LMFDB - Embedded newform 273.2.cg.a.115.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.5
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.511829 + 0.137144i) q^{2} +1.00000i q^{3} +(-1.48889 + 0.859611i) q^{4} +(-2.03763 - 0.545981i) q^{5} +(-0.137144 - 0.511829i) q^{6} +(0.917679 - 2.48150i) q^{7} +(1.39354 - 1.39354i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.511829 + 0.137144i) q^{2} +1.00000i q^{3} +(-1.48889 + 0.859611i) q^{4} +(-2.03763 - 0.545981i) q^{5} +(-0.137144 - 0.511829i) q^{6} +(0.917679 - 2.48150i) q^{7} +(1.39354 - 1.39354i) q^{8} -1.00000 q^{9} +1.11780 q^{10} +(-2.03793 + 2.03793i) q^{11} +(-0.859611 - 1.48889i) q^{12} +(-2.80107 - 2.27024i) q^{13} +(-0.129371 + 1.39596i) q^{14} +(0.545981 - 2.03763i) q^{15} +(1.19709 - 2.07341i) q^{16} +(-1.64880 - 2.85581i) q^{17} +(0.511829 - 0.137144i) q^{18} +(4.78288 - 4.78288i) q^{19} +(3.50314 - 0.938663i) q^{20} +(2.48150 + 0.917679i) q^{21} +(0.763581 - 1.32256i) q^{22} +(-6.79410 - 3.92258i) q^{23} +(1.39354 + 1.39354i) q^{24} +(-0.476290 - 0.274986i) q^{25} +(1.74502 + 0.777826i) q^{26} -1.00000i q^{27} +(0.766806 + 4.48354i) q^{28} +(0.677462 + 1.17340i) q^{29} +1.11780i q^{30} +(1.71085 + 6.38499i) q^{31} +(-1.34849 + 5.03262i) q^{32} +(-2.03793 - 2.03793i) q^{33} +(1.23556 + 1.23556i) q^{34} +(-3.22474 + 4.55535i) q^{35} +(1.48889 - 0.859611i) q^{36} +(1.05363 + 3.93218i) q^{37} +(-1.79207 + 3.10396i) q^{38} +(2.27024 - 2.80107i) q^{39} +(-3.60036 + 2.07867i) q^{40} +(-6.61712 - 1.77305i) q^{41} +(-1.39596 - 0.129371i) q^{42} +(-4.36301 - 2.51899i) q^{43} +(1.28243 - 4.78608i) q^{44} +(2.03763 + 0.545981i) q^{45} +(4.01538 + 1.07592i) q^{46} +(-0.947124 + 3.53471i) q^{47} +(2.07341 + 1.19709i) q^{48} +(-5.31573 - 4.55445i) q^{49} +(0.281492 + 0.0754255i) q^{50} +(2.85581 - 1.64880i) q^{51} +(6.12201 + 0.972311i) q^{52} +(-3.87961 + 6.71968i) q^{53} +(0.137144 + 0.511829i) q^{54} +(5.26521 - 3.03987i) q^{55} +(-2.17925 - 4.73689i) q^{56} +(4.78288 + 4.78288i) q^{57} +(-0.507670 - 0.507670i) q^{58} +(0.737061 - 2.75075i) q^{59} +(0.938663 + 3.50314i) q^{60} +3.63687i q^{61} +(-1.75133 - 3.03339i) q^{62} +(-0.917679 + 2.48150i) q^{63} +2.02756i q^{64} +(4.46803 + 6.15525i) q^{65} +(1.32256 + 0.763581i) q^{66} +(-1.33686 - 1.33686i) q^{67} +(4.90977 + 2.83466i) q^{68} +(3.92258 - 6.79410i) q^{69} +(1.02578 - 2.77382i) q^{70} +(-9.87427 + 2.64580i) q^{71} +(-1.39354 + 1.39354i) q^{72} +(6.80337 - 1.82296i) q^{73} +(-1.07855 - 1.86811i) q^{74} +(0.274986 - 0.476290i) q^{75} +(-3.00977 + 11.2326i) q^{76} +(3.18696 + 6.92729i) q^{77} +(-0.777826 + 1.74502i) q^{78} +(-1.13108 - 1.95909i) q^{79} +(-3.57126 + 3.57126i) q^{80} +1.00000 q^{81} +3.63000 q^{82} +(3.97225 - 3.97225i) q^{83} +(-4.48354 + 0.766806i) q^{84} +(1.80043 + 6.71929i) q^{85} +(2.57858 + 0.690929i) q^{86} +(-1.17340 + 0.677462i) q^{87} +5.67985i q^{88} +(11.9316 - 3.19707i) q^{89} -1.11780 q^{90} +(-8.20410 + 4.86751i) q^{91} +13.4876 q^{92} +(-6.38499 + 1.71085i) q^{93} -1.93906i q^{94} +(-12.3571 + 7.13438i) q^{95} +(-5.03262 - 1.34849i) q^{96} +(-3.94107 - 14.7083i) q^{97} +(3.34536 + 1.60208i) q^{98} +(2.03793 - 2.03793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.511829	+	0.137144i	−0.361918	+	0.0969756i	−0.435196	−	0.900336i	$-0.643321\pi$
$2$	−0.511829	+	0.137144i	−0.361918	+	0.0969756i	0.0732776	+	0.997312i	$0.476654\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.48889	+	0.859611i	−0.744445	+	0.429806i
$5$	−2.03763	−	0.545981i	−0.911255	−	0.244170i	−0.227412	−	0.973799i	$-0.573026\pi$
$5$	−2.03763	−	0.545981i	−0.911255	−	0.244170i	−0.683844	+	0.729629i	$0.739693\pi$
$6$	−0.137144	−	0.511829i	−0.0559889	−	0.208953i
$7$	0.917679	−	2.48150i	0.346850	−	0.937921i
$7$	0.917679	−	2.48150i	0.346850	−	0.937921i
$8$	1.39354	−	1.39354i	0.492690	−	0.492690i
$9$	−1.00000			−0.333333
$10$	1.11780			0.353478
$11$	−2.03793	+	2.03793i	−0.614458	+	0.614458i	−0.944105	−	0.329646i	$-0.893071\pi$
$11$	−2.03793	+	2.03793i	−0.614458	+	0.614458i	0.329646	+	0.944105i	$0.393071\pi$
$12$	−0.859611	−	1.48889i	−0.248148	−	0.429806i
$13$	−2.80107	−	2.27024i	−0.776877	−	0.629652i
$13$	−2.80107	−	2.27024i	−0.776877	−	0.629652i
$14$	−0.129371	+	1.39596i	−0.0345758	+	0.373086i
$15$	0.545981	−	2.03763i	0.140972	−	0.526114i
$16$	1.19709	−	2.07341i	0.299271	−	0.518353i
$17$	−1.64880	−	2.85581i	−0.399893	−	0.692635i	0.593819	−	0.804599i	$-0.297619\pi$
$17$	−1.64880	−	2.85581i	−0.399893	−	0.692635i	−0.993712	+	0.111963i	$0.964286\pi$
$18$	0.511829	−	0.137144i	0.120639	−	0.0323252i
$19$	4.78288	−	4.78288i	1.09727	−	1.09727i	0.102539	−	0.994729i	$-0.467303\pi$
$19$	4.78288	−	4.78288i	1.09727	−	1.09727i	0.994729	−	0.102539i	$-0.0326968\pi$
$20$	3.50314	−	0.938663i	0.783325	−	0.209891i
$21$	2.48150	+	0.917679i	0.541509	+	0.200254i
$22$	0.763581	−	1.32256i	0.162796	−	0.281971i
$23$	−6.79410	−	3.92258i	−1.41667	−	0.817914i	−0.420664	−	0.907217i	$-0.638203\pi$
$23$	−6.79410	−	3.92258i	−1.41667	−	0.817914i	−0.996005	+	0.0893026i	$0.971536\pi$
$24$	1.39354	+	1.39354i	0.284454	+	0.284454i
$25$	−0.476290	−	0.274986i	−0.0952579	−	0.0549972i
$26$	1.74502	+	0.777826i	0.342227	+	0.152544i
$27$		−	1.00000i		−	0.192450i
$28$	0.766806	+	4.48354i	0.144913	+	0.847308i
$29$	0.677462	+	1.17340i	0.125802	+	0.217895i	0.922046	−	0.387080i	$-0.126516\pi$
$29$	0.677462	+	1.17340i	0.125802	+	0.217895i	−0.796244	+	0.604975i	$0.793183\pi$
$30$			1.11780i			0.204081i
$31$	1.71085	+	6.38499i	0.307278	+	1.14678i	0.930966	+	0.365105i	$0.118967\pi$
$31$	1.71085	+	6.38499i	0.307278	+	1.14678i	−0.623688	+	0.781673i	$0.714366\pi$
$32$	−1.34849	+	5.03262i	−0.238381	+	0.889650i
$33$	−2.03793	−	2.03793i	−0.354758	−	0.354758i
$34$	1.23556	+	1.23556i	0.211897	+	0.211897i
$35$	−3.22474	+	4.55535i	−0.545081	+	0.769995i
$36$	1.48889	−	0.859611i	0.248148	−	0.143269i
$37$	1.05363	+	3.93218i	0.173215	+	0.646447i	0.996849	+	0.0793250i	$0.0252765\pi$
$37$	1.05363	+	3.93218i	0.173215	+	0.646447i	−0.823634	+	0.567122i	$0.808057\pi$
$38$	−1.79207	+	3.10396i	−0.290713	+	0.503529i
$39$	2.27024	−	2.80107i	0.363530	−	0.448530i
$40$	−3.60036	+	2.07867i	−0.569266	+	0.328666i
$41$	−6.61712	−	1.77305i	−1.03342	−	0.276904i	−0.298036	−	0.954555i	$-0.596332\pi$
$41$	−6.61712	−	1.77305i	−1.03342	−	0.276904i	−0.735384	+	0.677651i	$0.762998\pi$
$42$	−1.39596	−	0.129371i	−0.215401	−	0.0199624i
$43$	−4.36301	−	2.51899i	−0.665353	−	0.384142i	0.128961	−	0.991650i	$-0.458836\pi$
$43$	−4.36301	−	2.51899i	−0.665353	−	0.384142i	−0.794314	+	0.607508i	$0.792169\pi$
$44$	1.28243	−	4.78608i	0.193333	−	0.721528i
$45$	2.03763	+	0.545981i	0.303752	+	0.0813901i
$46$	4.01538	+	1.07592i	0.592035	+	0.158635i
$47$	−0.947124	+	3.53471i	−0.138152	+	0.515591i	0.861813	+	0.507226i	$0.169329\pi$
$47$	−0.947124	+	3.53471i	−0.138152	+	0.515591i	−0.999965	+	0.00836456i	$0.997337\pi$
$48$	2.07341	+	1.19709i	0.299271	+	0.172784i
$49$	−5.31573	−	4.55445i	−0.759390	−	0.650636i
$50$	0.281492	+	0.0754255i	0.0398089	+	0.0106668i
$51$	2.85581	−	1.64880i	0.399893	−	0.230878i
$52$	6.12201	+	0.972311i	0.848970	+	0.134835i
$53$	−3.87961	+	6.71968i	−0.532905	+	0.923019i	0.466356	+	0.884597i	$0.345567\pi$
$53$	−3.87961	+	6.71968i	−0.532905	+	0.923019i	−0.999262	+	0.0384223i	$0.987767\pi$
$54$	0.137144	+	0.511829i	0.0186630	+	0.0696511i
$55$	5.26521	−	3.03987i	0.709961	−	0.409896i
$56$	−2.17925	−	4.73689i	−0.291214	−	0.632993i
$57$	4.78288	+	4.78288i	0.633508	+	0.633508i
$58$	−0.507670	−	0.507670i	−0.0666603	−	0.0666603i
$59$	0.737061	−	2.75075i	0.0959571	−	0.358117i	−0.901206	−	0.433392i	$-0.857317\pi$
$59$	0.737061	−	2.75075i	0.0959571	−	0.358117i	0.997163	+	0.0752747i	$0.0239834\pi$
$60$	0.938663	+	3.50314i	0.121181	+	0.452253i
$61$			3.63687i			0.465653i	0.972518	+	0.232827i	$0.0747975\pi$
$61$			3.63687i			0.465653i	−0.972518	+	0.232827i	$0.925203\pi$
$62$	−1.75133	−	3.03339i	−0.222419	−	0.385241i
$63$	−0.917679	+	2.48150i	−0.115617	+	0.312640i
$64$			2.02756i			0.253445i
$65$	4.46803	+	6.15525i	0.554191	+	0.763464i
$66$	1.32256	+	0.763581i	0.162796	+	0.0939903i
$67$	−1.33686	−	1.33686i	−0.163324	−	0.163324i	0.620714	−	0.784037i	$-0.286843\pi$
$67$	−1.33686	−	1.33686i	−0.163324	−	0.163324i	−0.784037	+	0.620714i	$0.786843\pi$
$68$	4.90977	+	2.83466i	0.595397	+	0.343753i
$69$	3.92258	−	6.79410i	0.472223	−	0.817914i
$70$	1.02578	−	2.77382i	0.122604	−	0.331534i
$71$	−9.87427	+	2.64580i	−1.17186	+	0.313999i	−0.791693	−	0.610919i	$-0.790800\pi$
$71$	−9.87427	+	2.64580i	−1.17186	+	0.313999i	−0.380167	+	0.924918i	$0.624134\pi$
$72$	−1.39354	+	1.39354i	−0.164230	+	0.164230i
$73$	6.80337	−	1.82296i	0.796274	−	0.213361i	0.162326	−	0.986737i	$-0.448100\pi$
$73$	6.80337	−	1.82296i	0.796274	−	0.213361i	0.633947	+	0.773376i	$0.281434\pi$
$74$	−1.07855	−	1.86811i	−0.125379	−	0.217163i
$75$	0.274986	−	0.476290i	0.0317526	−	0.0549972i
$76$	−3.00977	+	11.2326i	−0.345244	+	1.28847i
$77$	3.18696	+	6.92729i	0.363188	+	0.789438i
$78$	−0.777826	+	1.74502i	−0.0880715	+	0.197585i
$79$	−1.13108	−	1.95909i	−0.127256	−	0.220414i	0.795356	−	0.606142i	$-0.207284\pi$
$79$	−1.13108	−	1.95909i	−0.127256	−	0.220414i	−0.922613	+	0.385728i	$0.873950\pi$
$80$	−3.57126	+	3.57126i	−0.399279	+	0.399279i
$81$	1.00000			0.111111
$82$	3.63000			0.400866
$83$	3.97225	−	3.97225i	0.436011	−	0.436011i	−0.454656	−	0.890667i	$-0.650238\pi$
$83$	3.97225	−	3.97225i	0.436011	−	0.436011i	0.890667	+	0.454656i	$0.150238\pi$
$84$	−4.48354	+	0.766806i	−0.489194	+	0.0836654i
$85$	1.80043	+	6.71929i	0.195284	+	0.728810i
$86$	2.57858	+	0.690929i	0.278056	+	0.0745048i
$87$	−1.17340	+	0.677462i	−0.125802	+	0.0726316i
$88$			5.67985i			0.605475i
$89$	11.9316	−	3.19707i	1.26475	−	0.338889i	0.436732	−	0.899591i	$-0.356136\pi$
$89$	11.9316	−	3.19707i	1.26475	−	0.338889i	0.828017	+	0.560703i	$0.189469\pi$
$90$	−1.11780			−0.117826
$91$	−8.20410	+	4.86751i	−0.860024	+	0.510254i
$92$	13.4876			1.40618
$93$	−6.38499	+	1.71085i	−0.662093	+	0.177407i
$94$		−	1.93906i		−	0.199999i
$95$	−12.3571	+	7.13438i	−1.26781	+	0.731972i
$96$	−5.03262	−	1.34849i	−0.513640	−	0.137629i
$97$	−3.94107	−	14.7083i	−0.400155	−	1.49340i	−0.812819	−	0.582516i	$-0.802068\pi$
$97$	−3.94107	−	14.7083i	−0.400155	−	1.49340i	0.412664	−	0.910883i	$-0.364598\pi$
$98$	3.34536	+	1.60208i	0.337933	+	0.161834i
$99$	2.03793	−	2.03793i	0.204819	−	0.204819i
$100$	0.945524			0.0945524
$101$	8.37472			0.833316			0.416658	−	0.909063i	$-0.363201\pi$
$101$	8.37472			0.833316			0.416658	+	0.909063i	$0.363201\pi$
$102$	−1.23556	+	1.23556i	−0.122339	+	0.122339i
$103$	−3.94643	−	6.83541i	−0.388853	−	0.673513i	0.603442	−	0.797407i	$-0.293795\pi$
$103$	−3.94643	−	6.83541i	−0.388853	−	0.673513i	−0.992296	+	0.123893i	$0.960462\pi$
$104$	−7.06706	+	0.739728i	−0.692982	+	0.0725363i
$105$	−4.55535	−	3.22474i	−0.444557	−	0.314703i
$106$	1.06413	−	3.97140i	0.103358	−	0.385736i
$107$	10.0079	−	17.3341i	0.967497	−	1.67575i	0.264746	−	0.964318i	$-0.414712\pi$
$107$	10.0079	−	17.3341i	0.967497	−	1.67575i	0.702751	−	0.711436i	$-0.251955\pi$
$108$	0.859611	+	1.48889i	0.0827161	+	0.143269i
$109$	6.75874	−	1.81100i	0.647370	−	0.173462i	0.0798304	−	0.996808i	$-0.474562\pi$
$109$	6.75874	−	1.81100i	0.647370	−	0.173462i	0.567539	+	0.823346i	$0.307895\pi$
$110$	−2.27799	+	2.27799i	−0.217198	+	0.217198i
$111$	−3.93218	+	1.05363i	−0.373226	+	0.100006i
$112$	−4.04664	−	4.87330i	−0.382372	−	0.460483i
$113$	2.05899	−	3.56627i	0.193693	−	0.335486i	−0.752778	−	0.658274i	$-0.771287\pi$
$113$	2.05899	−	3.56627i	0.193693	−	0.335486i	0.946471	+	0.322788i	$0.104620\pi$
$114$	−3.10396	−	1.79207i	−0.290713	−	0.167843i
$115$	11.7022	+	11.7022i	1.09124	+	1.09124i
$116$	−2.01733	−	1.16471i	−0.187305	−	0.108140i
$117$	2.80107	+	2.27024i	0.258959	+	0.209884i
$118$			1.50900i			0.138914i
$119$	−8.59977	+	1.47079i	−0.788340	+	0.134827i
$120$	−2.07867	−	3.60036i	−0.189755	−	0.328666i
$121$			2.69370i			0.244882i
$122$	−0.498775	−	1.86145i	−0.0451570	−	0.168528i
$123$	1.77305	−	6.61712i	0.159871	−	0.596645i
$124$	−8.03588	−	8.03588i	−0.721643	−	0.721643i
$125$	8.27861	+	8.27861i	0.740461	+	0.740461i
$126$	0.129371	−	1.39596i	0.0115253	−	0.124362i
$127$	−15.0417	+	8.68434i	−1.33474	+	0.770611i	−0.986022	−	0.166618i	$-0.946715\pi$
$127$	−15.0417	+	8.68434i	−1.33474	+	0.770611i	−0.348716	+	0.937229i	$0.613382\pi$
$128$	−2.97504	−	11.1030i	−0.262959	−	0.981376i
$129$	2.51899	−	4.36301i	0.221784	−	0.384142i
$130$	−3.13103	−	2.53767i	−0.274609	−	0.222568i
$131$	6.59348	−	3.80675i	0.576075	−	0.332597i	−0.183497	−	0.983020i	$-0.558742\pi$
$131$	6.59348	−	3.80675i	0.576075	−	0.332597i	0.759572	+	0.650423i	$0.225408\pi$
$132$	4.78608	+	1.28243i	0.416575	+	0.111621i
$133$	−7.47959	−	16.2579i	−0.648563	−	1.40974i
$134$	0.867588	+	0.500902i	0.0749482	+	0.0432714i
$135$	−0.545981	+	2.03763i	−0.0469906	+	0.175371i
$136$	−6.27734	−	1.68201i	−0.538277	−	0.144231i
$137$	−15.1843	−	4.06862i	−1.29728	−	0.347606i	−0.456860	−	0.889538i	$-0.651026\pi$
$137$	−15.1843	−	4.06862i	−1.29728	−	0.347606i	−0.840422	+	0.541933i	$0.817693\pi$
$138$	−1.07592	+	4.01538i	−0.0915882	+	0.341812i
$139$	−16.0562	−	9.27005i	−1.36187	−	0.786275i	−0.371996	−	0.928234i	$-0.621326\pi$
$139$	−16.0562	−	9.27005i	−1.36187	−	0.786275i	−0.989873	+	0.141959i	$0.954660\pi$
$140$	0.885460	−	9.55444i	0.0748350	−	0.807498i
$141$	−3.53471	−	0.947124i	−0.297677	−	0.0797622i
$142$	4.69109	−	2.70840i	0.393667	−	0.227284i
$143$	10.3350	−	1.08179i	0.864254	−	0.0904637i
$144$	−1.19709	+	2.07341i	−0.0997571	+	0.172784i
$145$	−0.739763	−	2.76083i	−0.0614340	−	0.229275i
$146$	−3.23215	+	1.86608i	−0.267495	+	0.154438i
$147$	4.55445	−	5.31573i	0.375645	−	0.438434i
$148$	−4.94888	−	4.94888i	−0.406795	−	0.406795i
$149$	15.6133	+	15.6133i	1.27909	+	1.27909i	0.941176	+	0.337917i	$0.109722\pi$
$149$	15.6133	+	15.6133i	1.27909	+	1.27909i	0.337917	+	0.941176i	$0.390278\pi$
$150$	−0.0754255	+	0.281492i	−0.00615846	+	0.0229837i
$151$	4.61110	+	17.2088i	0.375246	+	1.40044i	0.852986	+	0.521935i	$0.174789\pi$
$151$	4.61110	+	17.2088i	0.375246	+	1.40044i	−0.477740	+	0.878501i	$0.658544\pi$
$152$		−	13.3302i		−	1.08123i
$153$	1.64880	+	2.85581i	0.133298	+	0.230878i
$154$	−2.58122	−	3.10852i	−0.208001	−	0.250491i
$155$		−	13.9443i		−	1.12004i
$156$	−0.972311	+	6.12201i	−0.0778472	+	0.490153i
$157$	3.29871	+	1.90451i	0.263265	+	0.151996i	0.625823	−	0.779965i	$-0.284763\pi$
$157$	3.29871	+	1.90451i	0.263265	+	0.151996i	−0.362558	+	0.931961i	$0.618096\pi$
$158$	0.847596	+	0.847596i	0.0674311	+	0.0674311i
$159$	−6.71968	−	3.87961i	−0.532905	−	0.307673i
$160$	5.49543	−	9.51836i	0.434452	−	0.752493i
$161$	−15.9687	+	13.2599i	−1.25851	+	1.04503i
$162$	−0.511829	+	0.137144i	−0.0402131	+	0.0107751i
$163$	−5.61169	+	5.61169i	−0.439541	+	0.439541i	−0.891858	−	0.452316i	$-0.850598\pi$
$163$	−5.61169	+	5.61169i	−0.439541	+	0.439541i	0.452316	+	0.891858i	$0.350598\pi$
$164$	11.3763	−	3.04827i	0.888339	−	0.238030i
$165$	3.03987	+	5.26521i	0.236654	+	0.409896i
$166$	−1.48834	+	2.57788i	−0.115518	+	0.200082i
$167$	2.98897	−	11.1550i	0.231294	−	0.863200i	−0.748491	−	0.663145i	$-0.769221\pi$
$167$	2.98897	−	11.1550i	0.231294	−	0.863200i	0.979785	−	0.200055i	$-0.0641120\pi$
$168$	4.73689	−	2.17925i	0.365459	−	0.168133i
$169$	2.69199	+	12.7182i	0.207076	+	0.978325i
$170$	−1.84302	−	3.19221i	−0.141354	−	0.244832i
$171$	−4.78288	+	4.78288i	−0.365756	+	0.365756i
$172$	8.66139			0.660425
$173$	19.0583			1.44897			0.724486	−	0.689289i	$-0.242077\pi$
$173$	19.0583			1.44897			0.724486	+	0.689289i	$0.242077\pi$
$174$	0.507670	−	0.507670i	0.0384864	−	0.0384864i
$175$	−1.11946	+	0.929566i	−0.0846232	+	0.0702686i
$176$	1.78589	+	6.66504i	0.134617	+	0.502396i
$177$	2.75075	+	0.737061i	0.206759	+	0.0554009i
$178$	−5.66849	+	3.27271i	−0.424872	+	0.245300i
$179$		−	10.8477i		−	0.810799i	−0.914140	−	0.405399i	$-0.867132\pi$
$179$		−	10.8477i		−	0.810799i	0.914140	−	0.405399i	$-0.132868\pi$
$180$	−3.50314	+	0.938663i	−0.261108	+	0.0699638i
$181$	5.71631			0.424890			0.212445	−	0.977173i	$-0.431857\pi$
$181$	5.71631			0.424890			0.212445	+	0.977173i	$0.431857\pi$
$182$	3.53155	−	3.61648i	0.261776	−	0.268071i
$183$	−3.63687			−0.268845
$184$	−14.9341	+	4.00158i	−1.10096	+	0.295000i
$185$		−	8.58759i		−	0.631372i
$186$	3.03339	−	1.75133i	0.222419	−	0.128414i
$187$	9.18007	+	2.45979i	0.671313	+	0.179878i
$188$	−1.62832	−	6.07696i	−0.118757	−	0.443208i
$189$	−2.48150	−	0.917679i	−0.180503	−	0.0667513i
$190$	5.34629	−	5.34629i	0.387860	−	0.387860i
$191$	−23.0051			−1.66459			−0.832294	−	0.554335i	$-0.812973\pi$
$191$	−23.0051			−1.66459			−0.832294	+	0.554335i	$0.812973\pi$
$192$	−2.02756			−0.146327
$193$	−3.52631	+	3.52631i	−0.253829	+	0.253829i	−0.822539	−	0.568709i	$-0.807443\pi$
$193$	−3.52631	+	3.52631i	−0.253829	+	0.253829i	0.568709	+	0.822539i	$0.307443\pi$
$194$	4.03431	+	6.98763i	0.289647	+	0.501683i
$195$	−6.15525	+	4.46803i	−0.440786	+	0.319963i
$196$	11.8296	+	2.21161i	0.844971	+	0.157972i
$197$	1.17127	−	4.37125i	0.0834496	−	0.311438i	−0.911566	−	0.411153i	$-0.865126\pi$
$197$	1.17127	−	4.37125i	0.0834496	−	0.311438i	0.995016	+	0.0997145i	$0.0317929\pi$
$198$	−0.763581	+	1.32256i	−0.0542653	+	0.0939903i
$199$	−10.9036	−	18.8855i	−0.772934	−	1.33876i	−0.935949	−	0.352137i	$-0.885455\pi$
$199$	−10.9036	−	18.8855i	−0.772934	−	1.33876i	0.163015	−	0.986624i	$-0.447878\pi$
$200$	−1.04693	+	0.280524i	−0.0740292	+	0.0198361i
$201$	1.33686	−	1.33686i	0.0942950	−	0.0942950i
$202$	−4.28643	+	1.14855i	−0.301592	+	0.0808114i
$203$	3.53349	−	0.604322i	0.248002	−	0.0424151i
$204$	−2.83466	+	4.90977i	−0.198466	+	0.343753i
$205$	12.5152	+	7.22564i	0.874098	+	0.504661i
$206$	2.95733	+	2.95733i	0.206047	+	0.206047i
$207$	6.79410	+	3.92258i	0.472223	+	0.272638i
$208$	−8.06027	+	3.09010i	−0.558879	+	0.214260i
$209$			19.4943i			1.34845i
$210$	2.77382	+	1.02578i	0.191412	+	0.0707854i
$211$	5.12257	+	8.87255i	0.352652	+	0.610811i	0.986713	−	0.162472i	$-0.0519466\pi$
$211$	5.12257	+	8.87255i	0.352652	+	0.610811i	−0.634061	+	0.773283i	$0.718613\pi$
$212$		−	13.3398i		−	0.916183i
$213$	−2.64580	−	9.87427i	−0.181288	−	0.676574i
$214$	−2.74504	+	10.2446i	−0.187647	+	0.700309i
$215$	7.51488	+	7.51488i	0.512511	+	0.512511i
$216$	−1.39354	−	1.39354i	−0.0948182	−	0.0948182i
$217$	17.4144	+	1.61388i	1.18217	+	0.109557i
$218$	−3.21095	+	1.85384i	−0.217473	+	0.125558i
$219$	1.82296	+	6.80337i	0.123184	+	0.459729i
$220$	−5.22621	+	9.05207i	−0.352351	+	0.610290i
$221$	−1.86497	+	11.7425i	−0.125451	+	0.789886i
$222$	1.86811	−	1.07855i	0.125379	−	0.0723877i
$223$	20.9821	+	5.62213i	1.40506	+	0.376486i	0.880161	−	0.474675i	$-0.157435\pi$
$223$	20.9821	+	5.62213i	1.40506	+	0.376486i	0.524904	+	0.851161i	$0.324101\pi$
$224$	11.2510	+	7.96460i	0.751738	+	0.532158i
$225$	0.476290	+	0.274986i	0.0317526	+	0.0183324i
$226$	−0.564756	+	2.10770i	−0.0375670	+	0.140202i
$227$	−11.2825	−	3.02314i	−0.748848	−	0.200653i	−0.135841	−	0.990731i	$-0.543374\pi$
$227$	−11.2825	−	3.02314i	−0.748848	−	0.200653i	−0.613007	+	0.790078i	$0.710040\pi$
$228$	−11.2326	−	3.00977i	−0.743897	−	0.199327i
$229$	−1.25682	+	4.69053i	−0.0830532	+	0.309959i	−0.994938	−	0.100487i	$-0.967960\pi$
$229$	−1.25682	+	4.69053i	−0.0830532	+	0.309959i	0.911885	+	0.410445i	$0.134627\pi$
$230$	−7.59442	−	4.38464i	−0.500761	−	0.289115i
$231$	−6.92729	+	3.18696i	−0.455782	+	0.209687i
$232$	2.57924	+	0.691106i	0.169336	+	0.0453733i
$233$	−1.91696	+	1.10676i	−0.125584	+	0.0725060i	−0.561476	−	0.827493i	$-0.689766\pi$
$233$	−1.91696	+	1.10676i	−0.125584	+	0.0725060i	0.435892	+	0.899999i	$0.356433\pi$
$234$	−1.74502	−	0.777826i	−0.114076	−	0.0508481i
$235$	3.85977	−	6.68532i	0.251784	−	0.436102i
$236$	1.26717	+	4.72915i	0.0824858	+	0.307841i
$237$	1.95909	−	1.13108i	0.127256	−	0.0734715i
$238$	4.19990	−	1.93220i	0.272239	−	0.125246i
$239$	−5.82013	−	5.82013i	−0.376473	−	0.376473i	0.493355	−	0.869828i	$-0.335770\pi$
$239$	−5.82013	−	5.82013i	−0.376473	−	0.376473i	−0.869828	+	0.493355i	$0.835770\pi$
$240$	−3.57126	−	3.57126i	−0.230524	−	0.230524i
$241$	3.76485	−	14.0506i	0.242515	−	0.905079i	−0.732101	−	0.681196i	$-0.761460\pi$
$241$	3.76485	−	14.0506i	0.242515	−	0.905079i	0.974616	−	0.223883i	$-0.0718733\pi$
$242$	−0.369425	−	1.37871i	−0.0237476	−	0.0886271i
$243$			1.00000i			0.0641500i
$244$	−3.12629	−	5.41490i	−0.200140	−	0.346653i
$245$	8.34484	+	12.1826i	0.533132	+	0.778316i
$246$			3.63000i			0.231440i
$247$	−24.2555	+	2.53889i	−1.54334	+	0.161545i
$248$	11.2819	+	6.51358i	0.716399	+	0.413613i
$249$	3.97225	+	3.97225i	0.251731	+	0.251731i
$250$	−5.37259	−	3.10187i	−0.339793	−	0.196179i
$251$	−10.7479	+	18.6160i	−0.678403	+	1.17503i	0.297058	+	0.954859i	$0.403994\pi$
$251$	−10.7479	+	18.6160i	−0.678403	+	1.17503i	−0.975462	+	0.220169i	$0.929339\pi$
$252$	−0.766806	−	4.48354i	−0.0483042	−	0.282436i
$253$	21.8398	−	5.85196i	1.37306	−	0.367910i
$254$	6.50779	−	6.50779i	0.408335	−	0.408335i
$255$	−6.71929	+	1.80043i	−0.420779	+	0.112747i
$256$	1.01786	+	1.76299i	0.0636165	+	0.110187i
$257$	−3.77139	+	6.53224i	−0.235253	+	0.407470i	−0.959346	−	0.282232i	$-0.908925\pi$
$257$	−3.77139	+	6.53224i	−0.235253	+	0.407470i	0.724093	+	0.689702i	$0.242258\pi$
$258$	−0.690929	+	2.57858i	−0.0430153	+	0.160535i
$259$	10.7246	+	0.993906i	0.666395	+	0.0617583i
$260$	−11.9435	−	5.32371i	−0.740706	−	0.330163i
$261$	−0.677462	−	1.17340i	−0.0419339	−	0.0726316i
$262$	−2.85266	+	2.85266i	−0.176238	+	0.176238i
$263$	23.8379			1.46991			0.734955	−	0.678115i	$-0.237203\pi$
$263$	23.8379			1.46991			0.734955	+	0.678115i	$0.237203\pi$
$264$	−5.67985			−0.349571
$265$	11.5740	−	11.5740i	0.710987	−	0.710987i
$266$	6.05795	+	7.29548i	0.371437	+	0.447315i
$267$	3.19707	+	11.9316i	0.195657	+	0.730203i
$268$	3.13962	+	0.841260i	0.191783	+	0.0513881i
$269$	−23.9283	+	13.8150i	−1.45893	+	0.842316i	−0.998959	−	0.0456166i	$-0.985475\pi$
$269$	−23.9283	+	13.8150i	−1.45893	+	0.842316i	−0.459974	+	0.887932i	$0.652141\pi$
$270$		−	1.11780i		−	0.0680269i
$271$	−19.9776	+	5.35298i	−1.21355	+	0.325170i	−0.808155	−	0.588970i	$-0.799533\pi$
$271$	−19.9776	+	5.35298i	−1.21355	+	0.325170i	−0.405397	+	0.914141i	$0.632867\pi$
$272$	−7.89502			−0.478706
$273$	−4.86751	−	8.20410i	−0.294595	−	0.496535i
$274$	8.32976			0.503219
$275$	1.53105	−	0.410242i	0.0923255	−	0.0247386i
$276$			13.4876i			0.811856i
$277$	7.78035	−	4.49199i	0.467476	−	0.269897i	−0.247707	−	0.968835i	$-0.579677\pi$
$277$	7.78035	−	4.49199i	0.467476	−	0.269897i	0.715183	+	0.698938i	$0.246344\pi$
$278$	9.48936	+	2.54267i	0.569134	+	0.152499i
$279$	−1.71085	−	6.38499i	−0.102426	−	0.382259i
$280$	1.85425	+	10.8418i	0.110813	+	0.647924i
$281$	13.3221	−	13.3221i	0.794731	−	0.794731i	−0.187528	−	0.982259i	$-0.560048\pi$
$281$	13.3221	−	13.3221i	0.794731	−	0.794731i	0.982259	+	0.187528i	$0.0600476\pi$
$282$	1.93906			0.115469
$283$	−19.3973			−1.15305			−0.576525	−	0.817080i	$-0.695592\pi$
$283$	−19.3973			−1.15305			−0.576525	+	0.817080i	$0.695592\pi$
$284$	12.4273	−	12.4273i	0.737427	−	0.737427i
$285$	−7.13438	−	12.3571i	−0.422604	−	0.731972i
$286$	−5.14138	+	1.97107i	−0.304016	+	0.116552i
$287$	−10.4722	+	14.7933i	−0.618156	+	0.873222i
$288$	1.34849	−	5.03262i	0.0794603	−	0.296550i
$289$	3.06290	−	5.30511i	0.180171	−	0.312065i
$290$	0.757265	+	1.31162i	0.0444681	+	0.0770210i
$291$	14.7083	−	3.94107i	0.862215	−	0.231030i
$292$	−8.56243	+	8.56243i	−0.501078	+	0.501078i
$293$	25.2467	−	6.76482i	1.47493	−	0.395205i	0.570309	−	0.821431i	$-0.306824\pi$
$293$	25.2467	−	6.76482i	1.47493	−	0.395205i	0.904617	+	0.426225i	$0.140157\pi$
$294$	−1.60208	+	3.34536i	−0.0934351	+	0.195105i
$295$	−3.00371	+	5.20258i	−0.174883	+	0.302906i
$296$	6.94791	+	4.01138i	0.403839	+	0.233156i
$297$	2.03793	+	2.03793i	0.118253	+	0.118253i
$298$	−10.1326	−	5.85008i	−0.586967	−	0.338886i
$299$	10.1256	+	26.4117i	0.585576	+	1.52743i
$300$			0.945524i			0.0545899i
$301$	−10.2547	+	8.51521i	−0.591072	+	0.490809i
$302$	−4.72019	−	8.17560i	−0.271616	−	0.470453i
$303$			8.37472i			0.481115i
$304$	−4.19137	−	15.6424i	−0.240391	−	0.897153i
$305$	1.98566	−	7.41059i	0.113699	−	0.424329i
$306$	−1.23556	−	1.23556i	−0.0706324	−	0.0706324i
$307$	−1.58354	−	1.58354i	−0.0903771	−	0.0903771i	0.660473	−	0.750850i	$-0.270356\pi$
$307$	−1.58354	−	1.58354i	−0.0903771	−	0.0903771i	−0.750850	+	0.660473i	$0.770356\pi$
$308$	−10.6998	−	7.57443i	−0.609679	−	0.431593i
$309$	6.83541	−	3.94643i	0.388853	−	0.224504i
$310$	1.91239	+	7.13712i	0.108616	+	0.405361i
$311$	7.59574	−	13.1562i	0.430715	−	0.746020i	−0.566220	−	0.824254i	$-0.691595\pi$
$311$	7.59574	−	13.1562i	0.430715	−	0.746020i	0.996935	+	0.0782342i	$0.0249282\pi$
$312$	−0.739728	−	7.06706i	−0.0418788	−	0.400094i
$313$	−2.66705	+	1.53982i	−0.150750	+	0.0870358i	−0.573478	−	0.819221i	$-0.694406\pi$
$313$	−2.66705	+	1.53982i	−0.150750	+	0.0870358i	0.422727	+	0.906257i	$0.361073\pi$
$314$	−1.94957	−	0.522385i	−0.110020	−	0.0294799i
$315$	3.22474	−	4.55535i	0.181694	−	0.256665i
$316$	3.36810	+	1.94458i	0.189471	+	0.109391i
$317$	2.12956	−	7.94761i	0.119608	−	0.446382i	−0.879982	−	0.475006i	$-0.842446\pi$
$317$	2.12956	−	7.94761i	0.119608	−	0.446382i	0.999590	+	0.0286238i	$0.00911247\pi$
$318$	3.97140	+	1.06413i	0.222705	+	0.0596736i
$319$	−3.77192	−	1.01068i	−0.211187	−	0.0565874i
$320$	1.10701	−	4.13142i	0.0618838	−	0.230953i
$321$	17.3341	+	10.0079i	0.967497	+	0.558585i
$322$	6.35472	−	8.97683i	0.354135	−	0.500259i
$323$	−21.5450	−	5.77297i	−1.19880	−	0.321217i
$324$	−1.48889	+	0.859611i	−0.0827161	+	0.0477562i
$325$	0.709836	+	1.85155i	0.0393746	+	0.102705i
$326$	2.10261	−	3.64184i	0.116453	−	0.201703i
$327$	1.81100	+	6.75874i	0.100148	+	0.373759i
$328$	−11.6920	+	6.75038i	−0.645583	+	0.372728i
$329$	7.90225	+	5.59402i	0.435665	+	0.308409i
$330$	−2.27799	−	2.27799i	−0.125399	−	0.125399i
$331$	15.5865	+	15.5865i	0.856711	+	0.856711i	0.990949	−	0.134239i	$-0.0428588\pi$
$331$	15.5865	+	15.5865i	0.856711	+	0.856711i	−0.134239	+	0.990949i	$0.542859\pi$
$332$	−2.49965	+	9.32883i	−0.137186	+	0.511986i
$333$	−1.05363	−	3.93218i	−0.0577383	−	0.215482i
$334$			6.11937i			0.334837i
$335$	1.99413	+	3.45393i	0.108951	+	0.188709i
$336$	4.87330	−	4.04664i	0.265860	−	0.220762i
$337$			6.60942i			0.360038i	0.983663	+	0.180019i	$0.0576159\pi$
$337$			6.60942i			0.360038i	−0.983663	+	0.180019i	$0.942384\pi$
$338$	−3.12207	−	6.14037i	−0.169818	−	0.333992i
$339$	3.56627	+	2.05899i	0.193693	+	0.111829i
$340$	−8.45662	−	8.45662i	−0.458625	−	0.458625i
$341$	−16.4987	−	9.52556i	−0.893457	−	0.515838i
$342$	1.79207	−	3.10396i	0.0969043	−	0.167843i
$343$	−16.1800	+	9.01149i	−0.873639	+	0.486574i
$344$	−9.59032	+	2.56972i	−0.517075	+	0.138550i
$345$	−11.7022	+	11.7022i	−0.630026	+	0.630026i
$346$	−9.75457	+	2.61373i	−0.524409	+	0.140515i
$347$	−7.70530	−	13.3460i	−0.413642	−	0.716450i	0.581643	−	0.813445i	$-0.302410\pi$
$347$	−7.70530	−	13.3460i	−0.413642	−	0.716450i	−0.995285	+	0.0969950i	$0.969077\pi$
$348$	1.16471	−	2.01733i	0.0624349	−	0.108140i
$349$	−0.658426	+	2.45728i	−0.0352447	+	0.131535i	−0.981307	−	0.192451i	$-0.938356\pi$
$349$	−0.658426	+	2.45728i	−0.0352447	+	0.131535i	0.946062	+	0.323986i	$0.105023\pi$
$350$	0.445488	−	0.629307i	0.0238123	−	0.0336379i
$351$	−2.27024	+	2.80107i	−0.121177	+	0.149510i
$352$	−7.50800	−	13.0042i	−0.400178	−	0.693128i
$353$	3.56642	−	3.56642i	0.189821	−	0.189821i	−0.605798	−	0.795619i	$-0.707146\pi$
$353$	3.56642	−	3.56642i	0.189821	−	0.189821i	0.795619	+	0.605798i	$0.207146\pi$
$354$	−1.50900			−0.0802023
$355$	21.5647			1.14453
$356$	−15.0166	+	15.0166i	−0.795880	+	0.795880i
$357$	−1.47079	−	8.59977i	−0.0778426	−	0.455148i
$358$	1.48771	+	5.55219i	0.0786277	+	0.293443i
$359$	9.36366	+	2.50899i	0.494195	+	0.132419i	0.497305	−	0.867576i	$-0.334323\pi$
$359$	9.36366	+	2.50899i	0.494195	+	0.132419i	−0.00310948	+	0.999995i	$0.500990\pi$
$360$	3.60036	−	2.07867i	0.189755	−	0.109555i
$361$		−	26.7519i		−	1.40800i
$362$	−2.92577	+	0.783959i	−0.153775	+	0.0412039i
$363$	−2.69370			−0.141383
$364$	8.03084	−	14.2995i	0.420930	−	0.749499i
$365$	−14.8580			−0.777705
$366$	1.86145	−	0.498775i	0.0972998	−	0.0260714i
$367$		−	7.48563i		−	0.390747i	−0.980729	−	0.195373i	$-0.937408\pi$
$367$		−	7.48563i		−	0.390747i	0.980729	−	0.195373i	$-0.0625919\pi$
$368$	−16.2662	+	9.39132i	−0.847936	+	0.489556i
$369$	6.61712	+	1.77305i	0.344473	+	0.0923013i
$370$	1.17774	+	4.39538i	0.0612277	+	0.228505i
$371$	13.1147	+	15.7938i	0.680881	+	0.819972i
$372$	8.03588	−	8.03588i	0.416641	−	0.416641i
$373$	18.9380			0.980571			0.490285	−	0.871562i	$-0.336893\pi$
$373$	18.9380			0.980571			0.490285	+	0.871562i	$0.336893\pi$
$374$	−5.03598			−0.260404
$375$	−8.27861	+	8.27861i	−0.427505	+	0.427505i
$376$	3.60590	+	6.24561i	0.185960	+	0.322092i
$377$	0.766281	−	4.82478i	0.0394655	−	0.248489i
$378$	1.39596	+	0.129371i	0.0718005	+	0.00665412i
$379$	6.61698	−	24.6949i	0.339891	−	1.26849i	−0.558577	−	0.829453i	$-0.688652\pi$
$379$	6.61698	−	24.6949i	0.339891	−	1.26849i	0.898468	−	0.439039i	$-0.144681\pi$
$380$	12.2656	−	21.2446i	0.629211	−	1.08983i
$381$	−8.68434	−	15.0417i	−0.444912	−	0.770611i
$382$	11.7747	−	3.15501i	0.602444	−	0.161424i
$383$	6.37270	−	6.37270i	0.325630	−	0.325630i	−0.525292	−	0.850922i	$-0.676044\pi$
$383$	6.37270	−	6.37270i	0.325630	−	0.325630i	0.850922	+	0.525292i	$0.176044\pi$
$384$	11.1030	−	2.97504i	0.566598	−	0.151819i
$385$	−2.71168	−	15.8553i	−0.138200	−	0.808060i
$386$	1.32126	−	2.28848i	0.0672501	−	0.116481i
$387$	4.36301	+	2.51899i	0.221784	+	0.128047i
$388$	18.5112	+	18.5112i	0.939765	+	0.939765i
$389$	−24.4866	−	14.1373i	−1.24152	−	0.716792i	−0.272116	−	0.962264i	$-0.587724\pi$
$389$	−24.4866	−	14.1373i	−1.24152	−	0.716792i	−0.969404	+	0.245472i	$0.921057\pi$
$390$	2.53767	−	3.13103i	0.128500	−	0.158546i
$391$			25.8702i			1.30831i
$392$	−13.7545	+	1.06087i	−0.694705	+	0.0535821i
$393$	3.80675	+	6.59348i	0.192025	+	0.332597i
$394$			2.39796i			0.120808i
$395$	1.23510	+	4.60944i	0.0621444	+	0.231926i
$396$	−1.28243	+	4.78608i	−0.0644443	+	0.240509i
$397$	−12.0304	−	12.0304i	−0.603789	−	0.603789i	0.337527	−	0.941316i	$-0.390410\pi$
$397$	−12.0304	−	12.0304i	−0.603789	−	0.603789i	−0.941316	+	0.337527i	$0.890410\pi$
$398$	8.17081	+	8.17081i	0.409566	+	0.409566i
$399$	16.2579	−	7.47959i	0.813913	−	0.374448i
$400$	−1.14032	+	0.658363i	−0.0570159	+	0.0329182i
$401$	1.47514	+	5.50530i	0.0736650	+	0.274921i	0.992927	−	0.118724i	$-0.0378804\pi$
$401$	1.47514	+	5.50530i	0.0736650	+	0.274921i	−0.919262	+	0.393646i	$0.871214\pi$
$402$	−0.500902	+	0.867588i	−0.0249827	+	0.0432714i
$403$	9.70326	−	21.7689i	0.483354	−	1.08438i
$404$	−12.4690	+	7.19901i	−0.620358	+	0.358164i
$405$	−2.03763	−	0.545981i	−0.101251	−	0.0271300i
$406$	−1.72566	+	0.793907i	−0.0856432	+	0.0394009i
$407$	−10.1607	−	5.86629i	−0.503648	−	0.290781i
$408$	1.68201	−	6.27734i	0.0832718	−	0.310775i
$409$	−11.4404	−	3.06546i	−0.565693	−	0.151577i	−0.0353725	−	0.999374i	$-0.511262\pi$
$409$	−11.4404	−	3.06546i	−0.565693	−	0.151577i	−0.530321	+	0.847797i	$0.677928\pi$
$410$	−7.39659	−	1.98191i	−0.365291	−	0.0978795i
$411$	4.06862	−	15.1843i	0.200690	−	0.748986i
$412$	11.7516	+	6.78479i	0.578960	+	0.334262i
$413$	−6.14961	−	4.35332i	−0.302602	−	0.214213i
$414$	−4.01538	−	1.07592i	−0.197345	−	0.0528785i
$415$	−10.2627	+	5.92519i	−0.503778	+	0.290856i
$416$	15.2025	−	11.0353i	0.745363	−	0.541052i
$417$	9.27005	−	16.0562i	0.453956	−	0.786275i
$418$	−2.67354	−	9.97777i	−0.130767	−	0.488029i
$419$	9.24123	−	5.33542i	0.451463	−	0.260653i	−0.256985	−	0.966415i	$-0.582729\pi$
$419$	9.24123	−	5.33542i	0.451463	−	0.260653i	0.708448	+	0.705763i	$0.249396\pi$
$420$	9.55444	+	0.885460i	0.466209	+	0.0432060i
$421$	−7.86566	−	7.86566i	−0.383349	−	0.383349i	0.488958	−	0.872307i	$-0.337377\pi$
$421$	−7.86566	−	7.86566i	−0.383349	−	0.383349i	−0.872307	+	0.488958i	$0.837377\pi$
$422$	−3.83870	−	3.83870i	−0.186865	−	0.186865i
$423$	0.947124	−	3.53471i	0.0460507	−	0.171864i
$424$	3.95774	+	14.7705i	0.192205	+	0.717319i
$425$			1.81359i			0.0879720i
$426$	2.70840	+	4.69109i	0.131222	+	0.227284i
$427$	9.02490	+	3.33748i	0.436746	+	0.161512i
$428$			34.4115i			1.66334i
$429$	1.08179	+	10.3350i	0.0522292	+	0.498977i
$430$	−4.87696	−	2.81571i	−0.235188	−	0.135786i
$431$	−4.61007	−	4.61007i	−0.222059	−	0.222059i	0.587306	−	0.809365i	$-0.300189\pi$
$431$	−4.61007	−	4.61007i	−0.222059	−	0.222059i	−0.809365	+	0.587306i	$0.800189\pi$
$432$	−2.07341	−	1.19709i	−0.0997571	−	0.0575948i
$433$	−11.6587	+	20.1934i	−0.560281	+	0.970435i	0.437191	+	0.899369i	$0.355974\pi$
$433$	−11.6587	+	20.1934i	−0.560281	+	0.970435i	−0.997472	+	0.0710664i	$0.977360\pi$
$434$	−9.13453	+	1.56225i	−0.438472	+	0.0749905i
$435$	2.76083	−	0.739763i	0.132372	−	0.0354689i
$436$	−8.50626	+	8.50626i	−0.407376	+	0.407376i
$437$	−51.2566	+	13.7342i	−2.45194	+	0.656994i
$438$	−1.86608	−	3.23215i	−0.0891650	−	0.154438i
$439$	2.93624	−	5.08572i	0.140139	−	0.242728i	−0.787410	−	0.616430i	$-0.788578\pi$
$439$	2.93624	−	5.08572i	0.140139	−	0.242728i	0.927549	+	0.373702i	$0.121912\pi$
$440$	3.10109	−	11.5734i	0.147839	−	0.551742i
$441$	5.31573	+	4.55445i	0.253130	+	0.216879i
$442$	−0.655871	−	6.26593i	−0.0311966	−	0.298040i
$443$	−11.2685	−	19.5176i	−0.535381	−	0.927308i	−0.999145	−	0.0413488i	$-0.986835\pi$
$443$	−11.2685	−	19.5176i	−0.535381	−	0.927308i	0.463763	−	0.885959i	$-0.346499\pi$
$444$	4.94888	−	4.94888i	0.234863	−	0.234863i
$445$	−26.0578			−1.23526
$446$	−11.5103			−0.545028
$447$	−15.6133	+	15.6133i	−0.738485	+	0.738485i
$448$	5.03140	+	1.86065i	0.237711	+	0.0879075i
$449$	−1.20603	−	4.50095i	−0.0569159	−	0.212413i	0.931611	−	0.363456i	$-0.118403\pi$
$449$	−1.20603	−	4.50095i	−0.0569159	−	0.212413i	−0.988527	+	0.151043i	$0.951737\pi$
$450$	−0.281492	−	0.0754255i	−0.0132696	−	0.00355559i
$451$	17.0986	−	9.87186i	0.805140	−	0.464848i
$452$			7.07971i			0.333002i
$453$	−17.2088	+	4.61110i	−0.808542	+	0.216648i
$454$	6.18933			0.290480
$455$	19.3745	−	5.43891i	0.908290	−	0.254980i
$456$	13.3302			0.624246
$457$	26.3311	−	7.05539i	1.23172	−	0.330037i	0.416468	−	0.909150i	$-0.363268\pi$
$457$	26.3311	−	7.05539i	1.23172	−	0.330037i	0.815247	+	0.579113i	$0.196601\pi$
$458$		−	2.57311i		−	0.120234i
$459$	−2.85581	+	1.64880i	−0.133298	+	0.0769595i
$460$	−27.4827	−	7.36396i	−1.28139	−	0.343346i
$461$	5.21155	+	19.4498i	0.242726	+	0.905866i	0.974513	+	0.224332i	$0.0720200\pi$
$461$	5.21155	+	19.4498i	0.242726	+	0.905866i	−0.731787	+	0.681534i	$0.761313\pi$
$462$	3.10852	−	2.58122i	0.144621	−	0.120089i
$463$	6.95272	−	6.95272i	0.323120	−	0.323120i	−0.526843	−	0.849963i	$-0.676624\pi$
$463$	6.95272	−	6.95272i	0.323120	−	0.323120i	0.849963	+	0.526843i	$0.176624\pi$
$464$	3.24392			0.150595
$465$	13.9443			0.646653
$466$	0.829370	−	0.829370i	0.0384198	−	0.0384198i
$467$	−7.90161	−	13.6860i	−0.365643	−	0.633312i	0.623236	−	0.782034i	$-0.285817\pi$
$467$	−7.90161	−	13.6860i	−0.365643	−	0.633312i	−0.988879	+	0.148722i	$0.952484\pi$
$468$	−6.12201	−	0.972311i	−0.282990	−	0.0449451i
$469$	−4.54424	+	2.09062i	−0.209834	+	0.0965359i
$470$	−1.05869	+	3.95109i	−0.0488338	+	0.182250i
$471$	−1.90451	+	3.29871i	−0.0877551	+	0.151996i
$472$	−2.80615	−	4.86039i	−0.129163	−	0.223718i
$473$	14.0250	−	3.75799i	0.644871	−	0.172793i
$474$	−0.847596	+	0.847596i	−0.0389314	+	0.0389314i
$475$	−3.59326	+	0.962812i	−0.164870	+	0.0441768i
$476$	11.5398	−	9.58231i	0.528926	−	0.439205i
$477$	3.87961	−	6.71968i	0.177635	−	0.307673i
$478$	3.77711	+	2.18072i	0.172761	+	0.0997436i
$479$	−23.3192	−	23.3192i	−1.06548	−	1.06548i	−0.997700	−	0.0677829i	$-0.978407\pi$
$479$	−23.3192	−	23.3192i	−1.06548	−	1.06548i	−0.0677829	−	0.997700i	$-0.521593\pi$
$480$	9.51836	+	5.49543i	0.434452	+	0.250831i
$481$	5.97573	−	13.4063i	0.272470	−	0.611275i
$482$			7.70784i			0.351082i
$483$	−13.2599	−	15.9687i	−0.603348	−	0.726601i
$484$	−2.31553	−	4.01062i	−0.105252	−	0.182301i
$485$			32.1218i			1.45857i
$486$	−0.137144	−	0.511829i	−0.00622099	−	0.0232170i
$487$	7.00807	−	26.1545i	0.317566	−	1.18517i	−0.604011	−	0.796976i	$-0.706432\pi$
$487$	7.00807	−	26.1545i	0.317566	−	1.18517i	0.921577	−	0.388196i	$-0.126902\pi$
$488$	5.06811	+	5.06811i	0.229422	+	0.229422i
$489$	−5.61169	−	5.61169i	−0.253769	−	0.253769i
$490$	−5.94190	−	5.09095i	−0.268428	−	0.229986i
$491$	−10.9028	+	6.29476i	−0.492038	+	0.284078i	−0.725420	−	0.688307i	$-0.758354\pi$
$491$	−10.9028	+	6.29476i	−0.492038	+	0.284078i	0.233381	+	0.972385i	$0.425021\pi$
$492$	3.04827	+	11.3763i	0.137427	+	0.512883i
$493$	2.23400	−	3.86941i	0.100614	−	0.174269i
$494$	12.0665	−	4.62598i	0.542896	−	0.208133i
$495$	−5.26521	+	3.03987i	−0.236654	+	0.136632i
$496$	15.2868	+	4.09607i	0.686396	+	0.183919i
$497$	−2.49584	+	26.9311i	−0.111954	+	1.20802i
$498$	−2.57788	−	1.48834i	−0.115518	−	0.0666942i
$499$	−6.44253	+	24.0438i	−0.288407	+	1.07635i	0.657906	+	0.753100i	$0.271442\pi$
$499$	−6.44253	+	24.0438i	−0.288407	+	1.07635i	−0.946313	+	0.323251i	$0.895224\pi$
$500$	−19.4423	−	5.20955i	−0.869487	−	0.232978i
$501$	11.1550	+	2.98897i	0.498369	+	0.133537i
$502$	2.94803	−	11.0022i	0.131577	−	0.491052i
$503$	−22.2573	−	12.8503i	−0.992404	−	0.572965i	−0.0864120	−	0.996259i	$-0.527540\pi$
$503$	−22.2573	−	12.8503i	−0.992404	−	0.572965i	−0.905992	+	0.423295i	$0.860873\pi$
$504$	2.17925	+	4.73689i	0.0970714	+	0.210998i
$505$	−17.0646	−	4.57244i	−0.759364	−	0.203471i
$506$	−10.3757	+	5.99041i	−0.461256	+	0.266306i
$507$	−12.7182	+	2.69199i	−0.564836	+	0.119556i
$508$	14.9303	−	25.8601i	0.662426	−	1.14735i
$509$	−2.33254	−	8.70515i	−0.103388	−	0.385849i	0.894769	−	0.446529i	$-0.147340\pi$
$509$	−2.33254	−	8.70515i	−0.103388	−	0.385849i	−0.998157	+	0.0606796i	$0.980673\pi$
$510$	3.19221	−	1.84302i	0.141354	−	0.0816105i
$511$	1.71963	−	18.5555i	0.0760720	−	0.820846i
$512$	15.4932	+	15.4932i	0.684708	+	0.684708i
$513$	−4.78288	−	4.78288i	−0.211169	−	0.211169i
$514$	1.03445	−	3.86061i	0.0456276	−	0.170284i
$515$	4.30935	+	16.0827i	0.189893	+	0.708689i
$516$			8.66139i			0.381297i
$517$	−5.27332	−	9.13366i	−0.231920	−	0.401698i
$518$	−5.62548	+	0.962109i	−0.247169	+	0.0422727i
$519$			19.0583i			0.836564i
$520$	14.8039	+	2.35119i	0.649195	+	0.103107i
$521$	−10.2174	−	5.89904i	−0.447634	−	0.258442i	0.259196	−	0.965825i	$-0.416542\pi$
$521$	−10.2174	−	5.89904i	−0.447634	−	0.258442i	−0.706831	+	0.707383i	$0.749876\pi$
$522$	0.507670	+	0.507670i	0.0222201	+	0.0222201i
$523$	24.7931	+	14.3143i	1.08412	+	0.625920i	0.932006	−	0.362443i	$-0.118057\pi$
$523$	24.7931	+	14.3143i	1.08412	+	0.625920i	0.152119	+	0.988362i	$0.451390\pi$
$524$	−6.54464	+	11.3357i	−0.285904	+	0.495200i
$525$	−0.929566	−	1.11946i	−0.0405696	−	0.0488572i
$526$	−12.2010	+	3.26924i	−0.531987	+	0.142545i
$527$	15.4135	−	15.4135i	0.671421	−	0.671421i
$528$	−6.66504	+	1.78589i	−0.290059	+	0.0777210i
$529$	19.2732	+	33.3822i	0.837966	+	1.45140i
$530$	−4.33661	+	7.51124i	−0.188370	+	0.326267i
$531$	−0.737061	+	2.75075i	−0.0319857	+	0.119372i
$532$	25.1118	+	17.7767i	1.08873	+	0.770717i
$533$	14.5098	+	19.9889i	0.628487	+	0.865815i
$534$	−3.27271	−	5.66849i	−0.141624	−	0.245300i
$535$	−29.8564	+	29.8564i	−1.29081	+	1.29081i
$536$	−3.72594			−0.160936
$537$	10.8477			0.468115
$538$	10.3525	−	10.3525i	0.446330	−	0.446330i
$539$	20.1147	−	1.55143i	0.866402	−	0.0668250i
$540$	−0.938663	−	3.50314i	−0.0403936	−	0.150751i
$541$	−20.6881	−	5.54336i	−0.889451	−	0.238328i	−0.214971	−	0.976621i	$-0.568966\pi$
$541$	−20.6881	−	5.54336i	−0.889451	−	0.238328i	−0.674480	+	0.738293i	$0.735632\pi$
$542$	9.49098	−	5.47962i	0.407673	−	0.235370i
$543$			5.71631i			0.245310i
$544$	16.5956	−	4.44677i	0.711530	−	0.190654i
$545$	−14.7606			−0.632273
$546$	3.61648	+	3.53155i	0.154771	+	0.151136i
$547$	−26.1223			−1.11691			−0.558455	−	0.829535i	$-0.688606\pi$
$547$	−26.1223			−1.11691			−0.558455	+	0.829535i	$0.688606\pi$
$548$	26.1052	−	6.99486i	1.11516	−	0.298806i
$549$		−	3.63687i		−	0.155218i
$550$	−0.727372	+	0.419948i	−0.0310152	+	0.0179066i
$551$	8.85245	+	2.37201i	0.377127	+	0.101051i
$552$	−4.00158	−	14.9341i	−0.170318	−	0.635637i
$553$	−5.89945	+	1.00896i	−0.250870	+	0.0429055i
$554$	−3.36616	+	3.36616i	−0.143014	+	0.143014i
$555$	8.58759			0.364523
$556$	31.8745			1.35178
$557$	24.3809	−	24.3809i	1.03305	−	1.03305i	0.0336154	−	0.999435i	$-0.489298\pi$
$557$	24.3809	−	24.3809i	1.03305	−	1.03305i	0.999435	−	0.0336154i	$-0.0107021\pi$
$558$	1.75133	+	3.03339i	0.0741397	+	0.128414i
$559$	6.50239	+	16.9610i	0.275022	+	0.717372i
$560$	5.58483	+	12.1394i	0.236002	+	0.512982i
$561$	−2.45979	+	9.18007i	−0.103853	+	0.387583i
$562$	−4.99160	+	8.64570i	−0.210558	+	0.364697i
$563$	8.01096	+	13.8754i	0.337622	+	0.584778i	0.983985	−	0.178252i	$-0.0570442\pi$
$563$	8.01096	+	13.8754i	0.337622	+	0.584778i	−0.646363	+	0.763030i	$0.723711\pi$
$564$	6.07696	−	1.62832i	0.255886	−	0.0685645i
$565$	−6.14257	+	6.14257i	−0.258420	+	0.258420i
$566$	9.92810	−	2.66023i	0.417309	−	0.111818i
$567$	0.917679	−	2.48150i	0.0385389	−	0.104213i
$568$	−10.0731	+	17.4472i	−0.422660	+	0.732068i
$569$	−22.9269	−	13.2368i	−0.961145	−	0.554917i	−0.0646197	−	0.997910i	$-0.520583\pi$
$569$	−22.9269	−	13.2368i	−0.961145	−	0.554917i	−0.896525	+	0.442993i	$0.853917\pi$
$570$	5.34629	+	5.34629i	0.223931	+	0.223931i
$571$	13.5784	+	7.83948i	0.568237	+	0.328072i	0.756445	−	0.654057i	$-0.226935\pi$
$571$	13.5784	+	7.83948i	0.568237	+	0.328072i	−0.188208	+	0.982129i	$0.560268\pi$
$572$	−14.4577	+	10.4947i	−0.604508	+	0.438806i
$573$		−	23.0051i		−	0.961050i
$574$	3.33117	−	9.00785i	0.139040	−	0.375981i
$575$	2.15731	+	3.73657i	0.0899660	+	0.155826i
$576$		−	2.02756i		−	0.0844817i
$577$	7.54746	+	28.1675i	0.314205	+	1.17263i	0.924728	+	0.380630i	$0.124293\pi$
$577$	7.54746	+	28.1675i	0.314205	+	1.17263i	−0.610523	+	0.791999i	$0.709041\pi$
$578$	−0.840119	+	3.13537i	−0.0349444	+	0.130414i
$579$	−3.52631	−	3.52631i	−0.146548	−	0.146548i
$580$	3.47467	+	3.47467i	0.144278	+	0.144278i
$581$	−6.21190	−	13.5024i	−0.257713	−	0.560174i
$582$	−6.98763	+	4.03431i	−0.289647	+	0.167228i
$583$	−5.78786	−	21.6006i	−0.239709	−	0.894605i
$584$	6.94038	−	12.0211i	0.287195	−	0.497436i
$585$	−4.46803	−	6.15525i	−0.184730	−	0.254488i
$586$	−11.9942	+	6.92487i	−0.495477	+	0.286064i
$587$	−7.40030	−	1.98290i	−0.305443	−	0.0818432i	0.102842	−	0.994698i	$-0.467206\pi$
$587$	−7.40030	−	1.98290i	−0.305443	−	0.0818432i	−0.408285	+	0.912854i	$0.633873\pi$
$588$	−2.21161	+	11.8296i	−0.0912055	+	0.487844i
$589$	38.7215	+	22.3558i	1.59549	+	0.921157i
$590$	0.823884	−	3.07478i	0.0339188	−	0.126587i
$591$	4.37125	+	1.17127i	0.179809	+	0.0481797i
$592$	9.41431	+	2.52256i	0.386926	+	0.103676i
$593$	−4.71470	+	17.5955i	−0.193610	+	0.722561i	0.799013	+	0.601314i	$0.205356\pi$
$593$	−4.71470	+	17.5955i	−0.193610	+	0.722561i	−0.992622	+	0.121247i	$0.961311\pi$
$594$	−1.32256	−	0.763581i	−0.0542653	−	0.0313301i
$595$	18.3262	+	1.69838i	0.751300	+	0.0696269i
$596$	−36.6679	−	9.82514i	−1.50198	−	0.402453i
$597$	18.8855	−	10.9036i	0.772934	−	0.446253i
$598$	−8.80477	−	12.1296i	−0.360054	−	0.496017i
$599$	−7.09934	+	12.2964i	−0.290071	+	0.502418i	−0.973826	−	0.227293i	$-0.927012\pi$
$599$	−7.09934	+	12.2964i	−0.290071	+	0.502418i	0.683755	+	0.729712i	$0.260346\pi$
$600$	−0.280524	−	1.04693i	−0.0114523	−	0.0427408i
$601$	−11.4194	+	6.59300i	−0.465807	+	0.268934i	−0.714483	−	0.699653i	$-0.753338\pi$
$601$	−11.4194	+	6.59300i	−0.465807	+	0.268934i	0.248676	+	0.968587i	$0.420005\pi$
$602$	4.08085	−	5.76471i	0.166323	−	0.234952i
$603$	1.33686	+	1.33686i	0.0544413	+	0.0544413i
$604$	−21.6583	−	21.6583i	−0.881265	−	0.881265i
$605$	1.47071	−	5.48876i	0.0597928	−	0.223150i
$606$	−1.14855	−	4.28643i	−0.0466565	−	0.174124i
$607$		−	11.2832i		−	0.457970i	−0.973430	−	0.228985i	$-0.926459\pi$
$607$		−	11.2832i		−	0.457970i	0.973430	−	0.228985i	$-0.0735406\pi$
$608$	17.6208	+	30.5201i	0.714617	+	1.23775i
$609$	0.604322	+	3.53349i	0.0244884	+	0.143184i
$610$			4.06528i			0.164598i
$611$	10.6776	−	7.75078i	0.431970	−	0.313563i
$612$	−4.90977	−	2.83466i	−0.198466	−	0.114584i
$613$	7.04738	+	7.04738i	0.284641	+	0.284641i	0.834957	−	0.550316i	$-0.185493\pi$
$613$	7.04738	+	7.04738i	0.284641	+	0.284641i	−0.550316	+	0.834957i	$0.685493\pi$
$614$	1.02767	+	0.593327i	0.0414735	+	0.0239447i
$615$	−7.22564	+	12.5152i	−0.291366	+	0.504661i
$616$	14.0946	+	5.21228i	0.567887	+	0.210009i
$617$	37.7991	−	10.1282i	1.52173	−	0.407747i	0.601422	−	0.798932i	$-0.294601\pi$
$617$	37.7991	−	10.1282i	1.52173	−	0.407747i	0.920312	+	0.391184i	$0.127935\pi$
$618$	−2.95733	+	2.95733i	−0.118961	+	0.118961i
$619$	−18.7706	+	5.02957i	−0.754455	+	0.202156i	−0.615493	−	0.788142i	$-0.711043\pi$
$619$	−18.7706	+	5.02957i	−0.754455	+	0.202156i	−0.138962	+	0.990298i	$0.544376\pi$
$620$	11.9867	+	20.7616i	0.481398	+	0.833805i
$621$	−3.92258	+	6.79410i	−0.157408	+	0.272638i
$622$	−2.08342	+	7.77544i	−0.0835376	+	0.311767i
$623$	3.01586	−	32.5423i	0.120828	−	1.30378i
$624$	−3.09010	−	8.06027i	−0.123703	−	0.322669i
$625$	−10.9738	−	19.0072i	−0.438953	−	0.760290i
$626$	1.15390	−	1.15390i	0.0461189	−	0.0461189i
$627$	−19.4943			−0.778529
$628$	−6.54855			−0.261316
$629$	9.49234	−	9.49234i	0.378484	−	0.378484i
$630$	−1.02578	+	2.77382i	−0.0408680	+	0.110511i
$631$	−2.13268	−	7.95928i	−0.0849008	−	0.316854i	0.910395	−	0.413741i	$-0.135778\pi$
$631$	−2.13268	−	7.95928i	−0.0849008	−	0.316854i	−0.995295	+	0.0968871i	$0.969111\pi$
$632$	−4.30626	−	1.15386i	−0.171294	−	0.0458980i
$633$	−8.87255	+	5.12257i	−0.352652	+	0.203604i
$634$			4.35988i			0.173153i
$635$	35.3909	−	9.48297i	1.40445	−	0.376320i
$636$	13.3398			0.528958
$637$	4.55003	+	24.8253i	0.180279	+	0.983616i
$638$	2.06919			0.0819200
$639$	9.87427	−	2.64580i	0.390620	−	0.104666i
$640$			24.2481i			0.958491i
$641$	−34.5796	+	19.9646i	−1.36581	+	0.788552i	−0.990390	−	0.138301i	$-0.955836\pi$
$641$	−34.5796	+	19.9646i	−1.36581	+	0.788552i	−0.375423	+	0.926854i	$0.622502\pi$
$642$	−10.2446	−	2.74504i	−0.404324	−	0.108338i
$643$	−3.71724	−	13.8729i	−0.146594	−	0.547095i	−0.999679	−	0.0253239i	$-0.991938\pi$
$643$	−3.71724	−	13.8729i	−0.146594	−	0.547095i	0.853086	−	0.521771i	$-0.174728\pi$
$644$	12.3773	−	33.4695i	0.487732	−	1.31888i
$645$	−7.51488	+	7.51488i	−0.295898	+	0.295898i
$646$	11.8191			0.465016
$647$	9.05314			0.355916			0.177958	−	0.984038i	$-0.443051\pi$
$647$	9.05314			0.355916			0.177958	+	0.984038i	$0.443051\pi$
$648$	1.39354	−	1.39354i	0.0547433	−	0.0547433i
$649$	4.10375	+	7.10790i	0.161086	+	0.279010i
$650$	−0.617244	−	0.850327i	−0.0242103	−	0.0333526i
$651$	−1.61388	+	17.4144i	−0.0632531	+	0.682524i
$652$	3.53132	−	13.1791i	0.138297	−	0.516132i
$653$	−16.9246	+	29.3143i	−0.662312	+	1.14716i	0.317694	+	0.948193i	$0.397092\pi$
$653$	−16.9246	+	29.3143i	−0.662312	+	1.14716i	−0.980006	+	0.198966i	$0.936242\pi$
$654$	−1.85384	−	3.21095i	−0.0724910	−	0.125558i
$655$	−15.5135	+	4.15682i	−0.606161	+	0.162420i
$656$	−11.5975	+	11.5975i	−0.452807	+	0.452807i
$657$	−6.80337	+	1.82296i	−0.265425	+	0.0711203i
$658$	−4.81179	−	1.77944i	−0.187583	−	0.0693697i
$659$	14.7702	−	25.5827i	0.575365	−	0.996561i	−0.420637	−	0.907229i	$-0.638193\pi$
$659$	14.7702	−	25.5827i	0.575365	−	0.996561i	0.996002	−	0.0893323i	$-0.0284733\pi$
$660$	−9.05207	−	5.22621i	−0.352351	−	0.203430i
$661$	−15.2821	−	15.2821i	−0.594406	−	0.594406i	0.344413	−	0.938818i	$-0.388078\pi$
$661$	−15.2821	−	15.2821i	−0.594406	−	0.594406i	−0.938818	+	0.344413i	$0.888078\pi$
$662$	−10.1152	−	5.84002i	−0.393139	−	0.226979i
$663$	−11.7425	−	1.86497i	−0.456041	−	0.0724294i
$664$		−	11.0709i		−	0.429636i
$665$	6.36413	+	37.2113i	0.246790	+	1.44299i
$666$	1.07855	+	1.86811i	0.0417931	+	0.0723877i
$667$		−	10.6296i		−	0.411579i
$668$	5.13871	+	19.1779i	0.198823	+	0.742016i
$669$	−5.62213	+	20.9821i	−0.217364	+	0.811215i
$670$	−1.49434	−	1.49434i	−0.0577314	−	0.0577314i
$671$	−7.41167	−	7.41167i	−0.286124	−	0.286124i
$672$	−7.96460	+	11.2510i	−0.307241	+	0.434016i
$673$	−40.0862	+	23.1438i	−1.54521	+	0.892126i	−0.546711	+	0.837321i	$0.684120\pi$
$673$	−40.0862	+	23.1438i	−1.54521	+	0.892126i	−0.998497	+	0.0548050i	$0.982546\pi$
$674$	−0.906443	−	3.38289i	−0.0349149	−	0.130304i
$675$	−0.274986	+	0.476290i	−0.0105842	+	0.0183324i
$676$	−14.9408	−	16.6220i	−0.574646	−	0.639307i
$677$	3.29683	−	1.90343i	0.126707	−	0.0731546i	−0.435307	−	0.900282i	$-0.643360\pi$
$677$	3.29683	−	1.90343i	0.126707	−	0.0731546i	0.562014	+	0.827128i	$0.310027\pi$
$678$	−2.10770	−	0.564756i	−0.0809457	−	0.0216893i
$679$	−40.1153	−	3.71769i	−1.53948	−	0.142672i
$680$	11.8725	+	6.85462i	0.455291	+	0.262863i
$681$	3.02314	−	11.2825i	0.115847	−	0.432347i
$682$	9.75091	+	2.61275i	0.373382	+	0.100047i
$683$	10.5464	+	2.82590i	0.403547	+	0.108130i	0.454883	−	0.890551i	$-0.349681\pi$
$683$	10.5464	+	2.82590i	0.403547	+	0.108130i	−0.0513357	+	0.998681i	$0.516348\pi$
$684$	3.00977	−	11.2326i	0.115081	−	0.429489i
$685$	28.7186	+	16.5807i	1.09728	+	0.633515i
$686$	7.04553	−	6.83134i	0.269000	−	0.260822i
$687$	−4.69053	−	1.25682i	−0.178955	−	0.0479508i
$688$	−10.4458	+	6.03088i	−0.398242	+	0.229925i
$689$	26.1224	−	10.0146i	0.995183	−	0.381528i
$690$	4.38464	−	7.59442i	0.166920	−	0.289115i
$691$	5.97064	+	22.2827i	0.227134	+	0.847675i	0.981538	+	0.191265i	$0.0612590\pi$
$691$	5.97064	+	22.2827i	0.227134	+	0.847675i	−0.754405	+	0.656410i	$0.772074\pi$
$692$	−28.3756	+	16.3827i	−1.07868	+	0.622776i
$693$	−3.18696	−	6.92729i	−0.121063	−	0.263146i
$694$	5.77412	+	5.77412i	0.219183	+	0.219183i
$695$	27.6553	+	27.6553i	1.04903	+	1.04903i
$696$	−0.691106	+	2.57924i	−0.0261963	+	0.0977660i
$697$	5.84682	+	21.8206i	0.221464	+	0.826515i
$698$		−	1.34801i		−	0.0510228i
$699$	−1.10676	−	1.91696i	−0.0418614	−	0.0725060i
$700$	0.867688	−	2.34632i	0.0327955	−	0.0886827i
$701$			12.3895i			0.467945i	0.972243	+	0.233973i	$0.0751726\pi$
$701$			12.3895i			0.467945i	−0.972243	+	0.233973i	$0.924827\pi$
$702$	0.777826	−	1.74502i	0.0293572	−	0.0658616i
$703$	23.8465	+	13.7678i	0.899389	+	0.519262i
$704$	−4.13202	−	4.13202i	−0.155732	−	0.155732i
$705$	6.68532	+	3.85977i	0.251784	+	0.145367i
$706$	−1.33628	+	2.31451i	−0.0502917	+	0.0871077i
$707$	7.68531	−	20.7819i	0.289036	−	0.781584i
$708$	−4.72915	+	1.26717i	−0.177732	+	0.0476232i
$709$	−16.8696	+	16.8696i	−0.633553	+	0.633553i	−0.948957	−	0.315405i	$-0.897860\pi$
$709$	−16.8696	+	16.8696i	−0.633553	+	0.633553i	0.315405	+	0.948957i	$0.397860\pi$
$710$	−11.0374	+	2.95747i	−0.414227	+	0.110992i
$711$	1.13108	+	1.95909i	0.0424188	+	0.0734715i
$712$	12.1719	−	21.0824i	0.456162	−	0.790096i
$713$	13.4219	−	50.0912i	0.502654	−	1.87593i
$714$	1.93220	+	4.19990i	0.0723109	+	0.157177i
$715$	−21.6495	−	3.43842i	−0.809645	−	0.128589i
$716$	9.32484	+	16.1511i	0.348486	+	0.603595i
$717$	5.82013	−	5.82013i	0.217357	−	0.217357i
$718$	−5.13669			−0.191700
$719$	41.6555			1.55349			0.776744	−	0.629817i	$-0.216870\pi$
$719$	41.6555			1.55349			0.776744	+	0.629817i	$0.216870\pi$
$720$	3.57126	−	3.57126i	0.133093	−	0.133093i
$721$	−20.5837	+	3.52036i	−0.766576	+	0.131105i
$722$	3.66887	+	13.6924i	0.136541	+	0.509579i
$723$	14.0506	+	3.76485i	0.522548	+	0.140016i
$724$	−8.51095	+	4.91380i	−0.316307	+	0.182620i
$725$		−	0.745171i		−	0.0276749i
$726$	1.37871	−	0.369425i	0.0511689	−	0.0137107i
$727$	−31.5386			−1.16970			−0.584851	−	0.811141i	$-0.698847\pi$
$727$	−31.5386			−1.16970			−0.584851	+	0.811141i	$0.698847\pi$
$728$	−4.64966	+	18.2158i	−0.172328	+	0.675122i
$729$	−1.00000			−0.0370370
$730$	7.60478	−	2.03769i	0.281465	−	0.0754184i
$731$			16.6132i			0.614463i
$732$	5.41490	−	3.12629i	0.200140	−	0.115551i
$733$	−31.5148	−	8.44436i	−1.16402	−	0.311899i	−0.375452	−	0.926842i	$-0.622513\pi$
$733$	−31.5148	−	8.44436i	−1.16402	−	0.311899i	−0.788572	+	0.614942i	$0.789179\pi$
$734$	1.02661	+	3.83137i	0.0378929	+	0.141418i
$735$	−12.1826	+	8.34484i	−0.449361	+	0.307804i
$736$	28.9026	−	28.9026i	1.06536	−	1.06536i
$737$	5.44886			0.200711
$738$	−3.63000			−0.133622
$739$	23.5095	−	23.5095i	0.864813	−	0.864813i	−0.127080	−	0.991892i	$-0.540560\pi$
$739$	23.5095	−	23.5095i	0.864813	−	0.864813i	0.991892	+	0.127080i	$0.0405605\pi$
$740$	7.38199	+	12.7860i	0.271367	+	0.470022i
$741$	−2.53889	−	24.2555i	−0.0932683	−	0.891048i
$742$	−8.87850	−	6.28512i	−0.325940	−	0.230734i
$743$	8.41303	−	31.3979i	0.308644	−	1.15188i	−0.621118	−	0.783717i	$-0.713321\pi$
$743$	8.41303	−	31.3979i	0.308644	−	1.15188i	0.929763	−	0.368159i	$-0.120012\pi$
$744$	−6.51358	+	11.2819i	−0.238800	+	0.413613i
$745$	−23.2896	−	40.3387i	−0.853264	−	1.47790i
$746$	−9.69301	+	2.59723i	−0.354886	+	0.0950915i
$747$	−3.97225	+	3.97225i	−0.145337	+	0.145337i
$748$	−15.7826	+	4.22893i	−0.577068	+	0.154625i
$749$	−33.8307	−	40.7417i	−1.23615	−	1.48867i
$750$	3.10187	−	5.37259i	0.113264	−	0.196179i
$751$	37.1727	+	21.4617i	1.35645	+	0.783148i	0.989144	−	0.146951i	$-0.0469459\pi$
$751$	37.1727	+	21.4617i	1.35645	+	0.783148i	0.367309	+	0.930099i	$0.380279\pi$
$752$	6.19513	+	6.19513i	0.225913	+	0.225913i
$753$	−18.6160	−	10.7479i	−0.678403	−	0.391676i
$754$	0.269485	+	2.57455i	0.00981407	+	0.0937597i
$755$		−	37.5828i		−	1.36778i
$756$	4.48354	−	0.766806i	0.163065	−	0.0278885i
$757$	6.45620	+	11.1825i	0.234654	+	0.406433i	0.959172	−	0.282823i	$-0.0912708\pi$
$757$	6.45620	+	11.1825i	0.234654	+	0.406433i	−0.724518	+	0.689256i	$0.757937\pi$
$758$			13.5471i			0.492051i
$759$	5.85196	+	21.8398i	0.212413	+	0.792735i
$760$	−7.27806	+	27.1621i	−0.264003	+	0.985273i
$761$	−26.9660	−	26.9660i	−0.977516	−	0.977516i	0.0222364	−	0.999753i	$-0.492921\pi$
$761$	−26.9660	−	26.9660i	−0.977516	−	0.977516i	−0.999753	+	0.0222364i	$0.992921\pi$
$762$	6.50779	+	6.50779i	0.235752	+	0.235752i
$763$	1.70835	−	18.4338i	0.0618465	−	0.667347i
$764$	34.2520	−	19.7754i	1.23919	−	0.715449i
$765$	−1.80043	−	6.71929i	−0.0650947	−	0.242937i
$766$	−2.38776	+	4.13571i	−0.0862731	+	0.149429i
$767$	−8.30943	+	6.03173i	−0.300036	+	0.217793i
$768$	−1.76299	+	1.01786i	−0.0636165	+	0.0367290i
$769$	−0.0137463	−	0.00368331i	−0.000495704	−	0.000132824i	0.258571	−	0.965992i	$-0.416748\pi$
$769$	−0.0137463	−	0.00368331i	−0.000495704	−	0.000132824i	−0.259067	+	0.965859i	$0.583415\pi$
$770$	3.56238	+	7.74330i	0.128379	+	0.279049i
$771$	−6.53224	−	3.77139i	−0.235253	−	0.135823i
$772$	2.21903	−	8.28154i	0.0798647	−	0.298059i
$773$	16.6107	+	4.45082i	0.597445	+	0.160085i	0.544854	−	0.838531i	$-0.316585\pi$
$773$	16.6107	+	4.45082i	0.597445	+	0.160085i	0.0525914	+	0.998616i	$0.483252\pi$
$774$	−2.57858	−	0.690929i	−0.0926852	−	0.0248349i
$775$	0.940921	−	3.51157i	0.0337989	−	0.126139i
$776$	−25.9886	−	15.0045i	−0.932935	−	0.538630i
$777$	−0.993906	+	10.7246i	−0.0356562	+	0.384744i
$778$	14.4718	+	3.87771i	0.518840	+	0.139023i
$779$	−40.1292	+	23.1686i	−1.43778	+	0.830101i
$780$	5.32371	−	11.9435i	0.190619	−	0.427647i
$781$	14.7311	−	25.5150i	0.527120	−	0.912999i
$782$	−3.54795	−	13.2411i	−0.126874	−	0.473502i
$783$	1.17340	−	0.677462i	0.0419339	−	0.0242105i
$784$	−15.8066	+	5.56964i	−0.564523	+	0.198916i
$785$	−5.68171	−	5.68171i	−0.202789	−	0.202789i
$786$	−2.85266	−	2.85266i	−0.101751	−	0.101751i
$787$	8.75711	−	32.6820i	0.312157	−	1.16499i	−0.614450	−	0.788956i	$-0.710622\pi$
$787$	8.75711	−	32.6820i	0.312157	−	1.16499i	0.926607	−	0.376031i	$-0.122711\pi$
$788$	2.01368	+	7.51514i	0.0717343	+	0.267716i
$789$			23.8379i			0.848653i
$790$	−1.26432	−	2.18986i	−0.0449823	−	0.0779117i
$791$	−6.96022	−	8.38207i	−0.247477	−	0.298032i
$792$		−	5.67985i		−	0.201825i
$793$	8.25657	−	10.1871i	0.293199	−	0.361755i
$794$	7.80742	+	4.50761i	0.277075	+	0.159969i
$795$	11.5740	+	11.5740i	0.410488	+	0.410488i
$796$	32.4684	+	18.7457i	1.15081	+	0.664422i
$797$	10.7585	−	18.6343i	0.381087	−	0.660062i	−0.610131	−	0.792300i	$-0.708883\pi$
$797$	10.7585	−	18.6343i	0.381087	−	0.660062i	0.991218	+	0.132239i	$0.0422166\pi$
$798$	−7.29548	+	6.05795i	−0.258257	+	0.214449i
$799$	11.6561	−	3.12324i	0.412363	−	0.110492i
$800$	2.02617	−	2.02617i	0.0716359	−	0.0716359i
$801$	−11.9316	+	3.19707i	−0.421583	+	0.112963i
$802$	−1.51004	−	2.61547i	−0.0533214	−	0.0923553i
$803$	−10.1497	+	17.5798i	−0.358176	+	0.620378i
$804$	−0.841260	+	3.13962i	−0.0296689	+	0.110726i
$805$	39.7780	−	18.3002i	1.40199	−	0.644998i
$806$	−1.98094	+	12.4727i	−0.0697756	+	0.439332i
$807$	−13.8150	−	23.9283i	−0.486311	−	0.842316i
$808$	11.6705	−	11.6705i	0.410566	−	0.410566i
$809$	−3.38903			−0.119152			−0.0595761	−	0.998224i	$-0.518975\pi$
$809$	−3.38903			−0.119152			−0.0595761	+	0.998224i	$0.518975\pi$
$810$	1.11780			0.0392754
$811$	10.1944	−	10.1944i	0.357974	−	0.357974i	−0.505092	−	0.863066i	$-0.668541\pi$
$811$	10.1944	−	10.1944i	0.357974	−	0.357974i	0.863066	+	0.505092i	$0.168541\pi$
$812$	−4.74149	+	3.93719i	−0.166394	+	0.138168i
$813$	−5.35298	−	19.9776i	−0.187737	−	0.700644i
$814$	6.00508	+	1.60906i	0.210478	+	0.0563974i
$815$	14.4984	−	8.37066i	0.507857	−	0.293212i
$816$		−	7.89502i		−	0.276381i
$817$	−32.9158	+	8.81976i	−1.15158	+	0.308564i
$818$	6.27596			0.219434
$819$	8.20410	−	4.86751i	0.286675	−	0.170085i
$820$	−24.8450			−0.867624
$821$	−4.00847	+	1.07407i	−0.139896	+	0.0374851i	−0.328088	−	0.944647i	$-0.606404\pi$
$821$	−4.00847	+	1.07407i	−0.139896	+	0.0374851i	0.188191	+	0.982132i	$0.439738\pi$
$822$			8.32976i			0.290534i
$823$	−43.4703	+	25.0976i	−1.51528	+	0.874847i	−0.515441	+	0.856925i	$0.672372\pi$
$823$	−43.4703	+	25.0976i	−1.51528	+	0.874847i	−0.999839	+	0.0179221i	$0.994295\pi$
$824$	−15.0249	−	4.02591i	−0.523417	−	0.140249i
$825$	0.410242	+	1.53105i	0.0142828	+	0.0533042i
$826$	3.74458	+	1.38477i	0.130291	+	0.0481825i
$827$	17.6628	−	17.6628i	0.614195	−	0.614195i	−0.329842	−	0.944036i	$-0.606995\pi$
$827$	17.6628	−	17.6628i	0.614195	−	0.614195i	0.944036	+	0.329842i	$0.106995\pi$
$828$	−13.4876			−0.468725
$829$	32.8033			1.13930			0.569652	−	0.821886i	$-0.307078\pi$
$829$	32.8033			1.13930			0.569652	+	0.821886i	$0.307078\pi$
$830$	4.44016	−	4.44016i	0.154120	−	0.154120i
$831$	4.49199	+	7.78035i	0.155825	+	0.269897i
$832$	4.60306	−	5.67934i	0.159582	−	0.196896i
$833$	−4.24205	+	22.6901i	−0.146978	+	0.786165i
$834$	−2.54267	+	9.48936i	−0.0880454	+	0.328590i
$835$	−12.1808	+	21.0978i	−0.421535	+	0.730121i
$836$	−16.7575	−	29.0249i	−0.579572	−	1.00385i
$837$	6.38499	−	1.71085i	0.220698	−	0.0591357i
$838$	−3.99821	+	3.99821i	−0.138116	+	0.138116i
$839$	12.9458	−	3.46880i	0.446937	−	0.119756i	−0.0283288	−	0.999599i	$-0.509019\pi$
$839$	12.9458	−	3.46880i	0.446937	−	0.119756i	0.475266	+	0.879842i	$0.342352\pi$
$840$	−10.8418	+	1.85425i	−0.374079	+	0.0639777i
$841$	13.5821	−	23.5249i	0.468348	−	0.811202i
$842$	5.10461	+	2.94715i	0.175916	+	0.101565i
$843$	13.3221	+	13.3221i	0.458838	+	0.458838i
$844$	−15.2539	−	8.80683i	−0.525060	−	0.303144i
$845$	1.45863	−	27.3848i	0.0501782	−	0.942066i
$846$			1.93906i			0.0666663i
$847$	6.68443	+	2.47195i	0.229680	+	0.0849373i
$848$	9.28845	+	16.0881i	0.318967	+	0.552466i
$849$		−	19.3973i		−	0.665713i
$850$	−0.248723	−	0.928248i	−0.00853114	−	0.0318387i
$851$	8.26585	−	30.8486i	0.283350	−	1.05748i
$852$	12.4273	+	12.4273i	0.425754	+	0.425754i
$853$	−26.6788	−	26.6788i	−0.913466	−	0.913466i	0.0830772	−	0.996543i	$-0.473525\pi$
$853$	−26.6788	−	26.6788i	−0.913466	−	0.913466i	−0.996543	+	0.0830772i	$0.973525\pi$
$854$	−5.07692	−	0.470505i	−0.173729	−	0.0161003i
$855$	12.3571	−	7.13438i	0.422604	−	0.243991i
$856$	−10.2094	−	38.1021i	−0.348951	−	1.30230i
$857$	23.1022	−	40.0142i	0.789156	−	1.36686i	−0.137328	−	0.990526i	$-0.543852\pi$
$857$	23.1022	−	40.0142i	0.789156	−	1.36686i	0.926484	−	0.376333i	$-0.122815\pi$
$858$	−1.97107	−	5.14138i	−0.0672913	−	0.175524i
$859$	23.6394	−	13.6482i	0.806565	−	0.465671i	−0.0391966	−	0.999232i	$-0.512480\pi$
$859$	23.6394	−	13.6482i	0.806565	−	0.465671i	0.845762	+	0.533561i	$0.179147\pi$
$860$	−17.6487	−	4.72896i	−0.601816	−	0.161256i
$861$	−14.7933	−	10.4722i	−0.504155	−	0.356892i
$862$	2.99181	+	1.72732i	0.101902	+	0.0588329i
$863$	4.68768	−	17.4947i	0.159570	−	0.595525i	−0.839100	−	0.543977i	$-0.816918\pi$
$863$	4.68768	−	17.4947i	0.159570	−	0.595525i	0.998671	−	0.0515479i	$-0.0164155\pi$
$864$	5.03262	+	1.34849i	0.171213	+	0.0458764i
$865$	−38.8337	−	10.4054i	−1.32038	−	0.353796i
$866$	3.19784	−	11.9345i	0.108667	−	0.405551i
$867$	5.30511	+	3.06290i	0.180171	+	0.104022i
$868$	−27.3154	+	12.5667i	−0.927146	+	0.426542i
$869$	6.29753	+	1.68742i	0.213629	+	0.0572418i
$870$	−1.31162	+	0.757265i	−0.0444681	+	0.0256737i
$871$	0.709644	+	6.77965i	0.0240454	+	0.229720i
$872$	6.89486	−	11.9422i	0.233489	−	0.404415i
$873$	3.94107	+	14.7083i	0.133385	+	0.497800i
$874$	24.3511	−	14.0591i	0.823687	−	0.475556i
$875$	28.1405	−	12.9463i	0.951323	−	0.437665i
$876$	−8.56243	−	8.56243i	−0.289298	−	0.289298i
$877$	−7.83820	−	7.83820i	−0.264677	−	0.264677i	0.562274	−	0.826951i	$-0.309927\pi$
$877$	−7.83820	−	7.83820i	−0.264677	−	0.264677i	−0.826951	+	0.562274i	$0.809927\pi$
$878$	−0.805377	+	3.00571i	−0.0271802	+	0.101438i
$879$	6.76482	+	25.2467i	0.228172	+	0.851549i
$880$		−	14.5559i		−	0.490681i
$881$	5.59477	+	9.69042i	0.188492	+	0.326479i	0.944748	−	0.327798i	$-0.106307\pi$
$881$	5.59477	+	9.69042i	0.188492	+	0.326479i	−0.756255	+	0.654277i	$0.772973\pi$
$882$	−3.34536	−	1.60208i	−0.112644	−	0.0539448i
$883$		−	45.3449i		−	1.52598i	−0.646411	−	0.762989i	$-0.723731\pi$
$883$		−	45.3449i		−	1.52598i	0.646411	−	0.762989i	$-0.276269\pi$
$884$	−7.31725	−	19.0864i	−0.246106	−	0.641947i
$885$	−5.20258	−	3.00371i	−0.174883	−	0.100969i
$886$	8.44426	+	8.44426i	0.283690	+	0.283690i
$887$	−32.1643	−	18.5701i	−1.07997	−	0.623522i	−0.149084	−	0.988825i	$-0.547632\pi$
$887$	−32.1643	−	18.5701i	−1.07997	−	0.623522i	−0.930889	+	0.365302i	$0.880966\pi$
$888$	−4.01138	+	6.94791i	−0.134613	+	0.233156i
$889$	7.74676	+	45.2955i	0.259818	+	1.51916i
$890$	13.3371	−	3.57367i	0.447061	−	0.119790i
$891$	−2.03793	+	2.03793i	−0.0682732	+	0.0682732i
$892$	−36.0729	+	9.66570i	−1.20781	+	0.323632i
$893$	12.3761	+	21.4361i	0.414152	+	0.717332i
$894$	5.85008	−	10.1326i	0.195656	−	0.338886i
$895$	−5.92266	+	22.1037i	−0.197973	+	0.738845i
$896$	−30.2823	−	2.80642i	−1.01166	−	0.0937558i
$897$	−26.4117	+	10.1256i	−0.881860	+	0.338083i
$898$	1.23456	+	2.13832i	0.0411978	+	0.0713567i
$899$	−6.33310	+	6.33310i	−0.211221	+	0.211221i
$900$	−0.945524			−0.0315175
$901$	25.5868			0.852421
$902$	−7.39767	+	7.39767i	−0.246316	+	0.246316i
$903$	−8.51521	−	10.2547i	−0.283369	−	0.341256i
$904$	−2.10045	−	7.83900i	−0.0698601	−	0.260721i
$905$	−11.6477	−	3.12100i	−0.387183	−	0.103745i
$906$	8.17560	−	4.72019i	0.271616	−	0.156818i
$907$			46.8710i			1.55633i	0.628063	+	0.778163i	$0.283848\pi$
$907$			46.8710i			1.55633i	−0.628063	+	0.778163i	$0.716152\pi$
$908$	19.3972	−	5.19746i	0.643718	−	0.172484i
$909$	−8.37472			−0.277772
$910$	−9.17052	+	5.44089i	−0.304000	+	0.180364i
$911$	−29.2953			−0.970596			−0.485298	−	0.874349i	$-0.661289\pi$
$911$	−29.2953			−0.970596			−0.485298	+	0.874349i	$0.661289\pi$
$912$	15.6424	−	4.19137i	0.517972	−	0.138790i
$913$			16.1903i			0.535821i
$914$	−12.5094	+	7.22231i	−0.413774	+	0.238893i
$915$	7.41059	+	1.98566i	0.244986	+	0.0656439i
$916$	−2.16076	−	8.06406i	−0.0713934	−	0.266444i
$917$	−3.39576	−	19.8551i	−0.112138	−	0.655674i
$918$	1.23556	−	1.23556i	0.0407796	−	0.0407796i
$919$	−22.9342			−0.756529			−0.378265	−	0.925698i	$-0.623479\pi$
$919$	−22.9342			−0.756529			−0.378265	+	0.925698i	$0.623479\pi$
$920$	32.6149			1.07528
$921$	1.58354	−	1.58354i	0.0521793	−	0.0521793i
$922$	−5.33484	−	9.24022i	−0.175694	−	0.304311i
$923$	33.6652	+	15.0059i	1.10810	+	0.493926i
$924$	7.57443	−	10.6998i	0.249180	−	0.351998i
$925$	0.579464	−	2.16259i	0.0190527	−	0.0711055i
$926$	−2.60508	+	4.51213i	−0.0856083	+	0.148278i
$927$	3.94643	+	6.83541i	0.129618	+	0.224504i
$928$	−6.81882	+	1.82710i	−0.223839	+	0.0599774i
$929$	−11.9263	+	11.9263i	−0.391289	+	0.391289i	−0.875147	−	0.483857i	$-0.839235\pi$
$929$	−11.9263	+	11.9263i	−0.391289	+	0.391289i	0.483857	+	0.875147i	$0.339235\pi$
$930$	−7.13712	+	1.91239i	−0.234035	+	0.0627096i
$931$	−47.2079	+	3.64111i	−1.54718	+	0.119333i
$932$	1.90276	−	3.29568i	0.0623270	−	0.107953i
$933$	13.1562	+	7.59574i	0.430715	+	0.248673i
$934$	5.92123	+	5.92123i	0.193748	+	0.193748i
$935$	−17.3626	−	10.0243i	−0.567817	−	0.327829i
$936$	7.06706	−	0.739728i	0.230994	−	0.0241788i
$937$		−	42.9957i		−	1.40461i	−0.711877	−	0.702304i	$-0.752155\pi$
$937$		−	42.9957i		−	1.40461i	0.711877	−	0.702304i	$-0.247845\pi$
$938$	2.03916	−	1.69326i	0.0665809	−	0.0552868i
$939$	−1.53982	−	2.66705i	−0.0502502	−	0.0870358i
$940$			13.2716i			0.432872i
$941$	14.3161	+	53.4286i	0.466693	+	1.74172i	0.651215	+	0.758893i	$0.274260\pi$
$941$	14.3161	+	53.4286i	0.466693	+	1.74172i	−0.184522	+	0.982828i	$0.559074\pi$
$942$	0.522385	−	1.94957i	0.0170202	−	0.0635203i
$943$	38.0024	+	38.0024i	1.23753	+	1.23753i
$944$	−4.82111	−	4.82111i	−0.156914	−	0.156914i
$945$	4.55535	+	3.22474i	0.148186	+	0.104901i
$946$	−6.66303	+	3.84690i	−0.216634	+	0.125074i
$947$	7.38225	+	27.5509i	0.239891	+	0.895284i	0.975883	+	0.218294i	$0.0700493\pi$
$947$	7.38225	+	27.5509i	0.239891	+	0.895284i	−0.735992	+	0.676990i	$0.763284\pi$
$948$	−1.94458	+	3.36810i	−0.0631569	+	0.109391i
$949$	−23.1953	−	10.3391i	−0.752950	−	0.335620i
$950$	1.70709	−	0.985590i	0.0553854	−	0.0319768i
$951$	7.94761	+	2.12956i	0.257719	+	0.0690556i
$952$	−9.93450	+	14.0337i	−0.321979	+	0.454835i
$953$	15.2652	+	8.81337i	0.494488	+	0.285493i	0.726435	−	0.687236i	$-0.241176\pi$
$953$	15.2652	+	8.81337i	0.494488	+	0.285493i	−0.231946	+	0.972729i	$0.574509\pi$
$954$	−1.06413	+	3.97140i	−0.0344526	+	0.128579i
$955$	46.8758	+	12.5603i	1.51686	+	0.406443i
$956$	13.6686	+	3.66249i	0.442074	+	0.118453i
$957$	1.01068	−	3.77192i	0.0326708	−	0.121929i
$958$	15.1336	+	8.73737i	0.488943	+	0.282292i
$959$	−24.0306	+	33.9462i	−0.775989	+	1.09618i
$960$	4.13142	+	1.10701i	0.133341	+	0.0357286i
$961$	−10.9943	+	6.34756i	−0.354655	+	0.204760i
$962$	−1.21996	+	7.68128i	−0.0393330	+	0.247654i
$963$	−10.0079	+	17.3341i	−0.322499	+	0.558585i
$964$	6.47261	+	24.1561i	0.208469	+	0.778016i
$965$	9.11061	−	5.26001i	0.293281	−	0.169326i
$966$	8.97683	+	6.35472i	0.288825	+	0.204460i
$967$	−0.451783	−	0.451783i	−0.0145284	−	0.0145284i	0.699805	−	0.714334i	$-0.253270\pi$
$967$	−0.451783	−	0.451783i	−0.0145284	−	0.0145284i	−0.714334	+	0.699805i	$0.753270\pi$
$968$	3.75377	+	3.75377i	0.120651	+	0.120651i
$969$	5.77297	−	21.5450i	0.185455	−	0.692126i
$970$	−4.40531	−	16.4409i	−0.141446	−	0.527884i
$971$		−	48.0359i		−	1.54154i	−0.637111	−	0.770772i	$-0.719871\pi$
$971$		−	48.0359i		−	1.54154i	0.637111	−	0.770772i	$-0.280129\pi$
$972$	−0.859611	−	1.48889i	−0.0275720	−	0.0477562i
$973$	−37.7381	+	31.3366i	−1.20983	+	1.00460i
$974$			14.3477i			0.459731i
$975$	−1.85155	+	0.709836i	−0.0592970	+	0.0227329i
$976$	7.54072	+	4.35364i	0.241373	+	0.139357i
$977$	38.6070	+	38.6070i	1.23515	+	1.23515i	0.961962	+	0.273184i	$0.0880768\pi$
$977$	38.6070	+	38.6070i	1.23515	+	1.23515i	0.273184	+	0.961962i	$0.411923\pi$
$978$	3.64184	+	2.10261i	0.116453	+	0.0672342i
$979$	−17.8004	+	30.8312i	−0.568903	+	0.985369i
$980$	−22.8968	−	10.9652i	−0.731412	−	0.350270i
$981$	−6.75874	+	1.81100i	−0.215790	+	0.0578207i
$982$	4.71710	−	4.71710i	0.150529	−	0.150529i
$983$	−43.8637	+	11.7532i	−1.39903	+	0.374870i	−0.877998	−	0.478664i	$-0.841121\pi$
$983$	−43.8637	+	11.7532i	−1.39903	+	0.374870i	−0.521036	+	0.853534i	$0.674454\pi$
$984$	−6.75038	−	11.6920i	−0.215194	−	0.372728i
$985$	−4.77323	+	8.26748i	−0.152088	+	0.263424i
$986$	−0.612761	+	2.28686i	−0.0195143	+	0.0728283i
$987$	−5.59402	+	7.90225i	−0.178060	+	0.251531i
$988$	33.9313	−	24.6304i	1.07950	−	0.783598i
$989$	19.7618	+	34.2285i	0.628390	+	1.08840i
$990$	2.27799	−	2.27799i	0.0723992	−	0.0723992i
$991$	42.6152			1.35372			0.676858	−	0.736114i	$-0.263341\pi$
$991$	42.6152			1.35372			0.676858	+	0.736114i	$0.263341\pi$
$992$	−34.4403			−1.09348
$993$	−15.5865	+	15.5865i	−0.494622	+	0.494622i
$994$	−2.41599	−	14.1264i	−0.0766307	−	0.448062i
$995$	11.9063	+	44.4349i	0.377455	+	1.40868i
$996$	−9.32883	−	2.49965i	−0.295595	−	0.0792045i
$997$	−26.0063	+	15.0148i	−0.823629	+	0.475523i	−0.851666	−	0.524084i	$-0.824408\pi$
$997$	−26.0063	+	15.0148i	−0.823629	+	0.475523i	0.0280372	+	0.999607i	$0.491074\pi$
$998$		−	13.1899i		−	0.417519i
$999$	3.93218	−	1.05363i	0.124409	−	0.0333352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.115.5	yes	36
3.2	odd	2		819.2.gh.c.388.5		36
7.5	odd	6		273.2.bt.a.271.5	yes	36
13.6	odd	12		273.2.bt.a.136.5	✓	36
21.5	even	6		819.2.et.c.271.5		36
39.32	even	12		819.2.et.c.136.5		36
91.19	even	12	inner	273.2.cg.a.19.5	yes	36
273.110	odd	12		819.2.gh.c.19.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.5	✓	36	13.6	odd	12
273.2.bt.a.271.5	yes	36	7.5	odd	6
273.2.cg.a.19.5	yes	36	91.19	even	12	inner
273.2.cg.a.115.5	yes	36	1.1	even	1	trivial
819.2.et.c.136.5		36	39.32	even	12
819.2.et.c.271.5		36	21.5	even	6
819.2.gh.c.19.5		36	273.110	odd	12
819.2.gh.c.388.5		36	3.2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.511829 + 0.137144i) q^{2} +1.00000i q^{3} +(-1.48889 + 0.859611i) q^{4} +(-2.03763 - 0.545981i) q^{5} +(-0.137144 - 0.511829i) q^{6} +(0.917679 - 2.48150i) q^{7} +(1.39354 - 1.39354i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.511829 + 0.137144i) q^{2} +1.00000i q^{3} +(-1.48889 + 0.859611i) q^{4} +(-2.03763 - 0.545981i) q^{5} +(-0.137144 - 0.511829i) q^{6} +(0.917679 - 2.48150i) q^{7} +(1.39354 - 1.39354i) q^{8} -1.00000 q^{9} +1.11780 q^{10} +(-2.03793 + 2.03793i) q^{11} +(-0.859611 - 1.48889i) q^{12} +(-2.80107 - 2.27024i) q^{13} +(-0.129371 + 1.39596i) q^{14} +(0.545981 - 2.03763i) q^{15} +(1.19709 - 2.07341i) q^{16} +(-1.64880 - 2.85581i) q^{17} +(0.511829 - 0.137144i) q^{18} +(4.78288 - 4.78288i) q^{19} +(3.50314 - 0.938663i) q^{20} +(2.48150 + 0.917679i) q^{21} +(0.763581 - 1.32256i) q^{22} +(-6.79410 - 3.92258i) q^{23} +(1.39354 + 1.39354i) q^{24} +(-0.476290 - 0.274986i) q^{25} +(1.74502 + 0.777826i) q^{26} -1.00000i q^{27} +(0.766806 + 4.48354i) q^{28} +(0.677462 + 1.17340i) q^{29} +1.11780i q^{30} +(1.71085 + 6.38499i) q^{31} +(-1.34849 + 5.03262i) q^{32} +(-2.03793 - 2.03793i) q^{33} +(1.23556 + 1.23556i) q^{34} +(-3.22474 + 4.55535i) q^{35} +(1.48889 - 0.859611i) q^{36} +(1.05363 + 3.93218i) q^{37} +(-1.79207 + 3.10396i) q^{38} +(2.27024 - 2.80107i) q^{39} +(-3.60036 + 2.07867i) q^{40} +(-6.61712 - 1.77305i) q^{41} +(-1.39596 - 0.129371i) q^{42} +(-4.36301 - 2.51899i) q^{43} +(1.28243 - 4.78608i) q^{44} +(2.03763 + 0.545981i) q^{45} +(4.01538 + 1.07592i) q^{46} +(-0.947124 + 3.53471i) q^{47} +(2.07341 + 1.19709i) q^{48} +(-5.31573 - 4.55445i) q^{49} +(0.281492 + 0.0754255i) q^{50} +(2.85581 - 1.64880i) q^{51} +(6.12201 + 0.972311i) q^{52} +(-3.87961 + 6.71968i) q^{53} +(0.137144 + 0.511829i) q^{54} +(5.26521 - 3.03987i) q^{55} +(-2.17925 - 4.73689i) q^{56} +(4.78288 + 4.78288i) q^{57} +(-0.507670 - 0.507670i) q^{58} +(0.737061 - 2.75075i) q^{59} +(0.938663 + 3.50314i) q^{60} +3.63687i q^{61} +(-1.75133 - 3.03339i) q^{62} +(-0.917679 + 2.48150i) q^{63} +2.02756i q^{64} +(4.46803 + 6.15525i) q^{65} +(1.32256 + 0.763581i) q^{66} +(-1.33686 - 1.33686i) q^{67} +(4.90977 + 2.83466i) q^{68} +(3.92258 - 6.79410i) q^{69} +(1.02578 - 2.77382i) q^{70} +(-9.87427 + 2.64580i) q^{71} +(-1.39354 + 1.39354i) q^{72} +(6.80337 - 1.82296i) q^{73} +(-1.07855 - 1.86811i) q^{74} +(0.274986 - 0.476290i) q^{75} +(-3.00977 + 11.2326i) q^{76} +(3.18696 + 6.92729i) q^{77} +(-0.777826 + 1.74502i) q^{78} +(-1.13108 - 1.95909i) q^{79} +(-3.57126 + 3.57126i) q^{80} +1.00000 q^{81} +3.63000 q^{82} +(3.97225 - 3.97225i) q^{83} +(-4.48354 + 0.766806i) q^{84} +(1.80043 + 6.71929i) q^{85} +(2.57858 + 0.690929i) q^{86} +(-1.17340 + 0.677462i) q^{87} +5.67985i q^{88} +(11.9316 - 3.19707i) q^{89} -1.11780 q^{90} +(-8.20410 + 4.86751i) q^{91} +13.4876 q^{92} +(-6.38499 + 1.71085i) q^{93} -1.93906i q^{94} +(-12.3571 + 7.13438i) q^{95} +(-5.03262 - 1.34849i) q^{96} +(-3.94107 - 14.7083i) q^{97} +(3.34536 + 1.60208i) q^{98} +(2.03793 - 2.03793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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