LMFDB - Embedded newform 65.2.f.b.18.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(18,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("65.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.4
Root			$1.18254 - 1.18254i$ of defining polynomial
Character	$\chi$	$=$	65.18
Dual form			65.2.f.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +O(q^{10})$	\(q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +(-3.71844 - 3.60536i) q^{10} +(-0.556540 - 0.556540i) q^{11} +(0.808545 + 0.808545i) q^{12} +(3.60536 + 0.0370899i) q^{13} +9.16944i q^{14} +(0.759725 - 0.0117303i) q^{15} +0.593630 q^{16} +(-1.16190 - 1.16190i) q^{17} +6.68135 q^{18} +(-1.24027 - 1.24027i) q^{19} +(5.23789 - 5.40218i) q^{20} +(-0.951180 - 0.951180i) q^{21} +(1.28910 - 1.28910i) q^{22} +(-2.80855 + 2.80855i) q^{23} +(-0.759725 + 0.759725i) q^{24} +(-0.154365 - 4.99762i) q^{25} +(-0.0859102 + 8.35097i) q^{26} +(-1.41391 + 1.41391i) q^{27} -13.3214 q^{28} -3.47817i q^{29} +(0.0271704 + 1.75973i) q^{30} +(-2.07599 + 2.07599i) q^{31} -4.94880i q^{32} +0.267445i q^{33} +(2.69127 - 2.69127i) q^{34} +(-6.16190 + 6.35517i) q^{35} +9.70671i q^{36} -6.84564 q^{37} +(2.87281 - 2.87281i) q^{38} +(-0.857366 - 0.875189i) q^{39} +(5.07599 + 4.92163i) q^{40} +(7.52699 - 7.52699i) q^{41} +(2.20318 - 2.20318i) q^{42} +(-7.03471 + 7.03471i) q^{43} +(1.87281 + 1.87281i) q^{44} +(4.63072 + 4.48990i) q^{45} +(-6.50534 - 6.50534i) q^{46} +9.09526 q^{47} +(-0.142634 - 0.142634i) q^{48} +8.67143 q^{49} +(11.5758 - 0.357550i) q^{50} +0.558351i q^{51} +(-12.1323 - 0.124811i) q^{52} +(0.958716 + 0.958716i) q^{53} +(-3.27498 - 3.27498i) q^{54} +(1.75973 - 0.0271704i) q^{55} -12.5171i q^{56} +0.596014i q^{57} +8.05636 q^{58} +(-7.46644 + 7.46644i) q^{59} +(-2.55654 + 0.0394734i) q^{60} +3.68926 q^{61} +(-4.80855 - 4.80855i) q^{62} -11.4191i q^{63} +12.6500 q^{64} +(-5.67143 + 5.73017i) q^{65} -0.619474 q^{66} +3.78690i q^{67} +(3.90990 + 3.90990i) q^{68} +1.34965 q^{69} +(-14.7203 - 14.2726i) q^{70} +(-3.67954 + 3.67954i) q^{71} -9.12062 q^{72} +5.57581i q^{73} -15.8563i q^{74} +(-1.16371 + 1.23789i) q^{75} +(4.17363 + 4.17363i) q^{76} +(-2.20318 - 2.20318i) q^{77} +(2.02717 - 1.98589i) q^{78} -9.03051i q^{79} +(-0.924009 + 0.952991i) q^{80} -7.97416 q^{81} +(17.4345 + 17.4345i) q^{82} +6.16980 q^{83} +(3.20080 + 3.20080i) q^{84} +(3.67382 - 0.0567242i) q^{85} +(-16.2942 - 16.2942i) q^{86} +(-0.835716 + 0.835716i) q^{87} +(-1.75973 + 1.75973i) q^{88} +(-3.51707 + 3.51707i) q^{89} +(-10.3998 + 10.7260i) q^{90} +(14.2726 + 0.146829i) q^{91} +(9.45100 - 9.45100i) q^{92} +0.997617 q^{93} +21.0670i q^{94} +(3.92163 - 0.0605505i) q^{95} +(-1.18907 + 1.18907i) q^{96} +9.03051i q^{97} +20.0853i q^{98} +(-1.60536 + 1.60536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.31627i			1.63785i	0.573903	+	0.818924i	$0.305429\pi$
$2$			2.31627i			1.63785i	−0.573903	+	0.818924i	$0.694571\pi$
$3$	−0.240275	−	0.240275i	−0.138723	−	0.138723i	0.634335	−	0.773058i	$-0.281274\pi$
$3$	−0.240275	−	0.240275i	−0.138723	−	0.138723i	−0.773058	+	0.634335i	$0.781274\pi$
$4$	−3.36509			−1.68254
$5$	−1.55654	+	1.60536i	−0.696106	+	0.717939i
$5$	−1.55654	+	1.60536i	−0.696106	+	0.717939i
$6$	0.556540	−	0.556540i	0.227207	−	0.227207i
$7$	3.95872			1.49625			0.748127	−	0.663556i	$-0.230953\pi$
$7$	3.95872			1.49625			0.748127	+	0.663556i	$0.230953\pi$
$8$		−	3.16190i		−	1.11790i
$9$		−	2.88454i		−	0.961512i
$10$	−3.71844	−	3.60536i	−1.17587	−	1.14012i
$11$	−0.556540	−	0.556540i	−0.167803	−	0.167803i	0.618210	−	0.786013i	$-0.287858\pi$
$11$	−0.556540	−	0.556540i	−0.167803	−	0.167803i	−0.786013	+	0.618210i	$0.787858\pi$
$12$	0.808545	+	0.808545i	0.233407	+	0.233407i
$13$	3.60536	+	0.0370899i	0.999947	+	0.0102869i
$13$	3.60536	+	0.0370899i	0.999947	+	0.0102869i
$14$			9.16944i			2.45064i
$15$	0.759725	−	0.0117303i	0.196160	−	0.00302874i
$16$	0.593630			0.148408
$17$	−1.16190	−	1.16190i	−0.281802	−	0.281802i	0.552025	−	0.833827i	$-0.313855\pi$
$17$	−1.16190	−	1.16190i	−0.281802	−	0.281802i	−0.833827	+	0.552025i	$0.813855\pi$
$18$	6.68135			1.57481
$19$	−1.24027	−	1.24027i	−0.284539	−	0.284539i	0.550377	−	0.834916i	$-0.314484\pi$
$19$	−1.24027	−	1.24027i	−0.284539	−	0.284539i	−0.834916	+	0.550377i	$0.814484\pi$
$20$	5.23789	−	5.40218i	1.17123	−	1.20796i
$21$	−0.951180	−	0.951180i	−0.207564	−	0.207564i
$22$	1.28910	−	1.28910i	0.274836	−	0.274836i
$23$	−2.80855	+	2.80855i	−0.585622	+	0.585622i	−0.936443	−	0.350821i	$-0.885903\pi$
$23$	−2.80855	+	2.80855i	−0.585622	+	0.585622i	0.350821	+	0.936443i	$0.385903\pi$
$24$	−0.759725	+	0.759725i	−0.155078	+	0.155078i
$25$	−0.154365	−	4.99762i	−0.0308729	−	0.999523i
$26$	−0.0859102	+	8.35097i	−0.0168484	+	1.63776i
$27$	−1.41391	+	1.41391i	−0.272106	+	0.272106i
$28$	−13.3214			−2.51751
$29$		−	3.47817i		−	0.645879i	−0.946420	−	0.322940i	$-0.895329\pi$
$29$		−	3.47817i		−	0.645879i	0.946420	−	0.322940i	$-0.104671\pi$
$30$	0.0271704	+	1.75973i	0.00496062	+	0.321280i
$31$	−2.07599	+	2.07599i	−0.372859	+	0.372859i	−0.868517	−	0.495659i	$-0.834927\pi$
$31$	−2.07599	+	2.07599i	−0.372859	+	0.372859i	0.495659	+	0.868517i	$0.334927\pi$
$32$		−	4.94880i		−	0.874832i
$33$			0.267445i			0.0465562i
$34$	2.69127	−	2.69127i	0.461549	−	0.461549i
$35$	−6.16190	+	6.35517i	−1.04155	+	1.07422i
$36$			9.70671i			1.61779i
$37$	−6.84564			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$37$	−6.84564			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$38$	2.87281	−	2.87281i	0.466031	−	0.466031i
$39$	−0.857366	−	0.875189i	−0.137288	−	0.140142i
$40$	5.07599	+	4.92163i	0.802585	+	0.778177i
$41$	7.52699	−	7.52699i	1.17552	−	1.17552i	0.194644	−	0.980874i	$-0.437645\pi$
$41$	7.52699	−	7.52699i	1.17552	−	1.17552i	0.980874	−	0.194644i	$-0.0623551\pi$
$42$	2.20318	−	2.20318i	0.339959	−	0.339959i
$43$	−7.03471	+	7.03471i	−1.07278	+	1.07278i	−0.0756481	+	0.997135i	$0.524103\pi$
$43$	−7.03471	+	7.03471i	−1.07278	+	1.07278i	−0.997135	+	0.0756481i	$0.975897\pi$
$44$	1.87281	+	1.87281i	0.282336	+	0.282336i
$45$	4.63072	+	4.48990i	0.690307	+	0.669314i
$46$	−6.50534	−	6.50534i	−0.959160	−	0.959160i
$47$	9.09526			1.32668			0.663340	−	0.748318i	$-0.269138\pi$
$47$	9.09526			1.32668			0.663340	+	0.748318i	$0.269138\pi$
$48$	−0.142634	−	0.142634i	−0.0205875	−	0.0205875i
$49$	8.67143			1.23878
$50$	11.5758	−	0.357550i	1.63707	−	0.0505651i
$51$			0.558351i			0.0781848i
$52$	−12.1323	−	0.124811i	−1.68245	−	0.0173081i
$53$	0.958716	+	0.958716i	0.131690	+	0.131690i	0.769879	−	0.638190i	$-0.220316\pi$
$53$	0.958716	+	0.958716i	0.131690	+	0.131690i	−0.638190	+	0.769879i	$0.720316\pi$
$54$	−3.27498	−	3.27498i	−0.445669	−	0.445669i
$55$	1.75973	−	0.0271704i	0.237281	−	0.00366366i
$56$		−	12.5171i		−	1.67266i
$57$			0.596014i			0.0789439i
$58$	8.05636			1.05785
$59$	−7.46644	+	7.46644i	−0.972047	+	0.972047i	−0.999620	−	0.0275726i	$-0.991222\pi$
$59$	−7.46644	+	7.46644i	−0.972047	+	0.972047i	0.0275726	+	0.999620i	$0.491222\pi$
$60$	−2.55654	+	0.0394734i	−0.330048	+	0.00509599i
$61$	3.68926			0.472361			0.236180	−	0.971709i	$-0.424104\pi$
$61$	3.68926			0.472361			0.236180	+	0.971709i	$0.424104\pi$
$62$	−4.80855	−	4.80855i	−0.610686	−	0.610686i
$63$		−	11.4191i		−	1.43867i
$64$	12.6500			1.58125
$65$	−5.67143	+	5.73017i	−0.703455	+	0.710740i
$66$	−0.619474			−0.0762520
$67$			3.78690i			0.462643i	0.972877	+	0.231321i	$0.0743049\pi$
$67$			3.78690i			0.462643i	−0.972877	+	0.231321i	$0.925695\pi$
$68$	3.90990	+	3.90990i	0.474144	+	0.474144i
$69$	1.34965			0.162478
$70$	−14.7203	−	14.2726i	−1.75941	−	1.70590i
$71$	−3.67954	+	3.67954i	−0.436681	+	0.436681i	−0.890893	−	0.454212i	$-0.849921\pi$
$71$	−3.67954	+	3.67954i	−0.436681	+	0.436681i	0.454212	+	0.890893i	$0.349921\pi$
$72$	−9.12062			−1.07487
$73$			5.57581i			0.652599i	0.945266	+	0.326299i	$0.105802\pi$
$73$			5.57581i			0.652599i	−0.945266	+	0.326299i	$0.894198\pi$
$74$		−	15.8563i		−	1.84326i
$75$	−1.16371	+	1.23789i	−0.134374	+	0.142939i
$76$	4.17363	+	4.17363i	0.478748	+	0.478748i
$77$	−2.20318	−	2.20318i	−0.251076	−	0.251076i
$78$	2.02717	−	1.98589i	0.229532	−	0.224857i
$79$		−	9.03051i		−	1.01601i	−0.861354	−	0.508006i	$-0.830383\pi$
$79$		−	9.03051i		−	1.01601i	0.861354	−	0.508006i	$-0.169617\pi$
$80$	−0.924009	+	0.952991i	−0.103307	+	0.106548i
$81$	−7.97416			−0.886017
$82$	17.4345	+	17.4345i	1.92532	+	1.92532i
$83$	6.16980			0.677224			0.338612	−	0.940926i	$-0.390043\pi$
$83$	6.16980			0.677224			0.338612	+	0.940926i	$0.390043\pi$
$84$	3.20080	+	3.20080i	0.349236	+	0.349236i
$85$	3.67382	−	0.0567242i	0.398481	−	0.00615261i
$86$	−16.2942	−	16.2942i	−1.75705	−	1.75705i
$87$	−0.835716	+	0.835716i	−0.0895981	+	0.0895981i
$88$	−1.75973	+	1.75973i	−0.187587	+	0.187587i
$89$	−3.51707	+	3.51707i	−0.372808	+	0.372808i	−0.868499	−	0.495691i	$-0.834915\pi$
$89$	−3.51707	+	3.51707i	−0.372808	+	0.372808i	0.495691	+	0.868499i	$0.334915\pi$
$90$	−10.3998	+	10.7260i	−1.09623	+	1.13062i
$91$	14.2726	+	0.146829i	1.49617	+	0.0153918i
$92$	9.45100	−	9.45100i	0.985334	−	0.985334i
$93$	0.997617			0.103448
$94$			21.0670i			2.17290i
$95$	3.92163	−	0.0605505i	0.402350	−	0.00621235i
$96$	−1.18907	+	1.18907i	−0.121359	+	0.121359i
$97$			9.03051i			0.916910i	0.888718	+	0.458455i	$0.151597\pi$
$97$			9.03051i			0.916910i	−0.888718	+	0.458455i	$0.848403\pi$
$98$			20.0853i			2.02893i
$99$	−1.60536	+	1.60536i	−0.161345	+	0.161345i
$100$	0.519450	+	16.8174i	0.0519450	+	1.68174i
$101$		−	3.28490i		−	0.326860i	−0.986555	−	0.163430i	$-0.947744\pi$
$101$		−	3.28490i		−	0.326860i	0.986555	−	0.163430i	$-0.0522558\pi$
$102$	−1.29329			−0.128055
$103$	3.64426	−	3.64426i	0.359080	−	0.359080i	−0.504394	−	0.863474i	$-0.668284\pi$
$103$	3.64426	−	3.64426i	0.359080	−	0.359080i	0.863474	+	0.504394i	$0.168284\pi$
$104$	0.117275	−	11.3998i	0.0114997	−	1.11784i
$105$	3.00754	−	0.0464368i	0.293505	−	0.00453177i
$106$	−2.22064	+	2.22064i	−0.215688	+	0.215688i
$107$	−4.69308	+	4.69308i	−0.453697	+	0.453697i	−0.896580	−	0.442882i	$-0.853956\pi$
$107$	−4.69308	+	4.69308i	−0.453697	+	0.453697i	0.442882	+	0.896580i	$0.353956\pi$
$108$	4.75791	−	4.75791i	0.457831	−	0.457831i
$109$	−4.12300	−	4.12300i	−0.394912	−	0.394912i	0.481522	−	0.876434i	$-0.340084\pi$
$109$	−4.12300	−	4.12300i	−0.394912	−	0.394912i	−0.876434	+	0.481522i	$0.840084\pi$
$110$	0.0629339	+	4.07599i	0.00600051	+	0.388630i
$111$	1.64483	+	1.64483i	0.156121	+	0.156121i
$112$	2.35001			0.222055
$113$	−12.7920	−	12.7920i	−1.20337	−	1.20337i	−0.973134	−	0.230241i	$-0.926049\pi$
$113$	−12.7920	−	12.7920i	−1.20337	−	1.20337i	−0.230241	−	0.973134i	$-0.573951\pi$
$114$	−1.38053			−0.129298
$115$	−0.137114	−	8.88034i	−0.0127859	−	0.828096i
$116$			11.7043i			1.08672i
$117$	0.106987	−	10.3998i	0.00989098	−	0.961461i
$118$	−17.2942	−	17.2942i	−1.59206	−	1.59206i
$119$	−4.59964	−	4.59964i	−0.421648	−	0.421648i
$120$	−0.0370899	−	2.40218i	−0.00338583	−	0.219288i
$121$		−	10.3805i		−	0.943684i
$122$			8.54529i			0.773655i
$123$	−3.61709			−0.326142
$124$	6.98589	−	6.98589i	0.627351	−	0.627351i
$125$	8.26325	+	7.53118i	0.739088	+	0.673609i
$126$	26.4496			2.35632
$127$	−5.44898	−	5.44898i	−0.483519	−	0.483519i	0.422735	−	0.906253i	$-0.361070\pi$
$127$	−5.44898	−	5.44898i	−0.483519	−	0.483519i	−0.906253	+	0.422735i	$0.861070\pi$
$128$			19.4031i			1.71501i
$129$	3.38053			0.297639
$130$	−13.2726	−	13.1365i	−1.16408	−	1.15215i
$131$	2.42144			0.211562			0.105781	−	0.994389i	$-0.466266\pi$
$131$	2.42144			0.211562			0.105781	+	0.994389i	$0.466266\pi$
$132$		−	0.899976i		−	0.0783329i
$133$	−4.90990	−	4.90990i	−0.425742	−	0.425742i
$134$	−8.77146			−0.757738
$135$	−0.0690272	−	4.47063i	−0.00594091	−	0.384771i
$136$	−3.67382	+	3.67382i	−0.315027	+	0.315027i
$137$	−0.578190			−0.0493981			−0.0246991	−	0.999695i	$-0.507863\pi$
$137$	−0.578190			−0.0493981			−0.0246991	+	0.999695i	$0.507863\pi$
$138$			3.12614i			0.266114i
$139$			16.6241i			1.41004i	0.709187	+	0.705021i	$0.249062\pi$
$139$			16.6241i			1.41004i	−0.709187	+	0.705021i	$0.750938\pi$
$140$	20.7353	−	21.3857i	1.75245	−	1.80742i
$141$	−2.18536	−	2.18536i	−0.184041	−	0.184041i
$142$	−8.52279	−	8.52279i	−0.715217	−	0.715217i
$143$	−1.98589	−	2.02717i	−0.166068	−	0.169521i
$144$		−	1.71235i		−	0.142696i
$145$	5.58371	+	5.41391i	0.463702	+	0.449600i
$146$	−12.9150			−1.06886
$147$	−2.08353	−	2.08353i	−0.171846	−	0.171846i
$148$	23.0361			1.89356
$149$	0.953563	+	0.953563i	0.0781189	+	0.0781189i	0.745087	−	0.666968i	$-0.232408\pi$
$149$	0.953563	+	0.953563i	0.0781189	+	0.0781189i	−0.666968	+	0.745087i	$0.732408\pi$
$150$	−2.86729	−	2.69546i	−0.234113	−	0.220084i
$151$	9.13988	+	9.13988i	0.743793	+	0.743793i	0.973306	−	0.229513i	$-0.0737132\pi$
$151$	9.13988	+	9.13988i	0.743793	+	0.743793i	−0.229513	+	0.973306i	$0.573713\pi$
$152$	−3.92163	+	3.92163i	−0.318086	+	0.318086i
$153$	−3.35154	+	3.35154i	−0.270956	+	0.270956i
$154$	5.10316	−	5.10316i	0.411224	−	0.411224i
$155$	−0.101350	−	6.56408i	−0.00814065	−	0.527239i
$156$	2.88511	+	2.94509i	0.230994	+	0.235796i
$157$	2.45519	−	2.45519i	0.195945	−	0.195945i	−0.602314	−	0.798259i	$-0.705754\pi$
$157$	2.45519	−	2.45519i	0.195945	−	0.195945i	0.798259	+	0.602314i	$0.205754\pi$
$158$	20.9171			1.66407
$159$		−	0.460711i		−	0.0365367i
$160$	7.94460	+	7.70300i	0.628076	+	0.608976i
$161$	−11.1182	+	11.1182i	−0.876240	+	0.876240i
$162$		−	18.4703i		−	1.45116i
$163$		−	4.11546i		−	0.322348i	−0.986926	−	0.161174i	$-0.948472\pi$
$163$		−	4.11546i		−	0.322348i	0.986926	−	0.161174i	$-0.0515280\pi$
$164$	−25.3290	+	25.3290i	−1.97786	+	1.97786i
$165$	−0.429346	−	0.416289i	−0.0334245	−	0.0324081i
$166$			14.2909i			1.10919i
$167$	5.27547			0.408228			0.204114	−	0.978947i	$-0.434569\pi$
$167$	5.27547			0.408228			0.204114	+	0.978947i	$0.434569\pi$
$168$	−3.00754	+	3.00754i	−0.232036	+	0.232036i
$169$	12.9972	+	0.267445i	0.999788	+	0.0205727i
$170$	0.131388	+	8.50953i	0.0100770	+	0.652651i
$171$	−3.57762	+	3.57762i	−0.273587	+	0.273587i
$172$	23.6724	−	23.6724i	1.80500	−	1.80500i
$173$	3.42144	−	3.42144i	0.260127	−	0.260127i	−0.564978	−	0.825106i	$-0.691115\pi$
$173$	3.42144	−	3.42144i	0.260127	−	0.260127i	0.825106	+	0.564978i	$0.191115\pi$
$174$	−1.93574	−	1.93574i	−0.146748	−	0.146748i
$175$	−0.611086	−	19.7841i	−0.0461938	−	1.49554i
$176$	−0.330379	−	0.330379i	−0.0249033	−	0.0249033i
$177$	3.58799			0.269690
$178$	−8.14646	−	8.14646i	−0.610603	−	0.610603i
$179$	13.0849			0.978008			0.489004	−	0.872282i	$-0.337360\pi$
$179$	13.0849			0.978008			0.489004	+	0.872282i	$0.337360\pi$
$180$	−15.5828	−	15.1089i	−1.16147	−	1.12615i
$181$			4.65035i			0.345658i	0.984952	+	0.172829i	$0.0552908\pi$
$181$			4.65035i			0.345658i	−0.984952	+	0.172829i	$0.944709\pi$
$182$	−0.340094	+	33.0591i	−0.0252094	+	2.45051i
$183$	−0.886435	−	0.886435i	−0.0655272	−	0.0655272i
$184$	8.88034	+	8.88034i	0.654667	+	0.654667i
$185$	10.6555	−	10.9897i	0.783408	−	0.807980i
$186$			2.31074i			0.169432i
$187$			1.29329i			0.0945747i
$188$	−30.6063			−2.23220
$189$	−5.59725	+	5.59725i	−0.407140	+	0.407140i
$190$	0.140251	+	9.08353i	0.0101749	+	0.658988i
$191$	−4.01984			−0.290865			−0.145433	−	0.989368i	$-0.546457\pi$
$191$	−4.01984			−0.290865			−0.145433	+	0.989368i	$0.546457\pi$
$192$	−3.03947	−	3.03947i	−0.219355	−	0.219355i
$193$			23.0576i			1.65972i	0.557970	+	0.829861i	$0.311580\pi$
$193$			23.0576i			1.65972i	−0.557970	+	0.829861i	$0.688420\pi$
$194$	−20.9171			−1.50176
$195$	2.73952	−	0.0141137i	0.196181	−	0.00101070i
$196$	−29.1801			−2.08429
$197$			0.249622i			0.0177848i	0.999960	+	0.00889240i	$0.00283058\pi$
$197$			0.249622i			0.0177848i	−0.999960	+	0.00889240i	$0.997169\pi$
$198$	−3.71844	−	3.71844i	−0.264258	−	0.264258i
$199$	−17.6865			−1.25376			−0.626882	−	0.779115i	$-0.715669\pi$
$199$	−17.6865			−1.25376			−0.626882	+	0.779115i	$0.715669\pi$
$200$	−15.8020	+	0.488086i	−1.11737	+	0.0345129i
$201$	0.909896	−	0.909896i	0.0641791	−	0.0641791i
$202$	7.60870			0.535346
$203$		−	13.7691i		−	0.966399i
$204$		−	1.87890i		−	0.131549i
$205$	0.367469	+	23.7996i	0.0256652	+	1.66224i
$206$	8.44108	+	8.44108i	0.588118	+	0.588118i
$207$	8.10135	+	8.10135i	0.563083	+	0.563083i
$208$	2.14025	+	0.0220177i	0.148400	+	0.00152665i
$209$			1.38053i			0.0954930i
$210$	0.107560	+	6.96625i	0.00742234	+	0.480717i
$211$	9.10469			0.626793			0.313396	−	0.949622i	$-0.398533\pi$
$211$	9.10469			0.626793			0.313396	+	0.949622i	$0.398533\pi$
$212$	−3.22616	−	3.22616i	−0.221574	−	0.221574i
$213$	1.76820			0.121155
$214$	−10.8704	−	10.8704i	−0.743087	−	0.743087i
$215$	−0.343436	−	22.2430i	−0.0234221	−	1.51696i
$216$	4.47063	+	4.47063i	0.304188	+	0.304188i
$217$	−8.21826	+	8.21826i	−0.557892	+	0.557892i
$218$	9.54996	−	9.54996i	0.646805	−	0.646805i
$219$	1.33973	−	1.33973i	0.0905303	−	0.0905303i
$220$	−5.92163	+	0.0914308i	−0.399236	+	0.00616426i
$221$	−4.14598	−	4.23217i	−0.278889	−	0.284686i
$222$	−3.80987	+	3.80987i	−0.255702	+	0.255702i
$223$	14.2674			0.955419			0.477709	−	0.878518i	$-0.341467\pi$
$223$	14.2674			0.955419			0.477709	+	0.878518i	$0.341467\pi$
$224$		−	19.5909i		−	1.30897i
$225$	−14.4158	+	0.445270i	−0.961054	+	0.0296847i
$226$	29.6298	−	29.6298i	1.97094	−	1.97094i
$227$			12.3687i			0.820940i	0.911874	+	0.410470i	$0.134635\pi$
$227$			12.3687i			0.820940i	−0.911874	+	0.410470i	$0.865365\pi$
$228$		−	2.00564i		−	0.132827i
$229$	6.93888	−	6.93888i	0.458534	−	0.458534i	−0.439640	−	0.898174i	$-0.644894\pi$
$229$	6.93888	−	6.93888i	0.458534	−	0.458534i	0.898174	+	0.439640i	$0.144894\pi$
$230$	20.5692	−	0.317592i	1.35629	−	0.0209414i
$231$			1.05874i			0.0696600i
$232$	−10.9976			−0.722029
$233$	−3.17544	+	3.17544i	−0.208030	+	0.208030i	−0.803430	−	0.595400i	$-0.796994\pi$
$233$	−3.17544	+	3.17544i	−0.208030	+	0.208030i	0.595400	+	0.803430i	$0.296994\pi$
$234$	24.0887	+	0.247811i	1.57473	+	0.0161999i
$235$	−14.1571	+	14.6012i	−0.923510	+	0.952475i
$236$	25.1252	−	25.1252i	1.63551	−	1.63551i
$237$	−2.16980	+	2.16980i	−0.140944	+	0.140944i
$238$	10.6540	−	10.6540i	0.690595	−	0.690595i
$239$	12.3783	+	12.3783i	0.800689	+	0.800689i	0.983203	−	0.182514i	$-0.0584236\pi$
$239$	12.3783	+	12.3783i	0.800689	+	0.800689i	−0.182514	+	0.983203i	$0.558424\pi$
$240$	0.450996	−	0.00696344i	0.0291117	−	0.000449488i
$241$	12.3115	+	12.3115i	0.793053	+	0.793053i	0.981989	−	0.188936i	$-0.0605039\pi$
$241$	12.3115	+	12.3115i	0.793053	+	0.793053i	−0.188936	+	0.981989i	$0.560504\pi$
$242$	24.0441			1.54561
$243$	6.15771	+	6.15771i	0.395017	+	0.395017i
$244$	−12.4147			−0.794767
$245$	−13.4974	+	13.9208i	−0.862319	+	0.889366i
$246$		−	8.37814i		−	0.534171i
$247$	−4.42564	−	4.51764i	−0.281596	−	0.287451i
$248$	6.56408	+	6.56408i	0.416819	+	0.416819i
$249$	−1.48245	−	1.48245i	−0.0939464	−	0.0939464i
$250$	−17.4442	+	19.1399i	−1.10327	+	1.21051i
$251$		−	19.7805i		−	1.24854i	−0.781210	−	0.624268i	$-0.785397\pi$
$251$		−	19.7805i		−	1.24854i	0.781210	−	0.624268i	$-0.214603\pi$
$252$			38.4261i			2.42062i
$253$	3.12614			0.196539
$254$	12.6213	−	12.6213i	0.791930	−	0.791930i
$255$	−0.896355	−	0.869096i	−0.0561319	−	0.0544249i
$256$	−19.6428			−1.22768
$257$	−14.5758	−	14.5758i	−0.909214	−	0.909214i	0.0869949	−	0.996209i	$-0.472274\pi$
$257$	−14.5758	−	14.5758i	−0.909214	−	0.909214i	−0.996209	+	0.0869949i	$0.972274\pi$
$258$			7.83020i			0.487487i
$259$	−27.0999			−1.68391
$260$	19.0849	−	19.2825i	1.18359	−	1.19585i
$261$	−10.0329			−0.621021
$262$			5.60870i			0.346507i
$263$	14.5593	+	14.5593i	0.897765	+	0.897765i	0.995238	−	0.0974727i	$-0.0310759\pi$
$263$	14.5593	+	14.5593i	0.897765	+	0.897765i	−0.0974727	+	0.995238i	$0.531076\pi$
$264$	0.845635			0.0520453
$265$	−3.03136	+	0.0468047i	−0.186215	+	0.00287519i
$266$	11.3726	−	11.3726i	0.697300	−	0.697300i
$267$	1.69013			0.103434
$268$		−	12.7432i		−	0.778417i
$269$			8.65961i			0.527986i	0.964525	+	0.263993i	$0.0850396\pi$
$269$			8.65961i			0.527986i	−0.964525	+	0.263993i	$0.914960\pi$
$270$	10.3552	−	0.159885i	0.630195	−	0.00973031i
$271$	−14.1589	−	14.1589i	−0.860095	−	0.860095i	0.131254	−	0.991349i	$-0.458100\pi$
$271$	−14.1589	−	14.1589i	−0.860095	−	0.860095i	−0.991349	+	0.131254i	$0.958100\pi$
$272$	−0.689739	−	0.689739i	−0.0418216	−	0.0418216i
$273$	−3.39407	−	3.46463i	−0.205418	−	0.209689i
$274$		−	1.33924i		−	0.0809066i
$275$	−2.69546	+	2.86729i	−0.162543	+	0.172904i
$276$	−4.54167			−0.273377
$277$	0.848019	+	0.848019i	0.0509525	+	0.0509525i	0.732124	−	0.681171i	$-0.238529\pi$
$277$	0.848019	+	0.848019i	0.0509525	+	0.0509525i	−0.681171	+	0.732124i	$0.738529\pi$
$278$	−38.5059			−2.30943
$279$	5.98827	+	5.98827i	0.358508	+	0.358508i
$280$	20.0944	+	19.4833i	1.20087	+	1.16435i
$281$	−13.1441	−	13.1441i	−0.784110	−	0.784110i	0.196412	−	0.980522i	$-0.437071\pi$
$281$	−13.1441	−	13.1441i	−0.784110	−	0.784110i	−0.980522	+	0.196412i	$0.937071\pi$
$282$	5.06188	−	5.06188i	0.301430	−	0.301430i
$283$	7.40181	−	7.40181i	0.439992	−	0.439992i	−0.452017	−	0.892009i	$-0.649295\pi$
$283$	7.40181	−	7.40181i	0.439992	−	0.439992i	0.892009	+	0.452017i	$0.149295\pi$
$284$	12.3820	−	12.3820i	0.734735	−	0.734735i
$285$	−0.956817	−	0.927719i	−0.0566769	−	0.0549533i
$286$	4.69546	−	4.59984i	0.277649	−	0.271994i
$287$	29.7972	−	29.7972i	1.75887	−	1.75887i
$288$	−14.2750			−0.841161
$289$		−	14.3000i		−	0.841175i
$290$	−12.5400	+	12.9334i	−0.736377	+	0.759473i
$291$	2.16980	−	2.16980i	0.127196	−	0.127196i
$292$		−	18.7631i		−	1.09803i
$293$		−	11.2274i		−	0.655912i	−0.944693	−	0.327956i	$-0.893640\pi$
$293$		−	11.2274i		−	0.655912i	0.944693	−	0.327956i	$-0.106360\pi$
$294$	4.82600	−	4.82600i	0.281458	−	0.281458i
$295$	−0.364513	−	23.6081i	−0.0212228	−	1.37452i
$296$			21.6452i			1.25810i
$297$	1.57379			0.0913206
$298$	−2.20871	+	2.20871i	−0.127947	+	0.127947i
$299$	−10.2300	+	10.0216i	−0.591615	+	0.579567i
$300$	3.91599	−	4.16561i	0.226090	−	0.240502i
$301$	−27.8484	+	27.8484i	−1.60516	+	1.60516i
$302$	−21.1704	+	21.1704i	−1.21822	+	1.21822i
$303$	−0.789279	+	0.789279i	−0.0453429	+	0.0453429i
$304$	−0.736265	−	0.736265i	−0.0422277	−	0.0422277i
$305$	−5.74247	+	5.92258i	−0.328813	+	0.339126i
$306$	−7.76307	−	7.76307i	−0.443785	−	0.443785i
$307$	−28.2579			−1.61276			−0.806382	−	0.591395i	$-0.798577\pi$
$307$	−28.2579			−1.61276			−0.806382	+	0.591395i	$0.798577\pi$
$308$	7.41391	+	7.41391i	0.422446	+	0.422446i
$309$	−1.75125			−0.0996250
$310$	15.2041	−	0.234754i	0.863537	−	0.0133331i
$311$			9.55436i			0.541778i	0.962611	+	0.270889i	$0.0873177\pi$
$311$			9.55436i			0.541778i	−0.962611	+	0.270889i	$0.912682\pi$
$312$	−2.76726	+	2.71090i	−0.156665	+	0.153475i
$313$	17.7119	+	17.7119i	1.00113	+	1.00113i	0.999999	+	0.00113436i	$0.000361078\pi$
$313$	17.7119	+	17.7119i	1.00113	+	1.00113i	0.00113436	+	0.999999i	$0.499639\pi$
$314$	5.68687	+	5.68687i	0.320929	+	0.320929i
$315$	18.3317	+	17.7742i	1.03287	+	1.00146i
$316$			30.3884i			1.70948i
$317$		−	0.912395i		−	0.0512452i	−0.999672	−	0.0256226i	$-0.991843\pi$
$317$		−	0.912395i		−	0.0512452i	0.999672	−	0.0256226i	$-0.00815683\pi$
$318$	1.06713			0.0598416
$319$	−1.93574	+	1.93574i	−0.108381	+	0.108381i
$320$	−19.6902	+	20.3078i	−1.10072	+	1.13524i
$321$	2.25526			0.125876
$322$	−25.7528	−	25.7528i	−1.43515	−	1.43515i
$323$			2.88215i			0.160367i
$324$	26.8337			1.49076
$325$	−0.371179	−	18.0239i	−0.0205893	−	0.999788i
$326$	9.53251			0.527957
$327$			1.98131i			0.109566i
$328$	−23.7996	−	23.7996i	−1.31411	−	1.31411i
$329$	36.0055			1.98505
$330$	0.964237	−	0.994479i	0.0530795	−	0.0547443i
$331$	−15.2585	+	15.2585i	−0.838682	+	0.838682i	−0.988685	−	0.150003i	$-0.952072\pi$
$331$	−15.2585	+	15.2585i	−0.838682	+	0.838682i	0.150003	+	0.988685i	$0.452072\pi$
$332$	−20.7619			−1.13946
$333$			19.7465i			1.08210i
$334$			12.2194i			0.668615i
$335$	−6.07933	−	5.89446i	−0.332149	−	0.322049i
$336$	−0.564649	−	0.564649i	−0.0308041	−	0.0308041i
$337$	8.33973	+	8.33973i	0.454294	+	0.454294i	0.896777	−	0.442483i	$-0.145902\pi$
$337$	8.33973	+	8.33973i	0.454294	+	0.454294i	−0.442483	+	0.896777i	$0.645902\pi$
$338$	−0.619474	+	30.1051i	−0.0336950	+	1.63750i
$339$			6.14721i			0.333871i
$340$	−12.3627	+	0.190882i	−0.670462	+	0.0103520i
$341$	2.31074			0.125134
$342$	−8.28671	−	8.28671i	−0.448094	−	0.448094i
$343$	6.61672			0.357269
$344$	22.2430	+	22.2430i	1.19926	+	1.19926i
$345$	−2.10078	+	2.16667i	−0.113102	+	0.116649i
$346$	7.92497	+	7.92497i	0.426049	+	0.426049i
$347$	22.4851	−	22.4851i	1.20707	−	1.20707i	0.235092	−	0.971973i	$-0.424461\pi$
$347$	22.4851	−	22.4851i	1.20707	−	1.20707i	0.971973	−	0.235092i	$-0.0755391\pi$
$348$	2.81226	−	2.81226i	0.150753	−	0.150753i
$349$	19.2262	−	19.2262i	1.02915	−	1.02915i	0.0295907	−	0.999562i	$-0.490580\pi$
$349$	19.2262	−	19.2262i	1.02915	−	1.02915i	0.999562	−	0.0295907i	$-0.00942039\pi$
$350$	45.8253	−	1.41544i	2.44947	−	0.0756583i
$351$	−5.15008	+	5.04520i	−0.274891	+	0.269293i
$352$	−2.75420	+	2.75420i	−0.146800	+	0.146800i
$353$	−4.45434			−0.237080			−0.118540	−	0.992949i	$-0.537821\pi$
$353$	−4.45434			−0.237080			−0.118540	+	0.992949i	$0.537821\pi$
$354$			8.31074i			0.441711i
$355$	−0.179636	−	11.6343i	−0.00953409	−	0.617487i
$356$	11.8352	−	11.8352i	0.627266	−	0.627266i
$357$			2.21035i			0.116984i
$358$			30.3080i			1.60183i
$359$	11.6335	−	11.6335i	0.613992	−	0.613992i	−0.329992	−	0.943984i	$-0.607046\pi$
$359$	11.6335	−	11.6335i	0.613992	−	0.613992i	0.943984	+	0.329992i	$0.107046\pi$
$360$	14.1966	−	14.6419i	0.748227	−	0.771695i
$361$		−	15.9234i		−	0.838076i
$362$	−10.7715			−0.566135
$363$	−2.49418	+	2.49418i	−0.130910	+	0.130910i
$364$	−48.0285	−	0.494091i	−2.51738	−	0.0258974i
$365$	−8.95118	−	8.67897i	−0.468526	−	0.454278i
$366$	2.05322	−	2.05322i	0.107323	−	0.107323i
$367$	0.881194	−	0.881194i	0.0459980	−	0.0459980i	−0.683734	−	0.729732i	$-0.739645\pi$
$367$	0.881194	−	0.881194i	0.0459980	−	0.0459980i	0.729732	+	0.683734i	$0.239645\pi$
$368$	−1.66724	+	1.66724i	−0.0869108	+	0.0869108i
$369$	−21.7119	−	21.7119i	−1.13027	−	1.13027i
$370$	25.4551	+	24.6810i	1.32335	+	1.28310i
$371$	3.79528	+	3.79528i	0.197041	+	0.197041i
$372$	−3.35707			−0.174056
$373$	8.48607	+	8.48607i	0.439392	+	0.439392i	0.891807	−	0.452415i	$-0.149438\pi$
$373$	8.48607	+	8.48607i	0.439392	+	0.439392i	−0.452415	+	0.891807i	$0.649438\pi$
$374$	−2.99560			−0.154899
$375$	−0.175898	−	3.79500i	−0.00908334	−	0.195973i
$376$		−	28.7583i		−	1.48310i
$377$	0.129005	−	12.5400i	0.00664410	−	0.645845i
$378$	−12.9647	−	12.9647i	−0.666833	−	0.666833i
$379$	−21.9165	−	21.9165i	−1.12577	−	1.12577i	−0.990857	−	0.134918i	$-0.956923\pi$
$379$	−21.9165	−	21.9165i	−1.12577	−	1.12577i	−0.134918	−	0.990857i	$-0.543077\pi$
$380$	−13.1966	+	0.203758i	−0.676972	+	0.0104525i
$381$			2.61851i			0.134150i
$382$		−	9.31101i		−	0.476393i
$383$	−11.8412			−0.605059			−0.302529	−	0.953140i	$-0.597831\pi$
$383$	−11.8412			−0.605059			−0.302529	+	0.953140i	$0.597831\pi$
$384$	4.66208	−	4.66208i	0.237911	−	0.237911i
$385$	6.96625	−	0.107560i	0.355033	−	0.00548176i
$386$	−53.4075			−2.71837
$387$	20.2919	+	20.2919i	1.03149	+	1.03149i
$388$		−	30.3884i		−	1.54274i
$389$	22.0771			1.11935			0.559676	−	0.828712i	$-0.310926\pi$
$389$	22.0771			1.11935			0.559676	+	0.828712i	$0.310926\pi$
$390$	0.0326910	+	6.34545i	0.00165537	+	0.321314i
$391$	6.52650			0.330059
$392$		−	27.4182i		−	1.38483i
$393$	−0.581812	−	0.581812i	−0.0293485	−	0.0293485i
$394$	−0.578190			−0.0291288
$395$	14.4972	+	14.0564i	0.729435	+	0.707252i
$396$	5.40218	−	5.40218i	0.271470	−	0.271470i
$397$	−16.1305			−0.809568			−0.404784	−	0.914412i	$-0.632653\pi$
$397$	−16.1305			−0.809568			−0.404784	+	0.914412i	$0.632653\pi$
$398$		−	40.9666i		−	2.05347i
$399$			2.35945i			0.118120i
$400$	−0.0916355	−	2.96674i	−0.00458178	−	0.148337i
$401$	22.8020	+	22.8020i	1.13868	+	1.13868i	0.988688	+	0.149988i	$0.0479236\pi$
$401$	22.8020	+	22.8020i	1.13868	+	1.13868i	0.149988	+	0.988688i	$0.452076\pi$
$402$	2.10756	+	2.10756i	0.105116	+	0.105116i
$403$	−7.56169	+	7.40770i	−0.376675	+	0.369004i
$404$			11.0540i			0.549956i
$405$	12.4121	−	12.8014i	0.616762	−	0.636106i
$406$	31.8928			1.58281
$407$	3.80987	+	3.80987i	0.188848	+	0.188848i
$408$	1.76545			0.0874028
$409$	3.08611	+	3.08611i	0.152599	+	0.152599i	0.779278	−	0.626679i	$-0.215586\pi$
$409$	3.08611	+	3.08611i	0.152599	+	0.152599i	−0.626679	+	0.779278i	$0.715586\pi$
$410$	−55.1262	+	0.851156i	−2.72249	+	0.0420356i
$411$	0.138925	+	0.138925i	0.00685264	+	0.00685264i
$412$	−12.2633	+	12.2633i	−0.604167	+	0.604167i
$413$	−29.5575	+	29.5575i	−1.45443	+	1.45443i
$414$	−18.7649	+	18.7649i	−0.922243	+	0.922243i
$415$	−9.60355	+	9.90476i	−0.471420	+	0.486206i
$416$	0.183551	−	17.8422i	0.00899931	−	0.874786i
$417$	3.99436	−	3.99436i	0.195605	−	0.195605i
$418$	−3.19766			−0.156403
$419$			9.51871i			0.465020i	0.972594	+	0.232510i	$0.0746938\pi$
$419$			9.51871i			0.465020i	−0.972594	+	0.232510i	$0.925306\pi$
$420$	−10.1206	+	0.156264i	−0.493836	+	0.00762489i
$421$	20.6718	−	20.6718i	1.00748	−	1.00748i	0.00751095	−	0.999972i	$-0.497609\pi$
$421$	20.6718	−	20.6718i	1.00748	−	1.00748i	0.999972	−	0.00751095i	$-0.00239083\pi$
$422$			21.0889i			1.02659i
$423$		−	26.2356i		−	1.27562i
$424$	3.03136	−	3.03136i	0.147216	−	0.147216i
$425$	−5.62738	+	5.98609i	−0.272968	+	0.290368i
$426$			4.09562i			0.198434i
$427$	14.6047			0.706772
$428$	15.7926	−	15.7926i	0.763365	−	0.763365i
$429$	−0.00991953	+	0.964237i	−0.000478919	+	0.0465538i
$430$	51.5208	−	0.795489i	2.48455	−	0.0383619i
$431$	−16.8370	+	16.8370i	−0.811012	+	0.811012i	−0.984786	−	0.173774i	$-0.944404\pi$
$431$	−16.8370	+	16.8370i	−0.811012	+	0.811012i	0.173774	+	0.984786i	$0.444404\pi$
$432$	−0.839337	+	0.839337i	−0.0403826	+	0.0403826i
$433$	18.0614	−	18.0614i	0.867975	−	0.867975i	−0.124273	−	0.992248i	$-0.539660\pi$
$433$	18.0614	−	18.0614i	0.867975	−	0.867975i	0.992248	+	0.124273i	$0.0396598\pi$
$434$	−19.0357	−	19.0357i	−0.913741	−	0.913741i
$435$	−0.0407998	−	2.64245i	−0.00195620	−	0.126696i
$436$	13.8742	+	13.8742i	0.664456	+	0.664456i
$437$	6.96674			0.333264
$438$	3.10316	+	3.10316i	0.148275	+	0.148275i
$439$	32.7984			1.56538			0.782692	−	0.622409i	$-0.213846\pi$
$439$	32.7984			1.56538			0.782692	+	0.622409i	$0.213846\pi$
$440$	−0.0859102	−	5.56408i	−0.00409561	−	0.265257i
$441$		−	25.0131i		−	1.19110i
$442$	9.80282	−	9.60318i	0.466273	−	0.456777i
$443$	−11.4661	−	11.4661i	−0.544769	−	0.544769i	0.380154	−	0.924923i	$-0.375871\pi$
$443$	−11.4661	−	11.4661i	−0.544769	−	0.544769i	−0.924923	+	0.380154i	$0.875871\pi$
$444$	−5.53501	−	5.53501i	−0.262680	−	0.262680i
$445$	−0.171704	−	11.1206i	−0.00813955	−	0.527168i
$446$			33.0472i			1.56483i
$447$		−	0.458234i		−	0.0216737i
$448$	50.0777			2.36595
$449$	−20.0441	+	20.0441i	−0.945937	+	0.945937i	−0.998612	−	0.0526744i	$-0.983225\pi$
$449$	−20.0441	+	20.0441i	−0.945937	+	0.945937i	0.0526744	+	0.998612i	$0.483225\pi$
$450$	−1.03136	−	33.3908i	−0.0486190	−	1.57406i
$451$	−8.37814			−0.394511
$452$	43.0463	+	43.0463i	2.02473	+	2.02473i
$453$		−	4.39217i		−	0.206362i
$454$	−28.6492			−1.34457
$455$	−22.4516	+	22.6841i	−1.05255	+	1.06345i
$456$	1.88454			0.0882515
$457$			3.16380i			0.147996i	0.997258	+	0.0739982i	$0.0235759\pi$
$457$			3.16380i			0.147996i	−0.997258	+	0.0739982i	$0.976424\pi$
$458$	16.0723	+	16.0723i	0.751008	+	0.751008i
$459$	3.28564			0.153360
$460$	0.461400	+	29.8831i	0.0215129	+	1.39331i
$461$	20.0071	−	20.0071i	0.931821	−	0.931821i	−0.0659984	−	0.997820i	$-0.521023\pi$
$461$	20.0071	−	20.0071i	0.931821	−	0.931821i	0.997820	+	0.0659984i	$0.0210232\pi$
$462$	−2.45232			−0.114092
$463$		−	4.68050i		−	0.217521i	−0.994068	−	0.108761i	$-0.965312\pi$
$463$		−	4.68050i		−	0.217521i	0.994068	−	0.108761i	$-0.0346882\pi$
$464$		−	2.06474i		−	0.0958534i
$465$	−1.55283	+	1.60153i	−0.0720108	+	0.0742694i
$466$	−7.35517	−	7.35517i	−0.340721	−	0.340721i
$467$	−5.31207	−	5.31207i	−0.245813	−	0.245813i	0.573437	−	0.819250i	$-0.305610\pi$
$467$	−5.31207	−	5.31207i	−0.245813	−	0.245813i	−0.819250	+	0.573437i	$0.805610\pi$
$468$	−0.360021	+	34.9962i	−0.0166420	+	1.61770i
$469$			14.9912i			0.692231i
$470$	−33.8202	−	32.7917i	−1.56001	−	1.51257i
$471$	−1.17984			−0.0543642
$472$	23.6081	+	23.6081i	1.08665	+	1.08665i
$473$	7.83020			0.360033
$474$	−5.02584	−	5.02584i	−0.230845	−	0.230845i
$475$	−6.00696	+	6.38987i	−0.275618	+	0.293187i
$476$	15.4782	+	15.4782i	0.709441	+	0.709441i
$477$	2.76545	−	2.76545i	0.126621	−	0.126621i
$478$	−28.6715	+	28.6715i	−1.31141	+	1.31141i
$479$	−18.0482	+	18.0482i	−0.824645	+	0.824645i	−0.986770	−	0.162125i	$-0.948165\pi$
$479$	−18.0482	+	18.0482i	−0.824645	+	0.824645i	0.162125	+	0.986770i	$0.448165\pi$
$480$	−0.0580507	−	3.75973i	−0.00264964	−	0.171607i
$481$	−24.6810	−	0.253904i	−1.12536	−	0.0115770i
$482$	−28.5167	+	28.5167i	−1.29890	+	1.29890i
$483$	5.34286			0.243109
$484$			34.9314i			1.58779i
$485$	−14.4972	−	14.0564i	−0.658285	−	0.638266i
$486$	−14.2629	+	14.2629i	−0.646978	+	0.646978i
$487$		−	0.978187i		−	0.0443259i	−0.999754	−	0.0221629i	$-0.992945\pi$
$487$		−	0.978187i		−	0.0443259i	0.999754	−	0.0221629i	$-0.00705526\pi$
$488$		−	11.6651i		−	0.528052i
$489$	−0.988842	+	0.988842i	−0.0447170	+	0.0447170i
$490$	−32.2442	−	31.2636i	−1.45664	−	1.41235i
$491$		−	19.2368i		−	0.868146i	−0.900878	−	0.434073i	$-0.857076\pi$
$491$		−	19.2368i		−	0.868146i	0.900878	−	0.434073i	$-0.142924\pi$
$492$	12.1718			0.548748
$493$	−4.04128	+	4.04128i	−0.182010	+	0.182010i
$494$	10.4641	−	10.2509i	0.470800	−	0.461212i
$495$	−0.0783740	−	5.07599i	−0.00352265	−	0.228149i
$496$	−1.23237	+	1.23237i	−0.0553351	+	0.0553351i
$497$	−14.5663	+	14.5663i	−0.653386	+	0.653386i
$498$	3.43374	−	3.43374i	0.153870	−	0.153870i
$499$	−16.4546	−	16.4546i	−0.736610	−	0.736610i	0.235310	−	0.971920i	$-0.424389\pi$
$499$	−16.4546	−	16.4546i	−0.736610	−	0.736610i	−0.971920	+	0.235310i	$0.924389\pi$
$500$	−27.8065	−	25.3431i	−1.24355	−	1.13338i
$501$	−1.26756	−	1.26756i	−0.0566305	−	0.0566305i
$502$	45.8169			2.04491
$503$	12.8451	+	12.8451i	0.572733	+	0.572733i	0.932891	−	0.360158i	$-0.117277\pi$
$503$	12.8451	+	12.8451i	0.572733	+	0.572733i	−0.360158	+	0.932891i	$0.617277\pi$
$504$	−36.1059			−1.60829
$505$	5.27345	+	5.11308i	0.234665	+	0.227529i
$506$			7.24096i			0.321900i
$507$	−3.05865	−	3.18717i	−0.135839	−	0.141547i
$508$	18.3363	+	18.3363i	0.813541	+	0.813541i
$509$	−6.97177	−	6.97177i	−0.309018	−	0.309018i	0.535510	−	0.844529i	$-0.320119\pi$
$509$	−6.97177	−	6.97177i	−0.309018	−	0.309018i	−0.844529	+	0.535510i	$0.820119\pi$
$510$	2.01306	−	2.07620i	0.0891397	−	0.0919355i
$511$			22.0730i			0.976454i
$512$		−	6.69175i		−	0.295737i
$513$	3.50726			0.154849
$514$	33.7614	−	33.7614i	1.48915	−	1.48915i
$515$	0.177914	+	11.5228i	0.00783981	+	0.507755i
$516$	−11.3758			−0.500790
$517$	−5.06188	−	5.06188i	−0.222621	−	0.222621i
$518$		−	62.7706i		−	2.75798i
$519$	−1.64417			−0.0721712
$520$	18.1182	+	17.9325i	0.794537	+	0.786392i
$521$	9.45108			0.414060			0.207030	−	0.978335i	$-0.433620\pi$
$521$	9.45108			0.414060			0.207030	+	0.978335i	$0.433620\pi$
$522$		−	23.2388i		−	1.01714i
$523$	−15.1815	−	15.1815i	−0.663842	−	0.663842i	0.292441	−	0.956283i	$-0.405532\pi$
$523$	−15.1815	−	15.1815i	−0.663842	−	0.663842i	−0.956283	+	0.292441i	$0.905532\pi$
$524$	−8.14836			−0.355963
$525$	−4.60680	+	4.90046i	−0.201057	+	0.213874i
$526$	−33.7232	+	33.7232i	−1.47040	+	1.47040i
$527$	4.82419			0.210145
$528$			0.158764i			0.00690930i
$529$			7.22415i			0.314093i
$530$	−0.108412	−	7.02145i	−0.00470912	−	0.304992i
$531$	21.5372	+	21.5372i	0.934635	+	0.934635i
$532$	16.5222	+	16.5222i	0.716329	+	0.716329i
$533$	27.4167	−	26.8583i	1.18755	−	1.16336i
$534$			3.91478i			0.169409i
$535$	−0.229117	−	14.8391i	−0.00990560	−	0.641548i
$536$	11.9738			0.517189
$537$	−3.14396	−	3.14396i	−0.135672	−	0.135672i
$538$	−20.0580			−0.864760
$539$	−4.82600	−	4.82600i	−0.207871	−	0.207871i
$540$	0.232282	+	15.0441i	0.00999584	+	0.647393i
$541$	−15.2507	−	15.2507i	−0.655677	−	0.655677i	0.298677	−	0.954354i	$-0.403455\pi$
$541$	−15.2507	−	15.2507i	−0.655677	−	0.655677i	−0.954354	+	0.298677i	$0.903455\pi$
$542$	32.7959	−	32.7959i	1.40870	−	1.40870i
$543$	1.11736	−	1.11736i	0.0479506	−	0.0479506i
$544$	−5.75001	+	5.75001i	−0.246530	+	0.246530i
$545$	13.0365	−	0.201286i	0.558423	−	0.00862213i
$546$	8.02499	−	7.86156i	0.343438	−	0.336444i
$547$	−27.7930	+	27.7930i	−1.18834	+	1.18834i	−0.210818	+	0.977525i	$0.567613\pi$
$547$	−27.7930	+	27.7930i	−1.18834	+	1.18834i	−0.977525	+	0.210818i	$0.932387\pi$
$548$	1.94566			0.0831144
$549$		−	10.6418i		−	0.454181i
$550$	−6.64139	−	6.24341i	−0.283190	−	0.266220i
$551$	−4.31388	+	4.31388i	−0.183778	+	0.183778i
$552$		−	4.26745i		−	0.181635i
$553$		−	35.7492i		−	1.52021i
$554$	−1.96424	+	1.96424i	−0.0834524	+	0.0834524i
$555$	−5.20080	+	0.0803011i	−0.220762	+	0.00340859i
$556$		−	55.9417i		−	2.37246i
$557$	−24.9933			−1.05900			−0.529499	−	0.848310i	$-0.677620\pi$
$557$	−24.9933			−1.05900			−0.529499	+	0.848310i	$0.677620\pi$
$558$	−13.8704	+	13.8704i	−0.587182	+	0.587182i
$559$	−25.6236	+	25.1017i	−1.08376	+	1.06169i
$560$	−3.65789	+	3.77262i	−0.154574	+	0.159422i
$561$	0.310745	−	0.310745i	0.0131197	−	0.0131197i
$562$	30.4452	−	30.4452i	1.28425	−	1.28425i
$563$	−29.3156	+	29.3156i	−1.23551	+	1.23551i	−0.273687	+	0.961819i	$0.588243\pi$
$563$	−29.3156	+	29.3156i	−1.23551	+	1.23551i	−0.961819	+	0.273687i	$0.911757\pi$
$564$	7.35393	+	7.35393i	0.309656	+	0.309656i
$565$	40.4472	−	0.624511i	1.70163	−	0.0262734i
$566$	17.1446	+	17.1446i	0.720639	+	0.720639i
$567$	−31.5674			−1.32571
$568$	11.6343	+	11.6343i	0.488166	+	0.488166i
$569$	−25.9559			−1.08813			−0.544063	−	0.839044i	$-0.683115\pi$
$569$	−25.9559			−1.08813			−0.544063	+	0.839044i	$0.683115\pi$
$570$	2.14884	−	2.21624i	0.0900052	−	0.0928281i
$571$		−	10.3822i		−	0.434480i	−0.976118	−	0.217240i	$-0.930295\pi$
$571$		−	10.3822i		−	0.434480i	0.976118	−	0.217240i	$-0.0697055\pi$
$572$	6.68268	+	6.82160i	0.279417	+	0.285226i
$573$	0.965866	+	0.965866i	0.0403496	+	0.0403496i
$574$	69.0182	+	69.0182i	2.88077	+	2.88077i
$575$	14.4696	+	13.6025i	0.603423	+	0.567263i
$576$		−	36.4893i		−	1.52039i
$577$			12.1813i			0.507112i	0.967321	+	0.253556i	$0.0816003\pi$
$577$			12.1813i			0.507112i	−0.967321	+	0.253556i	$0.918400\pi$
$578$	33.1225			1.37772
$579$	5.54016	−	5.54016i	0.230241	−	0.230241i
$580$	−18.7897	−	18.2183i	−0.780198	−	0.756472i
$581$	24.4245			1.01330
$582$	5.02584	+	5.02584i	0.208328	+	0.208328i
$583$		−	1.06713i		−	0.0441959i
$584$	17.6301			0.729541
$585$	16.5289	+	16.3594i	0.683385	+	0.676380i
$586$	26.0056			1.07428
$587$			38.0854i			1.57195i	0.618258	+	0.785975i	$0.287839\pi$
$587$			38.0854i			1.57195i	−0.618258	+	0.785975i	$0.712161\pi$
$588$	7.01125	+	7.01125i	0.289139	+	0.289139i
$589$	5.14960			0.212185
$590$	54.6827	−	0.844309i	2.25125	−	0.0347596i
$591$	0.0599778	−	0.0599778i	0.00246716	−	0.00246716i
$592$	−4.06378			−0.167020
$593$			5.30739i			0.217949i	0.994045	+	0.108974i	$0.0347566\pi$
$593$			5.30739i			0.217949i	−0.994045	+	0.108974i	$0.965243\pi$
$594$			3.64532i			0.149569i
$595$	14.5436	−	0.224555i	0.596229	−	0.00920586i
$596$	−3.20882	−	3.20882i	−0.131438	−	0.131438i
$597$	4.24962	+	4.24962i	0.173925	+	0.173925i
$598$	−23.2128	−	23.6954i	−0.949242	−	0.968976i
$599$			0.0345018i			0.00140970i	1.00000		0.000704852i	$0.000224361\pi$
$599$			0.0345018i			0.00140970i	−1.00000		0.000704852i	$0.999776\pi$
$600$	3.91409	+	3.67954i	0.159792	+	0.150217i
$601$	−16.5133			−0.673593			−0.336797	−	0.941577i	$-0.609344\pi$
$601$	−16.5133			−0.673593			−0.336797	+	0.941577i	$0.609344\pi$
$602$	−64.5043	−	64.5043i	−2.62900	−	2.62900i
$603$	10.9234			0.444837
$604$	−30.7565	−	30.7565i	−1.25146	−	1.25146i
$605$	16.6645	+	16.1577i	0.677508	+	0.656904i
$606$	−1.82818	−	1.82818i	−0.0742647	−	0.0742647i
$607$	0.302520	−	0.302520i	0.0122789	−	0.0122789i	−0.700941	−	0.713220i	$-0.747236\pi$
$607$	0.302520	−	0.302520i	0.0122789	−	0.0122789i	0.713220	+	0.700941i	$0.247236\pi$
$608$	−6.13787	+	6.13787i	−0.248923	+	0.248923i
$609$	−3.30836	+	3.30836i	−0.134062	+	0.134062i
$610$	−13.7183	−	13.3011i	−0.555437	−	0.538546i
$611$	32.7917	+	0.337343i	1.32661	+	0.0136474i
$612$	11.2782	−	11.2782i	0.455896	−	0.455896i
$613$	−9.77269			−0.394715			−0.197358	−	0.980332i	$-0.563236\pi$
$613$	−9.77269			−0.394715			−0.197358	+	0.980332i	$0.563236\pi$
$614$		−	65.4528i		−	2.64146i
$615$	5.63015	−	5.80673i	0.227029	−	0.234150i
$616$	−6.96625	+	6.96625i	−0.280678	+	0.280678i
$617$		−	28.8877i		−	1.16297i	−0.813555	−	0.581487i	$-0.802471\pi$
$617$		−	28.8877i		−	1.16297i	0.813555	−	0.581487i	$-0.197529\pi$
$618$		−	4.05636i		−	0.163171i
$619$	21.1034	−	21.1034i	0.848216	−	0.848216i	−0.141695	−	0.989910i	$-0.545255\pi$
$619$	21.1034	−	21.1034i	0.848216	−	0.848216i	0.989910	+	0.141695i	$0.0452551\pi$
$620$	0.341052	+	22.0887i	0.0136970	+	0.887103i
$621$		−	7.94204i		−	0.318703i
$622$	−22.1304			−0.887350
$623$	−13.9231	+	13.9231i	−0.557816	+	0.557816i
$624$	−0.508958	−	0.519539i	−0.0203746	−	0.0207982i
$625$	−24.9523	+	1.54291i	−0.998094	+	0.0617164i
$626$	−41.0254	+	41.0254i	−1.63970	+	1.63970i
$627$	0.331706	−	0.331706i	0.0132470	−	0.0132470i
$628$	−8.26192	+	8.26192i	−0.329687	+	0.329687i
$629$	7.95395	+	7.95395i	0.317145	+	0.317145i
$630$	−41.1698	+	42.4611i	−1.64025	+	1.69169i
$631$	22.6176	+	22.6176i	0.900391	+	0.900391i	0.995470	−	0.0950787i	$-0.0303103\pi$
$631$	22.6176	+	22.6176i	0.900391	+	0.900391i	−0.0950787	+	0.995470i	$0.530310\pi$
$632$	−28.5536			−1.13580
$633$	−2.18763	−	2.18763i	−0.0869504	−	0.0869504i
$634$	2.11335			0.0839319
$635$	17.2291	−	0.266020i	0.683717	−	0.0105567i
$636$			1.55033i			0.0614746i
$637$	31.2636	+	0.321623i	1.23871	+	0.0127432i
$638$	−4.48369	−	4.48369i	−0.177511	−	0.177511i
$639$	10.6138	+	10.6138i	0.419874	+	0.419874i
$640$	−31.1490	−	30.2018i	−1.23127	−	1.19383i
$641$			18.9874i			0.749959i	0.927033	+	0.374980i	$0.122350\pi$
$641$			18.9874i			0.749959i	−0.927033	+	0.374980i	$0.877650\pi$
$642$			5.22378i			0.206166i
$643$	−39.2961			−1.54969			−0.774843	−	0.632154i	$-0.782171\pi$
$643$	−39.2961			−1.54969			−0.774843	+	0.632154i	$0.782171\pi$
$644$	37.4138	−	37.4138i	1.47431	−	1.47431i
$645$	−5.26192	+	5.42696i	−0.207188	+	0.213686i
$646$	−6.67583			−0.262657
$647$	−13.7831	−	13.7831i	−0.541869	−	0.541869i	0.382207	−	0.924077i	$-0.375164\pi$
$647$	−13.7831	−	13.7831i	−0.541869	−	0.541869i	−0.924077	+	0.382207i	$0.875164\pi$
$648$			25.2135i			0.990479i
$649$	8.31074			0.326225
$650$	41.7482	−	0.859749i	1.63750	−	0.0337221i
$651$	3.94928			0.154785
$652$			13.8489i			0.542364i
$653$	−18.6515	−	18.6515i	−0.729890	−	0.729890i	0.240707	−	0.970598i	$-0.422621\pi$
$653$	−18.6515	−	18.6515i	−0.729890	−	0.729890i	−0.970598	+	0.240707i	$0.922621\pi$
$654$	−4.58923			−0.179453
$655$	−3.76907	+	3.88729i	−0.147270	+	0.151889i
$656$	4.46825	−	4.46825i	0.174456	−	0.174456i
$657$	16.0836			0.627482
$658$			83.3984i			3.25121i
$659$		−	24.9329i		−	0.971247i	−0.874168	−	0.485623i	$-0.838593\pi$
$659$		−	24.9329i		−	0.971247i	0.874168	−	0.485623i	$-0.161407\pi$
$660$	1.44479	+	1.40085i	0.0562382	+	0.0545280i
$661$	−2.83810	−	2.83810i	−0.110389	−	0.110389i	0.649755	−	0.760144i	$-0.274872\pi$
$661$	−2.83810	−	2.83810i	−0.110389	−	0.110389i	−0.760144	+	0.649755i	$0.774872\pi$
$662$	−35.3427	−	35.3427i	−1.37363	−	1.37363i
$663$	−0.0207092	+	2.01306i	−0.000804279	+	0.0781806i
$664$		−	19.5083i		−	0.757069i
$665$	15.5246	−	0.239702i	0.602018	−	0.00929525i
$666$	−45.7381			−1.77232
$667$	9.76859	+	9.76859i	0.378241	+	0.378241i
$668$	−17.7524			−0.686861
$669$	−3.42811	−	3.42811i	−0.132538	−	0.132538i
$670$	13.6531	−	14.0813i	0.527466	−	0.544010i
$671$	−2.05322	−	2.05322i	−0.0792636	−	0.0792636i
$672$	−4.70720	+	4.70720i	−0.181584	+	0.181584i
$673$	1.00992	−	1.00992i	0.0389295	−	0.0389295i	−0.687374	−	0.726304i	$-0.741237\pi$
$673$	1.00992	−	1.00992i	0.0389295	−	0.0389295i	0.726304	+	0.687374i	$0.241237\pi$
$674$	−19.3170	+	19.3170i	−0.744064	+	0.744064i
$675$	7.28442	+	6.84790i	0.280377	+	0.263576i
$676$	−43.7369	−	0.899976i	−1.68219	−	0.0346145i
$677$	0.154365	−	0.154365i	0.00593272	−	0.00593272i	−0.704134	−	0.710067i	$-0.748665\pi$
$677$	0.154365	−	0.154365i	0.00593272	−	0.00593272i	0.710067	+	0.704134i	$0.248665\pi$
$678$	−14.2386			−0.546829
$679$			35.7492i			1.37193i
$680$	−0.179356	−	11.6162i	−0.00687801	−	0.445462i
$681$	2.97189	−	2.97189i	0.113883	−	0.113883i
$682$			5.35230i			0.204950i
$683$		−	19.3092i		−	0.738847i	−0.929261	−	0.369424i	$-0.879555\pi$
$683$		−	19.3092i		−	0.738847i	0.929261	−	0.369424i	$-0.120445\pi$
$684$	12.0390	−	12.0390i	0.460322	−	0.460322i
$685$	0.899976	−	0.928204i	0.0343863	−	0.0354648i
$686$			15.3261i			0.585153i
$687$	−3.33447			−0.127218
$688$	−4.17601	+	4.17601i	−0.159209	+	0.159209i
$689$	3.42096	+	3.49208i	0.130328	+	0.133037i
$690$	−5.01858	−	4.86596i	−0.191054	−	0.185244i
$691$	29.1769	−	29.1769i	1.10994	−	1.10994i	0.116784	−	0.993157i	$-0.462742\pi$
$691$	29.1769	−	29.1769i	1.10994	−	1.10994i	0.993157	−	0.116784i	$-0.0372584\pi$
$692$	−11.5134	+	11.5134i	−0.437676	+	0.437676i
$693$	−6.35517	+	6.35517i	−0.241413	+	0.241413i
$694$	52.0815	+	52.0815i	1.97699	+	1.97699i
$695$	−26.6877	−	25.8761i	−1.01232	−	0.981538i
$696$	2.64245	+	2.64245i	0.100162	+	0.100162i
$697$	−17.4912			−0.662527
$698$	44.5329	+	44.5329i	1.68559	+	1.68559i
$699$	1.52596			0.0577170
$700$	2.05636	+	66.5753i	0.0777230	+	2.51631i
$701$			21.8818i			0.826464i	0.910626	+	0.413232i	$0.135600\pi$
$701$			21.8818i			0.826464i	−0.910626	+	0.413232i	$0.864400\pi$
$702$	−11.6860	−	11.9290i	−0.441060	−	0.450229i
$703$	8.49047	+	8.49047i	0.320224	+	0.320224i
$704$	−7.04023	−	7.04023i	−0.265339	−	0.265339i
$705$	6.90990	−	0.106690i	0.260242	−	0.00401817i
$706$		−	10.3174i		−	0.388302i
$707$		−	13.0040i		−	0.489065i
$708$	−12.0739			−0.453765
$709$	−18.0869	+	18.0869i	−0.679267	+	0.679267i	−0.959834	−	0.280568i	$-0.909477\pi$
$709$	−18.0869	+	18.0869i	−0.679267	+	0.679267i	0.280568	+	0.959834i	$0.409477\pi$
$710$	26.9482	−	0.416085i	1.01135	−	0.0156154i
$711$	−26.0488			−0.976908
$712$	11.1206	+	11.1206i	0.416763	+	0.416763i
$713$		−	11.6610i		−	0.436709i
$714$	−5.11976			−0.191602
$715$	6.34545	−	0.0326910i	0.237306	−	0.00122258i
$716$	−44.0317			−1.64554
$717$		−	5.94841i		−	0.222147i
$718$	26.9462	+	26.9462i	1.00563	+	1.00563i
$719$	26.5866			0.991512			0.495756	−	0.868462i	$-0.334891\pi$
$719$	26.5866			0.991512			0.495756	+	0.868462i	$0.334891\pi$
$720$	2.74894	+	2.66534i	0.102447	+	0.0993313i
$721$	14.4266	−	14.4266i	0.537274	−	0.537274i
$722$	36.8829			1.37264
$723$		−	5.91629i		−	0.220029i
$724$		−	15.6488i		−	0.581585i
$725$	−17.3825	+	0.536906i	−0.645571	+	0.0199402i
$726$	−5.77718	−	5.77718i	−0.214411	−	0.214411i
$727$	13.8783	+	13.8783i	0.514719	+	0.514719i	0.915969	−	0.401250i	$-0.131424\pi$
$727$	13.8783	+	13.8783i	0.514719	+	0.514719i	−0.401250	+	0.915969i	$0.631424\pi$
$728$	0.464257	−	45.1285i	0.0172065	−	1.67257i
$729$			20.9634i			0.776422i
$730$	20.1028	−	20.7333i	0.744038	−	0.767374i
$731$	16.3473			0.604625
$732$	2.98293	+	2.98293i	0.110252	+	0.110252i
$733$	−38.2590			−1.41313			−0.706563	−	0.707650i	$-0.749756\pi$
$733$	−38.2590			−1.41313			−0.706563	+	0.707650i	$0.749756\pi$
$734$	2.04108	+	2.04108i	0.0753376	+	0.0753376i
$735$	6.58790	−	0.101718i	0.242999	−	0.00375193i
$736$	13.8989	+	13.8989i	0.512321	+	0.512321i
$737$	2.10756	−	2.10756i	0.0776330	−	0.0776330i
$738$	50.2904	−	50.2904i	1.85122	−	1.85122i
$739$	36.5799	−	36.5799i	1.34561	−	1.34561i	0.455250	−	0.890364i	$-0.349550\pi$
$739$	36.5799	−	36.5799i	1.34561	−	1.34561i	0.890364	−	0.455250i	$-0.150450\pi$
$740$	−35.8567	+	36.9813i	−1.31812	+	1.35946i
$741$	−0.0221061	+	2.14884i	−0.000812088	+	0.0789398i
$742$	−8.79088	+	8.79088i	−0.322724	+	0.322724i
$743$	32.7040			1.19979			0.599896	−	0.800078i	$-0.295209\pi$
$743$	32.7040			1.19979			0.599896	+	0.800078i	$0.295209\pi$
$744$		−	3.15436i		−	0.115645i
$745$	−3.01507	+	0.0465532i	−0.110464	+	0.00170558i
$746$	−19.6560	+	19.6560i	−0.719657	+	0.719657i
$747$		−	17.7970i		−	0.651159i
$748$		−	4.35203i		−	0.159126i
$749$	−18.5786	+	18.5786i	−0.678846	+	0.678846i
$750$	8.79024	−	0.407427i	0.320974	−	0.0148771i
$751$		−	19.6083i		−	0.715517i	−0.933814	−	0.357758i	$-0.883541\pi$
$751$		−	19.6083i		−	0.715517i	0.933814	−	0.357758i	$-0.116459\pi$
$752$	5.39922			0.196889
$753$	−4.75276	+	4.75276i	−0.173200	+	0.173200i
$754$	29.0461	+	0.298810i	1.05780	+	0.0108820i
$755$	−28.8994	+	0.446211i	−1.05176	+	0.0162393i
$756$	18.8352	−	18.8352i	0.685031	−	0.685031i
$757$	1.81942	−	1.81942i	0.0661281	−	0.0661281i	−0.673269	−	0.739397i	$-0.735111\pi$
$757$	1.81942	−	1.81942i	0.0661281	−	0.0661281i	0.739397	+	0.673269i	$0.235111\pi$
$758$	50.7644	−	50.7644i	1.84385	−	1.84385i
$759$	−0.751132	−	0.751132i	−0.0272644	−	0.0272644i
$760$	−0.191455	−	12.3998i	−0.00694479	−	0.449788i
$761$	−5.35106	−	5.35106i	−0.193976	−	0.193976i	0.603436	−	0.797412i	$-0.293798\pi$
$761$	−5.35106	−	5.35106i	−0.193976	−	0.193976i	−0.797412	+	0.603436i	$0.793798\pi$
$762$	−6.06515			−0.219717
$763$	−16.3218	−	16.3218i	−0.590888	−	0.590888i
$764$	13.5271			0.489393
$765$	−0.163623	−	10.5973i	−0.00591581	−	0.383144i
$766$		−	27.4274i		−	0.990994i
$767$	−27.1961	+	26.6423i	−0.981995	+	0.961996i
$768$	4.71968	+	4.71968i	0.170307	+	0.170307i
$769$	−23.5462	−	23.5462i	−0.849096	−	0.849096i	0.140924	−	0.990020i	$-0.454993\pi$
$769$	−23.5462	−	23.5462i	−0.849096	−	0.849096i	−0.990020	+	0.140924i	$0.954993\pi$
$770$	0.249137	+	16.1357i	0.00897829	+	0.581490i
$771$			7.00440i			0.252257i
$772$		−	77.5908i		−	2.79255i
$773$	14.1988			0.510695			0.255348	−	0.966849i	$-0.417810\pi$
$773$	14.1988			0.510695			0.255348	+	0.966849i	$0.417810\pi$
$774$	−47.0013	+	47.0013i	−1.68943	+	1.68943i
$775$	10.6955	+	10.0545i	0.384192	+	0.361170i
$776$	28.5536			1.02501
$777$	6.51143	+	6.51143i	0.233596	+	0.233596i
$778$			51.1363i			1.83333i
$779$	−18.6711			−0.668960
$780$	−9.21871	+	0.0474937i	−0.330083	+	0.00170055i
$781$	4.09562			0.146553
$782$			15.1171i			0.540587i
$783$	4.91780	+	4.91780i	0.175748	+	0.175748i
$784$	5.14762			0.183844
$785$	0.119863	+	7.76307i	0.00427809	+	0.277076i
$786$	1.34763	−	1.34763i	0.0480684	−	0.0480684i
$787$	−19.0199			−0.677987			−0.338994	−	0.940789i	$-0.610087\pi$
$787$	−19.0199			−0.677987			−0.338994	+	0.940789i	$0.610087\pi$
$788$		−	0.839998i		−	0.0299237i
$789$		−	6.99647i		−	0.249081i
$790$	−32.5583	+	33.5794i	−1.15837	+	1.19470i
$791$	−50.6401	−	50.6401i	−1.80055	−	1.80055i
$792$	5.07599	+	5.07599i	0.180367	+	0.180367i
$793$	13.3011	+	0.136834i	0.472336	+	0.00485913i
$794$		−	37.3626i		−	1.32595i
$795$	0.739607	+	0.717115i	0.0262311	+	0.0254334i
$796$	59.5166			2.10951
$797$	36.3558	+	36.3558i	1.28779	+	1.28779i	0.936126	+	0.351664i	$0.114384\pi$
$797$	36.3558	+	36.3558i	1.28779	+	1.28779i	0.351664	+	0.936126i	$0.385616\pi$
$798$	−5.46511			−0.193463
$799$	−10.5678	−	10.5678i	−0.373861	−	0.373861i
$800$	−24.7322	+	0.763919i	−0.874415	+	0.0270086i
$801$	10.1451	+	10.1451i	0.358460	+	0.358460i
$802$	−52.8154	+	52.8154i	−1.86498	+	1.86498i
$803$	3.10316	−	3.10316i	0.109508	−	0.109508i
$804$	−3.06188	+	3.06188i	−0.107984	+	0.107984i
$805$	−0.542795	−	35.1548i	−0.0191310	−	1.23904i
$806$	−17.1582	−	17.5149i	−0.604371	−	0.616936i
$807$	2.08069	−	2.08069i	0.0732437	−	0.0732437i
$808$	−10.3865			−0.365397
$809$		−	40.6511i		−	1.42922i	−0.699524	−	0.714609i	$-0.746605\pi$
$809$		−	40.6511i		−	1.42922i	0.699524	−	0.714609i	$-0.253395\pi$
$810$	29.6514	+	28.7497i	1.04185	+	1.01016i
$811$	−0.182019	+	0.182019i	−0.00639156	+	0.00639156i	−0.710295	−	0.703904i	$-0.751439\pi$
$811$	−0.182019	+	0.182019i	−0.00639156	+	0.00639156i	0.703904	+	0.710295i	$0.251439\pi$
$812$			46.3341i			1.62601i
$813$			6.80408i			0.238629i
$814$	−8.82467	+	8.82467i	−0.309305	+	0.309305i
$815$	6.60680	+	6.40589i	0.231426	+	0.224388i
$816$			0.331454i			0.0116032i
$817$	17.4499			0.610496
$818$	−7.14826	+	7.14826i	−0.249933	+	0.249933i
$819$	0.423532	−	41.1698i	0.0147994	−	1.43859i
$820$	−1.23656	−	80.0876i	−0.0431827	−	2.79678i
$821$	20.1229	−	20.1229i	0.702294	−	0.702294i	−0.262608	−	0.964902i	$-0.584583\pi$
$821$	20.1229	−	20.1229i	0.702294	−	0.702294i	0.964902	+	0.262608i	$0.0845827\pi$
$822$	−0.321786	+	0.321786i	−0.0112236	+	0.0112236i
$823$	−34.7291	+	34.7291i	−1.21058	+	1.21058i	−0.239745	+	0.970836i	$0.577064\pi$
$823$	−34.7291	+	34.7291i	−1.21058	+	1.21058i	−0.970836	+	0.239745i	$0.922936\pi$
$824$	−11.5228	−	11.5228i	−0.401415	−	0.401415i
$825$	1.33659	−	0.0412841i	0.0465340	−	0.00143733i
$826$	−68.4630	−	68.4630i	−2.38213	−	2.38213i
$827$	13.4572			0.467952			0.233976	−	0.972242i	$-0.424826\pi$
$827$	13.4572			0.467952			0.233976	+	0.972242i	$0.424826\pi$
$828$	−27.2617	−	27.2617i	−0.947411	−	0.947411i
$829$	26.7217			0.928082			0.464041	−	0.885814i	$-0.346399\pi$
$829$	26.7217			0.928082			0.464041	+	0.885814i	$0.346399\pi$
$830$	−22.9421	−	22.2444i	−0.796330	−	0.772113i
$831$		−	0.407515i		−	0.0141365i
$832$	45.6078	+	0.469187i	1.58116	+	0.0162661i
$833$	−10.0753	−	10.0753i	−0.349090	−	0.349090i
$834$	9.25201	+	9.25201i	0.320371	+	0.320371i
$835$	−8.21147	+	8.46902i	−0.284170	+	0.293083i
$836$		−	4.64559i		−	0.160671i
$837$		−	5.87051i		−	0.202915i
$838$	−22.0479			−0.761631
$839$	−19.5692	+	19.5692i	−0.675605	+	0.675605i	−0.959002	−	0.283398i	$-0.908538\pi$
$839$	−19.5692	+	19.5692i	−0.675605	+	0.675605i	0.283398	+	0.959002i	$0.408538\pi$
$840$	−0.146829	−	9.50953i	−0.00506607	−	0.328110i
$841$	16.9024			0.582840
$842$	47.8814	+	47.8814i	1.65010	+	1.65010i
$843$			6.31638i			0.217548i
$844$	−30.6381			−1.05461
$845$	−20.6601	+	20.4490i	−0.710729	+	0.703466i
$846$	60.7686			2.08927
$847$		−	41.0936i		−	1.41199i
$848$	0.569123	+	0.569123i	0.0195438	+	0.0195438i
$849$	−3.55694			−0.122074
$850$	−13.8654	−	13.0345i	−0.475578	−	0.447080i
$851$	19.2263	−	19.2263i	0.659068	−	0.659068i
$852$	−5.95015			−0.203849
$853$		−	19.6378i		−	0.672385i	−0.941793	−	0.336193i	$-0.890861\pi$
$853$		−	19.6378i		−	0.672385i	0.941793	−	0.336193i	$-0.109139\pi$
$854$			33.8284i			1.15758i
$855$	−0.174660	−	11.3121i	−0.00597325	−	0.386865i
$856$	14.8391	+	14.8391i	0.507189	+	0.507189i
$857$	−20.8611	−	20.8611i	−0.712601	−	0.712601i	0.254478	−	0.967079i	$-0.418096\pi$
$857$	−20.8611	−	20.8611i	−0.712601	−	0.712601i	−0.967079	+	0.254478i	$0.918096\pi$
$858$	−2.23343	−	0.0229763i	−0.0762480	−	0.000784397i
$859$		−	41.8545i		−	1.42806i	−0.700116	−	0.714029i	$-0.746868\pi$
$859$		−	41.8545i		−	1.42806i	0.700116	−	0.714029i	$-0.253132\pi$
$860$	1.15569	+	74.8497i	0.0394087	+	2.55236i
$861$	−14.3190			−0.487991
$862$	−38.9991	−	38.9991i	−1.32831	−	1.32831i
$863$	41.0888			1.39868			0.699339	−	0.714790i	$-0.253478\pi$
$863$	41.0888			1.39868			0.699339	+	0.714790i	$0.253478\pi$
$864$	6.99713	+	6.99713i	0.238047	+	0.238047i
$865$	0.167036	+	10.8183i	0.00567938	+	0.367832i
$866$	41.8350	+	41.8350i	1.42161	+	1.42161i
$867$	−3.43592	+	3.43592i	−0.116690	+	0.116690i
$868$	27.6551	−	27.6551i	0.938677	−	0.938677i
$869$	−5.02584	+	5.02584i	−0.170490	+	0.170490i
$870$	6.12062	−	0.0945032i	0.207508	−	0.00320396i
$871$	−0.140456	+	13.6531i	−0.00475916	+	0.462618i
$872$	−13.0365	+	13.0365i	−0.441472	+	0.441472i
$873$	26.0488			0.881620
$874$			16.1368i			0.545836i
$875$	32.7119	+	29.8138i	1.10586	+	1.00789i
$876$	−4.50829	+	4.50829i	−0.152321	+	0.152321i
$877$			56.0870i			1.89392i	0.321348	+	0.946961i	$0.395864\pi$
$877$			56.0870i			1.89392i	−0.321348	+	0.946961i	$0.604136\pi$
$878$			75.9699i			2.56386i
$879$	−2.69766	+	2.69766i	−0.0909899	+	0.0909899i
$880$	1.04463	−	0.0161292i	0.0352143	−	0.000543715i
$881$			51.8432i			1.74664i	0.487147	+	0.873320i	$0.338038\pi$
$881$			51.8432i			1.74664i	−0.487147	+	0.873320i	$0.661962\pi$
$882$	57.9369			1.95084
$883$	24.3974	−	24.3974i	0.821038	−	0.821038i	−0.165219	−	0.986257i	$-0.552833\pi$
$883$	24.3974	−	24.3974i	0.821038	−	0.821038i	0.986257	+	0.165219i	$0.0528330\pi$
$884$	13.9516	+	14.2416i	0.469242	+	0.478997i
$885$	−5.58486	+	5.76002i	−0.187733	+	0.193621i
$886$	26.5585	−	26.5585i	0.892249	−	0.892249i
$887$	−18.6955	+	18.6955i	−0.627733	+	0.627733i	−0.947497	−	0.319764i	$-0.896396\pi$
$887$	−18.6955	+	18.6955i	−0.627733	+	0.627733i	0.319764	+	0.947497i	$0.396396\pi$
$888$	5.20080	−	5.20080i	0.174527	−	0.174527i
$889$	−21.5710	−	21.5710i	−0.723467	−	0.723467i
$890$	25.7583	−	0.397712i	0.863420	−	0.0133313i
$891$	4.43794	+	4.43794i	0.148677	+	0.148677i
$892$	−48.0112			−1.60753
$893$	−11.2806	−	11.2806i	−0.377491	−	0.377491i
$894$	1.06139			0.0354983
$895$	−20.3671	+	21.0059i	−0.680797	+	0.702150i
$896$			76.8115i			2.56609i
$897$	4.86596	+	0.0500583i	0.162470	+	0.00167140i
$898$	−46.4273	−	46.4273i	−1.54930	−	1.54930i
$899$	7.22064	+	7.22064i	0.240822	+	0.240822i
$900$	48.5104	−	1.49837i	1.61701	−	0.0499458i
$901$		−	2.22787i		−	0.0742210i
$902$		−	19.4060i		−	0.646149i
$903$	13.3825			0.445343
$904$	−40.4472	+	40.4472i	−1.34525	+	1.34525i
$905$	−7.46550	−	7.23846i	−0.248161	−	0.240615i
$906$	10.1734			0.337989
$907$	−9.50332	−	9.50332i	−0.315553	−	0.315553i	0.531503	−	0.847056i	$-0.321627\pi$
$907$	−9.50332	−	9.50332i	−0.315553	−	0.315553i	−0.847056	+	0.531503i	$0.821627\pi$
$908$		−	41.6218i		−	1.38127i
$909$	−9.47541			−0.314280
$910$	−52.5424	−	52.0038i	−1.74177	−	1.72391i
$911$	−29.9373			−0.991866			−0.495933	−	0.868361i	$-0.665174\pi$
$911$	−29.9373			−0.991866			−0.495933	+	0.868361i	$0.665174\pi$
$912$			0.353812i			0.0117159i
$913$	−3.43374	−	3.43374i	−0.113640	−	0.113640i
$914$	−7.32820			−0.242395
$915$	2.80282	−	0.0432760i	0.0926584	−	0.00143066i
$916$	−23.3499	+	23.3499i	−0.771503	+	0.771503i
$917$	9.58580			0.316551
$918$			7.61041i			0.251181i
$919$			37.1394i			1.22512i	0.790425	+	0.612558i	$0.209860\pi$
$919$			37.1394i			1.22512i	−0.790425	+	0.612558i	$0.790140\pi$
$920$	−28.0788	+	0.433540i	−0.925729	+	0.0142934i
$921$	6.78966	+	6.78966i	0.223727	+	0.223727i
$922$	46.3416	+	46.3416i	1.52618	+	1.52618i
$923$	−13.4025	+	13.1296i	−0.441150	+	0.432166i
$924$		−	3.56275i		−	0.117206i
$925$	1.05672	+	34.2119i	0.0347449	+	1.12488i
$926$	10.8413			0.356267
$927$	−10.5120	−	10.5120i	−0.345259	−	0.345259i
$928$	−17.2127			−0.565036
$929$	40.4571	+	40.4571i	1.32735	+	1.32735i	0.907670	+	0.419685i	$0.137859\pi$
$929$	40.4571	+	40.4571i	1.32735	+	1.32735i	0.419685	+	0.907670i	$0.362141\pi$
$930$	−3.70958	−	3.59677i	−0.121642	−	0.117943i
$931$	−10.7550	−	10.7550i	−0.352480	−	0.352480i
$932$	10.6856	−	10.6856i	0.350020	−	0.350020i
$933$	2.29567	−	2.29567i	0.0751569	−	0.0751569i
$934$	12.3042	−	12.3042i	0.402605	−	0.402605i
$935$	−2.07620	−	2.01306i	−0.0678988	−	0.0658340i
$936$	−32.8831	−	0.338283i	−1.07482	−	0.0110571i
$937$	19.6392	−	19.6392i	0.641585	−	0.641585i	−0.309360	−	0.950945i	$-0.600115\pi$
$937$	19.6392	−	19.6392i	0.641585	−	0.641585i	0.950945	+	0.309360i	$0.100115\pi$
$938$	−34.7237			−1.13377
$939$		−	8.51143i		−	0.277760i
$940$	47.6400	−	49.1342i	1.55384	−	1.60258i
$941$	−34.3710	+	34.3710i	−1.12046	+	1.12046i	−0.128790	+	0.991672i	$0.541109\pi$
$941$	−34.3710	+	34.3710i	−1.12046	+	1.12046i	−0.991672	+	0.128790i	$0.958891\pi$
$942$		−	2.73282i		−	0.0890402i
$943$			42.2798i			1.37682i
$944$	−4.43230	+	4.43230i	−0.144259	+	0.144259i
$945$	−0.273259	−	17.6980i	−0.00888912	−	0.575715i
$946$			18.1368i			0.589679i
$947$	52.1483			1.69459			0.847295	−	0.531122i	$-0.178229\pi$
$947$	52.1483			1.69459			0.847295	+	0.531122i	$0.178229\pi$
$948$	7.30158	−	7.30158i	0.237144	−	0.237144i
$949$	−0.206806	+	20.1028i	−0.00671322	+	0.652564i
$950$	−14.8006	−	13.9137i	−0.480196	−	0.451421i
$951$	−0.219226	+	0.219226i	−0.00710888	+	0.00710888i
$952$	−14.5436	+	14.5436i	−0.471360	+	0.471360i
$953$	−10.2817	+	10.2817i	−0.333058	+	0.333058i	−0.853747	−	0.520689i	$-0.825675\pi$
$953$	−10.2817	+	10.2817i	−0.333058	+	0.333058i	0.520689	+	0.853747i	$0.325675\pi$
$954$	6.40552	+	6.40552i	0.207386	+	0.207386i
$955$	6.25704	−	6.45329i	0.202473	−	0.208824i
$956$	−41.6542	−	41.6542i	−1.34719	−	1.34719i
$957$	0.930219			0.0300697
$958$	−41.8045	−	41.8045i	−1.35064	−	1.35064i
$959$	−2.28889			−0.0739121
$960$	9.61051	−	0.148388i	0.310178	−	0.00478919i
$961$			22.3805i			0.721952i
$962$	0.588110	−	57.1677i	0.0189614	−	1.84316i
$963$	13.5374	+	13.5374i	0.436235	+	0.436235i
$964$	−41.4292	−	41.4292i	−1.33435	−	1.33435i
$965$	−37.0158	−	35.8901i	−1.19158	−	1.15534i
$966$			12.3755i			0.398175i
$967$		−	37.4312i		−	1.20371i	−0.798606	−	0.601854i	$-0.794429\pi$
$967$		−	37.4312i		−	1.20371i	0.798606	−	0.601854i	$-0.205571\pi$
$968$	−32.8222			−1.05495
$969$	0.692509	−	0.692509i	0.0222466	−	0.0222466i
$970$	32.5583	−	33.5794i	1.04538	−	1.07817i
$971$	38.5095			1.23583			0.617915	−	0.786245i	$-0.287978\pi$
$971$	38.5095			1.23583			0.617915	+	0.786245i	$0.287978\pi$
$972$	−20.7212	−	20.7212i	−0.664633	−	0.664633i
$973$			65.8103i			2.10978i
$974$	2.26574			0.0725990
$975$	−4.24151	+	4.41988i	−0.135837	+	0.141550i
$976$	2.19005			0.0701019
$977$		−	39.9972i		−	1.27963i	−0.768531	−	0.639813i	$-0.779012\pi$
$977$		−	39.9972i		−	1.27963i	0.768531	−	0.639813i	$-0.220988\pi$
$978$	−2.29042	−	2.29042i	−0.0732396	−	0.0732396i
$979$	3.91478			0.125117
$980$	45.4200	−	46.8446i	1.45089	−	1.49640i
$981$	−11.8929	+	11.8929i	−0.379712	+	0.379712i
$982$	44.5576			1.42189
$983$			16.8519i			0.537492i	0.963211	+	0.268746i	$0.0866093\pi$
$983$			16.8519i			0.537492i	−0.963211	+	0.268746i	$0.913391\pi$
$984$			11.4369i			0.364594i
$985$	−0.400733	−	0.388546i	−0.0127684	−	0.0123801i
$986$	−9.36069	−	9.36069i	−0.298105	−	0.298105i
$987$	−8.65122	−	8.65122i	−0.275372	−	0.275372i
$988$	14.8926	+	15.2022i	0.473798	+	0.483648i
$989$		−	39.5146i		−	1.25649i
$990$	11.7573	−	0.181535i	0.373673	−	0.00576956i
$991$	−42.4834			−1.34953			−0.674765	−	0.738032i	$-0.735755\pi$
$991$	−42.4834			−1.34953			−0.674765	+	0.738032i	$0.735755\pi$
$992$	10.2737	+	10.2737i	0.326189	+	0.326189i
$993$	7.33246			0.232689
$994$	−33.7393	−	33.7393i	−1.07015	−	1.07015i
$995$	27.5298	−	28.3932i	0.872752	−	0.900125i
$996$	4.98857	+	4.98857i	0.158069	+	0.158069i
$997$	14.2932	−	14.2932i	0.452670	−	0.452670i	−0.443570	−	0.896240i	$-0.646288\pi$
$997$	14.2932	−	14.2932i	0.452670	−	0.452670i	0.896240	+	0.443570i	$0.146288\pi$
$998$	38.1133	−	38.1133i	1.20645	−	1.20645i
$999$	9.67908	−	9.67908i	0.306233	−	0.306233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.f.b.18.4	✓	8
3.2	odd	2		585.2.n.e.343.1		8
4.3	odd	2		1040.2.cd.n.993.2		8
5.2	odd	4		65.2.k.b.57.1	yes	8
5.3	odd	4		325.2.k.b.57.4		8
5.4	even	2		325.2.f.b.18.1		8
13.2	odd	12		845.2.o.c.488.1		16
13.3	even	3		845.2.t.c.188.1		16
13.4	even	6		845.2.t.d.418.1		16
13.5	odd	4		845.2.k.b.268.4		8
13.6	odd	12		845.2.o.c.258.1		16
13.7	odd	12		845.2.o.d.258.4		16
13.8	odd	4		65.2.k.b.8.1	yes	8
13.9	even	3		845.2.t.c.418.4		16
13.10	even	6		845.2.t.d.188.4		16
13.11	odd	12		845.2.o.d.488.4		16
13.12	even	2		845.2.f.b.408.1		8
15.2	even	4		585.2.w.e.577.4		8
20.7	even	4		1040.2.bg.n.577.2		8
39.8	even	4		585.2.w.e.73.4		8
52.47	even	4		1040.2.bg.n.593.2		8
65.2	even	12		845.2.t.d.657.1		16
65.7	even	12		845.2.t.c.427.1		16
65.8	even	4		325.2.f.b.307.4		8
65.12	odd	4		845.2.k.b.577.4		8
65.17	odd	12		845.2.o.c.587.1		16
65.22	odd	12		845.2.o.d.587.4		16
65.32	even	12		845.2.t.d.427.4		16
65.34	odd	4		325.2.k.b.268.4		8
65.37	even	12		845.2.t.c.657.4		16
65.42	odd	12		845.2.o.d.357.4		16
65.47	even	4	inner	65.2.f.b.47.1	yes	8
65.57	even	4		845.2.f.b.437.4		8
65.62	odd	12		845.2.o.c.357.1		16
195.47	odd	4		585.2.n.e.307.4		8
260.47	odd	4		1040.2.cd.n.177.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.4	✓	8	1.1	even	1	trivial
65.2.f.b.47.1	yes	8	65.47	even	4	inner
65.2.k.b.8.1	yes	8	13.8	odd	4
65.2.k.b.57.1	yes	8	5.2	odd	4
325.2.f.b.18.1		8	5.4	even	2
325.2.f.b.307.4		8	65.8	even	4
325.2.k.b.57.4		8	5.3	odd	4
325.2.k.b.268.4		8	65.34	odd	4
585.2.n.e.307.4		8	195.47	odd	4
585.2.n.e.343.1		8	3.2	odd	2
585.2.w.e.73.4		8	39.8	even	4
585.2.w.e.577.4		8	15.2	even	4
845.2.f.b.408.1		8	13.12	even	2
845.2.f.b.437.4		8	65.57	even	4
845.2.k.b.268.4		8	13.5	odd	4
845.2.k.b.577.4		8	65.12	odd	4
845.2.o.c.258.1		16	13.6	odd	12
845.2.o.c.357.1		16	65.62	odd	12
845.2.o.c.488.1		16	13.2	odd	12
845.2.o.c.587.1		16	65.17	odd	12
845.2.o.d.258.4		16	13.7	odd	12
845.2.o.d.357.4		16	65.42	odd	12
845.2.o.d.488.4		16	13.11	odd	12
845.2.o.d.587.4		16	65.22	odd	12
845.2.t.c.188.1		16	13.3	even	3
845.2.t.c.418.4		16	13.9	even	3
845.2.t.c.427.1		16	65.7	even	12
845.2.t.c.657.4		16	65.37	even	12
845.2.t.d.188.4		16	13.10	even	6
845.2.t.d.418.1		16	13.4	even	6
845.2.t.d.427.4		16	65.32	even	12
845.2.t.d.657.1		16	65.2	even	12
1040.2.bg.n.577.2		8	20.7	even	4
1040.2.bg.n.593.2		8	52.47	even	4
1040.2.cd.n.177.2		8	260.47	odd	4
1040.2.cd.n.993.2		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +O(q^{10})\)	\(q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +(-3.71844 - 3.60536i) q^{10} +(-0.556540 - 0.556540i) q^{11} +(0.808545 + 0.808545i) q^{12} +(3.60536 + 0.0370899i) q^{13} +9.16944i q^{14} +(0.759725 - 0.0117303i) q^{15} +0.593630 q^{16} +(-1.16190 - 1.16190i) q^{17} +6.68135 q^{18} +(-1.24027 - 1.24027i) q^{19} +(5.23789 - 5.40218i) q^{20} +(-0.951180 - 0.951180i) q^{21} +(1.28910 - 1.28910i) q^{22} +(-2.80855 + 2.80855i) q^{23} +(-0.759725 + 0.759725i) q^{24} +(-0.154365 - 4.99762i) q^{25} +(-0.0859102 + 8.35097i) q^{26} +(-1.41391 + 1.41391i) q^{27} -13.3214 q^{28} -3.47817i q^{29} +(0.0271704 + 1.75973i) q^{30} +(-2.07599 + 2.07599i) q^{31} -4.94880i q^{32} +0.267445i q^{33} +(2.69127 - 2.69127i) q^{34} +(-6.16190 + 6.35517i) q^{35} +9.70671i q^{36} -6.84564 q^{37} +(2.87281 - 2.87281i) q^{38} +(-0.857366 - 0.875189i) q^{39} +(5.07599 + 4.92163i) q^{40} +(7.52699 - 7.52699i) q^{41} +(2.20318 - 2.20318i) q^{42} +(-7.03471 + 7.03471i) q^{43} +(1.87281 + 1.87281i) q^{44} +(4.63072 + 4.48990i) q^{45} +(-6.50534 - 6.50534i) q^{46} +9.09526 q^{47} +(-0.142634 - 0.142634i) q^{48} +8.67143 q^{49} +(11.5758 - 0.357550i) q^{50} +0.558351i q^{51} +(-12.1323 - 0.124811i) q^{52} +(0.958716 + 0.958716i) q^{53} +(-3.27498 - 3.27498i) q^{54} +(1.75973 - 0.0271704i) q^{55} -12.5171i q^{56} +0.596014i q^{57} +8.05636 q^{58} +(-7.46644 + 7.46644i) q^{59} +(-2.55654 + 0.0394734i) q^{60} +3.68926 q^{61} +(-4.80855 - 4.80855i) q^{62} -11.4191i q^{63} +12.6500 q^{64} +(-5.67143 + 5.73017i) q^{65} -0.619474 q^{66} +3.78690i q^{67} +(3.90990 + 3.90990i) q^{68} +1.34965 q^{69} +(-14.7203 - 14.2726i) q^{70} +(-3.67954 + 3.67954i) q^{71} -9.12062 q^{72} +5.57581i q^{73} -15.8563i q^{74} +(-1.16371 + 1.23789i) q^{75} +(4.17363 + 4.17363i) q^{76} +(-2.20318 - 2.20318i) q^{77} +(2.02717 - 1.98589i) q^{78} -9.03051i q^{79} +(-0.924009 + 0.952991i) q^{80} -7.97416 q^{81} +(17.4345 + 17.4345i) q^{82} +6.16980 q^{83} +(3.20080 + 3.20080i) q^{84} +(3.67382 - 0.0567242i) q^{85} +(-16.2942 - 16.2942i) q^{86} +(-0.835716 + 0.835716i) q^{87} +(-1.75973 + 1.75973i) q^{88} +(-3.51707 + 3.51707i) q^{89} +(-10.3998 + 10.7260i) q^{90} +(14.2726 + 0.146829i) q^{91} +(9.45100 - 9.45100i) q^{92} +0.997617 q^{93} +21.0670i q^{94} +(3.92163 - 0.0605505i) q^{95} +(-1.18907 + 1.18907i) q^{96} +9.03051i q^{97} +20.0853i q^{98} +(-1.60536 + 1.60536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Introduction

L-functions

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