LMFDB - Embedded newform 464.2.k.c.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(191,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("464.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.k (of order $4$, degree $2$, 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{17} - 6 x^{16} - 2 x^{15} + 18 x^{14} + 42 x^{13} + 9 x^{12} - 30 x^{11} - 142 x^{10} + \cdots + 1024 $ x^20 - 6x^17 - 6x^16 - 2x^15 + 18x^14 + 42x^13 + 9x^12 - 30x^11 - 142x^10 - 60x^9 + 36x^8 + 336x^7 + 288x^6 - 64x^5 - 384x^4 - 768*x^3 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.4
Root			$1.41029 + 0.105218i$ of defining polynomial
Character	$\chi$	$=$	464.191
Dual form			464.2.k.c.447.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30508 - 1.30508i) q^{3} -3.62458i q^{5} +1.31987i q^{7} +0.406445i q^{9} +O(q^{10})$	\(q+(-1.30508 - 1.30508i) q^{3} -3.62458i q^{5} +1.31987i q^{7} +0.406445i q^{9} +(0.158748 + 0.158748i) q^{11} -4.10656i q^{13} +(-4.73035 + 4.73035i) q^{15} +(-1.97758 + 1.97758i) q^{17} +(-0.759841 - 0.759841i) q^{19} +(1.72253 - 1.72253i) q^{21} +3.15705i q^{23} -8.13758 q^{25} +(-3.38479 + 3.38479i) q^{27} +(-0.639083 + 5.34711i) q^{29} +(-6.58066 - 6.58066i) q^{31} -0.414358i q^{33} +4.78397 q^{35} +(0.338500 + 0.338500i) q^{37} +(-5.35937 + 5.35937i) q^{39} +(0.459886 + 0.459886i) q^{41} +(-7.46477 - 7.46477i) q^{43} +1.47319 q^{45} +(4.11446 - 4.11446i) q^{47} +5.25795 q^{49} +5.16179 q^{51} +7.59645 q^{53} +(0.575397 - 0.575397i) q^{55} +1.98330i q^{57} -10.0339i q^{59} +(3.51872 - 3.51872i) q^{61} -0.536453 q^{63} -14.8845 q^{65} -2.87626 q^{67} +(4.12019 - 4.12019i) q^{69} +14.3931 q^{71} +(-8.40055 - 8.40055i) q^{73} +(10.6202 + 10.6202i) q^{75} +(-0.209527 + 0.209527i) q^{77} +(8.03404 + 8.03404i) q^{79} +10.0541 q^{81} +15.0176i q^{83} +(7.16791 + 7.16791i) q^{85} +(7.81243 - 6.14433i) q^{87} +(-7.68091 + 7.68091i) q^{89} +5.42012 q^{91} +17.1765i q^{93} +(-2.75411 + 2.75411i) q^{95} +(3.16000 + 3.16000i) q^{97} +(-0.0645225 + 0.0645225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 4 q^{17} - 16 q^{21} - 28 q^{25} - 4 q^{29} - 20 q^{37} - 4 q^{41} - 40 q^{45} + 28 q^{49} + 48 q^{53} + 4 q^{61} + 40 q^{65} - 24 q^{69} - 20 q^{73} - 16 q^{77} + 108 q^{81} + 16 q^{85} + 36 q^{89} - 36 q^{97}+O(q^{100}) $ 20 * q - 4 * q^17 - 16 * q^21 - 28 * q^25 - 4 * q^29 - 20 * q^37 - 4 * q^41 - 40 * q^45 + 28 * q^49 + 48 * q^53 + 4 * q^61 + 40 * q^65 - 24 * q^69 - 20 * q^73 - 16 * q^77 + 108 * q^81 + 16 * q^85 + 36 * q^89 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.30508	−	1.30508i	−0.753486	−	0.753486i	0.221642	−	0.975128i	$-0.428858\pi$
$3$	−1.30508	−	1.30508i	−0.753486	−	0.753486i	−0.975128	+	0.221642i	$0.928858\pi$
$4$		0			0
$5$		−	3.62458i		−	1.62096i	−0.585765	−	0.810481i	$-0.699206\pi$
$5$		−	3.62458i		−	1.62096i	0.585765	−	0.810481i	$-0.300794\pi$
$6$		0			0
$7$			1.31987i			0.498864i	0.968392	+	0.249432i	$0.0802438\pi$
$7$			1.31987i			0.498864i	−0.968392	+	0.249432i	$0.919756\pi$
$8$		0			0
$9$			0.406445i			0.135482i
$10$		0			0
$11$	0.158748	+	0.158748i	0.0478645	+	0.0478645i	0.730634	−	0.682769i	$-0.239225\pi$
$11$	0.158748	+	0.158748i	0.0478645	+	0.0478645i	−0.682769	+	0.730634i	$0.739225\pi$
$12$		0			0
$13$		−	4.10656i		−	1.13895i	−0.822007	−	0.569477i	$-0.807146\pi$
$13$		−	4.10656i		−	1.13895i	0.822007	−	0.569477i	$-0.192854\pi$
$14$		0			0
$15$	−4.73035	+	4.73035i	−1.22137	+	1.22137i
$16$		0			0
$17$	−1.97758	+	1.97758i	−0.479635	+	0.479635i	−0.905015	−	0.425380i	$-0.860140\pi$
$17$	−1.97758	+	1.97758i	−0.479635	+	0.479635i	0.425380	+	0.905015i	$0.360140\pi$
$18$		0			0
$19$	−0.759841	−	0.759841i	−0.174320	−	0.174320i	0.614555	−	0.788874i	$-0.289336\pi$
$19$	−0.759841	−	0.759841i	−0.174320	−	0.174320i	−0.788874	+	0.614555i	$0.789336\pi$
$20$		0			0
$21$	1.72253	−	1.72253i	0.375887	−	0.375887i
$22$		0			0
$23$			3.15705i			0.658290i	0.944279	+	0.329145i	$0.106761\pi$
$23$			3.15705i			0.658290i	−0.944279	+	0.329145i	$0.893239\pi$
$24$		0			0
$25$	−8.13758			−1.62752
$26$		0			0
$27$	−3.38479	+	3.38479i	−0.651402	+	0.651402i
$28$		0			0
$29$	−0.639083	+	5.34711i	−0.118675	+	0.992933i
$29$	−0.639083	+	5.34711i	−0.118675	+	0.992933i
$30$		0			0
$31$	−6.58066	−	6.58066i	−1.18192	−	1.18192i	−0.979246	−	0.202676i	$-0.935036\pi$
$31$	−6.58066	−	6.58066i	−1.18192	−	1.18192i	−0.202676	−	0.979246i	$-0.564964\pi$
$32$		0			0
$33$		−	0.414358i		−	0.0721304i
$34$		0			0
$35$	4.78397			0.808639
$36$		0			0
$37$	0.338500	+	0.338500i	0.0556491	+	0.0556491i	0.734384	−	0.678735i	$-0.237471\pi$
$37$	0.338500	+	0.338500i	0.0556491	+	0.0556491i	−0.678735	+	0.734384i	$0.737471\pi$
$38$		0			0
$39$	−5.35937	+	5.35937i	−0.858186	+	0.858186i
$40$		0			0
$41$	0.459886	+	0.459886i	0.0718221	+	0.0718221i	0.742105	−	0.670283i	$-0.233827\pi$
$41$	0.459886	+	0.459886i	0.0718221	+	0.0718221i	−0.670283	+	0.742105i	$0.733827\pi$
$42$		0			0
$43$	−7.46477	−	7.46477i	−1.13837	−	1.13837i	−0.988743	−	0.149624i	$-0.952194\pi$
$43$	−7.46477	−	7.46477i	−1.13837	−	1.13837i	−0.149624	−	0.988743i	$-0.547806\pi$
$44$		0			0
$45$	1.47319			0.219610
$46$		0			0
$47$	4.11446	−	4.11446i	0.600156	−	0.600156i	−0.340198	−	0.940354i	$-0.610494\pi$
$47$	4.11446	−	4.11446i	0.600156	−	0.600156i	0.940354	+	0.340198i	$0.110494\pi$
$48$		0			0
$49$	5.25795			0.751135
$50$		0			0
$51$	5.16179			0.722796
$52$		0			0
$53$	7.59645			1.04345			0.521726	−	0.853113i	$-0.325288\pi$
$53$	7.59645			1.04345			0.521726	+	0.853113i	$0.325288\pi$
$54$		0			0
$55$	0.575397	−	0.575397i	0.0775865	−	0.0775865i
$56$		0			0
$57$			1.98330i			0.262695i
$58$		0			0
$59$		−	10.0339i		−	1.30630i	−0.757230	−	0.653149i	$-0.773448\pi$
$59$		−	10.0339i		−	1.30630i	0.757230	−	0.653149i	$-0.226552\pi$
$60$		0			0
$61$	3.51872	−	3.51872i	0.450526	−	0.450526i	−0.445003	−	0.895529i	$-0.646797\pi$
$61$	3.51872	−	3.51872i	0.450526	−	0.450526i	0.895529	+	0.445003i	$0.146797\pi$
$62$		0			0
$63$	−0.536453			−0.0675868
$64$		0			0
$65$	−14.8845			−1.84620
$66$		0			0
$67$	−2.87626			−0.351391			−0.175695	−	0.984445i	$-0.556217\pi$
$67$	−2.87626			−0.351391			−0.175695	+	0.984445i	$0.556217\pi$
$68$		0			0
$69$	4.12019	−	4.12019i	0.496012	−	0.496012i
$70$		0			0
$71$	14.3931			1.70815			0.854073	−	0.520153i	$-0.174125\pi$
$71$	14.3931			1.70815			0.854073	+	0.520153i	$0.174125\pi$
$72$		0			0
$73$	−8.40055	−	8.40055i	−0.983210	−	0.983210i	0.0166514	−	0.999861i	$-0.494699\pi$
$73$	−8.40055	−	8.40055i	−0.983210	−	0.983210i	−0.999861	+	0.0166514i	$0.994699\pi$
$74$		0			0
$75$	10.6202	+	10.6202i	1.22631	+	1.22631i
$76$		0			0
$77$	−0.209527	+	0.209527i	−0.0238778	+	0.0238778i
$78$		0			0
$79$	8.03404	+	8.03404i	0.903900	+	0.903900i	0.995771	−	0.0918707i	$-0.0292847\pi$
$79$	8.03404	+	8.03404i	0.903900	+	0.903900i	−0.0918707	+	0.995771i	$0.529285\pi$
$80$		0			0
$81$	10.0541			1.11713
$82$		0			0
$83$			15.0176i			1.64840i	0.566298	+	0.824200i	$0.308375\pi$
$83$			15.0176i			1.64840i	−0.566298	+	0.824200i	$0.691625\pi$
$84$		0			0
$85$	7.16791	+	7.16791i	0.777469	+	0.777469i
$86$		0			0
$87$	7.81243	−	6.14433i	0.837581	−	0.658741i
$88$		0			0
$89$	−7.68091	+	7.68091i	−0.814175	+	0.814175i	−0.985257	−	0.171082i	$-0.945274\pi$
$89$	−7.68091	+	7.68091i	−0.814175	+	0.814175i	0.171082	+	0.985257i	$0.445274\pi$
$90$		0			0
$91$	5.42012			0.568183
$92$		0			0
$93$			17.1765i			1.78112i
$94$		0			0
$95$	−2.75411	+	2.75411i	−0.282565	+	0.282565i
$96$		0			0
$97$	3.16000	+	3.16000i	0.320849	+	0.320849i	0.849093	−	0.528244i	$-0.177149\pi$
$97$	3.16000	+	3.16000i	0.320849	+	0.320849i	−0.528244	+	0.849093i	$0.677149\pi$
$98$		0			0
$99$	−0.0645225	+	0.0645225i	−0.00648475	+	0.00648475i
$100$		0			0
$101$	9.65560	−	9.65560i	0.960769	−	0.960769i	−0.0384904	−	0.999259i	$-0.512255\pi$
$101$	9.65560	−	9.65560i	0.960769	−	0.960769i	0.999259	+	0.0384904i	$0.0122549\pi$
$102$		0			0
$103$		−	16.1493i		−	1.59124i	−0.605798	−	0.795619i	$-0.707146\pi$
$103$		−	16.1493i		−	1.59124i	0.605798	−	0.795619i	$-0.292854\pi$
$104$		0			0
$105$	−6.24344	−	6.24344i	−0.609298	−	0.609298i
$106$		0			0
$107$		−	1.66695i		−	0.161150i	−0.996749	−	0.0805752i	$-0.974324\pi$
$107$		−	1.66695i		−	0.161150i	0.996749	−	0.0805752i	$-0.0256757\pi$
$108$		0			0
$109$			2.30158i			0.220451i	0.993907	+	0.110226i	$0.0351574\pi$
$109$			2.30158i			0.220451i	−0.993907	+	0.110226i	$0.964843\pi$
$110$		0			0
$111$		−	0.883537i		−	0.0838616i
$112$		0			0
$113$	−1.52681	−	1.52681i	−0.143630	−	0.143630i	0.631635	−	0.775266i	$-0.282384\pi$
$113$	−1.52681	−	1.52681i	−0.143630	−	0.143630i	−0.775266	+	0.631635i	$0.782384\pi$
$114$		0			0
$115$	11.4430			1.06706
$116$		0			0
$117$	1.66909			0.154307
$118$		0			0
$119$	−2.61015	−	2.61015i	−0.239272	−	0.239272i
$120$		0			0
$121$		−	10.9496i		−	0.995418i
$122$		0			0
$123$		−	1.20037i		−	0.108234i
$124$		0			0
$125$			11.3724i			1.01718i
$126$		0			0
$127$	−11.0231	−	11.0231i	−0.978142	−	0.978142i	0.0216241	−	0.999766i	$-0.493116\pi$
$127$	−11.0231	−	11.0231i	−0.978142	−	0.978142i	−0.999766	+	0.0216241i	$0.993116\pi$
$128$		0			0
$129$			19.4842i			1.71549i
$130$		0			0
$131$	3.38044	−	3.38044i	0.295350	−	0.295350i	−0.543839	−	0.839189i	$-0.683030\pi$
$131$	3.38044	−	3.38044i	0.295350	−	0.295350i	0.839189	+	0.543839i	$0.183030\pi$
$132$		0			0
$133$	1.00289	−	1.00289i	0.0869617	−	0.0869617i
$134$		0			0
$135$	12.2684	+	12.2684i	1.05590	+	1.05590i
$136$		0			0
$137$	−11.0899	+	11.0899i	−0.947471	+	0.947471i	−0.998688	−	0.0512170i	$-0.983690\pi$
$137$	−11.0899	+	11.0899i	−0.947471	+	0.947471i	0.0512170	+	0.998688i	$0.483690\pi$
$138$		0			0
$139$		−	22.6926i		−	1.92476i	−0.271711	−	0.962379i	$-0.587590\pi$
$139$		−	22.6926i		−	1.92476i	0.271711	−	0.962379i	$-0.412410\pi$
$140$		0			0
$141$	−10.7394			−0.904419
$142$		0			0
$143$	0.651910	−	0.651910i	0.0545154	−	0.0545154i
$144$		0			0
$145$	19.3810	+	2.31641i	1.60951	+	0.192367i
$146$		0			0
$147$	−6.86202	−	6.86202i	−0.565970	−	0.565970i
$148$		0			0
$149$		−	19.4063i		−	1.58983i	−0.606722	−	0.794914i	$-0.707516\pi$
$149$		−	19.4063i		−	1.58983i	0.606722	−	0.794914i	$-0.292484\pi$
$150$		0			0
$151$	13.7683			1.12045			0.560225	−	0.828341i	$-0.310715\pi$
$151$	13.7683			1.12045			0.560225	+	0.828341i	$0.310715\pi$
$152$		0			0
$153$	−0.803778	−	0.803778i	−0.0649816	−	0.0649816i
$154$		0			0
$155$	−23.8521	+	23.8521i	−1.91585	+	1.91585i
$156$		0			0
$157$	16.8173	+	16.8173i	1.34217	+	1.34217i	0.893900	+	0.448266i	$0.147958\pi$
$157$	16.8173	+	16.8173i	1.34217	+	1.34217i	0.448266	+	0.893900i	$0.352042\pi$
$158$		0			0
$159$	−9.91394	−	9.91394i	−0.786226	−	0.786226i
$160$		0			0
$161$	−4.16689			−0.328397
$162$		0			0
$163$	−5.00902	+	5.00902i	−0.392337	+	0.392337i	−0.875520	−	0.483183i	$-0.839481\pi$
$163$	−5.00902	+	5.00902i	−0.392337	+	0.392337i	0.483183	+	0.875520i	$0.339481\pi$
$164$		0			0
$165$	−1.50187			−0.116921
$166$		0			0
$167$	1.73439			0.134211			0.0671057	−	0.997746i	$-0.478624\pi$
$167$	1.73439			0.134211			0.0671057	+	0.997746i	$0.478624\pi$
$168$		0			0
$169$	−3.86381			−0.297216
$170$		0			0
$171$	0.308833	−	0.308833i	0.0236171	−	0.0236171i
$172$		0			0
$173$		−	21.4781i		−	1.63295i	−0.577381	−	0.816475i	$-0.695925\pi$
$173$		−	21.4781i		−	1.63295i	0.577381	−	0.816475i	$-0.304075\pi$
$174$		0			0
$175$		−	10.7405i		−	0.811909i
$176$		0			0
$177$	−13.0949	+	13.0949i	−0.984276	+	0.984276i
$178$		0			0
$179$	−8.76538			−0.655155			−0.327578	−	0.944824i	$-0.606232\pi$
$179$	−8.76538			−0.655155			−0.327578	+	0.944824i	$0.606232\pi$
$180$		0			0
$181$	−5.78208			−0.429778			−0.214889	−	0.976638i	$-0.568939\pi$
$181$	−5.78208			−0.429778			−0.214889	+	0.976638i	$0.568939\pi$
$182$		0			0
$183$	−9.18439			−0.678929
$184$		0			0
$185$	1.22692	−	1.22692i	0.0902051	−	0.0902051i
$186$		0			0
$187$	−0.627877			−0.0459149
$188$		0			0
$189$	−4.46747	−	4.46747i	−0.324961	−	0.324961i
$190$		0			0
$191$	12.9379	+	12.9379i	0.936156	+	0.936156i	0.998081	−	0.0619248i	$-0.0197239\pi$
$191$	12.9379	+	12.9379i	0.936156	+	0.936156i	−0.0619248	+	0.998081i	$0.519724\pi$
$192$		0			0
$193$	5.05224	−	5.05224i	0.363668	−	0.363668i	−0.501493	−	0.865162i	$-0.667216\pi$
$193$	5.05224	−	5.05224i	0.363668	−	0.363668i	0.865162	+	0.501493i	$0.167216\pi$
$194$		0			0
$195$	19.4255	+	19.4255i	1.39109	+	1.39109i
$196$		0			0
$197$	−10.7853			−0.768419			−0.384209	−	0.923246i	$-0.625526\pi$
$197$	−10.7853			−0.768419			−0.384209	+	0.923246i	$0.625526\pi$
$198$		0			0
$199$		−	2.82753i		−	0.200438i	−0.994965	−	0.100219i	$-0.968046\pi$
$199$		−	2.82753i		−	0.200438i	0.994965	−	0.100219i	$-0.0319543\pi$
$200$		0			0
$201$	3.75373	+	3.75373i	0.264768	+	0.264768i
$202$		0			0
$203$	−7.05748	−	0.843506i	−0.495338	−	0.0592025i
$204$		0			0
$205$	1.66689	−	1.66689i	0.116421	−	0.116421i
$206$		0			0
$207$	−1.28317			−0.0891861
$208$		0			0
$209$		−	0.241247i		−	0.0166874i
$210$		0			0
$211$	1.59299	−	1.59299i	0.109666	−	0.109666i	−0.650145	−	0.759810i	$-0.725292\pi$
$211$	1.59299	−	1.59299i	0.109666	−	0.109666i	0.759810	+	0.650145i	$0.225292\pi$
$212$		0			0
$213$	−18.7841	−	18.7841i	−1.28706	−	1.28706i
$214$		0			0
$215$	−27.0567	+	27.0567i	−1.84525	+	1.84525i
$216$		0			0
$217$	8.68561	−	8.68561i	0.589618	−	0.589618i
$218$		0			0
$219$			21.9267i			1.48167i
$220$		0			0
$221$	8.12106	+	8.12106i	0.546282	+	0.546282i
$222$		0			0
$223$			18.8393i			1.26157i	0.775957	+	0.630786i	$0.217267\pi$
$223$			18.8393i			1.26157i	−0.775957	+	0.630786i	$0.782733\pi$
$224$		0			0
$225$		−	3.30748i		−	0.220498i
$226$		0			0
$227$		−	9.30184i		−	0.617385i	−0.951162	−	0.308692i	$-0.900109\pi$
$227$		−	9.30184i		−	0.617385i	0.951162	−	0.308692i	$-0.0998913\pi$
$228$		0			0
$229$	−0.834107	−	0.834107i	−0.0551194	−	0.0551194i	0.679010	−	0.734129i	$-0.262409\pi$
$229$	−0.834107	−	0.834107i	−0.0551194	−	0.0551194i	−0.734129	+	0.679010i	$0.762409\pi$
$230$		0			0
$231$	0.546898			0.0359832
$232$		0			0
$233$	5.96051			0.390486			0.195243	−	0.980755i	$-0.437450\pi$
$233$	5.96051			0.390486			0.195243	+	0.980755i	$0.437450\pi$
$234$		0			0
$235$	−14.9132	−	14.9132i	−0.972830	−	0.972830i
$236$		0			0
$237$		−	20.9701i		−	1.36215i
$238$		0			0
$239$		−	0.384705i		−	0.0248845i	−0.999923	−	0.0124422i	$-0.996039\pi$
$239$		−	0.384705i		−	0.0248845i	0.999923	−	0.0124422i	$-0.00396059\pi$
$240$		0			0
$241$			14.3854i			0.926642i	0.886191	+	0.463321i	$0.153342\pi$
$241$			14.3854i			0.926642i	−0.886191	+	0.463321i	$0.846658\pi$
$242$		0			0
$243$	−2.96705	−	2.96705i	−0.190336	−	0.190336i
$244$		0			0
$245$		−	19.0578i		−	1.21756i
$246$		0			0
$247$	−3.12033	+	3.12033i	−0.198542	+	0.198542i
$248$		0			0
$249$	19.5992	−	19.5992i	1.24205	−	1.24205i
$250$		0			0
$251$	−2.37640	−	2.37640i	−0.149997	−	0.149997i	0.628120	−	0.778117i	$-0.283825\pi$
$251$	−2.37640	−	2.37640i	−0.149997	−	0.149997i	−0.778117	+	0.628120i	$0.783825\pi$
$252$		0			0
$253$	−0.501177	+	0.501177i	−0.0315087	+	0.0315087i
$254$		0			0
$255$		−	18.7093i		−	1.17162i
$256$		0			0
$257$	−1.31539			−0.0820517			−0.0410258	−	0.999158i	$-0.513063\pi$
$257$	−1.31539			−0.0820517			−0.0410258	+	0.999158i	$0.513063\pi$
$258$		0			0
$259$	−0.446776	+	0.446776i	−0.0277613	+	0.0277613i
$260$		0			0
$261$	−2.17330	−	0.259752i	−0.134524	−	0.0160782i
$262$		0			0
$263$	−15.4544	−	15.4544i	−0.952961	−	0.952961i	0.0459810	−	0.998942i	$-0.485359\pi$
$263$	−15.4544	−	15.4544i	−0.952961	−	0.952961i	−0.998942	+	0.0459810i	$0.985359\pi$
$264$		0			0
$265$		−	27.5339i		−	1.69140i
$266$		0			0
$267$	20.0483			1.22694
$268$		0			0
$269$	14.2527	+	14.2527i	0.869005	+	0.869005i	0.992362	−	0.123357i	$-0.0393660\pi$
$269$	14.2527	+	14.2527i	0.869005	+	0.869005i	−0.123357	+	0.992362i	$0.539366\pi$
$270$		0			0
$271$	6.64099	−	6.64099i	0.403411	−	0.403411i	−0.476022	−	0.879433i	$-0.657922\pi$
$271$	6.64099	−	6.64099i	0.403411	−	0.403411i	0.879433	+	0.476022i	$0.157922\pi$
$272$		0			0
$273$	−7.07366	−	7.07366i	−0.428117	−	0.428117i
$274$		0			0
$275$	−1.29183	−	1.29183i	−0.0779002	−	0.0779002i
$276$		0			0
$277$	−17.1329			−1.02942			−0.514708	−	0.857366i	$-0.672100\pi$
$277$	−17.1329			−1.02942			−0.514708	+	0.857366i	$0.672100\pi$
$278$		0			0
$279$	2.67467	−	2.67467i	0.160129	−	0.160129i
$280$		0			0
$281$	0.939644			0.0560544			0.0280272	−	0.999607i	$-0.491077\pi$
$281$	0.939644			0.0560544			0.0280272	+	0.999607i	$0.491077\pi$
$282$		0			0
$283$	−19.7398			−1.17341			−0.586704	−	0.809801i	$-0.699575\pi$
$283$	−19.7398			−1.17341			−0.586704	+	0.809801i	$0.699575\pi$
$284$		0			0
$285$	7.18863			0.425818
$286$		0			0
$287$	−0.606989	+	0.606989i	−0.0358294	+	0.0358294i
$288$		0			0
$289$			9.17833i			0.539901i
$290$		0			0
$291$		−	8.24807i		−	0.483511i
$292$		0			0
$293$	−13.1920	+	13.1920i	−0.770687	+	0.770687i	−0.978227	−	0.207539i	$-0.933455\pi$
$293$	−13.1920	+	13.1920i	−0.770687	+	0.770687i	0.207539	+	0.978227i	$0.433455\pi$
$294$		0			0
$295$	−36.3685			−2.11746
$296$		0			0
$297$	−1.07466			−0.0623581
$298$		0			0
$299$	12.9646			0.749762
$300$		0			0
$301$	9.85252	−	9.85252i	0.567890	−	0.567890i
$302$		0			0
$303$	−25.2026			−1.44785
$304$		0			0
$305$	−12.7539	−	12.7539i	−0.730285	−	0.730285i
$306$		0			0
$307$	−2.17394	−	2.17394i	−0.124073	−	0.124073i	0.642344	−	0.766417i	$-0.277962\pi$
$307$	−2.17394	−	2.17394i	−0.124073	−	0.124073i	−0.766417	+	0.642344i	$0.777962\pi$
$308$		0			0
$309$	−21.0761	+	21.0761i	−1.19897	+	1.19897i
$310$		0			0
$311$	17.8625	+	17.8625i	1.01289	+	1.01289i	0.999916	+	0.0129762i	$0.00413057\pi$
$311$	17.8625	+	17.8625i	1.01289	+	1.01289i	0.0129762	+	0.999916i	$0.495869\pi$
$312$		0			0
$313$	26.2948			1.48627			0.743135	−	0.669141i	$-0.233338\pi$
$313$	26.2948			1.48627			0.743135	+	0.669141i	$0.233338\pi$
$314$		0			0
$315$			1.94442i			0.109556i
$316$		0			0
$317$	17.5916	+	17.5916i	0.988041	+	0.988041i	0.999929	−	0.0118882i	$-0.00378422\pi$
$317$	17.5916	+	17.5916i	0.988041	+	0.988041i	−0.0118882	+	0.999929i	$0.503784\pi$
$318$		0			0
$319$	−0.950299	+	0.747392i	−0.0532065	+	0.0418459i
$320$		0			0
$321$	−2.17550	+	2.17550i	−0.121425	+	0.121425i
$322$		0			0
$323$	3.00530			0.167219
$324$		0			0
$325$			33.4174i			1.85367i
$326$		0			0
$327$	3.00374	−	3.00374i	0.166107	−	0.166107i
$328$		0			0
$329$	5.43055	+	5.43055i	0.299396	+	0.299396i
$330$		0			0
$331$	1.64195	−	1.64195i	0.0902497	−	0.0902497i	−0.660541	−	0.750790i	$-0.729673\pi$
$331$	1.64195	−	1.64195i	0.0902497	−	0.0902497i	0.750790	+	0.660541i	$0.229673\pi$
$332$		0			0
$333$	−0.137582	+	0.137582i	−0.00753943	+	0.00753943i
$334$		0			0
$335$			10.4252i			0.569591i
$336$		0			0
$337$	−0.640281	−	0.640281i	−0.0348783	−	0.0348783i	0.689453	−	0.724331i	$-0.257851\pi$
$337$	−0.640281	−	0.640281i	−0.0348783	−	0.0348783i	−0.724331	+	0.689453i	$0.757851\pi$
$338$		0			0
$339$			3.98520i			0.216447i
$340$		0			0
$341$		−	2.08934i		−	0.113144i
$342$		0			0
$343$			16.1789i			0.873577i
$344$		0			0
$345$	−14.9339	−	14.9339i	−0.804017	−	0.804017i
$346$		0			0
$347$	5.34958			0.287181			0.143590	−	0.989637i	$-0.454135\pi$
$347$	5.34958			0.287181			0.143590	+	0.989637i	$0.454135\pi$
$348$		0			0
$349$	−26.0658			−1.39527			−0.697634	−	0.716454i	$-0.745764\pi$
$349$	−26.0658			−1.39527			−0.697634	+	0.716454i	$0.745764\pi$
$350$		0			0
$351$	13.8998	+	13.8998i	0.741917	+	0.741917i
$352$		0			0
$353$			17.1153i			0.910956i	0.890247	+	0.455478i	$0.150532\pi$
$353$			17.1153i			0.910956i	−0.890247	+	0.455478i	$0.849468\pi$
$354$		0			0
$355$		−	52.1689i		−	2.76884i
$356$		0			0
$357$			6.81289i			0.360576i
$358$		0			0
$359$	13.3661	+	13.3661i	0.705434	+	0.705434i	0.965572	−	0.260138i	$-0.0837680\pi$
$359$	13.3661	+	13.3661i	0.705434	+	0.705434i	−0.260138	+	0.965572i	$0.583768\pi$
$360$		0			0
$361$		−	17.8453i		−	0.939225i
$362$		0			0
$363$	−14.2901	+	14.2901i	−0.750033	+	0.750033i
$364$		0			0
$365$	−30.4485	+	30.4485i	−1.59375	+	1.59375i
$366$		0			0
$367$	6.30900	+	6.30900i	0.329327	+	0.329327i	0.852331	−	0.523003i	$-0.175188\pi$
$367$	6.30900	+	6.30900i	0.329327	+	0.329327i	−0.523003	+	0.852331i	$0.675188\pi$
$368$		0			0
$369$	−0.186918	+	0.186918i	−0.00973056	+	0.00973056i
$370$		0			0
$371$			10.0263i			0.520540i
$372$		0			0
$373$	−4.19470			−0.217193			−0.108597	−	0.994086i	$-0.534636\pi$
$373$	−4.19470			−0.217193			−0.108597	+	0.994086i	$0.534636\pi$
$374$		0			0
$375$	14.8419	−	14.8419i	0.766430	−	0.766430i
$376$		0			0
$377$	21.9582	+	2.62443i	1.13091	+	0.135165i
$378$		0			0
$379$	3.31860	+	3.31860i	0.170465	+	0.170465i	0.787184	−	0.616719i	$-0.211538\pi$
$379$	3.31860	+	3.31860i	0.170465	+	0.170465i	−0.616719	+	0.787184i	$0.711538\pi$
$380$		0			0
$381$			28.7720i			1.47403i
$382$		0			0
$383$	−0.00735121			−0.000375629			−0.000187815	−	1.00000i	$-0.500060\pi$
$383$	−0.00735121			−0.000375629			−0.000187815		1.00000i	$0.500060\pi$
$384$		0			0
$385$	0.759448	+	0.759448i	0.0387051	+	0.0387051i
$386$		0			0
$387$	3.03402	−	3.03402i	0.154228	−	0.154228i
$388$		0			0
$389$	−20.7929	−	20.7929i	−1.05424	−	1.05424i	−0.998442	−	0.0557978i	$-0.982230\pi$
$389$	−20.7929	−	20.7929i	−1.05424	−	1.05424i	−0.0557978	−	0.998442i	$-0.517770\pi$
$390$		0			0
$391$	−6.24333	−	6.24333i	−0.315739	−	0.315739i
$392$		0			0
$393$	−8.82345			−0.445084
$394$		0			0
$395$	29.1200	−	29.1200i	1.46519	−	1.46519i
$396$		0			0
$397$	10.8751			0.545807			0.272904	−	0.962041i	$-0.412016\pi$
$397$	10.8751			0.545807			0.272904	+	0.962041i	$0.412016\pi$
$398$		0			0
$399$	−2.61770			−0.131049
$400$		0			0
$401$	36.1804			1.80677			0.903383	−	0.428835i	$-0.141076\pi$
$401$	36.1804			1.80677			0.903383	+	0.428835i	$0.141076\pi$
$402$		0			0
$403$	−27.0239	+	27.0239i	−1.34615	+	1.34615i
$404$		0			0
$405$		−	36.4420i		−	1.81082i
$406$		0			0
$407$			0.107473i			0.00532723i
$408$		0			0
$409$	11.4711	−	11.4711i	0.567207	−	0.567207i	−0.364138	−	0.931345i	$-0.618636\pi$
$409$	11.4711	−	11.4711i	0.567207	−	0.567207i	0.931345	+	0.364138i	$0.118636\pi$
$410$		0			0
$411$	28.9462			1.42781
$412$		0			0
$413$	13.2434			0.651664
$414$		0			0
$415$	54.4327			2.67199
$416$		0			0
$417$	−29.6155	+	29.6155i	−1.45028	+	1.45028i
$418$		0			0
$419$	19.2783			0.941805			0.470903	−	0.882185i	$-0.343928\pi$
$419$	19.2783			0.941805			0.470903	+	0.882185i	$0.343928\pi$
$420$		0			0
$421$	11.3169	+	11.3169i	0.551553	+	0.551553i	0.926889	−	0.375336i	$-0.122473\pi$
$421$	11.3169	+	11.3169i	0.551553	+	0.551553i	−0.375336	+	0.926889i	$0.622473\pi$
$422$		0			0
$423$	1.67230	+	1.67230i	0.0813101	+	0.0813101i
$424$		0			0
$425$	16.0927	−	16.0927i	0.780613	−	0.780613i
$426$		0			0
$427$	4.64425	+	4.64425i	0.224751	+	0.224751i
$428$		0			0
$429$	−1.70158			−0.0821532
$430$		0			0
$431$		−	9.42869i		−	0.454164i	−0.973876	−	0.227082i	$-0.927081\pi$
$431$		−	9.42869i		−	0.454164i	0.973876	−	0.227082i	$-0.0729185\pi$
$432$		0			0
$433$	1.81117	+	1.81117i	0.0870394	+	0.0870394i	0.749286	−	0.662247i	$-0.230397\pi$
$433$	1.81117	+	1.81117i	0.0870394	+	0.0870394i	−0.662247	+	0.749286i	$0.730397\pi$
$434$		0			0
$435$	−22.2706	−	28.3168i	−1.06779	−	1.35769i
$436$		0			0
$437$	2.39886	−	2.39886i	0.114753	−	0.114753i
$438$		0			0
$439$	14.8886			0.710594			0.355297	−	0.934753i	$-0.384380\pi$
$439$	14.8886			0.710594			0.355297	+	0.934753i	$0.384380\pi$
$440$		0			0
$441$			2.13706i			0.101765i
$442$		0			0
$443$	3.03003	−	3.03003i	0.143961	−	0.143961i	−0.631453	−	0.775414i	$-0.717541\pi$
$443$	3.03003	−	3.03003i	0.143961	−	0.143961i	0.775414	+	0.631453i	$0.217541\pi$
$444$		0			0
$445$	27.8401	+	27.8401i	1.31975	+	1.31975i
$446$		0			0
$447$	−25.3267	+	25.3267i	−1.19791	+	1.19791i
$448$		0			0
$449$	−8.18122	+	8.18122i	−0.386095	+	0.386095i	−0.873292	−	0.487197i	$-0.838019\pi$
$449$	−8.18122	+	8.18122i	−0.386095	+	0.386095i	0.487197	+	0.873292i	$0.338019\pi$
$450$		0			0
$451$			0.146012i			0.00687545i
$452$		0			0
$453$	−17.9687	−	17.9687i	−0.844242	−	0.844242i
$454$		0			0
$455$		−	19.6456i		−	0.921002i
$456$		0			0
$457$		−	8.85533i		−	0.414235i	−0.978316	−	0.207117i	$-0.933592\pi$
$457$		−	8.85533i		−	0.414235i	0.978316	−	0.207117i	$-0.0664082\pi$
$458$		0			0
$459$		−	13.3874i		−	0.624870i
$460$		0			0
$461$	−5.48110	−	5.48110i	−0.255280	−	0.255280i	0.567851	−	0.823131i	$-0.307775\pi$
$461$	−5.48110	−	5.48110i	−0.255280	−	0.255280i	−0.823131	+	0.567851i	$0.807775\pi$
$462$		0			0
$463$	−12.0188			−0.558561			−0.279280	−	0.960210i	$-0.590096\pi$
$463$	−12.0188			−0.558561			−0.279280	+	0.960210i	$0.590096\pi$
$464$		0			0
$465$	62.2577			2.88713
$466$		0			0
$467$	24.1723	+	24.1723i	1.11856	+	1.11856i	0.991953	+	0.126609i	$0.0404094\pi$
$467$	24.1723	+	24.1723i	1.11856	+	1.11856i	0.126609	+	0.991953i	$0.459591\pi$
$468$		0			0
$469$		−	3.79628i		−	0.175296i
$470$		0			0
$471$		−	43.8957i		−	2.02261i
$472$		0			0
$473$		−	2.37004i		−	0.108975i
$474$		0			0
$475$	6.18327	+	6.18327i	0.283708	+	0.283708i
$476$		0			0
$477$			3.08753i			0.141368i
$478$		0			0
$479$	1.58667	−	1.58667i	0.0724966	−	0.0724966i	−0.669929	−	0.742425i	$-0.733675\pi$
$479$	1.58667	−	1.58667i	0.0724966	−	0.0724966i	0.742425	+	0.669929i	$0.233675\pi$
$480$		0			0
$481$	1.39007	−	1.39007i	0.0633818	−	0.0633818i
$482$		0			0
$483$	5.43811	+	5.43811i	0.247442	+	0.247442i
$484$		0			0
$485$	11.4537	−	11.4537i	0.520084	−	0.520084i
$486$		0			0
$487$		−	24.3457i		−	1.10321i	−0.834105	−	0.551605i	$-0.814015\pi$
$487$		−	24.3457i		−	1.10321i	0.834105	−	0.551605i	$-0.185985\pi$
$488$		0			0
$489$	13.0743			0.591240
$490$		0			0
$491$	16.2302	−	16.2302i	0.732457	−	0.732457i	−0.238649	−	0.971106i	$-0.576705\pi$
$491$	16.2302	−	16.2302i	0.732457	−	0.732457i	0.971106	+	0.238649i	$0.0767046\pi$
$492$		0			0
$493$	−9.31051	−	11.8382i	−0.419324	−	0.533166i
$494$		0			0
$495$	0.233867	+	0.233867i	0.0105115	+	0.0105115i
$496$		0			0
$497$			18.9970i			0.852132i
$498$		0			0
$499$	32.7378			1.46554			0.732772	−	0.680474i	$-0.238226\pi$
$499$	32.7378			1.46554			0.732772	+	0.680474i	$0.238226\pi$
$500$		0			0
$501$	−2.26352	−	2.26352i	−0.101126	−	0.101126i
$502$		0			0
$503$	19.4612	−	19.4612i	0.867732	−	0.867732i	−0.124489	−	0.992221i	$-0.539729\pi$
$503$	19.4612	−	19.4612i	0.867732	−	0.867732i	0.992221	+	0.124489i	$0.0397293\pi$
$504$		0			0
$505$	−34.9975	−	34.9975i	−1.55737	−	1.55737i
$506$		0			0
$507$	5.04256	+	5.04256i	0.223948	+	0.223948i
$508$		0			0
$509$	−13.4157			−0.594642			−0.297321	−	0.954778i	$-0.596093\pi$
$509$	−13.4157			−0.594642			−0.297321	+	0.954778i	$0.596093\pi$
$510$		0			0
$511$	11.0876	−	11.0876i	0.490488	−	0.490488i
$512$		0			0
$513$	5.14380			0.227104
$514$		0			0
$515$	−58.5344			−2.57933
$516$		0			0
$517$	1.30633			0.0574523
$518$		0			0
$519$	−28.0305	+	28.0305i	−1.23040	+	1.23040i
$520$		0			0
$521$			40.9342i			1.79336i	0.442681	+	0.896679i	$0.354027\pi$
$521$			40.9342i			1.79336i	−0.442681	+	0.896679i	$0.645973\pi$
$522$		0			0
$523$			24.5240i			1.07236i	0.844104	+	0.536179i	$0.180133\pi$
$523$			24.5240i			1.07236i	−0.844104	+	0.536179i	$0.819867\pi$
$524$		0			0
$525$	−14.0172	+	14.0172i	−0.611762	+	0.611762i
$526$		0			0
$527$	26.0276			1.13378
$528$		0			0
$529$	13.0330			0.566654
$530$		0			0
$531$	4.07821			0.176979
$532$		0			0
$533$	1.88855	−	1.88855i	0.0818020	−	0.0818020i
$534$		0			0
$535$	−6.04200			−0.261219
$536$		0			0
$537$	11.4395	+	11.4395i	0.493650	+	0.493650i
$538$		0			0
$539$	0.834691	+	0.834691i	0.0359527	+	0.0359527i
$540$		0			0
$541$	−18.5956	+	18.5956i	−0.799486	+	0.799486i	−0.983014	−	0.183528i	$-0.941248\pi$
$541$	−18.5956	+	18.5956i	−0.799486	+	0.799486i	0.183528	+	0.983014i	$0.441248\pi$
$542$		0			0
$543$	7.54605	+	7.54605i	0.323832	+	0.323832i
$544$		0			0
$545$	8.34226			0.357343
$546$		0			0
$547$			34.1340i			1.45946i	0.683734	+	0.729731i	$0.260355\pi$
$547$			34.1340i			1.45946i	−0.683734	+	0.729731i	$0.739645\pi$
$548$		0			0
$549$	1.43016	+	1.43016i	0.0610379	+	0.0610379i
$550$		0			0
$551$	4.54856	−	3.57735i	0.193775	−	0.152400i
$552$		0			0
$553$	−10.6039	+	10.6039i	−0.450923	+	0.450923i
$554$		0			0
$555$	−3.20245			−0.135936
$556$		0			0
$557$		−	11.5591i		−	0.489775i	−0.969551	−	0.244888i	$-0.921249\pi$
$557$		−	11.5591i		−	0.489775i	0.969551	−	0.244888i	$-0.0787511\pi$
$558$		0			0
$559$	−30.6545	+	30.6545i	−1.29655	+	1.29655i
$560$		0			0
$561$	0.819427	+	0.819427i	0.0345962	+	0.0345962i
$562$		0			0
$563$	−14.8665	+	14.8665i	−0.626546	+	0.626546i	−0.947197	−	0.320651i	$-0.896098\pi$
$563$	−14.8665	+	14.8665i	−0.626546	+	0.626546i	0.320651	+	0.947197i	$0.396098\pi$
$564$		0			0
$565$	−5.53404	+	5.53404i	−0.232819	+	0.232819i
$566$		0			0
$567$			13.2701i			0.557294i
$568$		0			0
$569$	13.7956	+	13.7956i	0.578340	+	0.578340i	0.934446	−	0.356106i	$-0.115896\pi$
$569$	13.7956	+	13.7956i	0.578340	+	0.578340i	−0.356106	+	0.934446i	$0.615896\pi$
$570$		0			0
$571$			27.4810i			1.15004i	0.818138	+	0.575022i	$0.195007\pi$
$571$			27.4810i			1.15004i	−0.818138	+	0.575022i	$0.804993\pi$
$572$		0			0
$573$		−	33.7700i		−	1.41076i
$574$		0			0
$575$		−	25.6907i		−	1.07138i
$576$		0			0
$577$	−18.3907	−	18.3907i	−0.765617	−	0.765617i	0.211715	−	0.977331i	$-0.432095\pi$
$577$	−18.3907	−	18.3907i	−0.765617	−	0.765617i	−0.977331	+	0.211715i	$0.932095\pi$
$578$		0			0
$579$	−13.1871			−0.548038
$580$		0			0
$581$	−19.8213			−0.822327
$582$		0			0
$583$	1.20592	+	1.20592i	0.0499443	+	0.0499443i
$584$		0			0
$585$		−	6.04974i		−	0.250126i
$586$		0			0
$587$		−	16.6544i		−	0.687401i	−0.939079	−	0.343701i	$-0.888319\pi$
$587$		−	16.6544i		−	0.687401i	0.939079	−	0.343701i	$-0.111681\pi$
$588$		0			0
$589$			10.0005i			0.412064i
$590$		0			0
$591$	14.0756	+	14.0756i	0.578993	+	0.578993i
$592$		0			0
$593$		−	8.82050i		−	0.362215i	−0.983463	−	0.181107i	$-0.942032\pi$
$593$		−	8.82050i		−	0.362215i	0.983463	−	0.181107i	$-0.0579681\pi$
$594$		0			0
$595$	−9.46070	+	9.46070i	−0.387851	+	0.387851i
$596$		0			0
$597$	−3.69014	+	3.69014i	−0.151027	+	0.151027i
$598$		0			0
$599$	−1.93353	−	1.93353i	−0.0790018	−	0.0790018i	0.666502	−	0.745504i	$-0.267791\pi$
$599$	−1.93353	−	1.93353i	−0.0790018	−	0.0790018i	−0.745504	+	0.666502i	$0.767791\pi$
$600$		0			0
$601$	−31.8434	+	31.8434i	−1.29892	+	1.29892i	−0.369814	+	0.929106i	$0.620579\pi$
$601$	−31.8434	+	31.8434i	−1.29892	+	1.29892i	−0.929106	+	0.369814i	$0.879421\pi$
$602$		0			0
$603$		−	1.16904i		−	0.0476069i
$604$		0			0
$605$	−39.6877			−1.61353
$606$		0			0
$607$	24.7745	−	24.7745i	1.00557	−	1.00557i	0.00558134	−	0.999984i	$-0.498223\pi$
$607$	24.7745	−	24.7745i	1.00557	−	1.00557i	0.999984	−	0.00558134i	$-0.00177661\pi$
$608$		0			0
$609$	8.10971	+	10.3114i	0.328622	+	0.417838i
$610$		0			0
$611$	−16.8963	−	16.8963i	−0.683550	−	0.683550i
$612$		0			0
$613$			9.51409i			0.384270i	0.981368	+	0.192135i	$0.0615412\pi$
$613$			9.51409i			0.384270i	−0.981368	+	0.192135i	$0.938459\pi$
$614$		0			0
$615$	−4.35084			−0.175443
$616$		0			0
$617$	−7.44325	−	7.44325i	−0.299654	−	0.299654i	0.541224	−	0.840878i	$-0.317961\pi$
$617$	−7.44325	−	7.44325i	−0.299654	−	0.299654i	−0.840878	+	0.541224i	$0.817961\pi$
$618$		0			0
$619$	28.3133	−	28.3133i	1.13801	−	1.13801i	0.149199	−	0.988807i	$-0.452331\pi$
$619$	28.3133	−	28.3133i	1.13801	−	1.13801i	0.988807	−	0.149199i	$-0.0476694\pi$
$620$		0			0
$621$	−10.6859	−	10.6859i	−0.428812	−	0.428812i
$622$		0			0
$623$	−10.1378	−	10.1378i	−0.406162	−	0.406162i
$624$		0			0
$625$	0.532326			0.0212931
$626$		0			0
$627$	−0.314846	+	0.314846i	−0.0125737	+	0.0125737i
$628$		0			0
$629$	−1.33883			−0.0533825
$630$		0			0
$631$	−37.7016			−1.50088			−0.750438	−	0.660941i	$-0.770157\pi$
$631$	−37.7016			−1.50088			−0.750438	+	0.660941i	$0.770157\pi$
$632$		0			0
$633$	−4.15793			−0.165263
$634$		0			0
$635$	−39.9541	+	39.9541i	−1.58553	+	1.58553i
$636$		0			0
$637$		−	21.5921i		−	0.855508i
$638$		0			0
$639$			5.84999i			0.231422i
$640$		0			0
$641$	−7.01502	+	7.01502i	−0.277077	+	0.277077i	−0.831941	−	0.554864i	$-0.812770\pi$
$641$	−7.01502	+	7.01502i	−0.277077	+	0.277077i	0.554864	+	0.831941i	$0.312770\pi$
$642$		0			0
$643$	−49.0251			−1.93336			−0.966680	−	0.255989i	$-0.917599\pi$
$643$	−49.0251			−1.93336			−0.966680	+	0.255989i	$0.917599\pi$
$644$		0			0
$645$	70.6220			2.78074
$646$		0			0
$647$	38.0184			1.49466			0.747329	−	0.664454i	$-0.231336\pi$
$647$	38.0184			1.49466			0.747329	+	0.664454i	$0.231336\pi$
$648$		0			0
$649$	1.59286	−	1.59286i	0.0625252	−	0.0625252i
$650$		0			0
$651$	−22.6708			−0.888537
$652$		0			0
$653$	−6.33630	−	6.33630i	−0.247959	−	0.247959i	0.572174	−	0.820132i	$-0.306100\pi$
$653$	−6.33630	−	6.33630i	−0.247959	−	0.247959i	−0.820132	+	0.572174i	$0.806100\pi$
$654$		0			0
$655$	−12.2527	−	12.2527i	−0.478751	−	0.478751i
$656$		0			0
$657$	3.41436	−	3.41436i	0.133207	−	0.133207i
$658$		0			0
$659$	−27.2704	−	27.2704i	−1.06230	−	1.06230i	−0.997925	−	0.0643794i	$-0.979493\pi$
$659$	−27.2704	−	27.2704i	−1.06230	−	1.06230i	−0.0643794	−	0.997925i	$-0.520507\pi$
$660$		0			0
$661$	12.7239			0.494901			0.247451	−	0.968900i	$-0.420407\pi$
$661$	12.7239			0.494901			0.247451	+	0.968900i	$0.420407\pi$
$662$		0			0
$663$		−	21.1972i		−	0.823231i
$664$		0			0
$665$	−3.63506	−	3.63506i	−0.140962	−	0.140962i
$666$		0			0
$667$	−16.8811	−	2.01762i	−0.653638	−	0.0781225i
$668$		0			0
$669$	24.5867	−	24.5867i	0.950576	−	0.950576i
$670$		0			0
$671$	1.11718			0.0431284
$672$		0			0
$673$		−	27.2188i		−	1.04921i	−0.851346	−	0.524605i	$-0.824213\pi$
$673$		−	27.2188i		−	1.04921i	0.851346	−	0.524605i	$-0.175787\pi$
$674$		0			0
$675$	27.5440	−	27.5440i	1.06017	−	1.06017i
$676$		0			0
$677$	−21.2693	−	21.2693i	−0.817444	−	0.817444i	0.168293	−	0.985737i	$-0.446175\pi$
$677$	−21.2693	−	21.2693i	−0.817444	−	0.817444i	−0.985737	+	0.168293i	$0.946175\pi$
$678$		0			0
$679$	−4.17078	+	4.17078i	−0.160060	+	0.160060i
$680$		0			0
$681$	−12.1396	+	12.1396i	−0.465190	+	0.465190i
$682$		0			0
$683$			47.8073i			1.82929i	0.404254	+	0.914647i	$0.367531\pi$
$683$			47.8073i			1.82929i	−0.404254	+	0.914647i	$0.632469\pi$
$684$		0			0
$685$	40.1961	+	40.1961i	1.53581	+	1.53581i
$686$		0			0
$687$			2.17715i			0.0830633i
$688$		0			0
$689$		−	31.1952i		−	1.18844i
$690$		0			0
$691$			13.4998i			0.513556i	0.966470	+	0.256778i	$0.0826609\pi$
$691$			13.4998i			0.513556i	−0.966470	+	0.256778i	$0.917339\pi$
$692$		0			0
$693$	−0.0851612	−	0.0851612i	−0.00323501	−	0.00323501i
$694$		0			0
$695$	−82.2510			−3.11996
$696$		0			0
$697$	−1.81892			−0.0688967
$698$		0			0
$699$	−7.77892	−	7.77892i	−0.294226	−	0.294226i
$700$		0			0
$701$			27.1986i			1.02728i	0.858006	+	0.513639i	$0.171703\pi$
$701$			27.1986i			1.02728i	−0.858006	+	0.513639i	$0.828297\pi$
$702$		0			0
$703$		−	0.514413i		−	0.0194015i
$704$		0			0
$705$			38.9257i			1.46603i
$706$		0			0
$707$	12.7441	+	12.7441i	0.479292	+	0.479292i
$708$		0			0
$709$		−	6.89109i		−	0.258800i	−0.991592	−	0.129400i	$-0.958695\pi$
$709$		−	6.89109i		−	0.258800i	0.991592	−	0.129400i	$-0.0413052\pi$
$710$		0			0
$711$	−3.26539	+	3.26539i	−0.122462	+	0.122462i
$712$		0			0
$713$	20.7755	−	20.7755i	0.778047	−	0.778047i
$714$		0			0
$715$	−2.36290	−	2.36290i	−0.0883674	−	0.0883674i
$716$		0			0
$717$	−0.502069	+	0.502069i	−0.0187501	+	0.0187501i
$718$		0			0
$719$		−	20.7114i		−	0.772406i	−0.922414	−	0.386203i	$-0.873786\pi$
$719$		−	20.7114i		−	0.772406i	0.922414	−	0.386203i	$-0.126214\pi$
$720$		0			0
$721$	21.3150			0.793810
$722$		0			0
$723$	18.7740	−	18.7740i	0.698211	−	0.698211i
$724$		0			0
$725$	5.20059	−	43.5125i	0.193145	−	1.61601i
$726$		0			0
$727$	14.3286	+	14.3286i	0.531417	+	0.531417i	0.920994	−	0.389577i	$-0.127379\pi$
$727$	14.3286	+	14.3286i	0.531417	+	0.531417i	−0.389577	+	0.920994i	$0.627379\pi$
$728$		0			0
$729$		−	22.4180i		−	0.830295i
$730$		0			0
$731$	29.5244			1.09200
$732$		0			0
$733$	−23.9466	−	23.9466i	−0.884488	−	0.884488i	0.109499	−	0.993987i	$-0.465075\pi$
$733$	−23.9466	−	23.9466i	−0.884488	−	0.884488i	−0.993987	+	0.109499i	$0.965075\pi$
$734$		0			0
$735$	−24.8719	+	24.8719i	−0.917415	+	0.917415i
$736$		0			0
$737$	−0.456601	−	0.456601i	−0.0168191	−	0.0168191i
$738$		0			0
$739$	31.5715	+	31.5715i	1.16138	+	1.16138i	0.984174	+	0.177202i	$0.0567047\pi$
$739$	31.5715	+	31.5715i	1.16138	+	1.16138i	0.177202	+	0.984174i	$0.443295\pi$
$740$		0			0
$741$	8.14454			0.299197
$742$		0			0
$743$	−21.0790	+	21.0790i	−0.773314	+	0.773314i	−0.978684	−	0.205371i	$-0.934160\pi$
$743$	−21.0790	+	21.0790i	−0.773314	+	0.773314i	0.205371	+	0.978684i	$0.434160\pi$
$744$		0			0
$745$	−70.3398			−2.57705
$746$		0			0
$747$	−6.10384			−0.223328
$748$		0			0
$749$	2.20016			0.0803920
$750$		0			0
$751$	18.0100	−	18.0100i	0.657196	−	0.657196i	−0.297520	−	0.954716i	$-0.596159\pi$
$751$	18.0100	−	18.0100i	0.657196	−	0.657196i	0.954716	+	0.297520i	$0.0961594\pi$
$752$		0			0
$753$			6.20277i			0.226041i
$754$		0			0
$755$		−	49.9043i		−	1.81621i
$756$		0			0
$757$	20.7974	−	20.7974i	0.755895	−	0.755895i	−0.219677	−	0.975573i	$-0.570500\pi$
$757$	20.7974	−	20.7974i	0.755895	−	0.755895i	0.975573	+	0.219677i	$0.0705005\pi$
$758$		0			0
$759$	1.30815			0.0474827
$760$		0			0
$761$	5.52228			0.200183			0.100091	−	0.994978i	$-0.468087\pi$
$761$	5.52228			0.200183			0.100091	+	0.994978i	$0.468087\pi$
$762$		0			0
$763$	−3.03778			−0.109975
$764$		0			0
$765$	−2.91336	+	2.91336i	−0.105333	+	0.105333i
$766$		0			0
$767$	−41.2046			−1.48781
$768$		0			0
$769$	−33.3883	−	33.3883i	−1.20401	−	1.20401i	−0.972936	−	0.231076i	$-0.925776\pi$
$769$	−33.3883	−	33.3883i	−1.20401	−	1.20401i	−0.231076	−	0.972936i	$-0.574224\pi$
$770$		0			0
$771$	1.71668	+	1.71668i	0.0618248	+	0.0618248i
$772$		0			0
$773$	−17.2207	+	17.2207i	−0.619384	+	0.619384i	−0.945373	−	0.325989i	$-0.894303\pi$
$773$	−17.2207	+	17.2207i	−0.619384	+	0.619384i	0.325989	+	0.945373i	$0.394303\pi$
$774$		0			0
$775$	53.5507	+	53.5507i	1.92360	+	1.92360i
$776$		0			0
$777$	1.16615			0.0418355
$778$		0			0
$779$		−	0.698880i		−	0.0250400i
$780$		0			0
$781$	2.28488	+	2.28488i	0.0817595	+	0.0817595i
$782$		0			0
$783$	−15.9357	−	20.2620i	−0.569494	−	0.724104i
$784$		0			0
$785$	60.9556	−	60.9556i	2.17560	−	2.17560i
$786$		0			0
$787$	−14.9600			−0.533266			−0.266633	−	0.963798i	$-0.585911\pi$
$787$	−14.9600			−0.533266			−0.266633	+	0.963798i	$0.585911\pi$
$788$		0			0
$789$			40.3384i			1.43609i
$790$		0			0
$791$	2.01519	−	2.01519i	0.0716518	−	0.0716518i
$792$		0			0
$793$	−14.4498	−	14.4498i	−0.513128	−	0.513128i
$794$		0			0
$795$	−35.9339	+	35.9339i	−1.27444	+	1.27444i
$796$		0			0
$797$	24.8899	−	24.8899i	0.881647	−	0.881647i	−0.112055	−	0.993702i	$-0.535743\pi$
$797$	24.8899	−	24.8899i	0.881647	−	0.881647i	0.993702	+	0.112055i	$0.0357433\pi$
$798$		0			0
$799$			16.2734i			0.575711i
$800$		0			0
$801$	−3.12186	−	3.12186i	−0.110306	−	0.110306i
$802$		0			0
$803$		−	2.66715i		−	0.0941217i
$804$		0			0
$805$			15.1032i			0.532319i
$806$		0			0
$807$		−	37.2018i		−	1.30957i
$808$		0			0
$809$	−2.76934	−	2.76934i	−0.0973650	−	0.0973650i	0.656746	−	0.754111i	$-0.271932\pi$
$809$	−2.76934	−	2.76934i	−0.0973650	−	0.0973650i	−0.754111	+	0.656746i	$0.771932\pi$
$810$		0			0
$811$	48.0311			1.68660			0.843299	−	0.537444i	$-0.180610\pi$
$811$	48.0311			1.68660			0.843299	+	0.537444i	$0.180610\pi$
$812$		0			0
$813$	−17.3340			−0.607929
$814$		0			0
$815$	18.1556	+	18.1556i	0.635963	+	0.635963i
$816$		0			0
$817$			11.3441i			0.396879i
$818$		0			0
$819$			2.20298i			0.0769782i
$820$		0			0
$821$		−	31.3808i		−	1.09520i	−0.836742	−	0.547598i	$-0.815542\pi$
$821$		−	31.3808i		−	1.09520i	0.836742	−	0.547598i	$-0.184458\pi$
$822$		0			0
$823$	14.5737	+	14.5737i	0.508008	+	0.508008i	0.913915	−	0.405907i	$-0.133044\pi$
$823$	14.5737	+	14.5737i	0.508008	+	0.508008i	−0.405907	+	0.913915i	$0.633044\pi$
$824$		0			0
$825$			3.37187i			0.117393i
$826$		0			0
$827$	0.898564	−	0.898564i	0.0312461	−	0.0312461i	−0.691311	−	0.722557i	$-0.742967\pi$
$827$	0.898564	−	0.898564i	0.0312461	−	0.0312461i	0.722557	+	0.691311i	$0.242967\pi$
$828$		0			0
$829$	−20.0381	+	20.0381i	−0.695953	+	0.695953i	−0.963535	−	0.267582i	$-0.913775\pi$
$829$	−20.0381	+	20.0381i	−0.695953	+	0.695953i	0.267582	+	0.963535i	$0.413775\pi$
$830$		0			0
$831$	22.3597	+	22.3597i	0.775650	+	0.775650i
$832$		0			0
$833$	−10.3980	+	10.3980i	−0.360270	+	0.360270i
$834$		0			0
$835$		−	6.28645i		−	0.217552i
$836$		0			0
$837$	44.5483			1.53981
$838$		0			0
$839$	−17.8338	+	17.8338i	−0.615691	+	0.615691i	−0.944423	−	0.328732i	$-0.893379\pi$
$839$	−17.8338	+	17.8338i	−0.615691	+	0.615691i	0.328732	+	0.944423i	$0.393379\pi$
$840$		0			0
$841$	−28.1831	−	6.83450i	−0.971833	−	0.235672i
$842$		0			0
$843$	−1.22631	−	1.22631i	−0.0422362	−	0.0422362i
$844$		0			0
$845$			14.0047i			0.481776i
$846$		0			0
$847$	14.4520			0.496578
$848$		0			0
$849$	25.7619	+	25.7619i	0.884146	+	0.884146i
$850$		0			0
$851$	−1.06866	+	1.06866i	−0.0366333	+	0.0366333i
$852$		0			0
$853$	18.7598	+	18.7598i	0.642323	+	0.642323i	0.951126	−	0.308803i	$-0.0999284\pi$
$853$	18.7598	+	18.7598i	0.642323	+	0.642323i	−0.308803	+	0.951126i	$0.599928\pi$
$854$		0			0
$855$	−1.11939	−	1.11939i	−0.0382824	−	0.0382824i
$856$		0			0
$857$	−26.2669			−0.897260			−0.448630	−	0.893718i	$-0.648088\pi$
$857$	−26.2669			−0.897260			−0.448630	+	0.893718i	$0.648088\pi$
$858$		0			0
$859$	−5.92377	+	5.92377i	−0.202117	+	0.202117i	−0.800906	−	0.598790i	$-0.795649\pi$
$859$	−5.92377	+	5.92377i	−0.202117	+	0.202117i	0.598790	+	0.800906i	$0.295649\pi$
$860$		0			0
$861$	1.58433			0.0539939
$862$		0			0
$863$	−2.67772			−0.0911506			−0.0455753	−	0.998961i	$-0.514512\pi$
$863$	−2.67772			−0.0911506			−0.0455753	+	0.998961i	$0.514512\pi$
$864$		0			0
$865$	−77.8491			−2.64695
$866$		0			0
$867$	11.9784	−	11.9784i	0.406808	−	0.406808i
$868$		0			0
$869$			2.55078i			0.0865294i
$870$		0			0
$871$			11.8115i			0.400218i
$872$		0			0
$873$	−1.28436	+	1.28436i	−0.0434691	+	0.0434691i
$874$		0			0
$875$	−15.0101			−0.507434
$876$		0			0
$877$	45.5570			1.53835			0.769176	−	0.639037i	$-0.220667\pi$
$877$	45.5570			1.53835			0.769176	+	0.639037i	$0.220667\pi$
$878$		0			0
$879$	34.4332			1.16140
$880$		0			0
$881$	−18.6854	+	18.6854i	−0.629528	+	0.629528i	−0.947949	−	0.318421i	$-0.896847\pi$
$881$	−18.6854	+	18.6854i	−0.629528	+	0.629528i	0.318421	+	0.947949i	$0.396847\pi$
$882$		0			0
$883$	−29.3384			−0.987315			−0.493658	−	0.869656i	$-0.664340\pi$
$883$	−29.3384			−0.987315			−0.493658	+	0.869656i	$0.664340\pi$
$884$		0			0
$885$	47.4637	+	47.4637i	1.59547	+	1.59547i
$886$		0			0
$887$	−4.71298	−	4.71298i	−0.158246	−	0.158246i	0.623543	−	0.781789i	$-0.285693\pi$
$887$	−4.71298	−	4.71298i	−0.158246	−	0.158246i	−0.781789	+	0.623543i	$0.785693\pi$
$888$		0			0
$889$	14.5490	−	14.5490i	0.487959	−	0.487959i
$890$		0			0
$891$	1.59608	+	1.59608i	0.0534707	+	0.0534707i
$892$		0			0
$893$	−6.25268			−0.209238
$894$		0			0
$895$			31.7708i			1.06198i
$896$		0			0
$897$	−16.9198	−	16.9198i	−0.564935	−	0.564935i
$898$		0			0
$899$	39.3931	−	30.9819i	1.31383	−	1.03330i
$900$		0			0
$901$	−15.0226	+	15.0226i	−0.500476	+	0.500476i
$902$		0			0
$903$	−25.7166			−0.855794
$904$		0			0
$905$			20.9576i			0.696654i
$906$		0			0
$907$	22.1276	−	22.1276i	0.734736	−	0.734736i	−0.236818	−	0.971554i	$-0.576105\pi$
$907$	22.1276	−	22.1276i	0.734736	−	0.734736i	0.971554	+	0.236818i	$0.0761046\pi$
$908$		0			0
$909$	3.92447	+	3.92447i	0.130166	+	0.130166i
$910$		0			0
$911$	−6.59269	+	6.59269i	−0.218425	+	0.218425i	−0.807835	−	0.589409i	$-0.799361\pi$
$911$	−6.59269	+	6.59269i	−0.218425	+	0.218425i	0.589409	+	0.807835i	$0.299361\pi$
$912$		0			0
$913$	−2.38403	+	2.38403i	−0.0788998	+	0.0788998i
$914$		0			0
$915$			33.2896i			1.10052i
$916$		0			0
$917$	4.46173	+	4.46173i	0.147339	+	0.147339i
$918$		0			0
$919$		−	14.3930i		−	0.474782i	−0.971414	−	0.237391i	$-0.923708\pi$
$919$		−	14.3930i		−	0.474782i	0.971414	−	0.237391i	$-0.0762923\pi$
$920$		0			0
$921$			5.67430i			0.186975i
$922$		0			0
$923$		−	59.1061i		−	1.94550i
$924$		0			0
$925$	−2.75457	−	2.75457i	−0.0905698	−	0.0905698i
$926$		0			0
$927$	6.56379			0.215583
$928$		0			0
$929$	−8.76445			−0.287552			−0.143776	−	0.989610i	$-0.545924\pi$
$929$	−8.76445			−0.287552			−0.143776	+	0.989610i	$0.545924\pi$
$930$		0			0
$931$	−3.99521	−	3.99521i	−0.130938	−	0.130938i
$932$		0			0
$933$		−	46.6239i		−	1.52640i
$934$		0			0
$935$			2.27579i			0.0744263i
$936$		0			0
$937$			11.3979i			0.372352i	0.982516	+	0.186176i	$0.0596095\pi$
$937$			11.3979i			0.372352i	−0.982516	+	0.186176i	$0.940390\pi$
$938$		0			0
$939$	−34.3167	−	34.3167i	−1.11988	−	1.11988i
$940$		0			0
$941$			44.2177i			1.44146i	0.693218	+	0.720728i	$0.256192\pi$
$941$			44.2177i			1.44146i	−0.693218	+	0.720728i	$0.743808\pi$
$942$		0			0
$943$	−1.45188	+	1.45188i	−0.0472798	+	0.0472798i
$944$		0			0
$945$	−16.1927	+	16.1927i	−0.526749	+	0.526749i
$946$		0			0
$947$	21.6876	+	21.6876i	0.704754	+	0.704754i	0.965427	−	0.260673i	$-0.0839446\pi$
$947$	21.6876	+	21.6876i	0.704754	+	0.704754i	−0.260673	+	0.965427i	$0.583945\pi$
$948$		0			0
$949$	−34.4973	+	34.4973i	−1.11983	+	1.11983i
$950$		0			0
$951$		−	45.9167i		−	1.48895i
$952$		0			0
$953$	44.8070			1.45144			0.725720	−	0.687990i	$-0.241507\pi$
$953$	44.8070			1.45144			0.725720	+	0.687990i	$0.241507\pi$
$954$		0			0
$955$	46.8946	−	46.8946i	1.51747	−	1.51747i
$956$		0			0
$957$	2.21561	+	0.264809i	0.0716207	+	0.00856006i
$958$		0			0
$959$	−14.6372	−	14.6372i	−0.472658	−	0.472658i
$960$		0			0
$961$			55.6102i			1.79388i
$962$		0			0
$963$	0.677524			0.0218329
$964$		0			0
$965$	−18.3123	−	18.3123i	−0.589493	−	0.589493i
$966$		0			0
$967$	7.39928	−	7.39928i	0.237945	−	0.237945i	−0.578054	−	0.815999i	$-0.696188\pi$
$967$	7.39928	−	7.39928i	0.237945	−	0.237945i	0.815999	+	0.578054i	$0.196188\pi$
$968$		0			0
$969$	−3.92214	−	3.92214i	−0.125997	−	0.125997i
$970$		0			0
$971$	−11.1100	−	11.1100i	−0.356538	−	0.356538i	0.505997	−	0.862535i	$-0.331125\pi$
$971$	−11.1100	−	11.1100i	−0.356538	−	0.356538i	−0.862535	+	0.505997i	$0.831125\pi$
$972$		0			0
$973$	29.9512			0.960191
$974$		0			0
$975$	43.6123	−	43.6123i	1.39671	−	1.39671i
$976$		0			0
$977$	12.0170			0.384458			0.192229	−	0.981350i	$-0.438428\pi$
$977$	12.0170			0.384458			0.192229	+	0.981350i	$0.438428\pi$
$978$		0			0
$979$	−2.43867			−0.0779401
$980$		0			0
$981$	−0.935465			−0.0298671
$982$		0			0
$983$	5.99283	−	5.99283i	0.191142	−	0.191142i	−0.605048	−	0.796189i	$-0.706846\pi$
$983$	5.99283	−	5.99283i	0.191142	−	0.191142i	0.796189	+	0.605048i	$0.206846\pi$
$984$		0			0
$985$			39.0921i			1.24558i
$986$		0			0
$987$		−	14.1746i		−	0.451181i
$988$		0			0
$989$	23.5667	−	23.5667i	0.749376	−	0.749376i
$990$		0			0
$991$	−36.8496			−1.17057			−0.585283	−	0.810829i	$-0.699017\pi$
$991$	−36.8496			−1.17057			−0.585283	+	0.810829i	$0.699017\pi$
$992$		0			0
$993$	−4.28574			−0.136004
$994$		0			0
$995$	−10.2486			−0.324902
$996$		0			0
$997$	26.0557	−	26.0557i	0.825194	−	0.825194i	−0.161654	−	0.986848i	$-0.551683\pi$
$997$	26.0557	−	26.0557i	0.825194	−	0.825194i	0.986848	+	0.161654i	$0.0516828\pi$
$998$		0			0
$999$	−2.29150			−0.0724999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.k.c.191.4	✓	20
4.3	odd	2	inner	464.2.k.c.191.7	yes	20
29.12	odd	4	inner	464.2.k.c.447.7	yes	20
116.99	even	4	inner	464.2.k.c.447.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.k.c.191.4	✓	20	1.1	even	1	trivial
464.2.k.c.191.7	yes	20	4.3	odd	2	inner
464.2.k.c.447.4	yes	20	116.99	even	4	inner
464.2.k.c.447.7	yes	20	29.12	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30508 - 1.30508i) q^{3} -3.62458i q^{5} +1.31987i q^{7} +0.406445i q^{9} +O(q^{10})\)	\(q+(-1.30508 - 1.30508i) q^{3} -3.62458i q^{5} +1.31987i q^{7} +0.406445i q^{9} +(0.158748 + 0.158748i) q^{11} -4.10656i q^{13} +(-4.73035 + 4.73035i) q^{15} +(-1.97758 + 1.97758i) q^{17} +(-0.759841 - 0.759841i) q^{19} +(1.72253 - 1.72253i) q^{21} +3.15705i q^{23} -8.13758 q^{25} +(-3.38479 + 3.38479i) q^{27} +(-0.639083 + 5.34711i) q^{29} +(-6.58066 - 6.58066i) q^{31} -0.414358i q^{33} +4.78397 q^{35} +(0.338500 + 0.338500i) q^{37} +(-5.35937 + 5.35937i) q^{39} +(0.459886 + 0.459886i) q^{41} +(-7.46477 - 7.46477i) q^{43} +1.47319 q^{45} +(4.11446 - 4.11446i) q^{47} +5.25795 q^{49} +5.16179 q^{51} +7.59645 q^{53} +(0.575397 - 0.575397i) q^{55} +1.98330i q^{57} -10.0339i q^{59} +(3.51872 - 3.51872i) q^{61} -0.536453 q^{63} -14.8845 q^{65} -2.87626 q^{67} +(4.12019 - 4.12019i) q^{69} +14.3931 q^{71} +(-8.40055 - 8.40055i) q^{73} +(10.6202 + 10.6202i) q^{75} +(-0.209527 + 0.209527i) q^{77} +(8.03404 + 8.03404i) q^{79} +10.0541 q^{81} +15.0176i q^{83} +(7.16791 + 7.16791i) q^{85} +(7.81243 - 6.14433i) q^{87} +(-7.68091 + 7.68091i) q^{89} +5.42012 q^{91} +17.1765i q^{93} +(-2.75411 + 2.75411i) q^{95} +(3.16000 + 3.16000i) q^{97} +(-0.0645225 + 0.0645225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 4 q^{17} - 16 q^{21} - 28 q^{25} - 4 q^{29} - 20 q^{37} - 4 q^{41} - 40 q^{45} + 28 q^{49} + 48 q^{53} + 4 q^{61} + 40 q^{65} - 24 q^{69} - 20 q^{73} - 16 q^{77} + 108 q^{81} + 16 q^{85} + 36 q^{89} - 36 q^{97}+O(q^{100}) \) 20 * q - 4 * q^17 - 16 * q^21 - 28 * q^25 - 4 * q^29 - 20 * q^37 - 4 * q^41 - 40 * q^45 + 28 * q^49 + 48 * q^53 + 4 * q^61 + 40 * q^65 - 24 * q^69 - 20 * q^73 - 16 * q^77 + 108 * q^81 + 16 * q^85 + 36 * q^89 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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