LMFDB - Embedded newform 354.2.c.a.353.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.41542366334681088.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 + 2x^6 + 14x^5 + 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.5
Root			$-0.0738304 - 1.73048i$ of defining polynomial
Character	$\chi$	$=$	354.353
Dual form			354.2.c.a.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.0738304 - 1.73048i) q^{3} +1.00000 q^{4} -2.30520i q^{5} +(-0.0738304 + 1.73048i) q^{6} +3.25240 q^{7} -1.00000 q^{8} +(-2.98910 - 0.255524i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.0738304 - 1.73048i) q^{3} +1.00000 q^{4} -2.30520i q^{5} +(-0.0738304 + 1.73048i) q^{6} +3.25240 q^{7} -1.00000 q^{8} +(-2.98910 - 0.255524i) q^{9} +2.30520i q^{10} +4.56636 q^{11} +(0.0738304 - 1.73048i) q^{12} -2.44397i q^{13} -3.25240 q^{14} +(-3.98910 - 0.170194i) q^{15} +1.00000 q^{16} +2.52929i q^{17} +(2.98910 + 0.255524i) q^{18} -1.31396 q^{19} -2.30520i q^{20} +(0.240126 - 5.62821i) q^{21} -4.56636 q^{22} -8.45845 q^{23} +(-0.0738304 + 1.73048i) q^{24} -0.313957 q^{25} +2.44397i q^{26} +(-0.662864 + 5.15370i) q^{27} +3.25240 q^{28} -7.58278i q^{29} +(3.98910 + 0.170194i) q^{30} +1.81032i q^{31} -1.00000 q^{32} +(0.337136 - 7.90198i) q^{33} -2.52929i q^{34} -7.49745i q^{35} +(-2.98910 - 0.255524i) q^{36} +2.83361i q^{37} +1.31396 q^{38} +(-4.22922 - 0.180439i) q^{39} +2.30520i q^{40} +5.77722i q^{41} +(-0.240126 + 5.62821i) q^{42} -11.5497i q^{43} +4.56636 q^{44} +(-0.589033 + 6.89048i) q^{45} +8.45845 q^{46} +0.674272 q^{47} +(0.0738304 - 1.73048i) q^{48} +3.57813 q^{49} +0.313957 q^{50} +(4.37689 + 0.186739i) q^{51} -2.44397i q^{52} +8.22118i q^{53} +(0.662864 - 5.15370i) q^{54} -10.5264i q^{55} -3.25240 q^{56} +(-0.0970099 + 2.27377i) q^{57} +7.58278i q^{58} +(7.51658 + 1.58147i) q^{59} +(-3.98910 - 0.170194i) q^{60} +0.133657i q^{61} -1.81032i q^{62} +(-9.72175 - 0.831066i) q^{63} +1.00000 q^{64} -5.63383 q^{65} +(-0.337136 + 7.90198i) q^{66} -3.33360i q^{67} +2.52929i q^{68} +(-0.624491 + 14.6371i) q^{69} +7.49745i q^{70} +6.35743i q^{71} +(2.98910 + 0.255524i) q^{72} +13.4703i q^{73} -2.83361i q^{74} +(-0.0231795 + 0.543295i) q^{75} -1.31396 q^{76} +14.8516 q^{77} +(4.22922 + 0.180439i) q^{78} +11.0366 q^{79} -2.30520i q^{80} +(8.86942 + 1.52757i) q^{81} -5.77722i q^{82} -9.52592 q^{83} +(0.240126 - 5.62821i) q^{84} +5.83054 q^{85} +11.5497i q^{86} +(-13.1218 - 0.559839i) q^{87} -4.56636 q^{88} +4.28529 q^{89} +(0.589033 - 6.89048i) q^{90} -7.94876i q^{91} -8.45845 q^{92} +(3.13272 + 0.133657i) q^{93} -0.674272 q^{94} +3.02894i q^{95} +(-0.0738304 + 1.73048i) q^{96} +8.58240i q^{97} -3.57813 q^{98} +(-13.6493 - 1.16681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - q^{3} + 10 q^{4} + q^{6} - 2 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - q^3 + 10 * q^4 + q^6 - 2 * q^7 - 10 * q^8 + 3 * q^9	$ 10 q - 10 q^{2} - q^{3} + 10 q^{4} + q^{6} - 2 q^{7} - 10 q^{8} + 3 q^{9} + 4 q^{11} - q^{12} + 2 q^{14} - 7 q^{15} + 10 q^{16} - 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} - 8 q^{23} + q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} + 7 q^{30} - 10 q^{32} + 3 q^{36} + 6 q^{38} - 4 q^{39} + 3 q^{42} + 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} - 4 q^{50} + 2 q^{51} + 10 q^{54} + 2 q^{56} - 3 q^{57} + 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} + 16 q^{65} + 14 q^{69} - 3 q^{72} - 4 q^{75} - 6 q^{76} + 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} + 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} - 16 q^{89} + 11 q^{90} - 8 q^{92} - 52 q^{93} + q^{96} - 8 q^{98} + 2 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 - q^3 + 10 * q^4 + q^6 - 2 * q^7 - 10 * q^8 + 3 * q^9 + 4 * q^11 - q^12 + 2 * q^14 - 7 * q^15 + 10 * q^16 - 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 - 8 * q^23 + q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 + 7 * q^30 - 10 * q^32 + 3 * q^36 + 6 * q^38 - 4 * q^39 + 3 * q^42 + 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 - 4 * q^50 + 2 * q^51 + 10 * q^54 + 2 * q^56 - 3 * q^57 + 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 + 16 * q^65 + 14 * q^69 - 3 * q^72 - 4 * q^75 - 6 * q^76 + 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 + 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 - 16 * q^89 + 11 * q^90 - 8 * q^92 - 52 * q^93 + q^96 - 8 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.0738304	−	1.73048i	0.0426260	−	0.999091i
$3$	0.0738304	−	1.73048i	0.0426260	−	0.999091i
$4$	1.00000			0.500000
$5$		−	2.30520i		−	1.03092i	−0.856914	−	0.515459i	$-0.827621\pi$
$5$		−	2.30520i		−	1.03092i	0.856914	−	0.515459i	$-0.172379\pi$
$6$	−0.0738304	+	1.73048i	−0.0301411	+	0.706464i
$7$	3.25240			1.22929			0.614647	−	0.788803i	$-0.289299\pi$
$7$	3.25240			1.22929			0.614647	+	0.788803i	$0.289299\pi$
$8$	−1.00000			−0.353553
$9$	−2.98910	−	0.255524i	−0.996366	−	0.0851745i
$10$			2.30520i			0.728969i
$11$	4.56636			1.37681			0.688405	−	0.725327i	$-0.258311\pi$
$11$	4.56636			1.37681			0.688405	+	0.725327i	$0.258311\pi$
$12$	0.0738304	−	1.73048i	0.0213130	−	0.499546i
$13$		−	2.44397i		−	0.677834i	−0.940816	−	0.338917i	$-0.889939\pi$
$13$		−	2.44397i		−	0.677834i	0.940816	−	0.338917i	$-0.110061\pi$
$14$	−3.25240			−0.869242
$15$	−3.98910	−	0.170194i	−1.02998	−	0.0439439i
$16$	1.00000			0.250000
$17$			2.52929i			0.613444i	0.951799	+	0.306722i	$0.0992322\pi$
$17$			2.52929i			0.613444i	−0.951799	+	0.306722i	$0.900768\pi$
$18$	2.98910	+	0.255524i	0.704537	+	0.0602275i
$19$	−1.31396			−0.301442			−0.150721	−	0.988576i	$-0.548160\pi$
$19$	−1.31396			−0.301442			−0.150721	+	0.988576i	$0.548160\pi$
$20$		−	2.30520i		−	0.515459i
$21$	0.240126	−	5.62821i	0.0523998	−	1.22818i
$22$	−4.56636			−0.973551
$23$	−8.45845			−1.76371			−0.881854	−	0.471522i	$-0.843705\pi$
$23$	−8.45845			−1.76371			−0.881854	+	0.471522i	$0.843705\pi$
$24$	−0.0738304	+	1.73048i	−0.0150706	+	0.353232i
$25$	−0.313957			−0.0627913
$26$			2.44397i			0.479301i
$27$	−0.662864	+	5.15370i	−0.127568	+	0.991830i
$28$	3.25240			0.614647
$29$		−	7.58278i		−	1.40809i	−0.710157	−	0.704043i	$-0.751376\pi$
$29$		−	7.58278i		−	1.40809i	0.710157	−	0.704043i	$-0.248624\pi$
$30$	3.98910	+	0.170194i	0.728306	+	0.0310730i
$31$			1.81032i			0.325144i	0.986697	+	0.162572i	$0.0519789\pi$
$31$			1.81032i			0.325144i	−0.986697	+	0.162572i	$0.948021\pi$
$32$	−1.00000			−0.176777
$33$	0.337136	−	7.90198i	0.0586879	−	1.37556i
$34$		−	2.52929i		−	0.433770i
$35$		−	7.49745i		−	1.26730i
$36$	−2.98910	−	0.255524i	−0.498183	−	0.0425873i
$37$			2.83361i			0.465843i	0.972496	+	0.232921i	$0.0748285\pi$
$37$			2.83361i			0.465843i	−0.972496	+	0.232921i	$0.925172\pi$
$38$	1.31396			0.213152
$39$	−4.22922	−	0.180439i	−0.677218	−	0.0288934i
$40$			2.30520i			0.364484i
$41$			5.77722i			0.902250i	0.892461	+	0.451125i	$0.148977\pi$
$41$			5.77722i			0.902250i	−0.892461	+	0.451125i	$0.851023\pi$
$42$	−0.240126	+	5.62821i	−0.0370523	+	0.868451i
$43$		−	11.5497i		−	1.76131i	−0.473760	−	0.880654i	$-0.657103\pi$
$43$		−	11.5497i		−	1.76131i	0.473760	−	0.880654i	$-0.342897\pi$
$44$	4.56636			0.688405
$45$	−0.589033	+	6.89048i	−0.0878079	+	1.02717i
$46$	8.45845			1.24713
$47$	0.674272			0.0983527			0.0491764	−	0.998790i	$-0.484340\pi$
$47$	0.674272			0.0983527			0.0491764	+	0.998790i	$0.484340\pi$
$48$	0.0738304	−	1.73048i	0.0106565	−	0.249773i
$49$	3.57813			0.511162
$50$	0.313957			0.0444002
$51$	4.37689	+	0.186739i	0.612887	+	0.0261487i
$52$		−	2.44397i		−	0.338917i
$53$			8.22118i			1.12927i	0.825342	+	0.564633i	$0.190982\pi$
$53$			8.22118i			1.12927i	−0.825342	+	0.564633i	$0.809018\pi$
$54$	0.662864	−	5.15370i	0.0902043	−	0.701330i
$55$		−	10.5264i		−	1.41938i
$56$	−3.25240			−0.434621
$57$	−0.0970099	+	2.27377i	−0.0128493	+	0.301168i
$58$			7.58278i			0.995668i
$59$	7.51658	+	1.58147i	0.978575	+	0.205890i
$59$	7.51658	+	1.58147i	0.978575	+	0.205890i
$60$	−3.98910	−	0.170194i	−0.514990	−	0.0219719i
$61$			0.133657i			0.0171130i	0.999963	+	0.00855650i	$0.00272365\pi$
$61$			0.133657i			0.0171130i	−0.999963	+	0.00855650i	$0.997276\pi$
$62$		−	1.81032i		−	0.229911i
$63$	−9.72175	−	0.831066i	−1.22483	−	0.104704i
$64$	1.00000			0.125000
$65$	−5.63383			−0.698791
$66$	−0.337136	+	7.90198i	−0.0414986	+	0.972666i
$67$		−	3.33360i		−	0.407264i	−0.979048	−	0.203632i	$-0.934725\pi$
$67$		−	3.33360i		−	0.407264i	0.979048	−	0.203632i	$-0.0652745\pi$
$68$			2.52929i			0.306722i
$69$	−0.624491	+	14.6371i	−0.0751798	+	1.76211i
$70$			7.49745i			0.896116i
$71$			6.35743i			0.754488i	0.926114	+	0.377244i	$0.123128\pi$
$71$			6.35743i			0.754488i	−0.926114	+	0.377244i	$0.876872\pi$
$72$	2.98910	+	0.255524i	0.352269	+	0.0301137i
$73$			13.4703i			1.57658i	0.615302	+	0.788292i	$0.289034\pi$
$73$			13.4703i			1.57658i	−0.615302	+	0.788292i	$0.710966\pi$
$74$		−	2.83361i		−	0.329401i
$75$	−0.0231795	+	0.543295i	−0.00267654	+	0.0627343i
$76$	−1.31396			−0.150721
$77$	14.8516			1.69250
$78$	4.22922	+	0.180439i	0.478865	+	0.0204307i
$79$	11.0366			1.24171			0.620856	−	0.783925i	$-0.286785\pi$
$79$	11.0366			1.24171			0.620856	+	0.783925i	$0.286785\pi$
$80$		−	2.30520i		−	0.257729i
$81$	8.86942	+	1.52757i	0.985491	+	0.169730i
$82$		−	5.77722i		−	0.637987i
$83$	−9.52592			−1.04561			−0.522803	−	0.852454i	$-0.675114\pi$
$83$	−9.52592			−1.04561			−0.522803	+	0.852454i	$0.675114\pi$
$84$	0.240126	−	5.62821i	0.0261999	−	0.614088i
$85$	5.83054			0.632410
$86$			11.5497i			1.24543i
$87$	−13.1218	−	0.559839i	−1.40681	−	0.0600211i
$88$	−4.56636			−0.486776
$89$	4.28529			0.454240			0.227120	−	0.973867i	$-0.427069\pi$
$89$	4.28529			0.454240			0.227120	+	0.973867i	$0.427069\pi$
$90$	0.589033	−	6.89048i	0.0620896	−	0.726320i
$91$		−	7.94876i		−	0.833257i
$92$	−8.45845			−0.881854
$93$	3.13272	+	0.133657i	0.324848	+	0.0138596i
$94$	−0.674272			−0.0695459
$95$			3.02894i			0.310762i
$96$	−0.0738304	+	1.73048i	−0.00753528	+	0.176616i
$97$			8.58240i			0.871411i	0.900089	+	0.435706i	$0.143501\pi$
$97$			8.58240i			0.871411i	−0.900089	+	0.435706i	$0.856499\pi$
$98$	−3.57813			−0.361446
$99$	−13.6493	−	1.16681i	−1.37181	−	0.117269i
$100$	−0.313957			−0.0313957
$101$	8.85165			0.880772			0.440386	−	0.897809i	$-0.354842\pi$
$101$	8.85165			0.880772			0.440386	+	0.897809i	$0.354842\pi$
$102$	−4.37689	−	0.186739i	−0.433376	−	0.0184899i
$103$		−	13.6040i		−	1.34044i	−0.742162	−	0.670221i	$-0.766200\pi$
$103$		−	13.6040i		−	1.34044i	0.742162	−	0.670221i	$-0.233800\pi$
$104$			2.44397i			0.239651i
$105$	−12.9742	−	0.553540i	−1.26615	−	0.0540199i
$106$		−	8.22118i		−	0.798512i
$107$			11.2988i			1.09230i	0.837689	+	0.546148i	$0.183906\pi$
$107$			11.2988i			1.09230i	−0.837689	+	0.546148i	$0.816094\pi$
$108$	−0.662864	+	5.15370i	−0.0637841	+	0.495915i
$109$			19.2424i			1.84309i	0.388269	+	0.921546i	$0.373073\pi$
$109$			19.2424i			1.84309i	−0.388269	+	0.921546i	$0.626927\pi$
$110$			10.5264i			1.00365i
$111$	4.90350	+	0.209207i	0.465419	+	0.0198570i
$112$	3.25240			0.307323
$113$	9.70743			0.913198			0.456599	−	0.889673i	$-0.349067\pi$
$113$	9.70743			0.913198			0.456599	+	0.889673i	$0.349067\pi$
$114$	0.0970099	−	2.27377i	0.00908581	−	0.212958i
$115$			19.4984i			1.81824i
$116$		−	7.58278i		−	0.704043i
$117$	−0.624491	+	7.30525i	−0.0577342	+	0.675371i
$118$	−7.51658	−	1.58147i	−0.691957	−	0.145586i
$119$			8.22629i			0.754103i
$120$	3.98910	+	0.170194i	0.364153	+	0.0155365i
$121$	9.85165			0.895604
$122$		−	0.133657i		−	0.0121007i
$123$	9.99734	+	0.426534i	0.901430	+	0.0384593i
$124$			1.81032i			0.162572i
$125$		−	10.8023i		−	0.966185i
$126$	9.72175	+	0.831066i	0.866083	+	0.0740372i
$127$	−3.14080			−0.278701			−0.139350	−	0.990243i	$-0.544501\pi$
$127$	−3.14080			−0.278701			−0.139350	+	0.990243i	$0.544501\pi$
$128$	−1.00000			−0.0883883
$129$	−19.9864	−	0.852717i	−1.75971	−	0.0750775i
$130$	5.63383			0.494120
$131$	10.9596			0.957541			0.478771	−	0.877940i	$-0.341083\pi$
$131$	10.9596			0.957541			0.478771	+	0.877940i	$0.341083\pi$
$132$	0.337136	−	7.90198i	0.0293439	−	0.687779i
$133$	−4.27352			−0.370561
$134$			3.33360i			0.287979i
$135$	11.8803	+	1.52803i	1.02249	+	0.131512i
$136$		−	2.52929i		−	0.216885i
$137$		−	13.7212i		−	1.17228i	−0.810209	−	0.586141i	$-0.800646\pi$
$137$		−	13.7212i		−	1.17228i	0.810209	−	0.586141i	$-0.199354\pi$
$138$	0.624491	−	14.6371i	0.0531602	−	1.24600i
$139$	−20.5507			−1.74309			−0.871545	−	0.490315i	$-0.836882\pi$
$139$	−20.5507			−1.74309			−0.871545	+	0.490315i	$0.836882\pi$
$140$		−	7.49745i		−	0.633650i
$141$	0.0497818	−	1.16681i	0.00419238	−	0.0982633i
$142$		−	6.35743i		−	0.533503i
$143$		−	11.1600i		−	0.933248i
$144$	−2.98910	−	0.255524i	−0.249092	−	0.0212936i
$145$	−17.4798			−1.45162
$146$		−	13.4703i		−	1.11481i
$147$	0.264175	−	6.19187i	0.0217888	−	0.510697i
$148$			2.83361i			0.232921i
$149$	17.0984			1.40076			0.700378	−	0.713772i	$-0.253015\pi$
$149$	17.0984			1.40076			0.700378	+	0.713772i	$0.253015\pi$
$150$	0.0231795	−	0.543295i	0.00189260	−	0.0443598i
$151$		−	13.9649i		−	1.13644i	−0.822875	−	0.568222i	$-0.807631\pi$
$151$		−	13.9649i		−	1.13644i	0.822875	−	0.568222i	$-0.192369\pi$
$152$	1.31396			0.106576
$153$	0.646294	−	7.56031i	0.0522498	−	0.611215i
$154$	−14.8516			−1.19678
$155$	4.17316			0.335196
$156$	−4.22922	−	0.180439i	−0.338609	−	0.0144467i
$157$		−	12.3655i		−	0.986872i	−0.869782	−	0.493436i	$-0.835741\pi$
$157$		−	12.3655i		−	0.986872i	0.869782	−	0.493436i	$-0.164259\pi$
$158$	−11.0366			−0.878023
$159$	14.2266	+	0.606973i	1.12824	+	0.0481361i
$160$			2.30520i			0.182242i
$161$	−27.5103			−2.16811
$162$	−8.86942	−	1.52757i	−0.696847	−	0.120017i
$163$	−2.07360			−0.162417			−0.0812083	−	0.996697i	$-0.525878\pi$
$163$	−2.07360			−0.162417			−0.0812083	+	0.996697i	$0.525878\pi$
$164$			5.77722i			0.451125i
$165$	−18.2157	−	0.777167i	−1.41809	−	0.0605024i
$166$	9.52592			0.739355
$167$		−	17.7195i		−	1.37118i	−0.727989	−	0.685589i	$-0.759545\pi$
$167$		−	17.7195i		−	1.37118i	0.727989	−	0.685589i	$-0.240455\pi$
$168$	−0.240126	+	5.62821i	−0.0185261	+	0.434226i
$169$	7.02703			0.540541
$170$	−5.83054			−0.447182
$171$	3.92755	+	0.335747i	0.300347	+	0.0256752i
$172$		−	11.5497i		−	0.880654i
$173$	1.06747			0.0811585			0.0405792	−	0.999176i	$-0.487080\pi$
$173$	1.06747			0.0811585			0.0405792	+	0.999176i	$0.487080\pi$
$174$	13.1218	+	0.559839i	0.994763	+	0.0424413i
$175$	−1.02111			−0.0771890
$176$	4.56636			0.344202
$177$	3.29165	−	12.8905i	0.247415	−	0.968910i
$178$	−4.28529			−0.321196
$179$	12.6586			0.946151			0.473076	−	0.881022i	$-0.343144\pi$
$179$	12.6586			0.946151			0.473076	+	0.881022i	$0.343144\pi$
$180$	−0.589033	+	6.89048i	−0.0439040	+	0.513586i
$181$	12.2036			0.907088			0.453544	−	0.891234i	$-0.350160\pi$
$181$	12.2036			0.907088			0.453544	+	0.891234i	$0.350160\pi$
$182$			7.94876i			0.589201i
$183$	0.231290	+	0.00986794i	0.0170975	+	0.000729459i
$184$	8.45845			0.623565
$185$	6.53205			0.480246
$186$	−3.13272	−	0.133657i	−0.229702	−	0.00980020i
$187$			11.5497i			0.844596i
$188$	0.674272			0.0491764
$189$	−2.15590	+	16.7619i	−0.156819	+	1.21925i
$190$		−	3.02894i		−	0.219742i
$191$	−17.4916			−1.26565			−0.632824	−	0.774296i	$-0.718104\pi$
$191$	−17.4916			−1.26565			−0.632824	+	0.774296i	$0.718104\pi$
$192$	0.0738304	−	1.73048i	0.00532825	−	0.124886i
$193$	3.92668			0.282648			0.141324	−	0.989963i	$-0.454864\pi$
$193$	3.92668			0.282648			0.141324	+	0.989963i	$0.454864\pi$
$194$		−	8.58240i		−	0.616181i
$195$	−0.415948	+	9.74922i	−0.0297867	+	0.698156i
$196$	3.57813			0.255581
$197$			1.63966i			0.116821i	0.998293	+	0.0584106i	$0.0186033\pi$
$197$			1.63966i			0.116821i	−0.998293	+	0.0584106i	$0.981397\pi$
$198$	13.6493	+	1.16681i	0.970014	+	0.0829218i
$199$	−20.5203			−1.45464			−0.727322	−	0.686297i	$-0.759235\pi$
$199$	−20.5203			−1.45464			−0.727322	+	0.686297i	$0.759235\pi$
$200$	0.313957			0.0222001
$201$	−5.76871	−	0.246121i	−0.406893	−	0.0173600i
$202$	−8.85165			−0.622800
$203$		−	24.6623i		−	1.73095i
$204$	4.37689	+	0.186739i	0.306443	+	0.0130743i
$205$	13.3177			0.930145
$206$			13.6040i			0.947835i
$207$	25.2831	+	2.16133i	1.75730	+	0.150223i
$208$		−	2.44397i		−	0.169458i
$209$	−6.00000			−0.415029
$210$	12.9742	+	0.553540i	0.895302	+	0.0381979i
$211$			17.9919i			1.23862i	0.785148	+	0.619308i	$0.212587\pi$
$211$			17.9919i			1.23862i	−0.785148	+	0.619308i	$0.787413\pi$
$212$			8.22118i			0.564633i
$213$	11.0014	+	0.469371i	0.753802	+	0.0321608i
$214$		−	11.2988i		−	0.772369i
$215$	−26.6243			−1.81576
$216$	0.662864	−	5.15370i	0.0451022	−	0.350665i
$217$			5.88790i			0.399697i
$218$		−	19.2424i		−	1.30326i
$219$	23.3101	+	0.994520i	1.57515	+	0.0672034i
$220$		−	10.5264i		−	0.709689i
$221$	6.18151			0.415813
$222$	−4.90350	−	0.209207i	−0.329101	−	0.0140410i
$223$	12.8745			0.862138			0.431069	−	0.902319i	$-0.358137\pi$
$223$	12.8745			0.862138			0.431069	+	0.902319i	$0.358137\pi$
$224$	−3.25240			−0.217310
$225$	0.938447	+	0.0802233i	0.0625632	+	0.00534822i
$226$	−9.70743			−0.645729
$227$	−6.85578			−0.455034			−0.227517	−	0.973774i	$-0.573061\pi$
$227$	−6.85578			−0.455034			−0.227517	+	0.973774i	$0.573061\pi$
$228$	−0.0970099	+	2.27377i	−0.00642464	+	0.150584i
$229$			19.9984i			1.32153i	0.750592	+	0.660766i	$0.229769\pi$
$229$			19.9984i			1.32153i	−0.750592	+	0.660766i	$0.770231\pi$
$230$		−	19.4984i		−	1.28569i
$231$	1.09650	−	25.7004i	0.0721446	−	1.69096i
$232$			7.58278i			0.497834i
$233$	3.71058			0.243088			0.121544	−	0.992586i	$-0.461215\pi$
$233$	3.71058			0.243088			0.121544	+	0.992586i	$0.461215\pi$
$234$	0.624491	−	7.30525i	0.0408242	−	0.477559i
$235$		−	1.55433i		−	0.101394i
$236$	7.51658	+	1.58147i	0.489288	+	0.102945i
$237$	0.814835	−	19.0985i	0.0529292	−	1.24058i
$238$		−	8.22629i		−	0.533231i
$239$			27.3300i			1.76783i	0.467649	+	0.883914i	$0.345101\pi$
$239$			27.3300i			1.76783i	−0.467649	+	0.883914i	$0.654899\pi$
$240$	−3.98910	−	0.170194i	−0.257495	−	0.0109860i
$241$	−20.6469			−1.32998			−0.664991	−	0.746851i	$-0.731565\pi$
$241$	−20.6469			−1.32998			−0.664991	+	0.746851i	$0.731565\pi$
$242$	−9.85165			−0.633288
$243$	3.29826	−	15.2355i	0.211583	−	0.977360i
$244$			0.133657i			0.00855650i
$245$		−	8.24832i		−	0.526966i
$246$	−9.99734	−	0.426534i	−0.637407	−	0.0271948i
$247$			3.21126i			0.204328i
$248$		−	1.81032i		−	0.114956i
$249$	−0.703303	+	16.4844i	−0.0445700	+	1.04466i
$250$			10.8023i			0.683196i
$251$			8.11629i			0.512296i	0.966638	+	0.256148i	$0.0824534\pi$
$251$			8.11629i			0.512296i	−0.966638	+	0.256148i	$0.917547\pi$
$252$	−9.72175	−	0.831066i	−0.612413	−	0.0523522i
$253$	−38.6243			−2.42829
$254$	3.14080			0.197071
$255$	0.430471	−	10.0896i	0.0269571	−	0.631836i
$256$	1.00000			0.0625000
$257$			4.73061i			0.295087i	0.989056	+	0.147544i	$0.0471367\pi$
$257$			4.73061i			0.295087i	−0.989056	+	0.147544i	$0.952863\pi$
$258$	19.9864	+	0.852717i	1.24430	+	0.0530878i
$259$			9.21605i			0.572657i
$260$	−5.63383			−0.349396
$261$	−1.93758	+	22.6657i	−0.119933	+	1.40297i
$262$	−10.9596			−0.677084
$263$		−	21.4373i		−	1.32188i	−0.750438	−	0.660941i	$-0.770158\pi$
$263$		−	21.4373i		−	1.32188i	0.750438	−	0.660941i	$-0.229842\pi$
$264$	−0.337136	+	7.90198i	−0.0207493	+	0.486333i
$265$	18.9515			1.16418
$266$	4.27352			0.262026
$267$	0.316385	−	7.41559i	0.0193624	−	0.453827i
$268$		−	3.33360i		−	0.203632i
$269$	−10.2002			−0.621917			−0.310958	−	0.950424i	$-0.600650\pi$
$269$	−10.2002			−0.621917			−0.310958	+	0.950424i	$0.600650\pi$
$270$	−11.8803	−	1.52803i	−0.723013	−	0.0929932i
$271$	−18.6667			−1.13392			−0.566961	−	0.823745i	$-0.691881\pi$
$271$	−18.6667			−1.13392			−0.566961	+	0.823745i	$0.691881\pi$
$272$			2.52929i			0.153361i
$273$	−13.7551	−	0.586860i	−0.832499	−	0.0355184i
$274$			13.7212i			0.828929i
$275$	−1.43364			−0.0864517
$276$	−0.624491	+	14.6371i	−0.0375899	+	0.881053i
$277$	−16.7548			−1.00670			−0.503349	−	0.864083i	$-0.667899\pi$
$277$	−16.7548			−1.00670			−0.503349	+	0.864083i	$0.667899\pi$
$278$	20.5507			1.23255
$279$	0.462580	−	5.41123i	0.0276939	−	0.323962i
$280$			7.49745i			0.448058i
$281$			20.1007i			1.19911i	0.800335	+	0.599553i	$0.204655\pi$
$281$			20.1007i			1.19911i	−0.800335	+	0.599553i	$0.795345\pi$
$282$	−0.0497818	+	1.16681i	−0.00296446	+	0.0694827i
$283$			16.1703i			0.961224i	0.876933	+	0.480612i	$0.159585\pi$
$283$			16.1703i			0.961224i	−0.876933	+	0.480612i	$0.840415\pi$
$284$			6.35743i			0.377244i
$285$	5.24150	+	0.223628i	0.310480	+	0.0132466i
$286$			11.1600i			0.659906i
$287$			18.7898i			1.10913i
$288$	2.98910	+	0.255524i	0.176134	+	0.0150569i
$289$	10.6027			0.623686
$290$	17.4798			1.02645
$291$	14.8516	+	0.633642i	0.870619	+	0.0371448i
$292$			13.4703i			0.788292i
$293$		−	13.7092i		−	0.800901i	−0.916318	−	0.400451i	$-0.868854\pi$
$293$		−	13.7092i		−	0.800901i	0.916318	−	0.400451i	$-0.131146\pi$
$294$	−0.264175	+	6.19187i	−0.0154070	+	0.361117i
$295$	3.64560	−	17.3272i	0.212255	−	1.00883i
$296$		−	2.83361i		−	0.164700i
$297$	−3.02688	+	23.5336i	−0.175637	+	1.36556i
$298$	−17.0984			−0.990484
$299$			20.6722i			1.19550i
$300$	−0.0231795	+	0.543295i	−0.00133827	+	0.0313671i
$301$		−	37.5642i		−	2.16516i
$302$			13.9649i			0.803588i
$303$	0.653521	−	15.3176i	0.0375438	−	0.879972i
$304$	−1.31396			−0.0753606
$305$	0.308106			0.0176421
$306$	−0.646294	+	7.56031i	−0.0369462	+	0.432194i
$307$	−4.75594			−0.271436			−0.135718	−	0.990748i	$-0.543334\pi$
$307$	−4.75594			−0.271436			−0.135718	+	0.990748i	$0.543334\pi$
$308$	14.8516			0.846251
$309$	−23.5414	−	1.00439i	−1.33922	−	0.0571376i
$310$	−4.17316			−0.237020
$311$			5.88211i			0.333544i	0.985996	+	0.166772i	$0.0533343\pi$
$311$			5.88211i			0.333544i	−0.985996	+	0.166772i	$0.946666\pi$
$312$	4.22922	+	0.180439i	0.239433	+	0.0102153i
$313$		−	1.28702i		−	0.0727467i	−0.999338	−	0.0363733i	$-0.988419\pi$
$313$		−	1.28702i		−	0.0727467i	0.999338	−	0.0363733i	$-0.0115806\pi$
$314$			12.3655i			0.697824i
$315$	−1.91577	+	22.4106i	−0.107942	+	1.26269i
$316$	11.0366			0.620856
$317$			26.3959i			1.48254i	0.671205	+	0.741272i	$0.265777\pi$
$317$			26.3959i			1.48254i	−0.671205	+	0.741272i	$0.734223\pi$
$318$	−14.2266	−	0.606973i	−0.797786	−	0.0340374i
$319$		−	34.6257i		−	1.93867i
$320$		−	2.30520i		−	0.128865i
$321$	19.5523	+	0.834194i	1.09130	+	0.0465602i
$322$	27.5103			1.53309
$323$		−	3.32338i		−	0.184918i
$324$	8.86942	+	1.52757i	0.492745	+	0.0848650i
$325$			0.767299i			0.0425621i
$326$	2.07360			0.114846
$327$	33.2986	+	1.42068i	1.84142	+	0.0785636i
$328$		−	5.77722i		−	0.318993i
$329$	2.19301			0.120904
$330$	18.2157	+	0.777167i	1.00274	+	0.0427816i
$331$	15.7151			0.863778			0.431889	−	0.901927i	$-0.357847\pi$
$331$	15.7151			0.863778			0.431889	+	0.901927i	$0.357847\pi$
$332$	−9.52592			−0.522803
$333$	0.724054	−	8.46994i	0.0396779	−	0.464150i
$334$			17.7195i			0.969569i
$335$	−7.68461			−0.419855
$336$	0.240126	−	5.62821i	0.0131000	−	0.307044i
$337$			14.1561i			0.771130i	0.922681	+	0.385565i	$0.125993\pi$
$337$			14.1561i			0.771130i	−0.922681	+	0.385565i	$0.874007\pi$
$338$	−7.02703			−0.382220
$339$	0.716703	−	16.7985i	0.0389260	−	0.912368i
$340$	5.83054			0.316205
$341$			8.26659i			0.447661i
$342$	−3.92755	−	0.335747i	−0.212377	−	0.0181551i
$343$	−11.1293			−0.600926
$344$			11.5497i			0.622717i
$345$	33.7416	+	1.43958i	1.81659	+	0.0775042i
$346$	−1.06747			−0.0573877
$347$	−17.5880			−0.944174			−0.472087	−	0.881552i	$-0.656499\pi$
$347$	−17.5880			−0.944174			−0.472087	+	0.881552i	$0.656499\pi$
$348$	−13.1218	−	0.559839i	−0.703403	−	0.0300105i
$349$		−	7.43449i		−	0.397959i	−0.980004	−	0.198980i	$-0.936237\pi$
$349$		−	7.43449i		−	0.397959i	0.980004	−	0.198980i	$-0.0637628\pi$
$350$	1.02111			0.0545808
$351$	12.5955	+	1.62002i	0.672296	+	0.0864701i
$352$	−4.56636			−0.243388
$353$	−7.10990			−0.378422			−0.189211	−	0.981936i	$-0.560593\pi$
$353$	−7.10990			−0.378422			−0.189211	+	0.981936i	$0.560593\pi$
$354$	−3.29165	+	12.8905i	−0.174949	+	0.685123i
$355$	14.6552			0.777815
$356$	4.28529			0.227120
$357$	14.2354	+	0.607350i	0.753417	+	0.0321444i
$358$	−12.6586			−0.669030
$359$		−	23.3922i		−	1.23459i	−0.786731	−	0.617296i	$-0.788228\pi$
$359$		−	23.3922i		−	1.23459i	0.786731	−	0.617296i	$-0.211772\pi$
$360$	0.589033	−	6.89048i	0.0310448	−	0.363160i
$361$	−17.2735			−0.909133
$362$	−12.2036			−0.641408
$363$	0.727351	−	17.0480i	0.0381760	−	0.894790i
$364$		−	7.94876i		−	0.416628i
$365$	31.0518			1.62533
$366$	−0.231290	−	0.00986794i	−0.0120897	−	0.000515805i
$367$			5.80088i			0.302803i	0.988472	+	0.151402i	$0.0483787\pi$
$367$			5.80088i			0.302803i	−0.988472	+	0.151402i	$0.951621\pi$
$368$	−8.45845			−0.440927
$369$	1.47621	−	17.2687i	0.0768487	−	0.898971i
$370$	−6.53205			−0.339585
$371$			26.7386i			1.38820i
$372$	3.13272	+	0.133657i	0.162424	+	0.00692979i
$373$	10.9210			0.565469			0.282735	−	0.959198i	$-0.408758\pi$
$373$	10.9210			0.565469			0.282735	+	0.959198i	$0.408758\pi$
$374$		−	11.5497i		−	0.597219i
$375$	−18.6931	−	0.797536i	−0.965307	−	0.0411846i
$376$	−0.674272			−0.0347729
$377$	−18.5320			−0.954449
$378$	2.15590	−	16.7619i	0.110888	−	0.862140i
$379$	35.6952			1.83354			0.916770	−	0.399415i	$-0.130787\pi$
$379$	35.6952			1.83354			0.916770	+	0.399415i	$0.130787\pi$
$380$			3.02894i			0.155381i
$381$	−0.231886	+	5.43507i	−0.0118799	+	0.278447i
$382$	17.4916			0.894948
$383$			20.9229i			1.06911i	0.845134	+	0.534554i	$0.179521\pi$
$383$			20.9229i			1.06911i	−0.845134	+	0.534554i	$0.820479\pi$
$384$	−0.0738304	+	1.73048i	−0.00376764	+	0.0883080i
$385$		−	34.2361i		−	1.74483i
$386$	−3.92668			−0.199863
$387$	−2.95121	+	34.5231i	−0.150019	+	1.75491i
$388$			8.58240i			0.435706i
$389$		−	1.93248i		−	0.0979805i	−0.998799	−	0.0489903i	$-0.984400\pi$
$389$		−	1.93248i		−	0.0979805i	0.998799	−	0.0489903i	$-0.0156003\pi$
$390$	0.415948	−	9.74922i	0.0210624	−	0.493671i
$391$		−	21.3939i		−	1.08194i
$392$	−3.57813			−0.180723
$393$	0.809149	−	18.9653i	0.0408162	−	0.956671i
$394$		−	1.63966i		−	0.0826051i
$395$		−	25.4415i		−	1.28010i
$396$	−13.6493	−	1.16681i	−0.685903	−	0.0586345i
$397$		−	19.2875i		−	0.968012i	−0.875065	−	0.484006i	$-0.839181\pi$
$397$		−	19.2875i		−	0.968012i	0.875065	−	0.484006i	$-0.160819\pi$
$398$	20.5203			1.02859
$399$	−0.315516	+	7.39522i	−0.0157955	+	0.370224i
$400$	−0.313957			−0.0156978
$401$	4.84743			0.242069			0.121035	−	0.992648i	$-0.461379\pi$
$401$	4.84743			0.242069			0.121035	+	0.992648i	$0.461379\pi$
$402$	5.76871	+	0.246121i	0.287717	+	0.0122754i
$403$	4.42437			0.220393
$404$	8.85165			0.440386
$405$	3.52136	−	20.4458i	0.174978	−	1.01596i
$406$			24.6623i			1.22397i
$407$			12.9393i			0.641377i
$408$	−4.37689	−	0.186739i	−0.216688	−	0.00924495i
$409$			36.9306i			1.82610i	0.407849	+	0.913049i	$0.366279\pi$
$409$			36.9306i			1.82610i	−0.407849	+	0.913049i	$0.633721\pi$
$410$	−13.3177			−0.657712
$411$	−23.7442	−	1.01304i	−1.17122	−	0.0499697i
$412$		−	13.6040i		−	0.670221i
$413$	24.4470	+	5.14357i	1.20296	+	0.253099i
$414$	−25.2831	−	2.16133i	−1.24260	−	0.106224i
$415$			21.9592i			1.07793i
$416$			2.44397i			0.119825i
$417$	−1.51727	+	35.5626i	−0.0743010	+	1.74151i
$418$	6.00000			0.293470
$419$	−24.1961			−1.18206			−0.591028	−	0.806651i	$-0.701278\pi$
$419$	−24.1961			−1.18206			−0.591028	+	0.806651i	$0.701278\pi$
$420$	−12.9742	−	0.553540i	−0.633074	−	0.0270100i
$421$		−	23.5993i		−	1.15016i	−0.818097	−	0.575080i	$-0.804971\pi$
$421$		−	23.5993i		−	1.15016i	0.818097	−	0.575080i	$-0.195029\pi$
$422$		−	17.9919i		−	0.875834i
$423$	−2.01547	−	0.172292i	−0.0979953	−	0.00837715i
$424$		−	8.22118i		−	0.399256i
$425$		−	0.794089i		−	0.0385190i
$426$	−11.0014	−	0.469371i	−0.533018	−	0.0227411i
$427$			0.434706i			0.0210369i
$428$			11.2988i			0.546148i
$429$	−19.3122	−	0.823949i	−0.932400	−	0.0397806i
$430$	26.6243			1.28394
$431$	30.4771			1.46803			0.734016	−	0.679132i	$-0.237644\pi$
$431$	30.4771			1.46803			0.734016	+	0.679132i	$0.237644\pi$
$432$	−0.662864	+	5.15370i	−0.0318920	+	0.247957i
$433$	−37.7340			−1.81338			−0.906689	−	0.421799i	$-0.861399\pi$
$433$	−37.7340			−1.81338			−0.906689	+	0.421799i	$0.861399\pi$
$434$		−	5.88790i		−	0.282628i
$435$	−1.29054	+	30.2484i	−0.0618768	+	1.45030i
$436$			19.2424i			0.921546i
$437$	11.1140			0.531656
$438$	−23.3101	−	0.994520i	−1.11380	−	0.0475200i
$439$	−6.37650			−0.304334			−0.152167	−	0.988355i	$-0.548625\pi$
$439$	−6.37650			−0.304334			−0.152167	+	0.988355i	$0.548625\pi$
$440$			10.5264i			0.501826i
$441$	−10.6954	−	0.914297i	−0.509304	−	0.0435379i
$442$	−6.18151			−0.294024
$443$	−21.9885			−1.04471			−0.522353	−	0.852730i	$-0.674946\pi$
$443$	−21.9885			−1.04471			−0.522353	+	0.852730i	$0.674946\pi$
$444$	4.90350	+	0.209207i	0.232710	+	0.00992851i
$445$		−	9.87846i		−	0.468284i
$446$	−12.8745			−0.609624
$447$	1.26238	−	29.5884i	0.0597086	−	1.39948i
$448$	3.25240			0.153662
$449$		−	23.7841i		−	1.12244i	−0.827666	−	0.561221i	$-0.810332\pi$
$449$		−	23.7841i		−	1.12244i	0.827666	−	0.561221i	$-0.189668\pi$
$450$	−0.938447	−	0.0802233i	−0.0442388	−	0.00378176i
$451$			26.3809i			1.24223i
$452$	9.70743			0.456599
$453$	−24.1659	−	1.03103i	−1.13541	−	0.0484421i
$454$	6.85578			0.321758
$455$	−18.3235			−0.859019
$456$	0.0970099	−	2.27377i	0.00454291	−	0.106479i
$457$			8.86945i			0.414896i	0.978246	+	0.207448i	$0.0665157\pi$
$457$			8.86945i			0.414896i	−0.978246	+	0.207448i	$0.933484\pi$
$458$		−	19.9984i		−	0.934465i
$459$	−13.0352	−	1.67658i	−0.608432	−	0.0782560i
$460$			19.4984i			0.909119i
$461$		−	17.7652i		−	0.827408i	−0.910411	−	0.413704i	$-0.864235\pi$
$461$		−	17.7652i		−	0.827408i	0.910411	−	0.413704i	$-0.135765\pi$
$462$	−1.09650	+	25.7004i	−0.0510139	+	1.19569i
$463$		−	27.7798i		−	1.29104i	−0.763745	−	0.645518i	$-0.776641\pi$
$463$		−	27.7798i		−	1.29104i	0.763745	−	0.645518i	$-0.223359\pi$
$464$		−	7.58278i		−	0.352022i
$465$	0.308106	−	7.22156i	0.0142881	−	0.334892i
$466$	−3.71058			−0.171889
$467$	8.59729			0.397835			0.198918	−	0.980016i	$-0.436257\pi$
$467$	8.59729			0.397835			0.198918	+	0.980016i	$0.436257\pi$
$468$	−0.624491	+	7.30525i	−0.0288671	+	0.337685i
$469$		−	10.8422i		−	0.500646i
$470$			1.55433i			0.0716961i
$471$	−21.3982	−	0.912948i	−0.985975	−	0.0420664i
$472$	−7.51658	−	1.58147i	−0.345979	−	0.0727930i
$473$		−	52.7400i		−	2.42499i
$474$	−0.814835	+	19.0985i	−0.0374266	+	0.877225i
$475$	0.412525			0.0189280
$476$			8.22629i			0.377051i
$477$	2.10071	−	24.5739i	0.0961847	−	1.12516i
$478$		−	27.3300i		−	1.25004i
$479$		−	33.5116i		−	1.53119i	−0.643326	−	0.765593i	$-0.722446\pi$
$479$		−	33.5116i		−	1.53119i	0.643326	−	0.765593i	$-0.277554\pi$
$480$	3.98910	+	0.170194i	0.182077	+	0.00776826i
$481$	6.92525			0.315764
$482$	20.6469			0.940439
$483$	−2.03110	+	47.6059i	−0.0924181	+	2.16614i
$484$	9.85165			0.447802
$485$	19.7842			0.898353
$486$	−3.29826	+	15.2355i	−0.149612	+	0.691098i
$487$	15.2524			0.691152			0.345576	−	0.938391i	$-0.387683\pi$
$487$	15.2524			0.691152			0.345576	+	0.938391i	$0.387683\pi$
$488$		−	0.133657i		−	0.00605036i
$489$	−0.153094	+	3.58831i	−0.00692317	+	0.162269i
$490$			8.24832i			0.372621i
$491$		−	11.8006i		−	0.532552i	−0.963897	−	0.266276i	$-0.914207\pi$
$491$		−	11.8006i		−	0.532552i	0.963897	−	0.266276i	$-0.0857932\pi$
$492$	9.99734	+	0.426534i	0.450715	+	0.0192296i
$493$	19.1791			0.863782
$494$		−	3.21126i		−	0.144482i
$495$	−2.68974	+	31.4644i	−0.120895	+	1.41422i
$496$			1.81032i			0.0812859i
$497$			20.6769i			0.927486i
$498$	0.703303	−	16.4844i	0.0315157	−	0.738683i
$499$	−13.2132			−0.591506			−0.295753	−	0.955265i	$-0.595570\pi$
$499$	−13.2132			−0.591506			−0.295753	+	0.955265i	$0.595570\pi$
$500$		−	10.8023i		−	0.483093i
$501$	−30.6632	−	1.30824i	−1.36993	−	0.0584478i
$502$		−	8.11629i		−	0.362248i
$503$	−10.2884			−0.458739			−0.229369	−	0.973339i	$-0.573666\pi$
$503$	−10.2884			−0.458739			−0.229369	+	0.973339i	$0.573666\pi$
$504$	9.72175	+	0.831066i	0.433041	+	0.0370186i
$505$		−	20.4048i		−	0.908003i
$506$	38.6243			1.71706
$507$	0.518809	−	12.1601i	0.0230411	−	0.540050i
$508$	−3.14080			−0.139350
$509$	−20.9356			−0.927953			−0.463977	−	0.885847i	$-0.653578\pi$
$509$	−20.9356			−0.927953			−0.463977	+	0.885847i	$0.653578\pi$
$510$	−0.430471	+	10.0896i	−0.0190616	+	0.446775i
$511$			43.8110i			1.93808i
$512$	−1.00000			−0.0441942
$513$	0.870974	−	6.77174i	0.0384545	−	0.298979i
$514$		−	4.73061i		−	0.208658i
$515$	−31.3599			−1.38188
$516$	−19.9864	−	0.852717i	−0.879854	−	0.0375388i
$517$	3.07897			0.135413
$518$		−	9.21605i		−	0.404930i
$519$	0.0788120	−	1.84724i	0.00345946	−	0.0810847i
$520$	5.63383			0.247060
$521$			29.3907i			1.28763i	0.765181	+	0.643815i	$0.222649\pi$
$521$			29.3907i			1.28763i	−0.765181	+	0.643815i	$0.777351\pi$
$522$	1.93758	−	22.6657i	0.0848055	−	0.992049i
$523$	−21.0950			−0.922419			−0.461210	−	0.887291i	$-0.652584\pi$
$523$	−21.0950			−0.922419			−0.461210	+	0.887291i	$0.652584\pi$
$524$	10.9596			0.478771
$525$	−0.0753892	+	1.76701i	−0.00329026	+	0.0771188i
$526$			21.4373i			0.934711i
$527$	−4.57884			−0.199457
$528$	0.337136	−	7.90198i	0.0146720	−	0.343890i
$529$	48.5454			2.11067
$530$	−18.9515			−0.823200
$531$	−22.0637	−	6.64783i	−0.957483	−	0.288491i
$532$	−4.27352			−0.185280
$533$	14.1193			0.611575
$534$	−0.316385	+	7.41559i	−0.0136913	+	0.320904i
$535$	26.0460			1.12607
$536$			3.33360i			0.143989i
$537$	0.934593	−	21.9055i	0.0403306	−	0.945291i
$538$	10.2002			0.439762
$539$	16.3390			0.703772
$540$	11.8803	+	1.52803i	0.511247	+	0.0657562i
$541$		−	11.6743i		−	0.501917i	−0.967998	−	0.250959i	$-0.919254\pi$
$541$		−	11.6743i		−	0.501917i	0.967998	−	0.250959i	$-0.0807458\pi$
$542$	18.6667			0.801804
$543$	0.900998	−	21.1181i	0.0386655	−	0.906263i
$544$		−	2.52929i		−	0.108443i
$545$	44.3577			1.90008
$546$	13.7551	+	0.586860i	0.588666	+	0.0251153i
$547$	26.6015			1.13740			0.568699	−	0.822546i	$-0.307447\pi$
$547$	26.6015			1.13740			0.568699	+	0.822546i	$0.307447\pi$
$548$		−	13.7212i		−	0.586141i
$549$	0.0341525	−	0.399513i	0.00145759	−	0.0170508i
$550$	1.43364			0.0611306
$551$			9.96344i			0.424457i
$552$	0.624491	−	14.6371i	0.0265801	−	0.622998i
$553$	35.8954			1.52643
$554$	16.7548			0.711843
$555$	0.482263	−	11.3036i	0.0204709	−	0.479809i
$556$	−20.5507			−0.871545
$557$		−	1.86705i		−	0.0791096i	−0.999217	−	0.0395548i	$-0.987406\pi$
$557$		−	1.86705i		−	0.0791096i	0.999217	−	0.0395548i	$-0.0125940\pi$
$558$	−0.462580	+	5.41123i	−0.0195826	+	0.229076i
$559$	−28.2270			−1.19387
$560$		−	7.49745i		−	0.316825i
$561$	19.9864	+	0.852717i	0.843828	+	0.0360017i
$562$		−	20.1007i		−	0.847896i
$563$	−31.9221			−1.34536			−0.672678	−	0.739935i	$-0.734856\pi$
$563$	−31.9221			−1.34536			−0.672678	+	0.739935i	$0.734856\pi$
$564$	0.0497818	−	1.16681i	0.00209619	−	0.0491317i
$565$		−	22.3776i		−	0.941432i
$566$		−	16.1703i		−	0.679688i
$567$	28.8469	+	4.96827i	1.21146	+	0.208648i
$568$		−	6.35743i		−	0.266752i
$569$	−14.8215			−0.621348			−0.310674	−	0.950517i	$-0.600555\pi$
$569$	−14.8215			−0.621348			−0.310674	+	0.950517i	$0.600555\pi$
$570$	−5.24150	−	0.223628i	−0.219542	−	0.00936673i
$571$			34.3763i			1.43860i	0.694699	+	0.719301i	$0.255538\pi$
$571$			34.3763i			1.43860i	−0.694699	+	0.719301i	$0.744462\pi$
$572$		−	11.1600i		−	0.466624i
$573$	−1.29141	+	30.2688i	−0.0539495	+	1.26450i
$574$		−	18.7898i		−	0.784273i
$575$	2.65559			0.110746
$576$	−2.98910	−	0.255524i	−0.124546	−	0.0106468i
$577$	−16.7941			−0.699146			−0.349573	−	0.936909i	$-0.613673\pi$
$577$	−16.7941			−0.699146			−0.349573	+	0.936909i	$0.613673\pi$
$578$	−10.6027			−0.441013
$579$	0.289908	−	6.79502i	0.0120482	−	0.282391i
$580$	−17.4798			−0.725811
$581$	−30.9821			−1.28536
$582$	−14.8516	−	0.633642i	−0.615621	−	0.0262653i
$583$			37.5409i			1.55478i
$584$		−	13.4703i		−	0.557406i
$585$	16.8401	+	1.43958i	0.696252	+	0.0595192i
$586$			13.7092i			0.566323i
$587$	−33.8463			−1.39699			−0.698493	−	0.715617i	$-0.746146\pi$
$587$	−33.8463			−1.39699			−0.698493	+	0.715617i	$0.746146\pi$
$588$	0.264175	−	6.19187i	0.0108944	−	0.255349i
$589$		−	2.37869i		−	0.0980120i
$590$	−3.64560	+	17.3272i	−0.150087	+	0.713351i
$591$	2.83740	+	0.121057i	0.116715	+	0.00497962i
$592$			2.83361i			0.116461i
$593$		−	13.8626i		−	0.569269i	−0.958636	−	0.284635i	$-0.908128\pi$
$593$		−	13.8626i		−	0.569269i	0.958636	−	0.284635i	$-0.0918723\pi$
$594$	3.02688	−	23.5336i	0.124194	−	0.965597i
$595$	18.9633			0.777418
$596$	17.0984			0.700378
$597$	−1.51502	+	35.5099i	−0.0620056	+	1.45332i
$598$		−	20.6722i		−	0.845347i
$599$			3.89307i			0.159066i	0.996832	+	0.0795332i	$0.0253430\pi$
$599$			3.89307i			0.159066i	−0.996832	+	0.0795332i	$0.974657\pi$
$600$	0.0231795	−	0.543295i	0.000946301	−	0.0221799i
$601$			5.74105i			0.234182i	0.993121	+	0.117091i	$0.0373570\pi$
$601$			5.74105i			0.234182i	−0.993121	+	0.117091i	$0.962643\pi$
$602$			37.5642i			1.53100i
$603$	−0.851812	+	9.96445i	−0.0346885	+	0.405784i
$604$		−	13.9649i		−	0.568222i
$605$		−	22.7100i		−	0.923295i
$606$	−0.653521	+	15.3176i	−0.0265475	+	0.622234i
$607$	−18.3429			−0.744515			−0.372258	−	0.928129i	$-0.621416\pi$
$607$	−18.3429			−0.744515			−0.372258	+	0.928129i	$0.621416\pi$
$608$	1.31396			0.0532880
$609$	−42.6775	−	1.82082i	−1.72938	−	0.0737835i
$610$	−0.308106			−0.0124748
$611$		−	1.64790i		−	0.0666668i
$612$	0.646294	−	7.56031i	0.0261249	−	0.305607i
$613$			43.0978i			1.74070i	0.492432	+	0.870351i	$0.336108\pi$
$613$			43.0978i			1.74070i	−0.492432	+	0.870351i	$0.663892\pi$
$614$	4.75594			0.191934
$615$	0.983248	−	23.0459i	0.0396484	−	0.929300i
$616$	−14.8516			−0.598390
$617$			15.0453i			0.605703i	0.953038	+	0.302851i	$0.0979386\pi$
$617$			15.0453i			0.605703i	−0.953038	+	0.302851i	$0.902061\pi$
$618$	23.5414	+	1.00439i	0.946974	+	0.0404024i
$619$	31.6765			1.27319			0.636594	−	0.771199i	$-0.280343\pi$
$619$	31.6765			1.27319			0.636594	+	0.771199i	$0.280343\pi$
$620$	4.17316			0.167598
$621$	5.60680	−	43.5923i	0.224993	−	1.74930i
$622$		−	5.88211i		−	0.235851i
$623$	13.9375			0.558394
$624$	−4.22922	−	0.180439i	−0.169304	−	0.00722334i
$625$	−26.4712			−1.05885
$626$			1.28702i			0.0514397i
$627$	−0.442982	+	10.3829i	−0.0176910	+	0.414651i
$628$		−	12.3655i		−	0.493436i
$629$	−7.16704			−0.285768
$630$	1.91577	−	22.4106i	0.0763263	−	0.892860i
$631$	6.52370			0.259704			0.129852	−	0.991533i	$-0.458550\pi$
$631$	6.52370			0.259704			0.129852	+	0.991533i	$0.458550\pi$
$632$	−11.0366			−0.439012
$633$	31.1346	+	1.32835i	1.23749	+	0.0527972i
$634$		−	26.3959i		−	1.04832i
$635$			7.24017i			0.287317i
$636$	14.2266	+	0.606973i	0.564120	+	0.0240680i
$637$		−	8.74483i		−	0.346483i
$638$			34.6257i			1.37084i
$639$	1.62447	−	19.0030i	0.0642631	−	0.751746i
$640$			2.30520i			0.0911211i
$641$			17.7734i			0.702009i	0.936374	+	0.351004i	$0.114160\pi$
$641$			17.7734i			0.702009i	−0.936374	+	0.351004i	$0.885840\pi$
$642$	−19.5523	−	0.834194i	−0.771667	−	0.0329230i
$643$	4.15400			0.163818			0.0819088	−	0.996640i	$-0.473898\pi$
$643$	4.15400			0.163818			0.0819088	+	0.996640i	$0.473898\pi$
$644$	−27.5103			−1.08406
$645$	−1.96568	+	46.0728i	−0.0773988	+	1.81411i
$646$			3.32338i			0.130757i
$647$		−	9.60059i		−	0.377438i	−0.982031	−	0.188719i	$-0.939566\pi$
$647$		−	9.60059i		−	0.377438i	0.982031	−	0.188719i	$-0.0604335\pi$
$648$	−8.86942	−	1.52757i	−0.348424	−	0.0600086i
$649$	34.3234	+	7.22156i	1.34731	+	0.283471i
$650$		−	0.767299i		−	0.0300959i
$651$	10.1889	+	0.434706i	0.399333	+	0.0170375i
$652$	−2.07360			−0.0812083
$653$		−	0.316162i		−	0.0123724i	−0.999981	−	0.00618618i	$-0.998031\pi$
$653$		−	0.316162i		−	0.0123724i	0.999981	−	0.00618618i	$-0.00196914\pi$
$654$	−33.2986	−	1.42068i	−1.30208	−	0.0555529i
$655$		−	25.2640i		−	0.987146i
$656$			5.77722i			0.225562i
$657$	3.44199	−	40.2642i	0.134285	−	1.57085i
$658$	−2.19301			−0.0854923
$659$	−14.2468			−0.554975			−0.277487	−	0.960729i	$-0.589502\pi$
$659$	−14.2468			−0.554975			−0.277487	+	0.960729i	$0.589502\pi$
$660$	−18.2157	−	0.777167i	−0.709044	−	0.0302512i
$661$	−36.5390			−1.42120			−0.710600	−	0.703596i	$-0.751577\pi$
$661$	−36.5390			−1.42120			−0.710600	+	0.703596i	$0.751577\pi$
$662$	−15.7151			−0.610784
$663$	0.456383	−	10.6970i	0.0177245	−	0.415435i
$664$	9.52592			0.369677
$665$			9.85132i			0.382018i
$666$	−0.724054	+	8.46994i	−0.0280565	+	0.328204i
$667$			64.1385i			2.48345i
$668$		−	17.7195i		−	0.685589i
$669$	0.950527	−	22.2790i	0.0367495	−	0.861354i
$670$	7.68461			0.296882
$671$			0.610325i			0.0235614i
$672$	−0.240126	+	5.62821i	−0.00926307	+	0.217113i
$673$		−	25.5961i		−	0.986658i	−0.869843	−	0.493329i	$-0.835780\pi$
$673$		−	25.5961i		−	0.986658i	0.869843	−	0.493329i	$-0.164220\pi$
$674$		−	14.1561i		−	0.545271i
$675$	0.208111	−	1.61804i	0.00801018	−	0.0622783i
$676$	7.02703			0.270271
$677$		−	11.7568i		−	0.451852i	−0.974144	−	0.225926i	$-0.927459\pi$
$677$		−	11.7568i		−	0.451852i	0.974144	−	0.225926i	$-0.0725408\pi$
$678$	−0.716703	+	16.7985i	−0.0275248	+	0.645142i
$679$			27.9134i			1.07122i
$680$	−5.83054			−0.223591
$681$	−0.506165	+	11.8638i	−0.0193963	+	0.454621i
$682$		−	8.26659i		−	0.316544i
$683$	45.3837			1.73656			0.868279	−	0.496075i	$-0.165226\pi$
$683$	45.3837			1.73656			0.868279	+	0.496075i	$0.165226\pi$
$684$	3.92755	+	0.335747i	0.150173	+	0.0128376i
$685$	−31.6302			−1.20853
$686$	11.1293			0.424919
$687$	34.6068	+	1.47649i	1.32033	+	0.0563317i
$688$		−	11.5497i		−	0.440327i
$689$	20.0923			0.765455
$690$	−33.7416	−	1.43958i	−1.28452	−	0.0548038i
$691$		−	22.1246i		−	0.841658i	−0.907140	−	0.420829i	$-0.861739\pi$
$691$		−	22.1246i		−	0.841658i	0.907140	−	0.420829i	$-0.138261\pi$
$692$	1.06747			0.0405792
$693$	−44.3930	−	3.79495i	−1.68635	−	0.144158i
$694$	17.5880			0.667632
$695$			47.3736i			1.79698i
$696$	13.1218	+	0.559839i	0.497381	+	0.0212207i
$697$	−14.6123			−0.553480
$698$			7.43449i			0.281400i
$699$	0.273954	−	6.42107i	0.0103619	−	0.242867i
$700$	−1.02111			−0.0385945
$701$	−22.4779			−0.848978			−0.424489	−	0.905433i	$-0.639546\pi$
$701$	−22.4779			−0.848978			−0.424489	+	0.905433i	$0.639546\pi$
$702$	−12.5955	−	1.62002i	−0.475385	−	0.0611436i
$703$		−	3.72324i		−	0.140425i
$704$	4.56636			0.172101
$705$	−2.68974	−	0.114757i	−0.101301	−	0.00432200i
$706$	7.10990			0.267585
$707$	28.7891			1.08273
$708$	3.29165	−	12.8905i	0.123708	−	0.484455i
$709$	30.1704			1.13307			0.566536	−	0.824037i	$-0.308283\pi$
$709$	30.1704			1.13307			0.566536	+	0.824037i	$0.308283\pi$
$710$	−14.6552			−0.549998
$711$	−32.9894	−	2.82011i	−1.23720	−	0.105762i
$712$	−4.28529			−0.160598
$713$		−	15.3125i		−	0.573459i
$714$	−14.2354	−	0.607350i	−0.532746	−	0.0227295i
$715$	−25.7261			−0.962102
$716$	12.6586			0.473076
$717$	47.2939	+	2.01778i	1.76622	+	0.0753555i
$718$			23.3922i			0.872989i
$719$	26.3466			0.982564			0.491282	−	0.871001i	$-0.336528\pi$
$719$	26.3466			0.982564			0.491282	+	0.871001i	$0.336528\pi$
$720$	−0.589033	+	6.89048i	−0.0219520	+	0.256793i
$721$		−	44.2457i		−	1.64780i
$722$	17.2735			0.642854
$723$	−1.52437	+	35.7289i	−0.0566918	+	1.32877i
$724$	12.2036			0.453544
$725$			2.38066i			0.0884156i
$726$	−0.727351	+	17.0480i	−0.0269945	+	0.632712i
$727$	3.12553			0.115920			0.0579598	−	0.998319i	$-0.481540\pi$
$727$	3.12553			0.115920			0.0579598	+	0.998319i	$0.481540\pi$
$728$			7.94876i			0.294601i
$729$	−26.1212	−	6.83240i	−0.967453	−	0.253052i
$730$	−31.0518			−1.14928
$731$	29.2125			1.08046
$732$	0.231290	+	0.00986794i	0.00854873	+	0.000364730i
$733$	19.7033			0.727758			0.363879	−	0.931446i	$-0.381452\pi$
$733$	19.7033			0.727758			0.363879	+	0.931446i	$0.381452\pi$
$734$		−	5.80088i		−	0.214114i
$735$	−14.2735	−	0.608976i	−0.526487	−	0.0224624i
$736$	8.45845			0.311783
$737$		−	15.2224i		−	0.560724i
$738$	−1.47621	+	17.2687i	−0.0543402	+	0.635668i
$739$		−	40.8815i		−	1.50385i	−0.659248	−	0.751925i	$-0.729125\pi$
$739$		−	40.8815i		−	1.50385i	0.659248	−	0.751925i	$-0.270875\pi$
$740$	6.53205			0.240123
$741$	5.55702	+	0.237089i	0.204142	+	0.00870968i
$742$		−	26.7386i		−	0.981605i
$743$		−	7.23882i		−	0.265567i	−0.991145	−	0.132783i	$-0.957609\pi$
$743$		−	7.23882i		−	0.265567i	0.991145	−	0.132783i	$-0.0423914\pi$
$744$	−3.13272	−	0.133657i	−0.114851	−	0.00490010i
$745$		−	39.4153i		−	1.44406i
$746$	−10.9210			−0.399847
$747$	28.4739	+	2.43410i	1.04181	+	0.0890590i
$748$			11.5497i			0.422298i
$749$			36.7482i			1.34275i
$750$	18.6931	+	0.797536i	0.682575	+	0.0291219i
$751$		−	38.6007i		−	1.40856i	−0.709923	−	0.704279i	$-0.751270\pi$
$751$		−	38.6007i		−	1.40856i	0.709923	−	0.704279i	$-0.248730\pi$
$752$	0.674272			0.0245882
$753$	14.0451	+	0.599229i	0.511830	+	0.0218371i
$754$	18.5320			0.674897
$755$	−32.1918			−1.17158
$756$	−2.15590	+	16.7619i	−0.0784094	+	0.609625i
$757$	14.8860			0.541041			0.270521	−	0.962714i	$-0.412804\pi$
$757$	14.8860			0.541041			0.270521	+	0.962714i	$0.412804\pi$
$758$	−35.6952			−1.29651
$759$	−2.85165	+	66.8385i	−0.103508	+	2.42608i
$760$		−	3.02894i		−	0.109871i
$761$			38.9612i			1.41234i	0.708041	+	0.706171i	$0.249579\pi$
$761$			38.9612i			1.41234i	−0.708041	+	0.706171i	$0.750421\pi$
$762$	0.231886	−	5.43507i	0.00840035	−	0.196892i
$763$			62.5842i			2.26570i
$764$	−17.4916			−0.632824
$765$	−17.4280	−	1.48984i	−0.630112	−	0.0538652i
$766$		−	20.9229i		−	0.755974i
$767$	3.86505	−	18.3703i	0.139559	−	0.663312i
$768$	0.0738304	−	1.73048i	0.00266412	−	0.0624432i
$769$			9.07465i			0.327240i	0.986523	+	0.163620i	$0.0523171\pi$
$769$			9.07465i			0.327240i	−0.986523	+	0.163620i	$0.947683\pi$
$770$			34.2361i			1.23378i
$771$	8.18621	+	0.349263i	0.294819	+	0.0125784i
$772$	3.92668			0.141324
$773$	−6.98553			−0.251252			−0.125626	−	0.992078i	$-0.540094\pi$
$773$	−6.98553			−0.251252			−0.125626	+	0.992078i	$0.540094\pi$
$774$	2.95121	−	34.5231i	0.106079	−	1.24091i
$775$		−	0.568363i		−	0.0204162i
$776$		−	8.58240i		−	0.308090i
$777$	15.9482	+	0.680424i	0.572137	+	0.0244101i
$778$			1.93248i			0.0692827i
$779$		−	7.59101i		−	0.271976i
$780$	−0.415948	+	9.74922i	−0.0148933	+	0.349078i
$781$			29.0303i			1.03879i
$782$			21.3939i			0.765045i
$783$	39.0794	+	5.02635i	1.39658	+	0.179627i
$784$	3.57813			0.127790
$785$	−28.5049			−1.01738
$786$	−0.809149	+	18.9653i	−0.0288614	+	0.676469i
$787$	12.5507			0.447385			0.223693	−	0.974660i	$-0.428189\pi$
$787$	12.5507			0.447385			0.223693	+	0.974660i	$0.428189\pi$
$788$			1.63966i			0.0584106i
$789$	−37.0968	−	1.58272i	−1.32068	−	0.0563465i
$790$			25.4415i			0.905170i
$791$	31.5725			1.12259
$792$	13.6493	+	1.16681i	0.485007	+	0.0414609i
$793$	0.326653			0.0115998
$794$			19.2875i			0.684488i
$795$	1.39920	−	32.7951i	0.0496244	−	1.16312i
$796$	−20.5203			−0.727322
$797$	−3.93475			−0.139376			−0.0696880	−	0.997569i	$-0.522200\pi$
$797$	−3.93475			−0.139376			−0.0696880	+	0.997569i	$0.522200\pi$
$798$	0.315516	−	7.39522i	0.0111691	−	0.261788i
$799$			1.70543i			0.0603339i
$800$	0.313957			0.0111000
$801$	−12.8091	−	1.09499i	−0.452589	−	0.0386896i
$802$	−4.84743			−0.171169
$803$			61.5104i			2.17066i
$804$	−5.76871	−	0.246121i	−0.203447	−	0.00868001i
$805$			63.4168i			2.23515i
$806$	−4.42437			−0.155842
$807$	−0.753084	+	17.6512i	−0.0265098	+	0.621352i
$808$	−8.85165			−0.311400
$809$	10.6503			0.374444			0.187222	−	0.982318i	$-0.440052\pi$
$809$	10.6503			0.374444			0.187222	+	0.982318i	$0.440052\pi$
$810$	−3.52136	+	20.4458i	−0.123728	+	0.718392i
$811$		−	36.7153i		−	1.28925i	−0.764499	−	0.644625i	$-0.777014\pi$
$811$		−	36.7153i		−	1.28925i	0.764499	−	0.644625i	$-0.222986\pi$
$812$		−	24.6623i		−	0.865476i
$813$	−1.37817	+	32.3023i	−0.0483346	+	1.13289i
$814$		−	12.9393i		−	0.453522i
$815$			4.78006i			0.167438i
$816$	4.37689	+	0.186739i	0.153222	+	0.00653717i
$817$			15.1758i			0.530933i
$818$		−	36.9306i		−	1.29125i
$819$	−2.03110	+	23.7596i	−0.0709722	+	0.830229i
$820$	13.3177			0.465073
$821$	−40.0031			−1.39612			−0.698058	−	0.716041i	$-0.745952\pi$
$821$	−40.0031			−1.39612			−0.698058	+	0.716041i	$0.745952\pi$
$822$	23.7442	+	1.01304i	0.828176	+	0.0353339i
$823$			47.8113i			1.66660i	0.552824	+	0.833298i	$0.313550\pi$
$823$			47.8113i			1.66660i	−0.552824	+	0.833298i	$0.686450\pi$
$824$			13.6040i			0.473918i
$825$	−0.105846	+	2.48088i	−0.00368509	+	0.0863731i
$826$	−24.4470	−	5.14357i	−0.850618	−	0.178968i
$827$			43.6206i			1.51684i	0.651768	+	0.758418i	$0.274027\pi$
$827$			43.6206i			1.51684i	−0.651768	+	0.758418i	$0.725973\pi$
$828$	25.2831	+	2.16133i	0.878650	+	0.0751115i
$829$	18.2431			0.633610			0.316805	−	0.948491i	$-0.397390\pi$
$829$	18.2431			0.633610			0.316805	+	0.948491i	$0.397390\pi$
$830$		−	21.9592i		−	0.762214i
$831$	−1.23701	+	28.9938i	−0.0429115	+	1.00578i
$832$		−	2.44397i		−	0.0847292i
$833$			9.05015i			0.313569i
$834$	1.51727	−	35.5626i	0.0525387	−	1.23143i
$835$	−40.8471			−1.41357
$836$	−6.00000			−0.207514
$837$	−9.32986	−	1.20000i	−0.322487	−	0.0414780i
$838$	24.1961			0.835839
$839$	−33.0019			−1.13935			−0.569676	−	0.821869i	$-0.692931\pi$
$839$	−33.0019			−1.13935			−0.569676	+	0.821869i	$0.692931\pi$
$840$	12.9742	+	0.553540i	0.447651	+	0.0190989i
$841$	−28.4985			−0.982708
$842$			23.5993i			0.813287i
$843$	34.7837	+	1.48404i	1.19802	+	0.0511131i
$844$			17.9919i			0.619308i
$845$		−	16.1987i		−	0.557253i
$846$	2.01547	+	0.172292i	0.0692932	+	0.00592354i
$847$	32.0415			1.10096
$848$			8.22118i			0.282317i
$849$	27.9823	+	1.19386i	0.960350	+	0.0409731i
$850$			0.794089i			0.0272370i
$851$		−	23.9680i		−	0.821611i
$852$	11.0014	+	0.469371i	0.376901	+	0.0160804i
$853$	29.6827			1.01631			0.508157	−	0.861264i	$-0.330327\pi$
$853$	29.6827			1.01631			0.508157	+	0.861264i	$0.330327\pi$
$854$		−	0.434706i		−	0.0148753i
$855$	0.773964	−	9.05379i	0.0264690	−	0.309633i
$856$		−	11.2988i		−	0.386185i
$857$	−46.4927			−1.58816			−0.794080	−	0.607814i	$-0.792047\pi$
$857$	−46.4927			−1.58816			−0.794080	+	0.607814i	$0.792047\pi$
$858$	19.3122	+	0.823949i	0.659306	+	0.0281292i
$859$		−	9.94325i		−	0.339259i	−0.985508	−	0.169630i	$-0.945743\pi$
$859$		−	9.94325i		−	0.339259i	0.985508	−	0.169630i	$-0.0542572\pi$
$860$	−26.6243			−0.907882
$861$	32.5154	+	1.38726i	1.10812	+	0.0472777i
$862$	−30.4771			−1.03806
$863$	−19.8257			−0.674874			−0.337437	−	0.941348i	$-0.609560\pi$
$863$	−19.8257			−0.674874			−0.337437	+	0.941348i	$0.609560\pi$
$864$	0.662864	−	5.15370i	0.0225511	−	0.175332i
$865$		−	2.46074i		−	0.0836677i
$866$	37.7340			1.28225
$867$	0.782799	−	18.3477i	0.0265853	−	0.623119i
$868$			5.88790i			0.199848i
$869$	50.3970			1.70960
$870$	1.29054	−	30.2484i	0.0437535	−	1.02552i
$871$	−8.14719			−0.276057
$872$		−	19.2424i		−	0.651631i
$873$	2.19301	−	25.6536i	0.0742220	−	0.868244i
$874$	−11.1140			−0.375938
$875$		−	35.1334i		−	1.18772i
$876$	23.3101	+	0.994520i	0.787575	+	0.0336017i
$877$	9.44847			0.319052			0.159526	−	0.987194i	$-0.449003\pi$
$877$	9.44847			0.319052			0.159526	+	0.987194i	$0.449003\pi$
$878$	6.37650			0.215197
$879$	−23.7235	−	1.01216i	−0.800174	−	0.0341392i
$880$		−	10.5264i		−	0.354844i
$881$	−22.2975			−0.751223			−0.375612	−	0.926777i	$-0.622567\pi$
$881$	−22.2975			−0.751223			−0.375612	+	0.926777i	$0.622567\pi$
$882$	10.6954	+	0.914297i	0.360132	+	0.0307860i
$883$	−46.4123			−1.56190			−0.780949	−	0.624595i	$-0.785264\pi$
$883$	−46.4123			−1.56190			−0.780949	+	0.624595i	$0.785264\pi$
$884$	6.18151			0.207907
$885$	−29.7152	−	7.58791i	−0.998866	−	0.255065i
$886$	21.9885			0.738718
$887$	1.77193			0.0594956			0.0297478	−	0.999557i	$-0.490530\pi$
$887$	1.77193			0.0594956			0.0297478	+	0.999557i	$0.490530\pi$
$888$	−4.90350	−	0.209207i	−0.164551	−	0.00702051i
$889$	−10.2151			−0.342605
$890$			9.87846i			0.331127i
$891$	40.5009	+	6.97543i	1.35683	+	0.233686i
$892$	12.8745			0.431069
$893$	−0.885965			−0.0296477
$894$	−1.26238	+	29.5884i	−0.0422204	+	0.989584i
$895$		−	29.1807i		−	0.975404i
$896$	−3.25240			−0.108655
$897$	35.7727	+	1.52623i	1.19441	+	0.0509594i
$898$			23.7841i			0.793687i
$899$	13.7273			0.457830
$900$	0.938447	+	0.0802233i	0.0312816	+	0.00267411i
$901$	−20.7938			−0.692742
$902$		−	26.3809i		−	0.878386i
$903$	−65.0040	−	2.77338i	−2.16320	−	0.0922923i
$904$	−9.70743			−0.322864
$905$		−	28.1318i		−	0.935133i
$906$	24.1659	+	1.03103i	0.802858	+	0.0342537i
$907$	9.37900			0.311425			0.155712	−	0.987802i	$-0.450233\pi$
$907$	9.37900			0.311425			0.155712	+	0.987802i	$0.450233\pi$
$908$	−6.85578			−0.227517
$909$	−26.4584	−	2.26180i	−0.877571	−	0.0750193i
$910$	18.3235			0.607418
$911$		−	52.5106i		−	1.73975i	−0.493269	−	0.869877i	$-0.664198\pi$
$911$		−	52.5106i		−	1.73975i	0.493269	−	0.869877i	$-0.335802\pi$
$912$	−0.0970099	+	2.27377i	−0.00321232	+	0.0752921i
$913$	−43.4988			−1.43960
$914$		−	8.86945i		−	0.293375i
$915$	0.0227476	−	0.533170i	0.000752012	−	0.0176261i
$916$			19.9984i			0.660766i
$917$	35.6449			1.17710
$918$	13.0352	+	1.67658i	0.430226	+	0.0553353i
$919$		−	43.5065i		−	1.43515i	−0.696483	−	0.717573i	$-0.745253\pi$
$919$		−	43.5065i		−	1.43515i	0.696483	−	0.717573i	$-0.254747\pi$
$920$		−	19.4984i		−	0.642844i
$921$	−0.351133	+	8.23005i	−0.0115702	+	0.271189i
$922$			17.7652i			0.585066i
$923$	15.5373			0.511417
$924$	1.09650	−	25.7004i	0.0360723	−	0.845482i
$925$		−	0.889631i		−	0.0292509i
$926$			27.7798i			0.912901i
$927$	−3.47614	+	40.6637i	−0.114171	+	1.33557i
$928$			7.58278i			0.248917i
$929$	16.6357			0.545801			0.272900	−	0.962042i	$-0.412017\pi$
$929$	16.6357			0.545801			0.272900	+	0.962042i	$0.412017\pi$
$930$	−0.308106	+	7.22156i	−0.0101032	+	0.236804i
$931$	−4.70151			−0.154086
$932$	3.71058			0.121544
$933$	10.1788	+	0.434278i	0.333240	+	0.0142176i
$934$	−8.59729			−0.281312
$935$	26.6243			0.870709
$936$	0.624491	−	7.30525i	0.0204121	−	0.238780i
$937$			41.3803i			1.35184i	0.736977	+	0.675918i	$0.236253\pi$
$937$			41.3803i			1.35184i	−0.736977	+	0.675918i	$0.763747\pi$
$938$			10.8422i			0.354010i
$939$	−2.22716	−	0.0950212i	−0.0726806	−	0.00310090i
$940$		−	1.55433i		−	0.0506968i
$941$	6.61621			0.215682			0.107841	−	0.994168i	$-0.465606\pi$
$941$	6.61621			0.215682			0.107841	+	0.994168i	$0.465606\pi$
$942$	21.3982	+	0.912948i	0.697190	+	0.0297454i
$943$		−	48.8663i		−	1.59131i
$944$	7.51658	+	1.58147i	0.244644	+	0.0514724i
$945$	38.6396	+	4.96979i	1.25695	+	0.161667i
$946$			52.7400i			1.71472i
$947$		−	29.6511i		−	0.963531i	−0.876300	−	0.481765i	$-0.839996\pi$
$947$		−	29.6511i		−	0.963531i	0.876300	−	0.481765i	$-0.160004\pi$
$948$	0.814835	−	19.0985i	0.0264646	−	0.620292i
$949$	32.9210			1.06866
$950$	−0.412525			−0.0133841
$951$	45.6776	+	1.94882i	1.48120	+	0.0631949i
$952$		−	8.22629i		−	0.266616i
$953$			8.40629i			0.272307i	0.990688	+	0.136153i	$0.0434740\pi$
$953$			8.40629i			0.272307i	−0.990688	+	0.136153i	$0.956526\pi$
$954$	−2.10071	+	24.5739i	−0.0680129	+	0.795610i
$955$			40.3217i			1.30478i
$956$			27.3300i			0.883914i
$957$	−59.9190	−	2.55643i	−1.93690	−	0.0826376i
$958$			33.5116i			1.08271i
$959$		−	44.6269i		−	1.44108i
$960$	−3.98910	−	0.170194i	−0.128748	−	0.00549299i
$961$	27.7227			0.894282
$962$	−6.92525			−0.223279
$963$	2.88711	−	33.7732i	0.0930357	−	1.08833i
$964$	−20.6469			−0.664991
$965$		−	9.05178i		−	0.291387i
$966$	2.03110	−	47.6059i	0.0653494	−	1.53170i
$967$		−	1.73649i		−	0.0558419i	−0.999610	−	0.0279210i	$-0.991111\pi$
$967$		−	1.73649i		−	0.0558419i	0.999610	−	0.0279210i	$-0.00888867\pi$
$968$	−9.85165			−0.316644
$969$	−5.75104	−	0.245367i	−0.184750	−	0.00788232i
$970$	−19.7842			−0.635232
$971$		−	10.7342i		−	0.344477i	−0.985055	−	0.172239i	$-0.944900\pi$
$971$		−	10.7342i		−	0.344477i	0.985055	−	0.172239i	$-0.0551000\pi$
$972$	3.29826	−	15.2355i	0.105792	−	0.488680i
$973$	−66.8393			−2.14277
$974$	−15.2524			−0.488719
$975$	1.32779	+	0.0566500i	0.0425234	+	0.00181425i
$976$			0.133657i			0.00427825i
$977$	−54.0683			−1.72980			−0.864899	−	0.501946i	$-0.832618\pi$
$977$	−54.0683			−1.72980			−0.864899	+	0.501946i	$0.832618\pi$
$978$	0.153094	−	3.58831i	0.00489542	−	0.114742i
$979$	19.5682			0.625402
$980$		−	8.24832i		−	0.263483i
$981$	4.91690	−	57.5176i	0.156984	−	1.83639i
$982$			11.8006i			0.376571i
$983$	10.8443			0.345879			0.172939	−	0.984932i	$-0.444674\pi$
$983$	10.8443			0.345879			0.172939	+	0.984932i	$0.444674\pi$
$984$	−9.99734	−	0.426534i	−0.318704	−	0.0135974i
$985$	3.77976			0.120433
$986$	−19.1791			−0.610786
$987$	0.161911	−	3.79495i	0.00515367	−	0.120794i
$988$			3.21126i			0.102164i
$989$			97.6923i			3.10643i
$990$	2.68974	−	31.4644i	0.0854855	−	1.00000i
$991$		−	46.3054i		−	1.47094i	−0.677557	−	0.735470i	$-0.736961\pi$
$991$		−	46.3054i		−	1.47094i	0.677557	−	0.735470i	$-0.263039\pi$
$992$		−	1.81032i		−	0.0574778i
$993$	1.16025	−	27.1946i	0.0368194	−	0.862993i
$994$		−	20.6769i		−	0.655832i
$995$			47.3034i			1.49962i
$996$	−0.703303	+	16.4844i	−0.0222850	+	0.522328i
$997$	−30.0886			−0.952916			−0.476458	−	0.879197i	$-0.658080\pi$
$997$	−30.0886			−0.952916			−0.476458	+	0.879197i	$0.658080\pi$
$998$	13.2132			0.418258
$999$	−14.6036	−	1.87830i	−0.462037	−	0.0594267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.c.a.353.5	✓	10
3.2	odd	2		354.2.c.b.353.6	yes	10
59.58	odd	2		354.2.c.b.353.5	yes	10
177.176	even	2	inner	354.2.c.a.353.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.c.a.353.5	✓	10	1.1	even	1	trivial
354.2.c.a.353.6	yes	10	177.176	even	2	inner
354.2.c.b.353.5	yes	10	59.58	odd	2
354.2.c.b.353.6	yes	10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.0738304 - 1.73048i) q^{3} +1.00000 q^{4} -2.30520i q^{5} +(-0.0738304 + 1.73048i) q^{6} +3.25240 q^{7} -1.00000 q^{8} +(-2.98910 - 0.255524i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.0738304 - 1.73048i) q^{3} +1.00000 q^{4} -2.30520i q^{5} +(-0.0738304 + 1.73048i) q^{6} +3.25240 q^{7} -1.00000 q^{8} +(-2.98910 - 0.255524i) q^{9} +2.30520i q^{10} +4.56636 q^{11} +(0.0738304 - 1.73048i) q^{12} -2.44397i q^{13} -3.25240 q^{14} +(-3.98910 - 0.170194i) q^{15} +1.00000 q^{16} +2.52929i q^{17} +(2.98910 + 0.255524i) q^{18} -1.31396 q^{19} -2.30520i q^{20} +(0.240126 - 5.62821i) q^{21} -4.56636 q^{22} -8.45845 q^{23} +(-0.0738304 + 1.73048i) q^{24} -0.313957 q^{25} +2.44397i q^{26} +(-0.662864 + 5.15370i) q^{27} +3.25240 q^{28} -7.58278i q^{29} +(3.98910 + 0.170194i) q^{30} +1.81032i q^{31} -1.00000 q^{32} +(0.337136 - 7.90198i) q^{33} -2.52929i q^{34} -7.49745i q^{35} +(-2.98910 - 0.255524i) q^{36} +2.83361i q^{37} +1.31396 q^{38} +(-4.22922 - 0.180439i) q^{39} +2.30520i q^{40} +5.77722i q^{41} +(-0.240126 + 5.62821i) q^{42} -11.5497i q^{43} +4.56636 q^{44} +(-0.589033 + 6.89048i) q^{45} +8.45845 q^{46} +0.674272 q^{47} +(0.0738304 - 1.73048i) q^{48} +3.57813 q^{49} +0.313957 q^{50} +(4.37689 + 0.186739i) q^{51} -2.44397i q^{52} +8.22118i q^{53} +(0.662864 - 5.15370i) q^{54} -10.5264i q^{55} -3.25240 q^{56} +(-0.0970099 + 2.27377i) q^{57} +7.58278i q^{58} +(7.51658 + 1.58147i) q^{59} +(-3.98910 - 0.170194i) q^{60} +0.133657i q^{61} -1.81032i q^{62} +(-9.72175 - 0.831066i) q^{63} +1.00000 q^{64} -5.63383 q^{65} +(-0.337136 + 7.90198i) q^{66} -3.33360i q^{67} +2.52929i q^{68} +(-0.624491 + 14.6371i) q^{69} +7.49745i q^{70} +6.35743i q^{71} +(2.98910 + 0.255524i) q^{72} +13.4703i q^{73} -2.83361i q^{74} +(-0.0231795 + 0.543295i) q^{75} -1.31396 q^{76} +14.8516 q^{77} +(4.22922 + 0.180439i) q^{78} +11.0366 q^{79} -2.30520i q^{80} +(8.86942 + 1.52757i) q^{81} -5.77722i q^{82} -9.52592 q^{83} +(0.240126 - 5.62821i) q^{84} +5.83054 q^{85} +11.5497i q^{86} +(-13.1218 - 0.559839i) q^{87} -4.56636 q^{88} +4.28529 q^{89} +(0.589033 - 6.89048i) q^{90} -7.94876i q^{91} -8.45845 q^{92} +(3.13272 + 0.133657i) q^{93} -0.674272 q^{94} +3.02894i q^{95} +(-0.0738304 + 1.73048i) q^{96} +8.58240i q^{97} -3.57813 q^{98} +(-13.6493 - 1.16681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - q^{3} + 10 q^{4} + q^{6} - 2 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - q^3 + 10 * q^4 + q^6 - 2 * q^7 - 10 * q^8 + 3 * q^9	\( 10 q - 10 q^{2} - q^{3} + 10 q^{4} + q^{6} - 2 q^{7} - 10 q^{8} + 3 q^{9} + 4 q^{11} - q^{12} + 2 q^{14} - 7 q^{15} + 10 q^{16} - 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} - 8 q^{23} + q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} + 7 q^{30} - 10 q^{32} + 3 q^{36} + 6 q^{38} - 4 q^{39} + 3 q^{42} + 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} - 4 q^{50} + 2 q^{51} + 10 q^{54} + 2 q^{56} - 3 q^{57} + 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} + 16 q^{65} + 14 q^{69} - 3 q^{72} - 4 q^{75} - 6 q^{76} + 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} + 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} - 16 q^{89} + 11 q^{90} - 8 q^{92} - 52 q^{93} + q^{96} - 8 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - q^3 + 10 * q^4 + q^6 - 2 * q^7 - 10 * q^8 + 3 * q^9 + 4 * q^11 - q^12 + 2 * q^14 - 7 * q^15 + 10 * q^16 - 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 - 8 * q^23 + q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 + 7 * q^30 - 10 * q^32 + 3 * q^36 + 6 * q^38 - 4 * q^39 + 3 * q^42 + 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 - 4 * q^50 + 2 * q^51 + 10 * q^54 + 2 * q^56 - 3 * q^57 + 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 + 16 * q^65 + 14 * q^69 - 3 * q^72 - 4 * q^75 - 6 * q^76 + 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 + 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 - 16 * q^89 + 11 * q^90 - 8 * q^92 - 52 * q^93 + q^96 - 8 * q^98 + 2 * q^99

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