LMFDB - Embedded newform 882.2.t.a.815.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(803,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("882.803");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.t (of order $6$, degree $2$, not 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			815.7
Root			$-1.68301 + 0.409224i$ of defining polynomial
Character	$\chi$	$=$	882.815
Dual form			882.2.t.a.803.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.206076 - 1.71975i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(1.03834 - 1.38631i) q^{6} +1.00000i q^{8} +(-2.91507 - 0.708796i) q^{9} +(-1.23829 - 0.714925i) q^{10} -3.41945i q^{11} +(1.59238 - 0.681407i) q^{12} +(-5.48813 - 3.16857i) q^{13} +(-0.294657 + 2.45898i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-2.17012 - 2.07137i) q^{18} +(1.87673 - 1.08353i) q^{19} +(-0.714925 - 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} -8.05411i q^{23} +(1.71975 + 0.206076i) q^{24} -2.95553 q^{25} +(-3.16857 - 5.48813i) q^{26} +(-1.81967 + 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} +(-1.48467 + 1.98221i) q^{30} +(3.76052 - 2.17114i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.88058 - 0.704664i) q^{33} +(-1.97802 + 1.14201i) q^{34} +(-0.843698 - 2.87892i) q^{36} +(1.07786 + 1.86690i) q^{37} +2.16707 q^{38} +(-6.58012 + 8.78524i) q^{39} -1.42985i q^{40} +(0.202180 - 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(2.96133 - 1.70972i) q^{44} +(4.16811 + 1.01347i) q^{45} +(4.02706 - 6.97507i) q^{46} +(2.75915 - 4.77898i) q^{47} +(1.38631 + 1.03834i) q^{48} +(-2.55956 - 1.47776i) q^{50} +(3.16635 + 2.37159i) q^{51} -6.33715i q^{52} +(-8.56310 - 4.94391i) q^{53} +(-4.00944 + 3.30521i) q^{54} +4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} -0.345115 q^{58} +(-5.51480 - 9.55191i) q^{59} +(-2.27687 + 0.974311i) q^{60} +(9.94175 + 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(7.84721 + 4.53059i) q^{65} +(-4.74040 - 3.55055i) q^{66} +(-2.12683 - 3.68377i) q^{67} -2.28402 q^{68} +(-13.8510 - 1.65976i) q^{69} +3.55393i q^{71} +(0.708796 - 2.91507i) q^{72} +(0.201057 + 0.116080i) q^{73} +2.15571i q^{74} +(-0.609062 + 5.08276i) q^{75} +(1.87673 + 1.08353i) q^{76} +(-10.0912 + 4.31818i) q^{78} +(-7.28100 + 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(7.99522 + 4.13237i) q^{81} +(0.350186 - 0.202180i) q^{82} +(0.811624 + 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +5.81766i q^{86} +(0.235164 + 0.549556i) q^{87} +3.41945 q^{88} +(-2.02974 - 3.51562i) q^{89} +(3.10295 + 2.96175i) q^{90} +(6.97507 - 4.02706i) q^{92} +(-2.95886 - 6.91457i) q^{93} +(4.77898 - 2.75915i) q^{94} +(-2.68345 + 1.54929i) q^{95} +(0.681407 + 1.59238i) q^{96} +(-9.18719 + 5.30423i) q^{97} +(-2.42369 + 9.96791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.206076	−	1.71975i	0.118978	−	0.992897i
$3$	0.206076	−	1.71975i	0.118978	−	0.992897i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.42985			−0.639449			−0.319724	−	0.947511i	$-0.603590\pi$
$5$	−1.42985			−0.639449			−0.319724	+	0.947511i	$0.603590\pi$
$6$	1.03834	−	1.38631i	0.423901	−	0.565958i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.91507	−	0.708796i	−0.971689	−	0.236265i
$10$	−1.23829	−	0.714925i	−0.391581	−	0.226079i
$11$		−	3.41945i		−	1.03100i	−0.856889	−	0.515501i	$-0.827606\pi$
$11$		−	3.41945i		−	1.03100i	0.856889	−	0.515501i	$-0.172394\pi$
$12$	1.59238	−	0.681407i	0.459681	−	0.196705i
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.999658	−	0.0261501i	$-0.991675\pi$
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.522476	−	0.852654i	$-0.674991\pi$
$14$		0			0
$15$	−0.294657	+	2.45898i	−0.0760802	+	0.634907i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	−0.970632	−	0.240569i	$-0.922666\pi$
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	0.693655	+	0.720308i	$0.255999\pi$
$18$	−2.17012	−	2.07137i	−0.511503	−	0.488226i
$19$	1.87673	−	1.08353i	0.430553	−	0.248580i	−0.269029	−	0.963132i	$-0.586703\pi$
$19$	1.87673	−	1.08353i	0.430553	−	0.248580i	0.699582	+	0.714552i	$0.253370\pi$
$20$	−0.714925	−	1.23829i	−0.159862	−	0.276889i
$21$		0			0
$22$	1.70972	−	2.96133i	0.364514	−	0.631357i
$23$		−	8.05411i		−	1.67940i	−0.543052	−	0.839699i	$-0.682731\pi$
$23$		−	8.05411i		−	1.67940i	0.543052	−	0.839699i	$-0.317269\pi$
$24$	1.71975	+	0.206076i	0.351042	+	0.0420650i
$25$	−2.95553			−0.591106
$26$	−3.16857	−	5.48813i	−0.621408	−	1.07631i
$27$	−1.81967	+	4.86711i	−0.350196	+	0.936676i
$28$		0			0
$29$	−0.298879	+	0.172558i	−0.0555003	+	0.0320431i	−0.527493	−	0.849559i	$-0.676868\pi$
$29$	−0.298879	+	0.172558i	−0.0555003	+	0.0320431i	0.471993	+	0.881602i	$0.343535\pi$
$30$	−1.48467	+	1.98221i	−0.271063	+	0.361901i
$31$	3.76052	−	2.17114i	0.675410	−	0.389948i	−0.122713	−	0.992442i	$-0.539160\pi$
$31$	3.76052	−	2.17114i	0.675410	−	0.389948i	0.798123	+	0.602494i	$0.205826\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.88058	−	0.704664i	−1.02368	−	0.122666i
$34$	−1.97802	+	1.14201i	−0.339227	+	0.195853i
$35$		0			0
$36$	−0.843698	−	2.87892i	−0.140616	−	0.479820i
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	0.940920	−	0.338629i	$-0.109963\pi$
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	−0.763721	+	0.645546i	$0.776630\pi$
$38$	2.16707			0.351545
$39$	−6.58012	+	8.78524i	−1.05366	+	1.40676i
$40$		−	1.42985i		−	0.226079i
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	−0.849806	−	0.527096i	$-0.823281\pi$
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	0.881381	+	0.472406i	$0.156614\pi$
$42$		0			0
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	0.997953	−	0.0639521i	$-0.0203705\pi$
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	−0.554361	+	0.832277i	$0.687037\pi$
$44$	2.96133	−	1.70972i	0.446437	−	0.257750i
$45$	4.16811	+	1.01347i	0.621345	+	0.151080i
$46$	4.02706	−	6.97507i	0.593757	−	1.02842i
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	−0.591560	−	0.806261i	$-0.701488\pi$
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	0.994023	+	0.109175i	$0.0348209\pi$
$48$	1.38631	+	1.03834i	0.200096	+	0.149872i
$49$		0			0
$50$	−2.55956	−	1.47776i	−0.361977	−	0.208987i
$51$	3.16635	+	2.37159i	0.443378	+	0.332089i
$52$		−	6.33715i		−	0.878804i
$53$	−8.56310	−	4.94391i	−1.17623	−	0.679098i	−0.221093	−	0.975253i	$-0.570962\pi$
$53$	−8.56310	−	4.94391i	−1.17623	−	0.679098i	−0.955140	+	0.296155i	$0.904296\pi$
$54$	−4.00944	+	3.30521i	−0.545616	+	0.449782i
$55$			4.88930i			0.659273i
$56$		0			0
$57$	−1.47666	−	3.45080i	−0.195588	−	0.457070i
$58$	−0.345115			−0.0453158
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	−0.961805	−	0.273737i	$-0.911740\pi$
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	0.243839	−	0.969816i	$-0.421593\pi$
$60$	−2.27687	+	0.974311i	−0.293943	+	0.125783i
$61$	9.94175	+	5.73987i	1.27291	+	0.734915i	0.975535	−	0.219845i	$-0.0705551\pi$
$61$	9.94175	+	5.73987i	1.27291	+	0.734915i	0.297376	+	0.954760i	$0.403888\pi$
$62$	4.34228			0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.84721	+	4.53059i	0.973326	+	0.561950i
$66$	−4.74040	−	3.55055i	−0.583503	−	0.437042i
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	0.706364	−	0.707849i	$-0.250334\pi$
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	−0.966197	+	0.257804i	$0.917001\pi$
$68$	−2.28402			−0.276978
$69$	−13.8510	−	1.65976i	−1.66747	−	0.199811i
$70$		0			0
$71$			3.55393i			0.421773i	0.977511	+	0.210887i	$0.0676351\pi$
$71$			3.55393i			0.421773i	−0.977511	+	0.210887i	$0.932365\pi$
$72$	0.708796	−	2.91507i	0.0835324	−	0.343544i
$73$	0.201057	+	0.116080i	0.0235320	+	0.0135862i	0.511720	−	0.859152i	$-0.329009\pi$
$73$	0.201057	+	0.116080i	0.0235320	+	0.0135862i	−0.488188	+	0.872739i	$0.662342\pi$
$74$			2.15571i			0.250597i
$75$	−0.609062	+	5.08276i	−0.0703284	+	0.586907i
$76$	1.87673	+	1.08353i	0.215276	+	0.124290i
$77$		0			0
$78$	−10.0912	+	4.31818i	−1.14260	+	0.488937i
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	0.0871130	+	0.996198i	$0.472236\pi$
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	−0.906290	+	0.422657i	$0.861097\pi$
$80$	0.714925	−	1.23829i	0.0799311	−	0.138445i
$81$	7.99522	+	4.13237i	0.888357	+	0.459153i
$82$	0.350186	−	0.202180i	0.0386716	−	0.0223270i
$83$	0.811624	+	1.40577i	0.0890873	+	0.154304i	0.907126	−	0.420860i	$-0.138272\pi$
$83$	0.811624	+	1.40577i	0.0890873	+	0.154304i	−0.818038	+	0.575164i	$0.804938\pi$
$84$		0			0
$85$	1.63290	−	2.82827i	0.177113	−	0.306769i
$86$			5.81766i			0.627334i
$87$	0.235164	+	0.549556i	0.0252122	+	0.0589185i
$88$	3.41945			0.364514
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	0.738167	−	0.674618i	$-0.235691\pi$
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	−0.953320	+	0.301963i	$0.902358\pi$
$90$	3.10295	+	2.96175i	0.327080	+	0.312196i
$91$		0			0
$92$	6.97507	−	4.02706i	0.727201	−	0.419850i
$93$	−2.95886	−	6.91457i	−0.306820	−	0.717008i
$94$	4.77898	−	2.75915i	0.492914	−	0.284584i
$95$	−2.68345	+	1.54929i	−0.275316	+	0.158954i
$96$	0.681407	+	1.59238i	0.0695458	+	0.162522i
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.887702	−	0.460419i	$-0.847699\pi$
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.0451164	+	0.998982i	$0.514366\pi$
$98$		0			0
$99$	−2.42369	+	9.96791i	−0.243590	+	1.00181i
$100$	−1.47776	−	2.55956i	−0.147776	−	0.255956i
$101$	8.04886			0.800892			0.400446	−	0.916320i	$-0.368855\pi$
$101$	8.04886			0.800892			0.400446	+	0.916320i	$0.368855\pi$
$102$	1.55635	+	3.63703i	0.154101	+	0.360120i
$103$		−	2.81391i		−	0.277263i	−0.990344	−	0.138631i	$-0.955730\pi$
$103$		−	2.81391i		−	0.277263i	0.990344	−	0.138631i	$-0.0442703\pi$
$104$	3.16857	−	5.48813i	0.310704	−	0.538156i
$105$		0			0
$106$	−4.94391	−	8.56310i	−0.480195	−	0.831722i
$107$	13.7019	−	7.91078i	1.32461	−	0.764764i	0.340150	−	0.940371i	$-0.389522\pi$
$107$	13.7019	−	7.91078i	1.32461	−	0.764764i	0.984460	+	0.175607i	$0.0561888\pi$
$108$	−5.12488	+	0.857672i	−0.493142	+	0.0825296i
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	−0.510784	−	0.859709i	$-0.670645\pi$
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	0.999922	+	0.0124977i	$0.00397826\pi$
$110$	−2.44465	+	4.23425i	−0.233088	+	0.403720i
$111$	3.43272	−	1.46892i	0.325819	−	0.139424i
$112$		0			0
$113$	7.28808	+	4.20778i	0.685605	+	0.395834i	0.801963	−	0.597373i	$-0.203789\pi$
$113$	7.28808	+	4.20778i	0.685605	+	0.395834i	−0.116359	+	0.993207i	$0.537122\pi$
$114$	0.446579	−	3.72681i	0.0418260	−	0.349048i
$115$			11.5162i			1.07389i
$116$	−0.298879	−	0.172558i	−0.0277502	−	0.0160216i
$117$	13.7524	+	13.1266i	1.27141	+	1.21355i
$118$		−	11.0296i		−	1.01536i
$119$		0			0
$120$	−2.45898	−	0.294657i	−0.224473	−	0.0268984i
$121$	−0.692610			−0.0629646
$122$	5.73987	+	9.94175i	0.519664	+	0.900084i
$123$	−0.560567	−	0.419863i	−0.0505446	−	0.0378578i
$124$	3.76052	+	2.17114i	0.337705	+	0.194974i
$125$	11.3752			1.01743
$126$		0			0
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	9.26394	−	3.96420i	0.815645	−	0.349028i
$130$	4.53059	+	7.84721i	0.397359	+	0.688246i
$131$	−4.45667			−0.389381			−0.194690	−	0.980865i	$-0.562370\pi$
$131$	−4.45667			−0.389381			−0.194690	+	0.980865i	$0.562370\pi$
$132$	−2.33004	−	5.44507i	−0.202804	−	0.473932i
$133$		0			0
$134$		−	4.25366i		−	0.367460i
$135$	2.60186	−	6.95924i	0.223933	−	0.598956i
$136$	−1.97802	−	1.14201i	−0.169613	−	0.0979264i
$137$		−	9.65668i		−	0.825026i	−0.910952	−	0.412513i	$-0.864651\pi$
$137$		−	9.65668i		−	0.825026i	0.910952	−	0.412513i	$-0.135349\pi$
$138$	−11.1655	−	8.36291i	−0.950469	−	0.711898i
$139$	16.0680	+	9.27686i	1.36287	+	0.786853i	0.990005	−	0.141033i	$-0.0450423\pi$
$139$	16.0680	+	9.27686i	1.36287	+	0.786853i	0.372864	+	0.927886i	$0.378376\pi$
$140$		0			0
$141$	−7.65005	−	5.72987i	−0.644251	−	0.482542i
$142$	−1.77696	+	3.07779i	−0.149119	+	0.258282i
$143$	−10.8348	+	18.7664i	−0.906049	+	1.56932i
$144$	2.07137	−	2.17012i	0.172614	−	0.180844i
$145$	0.427352	−	0.246732i	0.0354896	−	0.0204899i
$146$	0.116080	+	0.201057i	0.00960689	+	0.0166396i
$147$		0			0
$148$	−1.07786	+	1.86690i	−0.0885993	+	0.153458i
$149$		−	6.50694i		−	0.533069i	−0.963825	−	0.266535i	$-0.914121\pi$
$149$		−	6.50694i		−	0.533069i	0.963825	−	0.266535i	$-0.0858786\pi$
$150$	−3.06884	+	4.09727i	−0.250570	+	0.334541i
$151$	5.75901			0.468661			0.234331	−	0.972157i	$-0.424710\pi$
$151$	5.75901			0.468661			0.234331	+	0.972157i	$0.424710\pi$
$152$	1.08353	+	1.87673i	0.0878862	+	0.152223i
$153$	4.73104	−	4.95660i	0.382482	−	0.400717i
$154$		0			0
$155$	−5.37699	+	3.10441i	−0.431890	+	0.249352i
$156$	−10.8983	−	1.30593i	−0.872562	−	0.104558i
$157$	−6.89669	+	3.98180i	−0.550415	+	0.317783i	−0.749290	−	0.662243i	$-0.769605\pi$
$157$	−6.89669	+	3.98180i	−0.550415	+	0.317783i	0.198874	+	0.980025i	$0.436272\pi$
$158$	−12.6111	+	7.28100i	−1.00328	+	0.579245i
$159$	−10.2669	+	13.7076i	−0.814220	+	1.08708i
$160$	1.23829	−	0.714925i	0.0978952	−	0.0565198i
$161$		0			0
$162$	4.85787	+	7.57635i	0.381671	+	0.595254i
$163$	5.69256	+	9.85980i	0.445876	+	0.772279i	0.998113	−	0.0614080i	$-0.0195591\pi$
$163$	5.69256	+	9.85980i	0.445876	+	0.772279i	−0.552237	+	0.833687i	$0.686226\pi$
$164$	0.404360			0.0315752
$165$	8.40836	+	1.00756i	0.654590	+	0.0784388i
$166$			1.62325i			0.125988i
$167$	−5.66418	+	9.81065i	−0.438308	+	0.759171i	−0.997559	−	0.0698271i	$-0.977755\pi$
$167$	−5.66418	+	9.81065i	−0.438308	+	0.759171i	0.559252	+	0.828998i	$0.311089\pi$
$168$		0			0
$169$	13.5797	+	23.5208i	1.04459	+	1.80929i
$170$	2.82827	−	1.63290i	0.216918	−	0.125238i
$171$	−6.23881	+	1.82835i	−0.477094	+	0.139817i
$172$	−2.90883	+	5.03824i	−0.221796	+	0.384162i
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	−0.0776528	−	0.996980i	$-0.524743\pi$
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	0.902237	−	0.431241i	$-0.141924\pi$
$174$	−0.0711198	+	0.593511i	−0.00539158	+	0.0449940i
$175$		0			0
$176$	2.96133	+	1.70972i	0.223218	+	0.128875i
$177$	−17.5633	+	7.51565i	−1.32014	+	0.564911i
$178$		−	4.05949i		−	0.304271i
$179$	18.0057	+	10.3956i	1.34581	+	0.777002i	0.987653	−	0.156660i	$-0.0500726\pi$
$179$	18.0057	+	10.3956i	1.34581	+	0.777002i	0.358155	+	0.933662i	$0.383406\pi$
$180$	1.20636	+	4.11642i	0.0899169	+	0.306820i
$181$		−	21.5301i		−	1.60032i	−0.599788	−	0.800159i	$-0.704748\pi$
$181$		−	21.5301i		−	1.60032i	0.599788	−	0.800159i	$-0.295252\pi$
$182$		0			0
$183$	11.9199	−	15.9145i	0.881143	−	1.17643i
$184$	8.05411			0.593757
$185$	−1.54117	−	2.66939i	−0.113309	−	0.196258i
$186$	0.894838	−	7.46763i	0.0656127	−	0.547553i
$187$	6.76372	+	3.90503i	0.494612	+	0.285564i
$188$	5.51829			0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$	−6.38207	−	3.68469i	−0.461791	−	0.266615i	0.251006	−	0.967985i	$-0.419239\pi$
$191$	−6.38207	−	3.68469i	−0.461791	−	0.266615i	−0.712797	+	0.701371i	$0.752572\pi$
$192$	−0.206076	+	1.71975i	−0.0148722	+	0.124112i
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	0.912383	−	0.409337i	$-0.134240\pi$
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	−0.810688	+	0.585478i	$0.800907\pi$
$194$	−10.6085			−0.761643
$195$	9.40859	−	12.5616i	0.673763	−	0.899553i
$196$		0			0
$197$		−	26.0883i		−	1.85871i	−0.369183	−	0.929357i	$-0.620363\pi$
$197$		−	26.0883i		−	1.85871i	0.369183	−	0.929357i	$-0.379637\pi$
$198$	−7.08293	+	7.42062i	−0.503362	+	0.527360i
$199$	−13.3511	−	7.70826i	−0.946434	−	0.546424i	−0.0544625	−	0.998516i	$-0.517345\pi$
$199$	−13.3511	−	7.70826i	−0.946434	−	0.546424i	−0.891971	+	0.452092i	$0.850678\pi$
$200$		−	2.95553i		−	0.208987i
$201$	−6.77345	+	2.89847i	−0.477762	+	0.204442i
$202$	6.97052	+	4.02443i	0.490444	+	0.283158i
$203$		0			0
$204$	−0.470680	+	3.92793i	−0.0329542	+	0.275010i
$205$	−0.289087	+	0.500713i	−0.0201907	+	0.0349713i
$206$	1.40695	−	2.43692i	0.0980272	−	0.169788i
$207$	−5.70872	+	23.4783i	−0.396784	+	1.63185i
$208$	5.48813	−	3.16857i	0.380533	−	0.219701i
$209$	−3.70508	−	6.41739i	−0.256286	−	0.443900i
$210$		0			0
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	−0.672568	−	0.740035i	$-0.734809\pi$
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	0.977173	+	0.212443i	$0.0681421\pi$
$212$		−	9.88782i		−	0.679098i
$213$	6.11186	+	0.732377i	0.418778	+	0.0501817i
$214$	15.8216			1.08154
$215$	−4.15919	−	7.20393i	−0.283655	−	0.491304i
$216$	−4.86711	−	1.81967i	−0.331165	−	0.123813i
$217$		0			0
$218$	8.84514	−	5.10675i	0.599069	−	0.345873i
$219$	0.241062	−	0.321846i	0.0162895	−	0.0217484i
$220$	−4.23425	+	2.44465i	−0.285473	+	0.164818i
$221$	12.5350	−	7.23707i	0.843194	−	0.486818i
$222$	3.70728	+	0.444240i	0.248817	+	0.0298154i
$223$	−6.88961	+	3.97772i	−0.461363	+	0.266368i	−0.712617	−	0.701553i	$-0.752490\pi$
$223$	−6.88961	+	3.97772i	−0.461363	+	0.266368i	0.251254	+	0.967921i	$0.419157\pi$
$224$		0			0
$225$	8.61556	+	2.09487i	0.574370	+	0.139658i
$226$	4.20778	+	7.28808i	0.279897	+	0.484796i
$227$	−9.23968			−0.613259			−0.306630	−	0.951829i	$-0.599201\pi$
$227$	−9.23968			−0.613259			−0.306630	+	0.951829i	$0.599201\pi$
$228$	2.25015	−	3.00422i	0.149020	−	0.198959i
$229$		−	8.44454i		−	0.558031i	−0.960287	−	0.279016i	$-0.909992\pi$
$229$		−	8.44454i		−	0.558031i	0.960287	−	0.279016i	$-0.0900081\pi$
$230$	−5.75809	+	9.97330i	−0.379677	+	0.657620i
$231$		0			0
$232$	−0.172558	−	0.298879i	−0.0113290	−	0.0196223i
$233$	−14.4176	+	8.32399i	−0.944526	+	0.545323i	−0.891376	−	0.453264i	$-0.850259\pi$
$233$	−14.4176	+	8.32399i	−0.944526	+	0.545323i	−0.0531500	+	0.998587i	$0.516926\pi$
$234$	5.34664	+	18.2441i	0.349521	+	1.19266i
$235$	−3.94517	+	6.83323i	−0.257354	+	0.445751i
$236$	5.51480	−	9.55191i	0.358983	−	0.621776i
$237$	20.1874	+	15.1203i	1.31131	+	0.982170i
$238$		0			0
$239$	−23.6325	−	13.6442i	−1.52866	−	0.882572i	−0.999418	−	0.0341012i	$-0.989143\pi$
$239$	−23.6325	−	13.6442i	−1.52866	−	0.882572i	−0.529242	−	0.848471i	$-0.677524\pi$
$240$	−1.98221	−	1.48467i	−0.127951	−	0.0958352i
$241$			25.2900i			1.62907i	0.580111	+	0.814537i	$0.303009\pi$
$241$			25.2900i			1.62907i	−0.580111	+	0.814537i	$0.696991\pi$
$242$	−0.599818	−	0.346305i	−0.0385578	−	0.0222613i
$243$	8.75426	−	12.8982i	0.561586	−	0.827418i
$244$			11.4797i			0.734915i
$245$		0			0
$246$	−0.275534	−	0.643896i	−0.0175674	−	0.0410533i
$247$	−13.7330			−0.873811
$248$	2.17114	+	3.76052i	0.137868	+	0.238794i
$249$	2.58483	−	1.10609i	0.163807	−	0.0700958i
$250$	9.85123	+	5.68761i	0.623046	+	0.359716i
$251$	−8.19337			−0.517161			−0.258581	−	0.965990i	$-0.583255\pi$
$251$	−8.19337			−0.517161			−0.258581	+	0.965990i	$0.583255\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$	5.00366	+	2.88886i	0.313958	+	0.181264i
$255$	−4.52741	−	3.39101i	−0.283517	−	0.212354i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.63445			0.413846			0.206923	−	0.978357i	$-0.433655\pi$
$257$	6.63445			0.413846			0.206923	+	0.978357i	$0.433655\pi$
$258$	10.0049	+	1.19888i	0.622878	+	0.0746388i
$259$		0			0
$260$			9.06117i			0.561950i
$261$	0.993559	−	0.291173i	0.0614997	−	0.0180231i
$262$	−3.85959	−	2.22833i	−0.238446	−	0.137667i
$263$		−	6.04590i		−	0.372806i	−0.982473	−	0.186403i	$-0.940317\pi$
$263$		−	6.04590i		−	0.372806i	0.982473	−	0.186403i	$-0.0596830\pi$
$264$	0.704664	−	5.88058i	0.0433691	−	0.361925i
$265$	12.2440	+	7.06905i	0.752140	+	0.434248i
$266$		0			0
$267$	−6.46426	+	2.76616i	−0.395606	+	0.169286i
$268$	2.12683	−	3.68377i	0.129917	−	0.225022i
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	−0.743116	−	0.669163i	$-0.766653\pi$
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	0.951070	+	0.308976i	$0.0999863\pi$
$270$	5.73290	−	4.72595i	0.348893	−	0.287612i
$271$	4.39780	−	2.53907i	0.267148	−	0.154238i	−0.360443	−	0.932781i	$-0.617375\pi$
$271$	4.39780	−	2.53907i	0.267148	−	0.154238i	0.627591	+	0.778543i	$0.284041\pi$
$272$	−1.14201	−	1.97802i	−0.0692444	−	0.119935i
$273$		0			0
$274$	4.82834	−	8.36293i	0.291691	−	0.505223i
$275$			10.1063i			0.609431i
$276$	−5.48813	−	12.8252i	−0.330347	−	0.771988i
$277$	−1.97913			−0.118915			−0.0594573	−	0.998231i	$-0.518937\pi$
$277$	−1.97913			−0.118915			−0.0594573	+	0.998231i	$0.518937\pi$
$278$	9.27686	+	16.0680i	0.556389	+	0.963694i
$279$	−12.5011	+	3.66357i	−0.748420	+	0.219332i
$280$		0			0
$281$	−15.2703	+	8.81631i	−0.910950	+	0.525937i	−0.880737	−	0.473606i	$-0.842952\pi$
$281$	−15.2703	+	8.81631i	−0.910950	+	0.525937i	−0.0302131	+	0.999543i	$0.509619\pi$
$282$	−3.76021	−	8.78724i	−0.223917	−	0.523272i
$283$	−4.46337	+	2.57693i	−0.265320	+	0.153182i	−0.626759	−	0.779213i	$-0.715619\pi$
$283$	−4.46337	+	2.57693i	−0.265320	+	0.153182i	0.361439	+	0.932396i	$0.382286\pi$
$284$	−3.07779	+	1.77696i	−0.182633	+	0.105443i
$285$	2.11140	+	4.93413i	0.125068	+	0.292273i
$286$	−18.7664	+	10.8348i	−1.10968	+	0.640673i
$287$		0			0
$288$	2.87892	−	0.843698i	0.169642	−	0.0497154i
$289$	5.89164	+	10.2046i	0.346567	+	0.600271i
$290$	0.493463			0.0289772
$291$	7.22868	+	16.8927i	0.423753	+	0.990269i
$292$			0.232161i			0.0135862i
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	−0.834289	−	0.551327i	$-0.814122\pi$
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	0.894608	+	0.446852i	$0.147455\pi$
$294$		0			0
$295$	7.88534	+	13.6578i	0.459102	+	0.795188i
$296$	−1.86690	+	1.07786i	−0.108511	+	0.0626491i
$297$	16.6428	+	6.22228i	0.965715	+	0.361053i
$298$	3.25347	−	5.63517i	0.188468	−	0.326437i
$299$	−25.5201	+	44.2020i	−1.47586	+	2.55627i
$300$	−4.70633	+	2.01392i	−0.271720	+	0.116274i
$301$		0			0
$302$	4.98745	+	2.87950i	0.286995	+	0.165697i
$303$	1.65867	−	13.8420i	0.0952883	−	0.795203i
$304$			2.16707i			0.124290i
$305$	−14.2152	−	8.20716i	−0.813961	−	0.469941i
$306$	6.57550	−	1.92702i	0.375896	−	0.110160i
$307$			1.09119i			0.0622772i	0.999515	+	0.0311386i	$0.00991333\pi$
$307$			1.09119i			0.0622772i	−0.999515	+	0.0311386i	$0.990087\pi$
$308$		0			0
$309$	−4.83921	−	0.579878i	−0.275293	−	0.0329881i
$310$	−6.20881			−0.352637
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	0.565429	−	0.824797i	$-0.308711\pi$
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	−0.997010	+	0.0772777i	$0.975377\pi$
$312$	−8.78524	−	6.58012i	−0.497366	−	0.372526i
$313$	−10.0202	−	5.78518i	−0.566377	−	0.326998i	0.189324	−	0.981915i	$-0.439370\pi$
$313$	−10.0202	−	5.78518i	−0.566377	−	0.326998i	−0.755701	+	0.654917i	$0.772704\pi$
$314$	−7.96361			−0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$	14.8613	+	8.58020i	0.834696	+	0.481912i	0.855458	−	0.517872i	$-0.173276\pi$
$317$	14.8613	+	8.58020i	0.834696	+	0.481912i	−0.0207618	+	0.999784i	$0.506609\pi$
$318$	−15.7452	+	6.73763i	−0.882947	+	0.377828i
$319$	0.590051	+	1.02200i	0.0330365	+	0.0572210i
$320$	1.42985			0.0799311
$321$	−10.7809	−	25.1940i	−0.601733	−	1.40619i
$322$		0			0
$323$			4.94962i			0.275404i
$324$	0.418868	+	8.99025i	0.0232704	+	0.499458i
$325$	16.2203	+	9.36481i	0.899742	+	0.519466i
$326$			11.3851i			0.630563i
$327$	−14.1590	−	10.6051i	−0.782997	−	0.586463i
$328$	0.350186	+	0.202180i	0.0193358	+	0.0111635i
$329$		0			0
$330$	6.77807	+	5.07676i	0.373120	+	0.279466i
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	−0.229591	−	0.973287i	$-0.573739\pi$
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	0.957687	−	0.287812i	$-0.0929280\pi$
$332$	−0.811624	+	1.40577i	−0.0445436	+	0.0771519i
$333$	−1.81877	−	6.20612i	−0.0996680	−	0.340093i
$334$	−9.81065	+	5.66418i	−0.536815	+	0.309930i
$335$	3.04105	+	5.26725i	0.166150	+	0.287780i
$336$		0			0
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	−0.733828	−	0.679335i	$-0.762268\pi$
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	0.955236	+	0.295846i	$0.0956015\pi$
$338$			27.1594i			1.47728i
$339$	8.73821	−	11.6665i	0.474594	−	0.633640i
$340$	3.26580			0.177113
$341$	−7.42410	−	12.8589i	−0.402037	−	0.696349i
$342$	−6.31714	−	1.53601i	−0.341592	−	0.0830578i
$343$		0			0
$344$	−5.03824	+	2.90883i	−0.271644	+	0.156834i
$345$	19.8049	+	2.37320i	1.06626	+	0.127769i
$346$	18.7853	−	10.8457i	1.00991	−	0.583069i
$347$	−22.1851	+	12.8086i	−1.19096	+	0.687599i	−0.958524	−	0.285013i	$-0.908002\pi$
$347$	−22.1851	+	12.8086i	−1.19096	+	0.687599i	−0.232433	+	0.972612i	$0.574669\pi$
$348$	−0.358347	+	0.478436i	−0.0192094	+	0.0256469i
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	−0.235659	−	0.971836i	$-0.575725\pi$
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	0.723805	+	0.690005i	$0.242391\pi$
$350$		0			0
$351$	25.4084	−	20.9456i	1.35620	−	1.11799i
$352$	1.70972	+	2.96133i	0.0911285	+	0.157839i
$353$	−12.8437			−0.683602			−0.341801	−	0.939772i	$-0.611037\pi$
$353$	−12.8437			−0.683602			−0.341801	+	0.939772i	$0.611037\pi$
$354$	−18.9681	−	2.27293i	−1.00814	−	0.120805i
$355$		−	5.08158i		−	0.269702i
$356$	2.02974	−	3.51562i	0.107576	−	0.186327i
$357$		0			0
$358$	10.3956	+	18.0057i	0.549424	+	0.951630i
$359$	−25.6881	+	14.8311i	−1.35577	+	0.782753i	−0.989050	−	0.147579i	$-0.952852\pi$
$359$	−25.6881	+	14.8311i	−1.35577	+	0.782753i	−0.366718	+	0.930332i	$0.619518\pi$
$360$	−1.01347	+	4.16811i	−0.0534147	+	0.219679i
$361$	−7.15191	+	12.3875i	−0.376416	+	0.651972i
$362$	10.7650	−	18.6456i	0.565798	−	0.979991i
$363$	−0.142730	+	1.19112i	−0.00749139	+	0.0625173i
$364$		0			0
$365$	−0.287482	−	0.165978i	−0.0150475	−	0.00868767i
$366$	18.2802	−	7.82238i	0.955519	−	0.408883i
$367$		−	23.9979i		−	1.25268i	−0.779550	−	0.626340i	$-0.784552\pi$
$367$		−	23.9979i		−	1.25268i	0.779550	−	0.626340i	$-0.215448\pi$
$368$	6.97507	+	4.02706i	0.363600	+	0.209925i
$369$	−0.837578	+	0.877510i	−0.0436026	+	0.0456814i
$370$		−	3.08235i		−	0.160244i
$371$		0			0
$372$	4.50877	−	6.01974i	0.233769	−	0.312109i
$373$	−11.8390			−0.612998			−0.306499	−	0.951871i	$-0.599158\pi$
$373$	−11.8390			−0.612998			−0.306499	+	0.951871i	$0.599158\pi$
$374$	3.90503	+	6.76372i	0.201925	+	0.349744i
$375$	2.34415	−	19.5625i	0.121052	−	1.01020i
$376$	4.77898	+	2.75915i	0.246457	+	0.142292i
$377$	2.18705			0.112639
$378$		0			0
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$	−2.68345	−	1.54929i	−0.137658	−	0.0794769i
$381$	1.19065	−	9.93624i	0.0609988	−	0.509049i
$382$	−3.68469	−	6.38207i	−0.188525	−	0.326535i
$383$	17.5521			0.896868			0.448434	−	0.893816i	$-0.351982\pi$
$383$	17.5521			0.896868			0.448434	+	0.893816i	$0.351982\pi$
$384$	−1.03834	+	1.38631i	−0.0529876	+	0.0707447i
$385$		0			0
$386$			2.82559i			0.143819i
$387$	−4.90834	−	16.7486i	−0.249505	−	0.851378i
$388$	−9.18719	−	5.30423i	−0.466409	−	0.269281i
$389$		−	21.8410i		−	1.10738i	−0.832722	−	0.553691i	$-0.813219\pi$
$389$		−	21.8410i		−	1.10738i	0.832722	−	0.553691i	$-0.186781\pi$
$390$	14.4289	−	6.17435i	0.730634	−	0.312650i
$391$	15.9312	+	9.19786i	0.805674	+	0.465156i
$392$		0			0
$393$	−0.918411	+	7.66435i	−0.0463277	+	0.386615i
$394$	13.0441	−	22.5931i	0.657154	−	1.13822i
$395$	10.4107	−	18.0319i	0.523821	−	0.907285i
$396$	−9.84431	+	2.88498i	−0.494695	+	0.144976i
$397$	−33.7636	+	19.4935i	−1.69455	+	0.978348i	−0.743792	+	0.668411i	$0.766975\pi$
$397$	−33.7636	+	19.4935i	−1.69455	+	0.978348i	−0.950757	+	0.309937i	$0.899692\pi$
$398$	−7.70826	−	13.3511i	−0.386380	−	0.669230i
$399$		0			0
$400$	1.47776	−	2.55956i	0.0738882	−	0.127978i
$401$		−	23.1979i		−	1.15845i	−0.815169	−	0.579223i	$-0.803356\pi$
$401$		−	23.1979i		−	1.15845i	0.815169	−	0.579223i	$-0.196644\pi$
$402$	−7.31522	−	0.876575i	−0.364850	−	0.0437196i
$403$	−27.5177			−1.37075
$404$	4.02443	+	6.97052i	0.200223	+	0.346796i
$405$	−11.4320	−	5.90868i	−0.568059	−	0.293605i
$406$		0			0
$407$	6.38377	−	3.68567i	0.316432	−	0.182692i
$408$	−2.37159	+	3.16635i	−0.117411	+	0.156758i
$409$	21.3205	−	12.3094i	1.05423	−	0.608659i	0.130398	−	0.991462i	$-0.458374\pi$
$409$	21.3205	−	12.3094i	1.05423	−	0.608659i	0.923830	+	0.382803i	$0.125041\pi$
$410$	−0.500713	+	0.289087i	−0.0247285	+	0.0142770i
$411$	−16.6071	−	1.99001i	−0.819166	−	0.0981597i
$412$	2.43692	−	1.40695i	0.120058	−	0.0693157i
$413$		0			0
$414$	−16.6830	+	17.4784i	−0.819926	+	0.859017i
$415$	−1.16050	−	2.01005i	−0.0569667	−	0.0986693i
$416$	6.33715			0.310704
$417$	19.2651	−	25.7212i	0.943415	−	1.25957i
$418$		−	7.41017i		−	0.362443i
$419$	8.53996	−	14.7916i	0.417204	−	0.722619i	−0.578453	−	0.815716i	$-0.696343\pi$
$419$	8.53996	−	14.7916i	0.417204	−	0.722619i	0.995657	+	0.0930969i	$0.0296766\pi$
$420$		0			0
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	0.629182	−	0.777258i	$-0.283390\pi$
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	−0.987716	+	0.156258i	$0.950057\pi$
$422$	7.66371	−	4.42465i	0.373064	−	0.215388i
$423$	−11.4304	+	11.9754i	−0.555766	+	0.582263i
$424$	4.94391	−	8.56310i	0.240097	−	0.415861i
$425$	3.37524	−	5.84608i	0.163723	−	0.283577i
$426$	4.92684	+	3.69019i	0.238706	+	0.178790i
$427$		0			0
$428$	13.7019	+	7.91078i	0.662305	+	0.382382i
$429$	30.0406	+	22.5004i	1.45038	+	1.08633i
$430$		−	8.31838i		−	0.401148i
$431$	8.32286	+	4.80521i	0.400898	+	0.231459i	0.686871	−	0.726779i	$-0.258984\pi$
$431$	8.32286	+	4.80521i	0.400898	+	0.231459i	−0.285973	+	0.958238i	$0.592317\pi$
$432$	−3.30521	−	4.00944i	−0.159022	−	0.192904i
$433$		−	9.04314i		−	0.434585i	−0.976106	−	0.217293i	$-0.930277\pi$
$433$		−	9.04314i		−	0.434585i	0.976106	−	0.217293i	$-0.0697226\pi$
$434$		0			0
$435$	−0.336249	−	0.785782i	−0.0161219	−	0.0376754i
$436$	10.2135			0.489138
$437$	−8.72690	−	15.1154i	−0.417464	−	0.723069i
$438$	0.369689	−	0.158196i	0.0176644	−	0.00755890i
$439$	−0.791370	−	0.456897i	−0.0377700	−	0.0218065i	0.480996	−	0.876723i	$-0.340275\pi$
$439$	−0.791370	−	0.456897i	−0.0377700	−	0.0218065i	−0.518766	+	0.854916i	$0.673608\pi$
$440$	−4.88930			−0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$	−25.4279	−	14.6808i	−1.20812	−	0.697507i	−0.245770	−	0.969328i	$-0.579041\pi$
$443$	−25.4279	−	14.6808i	−1.20812	−	0.697507i	−0.962348	+	0.271821i	$0.912374\pi$
$444$	2.98848	+	2.23836i	0.141827	+	0.106228i
$445$	2.90223	+	5.02681i	0.137579	+	0.238294i
$446$	−7.95544			−0.376701
$447$	−11.1903	−	1.34092i	−0.529283	−	0.0634234i
$448$		0			0
$449$		−	3.36736i		−	0.158915i	−0.996838	−	0.0794577i	$-0.974681\pi$
$449$		−	3.36736i		−	0.158915i	0.996838	−	0.0794577i	$-0.0253189\pi$
$450$	6.41386	+	6.12199i	0.302352	+	0.288593i
$451$	−1.19744	−	0.691343i	−0.0563853	−	0.0325541i
$452$			8.41555i			0.395834i
$453$	1.18679	−	9.90404i	0.0557603	−	0.465332i
$454$	−8.00180	−	4.61984i	−0.375543	−	0.216820i
$455$		0			0
$456$	3.45080	−	1.47666i	0.161599	−	0.0691507i
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	−0.633362	−	0.773856i	$-0.718325\pi$
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	0.986860	+	0.161579i	$0.0516588\pi$
$458$	4.22227	−	7.31319i	0.197294	−	0.341723i
$459$	−7.54914	−	9.15763i	−0.352364	−	0.427441i
$460$	−9.97330	+	5.75809i	−0.465008	+	0.268472i
$461$	5.19445	+	8.99706i	0.241930	+	0.419035i	0.961264	−	0.275629i	$-0.0888863\pi$
$461$	5.19445	+	8.99706i	0.241930	+	0.419035i	−0.719334	+	0.694664i	$0.755553\pi$
$462$		0			0
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	−0.921142	−	0.389226i	$-0.872743\pi$
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	0.797651	+	0.603120i	$0.206076\pi$
$464$		−	0.345115i		−	0.0160216i
$465$	4.23073	+	9.88681i	0.196195	+	0.458490i
$466$	−16.6480			−0.771203
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	0.998459	−	0.0554907i	$-0.0176723\pi$
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$468$	−4.49174	+	18.4732i	−0.207631	+	0.853924i
$469$		0			0
$470$	−6.83323	+	3.94517i	−0.315193	+	0.181977i
$471$	5.42646	+	12.6811i	0.250038	+	0.584315i
$472$	9.55191	−	5.51480i	0.439662	−	0.253839i
$473$	17.2280	−	9.94659i	0.792144	−	0.457345i
$474$	9.92265	+	23.1883i	0.455763	+	1.06507i
$475$	−5.54674	+	3.20241i	−0.254502	+	0.146937i
$476$		0			0
$477$	21.4578	+	20.4813i	0.982484	+	0.937775i
$478$	−13.6442	−	23.6325i	−0.624073	−	1.08093i
$479$	27.8024			1.27033			0.635163	−	0.772378i	$-0.280933\pi$
$479$	27.8024			1.27033			0.635163	+	0.772378i	$0.280933\pi$
$480$	−0.974311	−	2.27687i	−0.0444710	−	0.103924i
$481$		−	13.6611i		−	0.622891i
$482$	−12.6450	+	21.9018i	−0.575965	+	0.997600i
$483$		0			0
$484$	−0.346305	−	0.599818i	−0.0157411	−	0.0272645i
$485$	13.1363	−	7.58425i	0.596489	−	0.344383i
$486$	14.0305	−	6.79302i	0.636436	−	0.308138i
$487$	3.73838	−	6.47506i	0.169402	−	0.293413i	−0.768808	−	0.639480i	$-0.779150\pi$
$487$	3.73838	−	6.47506i	0.169402	−	0.293413i	0.938210	+	0.346067i	$0.112483\pi$
$488$	−5.73987	+	9.94175i	−0.259832	+	0.450042i
$489$	18.1295	−	7.75790i	0.819843	−	0.350824i
$490$		0			0
$491$	19.1466	+	11.0543i	0.864073	+	0.498873i	0.865374	−	0.501126i	$-0.167081\pi$
$491$	19.1466	+	11.0543i	0.864073	+	0.498873i	−0.00130103	+	0.999999i	$0.500414\pi$
$492$	0.0833287	−	0.695397i	0.00375675	−	0.0313509i
$493$		−	0.788249i		−	0.0355009i
$494$	−11.8931	−	6.86651i	−0.535098	−	0.308939i
$495$	3.46551	−	14.2526i	0.155763	−	0.640608i
$496$			4.34228i			0.194974i
$497$		0			0
$498$	2.79158	+	0.334512i	0.125094	+	0.0149898i
$499$	32.9042			1.47300			0.736498	−	0.676439i	$-0.236478\pi$
$499$	32.9042			1.47300			0.736498	+	0.676439i	$0.236478\pi$
$500$	5.68761	+	9.85123i	0.254358	+	0.440560i
$501$	15.7046	+	11.7627i	0.701630	+	0.525519i
$502$	−7.09567	−	4.09669i	−0.316695	−	0.182844i
$503$	−25.6142			−1.14208			−0.571039	−	0.820923i	$-0.693460\pi$
$503$	−25.6142			−1.14208			−0.571039	+	0.820923i	$0.693460\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$	−23.8509	−	13.7703i	−1.06030	−	0.612165i
$507$	43.2482	−	18.5066i	1.92072	−	0.821909i
$508$	2.88886	+	5.00366i	0.128173	+	0.222002i
$509$	21.4717			0.951715			0.475857	−	0.879522i	$-0.342138\pi$
$509$	21.4717			0.951715			0.475857	+	0.879522i	$0.342138\pi$
$510$	−2.22534	−	5.20041i	−0.0985398	−	0.230278i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	1.85863	+	11.1060i	0.0820607	+	0.490340i
$514$	5.74560	+	3.31723i	0.253428	+	0.146317i
$515$			4.02347i			0.177295i
$516$	8.06507	+	6.04071i	0.355045	+	0.265928i
$517$	−16.3415	−	9.43475i	−0.718697	−	0.414940i
$518$		0			0
$519$	−30.0710	−	22.5231i	−1.31997	−	0.988654i
$520$	−4.53059	+	7.84721i	−0.198679	+	0.344123i
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	−0.928079	−	0.372382i	$-0.878541\pi$
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	0.786532	+	0.617549i	$0.211874\pi$
$522$	1.00603	+	0.244616i	0.0440329	+	0.0107066i
$523$	−11.7830	+	6.80291i	−0.515234	+	0.297470i	−0.734982	−	0.678086i	$-0.762810\pi$
$523$	−11.7830	+	6.80291i	−0.515234	+	0.297470i	0.219749	+	0.975557i	$0.429476\pi$
$524$	−2.22833	−	3.85959i	−0.0973452	−	0.168607i
$525$		0			0
$526$	3.02295	−	5.23590i	0.131807	−	0.228296i
$527$			9.91784i			0.432028i
$528$	3.55055	−	4.74040i	0.154518	−	0.206300i
$529$	−41.8687			−1.82038
$530$	7.06905	+	12.2440i	0.307060	+	0.531843i
$531$	9.30564	+	31.7533i	0.403830	+	1.37798i
$532$		0			0
$533$	−2.21918	+	1.28124i	−0.0961233	+	0.0554968i
$534$	−6.98129	−	0.836561i	−0.302110	−	0.0362015i
$535$	−19.5916	+	11.3112i	−0.847020	+	0.489027i
$536$	3.68377	−	2.12683i	0.159115	−	0.0918650i
$537$	21.5883	−	28.8230i	0.931604	−	1.24380i
$538$	5.90750	−	3.41069i	0.254690	−	0.147045i
$539$		0			0
$540$	7.32781	−	1.22634i	0.315339	−	0.0527734i
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	−0.985022	−	0.172428i	$-0.944839\pi$
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	0.343184	−	0.939268i	$-0.388494\pi$
$542$	5.07815			0.218125
$543$	−37.0263	−	4.43682i	−1.58895	−	0.190402i
$544$		−	2.28402i		−	0.0979264i
$545$	−7.30188	+	12.6472i	−0.312778	+	0.541748i
$546$		0			0
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	0.604272	−	0.796778i	$-0.293464\pi$
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	−0.992166	+	0.124926i	$0.960131\pi$
$548$	8.36293	−	4.82834i	0.357247	−	0.206256i
$549$	−24.9125	−	23.7788i	−1.06324	−	1.01485i
$550$	−5.05313	+	8.75228i	−0.215466	+	0.373199i
$551$	−0.373944	+	0.647690i	−0.0159305	+	0.0275925i
$552$	1.65976	−	13.8510i	0.0706439	−	0.589540i
$553$		0			0
$554$	−1.71398	−	0.989567i	−0.0728201	−	0.0420427i
$555$	−4.90828	+	2.10033i	−0.208345	+	0.0891542i
$556$			18.5537i			0.786853i
$557$	32.5079	+	18.7684i	1.37740	+	0.795245i	0.991846	−	0.127439i	$-0.0406757\pi$
$557$	32.5079	+	18.7684i	1.37740	+	0.795245i	0.385558	+	0.922684i	$0.374009\pi$
$558$	−12.6580	−	3.07779i	−0.535857	−	0.130293i
$559$		−	36.8674i		−	1.55932i
$560$		0			0
$561$	8.10951	−	10.8272i	0.342384	−	0.457123i
$562$	−17.6326			−0.743787
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	0.781380	−	0.624056i	$-0.214516\pi$
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	−0.931138	+	0.364667i	$0.881183\pi$
$564$	1.13719	−	9.49008i	0.0478841	−	0.399604i
$565$	−10.4209	−	6.01649i	−0.438409	−	0.253116i
$566$	−5.15385			−0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$	35.6499	+	20.5825i	1.49452	+	0.862862i	0.999980	−	0.00629202i	$-0.00200283\pi$
$569$	35.6499	+	20.5825i	1.49452	+	0.862862i	0.494541	+	0.869154i	$0.335336\pi$
$570$	−0.638542	+	5.32878i	−0.0267456	+	0.223198i
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	0.816000	−	0.578052i	$-0.196187\pi$
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	−0.908608	+	0.417650i	$0.862854\pi$
$572$	−21.6695			−0.906049
$573$	−7.65193	+	10.2162i	−0.319664	+	0.426789i
$574$		0			0
$575$			23.8042i			0.992702i
$576$	2.91507	+	0.708796i	0.121461	+	0.0295332i
$577$	−2.37542	−	1.37145i	−0.0988900	−	0.0570941i	0.449739	−	0.893160i	$-0.351517\pi$
$577$	−2.37542	−	1.37145i	−0.0988900	−	0.0570941i	−0.548629	+	0.836066i	$0.684850\pi$
$578$			11.7833i			0.490119i
$579$	4.49942	−	1.92538i	0.186989	−	0.0800159i
$580$	0.427352	+	0.246732i	0.0177448	+	0.0102450i
$581$		0			0
$582$	−2.18614	+	18.2439i	−0.0906186	+	0.756233i
$583$	−16.9054	+	29.2811i	−0.700151	+	1.21270i
$584$	−0.116080	+	0.201057i	−0.00480344	+	0.00831981i
$585$	−19.6639	−	18.7690i	−0.813001	−	0.776004i
$586$	1.78831	−	1.03248i	0.0738745	−	0.0426515i
$587$	9.90248	+	17.1516i	0.408719	+	0.707922i	0.994747	−	0.102369i	$-0.0326422\pi$
$587$	9.90248	+	17.1516i	0.408719	+	0.707922i	−0.586027	+	0.810291i	$0.699309\pi$
$588$		0			0
$589$	4.70501	−	8.14931i	0.193866	−	0.335786i
$590$			15.7707i			0.649268i
$591$	−44.8653	−	5.37616i	−1.84551	−	0.221146i
$592$	−2.15571			−0.0885993
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	0.874816	−	0.484456i	$-0.160982\pi$
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	−0.856959	+	0.515385i	$0.827649\pi$
$594$	11.3020	+	13.7101i	0.463726	+	0.562531i
$595$		0			0
$596$	5.63517	−	3.25347i	0.230826	−	0.133267i
$597$	−16.0076	+	21.3720i	−0.655147	+	0.874699i
$598$	−44.2020	+	25.5201i	−1.80756	+	1.04359i
$599$	2.33277	−	1.34682i	0.0953143	−	0.0550297i	−0.451585	−	0.892228i	$-0.649141\pi$
$599$	2.33277	−	1.34682i	0.0953143	−	0.0550297i	0.546899	+	0.837198i	$0.315808\pi$
$600$	−5.08276	−	0.609062i	−0.207503	−	0.0248648i
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	−0.497646	−	0.867380i	$-0.665802\pi$
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	0.502350	+	0.864664i	$0.332469\pi$
$602$		0			0
$603$	3.58880	+	12.2459i	0.146147	+	0.498693i
$604$	2.87950	+	4.98745i	0.117165	+	0.202936i
$605$	0.990329			0.0402626
$606$	8.35746	−	11.1582i	0.339499	−	0.453271i
$607$		−	44.3243i		−	1.79907i	−0.436851	−	0.899534i	$-0.643906\pi$
$607$		−	44.3243i		−	1.79907i	0.436851	−	0.899534i	$-0.356094\pi$
$608$	−1.08353	+	1.87673i	−0.0439431	+	0.0761117i
$609$		0			0
$610$	−8.20716	−	14.2152i	−0.332298	−	0.575557i
$611$	−30.2851	+	17.4851i	−1.22520	+	0.707372i
$612$	6.65806	+	1.61890i	0.269136	+	0.0654402i
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	−0.791680	−	0.610936i	$-0.790793\pi$
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	0.924926	+	0.380147i	$0.124127\pi$
$614$	−0.545593	+	0.944994i	−0.0220183	+	0.0381369i
$615$	0.801527	+	0.600342i	0.0323207	+	0.0242081i
$616$		0			0
$617$	−7.99450	−	4.61563i	−0.321846	−	0.185818i	0.330369	−	0.943852i	$-0.392827\pi$
$617$	−7.99450	−	4.61563i	−0.321846	−	0.185818i	−0.652215	+	0.758034i	$0.726160\pi$
$618$	−3.90094	−	2.92180i	−0.156919	−	0.117532i
$619$			6.53894i			0.262822i	0.991328	+	0.131411i	$0.0419508\pi$
$619$			6.53894i			0.262822i	−0.991328	+	0.131411i	$0.958049\pi$
$620$	−5.37699	−	3.10441i	−0.215945	−	0.124676i
$621$	39.2003	+	14.6559i	1.57305	+	0.588119i
$622$		−	15.2220i		−	0.610347i
$623$		0			0
$624$	−4.31818	−	10.0912i	−0.172866	−	0.403970i
$625$	−1.48722			−0.0594888
$626$	−5.78518	−	10.0202i	−0.231222	−	0.400489i
$627$	−11.7998	+	5.04934i	−0.471240	+	0.201651i
$628$	−6.89669	−	3.98180i	−0.275208	−	0.158891i
$629$	−4.92368			−0.196320
$630$		0			0
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$	−12.6111	−	7.28100i	−0.501641	−	0.289623i
$633$	−12.2678	−	9.18858i	−0.487603	−	0.365213i
$634$	8.58020	+	14.8613i	0.340763	+	0.590219i
$635$	−8.26129			−0.327839
$636$	−17.0046	−	2.03764i	−0.674274	−	0.0807976i
$637$		0			0
$638$			1.18010i			0.0467207i
$639$	2.51901	−	10.3599i	0.0996504	−	0.409832i
$640$	1.23829	+	0.714925i	0.0489476	+	0.0282599i
$641$			15.2351i			0.601752i	0.953663	+	0.300876i	$0.0972790\pi$
$641$			15.2351i			0.601752i	−0.953663	+	0.300876i	$0.902721\pi$
$642$	3.26044	−	27.2091i	0.128679	−	1.07386i
$643$	−16.5813	−	9.57324i	−0.653904	−	0.377532i	0.136046	−	0.990702i	$-0.456560\pi$
$643$	−16.5813	−	9.57324i	−0.653904	−	0.377532i	−0.789950	+	0.613171i	$0.789894\pi$
$644$		0			0
$645$	−13.2461	+	5.66821i	−0.521563	+	0.223185i
$646$	−2.47481	+	4.28649i	−0.0973700	+	0.168650i
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	−0.849996	−	0.526789i	$-0.823396\pi$
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	0.881211	+	0.472723i	$0.156729\pi$
$648$	−4.13237	+	7.99522i	−0.162335	+	0.314082i
$649$	−32.6622	+	18.8576i	−1.28211	+	0.740224i
$650$	9.36481	+	16.2203i	0.367318	+	0.636213i
$651$		0			0
$652$	−5.69256	+	9.85980i	−0.222938	+	0.386140i
$653$		−	17.9639i		−	0.702983i	−0.936191	−	0.351492i	$-0.885675\pi$
$653$		−	17.9639i		−	0.702983i	0.936191	−	0.351492i	$-0.114325\pi$
$654$	−6.95955	−	16.2638i	−0.272140	−	0.635965i
$655$	6.37237			0.248989
$656$	0.202180	+	0.350186i	0.00789380	+	0.0136725i
$657$	−0.503818	−	0.480891i	−0.0196558	−	0.0187613i
$658$		0			0
$659$	10.0955	−	5.82866i	0.393266	−	0.227052i	−0.290308	−	0.956933i	$-0.593758\pi$
$659$	10.0955	−	5.82866i	0.393266	−	0.227052i	0.683574	+	0.729881i	$0.260424\pi$
$660$	3.33160	+	7.78563i	0.129682	+	0.303055i
$661$	15.7786	−	9.10975i	0.613715	−	0.354328i	−0.160703	−	0.987003i	$-0.551376\pi$
$661$	15.7786	−	9.10975i	0.613715	−	0.354328i	0.774418	+	0.632674i	$0.218043\pi$
$662$	22.9437	−	13.2466i	0.891732	−	0.514842i
$663$	−9.86279	−	23.0484i	−0.383039	−	0.895125i
$664$	−1.40577	+	0.811624i	−0.0545546	+	0.0314971i
$665$		0			0
$666$	1.52796	−	6.28404i	0.0592073	−	0.243502i
$667$	1.38980	+	2.40720i	0.0538132	+	0.0932072i
$668$	−11.3284			−0.438308
$669$	5.42090	+	12.6681i	0.209584	+	0.489777i
$670$			6.08209i			0.234972i
$671$	19.6272	−	33.9953i	0.757699	−	1.31237i
$672$		0			0
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	0.908747	−	0.417348i	$-0.137040\pi$
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	−0.815807	+	0.578324i	$0.803707\pi$
$674$	7.03993	−	4.06451i	0.271168	−	0.156559i
$675$	5.37810	−	14.3849i	0.207003	−	0.553675i
$676$	−13.5797	+	23.5208i	−0.522297	+	0.904645i
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	−0.998014	−	0.0629856i	$-0.979938\pi$
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	0.553554	+	0.832813i	$0.313271\pi$
$678$	13.4008	−	5.73442i	0.514654	−	0.220229i
$679$		0			0
$680$	2.82827	+	1.63290i	0.108459	+	0.0626189i
$681$	−1.90407	+	15.8899i	−0.0729642	+	0.608903i
$682$		−	14.8482i		−	0.568567i
$683$	6.80041	+	3.92622i	0.260210	+	0.150233i	0.624431	−	0.781080i	$-0.285331\pi$
$683$	6.80041	+	3.92622i	0.260210	+	0.150233i	−0.364220	+	0.931313i	$0.618664\pi$
$684$	−4.70280	−	4.48879i	−0.179816	−	0.171633i
$685$			13.8076i			0.527562i
$686$		0			0
$687$	−14.5225	−	1.74021i	−0.554067	−	0.0663933i
$688$	−5.81766			−0.221796
$689$	31.3303	+	54.2656i	1.19359	+	2.06736i
$690$	15.9650	+	11.9577i	0.607776	+	0.455222i
$691$	14.8676	+	8.58379i	0.565589	+	0.326543i	0.755386	−	0.655281i	$-0.227450\pi$
$691$	14.8676	+	8.58379i	0.565589	+	0.326543i	−0.189797	+	0.981823i	$0.560783\pi$
$692$	21.6914			0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$	−22.9748	−	13.2645i	−0.871485	−	0.503152i
$696$	−0.549556	+	0.235164i	−0.0208309	+	0.00891387i
$697$	0.461782	+	0.799830i	0.0174912	+	0.0302957i
$698$	10.5301			0.398570
$699$	11.3441	+	26.5100i	0.429071	+	1.00270i
$700$		0			0
$701$			34.9404i			1.31968i	0.751406	+	0.659840i	$0.229376\pi$
$701$			34.9404i			1.31968i	−0.751406	+	0.659840i	$0.770624\pi$
$702$	32.4771	−	5.43520i	1.22577	−	0.205138i
$703$	4.04570	+	2.33579i	0.152587	+	0.0880959i
$704$			3.41945i			0.128875i
$705$	10.9384	+	8.19286i	0.411965	+	0.308561i
$706$	−11.1230	−	6.42186i	−0.418619	−	0.241690i
$707$		0			0
$708$	−15.2904	−	11.4525i	−0.574649	−	0.430410i
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	−0.541864	−	0.840466i	$-0.682281\pi$
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	0.998797	+	0.0490345i	$0.0156144\pi$
$710$	2.54079	−	4.40078i	0.0953542	−	0.165158i
$711$	30.1633	−	31.6013i	1.13121	−	1.18514i
$712$	3.51562	−	2.02974i	0.131753	−	0.0760678i
$713$	−17.4866	−	30.2877i	−0.654879	−	1.13428i
$714$		0			0
$715$	15.4921	−	26.8331i	0.579372	−	1.00350i
$716$			20.7912i			0.777002i
$717$	−28.3347	+	37.8302i	−1.05818	+	1.41280i
$718$	−29.6621			−1.10698
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	0.981920	−	0.189297i	$-0.0606210\pi$
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	−0.654896	+	0.755719i	$0.727288\pi$
$720$	−2.96175	+	3.10295i	−0.110378	+	0.115640i
$721$		0			0
$722$	−12.3875	+	7.15191i	−0.461014	+	0.266167i
$723$	43.4925	+	5.21166i	1.61750	+	0.193824i
$724$	18.6456	−	10.7650i	0.692958	−	0.400079i
$725$	0.883344	−	0.509999i	0.0328066	−	0.0189409i
$726$	−0.719166	+	0.960171i	−0.0266907	+	0.0356353i
$727$	−33.8627	+	19.5507i	−1.25590	+	0.725094i	−0.972275	−	0.233841i	$-0.924870\pi$
$727$	−33.8627	+	19.5507i	−1.25590	+	0.725094i	−0.283625	+	0.958935i	$0.591537\pi$
$728$		0			0
$729$	−20.3776	−	17.7131i	−0.754725	−	0.656041i
$730$	−0.165978	−	0.287482i	−0.00614311	−	0.0106402i
$731$	−13.2876			−0.491461
$732$	19.7423	+	2.36570i	0.729695	+	0.0874386i
$733$			23.4489i			0.866105i	0.901369	+	0.433053i	$0.142564\pi$
$733$			23.4489i			0.866105i	−0.901369	+	0.433053i	$0.857436\pi$
$734$	11.9989	−	20.7828i	0.442889	−	0.767107i
$735$		0			0
$736$	4.02706	+	6.97507i	0.148439	+	0.257104i
$737$	−12.5965	+	7.27257i	−0.463997	+	0.267889i
$738$	−1.16412	+	0.341157i	−0.0428518	+	0.0125582i
$739$	13.3662	−	23.1509i	0.491682	−	0.851618i	−0.508272	−	0.861197i	$-0.669716\pi$
$739$	13.3662	−	23.1509i	0.491682	−	0.851618i	0.999954	+	0.00957820i	$0.00304888\pi$
$740$	1.54117	−	2.66939i	0.0566547	−	0.0981288i
$741$	−2.83004	+	23.6173i	−0.103964	+	0.867605i
$742$		0			0
$743$	−11.0914	−	6.40360i	−0.406903	−	0.234925i	0.282555	−	0.959251i	$-0.408818\pi$
$743$	−11.0914	−	6.40360i	−0.406903	−	0.234925i	−0.689458	+	0.724326i	$0.742151\pi$
$744$	6.91457	−	2.95886i	0.253501	−	0.108477i
$745$			9.30395i			0.340870i
$746$	−10.2528	−	5.91948i	−0.375383	−	0.216727i
$747$	−1.36953	−	4.67320i	−0.0501085	−	0.170983i
$748$			7.81007i			0.285564i
$749$		0			0
$750$	11.8113	−	15.7695i	0.431289	−	0.575822i
$751$	−10.2483			−0.373967			−0.186984	−	0.982363i	$-0.559871\pi$
$751$	−10.2483			−0.373967			−0.186984	+	0.982363i	$0.559871\pi$
$752$	2.75915	+	4.77898i	0.100616	+	0.174272i
$753$	−1.68845	+	14.0905i	−0.0615307	+	0.513488i
$754$	1.89404	+	1.09352i	0.0689768	+	0.0398238i
$755$	−8.23452			−0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$	−11.3778	−	6.56897i	−0.413260	−	0.238596i
$759$	−5.67544	+	47.3629i	−0.206006	+	1.71916i
$760$	−1.54929	−	2.68345i	−0.0561987	−	0.0973390i
$761$	16.2999			0.590870			0.295435	−	0.955363i	$-0.404535\pi$
$761$	16.2999			0.590870			0.295435	+	0.955363i	$0.404535\pi$
$762$	5.99925	−	8.00971i	0.217330	−	0.290161i
$763$		0			0
$764$		−	7.36938i		−	0.266615i
$765$	−6.76468	+	7.08719i	−0.244577	+	0.256238i
$766$	15.2005	+	8.77603i	0.549217	+	0.317091i
$767$			69.8962i			2.52380i
$768$	−1.59238	+	0.681407i	−0.0574602	+	0.0245882i
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.999968	−	0.00793771i	$-0.00252668\pi$
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.493110	+	0.869967i	$0.335860\pi$
$770$		0			0
$771$	1.36720	−	11.4096i	0.0492384	−	0.410906i
$772$	−1.41279	+	2.44703i	−0.0508476	+	0.0880706i
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	−0.956306	−	0.292367i	$-0.905557\pi$
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	0.731350	+	0.682002i	$0.238890\pi$
$774$	4.12353	−	16.9589i	0.148217	−	0.609574i
$775$	−11.1143	+	6.41686i	−0.399239	+	0.230501i
$776$	−5.30423	−	9.18719i	−0.190411	−	0.329801i
$777$		0			0
$778$	10.9205	−	18.9148i	0.391518	−	0.678130i
$779$		−	0.876275i		−	0.0313958i
$780$	15.5829	+	1.86729i	0.557959	+	0.0668596i
$781$	12.1525			0.434849
$782$	9.19786	+	15.9312i	0.328915	+	0.569697i
$783$	−0.295996	−	1.76867i	−0.0105780	−	0.0632073i
$784$		0			0
$785$	9.86123	−	5.69338i	0.351962	−	0.203206i
$786$	−4.62754	+	6.17831i	−0.165059	+	0.220373i
$787$	−0.226048	+	0.130509i	−0.00805773	+	0.00465213i	−0.504023	−	0.863690i	$-0.668147\pi$
$787$	−0.226048	+	0.130509i	−0.00805773	+	0.00465213i	0.495966	+	0.868342i	$0.334814\pi$
$788$	22.5931	−	13.0441i	0.804846	−	0.464678i
$789$	−10.3974	−	1.24591i	−0.370158	−	0.0443556i
$790$	18.0319	−	10.4107i	0.641548	−	0.370398i
$791$		0			0
$792$	−9.96791	−	2.42369i	−0.354194	−	0.0861221i
$793$	−36.3744	−	63.0024i	−1.29169	−	2.23728i
$794$	−38.9869			−1.38359
$795$	14.6802	−	19.5998i	0.520652	−	0.695132i
$796$		−	15.4165i		−	0.546424i
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	−0.831355	−	0.555741i	$-0.812435\pi$
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	0.896964	+	0.442104i	$0.145768\pi$
$798$		0			0
$799$	6.30194	+	10.9153i	0.222946	+	0.386155i
$800$	2.55956	−	1.47776i	0.0904942	−	0.0522468i
$801$	3.42498	+	11.6869i	0.121016	+	0.412937i
$802$	11.5989	−	20.0899i	0.409573	−	0.709400i
$803$	0.396931	−	0.687504i	0.0140074	−	0.0242615i
$804$	−5.89688	−	4.41674i	−0.207967	−	0.155767i
$805$		0			0
$806$	−23.8310	−	13.7588i	−0.839411	−	0.484634i
$807$	−9.45654	−	7.08292i	−0.332886	−	0.249331i
$808$			8.04886i			0.283158i
$809$	−5.94276	−	3.43105i	−0.208936	−	0.120629i	0.391881	−	0.920016i	$-0.371825\pi$
$809$	−5.94276	−	3.43105i	−0.208936	−	0.120629i	−0.600817	+	0.799387i	$0.705158\pi$
$810$	−6.94603	−	10.8330i	−0.244059	−	0.380634i
$811$			23.1945i			0.814470i	0.913323	+	0.407235i	$0.133507\pi$
$811$			23.1945i			0.814470i	−0.913323	+	0.407235i	$0.866493\pi$
$812$		0			0
$813$	−3.46029	−	8.08635i	−0.121358	−	0.283601i
$814$	7.37134			0.258365
$815$	−8.13951	−	14.0980i	−0.285114	−	0.493833i
$816$	−3.63703	+	1.55635i	−0.127321	+	0.0544830i
$817$	10.9182	+	6.30363i	0.381980	+	0.220536i
$818$	24.6187			0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$	−3.28550	−	1.89688i	−0.114665	−	0.0662017i	0.441571	−	0.897226i	$-0.354421\pi$
$821$	−3.28550	−	1.89688i	−0.114665	−	0.0662017i	−0.556236	+	0.831025i	$0.687755\pi$
$822$	−13.3871	−	10.0269i	−0.466930	−	0.349729i
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	0.966196	−	0.257810i	$-0.0830007\pi$
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	−0.706368	+	0.707845i	$0.749667\pi$
$824$	2.81391			0.0980272
$825$	17.3802	+	2.08265i	0.605102	+	0.0725087i
$826$		0			0
$827$			21.9819i			0.764384i	0.924083	+	0.382192i	$0.124831\pi$
$827$			21.9819i			0.764384i	−0.924083	+	0.382192i	$0.875169\pi$
$828$	−23.1871	+	6.79524i	−0.805809	+	0.236151i
$829$	−12.2406	−	7.06713i	−0.425135	−	0.245452i	0.272137	−	0.962259i	$-0.412270\pi$
$829$	−12.2406	−	7.06713i	−0.425135	−	0.245452i	−0.697272	+	0.716807i	$0.745603\pi$
$830$		−	2.32100i		−	0.0805631i
$831$	−0.407851	+	3.40361i	−0.0141482	+	0.118070i
$832$	5.48813	+	3.16857i	0.190267	+	0.109851i
$833$		0			0
$834$	29.5446	−	12.6426i	1.02305	−	0.437779i
$835$	8.09893	−	14.0278i	0.280275	−	0.485451i
$836$	3.70508	−	6.41739i	0.128143	−	0.221950i
$837$	3.72425	+	22.2537i	0.128729	+	0.769199i
$838$	14.7916	−	8.53996i	0.510969	−	0.295008i
$839$	8.92488	+	15.4583i	0.308121	+	0.533681i	0.977951	−	0.208833i	$-0.0669665\pi$
$839$	8.92488	+	15.4583i	0.308121	+	0.533681i	−0.669830	+	0.742514i	$0.733633\pi$
$840$		0			0
$841$	−14.4404	+	25.0116i	−0.497946	+	0.862469i
$842$		−	14.7130i		−	0.507045i
$843$	12.0150	+	28.0779i	0.413819	+	0.967054i
$844$	8.84930			0.304605
$845$	−19.4170	−	33.6312i	−0.667964	−	1.15695i
$846$	−15.8867	+	4.65577i	−0.546197	+	0.160069i
$847$		0			0
$848$	8.56310	−	4.94391i	0.294058	−	0.169775i
$849$	3.51187	+	8.20691i	0.120527	+	0.281660i
$850$	5.84608	−	3.37524i	0.200519	−	0.115770i
$851$	15.0362	−	8.68118i	0.515436	−	0.297587i
$852$	2.42167	+	5.65921i	0.0829651	+	0.193881i
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.244559	−	0.969634i	$-0.421357\pi$
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.962008	+	0.273022i	$0.0880233\pi$
$854$		0			0
$855$	8.92057	−	2.61427i	0.305077	−	0.0894060i
$856$	7.91078	+	13.7019i	0.270385	+	0.468320i
$857$	−5.45792			−0.186439			−0.0932194	−	0.995646i	$-0.529716\pi$
$857$	−5.45792			−0.186439			−0.0932194	+	0.995646i	$0.529716\pi$
$858$	14.7658	+	34.5062i	0.504095	+	1.17802i
$859$			44.8973i			1.53188i	0.642914	+	0.765938i	$0.277725\pi$
$859$			44.8973i			1.53188i	−0.642914	+	0.765938i	$0.722275\pi$
$860$	4.15919	−	7.20393i	0.141827	−	0.245652i
$861$		0			0
$862$	4.80521	+	8.32286i	0.163666	+	0.283478i
$863$	−19.6689	+	11.3559i	−0.669539	+	0.386558i	−0.795902	−	0.605426i	$-0.793003\pi$
$863$	−19.6689	+	11.3559i	−0.669539	+	0.386558i	0.126363	+	0.991984i	$0.459670\pi$
$864$	−0.857672	−	5.12488i	−0.0291786	−	0.174352i
$865$	−15.5077	+	26.8602i	−0.527279	+	0.913274i
$866$	4.52157	−	7.83159i	0.153649	−	0.266128i
$867$	18.7635	−	8.02921i	0.637241	−	0.272686i
$868$		0			0
$869$	43.1229	+	24.8970i	1.46284	+	0.844573i
$870$	0.101691	−	0.848632i	0.00344764	−	0.0287713i
$871$			26.9560i			0.913371i
$872$	8.84514	+	5.10675i	0.299534	+	0.172936i
$873$	30.5409	−	8.95033i	1.03365	−	0.302923i
$874$		−	17.4538i		−	0.590384i
$875$		0			0
$876$	0.399258	+	0.0478427i	0.0134897	+	0.00161645i
$877$	−30.4891			−1.02954			−0.514771	−	0.857327i	$-0.672123\pi$
$877$	−30.4891			−1.02954			−0.514771	+	0.857327i	$0.672123\pi$
$878$	−0.456897	−	0.791370i	−0.0154195	−	0.0267074i
$879$	−2.86268	−	2.14414i	−0.0965557	−	0.0723200i
$880$	−4.23425	−	2.44465i	−0.142737	−	0.0824091i
$881$	29.3810			0.989871			0.494935	−	0.868930i	$-0.335192\pi$
$881$	29.3810			0.989871			0.494935	+	0.868930i	$0.335192\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$	12.5350	+	7.23707i	0.421597	+	0.243409i
$885$	25.1130	−	10.7463i	0.844163	−	0.361231i
$886$	−14.6808	−	25.4279i	−0.493212	−	0.854268i
$887$	32.7073			1.09821			0.549103	−	0.835755i	$-0.314970\pi$
$887$	32.7073			1.09821			0.549103	+	0.835755i	$0.314970\pi$
$888$	1.46892	+	3.43272i	0.0492937	+	0.115195i
$889$		0			0
$890$			5.80446i			0.194566i
$891$	14.1304	−	27.3392i	0.473387	−	0.915898i
$892$	−6.88961	−	3.97772i	−0.230681	−	0.133184i
$893$		−	11.9585i		−	0.400176i
$894$	−9.02062	−	6.75642i	−0.301695	−	0.225968i
$895$	−25.7454	−	14.8641i	−0.860575	−	0.496853i
$896$		0			0
$897$	70.7573	+	52.9970i	2.36252	+	1.76952i
$898$	1.68368	−	2.91622i	0.0561851	−	0.0973154i
$899$	−0.749293	+	1.29781i	−0.0249903	+	0.0432845i
$900$	2.49357	+	8.50872i	0.0831190	+	0.283624i
$901$	19.5583	−	11.2920i	0.651580	−	0.376190i
$902$	−0.691343	−	1.19744i	−0.0230192	−	0.0398704i
$903$		0			0
$904$	−4.20778	+	7.28808i	−0.139949	+	0.242398i
$905$			30.7848i			1.02332i
$906$	5.97981	−	7.98375i	0.198666	−	0.265242i
$907$	56.6934			1.88248			0.941238	−	0.337745i	$-0.109664\pi$
$907$	56.6934			1.88248			0.941238	+	0.337745i	$0.109664\pi$
$908$	−4.61984	−	8.00180i	−0.153315	−	0.265549i
$909$	−23.4630	−	5.70500i	−0.778218	−	0.189223i
$910$		0			0
$911$	0.621795	−	0.358994i	0.0206010	−	0.0118940i	−0.489664	−	0.871911i	$-0.662881\pi$
$911$	0.621795	−	0.358994i	0.0206010	−	0.0118940i	0.510265	+	0.860017i	$0.329547\pi$
$912$	3.72681	+	0.446579i	0.123407	+	0.0147877i
$913$	4.80697	−	2.77530i	0.159087	−	0.0918492i
$914$	13.0890	−	7.55693i	0.432945	−	0.249961i
$915$	−17.0437	+	22.7553i	−0.563446	+	0.752267i
$916$	7.31319	−	4.22227i	0.241635	−	0.139508i
$917$		0			0
$918$	−1.95894	−	11.7053i	−0.0646546	−	0.386333i
$919$	18.9720	+	32.8605i	0.625829	+	1.08397i	0.988380	+	0.152004i	$0.0485727\pi$
$919$	18.9720	+	32.8605i	0.625829	+	1.08397i	−0.362550	+	0.931964i	$0.618094\pi$
$920$	−11.5162			−0.379677
$921$	1.87656	+	0.224867i	0.0618349	+	0.00740961i
$922$			10.3889i			0.342140i
$923$	11.2609	−	19.5044i	0.370656	−	0.641996i
$924$		0			0
$925$	−3.18563	−	5.51768i	−0.104743	−	0.181420i
$926$	−4.60244	+	2.65722i	−0.151246	+	0.0873217i
$927$	−1.99449	+	8.20273i	−0.0655076	+	0.269413i
$928$	0.172558	−	0.298879i	0.00566448	−	0.00981117i
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	0.264057	+	0.964507i	$0.414939\pi$
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	−0.967316	+	0.253574i	$0.918394\pi$
$930$	−1.27948	+	10.6776i	−0.0419559	+	0.350132i
$931$		0			0
$932$	−14.4176	−	8.32399i	−0.472263	−	0.272661i
$933$	−24.2393	+	10.3724i	−0.793558	+	0.339577i
$934$			19.4999i			0.638055i
$935$	−9.67111	−	5.58362i	−0.316279	−	0.182604i
$936$	−13.1266	+	13.7524i	−0.429055	+	0.449511i
$937$		−	8.64637i		−	0.282464i	−0.989976	−	0.141232i	$-0.954894\pi$
$937$		−	8.64637i		−	0.282464i	0.989976	−	0.141232i	$-0.0451064\pi$
$938$		0			0
$939$	−12.0140	+	16.0401i	−0.392061	+	0.523448i
$940$	−7.89034			−0.257354
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	0.771980	−	0.635646i	$-0.219266\pi$
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	−0.936476	+	0.350731i	$0.885933\pi$
$942$	−1.64110	+	13.6954i	−0.0534701	+	0.446220i
$943$	−2.82044	−	1.62838i	−0.0918460	−	0.0530273i
$944$	11.0296			0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$	50.4627	+	29.1346i	1.63982	+	0.946749i	0.980895	+	0.194537i	$0.0623205\pi$
$947$	50.4627	+	29.1346i	1.63982	+	0.946749i	0.658922	+	0.752212i	$0.271013\pi$
$948$	−3.00087	+	25.0430i	−0.0974638	+	0.813358i
$949$	−0.735619	−	1.27413i	−0.0238792	−	0.0413600i
$950$	−6.40483			−0.207800
$951$	17.8183	−	23.7896i	0.577799	−	0.771430i
$952$		0			0
$953$		−	46.9356i		−	1.52039i	−0.649694	−	0.760196i	$-0.725103\pi$
$953$		−	46.9356i		−	1.52039i	0.649694	−	0.760196i	$-0.274897\pi$
$954$	8.34233	+	28.4662i	0.270093	+	0.921628i
$955$	9.12541	+	5.26856i	0.295291	+	0.170487i
$956$		−	27.2885i		−	0.882572i
$957$	1.87918	−	0.804131i	0.0607451	−	0.0259939i
$958$	24.0776	+	13.9012i	0.777912	+	0.449128i
$959$		0			0
$960$	0.294657	−	2.45898i	0.00951002	−	0.0793633i
$961$	−6.07230	+	10.5175i	−0.195881	+	0.339275i
$962$	6.83054	−	11.8308i	0.220225	−	0.381441i
$963$	−45.5490	+	13.3486i	−1.46780	+	0.430153i
$964$	−21.9018	+	12.6450i	−0.705410	+	0.407269i
$965$	−2.02008	−	3.49889i	−0.0650288	−	0.112633i
$966$		0			0
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	−0.743890	−	0.668302i	$-0.767021\pi$
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	0.950712	+	0.310077i	$0.100355\pi$
$968$		−	0.692610i		−	0.0222613i
$969$	8.51209	+	1.01999i	0.273448	+	0.0327670i
$970$	15.1685			0.487031
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	0.997699	+	0.0677990i	$0.0215977\pi$
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	−0.440134	+	0.897932i	$0.645069\pi$
$972$	15.5473	+	1.13232i	0.498679	+	0.0363193i
$973$		0			0
$974$	6.47506	−	3.73838i	0.207474	−	0.119785i
$975$	19.4477	−	25.9650i	0.622826	−	0.831546i
$976$	−9.94175	+	5.73987i	−0.318228	+	0.183729i
$977$	−17.6381	+	10.1834i	−0.564293	+	0.325795i	−0.754867	−	0.655878i	$-0.772299\pi$
$977$	−17.6381	+	10.1834i	−0.564293	+	0.325795i	0.190574	+	0.981673i	$0.438965\pi$
$978$	19.5795	+	2.34619i	0.626084	+	0.0750230i
$979$	−12.0215	+	6.94060i	−0.384208	+	0.221822i
$980$		0			0
$981$	−21.1559	+	22.1645i	−0.675456	+	0.707659i
$982$	11.0543	+	19.1466i	0.352756	+	0.610992i
$983$	29.3364			0.935686			0.467843	−	0.883811i	$-0.345031\pi$
$983$	29.3364			0.935686			0.467843	+	0.883811i	$0.345031\pi$
$984$	0.419863	−	0.560567i	0.0133847	−	0.0178702i
$985$			37.3023i			1.18855i
$986$	0.394124	−	0.682643i	0.0125515	−	0.0217398i
$987$		0			0
$988$	−6.86651	−	11.8931i	−0.218453	−	0.378371i
$989$	40.5786	−	23.4280i	1.29032	−	0.744968i
$990$	10.1275	−	10.6104i	0.321874	−	0.337220i
$991$	−14.8114	+	25.6540i	−0.470498	+	0.814927i	−0.999431	−	0.0337371i	$-0.989259\pi$
$991$	−14.8114	+	25.6540i	−0.470498	+	0.814927i	0.528933	+	0.848664i	$0.322592\pi$
$992$	−2.17114	+	3.76052i	−0.0689338	+	0.119397i
$993$	−36.7276	−	27.5089i	−1.16551	−	0.872967i
$994$		0			0
$995$	19.0901	+	11.0217i	0.605196	+	0.349410i
$996$	2.25032	+	1.68548i	0.0713041	+	0.0534066i
$997$		−	27.0213i		−	0.855772i	−0.903833	−	0.427886i	$-0.859258\pi$
$997$		−	27.0213i		−	0.855772i	0.903833	−	0.427886i	$-0.140742\pi$
$998$	28.4959	+	16.4521i	0.902022	+	0.520783i
$999$	−11.0478	+	1.84890i	−0.349536	+	0.0584965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.t.a.815.7		16
3.2	odd	2		2646.2.t.b.2285.3		16
7.2	even	3		126.2.l.a.5.3	✓	16
7.3	odd	6		882.2.m.a.293.4		16
7.4	even	3		882.2.m.b.293.1		16
7.5	odd	6		882.2.l.b.509.2		16
7.6	odd	2		126.2.t.a.59.6	yes	16
9.2	odd	6		882.2.l.b.227.6		16
9.7	even	3		2646.2.l.a.521.3		16
21.2	odd	6		378.2.l.a.341.6		16
21.5	even	6		2646.2.l.a.1097.7		16
21.11	odd	6		2646.2.m.b.881.6		16
21.17	even	6		2646.2.m.a.881.7		16
21.20	even	2		378.2.t.a.17.2		16
28.23	odd	6		1008.2.ca.c.257.3		16
28.27	even	2		1008.2.df.c.689.6		16
63.2	odd	6		126.2.t.a.47.6	yes	16
63.11	odd	6		882.2.m.a.587.4		16
63.13	odd	6		1134.2.k.b.647.2		16
63.16	even	3		378.2.t.a.89.2		16
63.20	even	6		126.2.l.a.101.7	yes	16
63.23	odd	6		1134.2.k.b.971.2		16
63.25	even	3		2646.2.m.a.1763.7		16
63.34	odd	6		378.2.l.a.143.2		16
63.38	even	6		882.2.m.b.587.1		16
63.41	even	6		1134.2.k.a.647.7		16
63.47	even	6	inner	882.2.t.a.803.7		16
63.52	odd	6		2646.2.m.b.1763.6		16
63.58	even	3		1134.2.k.a.971.7		16
63.61	odd	6		2646.2.t.b.1979.3		16
84.23	even	6		3024.2.ca.c.2609.3		16
84.83	odd	2		3024.2.df.c.17.3		16
252.79	odd	6		3024.2.df.c.1601.3		16
252.83	odd	6		1008.2.ca.c.353.3		16
252.191	even	6		1008.2.df.c.929.6		16
252.223	even	6		3024.2.ca.c.2033.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	7.2	even	3
126.2.l.a.101.7	yes	16	63.20	even	6
126.2.t.a.47.6	yes	16	63.2	odd	6
126.2.t.a.59.6	yes	16	7.6	odd	2
378.2.l.a.143.2		16	63.34	odd	6
378.2.l.a.341.6		16	21.2	odd	6
378.2.t.a.17.2		16	21.20	even	2
378.2.t.a.89.2		16	63.16	even	3
882.2.l.b.227.6		16	9.2	odd	6
882.2.l.b.509.2		16	7.5	odd	6
882.2.m.a.293.4		16	7.3	odd	6
882.2.m.a.587.4		16	63.11	odd	6
882.2.m.b.293.1		16	7.4	even	3
882.2.m.b.587.1		16	63.38	even	6
882.2.t.a.803.7		16	63.47	even	6	inner
882.2.t.a.815.7		16	1.1	even	1	trivial
1008.2.ca.c.257.3		16	28.23	odd	6
1008.2.ca.c.353.3		16	252.83	odd	6
1008.2.df.c.689.6		16	28.27	even	2
1008.2.df.c.929.6		16	252.191	even	6
1134.2.k.a.647.7		16	63.41	even	6
1134.2.k.a.971.7		16	63.58	even	3
1134.2.k.b.647.2		16	63.13	odd	6
1134.2.k.b.971.2		16	63.23	odd	6
2646.2.l.a.521.3		16	9.7	even	3
2646.2.l.a.1097.7		16	21.5	even	6
2646.2.m.a.881.7		16	21.17	even	6
2646.2.m.a.1763.7		16	63.25	even	3
2646.2.m.b.881.6		16	21.11	odd	6
2646.2.m.b.1763.6		16	63.52	odd	6
2646.2.t.b.1979.3		16	63.61	odd	6
2646.2.t.b.2285.3		16	3.2	odd	2
3024.2.ca.c.2033.3		16	252.223	even	6
3024.2.ca.c.2609.3		16	84.23	even	6
3024.2.df.c.17.3		16	84.83	odd	2
3024.2.df.c.1601.3		16	252.79	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.206076 - 1.71975i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(1.03834 - 1.38631i) q^{6} +1.00000i q^{8} +(-2.91507 - 0.708796i) q^{9} +(-1.23829 - 0.714925i) q^{10} -3.41945i q^{11} +(1.59238 - 0.681407i) q^{12} +(-5.48813 - 3.16857i) q^{13} +(-0.294657 + 2.45898i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-2.17012 - 2.07137i) q^{18} +(1.87673 - 1.08353i) q^{19} +(-0.714925 - 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} -8.05411i q^{23} +(1.71975 + 0.206076i) q^{24} -2.95553 q^{25} +(-3.16857 - 5.48813i) q^{26} +(-1.81967 + 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} +(-1.48467 + 1.98221i) q^{30} +(3.76052 - 2.17114i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.88058 - 0.704664i) q^{33} +(-1.97802 + 1.14201i) q^{34} +(-0.843698 - 2.87892i) q^{36} +(1.07786 + 1.86690i) q^{37} +2.16707 q^{38} +(-6.58012 + 8.78524i) q^{39} -1.42985i q^{40} +(0.202180 - 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(2.96133 - 1.70972i) q^{44} +(4.16811 + 1.01347i) q^{45} +(4.02706 - 6.97507i) q^{46} +(2.75915 - 4.77898i) q^{47} +(1.38631 + 1.03834i) q^{48} +(-2.55956 - 1.47776i) q^{50} +(3.16635 + 2.37159i) q^{51} -6.33715i q^{52} +(-8.56310 - 4.94391i) q^{53} +(-4.00944 + 3.30521i) q^{54} +4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} -0.345115 q^{58} +(-5.51480 - 9.55191i) q^{59} +(-2.27687 + 0.974311i) q^{60} +(9.94175 + 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(7.84721 + 4.53059i) q^{65} +(-4.74040 - 3.55055i) q^{66} +(-2.12683 - 3.68377i) q^{67} -2.28402 q^{68} +(-13.8510 - 1.65976i) q^{69} +3.55393i q^{71} +(0.708796 - 2.91507i) q^{72} +(0.201057 + 0.116080i) q^{73} +2.15571i q^{74} +(-0.609062 + 5.08276i) q^{75} +(1.87673 + 1.08353i) q^{76} +(-10.0912 + 4.31818i) q^{78} +(-7.28100 + 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(7.99522 + 4.13237i) q^{81} +(0.350186 - 0.202180i) q^{82} +(0.811624 + 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +5.81766i q^{86} +(0.235164 + 0.549556i) q^{87} +3.41945 q^{88} +(-2.02974 - 3.51562i) q^{89} +(3.10295 + 2.96175i) q^{90} +(6.97507 - 4.02706i) q^{92} +(-2.95886 - 6.91457i) q^{93} +(4.77898 - 2.75915i) q^{94} +(-2.68345 + 1.54929i) q^{95} +(0.681407 + 1.59238i) q^{96} +(-9.18719 + 5.30423i) q^{97} +(-2.42369 + 9.96791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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