LMFDB - Embedded newform 1064.2.q.k.305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, 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:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.k.457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 + 2.95680i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})$	\(q+(-1.70711 + 2.95680i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} +(-4.32843 - 7.49706i) q^{9} +(1.62132 - 2.80821i) q^{11} -3.41421 q^{13} -3.41421 q^{15} +(3.41421 - 5.91359i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.41421 - 8.36308i) q^{21} +(-2.20711 - 3.82282i) q^{23} +(2.00000 - 3.46410i) q^{25} +19.3137 q^{27} -9.41421 q^{29} +(-2.29289 + 3.97141i) q^{31} +(5.53553 + 9.58783i) q^{33} +(-2.62132 - 0.358719i) q^{35} +(3.29289 + 5.70346i) q^{37} +(5.82843 - 10.0951i) q^{39} -5.65685 q^{41} -3.24264 q^{43} +(4.32843 - 7.49706i) q^{45} +(0.621320 + 1.07616i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(11.6569 + 20.1903i) q^{51} +(2.70711 - 4.68885i) q^{53} +3.24264 q^{55} -3.41421 q^{57} +(0.414214 - 0.717439i) q^{59} +(2.50000 + 4.33013i) q^{61} +(22.6924 + 3.10538i) q^{63} +(-1.70711 - 2.95680i) q^{65} +(-1.58579 + 2.74666i) q^{67} +15.0711 q^{69} -7.75736 q^{71} +(3.50000 - 6.06218i) q^{73} +(6.82843 + 11.8272i) q^{75} +(3.24264 + 7.94282i) q^{77} +(-1.94975 - 3.37706i) q^{79} +(-19.9853 + 34.6155i) q^{81} +14.8995 q^{83} +6.82843 q^{85} +(16.0711 - 27.8359i) q^{87} +(-6.77817 - 11.7401i) q^{89} +(5.53553 - 7.13834i) q^{91} +(-7.82843 - 13.5592i) q^{93} +(-0.500000 + 0.866025i) q^{95} -5.65685 q^{97} -28.0711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 2 q^{11} - 8 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{23} + 8 q^{25} + 32 q^{27} - 32 q^{29} - 12 q^{31} + 8 q^{33} - 2 q^{35} + 16 q^{37} + 12 q^{39} + 4 q^{43} + 6 q^{45} - 6 q^{47} + 10 q^{49} + 24 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{57} - 4 q^{59} + 10 q^{61} + 54 q^{63} - 4 q^{65} - 12 q^{67} + 32 q^{69} - 48 q^{71} + 14 q^{73} + 16 q^{75} - 4 q^{77} + 12 q^{79} - 46 q^{81} + 20 q^{83} + 16 q^{85} + 36 q^{87} + 4 q^{89} + 8 q^{91} - 20 q^{93} - 2 q^{95} - 84 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 2 * q^11 - 8 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^23 + 8 * q^25 + 32 * q^27 - 32 * q^29 - 12 * q^31 + 8 * q^33 - 2 * q^35 + 16 * q^37 + 12 * q^39 + 4 * q^43 + 6 * q^45 - 6 * q^47 + 10 * q^49 + 24 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^57 - 4 * q^59 + 10 * q^61 + 54 * q^63 - 4 * q^65 - 12 * q^67 + 32 * q^69 - 48 * q^71 + 14 * q^73 + 16 * q^75 - 4 * q^77 + 12 * q^79 - 46 * q^81 + 20 * q^83 + 16 * q^85 + 36 * q^87 + 4 * q^89 + 8 * q^91 - 20 * q^93 - 2 * q^95 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70711	+	2.95680i	−0.985599	+	1.70711i	−0.346353	+	0.938104i	$0.612580\pi$
$3$	−1.70711	+	2.95680i	−0.985599	+	1.70711i	−0.639246	+	0.769002i	$0.720753\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$		0			0
$9$	−4.32843	−	7.49706i	−1.44281	−	2.49902i
$10$		0			0
$11$	1.62132	−	2.80821i	0.488846	−	0.846707i	−0.511071	−	0.859538i	$-0.670751\pi$
$11$	1.62132	−	2.80821i	0.488846	−	0.846707i	0.999918	+	0.0128314i	$0.00408449\pi$
$12$		0			0
$13$	−3.41421			−0.946932			−0.473466	−	0.880812i	$-0.656997\pi$
$13$	−3.41421			−0.946932			−0.473466	+	0.880812i	$0.656997\pi$
$14$		0			0
$15$	−3.41421			−0.881546
$16$		0			0
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	−0.0714831	−	0.997442i	$-0.522773\pi$
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	0.899551	−	0.436815i	$-0.143893\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$		0			0
$21$	−3.41421	−	8.36308i	−0.745042	−	1.82497i
$22$		0			0
$23$	−2.20711	−	3.82282i	−0.460214	−	0.797113i	0.538758	−	0.842461i	$-0.318894\pi$
$23$	−2.20711	−	3.82282i	−0.460214	−	0.797113i	−0.998971	+	0.0453475i	$0.985561\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	19.3137			3.71692
$28$		0			0
$29$	−9.41421			−1.74818			−0.874088	−	0.485768i	$-0.838540\pi$
$29$	−9.41421			−1.74818			−0.874088	+	0.485768i	$0.838540\pi$
$30$		0			0
$31$	−2.29289	+	3.97141i	−0.411816	+	0.713286i	−0.995088	−	0.0989906i	$-0.968439\pi$
$31$	−2.29289	+	3.97141i	−0.411816	+	0.713286i	0.583273	+	0.812276i	$0.301772\pi$
$32$		0			0
$33$	5.53553	+	9.58783i	0.963613	+	1.66903i
$34$		0			0
$35$	−2.62132	−	0.358719i	−0.443084	−	0.0606347i
$36$		0			0
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	0.998827	+	0.0484222i	$0.0154193\pi$
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	−0.457479	+	0.889221i	$0.651247\pi$
$38$		0			0
$39$	5.82843	−	10.0951i	0.933295	−	1.61651i
$40$		0			0
$41$	−5.65685			−0.883452			−0.441726	−	0.897150i	$-0.645634\pi$
$41$	−5.65685			−0.883452			−0.441726	+	0.897150i	$0.645634\pi$
$42$		0			0
$43$	−3.24264			−0.494498			−0.247249	−	0.968952i	$-0.579527\pi$
$43$	−3.24264			−0.494498			−0.247249	+	0.968952i	$0.579527\pi$
$44$		0			0
$45$	4.32843	−	7.49706i	0.645244	−	1.11760i
$46$		0			0
$47$	0.621320	+	1.07616i	0.0906289	+	0.156974i	0.907776	−	0.419455i	$-0.137779\pi$
$47$	0.621320	+	1.07616i	0.0906289	+	0.156974i	−0.817147	+	0.576429i	$0.804446\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$	11.6569	+	20.1903i	1.63229	+	2.82720i
$52$		0			0
$53$	2.70711	−	4.68885i	0.371850	−	0.644063i	−0.618000	−	0.786178i	$-0.712057\pi$
$53$	2.70711	−	4.68885i	0.371850	−	0.644063i	0.989850	+	0.142115i	$0.0453903\pi$
$54$		0			0
$55$	3.24264			0.437238
$56$		0			0
$57$	−3.41421			−0.452224
$58$		0			0
$59$	0.414214	−	0.717439i	0.0539260	−	0.0934026i	−0.837802	−	0.545974i	$-0.816160\pi$
$59$	0.414214	−	0.717439i	0.0539260	−	0.0934026i	0.891728	+	0.452571i	$0.149493\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	22.6924	+	3.10538i	2.85897	+	0.391241i
$64$		0			0
$65$	−1.70711	−	2.95680i	−0.211741	−	0.366745i
$66$		0			0
$67$	−1.58579	+	2.74666i	−0.193735	+	0.335558i	−0.946485	−	0.322748i	$-0.895393\pi$
$67$	−1.58579	+	2.74666i	−0.193735	+	0.335558i	0.752750	+	0.658306i	$0.228727\pi$
$68$		0			0
$69$	15.0711			1.81434
$70$		0			0
$71$	−7.75736			−0.920629			−0.460315	−	0.887756i	$-0.652263\pi$
$71$	−7.75736			−0.920629			−0.460315	+	0.887756i	$0.652263\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$	6.82843	+	11.8272i	0.788479	+	1.36569i
$76$		0			0
$77$	3.24264	+	7.94282i	0.369533	+	0.905168i
$78$		0			0
$79$	−1.94975	−	3.37706i	−0.219364	−	0.379949i	0.735250	−	0.677796i	$-0.237065\pi$
$79$	−1.94975	−	3.37706i	−0.219364	−	0.379949i	−0.954614	+	0.297847i	$0.903731\pi$
$80$		0			0
$81$	−19.9853	+	34.6155i	−2.22059	+	3.84617i
$82$		0			0
$83$	14.8995			1.63543			0.817716	−	0.575622i	$-0.195240\pi$
$83$	14.8995			1.63543			0.817716	+	0.575622i	$0.195240\pi$
$84$		0			0
$85$	6.82843			0.740647
$86$		0			0
$87$	16.0711	−	27.8359i	1.72300	−	2.98432i
$88$		0			0
$89$	−6.77817	−	11.7401i	−0.718485	−	1.24445i	−0.961600	−	0.274455i	$-0.911503\pi$
$89$	−6.77817	−	11.7401i	−0.718485	−	1.24445i	0.243115	−	0.969998i	$-0.421831\pi$
$90$		0			0
$91$	5.53553	−	7.13834i	0.580282	−	0.748301i
$92$		0			0
$93$	−7.82843	−	13.5592i	−0.811770	−	1.40603i
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$		0			0
$97$	−5.65685			−0.574367			−0.287183	−	0.957876i	$-0.592719\pi$
$97$	−5.65685			−0.574367			−0.287183	+	0.957876i	$0.592719\pi$
$98$		0			0
$99$	−28.0711			−2.82125
$100$		0			0
$101$	−0.742641	+	1.28629i	−0.0738955	+	0.127991i	−0.900605	−	0.434638i	$-0.856876\pi$
$101$	−0.742641	+	1.28629i	−0.0738955	+	0.127991i	0.826710	+	0.562628i	$0.190210\pi$
$102$		0			0
$103$	−1.17157	−	2.02922i	−0.115439	−	0.199945i	0.802516	−	0.596630i	$-0.203494\pi$
$103$	−1.17157	−	2.02922i	−0.115439	−	0.199945i	−0.917955	+	0.396685i	$0.870161\pi$
$104$		0			0
$105$	5.53553	−	7.13834i	0.540213	−	0.696630i
$106$		0			0
$107$	−8.53553	−	14.7840i	−0.825161	−	1.42922i	−0.901796	−	0.432162i	$-0.857751\pi$
$107$	−8.53553	−	14.7840i	−0.825161	−	1.42922i	0.0766348	−	0.997059i	$-0.475582\pi$
$108$		0			0
$109$	9.65685	−	16.7262i	0.924959	−	1.60208i	0.133332	−	0.991071i	$-0.457432\pi$
$109$	9.65685	−	16.7262i	0.924959	−	1.60208i	0.791627	−	0.611004i	$-0.209234\pi$
$110$		0			0
$111$	−22.4853			−2.13421
$112$		0			0
$113$	11.0711			1.04148			0.520739	−	0.853716i	$-0.325656\pi$
$113$	11.0711			1.04148			0.520739	+	0.853716i	$0.325656\pi$
$114$		0			0
$115$	2.20711	−	3.82282i	0.205814	−	0.356480i
$116$		0			0
$117$	14.7782	+	25.5965i	1.36624	+	2.36640i
$118$		0			0
$119$	6.82843	+	16.7262i	0.625961	+	1.53328i
$120$		0			0
$121$	0.242641	+	0.420266i	0.0220582	+	0.0382060i
$122$		0			0
$123$	9.65685	−	16.7262i	0.870729	−	1.50815i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−19.5563			−1.73535			−0.867673	−	0.497136i	$-0.834385\pi$
$127$	−19.5563			−1.73535			−0.867673	+	0.497136i	$0.834385\pi$
$128$		0			0
$129$	5.53553	−	9.58783i	0.487377	−	0.844161i
$130$		0			0
$131$	−0.828427	−	1.43488i	−0.0723800	−	0.125366i	0.827564	−	0.561371i	$-0.189726\pi$
$131$	−0.828427	−	1.43488i	−0.0723800	−	0.125366i	−0.899944	+	0.436006i	$0.856393\pi$
$132$		0			0
$133$	−2.62132	−	0.358719i	−0.227297	−	0.0311049i
$134$		0			0
$135$	9.65685	+	16.7262i	0.831130	+	1.43956i
$136$		0			0
$137$	−0.328427	+	0.568852i	−0.0280594	+	0.0486003i	−0.879714	−	0.475503i	$-0.842266\pi$
$137$	−0.328427	+	0.568852i	−0.0280594	+	0.0486003i	0.851655	+	0.524103i	$0.175599\pi$
$138$		0			0
$139$	−18.5563			−1.57393			−0.786964	−	0.616998i	$-0.788349\pi$
$139$	−18.5563			−1.57393			−0.786964	+	0.616998i	$0.788349\pi$
$140$		0			0
$141$	−4.24264			−0.357295
$142$		0			0
$143$	−5.53553	+	9.58783i	−0.462905	+	0.801774i
$144$		0			0
$145$	−4.70711	−	8.15295i	−0.390904	−	0.677065i
$146$		0			0
$147$	23.0208	+	6.42090i	1.89872	+	0.529587i
$148$		0			0
$149$	3.32843	+	5.76500i	0.272675	+	0.472288i	0.969546	−	0.244909i	$-0.0787582\pi$
$149$	3.32843	+	5.76500i	0.272675	+	0.472288i	−0.696871	+	0.717197i	$0.745425\pi$
$150$		0			0
$151$	−2.82843	+	4.89898i	−0.230174	+	0.398673i	−0.957859	−	0.287238i	$-0.907263\pi$
$151$	−2.82843	+	4.89898i	−0.230174	+	0.398673i	0.727685	+	0.685911i	$0.240596\pi$
$152$		0			0
$153$	−59.1127			−4.77898
$154$		0			0
$155$	−4.58579			−0.368339
$156$		0			0
$157$	0.843146	−	1.46037i	0.0672904	−	0.116550i	−0.830417	−	0.557142i	$-0.811898\pi$
$157$	0.843146	−	1.46037i	0.0672904	−	0.116550i	0.897708	+	0.440592i	$0.145231\pi$
$158$		0			0
$159$	9.24264	+	16.0087i	0.732989	+	1.26957i
$160$		0			0
$161$	11.5711	+	1.58346i	0.911928	+	0.124794i
$162$		0			0
$163$	−7.03553	−	12.1859i	−0.551066	−	0.954474i	−0.998198	−	0.0600058i	$-0.980888\pi$
$163$	−7.03553	−	12.1859i	−0.551066	−	0.954474i	0.447132	−	0.894468i	$-0.352445\pi$
$164$		0			0
$165$	−5.53553	+	9.58783i	−0.430941	+	0.746411i
$166$		0			0
$167$	18.5858			1.43821			0.719106	−	0.694901i	$-0.244552\pi$
$167$	18.5858			1.43821			0.719106	+	0.694901i	$0.244552\pi$
$168$		0			0
$169$	−1.34315			−0.103319
$170$		0			0
$171$	4.32843	−	7.49706i	0.331003	−	0.573314i
$172$		0			0
$173$	4.82843	+	8.36308i	0.367099	+	0.635833i	0.989111	−	0.147174i	$-0.0470179\pi$
$173$	4.82843	+	8.36308i	0.367099	+	0.635833i	−0.622012	+	0.783008i	$0.713685\pi$
$174$		0			0
$175$	4.00000	+	9.79796i	0.302372	+	0.740656i
$176$		0			0
$177$	1.41421	+	2.44949i	0.106299	+	0.184115i
$178$		0			0
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	−0.961388	−	0.275197i	$-0.911257\pi$
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	0.719022	+	0.694988i	$0.244590\pi$
$180$		0			0
$181$	−14.7279			−1.09472			−0.547359	−	0.836898i	$-0.684367\pi$
$181$	−14.7279			−1.09472			−0.547359	+	0.836898i	$0.684367\pi$
$182$		0			0
$183$	−17.0711			−1.26193
$184$		0			0
$185$	−3.29289	+	5.70346i	−0.242098	+	0.419327i
$186$		0			0
$187$	−11.0711	−	19.1757i	−0.809597	−	1.40226i
$188$		0			0
$189$	−31.3137	+	40.3805i	−2.27774	+	2.93725i
$190$		0			0
$191$	−4.62132	−	8.00436i	−0.334387	−	0.579175i	0.648980	−	0.760806i	$-0.275196\pi$
$191$	−4.62132	−	8.00436i	−0.334387	−	0.579175i	−0.983367	+	0.181630i	$0.941863\pi$
$192$		0			0
$193$	−1.12132	+	1.94218i	−0.0807144	+	0.139801i	−0.903557	−	0.428468i	$-0.859054\pi$
$193$	−1.12132	+	1.94218i	−0.0807144	+	0.139801i	0.822843	+	0.568269i	$0.192387\pi$
$194$		0			0
$195$	11.6569			0.834765
$196$		0			0
$197$	−0.514719			−0.0366722			−0.0183361	−	0.999832i	$-0.505837\pi$
$197$	−0.514719			−0.0366722			−0.0183361	+	0.999832i	$0.505837\pi$
$198$		0			0
$199$	−1.03553	+	1.79360i	−0.0734071	+	0.127145i	−0.900392	−	0.435079i	$-0.856721\pi$
$199$	−1.03553	+	1.79360i	−0.0734071	+	0.127145i	0.826985	+	0.562223i	$0.190054\pi$
$200$		0			0
$201$	−5.41421	−	9.37769i	−0.381889	−	0.661451i
$202$		0			0
$203$	15.2635	−	19.6830i	1.07128	−	1.38147i
$204$		0			0
$205$	−2.82843	−	4.89898i	−0.197546	−	0.342160i
$206$		0			0
$207$	−19.1066	+	33.0936i	−1.32800	+	2.30016i
$208$		0			0
$209$	3.24264			0.224298
$210$		0			0
$211$	12.1421			0.835899			0.417950	−	0.908470i	$-0.362749\pi$
$211$	12.1421			0.835899			0.417950	+	0.908470i	$0.362749\pi$
$212$		0			0
$213$	13.2426	−	22.9369i	0.907371	−	1.57161i
$214$		0			0
$215$	−1.62132	−	2.80821i	−0.110573	−	0.191518i
$216$		0			0
$217$	−4.58579	−	11.2328i	−0.311303	−	0.762535i
$218$		0			0
$219$	11.9497	+	20.6976i	0.807489	+	1.39861i
$220$		0			0
$221$	−11.6569	+	20.1903i	−0.784125	+	1.35814i
$222$		0			0
$223$	−16.2426			−1.08769			−0.543844	−	0.839186i	$-0.683032\pi$
$223$	−16.2426			−1.08769			−0.543844	+	0.839186i	$0.683032\pi$
$224$		0			0
$225$	−34.6274			−2.30849
$226$		0			0
$227$	−0.707107	+	1.22474i	−0.0469323	+	0.0812892i	−0.888537	−	0.458804i	$-0.848278\pi$
$227$	−0.707107	+	1.22474i	−0.0469323	+	0.0812892i	0.841605	+	0.540094i	$0.181611\pi$
$228$		0			0
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$		0			0
$231$	−29.0208	−	3.97141i	−1.90943	−	0.261299i
$232$		0			0
$233$	3.17157	+	5.49333i	0.207777	+	0.359880i	0.951014	−	0.309148i	$-0.100044\pi$
$233$	3.17157	+	5.49333i	0.207777	+	0.359880i	−0.743237	+	0.669028i	$0.766711\pi$
$234$		0			0
$235$	−0.621320	+	1.07616i	−0.0405305	+	0.0702008i
$236$		0			0
$237$	13.3137			0.864818
$238$		0			0
$239$	−4.34315			−0.280935			−0.140467	−	0.990085i	$-0.544861\pi$
$239$	−4.34315			−0.280935			−0.140467	+	0.990085i	$0.544861\pi$
$240$		0			0
$241$	−4.36396	+	7.55860i	−0.281107	+	0.486892i	−0.971658	−	0.236392i	$-0.924035\pi$
$241$	−4.36396	+	7.55860i	−0.281107	+	0.486892i	0.690550	+	0.723284i	$0.257368\pi$
$242$		0			0
$243$	−39.2635	−	68.0063i	−2.51875	−	4.36261i
$244$		0			0
$245$	5.00000	−	4.89898i	0.319438	−	0.312984i
$246$		0			0
$247$	−1.70711	−	2.95680i	−0.108621	−	0.188136i
$248$		0			0
$249$	−25.4350	+	44.0548i	−1.61188	+	2.79186i
$250$		0			0
$251$	−22.2132			−1.40208			−0.701042	−	0.713120i	$-0.747282\pi$
$251$	−22.2132			−1.40208			−0.701042	+	0.713120i	$0.747282\pi$
$252$		0			0
$253$	−14.3137			−0.899895
$254$		0			0
$255$	−11.6569	+	20.1903i	−0.729981	+	1.26436i
$256$		0			0
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		0			0
$259$	−17.2635	−	2.36245i	−1.07270	−	0.146795i
$260$		0			0
$261$	40.7487	+	70.5789i	2.52228	+	4.36872i
$262$		0			0
$263$	10.5858	−	18.3351i	0.652748	−	1.13059i	−0.329706	−	0.944084i	$-0.606950\pi$
$263$	10.5858	−	18.3351i	0.652748	−	1.13059i	0.982453	−	0.186508i	$-0.0597171\pi$
$264$		0			0
$265$	5.41421			0.332592
$266$		0			0
$267$	46.2843			2.83255
$268$		0			0
$269$	8.00000	−	13.8564i	0.487769	−	0.844840i	−0.512132	−	0.858906i	$-0.671144\pi$
$269$	8.00000	−	13.8564i	0.487769	−	0.844840i	0.999901	+	0.0140665i	$0.00447764\pi$
$270$		0			0
$271$	−1.13604	−	1.96768i	−0.0690095	−	0.119528i	0.829456	−	0.558572i	$-0.188651\pi$
$271$	−1.13604	−	1.96768i	−0.0690095	−	0.119528i	−0.898466	+	0.439044i	$0.855317\pi$
$272$		0			0
$273$	11.6569	+	28.5533i	0.705505	+	1.72813i
$274$		0			0
$275$	−6.48528	−	11.2328i	−0.391077	−	0.677366i
$276$		0			0
$277$	13.9853	−	24.2232i	0.840294	−	1.45543i	−0.0493520	−	0.998781i	$-0.515716\pi$
$277$	13.9853	−	24.2232i	0.840294	−	1.45543i	0.889646	−	0.456651i	$-0.150951\pi$
$278$		0			0
$279$	39.6985			2.37669
$280$		0			0
$281$	−17.8995			−1.06779			−0.533897	−	0.845549i	$-0.679273\pi$
$281$	−17.8995			−1.06779			−0.533897	+	0.845549i	$0.679273\pi$
$282$		0			0
$283$	−7.27817	+	12.6062i	−0.432643	+	0.749359i	−0.997100	−	0.0761033i	$-0.975752\pi$
$283$	−7.27817	+	12.6062i	−0.432643	+	0.749359i	0.564457	+	0.825462i	$0.309085\pi$
$284$		0			0
$285$	−1.70711	−	2.95680i	−0.101120	−	0.175145i
$286$		0			0
$287$	9.17157	−	11.8272i	0.541381	−	0.698137i
$288$		0			0
$289$	−14.8137	−	25.6581i	−0.871395	−	1.50930i
$290$		0			0
$291$	9.65685	−	16.7262i	0.566095	−	0.980505i
$292$		0			0
$293$	9.65685			0.564159			0.282080	−	0.959391i	$-0.408976\pi$
$293$	9.65685			0.564159			0.282080	+	0.959391i	$0.408976\pi$
$294$		0			0
$295$	0.828427			0.0482329
$296$		0			0
$297$	31.3137	−	54.2369i	1.81701	−	3.14715i
$298$		0			0
$299$	7.53553	+	13.0519i	0.435791	+	0.754812i
$300$		0			0
$301$	5.25736	−	6.77962i	0.303029	−	0.390771i
$302$		0			0
$303$	−2.53553	−	4.39167i	−0.145663	−	0.252295i
$304$		0			0
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$		0			0
$307$	18.6274			1.06312			0.531561	−	0.847020i	$-0.321605\pi$
$307$	18.6274			1.06312			0.531561	+	0.847020i	$0.321605\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$		0			0
$313$	−0.571068	−	0.989118i	−0.0322787	−	0.0559083i	0.849435	−	0.527694i	$-0.176943\pi$
$313$	−0.571068	−	0.989118i	−0.0322787	−	0.0559083i	−0.881713	+	0.471785i	$0.843610\pi$
$314$		0			0
$315$	8.65685	+	21.2049i	0.487758	+	1.19476i
$316$		0			0
$317$	5.12132	+	8.87039i	0.287642	+	0.498211i	0.973246	−	0.229764i	$-0.0737953\pi$
$317$	5.12132	+	8.87039i	0.287642	+	0.498211i	−0.685604	+	0.727974i	$0.740462\pi$
$318$		0			0
$319$	−15.2635	+	26.4371i	−0.854589	+	1.48019i
$320$		0			0
$321$	58.2843			3.25311
$322$		0			0
$323$	6.82843			0.379944
$324$		0			0
$325$	−6.82843	+	11.8272i	−0.378773	+	0.656054i
$326$		0			0
$327$	32.9706	+	57.1067i	1.82328	+	3.15801i
$328$		0			0
$329$	−3.25736	−	0.445759i	−0.179584	−	0.0245755i
$330$		0			0
$331$	9.24264	+	16.0087i	0.508021	+	0.879919i	0.999957	+	0.00928730i	$0.00295628\pi$
$331$	9.24264	+	16.0087i	0.508021	+	0.879919i	−0.491935	+	0.870632i	$0.663710\pi$
$332$		0			0
$333$	28.5061	−	49.3740i	1.56212	−	2.70568i
$334$		0			0
$335$	−3.17157			−0.173282
$336$		0			0
$337$	5.07107			0.276239			0.138119	−	0.990416i	$-0.455894\pi$
$337$	5.07107			0.276239			0.138119	+	0.990416i	$0.455894\pi$
$338$		0			0
$339$	−18.8995	+	32.7349i	−1.02648	+	1.77791i
$340$		0			0
$341$	7.43503	+	12.8778i	0.402629	+	0.697375i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$		0			0
$345$	7.53553	+	13.0519i	0.405700	+	0.702692i
$346$		0			0
$347$	−6.20711	+	10.7510i	−0.333215	+	0.577145i	−0.983140	−	0.182853i	$-0.941467\pi$
$347$	−6.20711	+	10.7510i	−0.333215	+	0.577145i	0.649925	+	0.759998i	$0.274800\pi$
$348$		0			0
$349$	5.65685			0.302804			0.151402	−	0.988472i	$-0.451621\pi$
$349$	5.65685			0.302804			0.151402	+	0.988472i	$0.451621\pi$
$350$		0			0
$351$	−65.9411			−3.51968
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−3.87868	−	6.71807i	−0.205859	−	0.356558i
$356$		0			0
$357$	−61.1127	−	8.36308i	−3.23443	−	0.442621i
$358$		0			0
$359$	−18.3492	−	31.7818i	−0.968436	−	1.67738i	−0.700086	−	0.714059i	$-0.746855\pi$
$359$	−18.3492	−	31.7818i	−0.968436	−	1.67738i	−0.268350	−	0.963321i	$-0.586478\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	−1.65685			−0.0869623
$364$		0			0
$365$	7.00000			0.366397
$366$		0			0
$367$	−8.31371	+	14.3998i	−0.433972	+	0.751662i	−0.997211	−	0.0746323i	$-0.976222\pi$
$367$	−8.31371	+	14.3998i	−0.433972	+	0.751662i	0.563239	+	0.826294i	$0.309555\pi$
$368$		0			0
$369$	24.4853	+	42.4098i	1.27465	+	2.20776i
$370$		0			0
$371$	5.41421	+	13.2621i	0.281092	+	0.688532i
$372$		0			0
$373$	3.17157	+	5.49333i	0.164218	+	0.284434i	0.936377	−	0.350995i	$-0.114157\pi$
$373$	3.17157	+	5.49333i	0.164218	+	0.284434i	−0.772159	+	0.635429i	$0.780823\pi$
$374$		0			0
$375$	−15.3640	+	26.6112i	−0.793392	+	1.37419i
$376$		0			0
$377$	32.1421			1.65540
$378$		0			0
$379$	12.5858			0.646488			0.323244	−	0.946316i	$-0.395226\pi$
$379$	12.5858			0.646488			0.323244	+	0.946316i	$0.395226\pi$
$380$		0			0
$381$	33.3848	−	57.8241i	1.71035	−	2.96242i
$382$		0			0
$383$	1.87868	+	3.25397i	0.0959960	+	0.166270i	0.910024	−	0.414556i	$-0.136063\pi$
$383$	1.87868	+	3.25397i	0.0959960	+	0.166270i	−0.814028	+	0.580826i	$0.802730\pi$
$384$		0			0
$385$	−5.25736	+	6.77962i	−0.267940	+	0.345521i
$386$		0			0
$387$	14.0355	+	24.3103i	0.713466	+	1.23576i
$388$		0			0
$389$	7.65685	−	13.2621i	0.388218	−	0.672413i	−0.603992	−	0.796990i	$-0.706424\pi$
$389$	7.65685	−	13.2621i	0.388218	−	0.672413i	0.992210	+	0.124577i	$0.0397575\pi$
$390$		0			0
$391$	−30.1421			−1.52435
$392$		0			0
$393$	5.65685			0.285351
$394$		0			0
$395$	1.94975	−	3.37706i	0.0981024	−	0.169918i
$396$		0			0
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	0.963786	−	0.266678i	$-0.0859261\pi$
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	−0.712843	+	0.701324i	$0.752593\pi$
$398$		0			0
$399$	5.53553	−	7.13834i	0.277123	−	0.357364i
$400$		0			0
$401$	4.31371	+	7.47156i	0.215416	+	0.373112i	0.953401	−	0.301705i	$-0.0975558\pi$
$401$	4.31371	+	7.47156i	0.215416	+	0.373112i	−0.737985	+	0.674817i	$0.764222\pi$
$402$		0			0
$403$	7.82843	−	13.5592i	0.389962	−	0.675434i
$404$		0			0
$405$	−39.9706			−1.98615
$406$		0			0
$407$	21.3553			1.05854
$408$		0			0
$409$	14.6569	−	25.3864i	0.724735	−	1.25528i	−0.234348	−	0.972153i	$-0.575296\pi$
$409$	14.6569	−	25.3864i	0.724735	−	1.25528i	0.959083	−	0.283125i	$-0.0913711\pi$
$410$		0			0
$411$	−1.12132	−	1.94218i	−0.0553107	−	0.0958009i
$412$		0			0
$413$	0.828427	+	2.02922i	0.0407642	+	0.0998516i
$414$		0			0
$415$	7.44975	+	12.9033i	0.365694	+	0.633400i
$416$		0			0
$417$	31.6777	−	54.8673i	1.55126	−	2.68686i
$418$		0			0
$419$	−30.6985			−1.49972			−0.749860	−	0.661597i	$-0.769879\pi$
$419$	−30.6985			−1.49972			−0.749860	+	0.661597i	$0.769879\pi$
$420$		0			0
$421$	−24.5858			−1.19824			−0.599119	−	0.800660i	$-0.704482\pi$
$421$	−24.5858			−1.19824			−0.599119	+	0.800660i	$0.704482\pi$
$422$		0			0
$423$	5.37868	−	9.31615i	0.261520	−	0.452967i
$424$		0			0
$425$	−13.6569	−	23.6544i	−0.662455	−	1.14741i
$426$		0			0
$427$	−13.1066	−	1.79360i	−0.634273	−	0.0867983i
$428$		0			0
$429$	−18.8995	−	32.7349i	−0.912476	−	1.58046i
$430$		0			0
$431$	6.94975	−	12.0373i	0.334758	−	0.579817i	−0.648681	−	0.761061i	$-0.724679\pi$
$431$	6.94975	−	12.0373i	0.334758	−	0.579817i	0.983438	+	0.181244i	$0.0580122\pi$
$432$		0			0
$433$	12.0000			0.576683			0.288342	−	0.957528i	$-0.406896\pi$
$433$	12.0000			0.576683			0.288342	+	0.957528i	$0.406896\pi$
$434$		0			0
$435$	32.1421			1.54110
$436$		0			0
$437$	2.20711	−	3.82282i	0.105580	−	0.182870i
$438$		0			0
$439$	−13.2426	−	22.9369i	−0.632037	−	1.09472i	−0.987135	−	0.159891i	$-0.948886\pi$
$439$	−13.2426	−	22.9369i	−0.632037	−	1.09472i	0.355098	−	0.934829i	$-0.384448\pi$
$440$		0			0
$441$	−43.2843	+	42.4098i	−2.06116	+	2.01951i
$442$		0			0
$443$	8.34315	+	14.4508i	0.396395	+	0.686576i	0.993278	−	0.115752i	$-0.0369278\pi$
$443$	8.34315	+	14.4508i	0.396395	+	0.686576i	−0.596883	+	0.802328i	$0.703594\pi$
$444$		0			0
$445$	6.77817	−	11.7401i	0.321316	−	0.556536i
$446$		0			0
$447$	−22.7279			−1.07499
$448$		0			0
$449$	30.6274			1.44540			0.722699	−	0.691163i	$-0.242901\pi$
$449$	30.6274			1.44540			0.722699	+	0.691163i	$0.242901\pi$
$450$		0			0
$451$	−9.17157	+	15.8856i	−0.431872	+	0.748025i
$452$		0			0
$453$	−9.65685	−	16.7262i	−0.453719	−	0.785864i
$454$		0			0
$455$	8.94975	+	1.22474i	0.419571	+	0.0574169i
$456$		0			0
$457$	−2.91421	−	5.04757i	−0.136321	−	0.236115i	0.789780	−	0.613390i	$-0.210195\pi$
$457$	−2.91421	−	5.04757i	−0.136321	−	0.236115i	−0.926101	+	0.377275i	$0.876861\pi$
$458$		0			0
$459$	65.9411	−	114.213i	3.07787	−	5.33102i
$460$		0			0
$461$	10.7990			0.502959			0.251480	−	0.967863i	$-0.419083\pi$
$461$	10.7990			0.502959			0.251480	+	0.967863i	$0.419083\pi$
$462$		0			0
$463$	−27.7279			−1.28863			−0.644313	−	0.764762i	$-0.722857\pi$
$463$	−27.7279			−1.28863			−0.644313	+	0.764762i	$0.722857\pi$
$464$		0			0
$465$	7.82843	−	13.5592i	0.363035	−	0.628794i
$466$		0			0
$467$	3.86396	+	6.69258i	0.178803	+	0.309696i	0.941471	−	0.337095i	$-0.109444\pi$
$467$	3.86396	+	6.69258i	0.178803	+	0.309696i	−0.762668	+	0.646790i	$0.776111\pi$
$468$		0			0
$469$	−3.17157	−	7.76874i	−0.146450	−	0.358727i
$470$		0			0
$471$	2.87868	+	4.98602i	0.132643	+	0.229744i
$472$		0			0
$473$	−5.25736	+	9.10601i	−0.241734	+	0.418695i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−46.8701			−2.14603
$478$		0			0
$479$	4.96447	−	8.59871i	0.226832	−	0.392885i	−0.730035	−	0.683409i	$-0.760496\pi$
$479$	4.96447	−	8.59871i	0.226832	−	0.392885i	0.956868	+	0.290524i	$0.0938298\pi$
$480$		0			0
$481$	−11.2426	−	19.4728i	−0.512620	−	0.887884i
$482$		0			0
$483$	−24.4350	+	31.5101i	−1.11183	+	1.43376i
$484$		0			0
$485$	−2.82843	−	4.89898i	−0.128432	−	0.222451i
$486$		0			0
$487$	5.92893	−	10.2692i	0.268666	−	0.465342i	−0.699852	−	0.714288i	$-0.746751\pi$
$487$	5.92893	−	10.2692i	0.268666	−	0.465342i	0.968517	+	0.248946i	$0.0800840\pi$
$488$		0			0
$489$	48.0416			2.17252
$490$		0			0
$491$	−18.6985			−0.843851			−0.421925	−	0.906631i	$-0.638646\pi$
$491$	−18.6985			−0.843851			−0.421925	+	0.906631i	$0.638646\pi$
$492$		0			0
$493$	−32.1421	+	55.6718i	−1.44761	+	2.50733i
$494$		0			0
$495$	−14.0355	−	24.3103i	−0.630850	−	1.09266i
$496$		0			0
$497$	12.5772	−	16.2189i	0.564163	−	0.727515i
$498$		0			0
$499$	0.378680	+	0.655892i	0.0169520	+	0.0293618i	0.874377	−	0.485247i	$-0.161270\pi$
$499$	0.378680	+	0.655892i	0.0169520	+	0.0293618i	−0.857425	+	0.514609i	$0.827937\pi$
$500$		0			0
$501$	−31.7279	+	54.9544i	−1.41750	+	2.45518i
$502$		0			0
$503$	21.7279			0.968800			0.484400	−	0.874847i	$-0.339038\pi$
$503$	21.7279			0.968800			0.484400	+	0.874847i	$0.339038\pi$
$504$		0			0
$505$	−1.48528			−0.0660942
$506$		0			0
$507$	2.29289	−	3.97141i	0.101831	−	0.176376i
$508$		0			0
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	7.00000	+	17.1464i	0.309662	+	0.758513i
$512$		0			0
$513$	9.65685	+	16.7262i	0.426361	+	0.738478i
$514$		0			0
$515$	1.17157	−	2.02922i	0.0516257	−	0.0894183i
$516$		0			0
$517$	4.02944			0.177214
$518$		0			0
$519$	−32.9706			−1.44725
$520$		0			0
$521$	10.9497	−	18.9655i	0.479717	−	0.830894i	−0.520012	−	0.854159i	$-0.674073\pi$
$521$	10.9497	−	18.9655i	0.479717	−	0.830894i	0.999729	+	0.0232644i	$0.00740594\pi$
$522$		0			0
$523$	−3.65685	−	6.33386i	−0.159903	−	0.276960i	0.774930	−	0.632046i	$-0.217785\pi$
$523$	−3.65685	−	6.33386i	−0.159903	−	0.276960i	−0.934834	+	0.355086i	$0.884452\pi$
$524$		0			0
$525$	−35.7990	−	4.89898i	−1.56240	−	0.213809i
$526$		0			0
$527$	15.6569	+	27.1185i	0.682023	+	1.18130i
$528$		0			0
$529$	1.75736	−	3.04384i	0.0764069	−	0.132341i
$530$		0			0
$531$	−7.17157			−0.311220
$532$		0			0
$533$	19.3137			0.836570
$534$		0			0
$535$	8.53553	−	14.7840i	0.369023	−	0.639167i
$536$		0			0
$537$	−11.0711	−	19.1757i	−0.477752	−	0.827490i
$538$		0			0
$539$	−21.8640	−	6.09823i	−0.941747	−	0.262669i
$540$		0			0
$541$	14.5711	+	25.2378i	0.626459	+	1.08506i	0.988257	+	0.152802i	$0.0488298\pi$
$541$	14.5711	+	25.2378i	0.626459	+	1.08506i	−0.361798	+	0.932257i	$0.617837\pi$
$542$		0			0
$543$	25.1421	−	43.5475i	1.07895	−	1.86880i
$544$		0			0
$545$	19.3137			0.827308
$546$		0			0
$547$	−21.5563			−0.921683			−0.460841	−	0.887482i	$-0.652452\pi$
$547$	−21.5563			−0.921683			−0.460841	+	0.887482i	$0.652452\pi$
$548$		0			0
$549$	21.6421	−	37.4853i	0.923664	−	1.59983i
$550$		0			0
$551$	−4.70711	−	8.15295i	−0.200529	−	0.347327i
$552$		0			0
$553$	10.2218	+	1.39882i	0.434676	+	0.0594841i
$554$		0			0
$555$	−11.2426	−	19.4728i	−0.477224	−	0.826575i
$556$		0			0
$557$	−17.7426	+	30.7312i	−0.751780	+	1.30212i	0.195180	+	0.980768i	$0.437471\pi$
$557$	−17.7426	+	30.7312i	−0.751780	+	1.30212i	−0.946959	+	0.321353i	$0.895862\pi$
$558$		0			0
$559$	11.0711			0.468256
$560$		0			0
$561$	75.5980			3.19175
$562$		0			0
$563$	−21.4350	+	37.1266i	−0.903379	+	1.56470i	−0.0802999	+	0.996771i	$0.525588\pi$
$563$	−21.4350	+	37.1266i	−0.903379	+	1.56470i	−0.823079	+	0.567927i	$0.807746\pi$
$564$		0			0
$565$	5.53553	+	9.58783i	0.232882	+	0.403363i
$566$		0			0
$567$	−39.9706	−	97.9075i	−1.67861	−	4.11173i
$568$		0			0
$569$	2.65685	+	4.60181i	0.111381	+	0.192918i	0.916327	−	0.400430i	$-0.131139\pi$
$569$	2.65685	+	4.60181i	0.111381	+	0.192918i	−0.804946	+	0.593348i	$0.797806\pi$
$570$		0			0
$571$	21.3492	−	36.9780i	0.893438	−	1.54748i	0.0577120	−	0.998333i	$-0.481619\pi$
$571$	21.3492	−	36.9780i	0.893438	−	1.54748i	0.835726	−	0.549147i	$-0.185047\pi$
$572$		0			0
$573$	31.5563			1.31829
$574$		0			0
$575$	−17.6569			−0.736342
$576$		0			0
$577$	−14.0858	+	24.3973i	−0.586399	+	1.01567i	0.408300	+	0.912848i	$0.366122\pi$
$577$	−14.0858	+	24.3973i	−0.586399	+	1.01567i	−0.994699	+	0.102825i	$0.967212\pi$
$578$		0			0
$579$	−3.82843	−	6.63103i	−0.159104	−	0.275576i
$580$		0			0
$581$	−24.1569	+	31.1514i	−1.00220	+	1.29238i
$582$		0			0
$583$	−8.77817	−	15.2042i	−0.363555	−	0.629695i
$584$		0			0
$585$	−14.7782	+	25.5965i	−0.611002	+	1.05829i
$586$		0			0
$587$	−34.0000			−1.40333			−0.701665	−	0.712507i	$-0.747560\pi$
$587$	−34.0000			−1.40333			−0.701665	+	0.712507i	$0.747560\pi$
$588$		0			0
$589$	−4.58579			−0.188954
$590$		0			0
$591$	0.878680	−	1.52192i	0.0361441	−	0.0626033i
$592$		0			0
$593$	−2.15685	−	3.73578i	−0.0885714	−	0.153410i	0.818336	−	0.574740i	$-0.194897\pi$
$593$	−2.15685	−	3.73578i	−0.0885714	−	0.153410i	−0.906907	+	0.421330i	$0.861563\pi$
$594$		0			0
$595$	−11.0711	+	14.2767i	−0.453870	+	0.585287i
$596$		0			0
$597$	−3.53553	−	6.12372i	−0.144700	−	0.250627i
$598$		0			0
$599$	−10.6066	+	18.3712i	−0.433374	+	0.750626i	−0.997161	−	0.0752942i	$-0.976010\pi$
$599$	−10.6066	+	18.3712i	−0.433374	+	0.750626i	0.563787	+	0.825920i	$0.309344\pi$
$600$		0			0
$601$	−16.5269			−0.674147			−0.337073	−	0.941478i	$-0.609437\pi$
$601$	−16.5269			−0.674147			−0.337073	+	0.941478i	$0.609437\pi$
$602$		0			0
$603$	27.4558			1.11809
$604$		0			0
$605$	−0.242641	+	0.420266i	−0.00986475	+	0.0170862i
$606$		0			0
$607$	−7.94975	−	13.7694i	−0.322670	−	0.558881i	0.658368	−	0.752696i	$-0.271247\pi$
$607$	−7.94975	−	13.7694i	−0.322670	−	0.558881i	−0.981038	+	0.193815i	$0.937914\pi$
$608$		0			0
$609$	32.1421	+	78.7318i	1.30247	+	3.19037i
$610$		0			0
$611$	−2.12132	−	3.67423i	−0.0858194	−	0.148644i
$612$		0			0
$613$	16.2426	−	28.1331i	0.656034	−	1.13628i	−0.325599	−	0.945508i	$-0.605566\pi$
$613$	16.2426	−	28.1331i	0.656034	−	1.13628i	0.981633	−	0.190777i	$-0.0611006\pi$
$614$		0			0
$615$	19.3137			0.778804
$616$		0			0
$617$	27.2843			1.09842			0.549212	−	0.835683i	$-0.314928\pi$
$617$	27.2843			1.09842			0.549212	+	0.835683i	$0.314928\pi$
$618$		0			0
$619$	−4.55025	+	7.88127i	−0.182890	+	0.316775i	−0.942864	−	0.333179i	$-0.891879\pi$
$619$	−4.55025	+	7.88127i	−0.182890	+	0.316775i	0.759973	+	0.649954i	$0.225212\pi$
$620$		0			0
$621$	−42.6274	−	73.8329i	−1.71058	−	2.96281i
$622$		0			0
$623$	35.5355	+	4.86293i	1.42370	+	0.194829i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	−5.53553	+	9.58783i	−0.221068	+	0.382901i
$628$		0			0
$629$	44.9706			1.79309
$630$		0			0
$631$	−17.3848			−0.692077			−0.346039	−	0.938220i	$-0.612473\pi$
$631$	−17.3848			−0.692077			−0.346039	+	0.938220i	$0.612473\pi$
$632$		0			0
$633$	−20.7279	+	35.9018i	−0.823861	+	1.42697i
$634$		0			0
$635$	−9.77817	−	16.9363i	−0.388035	−	0.672096i
$636$		0			0
$637$	5.94975	+	23.1471i	0.235738	+	0.917120i
$638$		0			0
$639$	33.5772	+	58.1574i	1.32829	+	2.30067i
$640$		0			0
$641$	−5.34315	+	9.25460i	−0.211042	+	0.365535i	−0.952041	−	0.305971i	$-0.901019\pi$
$641$	−5.34315	+	9.25460i	−0.211042	+	0.365535i	0.740999	+	0.671506i	$0.234352\pi$
$642$		0			0
$643$	27.5147			1.08507			0.542537	−	0.840032i	$-0.317464\pi$
$643$	27.5147			1.08507			0.542537	+	0.840032i	$0.317464\pi$
$644$		0			0
$645$	11.0711			0.435923
$646$		0			0
$647$	−13.9645	+	24.1872i	−0.549000	+	0.950896i	0.449344	+	0.893359i	$0.351658\pi$
$647$	−13.9645	+	24.1872i	−0.549000	+	0.950896i	−0.998343	+	0.0575365i	$0.981675\pi$
$648$		0			0
$649$	−1.34315	−	2.32640i	−0.0527231	−	0.0913191i
$650$		0			0
$651$	41.0416	+	5.61642i	1.60855	+	0.220125i
$652$		0			0
$653$	15.0711	+	26.1039i	0.589776	+	1.02152i	0.994261	+	0.106978i	$0.0341175\pi$
$653$	15.0711	+	26.1039i	0.589776	+	1.02152i	−0.404485	+	0.914545i	$0.632549\pi$
$654$		0			0
$655$	0.828427	−	1.43488i	0.0323693	−	0.0560653i
$656$		0			0
$657$	−60.5980			−2.36415
$658$		0			0
$659$	24.3848			0.949896			0.474948	−	0.880014i	$-0.342467\pi$
$659$	24.3848			0.949896			0.474948	+	0.880014i	$0.342467\pi$
$660$		0			0
$661$	−4.43503	+	7.68170i	−0.172503	+	0.298783i	−0.939294	−	0.343113i	$-0.888519\pi$
$661$	−4.43503	+	7.68170i	−0.172503	+	0.298783i	0.766792	+	0.641896i	$0.221852\pi$
$662$		0			0
$663$	−39.7990	−	68.9339i	−1.54566	−	2.67717i
$664$		0			0
$665$	−1.00000	−	2.44949i	−0.0387783	−	0.0949871i
$666$		0			0
$667$	20.7782	+	35.9889i	0.804534	+	1.39349i
$668$		0			0
$669$	27.7279	−	48.0262i	1.07202	−	1.85680i
$670$		0			0
$671$	16.2132			0.625904
$672$		0			0
$673$	−40.6274			−1.56607			−0.783036	−	0.621976i	$-0.786330\pi$
$673$	−40.6274			−1.56607			−0.783036	+	0.621976i	$0.786330\pi$
$674$		0			0
$675$	38.6274	−	66.9046i	1.48677	−	2.57516i
$676$		0			0
$677$	−5.65685	−	9.79796i	−0.217411	−	0.376566i	0.736605	−	0.676323i	$-0.236428\pi$
$677$	−5.65685	−	9.79796i	−0.217411	−	0.376566i	−0.954016	+	0.299757i	$0.903094\pi$
$678$		0			0
$679$	9.17157	−	11.8272i	0.351973	−	0.453886i
$680$		0			0
$681$	−2.41421	−	4.18154i	−0.0925129	−	0.160237i
$682$		0			0
$683$	12.0711	−	20.9077i	0.461887	−	0.800011i	−0.537168	−	0.843475i	$-0.680506\pi$
$683$	12.0711	−	20.9077i	0.461887	−	0.800011i	0.999055	+	0.0434640i	$0.0138394\pi$
$684$		0			0
$685$	−0.656854			−0.0250971
$686$		0			0
$687$	54.6274			2.08417
$688$		0			0
$689$	−9.24264	+	16.0087i	−0.352117	+	0.609884i
$690$		0			0
$691$	8.31371	+	14.3998i	0.316268	+	0.547793i	0.979706	−	0.200438i	$-0.0642367\pi$
$691$	8.31371	+	14.3998i	0.316268	+	0.547793i	−0.663438	+	0.748231i	$0.730903\pi$
$692$		0			0
$693$	45.5122	−	58.6902i	1.72887	−	2.22945i
$694$		0			0
$695$	−9.27817	−	16.0703i	−0.351941	−	0.609580i
$696$		0			0
$697$	−19.3137	+	33.4523i	−0.731559	+	1.26710i
$698$		0			0
$699$	−21.6569			−0.819137
$700$		0			0
$701$	−20.7990			−0.785567			−0.392784	−	0.919631i	$-0.628488\pi$
$701$	−20.7990			−0.785567			−0.392784	+	0.919631i	$0.628488\pi$
$702$		0			0
$703$	−3.29289	+	5.70346i	−0.124194	+	0.215110i
$704$		0			0
$705$	−2.12132	−	3.67423i	−0.0798935	−	0.138380i
$706$		0			0
$707$	−1.48528	−	3.63818i	−0.0558598	−	0.136828i
$708$		0			0
$709$	−26.2990	−	45.5512i	−0.987679	−	1.71071i	−0.629365	−	0.777110i	$-0.716685\pi$
$709$	−26.2990	−	45.5512i	−0.987679	−	1.71071i	−0.358314	−	0.933601i	$-0.616648\pi$
$710$		0			0
$711$	−16.8787	+	29.2347i	−0.633000	+	1.09639i
$712$		0			0
$713$	20.2426			0.758093
$714$		0			0
$715$	−11.0711			−0.414034
$716$		0			0
$717$	7.41421	−	12.8418i	0.276889	−	0.479586i
$718$		0			0
$719$	−1.65685	−	2.86976i	−0.0617902	−	0.107024i	0.833475	−	0.552556i	$-0.186348\pi$
$719$	−1.65685	−	2.86976i	−0.0617902	−	0.107024i	−0.895266	+	0.445533i	$0.853014\pi$
$720$		0			0
$721$	6.14214	+	0.840532i	0.228745	+	0.0313030i
$722$		0			0
$723$	−14.8995	−	25.8067i	−0.554118	−	0.959761i
$724$		0			0
$725$	−18.8284	+	32.6118i	−0.699270	+	1.21117i
$726$		0			0
$727$	3.24264			0.120263			0.0601314	−	0.998190i	$-0.480848\pi$
$727$	3.24264			0.120263			0.0601314	+	0.998190i	$0.480848\pi$
$728$		0			0
$729$	148.196			5.48874
$730$		0			0
$731$	−11.0711	+	19.1757i	−0.409478	+	0.709237i
$732$		0			0
$733$	25.6569	+	44.4390i	0.947658	+	1.64139i	0.750341	+	0.661051i	$0.229889\pi$
$733$	25.6569	+	44.4390i	0.947658	+	1.64139i	0.197317	+	0.980340i	$0.436777\pi$
$734$		0			0
$735$	5.94975	+	23.1471i	0.219460	+	0.853792i
$736$		0			0
$737$	5.14214	+	8.90644i	0.189413	+	0.328073i
$738$		0			0
$739$	−22.3137	+	38.6485i	−0.820823	+	1.42171i	0.0842471	+	0.996445i	$0.473151\pi$
$739$	−22.3137	+	38.6485i	−0.820823	+	1.42171i	−0.905070	+	0.425262i	$0.860182\pi$
$740$		0			0
$741$	11.6569			0.428225
$742$		0			0
$743$	21.2721			0.780397			0.390198	−	0.920731i	$-0.372406\pi$
$743$	21.2721			0.780397			0.390198	+	0.920731i	$0.372406\pi$
$744$		0			0
$745$	−3.32843	+	5.76500i	−0.121944	+	0.211213i
$746$		0			0
$747$	−64.4914	−	111.702i	−2.35962	−	4.08698i
$748$		0			0
$749$	44.7487	+	6.12372i	1.63508	+	0.223756i
$750$		0			0
$751$	−2.75736	−	4.77589i	−0.100617	−	0.174275i	0.811322	−	0.584600i	$-0.198748\pi$
$751$	−2.75736	−	4.77589i	−0.100617	−	0.174275i	−0.911939	+	0.410325i	$0.865415\pi$
$752$		0			0
$753$	37.9203	−	65.6799i	1.38189	−	2.39351i
$754$		0			0
$755$	−5.65685			−0.205874
$756$		0			0
$757$	−31.6863			−1.15166			−0.575829	−	0.817570i	$-0.695321\pi$
$757$	−31.6863			−1.15166			−0.575829	+	0.817570i	$0.695321\pi$
$758$		0			0
$759$	24.4350	−	42.3227i	0.886935	−	1.53622i
$760$		0			0
$761$	6.57107	+	11.3814i	0.238201	+	0.412576i	0.960198	−	0.279320i	$-0.0901090\pi$
$761$	6.57107	+	11.3814i	0.238201	+	0.412576i	−0.721997	+	0.691896i	$0.756776\pi$
$762$		0			0
$763$	19.3137	+	47.3087i	0.699203	+	1.71269i
$764$		0			0
$765$	−29.5563	−	51.1931i	−1.06861	−	1.85089i
$766$		0			0
$767$	−1.41421	+	2.44949i	−0.0510643	+	0.0884459i
$768$		0			0
$769$	−3.54416			−0.127806			−0.0639028	−	0.997956i	$-0.520355\pi$
$769$	−3.54416			−0.127806			−0.0639028	+	0.997956i	$0.520355\pi$
$770$		0			0
$771$	47.7990			1.72144
$772$		0			0
$773$	0.464466	−	0.804479i	0.0167057	−	0.0289351i	−0.857552	−	0.514398i	$-0.828016\pi$
$773$	0.464466	−	0.804479i	0.0167057	−	0.0289351i	0.874257	+	0.485463i	$0.161349\pi$
$774$		0			0
$775$	9.17157	+	15.8856i	0.329453	+	0.570629i
$776$		0			0
$777$	36.4558	−	47.0116i	1.30785	−	1.68653i
$778$		0			0
$779$	−2.82843	−	4.89898i	−0.101339	−	0.175524i
$780$		0			0
$781$	−12.5772	+	21.7843i	−0.450046	+	0.779503i
$782$		0			0
$783$	−181.823			−6.49784
$784$		0			0
$785$	1.68629			0.0601863
$786$		0			0
$787$	−5.87868	+	10.1822i	−0.209552	+	0.362955i	−0.951574	−	0.307421i	$-0.900534\pi$
$787$	−5.87868	+	10.1822i	−0.209552	+	0.362955i	0.742021	+	0.670376i	$0.233867\pi$
$788$		0			0
$789$	36.1421	+	62.6000i	1.28669	+	2.22862i
$790$		0			0
$791$	−17.9497	+	23.1471i	−0.638220	+	0.823015i
$792$		0			0
$793$	−8.53553	−	14.7840i	−0.303106	−	0.524994i
$794$		0			0
$795$	−9.24264	+	16.0087i	−0.327803	+	0.567771i
$796$		0			0
$797$	−45.4975			−1.61160			−0.805802	−	0.592186i	$-0.798265\pi$
$797$	−45.4975			−1.61160			−0.805802	+	0.592186i	$0.798265\pi$
$798$		0			0
$799$	8.48528			0.300188
$800$		0			0
$801$	−58.6777	+	101.633i	−2.07327	+	3.59102i
$802$		0			0
$803$	−11.3492	−	19.6575i	−0.400506	−	0.693697i
$804$		0			0
$805$	4.41421	+	10.8126i	0.155581	+	0.381093i
$806$		0			0
$807$	27.3137	+	47.3087i	0.961488	+	1.66535i
$808$		0			0
$809$	13.9853	−	24.2232i	0.491696	−	0.851643i	−0.508258	−	0.861205i	$-0.669710\pi$
$809$	13.9853	−	24.2232i	0.491696	−	0.851643i	0.999954	+	0.00956188i	$0.00304369\pi$
$810$		0			0
$811$	32.4264			1.13865			0.569323	−	0.822114i	$-0.307206\pi$
$811$	32.4264			1.13865			0.569323	+	0.822114i	$0.307206\pi$
$812$		0			0
$813$	7.75736			0.272062
$814$		0			0
$815$	7.03553	−	12.1859i	0.246444	−	0.426854i
$816$		0			0
$817$	−1.62132	−	2.80821i	−0.0567228	−	0.0982468i
$818$		0			0
$819$	−77.4767	−	10.6024i	−2.70725	−	0.370479i
$820$		0			0
$821$	−4.01472	−	6.95370i	−0.140115	−	0.242686i	0.787425	−	0.616410i	$-0.211414\pi$
$821$	−4.01472	−	6.95370i	−0.140115	−	0.242686i	−0.927540	+	0.373725i	$0.878080\pi$
$822$		0			0
$823$	−4.86396	+	8.42463i	−0.169547	+	0.293664i	−0.938261	−	0.345929i	$-0.887564\pi$
$823$	−4.86396	+	8.42463i	−0.169547	+	0.293664i	0.768714	+	0.639593i	$0.220897\pi$
$824$		0			0
$825$	44.2843			1.54178
$826$		0			0
$827$	−0.686292			−0.0238647			−0.0119323	−	0.999929i	$-0.503798\pi$
$827$	−0.686292			−0.0238647			−0.0119323	+	0.999929i	$0.503798\pi$
$828$		0			0
$829$	−19.6569	+	34.0467i	−0.682711	+	1.18249i	0.291440	+	0.956589i	$0.405866\pi$
$829$	−19.6569	+	34.0467i	−0.682711	+	1.18249i	−0.974150	+	0.225901i	$0.927468\pi$
$830$		0			0
$831$	47.7487	+	82.7032i	1.65639	+	2.86894i
$832$		0			0
$833$	−46.0416	−	12.8418i	−1.59525	−	0.444942i
$834$		0			0
$835$	9.29289	+	16.0958i	0.321594	+	0.557017i
$836$		0			0
$837$	−44.2843	+	76.7026i	−1.53069	+	2.65123i
$838$		0			0
$839$	30.4853			1.05247			0.526234	−	0.850340i	$-0.323603\pi$
$839$	30.4853			1.05247			0.526234	+	0.850340i	$0.323603\pi$
$840$		0			0
$841$	59.6274			2.05612
$842$		0			0
$843$	30.5563	−	52.9251i	1.05242	−	1.82284i
$844$		0			0
$845$	−0.671573	−	1.16320i	−0.0231028	−	0.0400152i
$846$		0			0
$847$	−1.27208	−	0.174080i	−0.0437091	−	0.00598146i
$848$		0			0
$849$	−24.8492	−	43.0402i	−0.852824	−	1.47713i
$850$		0			0
$851$	14.5355	−	25.1763i	0.498272	−	0.863032i
$852$		0			0
$853$	−52.4558			−1.79605			−0.898027	−	0.439940i	$-0.855000\pi$
$853$	−52.4558			−1.79605			−0.898027	+	0.439940i	$0.855000\pi$
$854$		0			0
$855$	8.65685			0.296058
$856$		0			0
$857$	−3.51472	+	6.08767i	−0.120061	+	0.207951i	−0.919791	−	0.392408i	$-0.871642\pi$
$857$	−3.51472	+	6.08767i	−0.120061	+	0.207951i	0.799731	+	0.600359i	$0.204976\pi$
$858$		0			0
$859$	13.5919	+	23.5418i	0.463749	+	0.803237i	0.999144	−	0.0413648i	$-0.0131706\pi$
$859$	13.5919	+	23.5418i	0.463749	+	0.803237i	−0.535395	+	0.844602i	$0.679837\pi$
$860$		0			0
$861$	19.3137	+	47.3087i	0.658209	+	1.61228i
$862$		0			0
$863$	12.4350	+	21.5381i	0.423293	+	0.733166i	0.996259	−	0.0864136i	$-0.0275407\pi$
$863$	12.4350	+	21.5381i	0.423293	+	0.733166i	−0.572966	+	0.819579i	$0.694207\pi$
$864$		0			0
$865$	−4.82843	+	8.36308i	−0.164171	+	0.284353i
$866$		0			0
$867$	101.154			3.43538
$868$		0			0
$869$	−12.6447			−0.428941
$870$		0			0
$871$	5.41421	−	9.37769i	0.183454	−	0.317751i
$872$		0			0
$873$	24.4853	+	42.4098i	0.828701	+	1.43535i
$874$		0			0
$875$	−14.5919	+	18.8169i	−0.493296	+	0.636128i
$876$		0			0
$877$	−18.4350	−	31.9304i	−0.622507	−	1.07821i	−0.989017	−	0.147799i	$-0.952781\pi$
$877$	−18.4350	−	31.9304i	−0.622507	−	1.07821i	0.366511	−	0.930414i	$-0.380552\pi$
$878$		0			0
$879$	−16.4853	+	28.5533i	−0.556035	+	0.963080i
$880$		0			0
$881$	7.31371			0.246405			0.123203	−	0.992382i	$-0.460684\pi$
$881$	7.31371			0.246405			0.123203	+	0.992382i	$0.460684\pi$
$882$		0			0
$883$	−25.1716			−0.847091			−0.423545	−	0.905875i	$-0.639215\pi$
$883$	−25.1716			−0.847091			−0.423545	+	0.905875i	$0.639215\pi$
$884$		0			0
$885$	−1.41421	+	2.44949i	−0.0475383	+	0.0823387i
$886$		0			0
$887$	14.1421	+	24.4949i	0.474846	+	0.822458i	0.999585	−	0.0288053i	$-0.00917026\pi$
$887$	14.1421	+	24.4949i	0.474846	+	0.822458i	−0.524739	+	0.851263i	$0.675837\pi$
$888$		0			0
$889$	31.7071	−	40.8878i	1.06342	−	1.37133i
$890$		0			0
$891$	64.8051	+	112.246i	2.17105	+	3.76037i
$892$		0			0
$893$	−0.621320	+	1.07616i	−0.0207917	+	0.0360123i
$894$		0			0
$895$	−6.48528			−0.216779
$896$		0			0
$897$	−51.4558			−1.71806
$898$		0			0
$899$	21.5858	−	37.3877i	0.719926	−	1.24695i
$900$		0			0
$901$	−18.4853	−	32.0174i	−0.615834	−	1.06666i
$902$		0			0
$903$	11.0711	+	27.1185i	0.368422	+	0.902446i
$904$		0			0
$905$	−7.36396	−	12.7548i	−0.244786	−	0.423982i
$906$		0			0
$907$	24.7782	−	42.9171i	0.822746	−	1.42504i	−0.0808842	−	0.996724i	$-0.525774\pi$
$907$	24.7782	−	42.9171i	0.822746	−	1.42504i	0.903630	−	0.428314i	$-0.140892\pi$
$908$		0			0
$909$	12.8579			0.426468
$910$		0			0
$911$	−25.5563			−0.846720			−0.423360	−	0.905962i	$-0.639149\pi$
$911$	−25.5563			−0.846720			−0.423360	+	0.905962i	$0.639149\pi$
$912$		0			0
$913$	24.1569	−	41.8409i	0.799475	−	1.38473i
$914$		0			0
$915$	−8.53553	−	14.7840i	−0.282176	−	0.488743i
$916$		0			0
$917$	4.34315	+	0.594346i	0.143423	+	0.0196270i
$918$		0			0
$919$	−2.79289	−	4.83743i	−0.0921290	−	0.159572i	0.816278	−	0.577660i	$-0.196034\pi$
$919$	−2.79289	−	4.83743i	−0.0921290	−	0.159572i	−0.908407	+	0.418087i	$0.862701\pi$
$920$		0			0
$921$	−31.7990	+	55.0775i	−1.04781	+	1.81486i
$922$		0			0
$923$	26.4853			0.871774
$924$		0			0
$925$	26.3431			0.866157
$926$		0			0
$927$	−10.1421	+	17.5667i	−0.333111	+	0.576966i
$928$		0			0
$929$	17.8137	+	30.8542i	0.584449	+	1.01230i	0.994944	+	0.100432i	$0.0320226\pi$
$929$	17.8137	+	30.8542i	0.584449	+	1.01230i	−0.410495	+	0.911863i	$0.634644\pi$
$930$		0			0
$931$	5.00000	−	4.89898i	0.163868	−	0.160558i
$932$		0			0
$933$	−13.6569	−	23.6544i	−0.447105	−	0.774409i
$934$		0			0
$935$	11.0711	−	19.1757i	0.362063	−	0.627111i
$936$		0			0
$937$	30.5147			0.996872			0.498436	−	0.866926i	$-0.333908\pi$
$937$	30.5147			0.996872			0.498436	+	0.866926i	$0.333908\pi$
$938$		0			0
$939$	3.89949			0.127255
$940$		0			0
$941$	−13.7071	+	23.7414i	−0.446839	+	0.773948i	−0.998178	−	0.0603334i	$-0.980784\pi$
$941$	−13.7071	+	23.7414i	−0.446839	+	0.773948i	0.551339	+	0.834281i	$0.314117\pi$
$942$		0			0
$943$	12.4853	+	21.6251i	0.406577	+	0.704212i
$944$		0			0
$945$	−50.6274	−	6.92820i	−1.64691	−	0.225374i
$946$		0			0
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	0.996178	−	0.0873481i	$-0.0278392\pi$
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	−0.573735	+	0.819041i	$0.694506\pi$
$948$		0			0
$949$	−11.9497	+	20.6976i	−0.387905	+	0.671872i
$950$		0			0
$951$	−34.9706			−1.13400
$952$		0			0
$953$	−59.1543			−1.91620			−0.958098	−	0.286439i	$-0.907528\pi$
$953$	−59.1543			−1.91620			−0.958098	+	0.286439i	$0.907528\pi$
$954$		0			0
$955$	4.62132	−	8.00436i	0.149542	−	0.259015i
$956$		0			0
$957$	−52.1127	−	90.2618i	−1.68456	−	2.91775i
$958$		0			0
$959$	−0.656854	−	1.60896i	−0.0212109	−	0.0519560i
$960$		0			0
$961$	4.98528	+	8.63476i	0.160816	+	0.278541i
$962$		0			0
$963$	−73.8909	+	127.983i	−2.38110	+	4.12419i
$964$		0			0
$965$	−2.24264			−0.0721932
$966$		0			0
$967$	16.9706			0.545737			0.272868	−	0.962051i	$-0.412028\pi$
$967$	16.9706			0.545737			0.272868	+	0.962051i	$0.412028\pi$
$968$		0			0
$969$	−11.6569	+	20.1903i	−0.374472	+	0.648605i
$970$		0			0
$971$	−24.4350	−	42.3227i	−0.784157	−	1.35820i	−0.929501	−	0.368819i	$-0.879762\pi$
$971$	−24.4350	−	42.3227i	−0.784157	−	1.35820i	0.145344	−	0.989381i	$-0.453571\pi$
$972$		0			0
$973$	30.0858	−	38.7971i	0.964506	−	1.24378i
$974$		0			0
$975$	−23.3137	−	40.3805i	−0.746636	−	1.29321i
$976$		0			0
$977$	−8.65685	+	14.9941i	−0.276957	+	0.479704i	−0.970627	−	0.240589i	$-0.922659\pi$
$977$	−8.65685	+	14.9941i	−0.276957	+	0.479704i	0.693670	+	0.720293i	$0.255993\pi$
$978$		0			0
$979$	−43.9584			−1.40492
$980$		0			0
$981$	−167.196			−5.33816
$982$		0			0
$983$	24.9706	−	43.2503i	0.796437	−	1.37947i	−0.125485	−	0.992095i	$-0.540049\pi$
$983$	24.9706	−	43.2503i	0.796437	−	1.37947i	0.921923	−	0.387374i	$-0.126618\pi$
$984$		0			0
$985$	−0.257359	−	0.445759i	−0.00820015	−	0.0142031i
$986$		0			0
$987$	6.87868	−	8.87039i	0.218951	−	0.282348i
$988$		0			0
$989$	7.15685	+	12.3960i	0.227575	+	0.394171i
$990$		0			0
$991$	21.7279	−	37.6339i	0.690210	−	1.19548i	−0.281559	−	0.959544i	$-0.590851\pi$
$991$	21.7279	−	37.6339i	0.690210	−	1.19548i	0.971769	−	0.235935i	$-0.0758153\pi$
$992$		0			0
$993$	−63.1127			−2.00282
$994$		0			0
$995$	−2.07107			−0.0656573
$996$		0			0
$997$	−9.79899	+	16.9723i	−0.310337	+	0.537520i	−0.978435	−	0.206553i	$-0.933775\pi$
$997$	−9.79899	+	16.9723i	−0.310337	+	0.537520i	0.668098	+	0.744073i	$0.267109\pi$
$998$		0			0
$999$	63.5980	+	110.155i	2.01215	+	3.48515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.k.305.1	✓	4
7.2	even	3	inner	1064.2.q.k.457.1	yes	4
7.3	odd	6		7448.2.a.x.1.1		2
7.4	even	3		7448.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.k.305.1	✓	4	1.1	even	1	trivial
1064.2.q.k.457.1	yes	4	7.2	even	3	inner
7448.2.a.x.1.1		2	7.3	odd	6
7448.2.a.bd.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 + 2.95680i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})\)	\(q+(-1.70711 + 2.95680i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} +(-4.32843 - 7.49706i) q^{9} +(1.62132 - 2.80821i) q^{11} -3.41421 q^{13} -3.41421 q^{15} +(3.41421 - 5.91359i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.41421 - 8.36308i) q^{21} +(-2.20711 - 3.82282i) q^{23} +(2.00000 - 3.46410i) q^{25} +19.3137 q^{27} -9.41421 q^{29} +(-2.29289 + 3.97141i) q^{31} +(5.53553 + 9.58783i) q^{33} +(-2.62132 - 0.358719i) q^{35} +(3.29289 + 5.70346i) q^{37} +(5.82843 - 10.0951i) q^{39} -5.65685 q^{41} -3.24264 q^{43} +(4.32843 - 7.49706i) q^{45} +(0.621320 + 1.07616i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(11.6569 + 20.1903i) q^{51} +(2.70711 - 4.68885i) q^{53} +3.24264 q^{55} -3.41421 q^{57} +(0.414214 - 0.717439i) q^{59} +(2.50000 + 4.33013i) q^{61} +(22.6924 + 3.10538i) q^{63} +(-1.70711 - 2.95680i) q^{65} +(-1.58579 + 2.74666i) q^{67} +15.0711 q^{69} -7.75736 q^{71} +(3.50000 - 6.06218i) q^{73} +(6.82843 + 11.8272i) q^{75} +(3.24264 + 7.94282i) q^{77} +(-1.94975 - 3.37706i) q^{79} +(-19.9853 + 34.6155i) q^{81} +14.8995 q^{83} +6.82843 q^{85} +(16.0711 - 27.8359i) q^{87} +(-6.77817 - 11.7401i) q^{89} +(5.53553 - 7.13834i) q^{91} +(-7.82843 - 13.5592i) q^{93} +(-0.500000 + 0.866025i) q^{95} -5.65685 q^{97} -28.0711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 2 q^{11} - 8 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{23} + 8 q^{25} + 32 q^{27} - 32 q^{29} - 12 q^{31} + 8 q^{33} - 2 q^{35} + 16 q^{37} + 12 q^{39} + 4 q^{43} + 6 q^{45} - 6 q^{47} + 10 q^{49} + 24 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{57} - 4 q^{59} + 10 q^{61} + 54 q^{63} - 4 q^{65} - 12 q^{67} + 32 q^{69} - 48 q^{71} + 14 q^{73} + 16 q^{75} - 4 q^{77} + 12 q^{79} - 46 q^{81} + 20 q^{83} + 16 q^{85} + 36 q^{87} + 4 q^{89} + 8 q^{91} - 20 q^{93} - 2 q^{95} - 84 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 2 * q^11 - 8 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^23 + 8 * q^25 + 32 * q^27 - 32 * q^29 - 12 * q^31 + 8 * q^33 - 2 * q^35 + 16 * q^37 + 12 * q^39 + 4 * q^43 + 6 * q^45 - 6 * q^47 + 10 * q^49 + 24 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^57 - 4 * q^59 + 10 * q^61 + 54 * q^63 - 4 * q^65 - 12 * q^67 + 32 * q^69 - 48 * q^71 + 14 * q^73 + 16 * q^75 - 4 * q^77 + 12 * q^79 - 46 * q^81 + 20 * q^83 + 16 * q^85 + 36 * q^87 + 4 * q^89 + 8 * q^91 - 20 * q^93 - 2 * q^95 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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