LMFDB - Embedded newform 833.2.l.g.246.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(246,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("833.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.l (of order $8$, degree $4$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			246.3
Character	$\chi$	$=$	833.246
Dual form			833.2.l.g.491.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12386 + 1.12386i) q^{2} +(0.860453 - 2.07732i) q^{3} -0.526128i q^{4} +(2.47826 + 1.02653i) q^{5} +(1.36759 + 3.30165i) q^{6} +(-1.65643 - 1.65643i) q^{8} +(-1.45355 - 1.45355i) q^{9} +(-3.93890 + 1.63154i) q^{10} +(0.445138 + 1.07466i) q^{11} +(-1.09293 - 0.452708i) q^{12} +4.08176i q^{13} +(4.26485 - 4.26485i) q^{15} +4.77545 q^{16} +(4.10306 - 0.406033i) q^{17} +3.26718 q^{18} +(-4.40961 + 4.40961i) q^{19} +(0.540085 - 1.30388i) q^{20} +(-1.70804 - 0.707493i) q^{22} +(2.65538 + 6.41066i) q^{23} +(-4.86621 + 2.01565i) q^{24} +(1.55248 + 1.55248i) q^{25} +(-4.58733 - 4.58733i) q^{26} +(1.96175 - 0.812585i) q^{27} +(0.264539 + 0.109576i) q^{29} +9.58621i q^{30} +(0.241193 - 0.582292i) q^{31} +(-2.05408 + 2.05408i) q^{32} +2.61543 q^{33} +(-4.15495 + 5.06760i) q^{34} +(-0.764753 + 0.764753i) q^{36} +(4.22275 - 10.1946i) q^{37} -9.91158i q^{38} +(8.47912 + 3.51217i) q^{39} +(-2.40469 - 5.80543i) q^{40} +(-2.36854 + 0.981083i) q^{41} +(-0.0565224 - 0.0565224i) q^{43} +(0.565408 - 0.234199i) q^{44} +(-2.11016 - 5.09439i) q^{45} +(-10.1890 - 4.22041i) q^{46} +1.42190i q^{47} +(4.10905 - 9.92012i) q^{48} -3.48954 q^{50} +(2.68704 - 8.87274i) q^{51} +2.14753 q^{52} +(-1.16560 + 1.16560i) q^{53} +(-1.29151 + 3.11797i) q^{54} +3.12023i q^{55} +(5.36590 + 12.9544i) q^{57} +(-0.420453 + 0.174157i) q^{58} +(-4.41502 - 4.41502i) q^{59} +(-2.24386 - 2.24386i) q^{60} +(10.2340 - 4.23908i) q^{61} +(0.383348 + 0.925484i) q^{62} +4.93388i q^{64} +(-4.19005 + 10.1157i) q^{65} +(-2.93938 + 2.93938i) q^{66} +1.97520 q^{67} +(-0.213625 - 2.15874i) q^{68} +15.6018 q^{69} +(1.66870 - 4.02859i) q^{71} +4.81540i q^{72} +(13.7917 + 5.71269i) q^{73} +(6.71155 + 16.2031i) q^{74} +(4.56082 - 1.88915i) q^{75} +(2.32002 + 2.32002i) q^{76} +(-13.4765 + 5.58216i) q^{78} +(3.99744 + 9.65068i) q^{79} +(11.8348 + 4.90213i) q^{80} -10.9413i q^{81} +(1.55931 - 3.76452i) q^{82} +(-6.87240 + 6.87240i) q^{83} +(10.5853 + 3.20566i) q^{85} +0.127047 q^{86} +(0.455247 - 0.455247i) q^{87} +(1.04275 - 2.51743i) q^{88} +3.28777i q^{89} +(8.09692 + 3.35385i) q^{90} +(3.37283 - 1.39707i) q^{92} +(-1.00207 - 1.00207i) q^{93} +(-1.59802 - 1.59802i) q^{94} +(-15.4547 + 6.40157i) q^{95} +(2.49954 + 6.03442i) q^{96} +(-7.05111 - 2.92067i) q^{97} +(0.915039 - 2.20910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 16 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 28 q^{12} + 12 q^{15} - 8 q^{16} - 4 q^{17} + 24 q^{18} + 4 q^{19} - 24 q^{20} - 24 q^{22} - 8 q^{23} + 28 q^{24} + 8 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 - 16 * q^8 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 28 * q^12 + 12 * q^15 - 8 * q^16 - 4 * q^17 + 24 * q^18 + 4 * q^19 - 24 * q^20 - 24 * q^22 - 8 * q^23 + 28 * q^24 + 8 * q^25 - 36 * q^26 - 32 * q^27 - 8 * q^29 + 4 * q^31 - 48 * q^32 - 40 * q^33 - 8 * q^34 - 16 * q^36 + 36 * q^37 - 16 * q^39 - 28 * q^40 + 20 * q^41 + 8 * q^43 + 20 * q^44 - 8 * q^45 + 4 * q^46 + 28 * q^48 + 8 * q^50 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 24 * q^54 - 8 * q^57 - 28 * q^58 - 4 * q^59 - 76 * q^60 + 24 * q^61 + 44 * q^62 - 8 * q^65 - 12 * q^66 + 60 * q^68 + 96 * q^69 - 16 * q^71 + 24 * q^73 + 28 * q^74 + 108 * q^75 - 4 * q^76 + 80 * q^78 + 4 * q^79 + 44 * q^80 - 24 * q^82 - 44 * q^83 - 20 * q^85 - 64 * q^86 - 68 * q^87 - 104 * q^88 - 24 * q^90 - 40 * q^92 - 8 * q^93 - 44 * q^94 - 48 * q^95 + 12 * q^96 + 40 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.12386	+	1.12386i	−0.794690	+	0.794690i	−0.982253	−	0.187563i	$-0.939941\pi$
$2$	−1.12386	+	1.12386i	−0.794690	+	0.794690i	0.187563	+	0.982253i	$0.439941\pi$
$3$	0.860453	−	2.07732i	0.496783	−	1.19934i	−0.454424	−	0.890786i	$-0.650155\pi$
$3$	0.860453	−	2.07732i	0.496783	−	1.19934i	0.951207	−	0.308555i	$-0.0998452\pi$
$4$		−	0.526128i		−	0.263064i
$5$	2.47826	+	1.02653i	1.10831	+	0.459078i	0.860356	−	0.509694i	$-0.170241\pi$
$5$	2.47826	+	1.02653i	1.10831	+	0.459078i	0.247956	+	0.968771i	$0.420241\pi$
$6$	1.36759	+	3.30165i	0.558315	+	1.34789i
$7$		0			0
$7$		0			0
$8$	−1.65643	−	1.65643i	−0.585636	−	0.585636i
$9$	−1.45355	−	1.45355i	−0.484517	−	0.484517i
$10$	−3.93890	+	1.63154i	−1.24559	+	0.515940i
$11$	0.445138	+	1.07466i	0.134214	+	0.324022i	0.976671	−	0.214743i	$-0.0688913\pi$
$11$	0.445138	+	1.07466i	0.134214	+	0.324022i	−0.842456	+	0.538764i	$0.818891\pi$
$12$	−1.09293	−	0.452708i	−0.315503	−	0.130686i
$13$			4.08176i			1.13208i	0.824379	+	0.566039i	$0.191525\pi$
$13$			4.08176i			1.13208i	−0.824379	+	0.566039i	$0.808475\pi$
$14$		0			0
$15$	4.26485	−	4.26485i	1.10118	−	1.10118i
$16$	4.77545			1.19386
$17$	4.10306	−	0.406033i	0.995139	−	0.0984774i
$17$	4.10306	−	0.406033i	0.995139	−	0.0984774i
$18$	3.26718			0.770081
$19$	−4.40961	+	4.40961i	−1.01163	+	1.01163i	−0.0117021	+	0.999932i	$0.503725\pi$
$19$	−4.40961	+	4.40961i	−1.01163	+	1.01163i	−0.999932	+	0.0117021i	$0.996275\pi$
$20$	0.540085	−	1.30388i	0.120767	−	0.291557i
$21$		0			0
$22$	−1.70804	−	0.707493i	−0.364155	−	0.150838i
$23$	2.65538	+	6.41066i	0.553686	+	1.33672i	0.914692	+	0.404152i	$0.132433\pi$
$23$	2.65538	+	6.41066i	0.553686	+	1.33672i	−0.361006	+	0.932563i	$0.617567\pi$
$24$	−4.86621	+	2.01565i	−0.993310	+	0.411443i
$25$	1.55248	+	1.55248i	0.310495	+	0.310495i
$26$	−4.58733	−	4.58733i	−0.899650	−	0.899650i
$27$	1.96175	−	0.812585i	0.377540	−	0.156382i
$28$		0			0
$29$	0.264539	+	0.109576i	0.0491237	+	0.0203477i	0.407110	−	0.913379i	$-0.366537\pi$
$29$	0.264539	+	0.109576i	0.0491237	+	0.0203477i	−0.357986	+	0.933727i	$0.616537\pi$
$30$			9.58621i			1.75019i
$31$	0.241193	−	0.582292i	0.0433196	−	0.104583i	−0.900739	−	0.434361i	$-0.856974\pi$
$31$	0.241193	−	0.582292i	0.0433196	−	0.104583i	0.944058	+	0.329779i	$0.106974\pi$
$32$	−2.05408	+	2.05408i	−0.363114	+	0.363114i
$33$	2.61543			0.455287
$34$	−4.15495	+	5.06760i	−0.712568	+	0.869086i
$35$		0			0
$36$	−0.764753	+	0.764753i	−0.127459	+	0.127459i
$37$	4.22275	−	10.1946i	0.694215	−	1.67598i	−0.0418954	−	0.999122i	$-0.513340\pi$
$37$	4.22275	−	10.1946i	0.694215	−	1.67598i	0.736110	−	0.676861i	$-0.236660\pi$
$38$		−	9.91158i		−	1.60787i
$39$	8.47912	+	3.51217i	1.35775	+	0.562397i
$40$	−2.40469	−	5.80543i	−0.380214	−	0.917919i
$41$	−2.36854	+	0.981083i	−0.369904	+	0.153219i	−0.559889	−	0.828568i	$-0.689156\pi$
$41$	−2.36854	+	0.981083i	−0.369904	+	0.153219i	0.189985	+	0.981787i	$0.439156\pi$
$42$		0			0
$43$	−0.0565224	−	0.0565224i	−0.00861959	−	0.00861959i	0.702784	−	0.711403i	$-0.251940\pi$
$43$	−0.0565224	−	0.0565224i	−0.00861959	−	0.00861959i	−0.711403	+	0.702784i	$0.751940\pi$
$44$	0.565408	−	0.234199i	0.0852384	−	0.0353069i
$45$	−2.11016	−	5.09439i	−0.314565	−	0.759427i
$46$	−10.1890	−	4.22041i	−1.50228	−	0.622266i
$47$			1.42190i			0.207406i	0.994608	+	0.103703i	$0.0330692\pi$
$47$			1.42190i			0.207406i	−0.994608	+	0.103703i	$0.966931\pi$
$48$	4.10905	−	9.92012i	0.593090	−	1.43185i
$49$		0			0
$50$	−3.48954			−0.493495
$51$	2.68704	−	8.87274i	0.376260	−	1.24243i
$52$	2.14753			0.297809
$53$	−1.16560	+	1.16560i	−0.160107	+	0.160107i	−0.782614	−	0.622507i	$-0.786114\pi$
$53$	−1.16560	+	1.16560i	−0.160107	+	0.160107i	0.622507	+	0.782614i	$0.286114\pi$
$54$	−1.29151	+	3.11797i	−0.175752	+	0.424302i
$55$			3.12023i			0.420732i
$56$		0			0
$57$	5.36590	+	12.9544i	0.710731	+	1.71586i
$58$	−0.420453	+	0.174157i	−0.0552082	+	0.0228680i
$59$	−4.41502	−	4.41502i	−0.574787	−	0.574787i	0.358676	−	0.933462i	$-0.383228\pi$
$59$	−4.41502	−	4.41502i	−0.574787	−	0.574787i	−0.933462	+	0.358676i	$0.883228\pi$
$60$	−2.24386	−	2.24386i	−0.289681	−	0.289681i
$61$	10.2340	−	4.23908i	1.31033	−	0.542758i	0.385352	−	0.922769i	$-0.374080\pi$
$61$	10.2340	−	4.23908i	1.31033	−	0.542758i	0.924982	+	0.380011i	$0.124080\pi$
$62$	0.383348	+	0.925484i	0.0486852	+	0.117537i
$63$		0			0
$64$			4.93388i			0.616736i
$65$	−4.19005	+	10.1157i	−0.519711	+	1.25469i
$66$	−2.93938	+	2.93938i	−0.361812	+	0.361812i
$67$	1.97520			0.241309			0.120655	−	0.992695i	$-0.461501\pi$
$67$	1.97520			0.241309			0.120655	+	0.992695i	$0.461501\pi$
$68$	−0.213625	−	2.15874i	−0.0259059	−	0.261785i
$69$	15.6018			1.87824
$70$		0			0
$71$	1.66870	−	4.02859i	0.198038	−	0.478106i	−0.793397	−	0.608704i	$-0.791690\pi$
$71$	1.66870	−	4.02859i	0.198038	−	0.478106i	0.991435	+	0.130598i	$0.0416897\pi$
$72$			4.81540i			0.567501i
$73$	13.7917	+	5.71269i	1.61419	+	0.668620i	0.993331	−	0.115301i	$-0.0367834\pi$
$73$	13.7917	+	5.71269i	1.61419	+	0.668620i	0.620860	+	0.783921i	$0.286783\pi$
$74$	6.71155	+	16.2031i	0.780201	+	1.88357i
$75$	4.56082	−	1.88915i	0.526638	−	0.218141i
$76$	2.32002	+	2.32002i	0.266124	+	0.266124i
$77$		0			0
$78$	−13.4765	+	5.58216i	−1.52592	+	0.632056i
$79$	3.99744	+	9.65068i	0.449747	+	1.08579i	0.972417	+	0.233251i	$0.0749363\pi$
$79$	3.99744	+	9.65068i	0.449747	+	1.08579i	−0.522669	+	0.852536i	$0.675064\pi$
$80$	11.8348	+	4.90213i	1.32317	+	0.548075i
$81$		−	10.9413i		−	1.21570i
$82$	1.55931	−	3.76452i	0.172197	−	0.415721i
$83$	−6.87240	+	6.87240i	−0.754344	+	0.754344i	−0.975287	−	0.220943i	$-0.929087\pi$
$83$	−6.87240	+	6.87240i	−0.754344	+	0.754344i	0.220943	+	0.975287i	$0.429087\pi$
$84$		0			0
$85$	10.5853	+	3.20566i	1.14813	+	0.347703i
$86$	0.127047			0.0136998
$87$	0.455247	−	0.455247i	0.0488076	−	0.0488076i
$88$	1.04275	−	2.51743i	0.111158	−	0.268359i
$89$			3.28777i			0.348503i	0.984701	+	0.174251i	$0.0557505\pi$
$89$			3.28777i			0.348503i	−0.984701	+	0.174251i	$0.944250\pi$
$90$	8.09692	+	3.35385i	0.853490	+	0.353527i
$91$		0			0
$92$	3.37283	−	1.39707i	0.351642	−	0.145655i
$93$	−1.00207	−	1.00207i	−0.103910	−	0.103910i
$94$	−1.59802	−	1.59802i	−0.164823	−	0.164823i
$95$	−15.4547	+	6.40157i	−1.58562	+	0.656787i
$96$	2.49954	+	6.03442i	0.255108	+	0.615886i
$97$	−7.05111	−	2.92067i	−0.715932	−	0.296549i	−0.00517512	−	0.999987i	$-0.501647\pi$
$97$	−7.05111	−	2.92067i	−0.715932	−	0.296549i	−0.710757	+	0.703438i	$0.751647\pi$
$98$		0			0
$99$	0.915039	−	2.20910i	0.0919649	−	0.222023i
$100$	0.816801	−	0.816801i	0.0816801	−	0.0816801i
$101$	−13.0304			−1.29657			−0.648287	−	0.761396i	$-0.724514\pi$
$101$	−13.0304			−1.29657			−0.648287	+	0.761396i	$0.724514\pi$
$102$	6.95188	+	12.9916i	0.688338	+	1.28636i
$103$	−8.62782			−0.850125			−0.425062	−	0.905164i	$-0.639748\pi$
$103$	−8.62782			−0.850125			−0.425062	+	0.905164i	$0.639748\pi$
$104$	6.76114	−	6.76114i	0.662985	−	0.662985i
$105$		0			0
$106$		−	2.61994i		−	0.254471i
$107$	2.55720	+	1.05923i	0.247214	+	0.102400i	0.502850	−	0.864374i	$-0.332285\pi$
$107$	2.55720	+	1.05923i	0.247214	+	0.102400i	−0.255636	+	0.966773i	$0.582285\pi$
$108$	−0.427524	−	1.03213i	−0.0411385	−	0.0993171i
$109$	14.9539	−	6.19410i	1.43232	−	0.593288i	0.474399	−	0.880310i	$-0.342665\pi$
$109$	14.9539	−	6.19410i	1.43232	−	0.593288i	0.957924	+	0.287022i	$0.0926654\pi$
$110$	−3.50670	−	3.50670i	−0.334351	−	0.334351i
$111$	−17.5440	−	17.5440i	−1.66520	−	1.66520i
$112$		0			0
$113$	1.06517	+	2.57154i	0.100203	+	0.241911i	0.966029	−	0.258434i	$-0.0832066\pi$
$113$	1.06517	+	2.57154i	0.100203	+	0.241911i	−0.865826	+	0.500345i	$0.833207\pi$
$114$	−20.5895	−	8.52845i	−1.92838	−	0.798762i
$115$			18.6131i			1.73568i
$116$	0.0576508	−	0.139181i	0.00535274	−	0.0129227i
$117$	5.93305	−	5.93305i	0.548510	−	0.548510i
$118$	9.92374			0.913554
$119$		0			0
$120$	−14.1288			−1.28978
$121$	6.82143	−	6.82143i	0.620130	−	0.620130i
$122$	−6.73750	+	16.2658i	−0.609985	+	1.47263i
$123$			5.76440i			0.519758i
$124$	−0.306360	−	0.126899i	−0.0275120	−	0.0113958i
$125$	−2.87887	−	6.95020i	−0.257494	−	0.621644i
$126$		0			0
$127$	−6.71452	−	6.71452i	−0.595817	−	0.595817i	0.343380	−	0.939197i	$-0.388428\pi$
$127$	−6.71452	−	6.71452i	−0.595817	−	0.595817i	−0.939197	+	0.343380i	$0.888428\pi$
$128$	−9.65317	−	9.65317i	−0.853227	−	0.853227i
$129$	−0.166050	+	0.0687802i	−0.0146199	+	0.00605576i
$130$	−6.65957	−	16.0776i	−0.584083	−	1.41010i
$131$	−5.46306	−	2.26287i	−0.477310	−	0.197708i	0.131040	−	0.991377i	$-0.458168\pi$
$131$	−5.46306	−	2.26287i	−0.477310	−	0.197708i	−0.608350	+	0.793669i	$0.708168\pi$
$132$		−	1.37605i		−	0.119770i
$133$		0			0
$134$	−2.21985	+	2.21985i	−0.191766	+	0.191766i
$135$	5.69588			0.490223
$136$	−7.46899	−	6.12387i	−0.640461	−	0.525117i
$137$	−4.29533			−0.366975			−0.183488	−	0.983022i	$-0.558739\pi$
$137$	−4.29533			−0.366975			−0.183488	+	0.983022i	$0.558739\pi$
$138$	−17.5343	+	17.5343i	−1.49262	+	1.49262i
$139$	−0.986651	+	2.38199i	−0.0836866	+	0.202037i	−0.960183	−	0.279370i	$-0.909874\pi$
$139$	−0.986651	+	2.38199i	−0.0836866	+	0.202037i	0.876497	+	0.481408i	$0.159874\pi$
$140$		0			0
$141$	2.95375	+	1.22348i	0.248750	+	0.103036i
$142$	2.65219	+	6.40296i	0.222567	+	0.537325i
$143$	−4.38650	+	1.81695i	−0.366817	+	0.151941i
$144$	−6.94135	−	6.94135i	−0.578446	−	0.578446i
$145$	0.543114	+	0.543114i	0.0451032	+	0.0451032i
$146$	−21.9202	+	9.07963i	−1.81413	+	0.751436i
$147$		0			0
$148$	−5.36367	−	2.22170i	−0.440891	−	0.182623i
$149$			9.03047i			0.739805i	0.929071	+	0.369902i	$0.120609\pi$
$149$			9.03047i			0.739805i	−0.929071	+	0.369902i	$0.879391\pi$
$150$	−3.00258	+	7.24888i	−0.245160	+	0.591868i
$151$	7.82609	−	7.82609i	0.636878	−	0.636878i	−0.312906	−	0.949784i	$-0.601303\pi$
$151$	7.82609	−	7.82609i	0.636878	−	0.636878i	0.949784	+	0.312906i	$0.101303\pi$
$152$	14.6084			1.18490
$153$	−6.55420	−	5.37382i	−0.529876	−	0.434448i
$154$		0			0
$155$	1.19548	−	1.19548i	0.0960233	−	0.0960233i
$156$	1.84785	−	4.46110i	0.147946	−	0.357174i
$157$			0.272715i			0.0217650i	0.999941	+	0.0108825i	$0.00346408\pi$
$157$			0.272715i			0.0217650i	−0.999941	+	0.0108825i	$0.996536\pi$
$158$	−15.3386	−	6.35345i	−1.22027	−	0.505454i
$159$	1.41837	+	3.42426i	0.112484	+	0.271561i
$160$	−7.19912	+	2.98197i	−0.569141	+	0.235746i
$161$		0			0
$162$	12.2965	+	12.2965i	0.966102	+	0.966102i
$163$	−5.58967	+	2.31532i	−0.437817	+	0.181350i	−0.590694	−	0.806895i	$-0.701146\pi$
$163$	−5.58967	+	2.31532i	−0.437817	+	0.181350i	0.152877	+	0.988245i	$0.451146\pi$
$164$	0.516175	+	1.24616i	0.0403065	+	0.0973085i
$165$	6.48171	+	2.68481i	0.504600	+	0.209012i
$166$		−	15.4472i		−	1.19894i
$167$	−6.33480	+	15.2936i	−0.490202	+	1.18345i	0.464416	+	0.885617i	$0.346264\pi$
$167$	−6.33480	+	15.2936i	−0.490202	+	1.18345i	−0.954618	+	0.297834i	$0.903736\pi$
$168$		0			0
$169$	−3.66078			−0.281598
$170$	−15.4991	+	8.29365i	−1.18873	+	0.636094i
$171$	12.8192			0.980307
$172$	−0.0297380	+	0.0297380i	−0.00226750	+	0.00226750i
$173$	−7.26359	+	17.5358i	−0.552240	+	1.33323i	0.363552	+	0.931574i	$0.381564\pi$
$173$	−7.26359	+	17.5358i	−0.552240	+	1.33323i	−0.915792	+	0.401652i	$0.868436\pi$
$174$			1.02327i			0.0775738i
$175$		0			0
$176$	2.12573	+	5.13197i	0.160233	+	0.386837i
$177$	−12.9703	+	5.37248i	−0.974909	+	0.403821i
$178$	−3.69499	−	3.69499i	−0.276951	−	0.276951i
$179$	−15.4829	−	15.4829i	−1.15725	−	1.15725i	−0.985065	−	0.172184i	$-0.944918\pi$
$179$	−15.4829	−	15.4829i	−1.15725	−	1.15725i	−0.172184	−	0.985065i	$-0.555082\pi$
$180$	−2.68030	+	1.11022i	−0.199778	+	0.0827506i
$181$	−5.70974	−	13.7845i	−0.424401	−	1.02460i	−0.981034	−	0.193837i	$-0.937907\pi$
$181$	−5.70974	−	13.7845i	−0.424401	−	1.02460i	0.556632	−	0.830759i	$-0.312093\pi$
$182$		0			0
$183$		−	24.9069i		−	1.84117i
$184$	6.22035	−	15.0173i	0.458570	−	1.10709i
$185$	20.9301	−	20.9301i	1.53881	−	1.53881i
$186$	2.25238			0.165152
$187$	2.26278	+	4.22865i	0.165471	+	0.309230i
$188$	0.748103			0.0545610
$189$		0			0
$190$	10.1745	−	24.5635i	0.738137	−	1.78202i
$191$		−	22.6174i		−	1.63654i	−0.574837	−	0.818268i	$-0.694935\pi$
$191$		−	22.6174i		−	1.63654i	0.574837	−	0.818268i	$-0.305065\pi$
$192$	10.2492	+	4.24538i	0.739676	+	0.306384i
$193$	−4.66877	−	11.2714i	−0.336066	−	0.811335i	−0.998086	−	0.0618482i	$-0.980301\pi$
$193$	−4.66877	−	11.2714i	−0.336066	−	0.811335i	0.662020	−	0.749486i	$-0.269699\pi$
$194$	11.2069	−	4.64205i	0.804608	−	0.333280i
$195$	17.4081	+	17.4081i	1.24662	+	1.24662i
$196$		0			0
$197$	20.4484	−	8.47001i	1.45689	−	0.603463i	0.493062	−	0.869994i	$-0.335877\pi$
$197$	20.4484	−	8.47001i	1.45689	−	0.603463i	0.963826	+	0.266531i	$0.0858774\pi$
$198$	1.45435	+	3.51110i	0.103356	+	0.249523i
$199$	−11.6096	−	4.80885i	−0.822983	−	0.340891i	−0.0688618	−	0.997626i	$-0.521937\pi$
$199$	−11.6096	−	4.80885i	−0.822983	−	0.340891i	−0.754121	+	0.656736i	$0.771937\pi$
$200$		−	5.14313i		−	0.363674i
$201$	1.69957	−	4.10312i	0.119878	−	0.289412i
$202$	14.6444	−	14.6444i	1.03037	−	1.03037i
$203$		0			0
$204$	−4.66820	−	1.41372i	−0.326839	−	0.0989805i
$205$	−6.87698			−0.480309
$206$	9.69648	−	9.69648i	0.675586	−	0.675586i
$207$	5.45849	−	13.1780i	0.379391	−	0.915931i
$208$			19.4922i			1.35154i
$209$	−6.70171	−	2.77594i	−0.463567	−	0.192016i
$210$		0			0
$211$	18.0568	−	7.47936i	1.24308	−	0.514901i	0.338404	−	0.941001i	$-0.390113\pi$
$211$	18.0568	−	7.47936i	1.24308	−	0.514901i	0.904676	+	0.426100i	$0.140113\pi$
$212$	0.613253	+	0.613253i	0.0421184	+	0.0421184i
$213$	−6.93283	−	6.93283i	−0.475030	−	0.475030i
$214$	−4.06437	+	1.68352i	−0.277835	+	0.115083i
$215$	−0.0820554	−	0.198099i	−0.00559613	−	0.0135103i
$216$	−4.59549	−	1.90352i	−0.312684	−	0.129518i
$217$		0			0
$218$	−9.84478	+	23.7674i	−0.666773	+	1.60973i
$219$	23.7342	−	23.7342i	1.60381	−	1.60381i
$220$	1.64164			0.110679
$221$	1.65733	+	16.7477i	0.111484	+	1.12657i
$222$	39.4340			2.64664
$223$	4.69604	−	4.69604i	0.314470	−	0.314470i	−0.532168	−	0.846638i	$-0.678623\pi$
$223$	4.69604	−	4.69604i	0.314470	−	0.314470i	0.846638	+	0.532168i	$0.178623\pi$
$224$		0			0
$225$		−	4.51321i		−	0.300880i
$226$	−4.08716	−	1.69296i	−0.271874	−	0.112614i
$227$	0.589024	+	1.42203i	0.0390949	+	0.0943834i	0.942221	−	0.334992i	$-0.108734\pi$
$227$	0.589024	+	1.42203i	0.0390949	+	0.0943834i	−0.903126	+	0.429376i	$0.858734\pi$
$228$	6.81568	−	2.82315i	0.451380	−	0.186968i
$229$	−6.90063	−	6.90063i	−0.456006	−	0.456006i	0.441336	−	0.897342i	$-0.354505\pi$
$229$	−6.90063	−	6.90063i	−0.456006	−	0.456006i	−0.897342	+	0.441336i	$0.854505\pi$
$230$	−20.9186	−	20.9186i	−1.37933	−	1.37933i
$231$		0			0
$232$	−0.256686	−	0.619694i	−0.0168522	−	0.0406849i
$233$	−12.4570	−	5.15984i	−0.816082	−	0.338032i	−0.0647043	−	0.997904i	$-0.520610\pi$
$233$	−12.4570	−	5.15984i	−0.816082	−	0.338032i	−0.751378	+	0.659872i	$0.770610\pi$
$234$			13.3358i			0.871791i
$235$	−1.45963	+	3.52385i	−0.0952155	+	0.229871i
$236$	−2.32286	+	2.32286i	−0.151206	+	0.151206i
$237$	23.4871			1.52565
$238$		0			0
$239$	−29.8225			−1.92905			−0.964527	−	0.263984i	$-0.914963\pi$
$239$	−29.8225			−1.92905			−0.964527	+	0.263984i	$0.914963\pi$
$240$	20.3666	−	20.3666i	1.31466	−	1.31466i
$241$	−5.29971	+	12.7946i	−0.341384	+	0.824175i	0.656192	+	0.754594i	$0.272166\pi$
$241$	−5.29971	+	12.7946i	−0.341384	+	0.824175i	−0.997576	+	0.0695809i	$0.977834\pi$
$242$			15.3327i			0.985622i
$243$	−16.8432	−	6.97670i	−1.08049	−	0.447556i
$244$	−2.23030	−	5.38441i	−0.142780	−	0.344702i
$245$		0			0
$246$	−6.47838	−	6.47838i	−0.413046	−	0.413046i
$247$	−17.9990	−	17.9990i	−1.14525	−	1.14525i
$248$	−1.36404	+	0.565006i	−0.0866169	+	0.0358779i
$249$	8.36278	+	20.1895i	0.529970	+	1.27946i
$250$	11.0465	+	4.57561i	0.698642	+	0.289387i
$251$			19.9305i			1.25800i	0.777405	+	0.629000i	$0.216535\pi$
$251$			19.9305i			1.25800i	−0.777405	+	0.629000i	$0.783465\pi$
$252$		0			0
$253$	−5.70726	+	5.70726i	−0.358812	+	0.358812i
$254$	15.0924			0.946980
$255$	15.7673	−	19.2306i	0.987387	−	1.20427i
$256$	11.8299			0.739367
$257$	8.23547	−	8.23547i	0.513715	−	0.513715i	−0.401948	−	0.915663i	$-0.631667\pi$
$257$	8.23547	−	8.23547i	0.513715	−	0.513715i	0.915663	+	0.401948i	$0.131667\pi$
$258$	0.109318	−	0.263916i	0.00680583	−	0.0164307i
$259$		0			0
$260$	5.32213	+	2.20450i	0.330065	+	0.136717i
$261$	−0.225247	−	0.543795i	−0.0139425	−	0.0336601i
$262$	8.68287	−	3.59656i	0.536430	−	0.222196i
$263$	2.21073	+	2.21073i	0.136319	+	0.136319i	0.771974	−	0.635654i	$-0.219270\pi$
$263$	2.21073	+	2.21073i	0.136319	+	0.136319i	−0.635654	+	0.771974i	$0.719270\pi$
$264$	−4.33227	−	4.33227i	−0.266633	−	0.266633i
$265$	−4.08517	+	1.69213i	−0.250950	+	0.103947i
$266$		0			0
$267$	6.82974	+	2.82897i	0.417973	+	0.173130i
$268$		−	1.03921i		−	0.0634797i
$269$	7.23403	−	17.4645i	0.441067	−	1.06483i	−0.534509	−	0.845163i	$-0.679503\pi$
$269$	7.23403	−	17.4645i	0.441067	−	1.06483i	0.975575	−	0.219666i	$-0.0704967\pi$
$270$	−6.40138	+	6.40138i	−0.389576	+	0.389576i
$271$	−18.7320			−1.13789			−0.568944	−	0.822376i	$-0.692648\pi$
$271$	−18.7320			−1.13789			−0.568944	+	0.822376i	$0.692648\pi$
$272$	19.5940	−	1.93899i	1.18806	−	0.117568i
$273$		0			0
$274$	4.82736	−	4.82736i	0.291631	−	0.291631i
$275$	−0.977315	+	2.35945i	−0.0589343	+	0.142280i
$276$		−	8.20855i		−	0.494097i
$277$	−1.11159	−	0.460435i	−0.0667889	−	0.0276649i	0.349039	−	0.937108i	$-0.386508\pi$
$277$	−1.11159	−	0.460435i	−0.0667889	−	0.0276649i	−0.415828	+	0.909443i	$0.636508\pi$
$278$	−1.56816	−	3.78588i	−0.0940522	−	0.227062i
$279$	−1.19698	+	0.495805i	−0.0716612	+	0.0296831i
$280$		0			0
$281$	−18.8513	−	18.8513i	−1.12457	−	1.12457i	−0.991045	−	0.133528i	$-0.957370\pi$
$281$	−18.8513	−	18.8513i	−1.12457	−	1.12457i	−0.133528	−	0.991045i	$-0.542630\pi$
$282$	−4.69463	+	1.94458i	−0.279561	+	0.115798i
$283$	−3.08743	−	7.45372i	−0.183529	−	0.443078i	0.805160	−	0.593057i	$-0.202079\pi$
$283$	−3.08743	−	7.45372i	−0.183529	−	0.443078i	−0.988689	+	0.149980i	$0.952079\pi$
$284$	−2.11955	−	0.877948i	−0.125772	−	0.0520967i
$285$			37.6127i			2.22798i
$286$	2.88782	−	6.97181i	0.170760	−	0.412252i
$287$		0			0
$288$	5.97142			0.351870
$289$	16.6703	−	3.33196i	0.980604	−	0.195998i
$290$	−1.22077			−0.0716861
$291$	−12.1343	+	12.1343i	−0.711325	+	0.711325i
$292$	3.00560	−	7.25617i	0.175890	−	0.424635i
$293$			0.254207i			0.0148509i	0.999972	+	0.00742547i	$0.00236362\pi$
$293$			0.254207i			0.0148509i	−0.999972	+	0.00742547i	$0.997636\pi$
$294$		0			0
$295$	−6.40942	−	15.4737i	−0.373171	−	0.900914i
$296$	−23.8813	+	9.89196i	−1.38807	+	0.574959i
$297$	1.74650	+	1.74650i	0.101342	+	0.101342i
$298$	−10.1490	−	10.1490i	−0.587915	−	0.587915i
$299$	−26.1668	+	10.8386i	−1.51327	+	0.626815i
$300$	−0.993937	−	2.39958i	−0.0573850	−	0.138540i
$301$		0			0
$302$			17.5909i			1.01224i
$303$	−11.2121	+	27.0683i	−0.644116	+	1.55503i
$304$	−21.0578	+	21.0578i	−1.20775	+	1.20775i
$305$	29.7141			1.70143
$306$	13.4054	−	1.32658i	0.766338	−	0.0758356i
$307$	−6.63552			−0.378709			−0.189355	−	0.981909i	$-0.560640\pi$
$307$	−6.63552			−0.378709			−0.189355	+	0.981909i	$0.560640\pi$
$308$		0			0
$309$	−7.42384	+	17.9227i	−0.422328	+	1.01959i
$310$			2.68711i			0.152617i
$311$	5.75159	+	2.38239i	0.326143	+	0.135093i	0.539747	−	0.841828i	$-0.318520\pi$
$311$	5.75159	+	2.38239i	0.326143	+	0.135093i	−0.213604	+	0.976920i	$0.568520\pi$
$312$	−8.22740	−	19.8627i	−0.465785	−	1.12450i
$313$	−5.44850	+	2.25684i	−0.307967	+	0.127564i	−0.531314	−	0.847175i	$-0.678302\pi$
$313$	−5.44850	+	2.25684i	−0.307967	+	0.127564i	0.223347	+	0.974739i	$0.428302\pi$
$314$	−0.306494	−	0.306494i	−0.0172965	−	0.0172965i
$315$		0			0
$316$	5.07749	−	2.10317i	0.285631	−	0.118312i
$317$	1.84002	+	4.44220i	0.103346	+	0.249499i	0.967091	−	0.254429i	$-0.0818876\pi$
$317$	1.84002	+	4.44220i	0.103346	+	0.249499i	−0.863746	+	0.503928i	$0.831888\pi$
$318$	−5.44245	−	2.25434i	−0.305197	−	0.126417i
$319$			0.333065i			0.0186481i
$320$	−5.06478	+	12.2274i	−0.283130	+	0.683535i
$321$	4.40071	−	4.40071i	0.245624	−	0.245624i
$322$		0			0
$323$	−16.3025	+	19.8834i	−0.907093	+	1.10634i
$324$	−5.75651			−0.319806
$325$	−6.33684	+	6.33684i	−0.351505	+	0.351505i
$326$	3.67992	−	8.88411i	0.203812	−	0.492046i
$327$		−	36.3937i		−	2.01258i
$328$	5.54842	+	2.29823i	0.306360	+	0.126898i
$329$		0			0
$330$	−10.3019	+	4.26719i	−0.567101	+	0.234901i
$331$	2.73146	+	2.73146i	0.150135	+	0.150135i	0.778178	−	0.628043i	$-0.216144\pi$
$331$	2.73146	+	2.73146i	0.150135	+	0.150135i	−0.628043	+	0.778178i	$0.716144\pi$
$332$	3.61576	+	3.61576i	0.198441	+	0.198441i
$333$	−20.9564	+	8.68041i	−1.14840	+	0.475683i
$334$	−10.0684	−	24.3073i	−0.550919	−	1.33004i
$335$	4.89506	+	2.02760i	0.267446	+	0.110780i
$336$		0			0
$337$	0.0502989	−	0.121432i	0.00273995	−	0.00661483i	−0.922504	−	0.385988i	$-0.873860\pi$
$337$	0.0502989	−	0.121432i	0.00273995	−	0.00661483i	0.925244	+	0.379374i	$0.123860\pi$
$338$	4.11421	−	4.11421i	0.223783	−	0.223783i
$339$	6.25844			0.339912
$340$	1.68659	−	5.56920i	0.0914680	−	0.302032i
$341$	0.733130			0.0397012
$342$	−14.4070	+	14.4070i	−0.779040	+	0.779040i
$343$		0			0
$344$			0.187251i			0.0100959i
$345$	38.6654	+	16.0157i	2.08167	+	0.862257i
$346$	−11.5446	−	27.8711i	−0.620641	−	1.49836i
$347$	−16.8484	+	6.97884i	−0.904470	+	0.374644i	−0.785937	−	0.618307i	$-0.787819\pi$
$347$	−16.8484	+	6.97884i	−0.904470	+	0.374644i	−0.118533	+	0.992950i	$0.537819\pi$
$348$	−0.239518	−	0.239518i	−0.0128395	−	0.0128395i
$349$	−9.05100	−	9.05100i	−0.484489	−	0.484489i	0.422073	−	0.906562i	$-0.361303\pi$
$349$	−9.05100	−	9.05100i	−0.484489	−	0.484489i	−0.906562	+	0.422073i	$0.861303\pi$
$350$		0			0
$351$	3.31678	+	8.00742i	0.177037	+	0.427404i
$352$	−3.12179	−	1.29309i	−0.166392	−	0.0689217i
$353$			17.2983i			0.920694i	0.887739	+	0.460347i	$0.152275\pi$
$353$			17.2983i			0.920694i	−0.887739	+	0.460347i	$0.847725\pi$
$354$	8.53892	−	20.6148i	0.453838	−	1.09566i
$355$	8.27093	−	8.27093i	0.438976	−	0.438976i
$356$	1.72979			0.0916784
$357$		0			0
$358$	34.8013			1.83931
$359$	0.736537	−	0.736537i	0.0388729	−	0.0388729i	−0.687403	−	0.726276i	$-0.741249\pi$
$359$	0.736537	−	0.736537i	0.0388729	−	0.0388729i	0.726276	+	0.687403i	$0.241249\pi$
$360$	−4.94315	+	11.9338i	−0.260527	+	0.628968i
$361$		−	19.8893i		−	1.04681i
$362$	21.9088	+	9.07494i	1.15150	+	0.476968i
$363$	−8.30076	−	20.0398i	−0.435677	−	1.05182i
$364$		0			0
$365$	28.3151	+	28.3151i	1.48208	+	1.48208i
$366$	27.9919	+	27.9919i	1.46316	+	1.46316i
$367$	7.27629	−	3.01394i	0.379819	−	0.157326i	−0.184602	−	0.982813i	$-0.559100\pi$
$367$	7.27629	−	3.01394i	0.379819	−	0.157326i	0.564421	+	0.825487i	$0.309100\pi$
$368$	12.6806	+	30.6138i	0.661024	+	1.59585i
$369$	4.86885	+	2.01674i	0.253462	+	0.104988i
$370$			47.0451i			2.44576i
$371$		0			0
$372$	−0.527217	+	0.527217i	−0.0273350	+	0.0273350i
$373$	6.85899			0.355145			0.177573	−	0.984108i	$-0.443176\pi$
$373$	6.85899			0.355145			0.177573	+	0.984108i	$0.443176\pi$
$374$	−7.29546	−	2.20937i	−0.377239	−	0.114244i
$375$	−16.9149			−0.873482
$376$	2.35528	−	2.35528i	0.121464	−	0.121464i
$377$	−0.447262	+	1.07979i	−0.0230352	+	0.0556118i
$378$		0			0
$379$	−18.8817	−	7.82107i	−0.969889	−	0.401741i	−0.159218	−	0.987243i	$-0.550897\pi$
$379$	−18.8817	−	7.82107i	−0.969889	−	0.401741i	−0.810671	+	0.585502i	$0.800897\pi$
$380$	3.36804	+	8.13117i	0.172777	+	0.417120i
$381$	−19.7257	+	8.17066i	−1.01058	+	0.418596i
$382$	25.4188	+	25.4188i	1.30054	+	1.30054i
$383$	−2.90628	−	2.90628i	−0.148504	−	0.148504i	0.628946	−	0.777449i	$-0.283487\pi$
$383$	−2.90628	−	2.90628i	−0.148504	−	0.148504i	−0.777449	+	0.628946i	$0.783487\pi$
$384$	−28.3588	+	11.7466i	−1.44718	+	0.599441i
$385$		0			0
$386$	17.9146	+	7.42046i	0.911827	+	0.377691i
$387$			0.164316i			0.00835267i
$388$	−1.53664	+	3.70979i	−0.0780112	+	0.188336i
$389$	0.282915	−	0.282915i	0.0143443	−	0.0143443i	−0.699898	−	0.714243i	$-0.746771\pi$
$389$	0.282915	−	0.282915i	0.0143443	−	0.0143443i	0.714243	+	0.699898i	$0.246771\pi$
$390$	−39.1286			−1.98135
$391$	13.4981	+	25.2252i	0.682631	+	1.27569i
$392$		0			0
$393$	−9.40141	+	9.40141i	−0.474239	+	0.474239i
$394$	−13.4621	+	32.5003i	−0.678209	+	1.63734i
$395$			28.0204i			1.40986i
$396$	−1.16227	−	0.481428i	−0.0584062	−	0.0241927i
$397$	−10.0505	−	24.2641i	−0.504421	−	1.21778i	−0.947053	−	0.321077i	$-0.895955\pi$
$397$	−10.0505	−	24.2641i	−0.504421	−	1.21778i	0.442632	−	0.896703i	$-0.354045\pi$
$398$	18.4521	−	7.64309i	0.924918	−	0.383114i
$399$		0			0
$400$	7.41377	+	7.41377i	0.370688	+	0.370688i
$401$	14.4925	−	6.00300i	0.723722	−	0.299775i	0.00975271	−	0.999952i	$-0.496896\pi$
$401$	14.4925	−	6.00300i	0.723722	−	0.299775i	0.713969	+	0.700177i	$0.246896\pi$
$402$	2.70126	+	6.52142i	0.134727	+	0.325259i
$403$	2.37678	+	0.984494i	0.118396	+	0.0490411i
$404$			6.85566i			0.341082i
$405$	11.2315	−	27.1153i	0.558099	−	1.34737i
$406$		0			0
$407$	12.8354			0.636228
$408$	−19.1479	+	10.2462i	−0.947964	+	0.507261i
$409$	17.3418			0.857499			0.428749	−	0.903423i	$-0.358954\pi$
$409$	17.3418			0.857499			0.428749	+	0.903423i	$0.358954\pi$
$410$	7.72877	−	7.72877i	0.381697	−	0.381697i
$411$	−3.69593	+	8.92277i	−0.182307	+	0.440128i
$412$			4.53934i			0.223637i
$413$		0			0
$414$	8.67561	+	20.9448i	0.426383	+	1.02938i
$415$	−24.0863	+	9.97688i	−1.18235	+	0.489746i
$416$	−8.38427	−	8.38427i	−0.411073	−	0.411073i
$417$	4.09918	+	4.09918i	0.200738	+	0.200738i
$418$	10.6516	−	4.41202i	0.520985	−	0.215799i
$419$	1.47409	+	3.55877i	0.0720140	+	0.173857i	0.955788	−	0.294057i	$-0.0950056\pi$
$419$	1.47409	+	3.55877i	0.0720140	+	0.173857i	−0.883774	+	0.467914i	$0.845006\pi$
$420$		0			0
$421$		−	26.8094i		−	1.30661i	−0.757096	−	0.653304i	$-0.773382\pi$
$421$		−	26.8094i		−	1.30661i	0.757096	−	0.653304i	$-0.226618\pi$
$422$	−11.8876	+	28.6991i	−0.578677	+	1.39705i
$423$	2.06681	−	2.06681i	0.100492	−	0.100492i
$424$	3.86146			0.187529
$425$	7.00027	+	5.73956i	0.339563	+	0.278409i
$426$	15.5831			0.755003
$427$		0			0
$428$	0.557290	−	1.34542i	0.0269376	−	0.0650332i
$429$			10.6756i			0.515421i
$430$	0.314855	+	0.130417i	0.0151836	+	0.00628927i
$431$	−7.10217	−	17.1462i	−0.342099	−	0.825901i	−0.997503	−	0.0706223i	$-0.977501\pi$
$431$	−7.10217	−	17.1462i	−0.342099	−	0.825901i	0.655404	−	0.755279i	$-0.272499\pi$
$432$	9.36825	−	3.88046i	0.450730	−	0.186699i
$433$	7.24642	+	7.24642i	0.348241	+	0.348241i	0.859454	−	0.511213i	$-0.170804\pi$
$433$	7.24642	+	7.24642i	0.348241	+	0.348241i	−0.511213	+	0.859454i	$0.670804\pi$
$434$		0			0
$435$	1.59555	−	0.660896i	0.0765005	−	0.0316876i
$436$	−3.25889	−	7.86766i	−0.156073	−	0.376792i
$437$	−39.9777	−	16.5593i	−1.91239	−	0.792139i
$438$			53.3478i			2.54906i
$439$	14.7759	−	35.6722i	0.705215	−	1.70254i	−0.00641004	−	0.999979i	$-0.502040\pi$
$439$	14.7759	−	35.6722i	0.705215	−	1.70254i	0.711625	−	0.702560i	$-0.247960\pi$
$440$	5.16843	−	5.16843i	0.246395	−	0.246395i
$441$		0			0
$442$	−20.6847	−	16.9595i	−0.983872	−	0.806682i
$443$	8.63055			0.410050			0.205025	−	0.978757i	$-0.434272\pi$
$443$	8.63055			0.410050			0.205025	+	0.978757i	$0.434272\pi$
$444$	−9.23037	+	9.23037i	−0.438054	+	0.438054i
$445$	−3.37499	+	8.14794i	−0.159990	+	0.386249i
$446$			10.5554i			0.499812i
$447$	18.7592	+	7.77030i	0.887278	+	0.367522i
$448$		0			0
$449$	−18.9609	+	7.85388i	−0.894822	+	0.370647i	−0.782227	−	0.622994i	$-0.785916\pi$
$449$	−18.9609	+	7.85388i	−0.894822	+	0.370647i	−0.112595	+	0.993641i	$0.535916\pi$
$450$	5.07222	+	5.07222i	0.239107	+	0.239107i
$451$	−2.10866	−	2.10866i	−0.0992928	−	0.0992928i
$452$	1.35296	−	0.560415i	0.0636379	−	0.0263597i
$453$	−9.52329	−	22.9913i	−0.447443	−	1.08022i
$454$	−2.26014	−	0.936182i	−0.106074	−	0.0439372i
$455$		0			0
$456$	12.5698	−	30.3463i	0.588637	−	1.42110i
$457$	−21.2862	+	21.2862i	−0.995724	+	0.995724i	−0.999991	−	0.00426664i	$-0.998642\pi$
$457$	−21.2862	+	21.2862i	−0.995724	+	0.995724i	0.00426664	+	0.999991i	$0.498642\pi$
$458$	15.5107			0.724767
$459$	7.71927	−	4.13063i	0.360305	−	0.192801i
$460$	9.79288			0.456595
$461$	−8.81316	+	8.81316i	−0.410470	+	0.410470i	−0.881902	−	0.471433i	$-0.843737\pi$
$461$	−8.81316	+	8.81316i	−0.410470	+	0.410470i	0.471433	+	0.881902i	$0.343737\pi$
$462$		0			0
$463$			36.8030i			1.71038i	0.518315	+	0.855190i	$0.326559\pi$
$463$			36.8030i			1.71038i	−0.518315	+	0.855190i	$0.673441\pi$
$464$	1.26329	+	0.523273i	0.0586469	+	0.0242923i
$465$	−1.45474	−	3.51205i	−0.0674618	−	0.162867i
$466$	19.7988	−	8.20094i	0.917163	−	0.379901i
$467$	24.3676	+	24.3676i	1.12760	+	1.12760i	0.990566	+	0.137033i	$0.0437567\pi$
$467$	24.3676	+	24.3676i	1.12760	+	1.12760i	0.137033	+	0.990566i	$0.456243\pi$
$468$	−3.12154	−	3.12154i	−0.144293	−	0.144293i
$469$		0			0
$470$	−2.31990	−	5.60073i	−0.107009	−	0.258343i
$471$	0.566516	+	0.234659i	0.0261037	+	0.0108125i
$472$			14.6263i			0.673231i
$473$	0.0355820	−	0.0859026i	0.00163606	−	0.00394980i
$474$	−26.3963	+	26.3963i	−1.21242	+	1.21242i
$475$	−13.6916			−0.628215
$476$		0			0
$477$	3.38851			0.155149
$478$	33.5163	−	33.5163i	1.53300	−	1.53300i
$479$	−6.23165	+	15.0445i	−0.284731	+	0.687402i	−0.999934	−	0.0115154i	$-0.996334\pi$
$479$	−6.23165	+	15.0445i	−0.284731	+	0.687402i	0.715202	+	0.698917i	$0.246334\pi$
$480$			17.5207i			0.799708i
$481$	41.6120	+	17.2362i	1.89734	+	0.785905i
$482$	−8.42325	−	20.3355i	−0.383669	−	0.926258i
$483$		0			0
$484$	−3.58895	−	3.58895i	−0.163134	−	0.163134i
$485$	−14.4763	−	14.4763i	−0.657337	−	0.657337i
$486$	26.7703	−	11.0886i	1.21433	−	0.502990i
$487$	−10.9165	−	26.3548i	−0.494675	−	1.19425i	−0.952316	−	0.305114i	$-0.901305\pi$
$487$	−10.9165	−	26.3548i	−0.494675	−	1.19425i	0.457641	−	0.889137i	$-0.348695\pi$
$488$	−23.9737	−	9.93022i	−1.08524	−	0.449520i
$489$			13.6038i			0.615183i
$490$		0			0
$491$	23.6986	−	23.6986i	1.06950	−	1.06950i	0.0721073	−	0.997397i	$-0.477028\pi$
$491$	23.6986	−	23.6986i	1.06950	−	1.06950i	0.997397	−	0.0721073i	$-0.0229724\pi$
$492$	3.03281			0.136730
$493$	1.12991	+	0.342185i	0.0508887	+	0.0154112i
$494$	40.4567			1.82023
$495$	4.53541	−	4.53541i	0.203852	−	0.203852i
$496$	1.15181	−	2.78071i	0.0517176	−	0.124857i
$497$		0			0
$498$	−32.0888	−	13.2916i	−1.43794	−	0.595612i
$499$	9.66462	+	23.3325i	0.432648	+	1.04450i	0.978430	+	0.206577i	$0.0662325\pi$
$499$	9.66462	+	23.3325i	0.432648	+	1.04450i	−0.545782	+	0.837927i	$0.683767\pi$
$500$	−3.65669	+	1.51465i	−0.163532	+	0.0677373i
$501$	26.3188	+	26.3188i	1.17584	+	1.17584i
$502$	−22.3991	−	22.3991i	−0.999720	−	0.999720i
$503$	18.7880	−	7.78224i	0.837715	−	0.346993i	0.0777626	−	0.996972i	$-0.475222\pi$
$503$	18.7880	−	7.78224i	0.837715	−	0.346993i	0.759952	+	0.649979i	$0.225222\pi$
$504$		0			0
$505$	−32.2927	−	13.3761i	−1.43701	−	0.595228i
$506$		−	12.8283i		−	0.570289i
$507$	−3.14993	+	7.60461i	−0.139893	+	0.337732i
$508$	−3.53269	+	3.53269i	−0.156738	+	0.156738i
$509$	24.3088			1.07747			0.538734	−	0.842476i	$-0.318903\pi$
$509$	24.3088			1.07747			0.538734	+	0.842476i	$0.318903\pi$
$510$	3.89232	+	39.3328i	0.172355	+	1.74169i
$511$		0			0
$512$	6.01120	−	6.01120i	0.265660	−	0.265660i
$513$	−5.06739	+	12.2338i	−0.223731	+	0.540133i
$514$			18.5111i			0.816487i
$515$	−21.3820	−	8.85671i	−0.942203	−	0.390273i
$516$	0.0361872	+	0.0873635i	0.00159305	+	0.00384596i
$517$	−1.52806	+	0.632944i	−0.0672040	+	0.0278368i
$518$		0			0
$519$	30.1776	+	30.1776i	1.32465	+	1.32465i
$520$	23.6964	−	9.81536i	1.03916	−	0.430432i
$521$	3.16365	+	7.63773i	0.138602	+	0.334615i	0.977905	−	0.209049i	$-0.0670367\pi$
$521$	3.16365	+	7.63773i	0.138602	+	0.334615i	−0.839303	+	0.543664i	$0.817037\pi$
$522$	0.864297	+	0.358003i	0.0378292	+	0.0156694i
$523$		−	3.04018i		−	0.132938i	−0.997788	−	0.0664689i	$-0.978827\pi$
$523$		−	3.04018i		−	0.132938i	0.997788	−	0.0664689i	$-0.0211733\pi$
$524$	−1.19056	+	2.87427i	−0.0520099	+	0.125563i
$525$		0			0
$526$	−4.96911			−0.216663
$527$	0.753202	−	2.48712i	0.0328100	−	0.108340i
$528$	12.4898			0.543550
$529$	−17.7821	+	17.7821i	−0.773134	+	0.773134i
$530$	2.68944	−	6.49289i	0.116822	−	0.282033i
$531$			12.8349i			0.556988i
$532$		0			0
$533$	−4.00455	−	9.66783i	−0.173456	−	0.418760i
$534$	−10.8550	+	4.49631i	−0.469744	+	0.194574i
$535$	5.25009	+	5.25009i	0.226981	+	0.226981i
$536$	−3.27178	−	3.27178i	−0.141319	−	0.141319i
$537$	−45.4853	+	18.8406i	−1.96284	+	0.813033i
$538$	11.4976	+	27.7577i	0.495698	+	1.19672i
$539$		0			0
$540$		−	2.99676i		−	0.128960i
$541$	−2.55117	+	6.15908i	−0.109684	+	0.264800i	−0.969185	−	0.246334i	$-0.920774\pi$
$541$	−2.55117	+	6.15908i	−0.109684	+	0.264800i	0.859502	+	0.511133i	$0.170774\pi$
$542$	21.0522	−	21.0522i	0.904268	−	0.904268i
$543$	−33.5478			−1.43967
$544$	−7.59401	+	9.26205i	−0.325590	+	0.397107i
$545$	43.4181			1.85982
$546$		0			0
$547$	−10.5841	+	25.5523i	−0.452544	+	1.09254i	0.518808	+	0.854891i	$0.326376\pi$
$547$	−10.5841	+	25.5523i	−0.452544	+	1.09254i	−0.971352	+	0.237646i	$0.923624\pi$
$548$			2.25989i			0.0965379i
$549$	−21.0374	−	8.71398i	−0.897855	−	0.371904i
$550$	−1.55333	−	3.75006i	−0.0662340	−	0.159903i
$551$	−1.64970	+	0.683328i	−0.0702796	+	0.0291108i
$552$	−25.8433	−	25.8433i	−1.09996	−	1.09996i
$553$		0			0
$554$	1.76674	−	0.731806i	0.0750614	−	0.0310915i
$555$	−25.4691	−	61.4879i	−1.08110	−	2.61002i
$556$	1.25323	+	0.519105i	0.0531488	+	0.0220149i
$557$			7.31556i			0.309970i	0.987917	+	0.154985i	$0.0495330\pi$
$557$			7.31556i			0.309970i	−0.987917	+	0.154985i	$0.950467\pi$
$558$	0.788022	−	1.90245i	0.0333596	−	0.0805373i
$559$	0.230711	−	0.230711i	0.00975804	−	0.00975804i
$560$		0			0
$561$	10.7313	−	1.06195i	0.453074	−	0.0448355i
$562$	42.3724			1.78737
$563$	−21.4267	+	21.4267i	−0.903026	+	0.903026i	−0.995697	−	0.0926711i	$-0.970459\pi$
$563$	−21.4267	+	21.4267i	−0.903026	+	0.903026i	0.0926711	+	0.995697i	$0.470459\pi$
$564$	0.643708	−	1.55405i	0.0271050	−	0.0654372i
$565$			7.46638i			0.314113i
$566$	11.8468	+	4.90710i	0.497958	+	0.206261i
$567$		0			0
$568$	−9.43715	+	3.90900i	−0.395974	+	0.164018i
$569$	16.4931	+	16.4931i	0.691427	+	0.691427i	0.962546	−	0.271119i	$-0.0873936\pi$
$569$	16.4931	+	16.4931i	0.691427	+	0.691427i	−0.271119	+	0.962546i	$0.587394\pi$
$570$	−42.2714	−	42.2714i	−1.77056	−	1.77056i
$571$	37.5784	−	15.5655i	1.57261	−	0.651395i	0.585386	−	0.810755i	$-0.300943\pi$
$571$	37.5784	−	15.5655i	1.57261	−	0.651395i	0.987221	+	0.159359i	$0.0509429\pi$
$572$	0.955946	+	2.30786i	0.0399701	+	0.0964964i
$573$	−46.9835	−	19.4612i	−1.96276	−	0.813003i
$574$		0			0
$575$	−5.82998	+	14.0748i	−0.243127	+	0.586961i
$576$	7.17165	−	7.17165i	0.298819	−	0.298819i
$577$	35.4559			1.47605			0.738024	−	0.674774i	$-0.235759\pi$
$577$	35.4559			1.47605			0.738024	+	0.674774i	$0.235759\pi$
$578$	−14.9904	+	22.4797i	−0.623519	+	0.935034i
$579$	−27.4316			−1.14002
$580$	0.285747	−	0.285747i	0.0118650	−	0.0118650i
$581$		0			0
$582$		−	27.2745i		−	1.13057i
$583$	−1.77147	−	0.733767i	−0.0733668	−	0.0303895i
$584$	−13.3822	−	32.3075i	−0.553760	−	1.33690i
$585$	20.7941	−	8.61319i	0.859729	−	0.356112i
$586$	−0.285694	−	0.285694i	−0.0118019	−	0.0118019i
$587$	−6.75236	−	6.75236i	−0.278700	−	0.278700i	0.553890	−	0.832590i	$-0.313143\pi$
$587$	−6.75236	−	6.75236i	−0.278700	−	0.278700i	−0.832590	+	0.553890i	$0.813143\pi$
$588$		0			0
$589$	1.50411	+	3.63125i	0.0619759	+	0.149623i
$590$	24.5936	+	10.1870i	1.01250	+	0.419392i
$591$		−	49.7659i		−	2.04710i
$592$	20.1655	−	48.6838i	0.828796	−	2.00089i
$593$	−10.0599	+	10.0599i	−0.413112	+	0.413112i	−0.882821	−	0.469709i	$-0.844359\pi$
$593$	−10.0599	+	10.0599i	−0.413112	+	0.413112i	0.469709	+	0.882821i	$0.344359\pi$
$594$	−3.92565			−0.161072
$595$		0			0
$596$	4.75118			0.194616
$597$	−19.9790	+	19.9790i	−0.817688	+	0.817688i
$598$	17.2267	−	41.5890i	0.704453	−	1.70070i
$599$			15.3003i			0.625154i	0.949892	+	0.312577i	$0.101192\pi$
$599$			15.3003i			0.625154i	−0.949892	+	0.312577i	$0.898808\pi$
$600$	−10.6839	−	4.42542i	−0.436169	−	0.180667i
$601$	10.6505	+	25.7125i	0.434442	+	1.04884i	0.977839	+	0.209359i	$0.0671379\pi$
$601$	10.6505	+	25.7125i	0.434442	+	1.04884i	−0.543397	+	0.839476i	$0.682862\pi$
$602$		0			0
$603$	−2.87105	−	2.87105i	−0.116918	−	0.116918i
$604$	−4.11752	−	4.11752i	−0.167540	−	0.167540i
$605$	23.9077	−	9.90288i	0.971985	−	0.402610i
$606$	−17.8202	−	43.0218i	−0.723897	−	1.74764i
$607$	32.2787	+	13.3703i	1.31015	+	0.542682i	0.924928	−	0.380141i	$-0.124125\pi$
$607$	32.2787	+	13.3703i	1.31015	+	0.542682i	0.385223	+	0.922824i	$0.374125\pi$
$608$		−	18.1154i		−	0.734676i
$609$		0			0
$610$	−33.3946	+	33.3946i	−1.35211	+	1.35211i
$611$	−5.80387			−0.234800
$612$	−2.82732	+	3.44835i	−0.114288	+	0.139391i
$613$	−27.8898			−1.12646			−0.563230	−	0.826300i	$-0.690441\pi$
$613$	−27.8898			−1.12646			−0.563230	+	0.826300i	$0.690441\pi$
$614$	7.45741	−	7.45741i	0.300956	−	0.300956i
$615$	−5.91732	+	14.2857i	−0.238609	+	0.576054i
$616$		0			0
$617$	−0.737118	−	0.305324i	−0.0296753	−	0.0122919i	0.367796	−	0.929906i	$-0.380112\pi$
$617$	−0.737118	−	0.305324i	−0.0296753	−	0.0122919i	−0.397472	+	0.917614i	$0.630112\pi$
$618$	−11.7993	−	28.4860i	−0.474637	−	1.14588i
$619$	−3.28144	+	1.35922i	−0.131892	+	0.0546315i	−0.447653	−	0.894207i	$-0.647740\pi$
$619$	−3.28144	+	1.35922i	−0.131892	+	0.0546315i	0.315761	+	0.948839i	$0.397740\pi$
$620$	−0.628975	−	0.628975i	−0.0252603	−	0.0252603i
$621$	10.4184	+	10.4184i	0.418077	+	0.418077i
$622$	−9.14146	+	3.78652i	−0.366539	+	0.151826i
$623$		0			0
$624$	40.4916	+	16.7722i	1.62096	+	0.671424i
$625$		−	31.1573i		−	1.24629i
$626$	3.58698	−	8.65973i	0.143364	−	0.346112i
$627$	−11.5330	+	11.5330i	−0.460584	+	0.460584i
$628$	0.143483			0.00572560
$629$	13.1868	−	43.5437i	0.525794	−	1.73620i
$630$		0			0
$631$	10.2243	−	10.2243i	0.407024	−	0.407024i	−0.473675	−	0.880700i	$-0.657073\pi$
$631$	10.2243	−	10.2243i	0.407024	−	0.407024i	0.880700	+	0.473675i	$0.157073\pi$
$632$	9.36418	−	22.6071i	0.372487	−	0.899263i
$633$		−	43.9453i		−	1.74667i
$634$	−7.06034	−	2.92449i	−0.280402	−	0.116146i
$635$	−9.74767	−	23.5330i	−0.386825	−	0.933877i
$636$	1.80160	−	0.746246i	0.0714380	−	0.0295906i
$637$		0			0
$638$	−0.374319	−	0.374319i	−0.0148194	−	0.0148194i
$639$	−8.28130	+	3.43023i	−0.327603	+	0.135698i
$640$	−14.0138	−	33.8323i	−0.553944	−	1.33734i
$641$	34.1973	+	14.1650i	1.35071	+	0.559484i	0.936491	−	0.350692i	$-0.114054\pi$
$641$	34.1973	+	14.1650i	1.35071	+	0.559484i	0.414222	+	0.910176i	$0.364054\pi$
$642$			9.89158i			0.390389i
$643$	7.90410	−	19.0822i	0.311707	−	0.752528i	−0.687935	−	0.725773i	$-0.741482\pi$
$643$	7.90410	−	19.0822i	0.311707	−	0.752528i	0.999642	−	0.0267554i	$-0.00851751\pi$
$644$		0			0
$645$	−0.482120			−0.0189834
$646$	−4.02443	−	40.6678i	−0.158339	−	1.60005i
$647$	16.6582			0.654899			0.327450	−	0.944869i	$-0.393811\pi$
$647$	16.6582			0.654899			0.327450	+	0.944869i	$0.393811\pi$
$648$	−18.1234	+	18.1234i	−0.711956	+	0.711956i
$649$	2.77934	−	6.70993i	0.109099	−	0.263388i
$650$		−	14.2435i		−	0.558674i
$651$		0			0
$652$	1.21815	+	2.94088i	0.0477066	+	0.115174i
$653$	22.5240	−	9.32974i	0.881432	−	0.365101i	0.104380	−	0.994537i	$-0.466714\pi$
$653$	22.5240	−	9.32974i	0.881432	−	0.365101i	0.777052	+	0.629436i	$0.216714\pi$
$654$	40.9015	+	40.9015i	1.59937	+	1.59937i
$655$	−11.2160	−	11.2160i	−0.438244	−	0.438244i
$656$	−11.3109	+	4.68511i	−0.441615	+	0.182923i
$657$	−11.7432	−	28.3506i	−0.458145	−	1.10606i
$658$		0			0
$659$		−	43.9334i		−	1.71140i	−0.517471	−	0.855701i	$-0.673126\pi$
$659$		−	43.9334i		−	1.71140i	0.517471	−	0.855701i	$-0.326874\pi$
$660$	1.41255	−	3.41021i	0.0549836	−	0.132742i
$661$	0.652865	−	0.652865i	0.0253935	−	0.0253935i	−0.694296	−	0.719690i	$-0.744284\pi$
$661$	0.652865	−	0.652865i	0.0253935	−	0.0253935i	0.719690	+	0.694296i	$0.244284\pi$
$662$	−6.13957			−0.238621
$663$	36.2164	+	10.9678i	1.40653	+	0.425956i
$664$	22.7673			0.883541
$665$		0			0
$666$	13.7965	−	33.3076i	0.534602	−	1.29064i
$667$			1.98684i			0.0769306i
$668$	8.04637	+	3.33292i	0.311323	+	0.128954i
$669$	−5.71444	−	13.7959i	−0.220933	−	0.533380i
$670$	−7.78011	+	3.22263i	−0.300572	+	0.124501i
$671$	9.11112	+	9.11112i	0.351731	+	0.351731i
$672$		0			0
$673$	30.2805	−	12.5426i	1.16723	−	0.483481i	0.286951	−	0.957945i	$-0.407358\pi$
$673$	30.2805	−	12.5426i	1.16723	−	0.483481i	0.880275	+	0.474465i	$0.157358\pi$
$674$	0.0799440	+	0.193002i	0.00307933	+	0.00743416i
$675$	4.30710	+	1.78406i	0.165780	+	0.0686685i
$676$			1.92604i			0.0740784i
$677$	−0.0169885	+	0.0410139i	−0.000652921	+	0.00157629i	−0.924206	−	0.381895i	$-0.875272\pi$
$677$	−0.0169885	+	0.0410139i	−0.000652921	+	0.00157629i	0.923553	+	0.383471i	$0.125272\pi$
$678$	−7.03362	+	7.03362i	−0.270125	+	0.270125i
$679$		0			0
$680$	−12.2238	−	22.8437i	−0.468761	−	0.876015i
$681$	3.46083			0.132619
$682$	−0.823936	+	0.823936i	−0.0315501	+	0.0315501i
$683$	6.83157	−	16.4929i	0.261403	−	0.631082i	−0.737623	−	0.675213i	$-0.764052\pi$
$683$	6.83157	−	16.4929i	0.261403	−	0.631082i	0.999026	+	0.0441308i	$0.0140518\pi$
$684$		−	6.74453i		−	0.257883i
$685$	−10.6449	−	4.40928i	−0.406723	−	0.168470i
$686$		0			0
$687$	−20.2725	+	8.39713i	−0.773443	+	0.320370i
$688$	−0.269920	−	0.269920i	−0.0102906	−	0.0102906i
$689$	−4.75769	−	4.75769i	−0.181254	−	0.181254i
$690$	−61.4539	+	25.4551i	−2.33951	+	0.969058i
$691$	3.74638	+	9.04456i	0.142519	+	0.344071i	0.978980	−	0.203955i	$-0.0653795\pi$
$691$	3.74638	+	9.04456i	0.142519	+	0.344071i	−0.836461	+	0.548026i	$0.815380\pi$
$692$	9.22610	+	3.82157i	0.350724	+	0.145274i
$693$		0			0
$694$	11.0920	−	26.7785i	0.421047	−	1.01650i
$695$	−4.89036	+	4.89036i	−0.185502	+	0.185502i
$696$	−1.50817			−0.0571670
$697$	−9.31994	+	4.98715i	−0.353018	+	0.188902i
$698$	20.3441			0.770037
$699$	−21.4373	+	21.4373i	−0.810832	+	0.810832i
$700$		0			0
$701$			0.945148i			0.0356978i	0.999841	+	0.0178489i	$0.00568178\pi$
$701$			0.945148i			0.0356978i	−0.999841	+	0.0178489i	$0.994318\pi$
$702$	−12.7268	−	5.27162i	−0.480343	−	0.198965i
$703$	26.3336	+	63.5749i	0.993190	+	2.39777i
$704$	−5.30224	+	2.19626i	−0.199836	+	0.0827746i
$705$	6.06421	+	6.06421i	0.228392	+	0.228392i
$706$	−19.4409	−	19.4409i	−0.731666	−	0.731666i
$707$		0			0
$708$	2.82661	+	6.82405i	0.106231	+	0.256463i
$709$	−29.1678	−	12.0817i	−1.09542	−	0.453738i	−0.239527	−	0.970890i	$-0.576992\pi$
$709$	−29.1678	−	12.0817i	−1.09542	−	0.453738i	−0.855894	+	0.517152i	$0.826992\pi$
$710$			18.5908i			0.697699i
$711$	8.21727	−	19.8382i	0.308172	−	0.743992i
$712$	5.44595	−	5.44595i	0.204096	−	0.204096i
$713$	4.37334			0.163783
$714$		0			0
$715$	−12.7360			−0.476301
$716$	−8.14600	+	8.14600i	−0.304430	+	0.304430i
$717$	−25.6608	+	61.9507i	−0.958321	+	2.31359i
$718$			1.65553i			0.0617839i
$719$	−26.6728	−	11.0482i	−0.994727	−	0.412030i	−0.174866	−	0.984592i	$-0.555949\pi$
$719$	−26.6728	−	11.0482i	−0.994727	−	0.412030i	−0.819861	+	0.572563i	$0.805949\pi$
$720$	−10.0770	−	24.3280i	−0.375547	−	0.906650i
$721$		0			0
$722$	22.3528	+	22.3528i	0.831885	+	0.831885i
$723$	22.0184	+	22.0184i	0.818872	+	0.818872i
$724$	−7.25242	+	3.00405i	−0.269534	+	0.111645i
$725$	0.240577	+	0.580805i	0.00893481	+	0.0215705i
$726$	31.8509	+	13.1931i	1.18210	+	0.489640i
$727$		−	2.05022i		−	0.0760386i	−0.999277	−	0.0380193i	$-0.987895\pi$
$727$		−	2.05022i		−	0.0760386i	0.999277	−	0.0380193i	$-0.0121048\pi$
$728$		0			0
$729$	−5.77570	+	5.77570i	−0.213915	+	0.213915i
$730$	−63.6444			−2.35558
$731$	−0.254865	−	0.208965i	−0.00942653	−	0.00772886i
$732$	−13.1042			−0.484345
$733$	−3.91773	+	3.91773i	−0.144705	+	0.144705i	−0.775748	−	0.631043i	$-0.782627\pi$
$733$	−3.91773	+	3.91773i	−0.144705	+	0.144705i	0.631043	+	0.775748i	$0.282627\pi$
$734$	−4.79029	+	11.5648i	−0.176813	+	0.426864i
$735$		0			0
$736$	−18.6224	−	7.71365i	−0.686431	−	0.284329i
$737$	0.879237	+	2.12267i	0.0323871	+	0.0781894i
$738$	−7.73846	+	3.20537i	−0.284857	+	0.117991i
$739$	−28.5322	−	28.5322i	−1.04958	−	1.04958i	−0.998705	−	0.0508698i	$-0.983801\pi$
$739$	−28.5322	−	28.5322i	−1.04958	−	1.04958i	−0.0508698	−	0.998705i	$-0.516199\pi$
$740$	−11.0119	−	11.0119i	−0.404806	−	0.404806i
$741$	−52.8769	+	21.9023i	−1.94248	+	0.804602i
$742$		0			0
$743$	−29.8250	−	12.3539i	−1.09417	−	0.453221i	−0.238712	−	0.971090i	$-0.576725\pi$
$743$	−29.8250	−	12.3539i	−1.09417	−	0.453221i	−0.855460	+	0.517870i	$0.826725\pi$
$744$			3.31972i			0.121707i
$745$	−9.27004	+	22.3798i	−0.339628	+	0.819934i
$746$	−7.70855	+	7.70855i	−0.282230	+	0.282230i
$747$	19.9788			0.730985
$748$	2.22481	−	1.19051i	0.0813471	−	0.0435293i
$749$		0			0
$750$	19.0100	−	19.0100i	0.694147	−	0.694147i
$751$	−4.61230	+	11.1351i	−0.168305	+	0.406325i	−0.985418	−	0.170154i	$-0.945574\pi$
$751$	−4.61230	+	11.1351i	−0.168305	+	0.406325i	0.817112	+	0.576479i	$0.195574\pi$
$752$			6.79023i			0.247614i
$753$	41.4019	+	17.1492i	1.50877	+	0.624953i
$754$	−0.710869	−	1.71619i	−0.0258883	−	0.0624999i
$755$	27.4288	−	11.3614i	0.998236	−	0.413483i
$756$		0			0
$757$	29.3705	+	29.3705i	1.06749	+	1.06749i	0.997551	+	0.0699392i	$0.0222805\pi$
$757$	29.3705	+	29.3705i	1.06749	+	1.06749i	0.0699392	+	0.997551i	$0.477719\pi$
$758$	30.0102	−	12.4306i	1.09002	−	0.451501i
$759$	6.94496	+	16.7666i	0.252086	+	0.608590i
$760$	36.2034	+	14.9959i	1.31324	+	0.543960i
$761$			9.22390i			0.334366i	0.985926	+	0.167183i	$0.0534671\pi$
$761$			9.22390i			0.334366i	−0.985926	+	0.167183i	$0.946533\pi$
$762$	12.9863	−	31.3517i	0.470443	−	1.13575i
$763$		0			0
$764$	−11.8996			−0.430513
$765$	−10.7266	−	20.0458i	−0.387822	−	0.724758i
$766$	6.53250			0.236029
$767$	18.0211	−	18.0211i	0.650703	−	0.650703i
$768$	10.1790	−	24.5744i	0.367305	−	0.886752i
$769$		−	9.65507i		−	0.348171i	−0.984731	−	0.174085i	$-0.944303\pi$
$769$		−	9.65507i		−	0.348171i	0.984731	−	0.174085i	$-0.0556969\pi$
$770$		0			0
$771$	−10.0215	−	24.1939i	−0.360914	−	0.871323i
$772$	−5.93021	+	2.45637i	−0.213433	+	0.0884068i
$773$	−24.0454	−	24.0454i	−0.864854	−	0.864854i	0.127043	−	0.991897i	$-0.459451\pi$
$773$	−24.0454	−	24.0454i	−0.864854	−	0.864854i	−0.991897	+	0.127043i	$0.959451\pi$
$774$	−0.184669	−	0.184669i	−0.00663778	−	0.00663778i
$775$	1.27844	−	0.529548i	0.0459230	−	0.0190219i
$776$	6.84178	+	16.5175i	0.245606	+	0.592945i
$777$		0			0
$778$			0.635914i			0.0227986i
$779$	6.11816	−	14.7705i	0.219206	−	0.529210i
$780$	9.15890	−	9.15890i	0.327941	−	0.327941i
$781$	5.07216			0.181496
$782$	−43.5197	−	13.1796i	−1.55626	−	0.471300i
$783$	0.608001			0.0217282
$784$		0			0
$785$	−0.279950	+	0.675859i	−0.00999184	+	0.0241224i
$786$		−	21.1318i		−	0.753745i
$787$	−3.29656	−	1.36548i	−0.117510	−	0.0486742i	0.323154	−	0.946346i	$-0.395257\pi$
$787$	−3.29656	−	1.36548i	−0.117510	−	0.0486742i	−0.440664	+	0.897672i	$0.645257\pi$
$788$	−4.45631	−	10.7585i	−0.158749	−	0.383255i
$789$	6.49462	−	2.69016i	0.231215	−	0.0957722i
$790$	−31.4910	−	31.4910i	−1.12040	−	1.12040i
$791$		0			0
$792$	−5.17491	+	2.14352i	−0.183883	+	0.0761666i
$793$	17.3029	+	41.7729i	0.614444	+	1.48340i
$794$	38.5649	+	15.9741i	1.36862	+	0.566899i
$795$			9.94221i			0.352614i
$796$	−2.53007	+	6.10813i	−0.0896760	+	0.216497i
$797$	−37.6393	+	37.6393i	−1.33325	+	1.33325i	−0.430811	+	0.902442i	$0.641772\pi$
$797$	−37.6393	+	37.6393i	−1.33325	+	1.33325i	−0.902442	+	0.430811i	$0.858228\pi$
$798$		0			0
$799$	0.577340	+	5.83416i	0.0204248	+	0.206398i
$800$	−6.37783			−0.225490
$801$	4.77893	−	4.77893i	0.168855	−	0.168855i
$802$	−9.54105	+	23.0341i	−0.336906	+	0.813363i
$803$			17.3642i			0.612771i
$804$	−2.15877	−	0.894190i	−0.0761338	−	0.0315356i
$805$		0			0
$806$	−3.77760	+	1.56474i	−0.133060	+	0.0551154i
$807$	−30.0548	−	30.0548i	−1.05798	−	1.05798i
$808$	21.5839	+	21.5839i	0.759320	+	0.759320i
$809$	−5.76328	+	2.38723i	−0.202626	+	0.0839304i	−0.481688	−	0.876343i	$-0.659976\pi$
$809$	−5.76328	+	2.38723i	−0.202626	+	0.0839304i	0.279063	+	0.960273i	$0.409976\pi$
$810$	17.8512	+	43.0965i	0.627226	+	1.51426i
$811$	46.3967	+	19.2181i	1.62921	+	0.674840i	0.995143	−	0.0984386i	$-0.0313848\pi$
$811$	46.3967	+	19.2181i	1.62921	+	0.674840i	0.634066	+	0.773279i	$0.281385\pi$
$812$		0			0
$813$	−16.1180	+	38.9123i	−0.565283	+	1.36472i
$814$	−14.4252	+	14.4252i	−0.505604	+	0.505604i
$815$	−16.2294			−0.568491
$816$	12.8318	−	42.3713i	0.449203	−	1.48329i
$817$	0.498484			0.0174397
$818$	−19.4898	+	19.4898i	−0.681446	+	0.681446i
$819$		0			0
$820$			3.61817i			0.126352i
$821$	−41.0103	−	16.9870i	−1.43127	−	0.592851i	−0.473604	−	0.880738i	$-0.657047\pi$
$821$	−41.0103	−	16.9870i	−1.43127	−	0.592851i	−0.957664	+	0.287887i	$0.907047\pi$
$822$	−5.87424	−	14.1817i	−0.204888	−	0.494643i
$823$	26.2150	−	10.8586i	0.913797	−	0.378507i	0.124288	−	0.992246i	$-0.460335\pi$
$823$	26.2150	−	10.8586i	0.913797	−	0.378507i	0.789509	+	0.613739i	$0.210335\pi$
$824$	14.2914	+	14.2914i	0.497863	+	0.497863i
$825$	4.06039	+	4.06039i	0.141365	+	0.141365i
$826$		0			0
$827$	−5.17832	−	12.5016i	−0.180068	−	0.434722i	0.807912	−	0.589303i	$-0.200597\pi$
$827$	−5.17832	−	12.5016i	−0.180068	−	0.434722i	−0.987980	+	0.154580i	$0.950597\pi$
$828$	−6.93329	−	2.87186i	−0.240948	−	0.0998041i
$829$		−	10.3528i		−	0.359567i	−0.983706	−	0.179783i	$-0.942460\pi$
$829$		−	10.3528i		−	0.359567i	0.983706	−	0.179783i	$-0.0575397\pi$
$830$	15.8570	−	38.2823i	0.550406	−	1.32880i
$831$	−1.91294	+	1.91294i	−0.0663592	+	0.0663592i
$832$	−20.1389			−0.698192
$833$		0			0
$834$	−9.21381			−0.319048
$835$	−31.3986	+	31.3986i	−1.08659	+	1.08659i
$836$	−1.46050	+	3.52595i	−0.0505124	+	0.121948i
$837$		−	1.33831i		−	0.0462586i
$838$	−5.65623	−	2.34289i	−0.195391	−	0.0809337i
$839$	−8.53922	−	20.6155i	−0.294807	−	0.711726i	−0.999996	−	0.00270739i	$-0.999138\pi$
$839$	−8.53922	−	20.6155i	−0.294807	−	0.711726i	0.705190	−	0.709019i	$-0.250862\pi$
$840$		0			0
$841$	−20.4481	−	20.4481i	−0.705108	−	0.705108i
$842$	30.1300	+	30.1300i	1.03835	+	1.03835i
$843$	−55.3807	+	22.9395i	−1.90741	+	0.790077i
$844$	−3.93510	−	9.50018i	−0.135452	−	0.327010i
$845$	−9.07236	−	3.75790i	−0.312099	−	0.129276i
$846$			4.64561i			0.159720i
$847$		0			0
$848$	−5.56625	+	5.56625i	−0.191146	+	0.191146i
$849$	−18.1403			−0.622575
$850$	−14.3178	+	1.41687i	−0.491096	+	0.0485981i
$851$	76.5672			2.62469
$852$	−3.64756	+	3.64756i	−0.124963	+	0.124963i
$853$	−9.71313	+	23.4496i	−0.332571	+	0.802898i	0.665815	+	0.746116i	$0.268084\pi$
$853$	−9.71313	+	23.4496i	−0.332571	+	0.802898i	−0.998387	+	0.0567814i	$0.981916\pi$
$854$		0			0
$855$	31.7693	+	13.1593i	1.08649	+	0.450037i
$856$	−2.48129	−	5.99036i	−0.0848087	−	0.204746i
$857$	−20.4373	+	8.46541i	−0.698125	+	0.289173i	−0.703381	−	0.710813i	$-0.748327\pi$
$857$	−20.4373	+	8.46541i	−0.698125	+	0.289173i	0.00525584	+	0.999986i	$0.498327\pi$
$858$	−11.9978	−	11.9978i	−0.409599	−	0.409599i
$859$	11.0809	+	11.0809i	0.378076	+	0.378076i	0.870408	−	0.492332i	$-0.163855\pi$
$859$	11.0809	+	11.0809i	0.378076	+	0.378076i	−0.492332	+	0.870408i	$0.663855\pi$
$860$	−0.104225	+	0.0431716i	−0.00355406	+	0.00147214i
$861$		0			0
$862$	27.2517	+	11.2880i	0.928198	+	0.384472i
$863$			19.1310i			0.651227i	0.945503	+	0.325613i	$0.105571\pi$
$863$			19.1310i			0.651227i	−0.945503	+	0.325613i	$0.894429\pi$
$864$	−2.36049	+	5.69872i	−0.0803054	+	0.193874i
$865$	−36.0021	+	36.0021i	−1.22411	+	1.22411i
$866$	−16.2879			−0.553487
$867$	7.42246	−	37.4965i	0.252080	−	1.27345i
$868$		0			0
$869$	−8.59177	+	8.59177i	−0.291456	+	0.291456i
$870$	−1.05042	+	2.53593i	−0.0356124	+	0.0859760i
$871$			8.06230i			0.273181i
$872$	−35.0301	−	14.5100i	−1.18627	−	0.491369i
$873$	6.00381	+	14.4945i	0.203198	+	0.490564i
$874$	63.5398	−	26.3190i	2.14926	−	0.890255i
$875$		0			0
$876$	−12.4872	−	12.4872i	−0.421903	−	0.421903i
$877$	11.9852	−	4.96445i	0.404712	−	0.167637i	−0.171035	−	0.985265i	$-0.554711\pi$
$877$	11.9852	−	4.96445i	0.404712	−	0.167637i	0.575748	+	0.817628i	$0.304711\pi$
$878$	23.4845	+	56.6966i	0.792564	+	1.91342i
$879$	0.528069	+	0.218733i	0.0178113	+	0.00737770i
$880$			14.9005i			0.502295i
$881$	2.50641	−	6.05100i	0.0844429	−	0.203863i	−0.876018	−	0.482279i	$-0.839809\pi$
$881$	2.50641	−	6.05100i	0.0844429	−	0.203863i	0.960461	+	0.278416i	$0.0898092\pi$
$882$		0			0
$883$	3.47124			0.116816			0.0584082	−	0.998293i	$-0.481398\pi$
$883$	3.47124			0.116816			0.0584082	+	0.998293i	$0.481398\pi$
$884$	8.81145	−	0.871967i	0.296361	−	0.0293274i
$885$	−37.6588			−1.26589
$886$	−9.69954	+	9.69954i	−0.325862	+	0.325862i
$887$	2.04770	−	4.94358i	0.0687550	−	0.165989i	−0.885767	−	0.464131i	$-0.846367\pi$
$887$	2.04770	−	4.94358i	0.0687550	−	0.165989i	0.954522	+	0.298142i	$0.0963667\pi$
$888$			58.1206i			1.95040i
$889$		0			0
$890$	−5.36414	−	12.9502i	−0.179806	−	0.434091i
$891$	11.7581	−	4.87038i	0.393912	−	0.163164i
$892$	−2.47072	−	2.47072i	−0.0827257	−	0.0827257i
$893$	−6.27004	−	6.27004i	−0.209819	−	0.209819i
$894$	−29.8154	+	12.3500i	−0.997177	+	0.413044i
$895$	−22.4770	−	54.2644i	−0.751325	−	1.81386i
$896$		0			0
$897$			63.6829i			2.12631i
$898$	12.4828	−	30.1361i	0.416556	−	1.00566i
$899$	0.127610	−	0.127610i	0.00425604	−	0.00425604i
$900$	−2.37452			−0.0791508
$901$	−4.30925	+	5.25579i	−0.143562	+	0.175096i
$902$	4.73968			0.157814
$903$		0			0
$904$	2.49520	−	6.02395i	0.0829892	−	0.200354i
$905$		−	40.0228i		−	1.33040i
$906$	36.5418	+	15.1361i	1.21402	+	0.502864i
$907$	−2.89715	−	6.99435i	−0.0961985	−	0.232244i	0.868454	−	0.495770i	$-0.165114\pi$
$907$	−2.89715	−	6.99435i	−0.0961985	−	0.232244i	−0.964652	+	0.263527i	$0.915114\pi$
$908$	0.748169	−	0.309902i	0.0248289	−	0.0102844i
$909$	18.9404	+	18.9404i	0.628212	+	0.628212i
$910$		0			0
$911$	−15.5785	+	6.45282i	−0.516138	+	0.213791i	−0.625520	−	0.780208i	$-0.715113\pi$
$911$	−15.5785	+	6.45282i	−0.516138	+	0.213791i	0.109382	+	0.994000i	$0.465113\pi$
$912$	25.6246	+	61.8631i	0.848514	+	2.04849i
$913$	−10.4446	−	4.32631i	−0.345667	−	0.143180i
$914$		−	47.8454i		−	1.58258i
$915$	25.5676	−	61.7257i	0.845240	−	2.04059i
$916$	−3.63061	+	3.63061i	−0.119959	+	0.119959i
$917$		0			0
$918$	−4.03314	+	13.3176i	−0.133113	+	0.439548i
$919$	−20.2889			−0.669270			−0.334635	−	0.942348i	$-0.608613\pi$
$919$	−20.2889			−0.669270			−0.334635	+	0.942348i	$0.608613\pi$
$920$	30.8313	−	30.8313i	1.01648	−	1.01648i
$921$	−5.70956	+	13.7841i	−0.188136	+	0.454201i
$922$		−	19.8095i		−	0.652392i
$923$	16.4438	+	6.81123i	0.541253	+	0.224194i
$924$		0			0
$925$	22.3826	−	9.27118i	0.735936	−	0.304835i
$926$	−41.3614	−	41.3614i	−1.35922	−	1.35922i
$927$	12.5410	+	12.5410i	0.411900	+	0.411900i
$928$	−0.768462	+	0.318308i	−0.0252260	+	0.0104490i
$929$	−6.99298	−	16.8826i	−0.229432	−	0.553899i	0.766676	−	0.642034i	$-0.221909\pi$
$929$	−6.99298	−	16.8826i	−0.229432	−	0.553899i	−0.996109	+	0.0881354i	$0.971909\pi$
$930$	5.58198	+	2.31213i	0.183040	+	0.0758177i
$931$		0			0
$932$	−2.71473	+	6.55395i	−0.0889241	+	0.214682i
$933$	9.89796	−	9.89796i	0.324045	−	0.324045i
$934$	−54.7717			−1.79218
$935$	1.26692	+	12.8025i	0.0414326	+	0.418687i
$936$	−19.6553			−0.642455
$937$	−24.2616	+	24.2616i	−0.792593	+	0.792593i	−0.981915	−	0.189322i	$-0.939371\pi$
$937$	−24.2616	+	24.2616i	−0.792593	+	0.792593i	0.189322	+	0.981915i	$0.439371\pi$
$938$		0			0
$939$			13.2602i			0.432729i
$940$	1.85399	+	0.767950i	0.0604706	+	0.0250478i
$941$	−2.26516	−	5.46857i	−0.0738420	−	0.178270i	0.882649	−	0.470033i	$-0.155758\pi$
$941$	−2.26516	−	5.46857i	−0.0738420	−	0.178270i	−0.956491	+	0.291763i	$0.905758\pi$
$942$	−0.900409	+	0.372962i	−0.0293369	+	0.0121517i
$943$	−12.5788	−	12.5788i	−0.409622	−	0.409622i
$944$	−21.0837	−	21.0837i	−0.686216	−	0.686216i
$945$		0			0
$946$	0.0565533	+	0.136532i	0.00183871	+	0.00443903i
$947$	35.6762	+	14.7776i	1.15932	+	0.480206i	0.877648	−	0.479305i	$-0.159111\pi$
$947$	35.6762	+	14.7776i	1.15932	+	0.480206i	0.281671	+	0.959511i	$0.409111\pi$
$948$		−	12.3572i		−	0.401344i
$949$	−23.3178	+	56.2942i	−0.756929	+	1.82739i
$950$	15.3875	−	15.3875i	0.499236	−	0.499236i
$951$	10.8111			0.350574
$952$		0			0
$953$	−17.9346			−0.580959			−0.290479	−	0.956881i	$-0.593815\pi$
$953$	−17.9346			−0.580959			−0.290479	+	0.956881i	$0.593815\pi$
$954$	−3.80821	+	3.80821i	−0.123295	+	0.123295i
$955$	23.2174	−	56.0517i	0.751297	−	1.81379i
$956$			15.6904i			0.507464i
$957$	0.691883	+	0.286587i	0.0223654	+	0.00926405i
$958$	−9.90445	−	23.9115i	−0.319998	−	0.772544i
$959$		0			0
$960$	21.0423	+	21.0423i	0.679137	+	0.679137i
$961$	21.6394	+	21.6394i	0.698046	+	0.698046i
$962$	−66.1372	+	27.3949i	−2.13235	+	0.883248i
$963$	−2.17738	−	5.25667i	−0.0701652	−	0.169394i
$964$	6.73161	+	2.78833i	0.216811	+	0.0898059i
$965$		−	32.7261i		−	1.05349i
$966$		0			0
$967$	−0.674496	+	0.674496i	−0.0216903	+	0.0216903i	−0.717869	−	0.696178i	$-0.754882\pi$
$967$	−0.674496	+	0.674496i	−0.0216903	+	0.0216903i	0.696178	+	0.717869i	$0.254882\pi$
$968$	−22.5984			−0.726341
$969$	27.2765	+	50.9741i	0.876249	+	1.63752i
$970$	32.5388			1.04476
$971$	10.6714	−	10.6714i	0.342460	−	0.342460i	−0.514831	−	0.857291i	$-0.672145\pi$
$971$	10.6714	−	10.6714i	0.342460	−	0.342460i	0.857291	+	0.514831i	$0.172145\pi$
$972$	−3.67064	+	8.86170i	−0.117736	+	0.284239i
$973$		0			0
$974$	41.8878	+	17.3505i	1.34217	+	0.555946i
$975$	7.71108	+	18.6162i	0.246952	+	0.596195i
$976$	48.8721	−	20.2435i	1.56436	−	0.647978i
$977$	4.09894	+	4.09894i	0.131137	+	0.131137i	0.769629	−	0.638492i	$-0.220441\pi$
$977$	4.09894	+	4.09894i	0.131137	+	0.131137i	−0.638492	+	0.769629i	$0.720441\pi$
$978$	−15.2887	−	15.2887i	−0.488880	−	0.488880i
$979$	−3.53322	+	1.46351i	−0.112922	+	0.0467740i
$980$		0			0
$981$	−30.7397	−	12.7328i	−0.981442	−	0.406527i
$982$			53.2679i			1.69985i
$983$	2.08541	−	5.03463i	0.0665142	−	0.160580i	−0.887127	−	0.461525i	$-0.847302\pi$
$983$	2.08541	−	5.03463i	0.0665142	−	0.160580i	0.953641	+	0.300946i	$0.0973023\pi$
$984$	9.54831	−	9.54831i	0.304389	−	0.304389i
$985$	59.3712			1.89172
$986$	−1.65443	+	0.885297i	−0.0526879	+	0.0281936i
$987$		0			0
$988$	−9.46976	+	9.46976i	−0.301273	+	0.301273i
$989$	0.212258	−	0.512435i	0.00674940	−	0.0162945i
$990$			10.1943i			0.323998i
$991$	−22.4946	−	9.31757i	−0.714565	−	0.295982i	−0.00437276	−	0.999990i	$-0.501392\pi$
$991$	−22.4946	−	9.31757i	−0.714565	−	0.295982i	−0.710192	+	0.704008i	$0.751392\pi$
$992$	0.700645	+	1.69151i	0.0222455	+	0.0537054i
$993$	8.02441	−	3.32382i	0.254647	−	0.105478i
$994$		0			0
$995$	−23.8352	−	23.8352i	−0.755626	−	0.755626i
$996$	10.6223	−	4.39989i	0.336580	−	0.139416i
$997$	−2.32508	−	5.61324i	−0.0736360	−	0.177773i	0.882776	−	0.469795i	$-0.155672\pi$
$997$	−2.32508	−	5.61324i	−0.0736360	−	0.177773i	−0.956412	+	0.292022i	$0.905672\pi$
$998$	−37.0841	−	15.3608i	−1.17388	−	0.486236i
$999$		−	23.4307i		−	0.741313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.l.g.246.3		40
7.2	even	3		119.2.q.a.25.8	✓	80
7.3	odd	6		833.2.v.f.569.3		80
7.4	even	3		119.2.q.a.93.3	yes	80
7.5	odd	6		833.2.v.f.263.8		80
7.6	odd	2		833.2.l.f.246.3		40
17.15	even	8	inner	833.2.l.g.491.3		40
119.32	even	24		119.2.q.a.100.8	yes	80
119.66	odd	24		833.2.v.f.814.8		80
119.83	odd	8		833.2.l.f.491.3		40
119.100	even	24		119.2.q.a.32.3	yes	80
119.117	odd	24		833.2.v.f.508.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.q.a.25.8	✓	80	7.2	even	3
119.2.q.a.32.3	yes	80	119.100	even	24
119.2.q.a.93.3	yes	80	7.4	even	3
119.2.q.a.100.8	yes	80	119.32	even	24
833.2.l.f.246.3		40	7.6	odd	2
833.2.l.f.491.3		40	119.83	odd	8
833.2.l.g.246.3		40	1.1	even	1	trivial
833.2.l.g.491.3		40	17.15	even	8	inner
833.2.v.f.263.8		80	7.5	odd	6
833.2.v.f.508.3		80	119.117	odd	24
833.2.v.f.569.3		80	7.3	odd	6
833.2.v.f.814.8		80	119.66	odd	24

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12386 + 1.12386i) q^{2} +(0.860453 - 2.07732i) q^{3} -0.526128i q^{4} +(2.47826 + 1.02653i) q^{5} +(1.36759 + 3.30165i) q^{6} +(-1.65643 - 1.65643i) q^{8} +(-1.45355 - 1.45355i) q^{9} +(-3.93890 + 1.63154i) q^{10} +(0.445138 + 1.07466i) q^{11} +(-1.09293 - 0.452708i) q^{12} +4.08176i q^{13} +(4.26485 - 4.26485i) q^{15} +4.77545 q^{16} +(4.10306 - 0.406033i) q^{17} +3.26718 q^{18} +(-4.40961 + 4.40961i) q^{19} +(0.540085 - 1.30388i) q^{20} +(-1.70804 - 0.707493i) q^{22} +(2.65538 + 6.41066i) q^{23} +(-4.86621 + 2.01565i) q^{24} +(1.55248 + 1.55248i) q^{25} +(-4.58733 - 4.58733i) q^{26} +(1.96175 - 0.812585i) q^{27} +(0.264539 + 0.109576i) q^{29} +9.58621i q^{30} +(0.241193 - 0.582292i) q^{31} +(-2.05408 + 2.05408i) q^{32} +2.61543 q^{33} +(-4.15495 + 5.06760i) q^{34} +(-0.764753 + 0.764753i) q^{36} +(4.22275 - 10.1946i) q^{37} -9.91158i q^{38} +(8.47912 + 3.51217i) q^{39} +(-2.40469 - 5.80543i) q^{40} +(-2.36854 + 0.981083i) q^{41} +(-0.0565224 - 0.0565224i) q^{43} +(0.565408 - 0.234199i) q^{44} +(-2.11016 - 5.09439i) q^{45} +(-10.1890 - 4.22041i) q^{46} +1.42190i q^{47} +(4.10905 - 9.92012i) q^{48} -3.48954 q^{50} +(2.68704 - 8.87274i) q^{51} +2.14753 q^{52} +(-1.16560 + 1.16560i) q^{53} +(-1.29151 + 3.11797i) q^{54} +3.12023i q^{55} +(5.36590 + 12.9544i) q^{57} +(-0.420453 + 0.174157i) q^{58} +(-4.41502 - 4.41502i) q^{59} +(-2.24386 - 2.24386i) q^{60} +(10.2340 - 4.23908i) q^{61} +(0.383348 + 0.925484i) q^{62} +4.93388i q^{64} +(-4.19005 + 10.1157i) q^{65} +(-2.93938 + 2.93938i) q^{66} +1.97520 q^{67} +(-0.213625 - 2.15874i) q^{68} +15.6018 q^{69} +(1.66870 - 4.02859i) q^{71} +4.81540i q^{72} +(13.7917 + 5.71269i) q^{73} +(6.71155 + 16.2031i) q^{74} +(4.56082 - 1.88915i) q^{75} +(2.32002 + 2.32002i) q^{76} +(-13.4765 + 5.58216i) q^{78} +(3.99744 + 9.65068i) q^{79} +(11.8348 + 4.90213i) q^{80} -10.9413i q^{81} +(1.55931 - 3.76452i) q^{82} +(-6.87240 + 6.87240i) q^{83} +(10.5853 + 3.20566i) q^{85} +0.127047 q^{86} +(0.455247 - 0.455247i) q^{87} +(1.04275 - 2.51743i) q^{88} +3.28777i q^{89} +(8.09692 + 3.35385i) q^{90} +(3.37283 - 1.39707i) q^{92} +(-1.00207 - 1.00207i) q^{93} +(-1.59802 - 1.59802i) q^{94} +(-15.4547 + 6.40157i) q^{95} +(2.49954 + 6.03442i) q^{96} +(-7.05111 - 2.92067i) q^{97} +(0.915039 - 2.20910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 16 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 28 q^{12} + 12 q^{15} - 8 q^{16} - 4 q^{17} + 24 q^{18} + 4 q^{19} - 24 q^{20} - 24 q^{22} - 8 q^{23} + 28 q^{24} + 8 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 - 16 * q^8 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 28 * q^12 + 12 * q^15 - 8 * q^16 - 4 * q^17 + 24 * q^18 + 4 * q^19 - 24 * q^20 - 24 * q^22 - 8 * q^23 + 28 * q^24 + 8 * q^25 - 36 * q^26 - 32 * q^27 - 8 * q^29 + 4 * q^31 - 48 * q^32 - 40 * q^33 - 8 * q^34 - 16 * q^36 + 36 * q^37 - 16 * q^39 - 28 * q^40 + 20 * q^41 + 8 * q^43 + 20 * q^44 - 8 * q^45 + 4 * q^46 + 28 * q^48 + 8 * q^50 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 24 * q^54 - 8 * q^57 - 28 * q^58 - 4 * q^59 - 76 * q^60 + 24 * q^61 + 44 * q^62 - 8 * q^65 - 12 * q^66 + 60 * q^68 + 96 * q^69 - 16 * q^71 + 24 * q^73 + 28 * q^74 + 108 * q^75 - 4 * q^76 + 80 * q^78 + 4 * q^79 + 44 * q^80 - 24 * q^82 - 44 * q^83 - 20 * q^85 - 64 * q^86 - 68 * q^87 - 104 * q^88 - 24 * q^90 - 40 * q^92 - 8 * q^93 - 44 * q^94 - 48 * q^95 + 12 * q^96 + 40 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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