LMFDB - Embedded newform 155.2.n.a.4.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(4,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("155.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.n (of order $10$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	155.4
Dual form			155.2.n.a.39.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90735 - 0.619737i) q^{2} +(-0.725535 - 0.235741i) q^{3} +(1.63589 - 1.18855i) q^{4} +(2.06323 + 0.862016i) q^{5} -1.52995 q^{6} +(0.105855 + 0.145698i) q^{7} +(0.0260217 - 0.0358157i) q^{8} +(-1.95622 - 1.42128i) q^{9} +O(q^{10})$	\(q+(1.90735 - 0.619737i) q^{2} +(-0.725535 - 0.235741i) q^{3} +(1.63589 - 1.18855i) q^{4} +(2.06323 + 0.862016i) q^{5} -1.52995 q^{6} +(0.105855 + 0.145698i) q^{7} +(0.0260217 - 0.0358157i) q^{8} +(-1.95622 - 1.42128i) q^{9} +(4.46954 + 0.365508i) q^{10} +(1.75083 - 1.27206i) q^{11} +(-1.46709 + 0.476685i) q^{12} +(-5.76911 - 1.87450i) q^{13} +(0.292198 + 0.212294i) q^{14} +(-1.29374 - 1.11181i) q^{15} +(-1.22227 + 3.76177i) q^{16} +(0.322228 - 0.443509i) q^{17} +(-4.61203 - 1.49854i) q^{18} +(1.53326 + 4.71889i) q^{19} +(4.39977 - 1.04208i) q^{20} +(-0.0424550 - 0.130663i) q^{21} +(2.55112 - 3.51132i) q^{22} +(-0.938327 + 1.29150i) q^{23} +(-0.0273228 + 0.0198512i) q^{24} +(3.51386 + 3.55708i) q^{25} -12.1654 q^{26} +(2.42947 + 3.34388i) q^{27} +(0.346336 + 0.112531i) q^{28} +(-0.614635 - 1.89165i) q^{29} +(-3.15664 - 1.31884i) q^{30} +(-5.41535 + 1.29384i) q^{31} +8.02107i q^{32} +(-1.57017 + 0.510178i) q^{33} +(0.339744 - 1.04563i) q^{34} +(0.0928109 + 0.391857i) q^{35} -4.88943 q^{36} -7.17275i q^{37} +(5.84895 + 8.05038i) q^{38} +(3.74380 + 2.72003i) q^{39} +(0.0845625 - 0.0514651i) q^{40} +(-2.48328 - 7.64276i) q^{41} +(-0.161953 - 0.222910i) q^{42} +(5.21838 - 1.69555i) q^{43} +(1.35228 - 4.16189i) q^{44} +(-2.81098 - 4.61873i) q^{45} +(-0.989334 + 3.04486i) q^{46} +(7.15332 + 2.32425i) q^{47} +(1.77361 - 2.44116i) q^{48} +(2.15310 - 6.62655i) q^{49} +(8.90663 + 4.60694i) q^{50} +(-0.338341 + 0.245819i) q^{51} +(-11.6656 + 3.79037i) q^{52} +(2.82637 - 3.89017i) q^{53} +(6.70619 + 4.87233i) q^{54} +(4.70891 - 1.11530i) q^{55} +0.00797280 q^{56} -3.78517i q^{57} +(-2.34465 - 3.22714i) q^{58} +(-2.80623 + 8.63668i) q^{59} +(-3.43785 - 0.281139i) q^{60} +6.43798 q^{61} +(-9.52715 + 5.82389i) q^{62} -0.435467i q^{63} +(2.52640 + 7.77547i) q^{64} +(-10.2872 - 8.84059i) q^{65} +(-2.67869 + 1.94618i) q^{66} -6.31053i q^{67} -1.10852i q^{68} +(0.985247 - 0.715824i) q^{69} +(0.419872 + 0.689892i) q^{70} +(2.24909 + 1.63406i) q^{71} +(-0.101808 + 0.0330796i) q^{72} +(5.67998 + 7.81783i) q^{73} +(-4.44522 - 13.6810i) q^{74} +(-1.71088 - 3.40914i) q^{75} +(8.11687 + 5.89725i) q^{76} +(0.370671 + 0.120438i) q^{77} +(8.82645 + 2.86789i) q^{78} +(-4.97456 - 3.61423i) q^{79} +(-5.76455 + 6.70780i) q^{80} +(1.26726 + 3.90021i) q^{81} +(-9.47301 - 13.0385i) q^{82} +(-10.5004 + 3.41178i) q^{83} +(-0.224751 - 0.163291i) q^{84} +(1.04714 - 0.637297i) q^{85} +(8.90250 - 6.46804i) q^{86} +1.51735i q^{87} -0.0958085i q^{88} +(-9.81216 + 7.12895i) q^{89} +(-8.22393 - 7.06748i) q^{90} +(-0.337582 - 1.03897i) q^{91} +3.22799i q^{92} +(4.23403 + 0.337894i) q^{93} +15.0843 q^{94} +(-0.904284 + 11.0579i) q^{95} +(1.89089 - 5.81956i) q^{96} +(3.96471 + 5.45695i) q^{97} -13.9735i q^{98} -5.23297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9	$ 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9} + 4 q^{10} - 14 q^{11} - 16 q^{14} + 21 q^{15} - 22 q^{16} - 2 q^{19} - 29 q^{20} - 38 q^{21} - 30 q^{24} - 10 q^{25} + 12 q^{26} + 20 q^{29} - 30 q^{30} + 26 q^{31} - 2 q^{34} + 24 q^{35} - 44 q^{36} - 18 q^{39} + 36 q^{40} - 20 q^{41} + 62 q^{44} + 8 q^{45} - 70 q^{46} - 42 q^{49} - 11 q^{50} + 10 q^{51} - 26 q^{54} - 30 q^{55} + 208 q^{56} - 50 q^{59} - 67 q^{60} + 56 q^{61} + 12 q^{64} - 27 q^{65} + 60 q^{66} + 34 q^{69} + 5 q^{70} - 8 q^{71} - 84 q^{74} - 38 q^{75} - 20 q^{76} + 122 q^{79} - 80 q^{80} + 42 q^{81} - 40 q^{84} - 18 q^{85} + 78 q^{86} - 28 q^{89} + 144 q^{90} - 20 q^{91} + 160 q^{94} + 9 q^{95} - 70 q^{96} - 52 q^{99}+O(q^{100}) $ 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9 + 4 * q^10 - 14 * q^11 - 16 * q^14 + 21 * q^15 - 22 * q^16 - 2 * q^19 - 29 * q^20 - 38 * q^21 - 30 * q^24 - 10 * q^25 + 12 * q^26 + 20 * q^29 - 30 * q^30 + 26 * q^31 - 2 * q^34 + 24 * q^35 - 44 * q^36 - 18 * q^39 + 36 * q^40 - 20 * q^41 + 62 * q^44 + 8 * q^45 - 70 * q^46 - 42 * q^49 - 11 * q^50 + 10 * q^51 - 26 * q^54 - 30 * q^55 + 208 * q^56 - 50 * q^59 - 67 * q^60 + 56 * q^61 + 12 * q^64 - 27 * q^65 + 60 * q^66 + 34 * q^69 + 5 * q^70 - 8 * q^71 - 84 * q^74 - 38 * q^75 - 20 * q^76 + 122 * q^79 - 80 * q^80 + 42 * q^81 - 40 * q^84 - 18 * q^85 + 78 * q^86 - 28 * q^89 + 144 * q^90 - 20 * q^91 + 160 * q^94 + 9 * q^95 - 70 * q^96 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	1.90735	−	0.619737i	1.34870	−	0.438220i	0.456447	−	0.889750i	$-0.349122\pi$
$2$	1.90735	−	0.619737i	1.34870	−	0.438220i	0.892256	+	0.451530i	$0.149122\pi$
$3$	−0.725535	−	0.235741i	−0.418888	−	0.136105i	0.0919867	−	0.995760i	$-0.470678\pi$
$3$	−0.725535	−	0.235741i	−0.418888	−	0.136105i	−0.510874	+	0.859655i	$0.670678\pi$
$4$	1.63589	−	1.18855i	0.817946	−	0.594273i
$5$	2.06323	+	0.862016i	0.922706	+	0.385505i
$5$	2.06323	+	0.862016i	0.922706	+	0.385505i
$6$	−1.52995			−0.624599
$7$	0.105855	+	0.145698i	0.0400096	+	0.0550685i	0.828553	−	0.559910i	$-0.189164\pi$
$7$	0.105855	+	0.145698i	0.0400096	+	0.0550685i	−0.788544	+	0.614979i	$0.789164\pi$
$8$	0.0260217	−	0.0358157i	0.00920005	−	0.0126628i
$9$	−1.95622	−	1.42128i	−0.652075	−	0.473760i
$10$	4.46954	+	0.365508i	1.41339	+	0.115584i
$11$	1.75083	−	1.27206i	0.527897	−	0.383539i	−0.291674	−	0.956518i	$-0.594212\pi$
$11$	1.75083	−	1.27206i	0.527897	−	0.383539i	0.819570	+	0.572979i	$0.194212\pi$
$12$	−1.46709	+	0.476685i	−0.423511	+	0.137607i
$13$	−5.76911	−	1.87450i	−1.60006	−	0.519892i	−0.632940	−	0.774200i	$-0.718152\pi$
$13$	−5.76911	−	1.87450i	−1.60006	−	0.519892i	−0.967123	+	0.254308i	$0.918152\pi$
$14$	0.292198	+	0.212294i	0.0780932	+	0.0567380i
$15$	−1.29374	−	1.11181i	−0.334041	−	0.287068i
$16$	−1.22227	+	3.76177i	−0.305569	+	0.940444i
$17$	0.322228	−	0.443509i	0.0781518	−	0.107567i	−0.768151	−	0.640268i	$-0.778823\pi$
$17$	0.322228	−	0.443509i	0.0781518	−	0.107567i	0.846303	+	0.532702i	$0.178823\pi$
$18$	−4.61203	−	1.49854i	−1.08707	−	0.353209i
$19$	1.53326	+	4.71889i	0.351754	+	1.08259i	0.957868	+	0.287210i	$0.0927278\pi$
$19$	1.53326	+	4.71889i	0.351754	+	1.08259i	−0.606113	+	0.795378i	$0.707272\pi$
$20$	4.39977	−	1.04208i	0.983819	−	0.233016i
$21$	−0.0424550	−	0.130663i	−0.00926444	−	0.0285130i
$22$	2.55112	−	3.51132i	0.543901	−	0.748616i
$23$	−0.938327	+	1.29150i	−0.195655	+	0.269296i	−0.895561	−	0.444939i	$-0.853225\pi$
$23$	−0.938327	+	1.29150i	−0.195655	+	0.269296i	0.699906	+	0.714235i	$0.253225\pi$
$24$	−0.0273228	+	0.0198512i	−0.00557725	+	0.00405211i
$25$	3.51386	+	3.55708i	0.702772	+	0.711415i
$26$	−12.1654			−2.38584
$27$	2.42947	+	3.34388i	0.467552	+	0.643530i
$28$	0.346336	+	0.112531i	0.0654514	+	0.0212665i
$29$	−0.614635	−	1.89165i	−0.114135	−	0.351271i	0.877631	−	0.479337i	$-0.159123\pi$
$29$	−0.614635	−	1.89165i	−0.114135	−	0.351271i	−0.991766	+	0.128066i	$0.959123\pi$
$30$	−3.15664	−	1.31884i	−0.576321	−	0.240786i
$31$	−5.41535	+	1.29384i	−0.972625	+	0.232380i
$31$	−5.41535	+	1.29384i	−0.972625	+	0.232380i
$32$			8.02107i			1.41794i
$33$	−1.57017	+	0.510178i	−0.273331	+	0.0888106i
$34$	0.339744	−	1.04563i	0.0582657	−	0.179323i
$35$	0.0928109	+	0.391857i	0.0156879	+	0.0662359i
$36$	−4.88943			−0.814905
$37$		−	7.17275i		−	1.17919i	−0.807698	−	0.589596i	$-0.799287\pi$
$37$		−	7.17275i		−	1.17919i	0.807698	−	0.589596i	$-0.200713\pi$
$38$	5.84895	+	8.05038i	0.948824	+	1.30594i
$39$	3.74380	+	2.72003i	0.599487	+	0.435553i
$40$	0.0845625	−	0.0514651i	0.0133705	−	0.00813735i
$41$	−2.48328	−	7.64276i	−0.387824	−	1.19360i	−0.934411	−	0.356197i	$-0.884073\pi$
$41$	−2.48328	−	7.64276i	−0.387824	−	1.19360i	0.546587	−	0.837402i	$-0.315927\pi$
$42$	−0.161953	−	0.222910i	−0.0249900	−	0.0343957i
$43$	5.21838	−	1.69555i	0.795795	−	0.258569i	0.117225	−	0.993105i	$-0.462600\pi$
$43$	5.21838	−	1.69555i	0.795795	−	0.258569i	0.678570	+	0.734536i	$0.262600\pi$
$44$	1.35228	−	4.16189i	0.203864	−	0.627429i
$45$	−2.81098	−	4.61873i	−0.419036	−	0.688519i
$46$	−0.989334	+	3.04486i	−0.145869	+	0.448940i
$47$	7.15332	+	2.32425i	1.04342	+	0.339027i	0.780082	−	0.625677i	$-0.215177\pi$
$47$	7.15332	+	2.32425i	1.04342	+	0.339027i	0.263336	+	0.964704i	$0.415177\pi$
$48$	1.77361	−	2.44116i	0.255998	−	0.352351i
$49$	2.15310	−	6.62655i	0.307585	−	0.946650i
$50$	8.90663	+	4.60694i	1.25959	+	0.651520i
$51$	−0.338341	+	0.245819i	−0.0473772	+	0.0344215i
$52$	−11.6656	+	3.79037i	−1.61772	+	0.525630i
$53$	2.82637	−	3.89017i	0.388232	−	0.534355i	−0.569510	−	0.821984i	$-0.692867\pi$
$53$	2.82637	−	3.89017i	0.388232	−	0.534355i	0.957742	+	0.287629i	$0.0928670\pi$
$54$	6.70619	+	4.87233i	0.912596	+	0.663040i
$55$	4.70891	−	1.11530i	0.634949	−	0.150387i
$56$	0.00797280			0.00106541
$57$		−	3.78517i		−	0.501358i
$58$	−2.34465	−	3.22714i	−0.307868	−	0.423744i
$59$	−2.80623	+	8.63668i	−0.365340	+	1.12440i	0.584428	+	0.811445i	$0.301319\pi$
$59$	−2.80623	+	8.63668i	−0.365340	+	1.12440i	−0.949768	+	0.312955i	$0.898681\pi$
$60$	−3.43785	−	0.281139i	−0.443824	−	0.0362948i
$61$	6.43798			0.824299			0.412150	−	0.911116i	$-0.364778\pi$
$61$	6.43798			0.824299			0.412150	+	0.911116i	$0.364778\pi$
$62$	−9.52715	+	5.82389i	−1.20995	+	0.739635i
$63$		−	0.435467i		−	0.0548637i
$64$	2.52640	+	7.77547i	0.315800	+	0.971933i
$65$	−10.2872	−	8.84059i	−1.27597	−	1.09654i
$66$	−2.67869	+	1.94618i	−0.329724	+	0.239558i
$67$		−	6.31053i		−	0.770954i	−0.922717	−	0.385477i	$-0.874037\pi$
$67$		−	6.31053i		−	0.770954i	0.922717	−	0.385477i	$-0.125963\pi$
$68$		−	1.10852i		−	0.134427i
$69$	0.985247	−	0.715824i	0.118610	−	0.0861750i
$70$	0.419872	+	0.689892i	0.0501842	+	0.0824578i
$71$	2.24909	+	1.63406i	0.266918	+	0.193927i	0.713191	−	0.700969i	$-0.247249\pi$
$71$	2.24909	+	1.63406i	0.266918	+	0.193927i	−0.446273	+	0.894897i	$0.647249\pi$
$72$	−0.101808	+	0.0330796i	−0.0119982	+	0.00389846i
$73$	5.67998	+	7.81783i	0.664792	+	0.915007i	0.999628	−	0.0272690i	$-0.00868107\pi$
$73$	5.67998	+	7.81783i	0.664792	+	0.915007i	−0.334836	+	0.942276i	$0.608681\pi$
$74$	−4.44522	−	13.6810i	−0.516746	−	1.59038i
$75$	−1.71088	−	3.40914i	−0.197555	−	0.393654i
$76$	8.11687	+	5.89725i	0.931069	+	0.676461i
$77$	0.370671	+	0.120438i	0.0422419	+	0.0137252i
$78$	8.82645	+	2.86789i	0.999398	+	0.324724i
$79$	−4.97456	−	3.61423i	−0.559682	−	0.406632i	0.271661	−	0.962393i	$-0.412427\pi$
$79$	−4.97456	−	3.61423i	−0.559682	−	0.406632i	−0.831342	+	0.555761i	$0.812427\pi$
$80$	−5.76455	+	6.70780i	−0.644496	+	0.749954i
$81$	1.26726	+	3.90021i	0.140806	+	0.433357i
$82$	−9.47301	−	13.0385i	−1.04612	−	1.43986i
$83$	−10.5004	+	3.41178i	−1.15256	+	0.374491i	−0.822109	−	0.569330i	$-0.807203\pi$
$83$	−10.5004	+	3.41178i	−1.15256	+	0.374491i	−0.330456	+	0.943821i	$0.607203\pi$
$84$	−0.224751	−	0.163291i	−0.0245223	−	0.0178165i
$85$	1.04714	−	0.637297i	0.113579	−	0.0691245i
$86$	8.90250	−	6.46804i	0.959981	−	0.697467i
$87$			1.51735i			0.162677i
$88$		−	0.0958085i		−	0.0102132i
$89$	−9.81216	+	7.12895i	−1.04009	+	0.755667i	−0.970302	−	0.241895i	$-0.922231\pi$
$89$	−9.81216	+	7.12895i	−1.04009	+	0.755667i	−0.0697842	+	0.997562i	$0.522231\pi$
$90$	−8.22393	−	7.06748i	−0.866878	−	0.744978i
$91$	−0.337582	−	1.03897i	−0.0353882	−	0.108914i
$92$			3.22799i			0.336542i
$93$	4.23403	+	0.337894i	0.439049	+	0.0350380i
$94$	15.0843			1.55583
$95$	−0.904284	+	11.0579i	−0.0927776	+	1.13451i
$96$	1.89089	−	5.81956i	0.192988	−	0.593957i
$97$	3.96471	+	5.45695i	0.402555	+	0.554069i	0.961383	−	0.275214i	$-0.0887488\pi$
$97$	3.96471	+	5.45695i	0.402555	+	0.554069i	−0.558828	+	0.829284i	$0.688749\pi$
$98$		−	13.9735i		−	1.41154i
$99$	−5.23297			−0.525933
$100$	9.97604	+	1.64262i	0.997604	+	0.164262i
$101$	0.487183	+	0.353959i	0.0484766	+	0.0352203i	0.611760	−	0.791044i	$-0.290462\pi$
$101$	0.487183	+	0.353959i	0.0484766	+	0.0352203i	−0.563283	+	0.826264i	$0.690462\pi$
$102$	−0.492993	+	0.678546i	−0.0488136	+	0.0671861i
$103$	19.0957	−	6.20457i	1.88155	−	0.611354i	0.895466	−	0.445129i	$-0.146842\pi$
$103$	19.0957	−	6.20457i	1.88155	−	0.611354i	0.986088	−	0.166225i	$-0.0531578\pi$
$104$	−0.217258	+	0.157847i	−0.0213039	+	0.0154782i
$105$	0.0250390	−	0.306185i	0.00244356	−	0.0298806i
$106$	2.98001	−	9.17153i	0.289444	−	0.890818i
$107$	6.86738	−	9.45213i	0.663894	−	0.913772i	−0.335708	−	0.941966i	$-0.608976\pi$
$107$	6.86738	−	9.45213i	0.663894	−	0.913772i	0.999602	+	0.0281939i	$0.00897557\pi$
$108$	7.94871	+	2.58269i	0.764865	+	0.248520i
$109$	2.25977	−	6.95487i	0.216447	−	0.666156i	−0.782601	−	0.622524i	$-0.786107\pi$
$109$	2.25977	−	6.95487i	0.216447	−	0.666156i	0.999048	−	0.0436316i	$-0.0138928\pi$
$110$	8.29037	−	5.04556i	0.790456	−	0.481075i
$111$	−1.69091	+	5.20408i	−0.160494	+	0.493949i
$112$	−0.677466	+	0.220122i	−0.0640145	+	0.0207996i
$113$	−1.04221	−	1.43448i	−0.0980431	−	0.134945i	0.757177	−	0.653210i	$-0.226578\pi$
$113$	−1.04221	−	1.43448i	−0.0980431	−	0.134945i	−0.855220	+	0.518265i	$0.826578\pi$
$114$	−2.34581	−	7.21967i	−0.219705	−	0.676184i
$115$	−3.04928	+	1.85580i	−0.284346	+	0.173055i
$116$	−3.25379	−	2.36402i	−0.302107	−	0.219493i
$117$	8.62149	+	11.8665i	0.797057	+	1.09705i
$118$			18.2123i			1.67658i
$119$	0.0987278			0.00905036
$120$	−0.0734854	+	0.0174049i	−0.00670827	+	0.00158885i
$121$	−1.95189	+	6.00730i	−0.177445	+	0.546118i
$122$	12.2795	−	3.98986i	1.11173	−	0.361225i
$123$			6.13050i			0.552769i
$124$	−7.32114	+	8.55296i	−0.657458	+	0.768079i
$125$	4.18365	+	10.3681i	0.374197	+	0.927349i
$126$	−0.269875	−	0.830590i	−0.0240424	−	0.0739949i
$127$	−7.10659	−	2.30907i	−0.630608	−	0.204897i	−0.0237634	−	0.999718i	$-0.507565\pi$
$127$	−7.10659	−	2.30907i	−0.630608	−	0.204897i	−0.606844	+	0.794821i	$0.707565\pi$
$128$	0.208161	+	0.286509i	0.0183990	+	0.0253240i
$129$	−4.18583			−0.368541
$130$	−25.1001	−	10.4868i	−2.20143	−	0.919753i
$131$	−4.93765	+	3.58741i	−0.431405	+	0.313434i	−0.782210	−	0.623014i	$-0.785908\pi$
$131$	−4.93765	+	3.58741i	−0.431405	+	0.313434i	0.350806	+	0.936448i	$0.385908\pi$
$132$	−1.96225	+	2.70081i	−0.170792	+	0.235075i
$133$	−0.525227	+	0.722913i	−0.0455430	+	0.0626845i
$134$	−3.91087	−	12.0364i	−0.337848	−	1.03979i
$135$	2.13009	+	8.99344i	0.183329	+	0.774032i
$136$	−0.00749969	−	0.0230817i	−0.000643094	−	0.00197924i
$137$	−8.55973	−	2.78123i	−0.731307	−	0.237616i	−0.0803887	−	0.996764i	$-0.525616\pi$
$137$	−8.55973	−	2.78123i	−0.731307	−	0.237616i	−0.650919	+	0.759147i	$0.725616\pi$
$138$	1.43559	−	1.97592i	0.122206	−	0.168202i
$139$	−4.88476	+	15.0337i	−0.414320	+	1.27515i	0.498538	+	0.866868i	$0.333870\pi$
$139$	−4.88476	+	15.0337i	−0.414320	+	1.27515i	−0.912858	+	0.408278i	$0.866130\pi$
$140$	0.617569	+	0.530726i	0.0521941	+	0.0448545i
$141$	−4.64206	−	3.37265i	−0.390932	−	0.284029i
$142$	5.30251	+	1.72289i	0.444976	+	0.144582i
$143$	−12.4852	+	4.05670i	−1.04407	+	0.339238i
$144$	7.73758	−	5.62168i	0.644798	−	0.468473i
$145$	0.362498	−	4.43274i	0.0301038	−	0.368119i
$146$	15.6787	+	11.3913i	1.29758	+	0.942748i
$147$	−3.12429	+	4.30022i	−0.257687	+	0.354676i
$148$	−8.52514	−	11.7338i	−0.700762	−	0.964516i
$149$	−12.5426			−1.02753			−0.513766	−	0.857931i	$-0.671750\pi$
$149$	−12.5426			−1.02753			−0.513766	+	0.857931i	$0.671750\pi$
$150$	−5.37602	−	5.44215i	−0.438951	−	0.444349i
$151$	15.8751	−	11.5340i	1.29190	−	0.938621i	0.292059	−	0.956400i	$-0.405660\pi$
$151$	15.8751	−	11.5340i	1.29190	−	0.938621i	0.999842	+	0.0177797i	$0.00565974\pi$
$152$	0.208909	+	0.0678785i	0.0169447	+	0.00550568i
$153$	−1.26070	+	0.409627i	−0.101922	+	0.0331163i
$154$	0.781641			0.0629864
$155$	−12.2884	−	1.99863i	−0.987030	−	0.160534i
$156$	9.35732			0.749186
$157$	−7.39139	+	2.40161i	−0.589897	+	0.191669i	−0.588729	−	0.808330i	$-0.700372\pi$
$157$	−7.39139	+	2.40161i	−0.589897	+	0.191669i	−0.00116760	+	0.999999i	$0.500372\pi$
$158$	−11.7281	−	3.81070i	−0.933039	−	0.303163i
$159$	−2.96770	+	2.15616i	−0.235354	+	0.170995i
$160$	−6.91428	+	16.5493i	−0.546622	+	1.30834i
$161$	−0.287495			−0.0226578
$162$	4.83421	+	6.65372i	0.379811	+	0.522766i
$163$	0.692735	−	0.953468i	0.0542592	−	0.0746814i	−0.781025	−	0.624500i	$-0.785303\pi$
$163$	0.692735	−	0.953468i	0.0542592	−	0.0746814i	0.835284	+	0.549818i	$0.185303\pi$
$164$	−13.1462	−	9.55124i	−1.02654	−	0.745827i
$165$	−3.67940	−	0.300892i	−0.286441	−	0.0234244i
$166$	−17.9135	+	13.0149i	−1.39036	+	1.01015i
$167$	−0.965993	+	0.313870i	−0.0747508	+	0.0242880i	−0.346154	−	0.938178i	$-0.612512\pi$
$167$	−0.965993	+	0.313870i	−0.0747508	+	0.0242880i	0.271403	+	0.962466i	$0.412512\pi$
$168$	−0.00578454	−	0.00187951i	−0.000446287	−	0.000145008i
$169$	19.2517	+	13.9872i	1.48090	+	1.07594i
$170$	1.60232	−	1.86450i	0.122892	−	0.143001i
$171$	3.70747	−	11.4104i	0.283517	−	0.872575i
$172$	6.52146	−	8.97602i	0.497257	−	0.684415i
$173$	−23.2612	−	7.55804i	−1.76852	−	0.574627i	−0.770495	−	0.637446i	$-0.779991\pi$
$173$	−23.2612	−	7.55804i	−1.76852	−	0.574627i	−0.998025	+	0.0628189i	$0.979991\pi$
$174$	0.940360	+	2.89413i	0.0712885	+	0.219403i
$175$	−0.146296	+	0.888497i	−0.0110590	+	0.0671640i
$176$	2.64519	+	8.14105i	0.199388	+	0.613654i
$177$	4.07203	−	5.60467i	0.306073	−	0.421273i
$178$	−14.2972	+	19.6784i	−1.07162	+	1.47496i
$179$	−8.83485	+	6.41889i	−0.660348	+	0.479771i	−0.866780	−	0.498690i	$-0.833815\pi$
$179$	−8.83485	+	6.41889i	−0.660348	+	0.479771i	0.206433	+	0.978461i	$0.433815\pi$
$180$	−10.0880	−	4.21476i	−0.751917	−	0.314150i
$181$	5.65429			0.420280			0.210140	−	0.977671i	$-0.432608\pi$
$181$	5.65429			0.420280			0.210140	+	0.977671i	$0.432608\pi$
$182$	−1.28778	−	1.77247i	−0.0954564	−	0.131385i
$183$	−4.67098	−	1.51769i	−0.345289	−	0.112191i
$184$	0.0218391	+	0.0672137i	0.00161000	+	0.00495506i
$185$	6.18302	−	14.7991i	0.454585	−	1.08805i
$186$	8.28521	−	1.97950i	0.607501	−	0.145144i
$187$		−	1.18640i		−	0.0867584i
$188$	14.4645	−	4.69981i	1.05493	−	0.342769i
$189$	−0.230022	+	0.707936i	−0.0167317	+	0.0514948i
$190$	5.12818	+	21.6517i	0.372037	+	1.57078i
$191$	−12.5176			−0.905738			−0.452869	−	0.891577i	$-0.649600\pi$
$191$	−12.5176			−0.905738			−0.452869	+	0.891577i	$0.649600\pi$
$192$		−	6.23695i		−	0.450113i
$193$	−0.534356	−	0.735478i	−0.0384638	−	0.0529408i	0.789352	−	0.613941i	$-0.210417\pi$
$193$	−0.534356	−	0.735478i	−0.0384638	−	0.0529408i	−0.827816	+	0.561000i	$0.810417\pi$
$194$	10.9440	+	7.95126i	0.785732	+	0.570867i
$195$	5.37962	+	8.83926i	0.385242	+	0.632992i
$196$	−4.35372	−	13.3994i	−0.310980	−	0.957098i
$197$	10.7368	+	14.7779i	0.764963	+	1.05288i	0.996785	+	0.0801225i	$0.0255311\pi$
$197$	10.7368	+	14.7779i	0.764963	+	1.05288i	−0.231822	+	0.972758i	$0.574469\pi$
$198$	−9.98113	+	3.24307i	−0.709328	+	0.230475i
$199$	−6.23645	+	19.1938i	−0.442090	+	1.36061i	0.443553	+	0.896248i	$0.353718\pi$
$199$	−6.23645	+	19.1938i	−0.442090	+	1.36061i	−0.885643	+	0.464366i	$0.846282\pi$
$200$	0.218836	−	0.0332904i	0.0154740	−	0.00235399i
$201$	−1.48765	+	4.57851i	−0.104931	+	0.322943i
$202$	1.14859	+	0.373200i	0.0808147	+	0.0262583i
$203$	0.210546	−	0.289792i	0.0147775	−	0.0203394i
$204$	−0.261322	+	0.804267i	−0.0182962	+	0.0563100i
$205$	1.46459	−	17.9094i	0.102291	−	1.25085i
$206$	32.5770	−	23.6686i	2.26975	−	1.64907i
$207$	3.67115	−	1.19283i	0.255163	−	0.0829074i
$208$	14.1029	−	19.4109i	0.977859	−	1.34591i
$209$	8.68718	+	6.31161i	0.600905	+	0.436583i
$210$	−0.141996	−	0.599521i	−0.00979865	−	0.0413709i
$211$	23.6795			1.63016			0.815082	−	0.579345i	$-0.196692\pi$
$211$	23.6795			1.63016			0.815082	+	0.579345i	$0.196692\pi$
$212$		−	9.72317i		−	0.667790i
$213$	−1.24658	−	1.71577i	−0.0854143	−	0.117563i
$214$	7.24068	−	22.2845i	0.494963	−	1.52334i
$215$	12.2283	+	1.00000i	0.833965	+	0.0681995i
$216$	0.182982			0.0124504
$217$	−0.761753	−	0.652043i	−0.0517111	−	0.0442636i
$218$		−	14.6659i		−	0.993298i
$219$	−2.27805	−	7.01111i	−0.153936	−	0.473767i
$220$	6.37769	−	7.42127i	0.429984	−	0.500342i
$221$	−2.69033	+	1.95464i	−0.180971	+	0.131483i
$222$			10.9739i			0.736523i
$223$			26.8416i			1.79744i	0.438518	+	0.898722i	$0.355503\pi$
$223$			26.8416i			1.79744i	−0.438518	+	0.898722i	$0.644497\pi$
$224$	−1.16865	+	0.849074i	−0.0780837	+	0.0567311i
$225$	−1.81829	−	11.9526i	−0.121219	−	0.796841i
$226$	−2.87687	−	2.09017i	−0.191367	−	0.139036i
$227$	−0.468619	+	0.152264i	−0.0311033	+	0.0101061i	−0.324527	−	0.945876i	$-0.605205\pi$
$227$	−0.468619	+	0.152264i	−0.0311033	+	0.0101061i	0.293424	+	0.955982i	$0.405205\pi$
$228$	−4.49885	−	6.19214i	−0.297944	−	0.410084i
$229$	−9.30367	−	28.6337i	−0.614804	−	1.89217i	−0.404513	−	0.914532i	$-0.632559\pi$
$229$	−9.30367	−	28.6337i	−0.614804	−	1.89217i	−0.210290	−	0.977639i	$-0.567441\pi$
$230$	−4.66594	+	5.42943i	−0.307663	+	0.358006i
$231$	−0.240542	−	0.174764i	−0.0158265	−	0.0114986i
$232$	−0.0837447	−	0.0272103i	−0.00549811	−	0.00178644i
$233$	−5.90077	−	1.91728i	−0.386573	−	0.125605i	0.109282	−	0.994011i	$-0.465145\pi$
$233$	−5.90077	−	1.91728i	−0.386573	−	0.125605i	−0.495854	+	0.868406i	$0.665145\pi$
$234$	23.7983	+	17.2905i	1.55574	+	1.13031i
$235$	12.7554	+	10.9617i	0.832071	+	0.715065i
$236$	5.67440	+	17.4640i	0.369372	+	1.13681i
$237$	2.75720	+	3.79495i	0.179099	+	0.246509i
$238$	0.188309	−	0.0611853i	0.0122063	−	0.00396605i
$239$	−6.63673	−	4.82187i	−0.429295	−	0.311901i	0.352072	−	0.935973i	$-0.385477\pi$
$239$	−6.63673	−	4.82187i	−0.429295	−	0.311901i	−0.781367	+	0.624072i	$0.785477\pi$
$240$	5.76368	−	3.50780i	0.372044	−	0.226428i
$241$	5.01291	−	3.64209i	0.322910	−	0.234608i	−0.414506	−	0.910046i	$-0.636046\pi$
$241$	5.01291	−	3.64209i	0.322910	−	0.234608i	0.737416	+	0.675439i	$0.236046\pi$
$242$			12.6677i			0.814311i
$243$		−	15.5283i		−	0.996139i
$244$	10.5318	−	7.65184i	0.674232	−	0.489859i
$245$	10.1545	−	11.8161i	0.648749	−	0.754904i
$246$	3.79930	+	11.6930i	0.242234	+	0.745521i
$247$		−	30.0979i		−	1.91508i
$248$	−0.0945766	+	0.227622i	−0.00600562	+	0.0144540i
$249$	8.42267			0.533765
$250$	14.4052	+	17.1828i	0.911064	+	1.08674i
$251$	0.212179	−	0.653019i	0.0133926	−	0.0412182i	−0.944137	−	0.329554i	$-0.893102\pi$
$251$	0.212179	−	0.653019i	0.0133926	−	0.0412182i	0.957529	+	0.288335i	$0.0931018\pi$
$252$	−0.517573	−	0.712378i	−0.0326040	−	0.0448756i
$253$			3.45480i			0.217201i
$254$	−14.9858			−0.940293
$255$	−0.909976	+	0.215527i	−0.0569849	+	0.0134968i
$256$	−12.6538	−	9.19354i	−0.790864	−	0.574596i
$257$	−10.8090	+	14.8773i	−0.674248	+	0.928022i	−0.999847	−	0.0174856i	$-0.994434\pi$
$257$	−10.8090	+	14.8773i	−0.674248	+	0.928022i	0.325600	+	0.945508i	$0.394434\pi$
$258$	−7.98385	+	2.59411i	−0.497053	+	0.161502i
$259$	1.04505	−	0.759275i	0.0649364	−	0.0471790i
$260$	−27.3362	−	2.23548i	−1.69532	−	0.138639i
$261$	−1.48620	+	4.57406i	−0.0919936	+	0.283127i
$262$	−7.19460	+	9.90252i	−0.444484	+	0.611780i
$263$	23.1252	+	7.51383i	1.42596	+	0.463322i	0.917490	−	0.397758i	$-0.130212\pi$
$263$	23.1252	+	7.51383i	1.42596	+	0.463322i	0.508469	+	0.861080i	$0.330212\pi$
$264$	−0.0225859	+	0.0695124i	−0.00139007	+	0.00427819i
$265$	9.18485	−	5.58994i	0.564221	−	0.343387i
$266$	−0.553778	+	1.70435i	−0.0339543	+	0.104501i
$267$	8.79964	−	2.85918i	0.538529	−	0.174979i
$268$	−7.50036	−	10.3234i	−0.458157	−	0.630599i
$269$	−5.99403	−	18.4477i	−0.365462	−	1.12478i	−0.949691	−	0.313188i	$-0.898603\pi$
$269$	−5.99403	−	18.4477i	−0.365462	−	1.12478i	0.584229	−	0.811589i	$-0.301397\pi$
$270$	9.63640	+	15.8336i	0.586453	+	0.963602i
$271$	−8.11834	−	5.89832i	−0.493154	−	0.358297i	0.313242	−	0.949673i	$-0.398585\pi$
$271$	−8.11834	−	5.89832i	−0.493154	−	0.358297i	−0.806396	+	0.591376i	$0.798585\pi$
$272$	1.27453	+	1.75424i	0.0772797	+	0.106366i
$273$			0.833392i			0.0504392i
$274$	−18.0501			−1.09044
$275$	10.6770	+	1.75803i	0.643847	+	0.106013i
$276$	0.760969	−	2.34202i	0.0458049	−	0.140973i
$277$	−24.3814	+	7.92199i	−1.46494	+	0.475986i	−0.929574	−	0.368636i	$-0.879825\pi$
$277$	−24.3814	+	7.92199i	−1.46494	+	0.475986i	−0.535362	+	0.844623i	$0.679825\pi$
$278$			31.7019i			1.90136i
$279$	12.4325	+	5.16569i	0.744316	+	0.309262i
$280$	0.0164497	+	0.00687268i	0.000983060	+	0.000410721i
$281$	3.00369	+	9.24439i	0.179185	+	0.551474i	0.999800	−	0.0200072i	$-0.00636892\pi$
$281$	3.00369	+	9.24439i	0.179185	+	0.551474i	−0.820615	+	0.571481i	$0.806369\pi$
$282$	−10.9442	−	3.55599i	−0.651718	−	0.211756i
$283$	−12.4967	−	17.2003i	−0.742853	−	1.02245i	−0.998449	−	0.0556663i	$-0.982272\pi$
$283$	−12.4967	−	17.2003i	−0.742853	−	1.02245i	0.255596	−	0.966784i	$-0.417728\pi$
$284$	5.62143			0.333571
$285$	3.26288	−	7.80969i	0.193276	−	0.462606i
$286$	−21.2997	+	15.4751i	−1.25948	+	0.915063i
$287$	0.850663	−	1.17084i	0.0502130	−	0.0691123i
$288$	11.4002	−	15.6910i	0.671762	−	0.924601i
$289$	5.16042	+	15.8821i	0.303554	+	0.934243i
$290$	−2.05572	−	8.67946i	−0.120716	−	0.509676i
$291$	−1.59011	−	4.89385i	−0.0932138	−	0.286883i
$292$	18.5837	+	6.03820i	1.08753	+	0.353359i
$293$	3.86980	−	5.32632i	0.226076	−	0.311167i	−0.680878	−	0.732397i	$-0.738402\pi$
$293$	3.86980	−	5.32632i	0.226076	−	0.311167i	0.906954	+	0.421230i	$0.138402\pi$
$294$	−3.29413	+	10.1383i	−0.192117	+	0.591277i
$295$	−13.2349	+	15.4005i	−0.770563	+	0.896650i
$296$	−0.256897	−	0.186647i	−0.0149319	−	0.0108486i
$297$	8.50720	+	2.76416i	0.493638	+	0.160393i
$298$	−23.9232	+	7.77313i	−1.38584	+	0.450285i
$299$	7.83422	−	5.69189i	0.453065	−	0.329171i
$300$	−6.85074	−	3.54353i	−0.395527	−	0.204586i
$301$	0.799432	+	0.580821i	0.0460785	+	0.0334780i
$302$	23.1315	−	31.8378i	1.33107	−	1.83206i
$303$	−0.270026	−	0.371659i	−0.0155126	−	0.0213512i
$304$	−19.6255			−1.12560
$305$	13.2831	+	5.54964i	0.760586	+	0.317772i
$306$	−2.15074	+	1.56261i	−0.122950	+	0.0893282i
$307$	−21.2549	−	6.90613i	−1.21308	−	0.394154i	−0.368523	−	0.929619i	$-0.620136\pi$
$307$	−21.2549	−	6.90613i	−1.21308	−	0.394154i	−0.844558	+	0.535465i	$0.820136\pi$
$308$	0.749524	−	0.243535i	0.0427081	−	0.0138767i
$309$	−15.3173			−0.871368
$310$	−24.6770	+	3.80350i	−1.40156	+	0.216024i
$311$	14.5439			0.824707			0.412354	−	0.911024i	$-0.364707\pi$
$311$	14.5439			0.824707			0.412354	+	0.911024i	$0.364707\pi$
$312$	0.194840	−	0.0633072i	0.0110306	−	0.00358407i
$313$	26.4224	+	8.58516i	1.49348	+	0.485262i	0.938109	−	0.346339i	$-0.112575\pi$
$313$	26.4224	+	8.58516i	1.49348	+	0.485262i	0.555373	+	0.831601i	$0.312575\pi$
$314$	−12.6096	+	9.16143i	−0.711603	+	0.517010i
$315$	0.375380	−	0.898470i	0.0211502	−	0.0506231i
$316$	−12.4335			−0.699440
$317$	−7.17160	−	9.87086i	−0.402797	−	0.554403i	0.558646	−	0.829406i	$-0.311321\pi$
$317$	−7.17160	−	9.87086i	−0.402797	−	0.554403i	−0.961443	+	0.275003i	$0.911321\pi$
$318$	−4.32420	+	5.95176i	−0.242489	+	0.333758i
$319$	−3.48241	−	2.53012i	−0.194978	−	0.141659i
$320$	−1.49002	+	18.2204i	−0.0832945	+	1.01855i
$321$	−7.21077	+	5.23893i	−0.402466	+	0.292409i
$322$	−0.548354	+	0.178171i	−0.0305586	+	0.00992909i
$323$	2.58693	+	0.840545i	0.143941	+	0.0467692i
$324$	6.70867	+	4.87414i	0.372704	+	0.270785i
$325$	−13.6041	−	27.1079i	−0.754620	−	1.50368i
$326$	0.730392	−	2.24791i	0.0404527	−	0.124500i
$327$	−3.27909	+	4.51328i	−0.181334	+	0.249585i
$328$	−0.338350	−	0.109937i	−0.0186823	−	0.00607024i
$329$	0.418580	+	1.28826i	0.0230770	+	0.0710238i
$330$	−7.20439	+	1.70635i	−0.396589	+	0.0939316i
$331$	−5.98200	−	18.4107i	−0.328801	−	1.01194i	−0.969696	−	0.244316i	$-0.921437\pi$
$331$	−5.98200	−	18.4107i	−0.328801	−	1.01194i	0.640895	−	0.767629i	$-0.278563\pi$
$332$	−13.1224	+	18.0615i	−0.720186	+	0.991251i
$333$	−10.1945	+	14.0315i	−0.558654	+	0.768922i
$334$	−1.64797	+	1.19732i	−0.0901732	+	0.0655146i
$335$	5.43978	−	13.0201i	0.297207	−	0.711364i
$336$	0.543417			0.0296458
$337$	−7.11774	−	9.79673i	−0.387728	−	0.533662i	0.569883	−	0.821726i	$-0.306988\pi$
$337$	−7.11774	−	9.79673i	−0.387728	−	0.533662i	−0.957611	+	0.288064i	$0.906988\pi$
$338$	45.3881	+	14.7475i	2.46879	+	0.802158i
$339$	0.417996	+	1.28646i	0.0227024	+	0.0698709i
$340$	0.955558	−	2.28713i	0.0518224	−	0.124037i
$341$	−7.83555	+	9.15392i	−0.424319	+	0.495712i
$342$		−	24.0613i		−	1.30109i
$343$	2.39233	−	0.777316i	0.129174	−	0.0419711i
$344$	0.0750633	−	0.231021i	0.00404714	−	0.0124558i
$345$	2.64984	−	0.627613i	0.142663	−	0.0337895i
$346$	−49.0514			−2.63702
$347$			26.3499i			1.41454i	0.706945	+	0.707269i	$0.250073\pi$
$347$			26.3499i			1.41454i	−0.706945	+	0.707269i	$0.749927\pi$
$348$	1.80344	+	2.48223i	0.0966747	+	0.133061i
$349$	−11.4961	−	8.35238i	−0.615370	−	0.447092i	0.235931	−	0.971770i	$-0.424186\pi$
$349$	−11.4961	−	8.35238i	−0.615370	−	0.447092i	−0.851301	+	0.524677i	$0.824186\pi$
$350$	0.271595	+	1.78534i	0.0145174	+	0.0954306i
$351$	−7.74779	−	23.8453i	−0.413547	−	1.27277i
$352$	10.2032	+	14.0436i	0.543835	+	0.748524i
$353$	35.3446	−	11.4841i	1.88120	−	0.611239i	0.894905	−	0.446256i	$-0.147243\pi$
$353$	35.3446	−	11.4841i	1.88120	−	0.611239i	0.986296	−	0.164983i	$-0.0527571\pi$
$354$	4.29339	−	13.2137i	0.228191	−	0.702299i
$355$	3.23182	+	5.31020i	0.171527	+	0.281836i
$356$	−7.57855	+	23.3244i	−0.401663	+	1.23619i
$357$	−0.0716305	−	0.0232741i	−0.00379109	−	0.00123180i
$358$	−12.8732	+	17.7184i	−0.680368	+	0.936446i
$359$	6.76307	−	20.8146i	0.356941	−	1.09855i	−0.597934	−	0.801545i	$-0.704012\pi$
$359$	6.76307	−	20.8146i	0.356941	−	1.09855i	0.954875	−	0.297007i	$-0.0959884\pi$
$360$	−0.238569	−	0.0195096i	−0.0125737	−	0.00102825i
$361$	−4.54574	+	3.30267i	−0.239249	+	0.173825i
$362$	10.7847	−	3.50417i	0.566833	−	0.184175i
$363$	2.83233	−	3.89837i	0.148659	−	0.204611i
$364$	−1.78711	−	1.29841i	−0.0936702	−	0.0680554i
$365$	4.98004	+	21.0262i	0.260667	+	1.10056i
$366$	−9.84978			−0.514856
$367$			27.9988i			1.46152i	0.682632	+	0.730762i	$0.260835\pi$
$367$			27.9988i			1.46152i	−0.682632	+	0.730762i	$0.739165\pi$
$368$	−3.71142	−	5.10834i	−0.193471	−	0.266290i
$369$	−6.00465	+	18.4804i	−0.312589	+	0.962051i
$370$	2.62169	−	32.0589i	0.136295	−	1.66666i
$371$	0.865974			0.0449592
$372$	7.32803	−	4.47958i	0.379940	−	0.232256i
$373$		−	28.9851i		−	1.50079i	−0.660990	−	0.750395i	$-0.729864\pi$
$373$		−	28.9851i		−	1.50079i	0.660990	−	0.750395i	$-0.270136\pi$
$374$	−0.735258	−	2.26289i	−0.0380193	−	0.117011i
$375$	−0.591208	−	8.50866i	−0.0305298	−	0.439385i
$376$	0.269386	−	0.195720i	0.0138925	−	0.0100935i
$377$			12.0653i			0.621393i
$378$			1.49284i			0.0767833i
$379$	3.39847	−	2.46913i	0.174568	−	0.126831i	−0.497071	−	0.867710i	$-0.665591\pi$
$379$	3.39847	−	2.46913i	0.174568	−	0.126831i	0.671638	+	0.740879i	$0.265591\pi$
$380$	11.6635	+	19.1643i	0.598323	+	0.983106i
$381$	4.61174	+	3.35062i	0.236266	+	0.171658i
$382$	−23.8754	+	7.75759i	−1.22157	+	0.396913i
$383$	−2.86265	−	3.94010i	−0.146275	−	0.201330i	0.729593	−	0.683882i	$-0.239710\pi$
$383$	−2.86265	−	3.94010i	−0.146275	−	0.201330i	−0.875867	+	0.482553i	$0.839710\pi$
$384$	−0.0834861	−	0.256944i	−0.00426038	−	0.0131121i
$385$	0.660960	+	0.568016i	0.0336857	+	0.0289488i
$386$	−1.47501	−	1.07166i	−0.0750760	−	0.0545459i
$387$	−12.6182	−	4.09989i	−0.641418	−	0.208409i
$388$	12.9717	+	4.21475i	0.658537	+	0.213972i
$389$	6.86522	+	4.98787i	0.348080	+	0.252895i	0.748063	−	0.663627i	$-0.230984\pi$
$389$	6.86522	+	4.98787i	0.348080	+	0.252895i	−0.399983	+	0.916523i	$0.630984\pi$
$390$	15.7389	+	13.5257i	0.796968	+	0.684898i
$391$	0.270435	+	0.832313i	0.0136765	+	0.0420919i
$392$	−0.181308	−	0.249549i	−0.00915742	−	0.0126041i
$393$	4.42814	−	1.43879i	0.223370	−	0.0725773i
$394$	29.6372	+	21.5327i	1.49310	+	1.08480i
$395$	−7.14815	−	11.7451i	−0.359662	−	0.590962i
$396$	−8.56058	+	6.21963i	−0.430185	+	0.312548i
$397$		−	14.7591i		−	0.740736i	−0.928885	−	0.370368i	$-0.879232\pi$
$397$		−	14.7591i		−	0.740736i	0.928885	−	0.370368i	$-0.120768\pi$
$398$			40.4744i			2.02880i
$399$	0.551490	−	0.400681i	0.0276091	−	0.0200592i
$400$	−17.6758	+	8.87062i	−0.883791	+	0.443531i
$401$	7.75670	+	23.8727i	0.387351	+	1.19214i	0.934760	+	0.355279i	$0.115614\pi$
$401$	7.75670	+	23.8727i	0.387351	+	1.19214i	−0.547409	+	0.836865i	$0.684386\pi$
$402$			9.65479i			0.481537i
$403$	33.6670	+	2.68677i	1.67707	+	0.133838i
$404$	1.21768			0.0605817
$405$	−0.747400	+	9.13944i	−0.0371386	+	0.454142i
$406$	0.221992	−	0.683220i	0.0110173	−	0.0339076i
$407$	−9.12414	−	12.5583i	−0.452267	−	0.622492i
$408$			0.0185145i			0.000916607i
$409$	33.4547			1.65423			0.827114	−	0.562034i	$-0.189981\pi$
$409$	33.4547			1.65423			0.827114	+	0.562034i	$0.189981\pi$
$410$	−8.30565	−	35.0673i	−0.410187	−	1.73185i
$411$	5.55474	+	4.03575i	0.273995	+	0.199069i
$412$	23.8641	−	32.8461i	1.17570	−	1.61821i
$413$	−1.55540	+	0.505379i	−0.0765361	+	0.0248681i
$414$	6.26295	−	4.55030i	0.307807	−	0.223635i
$415$	−24.6057	−	2.01219i	−1.20785	−	0.0987746i
$416$	15.0355	−	46.2744i	0.737175	−	2.26879i
$417$	7.08813	−	9.75597i	0.347107	−	0.477752i
$418$	20.4811	+	6.65470i	1.00176	+	0.325492i
$419$	2.31899	−	7.13711i	0.113290	−	0.348671i	−0.878297	−	0.478116i	$-0.841320\pi$
$419$	2.31899	−	7.13711i	0.113290	−	0.348671i	0.991587	+	0.129446i	$0.0413198\pi$
$420$	−0.322954	−	0.530646i	−0.0157585	−	0.0258929i
$421$	6.14435	−	18.9104i	0.299457	−	0.921635i	−0.682230	−	0.731138i	$-0.738990\pi$
$421$	6.14435	−	18.9104i	0.299457	−	0.921635i	0.981688	−	0.190498i	$-0.0610102\pi$
$422$	45.1652	−	14.6751i	2.19861	−	0.714371i
$423$	−10.6901	−	14.7136i	−0.519769	−	0.715401i
$424$	−0.0657823	−	0.202457i	−0.00319467	−	0.00983219i
$425$	2.70986	−	0.412237i	0.131448	−	0.0199965i
$426$	−3.44100	−	2.50003i	−0.166717	−	0.121127i
$427$	0.681496	+	0.937998i	0.0329799	+	0.0453929i
$428$		−	23.6249i		−	1.14195i
$429$	10.0148			0.483519
$430$	23.9435	−	5.67099i	1.15466	−	0.273479i
$431$	5.30140	−	16.3160i	0.255359	−	0.785915i	−0.738399	−	0.674364i	$-0.764418\pi$
$431$	5.30140	−	16.3160i	0.255359	−	0.785915i	0.993759	−	0.111552i	$-0.0355820\pi$
$432$	−15.5484	+	5.05198i	−0.748073	+	0.243064i
$433$			9.39235i			0.451368i	0.974201	+	0.225684i	$0.0724616\pi$
$433$			9.39235i			0.451368i	−0.974201	+	0.225684i	$0.927538\pi$
$434$	−1.85703	−	0.771591i	−0.0891402	−	0.0370376i
$435$	−1.30798	+	3.13065i	−0.0627129	+	0.150103i
$436$	−4.56943	−	14.0633i	−0.218836	−	0.673508i
$437$	−7.53313	−	2.44766i	−0.360359	−	0.117088i
$438$	−8.69008	−	11.9609i	−0.415228	−	0.571513i
$439$	19.3253			0.922345			0.461173	−	0.887310i	$-0.347429\pi$
$439$	19.3253			0.922345			0.461173	+	0.887310i	$0.347429\pi$
$440$	0.0825884	−	0.197675i	0.00393725	−	0.00942379i
$441$	−13.6301	+	9.90286i	−0.649053	+	0.471565i
$442$	−3.92005	+	5.39548i	−0.186458	+	0.256637i
$443$	−22.4453	+	30.8934i	−1.06641	+	1.46779i	−0.192753	+	0.981247i	$0.561742\pi$
$443$	−22.4453	+	30.8934i	−1.06641	+	1.46779i	−0.873658	+	0.486541i	$0.838258\pi$
$444$	3.41914	+	10.5230i	0.162265	+	0.499401i
$445$	−26.3900	+	6.25045i	−1.25101	+	0.296300i
$446$	16.6347	+	51.1964i	0.787676	+	2.42422i
$447$	9.10011	+	2.95680i	0.430420	+	0.139852i
$448$	−0.865433	+	1.19117i	−0.0408879	+	0.0562773i
$449$	−2.19558	+	6.75731i	−0.103616	+	0.318897i	−0.989403	−	0.145195i	$-0.953619\pi$
$449$	−2.19558	+	6.75731i	−0.103616	+	0.318897i	0.885787	+	0.464092i	$0.153619\pi$
$450$	−10.8756	−	21.6710i	−0.512681	−	1.02158i
$451$	−14.0698	−	10.2223i	−0.662523	−	0.481351i
$452$	−3.40990	−	1.10794i	−0.160388	−	0.0521132i
$453$	−14.2370	+	4.62588i	−0.668912	+	0.217343i
$454$	−0.799459	+	0.580841i	−0.0375205	+	0.0272602i
$455$	0.199099	−	2.43464i	0.00933389	−	0.114138i
$456$	−0.135569	−	0.0984965i	−0.00634859	−	0.00461252i
$457$	8.00217	−	11.0140i	0.374326	−	0.515215i	−0.579744	−	0.814798i	$-0.696848\pi$
$457$	8.00217	−	11.0140i	0.374326	−	0.515215i	0.954070	+	0.299583i	$0.0968476\pi$
$458$	−35.4908	−	48.8489i	−1.65838	−	2.28256i
$459$	2.26588			0.105762
$460$	−2.78258	+	6.66010i	−0.129738	+	0.310529i
$461$	−27.8827	+	20.2580i	−1.29863	+	0.943508i	−0.999941	−	0.0108435i	$-0.996548\pi$
$461$	−27.8827	+	20.2580i	−1.29863	+	0.943508i	−0.298686	+	0.954351i	$0.596548\pi$
$462$	−0.567107	−	0.184264i	−0.0263842	−	0.00857275i
$463$	−11.4665	+	3.72571i	−0.532895	+	0.173148i	−0.563090	−	0.826396i	$-0.690387\pi$
$463$	−11.4665	+	3.72571i	−0.532895	+	0.173148i	0.0301942	+	0.999544i	$0.490387\pi$
$464$	7.86722			0.365226
$465$	8.44452	+	4.34696i	0.391605	+	0.201585i
$466$	−12.4431			−0.576414
$467$	−18.8126	+	6.11259i	−0.870544	+	0.282857i	−0.710025	−	0.704176i	$-0.751317\pi$
$467$	−18.8126	+	6.11259i	−0.870544	+	0.282857i	−0.160518	+	0.987033i	$0.551317\pi$
$468$	28.2077	+	9.16522i	1.30390	+	0.423663i
$469$	0.919429	−	0.668004i	0.0424553	−	0.0308456i
$470$	31.1225	+	13.0029i	1.43557	+	0.599780i
$471$	5.92887			0.273188
$472$	0.236307	+	0.325248i	0.0108769	+	0.0149708i
$473$	6.97968	−	9.60670i	0.320926	−	0.441717i
$474$	7.61082	+	5.52959i	0.349577	+	0.253982i
$475$	−11.3978	+	22.0355i	−0.522967	+	1.01106i
$476$	0.161508	−	0.117342i	0.00740271	−	0.00537838i
$477$	−11.0580	+	3.59297i	−0.506312	+	0.164511i
$478$	−15.6469	−	5.08398i	−0.715672	−	0.232536i
$479$	−3.28633	−	2.38766i	−0.150156	−	0.109095i	0.510171	−	0.860073i	$-0.329582\pi$
$479$	−3.28633	−	2.38766i	−0.150156	−	0.109095i	−0.660327	+	0.750978i	$0.729582\pi$
$480$	8.91790	−	10.3771i	0.407045	−	0.473649i
$481$	−13.4453	+	41.3804i	−0.613053	+	1.88678i
$482$	7.30425	−	10.0534i	0.332700	−	0.457922i
$483$	0.208587	+	0.0677742i	0.00949106	+	0.00308383i
$484$	3.94687	+	12.1472i	0.179403	+	0.552146i
$485$	3.47614	+	14.6766i	0.157843	+	0.666430i
$486$	−9.62344	−	29.6179i	−0.436528	−	1.34350i
$487$	−19.3142	+	26.5837i	−0.875211	+	1.20462i	0.102513	+	0.994732i	$0.467312\pi$
$487$	−19.3142	+	26.5837i	−0.875211	+	1.20462i	−0.977724	+	0.209893i	$0.932688\pi$
$488$	0.167527	−	0.230581i	0.00758359	−	0.0104379i
$489$	−0.727374	+	0.528468i	−0.0328930	+	0.0238982i
$490$	12.0454	−	28.8306i	0.544156	−	1.30244i
$491$	−9.05071			−0.408453			−0.204226	−	0.978924i	$-0.565468\pi$
$491$	−9.05071			−0.408453			−0.204226	+	0.978924i	$0.565468\pi$
$492$	7.28638	+	10.0288i	0.328495	+	0.452135i
$493$	−1.03702	−	0.336947i	−0.0467049	−	0.0151753i
$494$	−18.6528	−	57.4074i	−0.839229	−	2.58288i
$495$	−10.7968	−	4.51090i	−0.485282	−	0.202750i
$496$	1.75192	−	21.9527i	0.0786636	−	0.985707i
$497$			0.500662i			0.0224577i
$498$	16.0650	−	5.21984i	0.719891	−	0.233907i
$499$	2.89986	−	8.92484i	0.129815	−	0.399531i	−0.864932	−	0.501889i	$-0.832639\pi$
$499$	2.89986	−	8.92484i	0.129815	−	0.399531i	0.994748	+	0.102358i	$0.0326387\pi$
$500$	19.1669	+	11.9886i	0.857172	+	0.536147i
$501$	0.774854			0.0346179
$502$		−	1.37703i		−	0.0614601i
$503$	−9.57639	−	13.1808i	−0.426990	−	0.587702i	0.540269	−	0.841492i	$-0.318323\pi$
$503$	−9.57639	−	13.1808i	−0.426990	−	0.587702i	−0.967259	+	0.253791i	$0.918323\pi$
$504$	−0.0155966	−	0.0113316i	−0.000694727	−	0.000504749i
$505$	0.700054	+	1.15026i	0.0311520	+	0.0511859i
$506$	2.14107	+	6.58953i	0.0951821	+	0.292940i
$507$	−10.6704	−	14.6866i	−0.473890	−	0.652254i
$508$	−14.3701	+	4.66911i	−0.637568	+	0.207158i
$509$	4.92310	−	15.1517i	0.218213	−	0.671589i	−0.780697	−	0.624909i	$-0.785136\pi$
$509$	4.92310	−	15.1517i	0.218213	−	0.671589i	0.998910	−	0.0466799i	$-0.0148641\pi$
$510$	−1.60208	+	0.975032i	−0.0709411	+	0.0431751i
$511$	−0.537781	+	1.65512i	−0.0237900	+	0.0732182i
$512$	−30.5065	−	9.91217i	−1.34821	−	0.438060i
$513$	−12.0544	+	16.5915i	−0.532215	+	0.732531i
$514$	−11.3966	+	35.0751i	−0.502682	+	1.54710i
$515$	44.7473	+	3.65932i	1.97180	+	0.161249i
$516$	−6.84756	+	4.97504i	−0.301447	+	0.219014i
$517$	15.4809	−	5.03003i	0.680847	−	0.221221i
$518$	1.52273	−	2.09586i	0.0669051	−	0.0920869i
$519$	15.0951	+	10.9672i	0.662602	+	0.481408i
$520$	−0.584322	+	0.138396i	−0.0256242	+	0.00606906i
$521$	−2.33664			−0.102370			−0.0511849	−	0.998689i	$-0.516300\pi$
$521$	−2.33664			−0.102370			−0.0511849	+	0.998689i	$0.516300\pi$
$522$			9.64541i			0.422168i
$523$	−5.54650	−	7.63411i	−0.242532	−	0.333816i	0.670347	−	0.742048i	$-0.266145\pi$
$523$	−5.54650	−	7.63411i	−0.242532	−	0.333816i	−0.912878	+	0.408232i	$0.866145\pi$
$524$	−3.81366	+	11.7373i	−0.166601	+	0.512744i
$525$	0.315598	−	0.610147i	0.0137738	−	0.0266290i
$526$	48.7645			2.12623
$527$	−1.17115	+	2.81867i	−0.0510161	+	0.122783i
$528$		−	6.53019i		−	0.284190i
$529$	6.31989	+	19.4506i	0.274778	+	0.845679i
$530$	14.0545	−	16.3542i	0.610487	−	0.710381i
$531$	17.7648	−	12.9068i	0.770925	−	0.560110i
$532$			1.80686i			0.0783375i
$533$			48.7469i			2.11146i
$534$	15.0121	−	10.9069i	0.649637	−	0.471989i
$535$	22.3169	−	13.5822i	0.964843	−	0.587208i
$536$	−0.226016	−	0.164211i	−0.00976242	−	0.00709282i
$537$	7.92318	−	2.57440i	0.341911	−	0.111093i
$538$	−22.8655	−	31.4716i	−0.985800	−	1.35684i
$539$	−4.65963	−	14.3409i	−0.200704	−	0.617704i
$540$	14.1737	+	12.1806i	0.609939	+	0.524170i
$541$	7.33065	+	5.32603i	0.315169	+	0.228984i	0.734111	−	0.679029i	$-0.237599\pi$
$541$	7.33065	+	5.32603i	0.315169	+	0.228984i	−0.418942	+	0.908013i	$0.637599\pi$
$542$	−19.1399	−	6.21895i	−0.822131	−	0.267127i
$543$	−4.10239	−	1.33295i	−0.176050	−	0.0572022i
$544$	3.55742	+	2.58461i	0.152523	+	0.110814i
$545$	10.6576	−	12.4016i	0.456523	−	0.531224i
$546$	0.516484	+	1.58957i	0.0221035	+	0.0680274i
$547$	21.0580	+	28.9838i	0.900374	+	1.23926i	0.970349	+	0.241709i	$0.0777080\pi$
$547$	21.0580	+	28.9838i	0.900374	+	1.23926i	−0.0699752	+	0.997549i	$0.522292\pi$
$548$	−17.3084	+	5.62385i	−0.739379	+	0.240239i
$549$	−12.5941	−	9.15017i	−0.537505	−	0.390520i
$550$	21.4543	−	3.26374i	0.914815	−	0.139166i
$551$	7.98410	−	5.80079i	0.340134	−	0.247122i
$552$		−	0.0539143i		−	0.00229474i
$553$		−	1.10737i		−	0.0470900i
$554$	−41.5944	+	30.2201i	−1.76718	+	1.28393i
$555$	−7.97473	+	9.27964i	−0.338509	+	0.393899i
$556$	9.87735	+	30.3993i	0.418893	+	1.28922i
$557$		−	5.33532i		−	0.226065i	−0.993591	−	0.113032i	$-0.963944\pi$
$557$		−	5.33532i		−	0.226065i	0.993591	−	0.113032i	$-0.0360564\pi$
$558$	26.9146	+	2.14790i	1.13939	+	0.0909279i
$559$	−33.2837			−1.40775
$560$	−1.58752	−	0.129823i	−0.0670849	−	0.00548603i
$561$	−0.279683	+	0.860777i	−0.0118082	+	0.0363420i
$562$	11.4582	+	15.7708i	0.483334	+	0.665253i
$563$		−	23.1355i		−	0.975043i	−0.873111	−	0.487522i	$-0.837901\pi$
$563$		−	23.1355i		−	0.975043i	0.873111	−	0.487522i	$-0.162099\pi$
$564$	−11.6025			−0.488552
$565$	−0.913781	−	3.85808i	−0.0384430	−	0.162310i
$566$	−34.4953	−	25.0623i	−1.44995	−	1.05345i
$567$	−0.434105	+	0.597495i	−0.0182307	+	0.0250924i
$568$	0.117050	−	0.0380319i	0.00491132	−	0.00159578i
$569$	−4.88293	+	3.54766i	−0.204703	+	0.148726i	−0.685414	−	0.728154i	$-0.740379\pi$
$569$	−4.88293	+	3.54766i	−0.204703	+	0.148726i	0.480711	+	0.876879i	$0.340379\pi$
$570$	1.38351	−	16.9180i	0.0579488	−	0.708616i
$571$	−2.73084	+	8.40465i	−0.114282	+	0.351724i	−0.991797	−	0.127826i	$-0.959200\pi$
$571$	−2.73084	+	8.40465i	−0.114282	+	0.351724i	0.877515	+	0.479550i	$0.159200\pi$
$572$	−15.6029	+	21.4756i	−0.652391	+	0.897939i
$573$	9.08192	+	2.95090i	0.379403	+	0.123275i
$574$	0.896904	−	2.76039i	0.0374361	−	0.115216i
$575$	−7.89110	+	1.20043i	−0.329082	+	0.0500615i
$576$	6.10891	−	18.8013i	0.254538	−	0.783387i
$577$	12.2771	−	3.98908i	0.511104	−	0.166068i	−0.0421002	−	0.999113i	$-0.513405\pi$
$577$	12.2771	−	3.98908i	0.511104	−	0.166068i	0.553204	+	0.833046i	$0.313405\pi$
$578$	19.6855	+	27.0948i	0.818809	+	1.12699i
$579$	0.214312	+	0.659584i	0.00890650	+	0.0274114i
$580$	−4.67551	−	7.68233i	−0.194140	−	0.318992i
$581$	−1.60861	−	1.16872i	−0.0667363	−	0.0484868i
$582$	−6.06580	−	8.34886i	−0.251435	−	0.346071i
$583$		−	10.4063i		−	0.430987i
$584$	0.427804			0.0177026
$585$	7.55906	+	31.9151i	0.312529	+	1.31953i
$586$	4.08016	−	12.5574i	0.168550	−	0.518743i
$587$	25.3793	−	8.24622i	1.04751	−	0.340358i	0.265822	−	0.964022i	$-0.414357\pi$
$587$	25.3793	−	8.24622i	1.04751	−	0.340358i	0.781693	+	0.623664i	$0.214357\pi$
$588$			10.7481i			0.443243i
$589$	−14.4086	−	23.5707i	−0.593697	−	0.971212i
$590$	−15.6993	+	37.5763i	−0.646331	+	1.54699i
$591$	−4.30615	−	13.2530i	−0.177131	−	0.545154i
$592$	26.9823	+	8.76707i	1.10896	+	0.360324i
$593$	−21.8016	−	30.0073i	−0.895283	−	1.23225i	−0.971948	−	0.235194i	$-0.924427\pi$
$593$	−21.8016	−	30.0073i	−0.895283	−	1.23225i	0.0766654	−	0.997057i	$-0.475573\pi$
$594$	17.9393			0.736058
$595$	0.203698	+	0.0851049i	0.00835082	+	0.00348896i
$596$	−20.5184	+	14.9075i	−0.840466	+	0.610634i
$597$	9.04952	−	12.4556i	0.370372	−	0.509774i
$598$	11.4152	−	15.7116i	0.466800	−	0.642496i
$599$	−3.22738	−	9.93285i	−0.131867	−	0.405845i	0.863222	−	0.504824i	$-0.168443\pi$
$599$	−3.22738	−	9.93285i	−0.131867	−	0.405845i	−0.995090	+	0.0989784i	$0.968443\pi$
$600$	−0.166621	−	0.0274351i	−0.00680227	−	0.00112003i
$601$	5.35886	+	16.4929i	0.218593	+	0.672759i	0.998879	+	0.0473364i	$0.0150733\pi$
$601$	5.35886	+	16.4929i	0.218593	+	0.672759i	−0.780286	+	0.625422i	$0.784927\pi$
$602$	1.88476	+	0.612394i	0.0768169	+	0.0249593i
$603$	−8.96903	+	12.3448i	−0.365247	+	0.502720i
$604$	12.2614	−	37.7367i	0.498909	−	1.53548i
$605$	−9.20559	+	10.7119i	−0.374261	+	0.435501i
$606$	−0.745366	−	0.541540i	−0.0302784	−	0.0219986i
$607$	21.9115	+	7.11948i	0.889361	+	0.288971i	0.717839	−	0.696210i	$-0.245132\pi$
$607$	21.9115	+	7.11948i	0.889361	+	0.288971i	0.171522	+	0.985180i	$0.445132\pi$
$608$	−37.8506	+	12.2984i	−1.53504	+	0.498766i
$609$	−0.221075	+	0.160620i	−0.00895839	+	0.00650865i
$610$	28.7748	+	2.35313i	1.16506	+	0.0952755i
$611$	−36.9115	−	26.8178i	−1.49328	−	1.08493i
$612$	−1.57551	+	2.16851i	−0.0636863	+	0.0876567i
$613$	5.28082	+	7.26842i	0.213290	+	0.293569i	0.902235	−	0.431245i	$-0.141926\pi$
$613$	5.28082	+	7.26842i	0.213290	+	0.293569i	−0.688944	+	0.724814i	$0.741926\pi$
$614$	−44.8206			−1.80881
$615$	−5.28459	+	12.6487i	−0.213095	+	0.510043i
$616$	0.0139591	−	0.0101418i	0.000562426	−	0.000408627i
$617$	33.8523	+	10.9993i	1.36284	+	0.442814i	0.896991	−	0.442049i	$-0.145748\pi$
$617$	33.8523	+	10.9993i	1.36284	+	0.442814i	0.465851	+	0.884863i	$0.345748\pi$
$618$	−29.2154	+	9.49267i	−1.17522	+	0.381851i
$619$	−8.96083			−0.360166			−0.180083	−	0.983651i	$-0.557637\pi$
$619$	−8.96083			−0.360166			−0.180083	+	0.983651i	$0.557637\pi$
$620$	−22.4780	+	11.3358i	−0.902739	+	0.455257i
$621$	−6.59824			−0.264778
$622$	27.7403	−	9.01338i	1.11229	−	0.361403i
$623$	−2.07734	−	0.674969i	−0.0832269	−	0.0270421i
$624$	−14.8081	+	10.7587i	−0.592797	+	0.430693i
$625$	−0.305600	+	24.9981i	−0.0122240	+	0.999925i
$626$	55.7174			2.22692
$627$	−4.81495	−	6.62721i	−0.192291	−	0.264665i
$628$	−9.23710	+	12.7138i	−0.368600	+	0.507335i
$629$	−3.18118	−	2.31126i	−0.126842	−	0.0921561i
$630$	0.159167	−	1.94634i	0.00634135	−	0.0775439i
$631$	13.2997	−	9.66277i	0.529451	−	0.384669i	−0.290701	−	0.956814i	$-0.593889\pi$
$631$	13.2997	−	9.66277i	0.529451	−	0.384669i	0.820152	+	0.572145i	$0.193889\pi$
$632$	−0.258893	+	0.0841193i	−0.0102982	+	0.00334609i
$633$	−17.1803	−	5.58222i	−0.682856	−	0.221873i
$634$	−19.7961	−	14.3827i	−0.786204	−	0.571211i
$635$	−12.6721	−	10.8901i	−0.502877	−	0.432162i
$636$	−2.29214	+	7.05450i	−0.0908894	+	0.279729i
$637$	−24.8429	+	34.1933i	−0.984312	+	1.35479i
$638$	−8.21020	−	2.66765i	−0.325045	−	0.105613i
$639$	−2.07727	−	6.39318i	−0.0821755	−	0.252910i
$640$	0.182509	+	0.770571i	0.00721430	+	0.0304595i
$641$	7.92650	+	24.3953i	0.313078	+	0.963555i	0.976538	+	0.215344i	$0.0690872\pi$
$641$	7.92650	+	24.3953i	0.313078	+	0.963555i	−0.663460	+	0.748211i	$0.730913\pi$
$642$	−10.5067	+	14.4613i	−0.414668	+	0.570741i
$643$	−6.39361	+	8.80005i	−0.252139	+	0.347040i	−0.916259	−	0.400586i	$-0.868806\pi$
$643$	−6.39361	+	8.80005i	−0.252139	+	0.347040i	0.664120	+	0.747626i	$0.268806\pi$
$644$	−0.470311	+	0.341701i	−0.0185328	+	0.0134649i
$645$	−8.63633	−	3.60825i	−0.340055	−	0.142075i
$646$	5.45511			0.214629
$647$	−18.1234	−	24.9448i	−0.712506	−	0.980680i	−0.999740	−	0.0228198i	$-0.992736\pi$
$647$	−18.1234	−	24.9448i	−0.712506	−	0.980680i	0.287234	−	0.957861i	$-0.407264\pi$
$648$	0.172665	+	0.0561023i	0.00678292	+	0.00220391i
$649$	6.07310	+	18.6911i	0.238390	+	0.733689i
$650$	−42.7476	−	43.2734i	−1.67670	−	1.69732i
$651$	0.398965	+	0.652656i	0.0156367	+	0.0255796i
$652$		−	2.38312i		−	0.0933301i
$653$	25.6701	−	8.34073i	1.00455	−	0.326398i	0.239868	−	0.970806i	$-0.422896\pi$
$653$	25.6701	−	8.34073i	1.00455	−	0.326398i	0.764682	+	0.644408i	$0.222896\pi$
$654$	−3.45734	+	10.6406i	−0.135193	+	0.416080i
$655$	−13.2799	+	3.14534i	−0.518890	+	0.122899i
$656$	31.7856			1.24102
$657$		−	23.3663i		−	0.911605i
$658$	1.59676	+	2.19775i	0.0622481	+	0.0856772i
$659$	36.9987	+	26.8811i	1.44126	+	1.04714i	0.987776	+	0.155877i	$0.0498203\pi$
$659$	36.9987	+	26.8811i	1.44126	+	1.04714i	0.453487	+	0.891263i	$0.350180\pi$
$660$	−6.37673	+	3.88091i	−0.248214	+	0.151064i
$661$	6.88657	+	21.1947i	0.267856	+	0.824377i	0.991022	+	0.133702i	$0.0426865\pi$
$661$	6.88657	+	21.1947i	0.267856	+	0.824377i	−0.723165	+	0.690675i	$0.757313\pi$
$662$	−22.8196	−	31.4085i	−0.886909	−	1.22073i
$663$	2.41271	−	0.783938i	0.0937020	−	0.0304456i
$664$	−0.151042	+	0.464858i	−0.00586155	+	0.0180400i
$665$	−1.70683	+	1.03878i	−0.0661879	+	0.0402823i
$666$	−10.7487	+	33.0809i	−0.416502	+	1.28186i
$667$	3.01979	+	0.981189i	0.116927	+	0.0379918i
$668$	−1.20721	+	1.66159i	−0.0467084	+	0.0642887i
$669$	6.32765	−	19.4745i	0.244641	−	0.752927i
$670$	2.30655	−	28.2052i	0.0891097	−	1.08966i
$671$	11.2718	−	8.18947i	0.435145	−	0.316151i
$672$	1.04806	−	0.340534i	0.0404297	−	0.0131364i
$673$	5.58016	−	7.68043i	0.215099	−	0.296059i	−0.687809	−	0.725891i	$-0.741427\pi$
$673$	5.58016	−	7.68043i	0.215099	−	0.296059i	0.902909	+	0.429833i	$0.141427\pi$
$674$	−19.6474	−	14.2747i	−0.756791	−	0.549841i
$675$	−3.35762	+	20.3917i	−0.129235	+	0.784878i
$676$	48.1181			1.85070
$677$			5.22046i			0.200639i	0.994955	+	0.100319i	$0.0319864\pi$
$677$			5.22046i			0.200639i	−0.994955	+	0.100319i	$0.968014\pi$
$678$	1.59453	+	2.19469i	0.0612376	+	0.0842864i
$679$	−0.375378	+	1.15530i	−0.0144057	+	0.0443362i
$680$	0.00442316	−	0.0540877i	0.000169620	−	0.00207417i
$681$	0.375894			0.0144043
$682$	−9.27214	+	22.3157i	−0.355049	+	0.854514i
$683$		−	18.7655i		−	0.718042i	−0.933329	−	0.359021i	$-0.883111\pi$
$683$		−	18.7655i		−	0.718042i	0.933329	−	0.359021i	$-0.116889\pi$
$684$	−7.49677	−	23.0727i	−0.286646	−	0.882206i
$685$	−15.2633	−	13.1169i	−0.583179	−	0.501173i
$686$	4.08130	−	2.96523i	0.155825	−	0.113213i
$687$			22.9680i			0.876285i
$688$			21.7028i			0.827411i
$689$	−23.5978	+	17.1448i	−0.899003	+	0.653164i
$690$	4.66524	−	2.83929i	0.177603	−	0.108090i
$691$	−13.4077	−	9.74128i	−0.510054	−	0.370576i	0.302790	−	0.953057i	$-0.402082\pi$
$691$	−13.4077	−	9.74128i	−0.510054	−	0.370576i	−0.812844	+	0.582481i	$0.802082\pi$
$692$	−47.0360	+	15.2829i	−1.78804	+	0.580969i
$693$	−0.553939	−	0.762431i	−0.0210424	−	0.0289624i
$694$	16.3300	+	50.2586i	0.619879	+	1.90779i
$695$	−23.0377	+	26.8074i	−0.873870	+	1.01686i
$696$	0.0543451	+	0.0394840i	0.00205995	+	0.00149664i
$697$	−4.18982	−	1.36135i	−0.158701	−	0.0515650i
$698$	−27.1033	−	8.80641i	−1.02588	−	0.333327i
$699$	3.82924	+	2.78210i	0.144835	+	0.105229i
$700$	0.816694	+	1.62736i	0.0308681	+	0.0615086i
$701$	1.29014	+	3.97063i	0.0487277	+	0.149969i	0.972460	−	0.233071i	$-0.0748774\pi$
$701$	1.29014	+	3.97063i	0.0487277	+	0.149969i	−0.923732	+	0.383039i	$0.874877\pi$
$702$	−29.5556	−	40.6798i	−1.11550	−	1.53536i
$703$	33.8474	−	10.9977i	1.27658	−	0.414786i
$704$	14.3141	+	10.3998i	0.539485	+	0.391958i
$705$	−6.67037	−	10.9601i	−0.251221	−	0.412781i
$706$	60.2975	−	43.8087i	2.26933	−	1.64876i
$707$			0.108450i			0.00407868i
$708$		−	14.0084i		−	0.526469i
$709$	41.9260	−	30.4610i	1.57456	−	1.14399i	0.651948	−	0.758264i	$-0.273952\pi$
$709$	41.9260	−	30.4610i	1.57456	−	1.14399i	0.922615	−	0.385723i	$-0.126048\pi$
$710$	9.45515	+	8.12556i	0.354845	+	0.304947i
$711$	4.59452	+	14.1405i	0.172308	+	0.530309i
$712$			0.536937i			0.0201226i
$713$	3.41038	−	8.20794i	0.127720	−	0.307390i
$714$	−0.151048			−0.00565285
$715$	−29.2569	−	2.39255i	−1.09414	−	0.0894764i
$716$	−6.82372	+	21.0012i	−0.255014	+	0.784853i
$717$	3.67847	+	5.06298i	0.137375	+	0.189080i
$718$		−	43.8921i		−	1.63804i
$719$	1.79744			0.0670332			0.0335166	−	0.999438i	$-0.489329\pi$
$719$	1.79744			0.0670332			0.0335166	+	0.999438i	$0.489329\pi$
$720$	20.8104	−	4.92892i	0.775558	−	0.183690i
$721$	2.92537	+	2.12541i	0.108947	+	0.0791543i
$722$	−6.62355	+	9.11653i	−0.246503	+	0.339282i
$723$	−4.49563	+	1.46072i	−0.167194	+	0.0543247i
$724$	9.24982	−	6.72039i	0.343767	−	0.249761i
$725$	4.56901	−	8.83330i	0.169689	−	0.328060i
$726$	2.98629	−	9.19087i	0.110832	−	0.341105i
$727$	22.2301	−	30.5972i	0.824470	−	1.13479i	−0.164457	−	0.986384i	$-0.552587\pi$
$727$	22.2301	−	30.5972i	0.824470	−	1.13479i	0.988927	−	0.148402i	$-0.0474128\pi$
$728$	−0.0459960	−	0.0149450i	−0.00170472	−	0.000553899i
$729$	0.141124	−	0.434335i	0.00522681	−	0.0160865i
$730$	22.5294	+	37.0182i	0.833852	+	1.37010i
$731$	0.929515	−	2.86075i	0.0343794	−	0.105809i
$732$	−9.44507	+	3.06889i	−0.349100	+	0.113429i
$733$	3.35220	+	4.61391i	0.123816	+	0.170419i	0.866425	−	0.499307i	$-0.166412\pi$
$733$	3.35220	+	4.61391i	0.123816	+	0.170419i	−0.742609	+	0.669725i	$0.766412\pi$
$734$	17.3519	+	53.4036i	0.640470	+	1.97116i
$735$	−10.1530	+	6.17917i	−0.374499	+	0.227922i
$736$	−10.3592	−	7.52638i	−0.381844	−	0.277426i
$737$	−8.02735	−	11.0487i	−0.295691	−	0.406984i
$738$			38.9700i			1.43450i
$739$	−6.87196			−0.252789			−0.126395	−	0.991980i	$-0.540341\pi$
$739$	−6.87196			−0.252789			−0.126395	+	0.991980i	$0.540341\pi$
$740$	−7.47459	−	31.5585i	−0.274771	−	1.16011i
$741$	−7.09530	+	21.8371i	−0.260652	+	0.802205i
$742$	1.65172	−	0.536676i	0.0606366	−	0.0197020i
$743$			41.1148i			1.50836i	0.656671	+	0.754178i	$0.271964\pi$
$743$			41.1148i			1.50836i	−0.656671	+	0.754178i	$0.728036\pi$
$744$	0.122278	−	0.142852i	0.00448295	−	0.00523723i
$745$	−25.8783	−	10.8119i	−0.948109	−	0.396119i
$746$	−17.9631	−	55.2848i	−0.657676	−	2.02412i
$747$	25.3902	+	8.24976i	0.928977	+	0.301843i
$748$	−1.41009	−	1.94083i	−0.0515582	−	0.0709637i
$749$	2.10410			0.0768822
$750$	−6.40077	−	15.8626i	−0.233723	−	0.579221i
$751$	0.543513	−	0.394885i	0.0198331	−	0.0144096i	−0.577825	−	0.816161i	$-0.696098\pi$
$751$	0.543513	−	0.394885i	0.0198331	−	0.0144096i	0.597658	+	0.801751i	$0.296098\pi$
$752$	−17.4866	+	24.0683i	−0.637672	+	0.877680i
$753$	−0.307886	+	0.423769i	−0.0112200	+	0.0154430i
$754$	7.47730	+	23.0128i	0.272307	+	0.838075i
$755$	42.6966	−	10.1126i	1.55389	−	0.368036i
$756$	0.465122	+	1.43150i	0.0169163	+	0.0520631i
$757$	3.69822	+	1.20162i	0.134414	+	0.0436737i	0.375451	−	0.926842i	$-0.377488\pi$
$757$	3.69822	+	1.20162i	0.134414	+	0.0436737i	−0.241037	+	0.970516i	$0.577488\pi$
$758$	4.95187	−	6.81567i	0.179860	−	0.247556i
$759$	0.814436	−	2.50658i	0.0295622	−	0.0909830i
$760$	0.372515	+	0.320132i	0.0135125	+	0.0116124i
$761$	−34.4657	−	25.0408i	−1.24938	−	0.907728i	−0.251194	−	0.967937i	$-0.580823\pi$
$761$	−34.4657	−	25.0408i	−1.24938	−	0.907728i	−0.998186	+	0.0602091i	$0.980823\pi$
$762$	10.8727	+	3.53276i	0.393877	+	0.127978i
$763$	1.25252	−	0.406967i	0.0453442	−	0.0147332i
$764$	−20.4774	+	14.8777i	−0.740845	+	0.538256i
$765$	−2.95422	−	0.241589i	−0.106810	−	0.00873467i
$766$	−7.90191	−	5.74107i	−0.285508	−	0.207433i
$767$	32.3789	−	44.5657i	1.16913	−	1.60917i
$768$	7.01350	+	9.65325i	0.253078	+	0.348332i
$769$	13.1205			0.473137			0.236569	−	0.971615i	$-0.423977\pi$
$769$	13.1205			0.473137			0.236569	+	0.971615i	$0.423977\pi$
$770$	1.61271	+	0.673786i	0.0581179	+	0.0242816i
$771$	11.3495	−	8.24590i	0.408742	−	0.296969i
$772$	−1.74830	−	0.568056i	−0.0629226	−	0.0204448i
$773$	21.8362	−	7.09503i	0.785395	−	0.255190i	0.111253	−	0.993792i	$-0.464514\pi$
$773$	21.8362	−	7.09503i	0.785395	−	0.255190i	0.674142	+	0.738602i	$0.264514\pi$
$774$	−26.6082			−0.956411
$775$	−23.6310	−	14.7165i	−0.848852	−	0.528631i
$776$	0.298613			0.0107196
$777$	−0.937213	+	0.304519i	−0.0336223	+	0.0109246i
$778$	16.1856	+	5.25901i	0.580281	+	0.188545i
$779$	32.2579	−	23.4367i	1.15576	−	0.839707i
$780$	19.3063	+	8.06616i	0.691278	+	0.288815i
$781$	6.01641			0.215284
$782$	1.03163	+	1.41992i	0.0368910	+	0.0507761i
$783$	4.83222	−	6.65097i	0.172689	−	0.237686i
$784$	22.2959	+	16.1989i	0.796283	+	0.578533i
$785$	−17.3204	−	1.41642i	−0.618191	−	0.0505541i
$786$	7.55436	−	5.48856i	0.269455	−	0.195771i
$787$	1.28498	−	0.417514i	0.0458045	−	0.0148828i	−0.286025	−	0.958222i	$-0.592334\pi$
$787$	1.28498	−	0.417514i	0.0458045	−	0.0148828i	0.331830	+	0.943339i	$0.392334\pi$
$788$	35.1284	+	11.4139i	1.25140	+	0.406603i
$789$	−15.0068	−	10.9031i	−0.534257	−	0.388160i
$790$	−20.9130	−	17.9722i	−0.744050	−	0.639421i
$791$	0.0986767	−	0.303696i	0.00350854	−	0.0107982i
$792$	−0.136171	+	0.187423i	−0.00483861	+	0.00665978i
$793$	−37.1414	−	12.0680i	−1.31893	−	0.428547i
$794$	−9.14674	−	28.1508i	−0.324606	−	0.999033i
$795$	−7.98170	+	1.89046i	−0.283082	+	0.0670476i
$796$	12.6106	+	38.8113i	0.446970	+	1.37563i
$797$	20.1640	−	27.7534i	0.714247	−	0.983076i	−0.285448	−	0.958394i	$-0.592143\pi$
$797$	20.1640	−	27.7534i	0.714247	−	0.983076i	0.999695	−	0.0246824i	$-0.00785745\pi$
$798$	0.803571	−	1.10602i	0.0284461	−	0.0391527i
$799$	3.33583	−	2.42362i	0.118013	−	0.0857415i
$800$	−28.5316	+	28.1849i	−1.00874	+	0.996486i
$801$	29.3270			1.03622
$802$	29.5896	+	40.7265i	1.04484	+	1.43810i
$803$	19.8894	+	6.46246i	0.701882	+	0.228055i
$804$	3.00814	+	9.25809i	0.106089	+	0.326508i
$805$	−0.593169	−	0.247825i	−0.0209064	−	0.00873468i
$806$	65.8801	−	15.7401i	2.32053	−	0.554421i
$807$			14.7975i			0.520896i
$808$	0.0253546	−	0.00823822i	0.000891973	−	0.000289820i
$809$	6.34958	−	19.5420i	0.223239	−	0.687060i	−0.775226	−	0.631684i	$-0.782364\pi$
$809$	6.34958	−	19.5420i	0.223239	−	0.687060i	0.998466	−	0.0553765i	$-0.0176359\pi$
$810$	4.23849	+	17.8953i	0.148925	+	0.628778i
$811$	−10.7477			−0.377403			−0.188702	−	0.982034i	$-0.560428\pi$
$811$	−10.7477			−0.377403			−0.188702	+	0.982034i	$0.560428\pi$
$812$		−	0.724313i		−	0.0254184i
$813$	4.49966	+	6.19326i	0.157810	+	0.217207i
$814$	−25.1858	−	18.2986i	−0.882762	−	0.641364i
$815$	2.25118	−	1.37008i	0.0788553	−	0.0479917i
$816$	−0.511170	−	1.57322i	−0.0178945	−	0.0550737i
$817$	16.0023	+	22.0252i	0.559849	+	0.770566i
$818$	63.8100	−	20.7331i	2.23106	−	0.724916i
$819$	−0.816282	+	2.51226i	−0.0285232	+	0.0877854i
$820$	−18.8903	−	31.0386i	−0.659677	−	1.08392i
$821$	1.37527	−	4.23266i	0.0479974	−	0.147721i	−0.924185	−	0.381944i	$-0.875255\pi$
$821$	1.37527	−	4.23266i	0.0479974	−	0.147721i	0.972183	+	0.234223i	$0.0752547\pi$
$822$	13.0960	+	4.25513i	0.456774	+	0.148415i
$823$	−18.9143	+	26.0333i	−0.659312	+	0.907465i	−0.999458	−	0.0329074i	$-0.989523\pi$
$823$	−18.9143	+	26.0333i	−0.659312	+	0.907465i	0.340146	+	0.940372i	$0.389523\pi$
$824$	0.274680	−	0.845379i	0.00956895	−	0.0294502i
$825$	−7.33209	−	3.79251i	−0.255270	−	0.132038i
$826$	−2.65349	+	1.92788i	−0.0923268	+	0.0670794i
$827$	−11.1446	+	3.62110i	−0.387536	+	0.125918i	−0.496303	−	0.868149i	$-0.665310\pi$
$827$	−11.1446	+	3.62110i	−0.387536	+	0.125918i	0.108768	+	0.994067i	$0.465310\pi$
$828$	4.58788	−	6.31468i	0.159440	−	0.219450i
$829$	3.59724	+	2.61355i	0.124937	+	0.0907722i	0.648499	−	0.761215i	$-0.275397\pi$
$829$	3.59724	+	2.61355i	0.124937	+	0.0907722i	−0.523562	+	0.851988i	$0.675397\pi$
$830$	−48.1788	+	11.4111i	−1.67231	+	0.396085i
$831$	19.5571			0.678428
$832$		−	49.5933i		−	1.71934i
$833$	−2.24515	−	3.09018i	−0.0777897	−	0.107068i
$834$	7.47343	−	23.0009i	0.258784	−	0.796455i
$835$	−2.26363	−	0.185114i	−0.0783362	−	0.00640613i
$836$	21.7129			0.750957
$837$	−17.4829	−	14.9649i	−0.604296	−	0.517264i
$838$		−	15.0502i		−	0.519899i
$839$	5.19266	+	15.9814i	0.179271	+	0.551738i	0.999803	−	0.0198624i	$-0.00632282\pi$
$839$	5.19266	+	15.9814i	0.179271	+	0.551738i	−0.820532	+	0.571600i	$0.806323\pi$
$840$	−0.0103147	−	0.00886424i	−0.000355891	−	0.000305845i
$841$	20.2609	−	14.7204i	0.698653	−	0.507601i
$842$		−	39.8767i		−	1.37424i
$843$		−	7.41522i		−	0.255394i
$844$	38.7371	−	28.1442i	1.33339	−	0.968762i
$845$	27.6635	+	45.4540i	0.951655	+	1.56367i
$846$	−29.5083	−	21.4391i	−1.01452	−	0.737090i
$847$	−1.08187	+	0.351520i	−0.0371734	+	0.0120784i
$848$	11.1793	+	15.3870i	0.383900	+	0.528393i
$849$	5.01201	+	15.4254i	0.172012	+	0.529398i
$850$	4.91319	−	2.46568i	0.168521	−	0.0845722i
$851$	9.26358	+	6.73038i	0.317551	+	0.230715i
$852$	−4.07854	−	1.32520i	−0.139729	−	0.0454006i
$853$	28.4685	+	9.24998i	0.974743	+	0.316713i	0.752729	−	0.658330i	$-0.228737\pi$
$853$	28.4685	+	9.24998i	0.974743	+	0.316713i	0.222014	+	0.975044i	$0.428737\pi$
$854$	1.88117	+	1.36675i	0.0643722	+	0.0467691i
$855$	17.4853	−	20.3464i	0.597985	−	0.695833i
$856$	−0.159835	−	0.491920i	−0.00546304	−	0.0168135i
$857$	6.89338	+	9.48792i	0.235473	+	0.324101i	0.910358	−	0.413822i	$-0.135806\pi$
$857$	6.89338	+	9.48792i	0.235473	+	0.324101i	−0.674884	+	0.737924i	$0.735806\pi$
$858$	19.1018	−	6.20654i	0.652123	−	0.211888i
$859$	−7.91122	−	5.74784i	−0.269927	−	0.196114i	0.444585	−	0.895737i	$-0.353351\pi$
$859$	−7.91122	−	5.74784i	−0.269927	−	0.196114i	−0.714512	+	0.699623i	$0.753351\pi$
$860$	21.1928	−	12.8980i	0.722667	−	0.439819i
$861$	−0.893199	+	0.648947i	−0.0304401	+	0.0221161i
$862$		−	34.4059i		−	1.17187i
$863$			13.1212i			0.446651i	0.974744	+	0.223325i	$0.0716912\pi$
$863$			13.1212i			0.446651i	−0.974744	+	0.223325i	$0.928309\pi$
$864$	−26.8215	+	19.4869i	−0.912485	+	0.662959i
$865$	−41.4782	−	35.6456i	−1.41030	−	1.21199i
$866$	5.82079	+	17.9145i	0.197798	+	0.608761i
$867$		−	12.7396i		−	0.432658i
$868$	−2.02113	−	0.161295i	−0.0686016	−	0.00547470i
$869$	−13.3071			−0.451413
$870$	−0.554604	+	6.78187i	−0.0188028	+	0.229927i
$871$	−11.8291	+	36.4062i	−0.400813	+	1.23358i
$872$	−0.190291	−	0.261913i	−0.00644406	−	0.00886949i
$873$		−	16.3100i		−	0.552009i
$874$	−15.8853			−0.537327
$875$	−1.06774	+	1.70707i	−0.0360962	+	0.0577093i
$876$	−12.0597	−	8.76186i	−0.407458	−	0.296036i
$877$	−11.8536	+	16.3151i	−0.400268	+	0.550922i	−0.960811	−	0.277203i	$-0.910592\pi$
$877$	−11.8536	+	16.3151i	−0.400268	+	0.550922i	0.560543	+	0.828125i	$0.310592\pi$
$878$	36.8602	−	11.9766i	1.24397	−	0.404190i
$879$	−4.06330	+	2.95216i	−0.137052	+	0.0995740i
$880$	−1.56007	+	19.0771i	−0.0525901	+	0.643088i
$881$	−3.06067	+	9.41976i	−0.103116	+	0.317360i	−0.989284	−	0.146006i	$-0.953358\pi$
$881$	−3.06067	+	9.41976i	−0.103116	+	0.317360i	0.886167	+	0.463365i	$0.153358\pi$
$882$	−19.8603	+	27.3354i	−0.668731	+	0.920429i
$883$	−21.0930	−	6.85354i	−0.709836	−	0.230640i	−0.0682253	−	0.997670i	$-0.521734\pi$
$883$	−21.0930	−	6.85354i	−0.709836	−	0.230640i	−0.641611	+	0.767030i	$0.721734\pi$
$884$	−2.07791	+	6.39515i	−0.0698877	+	0.215092i
$885$	13.2329	−	8.05359i	0.444818	−	0.270718i
$886$	−23.6655	+	72.8348i	−0.795057	+	2.44693i
$887$	−50.8624	+	16.5262i	−1.70779	+	0.554896i	−0.989964	−	0.141323i	$-0.954864\pi$
$887$	−50.8624	+	16.5262i	−1.70779	+	0.554896i	−0.717830	+	0.696219i	$0.754864\pi$
$888$	0.142388	+	0.195980i	0.00477822	+	0.00657666i
$889$	−0.415845	−	1.27984i	−0.0139470	−	0.0429245i
$890$	−46.4615	+	28.2767i	−1.55739	+	0.947837i
$891$	7.18004	+	5.21661i	0.240540	+	0.174763i
$892$	31.9024	+	43.9099i	1.06817	+	1.47021i
$893$			37.3194i			1.24885i
$894$	19.1896			0.641795
$895$	−23.7615	+	5.62789i	−0.794261	+	0.188120i
$896$	−0.0197086	+	0.0606570i	−0.000658420	+	0.00202641i
$897$	−7.02581	+	2.28282i	−0.234585	+	0.0762213i
$898$			14.2493i			0.475504i
$899$	5.77595	+	9.44871i	0.192639	+	0.315132i
$900$	−17.1808	−	17.3921i	−0.572692	−	0.579736i
$901$	−0.814588	−	2.50704i	−0.0271378	−	0.0835217i
$902$	−33.1713	−	10.7780i	−1.10448	−	0.358869i
$903$	−0.443092	−	0.609864i	−0.0147452	−	0.0202950i
$904$	−0.0784972			−0.00261078
$905$	11.6661	+	4.87409i	0.387795	+	0.162020i
$906$	−24.2882	+	17.6464i	−0.806920	+	0.586262i
$907$	6.41314	−	8.82693i	0.212945	−	0.293093i	−0.689161	−	0.724608i	$-0.742021\pi$
$907$	6.41314	−	8.82693i	0.212945	−	0.293093i	0.902106	+	0.431515i	$0.142021\pi$
$908$	−0.585638	+	0.806062i	−0.0194351	+	0.0267501i
$909$	−0.449964	−	1.38485i	−0.0149244	−	0.0459325i
$910$	−1.12908	−	4.76711i	−0.0374288	−	0.158028i
$911$	−17.7214	−	54.5409i	−0.587137	−	1.80702i	−0.590515	−	0.807026i	$-0.701076\pi$
$911$	−17.7214	−	54.5409i	−0.587137	−	1.80702i	0.00337886	−	0.999994i	$-0.498924\pi$
$912$	14.2390	+	4.62652i	0.471499	+	0.153199i
$913$	−14.0444	+	19.3305i	−0.464803	+	0.639746i
$914$	8.43717	−	25.9669i	0.279077	−	0.858910i
$915$	−8.32904	−	7.15781i	−0.275350	−	0.236630i
$916$	−49.2523	−	35.7839i	−1.62734	−	1.18233i
$917$	−1.04536	−	0.339656i	−0.0345207	−	0.0112164i
$918$	4.32185	−	1.40425i	0.142642	−	0.0463472i
$919$	−40.5336	+	29.4494i	−1.33708	+	0.971446i	−0.337535	+	0.941313i	$0.609593\pi$
$919$	−40.5336	+	29.4494i	−1.33708	+	0.971446i	−0.999546	+	0.0301334i	$0.990407\pi$
$920$	−0.0128802	+	0.157503i	−0.000424648	+	0.00519273i
$921$	13.7931	+	10.0213i	0.454498	+	0.330212i
$922$	−40.6276	+	55.9191i	−1.33800	+	1.84160i
$923$	−9.91222	−	13.6430i	−0.326265	−	0.449065i
$924$	−0.601217			−0.0197786
$925$	25.5140	−	25.2040i	0.838896	−	0.828703i
$926$	−19.5618	+	14.2125i	−0.642841	+	0.467051i
$927$	−46.1739	−	15.0028i	−1.51655	−	0.492757i
$928$	15.1731	−	4.93003i	0.498080	−	0.161836i
$929$	13.9448			0.457515			0.228758	−	0.973483i	$-0.426534\pi$
$929$	13.9448			0.457515			0.228758	+	0.973483i	$0.426534\pi$
$930$	18.8007	+	3.05780i	0.616498	+	0.100269i
$931$	34.5712			1.13303
$932$	−11.9318	+	3.87688i	−0.390839	+	0.126991i
$933$	−10.5521	−	3.42858i	−0.345460	−	0.112247i
$934$	−32.0941	+	23.3177i	−1.05015	+	0.762980i
$935$	1.02270	−	2.44783i	0.0334458	−	0.0800525i
$936$	0.649352			0.0212247
$937$	−11.2703	−	15.5123i	−0.368185	−	0.506764i	0.584221	−	0.811594i	$-0.301400\pi$
$937$	−11.2703	−	15.5123i	−0.368185	−	0.506764i	−0.952406	+	0.304831i	$0.901400\pi$
$938$	1.33969	−	1.84393i	0.0437424	−	0.0602063i
$939$	−17.1465	−	12.4577i	−0.559555	−	0.406541i
$940$	33.8950	+	2.77185i	1.10553	+	0.0904077i
$941$	−22.5887	+	16.4116i	−0.736370	+	0.535004i	−0.891572	−	0.452879i	$-0.850397\pi$
$941$	−22.5887	+	16.4116i	−0.736370	+	0.535004i	0.155202	+	0.987883i	$0.450397\pi$
$942$	11.3084	−	3.67434i	0.368449	−	0.119716i
$943$	12.2007	+	3.96426i	0.397310	+	0.129094i
$944$	−29.0593	−	21.1128i	−0.945799	−	0.687163i
$945$	−1.08484	+	1.26235i	−0.0352899	+	0.0410644i
$946$	7.35909	−	22.6489i	0.239265	−	0.736381i
$947$	11.1232	−	15.3098i	0.361455	−	0.497500i	−0.589098	−	0.808061i	$-0.700517\pi$
$947$	11.1232	−	15.3098i	0.361455	−	0.497500i	0.950553	+	0.310561i	$0.100517\pi$
$948$	9.02095	+	2.93108i	0.292987	+	0.0951972i
$949$	−18.1140	−	55.7490i	−0.588004	−	1.80969i
$950$	−8.08347	+	49.0931i	−0.262262	+	1.59279i
$951$	2.87628	+	8.85229i	0.0932699	+	0.287055i
$952$	0.00256906	−	0.00353601i	8.32638e−5	−	0.000114603i
$953$	−18.5702	+	25.5597i	−0.601548	+	0.827959i	−0.995849	−	0.0910220i	$-0.970987\pi$
$953$	−18.5702	+	25.5597i	−0.601548	+	0.827959i	0.394301	+	0.918981i	$0.370987\pi$
$954$	−18.8649	+	13.7061i	−0.610773	+	0.443753i
$955$	−25.8266	−	10.7903i	−0.835730	−	0.349167i
$956$	−16.5880			−0.536494
$957$	1.93016	+	2.65663i	0.0623931	+	0.0858768i
$958$	−7.74792	−	2.51745i	−0.250324	−	0.0813352i
$959$	−0.500877	−	1.54154i	−0.0161742	−	0.0497789i
$960$	5.37635	−	12.8683i	0.173521	−	0.415322i
$961$	27.6520	−	14.0131i	0.891999	−	0.452037i
$962$			87.2596i			2.81336i
$963$	−26.8683	+	8.73002i	−0.865817	+	0.281321i
$964$	3.87179	−	11.9161i	0.124702	−	0.383793i
$965$	−0.468507	−	1.97808i	−0.0150818	−	0.0636768i
$966$	0.439852			0.0141520
$967$		−	29.7465i		−	0.956584i	−0.878201	−	0.478292i	$-0.841256\pi$
$967$		−	29.7465i		−	0.956584i	0.878201	−	0.478292i	$-0.158744\pi$
$968$	0.164365	+	0.226228i	0.00528288	+	0.00727126i
$969$	−1.67876	−	1.21969i	−0.0539295	−	0.0391821i
$970$	15.7259	+	25.8392i	0.504927	+	0.829646i
$971$	−7.55506	−	23.2521i	−0.242453	−	0.746195i	−0.996045	−	0.0888517i	$-0.971680\pi$
$971$	−7.55506	−	23.2521i	−0.242453	−	0.746195i	0.753592	−	0.657343i	$-0.228320\pi$
$972$	−18.4561	−	25.4026i	−0.591978	−	0.814788i
$973$	−2.70746	+	0.879706i	−0.0867971	+	0.0282021i
$974$	−20.3641	+	62.6744i	−0.652509	+	2.00822i
$975$	3.47982	+	22.8748i	0.111443	+	0.732579i
$976$	−7.86898	+	24.2182i	−0.251880	+	0.775207i
$977$	28.5145	+	9.26492i	0.912259	+	0.296411i	0.727287	−	0.686333i	$-0.240781\pi$
$977$	28.5145	+	9.26492i	0.912259	+	0.296411i	0.184972	+	0.982744i	$0.440781\pi$
$978$	−1.05985	+	1.45876i	−0.0338902	+	0.0466459i
$979$	−8.11104	+	24.9632i	−0.259230	+	0.797828i
$980$	2.56773	−	31.3990i	0.0820232	−	1.00300i
$981$	−14.3054	+	10.3935i	−0.456738	+	0.331839i
$982$	−17.2629	+	5.60906i	−0.550882	+	0.178992i
$983$	4.15147	−	5.71401i	0.132411	−	0.182249i	−0.737663	−	0.675169i	$-0.764071\pi$
$983$	4.15147	−	5.71401i	0.132411	−	0.182249i	0.870074	+	0.492921i	$0.164071\pi$
$984$	0.219569	+	0.159526i	0.00699959	+	0.00508550i
$985$	9.41367	+	39.7455i	0.299944	+	1.26640i
$986$	−2.18678			−0.0696412
$987$		−	1.03335i		−	0.0328919i
$988$	−35.7727	−	49.2370i	−1.13808	−	1.56644i
$989$	−2.70674	+	8.33050i	−0.0860694	+	0.264894i
$990$	−23.3890	−	1.91269i	−0.743350	−	0.0607893i
$991$	16.2093			0.514905			0.257453	−	0.966291i	$-0.417117\pi$
$991$	16.2093			0.514905			0.257453	+	0.966291i	$0.417117\pi$
$992$	−10.3779	−	43.4369i	−0.329500	−	1.37912i
$993$			14.7678i			0.468642i
$994$	0.310279	+	0.954939i	0.00984144	+	0.0302888i
$995$	−29.4126	+	34.2254i	−0.932443	+	1.08502i
$996$	13.7786	−	10.0107i	0.436591	−	0.317202i
$997$		−	16.0753i		−	0.509109i	−0.967058	−	0.254554i	$-0.918071\pi$
$997$		−	16.0753i		−	0.509109i	0.967058	−	0.254554i	$-0.0819288\pi$
$998$		−	18.8200i		−	0.595736i
$999$	23.9848	−	17.4260i	0.758846	−	0.551334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.n.a.4.13	yes	56
5.2	odd	4		775.2.k.h.376.13		56
5.3	odd	4		775.2.k.h.376.2		56
5.4	even	2	inner	155.2.n.a.4.2	✓	56
31.8	even	5	inner	155.2.n.a.39.2	yes	56
155.8	odd	20		775.2.k.h.101.2		56
155.39	even	10	inner	155.2.n.a.39.13	yes	56
155.132	odd	20		775.2.k.h.101.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.n.a.4.2	✓	56	5.4	even	2	inner
155.2.n.a.4.13	yes	56	1.1	even	1	trivial
155.2.n.a.39.2	yes	56	31.8	even	5	inner
155.2.n.a.39.13	yes	56	155.39	even	10	inner
775.2.k.h.101.2		56	155.8	odd	20
775.2.k.h.101.13		56	155.132	odd	20
775.2.k.h.376.2		56	5.3	odd	4
775.2.k.h.376.13		56	5.2	odd	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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.90735 - 0.619737i) q^{2} +(-0.725535 - 0.235741i) q^{3} +(1.63589 - 1.18855i) q^{4} +(2.06323 + 0.862016i) q^{5} -1.52995 q^{6} +(0.105855 + 0.145698i) q^{7} +(0.0260217 - 0.0358157i) q^{8} +(-1.95622 - 1.42128i) q^{9} +O(q^{10})\)	\(q+(1.90735 - 0.619737i) q^{2} +(-0.725535 - 0.235741i) q^{3} +(1.63589 - 1.18855i) q^{4} +(2.06323 + 0.862016i) q^{5} -1.52995 q^{6} +(0.105855 + 0.145698i) q^{7} +(0.0260217 - 0.0358157i) q^{8} +(-1.95622 - 1.42128i) q^{9} +(4.46954 + 0.365508i) q^{10} +(1.75083 - 1.27206i) q^{11} +(-1.46709 + 0.476685i) q^{12} +(-5.76911 - 1.87450i) q^{13} +(0.292198 + 0.212294i) q^{14} +(-1.29374 - 1.11181i) q^{15} +(-1.22227 + 3.76177i) q^{16} +(0.322228 - 0.443509i) q^{17} +(-4.61203 - 1.49854i) q^{18} +(1.53326 + 4.71889i) q^{19} +(4.39977 - 1.04208i) q^{20} +(-0.0424550 - 0.130663i) q^{21} +(2.55112 - 3.51132i) q^{22} +(-0.938327 + 1.29150i) q^{23} +(-0.0273228 + 0.0198512i) q^{24} +(3.51386 + 3.55708i) q^{25} -12.1654 q^{26} +(2.42947 + 3.34388i) q^{27} +(0.346336 + 0.112531i) q^{28} +(-0.614635 - 1.89165i) q^{29} +(-3.15664 - 1.31884i) q^{30} +(-5.41535 + 1.29384i) q^{31} +8.02107i q^{32} +(-1.57017 + 0.510178i) q^{33} +(0.339744 - 1.04563i) q^{34} +(0.0928109 + 0.391857i) q^{35} -4.88943 q^{36} -7.17275i q^{37} +(5.84895 + 8.05038i) q^{38} +(3.74380 + 2.72003i) q^{39} +(0.0845625 - 0.0514651i) q^{40} +(-2.48328 - 7.64276i) q^{41} +(-0.161953 - 0.222910i) q^{42} +(5.21838 - 1.69555i) q^{43} +(1.35228 - 4.16189i) q^{44} +(-2.81098 - 4.61873i) q^{45} +(-0.989334 + 3.04486i) q^{46} +(7.15332 + 2.32425i) q^{47} +(1.77361 - 2.44116i) q^{48} +(2.15310 - 6.62655i) q^{49} +(8.90663 + 4.60694i) q^{50} +(-0.338341 + 0.245819i) q^{51} +(-11.6656 + 3.79037i) q^{52} +(2.82637 - 3.89017i) q^{53} +(6.70619 + 4.87233i) q^{54} +(4.70891 - 1.11530i) q^{55} +0.00797280 q^{56} -3.78517i q^{57} +(-2.34465 - 3.22714i) q^{58} +(-2.80623 + 8.63668i) q^{59} +(-3.43785 - 0.281139i) q^{60} +6.43798 q^{61} +(-9.52715 + 5.82389i) q^{62} -0.435467i q^{63} +(2.52640 + 7.77547i) q^{64} +(-10.2872 - 8.84059i) q^{65} +(-2.67869 + 1.94618i) q^{66} -6.31053i q^{67} -1.10852i q^{68} +(0.985247 - 0.715824i) q^{69} +(0.419872 + 0.689892i) q^{70} +(2.24909 + 1.63406i) q^{71} +(-0.101808 + 0.0330796i) q^{72} +(5.67998 + 7.81783i) q^{73} +(-4.44522 - 13.6810i) q^{74} +(-1.71088 - 3.40914i) q^{75} +(8.11687 + 5.89725i) q^{76} +(0.370671 + 0.120438i) q^{77} +(8.82645 + 2.86789i) q^{78} +(-4.97456 - 3.61423i) q^{79} +(-5.76455 + 6.70780i) q^{80} +(1.26726 + 3.90021i) q^{81} +(-9.47301 - 13.0385i) q^{82} +(-10.5004 + 3.41178i) q^{83} +(-0.224751 - 0.163291i) q^{84} +(1.04714 - 0.637297i) q^{85} +(8.90250 - 6.46804i) q^{86} +1.51735i q^{87} -0.0958085i q^{88} +(-9.81216 + 7.12895i) q^{89} +(-8.22393 - 7.06748i) q^{90} +(-0.337582 - 1.03897i) q^{91} +3.22799i q^{92} +(4.23403 + 0.337894i) q^{93} +15.0843 q^{94} +(-0.904284 + 11.0579i) q^{95} +(1.89089 - 5.81956i) q^{96} +(3.96471 + 5.45695i) q^{97} -13.9735i q^{98} -5.23297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9	\( 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9} + 4 q^{10} - 14 q^{11} - 16 q^{14} + 21 q^{15} - 22 q^{16} - 2 q^{19} - 29 q^{20} - 38 q^{21} - 30 q^{24} - 10 q^{25} + 12 q^{26} + 20 q^{29} - 30 q^{30} + 26 q^{31} - 2 q^{34} + 24 q^{35} - 44 q^{36} - 18 q^{39} + 36 q^{40} - 20 q^{41} + 62 q^{44} + 8 q^{45} - 70 q^{46} - 42 q^{49} - 11 q^{50} + 10 q^{51} - 26 q^{54} - 30 q^{55} + 208 q^{56} - 50 q^{59} - 67 q^{60} + 56 q^{61} + 12 q^{64} - 27 q^{65} + 60 q^{66} + 34 q^{69} + 5 q^{70} - 8 q^{71} - 84 q^{74} - 38 q^{75} - 20 q^{76} + 122 q^{79} - 80 q^{80} + 42 q^{81} - 40 q^{84} - 18 q^{85} + 78 q^{86} - 28 q^{89} + 144 q^{90} - 20 q^{91} + 160 q^{94} + 9 q^{95} - 70 q^{96} - 52 q^{99}+O(q^{100}) \) 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9 + 4 * q^10 - 14 * q^11 - 16 * q^14 + 21 * q^15 - 22 * q^16 - 2 * q^19 - 29 * q^20 - 38 * q^21 - 30 * q^24 - 10 * q^25 + 12 * q^26 + 20 * q^29 - 30 * q^30 + 26 * q^31 - 2 * q^34 + 24 * q^35 - 44 * q^36 - 18 * q^39 + 36 * q^40 - 20 * q^41 + 62 * q^44 + 8 * q^45 - 70 * q^46 - 42 * q^49 - 11 * q^50 + 10 * q^51 - 26 * q^54 - 30 * q^55 + 208 * q^56 - 50 * q^59 - 67 * q^60 + 56 * q^61 + 12 * q^64 - 27 * q^65 + 60 * q^66 + 34 * q^69 + 5 * q^70 - 8 * q^71 - 84 * q^74 - 38 * q^75 - 20 * q^76 + 122 * q^79 - 80 * q^80 + 42 * q^81 - 40 * q^84 - 18 * q^85 + 78 * q^86 - 28 * q^89 + 144 * q^90 - 20 * q^91 + 160 * q^94 + 9 * q^95 - 70 * q^96 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more