LMFDB - Embedded newform 91.2.c.a.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(64,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("91.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.c (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.4
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	91.64
Dual form			91.2.c.a.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} +O(q^{10})$	\(q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} -2.21432 q^{10} -2.68889i q^{11} -3.37778 q^{12} +(3.59210 + 0.311108i) q^{13} -0.688892 q^{14} -7.11753i q^{15} +1.37778 q^{16} -3.59210 q^{17} +1.31111i q^{18} -8.54617i q^{19} +4.90321i q^{20} -2.21432i q^{21} +1.85236 q^{22} +3.28100 q^{23} -5.37778i q^{24} -5.33185 q^{25} +(-0.214320 + 2.47457i) q^{26} +2.42864 q^{27} +1.52543i q^{28} +2.05086 q^{29} +4.90321 q^{30} +5.83654i q^{31} +5.80642i q^{32} +5.95407i q^{33} -2.47457i q^{34} -3.21432 q^{35} +2.90321 q^{36} -3.93332i q^{37} +5.88739 q^{38} +(-7.95407 - 0.688892i) q^{39} -7.80642 q^{40} +0.755569i q^{41} +1.52543 q^{42} -8.80642 q^{43} -4.10171i q^{44} +6.11753i q^{45} +2.26025i q^{46} -1.88247i q^{47} -3.05086 q^{48} -1.00000 q^{49} -3.67307i q^{50} +7.95407 q^{51} +(5.47949 + 0.474572i) q^{52} +2.52543 q^{53} +1.67307i q^{54} +8.64296 q^{55} -2.42864 q^{56} +18.9240i q^{57} +1.41282i q^{58} -7.33185i q^{59} -10.8573i q^{60} +9.05086 q^{61} -4.02074 q^{62} +1.90321i q^{63} -1.24443 q^{64} +(-1.00000 + 11.5462i) q^{65} -4.10171 q^{66} +0.428639i q^{67} -5.47949 q^{68} -7.26517 q^{69} -2.21432i q^{70} +8.98418i q^{71} +4.62222i q^{72} -5.79060i q^{73} +2.70964 q^{74} +11.8064 q^{75} -13.0366i q^{76} +2.68889 q^{77} +(0.474572 - 5.47949i) q^{78} -4.47949 q^{79} +4.42864i q^{80} -11.0874 q^{81} -0.520505 q^{82} -10.8272i q^{83} -3.37778i q^{84} -11.5462i q^{85} -6.06668i q^{86} -4.54125 q^{87} +6.53035 q^{88} -5.36196i q^{89} -4.21432 q^{90} +(-0.311108 + 3.59210i) q^{91} +5.00492 q^{92} -12.9240i q^{93} +1.29682 q^{94} +27.4701 q^{95} -12.8573i q^{96} +9.62867i q^{97} -0.688892i q^{98} -5.11753i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} - 2 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 - 2 * q^9	$ 6 q - 4 q^{4} - 2 q^{9} - 20 q^{12} + 8 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} + 24 q^{22} + 6 q^{23} + 8 q^{25} + 12 q^{26} - 12 q^{27} - 14 q^{29} + 16 q^{30} - 6 q^{35} + 4 q^{36} - 4 q^{38} - 8 q^{39} - 20 q^{40} - 4 q^{42} - 26 q^{43} + 8 q^{48} - 6 q^{49} + 8 q^{51} - 20 q^{52} + 2 q^{53} + 12 q^{55} + 12 q^{56} + 28 q^{61} + 16 q^{62} - 8 q^{64} - 6 q^{65} + 28 q^{66} + 20 q^{68} - 4 q^{69} - 24 q^{74} + 44 q^{75} + 16 q^{77} + 16 q^{78} + 26 q^{79} - 26 q^{81} - 56 q^{82} - 40 q^{87} - 40 q^{88} - 12 q^{90} - 2 q^{91} - 36 q^{92} + 20 q^{94} + 58 q^{95}+O(q^{100}) $ 6 * q - 4 * q^4 - 2 * q^9 - 20 * q^12 + 8 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 + 24 * q^22 + 6 * q^23 + 8 * q^25 + 12 * q^26 - 12 * q^27 - 14 * q^29 + 16 * q^30 - 6 * q^35 + 4 * q^36 - 4 * q^38 - 8 * q^39 - 20 * q^40 - 4 * q^42 - 26 * q^43 + 8 * q^48 - 6 * q^49 + 8 * q^51 - 20 * q^52 + 2 * q^53 + 12 * q^55 + 12 * q^56 + 28 * q^61 + 16 * q^62 - 8 * q^64 - 6 * q^65 + 28 * q^66 + 20 * q^68 - 4 * q^69 - 24 * q^74 + 44 * q^75 + 16 * q^77 + 16 * q^78 + 26 * q^79 - 26 * q^81 - 56 * q^82 - 40 * q^87 - 40 * q^88 - 12 * q^90 - 2 * q^91 - 36 * q^92 + 20 * q^94 + 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.688892i			0.487120i	0.969886	+	0.243560i	$0.0783153\pi$
$2$			0.688892i			0.487120i	−0.969886	+	0.243560i	$0.921685\pi$
$3$	−2.21432			−1.27844			−0.639219	−	0.769025i	$-0.720742\pi$
$3$	−2.21432			−1.27844			−0.639219	+	0.769025i	$0.720742\pi$
$4$	1.52543			0.762714
$5$			3.21432i			1.43749i	0.695275	+	0.718744i	$0.255283\pi$
$5$			3.21432i			1.43749i	−0.695275	+	0.718744i	$0.744717\pi$
$6$		−	1.52543i		−	0.622753i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			2.42864i			0.858654i
$9$	1.90321			0.634404
$10$	−2.21432			−0.700229
$11$		−	2.68889i		−	0.810731i	−0.914155	−	0.405366i	$-0.867144\pi$
$11$		−	2.68889i		−	0.810731i	0.914155	−	0.405366i	$-0.132856\pi$
$12$	−3.37778			−0.975082
$13$	3.59210	+	0.311108i	0.996270	+	0.0862858i
$13$	3.59210	+	0.311108i	0.996270	+	0.0862858i
$14$	−0.688892			−0.184114
$15$		−	7.11753i		−	1.83774i
$16$	1.37778			0.344446
$17$	−3.59210			−0.871213			−0.435607	−	0.900137i	$-0.643466\pi$
$17$	−3.59210			−0.871213			−0.435607	+	0.900137i	$0.643466\pi$
$18$			1.31111i			0.309031i
$19$		−	8.54617i		−	1.96063i	−0.197449	−	0.980313i	$-0.563266\pi$
$19$		−	8.54617i		−	1.96063i	0.197449	−	0.980313i	$-0.436734\pi$
$20$			4.90321i			1.09639i
$21$		−	2.21432i		−	0.483204i
$22$	1.85236			0.394924
$23$	3.28100			0.684135			0.342068	−	0.939675i	$-0.388873\pi$
$23$	3.28100			0.684135			0.342068	+	0.939675i	$0.388873\pi$
$24$		−	5.37778i		−	1.09774i
$25$	−5.33185			−1.06637
$26$	−0.214320	+	2.47457i	−0.0420316	+	0.485304i
$27$	2.42864			0.467392
$28$			1.52543i			0.288279i
$29$	2.05086			0.380834			0.190417	−	0.981703i	$-0.439016\pi$
$29$	2.05086			0.380834			0.190417	+	0.981703i	$0.439016\pi$
$30$	4.90321			0.895200
$31$			5.83654i			1.04827i	0.851634	+	0.524136i	$0.175612\pi$
$31$			5.83654i			1.04827i	−0.851634	+	0.524136i	$0.824388\pi$
$32$			5.80642i			1.02644i
$33$			5.95407i			1.03647i
$34$		−	2.47457i		−	0.424386i
$35$	−3.21432			−0.543319
$36$	2.90321			0.483869
$37$		−	3.93332i		−	0.646634i	−0.946291	−	0.323317i	$-0.895202\pi$
$37$		−	3.93332i		−	0.646634i	0.946291	−	0.323317i	$-0.104798\pi$
$38$	5.88739			0.955061
$39$	−7.95407	−	0.688892i	−1.27367	−	0.110311i
$40$	−7.80642			−1.23430
$41$			0.755569i			0.118000i	0.998258	+	0.0590000i	$0.0187912\pi$
$41$			0.755569i			0.118000i	−0.998258	+	0.0590000i	$0.981209\pi$
$42$	1.52543			0.235379
$43$	−8.80642			−1.34297			−0.671484	−	0.741019i	$-0.734343\pi$
$43$	−8.80642			−1.34297			−0.671484	+	0.741019i	$0.734343\pi$
$44$		−	4.10171i		−	0.618356i
$45$			6.11753i			0.911948i
$46$			2.26025i			0.333256i
$47$		−	1.88247i		−	0.274586i	−0.990530	−	0.137293i	$-0.956160\pi$
$47$		−	1.88247i		−	0.274586i	0.990530	−	0.137293i	$-0.0438402\pi$
$48$	−3.05086			−0.440353
$49$	−1.00000			−0.142857
$50$		−	3.67307i		−	0.519451i
$51$	7.95407			1.11379
$52$	5.47949	+	0.474572i	0.759869	+	0.0658114i
$53$	2.52543			0.346894			0.173447	−	0.984843i	$-0.444509\pi$
$53$	2.52543			0.346894			0.173447	+	0.984843i	$0.444509\pi$
$54$			1.67307i			0.227676i
$55$	8.64296			1.16542
$56$	−2.42864			−0.324541
$57$			18.9240i			2.50654i
$58$			1.41282i			0.185512i
$59$		−	7.33185i		−	0.954526i	−0.878761	−	0.477263i	$-0.841629\pi$
$59$		−	7.33185i		−	0.954526i	0.878761	−	0.477263i	$-0.158371\pi$
$60$		−	10.8573i		−	1.40167i
$61$	9.05086			1.15884			0.579422	−	0.815028i	$-0.303278\pi$
$61$	9.05086			1.15884			0.579422	+	0.815028i	$0.303278\pi$
$62$	−4.02074			−0.510635
$63$			1.90321i			0.239782i
$64$	−1.24443			−0.155554
$65$	−1.00000	+	11.5462i	−0.124035	+	1.43213i
$66$	−4.10171			−0.504886
$67$			0.428639i			0.0523666i	0.999657	+	0.0261833i	$0.00833536\pi$
$67$			0.428639i			0.0523666i	−0.999657	+	0.0261833i	$0.991665\pi$
$68$	−5.47949			−0.664486
$69$	−7.26517			−0.874624
$70$		−	2.21432i		−	0.264662i
$71$			8.98418i			1.06623i	0.846044	+	0.533113i	$0.178978\pi$
$71$			8.98418i			1.06623i	−0.846044	+	0.533113i	$0.821022\pi$
$72$			4.62222i			0.544733i
$73$		−	5.79060i		−	0.677739i	−0.940833	−	0.338869i	$-0.889956\pi$
$73$		−	5.79060i		−	0.677739i	0.940833	−	0.338869i	$-0.110044\pi$
$74$	2.70964			0.314989
$75$	11.8064			1.36329
$76$		−	13.0366i		−	1.49540i
$77$	2.68889			0.306428
$78$	0.474572	−	5.47949i	0.0537347	−	0.620431i
$79$	−4.47949			−0.503983			−0.251991	−	0.967730i	$-0.581085\pi$
$79$	−4.47949			−0.503983			−0.251991	+	0.967730i	$0.581085\pi$
$80$			4.42864i			0.495137i
$81$	−11.0874			−1.23194
$82$	−0.520505			−0.0574802
$83$		−	10.8272i		−	1.18844i	−0.804304	−	0.594218i	$-0.797462\pi$
$83$		−	10.8272i		−	1.18844i	0.804304	−	0.594218i	$-0.202538\pi$
$84$		−	3.37778i		−	0.368546i
$85$		−	11.5462i		−	1.25236i
$86$		−	6.06668i		−	0.654187i
$87$	−4.54125			−0.486873
$88$	6.53035			0.696138
$89$		−	5.36196i		−	0.568367i	−0.958770	−	0.284183i	$-0.908278\pi$
$89$		−	5.36196i		−	0.568367i	0.958770	−	0.284183i	$-0.0917225\pi$
$90$	−4.21432			−0.444228
$91$	−0.311108	+	3.59210i	−0.0326130	+	0.376555i
$92$	5.00492			0.521799
$93$		−	12.9240i		−	1.34015i
$94$	1.29682			0.133757
$95$	27.4701			2.81838
$96$		−	12.8573i		−	1.31224i
$97$			9.62867i			0.977643i	0.872384	+	0.488822i	$0.162573\pi$
$97$			9.62867i			0.977643i	−0.872384	+	0.488822i	$0.837427\pi$
$98$		−	0.688892i		−	0.0695886i
$99$		−	5.11753i		−	0.514331i
$100$	−8.13335			−0.813335
$101$	−13.6938			−1.36259			−0.681293	−	0.732011i	$-0.738582\pi$
$101$	−13.6938			−1.36259			−0.681293	+	0.732011i	$0.738582\pi$
$102$			5.47949i			0.542551i
$103$	−12.2953			−1.21149			−0.605745	−	0.795659i	$-0.707125\pi$
$103$	−12.2953			−1.21149			−0.605745	+	0.795659i	$0.707125\pi$
$104$	−0.755569	+	8.72393i	−0.0740896	+	0.855451i
$105$	7.11753			0.694600
$106$			1.73975i			0.168979i
$107$	−18.1891			−1.75841			−0.879205	−	0.476444i	$-0.841925\pi$
$107$	−18.1891			−1.75841			−0.879205	+	0.476444i	$0.841925\pi$
$108$	3.70471			0.356486
$109$			8.36196i			0.800931i	0.916312	+	0.400465i	$0.131152\pi$
$109$			8.36196i			0.800931i	−0.916312	+	0.400465i	$0.868848\pi$
$110$			5.95407i			0.567698i
$111$			8.70964i			0.826682i
$112$			1.37778i			0.130188i
$113$	−8.46520			−0.796339			−0.398170	−	0.917312i	$-0.630354\pi$
$113$	−8.46520			−0.796339			−0.398170	+	0.917312i	$0.630354\pi$
$114$	−13.0366			−1.22099
$115$			10.5462i			0.983436i
$116$	3.12843			0.290468
$117$	6.83654	+	0.592104i	0.632038	+	0.0547400i
$118$	5.05086			0.464969
$119$		−	3.59210i		−	0.329288i
$120$	17.2859			1.57798
$121$	3.76986			0.342714
$122$			6.23506i			0.564496i
$123$		−	1.67307i		−	0.150856i
$124$			8.90321i			0.799532i
$125$		−	1.06668i		−	0.0954065i
$126$	−1.31111			−0.116803
$127$	−4.08742			−0.362700			−0.181350	−	0.983419i	$-0.558047\pi$
$127$	−4.08742			−0.362700			−0.181350	+	0.983419i	$0.558047\pi$
$128$			10.7556i			0.950667i
$129$	19.5002			1.71690
$130$	−7.95407	−	0.688892i	−0.697618	−	0.0604198i
$131$	5.93978			0.518961			0.259480	−	0.965748i	$-0.416449\pi$
$131$	5.93978			0.518961			0.259480	+	0.965748i	$0.416449\pi$
$132$			9.08250i			0.790530i
$133$	8.54617			0.741047
$134$	−0.295286			−0.0255089
$135$			7.80642i			0.671870i
$136$		−	8.72393i		−	0.748070i
$137$		−	16.3620i		−	1.39790i	−0.715172	−	0.698948i	$-0.753652\pi$
$137$		−	16.3620i		−	1.39790i	0.715172	−	0.698948i	$-0.246348\pi$
$138$		−	5.00492i		−	0.426047i
$139$	3.03011			0.257011			0.128505	−	0.991709i	$-0.458982\pi$
$139$	3.03011			0.257011			0.128505	+	0.991709i	$0.458982\pi$
$140$	−4.90321			−0.414397
$141$			4.16839i			0.351041i
$142$	−6.18913			−0.519380
$143$	0.836535	−	9.65878i	0.0699546	−	0.807708i
$144$	2.62222			0.218518
$145$			6.59210i			0.547444i
$146$	3.98910			0.330140
$147$	2.21432			0.182634
$148$		−	6.00000i		−	0.493197i
$149$		−	14.5368i		−	1.19090i	−0.803392	−	0.595451i	$-0.796974\pi$
$149$		−	14.5368i		−	1.19090i	0.803392	−	0.595451i	$-0.203026\pi$
$150$			8.13335i			0.664085i
$151$			19.9748i			1.62553i	0.582594	+	0.812764i	$0.302038\pi$
$151$			19.9748i			1.62553i	−0.582594	+	0.812764i	$0.697962\pi$
$152$	20.7556			1.68350
$153$	−6.83654			−0.552701
$154$			1.85236i			0.149267i
$155$	−18.7605			−1.50688
$156$	−12.1334	−	1.05086i	−0.971446	−	0.0841357i
$157$	7.39853			0.590467			0.295233	−	0.955425i	$-0.404603\pi$
$157$	7.39853			0.590467			0.295233	+	0.955425i	$0.404603\pi$
$158$		−	3.08589i		−	0.245500i
$159$	−5.59210			−0.443483
$160$	−18.6637			−1.47550
$161$			3.28100i			0.258579i
$162$		−	7.63804i		−	0.600101i
$163$		−	2.32693i		−	0.182259i	−0.995839	−	0.0911296i	$-0.970952\pi$
$163$		−	2.32693i		−	0.182259i	0.995839	−	0.0911296i	$-0.0290477\pi$
$164$			1.15257i			0.0900002i
$165$	−19.1383			−1.48991
$166$	7.45875			0.578911
$167$			3.42219i			0.264817i	0.991195	+	0.132408i	$0.0422710\pi$
$167$			3.42219i			0.264817i	−0.991195	+	0.132408i	$0.957729\pi$
$168$	5.37778			0.414905
$169$	12.8064	+	2.23506i	0.985110	+	0.171928i
$170$	7.95407			0.610049
$171$		−	16.2652i		−	1.24383i
$172$	−13.4336			−1.02430
$173$	−8.27454			−0.629102			−0.314551	−	0.949241i	$-0.601854\pi$
$173$	−8.27454			−0.629102			−0.314551	+	0.949241i	$0.601854\pi$
$174$		−	3.12843i		−	0.237166i
$175$		−	5.33185i		−	0.403050i
$176$		−	3.70471i		−	0.279253i
$177$			16.2351i			1.22030i
$178$	3.69381			0.276863
$179$	16.2257			1.21277			0.606383	−	0.795173i	$-0.292620\pi$
$179$	16.2257			1.21277			0.606383	+	0.795173i	$0.292620\pi$
$180$			9.33185i			0.695555i
$181$	9.20495			0.684199			0.342099	−	0.939664i	$-0.388862\pi$
$181$	9.20495			0.684199			0.342099	+	0.939664i	$0.388862\pi$
$182$	−2.47457	−	0.214320i	−0.183428	−	0.0158864i
$183$	−20.0415			−1.48151
$184$			7.96836i			0.587435i
$185$	12.6430			0.929529
$186$	8.90321			0.652815
$187$			9.65878i			0.706320i
$188$		−	2.87157i		−	0.209431i
$189$			2.42864i			0.176658i
$190$			18.9240i			1.37289i
$191$	−6.66815			−0.482490			−0.241245	−	0.970464i	$-0.577556\pi$
$191$	−6.66815			−0.482490			−0.241245	+	0.970464i	$0.577556\pi$
$192$	2.75557			0.198866
$193$		−	20.6035i		−	1.48307i	−0.670914	−	0.741535i	$-0.734098\pi$
$193$		−	20.6035i		−	1.48307i	0.670914	−	0.741535i	$-0.265902\pi$
$194$	−6.63311			−0.476230
$195$	2.21432	−	25.5669i	0.158571	−	1.83088i
$196$	−1.52543			−0.108959
$197$		−	8.36842i		−	0.596225i	−0.954531	−	0.298112i	$-0.903643\pi$
$197$		−	8.36842i		−	0.596225i	0.954531	−	0.298112i	$-0.0963571\pi$
$198$	3.52543			0.250541
$199$	0.601472			0.0426372			0.0213186	−	0.999773i	$-0.493214\pi$
$199$	0.601472			0.0426372			0.0213186	+	0.999773i	$0.493214\pi$
$200$		−	12.9491i		−	0.915643i
$201$		−	0.949145i		−	0.0669475i
$202$		−	9.43356i		−	0.663743i
$203$			2.05086i			0.143942i
$204$	12.1334			0.849505
$205$	−2.42864			−0.169624
$206$		−	8.47013i		−	0.590142i
$207$	6.24443			0.434018
$208$	4.94914	+	0.428639i	0.343161	+	0.0297208i
$209$	−22.9797			−1.58954
$210$			4.90321i			0.338354i
$211$	−1.90321			−0.131023			−0.0655113	−	0.997852i	$-0.520868\pi$
$211$	−1.90321			−0.131023			−0.0655113	+	0.997852i	$0.520868\pi$
$212$	3.85236			0.264581
$213$		−	19.8938i		−	1.36310i
$214$		−	12.5303i		−	0.856557i
$215$		−	28.3067i		−	1.93050i
$216$			5.89829i			0.401328i
$217$	−5.83654			−0.396210
$218$	−5.76049			−0.390150
$219$			12.8222i			0.866447i
$220$	13.1842			0.888879
$221$	−12.9032	−	1.11753i	−0.867964	−	0.0751733i
$222$	−6.00000			−0.402694
$223$			10.6336i			0.712078i	0.934471	+	0.356039i	$0.115873\pi$
$223$			10.6336i			0.712078i	−0.934471	+	0.356039i	$0.884127\pi$
$224$	−5.80642			−0.387958
$225$	−10.1476			−0.676510
$226$		−	5.83161i		−	0.387913i
$227$			15.0509i			0.998960i	0.866325	+	0.499480i	$0.166476\pi$
$227$			15.0509i			0.998960i	−0.866325	+	0.499480i	$0.833524\pi$
$228$			28.8671i			1.91177i
$229$			6.53480i			0.431831i	0.976412	+	0.215916i	$0.0692736\pi$
$229$			6.53480i			0.431831i	−0.976412	+	0.215916i	$0.930726\pi$
$230$	−7.26517			−0.479051
$231$	−5.95407			−0.391749
$232$			4.98079i			0.327005i
$233$	27.9590			1.83165			0.915827	−	0.401573i	$-0.131536\pi$
$233$	27.9590			1.83165			0.915827	+	0.401573i	$0.131536\pi$
$234$	−0.407896	+	4.70964i	−0.0266650	+	0.307879i
$235$	6.05086			0.394714
$236$		−	11.1842i		−	0.728030i
$237$	9.91903			0.644310
$238$	2.47457			0.160403
$239$		−	19.5812i		−	1.26660i	−0.773905	−	0.633301i	$-0.781699\pi$
$239$		−	19.5812i		−	1.26660i	0.773905	−	0.633301i	$-0.218301\pi$
$240$		−	9.80642i		−	0.633002i
$241$			13.3575i			0.860433i	0.902726	+	0.430217i	$0.141563\pi$
$241$			13.3575i			0.860433i	−0.902726	+	0.430217i	$0.858437\pi$
$242$			2.59703i			0.166943i
$243$	17.2652			1.10756
$244$	13.8064			0.883866
$245$		−	3.21432i		−	0.205355i
$246$	1.15257			0.0734849
$247$	2.65878	−	30.6987i	0.169174	−	1.95331i
$248$	−14.1748			−0.900103
$249$			23.9748i			1.51934i
$250$	0.734825			0.0464744
$251$	−3.29682			−0.208093			−0.104047	−	0.994572i	$-0.533179\pi$
$251$	−3.29682			−0.208093			−0.104047	+	0.994572i	$0.533179\pi$
$252$			2.90321i			0.182885i
$253$		−	8.82225i		−	0.554650i
$254$		−	2.81579i		−	0.176678i
$255$			25.5669i			1.60106i
$256$	−9.89829			−0.618643
$257$	23.6938			1.47798			0.738990	−	0.673717i	$-0.235303\pi$
$257$	23.6938			1.47798			0.738990	+	0.673717i	$0.235303\pi$
$258$			13.4336i			0.836337i
$259$	3.93332			0.244405
$260$	−1.52543	+	17.6128i	−0.0946030	+	1.09230i
$261$	3.90321			0.241603
$262$			4.09187i			0.252796i
$263$	9.99063			0.616049			0.308024	−	0.951378i	$-0.400332\pi$
$263$	9.99063			0.616049			0.308024	+	0.951378i	$0.400332\pi$
$264$	−14.4603			−0.889969
$265$			8.11753i			0.498656i
$266$			5.88739i			0.360979i
$267$			11.8731i			0.726622i
$268$			0.653858i			0.0399408i
$269$	−18.2034			−1.10988			−0.554941	−	0.831890i	$-0.687259\pi$
$269$	−18.2034			−1.10988			−0.554941	+	0.831890i	$0.687259\pi$
$270$	−5.37778			−0.327282
$271$			24.1748i			1.46852i	0.678870	+	0.734258i	$0.262470\pi$
$271$			24.1748i			1.46852i	−0.678870	+	0.734258i	$0.737530\pi$
$272$	−4.94914			−0.300086
$273$	0.688892	−	7.95407i	0.0416937	−	0.481402i
$274$	11.2716			0.680944
$275$			14.3368i			0.864540i
$276$	−11.0825			−0.667088
$277$	−1.69535			−0.101863			−0.0509317	−	0.998702i	$-0.516219\pi$
$277$	−1.69535			−0.101863			−0.0509317	+	0.998702i	$0.516219\pi$
$278$			2.08742i			0.125195i
$279$			11.1082i			0.665028i
$280$		−	7.80642i		−	0.466523i
$281$		−	11.6479i		−	0.694854i	−0.937707	−	0.347427i	$-0.887055\pi$
$281$		−	11.6479i		−	0.694854i	0.937707	−	0.347427i	$-0.112945\pi$
$282$	−2.87157			−0.170999
$283$	−12.1334			−0.721253			−0.360626	−	0.932710i	$-0.617437\pi$
$283$	−12.1334			−0.721253			−0.360626	+	0.932710i	$0.617437\pi$
$284$			13.7047i			0.813225i
$285$	−60.8276			−3.60312
$286$	6.65386	+	0.576283i	0.393451	+	0.0340763i
$287$	−0.755569			−0.0445998
$288$			11.0509i			0.651178i
$289$	−4.09679			−0.240988
$290$	−4.54125			−0.266671
$291$		−	21.3210i		−	1.24986i
$292$		−	8.83314i		−	0.516921i
$293$		−	11.4538i		−	0.669140i	−0.942371	−	0.334570i	$-0.891409\pi$
$293$		−	11.4538i		−	0.669140i	0.942371	−	0.334570i	$-0.108591\pi$
$294$			1.52543i			0.0889647i
$295$	23.5669			1.37212
$296$	9.55262			0.555235
$297$		−	6.53035i		−	0.378929i
$298$	10.0143			0.580112
$299$	11.7857	+	1.02074i	0.681583	+	0.0590311i
$300$	18.0098			1.03980
$301$		−	8.80642i		−	0.507594i
$302$	−13.7605			−0.791827
$303$	30.3225			1.74198
$304$		−	11.7748i		−	0.675330i
$305$			29.0923i			1.66582i
$306$		−	4.70964i		−	0.269232i
$307$		−	3.96989i		−	0.226574i	−0.993562	−	0.113287i	$-0.963862\pi$
$307$		−	3.96989i		−	0.226574i	0.993562	−	0.113287i	$-0.0361379\pi$
$308$	4.10171			0.233717
$309$	27.2257			1.54882
$310$		−	12.9240i		−	0.734031i
$311$	−27.3481			−1.55077			−0.775386	−	0.631488i	$-0.782444\pi$
$311$	−27.3481			−1.55077			−0.775386	+	0.631488i	$0.782444\pi$
$312$	1.67307	−	19.3176i	0.0947190	−	1.09364i
$313$	−19.1032			−1.07978			−0.539890	−	0.841736i	$-0.681534\pi$
$313$	−19.1032			−1.07978			−0.539890	+	0.841736i	$0.681534\pi$
$314$			5.09679i			0.287628i
$315$	−6.11753			−0.344684
$316$	−6.83314			−0.384394
$317$			9.90813i			0.556496i	0.960509	+	0.278248i	$0.0897538\pi$
$317$			9.90813i			0.556496i	−0.960509	+	0.278248i	$0.910246\pi$
$318$		−	3.85236i		−	0.216029i
$319$		−	5.51453i		−	0.308754i
$320$		−	4.00000i		−	0.223607i
$321$	40.2766			2.24802
$322$	−2.26025			−0.125959
$323$			30.6987i			1.70812i
$324$	−16.9131			−0.939614
$325$	−19.1526	−	1.65878i	−1.06239	−	0.0920126i
$326$	1.60300			0.0887821
$327$		−	18.5161i		−	1.02394i
$328$	−1.83500			−0.101321
$329$	1.88247			0.103784
$330$		−	13.1842i		−	0.725767i
$331$			23.4193i			1.28724i	0.765345	+	0.643620i	$0.222568\pi$
$331$			23.4193i			1.28724i	−0.765345	+	0.643620i	$0.777432\pi$
$332$		−	16.5161i		−	0.906437i
$333$		−	7.48595i		−	0.410227i
$334$	−2.35752			−0.128998
$335$	−1.37778			−0.0752764
$336$		−	3.05086i		−	0.166438i
$337$	7.51606			0.409426			0.204713	−	0.978822i	$-0.434374\pi$
$337$	7.51606			0.409426			0.204713	+	0.978822i	$0.434374\pi$
$338$	−1.53972	+	8.82225i	−0.0837496	+	0.479867i
$339$	18.7447			1.01807
$340$		−	17.6128i		−	0.955191i
$341$	15.6938			0.849868
$342$	11.2050			0.605894
$343$		−	1.00000i		−	0.0539949i
$344$		−	21.3876i		−	1.15314i
$345$		−	23.3526i		−	1.25726i
$346$		−	5.70027i		−	0.306448i
$347$	5.64449			0.303012			0.151506	−	0.988456i	$-0.451588\pi$
$347$	5.64449			0.303012			0.151506	+	0.988456i	$0.451588\pi$
$348$	−6.92735			−0.371345
$349$		−	24.1590i		−	1.29320i	−0.762828	−	0.646601i	$-0.776190\pi$
$349$		−	24.1590i		−	1.29320i	0.762828	−	0.646601i	$-0.223810\pi$
$350$	3.67307			0.196334
$351$	8.72393	+	0.755569i	0.465649	+	0.0403293i
$352$	15.6128			0.832168
$353$			36.1289i			1.92295i	0.274896	+	0.961474i	$0.411356\pi$
$353$			36.1289i			1.92295i	−0.274896	+	0.961474i	$0.588644\pi$
$354$	−11.1842			−0.594434
$355$	−28.8780			−1.53269
$356$		−	8.17929i		−	0.433501i
$357$			7.95407i			0.420974i
$358$			11.1778i			0.590763i
$359$		−	17.4128i		−	0.919013i	−0.888174	−	0.459507i	$-0.848026\pi$
$359$		−	17.4128i		−	0.919013i	0.888174	−	0.459507i	$-0.151974\pi$
$360$	−14.8573			−0.783047
$361$	−54.0370			−2.84405
$362$			6.34122i			0.333287i
$363$	−8.34767			−0.438139
$364$	−0.474572	+	5.47949i	−0.0248744	+	0.287204i
$365$	18.6128			0.974241
$366$		−	13.8064i		−	0.721673i
$367$	2.93825			0.153375			0.0766876	−	0.997055i	$-0.475566\pi$
$367$	2.93825			0.153375			0.0766876	+	0.997055i	$0.475566\pi$
$368$	4.52051			0.235648
$369$			1.43801i			0.0748597i
$370$			8.70964i			0.452792i
$371$			2.52543i			0.131114i
$372$		−	19.7146i		−	1.02215i
$373$	−18.7699			−0.971866			−0.485933	−	0.873996i	$-0.661520\pi$
$373$	−18.7699			−0.971866			−0.485933	+	0.873996i	$0.661520\pi$
$374$	−6.65386			−0.344063
$375$			2.36196i			0.121971i
$376$	4.57184			0.235774
$377$	7.36689	+	0.638037i	0.379414	+	0.0328606i
$378$	−1.67307			−0.0860535
$379$			23.6894i			1.21684i	0.793615	+	0.608421i	$0.208197\pi$
$379$			23.6894i			1.21684i	−0.793615	+	0.608421i	$0.791803\pi$
$380$	41.9037			2.14961
$381$	9.05086			0.463689
$382$		−	4.59364i		−	0.235031i
$383$			31.6128i			1.61534i	0.589634	+	0.807671i	$0.299272\pi$
$383$			31.6128i			1.61534i	−0.589634	+	0.807671i	$0.700728\pi$
$384$		−	23.8163i		−	1.21537i
$385$			8.64296i			0.440486i
$386$	14.1936			0.722434
$387$	−16.7605			−0.851984
$388$			14.6878i			0.745662i
$389$	20.0558			1.01687			0.508434	−	0.861101i	$-0.330225\pi$
$389$	20.0558			1.01687			0.508434	+	0.861101i	$0.330225\pi$
$390$	17.6128	+	1.52543i	0.891861	+	0.0772430i
$391$	−11.7857			−0.596027
$392$		−	2.42864i		−	0.122665i
$393$	−13.1526			−0.663459
$394$	5.76494			0.290433
$395$		−	14.3985i		−	0.724469i
$396$		−	7.80642i		−	0.392288i
$397$		−	22.8731i		−	1.14797i	−0.818867	−	0.573984i	$-0.805397\pi$
$397$		−	22.8731i		−	1.14797i	0.818867	−	0.573984i	$-0.194603\pi$
$398$			0.414349i			0.0207695i
$399$	−18.9240			−0.947383
$400$	−7.34614			−0.367307
$401$			5.61285i			0.280292i	0.990131	+	0.140146i	$0.0447572\pi$
$401$			5.61285i			0.280292i	−0.990131	+	0.140146i	$0.955243\pi$
$402$	0.653858			0.0326115
$403$	−1.81579	+	20.9654i	−0.0904510	+	1.04436i
$404$	−20.8889			−1.03926
$405$		−	35.6385i		−	1.77089i
$406$	−1.41282			−0.0701170
$407$	−10.5763			−0.524247
$408$			19.3176i			0.956362i
$409$		−	26.1175i		−	1.29143i	−0.763579	−	0.645714i	$-0.776560\pi$
$409$		−	26.1175i		−	1.29143i	0.763579	−	0.645714i	$-0.223440\pi$
$410$		−	1.67307i		−	0.0826271i
$411$			36.2306i			1.78712i
$412$	−18.7556			−0.924021
$413$	7.33185			0.360777
$414$			4.30174i			0.211419i
$415$	34.8020			1.70836
$416$	−1.80642	+	20.8573i	−0.0885672	+	1.02261i
$417$	−6.70964			−0.328572
$418$		−	15.8306i		−	0.774298i
$419$	−25.2464			−1.23337			−0.616685	−	0.787210i	$-0.711525\pi$
$419$	−25.2464			−1.23337			−0.616685	+	0.787210i	$0.711525\pi$
$420$	10.8573			0.529781
$421$		−	8.22861i		−	0.401038i	−0.979690	−	0.200519i	$-0.935737\pi$
$421$		−	8.22861i		−	0.401038i	0.979690	−	0.200519i	$-0.0642628\pi$
$422$		−	1.31111i		−	0.0638237i
$423$		−	3.58274i		−	0.174199i
$424$			6.13335i			0.297862i
$425$	19.1526			0.929036
$426$	13.7047			0.663996
$427$			9.05086i			0.438002i
$428$	−27.7462			−1.34116
$429$	−1.85236	+	21.3876i	−0.0894326	+	1.03260i
$430$	19.5002			0.940385
$431$		−	1.43801i		−	0.0692664i	−0.999400	−	0.0346332i	$-0.988974\pi$
$431$		−	1.43801i		−	0.0692664i	0.999400	−	0.0346332i	$-0.0110263\pi$
$432$	3.34614			0.160991
$433$	16.5018			0.793024			0.396512	−	0.918029i	$-0.370220\pi$
$433$	16.5018			0.793024			0.396512	+	0.918029i	$0.370220\pi$
$434$		−	4.02074i		−	0.193002i
$435$		−	14.5970i		−	0.699874i
$436$			12.7556i			0.610881i
$437$		−	28.0400i		−	1.34133i
$438$	−8.83314			−0.422064
$439$	10.1619			0.485003			0.242501	−	0.970151i	$-0.422032\pi$
$439$	10.1619			0.485003			0.242501	+	0.970151i	$0.422032\pi$
$440$			20.9906i			1.00069i
$441$	−1.90321			−0.0906291
$442$	0.769859	−	8.88892i	0.0366185	−	0.422803i
$443$	3.20787			0.152410			0.0762052	−	0.997092i	$-0.475720\pi$
$443$	3.20787			0.152410			0.0762052	+	0.997092i	$0.475720\pi$
$444$			13.2859i			0.630522i
$445$	17.2351			0.817020
$446$	−7.32540			−0.346868
$447$			32.1891i			1.52249i
$448$		−	1.24443i		−	0.0587939i
$449$			18.4099i			0.868817i	0.900716	+	0.434409i	$0.143043\pi$
$449$			18.4099i			0.868817i	−0.900716	+	0.434409i	$0.856957\pi$
$450$		−	6.99063i		−	0.329542i
$451$	2.03164			0.0956663
$452$	−12.9131			−0.607379
$453$		−	44.2306i		−	2.07814i
$454$	−10.3684			−0.486614
$455$	−11.5462	−	1.00000i	−0.541293	−	0.0468807i
$456$	−45.9595			−2.15225
$457$			3.40297i			0.159184i	0.996828	+	0.0795922i	$0.0253618\pi$
$457$			3.40297i			0.159184i	−0.996828	+	0.0795922i	$0.974638\pi$
$458$	−4.50177			−0.210354
$459$	−8.72393			−0.407198
$460$			16.0874i			0.750080i
$461$			17.5714i			0.818380i	0.912449	+	0.409190i	$0.134189\pi$
$461$			17.5714i			0.818380i	−0.912449	+	0.409190i	$0.865811\pi$
$462$		−	4.10171i		−	0.190829i
$463$		−	15.7714i		−	0.732959i	−0.930426	−	0.366479i	$-0.880563\pi$
$463$		−	15.7714i		−	0.732959i	0.930426	−	0.366479i	$-0.119437\pi$
$464$	2.82564			0.131177
$465$	41.5417			1.92645
$466$			19.2607i			0.892236i
$467$	3.76694			0.174313			0.0871567	−	0.996195i	$-0.472222\pi$
$467$	3.76694			0.174313			0.0871567	+	0.996195i	$0.472222\pi$
$468$	10.4286	+	0.903212i	0.482064	+	0.0417510i
$469$	−0.428639			−0.0197927
$470$			4.16839i			0.192273i
$471$	−16.3827			−0.754875
$472$	17.8064			0.819607
$473$			23.6795i			1.08879i
$474$			6.83314i			0.313857i
$475$			45.5669i			2.09075i
$476$		−	5.47949i		−	0.251152i
$477$	4.80642			0.220071
$478$	13.4893			0.616988
$479$			12.1032i			0.553011i	0.961012	+	0.276506i	$0.0891764\pi$
$479$			12.1032i			0.553011i	−0.961012	+	0.276506i	$0.910824\pi$
$480$	41.3274			1.88633
$481$	1.22369	−	14.1289i	0.0557954	−	0.644223i
$482$	−9.20189			−0.419135
$483$		−	7.26517i		−	0.330577i
$484$	5.75065			0.261393
$485$	−30.9496			−1.40535
$486$			11.8938i			0.539516i
$487$		−	17.3778i		−	0.787463i	−0.919226	−	0.393731i	$-0.871184\pi$
$487$		−	17.3778i		−	0.787463i	0.919226	−	0.393731i	$-0.128816\pi$
$488$			21.9813i			0.995045i
$489$			5.15257i			0.233007i
$490$	2.21432			0.100033
$491$	19.3921			0.875152			0.437576	−	0.899181i	$-0.355837\pi$
$491$	19.3921			0.875152			0.437576	+	0.899181i	$0.355837\pi$
$492$		−	2.55215i		−	0.115060i
$493$	−7.36689			−0.331788
$494$	21.1481	+	1.83161i	0.951499	+	0.0824082i
$495$	16.4494			0.739345
$496$			8.04149i			0.361073i
$497$	−8.98418			−0.402995
$498$	−16.5161			−0.740102
$499$		−	10.6702i		−	0.477662i	−0.971061	−	0.238831i	$-0.923236\pi$
$499$		−	10.6702i		−	0.477662i	0.971061	−	0.238831i	$-0.0767642\pi$
$500$		−	1.62714i		−	0.0727678i
$501$		−	7.57781i		−	0.338552i
$502$		−	2.27115i		−	0.101366i
$503$	−4.27655			−0.190682			−0.0953410	−	0.995445i	$-0.530394\pi$
$503$	−4.27655			−0.190682			−0.0953410	+	0.995445i	$0.530394\pi$
$504$	−4.62222			−0.205890
$505$		−	44.0163i		−	1.95870i
$506$	6.07758			0.270181
$507$	−28.3575	−	4.94914i	−1.25940	−	0.219799i
$508$	−6.23506			−0.276636
$509$			33.0765i			1.46609i	0.680180	+	0.733046i	$0.261902\pi$
$509$			33.0765i			1.46609i	−0.680180	+	0.733046i	$0.738098\pi$
$510$	−17.6128			−0.779910
$511$	5.79060			0.256161
$512$			14.6923i			0.649313i
$513$		−	20.7556i		−	0.916381i
$514$			16.3225i			0.719954i
$515$		−	39.5210i		−	1.74150i
$516$	29.7462			1.30950
$517$	−5.06175			−0.222616
$518$			2.70964i			0.119055i
$519$	18.3225			0.804268
$520$	−28.0415	−	2.42864i	−1.22970	−	0.106503i
$521$	24.3783			1.06803			0.534015	−	0.845475i	$-0.320682\pi$
$521$	24.3783			1.06803			0.534015	+	0.845475i	$0.320682\pi$
$522$			2.68889i			0.117690i
$523$	34.9403			1.52783			0.763915	−	0.645317i	$-0.223275\pi$
$523$	34.9403			1.52783			0.763915	+	0.645317i	$0.223275\pi$
$524$	9.06070			0.395818
$525$			11.8064i			0.515275i
$526$			6.88247i			0.300090i
$527$		−	20.9654i		−	0.913269i
$528$			8.20342i			0.357008i
$529$	−12.2351			−0.531959
$530$	−5.59210			−0.242905
$531$		−	13.9541i		−	0.605555i
$532$	13.0366			0.565207
$533$	−0.235063	+	2.71408i	−0.0101817	+	0.117560i
$534$	−8.17929			−0.353952
$535$		−	58.4657i		−	2.52769i
$536$	−1.04101			−0.0449648
$537$	−35.9289			−1.55045
$538$		−	12.5402i		−	0.540646i
$539$			2.68889i			0.115819i
$540$			11.9081i			0.512445i
$541$			30.4953i			1.31110i	0.755153	+	0.655548i	$0.227562\pi$
$541$			30.4953i			1.31110i	−0.755153	+	0.655548i	$0.772438\pi$
$542$	−16.6539			−0.715344
$543$	−20.3827			−0.874706
$544$		−	20.8573i		−	0.894248i
$545$	−26.8780			−1.15133
$546$	5.47949	+	0.474572i	0.234501	+	0.0203098i
$547$	−10.0049			−0.427780			−0.213890	−	0.976858i	$-0.568613\pi$
$547$	−10.0049			−0.427780			−0.213890	+	0.976858i	$0.568613\pi$
$548$		−	24.9590i		−	1.06620i
$549$	17.2257			0.735175
$550$	−9.87649			−0.421135
$551$		−	17.5270i		−	0.746674i
$552$		−	17.6445i		−	0.750999i
$553$		−	4.47949i		−	0.190487i
$554$		−	1.16791i		−	0.0496198i
$555$	−27.9956			−1.18835
$556$	4.62222			0.196026
$557$		−	14.1936i		−	0.601401i	−0.953719	−	0.300701i	$-0.902780\pi$
$557$		−	14.1936i		−	0.601401i	0.953719	−	0.300701i	$-0.0972205\pi$
$558$	−7.65233			−0.323949
$559$	−31.6336	−	2.73975i	−1.33796	−	0.115879i
$560$	−4.42864			−0.187144
$561$		−	21.3876i		−	0.902986i
$562$	8.02413			0.338478
$563$	21.3590			0.900177			0.450088	−	0.892984i	$-0.351393\pi$
$563$	21.3590			0.900177			0.450088	+	0.892984i	$0.351393\pi$
$564$			6.35857i			0.267744i
$565$		−	27.2099i		−	1.14473i
$566$		−	8.35857i		−	0.351337i
$567$		−	11.0874i		−	0.465628i
$568$	−21.8193			−0.915519
$569$	−34.2672			−1.43656			−0.718278	−	0.695757i	$-0.755069\pi$
$569$	−34.2672			−1.43656			−0.718278	+	0.695757i	$0.755069\pi$
$570$		−	41.9037i		−	1.75515i
$571$	37.6494			1.57558			0.787789	−	0.615945i	$-0.211226\pi$
$571$	37.6494			1.57558			0.787789	+	0.615945i	$0.211226\pi$
$572$	1.27607	−	14.7338i	0.0533553	−	0.616050i
$573$	14.7654			0.616834
$574$		−	0.520505i		−	0.0217255i
$575$	−17.4938			−0.729541
$576$	−2.36842			−0.0986840
$577$			28.3970i			1.18218i	0.806605	+	0.591091i	$0.201303\pi$
$577$			28.3970i			1.18218i	−0.806605	+	0.591091i	$0.798697\pi$
$578$		−	2.82225i		−	0.117390i
$579$			45.6227i			1.89601i
$580$			10.0558i			0.417543i
$581$	10.8272			0.449187
$582$	14.6878			0.608830
$583$		−	6.79060i		−	0.281238i
$584$	14.0633			0.581943
$585$	−1.90321	+	21.9748i	−0.0786881	+	0.908547i
$586$	7.89045			0.325952
$587$		−	6.23659i		−	0.257412i	−0.991683	−	0.128706i	$-0.958918\pi$
$587$		−	6.23659i		−	0.257412i	0.991683	−	0.128706i	$-0.0410823\pi$
$588$	3.37778			0.139297
$589$	49.8800			2.05527
$590$			16.2351i			0.668387i
$591$			18.5303i			0.762237i
$592$		−	5.41927i		−	0.222731i
$593$		−	17.5698i		−	0.721506i	−0.932661	−	0.360753i	$-0.882520\pi$
$593$		−	17.5698i		−	0.721506i	0.932661	−	0.360753i	$-0.117480\pi$
$594$	4.49871			0.184584
$595$	11.5462			0.473347
$596$		−	22.1748i		−	0.908317i
$597$	−1.33185			−0.0545090
$598$	−0.703182	+	8.11906i	−0.0287553	+	0.332013i
$599$	16.9813			0.693836			0.346918	−	0.937896i	$-0.387228\pi$
$599$	16.9813			0.693836			0.346918	+	0.937896i	$0.387228\pi$
$600$			28.6735i			1.17059i
$601$	−18.7052			−0.763001			−0.381500	−	0.924369i	$-0.624592\pi$
$601$	−18.7052			−0.763001			−0.381500	+	0.924369i	$0.624592\pi$
$602$	6.06668			0.247259
$603$			0.815792i			0.0332216i
$604$			30.4701i			1.23981i
$605$			12.1175i			0.492648i
$606$			20.8889i			0.848554i
$607$	−10.3575			−0.420399			−0.210199	−	0.977659i	$-0.567411\pi$
$607$	−10.3575			−0.420399			−0.210199	+	0.977659i	$0.567411\pi$
$608$	49.6227			2.01247
$609$		−	4.54125i		−	0.184021i
$610$	−20.0415			−0.811456
$611$	0.585651	−	6.76202i	0.0236929	−	0.273562i
$612$	−10.4286			−0.421553
$613$		−	7.02227i		−	0.283627i	−0.989893	−	0.141814i	$-0.954707\pi$
$613$		−	7.02227i		−	0.283627i	0.989893	−	0.141814i	$-0.0452933\pi$
$614$	2.73483			0.110369
$615$	5.37778			0.216853
$616$			6.53035i			0.263115i
$617$			29.9813i			1.20700i	0.797363	+	0.603500i	$0.206228\pi$
$617$			29.9813i			1.20700i	−0.797363	+	0.603500i	$0.793772\pi$
$618$			18.7556i			0.754460i
$619$		−	0.0285802i		−	0.00114874i	−1.00000		0.000574368i	$-0.999817\pi$
$619$		−	0.0285802i		−	0.00114874i	1.00000		0.000574368i	$-0.000182827\pi$
$620$	−28.6178			−1.14932
$621$	7.96836			0.319759
$622$		−	18.8399i		−	0.755412i
$623$	5.36196			0.214823
$624$	−10.9590	−	0.949145i	−0.438711	−	0.0379962i
$625$	−23.2306			−0.929225
$626$		−	13.1601i		−	0.525982i
$627$	50.8845			2.03213
$628$	11.2859			0.450357
$629$			14.1289i			0.563356i
$630$		−	4.21432i		−	0.167903i
$631$			12.1936i			0.485419i	0.970099	+	0.242709i	$0.0780361\pi$
$631$			12.1936i			0.485419i	−0.970099	+	0.242709i	$0.921964\pi$
$632$		−	10.8791i		−	0.432746i
$633$	4.21432			0.167504
$634$	−6.82564			−0.271081
$635$		−	13.1383i		−	0.521377i
$636$	−8.53035			−0.338250
$637$	−3.59210	−	0.311108i	−0.142324	−	0.0123265i
$638$	3.79892			0.150401
$639$			17.0988i			0.676418i
$640$	−34.5718			−1.36657
$641$	2.82516			0.111587			0.0557935	−	0.998442i	$-0.482231\pi$
$641$	2.82516			0.111587			0.0557935	+	0.998442i	$0.482231\pi$
$642$			27.7462i			1.09506i
$643$		−	37.7275i		−	1.48783i	−0.668276	−	0.743913i	$-0.732968\pi$
$643$		−	37.7275i		−	1.48783i	0.668276	−	0.743913i	$-0.267032\pi$
$644$			5.00492i			0.197222i
$645$			62.6800i			2.46802i
$646$	−21.1481			−0.832062
$647$	−12.3664			−0.486174			−0.243087	−	0.970005i	$-0.578160\pi$
$647$	−12.3664			−0.486174			−0.243087	+	0.970005i	$0.578160\pi$
$648$		−	26.9273i		−	1.05781i
$649$	−19.7146			−0.773864
$650$	1.14272	−	13.1941i	0.0448212	−	0.517513i
$651$	12.9240			0.506530
$652$		−	3.54956i		−	0.139012i
$653$	−33.0005			−1.29141			−0.645704	−	0.763588i	$-0.723436\pi$
$653$	−33.0005			−1.29141			−0.645704	+	0.763588i	$0.723436\pi$
$654$	12.7556			0.498782
$655$			19.0923i			0.746000i
$656$			1.04101i			0.0406446i
$657$		−	11.0207i		−	0.429960i
$658$			1.29682i			0.0505552i
$659$	32.8118			1.27817			0.639084	−	0.769137i	$-0.279314\pi$
$659$	32.8118			1.27817			0.639084	+	0.769137i	$0.279314\pi$
$660$	−29.1941			−1.13638
$661$			14.7067i			0.572025i	0.958226	+	0.286013i	$0.0923299\pi$
$661$			14.7067i			0.572025i	−0.958226	+	0.286013i	$0.907670\pi$
$662$	−16.1334			−0.627041
$663$	28.5718	+	2.47457i	1.10964	+	0.0961044i
$664$	26.2953			1.02046
$665$			27.4701i			1.06525i
$666$	5.15701			0.199830
$667$	6.72885			0.260542
$668$			5.22030i			0.201979i
$669$		−	23.5462i		−	0.910348i
$670$		−	0.949145i		−	0.0366687i
$671$		−	24.3368i		−	0.939511i
$672$	12.8573			0.495980
$673$	−21.2908			−0.820702			−0.410351	−	0.911928i	$-0.634594\pi$
$673$	−21.2908			−0.820702			−0.410351	+	0.911928i	$0.634594\pi$
$674$			5.17775i			0.199440i
$675$	−12.9491			−0.498413
$676$	19.5353	+	3.40943i	0.751357	+	0.131132i
$677$	−3.07160			−0.118051			−0.0590256	−	0.998256i	$-0.518799\pi$
$677$	−3.07160			−0.118051			−0.0590256	+	0.998256i	$0.518799\pi$
$678$			12.9131i			0.495923i
$679$	−9.62867			−0.369514
$680$	28.0415			1.07534
$681$		−	33.3274i		−	1.27711i
$682$			10.8113i			0.413988i
$683$			24.7971i			0.948833i	0.880301	+	0.474416i	$0.157341\pi$
$683$			24.7971i			0.948833i	−0.880301	+	0.474416i	$0.842659\pi$
$684$		−	24.8113i		−	0.948686i
$685$	52.5926			2.00946
$686$	0.688892			0.0263020
$687$		−	14.4701i		−	0.552070i
$688$	−12.1334			−0.462580
$689$	9.07160	+	0.785680i	0.345600	+	0.0299320i
$690$	16.0874			0.612438
$691$		−	27.0953i		−	1.03075i	−0.856964	−	0.515376i	$-0.827652\pi$
$691$		−	27.0953i		−	1.03075i	0.856964	−	0.515376i	$-0.172348\pi$
$692$	−12.6222			−0.479825
$693$	5.11753			0.194399
$694$			3.88845i			0.147603i
$695$			9.73975i			0.369450i
$696$		−	11.0291i		−	0.418055i
$697$		−	2.71408i		−	0.102803i
$698$	16.6430			0.629945
$699$	−61.9101			−2.34166
$700$		−	8.13335i		−	0.307412i
$701$	−13.5205			−0.510662			−0.255331	−	0.966854i	$-0.582185\pi$
$701$	−13.5205			−0.510662			−0.255331	+	0.966854i	$0.582185\pi$
$702$	−0.520505	+	6.00984i	−0.0196452	+	0.226827i
$703$	−33.6149			−1.26781
$704$			3.34614i			0.126112i
$705$	−13.3985			−0.504618
$706$	−24.8889			−0.936707
$707$		−	13.6938i		−	0.515009i
$708$			24.7654i			0.930741i
$709$			50.9753i			1.91442i	0.289399	+	0.957209i	$0.406545\pi$
$709$			50.9753i			1.91442i	−0.289399	+	0.957209i	$0.593455\pi$
$710$		−	19.8938i		−	0.746603i
$711$	−8.52543			−0.319729
$712$	13.0223			0.488030
$713$			19.1497i			0.717160i
$714$	−5.47949			−0.205065
$715$	31.0464	+	2.68889i	1.16107	+	0.100559i
$716$	24.7511			0.924993
$717$			43.3590i			1.61927i
$718$	11.9956			0.447670
$719$	−41.5417			−1.54924			−0.774622	−	0.632424i	$-0.782060\pi$
$719$	−41.5417			−1.54924			−0.774622	+	0.632424i	$0.782060\pi$
$720$			8.42864i			0.314117i
$721$		−	12.2953i		−	0.457900i
$722$		−	37.2257i		−	1.38540i
$723$		−	29.5778i		−	1.10001i
$724$	14.0415			0.521848
$725$	−10.9349			−0.406110
$726$		−	5.75065i		−	0.213427i
$727$	20.8988			0.775092			0.387546	−	0.921850i	$-0.373323\pi$
$727$	20.8988			0.775092			0.387546	+	0.921850i	$0.373323\pi$
$728$	−8.72393	−	0.755569i	−0.323330	−	0.0280032i
$729$	−4.96836			−0.184013
$730$			12.8222i			0.474573i
$731$	31.6336			1.17001
$732$	−30.5718			−1.12997
$733$			19.3575i			0.714986i	0.933916	+	0.357493i	$0.116368\pi$
$733$			19.3575i			0.714986i	−0.933916	+	0.357493i	$0.883632\pi$
$734$			2.02413i			0.0747122i
$735$			7.11753i			0.262534i
$736$			19.0509i			0.702224i
$737$	1.15257			0.0424553
$738$	−0.990632			−0.0364657
$739$			1.31111i			0.0482299i	0.999709	+	0.0241149i	$0.00767677\pi$
$739$			1.31111i			0.0482299i	−0.999709	+	0.0241149i	$0.992323\pi$
$740$	19.2859			0.708964
$741$	−5.88739	+	67.9768i	−0.216279	+	2.49719i
$742$	−1.73975			−0.0638681
$743$		−	21.5210i		−	0.789528i	−0.918783	−	0.394764i	$-0.870826\pi$
$743$		−	21.5210i		−	0.789528i	0.918783	−	0.394764i	$-0.129174\pi$
$744$	31.3876			1.15073
$745$	46.7259			1.71191
$746$		−	12.9304i		−	0.473416i
$747$		−	20.6064i		−	0.753949i
$748$			14.7338i			0.538720i
$749$		−	18.1891i		−	0.664616i
$750$	−1.62714			−0.0594147
$751$	16.3176			0.595436			0.297718	−	0.954654i	$-0.403774\pi$
$751$	16.3176			0.595436			0.297718	+	0.954654i	$0.403774\pi$
$752$		−	2.59364i		−	0.0945802i
$753$	7.30021			0.266034
$754$	−0.439539	+	5.07499i	−0.0160071	+	0.184820i
$755$	−64.2054			−2.33667
$756$			3.70471i			0.134739i
$757$	−18.7462			−0.681342			−0.340671	−	0.940183i	$-0.610654\pi$
$757$	−18.7462			−0.681342			−0.340671	+	0.940183i	$0.610654\pi$
$758$	−16.3194			−0.592748
$759$			19.5353i			0.709085i
$760$			66.7150i			2.42001i
$761$			10.2968i			0.373259i	0.982430	+	0.186630i	$0.0597564\pi$
$761$			10.2968i			0.373259i	−0.982430	+	0.186630i	$0.940244\pi$
$762$			6.23506i			0.225873i
$763$	−8.36196			−0.302723
$764$	−10.1718			−0.368002
$765$		−	21.9748i		−	0.794501i
$766$	−21.7778			−0.786865
$767$	2.28100	−	26.3368i	0.0823620	−	0.950966i
$768$	21.9180			0.790897
$769$			9.36641i			0.337761i	0.985637	+	0.168881i	$0.0540153\pi$
$769$			9.36641i			0.337761i	−0.985637	+	0.168881i	$0.945985\pi$
$770$	−5.95407			−0.214570
$771$	−52.4657			−1.88951
$772$		−	31.4291i		−	1.13116i
$773$		−	3.71456i		−	0.133603i	−0.997766	−	0.0668017i	$-0.978721\pi$
$773$		−	3.71456i		−	0.133603i	0.997766	−	0.0668017i	$-0.0212795\pi$
$774$		−	11.5462i		−	0.415019i
$775$		−	31.1195i		−	1.11785i
$776$	−23.3846			−0.839457
$777$	−8.70964			−0.312456
$778$			13.8163i			0.495337i
$779$	6.45722			0.231354
$780$	3.37778	−	39.0005i	0.120944	−	1.39644i
$781$	24.1575			0.864423
$782$		−	8.11906i		−	0.290337i
$783$	4.98079			0.177999
$784$	−1.37778			−0.0492066
$785$			23.7812i			0.848789i
$786$		−	9.06070i		−	0.323184i
$787$		−	6.23659i		−	0.222311i	−0.993803	−	0.111155i	$-0.964545\pi$
$787$		−	6.23659i		−	0.222311i	0.993803	−	0.111155i	$-0.0354551\pi$
$788$		−	12.7654i		−	0.454749i
$789$	−22.1225			−0.787580
$790$	9.91903			0.352903
$791$		−	8.46520i		−	0.300988i
$792$	12.4286			0.441632
$793$	32.5116	+	2.81579i	1.15452	+	0.0999917i
$794$	15.7571			0.559199
$795$		−	17.9748i		−	0.637501i
$796$	0.917502			0.0325200
$797$	40.0701			1.41935			0.709677	−	0.704527i	$-0.248841\pi$
$797$	40.0701			1.41935			0.709677	+	0.704527i	$0.248841\pi$
$798$		−	13.0366i		−	0.461489i
$799$			6.76202i			0.239223i
$800$		−	30.9590i		−	1.09457i
$801$		−	10.2050i		−	0.360574i
$802$	−3.86665			−0.136536
$803$	−15.5703			−0.549464
$804$		−	1.44785i		−	0.0510618i
$805$	−10.5462			−0.371704
$806$	−14.4429	−	1.25088i	−0.508730	−	0.0440605i
$807$	40.3082			1.41892
$808$		−	33.2573i		−	1.16999i
$809$	−2.57136			−0.0904042			−0.0452021	−	0.998978i	$-0.514393\pi$
$809$	−2.57136			−0.0904042			−0.0452021	+	0.998978i	$0.514393\pi$
$810$	24.5511			0.862637
$811$		−	28.3654i		−	0.996042i	−0.867165	−	0.498021i	$-0.834060\pi$
$811$		−	28.3654i		−	0.996042i	0.867165	−	0.498021i	$-0.165940\pi$
$812$			3.12843i			0.109786i
$813$		−	53.5308i		−	1.87741i
$814$		−	7.28592i		−	0.255371i
$815$	7.47949			0.261995
$816$	10.9590			0.383641
$817$			75.2612i			2.63306i
$818$	17.9922			0.629081
$819$	−0.592104	+	6.83654i	−0.0206898	+	0.238888i
$820$	−3.70471			−0.129374
$821$		−	31.7846i		−	1.10929i	−0.832087	−	0.554646i	$-0.812854\pi$
$821$		−	31.7846i		−	1.10929i	0.832087	−	0.554646i	$-0.187146\pi$
$822$	−24.9590			−0.870545
$823$	−30.9131			−1.07756			−0.538781	−	0.842446i	$-0.681115\pi$
$823$	−30.9131			−1.07756			−0.538781	+	0.842446i	$0.681115\pi$
$824$		−	29.8608i		−	1.04025i
$825$		−	31.7462i		−	1.10526i
$826$			5.05086i			0.175742i
$827$		−	49.7560i		−	1.73019i	−0.501610	−	0.865094i	$-0.667259\pi$
$827$		−	49.7560i		−	1.73019i	0.501610	−	0.865094i	$-0.332741\pi$
$828$	9.52543			0.331031
$829$	19.9190			0.691817			0.345908	−	0.938268i	$-0.387571\pi$
$829$	19.9190			0.691817			0.345908	+	0.938268i	$0.387571\pi$
$830$			23.9748i			0.832178i
$831$	3.75404			0.130226
$832$	−4.47013	−	0.387152i	−0.154974	−	0.0134221i
$833$	3.59210			0.124459
$834$		−	4.62222i		−	0.160054i
$835$	−11.0000			−0.380671
$836$	−35.0539			−1.21237
$837$			14.1748i			0.489954i
$838$		−	17.3921i		−	0.600799i
$839$		−	11.5625i		−	0.399181i	−0.979879	−	0.199590i	$-0.936039\pi$
$839$		−	11.5625i		−	0.399181i	0.979879	−	0.199590i	$-0.0639611\pi$
$840$			17.2859i			0.596421i
$841$	−24.7940			−0.854965
$842$	5.66862			0.195354
$843$			25.7921i			0.888328i
$844$	−2.90321			−0.0999327
$845$	−7.18421	+	41.1639i	−0.247144	+	1.41608i
$846$	2.46812			0.0848557
$847$			3.76986i			0.129534i
$848$	3.47949			0.119486
$849$	26.8671			0.922077
$850$			13.1941i			0.452552i
$851$		−	12.9052i		−	0.442385i
$852$		−	30.3466i		−	1.03966i
$853$		−	1.74467i		−	0.0597363i	−0.999554	−	0.0298682i	$-0.990491\pi$
$853$		−	1.74467i		−	0.0597363i	0.999554	−	0.0298682i	$-0.00950875\pi$
$854$	−6.23506			−0.213359
$855$	52.2815			1.78799
$856$		−	44.1748i		−	1.50986i
$857$	42.3368			1.44620			0.723098	−	0.690745i	$-0.242717\pi$
$857$	42.3368			1.44620			0.723098	+	0.690745i	$0.242717\pi$
$858$	−14.7338	−	1.27607i	−0.503003	−	0.0435645i
$859$	−5.37778			−0.183488			−0.0917438	−	0.995783i	$-0.529244\pi$
$859$	−5.37778			−0.183488			−0.0917438	+	0.995783i	$0.529244\pi$
$860$		−	43.1798i		−	1.47242i
$861$	1.67307			0.0570181
$862$	0.990632			0.0337411
$863$			15.4291i			0.525213i	0.964903	+	0.262607i	$0.0845821\pi$
$863$			15.4291i			0.525213i	−0.964903	+	0.262607i	$0.915418\pi$
$864$			14.1017i			0.479750i
$865$		−	26.5970i		−	0.904326i
$866$			11.3679i			0.386298i
$867$	9.07160			0.308088
$868$	−8.90321			−0.302195
$869$			12.0449i			0.408595i
$870$	10.0558			0.340923
$871$	−0.133353	+	1.53972i	−0.00451850	+	0.0521713i
$872$	−20.3082			−0.687722
$873$			18.3254i			0.620221i
$874$	19.3165			0.653391
$875$	1.06668			0.0360602
$876$			19.5594i			0.660851i
$877$			38.5181i			1.30066i	0.759651	+	0.650331i	$0.225370\pi$
$877$			38.5181i			1.30066i	−0.759651	+	0.650331i	$0.774630\pi$
$878$			7.00048i			0.236255i
$879$			25.3624i			0.855454i
$880$	11.9081			0.401423
$881$	41.7373			1.40617			0.703083	−	0.711108i	$-0.251806\pi$
$881$	41.7373			1.40617			0.703083	+	0.711108i	$0.251806\pi$
$882$		−	1.31111i		−	0.0441473i
$883$	−52.8439			−1.77834			−0.889170	−	0.457577i	$-0.848717\pi$
$883$	−52.8439			−1.77834			−0.889170	+	0.457577i	$0.848717\pi$
$884$	−19.6829	−	1.70471i	−0.662008	−	0.0573357i
$885$	−52.1847			−1.75417
$886$			2.20987i			0.0742422i
$887$	8.99063			0.301876			0.150938	−	0.988543i	$-0.451771\pi$
$887$	8.99063			0.301876			0.150938	+	0.988543i	$0.451771\pi$
$888$	−21.1526			−0.709834
$889$		−	4.08742i		−	0.137088i
$890$			11.8731i			0.397987i
$891$			29.8129i			0.998769i
$892$			16.2208i			0.543112i
$893$	−16.0879			−0.538361
$894$	−22.1748			−0.741638
$895$			52.1546i			1.74334i
$896$	−10.7556			−0.359318
$897$	−26.0973	−	2.26025i	−0.871362	−	0.0754676i
$898$	−12.6824			−0.423218
$899$			11.9699i			0.399218i
$900$	−15.4795			−0.515983
$901$	−9.07160			−0.302219
$902$			1.39958i			0.0466010i
$903$			19.5002i			0.648927i
$904$		−	20.5589i		−	0.683780i
$905$			29.5877i			0.983527i
$906$	30.4701			1.01230
$907$	20.7003			0.687341			0.343671	−	0.939090i	$-0.388330\pi$
$907$	20.7003			0.687341			0.343671	+	0.939090i	$0.388330\pi$
$908$			22.9590i			0.761921i
$909$	−26.0622			−0.864430
$910$	0.688892	−	7.95407i	0.0228366	−	0.263675i
$911$	29.8988			0.990590			0.495295	−	0.868725i	$-0.335060\pi$
$911$	29.8988			0.990590			0.495295	+	0.868725i	$0.335060\pi$
$912$			26.0731i			0.863368i
$913$	−29.1131			−0.963503
$914$	−2.34428			−0.0775420
$915$		−	64.4197i		−	2.12965i
$916$			9.96836i			0.329364i
$917$			5.93978i			0.196149i
$918$		−	6.00984i		−	0.198354i
$919$	38.5847			1.27279			0.636397	−	0.771362i	$-0.280424\pi$
$919$	38.5847			1.27279			0.636397	+	0.771362i	$0.280424\pi$
$920$	−25.6128			−0.844431
$921$			8.79060i			0.289660i
$922$	−12.1048			−0.398649
$923$	−2.79505	+	32.2721i	−0.0920001	+	1.06225i
$924$	−9.08250			−0.298792
$925$			20.9719i			0.689552i
$926$	10.8648			0.357039
$927$	−23.4005			−0.768574
$928$			11.9081i			0.390904i
$929$			3.25581i			0.106820i	0.998573	+	0.0534098i	$0.0170090\pi$
$929$			3.25581i			0.106820i	−0.998573	+	0.0534098i	$0.982991\pi$
$930$			28.6178i			0.938414i
$931$			8.54617i			0.280089i
$932$	42.6494			1.39703
$933$	60.5575			1.98257
$934$			2.59502i			0.0849116i
$935$	−31.0464			−1.01533
$936$	−1.43801	+	16.6035i	−0.0470027	+	0.542702i
$937$	−11.6840			−0.381699			−0.190849	−	0.981619i	$-0.561124\pi$
$937$	−11.6840			−0.381699			−0.190849	+	0.981619i	$0.561124\pi$
$938$		−	0.295286i		−	0.00964144i
$939$	42.3007			1.38043
$940$	9.23014			0.301054
$941$		−	41.9699i		−	1.36818i	−0.729398	−	0.684090i	$-0.760200\pi$
$941$		−	41.9699i		−	1.36818i	0.729398	−	0.684090i	$-0.239800\pi$
$942$		−	11.2859i		−	0.367715i
$943$			2.47902i			0.0807279i
$944$		−	10.1017i		−	0.328783i
$945$	−7.80642			−0.253943
$946$	−16.3126			−0.530370
$947$			20.3555i			0.661465i	0.943725	+	0.330733i	$0.107296\pi$
$947$			20.3555i			0.661465i	−0.943725	+	0.330733i	$0.892704\pi$
$948$	15.1308			0.491424
$949$	1.80150	−	20.8004i	0.0584792	−	0.675211i
$950$	−31.3907			−1.01845
$951$		−	21.9398i		−	0.711446i
$952$	8.72393			0.282744
$953$	30.5496			0.989597			0.494799	−	0.869008i	$-0.335242\pi$
$953$	30.5496			0.989597			0.494799	+	0.869008i	$0.335242\pi$
$954$			3.31111i			0.107201i
$955$		−	21.4336i		−	0.693574i
$956$		−	29.8697i		−	0.966055i
$957$			12.2109i			0.394723i
$958$	−8.33783			−0.269383
$959$	16.3620			0.528355
$960$			8.85728i			0.285867i
$961$	−3.06515			−0.0988757
$962$	9.73329	+	0.842989i	0.313814	+	0.0271791i
$963$	−34.6178			−1.11554
$964$			20.3759i			0.656264i
$965$	66.2262			2.13190
$966$	5.00492			0.161031
$967$			54.4548i			1.75115i	0.483084	+	0.875574i	$0.339516\pi$
$967$			54.4548i			1.75115i	−0.483084	+	0.875574i	$0.660484\pi$
$968$			9.15563i			0.294273i
$969$		−	67.9768i		−	2.18373i
$970$		−	21.3210i		−	0.684575i
$971$	−54.6035			−1.75231			−0.876155	−	0.482030i	$-0.839899\pi$
$971$	−54.6035			−1.75231			−0.876155	+	0.482030i	$0.839899\pi$
$972$	26.3368			0.844752
$973$			3.03011i			0.0971409i
$974$	11.9714			0.383589
$975$	42.4099	+	3.67307i	1.35820	+	0.117632i
$976$	12.4701			0.399159
$977$			32.6474i			1.04448i	0.852798	+	0.522242i	$0.174904\pi$
$977$			32.6474i			1.04448i	−0.852798	+	0.522242i	$0.825096\pi$
$978$	−3.54956			−0.113502
$979$	−14.4177			−0.460793
$980$		−	4.90321i		−	0.156627i
$981$			15.9146i			0.508114i
$982$			13.3590i			0.426304i
$983$			27.5052i			0.877278i	0.898663	+	0.438639i	$0.144539\pi$
$983$			27.5052i			0.877278i	−0.898663	+	0.438639i	$0.855461\pi$
$984$	4.06329			0.129533
$985$	26.8988			0.857066
$986$		−	5.07499i		−	0.161621i
$987$	−4.16839			−0.132681
$988$	4.05578	−	46.8287i	0.129031	−	1.48982i
$989$	−28.8938			−0.918771
$990$			11.3319i			0.360150i
$991$	−6.29390			−0.199932			−0.0999662	−	0.994991i	$-0.531873\pi$
$991$	−6.29390			−0.199932			−0.0999662	+	0.994991i	$0.531873\pi$
$992$	−33.8894			−1.07599
$993$		−	51.8578i		−	1.64566i
$994$		−	6.18913i		−	0.196307i
$995$			1.93332i			0.0612905i
$996$			36.5718i			1.15882i
$997$	−20.8702			−0.660965			−0.330483	−	0.943812i	$-0.607212\pi$
$997$	−20.8702			−0.660965			−0.330483	+	0.943812i	$0.607212\pi$
$998$	7.35059			0.232679
$999$		−	9.55262i		−	0.302232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.c.a.64.4	yes	6
3.2	odd	2		819.2.c.b.64.3		6
4.3	odd	2		1456.2.k.c.337.6		6
7.2	even	3		637.2.r.e.116.4		12
7.3	odd	6		637.2.r.d.324.3		12
7.4	even	3		637.2.r.e.324.3		12
7.5	odd	6		637.2.r.d.116.4		12
7.6	odd	2		637.2.c.d.246.4		6
13.5	odd	4		1183.2.a.j.1.2		3
13.8	odd	4		1183.2.a.h.1.2		3
13.12	even	2	inner	91.2.c.a.64.3	✓	6
39.38	odd	2		819.2.c.b.64.4		6
52.51	odd	2		1456.2.k.c.337.5		6
91.12	odd	6		637.2.r.d.116.3		12
91.25	even	6		637.2.r.e.324.4		12
91.34	even	4		8281.2.a.be.1.2		3
91.38	odd	6		637.2.r.d.324.4		12
91.51	even	6		637.2.r.e.116.3		12
91.83	even	4		8281.2.a.bi.1.2		3
91.90	odd	2		637.2.c.d.246.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.3	✓	6	13.12	even	2	inner
91.2.c.a.64.4	yes	6	1.1	even	1	trivial
637.2.c.d.246.3		6	91.90	odd	2
637.2.c.d.246.4		6	7.6	odd	2
637.2.r.d.116.3		12	91.12	odd	6
637.2.r.d.116.4		12	7.5	odd	6
637.2.r.d.324.3		12	7.3	odd	6
637.2.r.d.324.4		12	91.38	odd	6
637.2.r.e.116.3		12	91.51	even	6
637.2.r.e.116.4		12	7.2	even	3
637.2.r.e.324.3		12	7.4	even	3
637.2.r.e.324.4		12	91.25	even	6
819.2.c.b.64.3		6	3.2	odd	2
819.2.c.b.64.4		6	39.38	odd	2
1183.2.a.h.1.2		3	13.8	odd	4
1183.2.a.j.1.2		3	13.5	odd	4
1456.2.k.c.337.5		6	52.51	odd	2
1456.2.k.c.337.6		6	4.3	odd	2
8281.2.a.be.1.2		3	91.34	even	4
8281.2.a.bi.1.2		3	91.83	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} +O(q^{10})\)	\(q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} -2.21432 q^{10} -2.68889i q^{11} -3.37778 q^{12} +(3.59210 + 0.311108i) q^{13} -0.688892 q^{14} -7.11753i q^{15} +1.37778 q^{16} -3.59210 q^{17} +1.31111i q^{18} -8.54617i q^{19} +4.90321i q^{20} -2.21432i q^{21} +1.85236 q^{22} +3.28100 q^{23} -5.37778i q^{24} -5.33185 q^{25} +(-0.214320 + 2.47457i) q^{26} +2.42864 q^{27} +1.52543i q^{28} +2.05086 q^{29} +4.90321 q^{30} +5.83654i q^{31} +5.80642i q^{32} +5.95407i q^{33} -2.47457i q^{34} -3.21432 q^{35} +2.90321 q^{36} -3.93332i q^{37} +5.88739 q^{38} +(-7.95407 - 0.688892i) q^{39} -7.80642 q^{40} +0.755569i q^{41} +1.52543 q^{42} -8.80642 q^{43} -4.10171i q^{44} +6.11753i q^{45} +2.26025i q^{46} -1.88247i q^{47} -3.05086 q^{48} -1.00000 q^{49} -3.67307i q^{50} +7.95407 q^{51} +(5.47949 + 0.474572i) q^{52} +2.52543 q^{53} +1.67307i q^{54} +8.64296 q^{55} -2.42864 q^{56} +18.9240i q^{57} +1.41282i q^{58} -7.33185i q^{59} -10.8573i q^{60} +9.05086 q^{61} -4.02074 q^{62} +1.90321i q^{63} -1.24443 q^{64} +(-1.00000 + 11.5462i) q^{65} -4.10171 q^{66} +0.428639i q^{67} -5.47949 q^{68} -7.26517 q^{69} -2.21432i q^{70} +8.98418i q^{71} +4.62222i q^{72} -5.79060i q^{73} +2.70964 q^{74} +11.8064 q^{75} -13.0366i q^{76} +2.68889 q^{77} +(0.474572 - 5.47949i) q^{78} -4.47949 q^{79} +4.42864i q^{80} -11.0874 q^{81} -0.520505 q^{82} -10.8272i q^{83} -3.37778i q^{84} -11.5462i q^{85} -6.06668i q^{86} -4.54125 q^{87} +6.53035 q^{88} -5.36196i q^{89} -4.21432 q^{90} +(-0.311108 + 3.59210i) q^{91} +5.00492 q^{92} -12.9240i q^{93} +1.29682 q^{94} +27.4701 q^{95} -12.8573i q^{96} +9.62867i q^{97} -0.688892i q^{98} -5.11753i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} - 2 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 - 2 * q^9	\( 6 q - 4 q^{4} - 2 q^{9} - 20 q^{12} + 8 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} + 24 q^{22} + 6 q^{23} + 8 q^{25} + 12 q^{26} - 12 q^{27} - 14 q^{29} + 16 q^{30} - 6 q^{35} + 4 q^{36} - 4 q^{38} - 8 q^{39} - 20 q^{40} - 4 q^{42} - 26 q^{43} + 8 q^{48} - 6 q^{49} + 8 q^{51} - 20 q^{52} + 2 q^{53} + 12 q^{55} + 12 q^{56} + 28 q^{61} + 16 q^{62} - 8 q^{64} - 6 q^{65} + 28 q^{66} + 20 q^{68} - 4 q^{69} - 24 q^{74} + 44 q^{75} + 16 q^{77} + 16 q^{78} + 26 q^{79} - 26 q^{81} - 56 q^{82} - 40 q^{87} - 40 q^{88} - 12 q^{90} - 2 q^{91} - 36 q^{92} + 20 q^{94} + 58 q^{95}+O(q^{100}) \) 6 * q - 4 * q^4 - 2 * q^9 - 20 * q^12 + 8 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 + 24 * q^22 + 6 * q^23 + 8 * q^25 + 12 * q^26 - 12 * q^27 - 14 * q^29 + 16 * q^30 - 6 * q^35 + 4 * q^36 - 4 * q^38 - 8 * q^39 - 20 * q^40 - 4 * q^42 - 26 * q^43 + 8 * q^48 - 6 * q^49 + 8 * q^51 - 20 * q^52 + 2 * q^53 + 12 * q^55 + 12 * q^56 + 28 * q^61 + 16 * q^62 - 8 * q^64 - 6 * q^65 + 28 * q^66 + 20 * q^68 - 4 * q^69 - 24 * q^74 + 44 * q^75 + 16 * q^77 + 16 * q^78 + 26 * q^79 - 26 * q^81 - 56 * q^82 - 40 * q^87 - 40 * q^88 - 12 * q^90 - 2 * q^91 - 36 * q^92 + 20 * q^94 + 58 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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