LMFDB - Embedded newform 750.2.o.b.229.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.10
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.18037 - 1.89914i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-1.62489 + 2.23646i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.18037 - 1.89914i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-1.62489 + 2.23646i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(1.54592 - 1.61559i) q^{10} +(5.34771 - 1.37306i) q^{11} +(0.770513 - 0.637424i) q^{12} +(-0.775277 - 1.95813i) q^{13} +(-2.57029 - 1.01765i) q^{14} +(1.51533 + 1.64432i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.961081 + 1.74820i) q^{17} +(0.587785 + 0.809017i) q^{18} +(0.682490 - 3.57774i) q^{19} +(1.94928 + 1.09558i) q^{20} +(1.17703 - 2.50132i) q^{21} +(2.65984 + 4.83823i) q^{22} +(1.09333 + 0.0687864i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-2.21344 + 4.48338i) q^{25} +(1.70380 - 1.23789i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.346474 - 2.74262i) q^{28} +(7.09032 + 0.895715i) q^{29} +(-1.21581 + 1.87665i) q^{30} +(8.26381 + 4.54307i) q^{31} +(0.951057 + 0.309017i) q^{32} +(-4.99570 + 2.35080i) q^{33} +(-1.93229 - 0.496127i) q^{34} +(6.16532 + 0.446019i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(1.48964 + 0.945351i) q^{37} +(3.63507 - 0.228699i) q^{38} +(1.12846 + 1.77817i) q^{39} +(-0.576390 + 2.16050i) q^{40} +(0.527269 + 8.38070i) q^{41} +(2.71546 + 0.518001i) q^{42} +(5.76846 - 1.87428i) q^{43} +(-4.02476 + 3.77950i) q^{44} +(-1.79660 - 1.33125i) q^{45} +(0.205274 + 1.07609i) q^{46} +(3.60363 - 3.83747i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-0.198397 - 0.610602i) q^{49} +(-4.89299 - 1.02893i) q^{50} +(0.616478 - 1.89732i) q^{51} +(1.62272 + 1.34243i) q^{52} +(8.74324 + 4.11426i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-8.91991 - 8.53531i) q^{55} +(2.74262 - 0.346474i) q^{56} +3.64225i q^{57} +(0.895715 + 7.09032i) q^{58} +(-1.78213 - 2.15423i) q^{59} +(-2.12005 - 0.710912i) q^{60} +(0.782961 - 12.4448i) q^{61} +(-2.34521 + 9.13400i) q^{62} +(-0.687484 + 2.67757i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-2.80363 + 3.78368i) q^{65} +(-3.51932 - 4.25413i) q^{66} +(-1.07998 - 8.54890i) q^{67} -1.99496i q^{68} +(-1.08685 + 0.137301i) q^{69} +(1.10125 + 6.08255i) q^{70} +(-0.857026 - 0.804801i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(-10.1380 - 8.38690i) q^{73} +(-0.545194 + 1.67794i) q^{74} +(1.33413 - 4.81872i) q^{75} +(1.12552 + 3.46399i) q^{76} +(-5.61862 + 14.1910i) q^{77} +(-1.44167 + 1.53522i) q^{78} +(-1.51220 - 7.92722i) q^{79} +(-2.23597 - 0.0209864i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-7.98628 + 2.59490i) q^{82} +(2.50902 + 0.478620i) q^{83} +(0.173579 + 2.75897i) q^{84} +(4.45451 - 0.238304i) q^{85} +(3.24996 + 5.12111i) q^{86} +(-7.13257 + 0.448743i) q^{87} +(-4.66167 - 2.95839i) q^{88} +(-1.02123 + 1.23446i) q^{89} +(0.842628 - 2.07123i) q^{90} +(5.63902 + 1.44785i) q^{91} +(-0.991229 + 0.466437i) q^{92} +(-8.96872 - 2.91411i) q^{93} +(4.61310 + 2.53607i) q^{94} +(-7.60021 + 2.92692i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(1.58942 - 12.5815i) q^{97} +(0.542079 - 0.344014i) q^{98} +(4.46672 - 3.24526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−1.18037	−	1.89914i	−0.527879	−	0.849320i
$5$	−1.18037	−	1.89914i	−0.527879	−	0.849320i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	−1.62489	+	2.23646i	−0.614149	+	0.845304i	−0.996911	−	0.0785433i	$-0.974973\pi$
$7$	−1.62489	+	2.23646i	−0.614149	+	0.845304i	0.382762	+	0.923847i	$0.374973\pi$
$8$	−0.684547	−	0.728969i	−0.242024	−	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	1.54592	−	1.61559i	0.488864	−	0.510893i
$11$	5.34771	−	1.37306i	1.61239	−	0.413993i	0.668360	−	0.743838i	$-0.266997\pi$
$11$	5.34771	−	1.37306i	1.61239	−	0.413993i	0.944035	+	0.329846i	$0.106997\pi$
$12$	0.770513	−	0.637424i	0.222428	−	0.184008i
$13$	−0.775277	−	1.95813i	−0.215023	−	0.543087i	0.781729	−	0.623619i	$-0.214338\pi$
$13$	−0.775277	−	1.95813i	−0.215023	−	0.543087i	−0.996752	+	0.0805319i	$0.974338\pi$
$14$	−2.57029	−	1.01765i	−0.686940	−	0.271979i
$15$	1.51533	+	1.64432i	0.391256	+	0.424561i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−0.961081	+	1.74820i	−0.233096	+	0.424001i	−0.966824	−	0.255443i	$-0.917779\pi$
$17$	−0.961081	+	1.74820i	−0.233096	+	0.424001i	0.733728	+	0.679444i	$0.237779\pi$
$18$	0.587785	+	0.809017i	0.138542	+	0.190687i
$19$	0.682490	−	3.57774i	0.156574	−	0.820790i	−0.814161	−	0.580639i	$-0.802803\pi$
$19$	0.682490	−	3.57774i	0.156574	−	0.820790i	0.970735	−	0.240151i	$-0.0771970\pi$
$20$	1.94928	+	1.09558i	0.435873	+	0.244978i
$21$	1.17703	−	2.50132i	0.256850	−	0.545833i
$22$	2.65984	+	4.83823i	0.567080	+	1.03151i
$23$	1.09333	+	0.0687864i	0.227975	+	0.0143430i	0.176367	−	0.984324i	$-0.443565\pi$
$23$	1.09333	+	0.0687864i	0.227975	+	0.0143430i	0.0516078	+	0.998667i	$0.483565\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−2.21344	+	4.48338i	−0.442688	+	0.896676i
$26$	1.70380	−	1.23789i	0.334144	−	0.242770i
$27$	−0.844328	+	0.535827i	−0.162491	+	0.103120i
$28$	0.346474	−	2.74262i	0.0654774	−	0.518307i
$29$	7.09032	+	0.895715i	1.31664	+	0.166330i	0.752085	−	0.659066i	$-0.229048\pi$
$29$	7.09032	+	0.895715i	1.31664	+	0.166330i	0.564554	+	0.825396i	$0.309048\pi$
$30$	−1.21581	+	1.87665i	−0.221976	+	0.342627i
$31$	8.26381	+	4.54307i	1.48422	+	0.815959i	0.998314	−	0.0580497i	$-0.0184882\pi$
$31$	8.26381	+	4.54307i	1.48422	+	0.815959i	0.485910	+	0.874009i	$0.338488\pi$
$32$	0.951057	+	0.309017i	0.168125	+	0.0546270i
$33$	−4.99570	+	2.35080i	−0.869640	+	0.409221i
$34$	−1.93229	−	0.496127i	−0.331385	−	0.0850851i
$35$	6.16532	+	0.446019i	1.04213	+	0.0753910i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	1.48964	+	0.945351i	0.244895	+	0.155415i	0.652609	−	0.757694i	$-0.273674\pi$
$37$	1.48964	+	0.945351i	0.244895	+	0.155415i	−0.407715	+	0.913109i	$0.633674\pi$
$38$	3.63507	−	0.228699i	0.589686	−	0.0370999i
$39$	1.12846	+	1.77817i	0.180698	+	0.284735i
$40$	−0.576390	+	2.16050i	−0.0911353	+	0.341606i
$41$	0.527269	+	8.38070i	0.0823456	+	1.30885i	0.794690	+	0.607015i	$0.207633\pi$
$41$	0.527269	+	8.38070i	0.0823456	+	1.30885i	−0.712345	+	0.701830i	$0.752367\pi$
$42$	2.71546	+	0.518001i	0.419004	+	0.0799293i
$43$	5.76846	−	1.87428i	0.879681	−	0.285826i	0.165856	−	0.986150i	$-0.446961\pi$
$43$	5.76846	−	1.87428i	0.879681	−	0.285826i	0.713825	+	0.700324i	$0.246961\pi$
$44$	−4.02476	+	3.77950i	−0.606755	+	0.569781i
$45$	−1.79660	−	1.33125i	−0.267822	−	0.198451i
$46$	0.205274	+	1.07609i	0.0302661	+	0.158660i
$47$	3.60363	−	3.83747i	0.525643	−	0.559753i	−0.410279	−	0.911960i	$-0.634569\pi$
$47$	3.60363	−	3.83747i	0.525643	−	0.559753i	0.935922	+	0.352207i	$0.114569\pi$
$48$	−0.368125	+	0.929776i	−0.0531342	+	0.134202i
$49$	−0.198397	−	0.610602i	−0.0283424	−	0.0872288i
$50$	−4.89299	−	1.02893i	−0.691973	−	0.145513i
$51$	0.616478	−	1.89732i	0.0863242	−	0.265678i
$52$	1.62272	+	1.34243i	0.225030	+	0.186161i
$53$	8.74324	+	4.11426i	1.20098	+	0.565136i	0.918990	−	0.394282i	$-0.129007\pi$
$53$	8.74324	+	4.11426i	1.20098	+	0.565136i	0.281986	+	0.959418i	$0.409007\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	−8.91991	−	8.53531i	−1.20276	−	1.15090i
$56$	2.74262	−	0.346474i	0.366498	−	0.0462995i
$57$			3.64225i			0.482428i
$58$	0.895715	+	7.09032i	0.117613	+	0.931004i
$59$	−1.78213	−	2.15423i	−0.232014	−	0.280456i	0.641639	−	0.767007i	$-0.278255\pi$
$59$	−1.78213	−	2.15423i	−0.232014	−	0.280456i	−0.873652	+	0.486551i	$0.838255\pi$
$60$	−2.12005	−	0.710912i	−0.273697	−	0.0917783i
$61$	0.782961	−	12.4448i	0.100248	−	1.59340i	−0.550984	−	0.834516i	$-0.685747\pi$
$61$	0.782961	−	12.4448i	0.100248	−	1.59340i	0.651231	−	0.758879i	$-0.274253\pi$
$62$	−2.34521	+	9.13400i	−0.297842	+	1.16002i
$63$	−0.687484	+	2.67757i	−0.0866148	+	0.337342i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−2.80363	+	3.78368i	−0.347748	+	0.469307i
$66$	−3.51932	−	4.25413i	−0.433199	−	0.523647i
$67$	−1.07998	−	8.54890i	−0.131940	−	1.04441i	−0.909529	−	0.415641i	$-0.863557\pi$
$67$	−1.07998	−	8.54890i	−0.131940	−	1.04441i	0.777589	−	0.628773i	$-0.216443\pi$
$68$		−	1.99496i		−	0.241925i
$69$	−1.08685	+	0.137301i	−0.130842	+	0.0165291i
$70$	1.10125	+	6.08255i	0.131624	+	0.727003i
$71$	−0.857026	−	0.804801i	−0.101710	−	0.0955123i	0.632024	−	0.774949i	$-0.282224\pi$
$71$	−0.857026	−	0.804801i	−0.101710	−	0.0955123i	−0.733734	+	0.679436i	$0.762224\pi$
$72$	−0.904827	−	0.425779i	−0.106635	−	0.0501786i
$73$	−10.1380	−	8.38690i	−1.18656	−	0.981612i	−0.186565	−	0.982443i	$-0.559736\pi$
$73$	−10.1380	−	8.38690i	−1.18656	−	0.981612i	−1.00000		0.000830635i	$0.999736\pi$
$74$	−0.545194	+	1.67794i	−0.0633775	+	0.195056i
$75$	1.33413	−	4.81872i	0.154052	−	0.556418i
$76$	1.12552	+	3.46399i	0.129106	+	0.397347i
$77$	−5.61862	+	14.1910i	−0.640301	+	1.61722i
$78$	−1.44167	+	1.53522i	−0.163237	+	0.173830i
$79$	−1.51220	−	7.92722i	−0.170136	−	0.891882i	−0.960296	−	0.278982i	$-0.910003\pi$
$79$	−1.51220	−	7.92722i	−0.170136	−	0.891882i	0.790161	−	0.612900i	$-0.209997\pi$
$80$	−2.23597	−	0.0209864i	−0.249989	−	0.00234635i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	−7.98628	+	2.59490i	−0.881937	+	0.286559i
$83$	2.50902	+	0.478620i	0.275400	+	0.0525354i	0.323231	−	0.946320i	$-0.395231\pi$
$83$	2.50902	+	0.478620i	0.275400	+	0.0525354i	−0.0478309	+	0.998855i	$0.515231\pi$
$84$	0.173579	+	2.75897i	0.0189391	+	0.301028i
$85$	4.45451	−	0.238304i	0.483159	−	0.0258477i
$86$	3.24996	+	5.12111i	0.350452	+	0.552224i
$87$	−7.13257	+	0.448743i	−0.764691	+	0.0481103i
$88$	−4.66167	−	2.95839i	−0.496936	−	0.315365i
$89$	−1.02123	+	1.23446i	−0.108250	+	0.130852i	−0.821856	−	0.569696i	$-0.807061\pi$
$89$	−1.02123	+	1.23446i	−0.108250	+	0.130852i	0.713605	+	0.700548i	$0.247061\pi$
$90$	0.842628	−	2.07123i	0.0888208	−	0.218326i
$91$	5.63902	+	1.44785i	0.591130	+	0.151776i
$92$	−0.991229	+	0.466437i	−0.103343	+	0.0486294i
$93$	−8.96872	−	2.91411i	−0.930013	−	0.302180i
$94$	4.61310	+	2.53607i	0.475804	+	0.261576i
$95$	−7.60021	+	2.92692i	−0.779765	+	0.300296i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	1.58942	−	12.5815i	0.161381	−	1.27746i	−0.678464	−	0.734633i	$-0.737354\pi$
$97$	1.58942	−	12.5815i	0.161381	−	1.27746i	0.839845	−	0.542826i	$-0.182646\pi$
$98$	0.542079	−	0.344014i	0.0547583	−	0.0347507i
$99$	4.46672	−	3.24526i	0.448922	−	0.326161i
$100$	−0.220233	−	4.99515i	−0.0220233	−	0.499515i
$101$	12.0425	+	8.74937i	1.19827	+	0.870595i	0.994114	−	0.108343i	$-0.0345544\pi$
$101$	12.0425	+	8.74937i	1.19827	+	0.870595i	0.204158	+	0.978938i	$0.434554\pi$
$102$	1.99103	+	0.125265i	0.197141	+	0.0124031i
$103$	5.07265	+	9.22711i	0.499823	+	0.909174i	0.999087	+	0.0427244i	$0.0136037\pi$
$103$	5.07265	+	9.22711i	0.499823	+	0.909174i	−0.499264	+	0.866450i	$0.666396\pi$
$104$	−0.896699	+	1.90558i	−0.0879286	+	0.186858i
$105$	−6.13969	+	0.717147i	−0.599173	+	0.0699864i
$106$	−1.81064	+	9.49173i	−0.175865	+	0.921918i
$107$	0.888595	+	1.22305i	0.0859038	+	0.118236i	0.849806	−	0.527096i	$-0.176719\pi$
$107$	0.888595	+	1.22305i	0.0859038	+	0.118236i	−0.763902	+	0.645332i	$0.776719\pi$
$108$	0.481754	−	0.876307i	0.0463568	−	0.0843226i
$109$	−8.29114	+	13.0647i	−0.794147	+	1.25138i	0.169852	+	0.985470i	$0.445671\pi$
$109$	−8.29114	+	13.0647i	−0.794147	+	1.25138i	−0.963999	+	0.265906i	$0.914329\pi$
$110$	6.04886	−	10.7623i	0.576736	−	1.02615i
$111$	−1.64039	−	0.649477i	−0.155699	−	0.0616456i
$112$	1.01765	+	2.57029i	0.0961590	+	0.242870i
$113$	−11.4343	+	9.45928i	−1.07565	+	0.889855i	−0.994277	−	0.106829i	$-0.965930\pi$
$113$	−11.4343	+	9.45928i	−1.07565	+	0.889855i	−0.0813720	+	0.996684i	$0.525930\pi$
$114$	−3.52783	+	0.905792i	−0.330411	+	0.0848352i
$115$	−1.15990	−	2.15757i	−0.108161	−	0.201195i
$116$	−6.64480	+	2.63086i	−0.616955	+	0.244270i
$117$	−1.44167	−	1.53522i	−0.133282	−	0.141931i
$118$	1.64335	−	2.26188i	0.151283	−	0.208223i
$119$	−2.34814	−	4.99005i	−0.215254	−	0.457437i
$120$	0.161343	−	2.23024i	0.0147285	−	0.203592i
$121$	17.0733	−	9.38613i	1.55212	−	0.853285i
$122$	12.2486	−	2.33654i	1.10893	−	0.211540i
$123$	−2.08832	−	8.13345i	−0.188297	−	0.733369i
$124$	−9.43027			−0.846863
$125$	11.1272	−	1.08844i	0.995250	−	0.0973527i
$126$	−2.76442			−0.246274
$127$	0.528239	+	2.05736i	0.0468737	+	0.182561i	0.987709	−	0.156303i	$-0.0499575\pi$
$127$	0.528239	+	2.05736i	0.0468737	+	0.182561i	−0.940836	+	0.338864i	$0.889958\pi$
$128$	−0.982287	+	0.187381i	−0.0868227	+	0.0165623i
$129$	−5.31507	+	2.92199i	−0.467966	+	0.257267i
$130$	−4.36204	−	1.77459i	−0.382576	−	0.155642i
$131$	−8.14196	−	17.3026i	−0.711367	−	1.51173i	−0.853056	−	0.521820i	$-0.825253\pi$
$131$	−8.14196	−	17.3026i	−0.711367	−	1.51173i	0.141689	−	0.989911i	$-0.454747\pi$
$132$	3.24526	−	4.46672i	0.282464	−	0.388778i
$133$	6.89252	+	7.33978i	0.597657	+	0.636440i
$134$	8.01174	−	3.17207i	0.692109	−	0.274025i
$135$	2.01423	+	0.971019i	0.173357	+	0.0835720i
$136$	1.93229	−	0.496127i	0.165692	−	0.0425426i
$137$	3.00961	−	2.48977i	0.257128	−	0.212715i	−0.499924	−	0.866069i	$-0.666639\pi$
$137$	3.00961	−	2.48977i	0.257128	−	0.212715i	0.757052	+	0.653354i	$0.226639\pi$
$138$	−0.403277	−	1.01856i	−0.0343292	−	0.0867057i
$139$	−18.0821	−	7.15920i	−1.53370	−	0.607235i	−0.558687	−	0.829378i	$-0.688695\pi$
$139$	−18.0821	−	7.15920i	−1.53370	−	0.607235i	−0.975014	+	0.222143i	$0.928695\pi$
$140$	−5.61758	+	2.57932i	−0.474772	+	0.217992i
$141$	−2.82072	+	4.44475i	−0.237548	+	0.374316i
$142$	0.566383	−	1.03025i	0.0475298	−	0.0864564i
$143$	−6.83458	−	9.40699i	−0.571536	−	0.786652i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	−6.66813	−	14.5228i	−0.553758	−	1.20605i
$146$	5.60218	−	11.9052i	0.463640	−	0.985285i
$147$	0.309298	+	0.562611i	0.0255105	+	0.0464033i
$148$	−1.76080	−	0.110780i	−0.144737	−	0.00910609i
$149$	2.33473	+	1.69628i	0.191269	+	0.138965i	0.679298	−	0.733862i	$-0.262284\pi$
$149$	2.33473	+	1.69628i	0.191269	+	0.138965i	−0.488030	+	0.872827i	$0.662284\pi$
$150$	4.99912	+	0.0938498i	0.408176	+	0.00766281i
$151$	10.7598	−	7.81748i	0.875623	−	0.636177i	−0.0564669	−	0.998404i	$-0.517984\pi$
$151$	10.7598	−	7.81748i	0.875623	−	0.636177i	0.932090	+	0.362227i	$0.117984\pi$
$152$	−3.07526	+	1.95162i	−0.249436	+	0.158297i
$153$	−0.250035	+	1.97923i	−0.0202142	+	0.160012i
$154$	−15.1425	−	1.91294i	−1.22022	−	0.154149i
$155$	−1.12647	−	21.0566i	−0.0904804	−	1.69131i
$156$	−1.84552	−	1.01458i	−0.147760	−	0.0812316i
$157$	−13.9352	−	4.52782i	−1.11215	−	0.361359i	−0.305383	−	0.952230i	$-0.598784\pi$
$157$	−13.9352	−	4.52782i	−1.11215	−	0.361359i	−0.806766	+	0.590871i	$0.798784\pi$
$158$	7.30210	−	3.43611i	0.580924	−	0.273362i
$159$	−9.35931	−	2.40306i	−0.742241	−	0.190575i
$160$	−0.535736	−	2.17094i	−0.0423536	−	0.171628i
$161$	−1.93037	+	2.33342i	−0.152135	+	0.183899i
$162$	0.844328	+	0.535827i	0.0663367	+	0.0420985i
$163$	−3.87933	+	0.244066i	−0.303852	+	0.0191168i	−0.213985	−	0.976837i	$-0.568644\pi$
$163$	−3.87933	+	0.244066i	−0.303852	+	0.0191168i	−0.0898674	+	0.995954i	$0.528644\pi$
$164$	−4.49948	−	7.09005i	−0.351350	−	0.553640i
$165$	10.3613	+	6.71270i	0.806624	+	0.522583i
$166$	0.160383	+	2.54922i	0.0124482	+	0.197858i
$167$	15.3567	+	2.92945i	1.18834	+	0.226688i	0.743383	−	0.668866i	$-0.233220\pi$
$167$	15.3567	+	2.92945i	1.18834	+	0.226688i	0.444954	+	0.895553i	$0.353220\pi$
$168$	−2.62912	+	0.854253i	−0.202841	+	0.0659071i
$169$	6.24339	−	5.86293i	0.480261	−	0.450995i
$170$	1.33861	+	4.25530i	0.102667	+	0.326366i
$171$	−0.682490	−	3.57774i	−0.0521913	−	0.273597i
$172$	−4.15199	+	4.42142i	−0.316586	+	0.337130i
$173$	−5.30717	+	13.4044i	−0.403497	+	1.01912i	0.575963	+	0.817476i	$0.304627\pi$
$173$	−5.30717	+	13.4044i	−0.403497	+	1.01912i	−0.979460	+	0.201640i	$0.935373\pi$
$174$	−2.20844	−	6.79689i	−0.167422	−	0.515271i
$175$	−6.43033	−	12.2353i	−0.486087	−	0.924898i
$176$	1.70613	−	5.25094i	0.128605	−	0.395805i
$177$	2.15423	+	1.78213i	0.161922	+	0.133953i
$178$	−1.44964	−	0.682150i	−0.108655	−	0.0511293i
$179$	−6.64366	−	6.23881i	−0.496570	−	0.466311i	0.395332	−	0.918538i	$-0.370629\pi$
$179$	−6.64366	−	6.23881i	−0.496570	−	0.466311i	−0.891903	+	0.452228i	$0.850629\pi$
$180$	2.21571	+	0.301062i	0.165149	+	0.0224399i
$181$	5.02964	−	0.635391i	0.373850	−	0.0472283i	0.0638365	−	0.997960i	$-0.479666\pi$
$181$	5.02964	−	0.635391i	0.373850	−	0.0472283i	0.310014	+	0.950732i	$0.399666\pi$
$182$			5.82192i			0.431550i
$183$	1.56283	+	12.3711i	0.115528	+	0.914498i
$184$	−0.698292	−	0.844090i	−0.0514788	−	0.0622271i
$185$	0.0370260	−	3.94489i	0.00272220	−	0.290034i
$186$	0.592132	−	9.41166i	0.0434172	−	0.690097i
$187$	−2.73920	+	10.6685i	−0.200310	+	0.780157i
$188$	−1.30917	+	5.09886i	−0.0954807	+	0.371873i
$189$	0.173579	−	2.75897i	0.0126260	−	0.200685i
$190$	−4.72507	−	6.63354i	−0.342792	−	0.481247i
$191$	3.42864	+	4.14451i	0.248087	+	0.299886i	0.879827	−	0.475295i	$-0.157659\pi$
$191$	3.42864	+	4.14451i	0.248087	+	0.299886i	−0.631739	+	0.775181i	$0.717659\pi$
$192$	−0.125333	−	0.992115i	−0.00904515	−	0.0715997i
$193$			5.93057i			0.426892i	0.976955	+	0.213446i	$0.0684687\pi$
$193$			5.93057i			0.426892i	−0.976955	+	0.213446i	$0.931531\pi$
$194$	12.5815	−	1.58942i	0.903300	−	0.114113i
$195$	2.04498	−	4.24201i	0.146444	−	0.303776i
$196$	0.468016	+	0.439496i	0.0334297	+	0.0313926i
$197$	22.6004	+	10.6350i	1.61021	+	0.757709i	0.999419	−	0.0340795i	$-0.0108500\pi$
$197$	22.6004	+	10.6350i	1.61021	+	0.757709i	0.610795	+	0.791789i	$0.290850\pi$
$198$	4.25413	+	3.51932i	0.302328	+	0.250107i
$199$	−6.18781	+	19.0441i	−0.438642	+	1.35000i	0.450666	+	0.892693i	$0.351187\pi$
$199$	−6.18781	+	19.0441i	−0.438642	+	1.35000i	−0.889308	+	0.457309i	$0.848813\pi$
$200$	4.78345	−	1.45556i	0.338241	−	0.102923i
$201$	2.66275	+	8.19511i	0.187816	+	0.578038i
$202$	−5.47965	+	13.8400i	−0.385547	+	0.973781i
$203$	−13.5242	+	14.4018i	−0.949212	+	1.01081i
$204$	0.373819	+	1.95963i	0.0261726	+	0.137201i
$205$	15.2937	−	10.8937i	1.06816	−	0.760849i
$206$	−7.67571	+	7.20797i	−0.534792	+	0.502203i
$207$	1.04187	−	0.338525i	0.0724152	−	0.0235291i
$208$	−2.06872	−	0.394629i	−0.143440	−	0.0273626i
$209$	−1.26269	−	20.0698i	−0.0873418	−	1.38826i
$210$	−2.22150	−	5.76846i	−0.153298	−	0.398061i
$211$	4.86648	+	7.66835i	0.335023	+	0.527911i	0.969519	−	0.245014i	$-0.0787927\pi$
$211$	4.86648	+	7.66835i	0.335023	+	0.527911i	−0.634497	+	0.772925i	$0.718793\pi$
$212$	−9.64381	+	0.606737i	−0.662340	+	0.0416709i
$213$	0.992650	+	0.629955i	0.0680153	+	0.0431638i
$214$	−0.963638	+	1.16484i	−0.0658729	+	0.0796267i
$215$	−10.3685	−	8.74273i	−0.707123	−	0.596249i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	−23.5882	+	11.0997i	−1.60127	+	0.753500i
$218$	−14.7162	−	4.78159i	−0.996708	−	0.323850i
$219$	11.5300	+	6.33867i	0.779125	+	0.428327i
$220$	11.9285	+	3.18234i	0.804219	+	0.214554i
$221$	4.16830	+	0.526579i	0.280390	+	0.0354215i
$222$	0.221124	−	1.75037i	0.0148408	−	0.117477i
$223$	0.392058	−	0.248807i	0.0262541	−	0.0166614i	−0.522635	−	0.852557i	$-0.675051\pi$
$223$	0.392058	−	0.248807i	0.0262541	−	0.0166614i	0.548889	+	0.835895i	$0.315051\pi$
$224$	−2.23646	+	1.62489i	−0.149430	+	0.108567i
$225$	−0.407562	+	4.98336i	−0.0271708	+	0.332224i
$226$	−12.0057	−	8.72265i	−0.798607	−	0.580222i
$227$	22.7591	+	1.43188i	1.51057	+	0.0950371i	0.796330	−	0.604862i	$-0.206772\pi$
$227$	22.7591	+	1.43188i	1.51057	+	0.0950371i	0.714242	+	0.699899i	$0.246772\pi$
$228$	−1.75467	−	3.19173i	−0.116206	−	0.211378i
$229$	−3.49159	+	7.42001i	−0.230731	+	0.490328i	−0.986346	−	0.164688i	$-0.947338\pi$
$229$	−3.49159	+	7.42001i	−0.230731	+	0.490328i	0.755615	+	0.655016i	$0.227338\pi$
$230$	1.80133	−	1.66003i	0.118776	−	0.109459i
$231$	2.85997	−	14.9925i	0.188172	−	0.986433i
$232$	−4.20071	−	5.78178i	−0.275790	−	0.379592i
$233$	2.86091	−	5.20398i	0.187425	−	0.340924i	−0.765855	−	0.643013i	$-0.777684\pi$
$233$	2.86091	−	5.20398i	0.187425	−	0.340924i	0.953280	+	0.302089i	$0.0976840\pi$
$234$	1.12846	−	1.77817i	0.0737698	−	0.116243i
$235$	−11.5415	−	2.31413i	−0.752885	−	0.150957i
$236$	2.59950	+	1.02921i	0.169213	+	0.0669962i
$237$	2.97083	+	7.50345i	0.192976	+	0.487401i
$238$	4.24932	−	3.51534i	0.275442	−	0.227866i
$239$	8.40801	−	2.15881i	0.543869	−	0.139642i	0.0332471	−	0.999447i	$-0.489415\pi$
$239$	8.40801	−	2.15881i	0.543869	−	0.139642i	0.510622	+	0.859805i	$0.329415\pi$
$240$	2.20030	−	0.398364i	0.142029	−	0.0257143i
$241$	−0.862734	+	0.341581i	−0.0555736	+	0.0220031i	−0.395747	−	0.918360i	$-0.629514\pi$
$241$	−0.862734	+	0.341581i	−0.0555736	+	0.0220031i	0.340173	+	0.940363i	$0.389514\pi$
$242$	13.3372	+	14.2027i	0.857349	+	0.912983i
$243$	−0.587785	+	0.809017i	−0.0377064	+	0.0518985i
$244$	5.30922	+	11.2827i	0.339888	+	0.722299i
$245$	−0.925434	+	1.09752i	−0.0591238	+	0.0701180i
$246$	7.35858	−	4.04541i	0.469166	−	0.257926i
$247$	−7.53479	+	1.43734i	−0.479427	+	0.0914556i
$248$	−2.34521	−	9.13400i	−0.148921	−	0.580010i
$249$	−2.55426			−0.161870
$250$	3.82147	+	10.5070i	0.241691	+	0.664519i
$251$	−19.2631			−1.21588			−0.607938	−	0.793984i	$-0.708003\pi$
$251$	−19.2631			−1.21588			−0.607938	+	0.793984i	$0.708003\pi$
$252$	−0.687484	−	2.67757i	−0.0433074	−	0.168671i
$253$	5.94125	−	1.13335i	0.373523	−	0.0712534i
$254$	−1.86135	+	1.02329i	−0.116792	+	0.0642068i
$255$	−4.33095	+	1.06877i	−0.271215	+	0.0669292i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	10.7441	−	14.7880i	0.670200	−	0.922451i	−0.329565	−	0.944133i	$-0.606902\pi$
$257$	10.7441	−	14.7880i	0.670200	−	0.922451i	0.999765	+	0.0216820i	$0.00690214\pi$
$258$	−4.15199	−	4.42142i	−0.258492	−	0.275266i
$259$	−4.53473	+	1.79543i	−0.281775	+	0.111562i
$260$	0.634043	−	4.66632i	0.0393217	−	0.289393i
$261$	6.92214	−	1.77730i	0.428470	−	0.110012i
$262$	14.7341	−	12.1891i	0.910278	−	0.753048i
$263$	3.59076	+	9.06923i	0.221416	+	0.559233i	0.997443	−	0.0714670i	$-0.0227681\pi$
$263$	3.59076	+	9.06923i	0.221416	+	0.559233i	−0.776027	+	0.630699i	$0.782768\pi$
$264$	5.13345	+	2.03248i	0.315942	+	0.125090i
$265$	−2.50675	−	21.4610i	−0.153988	−	1.31834i
$266$	−5.39509	+	8.50131i	−0.330794	+	0.521248i
$267$	0.771828	−	1.40395i	0.0472351	−	0.0859203i
$268$	5.06486	+	6.97118i	0.309385	+	0.425832i
$269$	1.44649	−	7.58276i	0.0881940	−	0.462329i	−0.910603	−	0.413283i	$-0.864382\pi$
$269$	1.44649	−	7.58276i	0.0881940	−	0.462329i	0.998797	−	0.0490459i	$-0.0156181\pi$
$270$	−0.439594	+	2.19243i	−0.0267528	+	0.133427i
$271$	−8.14216	+	17.3030i	−0.494601	+	1.05108i	0.489259	+	0.872139i	$0.337267\pi$
$271$	−8.14216	+	17.3030i	−0.494601	+	1.05108i	−0.983860	+	0.178942i	$0.942733\pi$
$272$	0.961081	+	1.74820i	0.0582741	+	0.106000i
$273$	−5.81043	−	0.365562i	−0.351664	−	0.0221248i
$274$	3.16000	+	2.29588i	0.190903	+	0.138699i
$275$	−5.68089	+	27.0150i	−0.342570	+	1.62906i
$276$	0.886270	−	0.643913i	0.0533472	−	0.0387590i
$277$	−24.4769	+	15.5335i	−1.47067	+	0.933317i	−0.472011	+	0.881593i	$0.656472\pi$
$277$	−24.4769	+	15.5335i	−1.47067	+	0.933317i	−0.998661	+	0.0517242i	$0.983528\pi$
$278$	2.43745	−	19.2944i	0.146189	−	1.15720i
$279$	9.35591	+	1.18193i	0.560124	+	0.0707601i
$280$	−3.89532	−	4.79965i	−0.232790	−	0.286834i
$281$	−13.9142	−	7.64940i	−0.830052	−	0.456325i	0.00927175	−	0.999957i	$-0.497049\pi$
$281$	−13.9142	−	7.64940i	−0.830052	−	0.456325i	−0.839324	+	0.543632i	$0.817049\pi$
$282$	−5.00660	−	1.62674i	−0.298138	−	0.0968711i
$283$	2.06174	−	0.970179i	0.122557	−	0.0576711i	−0.363523	−	0.931585i	$-0.618426\pi$
$283$	2.06174	−	0.970179i	0.122557	−	0.0576711i	0.486080	+	0.873914i	$0.338426\pi$
$284$	1.13873	+	0.292377i	0.0675714	+	0.0173494i
$285$	6.91714	−	4.29922i	0.409736	−	0.254664i
$286$	7.41176	−	8.95928i	0.438267	−	0.529773i
$287$	−19.5999	−	12.4385i	−1.15694	−	0.734219i
$288$	0.998027	−	0.0627905i	0.0588093	−	0.00369997i
$289$	6.97653	+	10.9932i	0.410384	+	0.646662i
$290$	12.4082	−	10.0703i	0.728635	−	0.591349i
$291$	0.796279	+	12.6565i	0.0466787	+	0.741937i
$292$	12.9244	+	2.46547i	0.756345	+	0.144281i
$293$	−18.9365	+	6.15283i	−1.10628	+	0.359452i	−0.804517	−	0.593930i	$-0.797576\pi$
$293$	−18.9365	+	6.15283i	−1.10628	+	0.359452i	−0.301764	+	0.953383i	$0.597576\pi$
$294$	−0.468016	+	0.439496i	−0.0272952	+	0.0256319i
$295$	−1.98759	+	5.92730i	−0.115722	+	0.345101i
$296$	−0.330594	−	1.73304i	−0.0192154	−	0.100731i
$297$	−3.77950	+	4.02476i	−0.219309	+	0.233540i
$298$	−1.06237	+	2.68323i	−0.0615413	+	0.155436i
$299$	−0.712940	−	2.19420i	−0.0412304	−	0.126894i
$300$	1.15233	+	4.86540i	0.0665297	+	0.280904i
$301$	−5.18131	+	15.9464i	−0.298646	+	0.919138i
$302$	10.2477	+	8.47767i	0.589691	+	0.487835i
$303$	−13.4686	−	6.33786i	−0.773753	−	0.364101i
$304$	−2.65509	−	2.49329i	−0.152280	−	0.143000i
$305$	−24.5586	+	13.2026i	−1.40622	+	0.755977i
$306$	−1.97923	+	0.250035i	−0.113145	+	0.0142936i
$307$		−	23.2102i		−	1.32468i	−0.749205	−	0.662338i	$-0.769564\pi$
$307$		−	23.2102i		−	1.32468i	0.749205	−	0.662338i	$-0.230436\pi$
$308$	−1.91294	−	15.1425i	−0.109000	−	0.862823i
$309$	−6.71178	−	8.11315i	−0.381820	−	0.461541i
$310$	20.1149	−	6.32765i	1.14245	−	0.359386i
$311$	1.88079	−	29.8943i	0.106650	−	1.69515i	−0.473623	−	0.880728i	$-0.657054\pi$
$311$	1.88079	−	29.8943i	0.106650	−	1.69515i	0.580273	−	0.814422i	$-0.302946\pi$
$312$	0.523746	−	2.03985i	0.0296513	−	0.115484i
$313$	−6.68288	+	26.0281i	−0.377738	+	1.47119i	0.441250	+	0.897384i	$0.354535\pi$
$313$	−6.68288	+	26.0281i	−0.377738	+	1.47119i	−0.818988	+	0.573810i	$0.805465\pi$
$314$	0.920027	−	14.6234i	0.0519201	−	0.825247i
$315$	5.89656	−	1.85491i	0.332234	−	0.104512i
$316$	5.14412	+	6.21817i	0.289379	+	0.349799i
$317$	0.113678	+	0.899854i	0.00638479	+	0.0505408i	0.994985	−	0.100022i	$-0.0318914\pi$
$317$	0.113678	+	0.899854i	0.00638479	+	0.0505408i	−0.988600	+	0.150563i	$0.951891\pi$
$318$		−	9.66288i		−	0.541868i
$319$	39.1468	−	4.94539i	2.19180	−	0.276889i
$320$	1.96951	−	1.05880i	0.110099	−	0.0591885i
$321$	−1.10203	−	1.03488i	−0.0615094	−	0.0577612i
$322$	−2.74018	−	1.28943i	−0.152704	−	0.0718571i
$323$	5.59868	+	4.63163i	0.311519	+	0.257711i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	10.4951	+	0.858333i	0.582161	+	0.0476118i
$326$	−1.20115	−	3.69675i	−0.0665254	−	0.204744i
$327$	5.69619	−	14.3869i	0.315000	−	0.795600i
$328$	5.74833	−	6.12134i	0.317398	−	0.337995i
$329$	2.72688	+	14.2948i	0.150338	+	0.788100i
$330$	−3.92506	+	11.7051i	−0.216068	+	0.644347i
$331$	8.03445	−	7.54485i	0.441613	−	0.414703i	−0.431581	−	0.902074i	$-0.642044\pi$
$331$	8.03445	−	7.54485i	0.441613	−	0.414703i	0.873195	+	0.487371i	$0.162044\pi$
$332$	−2.42924	+	0.789309i	−0.133322	+	0.0433190i
$333$	1.73304	+	0.330594i	0.0949697	+	0.0181164i
$334$	0.981643	+	15.6028i	0.0537131	+	0.853746i
$335$	−14.9608	+	12.1419i	−0.817393	+	0.663384i
$336$	−1.48125	−	2.33408i	−0.0808089	−	0.127334i
$337$	24.4696	−	1.53950i	1.33295	−	0.0838619i	0.619735	−	0.784811i	$-0.287240\pi$
$337$	24.4696	−	1.53950i	1.33295	−	0.0838619i	0.713211	+	0.700949i	$0.247240\pi$
$338$	7.23140	+	4.58919i	0.393336	+	0.249619i
$339$	9.45928	−	11.4343i	0.513758	−	0.621026i
$340$	−3.78871	+	2.35480i	−0.205472	+	0.127707i
$341$	50.4303	+	12.9483i	2.73096	+	0.701190i
$342$	3.29561	−	1.55080i	0.178206	−	0.0838575i
$343$	−16.7159	−	5.43132i	−0.902573	−	0.293264i
$344$	−5.31507	−	2.92199i	−0.286570	−	0.157543i
$345$	1.54364	+	1.90201i	0.0831070	+	0.102401i
$346$	−14.3031	−	1.80690i	−0.768939	−	0.0971396i
$347$	−2.13455	+	16.8967i	−0.114589	+	0.907062i	0.825090	+	0.565002i	$0.191125\pi$
$347$	−2.13455	+	16.8967i	−0.114589	+	0.907062i	−0.939678	+	0.342060i	$0.888875\pi$
$348$	6.03413	−	3.82938i	0.323463	−	0.205276i
$349$	−6.27406	+	4.55837i	−0.335843	+	0.244004i	−0.742906	−	0.669396i	$-0.766553\pi$
$349$	−6.27406	+	4.55837i	−0.335843	+	0.244004i	0.407063	+	0.913400i	$0.366553\pi$
$350$	10.2517	−	9.27109i	0.547977	−	0.495561i
$351$	1.70380	+	1.23789i	0.0909424	+	0.0660735i
$352$	5.51027	+	0.346677i	0.293698	+	0.0184779i
$353$	6.71655	+	12.2174i	0.357486	+	0.650265i	0.992501	−	0.122235i	$-0.0390061\pi$
$353$	6.71655	+	12.2174i	0.357486	+	0.650265i	−0.635015	+	0.772500i	$0.719006\pi$
$354$	−1.19041	+	2.52974i	−0.0632694	+	0.134454i
$355$	−0.516817	+	2.57757i	−0.0274298	+	0.136803i
$356$	0.300208	−	1.57374i	0.0159110	−	0.0834082i
$357$	3.24159	+	4.46166i	0.171563	+	0.236136i
$358$	4.39060	−	7.98647i	0.232050	−	0.422098i
$359$	4.36878	−	6.88410i	0.230575	−	0.363329i	−0.709265	−	0.704942i	$-0.750973\pi$
$359$	4.36878	−	6.88410i	0.230575	−	0.363329i	0.939841	+	0.341613i	$0.110973\pi$
$360$	0.259420	+	2.22097i	0.0136727	+	0.117055i
$361$	5.33133	+	2.11082i	0.280596	+	0.111096i
$362$	1.86625	+	4.71361i	0.0980879	+	0.247742i
$363$	−15.0121	+	12.4191i	−0.787932	+	0.651834i
$364$	−5.63902	+	1.44785i	−0.295565	+	0.0758881i
$365$	−3.96122	+	29.1531i	−0.207340	+	1.52595i
$366$	−11.5938	+	4.59030i	−0.606016	+	0.239939i
$367$	8.70508	+	9.26997i	0.454402	+	0.483889i	0.914848	−	0.403799i	$-0.132311\pi$
$367$	8.70508	+	9.26997i	0.454402	+	0.483889i	−0.460446	+	0.887688i	$0.652311\pi$
$368$	0.643913	−	0.886270i	0.0335663	−	0.0462000i
$369$	3.57538	+	7.59807i	0.186127	+	0.395540i
$370$	3.83016	−	0.945191i	0.199121	−	0.0491381i
$371$	−23.4081	+	12.8687i	−1.21529	+	0.668112i
$372$	9.26323	−	1.76706i	0.480276	−	0.0916176i
$373$	3.37772	+	13.1554i	0.174892	+	0.681158i	0.994176	+	0.107771i	$0.0343712\pi$
$373$	3.37772	+	13.1554i	0.174892	+	0.681158i	−0.819284	+	0.573388i	$0.805629\pi$
$374$	−11.0145			−0.569548
$375$	−10.7262	+	3.15419i	−0.553898	+	0.162882i
$376$	−5.26425			−0.271483
$377$	−3.74304	−	14.5782i	−0.192776	−	0.750814i
$378$	2.71546	−	0.518001i	0.139668	−	0.0266431i
$379$	6.87550	−	3.77984i	0.353171	−	0.194157i	−0.295286	−	0.955409i	$-0.595415\pi$
$379$	6.87550	−	3.77984i	0.353171	−	0.194157i	0.648456	+	0.761252i	$0.275415\pi$
$380$	5.25006	−	6.22631i	0.269322	−	0.319403i
$381$	−0.904393	−	1.92193i	−0.0463335	−	0.0984636i
$382$	−3.16164	+	4.35162i	−0.161763	+	0.222648i
$383$	16.4872	+	17.5571i	0.842455	+	0.897124i	0.995847	−	0.0910418i	$-0.0290197\pi$
$383$	16.4872	+	17.5571i	0.842455	+	0.897124i	−0.153392	+	0.988165i	$0.549020\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	33.5827	−	6.08016i	1.71154	−	0.309874i
$386$	−5.74425	+	1.47487i	−0.292375	+	0.0750691i
$387$	4.67340	−	3.86618i	0.237562	−	0.196529i
$388$	4.66838	+	11.7910i	0.237001	+	0.598596i
$389$	−15.9734	−	6.32433i	−0.809885	−	0.320656i	−0.0735658	−	0.997290i	$-0.523438\pi$
$389$	−15.9734	−	6.32433i	−0.809885	−	0.320656i	−0.736319	+	0.676634i	$0.763438\pi$
$390$	4.61730	+	0.925792i	0.233806	+	0.0468793i
$391$	−1.17103	+	1.84525i	−0.0592215	+	0.0933182i
$392$	−0.309298	+	0.562611i	−0.0156219	+	0.0284161i
$393$	11.2399	+	15.4704i	0.566979	+	0.780380i
$394$	−4.68034	+	24.5352i	−0.235792	+	1.23607i
$395$	−13.2699	+	12.2289i	−0.667682	+	0.615305i
$396$	−2.35080	+	4.99570i	−0.118132	+	0.251043i
$397$	−18.0476	−	32.8284i	−0.905782	−	1.64761i	−0.751651	−	0.659561i	$-0.770742\pi$
$397$	−18.0476	−	32.8284i	−0.905782	−	1.64761i	−0.154131	−	0.988050i	$-0.549258\pi$
$398$	−19.9847	−	1.25733i	−1.00174	−	0.0630242i
$399$	−8.14577	−	5.91825i	−0.407799	−	0.296283i
$400$	2.59942	+	4.27118i	0.129971	+	0.213559i
$401$	−14.9619	+	10.8705i	−0.747163	+	0.542845i	−0.894946	−	0.446174i	$-0.852786\pi$
$401$	−14.9619	+	10.8705i	−0.747163	+	0.542845i	0.147784	+	0.989020i	$0.452786\pi$
$402$	−7.27544	+	4.61714i	−0.362866	+	0.230282i
$403$	2.48916	−	19.7037i	0.123994	−	0.981512i
$404$	−14.7679	−	1.86563i	−0.734733	−	0.0928184i
$405$	−2.16050	−	0.576390i	−0.107356	−	0.0286411i
$406$	−17.3127	−	9.51772i	−0.859213	−	0.472357i
$407$	9.26416	+	3.01011i	0.459207	+	0.149205i
$408$	−1.80510	+	0.849414i	−0.0893656	+	0.0420523i
$409$	−36.7671	−	9.44020i	−1.81802	−	0.466788i	−0.823138	−	0.567842i	$-0.807778\pi$
$409$	−36.7671	−	9.44020i	−1.81802	−	0.466788i	−0.994881	+	0.101054i	$0.967778\pi$
$410$	14.3549	+	12.1041i	0.708936	+	0.597778i
$411$	−2.48977	+	3.00961i	−0.122811	+	0.148453i
$412$	−8.89039	−	5.64201i	−0.437998	−	0.277962i
$413$	7.71361	−	0.485299i	0.379562	−	0.0238800i
$414$	0.586993	+	0.924953i	0.0288491	+	0.0454590i
$415$	−2.05261	−	5.32991i	−0.100759	−	0.261635i
$416$	−0.132238	−	2.10186i	−0.00648350	−	0.103052i
$417$	19.1033	+	3.64415i	0.935492	+	0.178455i
$418$	19.1253	−	6.21417i	0.935447	−	0.303945i
$419$	−6.14570	+	5.77119i	−0.300237	+	0.281941i	−0.819993	−	0.572373i	$-0.806023\pi$
$419$	−6.14570	+	5.77119i	−0.300237	+	0.281941i	0.519756	+	0.854315i	$0.326023\pi$
$420$	5.03477	−	3.58626i	0.245671	−	0.174992i
$421$	7.22775	+	37.8892i	0.352259	+	1.84661i	0.511390	+	0.859348i	$0.329131\pi$
$421$	7.22775	+	37.8892i	0.352259	+	1.84661i	−0.159132	+	0.987257i	$0.550869\pi$
$422$	−6.21719	+	6.62064i	−0.302648	+	0.322288i
$423$	1.93790	−	4.89457i	0.0942239	−	0.237982i
$424$	−2.98599	−	9.18995i	−0.145013	−	0.446303i
$425$	−5.71055	−	8.17843i	−0.277002	−	0.396712i
$426$	−0.363302	+	1.11813i	−0.0176020	+	0.0541735i
$427$	26.5602	+	21.9725i	1.28534	+	1.06332i
$428$	−1.36789	−	0.643680i	−0.0661194	−	0.0311134i
$429$	8.47621	+	7.95969i	0.409235	+	0.384298i
$430$	5.88953	−	12.2169i	0.284018	−	0.589153i
$431$	−24.9382	+	3.15043i	−1.20123	+	0.151751i	−0.700372	−	0.713778i	$-0.746982\pi$
$431$	−24.9382	+	3.15043i	−1.20123	+	0.151751i	−0.500859	+	0.865529i	$0.666982\pi$
$432$			1.00000i			0.0481125i
$433$	−1.08742	−	8.60780i	−0.0522580	−	0.413665i	−0.996444	−	0.0842530i	$-0.973150\pi$
$433$	−1.08742	−	8.60780i	−0.0522580	−	0.413665i	0.944186	−	0.329412i	$-0.106850\pi$
$434$	−16.6172	−	20.0867i	−0.797649	−	0.964192i
$435$	9.27131	+	13.0160i	0.444525	+	0.624071i
$436$	0.971592	−	15.4430i	0.0465308	−	0.739586i
$437$	0.992286	−	3.86470i	0.0474675	−	0.184874i
$438$	−3.27213	+	12.7441i	−0.156349	+	0.608937i
$439$	1.22103	−	19.4077i	0.0582764	−	0.926277i	−0.854921	−	0.518759i	$-0.826394\pi$
$439$	1.22103	−	19.4077i	0.0582764	−	0.926277i	0.913197	−	0.407518i	$-0.133606\pi$
$440$	−0.115869	+	12.3452i	−0.00552385	+	0.588532i
$441$	−0.409242	−	0.494689i	−0.0194877	−	0.0235566i
$442$	0.526579	+	4.16830i	0.0250468	+	0.198266i
$443$		−	12.9626i		−	0.615874i	−0.951407	−	0.307937i	$-0.900361\pi$
$443$		−	12.9626i		−	0.615874i	0.951407	−	0.307937i	$-0.0996385\pi$
$444$	1.75037	−	0.221124i	0.0830691	−	0.0104941i
$445$	3.54983	+	0.482338i	0.168278	+	0.0228650i
$446$	0.338492	+	0.317865i	0.0160280	+	0.0150513i
$447$	−2.61123	−	1.22875i	−0.123507	−	0.0581180i
$448$	−2.13002	−	1.76211i	−0.100634	−	0.0832518i
$449$	1.62227	−	4.99284i	0.0765598	−	0.235627i	−0.905451	−	0.424450i	$-0.860467\pi$
$449$	1.62227	−	4.99284i	0.0765598	−	0.235627i	0.982011	+	0.188823i	$0.0604674\pi$
$450$	−4.92816	+	0.844554i	−0.232316	+	0.0398127i
$451$	14.3269	+	44.0935i	0.674626	+	2.07628i
$452$	5.46292	−	13.7978i	0.256954	−	0.648992i
$453$	−9.10440	+	9.69520i	−0.427762	+	0.455520i
$454$	4.27305	+	22.4001i	0.200544	+	1.05129i
$455$	−3.90647	−	12.4183i	−0.183138	−	0.582177i
$456$	2.65509	−	2.49329i	0.124336	−	0.116759i
$457$	−29.9127	+	9.71922i	−1.39926	+	0.454646i	−0.908951	−	0.416904i	$-0.863115\pi$
$457$	−29.9127	+	9.71922i	−1.39926	+	0.454646i	−0.490306	+	0.871550i	$0.663115\pi$
$458$	−8.05522	−	1.53662i	−0.376396	−	0.0718013i
$459$	−0.125265	−	1.99103i	−0.00584686	−	0.0929332i
$460$	2.05585	+	1.33191i	0.0958544	+	0.0621006i
$461$	−1.45164	−	2.28743i	−0.0676098	−	0.106536i	0.808841	−	0.588027i	$-0.200095\pi$
$461$	−1.45164	−	2.28743i	−0.0676098	−	0.106536i	−0.876451	+	0.481491i	$0.840095\pi$
$462$	15.2327	−	0.958361i	0.708690	−	0.0445870i
$463$	−8.73978	−	5.54643i	−0.406172	−	0.257765i	0.317010	−	0.948422i	$-0.397321\pi$
$463$	−8.73978	−	5.54643i	−0.406172	−	0.257765i	−0.723182	+	0.690658i	$0.757321\pi$
$464$	4.55546	−	5.50660i	0.211482	−	0.255638i
$465$	5.05213	+	20.4726i	0.234287	+	0.949393i
$466$	5.75197	+	1.47685i	0.266455	+	0.0684139i
$467$	18.6108	−	8.75760i	0.861207	−	0.405253i	0.0561300	−	0.998423i	$-0.482124\pi$
$467$	18.6108	−	8.75760i	0.861207	−	0.405253i	0.805077	+	0.593170i	$0.202124\pi$
$468$	2.00294	+	0.650796i	0.0925861	+	0.0300830i
$469$	20.8741	+	11.4757i	0.963879	+	0.529897i
$470$	−0.628829	−	11.7544i	−0.0290057	−	0.542190i
$471$	14.5368	+	1.83642i	0.669820	+	0.0846179i
$472$	−0.350411	+	2.77379i	−0.0161290	+	0.127674i
$473$	28.2745	−	17.9436i	1.30006	−	0.825045i
$474$	−6.52890	+	4.74352i	−0.299882	+	0.217877i
$475$	14.5297	+	10.9790i	0.666669	+	0.503750i
$476$	4.46166	+	3.24159i	0.204500	+	0.148578i
$477$	9.64381	+	0.606737i	0.441560	+	0.0277806i
$478$	4.18198	+	7.60699i	0.191279	+	0.347935i
$479$	2.44020	−	5.18570i	0.111496	−	0.236941i	−0.841290	−	0.540584i	$-0.818203\pi$
$479$	2.44020	−	5.18570i	0.111496	−	0.236941i	0.952786	+	0.303644i	$0.0982032\pi$
$480$	0.933040	+	2.03210i	0.0425873	+	0.0927523i
$481$	0.696237	−	3.64980i	0.0317457	−	0.166417i
$482$	−0.545402	−	0.750682i	−0.0248424	−	0.0341926i
$483$	1.45894	−	2.65380i	0.0663841	−	0.120752i
$484$	−10.4397	+	16.4503i	−0.474530	+	0.747739i
$485$	−25.7701	+	11.8324i	−1.17016	+	0.537280i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	−11.8423	−	29.9102i	−0.536625	−	1.35536i	−0.904892	−	0.425641i	$-0.860049\pi$
$487$	−11.8423	−	29.9102i	−0.536625	−	1.35536i	0.368267	−	0.929720i	$-0.379951\pi$
$488$	−9.60785	+	7.94831i	−0.434927	+	0.359803i
$489$	3.76488	−	0.966656i	0.170254	−	0.0437137i
$490$	−1.29319	−	0.623418i	−0.0584202	−	0.0281632i
$491$	15.7236	−	6.22542i	0.709596	−	0.280949i	0.0145297	−	0.999894i	$-0.495375\pi$
$491$	15.7236	−	6.22542i	0.709596	−	0.280949i	0.695067	+	0.718945i	$0.255375\pi$
$492$	5.74833	+	6.12134i	0.259155	+	0.275972i
$493$	−8.38026	+	11.5344i	−0.377428	+	0.519485i
$494$	−3.26601	−	6.94062i	−0.146945	−	0.312273i
$495$	−11.4356	−	4.65229i	−0.513991	−	0.209105i
$496$	8.26381	−	4.54307i	0.371056	−	0.203990i
$497$	3.19248	−	0.608998i	0.143202	−	0.0273173i
$498$	−0.635218	−	2.47401i	−0.0284648	−	0.110863i
$499$	10.6423			0.476415			0.238207	−	0.971214i	$-0.423440\pi$
$499$	10.6423			0.476415			0.238207	+	0.971214i	$0.423440\pi$
$500$	−9.22651	+	6.31439i	−0.412622	+	0.282388i
$501$	−15.6336			−0.698459
$502$	−4.79054	−	18.6579i	−0.213812	−	0.832744i
$503$	16.5739	−	3.16165i	0.738995	−	0.140971i	0.195878	−	0.980628i	$-0.437244\pi$
$503$	16.5739	−	3.16165i	0.738995	−	0.140971i	0.543116	+	0.839657i	$0.317244\pi$
$504$	2.42248	−	1.33177i	0.107906	−	0.0593218i
$505$	2.40164	−	33.1978i	0.106871	−	1.47728i
$506$	2.57528	+	5.47274i	0.114485	+	0.243293i
$507$	−5.03420	+	6.92898i	−0.223576	+	0.307727i
$508$	−1.45404	−	1.54839i	−0.0645126	−	0.0686989i
$509$	−11.3343	+	4.48757i	−0.502384	+	0.198908i	−0.605628	−	0.795748i	$-0.707078\pi$
$509$	−11.3343	+	4.48757i	−0.502384	+	0.198908i	0.103244	+	0.994656i	$0.467078\pi$
$510$	−2.11226	−	3.92909i	−0.0935324	−	0.173983i
$511$	35.2301	−	9.04555i	1.55849	−	0.400152i
$512$	0.770513	−	0.637424i	0.0340522	−	0.0281704i
$513$	1.34080	+	3.38648i	0.0591979	+	0.149517i
$514$	16.9954	+	6.72894i	0.749634	+	0.296801i
$515$	11.5359	−	20.5251i	0.508334	−	0.904443i
$516$	3.24996	−	5.12111i	0.143071	−	0.225444i
$517$	14.0021	−	25.4697i	0.615810	−	1.12015i
$518$	−2.86676	−	3.94576i	−0.125958	−	0.173367i
$519$	2.70143	−	14.1614i	0.118580	−	0.621617i
$520$	4.67740	−	0.546344i	0.205118	−	0.0239588i
$521$	−16.7756	+	35.6499i	−0.734951	+	1.56185i	0.0895447	+	0.995983i	$0.471459\pi$
$521$	−16.7756	+	35.6499i	−0.734951	+	1.56185i	−0.824496	+	0.565868i	$0.808541\pi$
$522$	3.44293	+	6.26267i	0.150693	+	0.274110i
$523$	5.46237	+	0.343663i	0.238853	+	0.0150273i	0.181766	−	0.983342i	$-0.441819\pi$
$523$	5.46237	+	0.343663i	0.238853	+	0.0150273i	0.0570871	+	0.998369i	$0.481819\pi$
$524$	15.4704	+	11.2399i	0.675829	+	0.491018i
$525$	8.60909	+	10.8136i	0.375731	+	0.471945i
$526$	−7.89131	+	5.73338i	−0.344078	+	0.249987i
$527$	−15.8844	+	10.0805i	−0.691935	+	0.439115i
$528$	−0.691985	+	5.47763i	−0.0301148	+	0.238383i
$529$	−21.6280	−	2.73225i	−0.940348	−	0.118794i
$530$	20.1633	−	7.76512i	0.875839	−	0.337295i
$531$	−2.45001	−	1.34690i	−0.106321	−	0.0584506i
$532$	−9.57593	−	3.11141i	−0.415169	−	0.134897i
$533$	16.0017	−	7.52982i	0.693110	−	0.326153i
$534$	1.55179	+	0.398431i	0.0671524	+	0.0172418i
$535$	1.27386	−	3.13122i	0.0550737	−	0.135374i
$536$	−5.49259	+	6.63939i	−0.237244	+	0.286778i
$537$	7.69502	+	4.88341i	0.332065	+	0.210735i
$538$	7.70426	−	0.484711i	0.332154	−	0.0208974i
$539$	−1.89936	−	2.99291i	−0.0818112	−	0.128914i
$540$	−2.23288	+	0.119453i	−0.0960876	+	0.00514043i
$541$	−0.590909	−	9.39224i	−0.0254052	−	0.403804i	−0.990093	−	0.140410i	$-0.955158\pi$
$541$	−0.590909	−	9.39224i	−0.0254052	−	0.403804i	0.964688	−	0.263394i	$-0.0848420\pi$
$542$	−18.7842	−	3.58329i	−0.806852	−	0.153915i
$543$	−4.82149	+	1.56660i	−0.206910	+	0.0672291i
$544$	−1.45427	+	1.36565i	−0.0623511	+	0.0585516i
$545$	34.5984	+	0.324734i	1.48203	+	0.0139101i
$546$	−1.09092	−	5.71880i	−0.0466870	−	0.244742i
$547$	−5.17128	+	5.50685i	−0.221108	+	0.235456i	−0.829953	−	0.557833i	$-0.811633\pi$
$547$	−5.17128	+	5.50685i	−0.221108	+	0.235456i	0.608845	+	0.793289i	$0.291633\pi$
$548$	−1.43789	+	3.63169i	−0.0614235	+	0.155138i
$549$	−3.85326	−	11.8591i	−0.164453	−	0.506135i
$550$	−27.5790	+	1.21594i	−1.17597	+	0.0518479i
$551$	8.04371	−	24.7560i	0.342673	−	1.05464i
$552$	0.844090	+	0.698292i	0.0359269	+	0.0297213i
$553$	20.1861	+	9.49885i	0.858400	+	0.403932i
$554$	−21.1326	−	19.8449i	−0.897839	−	0.843127i
$555$	0.702828	+	3.88195i	0.0298334	+	0.164780i
$556$	19.2944	−	2.43745i	0.818265	−	0.103371i
$557$		−	38.7380i		−	1.64138i	−0.571372	−	0.820691i	$-0.693589\pi$
$557$		−	38.7380i		−	1.64138i	0.571372	−	0.820691i	$-0.306411\pi$
$558$	1.18193	+	9.35591i	0.0500349	+	0.396067i
$559$	−8.14224	−	9.84228i	−0.344380	−	0.416284i
$560$	3.68013	−	4.96656i	0.155514	−	0.209876i
$561$	0.691608	−	10.9928i	0.0291997	−	0.464116i
$562$	3.94876	−	15.3794i	0.166568	−	0.648740i
$563$	−2.98070	+	11.6091i	−0.125622	+	0.489264i	0.874370	+	0.485259i	$0.161275\pi$
$563$	−2.98070	+	11.6091i	−0.125622	+	0.489264i	−0.999992	+	0.00400482i	$0.998725\pi$
$564$	0.330545	−	5.25386i	0.0139184	−	0.221227i
$565$	31.4612	+	10.5498i	1.32358	+	0.443835i
$566$	1.45243	+	1.75569i	0.0610503	+	0.0737971i
$567$	0.346474	+	2.74262i	0.0145505	+	0.115179i
$568$			1.17567i			0.0493300i
$569$	−22.0952	+	2.79128i	−0.926281	+	0.117016i	−0.573979	−	0.818870i	$-0.694601\pi$
$569$	−22.0952	+	2.79128i	−0.926281	+	0.117016i	−0.352302	+	0.935886i	$0.614601\pi$
$570$	5.88437	+	5.63065i	0.246469	+	0.235842i
$571$	13.7004	+	12.8655i	0.573344	+	0.538406i	0.916064	−	0.401032i	$-0.131348\pi$
$571$	13.7004	+	12.8655i	0.573344	+	0.538406i	−0.342720	+	0.939437i	$0.611348\pi$
$572$	10.5210	+	4.95082i	0.439907	+	0.207004i
$573$	−4.14451	−	3.42864i	−0.173139	−	0.143233i
$574$	7.17339	−	22.0774i	0.299412	−	0.921494i
$575$	−2.72841	+	4.74955i	−0.113783	+	0.198070i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−10.8649	+	27.4417i	−0.452313	+	1.14241i	0.507470	+	0.861670i	$0.330581\pi$
$577$	−10.8649	+	27.4417i	−0.452313	+	1.14241i	−0.959783	+	0.280743i	$0.909419\pi$
$578$	−8.91288	+	9.49126i	−0.370727	+	0.394784i
$579$	−1.11128	−	5.82553i	−0.0461832	−	0.242101i
$580$	12.8397	+	9.51399i	0.533140	+	0.395047i
$581$	−5.14728	+	4.83362i	−0.213545	+	0.200532i
$582$	−12.0608	+	3.91880i	−0.499938	+	0.162440i
$583$	52.4054	+	9.99686i	2.17041	+	0.414028i
$584$	0.826165	+	13.1315i	0.0341870	+	0.543386i
$585$	−1.21389	+	4.55006i	−0.0501881	+	0.188122i
$586$	−10.6688	−	16.8114i	−0.440726	−	0.694473i
$587$	−5.94714	+	0.374162i	−0.245465	+	0.0154433i	−0.185046	−	0.982730i	$-0.559244\pi$
$587$	−5.94714	+	0.374162i	−0.245465	+	0.0154433i	−0.0604184	+	0.998173i	$0.519244\pi$
$588$	−0.542079	−	0.344014i	−0.0223550	−	0.0141869i
$589$	21.8939	−	26.4652i	0.902122	−	1.09048i
$590$	−6.23538	−	0.451087i	−0.256706	−	0.0185710i
$591$	−24.1929	−	6.21168i	−0.995163	−	0.255514i
$592$	1.59637	−	0.751196i	0.0656105	−	0.0308740i
$593$	−19.9774	−	6.49106i	−0.820375	−	0.266556i	−0.131389	−	0.991331i	$-0.541944\pi$
$593$	−19.9774	−	6.49106i	−0.820375	−	0.266556i	−0.688986	+	0.724775i	$0.741944\pi$
$594$	−4.83823	−	2.65984i	−0.198515	−	0.109135i
$595$	−6.70511	+	10.3496i	−0.274883	+	0.424290i
$596$	−2.86313	−	0.361698i	−0.117279	−	0.0148157i
$597$	2.50969	−	19.8663i	0.102715	−	0.813072i
$598$	1.94797	−	1.23622i	0.0796584	−	0.0505527i
$599$	−2.71844	+	1.97506i	−0.111073	+	0.0806989i	−0.641935	−	0.766759i	$-0.721868\pi$
$599$	−2.71844	+	1.97506i	−0.111073	+	0.0806989i	0.530862	+	0.847458i	$0.321868\pi$
$600$	−4.42597	+	2.32610i	−0.180690	+	0.0949627i
$601$	−13.6190	−	9.89482i	−0.555532	−	0.403618i	0.274289	−	0.961647i	$-0.411558\pi$
$601$	−13.6190	−	9.89482i	−0.555532	−	0.403618i	−0.829821	+	0.558029i	$0.811558\pi$
$602$	−16.7340	−	1.05281i	−0.682027	−	0.0429095i
$603$	−4.15120	−	7.55100i	−0.169050	−	0.307501i
$604$	−5.66282	+	12.0341i	−0.230417	+	0.489661i
$605$	−37.9784	−	21.3454i	−1.54404	−	0.867815i
$606$	2.78923	−	14.6217i	0.113305	−	0.593965i
$607$	−15.5073	−	21.3440i	−0.629422	−	0.866326i	0.368574	−	0.929598i	$-0.379846\pi$
$607$	−15.5073	−	21.3440i	−0.629422	−	0.866326i	−0.997996	+	0.0632728i	$0.979846\pi$
$608$	1.75467	−	3.19173i	0.0711612	−	0.129442i
$609$	10.5860	−	16.6809i	0.428967	−	0.675944i
$610$	−18.8953	−	20.5037i	−0.765047	−	0.830170i
$611$	−10.3081	−	4.08125i	−0.417020	−	0.165110i
$612$	−0.734395	−	1.85487i	−0.0296862	−	0.0749787i
$613$	1.62025	−	1.34039i	0.0654414	−	0.0541378i	−0.604128	−	0.796887i	$-0.706479\pi$
$613$	1.62025	−	1.34039i	0.0654414	−	0.0541378i	0.669570	+	0.742749i	$0.266479\pi$
$614$	22.4810	−	5.77214i	0.907260	−	0.232945i
$615$	−12.9815	+	13.5665i	−0.523466	+	0.547054i
$616$	14.1910	−	5.61862i	0.571772	−	0.226381i
$617$	−13.3815	−	14.2499i	−0.538721	−	0.573679i	0.400802	−	0.916164i	$-0.368731\pi$
$617$	−13.3815	−	14.2499i	−0.538721	−	0.573679i	−0.939523	+	0.342485i	$0.888731\pi$
$618$	6.18911	−	8.51858i	0.248963	−	0.342668i
$619$	17.1572	+	36.4609i	0.689605	+	1.46549i	0.875651	+	0.482944i	$0.160433\pi$
$619$	17.1572	+	36.4609i	0.689605	+	1.46549i	−0.186046	+	0.982541i	$0.559567\pi$
$620$	11.1312	+	17.9094i	0.447041	+	0.719258i
$621$	−0.959986	+	0.527757i	−0.0385229	+	0.0211781i
$622$	29.4228	−	5.61271i	1.17975	−	0.225049i
$623$	−1.10143	−	4.28979i	−0.0441279	−	0.171867i
$624$	2.10602			0.0843082
$625$	−15.2014	−	19.8474i	−0.608055	−	0.793895i
$626$	−26.8723			−1.07403
$627$	5.00103	+	19.4777i	0.199722	+	0.777865i
$628$	14.3928	−	2.74557i	0.574335	−	0.109560i
$629$	−3.08432	+	1.69562i	−0.122980	+	0.0676089i
$630$	3.26305	+	5.25001i	0.130003	+	0.209166i
$631$	−2.12796	−	4.52214i	−0.0847126	−	0.180023i	0.857982	−	0.513679i	$-0.171718\pi$
$631$	−2.12796	−	4.52214i	−0.0847126	−	0.180023i	−0.942695	+	0.333656i	$0.891718\pi$
$632$	−4.74352	+	6.52890i	−0.188687	+	0.259706i
$633$	−6.21719	−	6.62064i	−0.247111	−	0.263147i
$634$	−0.843313	+	0.333891i	−0.0334922	+	0.0132605i
$635$	3.28368	−	3.43165i	0.130309	−	0.136181i
$636$	9.35931	−	2.40306i	0.371121	−	0.0952876i
$637$	−1.04182	+	0.861871i	−0.0412786	+	0.0341486i
$638$	14.5254	+	36.6871i	0.575068	+	1.45245i
$639$	−1.09311	−	0.432793i	−0.0432427	−	0.0171210i
$640$	1.51533	+	1.64432i	0.0598986	+	0.0649974i
$641$	−17.7018	+	27.8936i	−0.699180	+	1.10173i	0.290282	+	0.956941i	$0.406251\pi$
$641$	−17.7018	+	27.8936i	−0.699180	+	1.10173i	−0.989462	+	0.144791i	$0.953749\pi$
$642$	0.728300	−	1.32477i	0.0287437	−	0.0522846i
$643$	−27.5169	−	37.8737i	−1.08516	−	1.49359i	−0.853711	−	0.520748i	$-0.825653\pi$
$643$	−27.5169	−	37.8737i	−1.08516	−	1.49359i	−0.231449	−	0.972847i	$-0.574347\pi$
$644$	0.567465	−	2.97476i	0.0223613	−	0.117222i
$645$	11.8230	+	6.64502i	0.465531	+	0.261647i
$646$	−3.09378	+	6.57462i	−0.121723	+	0.258675i
$647$	−10.9865	−	19.9844i	−0.431924	−	0.785666i	0.567362	−	0.823469i	$-0.307964\pi$
$647$	−10.9865	−	19.9844i	−0.431924	−	0.785666i	−0.999285	+	0.0378025i	$0.987964\pi$
$648$	−0.998027	−	0.0627905i	−0.0392062	−	0.00246664i
$649$	−12.4882	−	9.07320i	−0.490204	−	0.356154i
$650$	1.77865	+	10.3788i	0.0697643	+	0.407090i
$651$	21.0905	−	15.3231i	0.826600	−	0.600560i
$652$	3.28190	−	2.08276i	0.128529	−	0.0815670i
$653$	−3.36693	+	26.6520i	−0.131758	+	1.04297i	0.778126	+	0.628108i	$0.216171\pi$
$653$	−3.36693	+	26.6520i	−0.131758	+	1.04297i	−0.909884	+	0.414863i	$0.863829\pi$
$654$	15.3515	+	1.93935i	0.600292	+	0.0758346i
$655$	−23.2494	+	35.8862i	−0.908428	+	1.40219i
$656$	7.35858	+	4.04541i	0.287304	+	0.157947i
$657$	−12.5135	−	4.06589i	−0.488199	−	0.158625i
$658$	−13.1676	+	6.19619i	−0.513326	+	0.241553i
$659$	31.9765	+	8.21017i	1.24563	+	0.319823i	0.813274	−	0.581882i	$-0.197683\pi$
$659$	31.9765	+	8.21017i	1.24563	+	0.319823i	0.432353	+	0.901704i	$0.357683\pi$
$660$	−12.3135	−	0.890799i	−0.479303	−	0.0346743i
$661$	−18.7603	+	22.6773i	−0.729690	+	0.882044i	−0.996660	−	0.0816607i	$-0.973978\pi$
$661$	−18.7603	+	22.6773i	−0.729690	+	0.882044i	0.266970	+	0.963705i	$0.413978\pi$
$662$	9.30590	+	5.90571i	0.361684	+	0.229532i
$663$	−4.19314	+	0.263810i	−0.162848	+	0.0102455i
$664$	−1.36864	−	2.15663i	−0.0531135	−	0.0836935i
$665$	5.80351	−	21.7535i	0.225051	−	0.843565i
$666$	0.110780	+	1.76080i	0.00429265	+	0.0682298i
$667$	7.69043	+	1.46703i	0.297775	+	0.0568036i
$668$	−14.8685	+	4.83105i	−0.575278	+	0.186919i
$669$	−0.338492	+	0.317865i	−0.0130868	+	0.0122894i
$670$	−15.4810	−	11.4712i	−0.598085	−	0.443170i
$671$	−12.9004	−	67.6263i	−0.498015	−	2.61068i
$672$	1.89238	−	2.01518i	0.0730000	−	0.0777371i
$673$	16.6943	−	42.1650i	0.643519	−	1.62534i	−0.129960	−	0.991519i	$-0.541485\pi$
$673$	16.6943	−	42.1650i	0.643519	−	1.62534i	0.773478	−	0.633823i	$-0.218515\pi$
$674$	7.57649	+	23.3180i	0.291835	+	0.898177i
$675$	−0.533446	−	4.97146i	−0.0205323	−	0.191352i
$676$	−2.64663	+	8.14550i	−0.101794	+	0.313288i
$677$	11.1012	+	9.18372i	0.426654	+	0.352959i	0.825834	−	0.563914i	$-0.190705\pi$
$677$	11.1012	+	9.18372i	0.426654	+	0.352959i	−0.399180	+	0.916873i	$0.630705\pi$
$678$	13.4275	+	6.31851i	0.515680	+	0.242661i
$679$	25.5555	+	23.9982i	0.980730	+	0.920967i
$680$	−3.22303	−	3.08406i	−0.123598	−	0.118268i
$681$	−22.6242	+	2.85811i	−0.866963	+	0.109523i
$682$			52.0661i			1.99371i
$683$	−2.27367	−	17.9980i	−0.0869996	−	0.688673i	−0.973943	−	0.226794i	$-0.927176\pi$
$683$	−2.27367	−	17.9980i	−0.0869996	−	0.688673i	0.886943	−	0.461879i	$-0.152824\pi$
$684$	2.32166	+	2.80640i	0.0887709	+	0.107306i
$685$	−8.28087	−	2.77681i	−0.316396	−	0.106096i
$686$	1.10361	−	17.5414i	0.0421362	−	0.669735i
$687$	2.03937	−	7.94284i	0.0778070	−	0.303038i
$688$	1.50838	−	5.87476i	0.0575065	−	0.223973i
$689$	1.27780	−	20.3101i	0.0486803	−	0.773751i
$690$	−1.45837	+	1.96816i	−0.0555192	+	0.0749266i
$691$	−0.100632	−	0.121643i	−0.00382822	−	0.00462752i	0.768596	−	0.639735i	$-0.220956\pi$
$691$	−0.100632	−	0.121643i	−0.00382822	−	0.00462752i	−0.772424	+	0.635107i	$0.780956\pi$
$692$	−1.80690	−	14.3031i	−0.0686881	−	0.543722i
$693$			15.2628i			0.579787i
$694$	−16.8967	+	2.13455i	−0.641389	+	0.0810263i
$695$	7.74729	+	42.7908i	0.293872	+	1.62315i
$696$	5.20970	+	4.89223i	0.197473	+	0.185440i
$697$	−15.1579	−	7.13276i	−0.574146	−	0.270173i
$698$	−5.97546	−	4.94333i	−0.226174	−	0.187108i
$699$	−1.83511	+	5.64788i	−0.0694102	+	0.213623i
$700$	11.5293	+	7.62400i	0.435767	+	0.288160i
$701$	−7.48137	−	23.0253i	−0.282567	−	0.869653i	−0.987117	−	0.159999i	$-0.948851\pi$
$701$	−7.48137	−	23.0253i	−0.282567	−	0.869653i	0.704550	−	0.709654i	$-0.251149\pi$
$702$	−0.775277	+	1.95813i	−0.0292610	+	0.0739047i
$703$	4.39888	−	4.68433i	0.165907	−	0.176673i
$704$	1.03456	+	5.42337i	0.0389916	+	0.204401i
$705$	11.7707	+	0.110478i	0.443310	+	0.00416082i
$706$	−10.1632	+	9.54388i	−0.382497	+	0.359189i
$707$	−39.1353	+	12.7158i	−1.47184	+	0.478228i
$708$	−2.74631	−	0.523887i	−0.103213	−	0.0196889i
$709$	−1.24727	−	19.8248i	−0.0468422	−	0.744535i	−0.949420	−	0.314008i	$-0.898328\pi$
$709$	−1.24727	−	19.8248i	−0.0468422	−	0.744535i	0.902578	−	0.430526i	$-0.141672\pi$
$710$	−2.62512	+	0.140437i	−0.0985191	+	0.00527050i
$711$	−4.32421	−	6.81387i	−0.162171	−	0.255540i
$712$	1.59896	−	0.100598i	0.0599236	−	0.00377007i
$713$	8.72256	+	5.53550i	0.326662	+	0.207306i
$714$	−3.51534	+	4.24932i	−0.131558	+	0.159027i
$715$	−9.79781	+	24.0836i	−0.366417	+	0.900674i
$716$	8.82745	+	2.26650i	0.329897	+	0.0847033i
$717$	−7.85456	+	3.69608i	−0.293334	+	0.138033i
$718$	7.75429	+	2.51952i	0.289388	+	0.0940277i
$719$	45.3594	+	24.9365i	1.69162	+	0.929976i	0.971797	+	0.235818i	$0.0757769\pi$
$719$	45.3594	+	24.9365i	1.69162	+	0.929976i	0.719823	+	0.694158i	$0.244223\pi$
$720$	−2.08668	+	0.803603i	−0.0777659	+	0.0299485i
$721$	−28.8786	−	3.64821i	−1.07549	−	0.135867i
$722$	−0.718659	+	5.68877i	−0.0267457	+	0.211714i
$723$	0.783447	−	0.497191i	0.0291367	−	0.0184907i
$724$	−4.10140	+	2.97984i	−0.152427	+	0.110745i
$725$	−19.7098	+	29.8060i	−0.732004	+	1.10697i
$726$	−15.7623	−	11.4520i	−0.584994	−	0.425023i
$727$	−12.7923	−	0.804821i	−0.474439	−	0.0298492i	−0.176228	−	0.984349i	$-0.556390\pi$
$727$	−12.7923	−	0.804821i	−0.474439	−	0.0298492i	−0.298210	+	0.954500i	$0.596390\pi$
$728$	−2.80473	−	5.10179i	−0.103950	−	0.189085i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−29.2224	+	3.41332i	−1.08157	+	0.126333i
$731$	−2.26733	+	11.8858i	−0.0838602	+	0.439611i
$732$	−7.32934	−	10.0880i	−0.270900	−	0.372862i
$733$	12.4712	−	22.6849i	0.460632	−	0.837887i	−0.539359	−	0.842076i	$-0.681333\pi$
$733$	12.4712	−	22.6849i	0.460632	−	0.837887i	0.999991	+	0.00418875i	$0.00133332\pi$
$734$	−6.81387	+	10.7369i	−0.251505	+	0.396308i
$735$	0.703388	−	1.25149i	0.0259448	−	0.0461619i
$736$	1.01856	+	0.403277i	0.0375447	+	0.0148650i
$737$	−17.5135	−	44.2342i	−0.645120	−	1.62939i
$738$	−6.47021	+	5.35262i	−0.238172	+	0.197033i
$739$	−37.7491	+	9.69231i	−1.38862	+	0.356537i	−0.867709	−	0.497073i	$-0.834408\pi$
$739$	−37.7491	+	9.69231i	−1.38862	+	0.356537i	−0.520912	+	0.853610i	$0.674408\pi$
$740$	1.86802	+	3.47477i	0.0686697	+	0.127735i
$741$	7.13199	−	2.82376i	0.262000	−	0.103733i
$742$	−18.2858	−	19.4724i	−0.671293	−	0.714855i
$743$	28.6194	−	39.3912i	1.04994	−	1.44512i	0.161086	−	0.986940i	$-0.448500\pi$
$743$	28.6194	−	39.3912i	1.04994	−	1.44512i	0.888858	−	0.458183i	$-0.151500\pi$
$744$	4.01521	+	8.53276i	0.147205	+	0.312826i
$745$	0.465617	−	6.43623i	0.0170589	−	0.235805i
$746$	−11.9020	+	6.54321i	−0.435765	+	0.239564i
$747$	2.50902	−	0.478620i	0.0918001	−	0.0175118i
$748$	−2.73920	−	10.6685i	−0.100155	−	0.390078i
$749$	−4.17917			−0.152703
$750$	−5.72259	−	9.60479i	−0.208959	−	0.350717i
$751$	−20.1155			−0.734027			−0.367013	−	0.930216i	$-0.619620\pi$
$751$	−20.1155			−0.734027			−0.367013	+	0.930216i	$0.619620\pi$
$752$	−1.30917	−	5.09886i	−0.0477403	−	0.185936i
$753$	18.9219	−	3.60955i	0.689552	−	0.131539i
$754$	13.1893	−	7.25088i	0.480326	−	0.264062i
$755$	−27.5471	−	11.2069i	−1.00254	−	0.407859i
$756$	1.17703	+	2.50132i	0.0428083	+	0.0909722i
$757$	6.28050	−	8.64437i	0.228269	−	0.314185i	−0.679484	−	0.733690i	$-0.737796\pi$
$757$	6.28050	−	8.64437i	0.228269	−	0.314185i	0.907753	+	0.419505i	$0.137796\pi$
$758$	5.37096	+	5.71949i	0.195082	+	0.207741i
$759$	−5.62364	+	2.22656i	−0.204125	+	0.0808190i
$760$	7.33634	+	3.53670i	0.266117	+	0.128289i
$761$	−8.62606	+	2.21480i	−0.312695	+	0.0802863i	−0.401776	−	0.915738i	$-0.631607\pi$
$761$	−8.62606	+	2.21480i	−0.312695	+	0.0802863i	0.0890813	+	0.996024i	$0.471607\pi$
$762$	1.63664	−	1.35395i	0.0592892	−	0.0490483i
$763$	−15.7467	−	39.7716i	−0.570068	−	1.43983i
$764$	−5.00117	−	1.98010i	−0.180936	−	0.0716376i
$765$	4.05397	−	1.86138i	0.146572	−	0.0672984i
$766$	−12.9053	+	20.3355i	−0.466287	+	0.734750i
$767$	−2.83660	+	5.15976i	−0.102424	+	0.186308i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	5.68831	−	29.8192i	0.205126	−	1.07531i	−0.719518	−	0.694473i	$-0.755637\pi$
$769$	5.68831	−	29.8192i	0.205126	−	1.07531i	0.924644	−	0.380833i	$-0.124363\pi$
$770$	14.2408	+	31.0156i	0.513204	+	1.11772i
$771$	−7.78281	+	16.5393i	−0.280291	+	0.595649i
$772$	−2.85708	−	5.19700i	−0.102828	−	0.187044i
$773$	23.8315	+	1.49935i	0.857158	+	0.0539278i	0.485285	−	0.874356i	$-0.338716\pi$
$773$	23.8315	+	1.49935i	0.857158	+	0.0539278i	0.371873	+	0.928284i	$0.378716\pi$
$774$	4.90694	+	3.56510i	0.176376	+	0.128145i
$775$	−38.6597	+	26.9940i	−1.38870	+	0.969653i
$776$	−10.2596	+	7.45401i	−0.368297	+	0.267583i
$777$	4.11798	−	2.61335i	0.147732	−	0.0937534i
$778$	2.15321	−	17.0444i	0.0771962	−	0.611071i
$779$	30.3438	+	3.83331i	1.08718	+	0.137343i
$780$	0.251570	+	4.70248i	0.00900764	+	0.168376i
$781$	−5.68816	−	3.12709i	−0.203538	−	0.111896i
$782$	−2.07850	−	0.675345i	−0.0743270	−	0.0241503i
$783$	−6.46650	+	3.04290i	−0.231094	+	0.108745i
$784$	−0.621854	−	0.159665i	−0.0222091	−	0.00570232i
$785$	7.84977	+	31.8093i	0.280170	+	1.13532i
$786$	−12.1891	+	14.7341i	−0.434772	+	0.525549i
$787$	3.73023	+	2.36727i	0.132968	+	0.0843842i	0.600647	−	0.799514i	$-0.294910\pi$
$787$	3.73023	+	2.36727i	0.132968	+	0.0843842i	−0.467679	+	0.883898i	$0.654910\pi$
$788$	−24.9283	+	1.56836i	−0.888035	+	0.0558704i
$789$	−5.22656	−	8.23574i	−0.186071	−	0.293200i
$790$	−15.1448	−	9.81180i	−0.538829	−	0.349088i
$791$	−2.57589	−	40.9427i	−0.0915883	−	1.45575i
$792$	−5.42337	−	1.03456i	−0.192711	−	0.0367616i
$793$	−24.9755	+	8.11504i	−0.886907	+	0.288174i
$794$	27.3088	−	25.6447i	0.969153	−	0.910096i
$795$	6.48373	+	20.6111i	0.229954	+	0.731001i
$796$	−3.75215	−	19.6695i	−0.132992	−	0.697166i
$797$	−10.8455	+	11.5492i	−0.384166	+	0.409095i	−0.891765	−	0.452498i	$-0.850533\pi$
$797$	−10.8455	+	11.5492i	−0.384166	+	0.409095i	0.507600	+	0.861593i	$0.330533\pi$
$798$	3.70654	−	9.36166i	0.131210	−	0.331399i
$799$	3.24529	+	9.98798i	0.114810	+	0.353349i
$800$	−3.49055	+	3.57996i	−0.123409	+	0.126571i
$801$	−0.495083	+	1.52371i	−0.0174929	+	0.0538376i
$802$	−14.2498	−	11.7885i	−0.503179	−	0.416266i
$803$	−65.7308	−	30.9306i	−2.31959	−	1.09152i
$804$	−6.28141	−	5.89864i	−0.221528	−	0.208029i
$805$	6.71004	+	0.911736i	0.236498	+	0.0321345i
$806$	19.7037	−	2.48916i	0.694034	−	0.0876769i
$807$			7.71950i			0.271739i
$808$	−1.86563	−	14.7679i	−0.0656325	−	0.519535i
$809$	8.53076	+	10.3119i	0.299926	+	0.362548i	0.898849	−	0.438259i	$-0.144405\pi$
$809$	8.53076	+	10.3119i	0.299926	+	0.362548i	−0.598923	+	0.800806i	$0.704405\pi$
$810$	0.0209864	−	2.23597i	0.000737386	−	0.0785640i
$811$	1.19125	−	18.9344i	0.0418304	−	0.664875i	−0.920117	−	0.391642i	$-0.871907\pi$
$811$	1.19125	−	18.9344i	0.0418304	−	0.664875i	0.961948	−	0.273233i	$-0.0880930\pi$
$812$	4.91322	−	19.1357i	0.172420	−	0.671532i
$813$	4.75569	−	18.5222i	0.166789	−	0.649601i
$814$	−0.611637	+	9.72169i	−0.0214379	+	0.340745i
$815$	5.04257	+	7.07928i	0.176633	+	0.247976i
$816$	−1.27164	−	1.53715i	−0.0445162	−	0.0538109i
$817$	−2.76879	−	21.9172i	−0.0968676	−	0.766786i
$818$		−	37.9597i		−	1.32723i
$819$	5.77602	−	0.729680i	0.201830	−	0.0254971i
$820$	−8.15390	+	16.9140i	−0.284747	+	0.590664i
$821$	27.4351	+	25.7633i	0.957491	+	0.899144i	0.994972	−	0.100153i	$-0.0319333\pi$
$821$	27.4351	+	25.7633i	0.957491	+	0.899144i	−0.0374806	+	0.999297i	$0.511933\pi$
$822$	−3.53424	−	1.66309i	−0.123271	−	0.0580068i
$823$	35.1283	+	29.0606i	1.22450	+	1.01299i	0.999251	+	0.0386881i	$0.0123179\pi$
$823$	35.1283	+	29.0606i	1.22450	+	1.01299i	0.225244	+	0.974302i	$0.427682\pi$
$824$	3.25381	−	10.0142i	0.113352	−	0.348861i
$825$	0.518160	−	27.6010i	0.0180400	−	0.960942i
$826$	2.38835	+	7.35058i	0.0831013	+	0.255759i
$827$	−5.67207	+	14.3260i	−0.197237	+	0.498165i	−0.994410	−	0.105587i	$-0.966328\pi$
$827$	−5.67207	+	14.3260i	−0.197237	+	0.498165i	0.797173	+	0.603751i	$0.206328\pi$
$828$	−0.749915	+	0.798578i	−0.0260613	+	0.0277525i
$829$	4.26842	+	22.3759i	0.148248	+	0.777145i	0.976288	+	0.216476i	$0.0694562\pi$
$829$	4.26842	+	22.3759i	0.148248	+	0.777145i	−0.828040	+	0.560670i	$0.810544\pi$
$830$	4.65200	−	3.31362i	0.161473	−	0.115017i
$831$	21.1326	−	19.8449i	0.733083	−	0.688410i
$832$	2.00294	−	0.650796i	0.0694395	−	0.0225623i
$833$	1.25813	+	0.240001i	0.0435916	+	0.00831554i
$834$	1.22114	+	19.4094i	0.0422844	+	0.672092i
$835$	−12.5632	−	32.6223i	−0.434768	−	1.12894i
$836$	10.7752	+	16.9790i	0.372668	+	0.587231i
$837$	−9.41166	+	0.592132i	−0.325315	+	0.0204671i
$838$	−7.11825	−	4.51738i	−0.245896	−	0.156050i
$839$	5.81135	−	7.02471i	0.200630	−	0.242520i	−0.660597	−	0.750741i	$-0.729697\pi$
$839$	5.81135	−	7.02471i	0.200630	−	0.242520i	0.861227	+	0.508221i	$0.169697\pi$
$840$	4.72569	+	3.98472i	0.163052	+	0.137486i
$841$	21.3814	+	5.48980i	0.737288	+	0.189303i
$842$	−34.9014	+	16.4233i	−1.20278	+	0.565985i
$843$	15.1011	+	4.90664i	0.520109	+	0.168994i
$844$	−7.95879	−	4.37538i	−0.273953	−	0.150607i
$845$	−18.5040	−	4.93660i	−0.636558	−	0.169824i
$846$	5.22274	+	0.659785i	0.179561	+	0.0226839i
$847$	−6.75044	+	53.4353i	−0.231948	+	1.83606i
$848$	8.15864	−	5.17763i	0.280169	−	0.177801i
$849$	−1.84342	+	1.33932i	−0.0632661	+	0.0459655i
$850$	6.50133	−	7.56503i	0.222994	−	0.259479i
$851$	1.56363	+	1.13605i	0.0536007	+	0.0389432i
$852$	−1.17335	−	0.0738209i	−0.0401983	−	0.00252906i
$853$	13.2593	+	24.1185i	0.453988	+	0.825802i	0.999928	−	0.0120228i	$-0.00382708\pi$
$853$	13.2593	+	24.1185i	0.453988	+	0.825802i	−0.545939	+	0.837825i	$0.683827\pi$
$854$	−14.6769	+	31.1900i	−0.502234	+	1.06730i
$855$	−5.98902	+	5.51921i	−0.204820	+	0.188753i
$856$	0.283277	−	1.48499i	0.00968222	−	0.0507560i
$857$	−24.8990	−	34.2706i	−0.850534	−	1.17066i	−0.983745	−	0.179572i	$-0.942529\pi$
$857$	−24.8990	−	34.2706i	−0.850534	−	1.17066i	0.133210	−	0.991088i	$-0.457471\pi$
$858$	−5.60168	+	10.1894i	−0.191238	+	0.347861i
$859$	−19.1568	+	30.1862i	−0.653620	+	1.02994i	0.342290	+	0.939594i	$0.388797\pi$
$859$	−19.1568	+	30.1862i	−0.653620	+	1.02994i	−0.995910	+	0.0903463i	$0.971203\pi$
$860$	13.2978	+	2.66627i	0.453451	+	0.0909191i
$861$	21.5834	+	8.54549i	0.735562	+	0.291230i
$862$	−9.25333	−	23.3712i	−0.315170	−	0.796028i
$863$	−6.25770	+	5.17682i	−0.213014	+	0.176221i	−0.737812	−	0.675006i	$-0.764141\pi$
$863$	−6.25770	+	5.17682i	−0.213014	+	0.176221i	0.524798	+	0.851227i	$0.324141\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	31.7212	−	5.74313i	1.07855	−	0.195272i
$866$	8.06694	−	3.19393i	0.274126	−	0.108534i
$867$	−8.91288	−	9.49126i	−0.302697	−	0.322340i
$868$	15.3231	−	21.0905i	0.520100	−	0.715857i
$869$	−18.9713	−	40.3161i	−0.643558	−	1.36763i
$870$	−10.3014	+	12.2170i	−0.349251	+	0.414195i
$871$	−15.9025	+	8.74250i	−0.538837	+	0.296228i
$872$	15.1995	−	2.89945i	0.514719	−	0.0981879i
$873$	−3.15377	−	12.2831i	−0.106739	−	0.415720i
$874$	3.99005			0.134966
$875$	−15.6462	+	26.6542i	−0.528939	+	0.901078i
$876$	−13.1575			−0.444550
$877$	5.04534	+	19.6503i	0.170369	+	0.663543i	0.995174	+	0.0981258i	$0.0312848\pi$
$877$	5.04534	+	19.6503i	0.170369	+	0.663543i	−0.824805	+	0.565417i	$0.808715\pi$
$878$	19.1016	−	3.64382i	0.644647	−	0.122973i
$879$	17.4481	−	9.59219i	0.588511	−	0.323537i
$880$	−11.9861	+	2.95789i	−0.404052	+	0.0997103i
$881$	−14.1343	−	30.0370i	−0.476197	−	1.01197i	−0.988226	−	0.153002i	$-0.951106\pi$
$881$	−14.1343	−	30.0370i	−0.476197	−	1.01197i	0.512029	−	0.858968i	$-0.328894\pi$
$882$	0.377373	−	0.519409i	0.0127068	−	0.0174894i
$883$	3.13950	+	3.34323i	0.105653	+	0.112509i	0.779621	−	0.626251i	$-0.215412\pi$
$883$	3.13950	+	3.34323i	0.105653	+	0.112509i	−0.673969	+	0.738760i	$0.735412\pi$
$884$	−3.90639	+	1.54665i	−0.131386	+	0.0520195i
$885$	0.841719	−	6.19475i	0.0282941	−	0.208234i
$886$	12.5554	−	3.22368i	0.421807	−	0.108302i
$887$	−22.8990	+	18.9437i	−0.768874	+	0.636068i	−0.936853	−	0.349722i	$-0.886276\pi$
$887$	−22.8990	+	18.9437i	−0.768874	+	0.636068i	0.167979	+	0.985791i	$0.446276\pi$
$888$	0.649477	+	1.64039i	0.0217950	+	0.0550479i
$889$	−5.45953	−	2.16158i	−0.183107	−	0.0724971i
$890$	0.415623	+	3.55826i	0.0139317	+	0.119273i
$891$	2.95839	−	4.66167i	0.0991097	−	0.156172i
$892$	−0.223699	+	0.406907i	−0.00749000	+	0.0136243i
$893$	−11.2700	−	15.5119i	−0.377137	−	0.519085i
$894$	0.540762	−	2.83477i	0.0180858	−	0.0948090i
$895$	−4.00636	+	19.9813i	−0.133918	+	0.667903i
$896$	1.17703	−	2.50132i	0.0393219	−	0.0835633i
$897$	1.11147	+	2.02175i	0.0371107	+	0.0675042i
$898$	5.23943	+	0.329637i	0.174842	+	0.0110001i
$899$	54.5237	+	39.6138i	1.81847	+	1.32119i
$900$	−2.04360	−	4.56330i	−0.0681201	−	0.152110i
$901$	−15.5955	+	11.3308i	−0.519562	+	0.377484i
$902$	−39.1453	+	24.8424i	−1.30340	+	0.827161i
$903$	2.10147	−	16.6349i	0.0699326	−	0.553574i
$904$	14.7228	+	1.85993i	0.489675	+	0.0618603i
$905$	−7.14354	−	8.80197i	−0.237459	−	0.292587i
$906$	−11.6548	−	6.40727i	−0.387204	−	0.212867i
$907$	19.9847	+	6.49342i	0.663581	+	0.215611i	0.621393	−	0.783499i	$-0.286567\pi$
$907$	19.9847	+	6.49342i	0.663581	+	0.215611i	0.0421882	+	0.999110i	$0.486567\pi$
$908$	−20.6337	+	9.70950i	−0.684754	+	0.322221i
$909$	14.4177	+	3.70183i	0.478204	+	0.122782i
$910$	11.0566	−	6.87204i	0.366524	−	0.227806i
$911$	30.3199	−	36.6504i	1.00454	−	1.21428i	0.0278553	−	0.999612i	$-0.491132\pi$
$911$	30.3199	−	36.6504i	1.00454	−	1.21428i	0.976687	−	0.214671i	$-0.0688678\pi$
$912$	3.07526	+	1.95162i	0.101832	+	0.0646245i
$913$	14.0747	−	0.885502i	0.465803	−	0.0293058i
$914$	−16.8529	−	26.5559i	−0.557443	−	0.878390i
$915$	21.6497	−	17.5705i	0.715716	−	0.580864i
$916$	−0.514912	−	8.18429i	−0.0170132	−	0.270417i
$917$	51.9263	+	9.90547i	1.71476	+	0.327108i
$918$	1.89732	−	0.616478i	0.0626210	−	0.0203468i
$919$	−9.80784	+	9.21018i	−0.323531	+	0.303816i	−0.829245	−	0.558886i	$-0.811229\pi$
$919$	−9.80784	+	9.21018i	−0.323531	+	0.303816i	0.505714	+	0.862701i	$0.331229\pi$
$920$	−0.778797	+	2.32249i	−0.0256762	+	0.0765703i
$921$	4.34916	+	22.7991i	0.143310	+	0.751255i
$922$	1.85455	−	1.97490i	0.0610764	−	0.0650398i
$923$	−0.911469	+	2.30211i	−0.0300014	+	0.0757748i
$924$	4.71647	+	14.5158i	0.155161	+	0.477535i
$925$	−7.53559	+	4.58612i	−0.247769	+	0.150791i
$926$	3.19869	−	9.84455i	0.105115	−	0.323512i
$927$	8.11315	+	6.71178i	0.266471	+	0.220444i
$928$	6.46650	+	3.04290i	0.212273	+	0.0998882i
$929$	17.2805	+	16.2274i	0.566954	+	0.532405i	0.914144	−	0.405390i	$-0.132864\pi$
$929$	17.2805	+	16.2274i	0.566954	+	0.532405i	−0.347190	+	0.937795i	$0.612864\pi$
$930$	−18.5730	+	9.98473i	−0.609032	+	0.327412i
$931$	−2.31998	+	0.293081i	−0.0760342	+	0.00960536i
$932$			5.93854i			0.194523i
$933$	3.75416	+	29.7172i	0.122906	+	0.972898i
$934$	13.1108	+	15.8482i	0.428998	+	0.518570i
$935$	23.4942	−	7.39067i	0.768342	−	0.241701i
$936$	−0.132238	+	2.10186i	−0.00432233	+	0.0687015i
$937$	12.6244	−	49.1689i	0.412422	−	1.60628i	−0.335194	−	0.942149i	$-0.608802\pi$
$937$	12.6244	−	49.1689i	0.412422	−	1.60628i	0.747617	−	0.664130i	$-0.231198\pi$
$938$	−5.92394	+	23.0722i	−0.193424	+	0.753335i
$939$	1.68733	−	26.8193i	0.0550638	−	0.875215i
$940$	11.2287	−	3.53227i	0.366241	−	0.115210i
$941$	−9.51610	−	11.5030i	−0.310216	−	0.374987i	0.592245	−	0.805758i	$-0.298242\pi$
$941$	−9.51610	−	11.5030i	−0.310216	−	0.374987i	−0.902461	+	0.430771i	$0.858242\pi$
$942$	1.83642	+	14.5368i	0.0598339	+	0.473634i
$943$			9.19913i			0.299565i
$944$	−2.77379	+	0.350411i	−0.0902790	+	0.0114049i
$945$	−5.44454	+	2.92696i	−0.177111	+	0.0952140i
$946$	24.4114	+	22.9238i	0.793683	+	0.745318i
$947$	45.1111	+	21.2276i	1.46591	+	0.689806i	0.982616	−	0.185651i	$-0.0594393\pi$
$947$	45.1111	+	21.2276i	1.46591	+	0.689806i	0.483296	+	0.875457i	$0.339439\pi$
$948$	−6.21817	−	5.14412i	−0.201957	−	0.167073i
$949$	−8.56283	+	26.3537i	−0.277961	+	0.855477i
$950$	−7.02066	+	16.8036i	−0.227780	+	0.545181i
$951$	−0.280280	−	0.862614i	−0.00908871	−	0.0279722i
$952$	−2.03018	+	5.12764i	−0.0657984	+	0.166188i
$953$	25.9880	−	27.6744i	0.841832	−	0.896460i	−0.153962	−	0.988077i	$-0.549203\pi$
$953$	25.9880	−	27.6744i	0.841832	−	0.896460i	0.995794	+	0.0916163i	$0.0292033\pi$
$954$	1.81064	+	9.49173i	0.0586218	+	0.307306i
$955$	3.82392	−	11.4035i	0.123739	−	0.369009i
$956$	−6.32798	+	5.94237i	−0.204662	+	0.192190i
$957$	−37.5267	+	12.1932i	−1.21307	+	0.394149i
$958$	5.62964	+	1.07391i	0.181885	+	0.0346965i
$959$	0.677998	+	10.7765i	0.0218937	+	0.347990i
$960$	−1.73622	+	1.40909i	−0.0560363	+	0.0454782i
$961$	31.0404	+	48.9119i	1.00130	+	1.57780i
$962$	3.70829	−	0.233306i	0.119560	−	0.00752207i
$963$	1.27643	+	0.810046i	0.0411323	+	0.0261034i
$964$	0.591462	−	0.714955i	0.0190497	−	0.0230271i
$965$	11.2630	−	7.00029i	0.362568	−	0.225347i
$966$	2.93325	+	0.753132i	0.0943759	+	0.0242316i
$967$	20.1508	−	9.48225i	0.648006	−	0.304929i	−0.0735425	−	0.997292i	$-0.523430\pi$
$967$	20.1508	−	9.48225i	0.648006	−	0.304929i	0.721549	+	0.692363i	$0.243430\pi$
$968$	−18.5297	−	6.02066i	−0.595567	−	0.193511i
$969$	−6.36739	−	3.50050i	−0.204550	−	0.112452i
$970$	−17.8694	−	22.0179i	−0.573752	−	0.706953i
$971$	−45.6318	−	5.76463i	−1.46439	−	0.184996i	−0.647624	−	0.761960i	$-0.724237\pi$
$971$	−45.6318	−	5.76463i	−1.46439	−	0.184996i	−0.816769	+	0.576964i	$0.804237\pi$
$972$	0.125333	−	0.992115i	0.00402007	−	0.0318221i
$973$	45.3926	−	28.8070i	1.45522	−	0.923511i
$974$	26.0255	−	18.9086i	0.833910	−	0.605871i
$975$	−10.4700	+	1.12345i	−0.335308	+	0.0359791i
$976$	−10.0880	−	7.32934i	−0.322908	−	0.234606i
$977$	12.8439	+	0.808070i	0.410913	+	0.0258525i	0.266902	−	0.963724i	$-0.414000\pi$
$977$	12.8439	+	0.808070i	0.410913	+	0.0258525i	0.144011	+	0.989576i	$0.454000\pi$
$978$	1.87257	+	3.40620i	0.0598783	+	0.108918i
$979$	−3.76626	+	8.00372i	−0.120370	+	0.255800i
$980$	0.282230	−	1.40760i	0.00901551	−	0.0449640i
$981$	−2.89945	+	15.1995i	−0.0925724	+	0.485282i
$982$	9.94013	+	13.6814i	0.317202	+	0.436592i
$983$	−26.9126	+	48.9538i	−0.858377	+	1.56138i	−0.0311506	+	0.999515i	$0.509917\pi$
$983$	−26.9126	+	48.9538i	−0.858377	+	1.56138i	−0.827227	+	0.561868i	$0.810083\pi$
$984$	−4.49948	+	7.09005i	−0.143438	+	0.226022i
$985$	−6.47971	−	55.4745i	−0.206461	−	1.76757i
$986$	−13.2561	−	5.24848i	−0.422162	−	0.167146i
$987$	−5.35717	−	13.5307i	−0.170521	−	0.430686i
$988$	5.91034	−	4.88946i	0.188033	−	0.155554i
$989$	6.43574	−	1.65242i	0.204645	−	0.0525438i
$990$	1.66221	−	12.2333i	0.0528286	−	0.388799i
$991$	−45.9930	+	18.2099i	−1.46102	+	0.578457i	−0.958242	−	0.285960i	$-0.907688\pi$
$991$	−45.9930	+	18.2099i	−1.46102	+	0.578457i	−0.502775	+	0.864417i	$0.667688\pi$
$992$	6.45546	+	6.87437i	0.204961	+	0.218262i
$993$	−6.47837	+	8.91672i	−0.205585	+	0.282963i
$994$	1.38380	+	2.94073i	0.0438915	+	0.0932742i
$995$	43.4713	−	10.7277i	1.37813	−	0.340090i
$996$	2.23831	−	1.23052i	0.0709237	−	0.0389906i
$997$	−37.9140	+	7.23249i	−1.20075	+	0.229055i	−0.748683	−	0.662929i	$-0.769313\pi$
$997$	−37.9140	+	7.23249i	−1.20075	+	0.229055i	−0.452067	+	0.891984i	$0.649313\pi$
$998$	2.64663	+	10.3079i	0.0837777	+	0.326292i
$999$	−1.76429			−0.0558195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.10	✓	280
125.119	even	50	inner	750.2.o.b.619.10	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.10	✓	280	1.1	even	1	trivial
750.2.o.b.619.10	yes	280	125.119	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.18037 - 1.89914i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-1.62489 + 2.23646i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.18037 - 1.89914i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-1.62489 + 2.23646i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(1.54592 - 1.61559i) q^{10} +(5.34771 - 1.37306i) q^{11} +(0.770513 - 0.637424i) q^{12} +(-0.775277 - 1.95813i) q^{13} +(-2.57029 - 1.01765i) q^{14} +(1.51533 + 1.64432i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.961081 + 1.74820i) q^{17} +(0.587785 + 0.809017i) q^{18} +(0.682490 - 3.57774i) q^{19} +(1.94928 + 1.09558i) q^{20} +(1.17703 - 2.50132i) q^{21} +(2.65984 + 4.83823i) q^{22} +(1.09333 + 0.0687864i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-2.21344 + 4.48338i) q^{25} +(1.70380 - 1.23789i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.346474 - 2.74262i) q^{28} +(7.09032 + 0.895715i) q^{29} +(-1.21581 + 1.87665i) q^{30} +(8.26381 + 4.54307i) q^{31} +(0.951057 + 0.309017i) q^{32} +(-4.99570 + 2.35080i) q^{33} +(-1.93229 - 0.496127i) q^{34} +(6.16532 + 0.446019i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(1.48964 + 0.945351i) q^{37} +(3.63507 - 0.228699i) q^{38} +(1.12846 + 1.77817i) q^{39} +(-0.576390 + 2.16050i) q^{40} +(0.527269 + 8.38070i) q^{41} +(2.71546 + 0.518001i) q^{42} +(5.76846 - 1.87428i) q^{43} +(-4.02476 + 3.77950i) q^{44} +(-1.79660 - 1.33125i) q^{45} +(0.205274 + 1.07609i) q^{46} +(3.60363 - 3.83747i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-0.198397 - 0.610602i) q^{49} +(-4.89299 - 1.02893i) q^{50} +(0.616478 - 1.89732i) q^{51} +(1.62272 + 1.34243i) q^{52} +(8.74324 + 4.11426i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-8.91991 - 8.53531i) q^{55} +(2.74262 - 0.346474i) q^{56} +3.64225i q^{57} +(0.895715 + 7.09032i) q^{58} +(-1.78213 - 2.15423i) q^{59} +(-2.12005 - 0.710912i) q^{60} +(0.782961 - 12.4448i) q^{61} +(-2.34521 + 9.13400i) q^{62} +(-0.687484 + 2.67757i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-2.80363 + 3.78368i) q^{65} +(-3.51932 - 4.25413i) q^{66} +(-1.07998 - 8.54890i) q^{67} -1.99496i q^{68} +(-1.08685 + 0.137301i) q^{69} +(1.10125 + 6.08255i) q^{70} +(-0.857026 - 0.804801i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(-10.1380 - 8.38690i) q^{73} +(-0.545194 + 1.67794i) q^{74} +(1.33413 - 4.81872i) q^{75} +(1.12552 + 3.46399i) q^{76} +(-5.61862 + 14.1910i) q^{77} +(-1.44167 + 1.53522i) q^{78} +(-1.51220 - 7.92722i) q^{79} +(-2.23597 - 0.0209864i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-7.98628 + 2.59490i) q^{82} +(2.50902 + 0.478620i) q^{83} +(0.173579 + 2.75897i) q^{84} +(4.45451 - 0.238304i) q^{85} +(3.24996 + 5.12111i) q^{86} +(-7.13257 + 0.448743i) q^{87} +(-4.66167 - 2.95839i) q^{88} +(-1.02123 + 1.23446i) q^{89} +(0.842628 - 2.07123i) q^{90} +(5.63902 + 1.44785i) q^{91} +(-0.991229 + 0.466437i) q^{92} +(-8.96872 - 2.91411i) q^{93} +(4.61310 + 2.53607i) q^{94} +(-7.60021 + 2.92692i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(1.58942 - 12.5815i) q^{97} +(0.542079 - 0.344014i) q^{98} +(4.46672 - 3.24526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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