LMFDB - Embedded newform 150.2.l.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, 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("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	150.17
Dual form			150.2.l.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(-1.69961 - 0.333634i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.62298 - 1.53816i) q^{5} +(-1.36290 - 1.06888i) q^{6} +(2.58285 + 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.77738 + 1.13410i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(-1.69961 - 0.333634i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.62298 - 1.53816i) q^{5} +(-1.36290 - 1.06888i) q^{6} +(2.58285 + 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.77738 + 1.13410i) q^{9} +(2.14440 - 0.633691i) q^{10} +(1.45719 - 0.473470i) q^{11} +(-0.729092 - 1.57112i) q^{12} +(-2.28489 - 4.48435i) q^{13} +(1.12875 + 3.47393i) q^{14} +(-3.27162 + 2.07279i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-5.09363 + 0.806752i) q^{17} +(1.95979 + 2.27139i) q^{18} +(-1.27450 + 1.75421i) q^{19} +(2.19836 + 0.408913i) q^{20} +(-3.52813 - 5.25158i) q^{21} +(1.51332 + 0.239686i) q^{22} +(-2.88760 + 5.66723i) q^{23} +(0.0636485 - 1.73088i) q^{24} +(0.268140 - 4.99280i) q^{25} -5.03290i q^{26} +(-4.34209 - 2.85416i) q^{27} +(-0.571409 + 3.60774i) q^{28} +(5.64831 - 4.10373i) q^{29} +(-3.85607 + 0.361585i) q^{30} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.63463 + 0.318547i) q^{33} +(-4.90472 - 1.59364i) q^{34} +(8.16476 + 0.219087i) q^{35} +(0.714995 + 2.91355i) q^{36} +(-6.84089 + 3.48561i) q^{37} +(-1.93198 + 0.984395i) q^{38} +(2.38730 + 8.38398i) q^{39} +(1.77311 + 1.36238i) q^{40} +(2.85939 + 0.929072i) q^{41} +(-0.759414 - 6.28093i) q^{42} +(3.24693 - 3.24693i) q^{43} +(1.23956 + 0.900593i) q^{44} +(6.25205 - 2.43142i) q^{45} +(-5.14573 + 3.73859i) q^{46} +(-0.446195 + 2.81716i) q^{47} +(0.842515 - 1.51333i) q^{48} +6.34226i q^{49} +(2.50560 - 4.32689i) q^{50} +(8.92637 + 0.328243i) q^{51} +(2.28489 - 4.48435i) q^{52} +(-1.02055 - 0.161639i) q^{53} +(-2.57307 - 4.51434i) q^{54} +(1.63672 - 3.00982i) q^{55} +(-2.14701 + 2.95510i) q^{56} +(2.75143 - 2.55625i) q^{57} +(6.89573 - 1.09218i) q^{58} +(-2.10801 + 6.48779i) q^{59} +(-3.59994 - 1.42844i) q^{60} +(1.78395 + 5.49044i) q^{61} +(-3.34066 - 6.55641i) q^{62} +(4.24434 + 10.1028i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-10.6060 - 3.76349i) q^{65} +(-2.49209 - 0.912268i) q^{66} +(-0.527466 - 3.33029i) q^{67} +(-3.64664 - 3.64664i) q^{68} +(6.79858 - 8.66870i) q^{69} +(7.17539 + 3.90193i) q^{70} +(-2.18090 - 3.00175i) q^{71} +(-0.685659 + 2.92059i) q^{72} +(-0.531390 - 0.270757i) q^{73} -7.67771 q^{74} +(-2.12150 + 8.39638i) q^{75} -2.16832 q^{76} +(4.98661 + 2.54081i) q^{77} +(-1.67915 + 8.55399i) q^{78} +(-0.782199 - 1.07660i) q^{79} +(0.961346 + 2.01886i) q^{80} +(6.42764 + 6.29964i) q^{81} +(2.12595 + 2.12595i) q^{82} +(-0.432953 - 2.73356i) q^{83} +(2.17484 - 5.94112i) q^{84} +(-7.02596 + 9.14415i) q^{85} +(4.36710 - 1.41896i) q^{86} +(-10.9691 + 5.09030i) q^{87} +(0.695596 + 1.36518i) q^{88} +(-1.98939 - 6.12272i) q^{89} +(6.67446 + 0.671961i) q^{90} +(5.68088 - 17.4839i) q^{91} +(-6.28217 + 0.994998i) q^{92} +(8.67494 + 9.33729i) q^{93} +(-1.67653 + 2.30754i) q^{94} +(0.629747 + 4.80743i) q^{95} +(1.43772 - 0.965894i) 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^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	−1.69961	−	0.333634i	−0.981273	−	0.192624i
$3$	−1.69961	−	0.333634i	−0.981273	−	0.192624i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	1.62298	−	1.53816i	0.725820	−	0.687885i
$5$	1.62298	−	1.53816i	0.725820	−	0.687885i
$6$	−1.36290	−	1.06888i	−0.556402	−	0.436368i
$7$	2.58285	+	2.58285i	0.976227	+	0.976227i	0.999724	−	0.0234972i	$-0.00748007\pi$
$7$	2.58285	+	2.58285i	0.976227	+	0.976227i	−0.0234972	+	0.999724i	$0.507480\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	2.77738	+	1.13410i	0.925792	+	0.378033i
$10$	2.14440	−	0.633691i	0.678118	−	0.200391i
$11$	1.45719	−	0.473470i	0.439360	−	0.142757i	−0.0809806	−	0.996716i	$-0.525805\pi$
$11$	1.45719	−	0.473470i	0.439360	−	0.142757i	0.520340	+	0.853959i	$0.325805\pi$
$12$	−0.729092	−	1.57112i	−0.210471	−	0.453544i
$13$	−2.28489	−	4.48435i	−0.633714	−	1.24373i	−0.954959	−	0.296738i	$-0.904101\pi$
$13$	−2.28489	−	4.48435i	−0.633714	−	1.24373i	0.321245	−	0.946996i	$-0.395899\pi$
$14$	1.12875	+	3.47393i	0.301671	+	0.928447i
$15$	−3.27162	+	2.07279i	−0.844730	+	0.535193i
$16$	−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	$0.665061\pi$
$18$	1.95979	+	2.27139i	0.461927	+	0.535372i
$19$	−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	$0.280011\pi$
$20$	2.19836	+	0.408913i	0.491568	+	0.0914358i
$21$	−3.52813	−	5.25158i	−0.769900	−	1.14599i
$22$	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
$25$	0.268140	−	4.99280i	0.0536279	−	0.998561i
$26$		−	5.03290i		−	0.987033i
$27$	−4.34209	−	2.85416i	−0.835636	−	0.549283i
$28$	−0.571409	+	3.60774i	−0.107986	+	0.681798i
$29$	5.64831	−	4.10373i	1.04886	−	0.762044i	0.0768679	−	0.997041i	$-0.475508\pi$
$29$	5.64831	−	4.10373i	1.04886	−	0.762044i	0.971996	+	0.234997i	$0.0755080\pi$
$30$	−3.85607	+	0.361585i	−0.704018	+	0.0660161i
$31$	−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
$33$	−2.63463	+	0.318547i	−0.458630	+	0.0554520i
$34$	−4.90472	−	1.59364i	−0.841152	−	0.273307i
$35$	8.16476	+	0.219087i	1.38010	+	0.0370325i
$36$	0.714995	+	2.91355i	0.119166	+	0.485592i
$37$	−6.84089	+	3.48561i	−1.12464	+	0.573031i	−0.914477	−	0.404637i	$-0.867398\pi$
$37$	−6.84089	+	3.48561i	−1.12464	+	0.573031i	−0.210158	+	0.977667i	$0.567398\pi$
$38$	−1.93198	+	0.984395i	−0.313409	+	0.159690i
$39$	2.38730	+	8.38398i	0.382274	+	1.34251i
$40$	1.77311	+	1.36238i	0.280353	+	0.215411i
$41$	2.85939	+	0.929072i	0.446562	+	0.145097i	0.523661	−	0.851927i	$-0.324566\pi$
$41$	2.85939	+	0.929072i	0.446562	+	0.145097i	−0.0770993	+	0.997023i	$0.524566\pi$
$42$	−0.759414	−	6.28093i	−0.117180	−	0.969168i
$43$	3.24693	−	3.24693i	0.495151	−	0.495151i	−0.414773	−	0.909925i	$-0.636139\pi$
$43$	3.24693	−	3.24693i	0.495151	−	0.495151i	0.909925	+	0.414773i	$0.136139\pi$
$44$	1.23956	+	0.900593i	0.186871	+	0.135770i
$45$	6.25205	−	2.43142i	0.932001	−	0.362455i
$46$	−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	$0.983297\pi$
$48$	0.842515	−	1.51333i	0.121607	−	0.218430i
$49$			6.34226i			0.906037i
$50$	2.50560	−	4.32689i	0.354345	−	0.611914i
$51$	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	$0.572608\pi$
$54$	−2.57307	−	4.51434i	−0.350151	−	0.614324i
$55$	1.63672	−	3.00982i	0.220696	−	0.405844i
$56$	−2.14701	+	2.95510i	−0.286906	+	0.394892i
$57$	2.75143	−	2.55625i	0.364436	−	0.338584i
$58$	6.89573	−	1.09218i	0.905454	−	0.143410i
$59$	−2.10801	+	6.48779i	−0.274439	+	0.844638i	0.714928	+	0.699198i	$0.246460\pi$
$59$	−2.10801	+	6.48779i	−0.274439	+	0.844638i	−0.989367	+	0.145439i	$0.953540\pi$
$60$	−3.59994	−	1.42844i	−0.464750	−	0.184411i
$61$	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
$63$	4.24434	+	10.1028i	0.534737	+	1.27283i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−10.6060	−	3.76349i	−1.31551	−	0.466804i
$66$	−2.49209	−	0.912268i	−0.306755	−	0.112292i
$67$	−0.527466	−	3.33029i	−0.0644402	−	0.406859i	−0.998732	−	0.0503493i	$-0.983967\pi$
$67$	−0.527466	−	3.33029i	−0.0644402	−	0.406859i	0.934291	−	0.356510i	$-0.116033\pi$
$68$	−3.64664	−	3.64664i	−0.442220	−	0.442220i
$69$	6.79858	−	8.66870i	0.818453	−	1.04359i
$70$	7.17539	+	3.90193i	0.857623	+	0.466370i
$71$	−2.18090	−	3.00175i	−0.258825	−	0.356242i	0.659752	−	0.751483i	$-0.270661\pi$
$71$	−2.18090	−	3.00175i	−0.258825	−	0.356242i	−0.918578	+	0.395241i	$0.870661\pi$
$72$	−0.685659	+	2.92059i	−0.0808057	+	0.344195i
$73$	−0.531390	−	0.270757i	−0.0621945	−	0.0316897i	0.422617	−	0.906309i	$-0.361112\pi$
$73$	−0.531390	−	0.270757i	−0.0621945	−	0.0316897i	−0.484811	+	0.874619i	$0.661112\pi$
$74$	−7.67771			−0.892516
$75$	−2.12150	+	8.39638i	−0.244970	+	0.969531i
$76$	−2.16832			−0.248723
$77$	4.98661	+	2.54081i	0.568277	+	0.289552i
$78$	−1.67915	+	8.55399i	−0.190126	+	0.968549i
$79$	−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	$0.823851\pi$
$80$	0.961346	+	2.01886i	0.107482	+	0.225716i
$81$	6.42764	+	6.29964i	0.714182	+	0.699960i
$82$	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	$0.998537\pi$
$84$	2.17484	−	5.94112i	0.237294	−	0.648229i
$85$	−7.02596	+	9.14415i	−0.762072	+	0.991823i
$86$	4.36710	−	1.41896i	0.470917	−	0.153010i
$87$	−10.9691	+	5.09030i	−1.17601	+	0.545737i
$88$	0.695596	+	1.36518i	0.0741507	+	0.145529i
$89$	−1.98939	−	6.12272i	−0.210875	−	0.649007i	−0.999421	−	0.0340306i	$-0.989166\pi$
$89$	−1.98939	−	6.12272i	−0.210875	−	0.649007i	0.788546	−	0.614976i	$-0.210834\pi$
$90$	6.67446	+	0.671961i	0.703550	+	0.0708309i
$91$	5.68088	−	17.4839i	0.595518	−	1.83282i
$92$	−6.28217	+	0.994998i	−0.654961	+	0.103736i
$93$	8.67494	+	9.33729i	0.899549	+	0.968232i
$94$	−1.67653	+	2.30754i	−0.172921	+	0.238005i
$95$	0.629747	+	4.80743i	0.0646107	+	0.493232i
$96$	1.43772	−	0.965894i	0.146737	−	0.0985811i
$97$	13.5156	+	2.14067i	1.37230	+	0.217352i	0.798675	−	0.601763i	$-0.205535\pi$
$97$	13.5156	+	2.14067i	1.37230	+	0.217352i	0.573630	+	0.819114i	$0.305535\pi$
$98$	−2.87933	+	5.65100i	−0.290856	+	0.570837i
$99$	4.58413	+	0.337594i	0.460722	+	0.0339295i
$100$	4.19687	−	2.71777i	0.419687	−	0.271777i
$101$		−	0.146560i		−	0.0145833i	−0.999973	−	0.00729163i	$-0.997679\pi$
$101$		−	0.146560i		−	0.0145833i	0.999973	−	0.00729163i	$-0.00232102\pi$
$102$	7.80443	+	4.34495i	0.772754	+	0.430214i
$103$	2.44405	−	15.4311i	0.240819	−	1.52047i	−0.510120	−	0.860103i	$-0.670399\pi$
$103$	2.44405	−	15.4311i	0.240819	−	1.52047i	0.750939	−	0.660371i	$-0.229601\pi$
$104$	4.07170	−	2.95827i	0.399263	−	0.290082i
$105$	−13.8038	−	3.09641i	−1.34712	−	0.302178i
$106$	−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	$0.211361\pi$
$108$	−0.243156	−	5.19046i	−0.0233977	−	0.499452i
$109$	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	$0.473961\pi$
$110$	2.82476	−	1.93872i	0.269330	−	0.184849i
$111$	12.7898	−	3.64183i	1.21395	−	0.345668i
$112$	−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	$0.179534\pi$
$114$	3.61206	−	1.02852i	0.338300	−	0.0963293i
$115$	4.03057	+	13.6394i	0.375853	+	1.27188i
$116$	6.63998	+	2.15746i	0.616507	+	0.200315i
$117$	−1.26030	−	15.0460i	−0.116515	−	1.39100i
$118$	−4.82364	+	4.82364i	−0.444052	+	0.444052i
$119$	−15.2398	−	11.0724i	−1.39703	−	1.01500i
$120$	−2.55907	−	2.90709i	−0.233610	−	0.265380i
$121$	−6.99996	+	5.08577i	−0.636360	+	0.462342i
$122$	−0.903094	+	5.70191i	−0.0817623	+	0.516227i
$123$	−4.54989	−	2.53305i	−0.410250	−	0.228398i
$124$		−	7.35843i		−	0.660807i
$125$	−7.24454	−	8.51567i	−0.647971	−	0.761665i
$126$	−0.804822	+	10.9285i	−0.0716992	+	0.973590i
$127$	−8.38871	+	16.4638i	−0.744378	+	1.46092i	0.138025	+	0.990429i	$0.455925\pi$
$127$	−8.38871	+	16.4638i	−0.744378	+	1.46092i	−0.882403	+	0.470495i	$0.844075\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	−6.60181	+	4.43523i	−0.581257	+	0.390501i
$130$	−7.74140	−	8.16831i	−0.678965	−	0.716408i
$131$	−7.79711	+	10.7318i	−0.681236	+	0.937641i	−0.999948	−	0.0102104i	$-0.996750\pi$
$131$	−7.79711	+	10.7318i	−0.681236	+	0.937641i	0.318712	+	0.947852i	$0.396750\pi$
$132$	−1.80631	−	1.94422i	−0.157219	−	0.169223i
$133$	−7.82271	+	1.23900i	−0.678315	+	0.107435i
$134$	1.04194	−	3.20677i	0.0900102	−	0.277023i
$135$	−11.4373	+	2.04658i	−0.984365	+	0.176141i
$136$	−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	$0.713095\pi$
$138$	9.99308	−	4.63737i	0.850668	−	0.394760i
$139$	−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	$0.466047\pi$
$140$	4.62188	+	6.73421i	0.390620	+	0.569144i
$141$	1.69826	−	4.63922i	0.143019	−	0.390693i
$142$	−0.580430	−	3.66469i	−0.0487086	−	0.307534i
$143$	−5.45272	−	5.45272i	−0.455980	−	0.455980i
$144$	−1.93685	+	2.29099i	−0.161404	+	0.190915i
$145$	2.85491	−	15.3483i	0.237087	−	1.27460i
$146$	−0.350551	−	0.482492i	−0.0290118	−	0.0399313i
$147$	2.11600	−	10.7794i	0.174524	−	0.889070i
$148$	−6.84089	−	3.48561i	−0.562318	−	0.286515i
$149$	6.55688			0.537160			0.268580	−	0.963257i	$-0.413446\pi$
$149$	6.55688			0.537160			0.268580	+	0.963257i	$0.413446\pi$
$150$	−5.70215	+	6.51809i	−0.465579	+	0.532200i
$151$	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
$153$	−15.0619	−	3.53603i	−1.21768	−	0.285871i
$154$	3.28960	+	4.52775i	0.265084	+	0.364856i
$155$	−16.3146	+	2.13712i	−1.31042	+	0.171657i
$156$	−5.37956	+	6.85934i	−0.430710	+	0.549187i
$157$	15.3342	+	15.3342i	1.22380	+	1.22380i	0.966271	+	0.257528i	$0.0829078\pi$
$157$	15.3342	+	15.3342i	1.22380	+	1.22380i	0.257528	+	0.966271i	$0.417092\pi$
$158$	−0.208176	−	1.31437i	−0.0165616	−	0.104566i
$159$	1.68061	+	0.615212i	0.133281	+	0.0487895i
$160$	−0.0599794	+	2.23526i	−0.00474179	+	0.176713i
$161$	−22.0958	+	7.17938i	−1.74140	+	0.565814i
$162$	2.86709	+	8.53111i	0.225260	+	0.670267i
$163$	−4.66780	−	9.16108i	−0.365610	−	0.717551i	0.632776	−	0.774335i	$-0.281915\pi$
$163$	−4.66780	−	9.16108i	−0.365610	−	0.717551i	−0.998386	+	0.0567839i	$0.981915\pi$
$164$	0.929072	+	2.85939i	0.0725483	+	0.223281i
$165$	−3.78598	+	4.56947i	−0.294738	+	0.355733i
$166$	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	$0.0677733\pi$
$168$	4.63501	−	4.30622i	0.357598	−	0.332232i
$169$	−7.24745	+	9.97526i	−0.557496	+	0.767327i
$170$	−10.4115	+	4.95778i	−0.798528	+	0.380244i
$171$	−5.52922	+	3.42667i	−0.422830	+	0.262044i
$172$	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
$175$	13.5882	−	12.2031i	1.02717	−	0.922469i
$176$			1.53218i			0.115492i
$177$	5.74735	−	10.3234i	0.431997	−	0.775956i
$178$	1.00709	−	6.35855i	0.0754849	−	0.476593i
$179$	−3.64757	+	2.65012i	−0.272632	+	0.198079i	−0.715697	−	0.698410i	$-0.753891\pi$
$179$	−3.64757	+	2.65012i	−0.272632	+	0.198079i	0.443065	+	0.896489i	$0.353891\pi$
$180$	5.64193	+	3.62886i	0.420524	+	0.270480i
$181$	−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
$183$	−1.20023	−	9.92681i	−0.0887236	−	0.733811i
$184$	−6.04917	−	1.96550i	−0.445951	−	0.144898i
$185$	−5.74123	+	16.1795i	−0.422103	+	1.18954i
$186$	3.49039	+	12.2579i	0.255928	+	0.898795i
$187$	−7.04042	+	3.58727i	−0.514846	+	0.262327i
$188$	−2.54140	+	1.29491i	−0.185351	+	0.0944409i
$189$	−3.84312	−	18.5869i	−0.279546	−	1.35200i
$190$	−1.62142	+	4.56935i	−0.117630	+	0.331496i
$191$	12.1952	+	3.96247i	0.882416	+	0.286714i	0.714960	−	0.699165i	$-0.246445\pi$
$191$	12.1952	+	3.96247i	0.882416	+	0.286714i	0.167456	+	0.985880i	$0.446445\pi$
$192$	1.71953	−	0.207905i	0.124096	−	0.0150042i
$193$	−9.89879	+	9.89879i	−0.712531	+	0.712531i	−0.967064	−	0.254533i	$-0.918078\pi$
$193$	−9.89879	+	9.89879i	−0.712531	+	0.712531i	0.254533	+	0.967064i	$0.418078\pi$
$194$	11.0707	+	8.04332i	0.794828	+	0.577477i
$195$	16.7704	+	9.93500i	1.20096	+	0.711460i
$196$	−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	$-0.0279691\pi$
$198$	3.93122	+	2.38195i	0.279380	+	0.169278i
$199$		−	5.40490i		−	0.383143i	−0.981479	−	0.191572i	$-0.938642\pi$
$199$		−	5.40490i		−	0.383143i	0.981479	−	0.191572i	$-0.0613585\pi$
$200$	4.97328	−	0.516208i	0.351664	−	0.0365014i
$201$	−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
$204$	4.98123	+	7.41452i	0.348756	+	0.519120i
$205$	6.06980	−	2.89033i	0.423933	−	0.201869i
$206$	9.18325	−	12.6397i	0.639827	−	0.880647i
$207$	−14.4471	+	12.4652i	−1.00415	+	0.866391i
$208$	4.97094	−	0.787319i	0.344673	−	0.0545908i
$209$	−1.02663	+	3.15965i	−0.0710137	+	0.218558i
$210$	−10.8936	−	9.02573i	−0.751728	−	0.622835i
$211$	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
$213$	2.70520	+	5.82944i	0.185357	+	0.399427i
$214$	2.38255	−	0.774136i	0.162868	−	0.0529189i
$215$	0.275416	−	10.2640i	0.0187832	−	0.699998i
$216$	2.13977	−	4.73512i	0.145593	−	0.322184i
$217$	−4.20467	−	26.5473i	−0.285432	−	1.80215i
$218$	5.69477	+	5.69477i	0.385698	+	0.385698i
$219$	0.812824	+	0.637472i	0.0549256	+	0.0430763i
$220$	3.39704	−	0.444993i	0.229028	−	0.0300014i
$221$	15.2561	+	20.9983i	1.02624	+	1.41250i
$222$	13.0491	+	2.56155i	0.875802	+	0.171920i
$223$	25.8694	+	13.1811i	1.73234	+	0.882673i	0.972611	+	0.232437i	$0.0746699\pi$
$223$	25.8694	+	13.1811i	1.73234	+	0.882673i	0.759732	+	0.650236i	$0.225330\pi$
$224$	−3.65271			−0.244057
$225$	6.40706	−	13.5628i	0.427137	−	0.904187i
$226$	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	$0.691864\pi$
$228$	3.68530	+	0.723425i	0.244065	+	0.0479100i
$229$	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	$0.656324\pi$
$230$	−2.60088	+	13.9826i	−0.171497	+	0.921987i
$231$	−7.62762	−	5.98209i	−0.501860	−	0.393593i
$232$	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	$0.857303\pi$
$234$	5.70781	−	13.9783i	0.373131	−	0.913787i
$235$	3.60908	+	5.25852i	0.235430	+	0.343028i
$236$	−6.48779	+	2.10801i	−0.422319	+	0.137220i
$237$	0.970244	+	2.09078i	0.0630241	+	0.135811i
$238$	−8.55203	−	16.7843i	−0.554345	−	1.08796i
$239$	−5.85405	−	18.0169i	−0.378667	−	1.16542i	−0.940971	−	0.338486i	$-0.890085\pi$
$239$	−5.85405	−	18.0169i	−0.378667	−	1.16542i	0.562305	−	0.826930i	$-0.309915\pi$
$240$	−0.960355	−	3.75203i	−0.0619907	−	0.242192i
$241$	−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
$243$	−8.82273	−	12.8514i	−0.565978	−	0.824420i
$244$	−3.39328	+	4.67045i	−0.217232	+	0.298995i
$245$	9.75540	+	10.2934i	0.623250	+	0.657620i
$246$	−2.90400	−	4.32257i	−0.185152	−	0.275597i
$247$	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
$250$	−2.58890	−	10.8765i	−0.163736	−	0.687888i
$251$		−	13.6488i		−	0.861504i	−0.902470	−	0.430752i	$-0.858248\pi$
$251$		−	13.6488i		−	0.861504i	0.902470	−	0.430752i	$-0.141752\pi$
$252$	−5.67855	+	9.37200i	−0.357715	+	0.590381i
$253$	−1.52452	+	9.62542i	−0.0958455	+	0.605145i
$254$	−14.9488	+	10.8609i	−0.937971	+	0.681476i
$255$	14.9922	−	13.1974i	0.938849	−	0.826455i
$256$	−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	$0.466834\pi$
$258$	−7.89581	+	0.954666i	−0.491571	+	0.0594349i
$259$	−26.6718	−	8.66620i	−1.65731	−	0.538492i
$260$	−3.18930	−	10.7925i	−0.197792	−	0.669325i
$261$	20.3415	−	4.99188i	1.25911	−	0.308989i
$262$	−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	$0.517537\pi$
$264$	−0.726772	−	2.55236i	−0.0447297	−	0.157087i
$265$	−1.90495	+	1.30742i	−0.117020	+	0.0803144i
$266$	−7.53258	−	2.44748i	−0.461852	−	0.150065i
$267$	1.33845	+	11.0700i	0.0819118	+	0.677472i
$268$	2.38422	−	2.38422i	0.145640	−	0.145640i
$269$	8.83824	+	6.42136i	0.538877	+	0.391517i	0.823668	−	0.567073i	$-0.191924\pi$
$269$	8.83824	+	6.42136i	0.538877	+	0.391517i	−0.284791	+	0.958590i	$0.591924\pi$
$270$	−11.1198	−	3.36890i	−0.676731	−	0.205025i
$271$	−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
$273$	−15.4885	+	27.8206i	−0.937409	+	1.68378i
$274$			9.76085i			0.589674i
$275$	−1.97321	−	7.40242i	−0.118989	−	0.446383i
$276$	11.0092	+	0.404835i	0.662678	+	0.0243682i
$277$	12.7426	−	25.0088i	0.765631	−	1.50263i	−0.0961574	−	0.995366i	$-0.530655\pi$
$277$	12.7426	−	25.0088i	0.765631	−	1.50263i	0.861788	−	0.507269i	$-0.169345\pi$
$278$	−4.79774	−	0.759888i	−0.287749	−	0.0455750i
$279$	−11.6288	−	18.7640i	−0.696198	−	1.12337i
$280$	1.06086	+	8.09851i	0.0633985	+	0.483979i
$281$	0.417572	−	0.574739i	0.0249103	−	0.0342861i	−0.796380	−	0.604796i	$-0.793255\pi$
$281$	0.417572	−	0.574739i	0.0249103	−	0.0342861i	0.821290	+	0.570510i	$0.193255\pi$
$282$	3.61933	−	3.36258i	0.215528	−	0.200239i
$283$	9.10320	−	1.44181i	0.541129	−	0.0857064i	0.120114	−	0.992760i	$-0.461674\pi$
$283$	9.10320	−	1.44181i	0.541129	−	0.0857064i	0.421015	+	0.907054i	$0.361674\pi$
$284$	1.14657	−	3.52877i	0.0680363	−	0.209394i
$285$	0.533598	−	8.38089i	0.0316076	−	0.496441i
$286$	−2.38293	−	7.33390i	−0.140905	−	0.433662i
$287$	4.98573	+	9.78504i	0.294298	+	0.577593i
$288$	−2.76583	+	1.16197i	−0.162978	+	0.0684699i
$289$	9.12626	−	2.96530i	0.536839	−	0.174430i
$290$	9.51171	−	12.3793i	0.558547	−	0.726938i
$291$	−22.2572	−	8.14759i	−1.30474	−	0.477620i
$292$	−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	$0.723969\pi$
$294$	6.77911	−	8.64387i	0.395366	−	0.504121i
$295$	6.55798	+	13.7720i	0.381820	+	0.801837i
$296$	−4.51285	−	6.21140i	−0.262304	−	0.361030i
$297$	−7.67862	−	2.10320i	−0.445559	−	0.122040i
$298$	5.84222	+	2.97676i	0.338431	+	0.172439i
$299$	32.0116			1.85128
$300$	−8.03980	+	3.21894i	−0.464178	+	0.185845i
$301$	16.7727			0.966760
$302$	0.949976	+	0.484037i	0.0546650	+	0.0278532i
$303$	−0.0488974	+	0.249095i	−0.00280908	+	0.0143102i
$304$	−1.27450	−	1.75421i	−0.0730979	−	0.100611i
$305$	11.3405	+	6.16688i	0.649354	+	0.353115i
$306$	−11.8149	−	9.98857i	−0.675413	−	0.571008i
$307$	−11.7511	−	11.7511i	−0.670673	−	0.670673i	0.287198	−	0.957871i	$-0.407276\pi$
$307$	−11.7511	−	11.7511i	−0.670673	−	0.670673i	−0.957871	+	0.287198i	$0.907276\pi$
$308$	0.875502	+	5.52770i	0.0498864	+	0.314970i
$309$	−9.30230	+	25.4115i	−0.529189	+	1.44561i
$310$	−15.5066	−	5.50247i	−0.880717	−	0.312520i
$311$	−3.30339	+	1.07334i	−0.187318	+	0.0608633i	−0.401174	−	0.916002i	$-0.631398\pi$
$311$	−3.30339	+	1.07334i	−0.187318	+	0.0608633i	0.213856	+	0.976865i	$0.431398\pi$
$312$	−7.90730	+	3.66945i	−0.447663	+	0.207742i
$313$	3.85400	+	7.56390i	0.217841	+	0.427537i	0.973904	−	0.226962i	$-0.0728795\pi$
$313$	3.85400	+	7.56390i	0.217841	+	0.427537i	−0.756063	+	0.654499i	$0.772879\pi$
$314$	6.70127	+	20.6244i	0.378175	+	1.16390i
$315$	22.4281	+	9.86813i	1.26368	+	0.556006i
$316$	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	$0.360690\pi$
$318$	1.21813	+	1.31114i	0.0683093	+	0.0735249i
$319$	6.28766	−	8.65423i	0.352042	−	0.484544i
$320$	−1.06823	+	1.96440i	−0.0597159	+	0.109814i
$321$	−3.60172	+	2.41972i	−0.201029	+	0.135055i
$322$	−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
$325$	−23.0021	+	10.2056i	−1.27593	+	0.566103i
$326$		−	10.2817i		−	0.569452i
$327$	−12.1878	−	6.78529i	−0.673986	−	0.375227i
$328$	−0.470327	+	2.96952i	−0.0259694	+	0.163965i
$329$	−8.42877	+	6.12386i	−0.464693	+	0.337619i
$330$	−5.44783	+	2.35263i	−0.299893	+	0.129508i
$331$	−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
$333$	−22.9528	+	1.92260i	−1.25780	+	0.105358i
$334$	22.9173	+	7.44629i	1.25398	+	0.407443i
$335$	−5.97858	−	4.59367i	−0.326644	−	0.250979i
$336$	6.08480	−	1.73262i	0.331953	−	0.0945221i
$337$	−23.3624	+	11.9038i	−1.27263	+	0.648439i	−0.954104	−	0.299475i	$-0.903189\pi$
$337$	−23.3624	+	11.9038i	−1.27263	+	0.648439i	−0.318528	+	0.947913i	$0.603189\pi$
$338$	−10.9862	+	5.59775i	−0.597570	+	0.304477i
$339$	−18.0729	+	5.14617i	−0.981585	+	0.279502i
$340$	−11.5275	−	0.309321i	−0.625168	−	0.0167753i
$341$	−10.7226	−	3.48400i	−0.580663	−	0.188669i
$342$	−6.48225	+	0.542974i	−0.350520	+	0.0293607i
$343$	1.69884	−	1.69884i	0.0917290	−	0.0917290i
$344$	3.71488	+	2.69902i	0.200293	+	0.145521i
$345$	−2.29985	−	24.5264i	−0.123820	−	1.32046i
$346$	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	$-0.0535027\pi$
$348$	−10.5656	−	5.88218i	−0.566376	−	0.315318i
$349$		−	25.4721i		−	1.36349i	−0.731591	−	0.681744i	$-0.761222\pi$
$349$		−	25.4721i		−	1.36349i	0.731591	−	0.681744i	$-0.238778\pi$
$350$	17.6473	−	4.70412i	0.943289	−	0.251446i
$351$	−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	$0.625301\pi$
$354$	9.80767	−	6.58900i	0.521272	−	0.350201i
$355$	−8.15673	−	1.51722i	−0.432914	−	0.0805256i
$356$	3.78405	−	5.20829i	0.200554	−	0.276039i
$357$	22.2077	+	23.9033i	1.17536	+	1.26510i
$358$	−4.45314	+	0.705308i	−0.235356	+	0.0372767i
$359$	−2.11987	+	6.52428i	−0.111882	+	0.344338i	−0.991284	−	0.131742i	$-0.957943\pi$
$359$	−2.11987	+	6.52428i	−0.111882	+	0.344338i	0.879402	+	0.476080i	$0.157943\pi$
$360$	3.37952	+	5.79472i	0.178117	+	0.305409i
$361$	4.41845	+	13.5986i	0.232550	+	0.715715i
$362$	−6.42000	−	12.6000i	−0.337428	−	0.662239i
$363$	13.5940	−	6.30841i	0.713500	−	0.331106i
$364$	17.4839	−	5.68088i	0.916408	−	0.297759i
$365$	−1.27890	+	0.377928i	−0.0669408	+	0.0197817i
$366$	3.43727	−	9.38975i	0.179669	−	0.490810i
$367$	−2.31983	−	14.6468i	−0.121094	−	0.764559i	−0.971256	−	0.238038i	$-0.923496\pi$
$367$	−2.31983	−	14.6468i	−0.121094	−	0.764559i	0.850162	−	0.526522i	$-0.176504\pi$
$368$	−4.49754	−	4.49754i	−0.234450	−	0.234450i
$369$	6.88794	+	5.82321i	0.358572	+	0.303144i
$370$	−12.4608	+	11.8095i	−0.647806	+	0.613949i
$371$	−2.21843	−	3.05341i	−0.115175	−	0.158525i
$372$	−2.45502	+	12.5065i	−0.127287	+	0.648431i
$373$	−15.4140	−	7.85384i	−0.798108	−	0.406656i	0.00685847	−	0.999976i	$-0.497817\pi$
$373$	−15.4140	−	7.85384i	−0.798108	−	0.406656i	−0.804967	+	0.593320i	$0.797817\pi$
$374$	−7.90165			−0.408584
$375$	9.47180	+	16.8904i	0.489122	+	0.872216i
$376$	−2.85228			−0.147095
$377$	−31.3083	−	15.9524i	−1.61246	−	0.821590i
$378$	5.01402	−	18.3058i	0.257893	−	0.941546i
$379$	−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	$0.846657\pi$
$380$	−3.51914	+	3.33521i	−0.180528	+	0.171093i
$381$	19.7505	−	25.1833i	1.01185	−	1.29018i
$382$	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	$0.667455\pi$
$384$	1.62650	+	0.595405i	0.0830018	+	0.0303841i
$385$	12.0013	−	3.54652i	0.611645	−	0.180747i
$386$	−13.3138	+	4.32593i	−0.677657	+	0.220184i
$387$	12.7003	−	5.33560i	0.645591	−	0.271224i
$388$	6.21246	+	12.1926i	0.315390	+	0.618987i
$389$	−0.407506	−	1.25417i	−0.0206613	−	0.0635891i	0.940194	−	0.340639i	$-0.110643\pi$
$389$	−0.407506	−	1.25417i	−0.0206613	−	0.0635891i	−0.960856	+	0.277050i	$0.910643\pi$
$390$	10.4322	+	16.4658i	0.528253	+	0.833776i
$391$	10.1363	−	31.1963i	0.512615	−	1.57767i
$392$	−6.26418	+	0.992148i	−0.316389	+	0.0501110i
$393$	16.8326	−	15.6385i	0.849091	−	0.788860i
$394$	4.00131	−	5.50734i	0.201583	−	0.277456i
$395$	−2.92548	−	0.544164i	−0.147197	−	0.0273798i
$396$	2.42136	+	3.90707i	0.121678	+	0.196338i
$397$	10.9634	+	1.73643i	0.550238	+	0.0871491i	0.425362	−	0.905023i	$-0.360147\pi$
$397$	10.9634	+	1.73643i	0.550238	+	0.0871491i	0.124876	+	0.992172i	$0.460147\pi$
$398$	2.45377	−	4.81580i	0.122997	−	0.241394i
$399$	13.7090	+	0.504110i	0.686307	+	0.0252371i
$400$	4.66558	+	1.79788i	0.233279	+	0.0898939i
$401$		−	38.4533i		−	1.92026i	−0.279545	−	0.960132i	$-0.590184\pi$
$401$		−	38.4533i		−	1.92026i	0.279545	−	0.960132i	$-0.409816\pi$
$402$	−2.84079	+	5.10265i	−0.141686	+	0.254497i
$403$	−5.79343	+	36.5783i	−0.288591	+	1.82209i
$404$	0.118569	−	0.0861458i	0.00589905	−	0.00428591i
$405$	20.1218	+	0.337476i	0.999859	+	0.0167693i
$406$	20.6316	+	14.9897i	1.02393	+	0.743928i
$407$	−8.31815	+	8.31815i	−0.412316	+	0.412316i
$408$	1.07219	+	8.86782i	0.0530813	+	0.439022i
$409$	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	$0.509332\pi$
$410$	6.72041	+	0.180331i	0.331897	+	0.00890589i
$411$	−4.62994	−	16.2600i	−0.228378	−	0.802044i
$412$	13.9206	−	7.09291i	0.685820	−	0.349443i
$413$	−22.2017	+	11.3123i	−1.09247	+	0.556643i
$414$	−18.5316	+	4.54771i	−0.910777	+	0.223508i
$415$	−4.90732	−	3.77057i	−0.240891	−	0.185090i
$416$	4.78657	+	1.55525i	0.234681	+	0.0762525i
$417$	8.35269	−	1.00991i	0.409033	−	0.0494553i
$418$	−2.34919	+	2.34919i	−0.114903	+	0.114903i
$419$	−4.06691	−	2.95479i	−0.198682	−	0.144351i	0.483996	−	0.875070i	$-0.339185\pi$
$419$	−4.06691	−	2.95479i	−0.198682	−	0.144351i	−0.682678	+	0.730719i	$0.739185\pi$
$420$	−5.60865	−	12.9876i	−0.273674	−	0.633728i
$421$	−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
$423$	−4.43419	+	7.31829i	−0.215598	+	0.355828i
$424$		−	1.03327i		−	0.0501799i
$425$	2.66215	+	25.6478i	0.129133	+	1.24410i
$426$	−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
$429$	7.44831	+	11.0867i	0.359608	+	0.535273i
$430$	4.90515	−	9.02024i	0.236547	−	0.434995i
$431$	14.5495	−	20.0257i	0.700824	−	0.964602i	−0.299122	−	0.954215i	$-0.596694\pi$
$431$	14.5495	−	20.0257i	0.700824	−	0.964602i	0.999946	−	0.0103868i	$-0.00330628\pi$
$432$	4.05625	−	3.24759i	0.195156	−	0.156250i
$433$	21.9052	−	3.46945i	1.05270	−	0.166731i	0.393979	−	0.919119i	$-0.371098\pi$
$433$	21.9052	−	3.46945i	1.05270	−	0.166731i	0.658720	+	0.752388i	$0.271098\pi$
$434$	8.30582	−	25.5627i	0.398692	−	1.22705i
$435$	−9.97295	+	25.1336i	−0.478166	+	1.20507i
$436$	2.48870	+	7.65945i	0.119187	+	0.366821i
$437$	−6.26122	−	12.2883i	−0.299515	−	0.587831i
$438$	0.434825	+	0.937006i	0.0207768	+	0.0447719i
$439$	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	$0.387053\pi$
$440$	3.22881	+	1.14573i	0.153927	+	0.0546206i
$441$	−7.19275	+	17.6148i	−0.342512	+	0.838802i
$442$	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	$0.757626\pi$
$444$	10.4640	+	8.20655i	0.496598	+	0.389465i
$445$	−12.6465	−	6.87706i	−0.599499	−	0.326004i
$446$	17.0657	+	23.4889i	0.808085	+	1.11223i
$447$	−11.1442	−	2.18760i	−0.527101	−	0.103470i
$448$	−3.25458	−	1.65829i	−0.153765	−	0.0783470i
$449$	12.4310			0.586657			0.293329	−	0.956012i	$-0.405237\pi$
$449$	12.4310			0.586657			0.293329	+	0.956012i	$0.405237\pi$
$450$	11.8661	−	9.17580i	0.559374	−	0.432551i
$451$	4.60656			0.216915
$452$	9.66667	+	4.92541i	0.454682	+	0.231672i
$453$	−1.81210	−	0.355715i	−0.0851398	−	0.0167130i
$454$	−2.32271	−	3.19694i	−0.109010	−	0.150040i
$455$	−17.6731	−	37.1142i	−0.828528	−	1.73994i
$456$	2.95520	+	2.31767i	0.138390	+	0.108535i
$457$	−25.4659	−	25.4659i	−1.19125	−	1.19125i	−0.976718	−	0.214529i	$-0.931178\pi$
$457$	−25.4659	−	25.4659i	−1.19125	−	1.19125i	−0.214529	−	0.976718i	$-0.568822\pi$
$458$	2.06521	+	13.0392i	0.0965011	+	0.609284i
$459$	24.4196	+	11.0350i	1.13981	+	0.515071i
$460$	−8.66538	+	11.2778i	−0.404025	+	0.525832i
$461$	−34.8009	+	11.3075i	−1.62084	+	0.526642i	−0.972140	−	0.234403i	$-0.924686\pi$
$461$	−34.8009	+	11.3075i	−1.62084	+	0.526642i	−0.648699	+	0.761045i	$0.724686\pi$
$462$	−4.08044	−	8.79295i	−0.189839	−	0.409085i
$463$	3.00399	+	5.89566i	0.139607	+	0.273994i	0.950215	−	0.311595i	$-0.100863\pi$
$463$	3.00399	+	5.89566i	0.139607	+	0.273994i	−0.810608	+	0.585589i	$0.800863\pi$
$464$	2.15746	+	6.63998i	0.100158	+	0.308253i
$465$	28.4415	+	1.81082i	1.31894	+	0.0839749i
$466$	−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	$0.794621\pi$
$468$	11.4317	−	9.86343i	0.528430	−	0.455937i
$469$	7.23928	−	9.96401i	0.334279	−	0.460095i
$470$	0.828391	+	6.32386i	0.0382108	+	0.291698i
$471$	−20.9461	−	31.1781i	−0.965147	−	1.43661i
$472$	−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
$475$	8.41666	+	6.83373i	0.386183	+	0.313553i
$476$		−	18.8375i		−	0.863413i
$477$	−2.65112	−	1.60633i	−0.121387	−	0.0735488i
$478$	2.96351	−	18.7109i	0.135548	−	0.855815i
$479$	−9.41843	+	6.84289i	−0.430339	+	0.312660i	−0.781785	−	0.623549i	$-0.785690\pi$
$479$	−9.41843	+	6.84289i	−0.430339	+	0.312660i	0.351445	+	0.936208i	$0.385690\pi$
$480$	0.847702	−	3.77907i	0.0386921	−	0.172490i
$481$	31.2614	+	22.7127i	1.42540	+	1.03561i
$482$	−16.6233	+	16.6233i	−0.757170	+	0.757170i
$483$	39.9497	−	4.83024i	1.81777	−	0.219783i
$484$	−8.22894	−	2.67375i	−0.374043	−	0.121534i
$485$	25.2283	−	17.3149i	1.14556	−	0.786230i
$486$	−2.02668	−	15.4561i	−0.0919320	−	0.701105i
$487$	31.6495	−	16.1262i	1.43418	−	0.730750i	0.447629	−	0.894219i	$-0.352269\pi$
$487$	31.6495	−	16.1262i	1.43418	−	0.730750i	0.986548	+	0.163470i	$0.0522686\pi$
$488$	−5.14377	+	2.62088i	−0.232848	+	0.118642i
$489$	4.87701	+	17.1276i	0.220546	+	0.774538i
$490$	4.01903	+	13.6003i	0.181561	+	0.614400i
$491$	−3.18688	−	1.03548i	−0.143822	−	0.0467305i	0.236222	−	0.971699i	$-0.424091\pi$
$491$	−3.18688	−	1.03548i	−0.143822	−	0.0467305i	−0.380043	+	0.924969i	$0.624091\pi$
$492$	−0.625074	−	5.16983i	−0.0281805	−	0.233074i
$493$	−25.4597	+	25.4597i	−1.14665	+	1.14665i
$494$	8.82874	+	6.41446i	0.397224	+	0.288600i
$495$	7.95923	−	6.50320i	0.357741	−	0.292297i
$496$	5.95310	−	4.32518i	0.267302	−	0.194206i
$497$	2.12014	−	13.3860i	0.0951012	−	0.600446i
$498$	−2.33177	+	4.18834i	−0.104489	+	0.187684i
$499$			2.56390i			0.114776i	0.998352	+	0.0573880i	$0.0182772\pi$
$499$			2.56390i			0.114776i	−0.998352	+	0.0573880i	$0.981723\pi$
$500$	2.63109	−	10.8663i	0.117666	−	0.485958i
$501$	−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	$0.444888\pi$
$504$	−9.31442	+	5.77251i	−0.414897	+	0.257128i
$505$	−0.225432	−	0.237864i	−0.0100316	−	0.0105848i
$506$	−5.72820	+	7.88419i	−0.254650	+	0.350495i
$507$	15.6460	−	14.5361i	0.694861	−	0.645570i
$508$	−18.2502	+	2.89055i	−0.809723	+	0.128248i
$509$	−2.88278	+	8.87228i	−0.127777	+	0.393257i	−0.994397	−	0.105712i	$-0.966288\pi$
$509$	−2.88278	+	8.87228i	−0.127777	+	0.393257i	0.866620	+	0.498969i	$0.166288\pi$
$510$	19.3497	−	4.95267i	0.856818	−	0.219308i
$511$	−0.673177	−	2.07183i	−0.0297796	−	0.0916522i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	10.5408	−	3.97929i	0.465388	−	0.175690i
$514$	−19.2024	+	6.23925i	−0.846983	+	0.275202i
$515$	−19.7689	−	28.8038i	−0.871120	−	1.26925i
$516$	−7.46862	−	2.73401i	−0.328788	−	0.120358i
$517$	0.683651	+	4.31640i	0.0300669	+	0.189835i
$518$	−19.8304	−	19.8304i	−0.871298	−	0.871298i
$519$	−25.6655	+	32.7254i	−1.12659	+	1.43649i
$520$	2.05802	−	11.0641i	0.0902501	−	0.485194i
$521$	19.0337	+	26.1976i	0.833881	+	1.14774i	0.987188	+	0.159560i	$0.0510075\pi$
$521$	19.0337	+	26.1976i	0.833881	+	1.14774i	−0.153308	+	0.988179i	$0.548993\pi$
$522$	20.3907	+	4.78706i	0.892476	+	0.209524i
$523$	−19.7913	−	10.0842i	−0.865413	−	0.440950i	−0.0358458	−	0.999357i	$-0.511413\pi$
$523$	−19.7913	−	10.0842i	−0.865413	−	0.440950i	−0.829567	+	0.558408i	$0.811413\pi$
$524$	−13.2652			−0.579494
$525$	−27.1662	+	16.2071i	−1.18563	+	0.707335i
$526$	−16.2940			−0.710454
$527$	33.8122	+	17.2282i	1.47288	+	0.750471i
$528$	0.511188	−	2.60412i	0.0222466	−	0.113330i
$529$	−10.2602	−	14.1219i	−0.446095	−	0.613997i
$530$	−2.29088	+	0.300093i	−0.0995096	+	0.0130352i
$531$	−13.2125	+	15.6283i	−0.573375	+	0.678212i
$532$	−5.60044	−	5.60044i	−0.242810	−	0.242810i
$533$	−2.36711	−	14.9453i	−0.102531	−	0.647354i
$534$	−3.83310	+	10.4711i	−0.165875	+	0.453128i
$535$	0.150258	−	5.59969i	0.00649622	−	0.242096i
$536$	3.20677	−	1.04194i	0.138511	−	0.0450051i
$537$	7.08363	−	3.28722i	0.305681	−	0.141854i
$538$	4.95969	+	9.73395i	0.213828	+	0.419660i
$539$	3.00287	+	9.24188i	0.129343	+	0.398076i
$540$	−8.37839	−	8.05001i	−0.360548	−	0.346417i
$541$	−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
$543$	16.6713	+	17.9442i	0.715434	+	0.770058i
$544$	3.03128	−	4.17220i	0.129965	−	0.178882i
$545$	16.2592	−	7.74232i	0.696466	−	0.331644i
$546$	−26.4307	+	17.7567i	−1.13113	+	0.759917i
$547$	−12.4044	−	1.96467i	−0.530376	−	0.0840033i	−0.114497	−	0.993424i	$-0.536526\pi$
$547$	−12.4044	−	1.96467i	−0.530376	−	0.0840033i	−0.415878	+	0.909420i	$0.636526\pi$
$548$	−4.43133	+	8.69698i	−0.189297	+	0.371517i
$549$	−1.27200	+	17.2722i	−0.0542875	+	0.737159i
$550$	1.60249	−	7.49143i	0.0683302	−	0.319436i
$551$			15.1385i			0.644922i
$552$	9.62550	+	5.35879i	0.409689	+	0.228085i
$553$	0.760406	−	4.80101i	0.0323357	−	0.204160i
$554$	22.7075	−	16.4980i	0.964751	−	0.700933i
$555$	15.1559	−	25.5834i	0.643332	−	1.08595i
$556$	−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	$0.0523018\pi$
$558$	−1.84265	−	21.9983i	−0.0780054	−	0.931260i
$559$	−21.9792	−	7.14148i	−0.929621	−	0.302052i
$560$	−2.73141	+	7.69745i	−0.115423	+	0.325276i
$561$	13.1628	−	3.74805i	0.555735	−	0.158243i
$562$	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	$0.528117\pi$
$564$	4.75142	−	1.35295i	0.200071	−	0.0569693i
$565$	8.11276	−	22.8627i	0.341307	−	0.961842i
$566$	8.76558	+	2.84811i	0.368445	+	0.119715i
$567$	0.330602	+	32.8727i	0.0138840	+	1.38052i
$568$	2.62363	−	2.62363i	0.110085	−	0.110085i
$569$	−24.7435	−	17.9772i	−1.03730	−	0.753643i	−0.0675439	−	0.997716i	$-0.521516\pi$
$569$	−24.7435	−	17.9772i	−1.03730	−	0.753643i	−0.969757	+	0.244073i	$0.921516\pi$
$570$	4.28028	−	7.22518i	0.179281	−	0.302629i
$571$	−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
$573$	−19.4052	−	10.8034i	−0.810663	−	0.451320i
$574$			10.9820i			0.458380i
$575$	27.5211	+	15.9368i	1.14771	+	0.664611i
$576$	−2.99190	−	0.220336i	−0.124662	−	0.00918066i
$577$	−1.76187	+	3.45787i	−0.0733478	+	0.143953i	−0.924768	−	0.380530i	$-0.875741\pi$
$577$	−1.76187	+	3.45787i	−0.0733478	+	0.143953i	0.851421	+	0.524483i	$0.175741\pi$
$578$	9.47778	+	1.50113i	0.394224	+	0.0624389i
$579$	20.1267	−	13.5216i	0.836437	−	0.561937i
$580$	14.0951	−	6.71182i	0.585266	−	0.278693i
$581$	5.94213	−	8.17864i	0.246521	−	0.339307i
$582$	−16.1324	−	17.3641i	−0.668708	−	0.719765i
$583$	−1.56366	+	0.247659i	−0.0647602	+	0.0102570i
$584$	0.184296	−	0.567203i	0.00762620	−	0.0234710i
$585$	−25.1886	−	22.4809i	−1.04142	−	0.929469i
$586$	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	$0.482223\pi$
$588$	9.96447	−	4.62409i	0.410928	−	0.190694i
$589$	15.1745	−	4.93049i	0.625254	−	0.203157i
$590$	−0.409159	+	15.2482i	−0.0168448	+	0.627759i
$591$	−4.05318	+	11.0723i	−0.166726	+	0.455453i
$592$	−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	$0.854145\pi$
$594$	−5.88686	−	5.35999i	−0.241541	−	0.219923i
$595$	−41.7650	+	5.47099i	−1.71220	+	0.224289i
$596$	3.85404	+	5.30463i	0.157868	+	0.217286i
$597$	−1.80326	+	9.18625i	−0.0738026	+	0.375968i
$598$	28.5226	+	14.5330i	1.16638	+	0.594298i
$599$	−39.0036			−1.59364			−0.796822	−	0.604215i	$-0.793487\pi$
$599$	−39.0036			−1.59364			−0.796822	+	0.604215i	$0.793487\pi$
$600$	−8.62488	−	0.781902i	−0.352109	−	0.0319210i
$601$	−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
$603$	2.31190	−	9.84766i	0.0941480	−	0.401028i
$604$	0.626686	+	0.862560i	0.0254995	+	0.0350971i
$605$	−3.53809	+	19.0211i	−0.143844	+	0.773319i
$606$	−0.156655	+	0.199747i	−0.00636367	+	0.00811415i
$607$	−14.3533	−	14.3533i	−0.582583	−	0.582583i	0.353030	−	0.935612i	$-0.385152\pi$
$607$	−14.3533	−	14.3533i	−0.582583	−	0.582583i	−0.935612	+	0.353030i	$0.885152\pi$
$608$	−0.339200	−	2.14162i	−0.0137564	−	0.0868542i
$609$	−41.4790	−	15.1841i	−1.68081	−	0.615289i
$610$	7.30474	+	10.6432i	0.295760	+	0.430931i
$611$	13.6526	−	4.43601i	0.552327	−	0.179462i
$612$	−5.99244	−	14.2637i	−0.242230	−	0.576577i
$613$	−12.7810	−	25.0841i	−0.516219	−	1.01314i	−0.991104	−	0.133089i	$-0.957510\pi$
$613$	−12.7810	−	25.0841i	−0.516219	−	1.01314i	0.474885	−	0.880048i	$-0.342490\pi$
$614$	−5.13543	−	15.8052i	−0.207249	−	0.637848i
$615$	−11.2806	+	2.88735i	−0.454879	+	0.116429i
$616$	−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	$0.296078\pi$
$618$	−19.8250	+	18.4187i	−0.797479	+	0.740909i
$619$	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	$0.143917\pi$
$620$	−11.3184	−	11.9426i	−0.454559	−	0.479626i
$621$	28.7134	−	16.3660i	1.15223	−	0.656744i
$622$	−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
$625$	−24.8562	−	2.67754i	−0.994248	−	0.107102i
$626$			8.48916i			0.339295i
$627$	2.79905	−	5.02767i	0.111783	−	0.200786i
$628$	−3.39240	+	21.4188i	−0.135372	+	0.854702i
$629$	32.0330	−	23.2733i	1.27724	−	0.927967i
$630$	15.5036	+	18.9747i	0.617678	+	0.755972i
$631$	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
$633$	−2.66066	−	22.0057i	−0.105752	−	0.874646i
$634$	9.37785	+	3.04705i	0.372442	+	0.121014i
$635$	11.7092	+	39.6236i	0.464664	+	1.57241i
$636$	0.490118	+	1.72125i	0.0194344	+	0.0682520i
$637$	28.4409	−	14.4914i	1.12687	−	0.574169i
$638$	9.53128	−	4.85643i	0.377347	−	0.192268i
$639$	−2.65290	−	10.8104i	−0.104947	−	0.427651i
$640$	−1.84362	+	1.26533i	−0.0728755	+	0.0500166i
$641$	30.1335	+	9.79096i	1.19020	+	0.386720i	0.836147	−	0.548505i	$-0.184803\pi$
$641$	30.1335	+	9.79096i	1.19020	+	0.386720i	0.354054	+	0.935225i	$0.384803\pi$
$642$	−4.30769	+	0.520834i	−0.170011	+	0.0205557i
$643$	11.3185	−	11.3185i	0.446357	−	0.446357i	−0.447785	−	0.894142i	$-0.647787\pi$
$643$	11.3185	−	11.3185i	0.446357	−	0.446357i	0.894142	+	0.447785i	$0.147787\pi$
$644$	−18.7959	−	13.6560i	−0.740660	−	0.538121i
$645$	−3.89252	+	17.3529i	−0.153268	+	0.683271i
$646$	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	$0.839732\pi$
$648$	−5.21658	+	7.33398i	−0.204926	+	0.288106i
$649$			10.4520i			0.410278i
$650$	−25.1283	−	1.34952i	−0.985613	−	0.0529325i
$651$	−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	$0.539929\pi$
$654$	−7.77894	−	11.5789i	−0.304181	−	0.452770i
$655$	3.85264	+	29.4107i	0.150535	+	1.14917i
$656$	−1.76720	+	2.43234i	−0.0689976	+	0.0949670i
$657$	−1.16880	−	1.35464i	−0.0455994	−	0.0528496i
$658$	−10.2903	+	1.62982i	−0.401156	+	0.0635369i
$659$	−1.49604	+	4.60434i	−0.0582774	+	0.179360i	−0.975958	−	0.217960i	$-0.930060\pi$
$659$	−1.49604	+	4.60434i	−0.0582774	+	0.179360i	0.917680	+	0.397320i	$0.130060\pi$
$660$	−5.92212	−	0.377052i	−0.230518	−	0.0146767i
$661$	−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
$663$	−18.9238	−	40.7789i	−0.734940	−	1.58372i
$664$	2.63218	−	0.855246i	0.102148	−	0.0331900i
$665$	−10.7903	+	14.0434i	−0.418432	+	0.544581i
$666$	−21.3239	−	8.70729i	−0.826284	−	0.337401i
$667$	6.94676	+	43.8601i	0.268980	+	1.69827i
$668$	17.0389	+	17.0389i	0.659256	+	0.659256i
$669$	−39.5703	−	31.0337i	−1.52988	−	1.19983i
$670$	−3.24147	−	6.80721i	−0.125229	−	0.262985i
$671$	5.19911	+	7.15597i	0.200710	+	0.276253i
$672$	6.20819	+	1.21867i	0.239486	+	0.0470111i
$673$	22.8312	+	11.6331i	0.880077	+	0.448422i	0.834800	−	0.550553i	$-0.185583\pi$
$673$	22.8312	+	11.6331i	0.880077	+	0.448422i	0.0452767	+	0.998974i	$0.485583\pi$
$674$	−26.2203			−1.00997
$675$	−15.4145	+	20.9139i	−0.593306	+	0.804977i
$676$	−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	$0.765474\pi$
$678$	−18.4394	−	3.61965i	−0.708160	−	0.139012i
$679$	29.3799	+	40.4379i	1.12750	+	1.55187i
$680$	−10.1307	−	5.50900i	−0.388494	−	0.211260i
$681$	5.38568	+	4.22382i	0.206380	+	0.161857i
$682$	−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	$0.847769\pi$
$684$	−6.02223	−	2.45909i	−0.230266	−	0.0940255i
$685$	20.5693	+	7.29895i	0.785912	+	0.278878i
$686$	2.28494	−	0.742422i	0.0872394	−	0.0283458i
$687$	−9.62532	−	20.7416i	−0.367229	−	0.791342i
$688$	2.08465	+	4.09136i	0.0794767	+	0.155982i
$689$	1.60699	+	4.94581i	0.0612214	+	0.188420i
$690$	9.08558	−	22.8973i	0.345882	−	0.871686i
$691$	−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
$693$	10.9682	+	12.7121i	0.416646	+	0.482892i
$694$	6.99576	−	9.62884i	0.265555	−	0.365506i
$695$	−5.18898	+	9.54218i	−0.196829	+	0.361956i
$696$	−6.74357	−	10.0377i	−0.255614	−	0.380480i
$697$	−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
$700$	17.8595	+	3.82031i	0.675026	+	0.144394i
$701$			14.8859i			0.562232i	0.959674	+	0.281116i	$0.0907045\pi$
$701$			14.8859i			0.562232i	−0.959674	+	0.281116i	$0.909295\pi$
$702$	−14.3647	+	21.8533i	−0.542161	+	0.824801i
$703$	2.60428	−	16.4428i	0.0982222	−	0.620150i
$704$	−1.23956	+	0.900593i	−0.0467177	+	0.0339424i
$705$	−4.37961	−	10.1416i	−0.164946	−	0.381954i
$706$	−7.12475	−	5.17643i	−0.268143	−	0.194818i
$707$	0.378543	−	0.378543i	0.0142366	−	0.0142366i
$708$	11.7300	−	1.41825i	0.440842	−	0.0533013i
$709$	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	$0.324638\pi$
$710$	−6.57890	−	5.05493i	−0.246902	−	0.189708i
$711$	−0.951484	−	3.87723i	−0.0356834	−	0.145407i
$712$	5.73613	−	2.92270i	0.214970	−	0.109533i
$713$	41.7019	−	21.2482i	1.56175	−	0.795750i
$714$	8.93533	+	31.3801i	0.334396	+	1.17437i
$715$	−17.2368	−	0.462520i	−0.644621	−	0.0172973i
$716$	−4.28798	−	1.39325i	−0.160249	−	0.0520681i
$717$	3.93856	+	32.5749i	0.147088	+	1.21653i
$718$	−4.85077	+	4.85077i	−0.181029	+	0.181029i
$719$	17.9319	+	13.0283i	0.668748	+	0.485874i	0.869606	−	0.493746i	$-0.164373\pi$
$719$	17.9319	+	13.0283i	0.668748	+	0.485874i	−0.200858	+	0.979620i	$0.564373\pi$
$720$	0.380428	+	6.69741i	0.0141777	+	0.249598i
$721$	46.1690	−	33.5437i	1.71942	−	1.24923i
$722$	−2.23676	+	14.1224i	−0.0832437	+	0.525580i
$723$	19.8066	−	35.5767i	0.736614	−	1.32311i
$724$		−	14.1413i		−	0.525556i
$725$	−18.9746	−	29.3013i	−0.704699	−	1.08822i
$726$	14.9763	+	0.550713i	0.555823	+	0.0204389i
$727$	−8.45889	+	16.6015i	−0.313723	+	0.615716i	−0.992993	−	0.118172i	$-0.962296\pi$
$727$	−8.45889	+	16.6015i	−0.313723	+	0.615716i	0.679270	+	0.733888i	$0.262296\pi$
$728$	18.1574	+	2.87585i	0.672957	+	0.106586i
$729$	10.7076	+	24.7860i	0.396576	+	0.918002i
$730$	−1.31109	−	0.243873i	−0.0485255	−	0.00902614i
$731$	−13.9192	+	19.1581i	−0.514819	+	0.708588i
$732$	7.32548	−	6.80584i	0.270758	−	0.251551i
$733$	2.14436	−	0.339633i	0.0792038	−	0.0125446i	−0.116707	−	0.993166i	$-0.537234\pi$
$733$	2.14436	−	0.339633i	0.0792038	−	0.0125446i	0.195911	+	0.980622i	$0.437234\pi$
$734$	4.58254	−	14.1036i	0.169145	−	0.520574i
$735$	−13.1462	−	20.7495i	−0.484905	−	0.765357i
$736$	−1.96550	−	6.04917i	−0.0724491	−	0.222975i
$737$	−2.34541	−	4.60312i	−0.0863942	−	0.169558i
$738$	3.49352	+	8.31558i	0.128598	+	0.306101i
$739$	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	$0.236059\pi$
$740$	−16.4641	+	4.86529i	−0.605231	+	0.178852i
$741$	−17.7498	−	6.49761i	−0.652057	−	0.238696i
$742$	−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	$-0.545273\pi$
$744$	−7.86527	+	10.0288i	−0.288355	+	0.367674i
$745$	10.6417	−	10.0855i	0.389882	−	0.369505i
$746$	−10.1684	−	13.9956i	−0.372293	−	0.512417i
$747$	1.89765	−	8.08314i	0.0694315	−	0.295746i
$748$	−7.04042	−	3.58727i	−0.257423	−	0.131164i
$749$	9.15060			0.334356
$750$	0.771360	+	19.3495i	0.0281661	+	0.706546i
$751$	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
$753$	−4.55370	+	23.1977i	−0.165946	+	0.845370i
$754$	−20.6537	−	28.4274i	−0.752163	−	1.03526i
$755$	1.73039	−	1.63996i	0.0629755	−	0.0596842i
$756$	12.7782	−	14.0342i	0.464737	−	0.510420i
$757$	2.64953	+	2.64953i	0.0962989	+	0.0962989i	0.753615	−	0.657316i	$-0.228308\pi$
$757$	2.64953	+	2.64953i	0.0962989	+	0.0962989i	−0.657316	+	0.753615i	$0.728308\pi$
$758$	−0.889598	−	5.61670i	−0.0323117	−	0.204008i
$759$	5.80246	−	15.8509i	0.210616	−	0.575350i
$760$	−4.64973	+	1.37404i	−0.168663	+	0.0498417i
$761$	−37.7032	+	12.2505i	−1.36674	+	0.444080i	−0.898287	−	0.439409i	$-0.855188\pi$
$761$	−37.7032	+	12.2505i	−1.36674	+	0.444080i	−0.468452	+	0.883489i	$0.655188\pi$
$762$	29.0308	−	13.4720i	1.05167	−	0.488038i
$763$	13.3553	+	26.2112i	0.483493	+	0.948909i
$764$	3.96247	+	12.1952i	0.143357	+	0.441208i
$765$	−29.8841	+	17.4286i	−1.08046	+	0.630133i
$766$	−9.38083	+	28.8712i	−0.338943	+	1.04316i
$767$	33.9101	−	5.37083i	1.22442	−	0.193929i
$768$	1.17891	+	1.26892i	0.0425403	+	0.0457883i
$769$	−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	$0.339816\pi$
$770$	12.3034	+	2.28853i	0.443382	+	0.0824728i
$771$	29.0286	−	19.5020i	1.04544	−	0.702348i
$772$	−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
$775$	−23.1910	+	28.5629i	−0.833046	+	1.02601i
$776$			13.6841i			0.491231i
$777$	42.4405	+	23.6278i	1.52254	+	0.847644i
$778$	0.206293	−	1.30248i	0.00739595	−	0.0466962i
$779$	−5.27409	+	3.83185i	−0.188964	+	0.137290i
$780$	1.81982	+	19.4072i	0.0651601	+	0.694889i
$781$	−4.59923	−	3.34153i	−0.164573	−	0.119570i
$782$	23.1943	−	23.1943i	0.829428	−	0.829428i
$783$	−36.2382	+	1.69764i	−1.29505	+	0.0606686i
$784$	−6.03185	−	1.95987i	−0.215423	−	0.0699952i
$785$	48.4734	+	1.30070i	1.73009	+	0.0464240i
$786$	22.0977	−	6.29221i	0.788198	−	0.224436i
$787$	4.03430	−	2.05558i	0.143807	−	0.0732734i	−0.380606	−	0.924737i	$-0.624285\pi$
$787$	4.03430	−	2.05558i	0.143807	−	0.0732734i	0.524413	+	0.851464i	$0.324285\pi$
$788$	6.06547	−	3.09051i	0.216074	−	0.110095i
$789$	27.1432	−	7.72889i	0.966322	−	0.275156i
$790$	−2.35958	−	1.81299i	−0.0839500	−	0.0645034i
$791$	37.6892	+	12.2460i	1.34007	+	0.435416i
$792$	0.383678	+	4.58050i	0.0136334	+	0.162761i
$793$	20.5449	−	20.5449i	0.729571	−	0.729571i
$794$	8.98015	+	6.52446i	0.318693	+	0.231544i
$795$	3.67388	−	1.58656i	0.130299	−	0.0562694i
$796$	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	$0.975456\pi$
$798$	11.9859	+	6.67291i	0.424297	+	0.236218i
$799$		−	14.7096i		−	0.520387i
$800$	3.34084	+	3.72005i	0.118117	+	0.131524i
$801$	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
$804$	−4.84772	+	3.25680i	−0.170966	+	0.114858i
$805$	−24.8181	+	45.6389i	−0.874725	+	1.60856i
$806$	−21.7682	+	29.9613i	−0.766752	+	1.05534i
$807$	−12.8792	−	13.8626i	−0.453370	−	0.487985i
$808$	0.144756	−	0.0229270i	0.00509248	−	0.000806570i
$809$	10.9215	−	33.6130i	0.383980	−	1.18177i	−0.553237	−	0.833024i	$-0.686608\pi$
$809$	10.9215	−	33.6130i	0.383980	−	1.18177i	0.937217	−	0.348746i	$-0.113392\pi$
$810$	17.7754	+	9.43579i	0.624565	+	0.331540i
$811$	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
$813$	5.27548	−	2.44813i	0.185019	−	0.0858597i
$814$	−11.1879	+	3.63517i	−0.392135	+	0.127413i
$815$	−21.6669	−	7.68844i	−0.758960	−	0.269314i
$816$	−3.07058	+	8.38805i	−0.107492	+	0.293640i
$817$	1.55755	+	9.83400i	0.0544918	+	0.344048i
$818$	8.03693	+	8.03693i	0.281005	+	0.281005i
$819$	35.6065	−	42.1168i	1.24419	−	1.47168i
$820$	5.90606	+	3.21168i	0.206249	+	0.112157i
$821$	1.62196	+	2.23243i	0.0566067	+	0.0779125i	0.836382	−	0.548147i	$-0.184667\pi$
$821$	1.62196	+	2.23243i	0.0566067	+	0.0779125i	−0.779775	+	0.626060i	$0.784667\pi$
$822$	3.25655	−	16.5897i	0.113585	−	0.578631i
$823$	−18.0680	−	9.20610i	−0.629811	−	0.320905i	0.109786	−	0.993955i	$-0.464984\pi$
$823$	−18.0680	−	9.20610i	−0.629811	−	0.320905i	−0.739596	+	0.673051i	$0.764984\pi$
$824$	15.6235			0.544270
$825$	0.883997	+	13.2396i	0.0307768	+	0.460944i
$826$	−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	$0.668441\pi$
$828$	−18.5764	−	4.36112i	−0.645574	−	0.151559i
$829$	−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	$0.972878\pi$
$830$	−2.66065	−	5.58748i	−0.0923527	−	0.193944i
$831$	−30.0014	+	38.2540i	−1.04074	+	1.32702i
$832$	3.55880	+	3.55880i	0.123379	+	0.123379i
$833$	−5.11663	−	32.3051i	−0.177281	−	1.11931i
$834$	7.90079	+	2.89221i	0.273582	+	0.100149i
$835$	32.8288	−	42.7261i	1.13609	−	1.47860i
$836$	−3.15965	+	1.02663i	−0.109279	+	0.0355068i
$837$	13.5042	+	35.7714i	0.466772	+	1.23644i
$838$	−2.28220	−	4.47907i	−0.0788374	−	0.154727i
$839$	−5.16619	−	15.8999i	−0.178357	−	0.548926i	0.821414	−	0.570332i	$-0.193186\pi$
$839$	−5.16619	−	15.8999i	−0.178357	−	0.548926i	−0.999771	+	0.0214067i	$0.993186\pi$
$840$	0.898888	−	14.1183i	0.0310146	−	0.487127i
$841$	6.10123	−	18.7776i	0.210387	−	0.647505i
$842$	−8.99583	+	1.42480i	−0.310017	+	0.0491018i
$843$	−0.901465	+	0.837518i	−0.0310481	+	0.0288457i
$844$	−7.52218	+	10.3534i	−0.258924	+	0.356379i
$845$	3.58104	+	27.3374i	0.123192	+	0.940434i
$846$	−7.27333	+	4.50757i	−0.250062	+	0.154973i
$847$	−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
$850$	−9.27188	+	24.0610i	−0.318023	+	0.825284i
$851$		−	48.8339i		−	1.67400i
$852$	−3.12604	+	5.61502i	−0.107096	+	0.192367i
$853$	−0.447638	+	2.82627i	−0.0153268	+	0.0967698i	−0.994166	−	0.107862i	$-0.965600\pi$
$853$	−0.447638	+	2.82627i	−0.0153268	+	0.0967698i	0.978839	+	0.204632i	$0.0655996\pi$
$854$	−17.0598	+	12.3946i	−0.583773	+	0.424136i
$855$	−3.70306	+	14.0662i	−0.126642	+	0.481055i
$856$	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	$0.314088\pi$
$858$	1.60322	+	13.2598i	0.0547330	+	0.452683i
$859$	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	$0.475053\pi$
$860$	8.46562	−	5.81020i	0.288675	−	0.198126i
$861$	−5.20919	−	18.2942i	−0.177529	−	0.623465i
$862$	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	$0.451208\pi$
$864$	5.08852	−	1.05213i	0.173115	−	0.0357942i
$865$	−15.2159	−	51.4904i	−0.517357	−	1.75073i
$866$	21.0928	+	6.85347i	0.716763	+	0.232890i
$867$	−16.5004	+	1.99504i	−0.560385	+	0.0677550i
$868$	19.0057	−	19.0057i	0.645097	−	0.645097i
$869$	−1.64955	−	1.19847i	−0.0559572	−	0.0406553i
$870$	−20.2964	+	17.8666i	−0.688112	+	0.605735i
$871$	−13.7290	+	9.97468i	−0.465188	+	0.337979i
$872$	−1.25986	+	7.95446i	−0.0426644	+	0.269372i
$873$	35.1103	+	21.2735i	1.18830	+	0.719999i
$874$		−	13.7915i		−	0.466505i
$875$	3.28316	−	40.7063i	0.110991	−	1.37612i
$876$	−0.0379595	+	1.03228i	−0.00128253	+	0.0348777i
$877$	−17.7609	+	34.8578i	−0.599744	+	1.17706i	0.369100	+	0.929390i	$0.379666\pi$
$877$	−17.7609	+	34.8578i	−0.599744	+	1.17706i	−0.968844	+	0.247673i	$0.920334\pi$
$878$	1.68299	+	0.266559i	0.0567981	+	0.00899594i
$879$	−2.70113	−	4.02061i	−0.0911069	−	0.135612i
$880$	2.35674	+	2.48670i	0.0794456	+	0.0838267i
$881$	−0.436643	+	0.600988i	−0.0147109	+	0.0202478i	−0.816309	−	0.577615i	$-0.803983\pi$
$881$	−0.436643	+	0.600988i	−0.0147109	+	0.0202478i	0.801598	+	0.597863i	$0.203983\pi$
$882$	−14.4058	+	12.4295i	−0.485067	+	0.418523i
$883$	−29.2220	+	4.62830i	−0.983397	+	0.155755i	−0.627371	−	0.778721i	$-0.715869\pi$
$883$	−29.2220	+	4.62830i	−0.983397	+	0.155755i	−0.356027	+	0.934476i	$0.615869\pi$
$884$	−8.02063	+	24.6849i	−0.269763	+	0.830245i
$885$	−6.55122	−	25.5951i	−0.220217	−	0.860369i
$886$	−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	$-0.599596\pi$
$888$	5.59776	+	12.0626i	0.187849	+	0.404795i
$889$	−64.1903	+	20.8567i	−2.15287	+	0.699511i
$890$	−8.14595	−	11.8689i	−0.273053	−	0.397846i
$891$	12.3490	+	6.13648i	0.413707	+	0.205580i
$892$	4.54190	+	28.6765i	0.152074	+	0.960159i
$893$	−4.37321	−	4.37321i	−0.146344	−	0.146344i
$894$	−8.93637	−	7.00851i	−0.298877	−	0.234400i
$895$	−1.84364	+	9.91163i	−0.0616263	+	0.331309i
$896$	−2.14701	−	2.95510i	−0.0717265	−	0.0987230i
$897$	−54.4075	−	10.6802i	−1.81661	−	0.356601i
$898$	11.0761	+	5.64357i	0.369616	+	0.188329i
$899$	−51.3743			−1.71343
$900$	14.7385	−	2.78859i	0.491284	−	0.0929531i
$901$	5.32868			0.177524
$902$	4.10448	+	2.09134i	0.136664	+	0.0696339i
$903$	−28.5071	−	5.59594i	−0.948655	−	0.186221i
$904$	6.37698	+	8.77715i	0.212095	+	0.291924i
$905$	−31.3530	+	4.10706i	−1.04221	+	0.136523i
$906$	−1.45310	−	1.13962i	−0.0482760	−	0.0378613i
$907$	−8.72011	−	8.72011i	−0.289547	−	0.289547i	0.547354	−	0.836901i	$-0.315635\pi$
$907$	−8.72011	−	8.72011i	−0.289547	−	0.289547i	−0.836901	+	0.547354i	$0.815635\pi$
$908$	−0.618172	−	3.90298i	−0.0205148	−	0.129525i
$909$	0.166213	−	0.407052i	0.00551295	−	0.0135011i
$910$	1.10264	−	41.0924i	0.0365523	−	1.36220i
$911$	35.6554	−	11.5852i	1.18132	−	0.383833i	0.348461	−	0.937323i	$-0.386704\pi$
$911$	35.6554	−	11.5852i	1.18132	−	0.383833i	0.832856	+	0.553490i	$0.186704\pi$
$912$	1.58090	+	3.40669i	0.0523489	+	0.112807i
$913$	−1.92515	−	3.77833i	−0.0637133	−	0.125044i
$914$	−11.1290	−	34.2516i	−0.368116	−	1.13294i
$915$	−17.2170	−	14.2649i	−0.569175	−	0.471583i
$916$	−4.07958	+	12.5556i	−0.134793	+	0.414850i
$917$	−47.8574	+	7.57987i	−1.58039	+	0.250309i
$918$	16.7482	+	20.9186i	0.552774	+	0.690416i
$919$	−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	$0.368267\pi$
$920$	−12.8409	+	6.11462i	−0.423353	+	0.201593i
$921$	16.0518	+	23.8930i	0.528925	+	0.787300i
$922$	−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
$925$	15.5687	+	35.0899i	0.511894	+	1.15375i
$926$			6.61685i			0.217443i
$927$	24.2885	−	40.0863i	0.797738	−	1.31661i
$928$	−1.09218	+	6.89573i	−0.0358525	+	0.226364i
$929$	0.652608	−	0.474147i	0.0214114	−	0.0155563i	−0.577028	−	0.816724i	$-0.695788\pi$
$929$	0.652608	−	0.474147i	0.0214114	−	0.0155563i	0.598439	+	0.801168i	$0.295788\pi$
$930$	24.5195	+	14.5256i	0.804025	+	0.476314i
$931$	−11.1256	−	8.08324i	−0.364628	−	0.264918i
$932$	−6.19799	+	6.19799i	−0.203022	+	0.203022i
$933$	5.97258	−	0.722133i	0.195534	−	0.0236416i
$934$	−36.3043	−	11.7960i	−1.18791	−	0.385976i
$935$	−5.90868	+	16.6514i	−0.193234	+	0.544557i
$936$	14.6636	−	3.59850i	0.479295	−	0.117621i
$937$	7.61042	−	3.87770i	0.248622	−	0.126679i	−0.325240	−	0.945632i	$-0.605445\pi$
$937$	7.61042	−	3.87770i	0.248622	−	0.126679i	0.573861	+	0.818953i	$0.305445\pi$
$938$	10.9738	−	5.59143i	0.358308	−	0.182567i
$939$	−4.02673	−	14.1415i	−0.131408	−	0.461492i
$940$	−2.13287	+	6.01069i	−0.0695666	+	0.196047i
$941$	−17.4242	−	5.66148i	−0.568014	−	0.184559i	0.0109101	−	0.999940i	$-0.496527\pi$
$941$	−17.4242	−	5.66148i	−0.568014	−	0.184559i	−0.578924	+	0.815382i	$0.696527\pi$
$942$	−4.50857	−	37.2893i	−0.146897	−	1.21495i
$943$	−13.5220	+	13.5220i	−0.440338	+	0.440338i
$944$	−5.51884	−	4.00967i	−0.179623	−	0.130504i
$945$	−34.8268	−	24.2548i	−1.13292	−	0.789009i
$946$	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	$-0.148586\pi$
$948$	−1.12118	+	2.01387i	−0.0364143	+	0.0654076i
$949$			3.00159i			0.0974356i
$950$	4.39685	+	9.90998i	0.142653	+	0.321522i
$951$	−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	$0.485529\pi$
$954$	−1.63291	−	2.63484i	−0.0528674	−	0.0853060i
$955$	25.8876	−	12.3272i	0.837702	−	0.398898i
$956$	11.1351	−	15.3261i	0.360133	−	0.495681i
$957$	−13.5739	+	12.6111i	−0.438783	+	0.407658i
$958$	−11.4985	+	1.82118i	−0.371500	+	0.0588397i
$959$	−11.0175	+	33.9085i	−0.355775	+	1.09496i
$960$	2.47097	−	2.98233i	0.0797503	−	0.0962543i
$961$	7.15266	+	22.0136i	0.230731	+	0.710117i
$962$	17.5427	+	34.4295i	0.565600	+	1.11005i
$963$	6.92884	−	2.91092i	0.223279	−	0.0938032i
$964$	−22.3583	+	7.26464i	−0.720111	+	0.233978i
$965$	−0.839653	+	31.2915i	−0.0270294	+	1.00731i
$966$	37.7883	+	13.8330i	1.21582	+	0.445070i
$967$	0.835271	+	5.27370i	0.0268605	+	0.169591i	0.997472	−	0.0710616i	$-0.0226387\pi$
$967$	0.835271	+	5.27370i	0.0268605	+	0.169591i	−0.970611	+	0.240652i	$0.922639\pi$
$968$	−6.11819	−	6.11819i	−0.196646	−	0.196646i
$969$	−11.9525	+	15.2403i	−0.383970	+	0.489590i
$970$	30.3394	−	3.97429i	0.974140	−	0.127607i
$971$	−33.9216	−	46.6890i	−1.08859	−	1.49832i	−0.849693	−	0.527278i	$-0.823212\pi$
$971$	−33.9216	−	46.6890i	−1.08859	−	1.49832i	−0.238902	−	0.971044i	$-0.576788\pi$
$972$	5.21116	−	14.6916i	0.167148	−	0.471234i
$973$	−15.8093	−	8.05524i	−0.506823	−	0.258239i
$974$	35.5211			1.13817
$975$	42.4997	−	9.67124i	1.36108	−	0.309727i
$976$	−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	$0.702767\pi$
$978$	−3.43033	+	17.4750i	−0.109690	+	0.558787i
$979$	−5.79785	−	7.98005i	−0.185300	−	0.255043i
$980$	−2.59343	+	13.9426i	−0.0828442	+	0.445379i
$981$	18.4507	+	15.5986i	0.589086	+	0.498026i
$982$	−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	$0.727927\pi$
$984$	1.79011	−	4.89013i	0.0570666	−	0.155892i
$985$	−8.61366	−	12.5503i	−0.274454	−	0.399887i
$986$	−34.2432	+	11.1263i	−1.09053	+	0.354333i
$987$	16.3688	−	7.59608i	0.521024	−	0.241786i
$988$	4.95436	+	9.72349i	0.157619	+	0.309345i
$989$	9.02525	+	27.7769i	0.286986	+	0.883253i
$990$	10.0441	−	2.18098i	0.319223	−	0.0693162i
$991$	−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
$993$	19.5108	+	21.0005i	0.619158	+	0.666432i
$994$	7.96619	−	10.9645i	0.252672	−	0.347773i
$995$	−8.31360	−	8.77206i	−0.263559	−	0.278093i
$996$	−3.97909	+	2.67324i	−0.126082	+	0.0847048i
$997$	36.6391	+	5.80306i	1.16037	+	0.183785i	0.706785	−	0.707428i	$-0.250145\pi$
$997$	36.6391	+	5.80306i	1.16037	+	0.183785i	0.453585	+	0.891213i	$0.350145\pi$
$998$	−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	150.2.l.a.17.6	yes	80
3.2	odd	2	inner	150.2.l.a.17.5	✓	80
5.2	odd	4		750.2.l.a.143.2		80
5.3	odd	4		750.2.l.c.143.9		80
5.4	even	2		750.2.l.b.107.5		80
15.2	even	4		750.2.l.a.143.8		80
15.8	even	4		750.2.l.c.143.3		80
15.14	odd	2		750.2.l.b.107.6		80
25.3	odd	20	inner	150.2.l.a.53.5	yes	80
25.4	even	10		750.2.l.a.257.8		80
25.21	even	5		750.2.l.c.257.3		80
25.22	odd	20		750.2.l.b.743.6		80
75.29	odd	10		750.2.l.a.257.2		80
75.47	even	20		750.2.l.b.743.5		80
75.53	even	20	inner	150.2.l.a.53.6	yes	80
75.71	odd	10		750.2.l.c.257.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.5	✓	80	3.2	odd	2	inner
150.2.l.a.17.6	yes	80	1.1	even	1	trivial
150.2.l.a.53.5	yes	80	25.3	odd	20	inner
150.2.l.a.53.6	yes	80	75.53	even	20	inner
750.2.l.a.143.2		80	5.2	odd	4
750.2.l.a.143.8		80	15.2	even	4
750.2.l.a.257.2		80	75.29	odd	10
750.2.l.a.257.8		80	25.4	even	10
750.2.l.b.107.5		80	5.4	even	2
750.2.l.b.107.6		80	15.14	odd	2
750.2.l.b.743.5		80	75.47	even	20
750.2.l.b.743.6		80	25.22	odd	20
750.2.l.c.143.3		80	15.8	even	4
750.2.l.c.143.9		80	5.3	odd	4
750.2.l.c.257.3		80	25.21	even	5
750.2.l.c.257.9		80	75.71	odd	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(-1.69961 - 0.333634i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.62298 - 1.53816i) q^{5} +(-1.36290 - 1.06888i) q^{6} +(2.58285 + 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.77738 + 1.13410i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(-1.69961 - 0.333634i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.62298 - 1.53816i) q^{5} +(-1.36290 - 1.06888i) q^{6} +(2.58285 + 2.58285i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.77738 + 1.13410i) q^{9} +(2.14440 - 0.633691i) q^{10} +(1.45719 - 0.473470i) q^{11} +(-0.729092 - 1.57112i) q^{12} +(-2.28489 - 4.48435i) q^{13} +(1.12875 + 3.47393i) q^{14} +(-3.27162 + 2.07279i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-5.09363 + 0.806752i) q^{17} +(1.95979 + 2.27139i) q^{18} +(-1.27450 + 1.75421i) q^{19} +(2.19836 + 0.408913i) q^{20} +(-3.52813 - 5.25158i) q^{21} +(1.51332 + 0.239686i) q^{22} +(-2.88760 + 5.66723i) q^{23} +(0.0636485 - 1.73088i) q^{24} +(0.268140 - 4.99280i) q^{25} -5.03290i q^{26} +(-4.34209 - 2.85416i) q^{27} +(-0.571409 + 3.60774i) q^{28} +(5.64831 - 4.10373i) q^{29} +(-3.85607 + 0.361585i) q^{30} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.63463 + 0.318547i) q^{33} +(-4.90472 - 1.59364i) q^{34} +(8.16476 + 0.219087i) q^{35} +(0.714995 + 2.91355i) q^{36} +(-6.84089 + 3.48561i) q^{37} +(-1.93198 + 0.984395i) q^{38} +(2.38730 + 8.38398i) q^{39} +(1.77311 + 1.36238i) q^{40} +(2.85939 + 0.929072i) q^{41} +(-0.759414 - 6.28093i) q^{42} +(3.24693 - 3.24693i) q^{43} +(1.23956 + 0.900593i) q^{44} +(6.25205 - 2.43142i) q^{45} +(-5.14573 + 3.73859i) q^{46} +(-0.446195 + 2.81716i) q^{47} +(0.842515 - 1.51333i) q^{48} +6.34226i q^{49} +(2.50560 - 4.32689i) q^{50} +(8.92637 + 0.328243i) q^{51} +(2.28489 - 4.48435i) q^{52} +(-1.02055 - 0.161639i) q^{53} +(-2.57307 - 4.51434i) q^{54} +(1.63672 - 3.00982i) q^{55} +(-2.14701 + 2.95510i) q^{56} +(2.75143 - 2.55625i) q^{57} +(6.89573 - 1.09218i) q^{58} +(-2.10801 + 6.48779i) q^{59} +(-3.59994 - 1.42844i) q^{60} +(1.78395 + 5.49044i) q^{61} +(-3.34066 - 6.55641i) q^{62} +(4.24434 + 10.1028i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-10.6060 - 3.76349i) q^{65} +(-2.49209 - 0.912268i) q^{66} +(-0.527466 - 3.33029i) q^{67} +(-3.64664 - 3.64664i) q^{68} +(6.79858 - 8.66870i) q^{69} +(7.17539 + 3.90193i) q^{70} +(-2.18090 - 3.00175i) q^{71} +(-0.685659 + 2.92059i) q^{72} +(-0.531390 - 0.270757i) q^{73} -7.67771 q^{74} +(-2.12150 + 8.39638i) q^{75} -2.16832 q^{76} +(4.98661 + 2.54081i) q^{77} +(-1.67915 + 8.55399i) q^{78} +(-0.782199 - 1.07660i) q^{79} +(0.961346 + 2.01886i) q^{80} +(6.42764 + 6.29964i) q^{81} +(2.12595 + 2.12595i) q^{82} +(-0.432953 - 2.73356i) q^{83} +(2.17484 - 5.94112i) q^{84} +(-7.02596 + 9.14415i) q^{85} +(4.36710 - 1.41896i) q^{86} +(-10.9691 + 5.09030i) q^{87} +(0.695596 + 1.36518i) q^{88} +(-1.98939 - 6.12272i) q^{89} +(6.67446 + 0.671961i) q^{90} +(5.68088 - 17.4839i) q^{91} +(-6.28217 + 0.994998i) q^{92} +(8.67494 + 9.33729i) q^{93} +(-1.67653 + 2.30754i) q^{94} +(0.629747 + 4.80743i) q^{95} +(1.43772 - 0.965894i) 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	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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