LMFDB - Embedded newform 1155.2.k.b.769.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.10
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83264 q^{2} +1.00000 q^{3} +1.35857 q^{4} +(0.538446 + 2.17027i) q^{5} -1.83264 q^{6} +(-0.996474 - 2.45093i) q^{7} +1.17551 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35857 q^{4} +(0.538446 + 2.17027i) q^{5} -1.83264 q^{6} +(-0.996474 - 2.45093i) q^{7} +1.17551 q^{8} +1.00000 q^{9} +(-0.986778 - 3.97732i) q^{10} +(-2.65195 - 1.99178i) q^{11} +1.35857 q^{12} -1.25331i q^{13} +(1.82618 + 4.49167i) q^{14} +(0.538446 + 2.17027i) q^{15} -4.87143 q^{16} +0.900604i q^{17} -1.83264 q^{18} -4.96271 q^{19} +(0.731517 + 2.94846i) q^{20} +(-0.996474 - 2.45093i) q^{21} +(4.86006 + 3.65021i) q^{22} -0.648612i q^{23} +1.17551 q^{24} +(-4.42015 + 2.33715i) q^{25} +2.29687i q^{26} +1.00000 q^{27} +(-1.35378 - 3.32975i) q^{28} +8.58387i q^{29} +(-0.986778 - 3.97732i) q^{30} +0.163881i q^{31} +6.57655 q^{32} +(-2.65195 - 1.99178i) q^{33} -1.65048i q^{34} +(4.78263 - 3.48231i) q^{35} +1.35857 q^{36} +5.80621i q^{37} +9.09485 q^{38} -1.25331i q^{39} +(0.632950 + 2.55118i) q^{40} -7.60600 q^{41} +(1.82618 + 4.49167i) q^{42} -10.5561 q^{43} +(-3.60285 - 2.70597i) q^{44} +(0.538446 + 2.17027i) q^{45} +1.18867i q^{46} +1.99140 q^{47} -4.87143 q^{48} +(-5.01408 + 4.88457i) q^{49} +(8.10054 - 4.28315i) q^{50} +0.900604i q^{51} -1.70271i q^{52} -12.1331i q^{53} -1.83264 q^{54} +(2.89477 - 6.82791i) q^{55} +(-1.17137 - 2.88109i) q^{56} -4.96271 q^{57} -15.7311i q^{58} +0.600825i q^{59} +(0.731517 + 2.94846i) q^{60} -5.24147 q^{61} -0.300334i q^{62} +(-0.996474 - 2.45093i) q^{63} -2.30959 q^{64} +(2.72003 - 0.674842i) q^{65} +(4.86006 + 3.65021i) q^{66} -6.57395i q^{67} +1.22353i q^{68} -0.648612i q^{69} +(-8.76483 + 6.38182i) q^{70} +10.8708 q^{71} +1.17551 q^{72} -1.42104i q^{73} -10.6407i q^{74} +(-4.42015 + 2.33715i) q^{75} -6.74218 q^{76} +(-2.23911 + 8.48448i) q^{77} +2.29687i q^{78} +6.04097i q^{79} +(-2.62300 - 10.5723i) q^{80} +1.00000 q^{81} +13.9391 q^{82} +6.80883i q^{83} +(-1.35378 - 3.32975i) q^{84} +(-1.95455 + 0.484927i) q^{85} +19.3456 q^{86} +8.58387i q^{87} +(-3.11739 - 2.34136i) q^{88} +13.9385i q^{89} +(-0.986778 - 3.97732i) q^{90} +(-3.07178 + 1.24889i) q^{91} -0.881184i q^{92} +0.163881i q^{93} -3.64951 q^{94} +(-2.67215 - 10.7704i) q^{95} +6.57655 q^{96} -19.2743 q^{97} +(9.18900 - 8.95165i) q^{98} +(-2.65195 - 1.99178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.83264			−1.29587			−0.647936	−	0.761695i	$-0.724368\pi$
$2$	−1.83264			−1.29587			−0.647936	+	0.761695i	$0.724368\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.35857			0.679284
$5$	0.538446	+	2.17027i	0.240801	+	0.970575i
$5$	0.538446	+	2.17027i	0.240801	+	0.970575i
$6$	−1.83264			−0.748172
$7$	−0.996474	−	2.45093i	−0.376632	−	0.926363i
$7$	−0.996474	−	2.45093i	−0.376632	−	0.926363i
$8$	1.17551			0.415606
$9$	1.00000			0.333333
$10$	−0.986778	−	3.97732i	−0.312047	−	1.25774i
$11$	−2.65195	−	1.99178i	−0.799592	−	0.600544i
$11$	−2.65195	−	1.99178i	−0.799592	−	0.600544i
$12$	1.35857			0.392185
$13$		−	1.25331i		−	0.347607i	−0.984780	−	0.173803i	$-0.944394\pi$
$13$		−	1.25331i		−	0.347607i	0.984780	−	0.173803i	$-0.0556057\pi$
$14$	1.82618	+	4.49167i	0.488066	+	1.20045i
$15$	0.538446	+	2.17027i	0.139026	+	0.560362i
$16$	−4.87143			−1.21786
$17$			0.900604i			0.218429i	0.994018	+	0.109214i	$0.0348335\pi$
$17$			0.900604i			0.218429i	−0.994018	+	0.109214i	$0.965167\pi$
$18$	−1.83264			−0.431957
$19$	−4.96271			−1.13852			−0.569261	−	0.822157i	$-0.692771\pi$
$19$	−4.96271			−1.13852			−0.569261	+	0.822157i	$0.692771\pi$
$20$	0.731517	+	2.94846i	0.163572	+	0.659296i
$21$	−0.996474	−	2.45093i	−0.217448	−	0.534836i
$22$	4.86006	+	3.65021i	1.03617	+	0.778228i
$23$		−	0.648612i		−	0.135245i	−0.997711	−	0.0676225i	$-0.978459\pi$
$23$		−	0.648612i		−	0.135245i	0.997711	−	0.0676225i	$-0.0215413\pi$
$24$	1.17551			0.239950
$25$	−4.42015	+	2.33715i	−0.884030	+	0.467430i
$26$			2.29687i			0.450454i
$27$	1.00000			0.192450
$28$	−1.35378	−	3.32975i	−0.255840	−	0.629264i
$29$			8.58387i			1.59398i	0.603989	+	0.796992i	$0.293577\pi$
$29$			8.58387i			1.59398i	−0.603989	+	0.796992i	$0.706423\pi$
$30$	−0.986778	−	3.97732i	−0.180160	−	0.726157i
$31$			0.163881i			0.0294338i	0.999892	+	0.0147169i	$0.00468471\pi$
$31$			0.163881i			0.0294338i	−0.999892	+	0.0147169i	$0.995315\pi$
$32$	6.57655			1.16258
$33$	−2.65195	−	1.99178i	−0.461644	−	0.346724i
$34$		−	1.65048i		−	0.283055i
$35$	4.78263	−	3.48231i	0.808411	−	0.588618i
$36$	1.35857			0.226428
$37$			5.80621i			0.954535i	0.878758	+	0.477268i	$0.158373\pi$
$37$			5.80621i			0.954535i	−0.878758	+	0.477268i	$0.841627\pi$
$38$	9.09485			1.47538
$39$		−	1.25331i		−	0.200691i
$40$	0.632950	+	2.55118i	0.100078	+	0.403377i
$41$	−7.60600			−1.18786			−0.593929	−	0.804517i	$-0.702424\pi$
$41$	−7.60600			−1.18786			−0.593929	+	0.804517i	$0.702424\pi$
$42$	1.82618	+	4.49167i	0.281785	+	0.693079i
$43$	−10.5561			−1.60980			−0.804898	−	0.593414i	$-0.797780\pi$
$43$	−10.5561			−1.60980			−0.804898	+	0.593414i	$0.797780\pi$
$44$	−3.60285	−	2.70597i	−0.543150	−	0.407940i
$45$	0.538446	+	2.17027i	0.0802669	+	0.323525i
$46$			1.18867i			0.175260i
$47$	1.99140			0.290475			0.145238	−	0.989397i	$-0.453605\pi$
$47$	1.99140			0.290475			0.145238	+	0.989397i	$0.453605\pi$
$48$	−4.87143			−0.703130
$49$	−5.01408	+	4.88457i	−0.716297	+	0.697795i
$50$	8.10054	−	4.28315i	1.14559	−	0.605729i
$51$			0.900604i			0.126110i
$52$		−	1.70271i		−	0.236124i
$53$		−	12.1331i		−	1.66662i	−0.552809	−	0.833308i	$-0.686444\pi$
$53$		−	12.1331i		−	1.66662i	0.552809	−	0.833308i	$-0.313556\pi$
$54$	−1.83264			−0.249391
$55$	2.89477	−	6.82791i	0.390331	−	0.920675i
$56$	−1.17137	−	2.88109i	−0.156530	−	0.385002i
$57$	−4.96271			−0.657326
$58$		−	15.7311i		−	2.06560i
$59$			0.600825i			0.0782207i	0.999235	+	0.0391104i	$0.0124524\pi$
$59$			0.600825i			0.0782207i	−0.999235	+	0.0391104i	$0.987548\pi$
$60$	0.731517	+	2.94846i	0.0944384	+	0.380645i
$61$	−5.24147			−0.671102			−0.335551	−	0.942022i	$-0.608922\pi$
$61$	−5.24147			−0.671102			−0.335551	+	0.942022i	$0.608922\pi$
$62$		−	0.300334i		−	0.0381425i
$63$	−0.996474	−	2.45093i	−0.125544	−	0.308788i
$64$	−2.30959			−0.288699
$65$	2.72003	−	0.674842i	0.337378	−	0.0837039i
$66$	4.86006	+	3.65021i	0.598232	+	0.449310i
$67$		−	6.57395i		−	0.803136i	−0.915829	−	0.401568i	$-0.868465\pi$
$67$		−	6.57395i		−	0.803136i	0.915829	−	0.401568i	$-0.131535\pi$
$68$			1.22353i			0.148375i
$69$		−	0.648612i		−	0.0780837i
$70$	−8.76483	+	6.38182i	−1.04760	+	0.762773i
$71$	10.8708			1.29012			0.645062	−	0.764130i	$-0.276832\pi$
$71$	10.8708			1.29012			0.645062	+	0.764130i	$0.276832\pi$
$72$	1.17551			0.138535
$73$		−	1.42104i		−	0.166321i	−0.996536	−	0.0831603i	$-0.973499\pi$
$73$		−	1.42104i		−	0.166321i	0.996536	−	0.0831603i	$-0.0265013\pi$
$74$		−	10.6407i		−	1.23696i
$75$	−4.42015	+	2.33715i	−0.510395	+	0.269871i
$76$	−6.74218			−0.773381
$77$	−2.23911	+	8.48448i	−0.255170	+	0.966896i
$78$			2.29687i			0.260070i
$79$			6.04097i			0.679662i	0.940486	+	0.339831i	$0.110370\pi$
$79$			6.04097i			0.679662i	−0.940486	+	0.339831i	$0.889630\pi$
$80$	−2.62300	−	10.5723i	−0.293261	−	1.18202i
$81$	1.00000			0.111111
$82$	13.9391			1.53931
$83$			6.80883i			0.747366i	0.927556	+	0.373683i	$0.121905\pi$
$83$			6.80883i			0.747366i	−0.927556	+	0.373683i	$0.878095\pi$
$84$	−1.35378	−	3.32975i	−0.147709	−	0.363306i
$85$	−1.95455	+	0.484927i	−0.212001	+	0.0525977i
$86$	19.3456			2.08609
$87$			8.58387i			0.920287i
$88$	−3.11739	−	2.34136i	−0.332315	−	0.249590i
$89$			13.9385i			1.47748i	0.673991	+	0.738739i	$0.264578\pi$
$89$			13.9385i			1.47748i	−0.673991	+	0.738739i	$0.735422\pi$
$90$	−0.986778	−	3.97732i	−0.104016	−	0.419247i
$91$	−3.07178	+	1.24889i	−0.322010	+	0.130920i
$92$		−	0.881184i		−	0.0918698i
$93$			0.163881i			0.0169936i
$94$	−3.64951			−0.376419
$95$	−2.67215	−	10.7704i	−0.274157	−	1.10502i
$96$	6.57655			0.671216
$97$	−19.2743			−1.95700			−0.978502	−	0.206236i	$-0.933879\pi$
$97$	−19.2743			−1.95700			−0.978502	+	0.206236i	$0.933879\pi$
$98$	9.18900	−	8.95165i	0.928230	−	0.904253i
$99$	−2.65195	−	1.99178i	−0.266531	−	0.200181i
$100$	−6.00508	+	3.17518i	−0.600508	+	0.317518i
$101$	−16.4453			−1.63637			−0.818186	−	0.574953i	$-0.805020\pi$
$101$	−16.4453			−1.63637			−0.818186	+	0.574953i	$0.805020\pi$
$102$		−	1.65048i		−	0.163422i
$103$	−9.53098			−0.939116			−0.469558	−	0.882902i	$-0.655587\pi$
$103$	−9.53098			−0.939116			−0.469558	+	0.882902i	$0.655587\pi$
$104$		−	1.47328i		−	0.144467i
$105$	4.78263	−	3.48231i	0.466737	−	0.339839i
$106$			22.2357i			2.15972i
$107$	0.883216			0.0853837			0.0426919	−	0.999088i	$-0.486407\pi$
$107$	0.883216			0.0853837			0.0426919	+	0.999088i	$0.486407\pi$
$108$	1.35857			0.130728
$109$		−	12.0458i		−	1.15378i	−0.816822	−	0.576890i	$-0.804266\pi$
$109$		−	12.0458i		−	1.15378i	0.816822	−	0.576890i	$-0.195734\pi$
$110$	−5.30507	+	12.5131i	−0.505819	+	1.19308i
$111$			5.80621i			0.551101i
$112$	4.85425	+	11.9395i	0.458684	+	1.12818i
$113$		−	10.2440i		−	0.963673i	−0.876261	−	0.481837i	$-0.839970\pi$
$113$		−	10.2440i		−	0.963673i	0.876261	−	0.481837i	$-0.160030\pi$
$114$	9.09485			0.851811
$115$	1.40766	−	0.349243i	0.131265	−	0.0325671i
$116$			11.6618i			1.08277i
$117$		−	1.25331i		−	0.115869i
$118$		−	1.10110i		−	0.101364i
$119$	2.20731	−	0.897428i	0.202344	−	0.0822671i
$120$	0.632950	+	2.55118i	0.0577802	+	0.232890i
$121$	3.06563	+	10.5642i	0.278694	+	0.960380i
$122$	9.60573			0.869662
$123$	−7.60600			−0.685810
$124$			0.222643i			0.0199939i
$125$	−7.45226	−	8.33449i	−0.666551	−	0.745460i
$126$	1.82618	+	4.49167i	0.162689	+	0.400149i
$127$	1.61785			0.143561			0.0717807	−	0.997420i	$-0.477132\pi$
$127$	1.61785			0.143561			0.0717807	+	0.997420i	$0.477132\pi$
$128$	−8.92045			−0.788464
$129$	−10.5561			−0.929416
$130$	−4.98483	+	1.23674i	−0.437199	+	0.108469i
$131$	7.90226			0.690423			0.345212	−	0.938525i	$-0.387807\pi$
$131$	7.90226			0.690423			0.345212	+	0.938525i	$0.387807\pi$
$132$	−3.60285	−	2.70597i	−0.313588	−	0.235524i
$133$	4.94521	+	12.1632i	0.428804	+	1.05469i
$134$			12.0477i			1.04076i
$135$	0.538446	+	2.17027i	0.0463421	+	0.186787i
$136$			1.05867i			0.0907803i
$137$			3.93225i			0.335955i	0.985791	+	0.167977i	$0.0537236\pi$
$137$			3.93225i			0.335955i	−0.985791	+	0.167977i	$0.946276\pi$
$138$			1.18867i			0.101186i
$139$	0.108206			0.00917793			0.00458897	−	0.999989i	$-0.498539\pi$
$139$	0.108206			0.00917793			0.00458897	+	0.999989i	$0.498539\pi$
$140$	6.49753	−	4.73096i	0.549141	−	0.399839i
$141$	1.99140			0.167706
$142$	−19.9222			−1.67184
$143$	−2.49632	+	3.32372i	−0.208753	+	0.277943i
$144$	−4.87143			−0.405952
$145$	−18.6293	+	4.62195i	−1.54708	+	0.383832i
$146$			2.60426i			0.215530i
$147$	−5.01408	+	4.88457i	−0.413554	+	0.402872i
$148$			7.88814i			0.648401i
$149$		−	4.27007i		−	0.349818i	−0.984585	−	0.174909i	$-0.944037\pi$
$149$		−	4.27007i		−	0.349818i	0.984585	−	0.174909i	$-0.0559631\pi$
$150$	8.10054	−	4.28315i	0.661407	−	0.349718i
$151$		−	16.1520i		−	1.31443i	−0.753704	−	0.657214i	$-0.771735\pi$
$151$		−	16.1520i		−	1.31443i	0.753704	−	0.657214i	$-0.228265\pi$
$152$	−5.83372			−0.473177
$153$			0.900604i			0.0728095i
$154$	4.10348	−	15.5490i	0.330668	−	1.25297i
$155$	−0.355665	+	0.0882409i	−0.0285677	+	0.00708768i
$156$		−	1.70271i		−	0.136326i
$157$	−16.5612			−1.32173			−0.660863	−	0.750506i	$-0.729810\pi$
$157$	−16.5612			−1.32173			−0.660863	+	0.750506i	$0.729810\pi$
$158$		−	11.0709i		−	0.880755i
$159$		−	12.1331i		−	0.962221i
$160$	3.54112	+	14.2729i	0.279950	+	1.12837i
$161$	−1.58970	+	0.646325i	−0.125286	+	0.0509375i
$162$	−1.83264			−0.143986
$163$		−	17.9624i		−	1.40692i	−0.710735	−	0.703460i	$-0.751637\pi$
$163$		−	17.9624i		−	1.40692i	0.710735	−	0.703460i	$-0.248363\pi$
$164$	−10.3333			−0.806894
$165$	2.89477	−	6.82791i	0.225358	−	0.531552i
$166$		−	12.4781i		−	0.968491i
$167$			3.86148i			0.298810i	0.988776	+	0.149405i	$0.0477359\pi$
$167$			3.86148i			0.298810i	−0.988776	+	0.149405i	$0.952264\pi$
$168$	−1.17137	−	2.88109i	−0.0903729	−	0.222281i
$169$	11.4292			0.879170
$170$	3.58199	−	0.888696i	0.274726	−	0.0681599i
$171$	−4.96271			−0.379508
$172$	−14.3412			−1.09351
$173$			9.17271i			0.697388i	0.937237	+	0.348694i	$0.113375\pi$
$173$			9.17271i			0.697388i	−0.937237	+	0.348694i	$0.886625\pi$
$174$		−	15.7311i		−	1.19257i
$175$	10.1327	+	8.50456i	0.765964	+	0.642884i
$176$	12.9188	+	9.70281i	0.973788	+	0.731377i
$177$			0.600825i			0.0451608i
$178$		−	25.5443i		−	1.91462i
$179$	−17.2783			−1.29144			−0.645719	−	0.763575i	$-0.723442\pi$
$179$	−17.2783			−1.29144			−0.645719	+	0.763575i	$0.723442\pi$
$180$	0.731517	+	2.94846i	0.0545240	+	0.219765i
$181$			14.8336i			1.10257i	0.834317	+	0.551285i	$0.185862\pi$
$181$			14.8336i			1.10257i	−0.834317	+	0.551285i	$0.814138\pi$
$182$	5.62946	−	2.28877i	0.417284	−	0.169655i
$183$	−5.24147			−0.387461
$184$		−	0.762451i		−	0.0562086i
$185$	−12.6011	+	3.12633i	−0.926448	+	0.229853i
$186$		−	0.300334i		−	0.0220216i
$187$	1.79380	−	2.38835i	0.131176	−	0.174654i
$188$	2.70545			0.197315
$189$	−0.996474	−	2.45093i	−0.0724828	−	0.178279i
$190$	4.89709	+	19.7383i	0.355272	+	1.43197i
$191$	−12.9155			−0.934532			−0.467266	−	0.884117i	$-0.654761\pi$
$191$	−12.9155			−0.934532			−0.467266	+	0.884117i	$0.654761\pi$
$192$	−2.30959			−0.166680
$193$	−1.42077			−0.102269			−0.0511347	−	0.998692i	$-0.516284\pi$
$193$	−1.42077			−0.102269			−0.0511347	+	0.998692i	$0.516284\pi$
$194$	35.3228			2.53603
$195$	2.72003	−	0.674842i	0.194785	−	0.0483264i
$196$	−6.81197	+	6.63602i	−0.486570	+	0.474002i
$197$	16.4316			1.17070			0.585351	−	0.810780i	$-0.300957\pi$
$197$	16.4316			1.17070			0.585351	+	0.810780i	$0.300957\pi$
$198$	4.86006	+	3.65021i	0.345390	+	0.259409i
$199$		−	12.7554i		−	0.904206i	−0.891966	−	0.452103i	$-0.850674\pi$
$199$		−	12.7554i		−	0.904206i	0.891966	−	0.452103i	$-0.149326\pi$
$200$	−5.19594	+	2.74735i	−0.367408	+	0.194267i
$201$		−	6.57395i		−	0.463691i
$202$	30.1384			2.12053
$203$	21.0384	−	8.55360i	1.47661	−	0.600345i
$204$			1.22353i			0.0856644i
$205$	−4.09543	−	16.5071i	−0.286037	−	1.15291i
$206$	17.4669			1.21697
$207$		−	0.648612i		−	0.0450816i
$208$			6.10543i			0.423335i
$209$	13.1608	+	9.88462i	0.910353	+	0.683733i
$210$	−8.76483	+	6.38182i	−0.604831	+	0.440387i
$211$			2.34216i			0.161241i	0.996745	+	0.0806204i	$0.0256901\pi$
$211$			2.34216i			0.161241i	−0.996745	+	0.0806204i	$0.974310\pi$
$212$		−	16.4837i		−	1.13211i
$213$	10.8708			0.744853
$214$	−1.61862			−0.110646
$215$	−5.68391	−	22.9097i	−0.387640	−	1.56243i
$216$	1.17551			0.0799835
$217$	0.401659	−	0.163303i	0.0272664	−	0.0110857i
$218$			22.0757i			1.49515i
$219$		−	1.42104i		−	0.0960252i
$220$	3.93274	−	9.27618i	0.265146	−	0.625400i
$221$	1.12874			0.0759272
$222$		−	10.6407i		−	0.714157i
$223$	−4.12809			−0.276437			−0.138219	−	0.990402i	$-0.544138\pi$
$223$	−4.12809			−0.276437			−0.138219	+	0.990402i	$0.544138\pi$
$224$	−6.55336	−	16.1186i	−0.437865	−	1.07697i
$225$	−4.42015	+	2.33715i	−0.294677	+	0.155810i
$226$			18.7735i			1.24880i
$227$			21.8296i			1.44888i	0.689336	+	0.724442i	$0.257902\pi$
$227$			21.8296i			1.44888i	−0.689336	+	0.724442i	$0.742098\pi$
$228$	−6.74218			−0.446512
$229$		−	1.37953i		−	0.0911616i	−0.998961	−	0.0455808i	$-0.985486\pi$
$229$		−	1.37953i		−	0.0911616i	0.998961	−	0.0455808i	$-0.0145139\pi$
$230$	−2.57974	+	0.640036i	−0.170103	+	0.0422027i
$231$	−2.23911	+	8.48448i	−0.147323	+	0.558238i
$232$			10.0904i			0.662470i
$233$	−2.59060			−0.169716			−0.0848578	−	0.996393i	$-0.527044\pi$
$233$	−2.59060			−0.169716			−0.0848578	+	0.996393i	$0.527044\pi$
$234$			2.29687i			0.150151i
$235$	1.07226	+	4.32187i	0.0699466	+	0.281928i
$236$			0.816262i			0.0531341i
$237$			6.04097i			0.392403i
$238$	−4.04521	+	1.64466i	−0.262212	+	0.106608i
$239$			9.02101i			0.583521i	0.956491	+	0.291760i	$0.0942410\pi$
$239$			9.02101i			0.583521i	−0.956491	+	0.291760i	$0.905759\pi$
$240$	−2.62300	−	10.5723i	−0.169314	−	0.682440i
$241$	0.695298			0.0447881			0.0223940	−	0.999749i	$-0.492871\pi$
$241$	0.695298			0.0447881			0.0223940	+	0.999749i	$0.492871\pi$
$242$	−5.61820	−	19.3603i	−0.361151	−	1.24453i
$243$	1.00000			0.0641500
$244$	−7.12090			−0.455869
$245$	−13.3006	−	8.25183i	−0.849747	−	0.527190i
$246$	13.9391			0.888722
$247$			6.21982i			0.395758i
$248$			0.192644i			0.0122329i
$249$			6.80883i			0.431492i
$250$	13.6573	+	15.2741i	0.863764	+	0.966021i
$251$		−	9.59678i		−	0.605744i	−0.953031	−	0.302872i	$-0.902055\pi$
$251$		−	9.59678i		−	0.605744i	0.953031	−	0.302872i	$-0.0979454\pi$
$252$	−1.35378	−	3.32975i	−0.0852800	−	0.209755i
$253$	−1.29189	+	1.72008i	−0.0812205	+	0.108141i
$254$	−2.96494			−0.186037
$255$	−1.95455	+	0.484927i	−0.122399	+	0.0303673i
$256$	20.9672			1.31045
$257$	4.38110			0.273285			0.136643	−	0.990620i	$-0.456369\pi$
$257$	4.38110			0.273285			0.136643	+	0.990620i	$0.456369\pi$
$258$	19.3456			1.20440
$259$	14.2306	−	5.78574i	0.884246	−	0.359508i
$260$	3.69535	−	0.916819i	0.229176	−	0.0568587i
$261$			8.58387i			0.531328i
$262$	−14.4820			−0.894700
$263$	2.67617			0.165020			0.0825100	−	0.996590i	$-0.473706\pi$
$263$	2.67617			0.165020			0.0825100	+	0.996590i	$0.473706\pi$
$264$	−3.11739	−	2.34136i	−0.191862	−	0.144101i
$265$	26.3322	−	6.53305i	1.61758	−	0.401322i
$266$	−9.06278	−	22.2908i	−0.555675	−	1.36674i
$267$			13.9385i			0.853023i
$268$		−	8.93117i		−	0.545558i
$269$			16.0604i			0.979219i	0.871942	+	0.489609i	$0.162861\pi$
$269$			16.0604i			0.979219i	−0.871942	+	0.489609i	$0.837139\pi$
$270$	−0.986778	−	3.97732i	−0.0600534	−	0.242052i
$271$	25.5100			1.54962			0.774812	−	0.632192i	$-0.217845\pi$
$271$	25.5100			1.54962			0.774812	+	0.632192i	$0.217845\pi$
$272$		−	4.38723i		−	0.266015i
$273$	−3.07178	+	1.24889i	−0.185912	+	0.0755865i
$274$		−	7.20640i		−	0.435354i
$275$	16.3771	+	2.60597i	0.987575	+	0.157146i
$276$		−	0.881184i		−	0.0530410i
$277$	23.7027			1.42416			0.712080	−	0.702099i	$-0.247753\pi$
$277$	23.7027			1.42416			0.712080	+	0.702099i	$0.247753\pi$
$278$	−0.198303			−0.0118934
$279$			0.163881i			0.00981127i
$280$	5.62204	−	4.09350i	0.335981	−	0.244633i
$281$			24.1777i			1.44232i	0.692769	+	0.721160i	$0.256391\pi$
$281$			24.1777i			1.44232i	−0.692769	+	0.721160i	$0.743609\pi$
$282$	−3.64951			−0.217325
$283$		−	28.5166i		−	1.69514i	−0.530687	−	0.847568i	$-0.678066\pi$
$283$		−	28.5166i		−	1.69514i	0.530687	−	0.847568i	$-0.321934\pi$
$284$	14.7687			0.876361
$285$	−2.67215	−	10.7704i	−0.158285	−	0.637984i
$286$	4.57486	−	6.09118i	0.270517	−	0.360179i
$287$	7.57918	+	18.6418i	0.447385	+	1.10039i
$288$	6.57655			0.387527
$289$	16.1889			0.952289
$290$	34.1408	−	8.47038i	2.00482	−	0.497398i
$291$	−19.2743			−1.12988
$292$		−	1.93059i		−	0.112979i
$293$		−	14.6498i		−	0.855851i	−0.903814	−	0.427926i	$-0.859245\pi$
$293$		−	14.6498i		−	0.855851i	0.903814	−	0.427926i	$-0.140755\pi$
$294$	9.18900	−	8.95165i	0.535914	−	0.522071i
$295$	−1.30395	+	0.323512i	−0.0759190	+	0.0188356i
$296$			6.82527i			0.396711i
$297$	−2.65195	−	1.99178i	−0.153881	−	0.115575i
$298$			7.82550i			0.453319i
$299$	−0.812914			−0.0470120
$300$	−6.00508	+	3.17518i	−0.346703	+	0.183319i
$301$	10.5189	+	25.8723i	0.606300	+	1.49125i
$302$			29.6007i			1.70333i
$303$	−16.4453			−0.944760
$304$	24.1755			1.38656
$305$	−2.82225	−	11.3754i	−0.161602	−	0.651354i
$306$		−	1.65048i		−	0.0943518i
$307$		−	27.6470i		−	1.57790i	−0.614459	−	0.788949i	$-0.710626\pi$
$307$		−	27.6470i		−	1.57790i	0.614459	−	0.788949i	$-0.289374\pi$
$308$	−3.04199	+	11.5267i	−0.173333	+	0.656798i
$309$	−9.53098			−0.542199
$310$	0.651806	−	0.161714i	0.0370201	−	0.00918473i
$311$		−	14.1431i		−	0.801981i	−0.916082	−	0.400990i	$-0.868666\pi$
$311$		−	14.1431i		−	0.801981i	0.916082	−	0.400990i	$-0.131334\pi$
$312$		−	1.47328i		−	0.0834083i
$313$	26.8476			1.51752			0.758758	−	0.651373i	$-0.225807\pi$
$313$	26.8476			1.51752			0.758758	+	0.651373i	$0.225807\pi$
$314$	30.3507			1.71279
$315$	4.78263	−	3.48231i	0.269470	−	0.196206i
$316$			8.20708i			0.461684i
$317$		−	16.0419i		−	0.901005i	−0.892775	−	0.450503i	$-0.851245\pi$
$317$		−	16.0419i		−	0.901005i	0.892775	−	0.450503i	$-0.148755\pi$
$318$			22.2357i			1.24692i
$319$	17.0972	−	22.7640i	0.957258	−	1.27454i
$320$	−1.24359	−	5.01244i	−0.0695188	−	0.280204i
$321$	0.883216			0.0492963
$322$	2.91335	−	1.18448i	0.162355	−	0.0660085i
$323$		−	4.46943i		−	0.248686i
$324$	1.35857			0.0754761
$325$	2.92918	+	5.53983i	0.162482	+	0.307295i
$326$			32.9185i			1.82319i
$327$		−	12.0458i		−	0.666136i
$328$	−8.94095			−0.493681
$329$	−1.98437	−	4.88077i	−0.109402	−	0.269085i
$330$	−5.30507	+	12.5131i	−0.292035	+	0.688823i
$331$	27.2861			1.49978			0.749890	−	0.661562i	$-0.230106\pi$
$331$	27.2861			1.49978			0.749890	+	0.661562i	$0.230106\pi$
$332$			9.25026i			0.507674i
$333$			5.80621i			0.318178i
$334$		−	7.07671i		−	0.387220i
$335$	14.2673	−	3.53972i	0.779504	−	0.193396i
$336$	4.85425	+	11.9395i	0.264821	+	0.651354i
$337$	7.08104			0.385729			0.192865	−	0.981225i	$-0.438222\pi$
$337$	7.08104			0.385729			0.192865	+	0.981225i	$0.438222\pi$
$338$	−20.9456			−1.13929
$339$		−	10.2440i		−	0.556377i
$340$	−2.65540	+	0.658807i	−0.144009	+	0.0357288i
$341$	0.326414	−	0.434602i	0.0176763	−	0.0235350i
$342$	9.09485			0.491793
$343$	16.9681	+	7.42180i	0.916192	+	0.400740i
$344$	−12.4089			−0.669041
$345$	1.40766	−	0.349243i	0.0757861	−	0.0188026i
$346$		−	16.8103i		−	0.903726i
$347$	15.8426			0.850477			0.425239	−	0.905081i	$-0.360190\pi$
$347$	15.8426			0.850477			0.425239	+	0.905081i	$0.360190\pi$
$348$			11.6618i			0.625137i
$349$	−16.4924			−0.882820			−0.441410	−	0.897305i	$-0.645522\pi$
$349$	−16.4924			−0.882820			−0.441410	+	0.897305i	$0.645522\pi$
$350$	−18.5697	−	15.5858i	−0.992591	−	0.833096i
$351$		−	1.25331i		−	0.0668969i
$352$	−17.4407	−	13.0990i	−0.929590	−	0.698181i
$353$	22.5281			1.19905			0.599525	−	0.800356i	$-0.295356\pi$
$353$	22.5281			1.19905			0.599525	+	0.800356i	$0.295356\pi$
$354$		−	1.10110i		−	0.0585226i
$355$	5.85333	+	23.5925i	0.310663	+	1.25216i
$356$			18.9364i			1.00363i
$357$	2.20731	−	0.897428i	0.116823	−	0.0474969i
$358$	31.6648			1.67354
$359$			14.2371i			0.751403i	0.926741	+	0.375702i	$0.122598\pi$
$359$			14.2371i			0.751403i	−0.926741	+	0.375702i	$0.877402\pi$
$360$	0.632950	+	2.55118i	0.0333594	+	0.134459i
$361$	5.62845			0.296234
$362$		−	27.1846i		−	1.42879i
$363$	3.06563	+	10.5642i	0.160904	+	0.554476i
$364$	−4.17322	+	1.69671i	−0.218736	+	0.0889317i
$365$	3.08405	−	0.765156i	0.161427	−	0.0400501i
$366$	9.60573			0.502100
$367$	−19.6640			−1.02645			−0.513226	−	0.858254i	$-0.671550\pi$
$367$	−19.6640			−1.02645			−0.513226	+	0.858254i	$0.671550\pi$
$368$			3.15967i			0.164709i
$369$	−7.60600			−0.395953
$370$	23.0932	−	5.72945i	1.20056	−	0.297860i
$371$	−29.7375	+	12.0904i	−1.54389	+	0.627700i
$372$			0.222643i			0.0115435i
$373$	−7.37461			−0.381843			−0.190922	−	0.981605i	$-0.561148\pi$
$373$	−7.37461			−0.381843			−0.190922	+	0.981605i	$0.561148\pi$
$374$	−3.28740	+	4.37699i	−0.169987	+	0.226329i
$375$	−7.45226	−	8.33449i	−0.384833	−	0.430391i
$376$	2.34091			0.120723
$377$	10.7583			0.554079
$378$	1.82618	+	4.49167i	0.0939284	+	0.231026i
$379$	−5.17238			−0.265687			−0.132844	−	0.991137i	$-0.542411\pi$
$379$	−5.17238			−0.265687			−0.132844	+	0.991137i	$0.542411\pi$
$380$	−3.63030	−	14.6324i	−0.186231	−	0.750624i
$381$	1.61785			0.0828852
$382$	23.6694			1.21103
$383$	−19.7084			−1.00705			−0.503527	−	0.863980i	$-0.667965\pi$
$383$	−19.7084			−1.00705			−0.503527	+	0.863980i	$0.667965\pi$
$384$	−8.92045			−0.455220
$385$	−19.6193	−	0.291038i	−0.999890	−	0.0148327i
$386$	2.60376			0.132528
$387$	−10.5561			−0.536598
$388$	−26.1854			−1.32936
$389$	−36.6557			−1.85852			−0.929258	−	0.369431i	$-0.879553\pi$
$389$	−36.6557			−1.85852			−0.929258	+	0.369431i	$0.879553\pi$
$390$	−4.98483	+	1.23674i	−0.252417	+	0.0626249i
$391$	0.584142			0.0295413
$392$	−5.89411	+	5.74187i	−0.297698	+	0.290008i
$393$	7.90226			0.398616
$394$	−30.1132			−1.51708
$395$	−13.1105	+	3.25274i	−0.659663	+	0.163663i
$396$	−3.60285	−	2.70597i	−0.181050	−	0.135980i
$397$	19.4173			0.974525			0.487263	−	0.873255i	$-0.337995\pi$
$397$	19.4173			0.974525			0.487263	+	0.873255i	$0.337995\pi$
$398$			23.3760i			1.17174i
$399$	4.94521	+	12.1632i	0.247570	+	0.608923i
$400$	21.5324	−	11.3853i	1.07662	−	0.569263i
$401$	22.8621			1.14168			0.570840	−	0.821061i	$-0.306618\pi$
$401$	22.8621			1.14168			0.570840	+	0.821061i	$0.306618\pi$
$402$			12.0477i			0.600884i
$403$	0.205394			0.0102314
$404$	−22.3421			−1.11156
$405$	0.538446	+	2.17027i	0.0267556	+	0.107842i
$406$	−38.5559	+	15.6757i	−1.91350	+	0.777970i
$407$	11.5647	−	15.3978i	0.573241	−	0.763239i
$408$			1.05867i			0.0524120i
$409$	−1.25943			−0.0622746			−0.0311373	−	0.999515i	$-0.509913\pi$
$409$	−1.25943			−0.0622746			−0.0311373	+	0.999515i	$0.509913\pi$
$410$	7.50544	+	30.2515i	0.370667	+	1.49402i
$411$			3.93225i			0.193964i
$412$	−12.9485			−0.637927
$413$	1.47258	−	0.598706i	0.0724608	−	0.0294604i
$414$			1.18867i			0.0584200i
$415$	−14.7770	+	3.66619i	−0.725374	+	0.179966i
$416$		−	8.24248i		−	0.404121i
$417$	0.108206			0.00529888
$418$	−24.1191	−	18.1149i	−1.17970	−	0.886031i
$419$			39.4012i			1.92487i	0.271508	+	0.962436i	$0.412478\pi$
$419$			39.4012i			1.92487i	−0.271508	+	0.962436i	$0.587522\pi$
$420$	6.49753	−	4.73096i	0.317047	−	0.230847i
$421$	6.21963			0.303126			0.151563	−	0.988448i	$-0.451569\pi$
$421$	6.21963			0.303126			0.151563	+	0.988448i	$0.451569\pi$
$422$		−	4.29233i		−	0.208947i
$423$	1.99140			0.0968250
$424$		−	14.2627i		−	0.692656i
$425$	−2.10485	−	3.98080i	−0.102100	−	0.193097i
$426$	−19.9222			−0.965235
$427$	5.22299	+	12.8465i	0.252758	+	0.621684i
$428$	1.19991			0.0579998
$429$	−2.49632	+	3.32372i	−0.120524	+	0.160471i
$430$	10.4166	+	41.9852i	0.502331	+	2.02470i
$431$			7.39679i			0.356291i	0.984004	+	0.178145i	$0.0570097\pi$
$431$			7.39679i			0.356291i	−0.984004	+	0.178145i	$0.942990\pi$
$432$	−4.87143			−0.234377
$433$	−25.6828			−1.23424			−0.617118	−	0.786870i	$-0.711700\pi$
$433$	−25.6828			−1.23424			−0.617118	+	0.786870i	$0.711700\pi$
$434$	−0.736097	+	0.299275i	−0.0353338	+	0.0143657i
$435$	−18.6293	+	4.62195i	−0.893208	+	0.221606i
$436$		−	16.3651i		−	0.783746i
$437$			3.21887i			0.153979i
$438$			2.60426i			0.124436i
$439$	−32.2236			−1.53795			−0.768975	−	0.639278i	$-0.779233\pi$
$439$	−32.2236			−1.53795			−0.768975	+	0.639278i	$0.779233\pi$
$440$	3.40284	−	8.02629i	0.162224	−	0.382638i
$441$	−5.01408	+	4.88457i	−0.238766	+	0.232598i
$442$	−2.06857			−0.0983919
$443$		−	29.6173i		−	1.40716i	−0.710617	−	0.703579i	$-0.751584\pi$
$443$		−	29.6173i		−	1.40716i	0.710617	−	0.703579i	$-0.248416\pi$
$444$			7.88814i			0.374355i
$445$	−30.2503	+	7.50514i	−1.43400	+	0.355778i
$446$	7.56530			0.358227
$447$		−	4.27007i		−	0.201967i
$448$	2.30145	+	5.66064i	0.108733	+	0.267440i
$449$	−3.86846			−0.182564			−0.0912819	−	0.995825i	$-0.529096\pi$
$449$	−3.86846			−0.182564			−0.0912819	+	0.995825i	$0.529096\pi$
$450$	8.10054	−	4.28315i	0.381863	−	0.201910i
$451$	20.1707	+	15.1495i	0.949802	+	0.713361i
$452$		−	13.9172i		−	0.654608i
$453$		−	16.1520i		−	0.758885i
$454$		−	40.0059i		−	1.87757i
$455$	−4.36443	−	5.99413i	−0.204607	−	0.281009i
$456$	−5.83372			−0.273189
$457$	−12.1915			−0.570295			−0.285148	−	0.958484i	$-0.592043\pi$
$457$	−12.1915			−0.570295			−0.285148	+	0.958484i	$0.592043\pi$
$458$			2.52817i			0.118134i
$459$			0.900604i			0.0420366i
$460$	1.91241	−	0.474470i	0.0891665	−	0.0221223i
$461$	−27.4628			−1.27907			−0.639534	−	0.768763i	$-0.720873\pi$
$461$	−27.4628			−1.27907			−0.639534	+	0.768763i	$0.720873\pi$
$462$	4.10348	−	15.5490i	0.190911	−	0.723405i
$463$			17.1399i			0.796557i	0.917265	+	0.398279i	$0.130392\pi$
$463$			17.1399i			0.796557i	−0.917265	+	0.398279i	$0.869608\pi$
$464$		−	41.8157i		−	1.94125i
$465$	−0.355665	+	0.0882409i	−0.0164936	+	0.00409207i
$466$	4.74763			0.219930
$467$	2.44194			0.113000			0.0564998	−	0.998403i	$-0.482006\pi$
$467$	2.44194			0.113000			0.0564998	+	0.998403i	$0.482006\pi$
$468$		−	1.70271i		−	0.0787079i
$469$	−16.1123	+	6.55077i	−0.743996	+	0.302487i
$470$	−1.96507	−	7.92043i	−0.0906418	−	0.365342i
$471$	−16.5612			−0.763099
$472$			0.706277i			0.0325090i
$473$	27.9943	+	21.0255i	1.28718	+	0.966753i
$474$		−	11.0709i		−	0.508504i
$475$	21.9359	−	11.5986i	1.00649	−	0.532180i
$476$	2.99879	−	1.21922i	0.137449	−	0.0558828i
$477$		−	12.1331i		−	0.555539i
$478$		−	16.5323i		−	0.756168i
$479$	27.3292			1.24870			0.624352	−	0.781143i	$-0.285363\pi$
$479$	27.3292			1.24870			0.624352	+	0.781143i	$0.285363\pi$
$480$	3.54112	+	14.2729i	0.161629	+	0.651465i
$481$	7.27700			0.331803
$482$	−1.27423			−0.0580396
$483$	−1.58970	+	0.646325i	−0.0723339	+	0.0294088i
$484$	4.16487	+	14.3522i	0.189312	+	0.652371i
$485$	−10.3782	−	41.8304i	−0.471248	−	1.89942i
$486$	−1.83264			−0.0831302
$487$			34.6540i			1.57032i	0.619292	+	0.785161i	$0.287420\pi$
$487$			34.6540i			1.57032i	−0.619292	+	0.785161i	$0.712580\pi$
$488$	−6.16142			−0.278914
$489$		−	17.9624i		−	0.812286i
$490$	24.3753	+	15.1226i	1.10116	+	0.683171i
$491$		−	26.4405i		−	1.19324i	−0.802522	−	0.596622i	$-0.796509\pi$
$491$		−	26.4405i		−	1.19324i	0.802522	−	0.596622i	$-0.203491\pi$
$492$	−10.3333			−0.465860
$493$	−7.73067			−0.348172
$494$		−	11.3987i		−	0.512852i
$495$	2.89477	−	6.82791i	0.130110	−	0.306892i
$496$		−	0.798333i		−	0.0358462i
$497$	−10.8324	−	26.6435i	−0.485901	−	1.19512i
$498$		−	12.4781i		−	0.559158i
$499$	2.98892			0.133803			0.0669013	−	0.997760i	$-0.478689\pi$
$499$	2.98892			0.133803			0.0669013	+	0.997760i	$0.478689\pi$
$500$	−10.1244	−	11.3230i	−0.452777	−	0.506379i
$501$			3.86148i			0.172518i
$502$			17.5874i			0.784966i
$503$			34.8409i			1.55348i	0.629823	+	0.776739i	$0.283127\pi$
$503$			34.8409i			1.55348i	−0.629823	+	0.776739i	$0.716873\pi$
$504$	−1.17137	−	2.88109i	−0.0521768	−	0.128334i
$505$	−8.85494	−	35.6908i	−0.394039	−	1.58822i
$506$	2.36757	−	3.15229i	0.105251	−	0.140137i
$507$	11.4292			0.507589
$508$	2.19797			0.0975190
$509$			20.3471i			0.901872i	0.892556	+	0.450936i	$0.148910\pi$
$509$			20.3471i			0.901872i	−0.892556	+	0.450936i	$0.851090\pi$
$510$	3.58199	−	0.888696i	0.158613	−	0.0393521i
$511$	−3.48287	+	1.41603i	−0.154073	+	0.0626416i
$512$	−20.5843			−0.909708
$513$	−4.96271			−0.219109
$514$	−8.02897			−0.354143
$515$	−5.13193	−	20.6848i	−0.226140	−	0.911482i
$516$	−14.3412			−0.631338
$517$	−5.28108	−	3.96642i	−0.232261	−	0.174443i
$518$	−26.0796	+	10.6032i	−1.14587	+	0.465877i
$519$			9.17271i			0.402637i
$520$	3.19743	−	0.793285i	0.140216	−	0.0347878i
$521$		−	14.1540i		−	0.620098i	−0.950721	−	0.310049i	$-0.899655\pi$
$521$		−	14.1540i		−	0.620098i	0.950721	−	0.310049i	$-0.100345\pi$
$522$		−	15.7311i		−	0.688533i
$523$			32.0815i			1.40283i	0.712754	+	0.701414i	$0.247447\pi$
$523$			32.0815i			1.40283i	−0.712754	+	0.701414i	$0.752553\pi$
$524$	10.7358			0.468994
$525$	10.1327	+	8.50456i	0.442229	+	0.371169i
$526$	−4.90446			−0.213845
$527$	−0.147591			−0.00642919
$528$	12.9188	+	9.70281i	0.562217	+	0.422261i
$529$	22.5793			0.981709
$530$	−48.2575	+	11.9727i	−2.09617	+	0.520062i
$531$			0.600825i			0.0260736i
$532$	6.71840	+	16.5246i	0.291280	+	0.716432i
$533$			9.53270i			0.412907i
$534$		−	25.5443i		−	1.10541i
$535$	0.475565	+	1.91682i	0.0205604	+	0.0828713i
$536$		−	7.72776i		−	0.333788i
$537$	−17.2783			−0.745612
$538$		−	29.4329i		−	1.26894i
$539$	23.0260	−	2.96667i	0.991802	−	0.127783i
$540$	0.731517	+	2.94846i	0.0314795	+	0.126882i
$541$		−	40.2041i		−	1.72851i	−0.503053	−	0.864255i	$-0.667790\pi$
$541$		−	40.2041i		−	1.72851i	0.503053	−	0.864255i	$-0.332210\pi$
$542$	−46.7507			−2.00811
$543$			14.8336i			0.636569i
$544$			5.92287i			0.253941i
$545$	26.1427	−	6.48603i	1.11983	−	0.277831i
$546$	5.62946	−	2.28877i	0.240919	−	0.0979504i
$547$	−7.50899			−0.321061			−0.160531	−	0.987031i	$-0.551321\pi$
$547$	−7.50899			−0.321061			−0.160531	+	0.987031i	$0.551321\pi$
$548$			5.34223i			0.228209i
$549$	−5.24147			−0.223701
$550$	−30.0133	−	4.77581i	−1.27977	−	0.203641i
$551$		−	42.5992i		−	1.81479i
$552$		−	0.762451i		−	0.0324521i
$553$	14.8060	−	6.01967i	0.629614	−	0.255982i
$554$	−43.4386			−1.84553
$555$	−12.6011	+	3.12633i	−0.534885	+	0.132706i
$556$	0.147006			0.00623443
$557$	−1.55694			−0.0659697			−0.0329848	−	0.999456i	$-0.510501\pi$
$557$	−1.55694			−0.0659697			−0.0329848	+	0.999456i	$0.510501\pi$
$558$		−	0.300334i		−	0.0127142i
$559$			13.2301i			0.559575i
$560$	−23.2982	+	16.9638i	−0.984530	+	0.716852i
$561$	1.79380	−	2.38835i	0.0757345	−	0.100836i
$562$		−	44.3090i		−	1.86906i
$563$			1.41618i			0.0596847i	0.999555	+	0.0298424i	$0.00950053\pi$
$563$			1.41618i			0.0596847i	−0.999555	+	0.0298424i	$0.990499\pi$
$564$	2.70545			0.113920
$565$	22.2322	−	5.51584i	0.935317	−	0.232053i
$566$			52.2607i			2.19668i
$567$	−0.996474	−	2.45093i	−0.0418480	−	0.102929i
$568$	12.7787			0.536184
$569$			43.4668i			1.82222i	0.412161	+	0.911111i	$0.364774\pi$
$569$			43.4668i			1.82222i	−0.412161	+	0.911111i	$0.635226\pi$
$570$	4.89709	+	19.7383i	0.205117	+	0.826746i
$571$		−	0.461909i		−	0.0193303i	−0.999953	−	0.00966514i	$-0.996923\pi$
$571$		−	0.461909i		−	0.0193303i	0.999953	−	0.00966514i	$-0.00307656\pi$
$572$	−3.39143	+	4.51550i	−0.141803	+	0.188803i
$573$	−12.9155			−0.539552
$574$	−13.8899	−	34.1636i	−0.579754	−	1.42596i
$575$	1.51590	+	2.86696i	0.0632175	+	0.119561i
$576$	−2.30959			−0.0962329
$577$	−9.50039			−0.395506			−0.197753	−	0.980252i	$-0.563364\pi$
$577$	−9.50039			−0.395506			−0.197753	+	0.980252i	$0.563364\pi$
$578$	−29.6684			−1.23404
$579$	−1.42077			−0.0590452
$580$	−25.3092	+	6.27924i	−1.05091	+	0.260731i
$581$	16.6879	−	6.78482i	0.692332	−	0.281482i
$582$	35.3228			1.46418
$583$	−24.1666	+	32.1765i	−1.00088	+	1.33261i
$584$		−	1.67045i		−	0.0691239i
$585$	2.72003	−	0.674842i	0.112459	−	0.0279013i
$586$			26.8478i			1.10907i
$587$	5.15760			0.212877			0.106439	−	0.994319i	$-0.466055\pi$
$587$	5.15760			0.212877			0.106439	+	0.994319i	$0.466055\pi$
$588$	−6.81197	+	6.63602i	−0.280921	+	0.273665i
$589$		−	0.813291i		−	0.0335111i
$590$	2.38968	−	0.592881i	0.0983814	−	0.0244085i
$591$	16.4316			0.675905
$592$		−	28.2845i		−	1.16249i
$593$			0.142190i			0.00583903i	0.999996	+	0.00291951i	$0.000929311\pi$
$593$			0.142190i			0.00583903i	−0.999996	+	0.00291951i	$0.999071\pi$
$594$	4.86006	+	3.65021i	0.199411	+	0.149770i
$595$	3.13618	+	4.30725i	0.128571	+	0.176580i
$596$		−	5.80118i		−	0.237626i
$597$		−	12.7554i		−	0.522044i
$598$	1.48978			0.0609216
$599$	47.1360			1.92592			0.962962	−	0.269639i	$-0.0869043\pi$
$599$	47.1360			1.92592			0.962962	+	0.269639i	$0.0869043\pi$
$600$	−5.19594	+	2.74735i	−0.212123	+	0.112160i
$601$	−33.9280			−1.38395			−0.691976	−	0.721920i	$-0.743260\pi$
$601$	−33.9280			−1.38395			−0.691976	+	0.721920i	$0.743260\pi$
$602$	−19.2774	−	47.4146i	−0.785687	−	1.93248i
$603$		−	6.57395i		−	0.267712i
$604$		−	21.9435i		−	0.892870i
$605$	−21.2765	+	12.3415i	−0.865011	+	0.501753i
$606$	30.1384			1.22429
$607$			34.6346i			1.40578i	0.711300	+	0.702888i	$0.248107\pi$
$607$			34.6346i			1.40578i	−0.711300	+	0.702888i	$0.751893\pi$
$608$	−32.6375			−1.32362
$609$	21.0384	−	8.55360i	0.852520	−	0.346609i
$610$	5.17217	+	20.8470i	0.209415	+	0.844072i
$611$		−	2.49584i		−	0.100971i
$612$			1.22353i			0.0494584i
$613$	−5.21722			−0.210721			−0.105361	−	0.994434i	$-0.533600\pi$
$613$	−5.21722			−0.210721			−0.105361	+	0.994434i	$0.533600\pi$
$614$			50.6670i			2.04475i
$615$	−4.09543	−	16.5071i	−0.165144	−	0.665630i
$616$	−2.63210	+	9.97361i	−0.106050	+	0.401848i
$617$			2.17670i			0.0876306i	0.999040	+	0.0438153i	$0.0139513\pi$
$617$			2.17670i			0.0876306i	−0.999040	+	0.0438153i	$0.986049\pi$
$618$	17.4669			0.702620
$619$		−	14.8762i		−	0.597926i	−0.954265	−	0.298963i	$-0.903359\pi$
$619$		−	14.8762i		−	0.597926i	0.954265	−	0.298963i	$-0.0966408\pi$
$620$	−0.483196	+	0.119881i	−0.0194056	+	0.00481455i
$621$		−	0.648612i		−	0.0260279i
$622$			25.9192i			1.03926i
$623$	34.1622	−	13.8894i	1.36868	−	0.556465i
$624$			6.10543i			0.244413i
$625$	14.0755	−	20.6611i	0.563019	−	0.826444i
$626$	−49.2019			−1.96651
$627$	13.1608	+	9.88462i	0.525593	+	0.394754i
$628$	−22.4995			−0.897829
$629$	−5.22910			−0.208498
$630$	−8.76483	+	6.38182i	−0.349199	+	0.254258i
$631$	−16.6415			−0.662487			−0.331243	−	0.943545i	$-0.607468\pi$
$631$	−16.6415			−0.662487			−0.331243	+	0.943545i	$0.607468\pi$
$632$			7.10123i			0.282472i
$633$			2.34216i			0.0930924i
$634$			29.3991i			1.16759i
$635$	0.871128	+	3.51118i	0.0345697	+	0.139337i
$636$		−	16.4837i		−	0.653622i
$637$	6.12189	+	6.28421i	0.242558	+	0.248990i
$638$	−31.3330	+	41.7181i	−1.24048	+	1.65164i
$639$	10.8708			0.430041
$640$	−4.80319	−	19.3598i	−0.189863	−	0.765263i
$641$	−39.2533			−1.55041			−0.775205	−	0.631709i	$-0.782354\pi$
$641$	−39.2533			−1.55041			−0.775205	+	0.631709i	$0.782354\pi$
$642$	−1.61862			−0.0638817
$643$	−1.64378			−0.0648245			−0.0324122	−	0.999475i	$-0.510319\pi$
$643$	−1.64378			−0.0648245			−0.0324122	+	0.999475i	$0.510319\pi$
$644$	−2.15972	+	0.878077i	−0.0851048	+	0.0346011i
$645$	−5.68391	−	22.9097i	−0.223804	−	0.902067i
$646$			8.19086i			0.322265i
$647$	−20.1321			−0.791476			−0.395738	−	0.918363i	$-0.629511\pi$
$647$	−20.1321			−0.791476			−0.395738	+	0.918363i	$0.629511\pi$
$648$	1.17551			0.0461785
$649$	1.19671	−	1.59335i	0.0469750	−	0.0625446i
$650$	−5.36813	−	10.1525i	−0.210555	−	0.398215i
$651$	0.401659	−	0.163303i	0.0157423	−	0.00640034i
$652$		−	24.4031i		−	0.955699i
$653$			28.2479i			1.10543i	0.833372	+	0.552713i	$0.186407\pi$
$653$			28.2479i			1.10543i	−0.833372	+	0.552713i	$0.813593\pi$
$654$			22.0757i			0.863227i
$655$	4.25494	+	17.1500i	0.166254	+	0.670107i
$656$	37.0521			1.44664
$657$		−	1.42104i		−	0.0554402i
$658$	3.63664	+	8.94469i	0.141771	+	0.348700i
$659$		−	5.74521i		−	0.223801i	−0.993719	−	0.111901i	$-0.964306\pi$
$659$		−	5.74521i		−	0.223801i	0.993719	−	0.111901i	$-0.0356939\pi$
$660$	3.93274	−	9.27618i	0.153082	−	0.361075i
$661$			26.7265i			1.03954i	0.854307	+	0.519769i	$0.173982\pi$
$661$			26.7265i			1.03954i	−0.854307	+	0.519769i	$0.826018\pi$
$662$	−50.0056			−1.94352
$663$	1.12874			0.0438366
$664$			8.00386i			0.310610i
$665$	−23.7348	+	17.2817i	−0.920395	+	0.670155i
$666$		−	10.6407i		−	0.412319i
$667$	5.56760			0.215578
$668$			5.24609i			0.202977i
$669$	−4.12809			−0.159601
$670$	−26.1468	+	6.48704i	−1.01014	+	0.250616i
$671$	13.9001	+	10.4399i	0.536607	+	0.403026i
$672$	−6.55336	−	16.1186i	−0.252801	−	0.621790i
$673$	23.9242			0.922210			0.461105	−	0.887346i	$-0.347453\pi$
$673$	23.9242			0.922210			0.461105	+	0.887346i	$0.347453\pi$
$674$	−12.9770			−0.499856
$675$	−4.42015	+	2.33715i	−0.170132	+	0.0899569i
$676$	15.5274			0.597206
$677$		−	42.9651i		−	1.65128i	−0.564195	−	0.825641i	$-0.690813\pi$
$677$		−	42.9651i		−	1.65128i	0.564195	−	0.825641i	$-0.309187\pi$
$678$			18.7735i			0.720993i
$679$	19.2063	+	47.2398i	0.737070	+	1.81290i
$680$	−2.29760	+	0.570037i	−0.0881090	+	0.0218599i
$681$			21.8296i			0.836513i
$682$	−0.598199	+	0.796470i	−0.0229062	+	0.0304984i
$683$			27.4806i			1.05151i	0.850635	+	0.525757i	$0.176218\pi$
$683$			27.4806i			1.05151i	−0.850635	+	0.525757i	$0.823782\pi$
$684$	−6.74218			−0.257794
$685$	−8.53405	+	2.11731i	−0.326069	+	0.0808981i
$686$	−31.0964	−	13.6015i	−1.18727	−	0.519307i
$687$		−	1.37953i		−	0.0526322i
$688$	51.4234			1.96050
$689$	−15.2066			−0.579327
$690$	−2.57974	+	0.640036i	−0.0982090	+	0.0243658i
$691$		−	40.6341i		−	1.54580i	−0.634531	−	0.772898i	$-0.718807\pi$
$691$		−	40.6341i		−	1.54580i	0.634531	−	0.772898i	$-0.281193\pi$
$692$			12.4618i			0.473725i
$693$	−2.23911	+	8.48448i	−0.0850568	+	0.322299i
$694$	−29.0339			−1.10211
$695$	0.0582633	+	0.234837i	0.00221005	+	0.00890787i
$696$			10.0904i			0.382477i
$697$		−	6.85000i		−	0.259462i
$698$	30.2247			1.14402
$699$	−2.59060			−0.0979854
$700$	13.7660	+	11.5540i	0.520307	+	0.436701i
$701$		−	41.0535i		−	1.55057i	−0.631611	−	0.775285i	$-0.717606\pi$
$701$		−	41.0535i		−	1.55057i	0.631611	−	0.775285i	$-0.282394\pi$
$702$			2.29687i			0.0866898i
$703$		−	28.8145i		−	1.08676i
$704$	6.12491	+	4.60019i	0.230841	+	0.173376i
$705$	1.07226	+	4.32187i	0.0403837	+	0.162771i
$706$	−41.2859			−1.55382
$707$	16.3873	+	40.3063i	0.616310	+	1.51588i
$708$			0.816262i			0.0306770i
$709$	−18.9113			−0.710230			−0.355115	−	0.934823i	$-0.615558\pi$
$709$	−18.9113			−0.710230			−0.355115	+	0.934823i	$0.615558\pi$
$710$	−10.7270	−	43.2366i	−0.402579	−	1.62264i
$711$			6.04097i			0.226554i
$712$			16.3849i			0.614049i
$713$	0.106295			0.00398078
$714$	−4.04521	+	1.64466i	−0.151388	+	0.0615499i
$715$	−8.55750	−	3.62805i	−0.320033	−	0.135681i
$716$	−23.4737			−0.877254
$717$			9.02101i			0.336896i
$718$		−	26.0914i		−	0.973723i
$719$		−	15.2306i		−	0.568005i	−0.958824	−	0.284002i	$-0.908338\pi$
$719$		−	15.2306i		−	0.568005i	0.958824	−	0.284002i	$-0.0916624\pi$
$720$	−2.62300	−	10.5723i	−0.0977536	−	0.394007i
$721$	9.49738	+	23.3597i	0.353701	+	0.869962i
$722$	−10.3149			−0.383882
$723$	0.695298			0.0258584
$724$			20.1524i			0.748959i
$725$	−20.0618	−	37.9420i	−0.745076	−	1.40913i
$726$	−5.61820	−	19.3603i	−0.208511	−	0.718530i
$727$	6.78304			0.251569			0.125785	−	0.992058i	$-0.459855\pi$
$727$	6.78304			0.251569			0.125785	+	0.992058i	$0.459855\pi$
$728$	−3.61091	+	1.46809i	−0.133829	+	0.0544110i
$729$	1.00000			0.0370370
$730$	−5.65195	+	1.40226i	−0.209188	+	0.0518998i
$731$		−	9.50689i		−	0.351625i
$732$	−7.12090			−0.263196
$733$			21.8456i			0.806886i	0.915005	+	0.403443i	$0.132187\pi$
$733$			21.8456i			0.806886i	−0.915005	+	0.403443i	$0.867813\pi$
$734$	36.0370			1.33015
$735$	−13.3006	−	8.25183i	−0.490602	−	0.304374i
$736$		−	4.26563i		−	0.157233i
$737$	−13.0939	+	17.4338i	−0.482319	+	0.642181i
$738$	13.9391			0.513104
$739$			29.0056i			1.06699i	0.845804	+	0.533493i	$0.179121\pi$
$739$			29.0056i			1.06699i	−0.845804	+	0.533493i	$0.820879\pi$
$740$	−17.1194	+	4.24734i	−0.629322	+	0.156135i
$741$			6.21982i			0.228491i
$742$	54.4980	−	22.1573i	2.00069	−	0.813419i
$743$	−12.8170			−0.470210			−0.235105	−	0.971970i	$-0.575543\pi$
$743$	−12.8170			−0.470210			−0.235105	+	0.971970i	$0.575543\pi$
$744$			0.192644i			0.00706266i
$745$	9.26721	−	2.29920i	0.339524	−	0.0842363i
$746$	13.5150			0.494820
$747$			6.80883i			0.249122i
$748$	2.43701	−	3.24474i	0.0891058	−	0.118639i
$749$	−0.880101	−	2.16470i	−0.0321582	−	0.0790963i
$750$	13.6573	+	15.2741i	0.498695	+	0.557732i
$751$	2.86925			0.104701			0.0523503	−	0.998629i	$-0.483329\pi$
$751$	2.86925			0.104701			0.0523503	+	0.998629i	$0.483329\pi$
$752$	−9.70095			−0.353757
$753$		−	9.59678i		−	0.349726i
$754$	−19.7160			−0.718016
$755$	35.0541	−	8.69696i	1.27575	−	0.316515i
$756$	−1.35378	−	3.32975i	−0.0492364	−	0.121102i
$757$			26.3576i			0.957982i	0.877820	+	0.478991i	$0.158997\pi$
$757$			26.3576i			0.957982i	−0.877820	+	0.478991i	$0.841003\pi$
$758$	9.47911			0.344297
$759$	−1.29189	+	1.72008i	−0.0468927	+	0.0624351i
$760$	−3.14115	−	12.6608i	−0.113941	−	0.459254i
$761$	22.7063			0.823102			0.411551	−	0.911387i	$-0.364987\pi$
$761$	22.7063			0.823102			0.411551	+	0.911387i	$0.364987\pi$
$762$	−2.96494			−0.107409
$763$	−29.5234	+	12.0033i	−1.06882	+	0.434550i
$764$	−17.5466			−0.634813
$765$	−1.95455	+	0.484927i	−0.0706671	+	0.0175326i
$766$	36.1185			1.30501
$767$	0.753022			0.0271900
$768$	20.9672			0.756587
$769$	−23.6591			−0.853169			−0.426585	−	0.904448i	$-0.640283\pi$
$769$	−23.6591			−0.853169			−0.426585	+	0.904448i	$0.640283\pi$
$770$	35.9550	+	0.533368i	1.29573	+	0.0192213i
$771$	4.38110			0.157781
$772$	−1.93021			−0.0694700
$773$	54.1026			1.94593			0.972967	−	0.230945i	$-0.0741816\pi$
$773$	54.1026			1.94593			0.972967	+	0.230945i	$0.0741816\pi$
$774$	19.3456			0.695363
$775$	−0.383013	−	0.724377i	−0.0137582	−	0.0260204i
$776$	−22.6571			−0.813343
$777$	14.2306	−	5.78574i	0.510520	−	0.207562i
$778$	67.1767			2.40840
$779$	37.7464			1.35240
$780$	3.69535	−	0.916819i	0.132315	−	0.0328274i
$781$	−28.8287	−	21.6522i	−1.03157	−	0.774776i
$782$	−1.07052			−0.0382818
$783$			8.58387i			0.306762i
$784$	24.4257	−	23.7948i	0.872348	−	0.849815i
$785$	−8.91731	−	35.9423i	−0.318273	−	1.28283i
$786$	−14.4820			−0.516556
$787$		−	8.62574i		−	0.307474i	−0.988112	−	0.153737i	$-0.950869\pi$
$787$		−	8.62574i		−	0.307474i	0.988112	−	0.153737i	$-0.0491309\pi$
$788$	22.3234			0.795239
$789$	2.67617			0.0952743
$790$	24.0269	−	5.96110i	0.854839	−	0.212086i
$791$	−25.1073	+	10.2079i	−0.892711	+	0.362950i
$792$	−3.11739	−	2.34136i	−0.110772	−	0.0831966i
$793$			6.56921i			0.233279i
$794$	−35.5849			−1.26286
$795$	26.3322	−	6.53305i	0.933908	−	0.231703i
$796$		−	17.3291i		−	0.614213i
$797$	−37.2277			−1.31867			−0.659336	−	0.751848i	$-0.729163\pi$
$797$	−37.2277			−1.31867			−0.659336	+	0.751848i	$0.729163\pi$
$798$	−9.06278	−	22.2908i	−0.320819	−	0.789086i
$799$			1.79346i			0.0634480i
$800$	−29.0693	+	15.3704i	−1.02776	+	0.543425i
$801$			13.9385i			0.492493i
$802$	−41.8981			−1.47947
$803$	−2.83041	+	3.76853i	−0.0998828	+	0.132989i
$804$		−	8.93117i		−	0.314978i
$805$	−2.25867	−	3.10207i	−0.0796076	−	0.109334i
$806$	−0.376413			−0.0132586
$807$			16.0604i			0.565352i
$808$	−19.3317			−0.680087
$809$			10.2662i			0.360940i	0.983581	+	0.180470i	$0.0577618\pi$
$809$			10.2662i			0.360940i	−0.983581	+	0.180470i	$0.942238\pi$
$810$	−0.986778	−	3.97732i	−0.0346719	−	0.139749i
$811$	5.33963			0.187500			0.0937499	−	0.995596i	$-0.470115\pi$
$811$	5.33963			0.187500			0.0937499	+	0.995596i	$0.470115\pi$
$812$	28.5822	−	11.6207i	1.00304	−	0.407805i
$813$	25.5100			0.894676
$814$	−21.1939	+	28.2185i	−0.742846	+	0.989060i
$815$	38.9832	−	9.67177i	1.36552	−	0.338787i
$816$		−	4.38723i		−	0.153584i
$817$	52.3870			1.83279
$818$	2.30807			0.0806999
$819$	−3.07178	+	1.24889i	−0.107337	+	0.0436399i
$820$	−5.56392	−	22.4260i	−0.194300	−	0.783151i
$821$		−	17.5107i		−	0.611128i	−0.952172	−	0.305564i	$-0.901155\pi$
$821$		−	17.5107i		−	0.611128i	0.952172	−	0.305564i	$-0.0988450\pi$
$822$		−	7.20640i		−	0.251352i
$823$		−	11.7968i		−	0.411211i	−0.978635	−	0.205606i	$-0.934084\pi$
$823$		−	11.7968i		−	0.411211i	0.978635	−	0.205606i	$-0.0659164\pi$
$824$	−11.2038			−0.390302
$825$	16.3771	+	2.60597i	0.570177	+	0.0907283i
$826$	−2.69870	+	1.09721i	−0.0938999	+	0.0381769i
$827$	29.9264			1.04064			0.520322	−	0.853970i	$-0.325812\pi$
$827$	29.9264			1.04064			0.520322	+	0.853970i	$0.325812\pi$
$828$		−	0.881184i		−	0.0306233i
$829$			37.7348i			1.31058i	0.755376	+	0.655292i	$0.227454\pi$
$829$			37.7348i			1.31058i	−0.755376	+	0.655292i	$0.772546\pi$
$830$	27.0809	−	6.71880i	0.939992	−	0.233213i
$831$	23.7027			0.822239
$832$			2.89464i			0.100354i
$833$	−4.39906	−	4.51570i	−0.152418	−	0.156460i
$834$	−0.198303			−0.00686667
$835$	−8.38046	+	2.07920i	−0.290018	+	0.0719537i
$836$	17.8799	+	13.4289i	0.618389	+	0.464449i
$837$			0.163881i			0.00566454i
$838$		−	72.2081i		−	2.49439i
$839$			13.9080i			0.480156i	0.970754	+	0.240078i	$0.0771731\pi$
$839$			13.9080i			0.480156i	−0.970754	+	0.240078i	$0.922827\pi$
$840$	5.62204	−	4.09350i	0.193979	−	0.141239i
$841$	−44.6828			−1.54079
$842$	−11.3983			−0.392813
$843$			24.1777i			0.832724i
$844$			3.18198i			0.109528i
$845$	6.15402	+	24.8045i	0.211705	+	0.853300i
$846$	−3.64951			−0.125473
$847$	22.8372	−	18.0406i	0.784696	−	0.619881i
$848$			59.1058i			2.02970i
$849$		−	28.5166i		−	0.978687i
$850$	3.85742	+	7.29538i	0.132309	+	0.250230i
$851$	3.76598			0.129096
$852$	14.7687			0.505967
$853$		−	30.0061i		−	1.02739i	−0.857973	−	0.513695i	$-0.828276\pi$
$853$		−	30.0061i		−	1.02739i	0.857973	−	0.513695i	$-0.171724\pi$
$854$	−9.57186	−	23.5429i	−0.327542	−	0.805623i
$855$	−2.67215	−	10.7704i	−0.0913857	−	0.368340i
$856$	1.03823			0.0354860
$857$		−	3.51078i		−	0.119926i	−0.998201	−	0.0599630i	$-0.980902\pi$
$857$		−	3.51078i		−	0.119926i	0.998201	−	0.0599630i	$-0.0190983\pi$
$858$	4.57486	−	6.09118i	0.156183	−	0.207949i
$859$		−	8.47192i		−	0.289058i	−0.989501	−	0.144529i	$-0.953833\pi$
$859$		−	8.47192i		−	0.289058i	0.989501	−	0.144529i	$-0.0461667\pi$
$860$	−7.72199	−	31.1244i	−0.263318	−	1.06133i
$861$	7.57918	+	18.6418i	0.258298	+	0.635309i
$862$		−	13.5556i		−	0.461707i
$863$			8.18498i			0.278620i	0.990249	+	0.139310i	$0.0444885\pi$
$863$			8.18498i			0.278620i	−0.990249	+	0.139310i	$0.955512\pi$
$864$	6.57655			0.223739
$865$	−19.9073	+	4.93901i	−0.676867	+	0.167931i
$866$	47.0673			1.59941
$867$	16.1889			0.549804
$868$	0.545682	−	0.221858i	0.0185216	−	0.00753035i
$869$	12.0323	−	16.0203i	0.408167	−	0.543452i
$870$	34.1408	−	8.47038i	1.15748	−	0.287173i
$871$	−8.23922			−0.279175
$872$		−	14.1600i		−	0.479519i
$873$	−19.2743			−0.652335
$874$		−	5.89903i		−	0.199538i
$875$	−13.0013	+	26.5700i	−0.439522	+	0.898232i
$876$		−	1.93059i		−	0.0652285i
$877$	46.2648			1.56225			0.781126	−	0.624373i	$-0.214646\pi$
$877$	46.2648			1.56225			0.781126	+	0.624373i	$0.214646\pi$
$878$	59.0543			1.99299
$879$		−	14.6498i		−	0.494126i
$880$	−14.1017	+	33.2617i	−0.475367	+	1.12125i
$881$			38.7271i			1.30475i	0.757897	+	0.652374i	$0.226227\pi$
$881$			38.7271i			1.30475i	−0.757897	+	0.652374i	$0.773773\pi$
$882$	9.18900	−	8.95165i	0.309410	−	0.301418i
$883$		−	48.1751i		−	1.62122i	−0.585585	−	0.810611i	$-0.699135\pi$
$883$		−	48.1751i		−	1.62122i	0.585585	−	0.810611i	$-0.300865\pi$
$884$	1.53347			0.0515762
$885$	−1.30395	+	0.323512i	−0.0438319	+	0.0108747i
$886$			54.2778i			1.82350i
$887$			6.20413i			0.208314i	0.994561	+	0.104157i	$0.0332145\pi$
$887$			6.20413i			0.208314i	−0.994561	+	0.104157i	$0.966785\pi$
$888$			6.82527i			0.229041i
$889$	−1.61215	−	3.96524i	−0.0540698	−	0.132990i
$890$	55.4380	−	13.7542i	1.85828	−	0.461042i
$891$	−2.65195	−	1.99178i	−0.0888435	−	0.0667271i
$892$	−5.60829			−0.187779
$893$	−9.88272			−0.330713
$894$			7.82550i			0.261724i
$895$	−9.30342	−	37.4985i	−0.310979	−	1.25344i
$896$	8.88899	+	21.8634i	0.296960	+	0.730404i
$897$	−0.812914			−0.0271424
$898$	7.08949			0.236579
$899$	−1.40673			−0.0469171
$900$	−6.00508	+	3.17518i	−0.200169	+	0.105839i
$901$	10.9272			0.364036
$902$	−36.9656	−	27.7635i	−1.23082	−	0.924425i
$903$	10.5189	+	25.8723i	0.350047	+	0.860976i
$904$		−	12.0419i		−	0.400509i
$905$	−32.1929	+	7.98708i	−1.07013	+	0.265500i
$906$			29.6007i			0.983418i
$907$		−	25.8651i		−	0.858835i	−0.903106	−	0.429418i	$-0.858719\pi$
$907$		−	25.8651i		−	0.858835i	0.903106	−	0.429418i	$-0.141281\pi$
$908$			29.6571i			0.984204i
$909$	−16.4453			−0.545457
$910$	7.99842	+	10.9851i	0.265145	+	0.364152i
$911$	−31.9293			−1.05787			−0.528933	−	0.848664i	$-0.677408\pi$
$911$	−31.9293			−1.05787			−0.528933	+	0.848664i	$0.677408\pi$
$912$	24.1755			0.800530
$913$	13.5617	−	18.0566i	0.448826	−	0.597588i
$914$	22.3427			0.739030
$915$	−2.82225	−	11.3754i	−0.0933008	−	0.376060i
$916$		−	1.87418i		−	0.0619247i
$917$	−7.87439	−	19.3679i	−0.260035	−	0.639583i
$918$		−	1.65048i		−	0.0544740i
$919$			15.4795i			0.510621i	0.966859	+	0.255311i	$0.0821777\pi$
$919$			15.4795i			0.510621i	−0.966859	+	0.255311i	$0.917822\pi$
$920$	1.65473	−	0.410539i	0.0545547	−	0.0135351i
$921$		−	27.6470i		−	0.911000i
$922$	50.3294			1.65751
$923$		−	13.6245i		−	0.448455i
$924$	−3.04199	+	11.5267i	−0.100074	+	0.379202i
$925$	−13.5700	−	25.6643i	−0.446178	−	0.843838i
$926$		−	31.4112i		−	1.03224i
$927$	−9.53098			−0.313039
$928$			56.4522i			1.85314i
$929$		−	12.0282i		−	0.394632i	−0.980340	−	0.197316i	$-0.936778\pi$
$929$		−	12.0282i		−	0.394632i	0.980340	−	0.197316i	$-0.0632225\pi$
$930$	0.651806	−	0.161714i	0.0213736	−	0.00530281i
$931$	24.8834	−	24.2407i	0.815521	−	0.794456i
$932$	−3.51950			−0.115285
$933$		−	14.1431i		−	0.463024i
$934$	−4.47520			−0.146433
$935$	6.14924	+	2.60704i	0.201102	+	0.0852593i
$936$		−	1.47328i		−	0.0481558i
$937$			26.8317i			0.876554i	0.898840	+	0.438277i	$0.144411\pi$
$937$			26.8317i			0.876554i	−0.898840	+	0.438277i	$0.855589\pi$
$938$	29.5280	−	12.0052i	0.964123	−	0.391984i
$939$	26.8476			0.876138
$940$	1.45674	+	5.87156i	0.0475136	+	0.191509i
$941$	21.7437			0.708824			0.354412	−	0.935089i	$-0.384681\pi$
$941$	21.7437			0.708824			0.354412	+	0.935089i	$0.384681\pi$
$942$	30.3507			0.988879
$943$			4.93335i			0.160652i
$944$		−	2.92687i		−	0.0952617i
$945$	4.78263	−	3.48231i	0.155579	−	0.113280i
$946$	−51.3035	−	38.5321i	−1.66802	−	1.25279i
$947$		−	23.4252i		−	0.761216i	−0.924736	−	0.380608i	$-0.875715\pi$
$947$		−	23.4252i		−	0.761216i	0.924736	−	0.380608i	$-0.124285\pi$
$948$			8.20708i			0.266553i
$949$	−1.78101			−0.0578141
$950$	−40.2006	+	21.2560i	−1.30428	+	0.689637i
$951$		−	16.0419i		−	0.520196i
$952$	2.59472	−	1.05494i	0.0840955	−	0.0341907i
$953$	−27.7086			−0.897568			−0.448784	−	0.893640i	$-0.648143\pi$
$953$	−27.7086			−0.897568			−0.448784	+	0.893640i	$0.648143\pi$
$954$			22.2357i			0.719907i
$955$	−6.95430	−	28.0301i	−0.225036	−	0.907033i
$956$			12.2557i			0.396376i
$957$	17.0972	−	22.7640i	0.552673	−	0.735854i
$958$	−50.0846			−1.61816
$959$	9.63765	−	3.91838i	0.311216	−	0.126531i
$960$	−1.24359	−	5.01244i	−0.0401367	−	0.161776i
$961$	30.9731			0.999134
$962$	−13.3361			−0.429974
$963$	0.883216			0.0284612
$964$	0.944610			0.0304238
$965$	−0.765009	−	3.08346i	−0.0246265	−	0.0992600i
$966$	2.91335	−	1.18448i	0.0937354	−	0.0381100i
$967$	−42.1076			−1.35409			−0.677044	−	0.735942i	$-0.736739\pi$
$967$	−42.1076			−1.35409			−0.677044	+	0.735942i	$0.736739\pi$
$968$	3.60369	+	12.4183i	0.115827	+	0.399140i
$969$		−	4.46943i		−	0.143579i
$970$	19.0194	+	76.6600i	0.610677	+	2.46140i
$971$		−	50.6587i		−	1.62572i	−0.582462	−	0.812858i	$-0.697910\pi$
$971$		−	50.6587i		−	1.62572i	0.582462	−	0.812858i	$-0.302090\pi$
$972$	1.35857			0.0435761
$973$	−0.107825	−	0.265205i	−0.00345670	−	0.00850210i
$974$		−	63.5083i		−	2.03494i
$975$	2.92918	+	5.53983i	0.0938088	+	0.177417i
$976$	25.5335			0.817306
$977$			42.2098i			1.35041i	0.737629	+	0.675206i	$0.235945\pi$
$977$			42.2098i			1.35041i	−0.737629	+	0.675206i	$0.764055\pi$
$978$			32.9185i			1.05262i
$979$	27.7624	−	36.9642i	0.887291	−	1.18138i
$980$	−18.0698	−	11.2107i	−0.577220	−	0.358112i
$981$		−	12.0458i		−	0.384594i
$982$			48.4559i			1.54629i
$983$	−6.75765			−0.215536			−0.107768	−	0.994176i	$-0.534370\pi$
$983$	−6.75765			−0.215536			−0.107768	+	0.994176i	$0.534370\pi$
$984$	−8.94095			−0.285027
$985$	8.84752	+	35.6610i	0.281906	+	1.13625i
$986$	14.1675			0.451186
$987$	−1.98437	−	4.88077i	−0.0631633	−	0.155357i
$988$			8.45006i			0.268832i
$989$			6.84683i			0.217717i
$990$	−5.30507	+	12.5131i	−0.168606	+	0.397692i
$991$	−49.0326			−1.55757			−0.778787	−	0.627289i	$-0.784165\pi$
$991$	−49.0326			−1.55757			−0.778787	+	0.627289i	$0.784165\pi$
$992$			1.07777i			0.0342192i
$993$	27.2861			0.865899
$994$	19.8520	+	48.8279i	0.629666	+	1.54873i
$995$	27.6827	−	6.86810i	0.877599	−	0.217733i
$996$			9.25026i			0.293106i
$997$		−	4.20775i		−	0.133261i	−0.997778	−	0.0666304i	$-0.978775\pi$
$997$		−	4.20775i		−	0.133261i	0.997778	−	0.0666304i	$-0.0212248\pi$
$998$	−5.47762			−0.173391
$999$			5.80621i			0.183700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.10	yes	48
5.4	even	2		1155.2.k.a.769.39	yes	48
7.6	odd	2		1155.2.k.a.769.9	✓	48
11.10	odd	2	inner	1155.2.k.b.769.39	yes	48
35.34	odd	2	inner	1155.2.k.b.769.40	yes	48
55.54	odd	2		1155.2.k.a.769.10	yes	48
77.76	even	2		1155.2.k.a.769.40	yes	48
385.384	even	2	inner	1155.2.k.b.769.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.9	✓	48	7.6	odd	2
1155.2.k.a.769.10	yes	48	55.54	odd	2
1155.2.k.a.769.39	yes	48	5.4	even	2
1155.2.k.a.769.40	yes	48	77.76	even	2
1155.2.k.b.769.9	yes	48	385.384	even	2	inner
1155.2.k.b.769.10	yes	48	1.1	even	1	trivial
1155.2.k.b.769.39	yes	48	11.10	odd	2	inner
1155.2.k.b.769.40	yes	48	35.34	odd	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35857 q^{4} +(0.538446 + 2.17027i) q^{5} -1.83264 q^{6} +(-0.996474 - 2.45093i) q^{7} +1.17551 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35857 q^{4} +(0.538446 + 2.17027i) q^{5} -1.83264 q^{6} +(-0.996474 - 2.45093i) q^{7} +1.17551 q^{8} +1.00000 q^{9} +(-0.986778 - 3.97732i) q^{10} +(-2.65195 - 1.99178i) q^{11} +1.35857 q^{12} -1.25331i q^{13} +(1.82618 + 4.49167i) q^{14} +(0.538446 + 2.17027i) q^{15} -4.87143 q^{16} +0.900604i q^{17} -1.83264 q^{18} -4.96271 q^{19} +(0.731517 + 2.94846i) q^{20} +(-0.996474 - 2.45093i) q^{21} +(4.86006 + 3.65021i) q^{22} -0.648612i q^{23} +1.17551 q^{24} +(-4.42015 + 2.33715i) q^{25} +2.29687i q^{26} +1.00000 q^{27} +(-1.35378 - 3.32975i) q^{28} +8.58387i q^{29} +(-0.986778 - 3.97732i) q^{30} +0.163881i q^{31} +6.57655 q^{32} +(-2.65195 - 1.99178i) q^{33} -1.65048i q^{34} +(4.78263 - 3.48231i) q^{35} +1.35857 q^{36} +5.80621i q^{37} +9.09485 q^{38} -1.25331i q^{39} +(0.632950 + 2.55118i) q^{40} -7.60600 q^{41} +(1.82618 + 4.49167i) q^{42} -10.5561 q^{43} +(-3.60285 - 2.70597i) q^{44} +(0.538446 + 2.17027i) q^{45} +1.18867i q^{46} +1.99140 q^{47} -4.87143 q^{48} +(-5.01408 + 4.88457i) q^{49} +(8.10054 - 4.28315i) q^{50} +0.900604i q^{51} -1.70271i q^{52} -12.1331i q^{53} -1.83264 q^{54} +(2.89477 - 6.82791i) q^{55} +(-1.17137 - 2.88109i) q^{56} -4.96271 q^{57} -15.7311i q^{58} +0.600825i q^{59} +(0.731517 + 2.94846i) q^{60} -5.24147 q^{61} -0.300334i q^{62} +(-0.996474 - 2.45093i) q^{63} -2.30959 q^{64} +(2.72003 - 0.674842i) q^{65} +(4.86006 + 3.65021i) q^{66} -6.57395i q^{67} +1.22353i q^{68} -0.648612i q^{69} +(-8.76483 + 6.38182i) q^{70} +10.8708 q^{71} +1.17551 q^{72} -1.42104i q^{73} -10.6407i q^{74} +(-4.42015 + 2.33715i) q^{75} -6.74218 q^{76} +(-2.23911 + 8.48448i) q^{77} +2.29687i q^{78} +6.04097i q^{79} +(-2.62300 - 10.5723i) q^{80} +1.00000 q^{81} +13.9391 q^{82} +6.80883i q^{83} +(-1.35378 - 3.32975i) q^{84} +(-1.95455 + 0.484927i) q^{85} +19.3456 q^{86} +8.58387i q^{87} +(-3.11739 - 2.34136i) q^{88} +13.9385i q^{89} +(-0.986778 - 3.97732i) q^{90} +(-3.07178 + 1.24889i) q^{91} -0.881184i q^{92} +0.163881i q^{93} -3.64951 q^{94} +(-2.67215 - 10.7704i) q^{95} +6.57655 q^{96} -19.2743 q^{97} +(9.18900 - 8.95165i) q^{98} +(-2.65195 - 1.99178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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