LMFDB - Embedded newform 833.2.o.e.30.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(30,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("833.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.o (of order $12$, degree $4$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			30.5
Character	$\chi$	$=$	833.30
Dual form			833.2.o.e.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48270 + 0.856038i) q^{2} +(-0.288085 + 1.07515i) q^{3} +(0.465602 + 0.806447i) q^{4} +(3.42458 - 0.917613i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} +(1.52513 + 0.880532i) q^{9} +O(q^{10})$	\(q+(1.48270 + 0.856038i) q^{2} +(-0.288085 + 1.07515i) q^{3} +(0.465602 + 0.806447i) q^{4} +(3.42458 - 0.917613i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} +(1.52513 + 0.880532i) q^{9} +(5.86314 + 1.57102i) q^{10} +(-5.29674 - 1.41926i) q^{11} +(-1.00118 + 0.268266i) q^{12} +3.78474 q^{13} +3.94628i q^{15} +(2.49763 - 4.32603i) q^{16} +(0.384149 + 4.10517i) q^{17} +(1.50754 + 2.61113i) q^{18} +(3.39847 + 1.96211i) q^{19} +(2.33450 + 2.33450i) q^{20} +(-6.63855 - 6.63855i) q^{22} +(-0.235457 - 0.878738i) q^{23} +(1.96737 + 0.527155i) q^{24} +(6.55560 - 3.78488i) q^{25} +(5.61164 + 3.23988i) q^{26} +(-3.74726 + 3.74726i) q^{27} +(1.69227 + 1.69227i) q^{29} +(-3.37817 + 5.85115i) q^{30} +(2.46882 - 9.21375i) q^{31} +(4.23708 - 2.44628i) q^{32} +(3.05182 - 5.28591i) q^{33} +(-2.94460 + 6.41559i) q^{34} +1.63991i q^{36} +(-10.3675 + 2.77797i) q^{37} +(3.35928 + 5.81844i) q^{38} +(-1.09033 + 4.06916i) q^{39} +(-1.67910 - 6.26650i) q^{40} +(-3.45091 + 3.45091i) q^{41} -1.18522i q^{43} +(-1.32162 - 4.93235i) q^{44} +(6.03090 + 1.61598i) q^{45} +(0.403120 - 1.50447i) q^{46} +(-1.34751 + 2.33396i) q^{47} +(3.93159 + 3.93159i) q^{48} +12.9600 q^{50} +(-4.52433 - 0.769621i) q^{51} +(1.76218 + 3.05219i) q^{52} +(-1.15780 + 0.668456i) q^{53} +(-8.76386 + 2.34827i) q^{54} -19.4414 q^{55} +(-3.08860 + 3.08860i) q^{57} +(1.06048 + 3.95777i) q^{58} +(-9.74112 + 5.62404i) q^{59} +(-3.18246 + 1.83740i) q^{60} +(2.28920 + 8.54343i) q^{61} +(11.5478 - 11.5478i) q^{62} -1.61410 q^{64} +(12.9611 - 3.47293i) q^{65} +(9.04989 - 5.22496i) q^{66} +(0.215124 + 0.372605i) q^{67} +(-3.13174 + 2.22117i) q^{68} +1.01260 q^{69} +(-1.60366 - 1.60366i) q^{71} +(1.61125 - 2.79077i) q^{72} +(2.45510 - 9.16255i) q^{73} +(-17.7500 - 4.75610i) q^{74} +(2.18073 + 8.13860i) q^{75} +3.65425i q^{76} +(-5.09998 + 5.09998i) q^{78} +(-1.76785 - 6.59771i) q^{79} +(4.58372 - 17.1067i) q^{80} +(-0.307732 - 0.533007i) q^{81} +(-8.07077 + 2.16256i) q^{82} +3.11707i q^{83} +(5.08251 + 13.7060i) q^{85} +(1.01459 - 1.75732i) q^{86} +(-2.30696 + 1.33192i) q^{87} +(-2.59704 + 9.69229i) q^{88} +(-1.46691 + 2.54076i) q^{89} +(7.55869 + 7.55869i) q^{90} +(0.599026 - 0.599026i) q^{92} +(9.19492 + 5.30869i) q^{93} +(-3.99591 + 2.30704i) q^{94} +(13.4388 + 3.60091i) q^{95} +(1.40947 + 5.26023i) q^{96} +(-8.64179 - 8.64179i) q^{97} +(-6.82850 - 6.82850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4}+O(q^{10}) $ 32 * q + 28 * q^4	$ 32 q + 28 q^{4} + 12 q^{11} - 20 q^{16} - 52 q^{18} - 8 q^{22} + 8 q^{23} + 24 q^{29} + 20 q^{30} - 32 q^{37} + 28 q^{39} - 12 q^{44} - 72 q^{46} - 56 q^{51} - 72 q^{57} + 28 q^{58} - 72 q^{64} + 8 q^{65} + 96 q^{67} - 48 q^{71} + 160 q^{72} - 88 q^{74} - 232 q^{78} + 36 q^{79} - 40 q^{81} - 104 q^{85} + 20 q^{86} + 48 q^{88} + 240 q^{92} + 84 q^{95} - 96 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 12 * q^11 - 20 * q^16 - 52 * q^18 - 8 * q^22 + 8 * q^23 + 24 * q^29 + 20 * q^30 - 32 * q^37 + 28 * q^39 - 12 * q^44 - 72 * q^46 - 56 * q^51 - 72 * q^57 + 28 * q^58 - 72 * q^64 + 8 * q^65 + 96 * q^67 - 48 * q^71 + 160 * q^72 - 88 * q^74 - 232 * q^78 + 36 * q^79 - 40 * q^81 - 104 * q^85 + 20 * q^86 + 48 * q^88 + 240 * q^92 + 84 * q^95 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.48270	+	0.856038i	1.04843	+	0.605310i	0.922209	−	0.386692i	$-0.126382\pi$
$2$	1.48270	+	0.856038i	1.04843	+	0.605310i	0.126219	+	0.992002i	$0.459716\pi$
$3$	−0.288085	+	1.07515i	−0.166326	+	0.620737i	0.831541	+	0.555463i	$0.187459\pi$
$3$	−0.288085	+	1.07515i	−0.166326	+	0.620737i	−0.997867	+	0.0652742i	$0.979208\pi$
$4$	0.465602	+	0.806447i	0.232801	+	0.403223i
$5$	3.42458	−	0.917613i	1.53152	−	0.410369i	0.608004	−	0.793934i	$-0.291970\pi$
$5$	3.42458	−	0.917613i	1.53152	−	0.410369i	0.923514	+	0.383565i	$0.125304\pi$
$6$	−1.34751	+	1.34751i	−0.550119	+	0.550119i
$7$		0			0
$7$		0			0
$8$		−	1.82986i		−	0.646953i
$9$	1.52513	+	0.880532i	0.508375	+	0.293511i
$10$	5.86314	+	1.57102i	1.85409	+	0.496801i
$11$	−5.29674	−	1.41926i	−1.59703	−	0.427922i	−0.652884	−	0.757458i	$-0.726441\pi$
$11$	−5.29674	−	1.41926i	−1.59703	−	0.427922i	−0.944143	+	0.329535i	$0.893108\pi$
$12$	−1.00118	+	0.268266i	−0.289017	+	0.0774418i
$13$	3.78474			1.04970			0.524849	−	0.851195i	$-0.324122\pi$
$13$	3.78474			1.04970			0.524849	+	0.851195i	$0.324122\pi$
$14$		0			0
$15$			3.94628i			1.01893i
$16$	2.49763	−	4.32603i	0.624408	−	1.08151i
$17$	0.384149	+	4.10517i	0.0931699	+	0.995650i
$17$	0.384149	+	4.10517i	0.0931699	+	0.995650i
$18$	1.50754	+	2.61113i	0.355330	+	0.615450i
$19$	3.39847	+	1.96211i	0.779662	+	0.450138i	0.836311	−	0.548256i	$-0.184708\pi$
$19$	3.39847	+	1.96211i	0.779662	+	0.450138i	−0.0566484	+	0.998394i	$0.518041\pi$
$20$	2.33450	+	2.33450i	0.522010	+	0.522010i
$21$		0			0
$22$	−6.63855	−	6.63855i	−1.41534	−	1.41534i
$23$	−0.235457	−	0.878738i	−0.0490962	−	0.183229i	0.937023	−	0.349267i	$-0.113569\pi$
$23$	−0.235457	−	0.878738i	−0.0490962	−	0.183229i	−0.986119	+	0.166038i	$0.946903\pi$
$24$	1.96737	+	0.527155i	0.401588	+	0.107605i
$25$	6.55560	−	3.78488i	1.31112	−	0.756975i
$26$	5.61164	+	3.23988i	1.10053	+	0.635393i
$27$	−3.74726	+	3.74726i	−0.721160	+	0.721160i
$28$		0			0
$29$	1.69227	+	1.69227i	0.314246	+	0.314246i	0.846552	−	0.532306i	$-0.178674\pi$
$29$	1.69227	+	1.69227i	0.314246	+	0.314246i	−0.532306	+	0.846552i	$0.678674\pi$
$30$	−3.37817	+	5.85115i	−0.616766	+	1.06827i
$31$	2.46882	−	9.21375i	0.443413	−	1.65484i	−0.276681	−	0.960962i	$-0.589234\pi$
$31$	2.46882	−	9.21375i	0.443413	−	1.65484i	0.720094	−	0.693877i	$-0.244099\pi$
$32$	4.23708	−	2.44628i	0.749017	−	0.432445i
$33$	3.05182	−	5.28591i	0.531254	−	0.920160i
$34$	−2.94460	+	6.41559i	−0.504995	+	1.10026i
$35$		0			0
$36$			1.63991i			0.273318i
$37$	−10.3675	+	2.77797i	−1.70441	+	0.456696i	−0.974044	−	0.226358i	$-0.927318\pi$
$37$	−10.3675	+	2.77797i	−1.70441	+	0.456696i	−0.730368	+	0.683054i	$0.760651\pi$
$38$	3.35928	+	5.81844i	0.544947	+	0.943875i
$39$	−1.09033	+	4.06916i	−0.174592	+	0.651587i
$40$	−1.67910	−	6.26650i	−0.265489	−	0.990820i
$41$	−3.45091	+	3.45091i	−0.538941	+	0.538941i	−0.923218	−	0.384277i	$-0.874451\pi$
$41$	−3.45091	+	3.45091i	−0.538941	+	0.538941i	0.384277	+	0.923218i	$0.374451\pi$
$42$		0			0
$43$		−	1.18522i		−	0.180744i	−0.995908	−	0.0903719i	$-0.971194\pi$
$43$		−	1.18522i		−	0.180744i	0.995908	−	0.0903719i	$-0.0288056\pi$
$44$	−1.32162	−	4.93235i	−0.199242	−	0.743580i
$45$	6.03090	+	1.61598i	0.899034	+	0.240895i
$46$	0.403120	−	1.50447i	0.0594369	−	0.221821i
$47$	−1.34751	+	2.33396i	−0.196555	+	0.340443i	−0.947409	−	0.320025i	$-0.896309\pi$
$47$	−1.34751	+	2.33396i	−0.196555	+	0.340443i	0.750854	+	0.660468i	$0.229642\pi$
$48$	3.93159	+	3.93159i	0.567476	+	0.567476i
$49$		0			0
$50$	12.9600			1.83282
$51$	−4.52433	−	0.769621i	−0.633534	−	0.107769i
$52$	1.76218	+	3.05219i	0.244371	+	0.423263i
$53$	−1.15780	+	0.668456i	−0.159036	+	0.0918195i	−0.577406	−	0.816457i	$-0.695935\pi$
$53$	−1.15780	+	0.668456i	−0.159036	+	0.0918195i	0.418370	+	0.908277i	$0.362602\pi$
$54$	−8.76386	+	2.34827i	−1.19261	+	0.319559i
$55$	−19.4414			−2.62148
$56$		0			0
$57$	−3.08860	+	3.08860i	−0.409096	+	0.409096i
$58$	1.06048	+	3.95777i	0.139248	+	0.519681i
$59$	−9.74112	+	5.62404i	−1.26819	+	0.732187i	−0.974644	−	0.223759i	$-0.928167\pi$
$59$	−9.74112	+	5.62404i	−1.26819	+	0.732187i	−0.293541	+	0.955946i	$0.594834\pi$
$60$	−3.18246	+	1.83740i	−0.410854	+	0.237207i
$61$	2.28920	+	8.54343i	0.293103	+	1.09387i	0.942713	+	0.333606i	$0.108266\pi$
$61$	2.28920	+	8.54343i	0.293103	+	1.09387i	−0.649610	+	0.760268i	$0.725068\pi$
$62$	11.5478	−	11.5478i	1.46658	−	1.46658i
$63$		0			0
$64$	−1.61410			−0.201763
$65$	12.9611	−	3.47293i	1.60763	−	0.430764i
$66$	9.04989	−	5.22496i	1.11396	−	0.643148i
$67$	0.215124	+	0.372605i	0.0262816	+	0.0455210i	0.878867	−	0.477067i	$-0.158300\pi$
$67$	0.215124	+	0.372605i	0.0262816	+	0.0455210i	−0.852585	+	0.522588i	$0.824967\pi$
$68$	−3.13174	+	2.22117i	−0.379779	+	0.269357i
$69$	1.01260			0.121903
$70$		0			0
$71$	−1.60366	−	1.60366i	−0.190320	−	0.190320i	0.605514	−	0.795834i	$-0.292967\pi$
$71$	−1.60366	−	1.60366i	−0.190320	−	0.190320i	−0.795834	+	0.605514i	$0.792967\pi$
$72$	1.61125	−	2.79077i	0.189888	−	0.328895i
$73$	2.45510	−	9.16255i	0.287347	−	1.07240i	−0.659759	−	0.751477i	$-0.729342\pi$
$73$	2.45510	−	9.16255i	0.287347	−	1.07240i	0.947107	−	0.320918i	$-0.103992\pi$
$74$	−17.7500	−	4.75610i	−2.06340	−	0.552885i
$75$	2.18073	+	8.13860i	0.251809	+	0.939765i
$76$			3.65425i			0.419171i
$77$		0			0
$78$	−5.09998	+	5.09998i	−0.577459	+	0.577459i
$79$	−1.76785	−	6.59771i	−0.198899	−	0.742300i	−0.991223	−	0.132200i	$-0.957796\pi$
$79$	−1.76785	−	6.59771i	−0.198899	−	0.742300i	0.792324	−	0.610100i	$-0.208871\pi$
$80$	4.58372	−	17.1067i	0.512476	−	1.91259i
$81$	−0.307732	−	0.533007i	−0.0341924	−	0.0592230i
$82$	−8.07077	+	2.16256i	−0.891268	+	0.238814i
$83$			3.11707i			0.342143i	0.985259	+	0.171072i	$0.0547229\pi$
$83$			3.11707i			0.342143i	−0.985259	+	0.171072i	$0.945277\pi$
$84$		0			0
$85$	5.08251	+	13.7060i	0.551275	+	1.48662i
$86$	1.01459	−	1.75732i	0.109406	−	0.189497i
$87$	−2.30696	+	1.33192i	−0.247332	+	0.142797i
$88$	−2.59704	+	9.69229i	−0.276846	+	1.03320i
$89$	−1.46691	+	2.54076i	−0.155492	+	0.269320i	−0.933238	−	0.359259i	$-0.883030\pi$
$89$	−1.46691	+	2.54076i	−0.155492	+	0.269320i	0.777746	+	0.628578i	$0.216363\pi$
$90$	7.55869	+	7.55869i	0.796756	+	0.796756i
$91$		0			0
$92$	0.599026	−	0.599026i	0.0624528	−	0.0624528i
$93$	9.19492	+	5.30869i	0.953469	+	0.550485i
$94$	−3.99591	+	2.30704i	−0.412147	+	0.237953i
$95$	13.4388	+	3.60091i	1.37879	+	0.369446i
$96$	1.40947	+	5.26023i	0.143854	+	0.536870i
$97$	−8.64179	−	8.64179i	−0.877441	−	0.877441i	0.115828	−	0.993269i	$-0.463048\pi$
$97$	−8.64179	−	8.64179i	−0.877441	−	0.877441i	−0.993269	+	0.115828i	$0.963048\pi$
$98$		0			0
$99$	−6.82850	−	6.82850i	−0.686290	−	0.686290i
$100$	6.10460	+	3.52449i	0.610460	+	0.352449i
$101$	−6.83026	−	11.8304i	−0.679636	−	1.17716i	−0.975090	−	0.221808i	$-0.928804\pi$
$101$	−6.83026	−	11.8304i	−0.679636	−	1.17716i	0.295454	−	0.955357i	$-0.404529\pi$
$102$	−6.04941	−	5.01412i	−0.598981	−	0.496472i
$103$	1.73549	−	3.00596i	0.171003	−	0.296186i	−0.767768	−	0.640728i	$-0.778632\pi$
$103$	1.73549	−	3.00596i	0.171003	−	0.296186i	0.938771	+	0.344542i	$0.111966\pi$
$104$		−	6.92554i		−	0.679105i
$105$		0			0
$106$	−2.28889			−0.222317
$107$	−8.18969	+	2.19442i	−0.791727	+	0.212143i	−0.631949	−	0.775010i	$-0.717745\pi$
$107$	−8.18969	+	2.19442i	−0.791727	+	0.212143i	−0.159778	+	0.987153i	$0.551078\pi$
$108$	−4.76669	−	1.27723i	−0.458675	−	0.122902i
$109$	5.11844	+	1.37148i	0.490258	+	0.131364i	0.495475	−	0.868622i	$-0.334994\pi$
$109$	5.11844	+	1.37148i	0.490258	+	0.131364i	−0.00521721	+	0.999986i	$0.501661\pi$
$110$	−28.8258	−	16.6426i	−2.74844	−	1.58681i
$111$		−	11.9469i		−	1.13395i
$112$		0			0
$113$	6.45333	−	6.45333i	0.607078	−	0.607078i	−0.335103	−	0.942181i	$-0.608771\pi$
$113$	6.45333	−	6.45333i	0.607078	−	0.607078i	0.942181	+	0.335103i	$0.108771\pi$
$114$	−7.22344	+	1.93551i	−0.676537	+	0.181278i
$115$	−1.61268	−	2.79325i	−0.150383	−	0.260472i
$116$	−0.576800	+	2.15265i	−0.0535546	+	0.199868i
$117$	5.77221	+	3.33258i	0.533641	+	0.308098i
$118$	−19.2576			−1.77280
$119$		0			0
$120$	7.22114			0.659197
$121$	16.5149	+	9.53488i	1.50135	+	0.866808i
$122$	−3.91929	+	14.6270i	−0.354836	+	1.32427i
$123$	−2.71608	−	4.70439i	−0.244901	−	0.424181i
$124$	8.57989	−	2.29897i	0.770497	−	0.206454i
$125$	6.44228	−	6.44228i	0.576215	−	0.576215i
$126$		0			0
$127$			0.446266i			0.0395997i	0.999804	+	0.0197999i	$0.00630290\pi$
$127$			0.446266i			0.0395997i	−0.999804	+	0.0197999i	$0.993697\pi$
$128$	−10.8674	−	6.27429i	−0.960551	−	0.554574i
$129$	1.27428	+	0.341443i	0.112194	+	0.0300624i
$130$	22.1905	+	5.94592i	1.94623	+	0.521491i
$131$	−0.0425928	+	0.0114127i	−0.00372135	+	0.000997132i	−0.260679	−	0.965425i	$-0.583946\pi$
$131$	−0.0425928	+	0.0114127i	−0.00372135	+	0.000997132i	0.256958	+	0.966423i	$0.417280\pi$
$132$	5.68375			0.494707
$133$		0			0
$134$			0.736617i			0.0636340i
$135$	−9.39424	+	16.2713i	−0.808528	+	1.40041i
$136$	7.51188	−	0.702939i	0.644139	−	0.0602765i
$137$	−0.962069	−	1.66635i	−0.0821951	−	0.142366i	0.821997	−	0.569491i	$-0.192860\pi$
$137$	−0.962069	−	1.66635i	−0.0821951	−	0.142366i	−0.904193	+	0.427125i	$0.859526\pi$
$138$	1.50139	+	0.866828i	0.127807	+	0.0737893i
$139$	4.26435	+	4.26435i	0.361698	+	0.361698i	0.864438	−	0.502740i	$-0.167675\pi$
$139$	4.26435	+	4.26435i	0.361698	+	0.361698i	−0.502740	+	0.864438i	$0.667675\pi$
$140$		0			0
$141$	−2.12115	−	2.12115i	−0.178633	−	0.178633i
$142$	−1.00496	−	3.75055i	−0.0843342	−	0.314740i
$143$	−20.0468	−	5.37152i	−1.67640	−	0.449189i
$144$	7.61841	−	4.39849i	0.634868	−	0.366541i
$145$	7.34815	+	4.24246i	0.610231	+	0.352317i
$146$	11.4837	−	11.4837i	0.950395	−	0.950395i
$147$		0			0
$148$	−7.06743	−	7.06743i	−0.580939	−	0.580939i
$149$	9.58651	−	16.6043i	0.785358	−	1.36028i	−0.143427	−	0.989661i	$-0.545812\pi$
$149$	9.58651	−	16.6043i	0.785358	−	1.36028i	0.928785	−	0.370619i	$-0.120854\pi$
$150$	−3.73358	+	13.9339i	−0.304846	+	1.13770i
$151$	−19.3681	+	11.1822i	−1.57615	+	0.909992i	−0.580763	+	0.814073i	$0.697246\pi$
$151$	−19.3681	+	11.1822i	−1.57615	+	0.909992i	−0.995389	+	0.0959194i	$0.969421\pi$
$152$	3.59038	−	6.21872i	0.291218	−	0.504405i
$153$	−3.02886	+	6.59916i	−0.244869	+	0.533510i
$154$		0			0
$155$		−	33.8186i		−	2.71638i
$156$	−3.78922	+	1.01532i	−0.303380	+	0.0812905i
$157$	−1.50439	−	2.60568i	−0.120063	−	0.207956i	0.799729	−	0.600361i	$-0.204976\pi$
$157$	−1.50439	−	2.60568i	−0.120063	−	0.207956i	−0.919792	+	0.392405i	$0.871643\pi$
$158$	3.02670	−	11.2958i	0.240791	−	0.898644i
$159$	−0.385144	−	1.43738i	−0.0305439	−	0.113991i
$160$	12.2655	−	12.2655i	0.969671	−	0.969671i
$161$		0			0
$162$		−	1.05372i		−	0.0827881i
$163$	−3.82827	−	14.2873i	−0.299853	−	1.11907i	−0.937286	−	0.348562i	$-0.886670\pi$
$163$	−3.82827	−	14.2873i	−0.299853	−	1.11907i	0.637432	−	0.770506i	$-0.279997\pi$
$164$	−4.38972	−	1.17622i	−0.342780	−	0.0918475i
$165$	5.60079	−	20.9024i	0.436021	−	1.62725i
$166$	−2.66833	+	4.62169i	−0.207103	+	0.358712i
$167$	9.61691	+	9.61691i	0.744179	+	0.744179i	0.973379	−	0.229200i	$-0.0736110\pi$
$167$	9.61691	+	9.61691i	0.744179	+	0.744179i	−0.229200	+	0.973379i	$0.573611\pi$
$168$		0			0
$169$	1.32426			0.101866
$170$	−4.19700	+	24.6727i	−0.321895	+	1.89231i
$171$	3.45540	+	5.98492i	0.264241	+	0.457678i
$172$	0.955814	−	0.551839i	0.0728801	−	0.0420773i
$173$	−8.35290	+	2.23815i	−0.635059	+	0.170164i	−0.561965	−	0.827161i	$-0.689954\pi$
$173$	−8.35290	+	2.23815i	−0.635059	+	0.170164i	−0.0730949	+	0.997325i	$0.523288\pi$
$174$	−4.56070			−0.345746
$175$		0			0
$176$	−19.3691	+	19.3691i	−1.46000	+	1.46000i
$177$	−3.24040	−	12.0933i	−0.243564	−	0.908992i
$178$	−4.34997	+	2.51145i	−0.326044	+	0.188241i
$179$	9.27283	−	5.35367i	0.693084	−	0.400152i	−0.111682	−	0.993744i	$-0.535624\pi$
$179$	9.27283	−	5.35367i	0.693084	−	0.400152i	0.804766	+	0.593592i	$0.202291\pi$
$180$	1.50480	+	5.61600i	0.112161	+	0.418592i
$181$	11.4187	−	11.4187i	0.848747	−	0.848747i	−0.141230	−	0.989977i	$-0.545106\pi$
$181$	11.4187	−	11.4187i	0.848747	−	0.848747i	0.989977	+	0.141230i	$0.0451056\pi$
$182$		0			0
$183$	−9.84493			−0.727758
$184$	−1.60797	+	0.430853i	−0.118541	+	0.0317629i
$185$	−32.9553	+	19.0268i	−2.42292	+	1.39888i
$186$	9.08888	+	15.7424i	0.666429	+	1.15429i
$187$	3.79156	−	22.2892i	0.277266	−	1.62995i
$188$	−2.50962			−0.183033
$189$		0			0
$190$	16.8432	+	16.8432i	1.22193	+	1.22193i
$191$	6.92720	−	11.9983i	0.501235	−	0.868164i	−0.498764	−	0.866738i	$-0.666213\pi$
$191$	6.92720	−	11.9983i	0.501235	−	0.868164i	0.999999	−	0.00142617i	$-0.000453966\pi$
$192$	0.464998	−	1.73540i	0.0335584	−	0.125242i
$193$	−14.6825	−	3.93416i	−1.05687	−	0.283187i	−0.311781	−	0.950154i	$-0.600925\pi$
$193$	−14.6825	−	3.93416i	−1.05687	−	0.283187i	−0.745087	+	0.666967i	$0.767592\pi$
$194$	−5.41550	−	20.2109i	−0.388810	−	1.45106i
$195$			14.9356i			1.06956i
$196$		0			0
$197$	−16.0288	+	16.0288i	−1.14200	+	1.14200i	−0.153921	+	0.988083i	$0.549190\pi$
$197$	−16.0288	+	16.0288i	−1.14200	+	1.14200i	−0.988083	+	0.153921i	$0.950810\pi$
$198$	−4.27917	−	15.9701i	−0.304107	−	1.13494i
$199$	−3.03917	+	11.3423i	−0.215441	+	0.804036i	0.770570	+	0.637355i	$0.219972\pi$
$199$	−3.03917	+	11.3423i	−0.215441	+	0.804036i	−0.986011	+	0.166681i	$0.946695\pi$
$200$	−6.92579	−	11.9958i	−0.489727	−	0.848233i
$201$	−0.462580	+	0.123948i	−0.0326279	+	0.00874261i
$202$		−	23.3879i		−	1.64556i
$203$		0			0
$204$	−1.48588	−	4.00697i	−0.104033	−	0.280544i
$205$	−8.65130	+	14.9845i	−0.604233	+	1.04656i
$206$	5.14643	−	2.97130i	0.358569	−	0.207020i
$207$	0.414655	−	1.54751i	0.0288205	−	0.107560i
$208$	9.45290	−	16.3729i	0.655440	−	1.13526i
$209$	−15.2161	−	15.2161i	−1.05252	−	1.05252i
$210$		0			0
$211$	15.4623	−	15.4623i	1.06447	−	1.06447i	0.0666961	−	0.997773i	$-0.478754\pi$
$211$	15.4623	−	15.4623i	1.06447	−	1.06447i	0.997773	−	0.0666961i	$-0.0212458\pi$
$212$	−1.07815	−	0.622469i	−0.0740475	−	0.0427513i
$213$	2.18617	−	1.26219i	0.149794	−	0.0864835i
$214$	−14.0214	−	3.75701i	−0.958481	−	0.256824i
$215$	−1.08757	−	4.05886i	−0.0741716	−	0.276812i
$216$	6.85695	+	6.85695i	0.466557	+	0.466557i
$217$		0			0
$218$	6.41508	+	6.41508i	0.434484	+	0.434484i
$219$	9.14382	+	5.27919i	0.617882	+	0.356734i
$220$	−9.05198	−	15.6785i	−0.610284	−	1.05704i
$221$	1.45391	+	15.5370i	0.0978003	+	1.04513i
$222$	10.2270	−	17.7137i	0.686393	−	1.18887i
$223$			24.5325i			1.64282i	0.570341	+	0.821408i	$0.306811\pi$
$223$			24.5325i			1.64282i	−0.570341	+	0.821408i	$0.693189\pi$
$224$		0			0
$225$	13.3308			0.888721
$226$	15.0927	−	4.04407i	1.00395	−	0.269007i
$227$	10.7023	+	2.86768i	0.710339	+	0.190335i	0.595857	−	0.803091i	$-0.296813\pi$
$227$	10.7023	+	2.86768i	0.710339	+	0.190335i	0.114482	+	0.993425i	$0.463479\pi$
$228$	−3.92885	−	1.05273i	−0.260195	−	0.0697190i
$229$	24.5967	+	14.2009i	1.62539	+	0.938421i	0.985443	+	0.170005i	$0.0543784\pi$
$229$	24.5967	+	14.2009i	1.62539	+	0.938421i	0.639950	+	0.768416i	$0.278955\pi$
$230$		−	5.52207i		−	0.364114i
$231$		0			0
$232$	3.09661	−	3.09661i	0.203303	−	0.203303i
$233$	−4.00596	+	1.07339i	−0.262439	+	0.0703204i	−0.387639	−	0.921811i	$-0.626709\pi$
$233$	−4.00596	+	1.07339i	−0.262439	+	0.0703204i	0.125200	+	0.992132i	$0.460043\pi$
$234$	5.70564	+	9.88246i	0.372989	+	0.646036i
$235$	−2.47299	+	9.22932i	−0.161320	+	0.602054i
$236$	−9.07097	−	5.23713i	−0.590470	−	0.340908i
$237$	7.60281			0.493855
$238$		0			0
$239$	17.2805			1.11778			0.558890	−	0.829242i	$-0.311227\pi$
$239$	17.2805			1.11778			0.558890	+	0.829242i	$0.311227\pi$
$240$	17.0717	+	9.85636i	1.10197	+	0.636225i
$241$	0.0970592	−	0.362230i	0.00625213	−	0.0233333i	−0.962729	−	0.270467i	$-0.912822\pi$
$241$	0.0970592	−	0.362230i	0.00625213	−	0.0233333i	0.968981	+	0.247134i	$0.0794886\pi$
$242$	16.3244	+	28.2748i	1.04938	+	1.81757i
$243$	−14.6948	+	3.93747i	−0.942674	+	0.252589i
$244$	−5.82396	+	5.82396i	−0.372841	+	0.372841i
$245$		0			0
$246$		−	9.30027i		−	0.592964i
$247$	12.8623	+	7.42607i	0.818410	+	0.472509i
$248$	−16.8599	−	4.51759i	−1.07060	−	0.286867i
$249$	−3.35131	−	0.897982i	−0.212381	−	0.0569073i
$250$	15.0668	−	4.03714i	0.952909	−	0.255331i
$251$	15.6012			0.984737			0.492369	−	0.870387i	$-0.336131\pi$
$251$	15.6012			0.984737			0.492369	+	0.870387i	$0.336131\pi$
$252$		0			0
$253$			4.98862i			0.313632i
$254$	−0.382021	+	0.661679i	−0.0239701	+	0.0415175i
$255$	−16.2002	+	1.51596i	−1.01449	+	0.0949331i
$256$	−9.12796	−	15.8101i	−0.570498	−	0.988131i
$257$	18.2668	+	10.5463i	1.13945	+	0.657863i	0.946295	−	0.323305i	$-0.104794\pi$
$257$	18.2668	+	10.5463i	1.13945	+	0.657863i	0.193157	+	0.981168i	$0.438127\pi$
$258$	1.59709	+	1.59709i	0.0994306	+	0.0994306i
$259$		0			0
$260$	8.83547	+	8.83547i	0.547953	+	0.547953i
$261$	1.09083	+	4.07102i	0.0675204	+	0.251990i
$262$	−0.0729221	−	0.0195394i	−0.00450514	−	0.00120715i
$263$	−9.18270	+	5.30164i	−0.566230	+	0.326913i	−0.755642	−	0.654985i	$-0.772675\pi$
$263$	−9.18270	+	5.30164i	−0.566230	+	0.326913i	0.189412	+	0.981898i	$0.439342\pi$
$264$	−9.67248	−	5.58441i	−0.595300	−	0.343697i
$265$	−3.35159	+	3.35159i	−0.205887	+	0.205887i
$266$		0			0
$267$	−2.30909	−	2.30909i	−0.141314	−	0.141314i
$268$	−0.200324	+	0.346972i	−0.0122368	+	0.0211947i
$269$	−7.23090	+	26.9861i	−0.440876	+	1.64537i	0.285725	+	0.958312i	$0.407766\pi$
$269$	−7.23090	+	26.9861i	−0.440876	+	1.64537i	−0.726601	+	0.687060i	$0.758901\pi$
$270$	−27.8577	+	16.0837i	−1.69537	+	0.978820i
$271$	1.44021	−	2.49452i	0.0874868	−	0.151532i	−0.818961	−	0.573849i	$-0.805450\pi$
$271$	1.44021	−	2.49452i	0.0874868	−	0.151532i	0.906448	+	0.422317i	$0.138783\pi$
$272$	18.7186	+	8.59137i	1.13498	+	0.520928i
$273$		0			0
$274$		−	3.29427i		−	0.199014i
$275$	−40.0950	+	10.7434i	−2.41782	+	0.647853i
$276$	0.471471	+	0.816612i	0.0283792	+	0.0491543i
$277$	−1.85581	+	6.92596i	−0.111505	+	0.416141i	−0.999002	−	0.0446725i	$-0.985776\pi$
$277$	−1.85581	+	6.92596i	−0.111505	+	0.416141i	0.887497	+	0.460813i	$0.152442\pi$
$278$	2.67231	+	9.97321i	0.160275	+	0.598153i
$279$	11.8783	−	11.8783i	0.711133	−	0.711133i
$280$		0			0
$281$			20.3361i			1.21315i	0.795026	+	0.606575i	$0.207457\pi$
$281$			20.3361i			1.21315i	−0.795026	+	0.606575i	$0.792543\pi$
$282$	−1.32925	−	4.96082i	−0.0791556	−	0.295413i
$283$	2.98372	+	0.799485i	0.177364	+	0.0475244i	0.346408	−	0.938084i	$-0.387401\pi$
$283$	2.98372	+	0.799485i	0.177364	+	0.0475244i	−0.169044	+	0.985608i	$0.554068\pi$
$284$	0.546600	−	2.03994i	0.0324348	−	0.121048i
$285$	−7.74302	+	13.4113i	−0.458657	+	0.794417i
$286$	−25.1252	−	25.1252i	−1.48568	−	1.48568i
$287$		0			0
$288$	8.61611			0.507709
$289$	−16.7049	+	3.15400i	−0.982639	+	0.185529i
$290$	7.26341	+	12.5806i	0.426522	+	0.738758i
$291$	11.7808	−	6.80164i	0.690602	−	0.398719i
$292$	8.53221	−	2.28620i	0.499310	−	0.133790i
$293$	20.4376			1.19398			0.596989	−	0.802249i	$-0.296364\pi$
$293$	20.4376			1.19398			0.596989	+	0.802249i	$0.296364\pi$
$294$		0			0
$295$	−28.1985	+	28.1985i	−1.64178	+	1.64178i
$296$	5.08330	+	18.9711i	0.295461	+	1.10267i
$297$	25.1666	−	14.5299i	1.46031	−	0.843112i
$298$	28.4279	−	16.4128i	1.64678	−	0.950770i
$299$	−0.891144	−	3.32579i	−0.0515362	−	0.192336i
$300$	−5.54800	+	5.54800i	−0.320314	+	0.320314i
$301$		0			0
$302$	−38.2894			−2.20331
$303$	14.6871	−	3.93539i	0.843751	−	0.226082i
$304$	16.9763	−	9.80125i	0.973655	−	0.562140i
$305$	15.6791	+	27.1570i	0.897784	+	1.55501i
$306$	−10.1400	+	7.19176i	−0.579666	+	0.411126i
$307$	−24.4776			−1.39701			−0.698504	−	0.715606i	$-0.746151\pi$
$307$	−24.4776			−1.39701			−0.698504	+	0.715606i	$0.746151\pi$
$308$		0			0
$309$	2.73188	+	2.73188i	0.155411	+	0.155411i
$310$	28.9500	−	50.1429i	1.64425	−	2.84793i
$311$	0.116599	−	0.435152i	0.00661170	−	0.0246752i	−0.962541	−	0.271136i	$-0.912601\pi$
$311$	0.116599	−	0.435152i	0.00661170	−	0.0246752i	0.969153	+	0.246460i	$0.0792675\pi$
$312$	7.44598	+	1.99515i	0.421546	+	0.112953i
$313$	−4.39395	−	16.3984i	−0.248361	−	0.926894i	−0.971664	−	0.236364i	$-0.924044\pi$
$313$	−4.39395	−	16.3984i	−0.248361	−	0.926894i	0.723304	−	0.690530i	$-0.242623\pi$
$314$		−	5.15126i		−	0.290702i
$315$		0			0
$316$	4.49759	−	4.49759i	0.253009	−	0.253009i
$317$	1.21191	+	4.52292i	0.0680678	+	0.254033i	0.991572	−	0.129555i	$-0.0413550\pi$
$317$	1.21191	+	4.52292i	0.0680678	+	0.254033i	−0.923504	+	0.383588i	$0.874688\pi$
$318$	0.659396	−	2.46090i	0.0369771	−	0.138000i
$319$	−6.56174	−	11.3653i	−0.367387	−	0.636333i
$320$	−5.52762	+	1.48112i	−0.309003	+	0.0827971i
$321$		−	9.43731i		−	0.526739i
$322$		0			0
$323$	−6.74927	+	14.7050i	−0.375539	+	0.818210i
$324$	0.286561	−	0.496339i	0.0159201	−	0.0275744i
$325$	24.8112	−	14.3248i	1.37628	−	0.794596i
$326$	6.55429	−	24.4610i	0.363009	−	1.35477i
$327$	−2.94909	+	5.10798i	−0.163085	+	0.282472i
$328$	6.31467	+	6.31467i	0.348669	+	0.348669i
$329$		0			0
$330$	26.1976	−	26.1976i	1.44213	−	1.44213i
$331$	−29.8812	−	17.2519i	−1.64242	−	0.948251i	−0.979970	−	0.199145i	$-0.936184\pi$
$331$	−29.8812	−	17.2519i	−1.64242	−	0.948251i	−0.662449	−	0.749107i	$-0.730483\pi$
$332$	−2.51375	+	1.45132i	−0.137960	+	0.0796513i
$333$	−18.2579	−	4.89219i	−1.00053	−	0.268090i
$334$	6.02657	+	22.4915i	0.329759	+	1.23068i
$335$	1.07862	+	1.07862i	0.0589311	+	0.0589311i
$336$		0			0
$337$	−19.0302	−	19.0302i	−1.03664	−	1.03664i	−0.999303	−	0.0373355i	$-0.988113\pi$
$337$	−19.0302	−	19.0302i	−1.03664	−	1.03664i	−0.0373355	−	0.999303i	$-0.511887\pi$
$338$	1.96349	+	1.13362i	0.106800	+	0.0616608i
$339$	5.07918	+	8.79740i	0.275863	+	0.477809i
$340$	−8.68672	+	10.4803i	−0.471103	+	0.568374i
$341$	−26.1534	+	45.2990i	−1.41628	+	2.45308i
$342$			11.8318i			0.639790i
$343$		0			0
$344$	−2.16878			−0.116933
$345$	3.46774	−	0.929179i	0.186697	−	0.0500253i
$346$	−14.3008	−	3.83189i	−0.768816	−	0.206004i
$347$	15.9779	+	4.28126i	0.857737	+	0.229830i	0.660778	−	0.750582i	$-0.270227\pi$
$347$	15.9779	+	4.28126i	0.857737	+	0.229830i	0.196959	+	0.980412i	$0.436893\pi$
$348$	−2.14825	−	1.24029i	−0.115158	−	0.0664866i
$349$			10.1340i			0.542461i	0.962514	+	0.271231i	$0.0874306\pi$
$349$			10.1340i			0.542461i	−0.962514	+	0.271231i	$0.912569\pi$
$350$		0			0
$351$	−14.1824	+	14.1824i	−0.757000	+	0.757000i
$352$	−25.9146	+	6.94380i	−1.38125	+	0.370106i
$353$	−0.398773	−	0.690696i	−0.0212246	−	0.0367620i	0.855218	−	0.518268i	$-0.173423\pi$
$353$	−0.398773	−	0.690696i	−0.0212246	−	0.0367620i	−0.876443	+	0.481506i	$0.840090\pi$
$354$	5.54782	−	20.7047i	0.294863	−	1.10044i
$355$	−6.96342	−	4.02033i	−0.369580	−	0.213377i
$356$	−2.73198			−0.144795
$357$		0			0
$358$	18.3318			0.968865
$359$	17.9552	+	10.3664i	0.947638	+	0.547119i	0.892346	−	0.451351i	$-0.149058\pi$
$359$	17.9552	+	10.3664i	0.947638	+	0.547119i	0.0552917	+	0.998470i	$0.482391\pi$
$360$	2.95701	−	11.0357i	0.155848	−	0.581632i
$361$	−1.80027	−	3.11817i	−0.0947512	−	0.164114i
$362$	26.7054	−	7.15570i	1.40361	−	0.376095i
$363$	−15.0091	+	15.0091i	−0.787774	+	0.787774i
$364$		0			0
$365$		−	33.6307i		−	1.76031i
$366$	−14.5971	−	8.42764i	−0.763003	−	0.440520i
$367$	4.72629	+	1.26641i	0.246710	+	0.0661058i	0.380055	−	0.924964i	$-0.375905\pi$
$367$	4.72629	+	1.26641i	0.246710	+	0.0661058i	−0.133345	+	0.991070i	$0.542572\pi$
$368$	−4.38953	−	1.17617i	−0.228820	−	0.0613121i
$369$	−8.30170	+	2.22443i	−0.432169	+	0.115799i
$370$	−65.1505			−3.38702
$371$		0			0
$372$			9.88695i			0.512614i
$373$	−3.32585	+	5.76055i	−0.172206	+	0.298270i	−0.939191	−	0.343395i	$-0.888423\pi$
$373$	−3.32585	+	5.76055i	−0.172206	+	0.298270i	0.766985	+	0.641665i	$0.221756\pi$
$374$	24.7022	−	29.8026i	1.27732	−	1.54105i
$375$	5.07048	+	8.78233i	0.261838	+	0.453518i
$376$	4.27082	+	2.46576i	0.220251	+	0.127162i
$377$	6.40480	+	6.40480i	0.329864	+	0.329864i
$378$		0			0
$379$	−4.33788	−	4.33788i	−0.222822	−	0.222822i	0.586864	−	0.809686i	$-0.300362\pi$
$379$	−4.33788	−	4.33788i	−0.222822	−	0.222822i	−0.809686	+	0.586864i	$0.800362\pi$
$380$	3.35318	+	12.5143i	0.172015	+	0.641968i
$381$	−0.479802	−	0.128563i	−0.0245810	−	0.00658646i
$382$	20.5419	−	11.8599i	1.05102	−	0.606805i
$383$	−25.0907	−	14.4861i	−1.28208	−	0.740207i	−0.304849	−	0.952401i	$-0.598606\pi$
$383$	−25.0907	−	14.4861i	−1.28208	−	0.740207i	−0.977228	+	0.212193i	$0.931939\pi$
$384$	9.87652	−	9.87652i	0.504009	−	0.504009i
$385$		0			0
$386$	−18.4019	−	18.4019i	−0.936634	−	0.936634i
$387$	1.04362	−	1.80760i	0.0530502	−	0.0918856i
$388$	2.94551	−	10.9928i	0.149536	−	0.558074i
$389$	−8.85496	+	5.11242i	−0.448964	+	0.259210i	−0.707393	−	0.706821i	$-0.750129\pi$
$389$	−8.85496	+	5.11242i	−0.448964	+	0.259210i	0.258428	+	0.966030i	$0.416795\pi$
$390$	−12.7855	+	22.1451i	−0.647418	+	1.12136i
$391$	3.51692	−	1.30416i	0.177858	−	0.0659541i
$392$		0			0
$393$		−	0.0490814i		−	0.00247583i
$394$	−37.4872	+	10.0447i	−1.88858	+	0.506042i
$395$	−12.1083	−	20.9722i	−0.609234	−	1.05522i
$396$	2.32746	−	8.68618i	0.116959	−	0.436497i
$397$	1.22117	+	4.55748i	0.0612890	+	0.228734i	0.989776	−	0.142632i	$-0.0455564\pi$
$397$	1.22117	+	4.55748i	0.0612890	+	0.228734i	−0.928487	+	0.371365i	$0.878890\pi$
$398$	−14.2156	+	14.2156i	−0.712566	+	0.712566i
$399$		0			0
$400$		−	37.8129i		−	1.89065i
$401$	−1.95330	−	7.28982i	−0.0975432	−	0.364036i	0.899850	−	0.436200i	$-0.143676\pi$
$401$	−1.95330	−	7.28982i	−0.0975432	−	0.364036i	−0.997393	+	0.0721641i	$0.977009\pi$
$402$	−0.791972	−	0.212208i	−0.0395000	−	0.0105840i
$403$	9.34383	−	34.8717i	0.465450	−	1.73708i
$404$	6.36037	−	11.0165i	0.316440	−	0.548091i
$405$	−1.54295	−	1.54295i	−0.0766696	−	0.0766696i
$406$		0			0
$407$	58.8568			2.91742
$408$	−1.40830	+	8.27889i	−0.0697212	+	0.409866i
$409$	−5.65042	−	9.78681i	−0.279395	−	0.483927i	0.691839	−	0.722051i	$-0.256801\pi$
$409$	−5.65042	−	9.78681i	−0.279395	−	0.483927i	−0.971235	+	0.238125i	$0.923467\pi$
$410$	−25.6546	+	14.8117i	−1.26699	+	0.731497i
$411$	2.06873	−	0.554316i	0.102043	−	0.0273424i
$412$	3.23220			0.159239
$413$		0			0
$414$	1.93954	−	1.93954i	0.0953232	−	0.0953232i
$415$	2.86027	+	10.6747i	0.140405	+	0.523998i
$416$	16.0363	−	9.25853i	0.786242	−	0.453937i
$417$	−5.81331	+	3.35631i	−0.284679	+	0.164359i
$418$	−9.53536	−	35.5864i	−0.466390	−	1.74059i
$419$	−20.0293	+	20.0293i	−0.978497	+	0.978497i	−0.999774	−	0.0212763i	$-0.993227\pi$
$419$	−20.0293	+	20.0293i	−0.978497	+	0.978497i	0.0212763	+	0.999774i	$0.493227\pi$
$420$		0			0
$421$	35.8374			1.74661			0.873304	−	0.487176i	$-0.161973\pi$
$421$	35.8374			1.74661			0.873304	+	0.487176i	$0.161973\pi$
$422$	36.1623	−	9.68966i	1.76035	−	0.471685i
$423$	−4.11025	+	2.37305i	−0.199847	+	0.115382i
$424$	1.22318	+	2.11861i	0.0594029	+	0.102889i
$425$	18.0559	+	25.4579i	0.875839	+	1.23489i
$426$	4.32191			0.209397
$427$		0			0
$428$	−5.58282	−	5.58282i	−0.269856	−	0.269856i
$429$	11.5504	−	20.0058i	0.557657	−	0.965890i
$430$	1.86200	−	6.94909i	0.0897937	−	0.335115i
$431$	−5.34307	−	1.43167i	−0.257366	−	0.0689611i	0.127829	−	0.991796i	$-0.459199\pi$
$431$	−5.34307	−	1.43167i	−0.257366	−	0.0689611i	−0.385195	+	0.922835i	$0.625866\pi$
$432$	6.85146	+	25.5700i	0.329641	+	1.23024i
$433$		−	2.97397i		−	0.142920i	−0.997443	−	0.0714599i	$-0.977234\pi$
$433$		−	2.97397i		−	0.142920i	0.997443	−	0.0714599i	$-0.0227658\pi$
$434$		0			0
$435$	−6.67816	+	6.67816i	−0.320193	+	0.320193i
$436$	1.27713	+	4.76632i	0.0611635	+	0.228265i
$437$	0.923984	−	3.44835i	0.0442001	−	0.164957i
$438$	9.03837	+	15.6549i	0.431870	+	0.748021i
$439$	−1.72376	+	0.461879i	−0.0822704	+	0.0220443i	−0.299719	−	0.954027i	$-0.596893\pi$
$439$	−1.72376	+	0.461879i	−0.0822704	+	0.0220443i	0.217449	+	0.976072i	$0.430226\pi$
$440$			35.5751i			1.69598i
$441$		0			0
$442$	−11.1446	+	24.2813i	−0.530093	+	1.15495i
$443$	4.35062	−	7.53550i	0.206704	−	0.358022i	−0.743970	−	0.668213i	$-0.767060\pi$
$443$	4.35062	−	7.53550i	0.206704	−	0.358022i	0.950674	+	0.310190i	$0.100393\pi$
$444$	9.63456	−	5.56251i	0.457236	−	0.263985i
$445$	−2.69210	+	10.0471i	−0.127618	+	0.476277i
$446$	−21.0007	+	36.3743i	−0.994414	+	1.72238i
$447$	15.0904	+	15.0904i	0.713750	+	0.713750i
$448$		0			0
$449$	−12.5684	+	12.5684i	−0.593139	+	0.593139i	−0.938478	−	0.345339i	$-0.887764\pi$
$449$	−12.5684	+	12.5684i	−0.593139	+	0.593139i	0.345339	+	0.938478i	$0.387764\pi$
$450$	19.7656	+	11.4117i	0.931760	+	0.537952i
$451$	23.1763	−	13.3808i	1.09133	−	0.630079i
$452$	8.20895	+	2.19958i	0.386117	+	0.103460i
$453$	−6.44283	−	24.0450i	−0.302711	−	1.12973i
$454$	13.4135	+	13.4135i	0.629528	+	0.629528i
$455$		0			0
$456$	5.65171	+	5.65171i	0.264666	+	0.264666i
$457$	19.4170	+	11.2104i	0.908287	+	0.524400i	0.879880	−	0.475196i	$-0.157623\pi$
$457$	19.4170	+	11.2104i	0.908287	+	0.524400i	0.0284077	+	0.999596i	$0.490956\pi$
$458$	24.3130	+	42.1114i	1.13607	+	1.96773i
$459$	−16.8226	−	13.9436i	−0.785213	−	0.650833i
$460$	1.50174	−	2.60108i	0.0700189	−	0.121276i
$461$		−	24.0555i		−	1.12038i	−0.828365	−	0.560189i	$-0.810729\pi$
$461$		−	24.0555i		−	1.12038i	0.828365	−	0.560189i	$-0.189271\pi$
$462$		0			0
$463$	−0.665002			−0.0309053			−0.0154526	−	0.999881i	$-0.504919\pi$
$463$	−0.665002			−0.0309053			−0.0154526	+	0.999881i	$0.504919\pi$
$464$	11.5475	−	3.09413i	0.536078	−	0.143642i
$465$	36.3600	+	9.74264i	1.68616	+	0.451804i
$466$	−6.85851	−	1.83773i	−0.317714	−	0.0851313i
$467$	17.8345	+	10.2968i	0.825283	+	0.476477i	0.852235	−	0.523160i	$-0.175247\pi$
$467$	17.8345	+	10.2968i	0.825283	+	0.476477i	−0.0269521	+	0.999637i	$0.508580\pi$
$468$			6.20664i			0.286902i
$469$		0			0
$470$	−11.5674	+	11.5674i	−0.533562	+	0.533562i
$471$	3.23488	−	0.866784i	0.149056	−	0.0399393i
$472$	10.2912	+	17.8249i	0.473691	+	0.820456i
$473$	−1.68213	+	6.27778i	−0.0773443	+	0.288653i
$474$	11.2727	+	6.50829i	0.517772	+	0.298936i
$475$	29.7053			1.36297
$476$		0			0
$477$	−2.35439			−0.107800
$478$	25.6218	+	14.7927i	1.17191	+	0.676604i
$479$	2.39514	−	8.93877i	0.109437	−	0.408423i	−0.889374	−	0.457180i	$-0.848859\pi$
$479$	2.39514	−	8.93877i	0.109437	−	0.408423i	0.998811	+	0.0487575i	$0.0155261\pi$
$480$	9.65370	+	16.7207i	0.440629	+	0.763192i
$481$	−39.2384	+	10.5139i	−1.78912	+	0.479393i
$482$	0.453992	−	0.453992i	0.0206788	−	0.0206788i
$483$		0			0
$484$			17.7579i			0.807175i
$485$	−37.5243	−	21.6647i	−1.70389	−	0.983742i
$486$	−25.1587	−	6.74124i	−1.14122	−	0.305789i
$487$	−1.48334	−	0.397459i	−0.0672164	−	0.0180106i	0.225054	−	0.974346i	$-0.427744\pi$
$487$	−1.48334	−	0.397459i	−0.0672164	−	0.0180106i	−0.292271	+	0.956336i	$0.594411\pi$
$488$	15.6333	−	4.18892i	0.707685	−	0.189624i
$489$	16.4638			0.744521
$490$		0			0
$491$			14.6140i			0.659521i	0.944065	+	0.329760i	$0.106968\pi$
$491$			14.6140i			0.659521i	−0.944065	+	0.329760i	$0.893032\pi$
$492$	2.52923	−	4.38075i	0.114026	−	0.197499i
$493$	−6.29697	+	7.59713i	−0.283601	+	0.342158i
$494$	12.7140	+	22.0213i	0.572029	+	0.990784i
$495$	−29.6506	−	17.1188i	−1.33270	−	0.769433i
$496$	−33.6928	−	33.6928i	−1.51285	−	1.51285i
$497$		0			0
$498$	−4.20029	−	4.20029i	−0.188220	−	0.188220i
$499$	5.14229	+	19.1913i	0.230200	+	0.859119i	0.980254	+	0.197742i	$0.0633610\pi$
$499$	5.14229	+	19.1913i	0.230200	+	0.859119i	−0.750054	+	0.661377i	$0.769972\pi$
$500$	8.19490	+	2.19582i	0.366487	+	0.0981999i
$501$	−13.1101	+	7.56912i	−0.585716	+	0.338163i
$502$	23.1319	+	13.3552i	1.03243	+	0.596072i
$503$	−25.4194	+	25.4194i	−1.13339	+	1.13339i	−0.143786	+	0.989609i	$0.545928\pi$
$503$	−25.4194	+	25.4194i	−1.13339	+	1.13339i	−0.989609	+	0.143786i	$0.954072\pi$
$504$		0			0
$505$	−34.2465	−	34.2465i	−1.52395	−	1.52395i
$506$	−4.27045	+	7.39663i	−0.189845	+	0.328821i
$507$	−0.381500	+	1.42378i	−0.0169430	+	0.0632322i
$508$	−0.359890	+	0.207782i	−0.0159675	+	0.00921886i
$509$	4.03432	−	6.98765i	0.178818	−	0.309722i	−0.762658	−	0.646802i	$-0.776106\pi$
$509$	4.03432	−	6.98765i	0.178818	−	0.309722i	0.941476	+	0.337080i	$0.109439\pi$
$510$	−25.3177	−	11.6202i	−1.12109	−	0.514552i
$511$		0			0
$512$		−	6.15837i		−	0.272164i
$513$	−20.0875	+	5.38242i	−0.886883	+	0.237640i
$514$	18.0561	+	31.2741i	0.796422	+	1.37944i
$515$	3.18502	−	11.8867i	0.140349	−	0.523789i
$516$	0.317953	+	1.18662i	0.0139971	+	0.0522379i
$517$	10.4499	−	10.4499i	0.459587	−	0.459587i
$518$		0			0
$519$		−	9.62539i		−	0.422508i
$520$	−6.35497	−	23.7171i	−0.278684	−	1.04006i
$521$	−7.40759	−	1.98486i	−0.324532	−	0.0869582i	0.0928746	−	0.995678i	$-0.470394\pi$
$521$	−7.40759	−	1.98486i	−0.324532	−	0.0869582i	−0.417407	+	0.908720i	$0.637061\pi$
$522$	−1.86758	+	6.96989i	−0.0817416	+	0.305064i
$523$	16.3473	−	28.3144i	0.714819	−	1.23810i	−0.248210	−	0.968706i	$-0.579842\pi$
$523$	16.3473	−	28.3144i	0.714819	−	1.23810i	0.963029	−	0.269397i	$-0.0868242\pi$
$524$	−0.0290350	−	0.0290350i	−0.00126840	−	0.00126840i
$525$		0			0
$526$	−18.1536			−0.791535
$527$	38.7724	+	6.59546i	1.68895	+	0.287303i
$528$	−15.2447	−	26.4046i	−0.663439	−	1.14911i
$529$	19.2018	−	11.0862i	0.834863	−	0.482008i
$530$	−7.83850	+	2.10032i	−0.340483	+	0.0912320i
$531$	−19.8086			−0.859619
$532$		0			0
$533$	−13.0608	+	13.0608i	−0.565725	+	0.565725i
$534$	−1.44702	−	5.40037i	−0.0626189	−	0.233697i
$535$	−26.0326	+	15.0299i	−1.12549	+	0.649800i
$536$	0.681815	−	0.393646i	0.0294499	−	0.0170029i
$537$	3.08463	+	11.5120i	0.133111	+	0.496779i
$538$	−33.8224	+	33.8224i	−1.45819	+	1.45819i
$539$		0			0
$540$	−17.4959			−0.752905
$541$	19.7308	−	5.28686i	0.848294	−	0.227300i	0.191615	−	0.981470i	$-0.438627\pi$
$541$	19.7308	−	5.28686i	0.848294	−	0.227300i	0.656679	+	0.754170i	$0.271961\pi$
$542$	4.27082	−	2.46576i	0.183447	−	0.105913i
$543$	8.98726	+	15.5664i	0.385680	+	0.668018i
$544$	11.6701	+	16.4542i	0.500350	+	0.705468i
$545$	18.7870			0.804746
$546$		0			0
$547$	30.6169	+	30.6169i	1.30908	+	1.30908i	0.922077	+	0.387007i	$0.126491\pi$
$547$	30.6169	+	30.6169i	1.30908	+	1.30908i	0.387007	+	0.922077i	$0.373509\pi$
$548$	0.895883	−	1.55172i	0.0382702	−	0.0662860i
$549$	−4.03143	+	15.0455i	−0.172057	+	0.642127i
$550$	−68.6457	−	18.3936i	−2.92706	−	0.784304i
$551$	2.43071	+	9.07153i	0.103552	+	0.386460i
$552$		−	1.85292i		−	0.0788657i
$553$		0			0
$554$	−8.68050	+	8.68050i	−0.368799	+	0.368799i
$555$	−10.9627	−	40.9132i	−0.465339	−	1.73667i
$556$	−1.45348	+	5.42446i	−0.0616413	+	0.230049i
$557$	−10.6080	−	18.3736i	−0.449476	−	0.778515i	0.548876	−	0.835904i	$-0.315056\pi$
$557$	−10.6080	−	18.3736i	−0.449476	−	0.778515i	−0.998352	+	0.0573890i	$0.981722\pi$
$558$	27.7802	−	7.44367i	1.17603	−	0.315116i
$559$		−	4.48573i		−	0.189726i
$560$		0			0
$561$	22.8719	+	10.4977i	0.965654	+	0.443212i
$562$	−17.4085	+	30.1524i	−0.734332	+	1.27190i
$563$	15.4255	−	8.90589i	0.650106	−	0.375339i	−0.138391	−	0.990378i	$-0.544193\pi$
$563$	15.4255	−	8.90589i	0.650106	−	0.375339i	0.788497	+	0.615039i	$0.210860\pi$
$564$	0.722983	−	2.69821i	0.0304431	−	0.113615i
$565$	16.1783	−	28.0216i	0.680625	−	1.17888i
$566$	3.73957	+	3.73957i	0.157186	+	0.157186i
$567$		0			0
$568$	−2.93448	+	2.93448i	−0.123128	+	0.123128i
$569$	18.1160	+	10.4593i	0.759461	+	0.438475i	0.829102	−	0.559097i	$-0.188852\pi$
$569$	18.1160	+	10.4593i	0.759461	+	0.438475i	−0.0696410	+	0.997572i	$0.522185\pi$
$570$	−22.9612	+	13.2566i	−0.961738	+	0.555260i
$571$	25.9951	+	6.96537i	1.08786	+	0.291492i	0.757813	−	0.652472i	$-0.226268\pi$
$571$	25.9951	+	6.96537i	1.08786	+	0.291492i	0.330049	+	0.943964i	$0.392935\pi$
$572$	−5.00199	−	18.6677i	−0.209144	−	0.780534i
$573$	10.9043	+	10.9043i	0.455533	+	0.455533i
$574$		0			0
$575$	−4.86947	−	4.86947i	−0.203071	−	0.203071i
$576$	−2.46171	−	1.42127i	−0.102571	−	0.0592195i
$577$	2.04925	+	3.54940i	0.0853113	+	0.147764i	0.905524	−	0.424295i	$-0.139478\pi$
$577$	2.04925	+	3.54940i	0.0853113	+	0.147764i	−0.820213	+	0.572059i	$0.806145\pi$
$578$	−27.4683	−	9.62356i	−1.14253	−	0.400287i
$579$	8.45961	−	14.6525i	0.351569	−	0.608936i
$580$			7.90119i			0.328079i
$581$		0			0
$582$	23.2898			0.965395
$583$	7.08128	−	1.89742i	0.293276	−	0.0785832i
$584$	−16.7662	−	4.49248i	−0.693789	−	0.185900i
$585$	22.8254	+	6.11605i	0.943714	+	0.252867i
$586$	30.3029	+	17.4954i	1.25180	+	0.722727i
$587$			30.1079i			1.24269i	0.783538	+	0.621344i	$0.213413\pi$
$587$			30.1079i			1.24269i	−0.783538	+	0.621344i	$0.786587\pi$
$588$		0			0
$589$	26.4686	−	26.4686i	1.09062	−	1.09062i
$590$	−65.9490	+	17.6710i	−2.71508	+	0.727503i
$591$	−12.6157	−	21.8510i	−0.518939	−	0.898829i
$592$	−13.8767	+	51.7886i	−0.570329	+	2.12850i
$593$	−14.5870	−	8.42179i	−0.599015	−	0.345842i	0.169639	−	0.985506i	$-0.445740\pi$
$593$	−14.5870	−	8.42179i	−0.599015	−	0.345842i	−0.768654	+	0.639665i	$0.779073\pi$
$594$	49.7527			2.04138
$595$		0			0
$596$	17.8540			0.731329
$597$	−11.3191	−	6.53511i	−0.463262	−	0.267464i
$598$	1.52571	−	5.69401i	0.0623908	−	0.232846i
$599$	3.18826	+	5.52223i	0.130269	+	0.225632i	0.923780	−	0.382923i	$-0.125083\pi$
$599$	3.18826	+	5.52223i	0.130269	+	0.225632i	−0.793511	+	0.608556i	$0.791749\pi$
$600$	14.8925	−	3.99043i	0.607984	−	0.162909i
$601$	22.6980	−	22.6980i	0.925870	−	0.925870i	−0.0715659	−	0.997436i	$-0.522800\pi$
$601$	22.6980	−	22.6980i	0.925870	−	0.925870i	0.997436	+	0.0715659i	$0.0227996\pi$
$602$		0			0
$603$			0.757694i			0.0308557i
$604$	−18.0356	−	10.4129i	−0.733860	−	0.423694i
$605$	65.3059	+	17.4987i	2.65506	+	0.711422i
$606$	25.1454	+	6.73769i	1.02146	+	0.273700i
$607$	−13.5012	+	3.61765i	−0.547998	+	0.146836i	−0.522187	−	0.852831i	$-0.674884\pi$
$607$	−13.5012	+	3.61765i	−0.547998	+	0.146836i	−0.0258115	+	0.999667i	$0.508217\pi$
$608$	19.1994			0.778640
$609$		0			0
$610$			53.6877i			2.17375i
$611$	−5.09998	+	8.83343i	−0.206323	+	0.357362i
$612$	−6.73211	+	0.629970i	−0.272130	+	0.0254650i
$613$	15.4989	+	26.8448i	0.625993	+	1.08425i	0.988348	+	0.152212i	$0.0486396\pi$
$613$	15.4989	+	26.8448i	0.625993	+	1.08425i	−0.362355	+	0.932040i	$0.618027\pi$
$614$	−36.2929	−	20.9537i	−1.46466	−	0.845624i
$615$	−13.6182	−	13.6182i	−0.549140	−	0.549140i
$616$		0			0
$617$	−22.1042	−	22.1042i	−0.889883	−	0.889883i	0.104629	−	0.994511i	$-0.466635\pi$
$617$	−22.1042	−	22.1042i	−0.889883	−	0.889883i	−0.994511	+	0.104629i	$0.966635\pi$
$618$	1.71197	+	6.38916i	0.0688656	+	0.257010i
$619$	6.77708	+	1.81591i	0.272394	+	0.0729877i	0.392430	−	0.919782i	$-0.371634\pi$
$619$	6.77708	+	1.81591i	0.272394	+	0.0729877i	−0.120036	+	0.992769i	$0.538301\pi$
$620$	27.2729	−	15.7460i	1.09531	−	0.632376i
$621$	4.17517	+	2.41054i	0.167544	+	0.0967315i
$622$	0.545387	−	0.545387i	0.0218680	−	0.0218680i
$623$		0			0
$624$	14.8800	+	14.8800i	0.595679	+	0.595679i
$625$	−2.77381	+	4.80437i	−0.110952	+	0.192175i
$626$	7.52277	−	28.0754i	0.300670	−	1.12212i
$627$	20.7431	−	11.9760i	0.828398	−	0.478276i
$628$	1.40089	−	2.42642i	0.0559018	−	0.0968247i
$629$	−15.3867	−	41.4933i	−0.613509	−	1.65445i
$630$		0			0
$631$		−	12.0354i		−	0.479123i	−0.970881	−	0.239562i	$-0.922996\pi$
$631$		−	12.0354i		−	0.479123i	0.970881	−	0.239562i	$-0.0770037\pi$
$632$	−12.0729	+	3.23492i	−0.480233	+	0.128678i
$633$	12.1698	+	21.0787i	0.483707	+	0.837804i
$634$	−2.07489	+	7.74359i	−0.0824043	+	0.307537i
$635$	0.409500	+	1.52827i	0.0162505	+	0.0606477i
$636$	0.979845	−	0.979845i	0.0388534	−	0.0388534i
$637$		0			0
$638$		−	22.4684i		−	0.889533i
$639$	−1.03371	−	3.85787i	−0.0408930	−	0.152615i
$640$	−42.9736	−	11.5147i	−1.69868	−	0.455160i
$641$	9.93203	−	37.0668i	0.392291	−	1.46405i	−0.434053	−	0.900887i	$-0.642917\pi$
$641$	9.93203	−	37.0668i	0.392291	−	1.46405i	0.826345	−	0.563164i	$-0.190416\pi$
$642$	8.07869	−	13.9927i	0.318841	−	0.552248i
$643$	4.98124	+	4.98124i	0.196441	+	0.196441i	0.798472	−	0.602031i	$-0.205642\pi$
$643$	4.98124	+	4.98124i	0.196441	+	0.196441i	−0.602031	+	0.798472i	$0.705642\pi$
$644$		0			0
$645$	4.67719			0.184164
$646$	−22.5952	+	16.0256i	−0.888997	+	0.630517i
$647$	22.7185	+	39.3496i	0.893156	+	1.54699i	0.836070	+	0.548623i	$0.184848\pi$
$647$	22.7185	+	39.3496i	0.893156	+	1.54699i	0.0570861	+	0.998369i	$0.481819\pi$
$648$	−0.975328	+	0.563106i	−0.0383145	+	0.0221209i
$649$	59.5781	−	15.9639i	2.33865	−	0.626639i
$650$	49.0502			1.92391
$651$		0			0
$652$	9.73950	−	9.73950i	0.381428	−	0.381428i
$653$	0.740855	+	2.76491i	0.0289919	+	0.108199i	0.978906	−	0.204313i	$-0.0654961\pi$
$653$	0.740855	+	2.76491i	0.0289919	+	0.108199i	−0.949914	+	0.312512i	$0.898829\pi$
$654$	−8.74525	+	5.04907i	−0.341966	+	0.197434i
$655$	−0.135390	+	0.0781674i	−0.00529012	+	0.00305425i
$656$	6.30962	+	23.5478i	0.246349	+	0.919388i
$657$	11.8122	−	11.8122i	0.460840	−	0.460840i
$658$		0			0
$659$	−3.39527			−0.132261			−0.0661305	−	0.997811i	$-0.521065\pi$
$659$	−3.39527			−0.132261			−0.0661305	+	0.997811i	$0.521065\pi$
$660$	19.4644	−	5.21548i	0.757652	−	0.203012i
$661$	13.0399	−	7.52858i	0.507193	−	0.292828i	−0.224486	−	0.974477i	$-0.572070\pi$
$661$	13.0399	−	7.52858i	0.507193	−	0.292828i	0.731679	+	0.681649i	$0.238737\pi$
$662$	−29.5366	−	51.1589i	−1.14797	−	1.98835i
$663$	−17.1234	−	2.91282i	−0.665019	−	0.113124i
$664$	5.70380			0.221350
$665$		0			0
$666$	−22.8831	−	22.8831i	−0.886702	−	0.886702i
$667$	1.08860	−	1.88552i	0.0421509	−	0.0730075i
$668$	−3.27787	+	12.2332i	−0.126825	+	0.473316i
$669$	−26.3760	−	7.06744i	−1.01976	−	0.273243i
$670$	0.675929	+	2.52260i	0.0261134	+	0.0974566i
$671$		−	48.5013i		−	1.87237i
$672$		0			0
$673$	16.6305	−	16.6305i	0.641060	−	0.641060i	−0.309756	−	0.950816i	$-0.600247\pi$
$673$	16.6305	−	16.6305i	0.641060	−	0.641060i	0.950816	+	0.309756i	$0.100247\pi$
$674$	−11.9255	−	44.5066i	−0.459353	−	1.71433i
$675$	−10.3826	+	38.7484i	−0.399627	+	1.49143i
$676$	0.616580	+	1.06795i	0.0237146	+	0.0410749i
$677$	36.5743	−	9.80007i	1.40567	−	0.376647i	0.525290	−	0.850923i	$-0.323957\pi$
$677$	36.5743	−	9.80007i	1.40567	−	0.376647i	0.880376	+	0.474276i	$0.157290\pi$
$678$			17.3919i			0.667931i
$679$		0			0
$680$	25.0800	−	9.30027i	0.961775	−	0.356649i
$681$	−6.16636	+	10.6805i	−0.236296	+	0.409276i
$682$	−77.5553	+	44.7766i	−2.96975	+	1.71458i
$683$	6.07995	−	22.6907i	0.232643	−	0.868235i	−0.746554	−	0.665324i	$-0.768293\pi$
$683$	6.07995	−	22.6907i	0.232643	−	0.868235i	0.979197	−	0.202910i	$-0.0650400\pi$
$684$	−3.21768	+	5.57318i	−0.123031	+	0.213096i
$685$	−4.82375	−	4.82375i	−0.184306	−	0.184306i
$686$		0			0
$687$	−22.3540	+	22.3540i	−0.852858	+	0.852858i
$688$	−5.12728	−	2.96023i	−0.195476	−	0.112858i
$689$	−4.38197	+	2.52993i	−0.166940	+	0.0963827i
$690$	5.93704	+	1.59083i	0.226019	+	0.0605617i
$691$	−2.21071	−	8.25050i	−0.0840995	−	0.313864i	0.911043	−	0.412312i	$-0.135279\pi$
$691$	−2.21071	−	8.25050i	−0.0840995	−	0.313864i	−0.995142	+	0.0984485i	$0.968612\pi$
$692$	−5.69408	−	5.69408i	−0.216457	−	0.216457i
$693$		0			0
$694$	20.0255	+	20.0255i	0.760157	+	0.760157i
$695$	18.5166	+	10.6906i	0.702376	+	0.405517i
$696$	2.43723	+	4.22140i	0.0923829	+	0.160012i
$697$	−15.4922	−	12.8409i	−0.586810	−	0.486384i
$698$	−8.67510	+	15.0257i	−0.328357	+	0.568732i
$699$		−	4.61623i		−	0.174602i
$700$		0			0
$701$	−9.16499			−0.346157			−0.173078	−	0.984908i	$-0.555371\pi$
$701$	−9.16499			−0.346157			−0.173078	+	0.984908i	$0.555371\pi$
$702$	−33.1689	+	8.88759i	−1.25188	+	0.335440i
$703$	−40.6844	−	10.9014i	−1.53444	−	0.411152i
$704$	8.54948	+	2.29083i	0.322220	+	0.0863387i
$705$	−9.21045	−	5.31766i	−0.346886	−	0.200275i
$706$		−	1.36546i		−	0.0513898i
$707$		0			0
$708$	8.24390	−	8.24390i	0.309825	−	0.309825i
$709$	−1.42573	+	0.382022i	−0.0535443	+	0.0143471i	−0.285492	−	0.958381i	$-0.592157\pi$
$709$	−1.42573	+	0.382022i	−0.0535443	+	0.0143471i	0.231947	+	0.972728i	$0.425490\pi$
$710$	−6.88312	−	11.9219i	−0.258319	−	0.447421i
$711$	3.11330	−	11.6190i	0.116758	−	0.435746i
$712$	4.64922	+	2.68423i	0.174237	+	0.100596i
$713$	−8.67777			−0.324985
$714$		0			0
$715$	−73.5808			−2.75177
$716$	8.63490	+	4.98536i	0.322701	+	0.186312i
$717$	−4.97824	+	18.5791i	−0.185916	+	0.693848i
$718$	17.7481	+	30.7406i	0.662354	+	1.14723i
$719$	10.7868	−	2.89031i	0.402280	−	0.107791i	−0.0520056	−	0.998647i	$-0.516561\pi$
$719$	10.7868	−	2.89031i	0.402280	−	0.107791i	0.454285	+	0.890856i	$0.349895\pi$
$720$	22.0537	−	22.0537i	0.821894	−	0.821894i
$721$		0			0
$722$		−	6.16441i		−	0.229416i
$723$	0.361489	+	0.208706i	0.0134439	+	0.00776186i
$724$	14.5252	+	3.89201i	0.539824	+	0.144645i
$725$	17.4989	+	4.68880i	0.649891	+	0.174138i
$726$	−35.1024	+	9.40566i	−1.30277	+	0.349077i
$727$	29.4789			1.09331			0.546656	−	0.837357i	$-0.315901\pi$
$727$	29.4789			1.09331			0.546656	+	0.837357i	$0.315901\pi$
$728$		0			0
$729$		−	18.7798i		−	0.695549i
$730$	28.7892	−	49.8643i	1.06553	−	1.84556i
$731$	4.86551	−	0.455300i	0.179958	−	0.0168399i
$732$	−4.58382	−	7.93942i	−0.169423	−	0.293449i
$733$	−12.5234	−	7.23042i	−0.462564	−	0.267062i	0.250558	−	0.968102i	$-0.419386\pi$
$733$	−12.5234	−	7.23042i	−0.462564	−	0.267062i	−0.713122	+	0.701040i	$0.752719\pi$
$734$	5.92358	+	5.92358i	0.218643	+	0.218643i
$735$		0			0
$736$	−3.14729	−	3.14729i	−0.116011	−	0.116011i
$737$	−0.610632	−	2.27891i	−0.0224929	−	0.0839448i
$738$	−14.2131	−	3.80840i	−0.523193	−	0.140189i
$739$	−15.6314	+	9.02477i	−0.575009	+	0.331982i	−0.759147	−	0.650919i	$-0.774384\pi$
$739$	−15.6314	+	9.02477i	−0.575009	+	0.331982i	0.184139	+	0.982900i	$0.441050\pi$
$740$	−30.6881	−	17.7178i	−1.12812	−	0.651320i
$741$	−11.6896	+	11.6896i	−0.429427	+	0.429427i
$742$		0			0
$743$	22.5374	+	22.5374i	0.826816	+	0.826816i	0.987075	−	0.160259i	$-0.0512331\pi$
$743$	22.5374	+	22.5374i	0.826816	+	0.826816i	−0.160259	+	0.987075i	$0.551233\pi$
$744$	9.71415	−	16.8254i	0.356138	−	0.616849i
$745$	17.5934	−	65.6595i	0.644573	−	2.40558i
$746$	−9.86250	+	5.69412i	−0.361092	+	0.208476i
$747$	−2.74468	+	4.75393i	−0.100423	+	0.173937i
$748$	19.7404	−	7.32023i	0.721782	−	0.267654i
$749$		0			0
$750$			17.3621i			0.633974i
$751$	38.1123	−	10.2122i	1.39074	−	0.372647i	0.515729	−	0.856752i	$-0.327521\pi$
$751$	38.1123	−	10.2122i	1.39074	−	0.372647i	0.875010	+	0.484104i	$0.160854\pi$
$752$	6.73118	+	11.6587i	0.245461	+	0.425151i
$753$	−4.49446	+	16.7736i	−0.163787	+	0.611263i
$754$	4.01365	+	14.9792i	0.146169	+	0.545508i
$755$	−56.0666	+	56.0666i	−2.04047	+	2.04047i
$756$		0			0
$757$			11.7657i			0.427633i	0.976874	+	0.213816i	$0.0685894\pi$
$757$			11.7657i			0.427633i	−0.976874	+	0.213816i	$0.931411\pi$
$758$	−2.71839	−	10.1452i	−0.0987364	−	0.368489i
$759$	−5.36351	−	1.43715i	−0.194683	−	0.0521651i
$760$	6.58916	−	24.5911i	0.239014	−	0.892012i
$761$	13.1983	−	22.8602i	0.478439	−	0.828680i	−0.521256	−	0.853400i	$-0.674536\pi$
$761$	13.1983	−	22.8602i	0.478439	−	0.828680i	0.999694	+	0.0247205i	$0.00786959\pi$
$762$	−0.601349	−	0.601349i	−0.0217846	−	0.0217846i
$763$		0			0
$764$	12.9013			0.466752
$765$	−4.31709	+	25.3787i	−0.156085	+	0.917567i
$766$	−24.8014	−	42.9572i	−0.896110	−	1.55211i
$767$	−36.8676	+	21.2855i	−1.33121	+	0.768576i
$768$	19.6278	−	5.25926i	0.708258	−	0.189777i
$769$	14.6383			0.527871			0.263936	−	0.964540i	$-0.414979\pi$
$769$	14.6383			0.527871			0.263936	+	0.964540i	$0.414979\pi$
$770$		0			0
$771$	−16.6013	+	16.6013i	−0.597880	+	0.597880i
$772$	−3.66351	−	13.6724i	−0.131852	−	0.492080i
$773$	−15.5409	+	8.97252i	−0.558966	+	0.322719i	−0.752730	−	0.658329i	$-0.771264\pi$
$773$	−15.5409	+	8.97252i	−0.558966	+	0.322719i	0.193764	+	0.981048i	$0.437930\pi$
$774$	3.09475	−	1.78676i	0.111239	−	0.0642237i
$775$	−18.6883	−	69.7458i	−0.671305	−	2.50534i
$776$	−15.8133	+	15.8133i	−0.567663	+	0.567663i
$777$		0			0
$778$	−17.5057			−0.627609
$779$	−18.4988	+	4.95675i	−0.662790	+	0.177594i
$780$	−12.0448	+	6.95407i	−0.431273	+	0.248996i
$781$	6.21819	+	10.7702i	0.222504	+	0.385389i
$782$	6.33095	+	1.07694i	0.226394	+	0.0385113i
$783$	−12.6827			−0.453244
$784$		0			0
$785$	−7.54291	−	7.54291i	−0.269218	−	0.269218i
$786$	0.0420155	−	0.0727730i	0.00149864	−	0.00259573i
$787$	−0.216944	+	0.809645i	−0.00773321	+	0.0288607i	−0.969685	−	0.244360i	$-0.921422\pi$
$787$	−0.216944	+	0.809645i	−0.00773321	+	0.0288607i	0.961951	+	0.273221i	$0.0880889\pi$
$788$	−20.3894	−	5.46332i	−0.726342	−	0.194623i
$789$	−3.05464	−	11.4001i	−0.108748	−	0.405854i
$790$		−	41.4606i		−	1.47510i
$791$		0			0
$792$	−12.4952	+	12.4952i	−0.443997	+	0.443997i
$793$	8.66405	+	32.3347i	0.307669	+	1.14824i
$794$	−2.09074	+	7.80276i	−0.0741977	+	0.276910i
$795$	−2.63791	−	4.56900i	−0.0935571	−	0.162046i
$796$	−10.5620	+	2.83009i	−0.374361	+	0.100310i
$797$		−	17.3052i		−	0.612981i	−0.951874	−	0.306490i	$-0.900845\pi$
$797$		−	17.3052i		−	0.612981i	0.951874	−	0.306490i	$-0.0991547\pi$
$798$		0			0
$799$	−10.0989	−	4.63518i	−0.357275	−	0.163981i
$800$	18.5177	−	32.0736i	0.654701	−	1.13397i
$801$	−4.47443	+	2.58331i	−0.158096	+	0.0912769i
$802$	3.34420	−	12.4807i	0.118088	−	0.440710i
$803$	−26.0080	+	45.0472i	−0.917804	+	1.58968i
$804$	−0.315336	−	0.315336i	−0.0111210	−	0.0111210i
$805$		0			0
$806$	43.7056	−	43.7056i	1.53946	−	1.53946i
$807$	−26.9309	−	15.5486i	−0.948014	−	0.547336i
$808$	−21.6479	+	12.4984i	−0.761570	+	0.439693i
$809$	−30.3584	−	8.13452i	−1.06735	−	0.285995i	−0.317944	−	0.948110i	$-0.602992\pi$
$809$	−30.3584	−	8.13452i	−1.06735	−	0.285995i	−0.749402	+	0.662115i	$0.769659\pi$
$810$	−0.966908	−	3.60855i	−0.0339737	−	0.126791i
$811$	−23.4079	−	23.4079i	−0.821964	−	0.821964i	0.164426	−	0.986389i	$-0.447423\pi$
$811$	−23.4079	−	23.4079i	−0.821964	−	0.821964i	−0.986389	+	0.164426i	$0.947423\pi$
$812$		0			0
$813$	2.26708	+	2.26708i	0.0795099	+	0.0795099i
$814$	87.2671	+	50.3837i	3.05871	+	1.76595i
$815$	−26.2204	−	45.4151i	−0.918462	−	1.59082i
$816$	−14.6295	+	17.6502i	−0.512136	+	0.617879i
$817$	2.32552	−	4.02792i	0.0813597	−	0.140919i
$818$		−	19.3479i		−	0.676483i
$819$		0			0
$820$	−16.1123			−0.562665
$821$	−20.8741	+	5.59319i	−0.728510	+	0.195204i	−0.603966	−	0.797010i	$-0.706414\pi$
$821$	−20.8741	+	5.59319i	−0.728510	+	0.195204i	−0.124545	+	0.992214i	$0.539747\pi$
$822$	3.54183	+	0.949030i	0.123536	+	0.0331012i
$823$	21.4722	+	5.75345i	0.748473	+	0.200553i	0.612841	−	0.790207i	$-0.290027\pi$
$823$	21.4722	+	5.75345i	0.748473	+	0.200553i	0.135632	+	0.990759i	$0.456693\pi$
$824$	−5.50049	−	3.17571i	−0.191619	−	0.110631i
$825$		−	46.2031i		−	1.60859i
$826$		0			0
$827$	31.0315	−	31.0315i	1.07907	−	1.07907i	0.0824786	−	0.996593i	$-0.473716\pi$
$827$	31.0315	−	31.0315i	1.07907	−	1.07907i	0.996593	−	0.0824786i	$-0.0262836\pi$
$828$	1.44105	−	0.386128i	0.0500800	−	0.0134189i
$829$	−24.1212	−	41.7792i	−0.837765	−	1.45105i	−0.891759	−	0.452510i	$-0.850529\pi$
$829$	−24.1212	−	41.7792i	−0.837765	−	1.45105i	0.0539946	−	0.998541i	$-0.482805\pi$
$830$	−4.89699	+	18.2758i	−0.169977	+	0.634363i
$831$	−6.91181	−	3.99053i	−0.239768	−	0.138430i
$832$	−6.10895			−0.211790
$833$		0			0
$834$	−11.4925			−0.397954
$835$	41.7585	+	24.1093i	1.44511	+	0.834336i
$836$	5.18632	−	19.3556i	0.179372	−	0.669427i
$837$	25.2750	+	43.7776i	0.873632	+	1.51317i
$838$	−46.8434	+	12.5517i	−1.61818	+	0.433590i
$839$	−18.6559	+	18.6559i	−0.644073	+	0.644073i	−0.951554	−	0.307482i	$-0.900514\pi$
$839$	−18.6559	+	18.6559i	−0.644073	+	0.644073i	0.307482	+	0.951554i	$0.400514\pi$
$840$		0			0
$841$		−	23.2725i		−	0.802499i
$842$	53.1361	+	30.6782i	1.83119	+	1.05724i
$843$	−21.8643	−	5.85853i	−0.753047	−	0.201778i
$844$	19.6688	+	5.27024i	0.677029	+	0.181409i
$845$	4.53504	−	1.21516i	0.156010	−	0.0418028i
$846$	−8.12570			−0.279367
$847$		0			0
$848$			6.67823i			0.229331i
$849$	−1.71913	+	2.97762i	−0.0590003	+	0.102192i
$850$	4.97857	+	53.2030i	0.170764	+	1.82485i
$851$	4.88222	+	8.45625i	0.167360	+	0.289876i
$852$	2.03577	+	1.17535i	0.0697443	+	0.0402669i
$853$	−12.6584	−	12.6584i	−0.433415	−	0.433415i	0.456374	−	0.889788i	$-0.349148\pi$
$853$	−12.6584	−	12.6584i	−0.433415	−	0.433415i	−0.889788	+	0.456374i	$0.849148\pi$
$854$		0			0
$855$	17.3251	+	17.3251i	0.592506	+	0.592506i
$856$	4.01548	+	14.9860i	0.137246	+	0.512210i
$857$	22.9576	+	6.15147i	0.784216	+	0.210130i	0.628643	−	0.777694i	$-0.283611\pi$
$857$	22.9576	+	6.15147i	0.784216	+	0.210130i	0.155574	+	0.987824i	$0.450277\pi$
$858$	34.2515	−	19.7751i	1.16933	−	0.675111i
$859$	−36.8299	−	21.2638i	−1.25662	−	0.725510i	−0.284205	−	0.958764i	$-0.591729\pi$
$859$	−36.8299	−	21.2638i	−1.25662	−	0.725510i	−0.972416	+	0.233253i	$0.925063\pi$
$860$	2.76688	−	2.76688i	0.0943499	−	0.0943499i
$861$		0			0
$862$	−6.69661	−	6.69661i	−0.228087	−	0.228087i
$863$	−17.8979	+	31.0001i	−0.609253	+	1.05526i	0.382111	+	0.924116i	$0.375197\pi$
$863$	−17.8979	+	31.0001i	−0.609253	+	1.05526i	−0.991364	+	0.131140i	$0.958136\pi$
$864$	−6.71059	+	25.0443i	−0.228299	+	0.852023i
$865$	−26.5514	+	15.3295i	−0.902775	+	0.521218i
$866$	2.54583	−	4.40951i	0.0865108	−	0.149841i
$867$	1.42141	−	18.8688i	0.0482735	−	0.640819i
$868$		0			0
$869$			37.4554i			1.27059i
$870$	−15.6185	+	4.18496i	−0.529516	+	0.141883i
$871$	0.814188	+	1.41021i	0.0275877	+	0.0477833i
$872$	2.50962	−	9.36603i	0.0849864	−	0.317174i
$873$	−5.57045	−	20.7892i	−0.188531	−	0.703608i
$874$	4.32191	−	4.32191i	0.146191	−	0.146191i
$875$		0			0
$876$			9.83200i			0.332193i
$877$	−5.52281	−	20.6114i	−0.186492	−	0.695998i	−0.994306	−	0.106561i	$-0.966016\pi$
$877$	−5.52281	−	20.6114i	−0.186492	−	0.695998i	0.807814	−	0.589437i	$-0.200651\pi$
$878$	−2.95120	−	0.790772i	−0.0995982	−	0.0266873i
$879$	−5.88777	+	21.9735i	−0.198590	+	0.741146i
$880$	−48.5576	+	84.1042i	−1.63688	+	2.83515i
$881$	24.2562	+	24.2562i	0.817212	+	0.817212i	0.985703	−	0.168491i	$-0.0538895\pi$
$881$	24.2562	+	24.2562i	0.817212	+	0.817212i	−0.168491	+	0.985703i	$0.553890\pi$
$882$		0			0
$883$	25.3180			0.852018			0.426009	−	0.904719i	$-0.359919\pi$
$883$	25.3180			0.852018			0.426009	+	0.904719i	$0.359919\pi$
$884$	−11.8528	+	8.40656i	−0.398654	+	0.282743i
$885$	−22.1940	−	38.4412i	−0.746044	−	1.29219i
$886$	12.9014	−	7.44860i	0.433429	−	0.250241i
$887$	−16.3255	+	4.37441i	−0.548157	+	0.146878i	−0.522260	−	0.852786i	$-0.674911\pi$
$887$	−16.3255	+	4.37441i	−0.548157	+	0.146878i	−0.0258971	+	0.999665i	$0.508244\pi$
$888$	−21.8612			−0.733613
$889$		0			0
$890$	−12.5923	+	12.5923i	−0.422093	+	0.422093i
$891$	0.873501	+	3.25995i	0.0292634	+	0.109212i
$892$	−19.7841	+	11.4224i	−0.662422	+	0.382450i
$893$	−9.15895	+	5.28792i	−0.306493	+	0.176954i
$894$	9.45659	+	35.2925i	0.316276	+	1.18036i
$895$	26.8429	−	26.8429i	0.897261	−	0.897261i
$896$		0			0
$897$	3.83245			0.127962
$898$	−29.3942	+	7.87615i	−0.980897	+	0.262830i
$899$	19.7700	−	11.4142i	0.659368	−	0.380686i
$900$	6.20686	+	10.7506i	0.206895	+	0.358353i
$901$	−3.18889	−	4.49618i	−0.106237	−	0.149789i
$902$	45.8180			1.52557
$903$		0			0
$904$	−11.8087	−	11.8087i	−0.392751	−	0.392751i
$905$	28.6264	−	49.5823i	0.951572	−	1.64817i
$906$	11.0306	−	41.1668i	0.366468	−	1.36768i
$907$	28.0784	+	7.52359i	0.932329	+	0.249817i	0.692847	−	0.721084i	$-0.256356\pi$
$907$	28.0784	+	7.52359i	0.932329	+	0.249817i	0.239481	+	0.970901i	$0.423023\pi$
$908$	2.67040	+	9.96606i	0.0886203	+	0.330735i
$909$		−	24.0571i		−	0.797922i
$910$		0			0
$911$	33.6975	−	33.6975i	1.11645	−	1.11645i	0.124188	−	0.992259i	$-0.460367\pi$
$911$	33.6975	−	33.6975i	1.11645	−	1.11645i	0.992259	−	0.124188i	$-0.0396326\pi$
$912$	5.64719	+	21.0756i	0.186997	+	0.697882i
$913$	4.42393	−	16.5103i	0.146411	−	0.546412i
$914$	19.1930	+	33.2433i	0.634849	+	1.09959i
$915$	−33.7148	+	9.03384i	−1.11458	+	0.298650i
$916$			26.4479i			0.873862i
$917$		0			0
$918$	−13.0067	−	35.0750i	−0.429284	−	1.15765i
$919$	−0.321216	+	0.556362i	−0.0105959	+	0.0183527i	−0.871275	−	0.490796i	$-0.836706\pi$
$919$	−0.321216	+	0.556362i	−0.0105959	+	0.0183527i	0.860679	+	0.509148i	$0.170040\pi$
$920$	−5.11125	+	2.95098i	−0.168513	+	0.0972910i
$921$	7.05162	−	26.3170i	0.232359	−	0.867175i
$922$	20.5924	−	35.6672i	0.678176	−	1.17464i
$923$	−6.06946	−	6.06946i	−0.199779	−	0.199779i
$924$		0			0
$925$	−57.4511	+	57.4511i	−1.88898	+	1.88898i
$926$	−0.986000	−	0.569267i	−0.0324020	−	0.0187073i
$927$	5.29369	−	3.05631i	0.173868	−	0.100382i
$928$	11.3100	+	3.03052i	0.371270	+	0.0994815i
$929$	2.22905	+	8.31892i	0.0731327	+	0.272935i	0.992803	−	0.119755i	$-0.0382111\pi$
$929$	2.22905	+	8.31892i	0.0731327	+	0.272935i	−0.919671	+	0.392690i	$0.871544\pi$
$930$	45.5710	+	45.5710i	1.49433	+	1.49433i
$931$		0			0
$932$	−2.73082	−	2.73082i	−0.0894510	−	0.0894510i
$933$	0.434262	+	0.250721i	0.0142171	+	0.00820825i
$934$	17.6288	+	30.5340i	0.576833	+	0.999104i
$935$	−7.46841	−	79.8104i	−0.244243	−	2.61008i
$936$	6.09816	−	10.5623i	0.199325	−	0.345240i
$937$		−	20.8080i		−	0.679766i	−0.940468	−	0.339883i	$-0.889612\pi$
$937$		−	20.8080i		−	0.679766i	0.940468	−	0.339883i	$-0.110388\pi$
$938$		0			0
$939$	18.8966			0.616666
$940$	−8.59438	+	2.30286i	−0.280318	+	0.0751110i
$941$	3.23771	+	0.867541i	0.105546	+	0.0282810i	0.311206	−	0.950343i	$-0.399267\pi$
$941$	3.23771	+	0.867541i	0.105546	+	0.0282810i	−0.205659	+	0.978624i	$0.565934\pi$
$942$	5.53837	+	1.48400i	0.180450	+	0.0483514i
$943$	3.84498	+	2.21990i	0.125210	+	0.0722899i
$944$			56.1871i			1.82874i
$945$		0			0
$946$	−7.86811	+	7.86811i	−0.255814	+	0.255814i
$947$	−11.6042	+	3.10934i	−0.377086	+	0.101040i	−0.442383	−	0.896826i	$-0.645867\pi$
$947$	−11.6042	+	3.10934i	−0.377086	+	0.101040i	0.0652977	+	0.997866i	$0.479200\pi$
$948$	3.53988	+	6.13126i	0.114970	+	0.199134i
$949$	9.29191	−	34.6779i	0.301628	−	1.12569i
$950$	44.0441	+	25.4289i	1.42898	+	0.825022i
$951$	−5.21194			−0.169009
$952$		0			0
$953$	13.0495			0.422716			0.211358	−	0.977409i	$-0.432211\pi$
$953$	13.0495			0.422716			0.211358	+	0.977409i	$0.432211\pi$
$954$	−3.49085	−	2.01544i	−0.113021	−	0.0652524i
$955$	12.7130	−	47.4455i	0.411382	−	1.53530i
$956$	8.04582	+	13.9358i	0.260221	+	0.450715i
$957$	14.1097	−	3.78068i	0.456102	−	0.122212i
$958$	11.2032	−	11.2032i	0.361959	−	0.361959i
$959$		0			0
$960$		−	6.36969i		−	0.205581i
$961$	−51.9514	−	29.9941i	−1.67585	−	0.967553i
$962$	−67.1792	−	18.0006i	−2.16594	−	0.580363i
$963$	−14.4226	−	3.86451i	−0.464761	−	0.124532i
$964$	0.337310	−	0.0903819i	0.0108640	−	0.00291101i
$965$	−53.8913			−1.73482
$966$		0			0
$967$		−	32.4078i		−	1.04216i	−0.853507	−	0.521082i	$-0.825529\pi$
$967$		−	32.4078i		−	1.04216i	0.853507	−	0.521082i	$-0.174471\pi$
$968$	17.4475	−	30.2199i	0.560784	−	0.971306i
$969$	−13.8657	−	11.4928i	−0.445431	−	0.369201i
$970$	−37.0916	−	64.2445i	−1.19094	−	2.06277i
$971$	21.5819	+	12.4603i	0.692595	+	0.399870i	0.804583	−	0.593840i	$-0.202389\pi$
$971$	21.5819	+	12.4603i	0.692595	+	0.399870i	−0.111989	+	0.993710i	$0.535722\pi$
$972$	−10.0173	−	10.0173i	−0.321305	−	0.321305i
$973$		0			0
$974$	−1.85911	−	1.85911i	−0.0595696	−	0.0595696i
$975$	8.25351	+	30.8025i	0.264324	+	0.986470i
$976$	42.6767	+	11.4352i	1.36605	+	0.366031i
$977$	−20.4301	+	11.7953i	−0.653616	+	0.377365i	−0.789840	−	0.613313i	$-0.789837\pi$
$977$	−20.4301	+	11.7953i	−0.653616	+	0.377365i	0.136224	+	0.990678i	$0.456503\pi$
$978$	24.4110	+	14.0937i	0.780576	+	0.450666i
$979$	11.3758	−	11.3758i	0.363572	−	0.363572i
$980$		0			0
$981$	6.59863	+	6.59863i	0.210678	+	0.210678i
$982$	−12.5101	+	21.6682i	−0.399215	+	0.691460i
$983$	−2.68709	+	10.0284i	−0.0857049	+	0.319855i	−0.995447	−	0.0953194i	$-0.969613\pi$
$983$	−2.68709	+	10.0284i	−0.0857049	+	0.319855i	0.909742	+	0.415174i	$0.136279\pi$
$984$	−8.60837	+	4.97005i	−0.274425	+	0.158439i
$985$	−40.1836	+	69.6001i	−1.28036	+	2.21764i
$986$	−15.8400	+	5.87384i	−0.504447	+	0.187061i
$987$		0			0
$988$			13.8304i			0.440003i
$989$	−1.04149	+	0.279067i	−0.0331176	+	0.00887383i
$990$	−29.3087	−	50.7642i	−0.931492	−	1.61339i
$991$	−5.87801	+	21.9370i	−0.186721	+	0.696853i	0.807534	+	0.589821i	$0.200802\pi$
$991$	−5.87801	+	21.9370i	−0.186721	+	0.696853i	−0.994256	+	0.107033i	$0.965865\pi$
$992$	−12.0788	−	45.0788i	−0.383503	−	1.43125i
$993$	27.1567	−	27.1567i	0.861792	−	0.861792i
$994$		0			0
$995$			41.6315i			1.31981i
$996$	−0.836205	−	3.12076i	−0.0264962	−	0.0988850i
$997$	37.3790	+	10.0157i	1.18380	+	0.317200i	0.796435	−	0.604725i	$-0.206717\pi$
$997$	37.3790	+	10.0157i	1.18380	+	0.317200i	0.387370	+	0.921924i	$0.373384\pi$
$998$	−8.80399	+	32.8569i	−0.278685	+	1.04007i
$999$	28.4400	−	49.2596i	0.899803	−	1.55850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.o.e.30.5		32
7.2	even	3		833.2.g.e.540.3	yes	16
7.3	odd	6	inner	833.2.o.e.557.3		32
7.4	even	3	inner	833.2.o.e.557.4		32
7.5	odd	6		833.2.g.e.540.4	yes	16
7.6	odd	2	inner	833.2.o.e.30.6		32
17.4	even	4	inner	833.2.o.e.667.4		32
119.4	even	12	inner	833.2.o.e.361.5		32
119.38	odd	12	inner	833.2.o.e.361.6		32
119.55	odd	4	inner	833.2.o.e.667.3		32
119.72	even	12		833.2.g.e.344.5	✓	16
119.89	odd	12		833.2.g.e.344.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.g.e.344.5	✓	16	119.72	even	12
833.2.g.e.344.6	yes	16	119.89	odd	12
833.2.g.e.540.3	yes	16	7.2	even	3
833.2.g.e.540.4	yes	16	7.5	odd	6
833.2.o.e.30.5		32	1.1	even	1	trivial
833.2.o.e.30.6		32	7.6	odd	2	inner
833.2.o.e.361.5		32	119.4	even	12	inner
833.2.o.e.361.6		32	119.38	odd	12	inner
833.2.o.e.557.3		32	7.3	odd	6	inner
833.2.o.e.557.4		32	7.4	even	3	inner
833.2.o.e.667.3		32	119.55	odd	4	inner
833.2.o.e.667.4		32	17.4	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48270 + 0.856038i) q^{2} +(-0.288085 + 1.07515i) q^{3} +(0.465602 + 0.806447i) q^{4} +(3.42458 - 0.917613i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} +(1.52513 + 0.880532i) q^{9} +O(q^{10})\)	\(q+(1.48270 + 0.856038i) q^{2} +(-0.288085 + 1.07515i) q^{3} +(0.465602 + 0.806447i) q^{4} +(3.42458 - 0.917613i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} +(1.52513 + 0.880532i) q^{9} +(5.86314 + 1.57102i) q^{10} +(-5.29674 - 1.41926i) q^{11} +(-1.00118 + 0.268266i) q^{12} +3.78474 q^{13} +3.94628i q^{15} +(2.49763 - 4.32603i) q^{16} +(0.384149 + 4.10517i) q^{17} +(1.50754 + 2.61113i) q^{18} +(3.39847 + 1.96211i) q^{19} +(2.33450 + 2.33450i) q^{20} +(-6.63855 - 6.63855i) q^{22} +(-0.235457 - 0.878738i) q^{23} +(1.96737 + 0.527155i) q^{24} +(6.55560 - 3.78488i) q^{25} +(5.61164 + 3.23988i) q^{26} +(-3.74726 + 3.74726i) q^{27} +(1.69227 + 1.69227i) q^{29} +(-3.37817 + 5.85115i) q^{30} +(2.46882 - 9.21375i) q^{31} +(4.23708 - 2.44628i) q^{32} +(3.05182 - 5.28591i) q^{33} +(-2.94460 + 6.41559i) q^{34} +1.63991i q^{36} +(-10.3675 + 2.77797i) q^{37} +(3.35928 + 5.81844i) q^{38} +(-1.09033 + 4.06916i) q^{39} +(-1.67910 - 6.26650i) q^{40} +(-3.45091 + 3.45091i) q^{41} -1.18522i q^{43} +(-1.32162 - 4.93235i) q^{44} +(6.03090 + 1.61598i) q^{45} +(0.403120 - 1.50447i) q^{46} +(-1.34751 + 2.33396i) q^{47} +(3.93159 + 3.93159i) q^{48} +12.9600 q^{50} +(-4.52433 - 0.769621i) q^{51} +(1.76218 + 3.05219i) q^{52} +(-1.15780 + 0.668456i) q^{53} +(-8.76386 + 2.34827i) q^{54} -19.4414 q^{55} +(-3.08860 + 3.08860i) q^{57} +(1.06048 + 3.95777i) q^{58} +(-9.74112 + 5.62404i) q^{59} +(-3.18246 + 1.83740i) q^{60} +(2.28920 + 8.54343i) q^{61} +(11.5478 - 11.5478i) q^{62} -1.61410 q^{64} +(12.9611 - 3.47293i) q^{65} +(9.04989 - 5.22496i) q^{66} +(0.215124 + 0.372605i) q^{67} +(-3.13174 + 2.22117i) q^{68} +1.01260 q^{69} +(-1.60366 - 1.60366i) q^{71} +(1.61125 - 2.79077i) q^{72} +(2.45510 - 9.16255i) q^{73} +(-17.7500 - 4.75610i) q^{74} +(2.18073 + 8.13860i) q^{75} +3.65425i q^{76} +(-5.09998 + 5.09998i) q^{78} +(-1.76785 - 6.59771i) q^{79} +(4.58372 - 17.1067i) q^{80} +(-0.307732 - 0.533007i) q^{81} +(-8.07077 + 2.16256i) q^{82} +3.11707i q^{83} +(5.08251 + 13.7060i) q^{85} +(1.01459 - 1.75732i) q^{86} +(-2.30696 + 1.33192i) q^{87} +(-2.59704 + 9.69229i) q^{88} +(-1.46691 + 2.54076i) q^{89} +(7.55869 + 7.55869i) q^{90} +(0.599026 - 0.599026i) q^{92} +(9.19492 + 5.30869i) q^{93} +(-3.99591 + 2.30704i) q^{94} +(13.4388 + 3.60091i) q^{95} +(1.40947 + 5.26023i) q^{96} +(-8.64179 - 8.64179i) q^{97} +(-6.82850 - 6.82850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4}+O(q^{10}) \) 32 * q + 28 * q^4	\( 32 q + 28 q^{4} + 12 q^{11} - 20 q^{16} - 52 q^{18} - 8 q^{22} + 8 q^{23} + 24 q^{29} + 20 q^{30} - 32 q^{37} + 28 q^{39} - 12 q^{44} - 72 q^{46} - 56 q^{51} - 72 q^{57} + 28 q^{58} - 72 q^{64} + 8 q^{65} + 96 q^{67} - 48 q^{71} + 160 q^{72} - 88 q^{74} - 232 q^{78} + 36 q^{79} - 40 q^{81} - 104 q^{85} + 20 q^{86} + 48 q^{88} + 240 q^{92} + 84 q^{95} - 96 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 12 * q^11 - 20 * q^16 - 52 * q^18 - 8 * q^22 + 8 * q^23 + 24 * q^29 + 20 * q^30 - 32 * q^37 + 28 * q^39 - 12 * q^44 - 72 * q^46 - 56 * q^51 - 72 * q^57 + 28 * q^58 - 72 * q^64 + 8 * q^65 + 96 * q^67 - 48 * q^71 + 160 * q^72 - 88 * q^74 - 232 * q^78 + 36 * q^79 - 40 * q^81 - 104 * q^85 + 20 * q^86 + 48 * q^88 + 240 * q^92 + 84 * q^95 - 96 * q^99

Introduction

L-functions

Modular forms

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Database

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