LMFDB - Embedded newform 65.2.k.b.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(8,65)]

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, 1]))

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

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

chi := DirichletCharacter("65.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.k (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			57.1
Root			$1.18254 + 1.18254i$ of defining polynomial
Character	$\chi$	$=$	65.57
Dual form			65.2.k.b.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31627 q^{2} +(-0.240275 + 0.240275i) q^{3} +3.36509 q^{4} +(-1.60536 + 1.55654i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872i q^{7} -3.16190 q^{8} +2.88454i q^{9} +O(q^{10})$	\(q-2.31627 q^{2} +(-0.240275 + 0.240275i) q^{3} +3.36509 q^{4} +(-1.60536 + 1.55654i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872i q^{7} -3.16190 q^{8} +2.88454i q^{9} +(3.71844 - 3.60536i) q^{10} +(-0.556540 - 0.556540i) q^{11} +(-0.808545 + 0.808545i) q^{12} +(0.0370899 - 3.60536i) q^{13} -9.16944i q^{14} +(0.0117303 - 0.759725i) q^{15} +0.593630 q^{16} +(1.16190 - 1.16190i) q^{17} -6.68135i q^{18} +(1.24027 + 1.24027i) q^{19} +(-5.40218 + 5.23789i) 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} +13.3214i q^{28} +3.47817i q^{29} +(-0.0271704 + 1.75973i) q^{30} +(-2.07599 + 2.07599i) q^{31} +4.94880 q^{32} +0.267445 q^{33} +(-2.69127 + 2.69127i) q^{34} +(-6.16190 - 6.35517i) q^{35} +9.70671i q^{36} -6.84564i 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} +(-4.48990 - 4.63072i) q^{45} +(-6.50534 - 6.50534i) q^{46} +9.09526i q^{47} +(-0.142634 + 0.142634i) q^{48} -8.67143 q^{49} +(-0.357550 + 11.5758i) q^{50} +0.558351i q^{51} +(0.124811 - 12.1323i) q^{52} +(0.958716 - 0.958716i) q^{53} +(3.27498 + 3.27498i) q^{54} +(1.75973 + 0.0271704i) q^{55} -12.5171i q^{56} -0.596014 q^{57} -8.05636i q^{58} +(7.46644 - 7.46644i) q^{59} +(0.0394734 - 2.55654i) q^{60} +3.68926 q^{61} +(4.80855 - 4.80855i) q^{62} -11.4191 q^{63} -12.6500 q^{64} +(5.55235 + 5.84564i) q^{65} -0.619474 q^{66} -3.78690 q^{67} +(3.90990 - 3.90990i) q^{68} -1.34965 q^{69} +(14.2726 + 14.7203i) q^{70} +(-3.67954 + 3.67954i) q^{71} -9.12062i q^{72} +5.57581 q^{73} +15.8563i q^{74} +(1.16371 + 1.23789i) q^{75} +(4.17363 + 4.17363i) q^{76} +(2.20318 - 2.20318i) q^{77} +(-1.98589 - 2.02717i) q^{78} +9.03051i q^{79} +(-0.952991 + 0.924009i) q^{80} -7.97416 q^{81} +(-17.4345 + 17.4345i) q^{82} -6.16980i q^{83} +(-3.20080 - 3.20080i) q^{84} +(-0.0567242 + 3.67382i) 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} -0.997617i q^{93} -21.0670i q^{94} +(-3.92163 - 0.0605505i) q^{95} +(-1.18907 + 1.18907i) q^{96} -9.03051 q^{97} +20.0853 q^{98} +(1.60536 - 1.60536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6	$ 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 8 q^{16} - 16 q^{17} + 14 q^{19} - 22 q^{20} - 12 q^{21} + 10 q^{22} + 14 q^{23} + 2 q^{24} + 12 q^{25} + 6 q^{26} + 12 q^{27} + 14 q^{30} + 2 q^{31} - 4 q^{32} - 8 q^{33} - 24 q^{35} + 2 q^{38} - 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} + 6 q^{43} + 10 q^{44} + 6 q^{45} + 2 q^{46} - 14 q^{48} - 24 q^{49} - 20 q^{50} - 22 q^{52} - 24 q^{53} - 20 q^{54} + 10 q^{55} - 40 q^{57} + 22 q^{59} + 46 q^{60} + 20 q^{61} + 30 q^{62} + 16 q^{63} - 48 q^{64} - 36 q^{66} - 12 q^{67} + 4 q^{68} - 4 q^{69} + 20 q^{70} - 10 q^{71} - 4 q^{73} - 30 q^{75} + 6 q^{76} + 24 q^{77} + 30 q^{78} + 2 q^{80} - 20 q^{81} - 20 q^{82} + 16 q^{84} - 20 q^{85} - 46 q^{86} + 16 q^{87} + 10 q^{88} - 28 q^{89} + 14 q^{90} + 20 q^{91} + 50 q^{92} - 2 q^{95} + 30 q^{96} + 12 q^{97} + 92 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 8 * q^16 - 16 * q^17 + 14 * q^19 - 22 * q^20 - 12 * q^21 + 10 * q^22 + 14 * q^23 + 2 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 14 * q^30 + 2 * q^31 - 4 * q^32 - 8 * q^33 - 24 * q^35 + 2 * q^38 - 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 + 6 * q^43 + 10 * q^44 + 6 * q^45 + 2 * q^46 - 14 * q^48 - 24 * q^49 - 20 * q^50 - 22 * q^52 - 24 * q^53 - 20 * q^54 + 10 * q^55 - 40 * q^57 + 22 * q^59 + 46 * q^60 + 20 * q^61 + 30 * q^62 + 16 * q^63 - 48 * q^64 - 36 * q^66 - 12 * q^67 + 4 * q^68 - 4 * q^69 + 20 * q^70 - 10 * q^71 - 4 * q^73 - 30 * q^75 + 6 * q^76 + 24 * q^77 + 30 * q^78 + 2 * q^80 - 20 * q^81 - 20 * q^82 + 16 * q^84 - 20 * q^85 - 46 * q^86 + 16 * q^87 + 10 * q^88 - 28 * q^89 + 14 * q^90 + 20 * q^91 + 50 * q^92 - 2 * q^95 + 30 * q^96 + 12 * q^97 + 92 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.31627			−1.63785			−0.818924	−	0.573903i	$-0.805429\pi$
$2$	−2.31627			−1.63785			−0.818924	+	0.573903i	$0.805429\pi$
$3$	−0.240275	+	0.240275i	−0.138723	+	0.138723i	−0.773058	−	0.634335i	$-0.781274\pi$
$3$	−0.240275	+	0.240275i	−0.138723	+	0.138723i	0.634335	+	0.773058i	$0.281274\pi$
$4$	3.36509			1.68254
$5$	−1.60536	+	1.55654i	−0.717939	+	0.696106i
$5$	−1.60536	+	1.55654i	−0.717939	+	0.696106i
$6$	0.556540	−	0.556540i	0.227207	−	0.227207i
$7$			3.95872i			1.49625i	0.663556	+	0.748127i	$0.269047\pi$
$7$			3.95872i			1.49625i	−0.663556	+	0.748127i	$0.730953\pi$
$8$	−3.16190			−1.11790
$9$			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
$13$	0.0370899	−	3.60536i	0.0102869	−	0.999947i
$13$	0.0370899	−	3.60536i	0.0102869	−	0.999947i
$14$		−	9.16944i		−	2.45064i
$15$	0.0117303	−	0.759725i	0.00302874	−	0.196160i
$16$	0.593630			0.148408
$17$	1.16190	−	1.16190i	0.281802	−	0.281802i	−0.552025	−	0.833827i	$-0.686145\pi$
$17$	1.16190	−	1.16190i	0.281802	−	0.281802i	0.833827	+	0.552025i	$0.186145\pi$
$18$		−	6.68135i		−	1.57481i
$19$	1.24027	+	1.24027i	0.284539	+	0.284539i	0.834916	−	0.550377i	$-0.185516\pi$
$19$	1.24027	+	1.24027i	0.284539	+	0.284539i	−0.550377	+	0.834916i	$0.685516\pi$
$20$	−5.40218	+	5.23789i	−1.20796	+	1.17123i
$21$	−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	$-0.114097\pi$
$23$	2.80855	+	2.80855i	0.585622	+	0.585622i	−0.350821	+	0.936443i	$0.614097\pi$
$24$	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
$28$			13.3214i			2.51751i
$29$			3.47817i			0.645879i	0.946420	+	0.322940i	$0.104671\pi$
$29$			3.47817i			0.645879i	−0.946420	+	0.322940i	$0.895329\pi$
$30$	−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	$0.334927\pi$
$32$	4.94880			0.874832
$33$	0.267445			0.0465562
$34$	−2.69127	+	2.69127i	−0.461549	+	0.461549i
$35$	−6.16190	−	6.35517i	−1.04155	−	1.07422i
$36$			9.70671i			1.61779i
$37$		−	6.84564i		−	1.12542i	−0.826656	−	0.562708i	$-0.809760\pi$
$37$		−	6.84564i		−	1.12542i	0.826656	−	0.562708i	$-0.190240\pi$
$38$	−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	0.997135	+	0.0756481i	$0.0241026\pi$
$43$	7.03471	+	7.03471i	1.07278	+	1.07278i	0.0756481	+	0.997135i	$0.475897\pi$
$44$	−1.87281	−	1.87281i	−0.282336	−	0.282336i
$45$	−4.48990	−	4.63072i	−0.669314	−	0.690307i
$46$	−6.50534	−	6.50534i	−0.959160	−	0.959160i
$47$			9.09526i			1.32668i	0.748318	+	0.663340i	$0.230862\pi$
$47$			9.09526i			1.32668i	−0.748318	+	0.663340i	$0.769138\pi$
$48$	−0.142634	+	0.142634i	−0.0205875	+	0.0205875i
$49$	−8.67143			−1.23878
$50$	−0.357550	+	11.5758i	−0.0505651	+	1.63707i
$51$			0.558351i			0.0781848i
$52$	0.124811	−	12.1323i	0.0173081	−	1.68245i
$53$	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	$0.220316\pi$
$54$	3.27498	+	3.27498i	0.445669	+	0.445669i
$55$	1.75973	+	0.0271704i	0.237281	+	0.00366366i
$56$		−	12.5171i		−	1.67266i
$57$	−0.596014			−0.0789439
$58$		−	8.05636i		−	1.05785i
$59$	7.46644	−	7.46644i	0.972047	−	0.972047i	−0.0275726	−	0.999620i	$-0.508778\pi$
$59$	7.46644	−	7.46644i	0.972047	−	0.972047i	0.999620	+	0.0275726i	$0.00877775\pi$
$60$	0.0394734	−	2.55654i	0.00509599	−	0.330048i
$61$	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
$63$	−11.4191			−1.43867
$64$	−12.6500			−1.58125
$65$	5.55235	+	5.84564i	0.688684	+	0.725062i
$66$	−0.619474			−0.0762520
$67$	−3.78690			−0.462643			−0.231321	−	0.972877i	$-0.574305\pi$
$67$	−3.78690			−0.462643			−0.231321	+	0.972877i	$0.574305\pi$
$68$	3.90990	−	3.90990i	0.474144	−	0.474144i
$69$	−1.34965			−0.162478
$70$	14.2726	+	14.7203i	1.70590	+	1.75941i
$71$	−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	$0.349921\pi$
$72$		−	9.12062i		−	1.07487i
$73$	5.57581			0.652599			0.326299	−	0.945266i	$-0.394198\pi$
$73$	5.57581			0.652599			0.326299	+	0.945266i	$0.394198\pi$
$74$			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
$78$	−1.98589	−	2.02717i	−0.224857	−	0.229532i
$79$			9.03051i			1.01601i	0.861354	+	0.508006i	$0.169617\pi$
$79$			9.03051i			1.01601i	−0.861354	+	0.508006i	$0.830383\pi$
$80$	−0.952991	+	0.924009i	−0.106548	+	0.103307i
$81$	−7.97416			−0.886017
$82$	−17.4345	+	17.4345i	−1.92532	+	1.92532i
$83$		−	6.16980i		−	0.677224i	−0.940926	−	0.338612i	$-0.890043\pi$
$83$		−	6.16980i		−	0.677224i	0.940926	−	0.338612i	$-0.109957\pi$
$84$	−3.20080	−	3.20080i	−0.349236	−	0.349236i
$85$	−0.0567242	+	3.67382i	−0.00615261	+	0.398481i
$86$	−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	−0.495691	−	0.868499i	$-0.665085\pi$
$89$	3.51707	−	3.51707i	0.372808	−	0.372808i	0.868499	+	0.495691i	$0.165085\pi$
$90$	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
$93$		−	0.997617i		−	0.103448i
$94$		−	21.0670i		−	2.17290i
$95$	−3.92163	−	0.0605505i	−0.402350	−	0.00621235i
$96$	−1.18907	+	1.18907i	−0.121359	+	0.121359i
$97$	−9.03051			−0.916910			−0.458455	−	0.888718i	$-0.651597\pi$
$97$	−9.03051			−0.916910			−0.458455	+	0.888718i	$0.651597\pi$
$98$	20.0853			2.02893
$99$	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	$-0.0522558\pi$
$102$		−	1.29329i		−	0.128055i
$103$	−3.64426	−	3.64426i	−0.359080	−	0.359080i	0.504394	−	0.863474i	$-0.331716\pi$
$103$	−3.64426	−	3.64426i	−0.359080	−	0.359080i	−0.863474	+	0.504394i	$0.831716\pi$
$104$	−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	0.442882	−	0.896580i	$-0.353956\pi$
$107$	−4.69308	−	4.69308i	−0.453697	−	0.453697i	−0.896580	+	0.442882i	$0.853956\pi$
$108$	−4.75791	−	4.75791i	−0.457831	−	0.457831i
$109$	4.12300	+	4.12300i	0.394912	+	0.394912i	0.876434	−	0.481522i	$-0.159916\pi$
$109$	4.12300	+	4.12300i	0.394912	+	0.394912i	−0.481522	+	0.876434i	$0.659916\pi$
$110$	−4.07599	−	0.0629339i	−0.388630	−	0.00600051i
$111$	1.64483	+	1.64483i	0.156121	+	0.156121i
$112$			2.35001i			0.222055i
$113$	−12.7920	+	12.7920i	−1.20337	+	1.20337i	−0.230241	+	0.973134i	$0.573951\pi$
$113$	−12.7920	+	12.7920i	−1.20337	+	1.20337i	−0.973134	+	0.230241i	$0.926049\pi$
$114$	1.38053			0.129298
$115$	−8.88034	−	0.137114i	−0.828096	−	0.0127859i
$116$			11.7043i			1.08672i
$117$	10.3998	+	0.106987i	0.961461	+	0.00989098i
$118$	−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
$122$	−8.54529			−0.773655
$123$			3.61709i			0.326142i
$124$	−6.98589	+	6.98589i	−0.627351	+	0.627351i
$125$	7.53118	+	8.26325i	0.673609	+	0.739088i
$126$	26.4496			2.35632
$127$	5.44898	−	5.44898i	0.483519	−	0.483519i	−0.422735	−	0.906253i	$-0.638930\pi$
$127$	5.44898	−	5.44898i	0.483519	−	0.483519i	0.906253	+	0.422735i	$0.138930\pi$
$128$	19.4031			1.71501
$129$	−3.38053			−0.297639
$130$	−12.8607	−	13.5400i	−1.12796	−	1.18754i
$131$	2.42144			0.211562			0.105781	−	0.994389i	$-0.466266\pi$
$131$	2.42144			0.211562			0.105781	+	0.994389i	$0.466266\pi$
$132$	0.899976			0.0783329
$133$	−4.90990	+	4.90990i	−0.425742	+	0.425742i
$134$	8.77146			0.757738
$135$	4.47063	+	0.0690272i	0.384771	+	0.00594091i
$136$	−3.67382	+	3.67382i	−0.315027	+	0.315027i
$137$		−	0.578190i		−	0.0493981i	−0.999695	−	0.0246991i	$-0.992137\pi$
$137$		−	0.578190i		−	0.0493981i	0.999695	−	0.0246991i	$-0.00786275\pi$
$138$	3.12614			0.266114
$139$		−	16.6241i		−	1.41004i	−0.709187	−	0.705021i	$-0.750938\pi$
$139$		−	16.6241i		−	1.41004i	0.709187	−	0.705021i	$-0.249062\pi$
$140$	−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
$143$	−2.02717	+	1.98589i	−0.169521	+	0.166068i
$144$			1.71235i			0.142696i
$145$	−5.41391	−	5.58371i	−0.449600	−	0.463702i
$146$	−12.9150			−1.06886
$147$	2.08353	−	2.08353i	0.171846	−	0.171846i
$148$		−	23.0361i		−	1.89356i
$149$	−0.953563	−	0.953563i	−0.0781189	−	0.0781189i	0.666968	−	0.745087i	$-0.267592\pi$
$149$	−0.953563	−	0.953563i	−0.0781189	−	0.0781189i	−0.745087	+	0.666968i	$0.767592\pi$
$150$	−2.69546	−	2.86729i	−0.220084	−	0.234113i
$151$	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	0.798259	−	0.602314i	$-0.205754\pi$
$157$	2.45519	+	2.45519i	0.195945	+	0.195945i	−0.602314	+	0.798259i	$0.705754\pi$
$158$		−	20.9171i		−	1.66407i
$159$			0.460711i			0.0365367i
$160$	−7.94460	+	7.70300i	−0.628076	+	0.608976i
$161$	−11.1182	+	11.1182i	−0.876240	+	0.876240i
$162$	18.4703			1.45116
$163$	−4.11546			−0.322348			−0.161174	−	0.986926i	$-0.551528\pi$
$163$	−4.11546			−0.322348			−0.161174	+	0.986926i	$0.551528\pi$
$164$	25.3290	−	25.3290i	1.97786	−	1.97786i
$165$	−0.429346	+	0.416289i	−0.0334245	+	0.0324081i
$166$			14.2909i			1.10919i
$167$			5.27547i			0.408228i	0.978947	+	0.204114i	$0.0654313\pi$
$167$			5.27547i			0.408228i	−0.978947	+	0.204114i	$0.934569\pi$
$168$	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	$-0.308885\pi$
$173$	−3.42144	−	3.42144i	−0.260127	−	0.260127i	−0.825106	+	0.564978i	$0.808885\pi$
$174$	1.93574	+	1.93574i	0.146748	+	0.146748i
$175$	19.7841	+	0.611086i	1.49554	+	0.0461938i
$176$	−0.330379	−	0.330379i	−0.0249033	−	0.0249033i
$177$			3.58799i			0.269690i
$178$	−8.14646	+	8.14646i	−0.610603	+	0.610603i
$179$	−13.0849			−0.978008			−0.489004	−	0.872282i	$-0.662640\pi$
$179$	−13.0849			−0.978008			−0.489004	+	0.872282i	$0.662640\pi$
$180$	−15.1089	−	15.5828i	−1.12615	−	1.16147i
$181$			4.65035i			0.345658i	0.984952	+	0.172829i	$0.0552908\pi$
$181$			4.65035i			0.345658i	−0.984952	+	0.172829i	$0.944709\pi$
$182$	−33.0591	−	0.340094i	−2.45051	−	0.0252094i
$183$	−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
$187$	−1.29329			−0.0945747
$188$			30.6063i			2.23220i
$189$	5.59725	−	5.59725i	0.407140	−	0.407140i
$190$	9.08353	+	0.140251i	0.658988	+	0.0101749i
$191$	−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
$193$	23.0576			1.65972			0.829861	−	0.557970i	$-0.188420\pi$
$193$	23.0576			1.65972			0.829861	+	0.557970i	$0.188420\pi$
$194$	20.9171			1.50176
$195$	−2.73865	−	0.0704700i	−0.196119	−	0.00504646i
$196$	−29.1801			−2.08429
$197$	−0.249622			−0.0177848			−0.00889240	−	0.999960i	$-0.502831\pi$
$197$	−0.249622			−0.0177848			−0.00889240	+	0.999960i	$0.502831\pi$
$198$	−3.71844	+	3.71844i	−0.264258	+	0.264258i
$199$	17.6865			1.25376			0.626882	−	0.779115i	$-0.284331\pi$
$199$	17.6865			1.25376			0.626882	+	0.779115i	$0.284331\pi$
$200$	−0.488086	+	15.8020i	−0.0345129	+	1.11737i
$201$	0.909896	−	0.909896i	0.0641791	−	0.0641791i
$202$			7.60870i			0.535346i
$203$	−13.7691			−0.966399
$204$			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
$208$	0.0220177	−	2.14025i	0.00152665	−	0.148400i
$209$		−	1.38053i		−	0.0954930i
$210$	−6.96625	−	0.107560i	−0.480717	−	0.00742234i
$211$	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
$213$		−	1.76820i		−	0.121155i
$214$	10.8704	+	10.8704i	0.743087	+	0.743087i
$215$	−22.2430	−	0.343436i	−1.51696	−	0.0234221i
$216$	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
$223$		−	14.2674i		−	0.955419i	−0.878518	−	0.477709i	$-0.841467\pi$
$223$		−	14.2674i		−	0.955419i	0.878518	−	0.477709i	$-0.158533\pi$
$224$			19.5909i			1.30897i
$225$	14.4158	+	0.445270i	0.961054	+	0.0296847i
$226$	29.6298	−	29.6298i	1.97094	−	1.97094i
$227$	−12.3687			−0.820940			−0.410470	−	0.911874i	$-0.634635\pi$
$227$	−12.3687			−0.820940			−0.410470	+	0.911874i	$0.634635\pi$
$228$	−2.00564			−0.132827
$229$	−6.93888	+	6.93888i	−0.458534	+	0.458534i	−0.898174	−	0.439640i	$-0.855106\pi$
$229$	−6.93888	+	6.93888i	−0.458534	+	0.458534i	0.439640	+	0.898174i	$0.355106\pi$
$230$	20.5692	+	0.317592i	1.35629	+	0.0209414i
$231$			1.05874i			0.0696600i
$232$		−	10.9976i		−	0.722029i
$233$	3.17544	+	3.17544i	0.208030	+	0.208030i	0.803430	−	0.595400i	$-0.203006\pi$
$233$	3.17544	+	3.17544i	0.208030	+	0.208030i	−0.595400	+	0.803430i	$0.703006\pi$
$234$	−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	0.182514	−	0.983203i	$-0.441576\pi$
$239$	−12.3783	−	12.3783i	−0.800689	−	0.800689i	−0.983203	+	0.182514i	$0.941576\pi$
$240$	0.00696344	−	0.450996i	0.000449488	−	0.0291117i
$241$	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	$0.560504\pi$
$242$			24.0441i			1.54561i
$243$	6.15771	−	6.15771i	0.395017	−	0.395017i
$244$	12.4147			0.794767
$245$	13.9208	−	13.4974i	0.889366	−	0.862319i
$246$		−	8.37814i		−	0.534171i
$247$	4.51764	−	4.42564i	0.287451	−	0.281596i
$248$	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	$-0.214603\pi$
$252$	−38.4261			−2.42062
$253$		−	3.12614i		−	0.196539i
$254$	−12.6213	+	12.6213i	−0.791930	+	0.791930i
$255$	−0.869096	−	0.896355i	−0.0544249	−	0.0561319i
$256$	−19.6428			−1.22768
$257$	14.5758	−	14.5758i	0.909214	−	0.909214i	−0.0869949	−	0.996209i	$-0.527726\pi$
$257$	14.5758	−	14.5758i	0.909214	−	0.909214i	0.996209	+	0.0869949i	$0.0277264\pi$
$258$	7.83020			0.487487
$259$	27.0999			1.68391
$260$	18.6841	+	19.6711i	1.15874	+	1.21995i
$261$	−10.0329			−0.621021
$262$	−5.60870			−0.346507
$263$	14.5593	−	14.5593i	0.897765	−	0.897765i	−0.0974727	−	0.995238i	$-0.531076\pi$
$263$	14.5593	−	14.5593i	0.897765	−	0.897765i	0.995238	+	0.0974727i	$0.0310759\pi$
$264$	−0.845635			−0.0520453
$265$	−0.0468047	+	3.03136i	−0.00287519	+	0.186215i
$266$	11.3726	−	11.3726i	0.697300	−	0.697300i
$267$			1.69013i			0.103434i
$268$	−12.7432			−0.778417
$269$		−	8.65961i		−	0.527986i	−0.964525	−	0.263993i	$-0.914960\pi$
$269$		−	8.65961i		−	0.527986i	0.964525	−	0.263993i	$-0.0850396\pi$
$270$	−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
$273$	−3.46463	+	3.39407i	−0.209689	+	0.205418i
$274$			1.33924i			0.0809066i
$275$	−2.86729	+	2.69546i	−0.172904	+	0.162543i
$276$	−4.54167			−0.273377
$277$	−0.848019	+	0.848019i	−0.0509525	+	0.0509525i	−0.732124	−	0.681171i	$-0.761471\pi$
$277$	−0.848019	+	0.848019i	−0.0509525	+	0.0509525i	0.681171	+	0.732124i	$0.261471\pi$
$278$			38.5059i			2.30943i
$279$	−5.98827	−	5.98827i	−0.358508	−	0.358508i
$280$	19.4833	+	20.0944i	1.16435	+	1.20087i
$281$	−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	$-0.350705\pi$
$283$	−7.40181	−	7.40181i	−0.439992	−	0.439992i	−0.892009	+	0.452017i	$0.850705\pi$
$284$	−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
$288$			14.2750i			0.841161i
$289$			14.3000i			0.841175i
$290$	12.5400	+	12.9334i	0.736377	+	0.759473i
$291$	2.16980	−	2.16980i	0.127196	−	0.127196i
$292$	18.7631			1.09803
$293$	−11.2274			−0.655912			−0.327956	−	0.944693i	$-0.606360\pi$
$293$	−11.2274			−0.655912			−0.327956	+	0.944693i	$0.606360\pi$
$294$	−4.82600	+	4.82600i	−0.281458	+	0.281458i
$295$	−0.364513	+	23.6081i	−0.0212228	+	1.37452i
$296$			21.6452i			1.25810i
$297$			1.57379i			0.0913206i
$298$	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
$305$	−5.92258	+	5.74247i	−0.339126	+	0.328813i
$306$	−7.76307	−	7.76307i	−0.443785	−	0.443785i
$307$		−	28.2579i		−	1.61276i	−0.591395	−	0.806382i	$-0.701423\pi$
$307$		−	28.2579i		−	1.61276i	0.591395	−	0.806382i	$-0.298577\pi$
$308$	7.41391	−	7.41391i	0.422446	−	0.422446i
$309$	1.75125			0.0996250
$310$	−0.234754	+	15.2041i	−0.0133331	+	0.863537i
$311$			9.55436i			0.541778i	0.962611	+	0.270889i	$0.0873177\pi$
$311$			9.55436i			0.541778i	−0.962611	+	0.270889i	$0.912682\pi$
$312$	−2.71090	−	2.76726i	−0.153475	−	0.156665i
$313$	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	$-0.000361078\pi$
$314$	−5.68687	−	5.68687i	−0.320929	−	0.320929i
$315$	18.3317	−	17.7742i	1.03287	−	1.00146i
$316$			30.3884i			1.70948i
$317$	0.912395			0.0512452			0.0256226	−	0.999672i	$-0.491843\pi$
$317$	0.912395			0.0512452			0.0256226	+	0.999672i	$0.491843\pi$
$318$		−	1.06713i		−	0.0598416i
$319$	1.93574	−	1.93574i	0.108381	−	0.108381i
$320$	20.3078	−	19.6902i	1.13524	−	1.10072i
$321$	2.25526			0.125876
$322$	25.7528	−	25.7528i	1.43515	−	1.43515i
$323$	2.88215			0.160367
$324$	−26.8337			−1.49076
$325$	−18.0125	−	0.741902i	−0.999153	−	0.0411533i
$326$	9.53251			0.527957
$327$	−1.98131			−0.109566
$328$	−23.7996	+	23.7996i	−1.31411	+	1.31411i
$329$	−36.0055			−1.98505
$330$	0.994479	−	0.964237i	0.0547443	−	0.0530795i
$331$	−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	$0.452072\pi$
$332$		−	20.7619i		−	1.13946i
$333$	19.7465			1.08210
$334$		−	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	$-0.854098\pi$
$337$	−8.33973	+	8.33973i	−0.454294	+	0.454294i	0.442483	+	0.896777i	$0.354098\pi$
$338$	30.1051	+	0.619474i	1.63750	+	0.0336950i
$339$		−	6.14721i		−	0.333871i
$340$	−0.190882	+	12.3627i	−0.0103520	+	0.670462i
$341$	2.31074			0.125134
$342$	8.28671	−	8.28671i	0.448094	−	0.448094i
$343$		−	6.61672i		−	0.357269i
$344$	−22.2430	−	22.2430i	−1.19926	−	1.19926i
$345$	2.16667	−	2.10078i	0.116649	−	0.113102i
$346$	7.92497	+	7.92497i	0.426049	+	0.426049i
$347$	22.4851	+	22.4851i	1.20707	+	1.20707i	0.971973	+	0.235092i	$0.0755391\pi$
$347$	22.4851	+	22.4851i	1.20707	+	1.20707i	0.235092	+	0.971973i	$0.424461\pi$
$348$	−2.81226	−	2.81226i	−0.150753	−	0.150753i
$349$	−19.2262	+	19.2262i	−1.02915	+	1.02915i	−0.0295907	+	0.999562i	$0.509420\pi$
$349$	−19.2262	+	19.2262i	−1.02915	+	1.02915i	−0.999562	+	0.0295907i	$0.990580\pi$
$350$	−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
$353$			4.45434i			0.237080i	0.992949	+	0.118540i	$0.0378215\pi$
$353$			4.45434i			0.237080i	−0.992949	+	0.118540i	$0.962179\pi$
$354$		−	8.31074i		−	0.441711i
$355$	0.179636	−	11.6343i	0.00953409	−	0.617487i
$356$	11.8352	−	11.8352i	0.627266	−	0.627266i
$357$	−2.21035			−0.116984
$358$	30.3080			1.60183
$359$	−11.6335	+	11.6335i	−0.613992	+	0.613992i	−0.943984	−	0.329992i	$-0.892954\pi$
$359$	−11.6335	+	11.6335i	−0.613992	+	0.613992i	0.329992	+	0.943984i	$0.392954\pi$
$360$	14.1966	+	14.6419i	0.748227	+	0.771695i
$361$		−	15.9234i		−	0.838076i
$362$		−	10.7715i		−	0.566135i
$363$	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	0.729732	−	0.683734i	$-0.239645\pi$
$367$	0.881194	+	0.881194i	0.0459980	+	0.0459980i	−0.683734	+	0.729732i	$0.739645\pi$
$368$	1.66724	+	1.66724i	0.0869108	+	0.0869108i
$369$	21.7119	+	21.7119i	1.13027	+	1.13027i
$370$	−24.6810	−	25.4551i	−1.28310	−	1.32335i
$371$	3.79528	+	3.79528i	0.197041	+	0.197041i
$372$		−	3.35707i		−	0.174056i
$373$	8.48607	−	8.48607i	0.439392	−	0.439392i	−0.452415	−	0.891807i	$-0.649438\pi$
$373$	8.48607	−	8.48607i	0.439392	−	0.439392i	0.891807	+	0.452415i	$0.149438\pi$
$374$	2.99560			0.154899
$375$	−3.79500	−	0.175898i	−0.195973	−	0.00908334i
$376$		−	28.7583i		−	1.48310i
$377$	12.5400	+	0.129005i	0.645845	+	0.00664410i
$378$	−12.9647	+	12.9647i	−0.666833	+	0.666833i
$379$	21.9165	+	21.9165i	1.12577	+	1.12577i	0.990857	+	0.134918i	$0.0430770\pi$
$379$	21.9165	+	21.9165i	1.12577	+	1.12577i	0.134918	+	0.990857i	$0.456923\pi$
$380$	−13.1966	−	0.203758i	−0.676972	−	0.0104525i
$381$			2.61851i			0.134150i
$382$	9.31101			0.476393
$383$			11.8412i			0.605059i	0.953140	+	0.302529i	$0.0978311\pi$
$383$			11.8412i			0.605059i	−0.953140	+	0.302529i	$0.902169\pi$
$384$	−4.66208	+	4.66208i	−0.237911	+	0.237911i
$385$	−0.107560	+	6.96625i	−0.00548176	+	0.355033i
$386$	−53.4075			−2.71837
$387$	−20.2919	+	20.2919i	−1.03149	+	1.03149i
$388$	−30.3884			−1.54274
$389$	−22.0771			−1.11935			−0.559676	−	0.828712i	$-0.689074\pi$
$389$	−22.0771			−1.11935			−0.559676	+	0.828712i	$0.689074\pi$
$390$	6.34344	+	0.163227i	0.321212	+	0.00826533i
$391$	6.52650			0.330059
$392$	27.4182			1.38483
$393$	−0.581812	+	0.581812i	−0.0293485	+	0.0293485i
$394$	0.578190			0.0291288
$395$	−14.0564	−	14.4972i	−0.707252	−	0.729435i
$396$	5.40218	−	5.40218i	0.271470	−	0.271470i
$397$		−	16.1305i		−	0.809568i	−0.914412	−	0.404784i	$-0.867347\pi$
$397$		−	16.1305i		−	0.809568i	0.914412	−	0.404784i	$-0.132653\pi$
$398$	−40.9666			−2.05347
$399$		−	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
$403$	7.40770	+	7.56169i	0.369004	+	0.376675i
$404$		−	11.0540i		−	0.549956i
$405$	12.8014	−	12.4121i	0.636106	−	0.616762i
$406$	31.8928			1.58281
$407$	−3.80987	+	3.80987i	−0.188848	+	0.188848i
$408$		−	1.76545i		−	0.0874028i
$409$	−3.08611	−	3.08611i	−0.152599	−	0.152599i	0.626679	−	0.779278i	$-0.284414\pi$
$409$	−3.08611	−	3.08611i	−0.152599	−	0.152599i	−0.779278	+	0.626679i	$0.784414\pi$
$410$	0.851156	−	55.1262i	0.0420356	−	2.72249i
$411$	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
$418$			3.19766i			0.156403i
$419$		−	9.51871i		−	0.465020i	−0.972594	−	0.232510i	$-0.925306\pi$
$419$		−	9.51871i		−	0.465020i	0.972594	−	0.232510i	$-0.0746938\pi$
$420$	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	$-0.00239083\pi$
$422$	−21.0889			−1.02659
$423$	−26.2356			−1.27562
$424$	−3.03136	+	3.03136i	−0.147216	+	0.147216i
$425$	−5.62738	−	5.98609i	−0.272968	−	0.290368i
$426$			4.09562i			0.198434i
$427$			14.6047i			0.706772i
$428$	−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	$-0.460340\pi$
$433$	−18.0614	−	18.0614i	−0.867975	−	0.867975i	−0.992248	+	0.124273i	$0.960340\pi$
$434$	19.0357	+	19.0357i	0.913741	+	0.913741i
$435$	2.64245	+	0.0407998i	0.126696	+	0.00195620i
$436$	13.8742	+	13.8742i	0.664456	+	0.664456i
$437$			6.96674i			0.333264i
$438$	3.10316	−	3.10316i	0.148275	−	0.148275i
$439$	−32.7984			−1.56538			−0.782692	−	0.622409i	$-0.786154\pi$
$439$	−32.7984			−1.56538			−0.782692	+	0.622409i	$0.786154\pi$
$440$	−5.56408	−	0.0859102i	−0.265257	−	0.00409561i
$441$		−	25.0131i		−	1.19110i
$442$	9.60318	+	9.80282i	0.456777	+	0.466273i
$443$	−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	$0.375871\pi$
$444$	5.53501	+	5.53501i	0.262680	+	0.262680i
$445$	−0.171704	+	11.1206i	−0.00813955	+	0.527168i
$446$			33.0472i			1.56483i
$447$	0.458234			0.0216737
$448$		−	50.0777i		−	2.36595i
$449$	20.0441	−	20.0441i	0.945937	−	0.945937i	−0.0526744	−	0.998612i	$-0.516775\pi$
$449$	20.0441	−	20.0441i	0.945937	−	0.945937i	0.998612	+	0.0526744i	$0.0167745\pi$
$450$	−33.3908	−	1.03136i	−1.57406	−	0.0486190i
$451$	−8.37814			−0.394511
$452$	−43.0463	+	43.0463i	−2.02473	+	2.02473i
$453$	−4.39217			−0.206362
$454$	28.6492			1.34457
$455$	−23.1412	+	21.9802i	−1.08488	+	1.03045i
$456$	1.88454			0.0882515
$457$	−3.16380			−0.147996			−0.0739982	−	0.997258i	$-0.523576\pi$
$457$	−3.16380			−0.147996			−0.0739982	+	0.997258i	$0.523576\pi$
$458$	16.0723	−	16.0723i	0.751008	−	0.751008i
$459$	−3.28564			−0.153360
$460$	−29.8831	−	0.461400i	−1.39331	−	0.0215129i
$461$	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	$0.0210232\pi$
$462$		−	2.45232i		−	0.114092i
$463$	−4.68050			−0.217521			−0.108761	−	0.994068i	$-0.534688\pi$
$463$	−4.68050			−0.217521			−0.108761	+	0.994068i	$0.534688\pi$
$464$			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	$-0.694390\pi$
$467$	5.31207	−	5.31207i	0.245813	−	0.245813i	0.819250	+	0.573437i	$0.194390\pi$
$468$	34.9962	+	0.360021i	1.61770	+	0.0166420i
$469$		−	14.9912i		−	0.692231i
$470$	32.7917	+	33.8202i	1.51257	+	1.56001i
$471$	−1.17984			−0.0543642
$472$	−23.6081	+	23.6081i	−1.08665	+	1.08665i
$473$		−	7.83020i		−	0.360033i
$474$	5.02584	+	5.02584i	0.230845	+	0.230845i
$475$	6.38987	−	6.00696i	0.293187	−	0.275618i
$476$	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	−0.162125	−	0.986770i	$-0.551835\pi$
$479$	18.0482	−	18.0482i	0.824645	−	0.824645i	0.986770	+	0.162125i	$0.0518347\pi$
$480$	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
$483$		−	5.34286i		−	0.243109i
$484$		−	34.9314i		−	1.58779i
$485$	14.4972	−	14.0564i	0.658285	−	0.638266i
$486$	−14.2629	+	14.2629i	−0.646978	+	0.646978i
$487$	0.978187			0.0443259			0.0221629	−	0.999754i	$-0.492945\pi$
$487$	0.978187			0.0443259			0.0221629	+	0.999754i	$0.492945\pi$
$488$	−11.6651			−0.528052
$489$	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	$-0.142924\pi$
$492$			12.1718i			0.548748i
$493$	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	0.971920	−	0.235310i	$-0.0756107\pi$
$499$	16.4546	+	16.4546i	0.736610	+	0.736610i	−0.235310	+	0.971920i	$0.575611\pi$
$500$	25.3431	+	27.8065i	1.13338	+	1.24355i
$501$	−1.26756	−	1.26756i	−0.0566305	−	0.0566305i
$502$			45.8169i			2.04491i
$503$	12.8451	−	12.8451i	0.572733	−	0.572733i	−0.360158	−	0.932891i	$-0.617277\pi$
$503$	12.8451	−	12.8451i	0.572733	−	0.572733i	0.932891	+	0.360158i	$0.117277\pi$
$504$	36.1059			1.60829
$505$	5.11308	+	5.27345i	0.227529	+	0.234665i
$506$			7.24096i			0.321900i
$507$	3.18717	−	3.05865i	0.141547	−	0.135839i
$508$	18.3363	−	18.3363i	0.813541	−	0.813541i
$509$	6.97177	+	6.97177i	0.309018	+	0.309018i	0.844529	−	0.535510i	$-0.179881\pi$
$509$	6.97177	+	6.97177i	0.309018	+	0.309018i	−0.535510	+	0.844529i	$0.679881\pi$
$510$	2.01306	+	2.07620i	0.0891397	+	0.0919355i
$511$			22.0730i			0.976454i
$512$	6.69175			0.295737
$513$		−	3.50726i		−	0.154849i
$514$	−33.7614	+	33.7614i	−1.48915	+	1.48915i
$515$	11.5228	+	0.177914i	0.507755	+	0.00783981i
$516$	−11.3758			−0.500790
$517$	5.06188	−	5.06188i	0.222621	−	0.222621i
$518$	−62.7706			−2.75798
$519$	1.64417			0.0721712
$520$	−17.5560	−	18.4833i	−0.769880	−	0.810547i
$521$	9.45108			0.414060			0.207030	−	0.978335i	$-0.433620\pi$
$521$	9.45108			0.414060			0.207030	+	0.978335i	$0.433620\pi$
$522$	23.2388			1.01714
$523$	−15.1815	+	15.1815i	−0.663842	+	0.663842i	−0.956283	−	0.292441i	$-0.905532\pi$
$523$	−15.1815	+	15.1815i	−0.663842	+	0.663842i	0.292441	+	0.956283i	$0.405532\pi$
$524$	8.14836			0.355963
$525$	−4.90046	+	4.60680i	−0.213874	+	0.201057i
$526$	−33.7232	+	33.7232i	−1.47040	+	1.47040i
$527$			4.82419i			0.210145i
$528$	0.158764			0.00690930
$529$		−	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
$533$	−26.8583	−	27.4167i	−1.16336	−	1.18755i
$534$		−	3.91478i		−	0.169409i
$535$	14.8391	+	0.229117i	0.641548	+	0.00990560i
$536$	11.9738			0.517189
$537$	3.14396	−	3.14396i	0.135672	−	0.135672i
$538$			20.0580i			0.864760i
$539$	4.82600	+	4.82600i	0.207871	+	0.207871i
$540$	15.0441	+	0.232282i	0.647393	+	0.00999584i
$541$	−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	−0.977525	−	0.210818i	$-0.932387\pi$
$547$	−27.7930	−	27.7930i	−1.18834	−	1.18834i	−0.210818	−	0.977525i	$-0.567613\pi$
$548$		−	1.94566i		−	0.0831144i
$549$			10.6418i			0.454181i
$550$	6.64139	−	6.24341i	0.283190	−	0.266220i
$551$	−4.31388	+	4.31388i	−0.183778	+	0.183778i
$552$	4.26745			0.181635
$553$	−35.7492			−1.52021
$554$	1.96424	−	1.96424i	0.0834524	−	0.0834524i
$555$	−5.20080	−	0.0803011i	−0.220762	−	0.00340859i
$556$		−	55.9417i		−	2.37246i
$557$		−	24.9933i		−	1.05900i	−0.848310	−	0.529499i	$-0.822380\pi$
$557$		−	24.9933i		−	1.05900i	0.848310	−	0.529499i	$-0.177620\pi$
$558$	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	0.961819	+	0.273687i	$0.0882433\pi$
$563$	29.3156	+	29.3156i	1.23551	+	1.23551i	0.273687	+	0.961819i	$0.411757\pi$
$564$	−7.35393	−	7.35393i	−0.309656	−	0.309656i
$565$	0.624511	−	40.4472i	0.0262734	−	1.70163i
$566$	17.1446	+	17.1446i	0.720639	+	0.720639i
$567$		−	31.5674i		−	1.32571i
$568$	11.6343	−	11.6343i	0.488166	−	0.488166i
$569$	25.9559			1.08813			0.544063	−	0.839044i	$-0.316885\pi$
$569$	25.9559			1.08813			0.544063	+	0.839044i	$0.316885\pi$
$570$	−2.21624	+	2.14884i	−0.0928281	+	0.0900052i
$571$		−	10.3822i		−	0.434480i	−0.976118	−	0.217240i	$-0.930295\pi$
$571$		−	10.3822i		−	0.434480i	0.976118	−	0.217240i	$-0.0697055\pi$
$572$	−6.82160	+	6.68268i	−0.285226	+	0.279417i
$573$	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
$577$	−12.1813			−0.507112			−0.253556	−	0.967321i	$-0.581600\pi$
$577$	−12.1813			−0.507112			−0.253556	+	0.967321i	$0.581600\pi$
$578$		−	33.1225i		−	1.37772i
$579$	−5.54016	+	5.54016i	−0.230241	+	0.230241i
$580$	−18.2183	−	18.7897i	−0.756472	−	0.780198i
$581$	24.4245			1.01330
$582$	−5.02584	+	5.02584i	−0.208328	+	0.208328i
$583$	−1.06713			−0.0441959
$584$	−17.6301			−0.729541
$585$	−16.8619	+	16.0159i	−0.697156	+	0.662178i
$586$	26.0056			1.07428
$587$	−38.0854			−1.57195			−0.785975	−	0.618258i	$-0.787839\pi$
$587$	−38.0854			−1.57195			−0.785975	+	0.618258i	$0.787839\pi$
$588$	7.01125	−	7.01125i	0.289139	−	0.289139i
$589$	−5.14960			−0.212185
$590$	0.844309	−	54.6827i	0.0347596	−	2.25125i
$591$	0.0599778	−	0.0599778i	0.00246716	−	0.00246716i
$592$		−	4.06378i		−	0.167020i
$593$	5.30739			0.217949			0.108974	−	0.994045i	$-0.465243\pi$
$593$	5.30739			0.217949			0.108974	+	0.994045i	$0.465243\pi$
$594$		−	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
$598$	−23.6954	+	23.2128i	−0.968976	+	0.949242i
$599$		−	0.0345018i		−	0.00140970i	−1.00000		0.000704852i	$-0.999776\pi$
$599$		−	0.0345018i		−	0.00140970i	1.00000		0.000704852i	$-0.000224361\pi$
$600$	−3.67954	−	3.91409i	−0.150217	−	0.159792i
$601$	−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
$603$		−	10.9234i		−	0.444837i
$604$	30.7565	+	30.7565i	1.25146	+	1.25146i
$605$	16.1577	+	16.6645i	0.656904	+	0.677508i
$606$	−1.82818	−	1.82818i	−0.0742647	−	0.0742647i
$607$	0.302520	+	0.302520i	0.0122789	+	0.0122789i	0.713220	−	0.700941i	$-0.247236\pi$
$607$	0.302520	+	0.302520i	0.0122789	+	0.0122789i	−0.700941	+	0.713220i	$0.747236\pi$
$608$	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
$613$			9.77269i			0.394715i	0.980332	+	0.197358i	$0.0632360\pi$
$613$			9.77269i			0.394715i	−0.980332	+	0.197358i	$0.936764\pi$
$614$			65.4528i			2.64146i
$615$	−5.63015	−	5.80673i	−0.227029	−	0.234150i
$616$	−6.96625	+	6.96625i	−0.280678	+	0.280678i
$617$	28.8877			1.16297			0.581487	−	0.813555i	$-0.302471\pi$
$617$	28.8877			1.16297			0.581487	+	0.813555i	$0.302471\pi$
$618$	−4.05636			−0.163171
$619$	−21.1034	+	21.1034i	−0.848216	+	0.848216i	−0.989910	−	0.141695i	$-0.954745\pi$
$619$	−21.1034	+	21.1034i	−0.848216	+	0.848216i	0.141695	+	0.989910i	$0.454745\pi$
$620$	0.341052	−	22.0887i	0.0136970	−	0.887103i
$621$		−	7.94204i		−	0.318703i
$622$		−	22.1304i		−	0.887350i
$623$	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
$630$	−42.4611	+	41.1698i	−1.69169	+	1.64025i
$631$	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	$0.530310\pi$
$632$		−	28.5536i		−	1.13580i
$633$	−2.18763	+	2.18763i	−0.0869504	+	0.0869504i
$634$	−2.11335			−0.0839319
$635$	−0.266020	+	17.2291i	−0.0105567	+	0.683717i
$636$			1.55033i			0.0614746i
$637$	−0.321623	+	31.2636i	−0.0127432	+	1.23871i
$638$	−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	$0.877650\pi$
$642$	−5.22378			−0.206166
$643$			39.2961i			1.54969i	0.632154	+	0.774843i	$0.282171\pi$
$643$			39.2961i			1.54969i	−0.632154	+	0.774843i	$0.717829\pi$
$644$	−37.4138	+	37.4138i	−1.47431	+	1.47431i
$645$	5.42696	−	5.26192i	0.213686	−	0.207188i
$646$	−6.67583			−0.262657
$647$	13.7831	−	13.7831i	0.541869	−	0.541869i	−0.382207	−	0.924077i	$-0.624836\pi$
$647$	13.7831	−	13.7831i	0.541869	−	0.541869i	0.924077	+	0.382207i	$0.124836\pi$
$648$	25.2135			0.990479
$649$	−8.31074			−0.326225
$650$	41.7217	+	1.71844i	1.63646	+	0.0674028i
$651$	3.94928			0.154785
$652$	−13.8489			−0.542364
$653$	−18.6515	+	18.6515i	−0.729890	+	0.729890i	−0.970598	−	0.240707i	$-0.922621\pi$
$653$	−18.6515	+	18.6515i	−0.729890	+	0.729890i	0.240707	+	0.970598i	$0.422621\pi$
$654$	4.58923			0.179453
$655$	−3.88729	+	3.76907i	−0.151889	+	0.147270i
$656$	4.46825	−	4.46825i	0.174456	−	0.174456i
$657$			16.0836i			0.627482i
$658$	83.3984			3.25121
$659$			24.9329i			0.971247i	0.874168	+	0.485623i	$0.161407\pi$
$659$			24.9329i			0.971247i	−0.874168	+	0.485623i	$0.838593\pi$
$660$	−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
$663$	2.01306	+	0.0207092i	0.0781806	+	0.000804279i
$664$			19.5083i			0.757069i
$665$	0.239702	−	15.5246i	0.00929525	−	0.602018i
$666$	−45.7381			−1.77232
$667$	−9.76859	+	9.76859i	−0.378241	+	0.378241i
$668$			17.7524i			0.686861i
$669$	3.42811	+	3.42811i	0.132538	+	0.132538i
$670$	−14.0813	+	13.6531i	−0.544010	+	0.527466i
$671$	−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	$-0.258763\pi$
$673$	−1.00992	−	1.00992i	−0.0389295	−	0.0389295i	−0.726304	+	0.687374i	$0.758763\pi$
$674$	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	0.710067	−	0.704134i	$-0.248665\pi$
$677$	0.154365	+	0.154365i	0.00593272	+	0.00593272i	−0.704134	+	0.710067i	$0.748665\pi$
$678$			14.2386i			0.546829i
$679$		−	35.7492i		−	1.37193i
$680$	0.179356	−	11.6162i	0.00687801	−	0.445462i
$681$	2.97189	−	2.97189i	0.113883	−	0.113883i
$682$	−5.35230			−0.204950
$683$	−19.3092			−0.738847			−0.369424	−	0.929261i	$-0.620445\pi$
$683$	−19.3092			−0.738847			−0.369424	+	0.929261i	$0.620445\pi$
$684$	−12.0390	+	12.0390i	−0.460322	+	0.460322i
$685$	0.899976	+	0.928204i	0.0343863	+	0.0354648i
$686$			15.3261i			0.585153i
$687$		−	3.33447i		−	0.127218i
$688$	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
$695$	25.8761	+	26.6877i	0.981538	+	1.01232i
$696$	2.64245	+	2.64245i	0.100162	+	0.100162i
$697$		−	17.4912i		−	0.662527i
$698$	44.5329	−	44.5329i	1.68559	−	1.68559i
$699$	−1.52596			−0.0577170
$700$	66.5753	+	2.05636i	2.51631	+	0.0777230i
$701$			21.8818i			0.826464i	0.910626	+	0.413232i	$0.135600\pi$
$701$			21.8818i			0.826464i	−0.910626	+	0.413232i	$0.864400\pi$
$702$	11.9290	−	11.6860i	0.450229	−	0.441060i
$703$	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
$707$	13.0040			0.489065
$708$			12.0739i			0.453765i
$709$	18.0869	−	18.0869i	0.679267	−	0.679267i	−0.280568	−	0.959834i	$-0.590523\pi$
$709$	18.0869	−	18.0869i	0.679267	−	0.679267i	0.959834	+	0.280568i	$0.0905227\pi$
$710$	−0.416085	+	26.9482i	−0.0156154	+	1.01135i
$711$	−26.0488			−0.976908
$712$	−11.1206	+	11.1206i	−0.416763	+	0.416763i
$713$	−11.6610			−0.436709
$714$	5.11976			0.191602
$715$	0.163227	−	6.34344i	0.00610435	−	0.237231i
$716$	−44.0317			−1.64554
$717$	5.94841			0.222147
$718$	26.9462	−	26.9462i	1.00563	−	1.00563i
$719$	−26.5866			−0.991512			−0.495756	−	0.868462i	$-0.665109\pi$
$719$	−26.5866			−0.991512			−0.495756	+	0.868462i	$0.665109\pi$
$720$	−2.66534	−	2.74894i	−0.0993313	−	0.102447i
$721$	14.4266	−	14.4266i	0.537274	−	0.537274i
$722$			36.8829i			1.37264i
$723$	−5.91629			−0.220029
$724$			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	$-0.868576\pi$
$727$	−13.8783	+	13.8783i	−0.514719	+	0.514719i	0.401250	+	0.915969i	$0.368576\pi$
$728$	−45.1285	−	0.464257i	−1.67257	−	0.0172065i
$729$		−	20.9634i		−	0.776422i
$730$	20.7333	−	20.1028i	0.767374	−	0.744038i
$731$	16.3473			0.604625
$732$	−2.98293	+	2.98293i	−0.110252	+	0.110252i
$733$			38.2590i			1.41313i	0.707650	+	0.706563i	$0.249756\pi$
$733$			38.2590i			1.41313i	−0.707650	+	0.706563i	$0.750244\pi$
$734$	−2.04108	−	2.04108i	−0.0753376	−	0.0753376i
$735$	−0.101718	+	6.58790i	−0.00375193	+	0.242999i
$736$	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	$0.650450\pi$
$739$	−36.5799	+	36.5799i	−1.34561	+	1.34561i	−0.890364	+	0.455250i	$0.849550\pi$
$740$	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
$743$		−	32.7040i		−	1.19979i	−0.800078	−	0.599896i	$-0.795209\pi$
$743$		−	32.7040i		−	1.19979i	0.800078	−	0.599896i	$-0.204791\pi$
$744$			3.15436i			0.115645i
$745$	3.01507	+	0.0465532i	0.110464	+	0.00170558i
$746$	−19.6560	+	19.6560i	−0.719657	+	0.719657i
$747$	17.7970			0.651159
$748$	−4.35203			−0.159126
$749$	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	$-0.116459\pi$
$752$			5.39922i			0.196889i
$753$	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	0.739397	−	0.673269i	$-0.235111\pi$
$757$	1.81942	+	1.81942i	0.0661281	+	0.0661281i	−0.673269	+	0.739397i	$0.735111\pi$
$758$	−50.7644	−	50.7644i	−1.84385	−	1.84385i
$759$	0.751132	+	0.751132i	0.0272644	+	0.0272644i
$760$	12.3998	+	0.191455i	0.449788	+	0.00694479i
$761$	−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	$0.793798\pi$
$762$		−	6.06515i		−	0.219717i
$763$	−16.3218	+	16.3218i	−0.590888	+	0.590888i
$764$	−13.5271			−0.489393
$765$	−10.5973	−	0.163623i	−0.383144	−	0.00591581i
$766$		−	27.4274i		−	0.990994i
$767$	−26.6423	−	27.1961i	−0.961996	−	0.981995i
$768$	4.71968	−	4.71968i	0.170307	−	0.170307i
$769$	23.5462	+	23.5462i	0.849096	+	0.849096i	0.990020	−	0.140924i	$-0.0450073\pi$
$769$	23.5462	+	23.5462i	0.849096	+	0.849096i	−0.140924	+	0.990020i	$0.545007\pi$
$770$	0.249137	−	16.1357i	0.00897829	−	0.581490i
$771$			7.00440i			0.252257i
$772$	77.5908			2.79255
$773$		−	14.1988i		−	0.510695i	−0.966849	−	0.255348i	$-0.917810\pi$
$773$		−	14.1988i		−	0.510695i	0.966849	−	0.255348i	$-0.0821900\pi$
$774$	47.0013	−	47.0013i	1.68943	−	1.68943i
$775$	10.0545	+	10.6955i	0.361170	+	0.384192i
$776$	28.5536			1.02501
$777$	−6.51143	+	6.51143i	−0.233596	+	0.233596i
$778$	51.1363			1.83333
$779$	18.6711			0.668960
$780$	−9.21579	−	0.237138i	−0.329978	−	0.00849089i
$781$	4.09562			0.146553
$782$	−15.1171			−0.540587
$783$	4.91780	−	4.91780i	0.175748	−	0.175748i
$784$	−5.14762			−0.183844
$785$	−7.76307	−	0.119863i	−0.277076	−	0.00427809i
$786$	1.34763	−	1.34763i	0.0480684	−	0.0480684i
$787$		−	19.0199i		−	0.677987i	−0.940789	−	0.338994i	$-0.889913\pi$
$787$		−	19.0199i		−	0.677987i	0.940789	−	0.338994i	$-0.110087\pi$
$788$	−0.839998			−0.0299237
$789$			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
$793$	0.136834	−	13.3011i	0.00485913	−	0.472336i
$794$			37.3626i			1.32595i
$795$	−0.717115	−	0.739607i	−0.0254334	−	0.0262311i
$796$	59.5166			2.10951
$797$	−36.3558	+	36.3558i	−1.28779	+	1.28779i	−0.351664	+	0.936126i	$0.614384\pi$
$797$	−36.3558	+	36.3558i	−1.28779	+	1.28779i	−0.936126	+	0.351664i	$0.885616\pi$
$798$			5.46511i			0.193463i
$799$	10.5678	+	10.5678i	0.373861	+	0.373861i
$800$	0.763919	−	24.7322i	0.0270086	−	0.874415i
$801$	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
$808$			10.3865i			0.365397i
$809$			40.6511i			1.42922i	0.699524	+	0.714609i	$0.253395\pi$
$809$			40.6511i			1.42922i	−0.699524	+	0.714609i	$0.746605\pi$
$810$	−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	$0.251439\pi$
$812$	−46.3341			−1.62601
$813$	6.80408			0.238629
$814$	8.82467	−	8.82467i	0.309305	−	0.309305i
$815$	6.60680	−	6.40589i	0.231426	−	0.224388i
$816$			0.331454i			0.0116032i
$817$			17.4499i			0.610496i
$818$	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	0.970836	+	0.239745i	$0.0770638\pi$
$823$	34.7291	+	34.7291i	1.21058	+	1.21058i	0.239745	+	0.970836i	$0.422936\pi$
$824$	11.5228	+	11.5228i	0.401415	+	0.401415i
$825$	0.0412841	−	1.33659i	0.00143733	−	0.0465340i
$826$	−68.4630	−	68.4630i	−2.38213	−	2.38213i
$827$			13.4572i			0.467952i	0.972242	+	0.233976i	$0.0751737\pi$
$827$			13.4572i			0.467952i	−0.972242	+	0.233976i	$0.924826\pi$
$828$	−27.2617	+	27.2617i	−0.947411	+	0.947411i
$829$	−26.7217			−0.928082			−0.464041	−	0.885814i	$-0.653601\pi$
$829$	−26.7217			−0.928082			−0.464041	+	0.885814i	$0.653601\pi$
$830$	−22.2444	−	22.9421i	−0.772113	−	0.796330i
$831$		−	0.407515i		−	0.0141365i
$832$	−0.469187	+	45.6078i	−0.0162661	+	1.58116i
$833$	−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
$837$	5.87051			0.202915
$838$			22.0479i			0.761631i
$839$	19.5692	−	19.5692i	0.675605	−	0.675605i	−0.283398	−	0.959002i	$-0.591462\pi$
$839$	19.5692	−	19.5692i	0.675605	−	0.675605i	0.959002	+	0.283398i	$0.0914616\pi$
$840$	−9.50953	−	0.146829i	−0.328110	−	0.00506607i
$841$	16.9024			0.582840
$842$	−47.8814	+	47.8814i	−1.65010	+	1.65010i
$843$	6.31638			0.217548
$844$	30.6381			1.05461
$845$	21.2816	−	19.8014i	0.732108	−	0.681189i
$846$	60.7686			2.08927
$847$	41.0936			1.41199
$848$	0.569123	−	0.569123i	0.0195438	−	0.0195438i
$849$	3.55694			0.122074
$850$	13.0345	+	13.8654i	0.447080	+	0.475578i
$851$	19.2263	−	19.2263i	0.659068	−	0.659068i
$852$		−	5.95015i		−	0.203849i
$853$	−19.6378			−0.672385			−0.336193	−	0.941793i	$-0.609139\pi$
$853$	−19.6378			−0.672385			−0.336193	+	0.941793i	$0.609139\pi$
$854$		−	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	$-0.581904\pi$
$857$	20.8611	−	20.8611i	0.712601	−	0.712601i	0.967079	+	0.254478i	$0.0819036\pi$
$858$	−0.0229763	+	2.23343i	−0.000784397	+	0.0762480i
$859$			41.8545i			1.42806i	0.700116	+	0.714029i	$0.253132\pi$
$859$			41.8545i			1.42806i	−0.700116	+	0.714029i	$0.746868\pi$
$860$	−74.8497	−	1.15569i	−2.55236	−	0.0394087i
$861$	−14.3190			−0.487991
$862$	38.9991	−	38.9991i	1.32831	−	1.32831i
$863$		−	41.0888i		−	1.39868i	−0.714790	−	0.699339i	$-0.753478\pi$
$863$		−	41.0888i		−	1.39868i	0.714790	−	0.699339i	$-0.246522\pi$
$864$	−6.99713	−	6.99713i	−0.238047	−	0.238047i
$865$	10.8183	+	0.167036i	0.367832	+	0.00567938i
$866$	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
$873$		−	26.0488i		−	0.881620i
$874$		−	16.1368i		−	0.545836i
$875$	−32.7119	+	29.8138i	−1.10586	+	1.00789i
$876$	−4.50829	+	4.50829i	−0.152321	+	0.152321i
$877$	−56.0870			−1.89392			−0.946961	−	0.321348i	$-0.895864\pi$
$877$	−56.0870			−1.89392			−0.946961	+	0.321348i	$0.895864\pi$
$878$	75.9699			2.56386
$879$	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	$0.661962\pi$
$882$			57.9369i			1.95084i
$883$	−24.3974	−	24.3974i	−0.821038	−	0.821038i	0.165219	−	0.986257i	$-0.447167\pi$
$883$	−24.3974	−	24.3974i	−0.821038	−	0.821038i	−0.986257	+	0.165219i	$0.947167\pi$
$884$	−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	0.319764	−	0.947497i	$-0.396396\pi$
$887$	−18.6955	−	18.6955i	−0.627733	−	0.627733i	−0.947497	+	0.319764i	$0.896396\pi$
$888$	−5.20080	−	5.20080i	−0.174527	−	0.174527i
$889$	21.5710	+	21.5710i	0.723467	+	0.723467i
$890$	0.397712	−	25.7583i	0.0133313	−	0.863420i
$891$	4.43794	+	4.43794i	0.148677	+	0.148677i
$892$		−	48.0112i		−	1.60753i
$893$	−11.2806	+	11.2806i	−0.377491	+	0.377491i
$894$	−1.06139			−0.0354983
$895$	21.0059	−	20.3671i	0.702150	−	0.680797i
$896$			76.8115i			2.56609i
$897$	−0.0500583	+	4.86596i	−0.00167140	+	0.162470i
$898$	−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
$902$	19.4060			0.646149
$903$		−	13.3825i		−	0.445343i
$904$	40.4472	−	40.4472i	1.34525	−	1.34525i
$905$	−7.23846	−	7.46550i	−0.240615	−	0.248161i
$906$	10.1734			0.337989
$907$	9.50332	−	9.50332i	0.315553	−	0.315553i	−0.531503	−	0.847056i	$-0.678373\pi$
$907$	9.50332	−	9.50332i	0.315553	−	0.315553i	0.847056	+	0.531503i	$0.178373\pi$
$908$	−41.6218			−1.38127
$909$	9.47541			0.314280
$910$	53.6012	−	50.9119i	1.77686	−	1.68771i
$911$	−29.9373			−0.991866			−0.495933	−	0.868361i	$-0.665174\pi$
$911$	−29.9373			−0.991866			−0.495933	+	0.868361i	$0.665174\pi$
$912$	−0.353812			−0.0117159
$913$	−3.43374	+	3.43374i	−0.113640	+	0.113640i
$914$	7.32820			0.242395
$915$	0.0432760	−	2.80282i	0.00143066	−	0.0926584i
$916$	−23.3499	+	23.3499i	−0.771503	+	0.771503i
$917$			9.58580i			0.316551i
$918$	7.61041			0.251181
$919$		−	37.1394i		−	1.22512i	−0.790425	−	0.612558i	$-0.790140\pi$
$919$		−	37.1394i		−	1.22512i	0.790425	−	0.612558i	$-0.209860\pi$
$920$	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
$923$	13.1296	+	13.4025i	0.432166	+	0.441150i
$924$			3.56275i			0.117206i
$925$	−34.2119	−	1.05672i	−1.12488	−	0.0347449i
$926$	10.8413			0.356267
$927$	10.5120	−	10.5120i	0.345259	−	0.345259i
$928$			17.2127i			0.565036i
$929$	−40.4571	−	40.4571i	−1.32735	−	1.32735i	−0.907670	−	0.419685i	$-0.862141\pi$
$929$	−40.4571	−	40.4571i	−1.32735	−	1.32735i	−0.419685	−	0.907670i	$-0.637859\pi$
$930$	−3.59677	−	3.70958i	−0.117943	−	0.121642i
$931$	−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	0.950945	−	0.309360i	$-0.100115\pi$
$937$	19.6392	+	19.6392i	0.641585	+	0.641585i	−0.309360	+	0.950945i	$0.600115\pi$
$938$			34.7237i			1.13377i
$939$			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	$0.958891\pi$
$942$	2.73282			0.0890402
$943$	42.2798			1.37682
$944$	4.43230	−	4.43230i	0.144259	−	0.144259i
$945$	−0.273259	+	17.6980i	−0.00888912	+	0.575715i
$946$			18.1368i			0.589679i
$947$			52.1483i			1.69459i	0.531122	+	0.847295i	$0.321771\pi$
$947$			52.1483i			1.69459i	−0.531122	+	0.847295i	$0.678229\pi$
$948$	−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	$-0.174325\pi$
$953$	10.2817	+	10.2817i	0.333058	+	0.333058i	−0.520689	+	0.853747i	$0.674325\pi$
$954$	−6.40552	−	6.40552i	−0.207386	−	0.207386i
$955$	6.45329	−	6.25704i	0.208824	−	0.202473i
$956$	−41.6542	−	41.6542i	−1.34719	−	1.34719i
$957$			0.930219i			0.0300697i
$958$	−41.8045	+	41.8045i	−1.35064	+	1.35064i
$959$	2.28889			0.0739121
$960$	−0.148388	+	9.61051i	−0.00478919	+	0.310178i
$961$			22.3805i			0.721952i
$962$	57.1677	+	0.588110i	1.84316	+	0.0189614i
$963$	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
$967$	37.4312			1.20371			0.601854	−	0.798606i	$-0.294429\pi$
$967$	37.4312			1.20371			0.601854	+	0.798606i	$0.294429\pi$
$968$			32.8222i			1.05495i
$969$	−0.692509	+	0.692509i	−0.0222466	+	0.0222466i
$970$	−33.5794	+	32.5583i	−1.07817	+	1.04538i
$971$	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
$973$	65.8103			2.10978
$974$	−2.26574			−0.0725990
$975$	4.50621	−	4.14969i	0.144314	−	0.132896i
$976$	2.19005			0.0701019
$977$	39.9972			1.27963			0.639813	−	0.768531i	$-0.279012\pi$
$977$	39.9972			1.27963			0.639813	+	0.768531i	$0.279012\pi$
$978$	−2.29042	+	2.29042i	−0.0732396	+	0.0732396i
$979$	−3.91478			−0.125117
$980$	46.8446	−	45.4200i	1.49640	−	1.45089i
$981$	−11.8929	+	11.8929i	−0.379712	+	0.379712i
$982$			44.5576i			1.42189i
$983$	16.8519			0.537492			0.268746	−	0.963211i	$-0.413391\pi$
$983$	16.8519			0.537492			0.268746	+	0.963211i	$0.413391\pi$
$984$		−	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
$988$	15.2022	−	14.8926i	0.483648	−	0.473798i
$989$			39.5146i			1.25649i
$990$	0.181535	−	11.7573i	0.00576956	−	0.373673i
$991$	−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
$993$		−	7.33246i		−	0.232689i
$994$	33.7393	+	33.7393i	1.07015	+	1.07015i
$995$	−28.3932	+	27.5298i	−0.900125	+	0.872752i
$996$	4.98857	+	4.98857i	0.158069	+	0.158069i
$997$	14.2932	+	14.2932i	0.452670	+	0.452670i	0.896240	−	0.443570i	$-0.146288\pi$
$997$	14.2932	+	14.2932i	0.452670	+	0.452670i	−0.443570	+	0.896240i	$0.646288\pi$
$998$	−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.k.b.57.1	yes	8
3.2	odd	2		585.2.w.e.577.4		8
4.3	odd	2		1040.2.bg.n.577.2		8
5.2	odd	4		325.2.f.b.18.1		8
5.3	odd	4		65.2.f.b.18.4	✓	8
5.4	even	2		325.2.k.b.57.4		8
13.2	odd	12		845.2.t.d.657.1		16
13.3	even	3		845.2.o.d.357.4		16
13.4	even	6		845.2.o.c.587.1		16
13.5	odd	4		845.2.f.b.437.4		8
13.6	odd	12		845.2.t.d.427.4		16
13.7	odd	12		845.2.t.c.427.1		16
13.8	odd	4		65.2.f.b.47.1	yes	8
13.9	even	3		845.2.o.d.587.4		16
13.10	even	6		845.2.o.c.357.1		16
13.11	odd	12		845.2.t.c.657.4		16
13.12	even	2		845.2.k.b.577.4		8
15.8	even	4		585.2.n.e.343.1		8
20.3	even	4		1040.2.cd.n.993.2		8
39.8	even	4		585.2.n.e.307.4		8
52.47	even	4		1040.2.cd.n.177.2		8
65.3	odd	12		845.2.t.c.188.1		16
65.8	even	4	inner	65.2.k.b.8.1	yes	8
65.18	even	4		845.2.k.b.268.4		8
65.23	odd	12		845.2.t.d.188.4		16
65.28	even	12		845.2.o.c.488.1		16
65.33	even	12		845.2.o.d.258.4		16
65.34	odd	4		325.2.f.b.307.4		8
65.38	odd	4		845.2.f.b.408.1		8
65.43	odd	12		845.2.t.d.418.1		16
65.47	even	4		325.2.k.b.268.4		8
65.48	odd	12		845.2.t.c.418.4		16
65.58	even	12		845.2.o.c.258.1		16
65.63	even	12		845.2.o.d.488.4		16
195.8	odd	4		585.2.w.e.73.4		8
260.203	odd	4		1040.2.bg.n.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.4	✓	8	5.3	odd	4
65.2.f.b.47.1	yes	8	13.8	odd	4
65.2.k.b.8.1	yes	8	65.8	even	4	inner
65.2.k.b.57.1	yes	8	1.1	even	1	trivial
325.2.f.b.18.1		8	5.2	odd	4
325.2.f.b.307.4		8	65.34	odd	4
325.2.k.b.57.4		8	5.4	even	2
325.2.k.b.268.4		8	65.47	even	4
585.2.n.e.307.4		8	39.8	even	4
585.2.n.e.343.1		8	15.8	even	4
585.2.w.e.73.4		8	195.8	odd	4
585.2.w.e.577.4		8	3.2	odd	2
845.2.f.b.408.1		8	65.38	odd	4
845.2.f.b.437.4		8	13.5	odd	4
845.2.k.b.268.4		8	65.18	even	4
845.2.k.b.577.4		8	13.12	even	2
845.2.o.c.258.1		16	65.58	even	12
845.2.o.c.357.1		16	13.10	even	6
845.2.o.c.488.1		16	65.28	even	12
845.2.o.c.587.1		16	13.4	even	6
845.2.o.d.258.4		16	65.33	even	12
845.2.o.d.357.4		16	13.3	even	3
845.2.o.d.488.4		16	65.63	even	12
845.2.o.d.587.4		16	13.9	even	3
845.2.t.c.188.1		16	65.3	odd	12
845.2.t.c.418.4		16	65.48	odd	12
845.2.t.c.427.1		16	13.7	odd	12
845.2.t.c.657.4		16	13.11	odd	12
845.2.t.d.188.4		16	65.23	odd	12
845.2.t.d.418.1		16	65.43	odd	12
845.2.t.d.427.4		16	13.6	odd	12
845.2.t.d.657.1		16	13.2	odd	12
1040.2.bg.n.577.2		8	4.3	odd	2
1040.2.bg.n.593.2		8	260.203	odd	4
1040.2.cd.n.177.2		8	52.47	even	4
1040.2.cd.n.993.2		8	20.3	even	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.31627 q^{2} +(-0.240275 + 0.240275i) q^{3} +3.36509 q^{4} +(-1.60536 + 1.55654i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872i q^{7} -3.16190 q^{8} +2.88454i q^{9} +O(q^{10})\)	\(q-2.31627 q^{2} +(-0.240275 + 0.240275i) q^{3} +3.36509 q^{4} +(-1.60536 + 1.55654i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872i q^{7} -3.16190 q^{8} +2.88454i q^{9} +(3.71844 - 3.60536i) q^{10} +(-0.556540 - 0.556540i) q^{11} +(-0.808545 + 0.808545i) q^{12} +(0.0370899 - 3.60536i) q^{13} -9.16944i q^{14} +(0.0117303 - 0.759725i) q^{15} +0.593630 q^{16} +(1.16190 - 1.16190i) q^{17} -6.68135i q^{18} +(1.24027 + 1.24027i) q^{19} +(-5.40218 + 5.23789i) 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} +13.3214i q^{28} +3.47817i q^{29} +(-0.0271704 + 1.75973i) q^{30} +(-2.07599 + 2.07599i) q^{31} +4.94880 q^{32} +0.267445 q^{33} +(-2.69127 + 2.69127i) q^{34} +(-6.16190 - 6.35517i) q^{35} +9.70671i q^{36} -6.84564i 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} +(-4.48990 - 4.63072i) q^{45} +(-6.50534 - 6.50534i) q^{46} +9.09526i q^{47} +(-0.142634 + 0.142634i) q^{48} -8.67143 q^{49} +(-0.357550 + 11.5758i) q^{50} +0.558351i q^{51} +(0.124811 - 12.1323i) q^{52} +(0.958716 - 0.958716i) q^{53} +(3.27498 + 3.27498i) q^{54} +(1.75973 + 0.0271704i) q^{55} -12.5171i q^{56} -0.596014 q^{57} -8.05636i q^{58} +(7.46644 - 7.46644i) q^{59} +(0.0394734 - 2.55654i) q^{60} +3.68926 q^{61} +(4.80855 - 4.80855i) q^{62} -11.4191 q^{63} -12.6500 q^{64} +(5.55235 + 5.84564i) q^{65} -0.619474 q^{66} -3.78690 q^{67} +(3.90990 - 3.90990i) q^{68} -1.34965 q^{69} +(14.2726 + 14.7203i) q^{70} +(-3.67954 + 3.67954i) q^{71} -9.12062i q^{72} +5.57581 q^{73} +15.8563i q^{74} +(1.16371 + 1.23789i) q^{75} +(4.17363 + 4.17363i) q^{76} +(2.20318 - 2.20318i) q^{77} +(-1.98589 - 2.02717i) q^{78} +9.03051i q^{79} +(-0.952991 + 0.924009i) q^{80} -7.97416 q^{81} +(-17.4345 + 17.4345i) q^{82} -6.16980i q^{83} +(-3.20080 - 3.20080i) q^{84} +(-0.0567242 + 3.67382i) 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} -0.997617i q^{93} -21.0670i q^{94} +(-3.92163 - 0.0605505i) q^{95} +(-1.18907 + 1.18907i) q^{96} -9.03051 q^{97} +20.0853 q^{98} +(1.60536 - 1.60536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6	\( 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 8 q^{16} - 16 q^{17} + 14 q^{19} - 22 q^{20} - 12 q^{21} + 10 q^{22} + 14 q^{23} + 2 q^{24} + 12 q^{25} + 6 q^{26} + 12 q^{27} + 14 q^{30} + 2 q^{31} - 4 q^{32} - 8 q^{33} - 24 q^{35} + 2 q^{38} - 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} + 6 q^{43} + 10 q^{44} + 6 q^{45} + 2 q^{46} - 14 q^{48} - 24 q^{49} - 20 q^{50} - 22 q^{52} - 24 q^{53} - 20 q^{54} + 10 q^{55} - 40 q^{57} + 22 q^{59} + 46 q^{60} + 20 q^{61} + 30 q^{62} + 16 q^{63} - 48 q^{64} - 36 q^{66} - 12 q^{67} + 4 q^{68} - 4 q^{69} + 20 q^{70} - 10 q^{71} - 4 q^{73} - 30 q^{75} + 6 q^{76} + 24 q^{77} + 30 q^{78} + 2 q^{80} - 20 q^{81} - 20 q^{82} + 16 q^{84} - 20 q^{85} - 46 q^{86} + 16 q^{87} + 10 q^{88} - 28 q^{89} + 14 q^{90} + 20 q^{91} + 50 q^{92} - 2 q^{95} + 30 q^{96} + 12 q^{97} + 92 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 8 * q^16 - 16 * q^17 + 14 * q^19 - 22 * q^20 - 12 * q^21 + 10 * q^22 + 14 * q^23 + 2 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 14 * q^30 + 2 * q^31 - 4 * q^32 - 8 * q^33 - 24 * q^35 + 2 * q^38 - 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 + 6 * q^43 + 10 * q^44 + 6 * q^45 + 2 * q^46 - 14 * q^48 - 24 * q^49 - 20 * q^50 - 22 * q^52 - 24 * q^53 - 20 * q^54 + 10 * q^55 - 40 * q^57 + 22 * q^59 + 46 * q^60 + 20 * q^61 + 30 * q^62 + 16 * q^63 - 48 * q^64 - 36 * q^66 - 12 * q^67 + 4 * q^68 - 4 * q^69 + 20 * q^70 - 10 * q^71 - 4 * q^73 - 30 * q^75 + 6 * q^76 + 24 * q^77 + 30 * q^78 + 2 * q^80 - 20 * q^81 - 20 * q^82 + 16 * q^84 - 20 * q^85 - 46 * q^86 + 16 * q^87 + 10 * q^88 - 28 * q^89 + 14 * q^90 + 20 * q^91 + 50 * q^92 - 2 * q^95 + 30 * q^96 + 12 * q^97 + 92 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more