2507i	−0.655677	+	0.655677i	−0.954354	−	0.298677i	$-0.903455\pi$
$541$	−15.2507	+	15.2507i	−0.655677	+	0.655677i	0.298677	+	0.954354i	$0.403455\pi$
$542$	−44.8000	+	12.0041i	−1.92432	+	0.515621i
$543$	0.408983	−	1.52635i	0.0175512	−	0.0655018i
$544$	−2.10465	+	7.85466i	−0.0902361	+	0.336766i
$545$	13.0365	+	0.201286i	0.558423	+	0.00862213i
$546$		0			0
$547$	−27.7930	−	27.7930i	−1.18834	−	1.18834i	−0.977525	−	0.210818i	$-0.932387\pi$
$547$	−27.7930	−	27.7930i	−1.18834	−	1.18834i	−0.210818	−	0.977525i	$-0.567613\pi$
$548$	−0.972830	−	1.68499i	−0.0415572	−	0.0719792i
$549$	9.21606	−	5.32089i	0.393332	−	0.227090i
$550$	−2.08626	−	8.87332i	−0.0889583	−	0.378360i
$551$	−4.31388	−	4.31388i	−0.183778	−	0.183778i
$552$	−3.69572	−	2.13372i	−0.157300	−	0.0908173i
$553$	−30.9597	−	17.8746i	−1.31654	−	0.760106i
$554$	−1.96424	−	1.96424i	−0.0834524	−	0.0834524i
$555$	2.66994	−	4.46388i	0.113333	−	0.189481i
$556$	48.4469	−	27.9708i	2.05461	−	1.18623i
$557$	12.4966	+	21.6448i	0.529499	+	0.917120i	0.999408	+	0.0344045i	$0.0109535\pi$
$557$	12.4966	+	21.6448i	0.529499	+	0.917120i	−0.469909	+	0.882715i	$0.655713\pi$
$558$	−13.8704	−	13.8704i	−0.587182	−	0.587182i
$559$		0			0
$560$	−3.65789	−	3.77262i	−0.154574	−	0.159422i
$561$	0.113741	−	0.424485i	0.00480213	−	0.0179218i
$562$	11.1437	−	41.5889i	0.470069	−	1.75432i
$563$	40.0459	−	10.7303i	1.68773	−	0.452227i	0.717929	−	0.696116i	$-0.245090\pi$
$563$	40.0459	−	10.7303i	1.68773	−	0.452227i	0.969803	+	0.243889i	$0.0784233\pi$
$564$	7.35393	−	7.35393i	0.309656	−	0.309656i
$565$	−20.7644	+	34.7160i	−0.873566	+	1.46051i
$566$	6.27534	+	23.4199i	0.263772	+	0.984412i
$567$	−31.5674			−1.32571
$568$	4.25846	+	15.8928i	0.178681	+	0.666847i
$569$	12.9779	+	22.4784i	0.544063	+	0.942345i	0.998665	+	0.0516505i	$0.0164482\pi$
$569$	12.9779	+	22.4784i	0.544063	+	0.942345i	−0.454602	+	0.890695i	$0.650218\pi$
$570$	0.844900	−	2.96907i	0.0353889	−	0.124361i
$571$			10.3822i			0.434480i	0.976118	+	0.217240i	$0.0697055\pi$
$571$			10.3822i			0.434480i	−0.976118	+	0.217240i	$0.930295\pi$
$572$		0			0
$573$	0.965866	−	0.965866i	0.0403496	−	0.0403496i
$574$	−94.2807	−	25.2624i	−3.93520	−	1.05443i
$575$	−19.0149	−	5.72977i	−0.792976	−	0.238948i
$576$	−31.6007	−	18.2447i	−1.31670	−	0.760195i
$577$		−	12.1813i		−	0.507112i	−0.967321	−	0.253556i	$-0.918400\pi$
$577$		−	12.1813i		−	0.507112i	0.967321	−	0.253556i	$-0.0816003\pi$
$578$	−16.5613	+	28.6850i	−0.688858	+	1.19314i
$579$	−7.56800	+	2.02784i	−0.314515	+	0.0842741i
$580$	−18.7897	+	18.2183i	−0.780198	+	0.756472i
$581$	−12.2123	+	21.1522i	−0.506650	+	0.877543i
$582$	−6.86543	−	1.83959i	−0.284581	−	0.0762533i
$583$	0.924160	−	0.533564i	0.0382748	−	0.0220980i
$584$	17.6301			0.729541
$585$		0			0
$586$	26.0056			1.07428
$587$	−32.9829	+	19.0427i	−1.36135	+	0.785975i	−0.989804	−	0.142439i	$-0.954505\pi$
$587$	−32.9829	+	19.0427i	−1.36135	+	0.785975i	−0.371546	+	0.928415i	$0.621172\pi$
$588$	−9.57754	−	2.56629i	−0.394971	−	0.105832i
$589$	−2.57480	+	4.45968i	−0.106093	+	0.183758i
$590$	54.6827	+	0.844309i	2.25125	+	0.0347596i
$591$	−0.0819312	+	0.0219534i	−0.00337020	+	0.000903042i
$592$	2.03189	−	3.51933i	0.0835101	−	0.144644i
$593$		−	5.30739i		−	0.217949i	−0.994045	−	0.108974i	$-0.965243\pi$
$593$		−	5.30739i		−	0.217949i	0.994045	−	0.108974i	$-0.0347566\pi$
$594$	3.15694	+	1.82266i	0.129531	+	0.0747846i
$595$	−7.07732	−	12.7074i	−0.290142	−	0.520952i
$596$	4.38333	+	1.17451i	0.179548	+	0.0481098i
$597$	4.24962	−	4.24962i	0.173925	−	0.173925i
$598$		0			0
$599$		−	0.0345018i		−	0.00140970i	−1.00000		0.000704852i	$-0.999776\pi$
$599$		−	0.0345018i		−	0.00140970i	1.00000		0.000704852i	$-0.000224361\pi$
$600$	−5.14362	−	1.54993i	−0.209987	−	0.0632757i
$601$	8.25667	+	14.3010i	0.336797	+	0.583349i	0.983828	−	0.179114i	$-0.0573231\pi$
$601$	8.25667	+	14.3010i	0.336797	+	0.583349i	−0.647032	+	0.762463i	$0.723990\pi$
$602$	−23.6102	−	88.1145i	−0.962280	−	3.59128i
$603$	10.9234			0.444837
$604$	−11.2577	−	42.0141i	−0.458068	−	1.70953i
$605$	5.66074	+	22.5107i	0.230142	+	0.915191i
$606$	−1.82818	+	1.82818i	−0.0742647	+	0.0742647i
$607$	−0.413250	+	0.110730i	−0.0167733	+	0.00449439i	−0.267196	−	0.963642i	$-0.586097\pi$
$607$	−0.413250	+	0.110730i	−0.0167733	+	0.00449439i	0.250423	+	0.968137i	$0.419430\pi$
$608$	−2.24662	+	8.38448i	−0.0911123	+	0.340036i
$609$	−1.21094	+	4.51931i	−0.0490699	+	0.183132i
$610$	−13.7183	+	13.3011i	−0.555437	+	0.538546i
$611$		0			0
$612$	11.2782	+	11.2782i	0.455896	+	0.455896i
$613$	4.88635	+	8.46340i	0.197358	+	0.341834i	0.947671	−	0.319249i	$-0.103431\pi$
$613$	4.88635	+	8.46340i	0.197358	+	0.341834i	−0.750313	+	0.661083i	$0.770097\pi$
$614$	56.6838	−	32.7264i	2.28757	−	1.32073i
$615$	−7.84385	+	1.97248i	−0.316295	+	0.0795382i
$616$	−6.96625	−	6.96625i	−0.280678	−	0.280678i
$617$	−25.0175	−	14.4438i	−1.00717	−	0.581487i	−0.0968051	−	0.995303i	$-0.530862\pi$
$617$	−25.0175	−	14.4438i	−1.00717	−	0.581487i	−0.910361	+	0.413816i	$0.864196\pi$
$618$	−3.51291	−	2.02818i	−0.141310	−	0.0815853i
$619$	21.1034	+	21.1034i	0.848216	+	0.848216i	0.989910	−	0.141695i	$-0.0452551\pi$
$619$	21.1034	+	21.1034i	0.848216	+	0.848216i	−0.141695	+	0.989910i	$0.545255\pi$
$620$	18.9588	+	11.3397i	0.761405	+	0.455413i
$621$	6.87801	−	3.97102i	0.276005	−	0.159351i
$622$	11.0652	+	19.1655i	0.443675	+	0.768467i
$623$	−13.9231	−	13.9231i	−0.557816	−	0.557816i
$624$		0			0
$625$	−24.9523	−	1.54291i	−0.998094	−	0.0617164i
$626$	−15.0163	+	56.0417i	−0.600173	+	2.23988i
$627$	0.121413	−	0.453118i	0.00484876	−	0.0180958i
$628$	11.2860	−	3.02407i	0.450360	−	0.120674i
$629$	7.95395	−	7.95395i	0.317145	−	0.317145i
$630$	57.3573	−	14.4236i	2.28517	−	0.574649i
$631$	8.27860	+	30.8962i	0.329566	+	1.22996i	0.909641	+	0.415394i	$0.136356\pi$
$631$	8.27860	+	30.8962i	0.329566	+	1.22996i	−0.580075	+	0.814563i	$0.696977\pi$
$632$	−28.5536			−1.13580
$633$	−0.800728	−	2.98836i	−0.0318261	−	0.118776i
$634$	−1.05668	−	1.83021i	−0.0419659	−	0.0726871i
$635$	−8.38419	−	15.0539i	−0.332716	−	0.597395i
$636$		−	1.55033i		−	0.0614746i
$637$		0			0
$638$	−4.48369	+	4.48369i	−0.177511	+	0.177511i
$639$	−14.4987	−	3.88491i	−0.573559	−	0.153685i
$640$	41.7300	+	11.8750i	1.64952	+	0.469399i
$641$	16.4436	+	9.49372i	0.649484	+	0.374980i	0.788258	−	0.615344i	$-0.210983\pi$
$641$	16.4436	+	9.49372i	0.649484	+	0.374980i	−0.138775	+	0.990324i	$0.544316\pi$
$642$		−	5.22378i		−	0.206166i
$643$	19.6480	−	34.0314i	0.774843	−	1.34207i	−0.160040	−	0.987111i	$-0.551162\pi$
$643$	19.6480	−	34.0314i	0.774843	−	1.34207i	0.934883	−	0.354957i	$-0.115504\pi$
$644$	−51.1082	+	13.6944i	−2.01395	+	0.539635i
$645$	−5.26192	−	5.42696i	−0.207188	−	0.213686i
$646$	3.33792	−	5.78144i	0.131329	−	0.227468i
$647$	18.8280	+	5.04496i	0.740207	+	0.198338i	0.609170	−	0.793040i	$-0.291503\pi$
$647$	18.8280	+	5.04496i	0.740207	+	0.198338i	0.131037	+	0.991377i	$0.458169\pi$
$648$	−21.8355	+	12.6067i	−0.857780	+	0.495240i
$649$	8.31074			0.326225
$650$		0			0
$651$	3.94928			0.154785
$652$	−11.9935	+	6.92444i	−0.469701	+	0.271182i
$653$	25.4784	+	6.82693i	0.997049	+	0.267158i	0.720209	−	0.693758i	$-0.244046\pi$
$653$	25.4784	+	6.82693i	0.997049	+	0.267158i	0.276840	+	0.960916i	$0.410713\pi$
$654$	2.29462	−	3.97439i	0.0897266	−	0.155411i
$655$	−3.76907	−	3.88729i	−0.147270	−	0.151889i
$656$	−6.10374	+	1.63549i	−0.238311	+	0.0638552i
$657$	−8.04181	+	13.9288i	−0.313741	+	0.543415i
$658$		−	83.3984i		−	3.25121i
$659$	−21.5925	−	12.4664i	−0.841124	−	0.485623i	0.0165219	−	0.999864i	$-0.494741\pi$
$659$	−21.5925	−	12.4664i	−0.841124	−	0.485623i	−0.857646	+	0.514240i	$0.828074\pi$
$660$	−1.93556	−	0.550797i	−0.0753417	−	0.0214397i
$661$	3.87692	+	1.03882i	0.150795	+	0.0404053i	0.333427	−	0.942776i	$-0.391795\pi$
$661$	3.87692	+	1.03882i	0.150795	+	0.0404053i	−0.182632	+	0.983181i	$0.558462\pi$
$662$	−35.3427	+	35.3427i	−1.37363	+	1.37363i
$663$		0			0
$664$			19.5083i			0.757069i
$665$	−7.55471	−	13.5646i	−0.292959	−	0.526011i
$666$	22.8690	+	39.6104i	0.886158	+	1.53487i
$667$	3.57555	+	13.3441i	0.138446	+	0.516687i
$668$	−17.7524			−0.686861
$669$	−1.25477	−	4.68288i	−0.0485124	−	0.181051i
$670$	−19.0214	+	4.78328i	−0.734860	+	0.184794i
$671$	−2.05322	+	2.05322i	−0.0792636	+	0.0792636i
$672$	6.43015	−	1.72295i	0.248048	−	0.0664644i
$673$	0.369656	−	1.37958i	0.0142492	−	0.0531787i	−0.958435	−	0.285310i	$-0.907903\pi$
$673$	0.369656	−	1.37958i	0.0142492	−	0.0531787i	0.972684	+	0.232132i	$0.0745700\pi$
$674$	−7.07052	+	26.3875i	−0.272346	+	1.01641i
$675$	7.28442	−	6.84790i	0.280377	−	0.263576i
$676$		0			0
$677$	0.154365	+	0.154365i	0.00593272	+	0.00593272i	0.710067	−	0.704134i	$-0.248665\pi$
$677$	0.154365	+	0.154365i	0.00593272	+	0.00593272i	−0.704134	+	0.710067i	$0.748665\pi$
$678$	7.11929	+	12.3310i	0.273415	+	0.473568i
$679$	−30.9597	+	17.8746i	−1.18813	+	0.685965i
$680$	−9.97028	−	5.96345i	−0.382343	−	0.228688i
$681$	2.97189	+	2.97189i	0.113883	+	0.113883i
$682$	4.63523	+	2.67615i	0.177492	+	0.102475i
$683$	−16.7223	−	9.65462i	−0.639860	−	0.369424i	0.144700	−	0.989476i	$-0.453778\pi$
$683$	−16.7223	−	9.65462i	−0.639860	−	0.369424i	−0.784561	+	0.620052i	$0.787112\pi$
$684$	12.0390	+	12.0390i	0.460322	+	0.460322i
$685$	−1.25384	+	0.315300i	−0.0479066	+	0.0120470i
$686$	−13.2728	+	7.66304i	−0.506757	+	0.292576i
$687$	1.66724	+	2.88774i	0.0636091	+	0.110174i
$688$	−4.17601	−	4.17601i	−0.159209	−	0.159209i
$689$		0			0
$690$	−5.01858	+	4.86596i	−0.191054	+	0.185244i
$691$	10.6795	−	39.8564i	0.406267	−	1.51621i	−0.395441	−	0.918491i	$-0.629408\pi$
$691$	10.6795	−	39.8564i	0.406267	−	1.51621i	0.801708	−	0.597716i	$-0.203925\pi$
$692$	−4.21421	+	15.7277i	−0.160200	+	0.597876i
$693$	8.68132	−	2.32615i	0.329776	−	0.0883632i
$694$	52.0815	−	52.0815i	1.97699	−	1.97699i
$695$	−9.06553	−	36.0503i	−0.343875	−	1.36747i
$696$	0.967204	+	3.60965i	0.0366618	+	0.136824i
$697$	−17.4912			−0.662527
$698$	16.3002	+	60.8331i	0.616971	+	2.30257i
$699$	−0.762979	−	1.32152i	−0.0288585	−	0.0499844i
$700$	−58.6841	+	31.5068i	−2.21805	+	1.19085i
$701$		−	21.8818i		−	0.826464i	−0.910626	−	0.413232i	$-0.864400\pi$
$701$		−	21.8818i		−	0.826464i	0.910626	−	0.413232i	$-0.135600\pi$
$702$		0			0
$703$	8.49047	−	8.49047i	0.320224	−	0.320224i
$704$	9.61713	+	2.57690i	0.362459	+	0.0971206i
$705$	−3.36255	−	6.03749i	−0.126641	−	0.227385i
$706$	−8.93516	−	5.15871i	−0.336279	−	0.194151i
$707$			13.0040i			0.489065i
$708$	6.03695	−	10.4563i	0.226883	−	0.392972i
$709$	24.7071	−	6.62025i	0.927895	−	0.248629i	0.236938	−	0.971525i	$-0.423856\pi$
$709$	24.7071	−	6.62025i	0.927895	−	0.248629i	0.690957	+	0.722896i	$0.257189\pi$
$710$	26.9482	+	0.416085i	1.01135	+	0.0156154i
$711$	13.0244	−	22.5590i	0.488454	−	0.846027i
$712$	−15.1910	−	4.07043i	−0.569308	−	0.152546i
$713$	10.0987	−	5.83051i	0.378201	−	0.218354i
$714$	−5.11976			−0.191602
$715$		0			0
$716$	−44.0317			−1.64554
$717$	5.15147	−	2.97421i	0.192385	−	0.111074i
$718$	−36.8093	−	9.86301i	−1.37371	−	0.368084i
$719$	−13.2933	+	23.0247i	−0.495756	+	0.858675i	−0.999988	−	0.00489360i	$-0.998442\pi$
$719$	−13.2933	+	23.0247i	−0.495756	+	0.858675i	0.504232	+	0.863568i	$0.331776\pi$
$720$	2.74894	−	2.66534i	0.102447	−	0.0993313i
$721$	−19.7071	+	5.28050i	−0.733931	+	0.196656i
$722$	−18.4415	+	31.9415i	−0.686320	+	1.18874i
$723$			5.91629i			0.220029i
$724$	−13.5523	−	7.82442i	−0.503667	−	0.290792i
$725$	8.22630	+	15.3222i	0.305517	+	0.569051i
$726$	7.89178	+	2.11459i	0.292891	+	0.0784800i
$727$	13.8783	−	13.8783i	0.514719	−	0.514719i	−0.401250	−	0.915969i	$-0.631424\pi$
$727$	13.8783	−	13.8783i	0.514719	−	0.514719i	0.915969	+	0.401250i	$0.131424\pi$
$728$		0			0
$729$		−	20.9634i		−	0.776422i
$730$	7.90418	−	27.7762i	0.292547	−	1.02804i
$731$	−8.17363	−	14.1571i	−0.302313	−	0.523621i
$732$	1.09183	+	4.07476i	0.0403551	+	0.150607i
$733$	−38.2590			−1.41313			−0.706563	−	0.707650i	$-0.749756\pi$
$733$	−38.2590			−1.41313			−0.706563	+	0.707650i	$0.749756\pi$
$734$	0.747087	+	2.78817i	0.0275755	+	0.102913i
$735$	−3.38204	+	5.65443i	−0.124749	+	0.208567i
$736$	13.8989	−	13.8989i	0.512321	−	0.512321i
$737$	−2.87898	+	0.771420i	−0.106049	+	0.0284156i
$738$	18.4076	−	68.6980i	0.677592	−	2.52881i
$739$	13.3892	−	49.9691i	0.492529	−	1.83814i	−0.0509242	−	0.998703i	$-0.516217\pi$
$739$	13.3892	−	49.9691i	0.492529	−	1.83814i	0.543453	−	0.839440i	$-0.317117\pi$
$740$	−35.8567	−	36.9813i	−1.31812	−	1.35946i
$741$		0			0
$742$	−8.79088	−	8.79088i	−0.322724	−	0.322724i
$743$	−16.3520	−	28.3225i	−0.599896	−	1.03905i	−0.992836	−	0.119486i	$-0.961875\pi$
$743$	−16.3520	−	28.3225i	−0.599896	−	1.03905i	0.392940	−	0.919564i	$-0.371458\pi$
$744$	2.73176	−	1.57718i	0.100151	−	0.0578223i
$745$	1.54785	−	2.58785i	0.0567089	−	0.0948116i
$746$	−19.6560	−	19.6560i	−0.719657	−	0.719657i
$747$	−15.4127	−	8.89851i	−0.563920	−	0.325580i
$748$	−3.76897	−	2.17601i	−0.137807	−	0.0795630i
$749$	−18.5786	−	18.5786i	−0.678846	−	0.678846i
$750$	−4.74796	+	7.40886i	−0.173371	+	0.270533i
$751$	16.9813	−	9.80415i	0.619656	−	0.357758i	−0.157079	−	0.987586i	$-0.550208\pi$
$751$	16.9813	−	9.80415i	0.619656	−	0.357758i	0.776735	+	0.629828i	$0.216874\pi$
$752$	−2.69961	−	4.67586i	−0.0984446	−	0.170511i
$753$	−4.75276	−	4.75276i	−0.173200	−	0.173200i
$754$		0			0
$755$	−28.8994	−	0.446211i	−1.05176	−	0.0162393i
$756$	6.89417	−	25.7294i	0.250739	−	0.935769i
$757$	0.665955	−	2.48538i	0.0242046	−	0.0903326i	−0.952767	−	0.303702i	$-0.901777\pi$
$757$	0.665955	−	2.48538i	0.0242046	−	0.0903326i	0.976972	+	0.213370i	$0.0684439\pi$
$758$	−69.3455	+	18.5811i	−2.51874	+	0.674895i
$759$	−0.751132	+	0.751132i	−0.0272644	+	0.0272644i
$760$	−10.6428	−	6.36570i	−0.386055	−	0.230908i
$761$	−1.95862	−	7.30968i	−0.0710001	−	0.264976i	0.921297	−	0.388861i	$-0.127131\pi$
$761$	−1.95862	−	7.30968i	−0.0710001	−	0.264976i	−0.992297	+	0.123885i	$0.960465\pi$
$762$	−6.06515			−0.219717
$763$	−5.97419	−	22.2960i	−0.216280	−	0.807168i
$764$	−6.76355	−	11.7148i	−0.244697	−	0.423827i
$765$	9.25930	−	5.15692i	0.334771	−	0.186449i
$766$			27.4274i			0.990994i
$767$		0			0
$768$	4.71968	−	4.71968i	0.170307	−	0.170307i
$769$	32.1647	+	8.61849i	1.15989	+	0.310791i	0.786921	−	0.617054i	$-0.211674\pi$
$769$	32.1647	+	8.61849i	1.15989	+	0.310791i	0.372966	+	0.927845i	$0.378341\pi$
$770$	−14.0985	+	7.85209i	−0.508074	+	0.282970i
$771$	6.06599	+	3.50220i	0.218461	+	0.126129i
$772$			77.5908i			2.79255i
$773$	−7.09940	+	12.2965i	−0.255348	+	0.442275i	−0.964990	−	0.262287i	$-0.915523\pi$
$773$	−7.09940	+	12.2965i	−0.255348	+	0.442275i	0.709642	+	0.704562i	$0.248857\pi$
$774$	64.2050	−	17.2037i	2.30780	−	0.618374i
$775$	10.6955	−	10.0545i	0.384192	−	0.361170i
$776$	−14.2768	+	24.7281i	−0.512507	+	0.887688i
$777$	−8.89478	−	2.38335i	−0.319098	−	0.0855022i
$778$	−44.2854	+	25.5682i	−1.58771	+	0.916663i
$779$	−18.6711			−0.668960
$780$		0			0
$781$	4.09562			0.146553
$782$	−13.0918	+	7.55856i	−0.468162	+	0.270293i
$783$	−6.71784	−	1.80004i	−0.240076	−	0.0643282i
$784$	−2.57381	+	4.45797i	−0.0919219	+	0.159213i
$785$	0.119863	−	7.76307i	0.00427809	−	0.277076i
$786$	−1.84090	+	0.493267i	−0.0656626	+	0.0175942i
$787$	9.50997	−	16.4717i	0.338994	−	0.587154i	−0.645250	−	0.763971i	$-0.723247\pi$
$787$	9.50997	−	16.4717i	0.338994	−	0.587154i	0.984244	+	0.176817i	$0.0565801\pi$
$788$			0.839998i			0.0299237i
$789$	−6.05912	−	3.49824i	−0.215710	−	0.124540i
$790$	−12.8015	+	44.9860i	−0.455457	+	1.60053i
$791$	69.1756	+	18.5356i	2.45960	+	0.659049i
$792$	5.07599	−	5.07599i	0.180367	−	0.180367i
$793$		0			0
$794$			37.3626i			1.32595i
$795$	−0.990843	−	0.281961i	−0.0351416	−	0.0100001i
$796$	−29.7583	−	51.5429i	−1.05475	−	1.82689i
$797$	13.3072	+	49.6630i	0.471364	+	1.75915i	0.634877	+	0.772613i	$0.281051\pi$
$797$	13.3072	+	49.6630i	0.471364	+	1.75915i	−0.163513	+	0.986541i	$0.552283\pi$
$798$	−5.46511			−0.193463
$799$	−3.86808	−	14.4359i	−0.136843	−	0.510704i
$800$	13.0277	−	21.0367i	0.460598	−	0.743761i
$801$	10.1451	−	10.1451i	0.358460	−	0.358460i
$802$	72.1472	−	19.3318i	2.54761	−	0.682629i
$803$	1.13584	−	4.23900i	0.0400828	−	0.149591i
$804$	−1.12072	+	4.18260i	−0.0395249	+	0.147509i
$805$	−0.542795	+	35.1548i	−0.0191310	+	1.23904i
$806$		0			0
$807$	2.08069	+	2.08069i	0.0732437	+	0.0732437i
$808$	5.19327	+	8.99500i	0.182698	+	0.316443i
$809$	35.2049	−	20.3256i	1.23774	−	0.714609i	0.269107	−	0.963110i	$-0.413271\pi$
$809$	35.2049	−	20.3256i	1.23774	−	0.714609i	0.968632	+	0.248502i	$0.0799381\pi$
$810$	10.0723	+	40.0537i	0.353903	+	1.40735i
$811$	−0.182019	−	0.182019i	−0.00639156	−	0.00639156i	0.703904	−	0.710295i	$-0.251439\pi$
$811$	−0.182019	−	0.182019i	−0.00639156	−	0.00639156i	−0.710295	+	0.703904i	$0.751439\pi$
$812$	40.1265	+	23.1671i	1.40816	+	0.813004i
$813$	5.89250	+	3.40204i	0.206659	+	0.119315i
$814$	−8.82467	−	8.82467i	−0.309305	−	0.309305i
$815$	2.24426	+	8.92460i	0.0786129	+	0.312615i
$816$	−0.287048	+	0.165727i	−0.0100487	+	0.00580161i
$817$	−8.72497	−	15.1121i	−0.305248	−	0.528705i
$818$	−7.14826	−	7.14826i	−0.249933	−	0.249933i
$819$		0			0
$820$	−1.23656	+	80.0876i	−0.0431827	+	2.79678i
$821$	7.36549	−	27.4884i	0.257057	−	0.959352i	−0.709877	−	0.704326i	$-0.751249\pi$
$821$	7.36549	−	27.4884i	0.257057	−	0.959352i	0.966934	−	0.255026i	$-0.0820839\pi$
$822$	−0.117782	+	0.439568i	−0.00410811	+	0.0153317i
$823$	47.4409	−	12.7117i	1.65368	−	0.443103i	0.693043	−	0.720896i	$-0.256270\pi$
$823$	47.4409	−	12.7117i	1.65368	−	0.443103i	0.960641	+	0.277793i	$0.0896029\pi$
$824$	−11.5228	+	11.5228i	−0.401415	+	0.401415i
$825$	−0.704047	+	1.13688i	−0.0245118	+	0.0395810i
$826$	−25.0592	−	93.5222i	−0.871921	−	3.25405i
$827$	13.4572			0.467952			0.233976	−	0.972242i	$-0.424826\pi$
$827$	13.4572			0.467952			0.233976	+	0.972242i	$0.424826\pi$
$828$	−9.97849	−	37.2402i	−0.346776	−	1.29419i
$829$	−13.3608	−	23.1417i	−0.464041	−	0.803743i	0.535116	−	0.844778i	$-0.320268\pi$
$829$	−13.3608	−	23.1417i	−0.464041	−	0.803743i	−0.999158	+	0.0410353i	$0.986934\pi$
$830$	30.7352	+	8.74622i	1.06683	+	0.303586i
$831$			0.407515i			0.0141365i
$832$		0			0
$833$	−10.0753	+	10.0753i	−0.349090	+	0.349090i
$834$	−12.6385	−	3.38647i	−0.437635	−	0.117264i
$835$	−3.22865	+	11.3459i	−0.111732	+	0.392640i
$836$	−4.02320	−	2.32279i	−0.139145	−	0.0803355i
$837$			5.87051i			0.202915i
$838$	11.0239	−	19.0940i	0.380816	−	0.659592i
$839$	26.7321	−	7.16283i	0.922893	−	0.247289i	0.234072	−	0.972219i	$-0.424795\pi$
$839$	26.7321	−	7.16283i	0.922893	−	0.247289i	0.688822	+	0.724931i	$0.258128\pi$
$840$	−0.146829	+	9.50953i	−0.00506607	+	0.328110i
$841$	−8.45118	+	14.6379i	−0.291420	+	0.504754i
$842$	−65.4072	−	17.5258i	−2.25408	−	0.603979i
$843$	−5.47015	+	3.15819i	−0.188402	+	0.108774i
$844$	−30.6381			−1.05461
$845$		0			0
$846$	60.7686			2.08927
$847$	35.5881	−	20.5468i	1.22282	−	0.705996i
$848$	−0.777436	−	0.208313i	−0.0266973	−	0.00715351i
$849$	1.77847	−	3.08040i	0.0610369	−	0.105719i
$850$	−13.8654	+	13.0345i	−0.475578	+	0.447080i
$851$	−26.2636	+	7.03731i	−0.900304	+	0.241236i
$852$	2.97508	−	5.15298i	0.101924	−	0.176538i
$853$			19.6378i			0.672385i	0.941793	+	0.336193i	$0.109139\pi$
$853$			19.6378i			0.672385i	−0.941793	+	0.336193i	$0.890861\pi$
$854$	29.2962	+	16.9142i	1.00250	+	0.578792i
$855$	9.88387	−	5.50478i	0.338021	−	0.188259i
$856$	−20.2705	−	5.43147i	−0.692832	−	0.185644i
$857$	−20.8611	+	20.8611i	−0.712601	+	0.712601i	−0.967079	−	0.254478i	$-0.918096\pi$
$857$	−20.8611	+	20.8611i	−0.712601	+	0.712601i	0.254478	+	0.967079i	$0.418096\pi$
$858$		0			0
$859$			41.8545i			1.42806i	0.700116	+	0.714029i	$0.253132\pi$
$859$			41.8545i			1.42806i	−0.700116	+	0.714029i	$0.746868\pi$
$860$	−65.3996	+	36.4240i	−2.23011	+	1.24205i
$861$	7.15952	+	12.4006i	0.243996	+	0.422613i
$862$	−14.2746	−	53.2737i	−0.486196	−	1.81451i
$863$	41.0888			1.39868			0.699339	−	0.714790i	$-0.253478\pi$
$863$	41.0888			1.39868			0.699339	+	0.714790i	$0.253478\pi$
$864$	2.56113	+	9.55826i	0.0871314	+	0.325179i
$865$	9.28537	+	5.55379i	0.315712	+	0.188834i
$866$	41.8350	−	41.8350i	1.42161	−	1.42161i
$867$	4.69356	−	1.25764i	0.159402	−	0.0427115i
$868$	10.1225	−	37.7776i	0.343579	−	1.28226i
$869$	−1.83959	+	6.86543i	−0.0624037	+	0.232894i
$870$	6.12062	+	0.0945032i	0.207508	+	0.00320396i
$871$		0			0
$872$	−13.0365	−	13.0365i	−0.441472	−	0.441472i
$873$	−13.0244	−	22.5590i	−0.440810	−	0.763505i
$874$	−13.9749	+	8.06841i	−0.472708	+	0.272918i
$875$	9.46358	+	43.2362i	0.319927	+	1.46165i
$876$	−4.50829	−	4.50829i	−0.152321	−	0.152321i
$877$	48.5727	+	28.0435i	1.64018	+	0.946961i	0.980767	+	0.195185i	$0.0625306\pi$
$877$	48.5727	+	28.0435i	1.64018	+	0.946961i	0.659418	+	0.751776i	$0.270803\pi$
$878$	65.7919	+	37.9849i	2.22037	+	1.28193i
$879$	−2.69766	−	2.69766i	−0.0909899	−	0.0909899i
$880$	−0.536281	+	0.896608i	−0.0180780	+	0.0302247i
$881$	−44.8975	+	25.9216i	−1.51263	+	0.873320i	−0.512744	+	0.858542i	$0.671371\pi$
$881$	−44.8975	+	25.9216i	−1.51263	+	0.873320i	−0.999891	+	0.0147786i	$0.995296\pi$
$882$	−28.9684	−	50.1748i	−0.975418	−	1.68947i
$883$	24.3974	+	24.3974i	0.821038	+	0.821038i	0.986257	−	0.165219i	$-0.0528330\pi$
$883$	24.3974	+	24.3974i	0.821038	+	0.821038i	−0.165219	+	0.986257i	$0.552833\pi$
$884$		0			0
$885$	−5.58486	−	5.76002i	−0.187733	−	0.193621i
$886$	9.72107	−	36.2795i	0.326586	−	1.21883i
$887$	−6.84302	+	25.5385i	−0.229766	+	0.857499i	0.750673	+	0.660674i	$0.229730\pi$
$887$	−6.84302	+	25.5385i	−0.229766	+	0.857499i	−0.980439	+	0.196825i	$0.936937\pi$
$888$	−7.10443	+	1.90363i	−0.238409	+	0.0638815i
$889$	−21.5710	+	21.5710i	−0.723467	+	0.723467i
$890$	−13.2236	+	22.1085i	−0.443255	+	0.741078i
$891$	1.62440	+	6.06234i	0.0544194	+	0.203096i
$892$	−48.0112			−1.60753
$893$	−4.12899	−	15.4096i	−0.138171	−	0.515663i
$894$	−0.530696	−	0.919193i	−0.0177491	−	0.0307424i
$895$	−8.00810	+	28.1414i	−0.267681	+	0.940663i
$896$		−	76.8115i		−	2.56609i
$897$		0			0
$898$	−46.4273	+	46.4273i	−1.54930	+	1.54930i
$899$	−9.86358	−	2.64294i	−0.328969	−	0.0881469i
$900$	−22.9576	−	42.7604i	−0.765253	−	1.42535i
$901$	−1.92939	−	1.11393i	−0.0642772	−	0.0371105i
$902$			19.4060i			0.646149i
$903$	−6.69127	+	11.5896i	−0.222672	+	0.385678i
$904$	55.2519	−	14.8047i	1.83765	−	0.492397i
$905$	−7.46550	+	7.23846i	−0.248161	+	0.240615i
$906$	−5.08671	+	8.81045i	−0.168995	+	0.292707i
$907$	12.9818	+	3.47846i	0.431053	+	0.115500i	0.467820	−	0.883824i	$-0.345039\pi$
$907$	12.9818	+	3.47846i	0.431053	+	0.115500i	−0.0367675	+	0.999324i	$0.511706\pi$
$908$	36.0455	−	20.8109i	1.19621	−	0.690633i
$909$	−9.47541			−0.314280
$910$		0			0
$911$	−29.9373			−0.991866			−0.495933	−	0.868361i	$-0.665174\pi$
$911$	−29.9373			−0.991866			−0.495933	+	0.868361i	$0.665174\pi$
$912$	−0.306410	+	0.176906i	−0.0101462	+	0.00585794i
$913$	4.69058	+	1.25684i	0.155236	+	0.0415953i
$914$	3.66410	−	6.34641i	0.121198	−	0.209921i
$915$	2.80282	+	0.0432760i	0.0926584	+	0.00143066i
$916$	31.8966	−	8.54666i	1.05389	−	0.282390i
$917$	−4.79290	+	8.30155i	−0.158276	+	0.274141i
$918$		−	7.61041i		−	0.251181i
$919$	32.1637	+	18.5697i	1.06098	+	0.612558i	0.925704	−	0.378249i	$-0.123474\pi$
$919$	32.1637	+	18.5697i	1.06098	+	0.612558i	0.135278	+	0.990808i	$0.456807\pi$
$920$	13.6639	+	24.5337i	0.450486	+	0.808852i
$921$	−9.27485	−	2.48519i	−0.305617	−	0.0818898i
$922$	46.3416	−	46.3416i	1.52618	−	1.52618i
$923$		0			0
$924$			3.56275i			0.117206i
$925$	−30.1567	+	16.1908i	−0.991546	+	0.532350i
$926$	−5.42064	−	9.38882i	−0.178133	−	0.308536i
$927$	−3.84766	−	14.3597i	−0.126374	−	0.471633i
$928$	−17.2127			−0.565036
$929$	14.8083	+	55.2654i	0.485846	+	1.81320i	0.576223	+	0.817293i	$0.304526\pi$
$929$	14.8083	+	55.2654i	0.485846	+	1.81320i	−0.0903774	+	0.995908i	$0.528807\pi$
$930$	−1.26010	−	5.01097i	−0.0413204	−	0.164316i
$931$	−10.7550	+	10.7550i	−0.352480	+	0.352480i
$932$	−14.5968	+	3.91121i	−0.478136	+	0.128116i
$933$	0.840274	−	3.13595i	0.0275094	−	0.102666i
$934$	4.50364	−	16.8078i	0.147364	−	0.549968i
$935$	−2.07620	+	2.01306i	−0.0678988	+	0.0658340i
$936$		0			0
$937$	19.6392	+	19.6392i	0.641585	+	0.641585i	0.950945	−	0.309360i	$-0.100115\pi$
$937$	19.6392	+	19.6392i	0.641585	+	0.641585i	−0.309360	+	0.950945i	$0.600115\pi$
$938$	17.3619	+	30.0716i	0.566884	+	0.981873i
$939$	7.37111	−	4.25571i	0.240547	−	0.138880i
$940$	−66.3714	+	16.6903i	−2.16480	+	0.544379i
$941$	−34.3710	−	34.3710i	−1.12046	−	1.12046i	−0.991672	−	0.128790i	$-0.958891\pi$
$941$	−34.3710	−	34.3710i	−1.12046	−	1.12046i	−0.128790	−	0.991672i	$-0.541109\pi$
$942$	−2.36670	−	1.36641i	−0.0771111	−	0.0445201i
$943$	36.6154	+	21.1399i	1.19236	+	0.688409i
$944$	−4.43230	−	4.43230i	−0.144259	−	0.144259i
$945$	−15.1902	−	9.08563i	−0.494139	−	0.295555i
$946$	−15.7069	+	9.06841i	−0.510677	+	0.294839i
$947$	−26.0741	−	45.1617i	−0.847295	−	1.46756i	−0.883613	−	0.468218i	$-0.844896\pi$
$947$	−26.0741	−	45.1617i	−0.847295	−	1.46756i	0.0363174	−	0.999340i	$-0.488437\pi$
$948$	7.30158	+	7.30158i	0.237144	+	0.237144i
$949$		0			0
$950$	−14.8006	+	13.9137i	−0.480196	+	0.451421i
$951$	−0.0802422	+	0.299468i	−0.00260203	+	0.00971091i
$952$	−5.32332	+	19.8669i	−0.172530	+	0.643890i
$953$	14.0451	−	3.76338i	0.454966	−	0.121908i	−0.0240561	−	0.999711i	$-0.507658\pi$
$953$	14.0451	−	3.76338i	0.454966	−	0.121908i	0.479022	+	0.877803i	$0.340991\pi$
$954$	6.40552	−	6.40552i	0.207386	−	0.207386i
$955$	−8.71723	+	2.19211i	−0.282083	+	0.0709351i
$956$	−15.2465	−	56.9007i	−0.493107	−	1.84030i
$957$	0.930219			0.0300697
$958$	−15.3015	−	57.1061i	−0.494370	−	1.84501i
$959$	1.14445	+	1.98224i	0.0369561	+	0.0640098i
$960$	−4.67675	−	8.39714i	−0.150941	−	0.271017i
$961$		−	22.3805i		−	0.721952i
$962$		0			0
$963$	13.5374	−	13.5374i	0.436235	−	0.436235i
$964$	56.5934	+	15.1642i	1.82275	+	0.488405i
$965$	49.5896	+	14.1115i	1.59635	+	0.454267i
$966$	10.7175	+	6.18774i	0.344830	+	0.199087i
$967$			37.4312i			1.20371i	0.798606	+	0.601854i	$0.205571\pi$
$967$			37.4312i			1.20371i	−0.798606	+	0.601854i	$0.794429\pi$
$968$	16.4111	−	28.4249i	0.527473	−	0.913609i
$969$	−0.945985	+	0.253476i	−0.0303894	+	0.00814282i
$970$	32.5583	+	33.5794i	1.04538	+	1.07817i
$971$	−19.2548	+	33.3502i	−0.617915	+	1.07026i	0.371950	+	0.928253i	$0.378689\pi$
$971$	−19.2548	+	33.3502i	−0.617915	+	1.07026i	−0.989866	+	0.142008i	$0.954644\pi$
$972$	28.3057	+	7.58449i	0.907906	+	0.243273i
$973$	−56.9934	+	32.9051i	−1.82712	+	1.05489i
$974$	2.26574			0.0725990
$975$		0			0
$976$	2.19005			0.0701019
$977$	34.6386	−	19.9986i	1.10819	−	0.639813i	0.169829	−	0.985474i	$-0.445679\pi$
$977$	34.6386	−	19.9986i	1.10819	−	0.639813i	0.938359	+	0.345661i	$0.112345\pi$
$978$	3.12877	+	0.838352i	0.100047	+	0.0268076i
$979$	−1.95739	+	3.39030i	−0.0625584	+	0.108354i
$980$	45.4200	+	46.8446i	1.45089	+	1.49640i
$981$	16.2461	−	4.35312i	0.518697	−	0.138984i
$982$	−22.2788	+	38.5880i	−0.710945	+	1.23139i
$983$		−	16.8519i		−	0.537492i	−0.963211	−	0.268746i	$-0.913391\pi$
$983$		−	16.8519i		−	0.537492i	0.963211	−	0.268746i	$-0.0866093\pi$
$984$	9.90463	+	5.71844i	0.315748	+	0.182297i
$985$	0.536857	+	0.152772i	0.0171057	+	0.00486771i
$986$	12.7869	+	3.42625i	0.407219	+	0.109114i
$987$	−8.65122	+	8.65122i	−0.275372	+	0.275372i
$988$		0			0
$989$			39.5146i			1.25649i
$990$	−5.72146	−	10.2729i	−0.181840	−	0.326495i
$991$	21.2417	+	36.7917i	0.674765	+	1.16873i	0.976537	+	0.215348i	$0.0690885\pi$
$991$	21.2417	+	36.7917i	0.674765	+	1.16873i	−0.301772	+	0.953380i	$0.597578\pi$
$992$	3.76042	+	14.0341i	0.119393	+	0.445582i
$993$	7.33246			0.232689
$994$	−12.3494	−	46.0888i	−0.391701	−	1.46185i
$995$	−38.3541	+	9.64486i	−1.21591	+	0.305763i
$996$	4.98857	−	4.98857i	0.158069	−	0.158069i
$997$	−19.5249	+	5.23167i	−0.618359	+	0.165689i	−0.554381	−	0.832263i	$-0.687045\pi$
$997$	−19.5249	+	5.23167i	−0.618359	+	0.165689i	−0.0639771	+	0.997951i	$0.520378\pi$
$998$	13.9504	−	52.0637i	0.441593	−	1.64805i
$999$	3.54279	−	13.2219i	0.112089	−	0.418322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.c.427.1		16
5.3	odd	4		845.2.o.d.258.4		16
13.2	odd	12		65.2.k.b.57.1	yes	8
13.3	even	3		65.2.f.b.47.1	yes	8
13.4	even	6		845.2.t.d.657.1		16
13.5	odd	4		845.2.o.d.587.4		16
13.6	odd	12		845.2.o.d.357.4		16
13.7	odd	12		845.2.o.c.357.1		16
13.8	odd	4		845.2.o.c.587.1		16
13.9	even	3	inner	845.2.t.c.657.4		16
13.10	even	6		845.2.f.b.437.4		8
13.11	odd	12		845.2.k.b.577.4		8
13.12	even	2		845.2.t.d.427.4		16
39.2	even	12		585.2.w.e.577.4		8
39.29	odd	6		585.2.n.e.307.4		8
52.3	odd	6		1040.2.cd.n.177.2		8
52.15	even	12		1040.2.bg.n.577.2		8
65.2	even	12		325.2.f.b.18.1		8
65.3	odd	12		65.2.k.b.8.1	yes	8
65.8	even	4		845.2.t.d.418.1		16
65.18	even	4	inner	845.2.t.c.418.4		16
65.23	odd	12		845.2.k.b.268.4		8
65.28	even	12		65.2.f.b.18.4	✓	8
65.29	even	6		325.2.f.b.307.4		8
65.33	even	12		845.2.t.d.188.4		16
65.38	odd	4		845.2.o.c.258.1		16
65.42	odd	12		325.2.k.b.268.4		8
65.43	odd	12		845.2.o.c.488.1		16
65.48	odd	12		845.2.o.d.488.4		16
65.54	odd	12		325.2.k.b.57.4		8
65.58	even	12	inner	845.2.t.c.188.1		16
65.63	even	12		845.2.f.b.408.1		8
195.68	even	12		585.2.w.e.73.4		8
195.158	odd	12		585.2.n.e.343.1		8
260.3	even	12		1040.2.bg.n.593.2		8
260.223	odd	12		1040.2.cd.n.993.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.4	✓	8	65.28	even	12
65.2.f.b.47.1	yes	8	13.3	even	3
65.2.k.b.8.1	yes	8	65.3	odd	12
65.2.k.b.57.1	yes	8	13.2	odd	12
325.2.f.b.18.1		8	65.2	even	12
325.2.f.b.307.4		8	65.29	even	6
325.2.k.b.57.4		8	65.54	odd	12
325.2.k.b.268.4		8	65.42	odd	12
585.2.n.e.307.4		8	39.29	odd	6
585.2.n.e.343.1		8	195.158	odd	12
585.2.w.e.73.4		8	195.68	even	12
585.2.w.e.577.4		8	39.2	even	12
845.2.f.b.408.1		8	65.63	even	12
845.2.f.b.437.4		8	13.10	even	6
845.2.k.b.268.4		8	65.23	odd	12
845.2.k.b.577.4		8	13.11	odd	12
845.2.o.c.258.1		16	65.38	odd	4
845.2.o.c.357.1		16	13.7	odd	12
845.2.o.c.488.1		16	65.43	odd	12
845.2.o.c.587.1		16	13.8	odd	4
845.2.o.d.258.4		16	5.3	odd	4
845.2.o.d.357.4		16	13.6	odd	12
845.2.o.d.488.4		16	65.48	odd	12
845.2.o.d.587.4		16	13.5	odd	4
845.2.t.c.188.1		16	65.58	even	12	inner
845.2.t.c.418.4		16	65.18	even	4	inner
845.2.t.c.427.1		16	1.1	even	1	trivial
845.2.t.c.657.4		16	13.9	even	3	inner
845.2.t.d.188.4		16	65.33	even	12
845.2.t.d.418.1		16	65.8	even	4
845.2.t.d.427.4		16	13.12	even	2
845.2.t.d.657.1		16	13.4	even	6
1040.2.bg.n.577.2		8	52.15	even	12
1040.2.bg.n.593.2		8	260.3	even	12
1040.2.cd.n.177.2		8	52.3	odd	6
1040.2.cd.n.993.2		8	260.223	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00594 + 1.15813i) q^{2} +(0.328222 + 0.0879467i) q^{3} +(1.68254 - 2.91425i) q^{4} +(-1.55654 - 1.60536i) q^{5} +(-0.760248 + 0.203708i) q^{6} +(-1.97936 + 3.42835i) q^{7} +3.16190i q^{8} +(-2.49808 - 1.44227i) q^{9} +O(q^{10})\)	\(q+(-2.00594 + 1.15813i) q^{2} +(0.328222 + 0.0879467i) q^{3} +(1.68254 - 2.91425i) q^{4} +(-1.55654 - 1.60536i) q^{5} +(-0.760248 + 0.203708i) q^{6} +(-1.97936 + 3.42835i) q^{7} +3.16190i q^{8} +(-2.49808 - 1.44227i) q^{9} +(4.98155 + 1.41758i) q^{10} +(0.760248 + 0.203708i) q^{11} +(0.808545 - 0.808545i) q^{12} -9.16944i q^{14} +(-0.369704 - 0.663806i) q^{15} +(-0.296815 - 0.514099i) q^{16} +(-0.425285 - 1.58719i) q^{17} +6.68135 q^{18} +(-0.453972 - 1.69425i) q^{19} +(-7.29737 + 1.83506i) q^{20} +(-0.951180 + 0.951180i) q^{21} +(-1.76094 + 0.471842i) q^{22} +(-1.02800 + 3.83654i) q^{23} +(-0.278079 + 1.03780i) q^{24} +(-0.154365 + 4.99762i) q^{25} +(-1.41391 - 1.41391i) q^{27} +(6.66071 + 11.5367i) q^{28} +(3.01218 - 1.73908i) q^{29} +(1.51038 + 0.903393i) q^{30} +(-2.07599 - 2.07599i) q^{31} +(-4.28578 - 2.47440i) q^{32} +(0.231614 + 0.133723i) q^{33} +(2.69127 + 2.69127i) q^{34} +(8.58469 - 2.15878i) q^{35} +(-8.40626 + 4.85336i) q^{36} +(3.42282 + 5.92849i) q^{37} +(2.87281 + 2.87281i) q^{38} +(5.07599 - 4.92163i) q^{40} +(2.75507 - 10.2821i) q^{41} +(0.806422 - 3.00961i) q^{42} +(9.60959 - 2.57488i) q^{43} +(1.87281 - 1.87281i) q^{44} +(1.57300 + 6.25527i) q^{45} +(-2.38112 - 8.88646i) q^{46} +9.09526 q^{47} +(-0.0522078 - 0.194842i) q^{48} +(-4.33572 - 7.50968i) q^{49} +(-5.47826 - 10.2037i) q^{50} -0.558351i q^{51} +(0.958716 - 0.958716i) q^{53} +(4.47371 + 1.19873i) q^{54} +(-0.856332 - 1.53755i) q^{55} +(-10.8401 - 6.25853i) q^{56} -0.596014i q^{57} +(-4.02818 + 6.97701i) q^{58} +(10.1993 - 2.73291i) q^{59} +(-2.55654 - 0.0394734i) q^{60} +(-1.84463 + 3.19499i) q^{61} +(6.56860 + 1.76005i) q^{62} +(9.88919 - 5.70953i) q^{63} +12.6500 q^{64} -0.619474 q^{66} +(-3.27955 + 1.89345i) q^{67} +(-5.34102 - 1.43112i) q^{68} +(-0.674823 + 1.16883i) q^{69} +(-14.7203 + 14.2726i) q^{70} +(5.02635 - 1.34681i) q^{71} +(4.56031 - 7.89869i) q^{72} -5.57581i q^{73} +(-13.7320 - 7.92815i) q^{74} +(-0.490190 + 1.62675i) q^{75} +(-5.70129 - 1.52765i) q^{76} +(-2.20318 + 2.20318i) q^{77} +9.03051i q^{79} +(-0.363309 + 1.27671i) q^{80} +(3.98708 + 6.90582i) q^{81} +(6.38147 + 23.8160i) q^{82} +6.16980 q^{83} +(1.17157 + 4.37238i) q^{84} +(-1.88603 + 3.15326i) q^{85} +(-16.2942 + 16.2942i) q^{86} +(1.14161 - 0.305893i) q^{87} +(-0.644104 + 2.40383i) q^{88} +(-1.28734 + 4.80440i) q^{89} +(-10.3998 - 10.7260i) q^{90} +(9.45100 + 9.45100i) q^{92} +(-0.498808 - 0.863961i) q^{93} +(-18.2446 + 10.5335i) q^{94} +(-2.01325 + 3.36595i) q^{95} +(-1.18907 - 1.18907i) q^{96} +(7.82065 + 4.51526i) q^{97} +(17.3944 + 10.0427i) q^{98} +(-1.60536 - 1.60536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} + 8 q^{4} - 4 q^{5} + 6 q^{6}+O(q^{10}) \) 16 * q + 6 * q^3 + 8 * q^4 - 4 * q^5 + 6 * q^6	\( 16 q + 6 q^{3} + 8 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{15} + 8 q^{16} - 16 q^{17} + 40 q^{18} + 14 q^{19} + 2 q^{20} - 24 q^{21} - 10 q^{22} + 14 q^{23} + 2 q^{24} - 24 q^{25} + 24 q^{27} + 8 q^{28} + 14 q^{30} + 4 q^{31} + 24 q^{35} + 44 q^{37} - 4 q^{38} + 44 q^{40} - 16 q^{41} - 24 q^{42} + 6 q^{43} - 20 q^{44} - 22 q^{45} - 2 q^{46} + 32 q^{47} + 14 q^{48} - 24 q^{49} - 44 q^{50} - 48 q^{53} - 20 q^{54} - 10 q^{55} - 24 q^{58} + 22 q^{59} - 20 q^{60} - 20 q^{61} + 30 q^{62} + 96 q^{64} - 72 q^{66} - 4 q^{68} - 4 q^{69} - 136 q^{70} + 10 q^{71} + 16 q^{72} - 30 q^{75} - 6 q^{76} - 48 q^{77} + 26 q^{80} + 20 q^{81} - 20 q^{82} + 96 q^{83} + 16 q^{84} - 32 q^{85} - 92 q^{86} - 16 q^{87} + 10 q^{88} - 28 q^{89} - 28 q^{90} + 100 q^{92} + 40 q^{93} - 2 q^{95} + 60 q^{96} + 4 q^{99}+O(q^{100}) \) 16 * q + 6 * q^3 + 8 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^15 + 8 * q^16 - 16 * q^17 + 40 * q^18 + 14 * q^19 + 2 * q^20 - 24 * q^21 - 10 * q^22 + 14 * q^23 + 2 * q^24 - 24 * q^25 + 24 * q^27 + 8 * q^28 + 14 * q^30 + 4 * q^31 + 24 * q^35 + 44 * q^37 - 4 * q^38 + 44 * q^40 - 16 * q^41 - 24 * q^42 + 6 * q^43 - 20 * q^44 - 22 * q^45 - 2 * q^46 + 32 * q^47 + 14 * q^48 - 24 * q^49 - 44 * q^50 - 48 * q^53 - 20 * q^54 - 10 * q^55 - 24 * q^58 + 22 * q^59 - 20 * q^60 - 20 * q^61 + 30 * q^62 + 96 * q^64 - 72 * q^66 - 4 * q^68 - 4 * q^69 - 136 * q^70 + 10 * q^71 + 16 * q^72 - 30 * q^75 - 6 * q^76 - 48 * q^77 + 26 * q^80 + 20 * q^81 - 20 * q^82 + 96 * q^83 + 16 * q^84 - 32 * q^85 - 92 * q^86 - 16 * q^87 + 10 * q^88 - 28 * q^89 - 28 * q^90 + 100 * q^92 + 40 * q^93 - 2 * q^95 + 60 * q^96 + 4 * q^99

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