LMFDB - Embedded newform 750.2.l.b.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	750.107
Dual form			750.2.l.b.743.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(-1.71953 - 0.207905i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(-2.58285 - 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.91355 + 0.714995i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(-1.71953 - 0.207905i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(-2.58285 - 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.91355 + 0.714995i) q^{9} +(-1.45719 + 0.473470i) q^{11} +(-0.842515 - 1.51333i) q^{12} +(2.28489 + 4.48435i) q^{13} +(-1.12875 - 3.47393i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.09363 + 0.806752i) q^{17} +(2.27139 + 1.95979i) q^{18} +(-1.27450 + 1.75421i) q^{19} +(3.90430 + 4.97827i) q^{21} +(-1.51332 - 0.239686i) q^{22} +(-2.88760 + 5.66723i) q^{23} +(-0.0636485 - 1.73088i) q^{24} +5.03290i q^{26} +(-4.86128 - 1.83520i) q^{27} +(0.571409 - 3.60774i) q^{28} +(-5.64831 + 4.10373i) q^{29} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.60412 - 0.511188i) q^{33} +(-4.90472 - 1.59364i) q^{34} +(1.13410 + 2.77738i) q^{36} +(6.84089 - 3.48561i) q^{37} +(-1.93198 + 0.984395i) q^{38} +(-2.99661 - 8.18600i) q^{39} +(-2.85939 - 0.929072i) q^{41} +(1.21867 + 6.20819i) q^{42} +(-3.24693 + 3.24693i) q^{43} +(-1.23956 - 0.900593i) q^{44} +(-5.14573 + 3.73859i) q^{46} +(-0.446195 + 2.81716i) q^{47} +(0.729092 - 1.57112i) q^{48} +6.34226i q^{49} +(8.92637 - 0.328243i) q^{51} +(-2.28489 + 4.48435i) q^{52} +(-1.02055 - 0.161639i) q^{53} +(-3.49827 - 3.84215i) q^{54} +(2.14701 - 2.95510i) q^{56} +(2.55625 - 2.75143i) q^{57} +(-6.89573 + 1.09218i) q^{58} +(2.10801 - 6.48779i) q^{59} +(1.78395 + 5.49044i) q^{61} +(-3.34066 - 6.55641i) q^{62} +(-5.67855 - 9.37200i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(2.55236 + 0.726772i) q^{66} +(0.527466 + 3.33029i) q^{67} +(-3.64664 - 3.64664i) q^{68} +(6.14354 - 9.14461i) q^{69} +(2.18090 + 3.00175i) q^{71} +(-0.250413 + 2.98953i) q^{72} +(0.531390 + 0.270757i) q^{73} +7.67771 q^{74} -2.16832 q^{76} +(4.98661 + 2.54081i) q^{77} +(1.04636 - 8.65421i) q^{78} +(-0.782199 - 1.07660i) q^{79} +(7.97756 + 4.16635i) q^{81} +(-2.12595 - 2.12595i) q^{82} +(-0.432953 - 2.73356i) q^{83} +(-1.73262 + 6.08480i) q^{84} +(-4.36710 + 1.41896i) q^{86} +(10.5656 - 5.88218i) q^{87} +(-0.695596 - 1.36518i) q^{88} +(1.98939 + 6.12272i) q^{89} +(5.68088 - 17.4839i) q^{91} +(-6.28217 + 0.994998i) q^{92} +(9.33729 + 8.67494i) q^{93} +(-1.67653 + 2.30754i) q^{94} +(1.36290 - 1.06888i) q^{96} +(-13.5156 - 2.14067i) q^{97} +(-2.87933 + 5.65100i) q^{98} +(-4.58413 + 0.337594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	−1.71953	−	0.207905i	−0.992770	−	0.120034i
$3$	−1.71953	−	0.207905i	−0.992770	−	0.120034i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.43772	−	0.965894i	−0.586948	−	0.394324i
$7$	−2.58285	−	2.58285i	−0.976227	−	0.976227i	0.0234972	−	0.999724i	$-0.492520\pi$
$7$	−2.58285	−	2.58285i	−0.976227	−	0.976227i	−0.999724	+	0.0234972i	$0.992520\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	2.91355	+	0.714995i	0.971184	+	0.238332i
$10$		0			0
$11$	−1.45719	+	0.473470i	−0.439360	+	0.142757i	−0.520340	−	0.853959i	$-0.674195\pi$
$11$	−1.45719	+	0.473470i	−0.439360	+	0.142757i	0.0809806	+	0.996716i	$0.474195\pi$
$12$	−0.842515	−	1.51333i	−0.243213	−	0.436861i
$13$	2.28489	+	4.48435i	0.633714	+	1.24373i	0.954959	+	0.296738i	$0.0958988\pi$
$13$	2.28489	+	4.48435i	0.633714	+	1.24373i	−0.321245	+	0.946996i	$0.604101\pi$
$14$	−1.12875	−	3.47393i	−0.301671	−	0.928447i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−5.09363	+	0.806752i	−1.23539	+	0.195666i	−0.739761	−	0.672870i	$-0.765061\pi$
$17$	−5.09363	+	0.806752i	−1.23539	+	0.195666i	−0.495626	+	0.868536i	$0.665061\pi$
$18$	2.27139	+	1.95979i	0.535372	+	0.461927i
$19$	−1.27450	+	1.75421i	−0.292391	+	0.402442i	−0.929789	−	0.368093i	$-0.880011\pi$
$19$	−1.27450	+	1.75421i	−0.292391	+	0.402442i	0.637398	+	0.770535i	$0.280011\pi$
$20$		0			0
$21$	3.90430	+	4.97827i	0.851988	+	1.08635i
$22$	−1.51332	−	0.239686i	−0.322640	−	0.0511012i
$23$	−2.88760	+	5.66723i	−0.602105	+	1.18170i	0.365873	+	0.930665i	$0.380770\pi$
$23$	−2.88760	+	5.66723i	−0.602105	+	1.18170i	−0.967978	+	0.251034i	$0.919230\pi$
$24$	−0.0636485	−	1.73088i	−0.0129922	−	0.353315i
$25$		0			0
$26$			5.03290i			0.987033i
$27$	−4.86128	−	1.83520i	−0.935554	−	0.353183i
$28$	0.571409	−	3.60774i	0.107986	−	0.681798i
$29$	−5.64831	+	4.10373i	−1.04886	+	0.762044i	−0.971996	−	0.234997i	$-0.924492\pi$
$29$	−5.64831	+	4.10373i	−1.04886	+	0.762044i	−0.0768679	+	0.997041i	$0.524492\pi$
$30$		0			0
$31$	−5.95310	−	4.32518i	−1.06921	−	0.776825i	−0.0934378	−	0.995625i	$-0.529786\pi$
$31$	−5.95310	−	4.32518i	−1.06921	−	0.776825i	−0.975770	+	0.218800i	$0.929786\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.60412	−	0.511188i	0.453318	−	0.0889864i
$34$	−4.90472	−	1.59364i	−0.841152	−	0.273307i
$35$		0			0
$36$	1.13410	+	2.77738i	0.189017	+	0.462896i
$37$	6.84089	−	3.48561i	1.12464	−	0.573031i	0.210158	−	0.977667i	$-0.432602\pi$
$37$	6.84089	−	3.48561i	1.12464	−	0.573031i	0.914477	+	0.404637i	$0.132602\pi$
$38$	−1.93198	+	0.984395i	−0.313409	+	0.159690i
$39$	−2.99661	−	8.18600i	−0.479842	−	1.31081i
$40$		0			0
$41$	−2.85939	−	0.929072i	−0.446562	−	0.145097i	0.0770993	−	0.997023i	$-0.475434\pi$
$41$	−2.85939	−	0.929072i	−0.446562	−	0.145097i	−0.523661	+	0.851927i	$0.675434\pi$
$42$	1.21867	+	6.20819i	0.188045	+	0.957945i
$43$	−3.24693	+	3.24693i	−0.495151	+	0.495151i	−0.909925	−	0.414773i	$-0.863861\pi$
$43$	−3.24693	+	3.24693i	−0.495151	+	0.495151i	0.414773	+	0.909925i	$0.363861\pi$
$44$	−1.23956	−	0.900593i	−0.186871	−	0.135770i
$45$		0			0
$46$	−5.14573	+	3.73859i	−0.758697	+	0.551226i
$47$	−0.446195	+	2.81716i	−0.0650842	+	0.410925i	0.933539	+	0.358475i	$0.116703\pi$
$47$	−0.446195	+	2.81716i	−0.0650842	+	0.410925i	−0.998624	+	0.0524505i	$0.983297\pi$
$48$	0.729092	−	1.57112i	0.105235	−	0.226772i
$49$			6.34226i			0.906037i
$50$		0			0
$51$	8.92637	−	0.328243i	1.24994	−	0.0459632i
$52$	−2.28489	+	4.48435i	−0.316857	+	0.621867i
$53$	−1.02055	−	0.161639i	−0.140183	−	0.0222028i	0.0859487	−	0.996300i	$-0.472608\pi$
$53$	−1.02055	−	0.161639i	−0.140183	−	0.0222028i	−0.226131	+	0.974097i	$0.572608\pi$
$54$	−3.49827	−	3.84215i	−0.476055	−	0.522850i
$55$		0			0
$56$	2.14701	−	2.95510i	0.286906	−	0.394892i
$57$	2.55625	−	2.75143i	0.338584	−	0.364436i
$58$	−6.89573	+	1.09218i	−0.905454	+	0.143410i
$59$	2.10801	−	6.48779i	0.274439	−	0.844638i	−0.714928	−	0.699198i	$-0.753540\pi$
$59$	2.10801	−	6.48779i	0.274439	−	0.844638i	0.989367	−	0.145439i	$-0.0464596\pi$
$60$		0			0
$61$	1.78395	+	5.49044i	0.228412	+	0.702979i	0.997927	+	0.0643507i	$0.0204976\pi$
$61$	1.78395	+	5.49044i	0.228412	+	0.702979i	−0.769516	+	0.638628i	$0.779502\pi$
$62$	−3.34066	−	6.55641i	−0.424264	−	0.832665i
$63$	−5.67855	−	9.37200i	−0.715430	−	1.18076i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	2.55236	+	0.726772i	0.314174	+	0.0894595i
$67$	0.527466	+	3.33029i	0.0644402	+	0.406859i	0.998732	+	0.0503493i	$0.0160334\pi$
$67$	0.527466	+	3.33029i	0.0644402	+	0.406859i	−0.934291	+	0.356510i	$0.883967\pi$
$68$	−3.64664	−	3.64664i	−0.442220	−	0.442220i
$69$	6.14354	−	9.14461i	0.739596	−	1.10088i
$70$		0			0
$71$	2.18090	+	3.00175i	0.258825	+	0.356242i	0.918578	−	0.395241i	$-0.129339\pi$
$71$	2.18090	+	3.00175i	0.258825	+	0.356242i	−0.659752	+	0.751483i	$0.729339\pi$
$72$	−0.250413	+	2.98953i	−0.0295114	+	0.352320i
$73$	0.531390	+	0.270757i	0.0621945	+	0.0316897i	0.484811	−	0.874619i	$-0.338888\pi$
$73$	0.531390	+	0.270757i	0.0621945	+	0.0316897i	−0.422617	+	0.906309i	$0.638888\pi$
$74$	7.67771			0.892516
$75$		0			0
$76$	−2.16832			−0.248723
$77$	4.98661	+	2.54081i	0.568277	+	0.289552i
$78$	1.04636	−	8.65421i	0.118477	−	0.979897i
$79$	−0.782199	−	1.07660i	−0.0880042	−	0.121127i	0.762745	−	0.646700i	$-0.223851\pi$
$79$	−0.782199	−	1.07660i	−0.0880042	−	0.121127i	−0.850749	+	0.525572i	$0.823851\pi$
$80$		0			0
$81$	7.97756	+	4.16635i	0.886396	+	0.462928i
$82$	−2.12595	−	2.12595i	−0.234771	−	0.234771i
$83$	−0.432953	−	2.73356i	−0.0475228	−	0.300047i	0.952467	−	0.304643i	$-0.0985371\pi$
$83$	−0.432953	−	2.73356i	−0.0475228	−	0.300047i	−0.999989	+	0.00459575i	$0.998537\pi$
$84$	−1.73262	+	6.08480i	−0.189044	+	0.663906i
$85$		0			0
$86$	−4.36710	+	1.41896i	−0.470917	+	0.153010i
$87$	10.5656	−	5.88218i	1.13275	−	0.630635i
$88$	−0.695596	−	1.36518i	−0.0741507	−	0.145529i
$89$	1.98939	+	6.12272i	0.210875	+	0.649007i	0.999421	+	0.0340306i	$0.0108344\pi$
$89$	1.98939	+	6.12272i	0.210875	+	0.649007i	−0.788546	+	0.614976i	$0.789166\pi$
$90$		0			0
$91$	5.68088	−	17.4839i	0.595518	−	1.83282i
$92$	−6.28217	+	0.994998i	−0.654961	+	0.103736i
$93$	9.33729	+	8.67494i	0.968232	+	0.899549i
$94$	−1.67653	+	2.30754i	−0.172921	+	0.238005i
$95$		0			0
$96$	1.36290	−	1.06888i	0.139100	−	0.109092i
$97$	−13.5156	−	2.14067i	−1.37230	−	0.217352i	−0.573630	−	0.819114i	$-0.694465\pi$
$97$	−13.5156	−	2.14067i	−1.37230	−	0.217352i	−0.798675	+	0.601763i	$0.794465\pi$
$98$	−2.87933	+	5.65100i	−0.290856	+	0.570837i
$99$	−4.58413	+	0.337594i	−0.460722	+	0.0339295i
$100$		0			0
$101$			0.146560i			0.0145833i	0.999973	+	0.00729163i	$0.00232102\pi$
$101$			0.146560i			0.0145833i	−0.999973	+	0.00729163i	$0.997679\pi$
$102$	8.10247	+	3.76002i	0.802264	+	0.372297i
$103$	−2.44405	+	15.4311i	−0.240819	+	1.52047i	0.510120	+	0.860103i	$0.329601\pi$
$103$	−2.44405	+	15.4311i	−0.240819	+	1.52047i	−0.750939	+	0.660371i	$0.770399\pi$
$104$	−4.07170	+	2.95827i	−0.399263	+	0.290082i
$105$		0			0
$106$	−0.835930	−	0.607339i	−0.0811927	−	0.0589900i
$107$	1.77141	−	1.77141i	0.171249	−	0.171249i	−0.616279	−	0.787528i	$-0.711361\pi$
$107$	1.77141	−	1.77141i	0.171249	−	0.171249i	0.787528	+	0.616279i	$0.211361\pi$
$108$	−1.37269	−	5.01156i	−0.132087	−	0.482238i
$109$	7.65945	+	2.48870i	0.733642	+	0.238375i	0.651928	−	0.758281i	$-0.273961\pi$
$109$	7.65945	+	2.48870i	0.733642	+	0.238375i	0.0817142	+	0.996656i	$0.473961\pi$
$110$		0			0
$111$	−12.4878	+	4.57135i	−1.18529	+	0.433893i
$112$	3.25458	−	1.65829i	0.307529	−	0.156694i
$113$	9.66667	−	4.92541i	0.909364	−	0.463344i	0.0642521	−	0.997934i	$-0.479534\pi$
$113$	9.66667	−	4.92541i	0.909364	−	0.463344i	0.845112	+	0.534590i	$0.179534\pi$
$114$	3.52676	−	1.29103i	0.330311	−	0.120916i
$115$		0			0
$116$	−6.63998	−	2.15746i	−0.616507	−	0.200315i
$117$	3.45085	+	14.6991i	0.319032	+	1.35893i
$118$	4.82364	−	4.82364i	0.444052	−	0.444052i
$119$	15.2398	+	11.0724i	1.39703	+	1.01500i
$120$		0			0
$121$	−6.99996	+	5.08577i	−0.636360	+	0.462342i
$122$	−0.903094	+	5.70191i	−0.0817623	+	0.516227i
$123$	4.72364	+	2.19205i	0.425916	+	0.197650i
$124$		−	7.35843i		−	0.660807i
$125$		0			0
$126$	−0.804822	−	10.9285i	−0.0716992	−	0.973590i
$127$	8.38871	−	16.4638i	0.744378	−	1.46092i	−0.138025	−	0.990429i	$-0.544075\pi$
$127$	8.38871	−	16.4638i	0.744378	−	1.46092i	0.882403	−	0.470495i	$-0.155925\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	6.25823	−	4.90813i	0.551006	−	0.432137i
$130$		0			0
$131$	7.79711	−	10.7318i	0.681236	−	0.937641i	−0.318712	−	0.947852i	$-0.603250\pi$
$131$	7.79711	−	10.7318i	0.681236	−	0.937641i	0.999948	+	0.0102104i	$0.00325012\pi$
$132$	1.94422	+	1.80631i	0.169223	+	0.157219i
$133$	7.82271	−	1.23900i	0.678315	−	0.107435i
$134$	−1.04194	+	3.20677i	−0.0900102	+	0.277023i
$135$		0			0
$136$	−1.59364	−	4.90472i	−0.136653	−	0.420576i
$137$	4.43133	+	8.69698i	0.378594	+	0.743033i	0.999154	−	0.0411262i	$-0.0130946\pi$
$137$	4.43133	+	8.69698i	0.378594	+	0.743033i	−0.620560	+	0.784159i	$0.713095\pi$
$138$	9.62550	−	5.35879i	0.819377	−	0.456171i
$139$	−4.61980	+	1.50106i	−0.391846	+	0.127319i	−0.498312	−	0.866998i	$-0.666047\pi$
$139$	−4.61980	+	1.50106i	−0.391846	+	0.127319i	0.106466	+	0.994316i	$0.466047\pi$
$140$		0			0
$141$	1.35295	−	4.75142i	0.113939	−	0.400142i
$142$	0.580430	+	3.66469i	0.0487086	+	0.307534i
$143$	−5.45272	−	5.45272i	−0.455980	−	0.455980i
$144$	−1.58034	+	2.55001i	−0.131695	+	0.212501i
$145$		0			0
$146$	0.350551	+	0.482492i	0.0290118	+	0.0399313i
$147$	1.31859	−	10.9057i	0.108755	−	0.899486i
$148$	6.84089	+	3.48561i	0.562318	+	0.286515i
$149$	−6.55688			−0.537160			−0.268580	−	0.963257i	$-0.586554\pi$
$149$	−6.55688			−0.537160			−0.268580	+	0.963257i	$0.586554\pi$
$150$		0			0
$151$	1.06618			0.0867647			0.0433824	−	0.999059i	$-0.486187\pi$
$151$	1.06618			0.0867647			0.0433824	+	0.999059i	$0.486187\pi$
$152$	−1.93198	−	0.984395i	−0.156705	−	0.0798450i
$153$	−15.4174	−	1.29141i	−1.24642	−	0.104404i
$154$	3.28960	+	4.52775i	0.265084	+	0.364856i
$155$		0			0
$156$	4.86125	−	7.23592i	0.389211	−	0.579337i
$157$	−15.3342	−	15.3342i	−1.22380	−	1.22380i	−0.966271	−	0.257528i	$-0.917092\pi$
$157$	−15.3342	−	15.3342i	−1.22380	−	1.22380i	−0.257528	−	0.966271i	$-0.582908\pi$
$158$	−0.208176	−	1.31437i	−0.0165616	−	0.104566i
$159$	1.72125	+	0.490118i	0.136504	+	0.0388689i
$160$		0			0
$161$	22.0958	−	7.17938i	1.74140	−	0.565814i
$162$	5.21658	+	7.33398i	0.409853	+	0.576212i
$163$	4.66780	+	9.16108i	0.365610	+	0.717551i	0.998386	−	0.0567839i	$-0.0180846\pi$
$163$	4.66780	+	9.16108i	0.365610	+	0.717551i	−0.632776	+	0.774335i	$0.718085\pi$
$164$	−0.929072	−	2.85939i	−0.0725483	−	0.223281i
$165$		0			0
$166$	0.855246	−	2.63218i	0.0663800	−	0.204297i
$167$	23.8000	−	3.76955i	1.84170	−	0.291697i	0.864282	−	0.503008i	$-0.167773\pi$
$167$	23.8000	−	3.76955i	1.84170	−	0.291697i	0.977419	+	0.211311i	$0.0677733\pi$
$168$	−4.30622	+	4.63501i	−0.332232	+	0.357598i
$169$	−7.24745	+	9.97526i	−0.557496	+	0.767327i
$170$		0			0
$171$	−4.96758	+	4.19970i	−0.379881	+	0.321159i
$172$	−4.53531	−	0.718323i	−0.345814	−	0.0547716i
$173$	10.9010	−	21.3945i	0.828791	−	1.62659i	0.0504717	−	0.998725i	$-0.483928\pi$
$173$	10.9010	−	21.3945i	0.828791	−	1.62659i	0.778319	−	0.627869i	$-0.216072\pi$
$174$	12.0845	−	0.444374i	0.916122	−	0.0336879i
$175$		0			0
$176$		−	1.53218i		−	0.115492i
$177$	−4.97362	+	10.7177i	−0.373840	+	0.805589i
$178$	−1.00709	+	6.35855i	−0.0754849	+	0.476593i
$179$	3.64757	−	2.65012i	0.272632	−	0.198079i	−0.443065	−	0.896489i	$-0.646109\pi$
$179$	3.64757	−	2.65012i	0.272632	−	0.198079i	0.715697	+	0.698410i	$0.246109\pi$
$180$		0			0
$181$	−11.4405	−	8.31202i	−0.850367	−	0.617828i	0.0748802	−	0.997193i	$-0.476143\pi$
$181$	−11.4405	−	8.31202i	−0.850367	−	0.617828i	−0.925247	+	0.379365i	$0.876143\pi$
$182$	12.9992	−	12.9992i	0.963568	−	0.963568i
$183$	−1.92607	−	9.81185i	−0.142379	−	0.725313i
$184$	−6.04917	−	1.96550i	−0.445951	−	0.144898i
$185$		0			0
$186$	4.38125	+	11.9685i	0.321249	+	0.877571i
$187$	7.04042	−	3.58727i	0.514846	−	0.262327i
$188$	−2.54140	+	1.29491i	−0.185351	+	0.0944409i
$189$	7.81594	+	17.2960i	0.568526	+	1.25810i
$190$		0			0
$191$	−12.1952	−	3.96247i	−0.882416	−	0.286714i	−0.167456	−	0.985880i	$-0.553555\pi$
$191$	−12.1952	−	3.96247i	−0.882416	−	0.286714i	−0.714960	+	0.699165i	$0.753555\pi$
$192$	1.69961	−	0.333634i	0.122659	−	0.0240780i
$193$	9.89879	−	9.89879i	0.712531	−	0.712531i	−0.254533	−	0.967064i	$-0.581922\pi$
$193$	9.89879	−	9.89879i	0.712531	−	0.712531i	0.967064	+	0.254533i	$0.0819218\pi$
$194$	−11.0707	−	8.04332i	−0.794828	−	0.577477i
$195$		0			0
$196$	−5.13100	+	3.72789i	−0.366500	+	0.266278i
$197$	1.06492	−	6.72363i	0.0758723	−	0.479039i	−0.920270	−	0.391284i	$-0.872031\pi$
$197$	1.06492	−	6.72363i	0.0758723	−	0.479039i	0.996142	−	0.0877545i	$-0.0279691\pi$
$198$	−4.23775	−	1.78035i	−0.301164	−	0.126524i
$199$		−	5.40490i		−	0.383143i	−0.981479	−	0.191572i	$-0.938642\pi$
$199$		−	5.40490i		−	0.383143i	0.981479	−	0.191572i	$-0.0613585\pi$
$200$		0			0
$201$	−0.214610	−	5.83618i	−0.0151374	−	0.411653i
$202$	−0.0665368	+	0.130586i	−0.00468151	+	0.00918799i
$203$	25.1881	+	3.98940i	1.76786	+	0.280001i
$204$	5.51234	+	7.02865i	0.385941	+	0.492104i
$205$		0			0
$206$	−9.18325	+	12.6397i	−0.639827	+	0.880647i
$207$	−12.4652	+	14.4471i	−0.866391	+	1.00415i
$208$	−4.97094	+	0.787319i	−0.344673	+	0.0545908i
$209$	1.02663	−	3.15965i	0.0710137	−	0.218558i
$210$		0			0
$211$	3.95464	+	12.1711i	0.272249	+	0.837896i	0.989934	+	0.141529i	$0.0452017\pi$
$211$	3.95464	+	12.1711i	0.272249	+	0.837896i	−0.717685	+	0.696368i	$0.754798\pi$
$212$	−0.469093	−	0.920647i	−0.0322175	−	0.0632303i
$213$	−3.12604	−	5.61502i	−0.214193	−	0.384735i
$214$	2.38255	−	0.774136i	0.162868	−	0.0529189i
$215$		0			0
$216$	1.05213	−	5.08852i	0.0715883	−	0.346230i
$217$	4.20467	+	26.5473i	0.285432	+	1.80215i
$218$	5.69477	+	5.69477i	0.385698	+	0.385698i
$219$	−0.857448	−	0.576052i	−0.0579410	−	0.0389260i
$220$		0			0
$221$	−15.2561	−	20.9983i	−1.02624	−	1.41250i
$222$	−13.2020	−	1.59623i	−0.886063	−	0.107132i
$223$	−25.8694	−	13.1811i	−1.73234	−	0.882673i	−0.972611	−	0.232437i	$-0.925330\pi$
$223$	−25.8694	−	13.1811i	−1.73234	−	0.882673i	−0.759732	−	0.650236i	$-0.774670\pi$
$224$	3.65271			0.244057
$225$		0			0
$226$	10.8492			0.721675
$227$	−3.52093	−	1.79400i	−0.233692	−	0.119072i	0.333224	−	0.942848i	$-0.391864\pi$
$227$	−3.52093	−	1.79400i	−0.233692	−	0.119072i	−0.566916	+	0.823776i	$0.691864\pi$
$228$	3.72848	+	0.450803i	0.246925	+	0.0298552i
$229$	7.75981	+	10.6805i	0.512783	+	0.705785i	0.984386	−	0.176026i	$-0.0563243\pi$
$229$	7.75981	+	10.6805i	0.512783	+	0.705785i	−0.471603	+	0.881811i	$0.656324\pi$
$230$		0			0
$231$	−8.04637	−	5.40573i	−0.529413	−	0.355671i
$232$	−4.93680	−	4.93680i	−0.324117	−	0.324117i
$233$	1.37119	+	8.65736i	0.0898297	+	0.567163i	0.991017	+	0.133733i	$0.0426966\pi$
$233$	1.37119	+	8.65736i	0.0898297	+	0.567163i	−0.901188	+	0.433429i	$0.857303\pi$
$234$	−3.59850	+	14.6636i	−0.235241	+	0.958591i
$235$		0			0
$236$	6.48779	−	2.10801i	0.422319	−	0.137220i
$237$	1.12118	+	2.01387i	0.0728285	+	0.130815i
$238$	8.55203	+	16.7843i	0.554345	+	1.08796i
$239$	5.85405	+	18.0169i	0.378667	+	1.16542i	0.940971	+	0.338486i	$0.109915\pi$
$239$	5.85405	+	18.0169i	0.378667	+	1.16542i	−0.562305	+	0.826930i	$0.690085\pi$
$240$		0			0
$241$	−7.26464	+	22.3583i	−0.467957	+	1.44022i	0.387269	+	0.921967i	$0.373418\pi$
$241$	−7.26464	+	22.3583i	−0.467957	+	1.44022i	−0.855226	+	0.518256i	$0.826582\pi$
$242$	−8.54590	+	1.35354i	−0.549351	+	0.0870087i
$243$	−12.8514	−	8.82273i	−0.824420	−	0.565978i
$244$	−3.39328	+	4.67045i	−0.217232	+	0.298995i
$245$		0			0
$246$	3.21363	+	4.09762i	0.204893	+	0.261254i
$247$	−10.7786	−	1.70716i	−0.685824	−	0.108624i
$248$	3.34066	−	6.55641i	0.212132	−	0.416332i
$249$	0.176156	+	4.79044i	0.0111634	+	0.303582i
$250$		0			0
$251$			13.6488i			0.861504i	0.902470	+	0.430752i	$0.141752\pi$
$251$			13.6488i			0.861504i	−0.902470	+	0.430752i	$0.858248\pi$
$252$	4.24434	−	10.1028i	0.267369	−	0.636414i
$253$	1.52452	−	9.62542i	0.0958455	−	0.605145i
$254$	14.9488	−	10.8609i	0.937971	−	0.681476i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.2769	+	14.2769i	−0.890571	+	0.890571i	−0.994577	−	0.104006i	$-0.966834\pi$
$257$	−14.2769	+	14.2769i	−0.890571	+	0.890571i	0.104006	+	0.994577i	$0.466834\pi$
$258$	7.80437	−	1.53200i	0.485879	−	0.0953780i
$259$	−26.6718	−	8.66620i	−1.65731	−	0.538492i
$260$		0			0
$261$	−19.3908	+	7.91793i	−1.20026	+	0.490107i
$262$	11.8194	−	6.02229i	0.730205	−	0.372058i
$263$	−14.5181	+	7.39734i	−0.895224	+	0.456139i	−0.840157	−	0.542343i	$-0.817537\pi$
$263$	−14.5181	+	7.39734i	−0.895224	+	0.456139i	−0.0550670	+	0.998483i	$0.517537\pi$
$264$	0.912268	+	2.49209i	0.0561462	+	0.153377i
$265$		0			0
$266$	7.53258	+	2.44748i	0.461852	+	0.150065i
$267$	−2.14787	−	10.9418i	−0.131448	−	0.669626i
$268$	−2.38422	+	2.38422i	−0.145640	+	0.145640i
$269$	−8.83824	−	6.42136i	−0.538877	−	0.391517i	0.284791	−	0.958590i	$-0.408076\pi$
$269$	−8.83824	−	6.42136i	−0.538877	−	0.391517i	−0.823668	+	0.567073i	$0.808076\pi$
$270$		0			0
$271$	−2.71650	+	1.97365i	−0.165016	+	0.119891i	−0.667228	−	0.744853i	$-0.732519\pi$
$271$	−2.71650	+	1.97365i	−0.165016	+	0.119891i	0.502213	+	0.864744i	$0.332519\pi$
$272$	0.806752	−	5.09363i	0.0489165	−	0.308847i
$273$	−13.4034	+	28.8830i	−0.811212	+	1.74808i
$274$			9.76085i			0.589674i
$275$		0			0
$276$	11.0092	−	0.404835i	0.662678	−	0.0243682i
$277$	−12.7426	+	25.0088i	−0.765631	+	1.50263i	0.0961574	+	0.995366i	$0.469345\pi$
$277$	−12.7426	+	25.0088i	−0.765631	+	1.50263i	−0.861788	+	0.507269i	$0.830655\pi$
$278$	−4.79774	−	0.759888i	−0.287749	−	0.0455750i
$279$	−14.2522	−	16.8581i	−0.853255	−	1.00927i
$280$		0			0
$281$	−0.417572	+	0.574739i	−0.0249103	+	0.0342861i	−0.821290	−	0.570510i	$-0.806745\pi$
$281$	−0.417572	+	0.574739i	−0.0249103	+	0.0342861i	0.796380	+	0.604796i	$0.206745\pi$
$282$	3.36258	−	3.61933i	0.200239	−	0.215528i
$283$	−9.10320	+	1.44181i	−0.541129	+	0.0857064i	−0.421015	−	0.907054i	$-0.638326\pi$
$283$	−9.10320	+	1.44181i	−0.541129	+	0.0857064i	−0.120114	+	0.992760i	$0.538326\pi$
$284$	−1.14657	+	3.52877i	−0.0680363	+	0.209394i
$285$		0			0
$286$	−2.38293	−	7.33390i	−0.140905	−	0.433662i
$287$	4.98573	+	9.78504i	0.294298	+	0.577593i
$288$	−2.56577	+	1.55461i	−0.151189	+	0.0916065i
$289$	9.12626	−	2.96530i	0.536839	−	0.174430i
$290$		0			0
$291$	22.7955	+	6.49090i	1.33629	+	0.380503i
$292$	0.0932964	+	0.589050i	0.00545976	+	0.0344716i
$293$	1.97743	+	1.97743i	0.115523	+	0.115523i	0.762505	−	0.646982i	$-0.223969\pi$
$293$	1.97743	+	1.97743i	0.115523	+	0.115523i	−0.646982	+	0.762505i	$0.723969\pi$
$294$	6.12595	−	9.11842i	0.357273	−	0.531797i
$295$		0			0
$296$	4.51285	+	6.21140i	0.262304	+	0.361030i
$297$	7.95272	+	0.372559i	0.461464	+	0.0216180i
$298$	−5.84222	−	2.97676i	−0.338431	−	0.172439i
$299$	−32.0116			−1.85128
$300$		0			0
$301$	16.7727			0.966760
$302$	0.949976	+	0.484037i	0.0546650	+	0.0278532i
$303$	0.0304705	−	0.252014i	0.00175048	−	0.0144778i
$304$	−1.27450	−	1.75421i	−0.0730979	−	0.100611i
$305$		0			0
$306$	−13.1507	−	8.15000i	−0.751775	−	0.465904i
$307$	11.7511	+	11.7511i	0.670673	+	0.670673i	0.957871	−	0.287198i	$-0.0927239\pi$
$307$	11.7511	+	11.7511i	0.670673	+	0.670673i	−0.287198	+	0.957871i	$0.592724\pi$
$308$	0.875502	+	5.52770i	0.0498864	+	0.314970i
$309$	7.41082	−	26.0261i	0.421587	−	1.48057i
$310$		0			0
$311$	3.30339	−	1.07334i	0.187318	−	0.0608633i	−0.213856	−	0.976865i	$-0.568602\pi$
$311$	3.30339	−	1.07334i	0.187318	−	0.0608633i	0.401174	+	0.916002i	$0.368602\pi$
$312$	7.61644	−	4.24029i	0.431196	−	0.240059i
$313$	−3.85400	−	7.56390i	−0.217841	−	0.427537i	0.756063	−	0.654499i	$-0.227121\pi$
$313$	−3.85400	−	7.56390i	−0.217841	−	0.427537i	−0.973904	+	0.226962i	$0.927121\pi$
$314$	−6.70127	−	20.6244i	−0.378175	−	1.16390i
$315$		0			0
$316$	0.411226	−	1.26562i	0.0231333	−	0.0711969i
$317$	9.73906	−	1.54252i	0.547000	−	0.0866363i	0.123183	−	0.992384i	$-0.460690\pi$
$317$	9.73906	−	1.54252i	0.547000	−	0.0866363i	0.423817	+	0.905748i	$0.360690\pi$
$318$	1.31114	+	1.21813i	0.0735249	+	0.0683093i
$319$	6.28766	−	8.65423i	0.352042	−	0.484544i
$320$		0			0
$321$	−3.41428	+	2.67771i	−0.190567	+	0.149455i
$322$	22.9469	+	3.63443i	1.27878	+	0.202539i
$323$	5.07665	−	9.96348i	0.282472	−	0.554383i
$324$	1.31844	+	8.90290i	0.0732469	+	0.494606i
$325$		0			0
$326$			10.2817i			0.569452i
$327$	−12.6532	−	5.87183i	−0.699724	−	0.324713i
$328$	0.470327	−	2.96952i	0.0259694	−	0.163965i
$329$	8.42877	−	6.12386i	0.464693	−	0.337619i
$330$		0			0
$331$	−13.3891	−	9.72777i	−0.735933	−	0.534687i	0.155502	−	0.987836i	$-0.450301\pi$
$331$	−13.3891	−	9.72777i	−0.735933	−	0.534687i	−0.891435	+	0.453149i	$0.850301\pi$
$332$	1.95701	−	1.95701i	0.107405	−	0.107405i
$333$	22.4235	−	5.26429i	1.22880	−	0.288481i
$334$	22.9173	+	7.44629i	1.25398	+	0.407443i
$335$		0			0
$336$	−5.94112	+	2.17484i	−0.324114	+	0.118647i
$337$	23.3624	−	11.9038i	1.27263	−	0.648439i	0.318528	−	0.947913i	$-0.396811\pi$
$337$	23.3624	−	11.9038i	1.27263	−	0.648439i	0.954104	+	0.299475i	$0.0968114\pi$
$338$	−10.9862	+	5.59775i	−0.597570	+	0.304477i
$339$	−17.6461	+	6.45964i	−0.958406	+	0.350840i
$340$		0			0
$341$	10.7226	+	3.48400i	0.580663	+	0.188669i
$342$	−6.33277	+	1.48673i	−0.342437	+	0.0803929i
$343$	−1.69884	+	1.69884i	−0.0917290	+	0.0917290i
$344$	−3.71488	−	2.69902i	−0.200293	−	0.145521i
$345$		0			0
$346$	19.4258	−	14.1137i	1.04434	−	0.758756i
$347$	1.86187	−	11.7554i	0.0999502	−	0.631061i	−0.885957	−	0.463768i	$-0.846497\pi$
$347$	1.86187	−	11.7554i	0.0999502	−	0.631061i	0.985907	−	0.167293i	$-0.0535027\pi$
$348$	10.9691	+	5.09030i	0.588005	+	0.272869i
$349$		−	25.4721i		−	1.36349i	−0.731591	−	0.681744i	$-0.761222\pi$
$349$		−	25.4721i		−	1.36349i	0.731591	−	0.681744i	$-0.238778\pi$
$350$		0			0
$351$	−2.87784	−	25.9929i	−0.153608	−	1.38740i
$352$	0.695596	−	1.36518i	0.0370754	−	0.0727645i
$353$	−8.69825	−	1.37767i	−0.462961	−	0.0733258i	−0.0794030	−	0.996843i	$-0.525301\pi$
$353$	−8.69825	−	1.37767i	−0.462961	−	0.0733258i	−0.383558	+	0.923517i	$0.625301\pi$
$354$	−9.29725	+	7.29153i	−0.494143	+	0.387541i
$355$		0			0
$356$	−3.78405	+	5.20829i	−0.200554	+	0.276039i
$357$	−23.9033	−	22.2077i	−1.26510	−	1.17536i
$358$	4.45314	−	0.705308i	0.235356	−	0.0372767i
$359$	2.11987	−	6.52428i	0.111882	−	0.344338i	−0.879402	−	0.476080i	$-0.842057\pi$
$359$	2.11987	−	6.52428i	0.111882	−	0.344338i	0.991284	+	0.131742i	$0.0420571\pi$
$360$		0			0
$361$	4.41845	+	13.5986i	0.232550	+	0.715715i
$362$	−6.42000	−	12.6000i	−0.337428	−	0.662239i
$363$	13.0940	−	7.28979i	0.687255	−	0.382615i
$364$	17.4839	−	5.68088i	0.916408	−	0.297759i
$365$		0			0
$366$	2.73835	−	9.61684i	0.143136	−	0.502680i
$367$	2.31983	+	14.6468i	0.121094	+	0.764559i	0.971256	+	0.238038i	$0.0765041\pi$
$367$	2.31983	+	14.6468i	0.121094	+	0.764559i	−0.850162	+	0.526522i	$0.823496\pi$
$368$	−4.49754	−	4.49754i	−0.234450	−	0.234450i
$369$	−7.66670	−	4.75135i	−0.399112	−	0.247345i
$370$		0			0
$371$	2.21843	+	3.05341i	0.115175	+	0.158525i
$372$	−1.52985	+	12.6530i	−0.0793191	+	0.656029i
$373$	15.4140	+	7.85384i	0.798108	+	0.406656i	0.804967	−	0.593320i	$-0.202183\pi$
$373$	15.4140	+	7.85384i	0.798108	+	0.406656i	−0.00685847	+	0.999976i	$0.502183\pi$
$374$	7.90165			0.408584
$375$		0			0
$376$	−2.85228			−0.147095
$377$	−31.3083	−	15.9524i	−1.61246	−	0.821590i
$378$	−0.888176	+	18.9592i	−0.0456829	+	0.975157i
$379$	−3.34257	−	4.60065i	−0.171696	−	0.236319i	0.714494	−	0.699642i	$-0.246657\pi$
$379$	−3.34257	−	4.60065i	−0.171696	−	0.236319i	−0.886190	+	0.463323i	$0.846657\pi$
$380$		0			0
$381$	−17.8475	+	26.5659i	−0.914356	+	1.36101i
$382$	−9.06711	−	9.06711i	−0.463914	−	0.463914i
$383$	4.74888	+	29.9833i	0.242657	+	1.53207i	0.744799	+	0.667289i	$0.232545\pi$
$383$	4.74888	+	29.9833i	0.242657	+	1.53207i	−0.502143	+	0.864785i	$0.667455\pi$
$384$	1.66583	+	0.474338i	0.0850092	+	0.0242060i
$385$		0			0
$386$	13.3138	−	4.32593i	0.677657	−	0.220184i
$387$	−11.7816	+	7.13855i	−0.598893	+	0.362873i
$388$	−6.21246	−	12.1926i	−0.315390	−	0.618987i
$389$	0.407506	+	1.25417i	0.0206613	+	0.0635891i	0.960856	−	0.277050i	$-0.0893567\pi$
$389$	0.407506	+	1.25417i	0.0206613	+	0.0635891i	−0.940194	+	0.340639i	$0.889357\pi$
$390$		0			0
$391$	10.1363	−	31.1963i	0.512615	−	1.57767i
$392$	−6.26418	+	0.992148i	−0.316389	+	0.0501110i
$393$	−15.6385	+	16.8326i	−0.788860	+	0.849091i
$394$	4.00131	−	5.50734i	0.201583	−	0.277456i
$395$		0			0
$396$	−2.96760	−	3.51020i	−0.149128	−	0.176394i
$397$	−10.9634	−	1.73643i	−0.550238	−	0.0871491i	−0.124876	−	0.992172i	$-0.539853\pi$
$397$	−10.9634	−	1.73643i	−0.550238	−	0.0871491i	−0.425362	+	0.905023i	$0.639853\pi$
$398$	2.45377	−	4.81580i	0.122997	−	0.241394i
$399$	−13.7090	+	0.504110i	−0.686307	+	0.0252371i
$400$		0			0
$401$			38.4533i			1.92026i	0.279545	+	0.960132i	$0.409816\pi$
$401$			38.4533i			1.92026i	−0.279545	+	0.960132i	$0.590184\pi$
$402$	2.45835	−	5.29751i	0.122612	−	0.264216i
$403$	5.79343	−	36.5783i	0.288591	−	1.82209i
$404$	−0.118569	+	0.0861458i	−0.00589905	+	0.00428591i
$405$		0			0
$406$	20.6316	+	14.9897i	1.02393	+	0.743928i
$407$	−8.31815	+	8.31815i	−0.412316	+	0.412316i
$408$	1.72059	+	8.76512i	0.0851820	+	0.433938i
$409$	10.8096	+	3.51227i	0.534502	+	0.173670i	0.563817	−	0.825900i	$-0.309332\pi$
$409$	10.8096	+	3.51227i	0.534502	+	0.173670i	−0.0293144	+	0.999570i	$0.509332\pi$
$410$		0			0
$411$	−5.81166	−	15.8760i	−0.286668	−	0.783105i
$412$	−13.9206	+	7.09291i	−0.685820	+	0.349443i
$413$	−22.2017	+	11.3123i	−1.09247	+	0.556643i
$414$	−17.6654	+	7.21341i	−0.868209	+	0.354520i
$415$		0			0
$416$	−4.78657	−	1.55525i	−0.234681	−	0.0762525i
$417$	8.25595	−	1.62064i	0.404296	−	0.0793633i
$418$	2.34919	−	2.34919i	0.114903	−	0.114903i
$419$	4.06691	+	2.95479i	0.198682	+	0.144351i	0.682678	−	0.730719i	$-0.260815\pi$
$419$	4.06691	+	2.95479i	0.198682	+	0.144351i	−0.483996	+	0.875070i	$0.660815\pi$
$420$		0			0
$421$	−7.36850	+	5.35353i	−0.359119	+	0.260915i	−0.752684	−	0.658382i	$-0.771241\pi$
$421$	−7.36850	+	5.35353i	−0.359119	+	0.260915i	0.393566	+	0.919296i	$0.371241\pi$
$422$	−2.00197	+	12.6399i	−0.0974544	+	0.615303i
$423$	−3.31427	+	7.88892i	−0.161145	+	0.383573i
$424$		−	1.03327i		−	0.0501799i
$425$		0			0
$426$	−0.236159	−	6.42221i	−0.0114420	−	0.311157i
$427$	9.57331	−	18.7887i	0.463285	−	0.909248i
$428$	2.47432	+	0.391893i	0.119601	+	0.0189429i
$429$	8.24246	+	10.5098i	0.397950	+	0.507416i
$430$		0			0
$431$	−14.5495	+	20.0257i	−0.700824	+	0.964602i	0.299122	+	0.954215i	$0.403306\pi$
$431$	−14.5495	+	20.0257i	−0.700824	+	0.964602i	−0.999946	+	0.0103868i	$0.996694\pi$
$432$	3.24759	−	4.05625i	0.156250	−	0.195156i
$433$	−21.9052	+	3.46945i	−1.05270	+	0.166731i	−0.658720	−	0.752388i	$-0.728902\pi$
$433$	−21.9052	+	3.46945i	−1.05270	+	0.166731i	−0.393979	+	0.919119i	$0.628902\pi$
$434$	−8.30582	+	25.5627i	−0.398692	+	1.22705i
$435$		0			0
$436$	2.48870	+	7.65945i	0.119187	+	0.366821i
$437$	−6.26122	−	12.2883i	−0.299515	−	0.587831i
$438$	−0.502470	−	0.902539i	−0.0240089	−	0.0431250i
$439$	1.62057	−	0.526555i	0.0773456	−	0.0251311i	−0.270089	−	0.962835i	$-0.587053\pi$
$439$	1.62057	−	0.526555i	0.0773456	−	0.0251311i	0.347434	+	0.937704i	$0.387053\pi$
$440$		0			0
$441$	−4.53469	+	18.4785i	−0.215937	+	0.879929i
$442$	−4.06030	−	25.6357i	−0.193129	−	1.21937i
$443$	−0.713085	−	0.713085i	−0.0338797	−	0.0338797i	0.689964	−	0.723844i	$-0.257626\pi$
$443$	−0.713085	−	0.713085i	−0.0338797	−	0.0338797i	−0.723844	+	0.689964i	$0.757626\pi$
$444$	−11.0384	−	7.41585i	−0.523861	−	0.351941i
$445$		0			0
$446$	−17.0657	−	23.4889i	−0.808085	−	1.11223i
$447$	11.2747	+	1.36321i	0.533277	+	0.0644774i
$448$	3.25458	+	1.65829i	0.153765	+	0.0783470i
$449$	−12.4310			−0.586657			−0.293329	−	0.956012i	$-0.594763\pi$
$449$	−12.4310			−0.586657			−0.293329	+	0.956012i	$0.594763\pi$
$450$		0			0
$451$	4.60656			0.216915
$452$	9.66667	+	4.92541i	0.454682	+	0.231672i
$453$	−1.83333	−	0.221664i	−0.0861374	−	0.0104147i
$454$	−2.32271	−	3.19694i	−0.109010	−	0.150040i
$455$		0			0
$456$	3.11744	+	2.09436i	0.145988	+	0.0980776i
$457$	25.4659	+	25.4659i	1.19125	+	1.19125i	0.976718	+	0.214529i	$0.0688217\pi$
$457$	25.4659	+	25.4659i	1.19125	+	1.19125i	0.214529	+	0.976718i	$0.431178\pi$
$458$	2.06521	+	13.0392i	0.0965011	+	0.609284i
$459$	26.2421	+	5.42596i	1.22488	+	0.253262i
$460$		0			0
$461$	34.8009	−	11.3075i	1.62084	−	0.526642i	0.648699	−	0.761045i	$-0.275314\pi$
$461$	34.8009	−	11.3075i	1.62084	−	0.526642i	0.972140	+	0.234403i	$0.0753135\pi$
$462$	−4.71522	−	8.46951i	−0.219372	−	0.394037i
$463$	−3.00399	−	5.89566i	−0.139607	−	0.273994i	0.810608	−	0.585589i	$-0.199137\pi$
$463$	−3.00399	−	5.89566i	−0.139607	−	0.273994i	−0.950215	+	0.311595i	$0.899137\pi$
$464$	−2.15746	−	6.63998i	−0.100158	−	0.308253i
$465$		0			0
$466$	−2.70862	+	8.33627i	−0.125474	+	0.386170i
$467$	−37.7026	+	5.97151i	−1.74467	+	0.276328i	−0.945699	−	0.325043i	$-0.894621\pi$
$467$	−37.7026	+	5.97151i	−1.74467	+	0.276328i	−0.798970	+	0.601371i	$0.794621\pi$
$468$	−9.86343	+	11.4317i	−0.455937	+	0.528430i
$469$	7.23928	−	9.96401i	0.334279	−	0.460095i
$470$		0			0
$471$	23.1795	+	29.5555i	1.06805	+	1.36185i
$472$	6.73768	+	1.06714i	0.310127	+	0.0491192i
$473$	3.19407	−	6.26871i	0.146863	−	0.288236i
$474$	0.0847006	+	2.30338i	0.00389043	+	0.105798i
$475$		0			0
$476$			18.8375i			0.863413i
$477$	−2.85784	−	1.20063i	−0.130852	−	0.0549730i
$478$	−2.96351	+	18.7109i	−0.135548	+	0.855815i
$479$	9.41843	−	6.84289i	0.430339	−	0.312660i	−0.351445	−	0.936208i	$-0.614310\pi$
$479$	9.41843	−	6.84289i	0.430339	−	0.312660i	0.781785	+	0.623549i	$0.214310\pi$
$480$		0			0
$481$	31.2614	+	22.7127i	1.42540	+	1.03561i
$482$	−16.6233	+	16.6233i	−0.757170	+	0.757170i
$483$	−39.4870	+	7.75131i	−1.79672	+	0.352697i
$484$	−8.22894	−	2.67375i	−0.374043	−	0.121534i
$485$		0			0
$486$	−7.44528	−	13.6955i	−0.337725	−	0.621242i
$487$	−31.6495	+	16.1262i	−1.43418	+	0.730750i	−0.986548	−	0.163470i	$-0.947731\pi$
$487$	−31.6495	+	16.1262i	−1.43418	+	0.730750i	−0.447629	+	0.894219i	$0.647731\pi$
$488$	−5.14377	+	2.62088i	−0.232848	+	0.118642i
$489$	−6.12178	−	16.7232i	−0.276837	−	0.756249i
$490$		0			0
$491$	3.18688	+	1.03548i	0.143822	+	0.0467305i	0.380043	−	0.924969i	$-0.375909\pi$
$491$	3.18688	+	1.03548i	0.143822	+	0.0467305i	−0.236222	+	0.971699i	$0.575909\pi$
$492$	1.00308	+	5.10996i	0.0452226	+	0.230375i
$493$	25.4597	−	25.4597i	1.14665	−	1.14665i
$494$	−8.82874	−	6.41446i	−0.397224	−	0.288600i
$495$		0			0
$496$	5.95310	−	4.32518i	0.267302	−	0.194206i
$497$	2.12014	−	13.3860i	0.0951012	−	0.600446i
$498$	−2.01786	+	4.34829i	−0.0904225	+	0.194852i
$499$			2.56390i			0.114776i	0.998352	+	0.0573880i	$0.0182772\pi$
$499$			2.56390i			0.114776i	−0.998352	+	0.0573880i	$0.981723\pi$
$500$		0			0
$501$	−41.7085	+	1.53372i	−1.86340	+	0.0685214i
$502$	−6.19642	+	12.1612i	−0.276560	+	0.542779i
$503$	14.3652	+	2.27523i	0.640515	+	0.101448i	0.468240	−	0.883601i	$-0.344888\pi$
$503$	14.3652	+	2.27523i	0.640515	+	0.101448i	0.172275	+	0.985049i	$0.444888\pi$
$504$	8.36830	−	7.07474i	0.372754	−	0.315134i
$505$		0			0
$506$	5.72820	−	7.88419i	0.254650	−	0.350495i
$507$	14.5361	−	15.6460i	0.645570	−	0.694861i
$508$	18.2502	−	2.89055i	0.809723	−	0.128248i
$509$	2.88278	−	8.87228i	0.127777	−	0.393257i	−0.866620	−	0.498969i	$-0.833712\pi$
$509$	2.88278	−	8.87228i	0.127777	−	0.393257i	0.994397	+	0.105712i	$0.0337122\pi$
$510$		0			0
$511$	−0.673177	−	2.07183i	−0.0297796	−	0.0916522i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	9.41504	−	6.18872i	0.415684	−	0.273239i
$514$	−19.2024	+	6.23925i	−0.846983	+	0.275202i
$515$		0			0
$516$	7.64925	+	2.17809i	0.336740	+	0.0958850i
$517$	−0.683651	−	4.31640i	−0.0300669	−	0.189835i
$518$	−19.8304	−	19.8304i	−0.871298	−	0.871298i
$519$	−23.1927	+	34.5221i	−1.01804	+	1.51535i
$520$		0			0
$521$	−19.0337	−	26.1976i	−0.833881	−	1.14774i	−0.987188	−	0.159560i	$-0.948993\pi$
$521$	−19.0337	−	26.1976i	−0.833881	−	1.14774i	0.153308	−	0.988179i	$-0.451007\pi$
$522$	−20.8720	−	1.74830i	−0.913541	−	0.0765212i
$523$	19.7913	+	10.0842i	0.865413	+	0.440950i	0.829567	−	0.558408i	$-0.188587\pi$
$523$	19.7913	+	10.0842i	0.865413	+	0.440950i	0.0358458	+	0.999357i	$0.488587\pi$
$524$	13.2652			0.579494
$525$		0			0
$526$	−16.2940			−0.710454
$527$	33.8122	+	17.2282i	1.47288	+	0.750471i
$528$	−0.318547	+	2.63463i	−0.0138630	+	0.114657i
$529$	−10.2602	−	14.1219i	−0.446095	−	0.613997i
$530$		0			0
$531$	10.7805	−	17.3953i	0.467835	−	0.754891i
$532$	5.60044	+	5.60044i	0.242810	+	0.242810i
$533$	−2.36711	−	14.9453i	−0.102531	−	0.647354i
$534$	3.05370	−	10.7243i	0.132146	−	0.464087i
$535$		0			0
$536$	−3.20677	+	1.04194i	−0.138511	+	0.0450051i
$537$	−6.82307	+	3.79860i	−0.294437	+	0.163922i
$538$	−4.95969	−	9.73395i	−0.213828	−	0.419660i
$539$	−3.00287	−	9.24188i	−0.129343	−	0.398076i
$540$		0			0
$541$	−0.547811	+	1.68599i	−0.0235522	+	0.0724863i	−0.962142	−	0.272549i	$-0.912133\pi$
$541$	−0.547811	+	1.68599i	−0.0235522	+	0.0724863i	0.938590	+	0.345036i	$0.112133\pi$
$542$	−3.31644	+	0.525272i	−0.142453	+	0.0225624i
$543$	17.9442	+	16.6713i	0.770058	+	0.715434i
$544$	3.03128	−	4.17220i	0.129965	−	0.178882i
$545$		0			0
$546$	−25.0552	+	19.6500i	−1.07226	+	0.840941i
$547$	12.4044	+	1.96467i	0.530376	+	0.0840033i	0.415878	−	0.909420i	$-0.363474\pi$
$547$	12.4044	+	1.96467i	0.530376	+	0.0840033i	0.114497	+	0.993424i	$0.463474\pi$
$548$	−4.43133	+	8.69698i	−0.189297	+	0.371517i
$549$	1.27200	+	17.2722i	0.0542875	+	0.737159i
$550$		0			0
$551$		−	15.1385i		−	0.644922i
$552$	9.99308	+	4.63737i	0.425334	+	0.197380i
$553$	−0.760406	+	4.80101i	−0.0323357	+	0.204160i
$554$	−22.7075	+	16.4980i	−0.964751	+	0.700933i
$555$		0			0
$556$	−3.92984	−	2.85519i	−0.166662	−	0.121087i
$557$	19.4225	−	19.4225i	0.822959	−	0.822959i	−0.163573	−	0.986531i	$-0.552302\pi$
$557$	19.4225	−	19.4225i	0.822959	−	0.822959i	0.986531	+	0.163573i	$0.0523018\pi$
$558$	−5.04537	−	21.4910i	−0.213588	−	0.909786i
$559$	−21.9792	−	7.14148i	−0.929621	−	0.302052i
$560$		0			0
$561$	−12.8520	+	4.70468i	−0.542612	+	0.198632i
$562$	−0.632986	+	0.322522i	−0.0267009	+	0.0136048i
$563$	−22.4447	+	11.4362i	−0.945933	+	0.481977i	−0.857716	−	0.514125i	$-0.828117\pi$
$563$	−22.4447	+	11.4362i	−0.945933	+	0.481977i	−0.0882171	+	0.996101i	$0.528117\pi$
$564$	4.63922	−	1.69826i	0.195347	−	0.0715097i
$565$		0			0
$566$	−8.76558	−	2.84811i	−0.368445	−	0.119715i
$567$	−9.84380	−	31.3659i	−0.413401	−	1.31725i
$568$	−2.62363	+	2.62363i	−0.110085	+	0.110085i
$569$	24.7435	+	17.9772i	1.03730	+	0.753643i	0.969757	−	0.244073i	$-0.0784837\pi$
$569$	24.7435	+	17.9772i	1.03730	+	0.753643i	0.0675439	+	0.997716i	$0.478484\pi$
$570$		0			0
$571$	−8.91080	+	6.47408i	−0.372905	+	0.270932i	−0.758415	−	0.651772i	$-0.774026\pi$
$571$	−8.91080	+	6.47408i	−0.372905	+	0.270932i	0.385509	+	0.922704i	$0.374026\pi$
$572$	1.20632	−	7.61638i	0.0504386	−	0.318457i
$573$	20.1462	+	9.34903i	0.841621	+	0.390561i
$574$			10.9820i			0.458380i
$575$		0			0
$576$	−2.99190	+	0.220336i	−0.124662	+	0.00918066i
$577$	1.76187	−	3.45787i	0.0733478	−	0.143953i	−0.851421	−	0.524483i	$-0.824259\pi$
$577$	1.76187	−	3.45787i	0.0733478	−	0.143953i	0.924768	+	0.380530i	$0.124259\pi$
$578$	9.47778	+	1.50113i	0.394224	+	0.0624389i
$579$	−19.0793	+	14.9632i	−0.792907	+	0.621851i
$580$		0			0
$581$	−5.94213	+	8.17864i	−0.246521	+	0.339307i
$582$	17.3641	+	16.1324i	0.719765	+	0.668708i
$583$	1.56366	−	0.247659i	0.0647602	−	0.0102570i
$584$	−0.184296	+	0.567203i	−0.00762620	+	0.0234710i
$585$		0			0
$586$	0.864170	+	2.65964i	0.0356985	+	0.109869i
$587$	20.1279	+	39.5031i	0.830766	+	1.63047i	0.774945	+	0.632028i	$0.217777\pi$
$587$	20.1279	+	39.5031i	0.830766	+	1.63047i	0.0558204	+	0.998441i	$0.482223\pi$
$588$	9.59794	−	5.34345i	0.395812	−	0.220360i
$589$	15.1745	−	4.93049i	0.625254	−	0.203157i
$590$		0			0
$591$	−3.22903	+	11.3401i	−0.132825	+	0.466468i
$592$	1.20106	+	7.58319i	0.0493632	+	0.311667i
$593$	−11.0677	−	11.0677i	−0.454495	−	0.454495i	0.442348	−	0.896843i	$-0.354145\pi$
$593$	−11.0677	−	11.0677i	−0.454495	−	0.454495i	−0.896843	+	0.442348i	$0.854145\pi$
$594$	6.91679	+	3.94241i	0.283799	+	0.161759i
$595$		0			0
$596$	−3.85404	−	5.30463i	−0.157868	−	0.217286i
$597$	−1.12370	+	9.29388i	−0.0459902	+	0.380373i
$598$	−28.5226	−	14.5330i	−1.16638	−	0.594298i
$599$	39.0036			1.59364			0.796822	−	0.604215i	$-0.206513\pi$
$599$	39.0036			1.59364			0.796822	+	0.604215i	$0.206513\pi$
$600$		0			0
$601$	−25.7471			−1.05025			−0.525123	−	0.851027i	$-0.675981\pi$
$601$	−25.7471			−1.05025			−0.525123	+	0.851027i	$0.675981\pi$
$602$	14.9446	+	7.61463i	0.609094	+	0.310349i
$603$	−0.844342	+	10.0801i	−0.0343843	+	0.410493i
$604$	0.626686	+	0.862560i	0.0254995	+	0.0350971i
$605$		0			0
$606$	0.141561	−	0.210713i	0.00575054	−	0.00855962i
$607$	14.3533	+	14.3533i	0.582583	+	0.582583i	0.935612	−	0.353030i	$-0.114848\pi$
$607$	14.3533	+	14.3533i	0.582583	+	0.582583i	−0.353030	+	0.935612i	$0.614848\pi$
$608$	−0.339200	−	2.14162i	−0.0137564	−	0.0868542i
$609$	−42.4822	−	12.0966i	−1.72147	−	0.490179i
$610$		0			0
$611$	−13.6526	+	4.43601i	−0.552327	+	0.179462i
$612$	−8.01733	−	13.2320i	−0.324082	−	0.534872i
$613$	12.7810	+	25.0841i	0.516219	+	1.01314i	0.991104	+	0.133089i	$0.0424895\pi$
$613$	12.7810	+	25.0841i	0.516219	+	1.01314i	−0.474885	+	0.880048i	$0.657510\pi$
$614$	5.13543	+	15.8052i	0.207249	+	0.637848i
$615$		0			0
$616$	−1.72945	+	5.32269i	−0.0696814	+	0.214457i
$617$	22.8131	−	3.61324i	0.918421	−	0.145464i	0.320712	−	0.947177i	$-0.396078\pi$
$617$	22.8131	−	3.61324i	0.918421	−	0.145464i	0.597709	+	0.801713i	$0.296078\pi$
$618$	18.4187	−	19.8250i	0.740909	−	0.797479i
$619$	5.12654	−	7.05608i	0.206053	−	0.283608i	−0.693466	−	0.720489i	$-0.743917\pi$
$619$	5.12654	−	7.05608i	0.206053	−	0.283608i	0.899519	+	0.436882i	$0.143917\pi$
$620$		0			0
$621$	24.4379	−	22.2507i	0.980658	−	0.892889i
$622$	3.43062	+	0.543357i	0.137555	+	0.0217866i
$623$	10.6758	−	20.9524i	0.427716	−	0.839440i
$624$	8.71135	−	0.320336i	0.348733	−	0.0128237i
$625$		0			0
$626$		−	8.48916i		−	0.339295i
$627$	−2.42223	+	5.21967i	−0.0967345	+	0.208453i
$628$	3.39240	−	21.4188i	0.135372	−	0.854702i
$629$	−32.0330	+	23.2733i	−1.27724	+	0.927967i
$630$		0			0
$631$	20.4095	+	14.8283i	0.812488	+	0.590307i	0.914551	−	0.404471i	$-0.132544\pi$
$631$	20.4095	+	14.8283i	0.812488	+	0.590307i	−0.102063	+	0.994778i	$0.532544\pi$
$632$	0.940986	−	0.940986i	0.0374304	−	0.0374304i
$633$	−4.26968	−	21.7508i	−0.169705	−	0.864517i
$634$	9.37785	+	3.04705i	0.372442	+	0.121014i
$635$		0			0
$636$	0.615212	+	1.68061i	0.0243947	+	0.0666403i
$637$	−28.4409	+	14.4914i	−1.12687	+	0.574169i
$638$	9.53128	−	4.85643i	0.377347	−	0.192268i
$639$	4.20793	+	10.3051i	0.166463	+	0.407663i
$640$		0			0
$641$	−30.1335	−	9.79096i	−1.19020	−	0.386720i	−0.354054	−	0.935225i	$-0.615197\pi$
$641$	−30.1335	−	9.79096i	−1.19020	−	0.386720i	−0.836147	+	0.548505i	$0.815197\pi$
$642$	−4.25780	+	0.835807i	−0.168042	+	0.0329867i
$643$	−11.3185	+	11.3185i	−0.446357	+	0.446357i	−0.894142	−	0.447785i	$-0.852213\pi$
$643$	−11.3185	+	11.3185i	−0.446357	+	0.446357i	0.447785	+	0.894142i	$0.352213\pi$
$644$	18.7959	+	13.6560i	0.740660	+	0.538121i
$645$		0			0
$646$	9.04665	−	6.57278i	0.355936	−	0.258602i
$647$	−4.88293	+	30.8296i	−0.191968	+	1.21204i	0.683933	+	0.729545i	$0.260268\pi$
$647$	−4.88293	+	30.8296i	−0.191968	+	1.21204i	−0.875901	+	0.482491i	$0.839732\pi$
$648$	−2.86709	+	8.53111i	−0.112630	+	0.335134i
$649$			10.4520i			0.410278i
$650$		0			0
$651$	−1.71075	−	46.5229i	−0.0670498	−	1.82338i
$652$	−4.66780	+	9.16108i	−0.182805	+	0.358775i
$653$	1.59686	+	0.252918i	0.0624900	+	0.00989744i	0.187601	−	0.982245i	$-0.439929\pi$
$653$	1.59686	+	0.252918i	0.0624900	+	0.00989744i	−0.125111	+	0.992143i	$0.539929\pi$
$654$	−8.60834	−	10.9763i	−0.336613	−	0.429207i
$655$		0			0
$656$	1.76720	−	2.43234i	0.0689976	−	0.0949670i
$657$	1.35464	+	1.16880i	0.0528496	+	0.0455994i
$658$	10.2903	−	1.62982i	0.401156	−	0.0635369i
$659$	1.49604	−	4.60434i	0.0582774	−	0.179360i	−0.917680	−	0.397320i	$-0.869940\pi$
$659$	1.49604	−	4.60434i	0.0582774	−	0.179360i	0.975958	+	0.217960i	$0.0699403\pi$
$660$		0			0
$661$	−14.5577	−	44.8040i	−0.566229	−	1.74267i	−0.664271	−	0.747492i	$-0.731258\pi$
$661$	−14.5577	−	44.8040i	−0.566229	−	1.74267i	0.0980414	−	0.995182i	$-0.468742\pi$
$662$	−7.51349	−	14.7460i	−0.292020	−	0.573121i
$663$	21.8677	+	39.2789i	0.849272	+	1.52547i
$664$	2.63218	−	0.855246i	0.102148	−	0.0331900i
$665$		0			0
$666$	22.3694	+	5.48953i	0.866797	+	0.212715i
$667$	−6.94676	−	43.8601i	−0.268980	−	1.69827i
$668$	17.0389	+	17.0389i	0.659256	+	0.659256i
$669$	41.7427	+	28.0437i	1.61387	+	1.08423i
$670$		0			0
$671$	−5.19911	−	7.15597i	−0.200710	−	0.276253i
$672$	−6.28093	−	0.759414i	−0.242292	−	0.0292950i
$673$	−22.8312	−	11.6331i	−0.880077	−	0.448422i	−0.0452767	−	0.998974i	$-0.514417\pi$
$673$	−22.8312	−	11.6331i	−0.880077	−	0.448422i	−0.834800	+	0.550553i	$0.814417\pi$
$674$	26.2203			1.00997
$675$		0			0
$676$	−12.3301			−0.474234
$677$	−16.4540	−	8.38373i	−0.632379	−	0.322213i	0.108254	−	0.994123i	$-0.465474\pi$
$677$	−16.4540	−	8.38373i	−0.632379	−	0.322213i	−0.740633	+	0.671910i	$0.765474\pi$
$678$	−18.6554	−	2.25559i	−0.716457	−	0.0866254i
$679$	29.3799	+	40.4379i	1.12750	+	1.55187i
$680$		0			0
$681$	5.68136	+	3.81686i	0.217710	+	0.146262i
$682$	7.97224	+	7.97224i	0.305273	+	0.305273i
$683$	2.58115	+	16.2967i	0.0987650	+	0.623578i	0.986568	+	0.163353i	$0.0522310\pi$
$683$	2.58115	+	16.2967i	0.0987650	+	0.623578i	−0.887803	+	0.460224i	$0.847769\pi$
$684$	−6.31750	−	1.55034i	−0.241556	−	0.0592786i
$685$		0			0
$686$	−2.28494	+	0.742422i	−0.0872394	+	0.0283458i
$687$	−11.1227	−	19.9787i	−0.424357	−	0.762234i
$688$	−2.08465	−	4.09136i	−0.0794767	−	0.155982i
$689$	−1.60699	−	4.94581i	−0.0612214	−	0.188420i
$690$		0			0
$691$	−10.6221	+	32.6914i	−0.404084	+	1.24364i	0.517574	+	0.855638i	$0.326835\pi$
$691$	−10.6221	+	32.6914i	−0.404084	+	1.24364i	−0.921658	+	0.388003i	$0.873165\pi$
$692$	23.7160	−	3.75624i	0.901547	−	0.142791i
$693$	12.7121	+	10.9682i	0.482892	+	0.416646i
$694$	6.99576	−	9.62884i	0.265555	−	0.365506i
$695$		0			0
$696$	7.46258	+	9.51535i	0.282868	+	0.360678i
$697$	15.3142	+	2.42553i	0.580067	+	0.0918736i
$698$	11.5641	−	22.6958i	0.437707	−	0.859048i
$699$	−0.557896	−	15.1717i	−0.0211016	−	0.573845i
$700$		0			0
$701$		−	14.8859i		−	0.562232i	−0.959674	−	0.281116i	$-0.909295\pi$
$701$		−	14.8859i		−	0.562232i	0.959674	−	0.281116i	$-0.0907045\pi$
$702$	9.23636	−	24.4663i	0.348604	−	0.923423i
$703$	−2.60428	+	16.4428i	−0.0982222	+	0.620150i
$704$	1.23956	−	0.900593i	0.0467177	−	0.0339424i
$705$		0			0
$706$	−7.12475	−	5.17643i	−0.268143	−	0.194818i
$707$	0.378543	−	0.378543i	0.0142366	−	0.0142366i
$708$	−11.5942	+	2.27594i	−0.435736	+	0.0855351i
$709$	38.5502	+	12.5257i	1.44778	+	0.470413i	0.924314	−	0.381632i	$-0.124638\pi$
$709$	38.5502	+	12.5257i	1.44778	+	0.470413i	0.523468	+	0.852045i	$0.324638\pi$
$710$		0			0
$711$	−1.50921	−	3.69601i	−0.0565998	−	0.138611i
$712$	−5.73613	+	2.92270i	−0.214970	+	0.109533i
$713$	41.7019	−	21.2482i	1.56175	−	0.795750i
$714$	−11.2159	−	30.6391i	−0.419745	−	1.14664i
$715$		0			0
$716$	4.28798	+	1.39325i	0.160249	+	0.0520681i
$717$	−6.32040	−	32.1976i	−0.236040	−	1.20244i
$718$	4.85077	−	4.85077i	0.181029	−	0.181029i
$719$	−17.9319	−	13.0283i	−0.668748	−	0.485874i	0.200858	−	0.979620i	$-0.435627\pi$
$719$	−17.9319	−	13.0283i	−0.668748	−	0.485874i	−0.869606	+	0.493746i	$0.835627\pi$
$720$		0			0
$721$	46.1690	−	33.5437i	1.71942	−	1.24923i
$722$	−2.23676	+	14.1224i	−0.0832437	+	0.525580i
$723$	17.1401	−	36.9353i	0.637449	−	1.37364i
$724$		−	14.1413i		−	0.525556i
$725$		0			0
$726$	14.9763	−	0.550713i	0.555823	−	0.0204389i
$727$	8.45889	−	16.6015i	0.313723	−	0.615716i	−0.679270	−	0.733888i	$-0.737704\pi$
$727$	8.45889	−	16.6015i	0.313723	−	0.615716i	0.992993	+	0.118172i	$0.0377036\pi$
$728$	18.1574	+	2.87585i	0.672957	+	0.106586i
$729$	20.2641	+	17.8428i	0.750523	+	0.660844i
$730$		0			0
$731$	13.9192	−	19.1581i	0.514819	−	0.708588i
$732$	6.80584	−	7.32548i	0.251551	−	0.270758i
$733$	−2.14436	+	0.339633i	−0.0792038	+	0.0125446i	−0.195911	−	0.980622i	$-0.562766\pi$
$733$	−2.14436	+	0.339633i	−0.0792038	+	0.0125446i	0.116707	+	0.993166i	$0.462766\pi$
$734$	−4.58254	+	14.1036i	−0.169145	+	0.520574i
$735$		0			0
$736$	−1.96550	−	6.04917i	−0.0724491	−	0.222975i
$737$	−2.34541	−	4.60312i	−0.0863942	−	0.169558i
$738$	−4.67401	−	7.71409i	−0.172053	−	0.283960i
$739$	25.4696	−	8.27559i	0.936916	−	0.304423i	0.199528	−	0.979892i	$-0.436059\pi$
$739$	25.4696	−	8.27559i	0.936916	−	0.304423i	0.737388	+	0.675470i	$0.236059\pi$
$740$		0			0
$741$	18.1791	+	5.17642i	0.667827	+	0.190161i
$742$	0.590418	+	3.72775i	0.0216749	+	0.136850i
$743$	−30.8466	−	30.8466i	−1.13165	−	1.13165i	−0.989903	−	0.141749i	$-0.954727\pi$
$743$	−30.8466	−	30.8466i	−1.13165	−	1.13165i	−0.141749	−	0.989903i	$-0.545273\pi$
$744$	−7.10746	+	10.5794i	−0.260572	+	0.387859i
$745$		0			0
$746$	10.1684	+	13.9956i	0.372293	+	0.512417i
$747$	0.693051	−	8.27393i	0.0253574	−	0.302727i
$748$	7.04042	+	3.58727i	0.257423	+	0.131164i
$749$	−9.15060			−0.334356
$750$		0			0
$751$	48.1007			1.75522			0.877610	−	0.479376i	$-0.159137\pi$
$751$	48.1007			1.75522			0.877610	+	0.479376i	$0.159137\pi$
$752$	−2.54140	−	1.29491i	−0.0926753	−	0.0472204i
$753$	2.83765	−	23.4695i	0.103410	−	0.855275i
$754$	−20.6537	−	28.4274i	−0.752163	−	1.03526i
$755$		0			0
$756$	−9.39868	+	16.4896i	−0.341827	+	0.599720i
$757$	−2.64953	−	2.64953i	−0.0962989	−	0.0962989i	0.657316	−	0.753615i	$-0.271692\pi$
$757$	−2.64953	−	2.64953i	−0.0962989	−	0.0962989i	−0.753615	+	0.657316i	$0.771692\pi$
$758$	−0.889598	−	5.61670i	−0.0323117	−	0.204008i
$759$	−4.62262	+	16.2342i	−0.167790	+	0.589265i
$760$		0			0
$761$	37.7032	−	12.2505i	1.36674	−	0.444080i	0.468452	−	0.883489i	$-0.344812\pi$
$761$	37.7032	−	12.2505i	1.36674	−	0.444080i	0.898287	+	0.439409i	$0.144812\pi$
$762$	−27.9629	+	15.5678i	−1.01299	+	0.563960i
$763$	−13.3553	−	26.2112i	−0.483493	−	0.948909i
$764$	−3.96247	−	12.1952i	−0.143357	−	0.441208i
$765$		0			0
$766$	−9.38083	+	28.8712i	−0.338943	+	1.04316i
$767$	33.9101	−	5.37083i	1.22442	−	0.193929i
$768$	1.26892	+	1.17891i	0.0457883	+	0.0425403i
$769$	−13.8631	+	19.0810i	−0.499918	+	0.688078i	−0.982179	−	0.187950i	$-0.939816\pi$
$769$	−13.8631	+	19.0810i	−0.499918	+	0.688078i	0.482261	+	0.876028i	$0.339816\pi$
$770$		0			0
$771$	27.5178	−	21.5814i	0.991031	−	0.777233i
$772$	13.8267	+	2.18993i	0.497632	+	0.0788172i
$773$	−18.8877	+	37.0692i	−0.679344	+	1.33329i	0.251495	+	0.967859i	$0.419078\pi$
$773$	−18.8877	+	37.0692i	−0.679344	+	1.33329i	−0.930839	+	0.365429i	$0.880922\pi$
$774$	−13.7383	+	1.01175i	−0.493814	+	0.0363665i
$775$		0			0
$776$		−	13.6841i		−	0.491231i
$777$	44.0612	+	20.4470i	1.58069	+	0.733531i
$778$	−0.206293	+	1.30248i	−0.00739595	+	0.0466962i
$779$	5.27409	−	3.83185i	0.188964	−	0.137290i
$780$		0			0
$781$	−4.59923	−	3.34153i	−0.164573	−	0.119570i
$782$	23.1943	−	23.1943i	0.829428	−	0.829428i
$783$	34.9892	−	9.58366i	1.25041	−	0.342492i
$784$	−6.03185	−	1.95987i	−0.215423	−	0.0699952i
$785$		0			0
$786$	−21.5759	+	7.89818i	−0.769585	+	0.281719i
$787$	−4.03430	+	2.05558i	−0.143807	+	0.0732734i	−0.524413	−	0.851464i	$-0.675715\pi$
$787$	−4.03430	+	2.05558i	−0.143807	+	0.0732734i	0.380606	+	0.924737i	$0.375715\pi$
$788$	6.06547	−	3.09051i	0.216074	−	0.110095i
$789$	26.5022	−	9.70155i	0.943503	−	0.345384i
$790$		0			0
$791$	−37.6892	−	12.2460i	−1.34007	−	0.435416i
$792$	−1.05055	−	4.47488i	−0.0373298	−	0.159008i
$793$	−20.5449	+	20.5449i	−0.729571	+	0.729571i
$794$	−8.98015	−	6.52446i	−0.318693	−	0.231544i
$795$		0			0
$796$	4.37266	−	3.17692i	0.154985	−	0.112603i
$797$	−2.04964	+	12.9409i	−0.0726021	+	0.458392i	0.924427	+	0.381360i	$0.124544\pi$
$797$	−2.04964	+	12.9409i	−0.0726021	+	0.458392i	−0.997029	+	0.0770316i	$0.975456\pi$
$798$	−12.4436	−	5.77457i	−0.440500	−	0.204418i
$799$		−	14.7096i		−	0.520387i
$800$		0			0
$801$	1.41848	+	19.2613i	0.0501195	+	0.680563i
$802$	−17.4574	+	34.2621i	−0.616443	+	1.20984i
$803$	−0.902532	−	0.142947i	−0.0318496	−	0.00504449i
$804$	4.59543	−	3.60405i	0.162068	−	0.127105i
$805$		0			0
$806$	21.7682	−	29.9613i	0.766752	−	1.05534i
$807$	13.8626	+	12.8792i	0.487985	+	0.453370i
$808$	−0.144756	+	0.0229270i	−0.00509248	+	0.000806570i
$809$	−10.9215	+	33.6130i	−0.383980	+	1.18177i	0.553237	+	0.833024i	$0.313392\pi$
$809$	−10.9215	+	33.6130i	−0.383980	+	1.18177i	−0.937217	+	0.348746i	$0.886608\pi$
$810$		0			0
$811$	0.0429712	+	0.132252i	0.00150892	+	0.00464399i	0.951808	−	0.306694i	$-0.0992228\pi$
$811$	0.0429712	+	0.132252i	0.00150892	+	0.00464399i	−0.950299	+	0.311338i	$0.899223\pi$
$812$	11.5777	+	22.7225i	0.406297	+	0.797403i
$813$	5.08143	−	2.82898i	0.178213	−	0.0992166i
$814$	−11.1879	+	3.63517i	−0.392135	+	0.127413i
$815$		0			0
$816$	−2.44622	+	8.59091i	−0.0856349	+	0.300742i
$817$	−1.55755	−	9.83400i	−0.0544918	−	0.344048i
$818$	8.03693	+	8.03693i	0.281005	+	0.281005i
$819$	29.0525	−	46.8786i	1.01518	−	1.63807i
$820$		0			0
$821$	−1.62196	−	2.23243i	−0.0566067	−	0.0779125i	0.779775	−	0.626060i	$-0.215333\pi$
$821$	−1.62196	−	2.23243i	−0.0566067	−	0.0779125i	−0.836382	+	0.548147i	$0.815333\pi$
$822$	2.02932	−	16.7840i	0.0707808	−	0.585411i
$823$	18.0680	+	9.20610i	0.629811	+	0.320905i	0.739596	−	0.673051i	$-0.235016\pi$
$823$	18.0680	+	9.20610i	0.629811	+	0.320905i	−0.109786	+	0.993955i	$0.535016\pi$
$824$	−15.6235			−0.544270
$825$		0			0
$826$	−24.9175			−0.866992
$827$	−2.96720	−	1.51186i	−0.103180	−	0.0525726i	0.401639	−	0.915798i	$-0.368441\pi$
$827$	−2.96720	−	1.51186i	−0.103180	−	0.0525726i	−0.504819	+	0.863225i	$0.668441\pi$
$828$	−19.0148	−	1.59274i	−0.660811	−	0.0553517i
$829$	−17.4925	−	24.0763i	−0.607539	−	0.836206i	0.388833	−	0.921308i	$-0.372878\pi$
$829$	−17.4925	−	24.0763i	−0.607539	−	0.836206i	−0.996372	+	0.0851024i	$0.972878\pi$
$830$		0			0
$831$	27.1108	−	40.3541i	0.940462	−	1.39987i
$832$	−3.55880	−	3.55880i	−0.123379	−	0.123379i
$833$	−5.11663	−	32.3051i	−0.177281	−	1.11931i
$834$	8.09187	+	2.30412i	0.280198	+	0.0797852i
$835$		0			0
$836$	3.15965	−	1.02663i	0.109279	−	0.0355068i
$837$	21.0021	+	31.9510i	0.725940	+	1.10439i
$838$	2.28220	+	4.47907i	0.0788374	+	0.154727i
$839$	5.16619	+	15.8999i	0.178357	+	0.548926i	0.999771	−	0.0214067i	$-0.00681447\pi$
$839$	5.16619	+	15.8999i	0.178357	+	0.548926i	−0.821414	+	0.570332i	$0.806814\pi$
$840$		0			0
$841$	6.10123	−	18.7776i	0.210387	−	0.647505i
$842$	−8.99583	+	1.42480i	−0.310017	+	0.0491018i
$843$	0.837518	−	0.901465i	0.0288457	−	0.0310481i
$844$	−7.52218	+	10.3534i	−0.258924	+	0.356379i
$845$		0			0
$846$	−6.53453	+	5.52443i	−0.224662	+	0.189934i
$847$	31.2156	+	4.94407i	1.07258	+	0.169880i
$848$	0.469093	−	0.920647i	0.0161087	−	0.0316152i
$849$	15.9530	−	0.586627i	0.547504	−	0.0201330i
$850$		0			0
$851$			48.8339i			1.67400i
$852$	2.70520	−	5.82944i	0.0926787	−	0.199713i
$853$	0.447638	−	2.82627i	0.0153268	−	0.0967698i	−0.978839	−	0.204632i	$-0.934400\pi$
$853$	0.447638	−	2.82627i	0.0153268	−	0.0967698i	0.994166	+	0.107862i	$0.0344004\pi$
$854$	17.0598	−	12.3946i	0.583773	−	0.424136i
$855$		0			0
$856$	2.02672	+	1.47249i	0.0692717	+	0.0503288i
$857$	−8.27926	+	8.27926i	−0.282814	+	0.282814i	−0.834230	−	0.551416i	$-0.814088\pi$
$857$	−8.27926	+	8.27926i	−0.282814	+	0.282814i	0.551416	+	0.834230i	$0.314088\pi$
$858$	2.57276	+	13.1063i	0.0878325	+	0.447440i
$859$	21.3255	+	6.92908i	0.727617	+	0.236417i	0.649323	−	0.760513i	$-0.275053\pi$
$859$	21.3255	+	6.92908i	0.727617	+	0.236417i	0.0782946	+	0.996930i	$0.475053\pi$
$860$		0			0
$861$	−6.53874	−	17.8622i	−0.222840	−	0.608742i
$862$	−22.0551	+	11.2377i	−0.751201	+	0.382756i
$863$	−16.3658	+	8.33881i	−0.557100	+	0.283857i	−0.709785	−	0.704418i	$-0.751208\pi$
$863$	−16.3658	+	8.33881i	−0.557100	+	0.283857i	0.152685	+	0.988275i	$0.451208\pi$
$864$	4.73512	−	2.13977i	0.161092	−	0.0727963i
$865$		0			0
$866$	−21.0928	−	6.85347i	−0.716763	−	0.232890i
$867$	−16.3094	+	3.20153i	−0.553895	+	0.108730i
$868$	−19.0057	+	19.0057i	−0.645097	+	0.645097i
$869$	1.64955	+	1.19847i	0.0559572	+	0.0406553i
$870$		0			0
$871$	−13.7290	+	9.97468i	−0.465188	+	0.337979i
$872$	−1.25986	+	7.95446i	−0.0426644	+	0.269372i
$873$	−37.8479	−	15.9006i	−1.28096	−	0.538152i
$874$		−	13.7915i		−	0.466505i
$875$		0			0
$876$	−0.0379595	−	1.03228i	−0.00128253	−	0.0348777i
$877$	17.7609	−	34.8578i	0.599744	−	1.17706i	−0.369100	−	0.929390i	$-0.620334\pi$
$877$	17.7609	−	34.8578i	0.599744	−	1.17706i	0.968844	−	0.247673i	$-0.0796660\pi$
$878$	1.68299	+	0.266559i	0.0567981	+	0.00899594i
$879$	−2.98913	−	3.81137i	−0.100821	−	0.128554i
$880$		0			0
$881$	0.436643	−	0.600988i	0.0147109	−	0.0202478i	−0.801598	−	0.597863i	$-0.796017\pi$
$881$	0.436643	−	0.600988i	0.0147109	−	0.0202478i	0.816309	+	0.577615i	$0.196017\pi$
$882$	−12.4295	+	14.4058i	−0.418523	+	0.485067i
$883$	29.2220	−	4.62830i	0.983397	−	0.155755i	0.356027	−	0.934476i	$-0.384131\pi$
$883$	29.2220	−	4.62830i	0.983397	−	0.155755i	0.627371	+	0.778721i	$0.284131\pi$
$884$	8.02063	−	24.6849i	0.269763	−	0.830245i
$885$		0			0
$886$	−0.311629	−	0.959097i	−0.0104694	−	0.0322215i
$887$	−26.7037	−	52.4089i	−0.896621	−	1.75972i	−0.588813	−	0.808270i	$-0.700404\pi$
$887$	−26.7037	−	52.4089i	−0.896621	−	1.75972i	−0.307809	−	0.951448i	$-0.599596\pi$
$888$	−6.46859	−	11.6189i	−0.217072	−	0.389905i
$889$	−64.1903	+	20.8567i	−2.15287	+	0.699511i
$890$		0			0
$891$	−13.5975	−	2.29403i	−0.455532	−	0.0768530i
$892$	−4.54190	−	28.6765i	−0.152074	−	0.960159i
$893$	−4.37321	−	4.37321i	−0.146344	−	0.146344i
$894$	9.42698	+	6.33325i	0.315285	+	0.211815i
$895$		0			0
$896$	2.14701	+	2.95510i	0.0717265	+	0.0987230i
$897$	55.0449	+	6.65537i	1.83790	+	0.222216i
$898$	−11.0761	−	5.64357i	−0.369616	−	0.188329i
$899$	51.3743			1.71343
$900$		0			0
$901$	5.32868			0.177524
$902$	4.10448	+	2.09134i	0.136664	+	0.0696339i
$903$	−28.8411	−	3.48711i	−0.959770	−	0.116044i
$904$	6.37698	+	8.77715i	0.212095	+	0.291924i
$905$		0			0
$906$	−1.53288	−	1.02982i	−0.0509264	−	0.0342134i
$907$	8.72011	+	8.72011i	0.289547	+	0.289547i	0.836901	−	0.547354i	$-0.184365\pi$
$907$	8.72011	+	8.72011i	0.289547	+	0.289547i	−0.547354	+	0.836901i	$0.684365\pi$
$908$	−0.618172	−	3.90298i	−0.0205148	−	0.129525i
$909$	−0.104790	+	0.427010i	−0.00347565	+	0.0141630i
$910$		0			0
$911$	−35.6554	+	11.5852i	−1.18132	+	0.383833i	−0.832856	−	0.553490i	$-0.813296\pi$
$911$	−35.6554	+	11.5852i	−1.18132	+	0.383833i	−0.348461	+	0.937323i	$0.613296\pi$
$912$	1.82684	+	3.28138i	0.0604927	+	0.108657i
$913$	1.92515	+	3.77833i	0.0637133	+	0.125044i
$914$	11.1290	+	34.2516i	0.368116	+	1.13294i
$915$		0			0
$916$	−4.07958	+	12.5556i	−0.134793	+	0.414850i
$917$	−47.8574	+	7.57987i	−1.58039	+	0.250309i
$918$	20.9186	+	16.7482i	0.690416	+	0.552774i
$919$	−17.9736	+	24.7386i	−0.592896	+	0.816051i	−0.995035	−	0.0995274i	$-0.968267\pi$
$919$	−17.9736	+	24.7386i	−0.592896	+	0.816051i	0.402139	+	0.915579i	$0.368267\pi$
$920$		0			0
$921$	−17.7633	−	22.6495i	−0.585320	−	0.746327i
$922$	36.1413	+	5.72422i	1.19025	+	0.188517i
$923$	−8.47779	+	16.6386i	−0.279050	+	0.547666i
$924$	−0.356215	−	9.68706i	−0.0117186	−	0.318681i
$925$		0			0
$926$		−	6.61685i		−	0.217443i
$927$	−18.1541	+	43.2119i	−0.596257	+	1.41926i
$928$	1.09218	−	6.89573i	0.0358525	−	0.226364i
$929$	−0.652608	+	0.474147i	−0.0214114	+	0.0155563i	−0.598439	−	0.801168i	$-0.704212\pi$
$929$	−0.652608	+	0.474147i	−0.0214114	+	0.0155563i	0.577028	+	0.816724i	$0.304212\pi$
$930$		0			0
$931$	−11.1256	−	8.08324i	−0.364628	−	0.264918i
$932$	−6.19799	+	6.19799i	−0.203022	+	0.203022i
$933$	−5.90342	+	1.15884i	−0.193269	+	0.0379387i
$934$	−36.3043	−	11.7960i	−1.18791	−	0.385976i
$935$		0			0
$936$	−13.9783	+	5.70781i	−0.456894	+	0.186566i
$937$	−7.61042	+	3.87770i	−0.248622	+	0.126679i	−0.573861	−	0.818953i	$-0.694555\pi$
$937$	−7.61042	+	3.87770i	−0.248622	+	0.126679i	0.325240	+	0.945632i	$0.394555\pi$
$938$	10.9738	−	5.59143i	0.358308	−	0.182567i
$939$	5.05449	+	13.8076i	0.164947	+	0.450594i
$940$		0			0
$941$	17.4242	+	5.66148i	0.568014	+	0.184559i	0.578924	−	0.815382i	$-0.303473\pi$
$941$	17.4242	+	5.66148i	0.568014	+	0.184559i	−0.0109101	+	0.999940i	$0.503473\pi$
$942$	7.23511	+	36.8574i	0.235733	+	1.20088i
$943$	13.5220	−	13.5220i	0.440338	−	0.440338i
$944$	5.51884	+	4.00967i	0.179623	+	0.130504i
$945$		0			0
$946$	5.69187	−	4.13539i	0.185059	−	0.134453i
$947$	5.62455	−	35.5120i	0.182773	−	1.15398i	−0.710242	−	0.703958i	$-0.751414\pi$
$947$	5.62455	−	35.5120i	0.182773	−	1.15398i	0.893015	−	0.450027i	$-0.148586\pi$
$948$	−0.970244	+	2.09078i	−0.0315121	+	0.0679054i
$949$			3.00159i			0.0974356i
$950$		0			0
$951$	−17.0673	+	0.627603i	−0.553444	+	0.0203514i
$952$	−8.55203	+	16.7843i	−0.277173	+	0.543982i
$953$	12.2669	+	1.94289i	0.397365	+	0.0629365i	0.351919	−	0.936030i	$-0.385529\pi$
$953$	12.2669	+	1.94289i	0.397365	+	0.0629365i	0.0454459	+	0.998967i	$0.485529\pi$
$954$	−2.00128	−	2.36720i	−0.0647939	−	0.0766409i
$955$		0			0
$956$	−11.1351	+	15.3261i	−0.360133	+	0.495681i
$957$	−12.6111	+	13.5739i	−0.407658	+	0.438783i
$958$	11.4985	−	1.82118i	0.371500	−	0.0588397i
$959$	11.0175	−	33.9085i	0.355775	−	1.09496i
$960$		0			0
$961$	7.15266	+	22.0136i	0.230731	+	0.710117i
$962$	17.5427	+	34.4295i	0.565600	+	1.11005i
$963$	6.42766	−	3.89455i	0.207128	−	0.125500i
$964$	−22.3583	+	7.26464i	−0.720111	+	0.233978i
$965$		0			0
$966$	−38.7022	−	11.0203i	−1.24522	−	0.354572i
$967$	−0.835271	−	5.27370i	−0.0268605	−	0.169591i	0.970611	−	0.240652i	$-0.0773613\pi$
$967$	−0.835271	−	5.27370i	−0.0268605	−	0.169591i	−0.997472	+	0.0710616i	$0.977361\pi$
$968$	−6.11819	−	6.11819i	−0.196646	−	0.196646i
$969$	−10.8009	+	16.0770i	−0.346975	+	0.516469i
$970$		0			0
$971$	33.9216	+	46.6890i	1.08859	+	1.49832i	0.849693	+	0.527278i	$0.176788\pi$
$971$	33.9216	+	46.6890i	1.08859	+	1.49832i	0.238902	+	0.971044i	$0.423212\pi$
$972$	−0.416147	−	15.5829i	−0.0133479	−	0.499822i
$973$	15.8093	+	8.05524i	0.506823	+	0.258239i
$974$	−35.5211			−1.13817
$975$		0			0
$976$	−5.77299			−0.184789
$977$	−9.19137	−	4.68324i	−0.294058	−	0.149830i	0.300738	−	0.953707i	$-0.402767\pi$
$977$	−9.19137	−	4.68324i	−0.294058	−	0.149830i	−0.594796	+	0.803877i	$0.702767\pi$
$978$	2.13762	−	17.6797i	0.0683534	−	0.565334i
$979$	−5.79785	−	7.98005i	−0.185300	−	0.255043i
$980$		0			0
$981$	20.5368	+	12.7274i	0.655689	+	0.406356i
$982$	2.36943	+	2.36943i	0.0756116	+	0.0756116i
$983$	6.30178	+	39.7879i	0.200996	+	1.26904i	0.857409	+	0.514635i	$0.172073\pi$
$983$	6.30178	+	39.7879i	0.200996	+	1.26904i	−0.656413	+	0.754401i	$0.727927\pi$
$984$	−1.42612	+	5.00840i	−0.0454630	+	0.159662i
$985$		0			0
$986$	34.2432	−	11.1263i	1.09053	−	0.354333i
$987$	−15.7667	+	8.77777i	−0.501859	+	0.279400i
$988$	−4.95436	−	9.72349i	−0.157619	−	0.309345i
$989$	−9.02525	−	27.7769i	−0.286986	−	0.883253i
$990$		0			0
$991$	−7.61373	+	23.4326i	−0.241858	+	0.744362i	0.754279	+	0.656554i	$0.227986\pi$
$991$	−7.61373	+	23.4326i	−0.241858	+	0.744362i	−0.996137	+	0.0878088i	$0.972014\pi$
$992$	7.26784	−	1.15111i	0.230754	−	0.0365478i
$993$	21.0005	+	19.5108i	0.666432	+	0.619158i
$994$	7.96619	−	10.9645i	0.252672	−	0.347773i
$995$		0			0
$996$	−3.77201	+	2.95827i	−0.119521	+	0.0937362i
$997$	−36.6391	−	5.80306i	−1.16037	−	0.183785i	−0.453585	−	0.891213i	$-0.649855\pi$
$997$	−36.6391	−	5.80306i	−1.16037	−	0.183785i	−0.706785	+	0.707428i	$0.749855\pi$
$998$	−1.16399	+	2.28445i	−0.0368454	+	0.0723131i
$999$	−39.6523	+	4.39015i	−1.25454	+	0.138898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.107.6		80
3.2	odd	2	inner	750.2.l.b.107.5		80
5.2	odd	4		750.2.l.c.143.3		80
5.3	odd	4		750.2.l.a.143.8		80
5.4	even	2		150.2.l.a.17.5	✓	80
15.2	even	4		750.2.l.c.143.9		80
15.8	even	4		750.2.l.a.143.2		80
15.14	odd	2		150.2.l.a.17.6	yes	80
25.3	odd	20	inner	750.2.l.b.743.5		80
25.4	even	10		750.2.l.c.257.9		80
25.21	even	5		750.2.l.a.257.2		80
25.22	odd	20		150.2.l.a.53.6	yes	80
75.29	odd	10		750.2.l.c.257.3		80
75.47	even	20		150.2.l.a.53.5	yes	80
75.53	even	20	inner	750.2.l.b.743.6		80
75.71	odd	10		750.2.l.a.257.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.5	✓	80	5.4	even	2
150.2.l.a.17.6	yes	80	15.14	odd	2
150.2.l.a.53.5	yes	80	75.47	even	20
150.2.l.a.53.6	yes	80	25.22	odd	20
750.2.l.a.143.2		80	15.8	even	4
750.2.l.a.143.8		80	5.3	odd	4
750.2.l.a.257.2		80	25.21	even	5
750.2.l.a.257.8		80	75.71	odd	10
750.2.l.b.107.5		80	3.2	odd	2	inner
750.2.l.b.107.6		80	1.1	even	1	trivial
750.2.l.b.743.5		80	25.3	odd	20	inner
750.2.l.b.743.6		80	75.53	even	20	inner
750.2.l.c.143.3		80	5.2	odd	4
750.2.l.c.143.9		80	15.2	even	4
750.2.l.c.257.3		80	75.29	odd	10
750.2.l.c.257.9		80	25.4	even	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(-1.71953 - 0.207905i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(-2.58285 - 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.91355 + 0.714995i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(-1.71953 - 0.207905i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(-2.58285 - 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.91355 + 0.714995i) q^{9} +(-1.45719 + 0.473470i) q^{11} +(-0.842515 - 1.51333i) q^{12} +(2.28489 + 4.48435i) q^{13} +(-1.12875 - 3.47393i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.09363 + 0.806752i) q^{17} +(2.27139 + 1.95979i) q^{18} +(-1.27450 + 1.75421i) q^{19} +(3.90430 + 4.97827i) q^{21} +(-1.51332 - 0.239686i) q^{22} +(-2.88760 + 5.66723i) q^{23} +(-0.0636485 - 1.73088i) q^{24} +5.03290i q^{26} +(-4.86128 - 1.83520i) q^{27} +(0.571409 - 3.60774i) q^{28} +(-5.64831 + 4.10373i) q^{29} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.60412 - 0.511188i) q^{33} +(-4.90472 - 1.59364i) q^{34} +(1.13410 + 2.77738i) q^{36} +(6.84089 - 3.48561i) q^{37} +(-1.93198 + 0.984395i) q^{38} +(-2.99661 - 8.18600i) q^{39} +(-2.85939 - 0.929072i) q^{41} +(1.21867 + 6.20819i) q^{42} +(-3.24693 + 3.24693i) q^{43} +(-1.23956 - 0.900593i) q^{44} +(-5.14573 + 3.73859i) q^{46} +(-0.446195 + 2.81716i) q^{47} +(0.729092 - 1.57112i) q^{48} +6.34226i q^{49} +(8.92637 - 0.328243i) q^{51} +(-2.28489 + 4.48435i) q^{52} +(-1.02055 - 0.161639i) q^{53} +(-3.49827 - 3.84215i) q^{54} +(2.14701 - 2.95510i) q^{56} +(2.55625 - 2.75143i) q^{57} +(-6.89573 + 1.09218i) q^{58} +(2.10801 - 6.48779i) q^{59} +(1.78395 + 5.49044i) q^{61} +(-3.34066 - 6.55641i) q^{62} +(-5.67855 - 9.37200i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(2.55236 + 0.726772i) q^{66} +(0.527466 + 3.33029i) q^{67} +(-3.64664 - 3.64664i) q^{68} +(6.14354 - 9.14461i) q^{69} +(2.18090 + 3.00175i) q^{71} +(-0.250413 + 2.98953i) q^{72} +(0.531390 + 0.270757i) q^{73} +7.67771 q^{74} -2.16832 q^{76} +(4.98661 + 2.54081i) q^{77} +(1.04636 - 8.65421i) q^{78} +(-0.782199 - 1.07660i) q^{79} +(7.97756 + 4.16635i) q^{81} +(-2.12595 - 2.12595i) q^{82} +(-0.432953 - 2.73356i) q^{83} +(-1.73262 + 6.08480i) q^{84} +(-4.36710 + 1.41896i) q^{86} +(10.5656 - 5.88218i) q^{87} +(-0.695596 - 1.36518i) q^{88} +(1.98939 + 6.12272i) q^{89} +(5.68088 - 17.4839i) q^{91} +(-6.28217 + 0.994998i) q^{92} +(9.33729 + 8.67494i) q^{93} +(-1.67653 + 2.30754i) q^{94} +(1.36290 - 1.06888i) q^{96} +(-13.5156 - 2.14067i) q^{97} +(-2.87933 + 5.65100i) q^{98} +(-4.58413 + 0.337594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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