LMFDB - Embedded newform 280.2.br.a.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	280.67
Dual form			280.2.br.a.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32896 + 0.483609i) q^{2} +(0.835437 + 3.11790i) q^{3} +(1.53224 - 1.28539i) q^{4} +(0.804876 + 2.08619i) q^{5} +(-2.61810 - 3.73952i) q^{6} +(-2.64531 + 0.0485395i) q^{7} +(-1.41466 + 2.44923i) q^{8} +(-6.42524 + 3.70961i) q^{9} +O(q^{10})$	\(q+(-1.32896 + 0.483609i) q^{2} +(0.835437 + 3.11790i) q^{3} +(1.53224 - 1.28539i) q^{4} +(0.804876 + 2.08619i) q^{5} +(-2.61810 - 3.73952i) q^{6} +(-2.64531 + 0.0485395i) q^{7} +(-1.41466 + 2.44923i) q^{8} +(-6.42524 + 3.70961i) q^{9} +(-2.07854 - 2.38320i) q^{10} +(1.23882 - 2.14570i) q^{11} +(5.28780 + 3.70352i) q^{12} +(0.837650 + 0.837650i) q^{13} +(3.49202 - 1.34380i) q^{14} +(-5.83209 + 4.25240i) q^{15} +(0.695547 - 3.93906i) q^{16} +(6.14695 - 1.64707i) q^{17} +(6.74485 - 8.03721i) q^{18} +(-0.588582 + 0.339818i) q^{19} +(3.91483 + 2.16197i) q^{20} +(-2.36133 - 8.20723i) q^{21} +(-0.608659 + 3.45065i) q^{22} +(-0.670633 + 2.50284i) q^{23} +(-8.81831 - 2.36458i) q^{24} +(-3.70435 + 3.35824i) q^{25} +(-1.51829 - 0.708105i) q^{26} +(-10.0867 - 10.0867i) q^{27} +(-3.99086 + 3.47462i) q^{28} +3.80356 q^{29} +(5.69408 - 8.47170i) q^{30} +(-4.91145 - 2.83563i) q^{31} +(0.980615 + 5.57121i) q^{32} +(7.72504 + 2.06992i) q^{33} +(-7.37248 + 5.16160i) q^{34} +(-2.23041 - 5.47953i) q^{35} +(-5.07674 + 13.9430i) q^{36} +(3.91379 + 1.04870i) q^{37} +(0.617860 - 0.736247i) q^{38} +(-1.91190 + 3.31151i) q^{39} +(-6.24818 - 0.979912i) q^{40} +0.957683 q^{41} +(7.10719 + 9.76509i) q^{42} +(-4.19558 + 4.19558i) q^{43} +(-0.859886 - 4.88011i) q^{44} +(-12.9105 - 10.4185i) q^{45} +(-0.319153 - 3.65048i) q^{46} +(0.868770 + 0.232786i) q^{47} +(12.8627 - 1.12220i) q^{48} +(6.99529 - 0.256804i) q^{49} +(3.29884 - 6.25441i) q^{50} +(10.2708 + 17.7895i) q^{51} +(2.36019 + 0.206778i) q^{52} +(-2.66036 + 0.712842i) q^{53} +(18.2828 + 8.52675i) q^{54} +(5.47344 + 0.857389i) q^{55} +(3.62332 - 6.54764i) q^{56} +(-1.55124 - 1.55124i) q^{57} +(-5.05476 + 1.83943i) q^{58} +(8.10063 + 4.67690i) q^{59} +(-3.47020 + 14.0122i) q^{60} +(1.10707 - 0.639170i) q^{61} +(7.89844 + 1.39320i) q^{62} +(16.8167 - 10.1249i) q^{63} +(-3.99748 - 6.92966i) q^{64} +(-1.07329 + 2.42170i) q^{65} +(-11.2673 + 0.985070i) q^{66} +(-6.43707 + 1.72481i) q^{67} +(7.30150 - 10.4249i) q^{68} -8.36385 q^{69} +(5.61406 + 6.20341i) q^{70} +0.973953i q^{71} +(0.00381367 - 20.9847i) q^{72} +(-0.439806 - 1.64138i) q^{73} +(-5.70841 + 0.499073i) q^{74} +(-13.5654 - 8.74417i) q^{75} +(-0.465053 + 1.27724i) q^{76} +(-3.17291 + 5.73618i) q^{77} +(0.939355 - 5.32546i) q^{78} +(7.01405 + 12.1487i) q^{79} +(8.77745 - 1.71942i) q^{80} +(11.8936 - 20.6003i) q^{81} +(-1.27272 + 0.463144i) q^{82} +(10.2393 - 10.2393i) q^{83} +(-14.1676 - 9.54026i) q^{84} +(8.38363 + 11.4980i) q^{85} +(3.54672 - 7.60476i) q^{86} +(3.17763 + 11.8591i) q^{87} +(3.50282 + 6.06961i) q^{88} +(-3.10863 + 1.79477i) q^{89} +(22.1959 + 7.60206i) q^{90} +(-2.25650 - 2.17518i) q^{91} +(2.18955 + 4.69698i) q^{92} +(4.73798 - 17.6824i) q^{93} +(-1.26713 + 0.110783i) q^{94} +(-1.18266 - 0.954381i) q^{95} +(-16.5512 + 7.71185i) q^{96} +(-1.33941 - 1.33941i) q^{97} +(-9.17223 + 3.72427i) q^{98} +18.3822i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.32896	+	0.483609i	−0.939713	+	0.341963i
$2$	−1.32896	+	0.483609i	−0.939713	+	0.341963i
$3$	0.835437	+	3.11790i	0.482340	+	1.80012i	0.591751	+	0.806121i	$0.298437\pi$
$3$	0.835437	+	3.11790i	0.482340	+	1.80012i	−0.109411	+	0.993997i	$0.534896\pi$
$4$	1.53224	−	1.28539i	0.766122	−	0.642695i
$5$	0.804876	+	2.08619i	0.359952	+	0.932971i
$5$	0.804876	+	2.08619i	0.359952	+	0.932971i
$6$	−2.61810	−	3.73952i	−1.06884	−	1.52665i
$7$	−2.64531	+	0.0485395i	−0.999832	+	0.0183462i
$7$	−2.64531	+	0.0485395i	−0.999832	+	0.0183462i
$8$	−1.41466	+	2.44923i	−0.500157	+	0.865935i
$9$	−6.42524	+	3.70961i	−2.14175	+	1.23654i
$10$	−2.07854	−	2.38320i	−0.657293	−	0.753635i
$11$	1.23882	−	2.14570i	0.373519	−	0.646954i	−0.616585	−	0.787288i	$-0.711484\pi$
$11$	1.23882	−	2.14570i	0.373519	−	0.646954i	0.990104	+	0.140334i	$0.0448177\pi$
$12$	5.28780	+	3.70352i	1.52646	+	1.06911i
$13$	0.837650	+	0.837650i	0.232322	+	0.232322i	0.813661	−	0.581339i	$-0.197471\pi$
$13$	0.837650	+	0.837650i	0.232322	+	0.232322i	−0.581339	+	0.813661i	$0.697471\pi$
$14$	3.49202	−	1.34380i	0.933281	−	0.359146i
$15$	−5.83209	+	4.25240i	−1.50584	+	1.09796i
$16$	0.695547	−	3.93906i	0.173887	−	0.984766i
$17$	6.14695	−	1.64707i	1.49085	−	0.399473i	0.580828	−	0.814026i	$-0.302729\pi$
$17$	6.14695	−	1.64707i	1.49085	−	0.399473i	0.910025	+	0.414553i	$0.136062\pi$
$18$	6.74485	−	8.03721i	1.58978	−	1.89439i
$19$	−0.588582	+	0.339818i	−0.135030	+	0.0779596i	−0.565993	−	0.824410i	$-0.691507\pi$
$19$	−0.588582	+	0.339818i	−0.135030	+	0.0779596i	0.430963	+	0.902369i	$0.358174\pi$
$20$	3.91483	+	2.16197i	0.875383	+	0.483431i
$21$	−2.36133	−	8.20723i	−0.515284	−	1.79097i
$22$	−0.608659	+	3.45065i	−0.129766	+	0.735681i
$23$	−0.670633	+	2.50284i	−0.139837	+	0.521877i	0.860094	+	0.510135i	$0.170404\pi$
$23$	−0.670633	+	2.50284i	−0.139837	+	0.521877i	−0.999931	+	0.0117425i	$0.996262\pi$
$24$	−8.81831	−	2.36458i	−1.80003	−	0.482667i
$25$	−3.70435	+	3.35824i	−0.740870	+	0.671649i
$26$	−1.51829	−	0.708105i	−0.297762	−	0.138871i
$27$	−10.0867	−	10.0867i	−1.94119	−	1.94119i
$28$	−3.99086	+	3.47462i	−0.754202	+	0.656642i
$29$	3.80356			0.706303			0.353152	−	0.935566i	$-0.385110\pi$
$29$	3.80356			0.706303			0.353152	+	0.935566i	$0.385110\pi$
$30$	5.69408	−	8.47170i	1.03959	−	1.54671i
$31$	−4.91145	−	2.83563i	−0.882123	−	0.509294i	−0.0107651	−	0.999942i	$-0.503427\pi$
$31$	−4.91145	−	2.83563i	−0.882123	−	0.509294i	−0.871358	+	0.490648i	$0.836760\pi$
$32$	0.980615	+	5.57121i	0.173350	+	0.984860i
$33$	7.72504	+	2.06992i	1.34476	+	0.360327i
$34$	−7.37248	+	5.16160i	−1.26437	+	0.885207i
$35$	−2.23041	−	5.47953i	−0.377008	−	0.926210i
$36$	−5.07674	+	13.9430i	−0.846123	+	2.32383i
$37$	3.91379	+	1.04870i	0.643423	+	0.172405i	0.565753	−	0.824574i	$-0.308585\pi$
$37$	3.91379	+	1.04870i	0.643423	+	0.172405i	0.0776697	+	0.996979i	$0.475252\pi$
$38$	0.617860	−	0.736247i	0.100230	−	0.119435i
$39$	−1.91190	+	3.31151i	−0.306149	+	0.530266i
$40$	−6.24818	−	0.979912i	−0.987924	−	0.154938i
$41$	0.957683			0.149565			0.0747825	−	0.997200i	$-0.476174\pi$
$41$	0.957683			0.149565			0.0747825	+	0.997200i	$0.476174\pi$
$42$	7.10719	+	9.76509i	1.09666	+	1.50679i
$43$	−4.19558	+	4.19558i	−0.639820	+	0.639820i	−0.950511	−	0.310691i	$-0.899440\pi$
$43$	−4.19558	+	4.19558i	−0.639820	+	0.639820i	0.310691	+	0.950511i	$0.399440\pi$
$44$	−0.859886	−	4.88011i	−0.129633	−	0.735705i
$45$	−12.9105	−	10.4185i	−1.92458	−	1.55309i
$46$	−0.319153	−	3.65048i	−0.0470565	−	0.538234i
$47$	0.868770	+	0.232786i	0.126723	+	0.0339554i	0.321623	−	0.946868i	$-0.395772\pi$
$47$	0.868770	+	0.232786i	0.126723	+	0.0339554i	−0.194900	+	0.980823i	$0.562438\pi$
$48$	12.8627	−	1.12220i	1.85657	−	0.161975i
$49$	6.99529	−	0.256804i	0.999327	−	0.0366863i
$50$	3.29884	−	6.25441i	0.466526	−	0.884508i
$51$	10.2708	+	17.7895i	1.43820	+	2.49103i
$52$	2.36019	+	0.206778i	0.327300	+	0.0286750i
$53$	−2.66036	+	0.712842i	−0.365429	+	0.0979164i	−0.436861	−	0.899529i	$-0.643910\pi$
$53$	−2.66036	+	0.712842i	−0.365429	+	0.0979164i	0.0714319	+	0.997445i	$0.477243\pi$
$54$	18.2828	+	8.52675i	2.48797	+	1.16034i
$55$	5.47344	+	0.857389i	0.738038	+	0.115610i
$56$	3.62332	−	6.54764i	0.484187	−	0.874965i
$57$	−1.55124	−	1.55124i	−0.205467	−	0.205467i
$58$	−5.05476	+	1.83943i	−0.663722	+	0.241530i
$59$	8.10063	+	4.67690i	1.05461	+	0.608881i	0.923937	−	0.382544i	$-0.124952\pi$
$59$	8.10063	+	4.67690i	1.05461	+	0.608881i	0.130675	+	0.991425i	$0.458285\pi$
$60$	−3.47020	+	14.0122i	−0.448000	+	1.80897i
$61$	1.10707	−	0.639170i	0.141746	−	0.0818373i	−0.427450	−	0.904039i	$-0.640588\pi$
$61$	1.10707	−	0.639170i	0.141746	−	0.0818373i	0.569196	+	0.822202i	$0.307255\pi$
$62$	7.89844	+	1.39320i	1.00310	+	0.176937i
$63$	16.8167	−	10.1249i	2.11870	−	1.27562i
$64$	−3.99748	−	6.92966i	−0.499685	−	0.866207i
$65$	−1.07329	+	2.42170i	−0.133125	+	0.300375i
$66$	−11.2673	+	0.985070i	−1.38690	+	0.121254i
$67$	−6.43707	+	1.72481i	−0.786413	+	0.210719i	−0.629610	−	0.776911i	$-0.716785\pi$
$67$	−6.43707	+	1.72481i	−0.786413	+	0.210719i	−0.156803	+	0.987630i	$0.550119\pi$
$68$	7.30150	−	10.4249i	0.885437	−	1.26421i
$69$	−8.36385			−1.00689
$70$	5.61406	+	6.20341i	0.671009	+	0.741449i
$71$			0.973953i			0.115587i	0.998329	+	0.0577935i	$0.0184065\pi$
$71$			0.973953i			0.115587i	−0.998329	+	0.0577935i	$0.981593\pi$
$72$	0.00381367	−	20.9847i	0.000449445	−	2.47308i
$73$	−0.439806	−	1.64138i	−0.0514754	−	0.192109i	0.935400	−	0.353591i	$-0.115039\pi$
$73$	−0.439806	−	1.64138i	−0.0514754	−	0.192109i	−0.986876	+	0.161482i	$0.948373\pi$
$74$	−5.70841	+	0.499073i	−0.663589	+	0.0580160i
$75$	−13.5654	−	8.74417i	−1.56640	−	1.00969i
$76$	−0.465053	+	1.27724i	−0.0533453	+	0.146510i
$77$	−3.17291	+	5.73618i	−0.361587	+	0.653698i
$78$	0.939355	−	5.32546i	0.106361	−	0.602990i
$79$	7.01405	+	12.1487i	0.789142	+	1.36683i	0.926493	+	0.376312i	$0.122808\pi$
$79$	7.01405	+	12.1487i	0.789142	+	1.36683i	−0.137351	+	0.990522i	$0.543859\pi$
$80$	8.77745	−	1.71942i	0.981349	−	0.192237i
$81$	11.8936	−	20.6003i	1.32151	−	2.28893i
$82$	−1.27272	+	0.463144i	−0.140548	+	0.0511457i
$83$	10.2393	−	10.2393i	1.12391	−	1.12391i	0.132767	−	0.991147i	$-0.457614\pi$
$83$	10.2393	−	10.2393i	1.12391	−	1.12391i	0.991147	−	0.132767i	$-0.0423862\pi$
$84$	−14.1676	−	9.54026i	−1.54581	−	1.04093i
$85$	8.38363	+	11.4980i	0.909332	+	1.24713i
$86$	3.54672	−	7.60476i	0.382453	−	0.820042i
$87$	3.17763	+	11.8591i	0.340678	+	1.27143i
$88$	3.50282	+	6.06961i	0.373402	+	0.647022i
$89$	−3.10863	+	1.79477i	−0.329514	+	0.190245i	−0.655625	−	0.755086i	$-0.727595\pi$
$89$	−3.10863	+	1.79477i	−0.329514	+	0.190245i	0.326111	+	0.945331i	$0.394262\pi$
$90$	22.1959	+	7.60206i	2.33965	+	0.801327i
$91$	−2.25650	−	2.17518i	−0.236546	−	0.228021i
$92$	2.18955	+	4.69698i	0.228276	+	0.489694i
$93$	4.73798	−	17.6824i	0.491306	−	1.83358i
$94$	−1.26713	+	0.110783i	−0.130695	+	0.0114263i
$95$	−1.18266	−	0.954381i	−0.121338	−	0.0979174i
$96$	−16.5512	+	7.71185i	−1.68925	+	0.787088i
$97$	−1.33941	−	1.33941i	−0.135997	−	0.135997i	0.635831	−	0.771828i	$-0.280657\pi$
$97$	−1.33941	−	1.33941i	−0.135997	−	0.135997i	−0.771828	+	0.635831i	$0.780657\pi$
$98$	−9.17223	+	3.72427i	−0.926535	+	0.376208i
$99$			18.3822i			1.84748i
$100$	−1.35932	+	9.90718i	−0.135932	+	0.990718i
$101$	13.6226	+	7.86501i	1.35550	+	0.782598i	0.989013	−	0.147826i	$-0.0472275\pi$
$101$	13.6226	+	7.86501i	1.35550	+	0.782598i	0.366486	+	0.930424i	$0.380561\pi$
$102$	−22.2526	−	18.6744i	−2.20333	−	1.84904i
$103$	−3.13644	+	11.7053i	−0.309042	+	1.15336i	0.620367	+	0.784312i	$0.286984\pi$
$103$	−3.13644	+	11.7053i	−0.309042	+	1.15336i	−0.929409	+	0.369050i	$0.879683\pi$
$104$	−3.23659	+	0.866611i	−0.317374	+	0.0849782i
$105$	15.2212	−	11.5320i	1.48544	−	1.12541i
$106$	3.19077	−	2.23391i	0.309915	−	0.216977i
$107$	1.83818	−	6.86020i	0.177704	−	0.663201i	−0.818371	−	0.574690i	$-0.805123\pi$
$107$	1.83818	−	6.86020i	0.177704	−	0.663201i	0.996075	−	0.0885105i	$-0.0282107\pi$
$108$	−28.4206	−	2.48995i	−2.73477	−	0.239596i
$109$	9.19843	−	15.9322i	0.881050	−	1.52602i	0.0308749	−	0.999523i	$-0.490171\pi$
$109$	9.19843	−	15.9322i	0.881050	−	1.52602i	0.850175	−	0.526500i	$-0.176496\pi$
$110$	−7.68860	+	1.50757i	−0.733079	+	0.143741i
$111$			13.0789i			1.24140i
$112$	−1.64874	+	10.4538i	−0.155791	+	0.987790i
$113$	−6.71821	+	6.71821i	−0.631996	+	0.631996i	−0.948568	−	0.316572i	$-0.897468\pi$
$113$	−6.71821	+	6.71821i	−0.631996	+	0.631996i	0.316572	+	0.948568i	$0.397468\pi$
$114$	2.81172	+	1.31134i	0.263342	+	0.122818i
$115$	−5.76116	+	0.615408i	−0.537231	+	0.0573871i
$116$	5.82798	−	4.88905i	0.541114	−	0.453937i
$117$	−8.48946	−	2.27474i	−0.784851	−	0.210300i
$118$	−13.0272	−	2.29786i	−1.19925	−	0.211535i
$119$	−16.1806	+	4.65537i	−1.48327	+	0.426757i
$120$	−2.16470	−	20.2998i	−0.197609	−	1.85311i
$121$	2.43063	+	4.20998i	0.220967	+	0.382726i
$122$	−1.16214	+	1.38482i	−0.105216	+	0.125376i
$123$	0.800084	+	2.98596i	0.0721412	+	0.269235i
$124$	−11.1704	+	1.96825i	−1.00313	+	0.176754i
$125$	−9.98747	−	5.02499i	−0.893306	−	0.449449i
$126$	−17.4521	+	21.5883i	−1.55475	+	1.92324i
$127$	5.67476	−	5.67476i	0.503554	−	0.503554i	−0.408987	−	0.912540i	$-0.634118\pi$
$127$	5.67476	−	5.67476i	0.503554	−	0.503554i	0.912540	+	0.408987i	$0.134118\pi$
$128$	8.66372	+	7.27599i	0.765772	+	0.643112i
$129$	−16.5865	−	9.57623i	−1.46036	−	0.843140i
$130$	0.255198	−	3.73738i	0.0223824	−	0.327790i
$131$	−2.36463	−	4.09566i	−0.206599	−	0.357839i	0.744042	−	0.668133i	$-0.232906\pi$
$131$	−2.36463	−	4.09566i	−0.206599	−	0.357839i	−0.950641	+	0.310293i	$0.899573\pi$
$132$	14.4973	−	6.75807i	1.26183	−	0.588214i
$133$	1.54049	−	0.927492i	0.133577	−	0.0804238i
$134$	7.72045	−	5.40522i	0.666945	−	0.466940i
$135$	12.9242	−	29.1613i	1.11234	−	2.50980i
$136$	−4.66178	+	17.3853i	−0.399744	+	1.49078i
$137$	−0.506402	+	0.135690i	−0.0432648	+	0.0115928i	−0.280387	−	0.959887i	$-0.590463\pi$
$137$	−0.506402	+	0.135690i	−0.0432648	+	0.0115928i	0.237122	+	0.971480i	$0.423796\pi$
$138$	11.1152	−	4.04483i	0.946187	−	0.344319i
$139$		−	11.7750i		−	0.998744i	−0.866388	−	0.499372i	$-0.833564\pi$
$139$		−	11.7750i		−	0.998744i	0.866388	−	0.499372i	$-0.166436\pi$
$140$	−10.4609	−	5.52904i	−0.884104	−	0.467290i
$141$			2.90321i			0.244495i
$142$	−0.471013	−	1.29434i	−0.0395265	−	0.108619i
$143$	2.83505	−	0.759649i	0.237079	−	0.0635251i
$144$	10.1433	+	27.8896i	0.845278	+	2.32414i
$145$	3.06139	+	7.93493i	0.254235	+	0.658960i
$146$	1.37827	+	1.96862i	0.114066	+	0.162924i
$147$	6.64481	+	21.5960i	0.548055	+	1.78121i
$148$	7.34487	−	3.42389i	0.603744	−	0.281442i
$149$	2.98171	+	5.16447i	0.244271	+	0.423090i	0.961926	−	0.273309i	$-0.0881180\pi$
$149$	2.98171	+	5.16447i	0.244271	+	0.423090i	−0.717655	+	0.696398i	$0.754785\pi$
$150$	22.2566	+	5.06025i	1.81724	+	0.413168i
$151$	−9.64976	−	5.57129i	−0.785286	−	0.453385i	0.0530143	−	0.998594i	$-0.483117\pi$
$151$	−9.64976	−	5.57129i	−0.785286	−	0.453385i	−0.838300	+	0.545209i	$0.816450\pi$
$152$	0.000349350	−	1.92230i	2.83361e−5	−	0.155919i
$153$	−33.3856	+	33.3856i	−2.69907	+	2.69907i
$154$	1.44260	−	9.15757i	0.116248	−	0.737938i
$155$	1.96254	−	12.5285i	0.157635	−	1.00632i
$156$	1.32708	+	7.53158i	0.106251	+	0.603009i
$157$	0.763144	+	2.84809i	0.0609055	+	0.227302i	0.989669	−	0.143370i	$-0.0457939\pi$
$157$	0.763144	+	2.84809i	0.0609055	+	0.227302i	−0.928764	+	0.370672i	$0.879127\pi$
$158$	−15.1966	−	12.7530i	−1.20897	−	1.01457i
$159$	−4.44513	−	7.69920i	−0.352522	−	0.610586i
$160$	−10.8333	+	6.52988i	−0.856448	+	0.516232i
$161$	1.65254	−	6.65332i	0.130239	−	0.524355i
$162$	−5.84357	+	33.1288i	−0.459114	+	2.60284i
$163$	−12.1767	−	3.26273i	−0.953750	−	0.255557i	−0.251797	−	0.967780i	$-0.581022\pi$
$163$	−12.1767	−	3.26273i	−0.953750	−	0.255557i	−0.701953	+	0.712223i	$0.747688\pi$
$164$	1.46740	−	1.23100i	0.114585	−	0.0961246i
$165$	1.89947	+	17.7819i	0.147873	+	1.38432i
$166$	−8.65579	+	18.5595i	−0.671820	+	1.44049i
$167$	5.02961	−	5.02961i	0.389203	−	0.389203i	−0.485200	−	0.874403i	$-0.661253\pi$
$167$	5.02961	−	5.02961i	0.389203	−	0.389203i	0.874403	+	0.485200i	$0.161253\pi$
$168$	23.4419	+	5.82699i	1.80858	+	0.449562i
$169$		−	11.5967i		−	0.892053i
$170$	−16.7020	−	11.2259i	−1.28098	−	0.860989i
$171$	2.52119	−	4.36682i	0.192800	−	0.333939i
$172$	−1.03570	+	11.8216i	−0.0789714	+	0.901389i
$173$	−3.31913	+	12.3872i	−0.252349	+	0.941780i	0.717197	+	0.696871i	$0.245425\pi$
$173$	−3.31913	+	12.3872i	−0.252349	+	0.941780i	−0.969546	+	0.244909i	$0.921242\pi$
$174$	−9.95810	−	14.2235i	−0.754922	−	1.07828i
$175$	9.63613	−	9.06339i	0.728423	−	0.685128i
$176$	−7.59040	−	6.37224i	−0.572148	−	0.480326i
$177$	−7.81452	+	29.1642i	−0.587375	+	2.19211i
$178$	3.26326	−	3.88853i	0.244592	−	0.291457i
$179$	10.1656	+	5.86914i	0.759816	+	0.438680i	0.829230	−	0.558908i	$-0.188780\pi$
$179$	10.1656	+	5.86914i	0.759816	+	0.438680i	−0.0694139	+	0.997588i	$0.522113\pi$
$180$	−33.1738	+	0.631342i	−2.47263	+	0.0470574i
$181$		−	23.5539i		−	1.75074i	−0.483449	−	0.875372i	$-0.660616\pi$
$181$		−	23.5539i		−	1.75074i	0.483449	−	0.875372i	$-0.339384\pi$
$182$	4.05073	+	1.79946i	0.300260	+	0.133385i
$183$	2.91776	+	2.91776i	0.215687	+	0.215687i
$184$	−5.18131	−	5.18319i	−0.381971	−	0.382110i
$185$	0.962340	+	9.00897i	0.0707526	+	0.662352i
$186$	2.25480	+	25.7904i	0.165330	+	1.89105i
$187$	4.08086	−	15.2300i	0.298422	−	1.11372i
$188$	1.63039	−	0.760023i	0.118908	−	0.0554304i
$189$	27.1720	+	26.1928i	1.97647	+	1.90525i
$190$	2.03325	+	0.696384i	0.147507	+	0.0505210i
$191$	0.802829	−	0.463513i	0.0580906	−	0.0335386i	−0.470673	−	0.882308i	$-0.655989\pi$
$191$	0.802829	−	0.463513i	0.0580906	−	0.0335386i	0.528764	+	0.848769i	$0.322656\pi$
$192$	18.2663	−	18.2530i	1.31826	−	1.31730i
$193$	−4.56175	−	17.0247i	−0.328362	−	1.22546i	−0.910889	−	0.412652i	$-0.864603\pi$
$193$	−4.56175	−	17.0247i	−0.328362	−	1.22546i	0.582527	−	0.812811i	$-0.302064\pi$
$194$	2.42777	+	1.13227i	0.174304	+	0.0812922i
$195$	−8.44727	−	1.32323i	−0.604922	−	0.0947582i
$196$	10.3884	−	9.38516i	0.742029	−	0.670368i
$197$	13.9403	−	13.9403i	0.993204	−	0.993204i	−0.00677298	−	0.999977i	$-0.502156\pi$
$197$	13.9403	−	13.9403i	0.993204	−	0.993204i	0.999977	+	0.00677298i	$0.00215592\pi$
$198$	−8.88981	−	24.4291i	−0.631771	−	1.73610i
$199$	11.7819	−	20.4068i	0.835197	−	1.44660i	−0.0586737	−	0.998277i	$-0.518687\pi$
$199$	11.7819	−	20.4068i	0.835197	−	1.44660i	0.893870	−	0.448326i	$-0.147980\pi$
$200$	−2.98473	−	13.8236i	−0.211053	−	0.977475i
$201$	−10.7555	−	18.6291i	−0.758637	−	1.31400i
$202$	−21.9074	−	3.86424i	−1.54140	−	0.271887i
$203$	−10.0616	+	0.184623i	−0.706184	+	0.0129580i
$204$	38.6038	+	14.0559i	2.70281	+	0.984112i
$205$	0.770816	+	1.99791i	0.0538362	+	0.139540i
$206$	−1.49262	−	17.0727i	−0.103996	−	1.18951i
$207$	−4.97558	−	18.5691i	−0.345826	−	1.29064i
$208$	3.88218	−	2.71693i	0.269181	−	0.188385i
$209$			1.68390i			0.116478i
$210$	−14.6514	+	22.6866i	−1.01104	+	1.56553i
$211$	15.8848			1.09356			0.546778	−	0.837277i	$-0.315854\pi$
$211$	15.8848			1.09356			0.546778	+	0.837277i	$0.315854\pi$
$212$	−3.16005	+	4.51185i	−0.217033	+	0.309875i
$213$	−3.03668	+	0.813677i	−0.208070	+	0.0557522i
$214$	0.874789	+	10.0059i	0.0597993	+	0.683987i
$215$	−12.1297	−	5.37584i	−0.827238	−	0.366629i
$216$	38.9739	−	10.4354i	2.65184	−	0.710041i
$217$	13.1299	+	7.26271i	0.891318	+	0.493025i
$218$	−4.51937	+	25.6216i	−0.306091	+	1.73531i
$219$	4.75021	−	2.74254i	0.320990	−	0.185323i
$220$	9.48873	−	5.72177i	0.639730	−	0.385762i
$221$	6.52866	+	3.76932i	0.439165	+	0.253552i
$222$	−6.32508	−	17.3813i	−0.424511	−	1.16656i
$223$	−10.5242	−	10.5242i	−0.704754	−	0.704754i	0.260673	−	0.965427i	$-0.416055\pi$
$223$	−10.5242	−	10.5242i	−0.704754	−	0.704754i	−0.965427	+	0.260673i	$0.916055\pi$
$224$	−2.86445	−	14.6900i	−0.191389	−	0.981514i
$225$	11.3435	−	35.3192i	0.756235	−	2.35461i
$226$	5.67922	−	12.1772i	0.377776	−	0.810015i
$227$	3.94156	−	1.05614i	0.261611	−	0.0700984i	−0.125630	−	0.992077i	$-0.540095\pi$
$227$	3.94156	−	1.05614i	0.261611	−	0.0700984i	0.387240	+	0.921979i	$0.373428\pi$
$228$	−4.37083	−	0.382932i	−0.289465	−	0.0253603i
$229$	−7.79525	−	13.5018i	−0.515124	−	0.892222i	−0.999846	−	0.0175530i	$-0.994412\pi$
$229$	−7.79525	−	13.5018i	−0.515124	−	0.892222i	0.484722	−	0.874669i	$-0.338921\pi$
$230$	7.35870	−	3.60400i	0.485219	−	0.237641i
$231$	−20.5356	−	5.10060i	−1.35114	−	0.335595i
$232$	−5.38074	+	9.31580i	−0.353263	+	0.611612i
$233$	7.73629	+	2.07293i	0.506821	+	0.135802i	0.503164	−	0.864191i	$-0.332169\pi$
$233$	7.73629	+	2.07293i	0.506821	+	0.135802i	0.00365716	+	0.999993i	$0.498836\pi$
$234$	12.3822	−	1.08255i	0.809450	−	0.0707683i
$235$	0.213617	+	1.99978i	0.0139348	+	0.130451i
$236$	18.4238	−	3.24631i	1.19929	−	0.211317i
$237$	−32.0185	+	32.0185i	−2.07983	+	2.07983i
$238$	19.2519	−	14.0119i	1.24792	−	0.908255i
$239$	−20.1233			−1.30166			−0.650832	−	0.759221i	$-0.725580\pi$
$239$	−20.1233			−1.30166			−0.650832	+	0.759221i	$0.725580\pi$
$240$	12.6940	+	25.9307i	0.819392	+	1.67382i
$241$	−13.0242	+	22.5586i	−0.838962	+	1.45313i	0.0518006	+	0.998657i	$0.483504\pi$
$241$	−13.0242	+	22.5586i	−0.838962	+	1.45313i	−0.890763	+	0.454468i	$0.849829\pi$
$242$	−5.26619	−	4.41940i	−0.338524	−	0.284090i
$243$	32.8300	+	8.79678i	2.10605	+	0.564314i
$244$	0.874727	−	2.40239i	0.0559987	−	0.153797i
$245$	6.16608	+	14.3868i	0.393937	+	0.919138i
$246$	−2.50731	−	3.58127i	−0.159860	−	0.228334i
$247$	−0.777675	−	0.208377i	−0.0494823	−	0.0132587i
$248$	13.8931	−	8.01784i	0.882215	−	0.509134i
$249$	40.4795	+	23.3709i	2.56529	+	1.48107i
$250$	15.7030	+	1.84796i	0.993147	+	0.116875i
$251$	6.32744			0.399385			0.199692	−	0.979859i	$-0.436006\pi$
$251$	6.32744			0.399385			0.199692	+	0.979859i	$0.436006\pi$
$252$	12.7527	−	37.1298i	0.803347	−	2.33896i
$253$	4.53955	+	4.53955i	0.285399	+	0.285399i
$254$	−4.79714	+	10.2859i	−0.300999	+	0.645393i
$255$	−28.8455	+	35.7451i	−1.80638	+	2.23845i
$256$	−15.0324	−	5.47961i	−0.939527	−	0.342476i
$257$	−1.31361	+	4.90245i	−0.0819406	+	0.305807i	−0.994717	−	0.102652i	$-0.967267\pi$
$257$	−1.31361	+	4.90245i	−0.0819406	+	0.305807i	0.912777	+	0.408459i	$0.133934\pi$
$258$	26.6739	+	4.70500i	1.66064	+	0.292920i
$259$	−10.4041	−	2.58415i	−0.646478	−	0.160571i
$260$	1.46828	+	5.09023i	0.0910592	+	0.315683i
$261$	−24.4388	+	14.1097i	−1.51272	+	0.873370i
$262$	5.12318	+	4.29939i	0.316511	+	0.265617i
$263$	−11.6494	+	3.12146i	−0.718335	+	0.192477i	−0.599429	−	0.800428i	$-0.704605\pi$
$263$	−11.6494	+	3.12146i	−0.718335	+	0.192477i	−0.118906	+	0.992905i	$0.537939\pi$
$264$	−15.9980	+	15.9922i	−0.984609	+	0.984252i
$265$	−3.62839	−	4.97626i	−0.222890	−	0.305689i
$266$	−1.59869	+	1.97759i	−0.0980221	+	0.121254i
$267$	−8.19296	−	8.19296i	−0.501401	−	0.501401i
$268$	−7.64612	+	10.9170i	−0.467061	+	0.666860i
$269$	5.01963	−	8.69425i	0.306052	−	0.530098i	−0.671443	−	0.741056i	$-0.734325\pi$
$269$	5.01963	−	8.69425i	0.306052	−	0.530098i	0.977495	+	0.210958i	$0.0676585\pi$
$270$	−3.07301	+	45.0043i	−0.187018	+	2.73887i
$271$	12.6819	−	7.32189i	0.770370	−	0.444773i	−0.0626365	−	0.998036i	$-0.519951\pi$
$271$	12.6819	−	7.32189i	0.770370	−	0.444773i	0.833007	+	0.553263i	$0.186618\pi$
$272$	−2.21242	−	25.3588i	−0.134148	−	1.53760i
$273$	4.89682	−	8.85276i	0.296369	−	0.535793i
$274$	0.607364	−	0.425226i	0.0366922	−	0.0256889i
$275$	2.61677	+	12.1087i	0.157797	+	0.730183i
$276$	−12.8155	+	10.7508i	−0.771400	+	0.647122i
$277$	2.60985	+	9.74008i	0.156810	+	0.585225i	0.998944	+	0.0459549i	$0.0146330\pi$
$277$	2.60985	+	9.74008i	0.156810	+	0.585225i	−0.842133	+	0.539270i	$0.818700\pi$
$278$	5.69450	+	15.6485i	0.341534	+	0.938533i
$279$	42.0763			2.51904
$280$	16.5759	+	2.28888i	0.990600	+	0.136787i
$281$	−26.8015			−1.59884			−0.799420	−	0.600772i	$-0.794860\pi$
$281$	−26.8015			−1.59884			−0.799420	+	0.600772i	$0.794860\pi$
$282$	−1.40402	−	3.85824i	−0.0836082	−	0.229755i
$283$	0.108013	+	0.403110i	0.00642071	+	0.0239624i	0.969062	−	0.246818i	$-0.0793850\pi$
$283$	0.108013	+	0.403110i	0.00642071	+	0.0239624i	−0.962641	+	0.270780i	$0.912718\pi$
$284$	1.25191	+	1.49233i	0.0742872	+	0.0885538i
$285$	1.98762	−	4.48473i	0.117736	−	0.265653i
$286$	−3.40028	+	2.38060i	−0.201063	+	0.140768i
$287$	−2.53336	+	0.0464855i	−0.149540	+	0.00274395i
$288$	−26.9677	−	32.1587i	−1.58909	−	1.89497i
$289$	20.3497	−	11.7489i	1.19704	−	0.691111i
$290$	−7.90586	−	9.06465i	−0.464248	−	0.532295i
$291$	3.05716	−	5.29515i	0.179214	−	0.310407i
$292$	−2.78370	−	1.94967i	−0.162904	−	0.114096i
$293$	19.1952	+	19.1952i	1.12139	+	1.12139i	0.991532	+	0.129862i	$0.0414535\pi$
$293$	19.1952	+	19.1952i	1.12139	+	1.12139i	0.129862	+	0.991532i	$0.458547\pi$
$294$	−19.2747	−	25.4867i	−1.12412	−	1.48641i
$295$	−3.23688	+	20.6638i	−0.188459	+	1.20309i
$296$	−8.10518	+	8.10223i	−0.471104	+	0.470933i
$297$	−34.1387	+	9.14744i	−1.98093	+	0.530788i
$298$	−6.46014	−	5.42137i	−0.374226	−	0.314051i
$299$	−2.65826	+	1.53475i	−0.153731	+	0.0887566i
$300$	−32.0252	+	4.03863i	−1.84897	+	0.233170i
$301$	10.8949	−	11.3022i	0.627974	−	0.651451i
$302$	15.5184	+	2.73729i	0.892985	+	0.157513i
$303$	−13.1414	+	49.0446i	−0.754957	+	2.81754i
$304$	0.929178	+	2.55482i	0.0532920	+	0.146529i
$305$	2.22449	+	1.79511i	0.127374	+	0.102788i
$306$	28.2224	−	60.5136i	1.61337	−	3.45933i
$307$	0.845235	+	0.845235i	0.0482401	+	0.0482401i	0.730815	−	0.682575i	$-0.239140\pi$
$307$	0.845235	+	0.845235i	0.0482401	+	0.0482401i	−0.682575	+	0.730815i	$0.739140\pi$
$308$	2.51154	+	12.8677i	0.143108	+	0.733203i
$309$	−39.1163			−2.22525
$310$	3.45079	+	17.5990i	0.195992	+	0.999554i
$311$	9.37338	+	5.41173i	0.531516	+	0.306871i	0.741634	−	0.670805i	$-0.234051\pi$
$311$	9.37338	+	5.41173i	0.531516	+	0.306871i	−0.210118	+	0.977676i	$0.567385\pi$
$312$	−5.40597	−	9.36735i	−0.306053	−	0.530322i
$313$	−7.99023	−	2.14097i	−0.451634	−	0.121015i	0.0258297	−	0.999666i	$-0.491777\pi$
$313$	−7.99023	−	2.14097i	−0.451634	−	0.121015i	−0.477464	+	0.878651i	$0.658444\pi$
$314$	−2.39155	−	3.41592i	−0.134963	−	0.192772i
$315$	34.6578	+	26.9334i	1.95275	+	1.51752i
$316$	26.3630	+	9.59898i	1.48304	+	0.539985i
$317$	−6.14770	−	1.64727i	−0.345289	−	0.0925199i	0.0820068	−	0.996632i	$-0.473867\pi$
$317$	−6.14770	−	1.64727i	−0.345289	−	0.0925199i	−0.427296	+	0.904112i	$0.640534\pi$
$318$	9.63079	+	8.08218i	0.540068	+	0.453226i
$319$	4.71194	−	8.16131i	0.263818	−	0.456946i
$320$	11.2391	−	13.9170i	0.628284	−	0.777984i
$321$	22.9251			1.27955
$322$	1.02145	+	9.64115i	0.0569232	+	0.537280i
$323$	−3.05828	+	3.05828i	−0.170167	+	0.170167i
$324$	−8.25554	−	46.8527i	−0.458641	−	2.60293i
$325$	−5.91598	−	0.289914i	−0.328160	−	0.0160815i
$326$	17.7601	−	1.55273i	0.983643	−	0.0859976i
$327$	57.3595	+	15.3694i	3.17199	+	0.849931i
$328$	−1.35479	+	2.34559i	−0.0748060	+	0.129513i
$329$	−2.30946	−	0.573621i	−0.127325	−	0.0316248i
$330$	−11.1238	−	22.7128i	−0.612345	−	1.25030i
$331$	6.11818	+	10.5970i	0.336285	+	0.582464i	0.983731	−	0.179648i	$-0.0574960\pi$
$331$	6.11818	+	10.5970i	0.336285	+	0.582464i	−0.647445	+	0.762112i	$0.724163\pi$
$332$	2.52763	−	28.8507i	0.138722	−	1.58339i
$333$	−29.0373	+	7.78052i	−1.59123	+	0.426370i
$334$	−4.25176	+	9.11649i	−0.232646	+	0.498832i
$335$	−8.77932	−	12.0407i	−0.479665	−	0.657852i
$336$	−33.9712	+	3.59290i	−1.85328	+	0.196009i
$337$	−6.59159	−	6.59159i	−0.359067	−	0.359067i	0.504402	−	0.863469i	$-0.331713\pi$
$337$	−6.59159	−	6.59159i	−0.359067	−	0.359067i	−0.863469	+	0.504402i	$0.831713\pi$
$338$	5.60826	+	15.4115i	0.305049	+	0.838274i
$339$	−26.5593	−	15.3340i	−1.44251	−	0.832831i
$340$	27.6252	+	6.84151i	1.49818	+	0.371033i
$341$	−12.1688	+	7.02568i	−0.658980	+	0.380462i
$342$	−1.23871	+	7.02258i	−0.0669817	+	0.379738i
$343$	−18.4922	+	1.01887i	−0.998486	+	0.0550139i
$344$	−4.34064	−	16.2113i	−0.234032	−	0.874053i
$345$	−6.73186	−	17.4486i	−0.362431	−	0.939398i
$346$	−1.57957	−	18.0672i	−0.0849182	−	0.971297i
$347$	−0.566595	+	0.151819i	−0.0304164	+	0.00815005i	−0.273995	−	0.961731i	$-0.588345\pi$
$347$	−0.566595	+	0.151819i	−0.0304164	+	0.00815005i	0.243579	+	0.969881i	$0.421679\pi$
$348$	20.1125	+	14.0865i	1.07814	+	0.755118i
$349$	−12.1672			−0.651293			−0.325647	−	0.945492i	$-0.605582\pi$
$349$	−12.1672			−0.651293			−0.325647	+	0.945492i	$0.605582\pi$
$350$	−8.42284	+	16.7050i	−0.450220	+	0.892918i
$351$		−	16.8982i		−	0.901961i
$352$	13.1690	+	4.79764i	0.701909	+	0.255715i
$353$	−6.73476	−	25.1345i	−0.358455	−	1.33777i	−0.876081	−	0.482165i	$-0.839851\pi$
$353$	−6.73476	−	25.1345i	−0.358455	−	1.33777i	0.517626	−	0.855607i	$-0.326816\pi$
$354$	−3.71891	−	42.5371i	−0.197658	−	2.26082i
$355$	−2.03185	+	0.783912i	−0.107839	+	0.0416057i
$356$	−2.45620	+	6.74582i	−0.130179	+	0.357528i
$357$	−28.0328	−	46.5602i	−1.48366	−	2.46423i
$358$	−16.3480	−	2.88362i	−0.864021	−	0.152404i
$359$	−16.4719	−	28.5301i	−0.869352	−	1.50576i	−0.862660	−	0.505785i	$-0.831203\pi$
$359$	−16.4719	−	28.5301i	−0.869352	−	1.50576i	−0.00669297	−	0.999978i	$-0.502130\pi$
$360$	43.7811	−	16.8822i	2.30747	−	0.889768i
$361$	−9.26905	+	16.0545i	−0.487845	+	0.844972i
$362$	11.3909	+	31.3020i	0.598690	+	1.64520i
$363$	−11.0956	+	11.0956i	−0.582370	+	0.582370i
$364$	−6.25347	−	0.432429i	−0.327771	−	0.0226654i
$365$	3.07023	−	2.23862i	0.160703	−	0.117175i
$366$	−5.28862	−	2.46651i	−0.276441	−	0.128927i
$367$	−6.33938	−	23.6589i	−0.330913	−	1.23498i	−0.908233	−	0.418465i	$-0.862568\pi$
$367$	−6.33938	−	23.6589i	−0.330913	−	1.23498i	0.577320	−	0.816518i	$-0.304098\pi$
$368$	9.39237	+	4.38250i	0.489611	+	0.228454i
$369$	−6.15334	+	3.55263i	−0.320330	+	0.184943i
$370$	−5.63572	−	11.5071i	−0.292987	−	0.598227i
$371$	7.00287	−	2.01482i	0.363571	−	0.104604i
$372$	−15.4690	−	33.1839i	−0.802031	−	1.72050i
$373$	6.87822	−	25.6699i	0.356141	−	1.32914i	−0.522902	−	0.852393i	$-0.675151\pi$
$373$	6.87822	−	25.6699i	0.356141	−	1.32914i	0.879043	−	0.476743i	$-0.158183\pi$
$374$	1.94207	+	22.2135i	0.100422	+	1.14863i
$375$	7.32349	−	35.3379i	0.378183	−	1.82484i
$376$	−1.79916	+	1.79851i	−0.0927847	+	0.0927509i
$377$	3.18605	+	3.18605i	0.164090	+	0.164090i
$378$	−48.7774	−	21.6684i	−2.50884	−	1.11450i
$379$			27.8207i			1.42905i	0.699608	+	0.714527i	$0.253358\pi$
$379$			27.8207i			1.42905i	−0.699608	+	0.714527i	$0.746642\pi$
$380$	−3.03888	+	0.0578339i	−0.155891	+	0.00296682i
$381$	22.4342	+	12.9524i	1.14934	+	0.663572i
$382$	−0.842764	+	1.00424i	−0.0431196	+	0.0513816i
$383$	4.49695	−	16.7829i	0.229784	−	0.857564i	−0.750648	−	0.660703i	$-0.770258\pi$
$383$	4.49695	−	16.7829i	0.229784	−	0.857564i	0.980431	−	0.196861i	$-0.0630749\pi$
$384$	−15.4478	+	33.0912i	−0.788315	+	1.68868i
$385$	−14.5205	−	2.00238i	−0.740035	−	0.102051i
$386$	14.2956	+	20.4189i	0.727629	+	1.03930i
$387$	11.3936	−	42.5216i	0.579170	−	2.16149i
$388$	−3.77398	−	0.330641i	−0.191595	−	0.0167858i
$389$	−11.9011	+	20.6132i	−0.603408	+	1.04513i	0.388893	+	0.921283i	$0.372857\pi$
$389$	−11.9011	+	20.6132i	−0.603408	+	1.04513i	−0.992301	+	0.123850i	$0.960476\pi$
$390$	11.8660	−	2.32667i	0.600857	−	0.117815i
$391$			16.4894i			0.833904i
$392$	−9.26697	+	17.4964i	−0.468053	+	0.883701i
$393$	10.7943	−	10.7943i	0.544502	−	0.544502i
$394$	−11.7844	+	25.2677i	−0.593688	+	1.27297i
$395$	−19.6990	+	24.4108i	−0.991164	+	1.22824i
$396$	23.6283	+	28.1661i	1.18737	+	1.41540i
$397$	−7.21071	−	1.93211i	−0.361895	−	0.0969696i	0.0732894	−	0.997311i	$-0.476650\pi$
$397$	−7.21071	−	1.93211i	−0.361895	−	0.0969696i	−0.435185	+	0.900341i	$0.643317\pi$
$398$	−5.78868	+	32.8176i	−0.290160	+	1.64500i
$399$	4.17880	+	4.02821i	0.209202	+	0.201663i
$400$	10.6518	+	16.9275i	0.532589	+	0.846374i
$401$	−6.05602	−	10.4893i	−0.302423	−	0.523813i	0.674261	−	0.738493i	$-0.264462\pi$
$401$	−6.05602	−	10.4893i	−0.302423	−	0.523813i	−0.976684	+	0.214681i	$0.931129\pi$
$402$	23.3029	+	19.5558i	1.16224	+	0.975356i
$403$	−1.73881	−	6.48934i	−0.0866165	−	0.323257i
$404$	30.9828	−	5.45923i	1.54145	−	0.271607i
$405$	52.5490	+	8.23157i	2.61118	+	0.409030i
$406$	13.2821	−	5.11122i	0.659179	−	0.253666i
$407$	7.09869	−	7.09869i	0.351869	−	0.351869i
$408$	−58.1003	−	0.0105589i	−2.87639	−	0.000522743i
$409$	4.03201	+	2.32788i	0.199370	+	0.115106i	0.596362	−	0.802716i	$-0.296612\pi$
$409$	4.03201	+	2.32788i	0.199370	+	0.115106i	−0.396991	+	0.917822i	$0.629946\pi$
$410$	−1.99059	−	2.28235i	−0.0983080	−	0.112717i
$411$	−0.846134	−	1.46555i	−0.0417367	−	0.0722901i
$412$	10.2401	+	21.9670i	0.504495	+	1.08224i
$413$	−21.6557	−	11.9786i	−1.06561	−	0.589430i
$414$	15.5925	+	22.2713i	0.766330	+	1.09457i
$415$	29.6026	+	13.1198i	1.45313	+	0.644025i
$416$	−3.84531	+	5.48814i	−0.188532	+	0.269078i
$417$	36.7133	−	9.83729i	1.79786	−	0.481734i
$418$	−0.814348	−	2.23783i	−0.0398311	−	0.109456i
$419$			29.5695i			1.44456i	0.691599	+	0.722282i	$0.256907\pi$
$419$			29.5695i			1.44456i	−0.691599	+	0.722282i	$0.743093\pi$
$420$	8.49958	−	37.2350i	0.414737	−	1.81688i
$421$		−	19.5111i		−	0.950915i	−0.879739	−	0.475457i	$-0.842283\pi$
$421$		−	19.5111i		−	0.950915i	0.879739	−	0.475457i	$-0.157717\pi$
$422$	−21.1102	+	7.68204i	−1.02763	+	0.373956i
$423$	−6.44560	+	1.72709i	−0.313396	+	0.0839742i
$424$	2.01759	−	7.52428i	0.0979828	−	0.365411i
$425$	−17.2392	+	26.7443i	−0.836223	+	1.29729i
$426$	3.64212	−	2.54991i	0.176461	−	0.123543i
$427$	−2.89753	+	1.74454i	−0.140221	+	0.0844241i
$428$	−6.00148	−	12.8743i	−0.290092	−	0.622302i
$429$	4.73701	+	8.20475i	0.228705	+	0.396129i
$430$	18.7196	+	1.27823i	0.902740	+	0.0616415i
$431$	25.4008	+	14.6652i	1.22351	+	0.706396i	0.965665	−	0.259790i	$-0.0836532\pi$
$431$	25.4008	+	14.6652i	1.22351	+	0.706396i	0.257848	+	0.966185i	$0.416987\pi$
$432$	−46.7479	+	32.7163i	−2.24916	+	1.57407i
$433$	13.6380	−	13.6380i	0.655402	−	0.655402i	−0.298887	−	0.954289i	$-0.596615\pi$
$433$	13.6380	−	13.6380i	0.655402	−	0.655402i	0.954289	+	0.298887i	$0.0966152\pi$
$434$	−20.9614	−	3.30206i	−1.00618	−	0.158504i
$435$	−22.1827	+	16.1742i	−1.06358	+	0.775496i
$436$	−6.38477	−	36.2355i	−0.305775	−	1.73537i
$437$	−0.455786	−	1.70102i	−0.0218032	−	0.0813707i
$438$	−4.98651	+	5.94196i	−0.238264	+	0.283918i
$439$	2.91490	+	5.04875i	0.139121	+	0.240964i	0.927164	−	0.374656i	$-0.122239\pi$
$439$	2.91490	+	5.04875i	0.139121	+	0.240964i	−0.788043	+	0.615620i	$0.788906\pi$
$440$	−9.84299	+	12.1928i	−0.469246	+	0.581270i
$441$	−43.9937	+	27.5998i	−2.09494	+	1.31428i
$442$	−10.4992	−	1.85194i	−0.499395	−	0.0880880i
$443$	19.0188	+	5.09607i	0.903610	+	0.242121i	0.680566	−	0.732687i	$-0.261734\pi$
$443$	19.0188	+	5.09607i	0.903610	+	0.242121i	0.223044	+	0.974808i	$0.428401\pi$
$444$	16.8115	+	20.0401i	0.797838	+	0.951060i
$445$	−6.24628	−	5.04061i	−0.296102	−	0.238948i
$446$	19.0758	+	8.89661i	0.903266	+	0.421267i
$447$	−13.6112	+	13.6112i	−0.643790	+	0.643790i
$448$	10.9109	+	18.1370i	0.515493	+	0.856894i
$449$			15.7430i			0.742959i	0.928441	+	0.371480i	$0.121149\pi$
$449$			15.7430i			0.742959i	−0.928441	+	0.371480i	$0.878851\pi$
$450$	2.00564	+	52.4235i	0.0945469	+	2.47127i
$451$	1.18640	−	2.05491i	0.0558654	−	0.0967617i
$452$	−1.65843	+	18.9295i	−0.0780058	+	0.890367i
$453$	9.30893	−	34.7414i	0.437372	−	1.63229i
$454$	−4.72740	+	3.30974i	−0.221868	+	0.155334i
$455$	2.72163	−	6.45823i	0.127592	−	0.302767i
$456$	5.99383	−	1.60487i	0.280687	−	0.0751551i
$457$	0.611909	−	2.28368i	0.0286239	−	0.106826i	−0.950136	−	0.311836i	$-0.899056\pi$
$457$	0.611909	−	2.28368i	0.0286239	−	0.106826i	0.978760	+	0.205010i	$0.0657227\pi$
$458$	16.8891	+	14.1734i	0.789176	+	0.662279i
$459$	−78.6159	−	45.3889i	−3.66947	−	2.11857i
$460$	−8.03646	+	8.34829i	−0.374702	+	0.389241i
$461$		−	14.0164i		−	0.652807i	−0.945231	−	0.326404i	$-0.894163\pi$
$461$		−	14.0164i		−	0.652807i	0.945231	−	0.326404i	$-0.105837\pi$
$462$	29.7576	−	3.15272i	1.38445	−	0.146678i
$463$	6.78988	+	6.78988i	0.315553	+	0.315553i	0.847056	−	0.531503i	$-0.178373\pi$
$463$	6.78988	+	6.78988i	0.315553	+	0.315553i	−0.531503	+	0.847056i	$0.678373\pi$
$464$	2.64555	−	14.9825i	0.122817	−	0.695543i
$465$	40.7022	−	4.34782i	1.88752	−	0.201625i
$466$	−11.2837	+	0.986504i	−0.522706	+	0.0456989i
$467$	8.10439	−	30.2460i	0.375026	−	1.39962i	−0.478280	−	0.878208i	$-0.658739\pi$
$467$	8.10439	−	30.2460i	0.375026	−	1.39962i	0.853306	−	0.521410i	$-0.174594\pi$
$468$	−15.9319	+	7.42680i	−0.736451	+	0.343304i
$469$	16.9443	−	4.87510i	0.782415	−	0.225111i
$470$	−1.25100	−	2.55431i	−0.0577043	−	0.117822i
$471$	−8.24249	+	4.75880i	−0.379794	+	0.219274i
$472$	−22.9145	+	13.2241i	−1.05472	+	0.608689i
$473$	3.80489	+	14.2001i	0.174949	+	0.652919i
$474$	27.0668	−	58.0357i	1.24322	−	2.66567i
$475$	1.03912	−	3.23541i	0.0476782	−	0.148451i
$476$	−18.8087	+	27.9316i	−0.862094	+	1.28024i
$477$	14.4491	−	14.4491i	0.661579	−	0.661579i
$478$	26.7429	−	9.73179i	1.22319	−	0.445122i
$479$	−0.389918	+	0.675358i	−0.0178158	+	0.0308579i	−0.874796	−	0.484492i	$-0.839005\pi$
$479$	−0.389918	+	0.675358i	−0.0178158	+	0.0308579i	0.856980	+	0.515350i	$0.172338\pi$
$480$	−29.4100	−	28.3218i	−1.34238	−	1.29271i
$481$	2.39995	+	4.15683i	0.109428	+	0.189535i
$482$	6.39905	−	36.2780i	0.291469	−	1.65242i
$483$	22.1249	−	0.405977i	1.00672	−	0.0184726i
$484$	9.13579	+	3.32641i	0.415263	+	0.151200i
$485$	1.71620	−	3.87233i	0.0779288	−	0.175833i
$486$	−47.8839	+	4.18637i	−2.17206	+	0.189898i
$487$	9.51051	+	35.4937i	0.430962	+	1.60837i	0.750548	+	0.660816i	$0.229790\pi$
$487$	9.51051	+	35.4937i	0.430962	+	1.60837i	−0.319586	+	0.947557i	$0.603544\pi$
$488$	−0.000657099		3.61569i	−2.97455e−5		0.163675i
$489$		−	40.6914i		−	1.84013i
$490$	−15.1520	−	16.1374i	−0.684499	−	0.729014i
$491$	16.9396			0.764474			0.382237	−	0.924064i	$-0.375154\pi$
$491$	16.9396			0.764474			0.382237	+	0.924064i	$0.375154\pi$
$492$	5.06404	+	3.54679i	0.228305	+	0.159902i
$493$	23.3803	−	6.26472i	1.05299	−	0.282149i
$494$	1.13427	−	0.0991664i	0.0510331	−	0.00446171i
$495$	−38.3487	+	14.7954i	−1.72365	+	0.665004i
$496$	−14.5859	+	17.3742i	−0.654925	+	0.780125i
$497$	−0.0472752	−	2.57640i	−0.00212058	−	0.115568i
$498$	−65.0979	−	11.4826i	−2.91710	−	0.514547i
$499$	−12.7875	+	7.38287i	−0.572448	+	0.330503i	−0.758126	−	0.652108i	$-0.773885\pi$
$499$	−12.7875	+	7.38287i	−0.572448	+	0.330503i	0.185679	+	0.982611i	$0.440552\pi$
$500$	−21.7623	+	5.13827i	−0.973240	+	0.229790i
$501$	19.8837	+	11.4799i	0.888338	+	0.512882i
$502$	−8.40889	+	3.06001i	−0.375307	+	0.136575i
$503$	−20.5187	−	20.5187i	−0.914884	−	0.914884i	0.0817674	−	0.996651i	$-0.473944\pi$
$503$	−20.5187	−	20.5187i	−0.914884	−	0.914884i	−0.996651	+	0.0817674i	$0.973944\pi$
$504$	1.00850	+	55.5112i	0.0449222	+	2.47267i
$505$	−5.44337	+	34.7496i	−0.242227	+	1.54634i
$506$	−8.22823	−	3.83749i	−0.365789	−	0.170597i
$507$	36.1572	−	9.68830i	1.60580	−	0.430273i
$508$	1.40084	−	15.9894i	0.0621524	−	0.709415i
$509$	12.8957	+	22.3361i	0.571593	+	0.990029i	0.996403	+	0.0847457i	$0.0270078\pi$
$509$	12.8957	+	22.3361i	0.571593	+	0.990029i	−0.424809	+	0.905283i	$0.639659\pi$
$510$	21.0478	−	61.4536i	0.932011	−	2.72121i
$511$	1.24309	+	4.32060i	0.0549912	+	0.191132i
$512$	22.6274	+	0.0123366i	1.00000	+	0.000545206i
$513$	9.36449	+	2.50921i	0.413452	+	0.110784i
$514$	−0.625144	−	7.15041i	−0.0275739	−	0.315391i
$515$	−26.9440	+	2.87816i	−1.18729	+	0.126827i
$516$	−37.7238	+	6.64701i	−1.66070	+	0.292618i
$517$	1.57574	−	1.57574i	0.0693011	−	0.0693011i
$518$	15.0763	−	1.59728i	0.662413	−	0.0701806i
$519$	−41.3948			−1.81703
$520$	−4.41297	−	6.05461i	−0.193521	−	0.265512i
$521$	12.1953	−	21.1229i	0.534286	−	0.925410i	−0.464912	−	0.885357i	$-0.653914\pi$
$521$	12.1953	−	21.1229i	0.534286	−	0.925410i	0.999198	−	0.0400529i	$-0.0127526\pi$
$522$	25.6544	−	30.5700i	1.12286	−	1.33801i
$523$	9.38717	+	2.51528i	0.410472	+	0.109986i	0.458145	−	0.888877i	$-0.348514\pi$
$523$	9.38717	+	2.51528i	0.410472	+	0.109986i	−0.0476732	+	0.998863i	$0.515181\pi$
$524$	−8.88771	−	3.23608i	−0.388261	−	0.141369i
$525$	36.3091	+	22.4725i	1.58466	+	0.980782i
$526$	13.9720	−	9.78205i	0.609209	−	0.426518i
$527$	−34.8609	−	9.34095i	−1.51857	−	0.406898i
$528$	13.5267	−	28.9897i	0.588673	−	1.26161i
$529$	14.1041	+	8.14303i	0.613224	+	0.354045i
$530$	7.22853	+	4.85851i	0.313987	+	0.211040i
$531$	−69.3980			−3.01162
$532$	1.16821	−	3.40127i	0.0506484	−	0.147464i
$533$	0.802203	+	0.802203i	0.0347473	+	0.0347473i
$534$	14.8503	+	6.92589i	0.642634	+	0.299713i
$535$	15.7912	−	1.68682i	0.682712	−	0.0729274i
$536$	4.88180	−	18.2059i	0.210862	−	0.786375i
$537$	−9.80659	+	36.5987i	−0.423186	+	1.57935i
$538$	−2.46624	+	13.9818i	−0.106327	+	0.602799i
$539$	8.11490	−	15.3280i	0.349533	−	0.660222i
$540$	−17.6806	−	61.2948i	−0.760851	−	2.63771i
$541$	−16.3797	+	9.45685i	−0.704220	+	0.406582i	−0.808917	−	0.587922i	$-0.799946\pi$
$541$	−16.3797	+	9.45685i	−0.704220	+	0.406582i	0.104697	+	0.994504i	$0.466613\pi$
$542$	−13.3127	+	15.8635i	−0.571831	+	0.681398i
$543$	73.4385	−	19.6778i	3.15155	−	0.844454i
$544$	15.2040	+	32.6308i	0.651864	+	1.39903i
$545$	40.6410	+	6.36623i	1.74087	+	0.272699i
$546$	−2.22639	+	14.1331i	−0.0952805	+	0.604840i
$547$	5.07311	+	5.07311i	0.216910	+	0.216910i	0.807195	−	0.590285i	$-0.200985\pi$
$547$	5.07311	+	5.07311i	0.216910	+	0.216910i	−0.590285	+	0.807195i	$0.700985\pi$
$548$	−0.601517	+	0.858834i	−0.0256955	+	0.0366876i
$549$	−4.74215	+	8.21364i	−0.202390	+	0.350549i
$550$	−9.33345	−	14.8264i	−0.397980	−	0.632202i
$551$	−2.23871	+	1.29252i	−0.0953721	+	0.0550631i
$552$	11.8320	−	20.4850i	0.503603	−	0.871900i
$553$	−19.1440	−	31.7965i	−0.814086	−	1.35213i
$554$	−8.17876	−	11.6820i	−0.347482	−	0.496320i
$555$	−27.2850	+	10.5269i	−1.15819	+	0.446842i
$556$	−15.1355	−	18.0422i	−0.641888	−	0.765160i
$557$	−2.61834	−	9.77177i	−0.110943	−	0.414043i	0.888009	−	0.459826i	$-0.152088\pi$
$557$	−2.61834	−	9.77177i	−0.110943	−	0.414043i	−0.998951	+	0.0457831i	$0.985422\pi$
$558$	−55.9176	+	20.3485i	−2.36718	+	0.861420i
$559$	−7.02886			−0.297289
$560$	−23.1356	+	4.97444i	−0.977657	+	0.210208i
$561$	50.8947			2.14878
$562$	35.6179	−	12.9614i	1.50245	−	0.546745i
$563$	−2.50655	−	9.35456i	−0.105638	−	0.394248i	0.892778	−	0.450496i	$-0.148753\pi$
$563$	−2.50655	−	9.35456i	−0.105638	−	0.394248i	−0.998417	+	0.0562482i	$0.982086\pi$
$564$	3.73176	+	4.44843i	0.157135	+	0.187313i
$565$	−19.4228	−	8.60812i	−0.817123	−	0.362146i
$566$	−0.338492	−	0.483480i	−0.0142279	−	0.0203222i
$567$	−30.4623	+	55.0715i	−1.27930	+	2.31279i
$568$	−2.38544	−	1.37781i	−0.100091	−	0.0578117i
$569$	−31.5070	+	18.1906i	−1.32084	+	0.762588i	−0.983863	−	0.178924i	$-0.942738\pi$
$569$	−31.5070	+	18.1906i	−1.32084	+	0.762588i	−0.336979	+	0.941512i	$0.609405\pi$
$570$	−0.472601	+	6.92124i	−0.0197951	+	0.289899i
$571$	3.18300	−	5.51312i	0.133204	−	0.230717i	−0.791706	−	0.610903i	$-0.790807\pi$
$571$	3.18300	−	5.51312i	0.133204	−	0.230717i	0.924910	+	0.380186i	$0.124140\pi$
$572$	3.36755	−	4.80811i	0.140804	−	0.201037i
$573$	2.11590	+	2.11590i	0.0883929	+	0.0883929i
$574$	3.34425	−	1.28694i	0.139586	−	0.0537156i
$575$	−5.92088	−	11.5235i	−0.246918	−	0.480564i
$576$	51.3911	+	29.6956i	2.14130	+	1.23732i
$577$	5.05788	−	1.35525i	0.210562	−	0.0564200i	−0.151996	−	0.988381i	$-0.548570\pi$
$577$	5.05788	−	1.35525i	0.210562	−	0.0564200i	0.362558	+	0.931961i	$0.381903\pi$
$578$	−21.3619	+	25.4550i	−0.888540	+	1.05879i
$579$	49.2701	−	28.4461i	2.04760	−	1.18218i
$580$	14.8903	+	8.22317i	0.618285	+	0.341449i
$581$	−26.5892	+	27.5832i	−1.10311	+	1.14434i
$582$	−1.50204	+	8.51548i	−0.0622616	+	0.352978i
$583$	−1.76617	+	6.59144i	−0.0731473	+	0.272990i
$584$	4.64229	+	1.24480i	0.192099	+	0.0515103i
$585$	−2.08743	−	19.5415i	−0.0863044	−	0.807941i
$586$	−34.7925	−	16.2266i	−1.43726	−	0.670314i
$587$	1.28429	+	1.28429i	0.0530084	+	0.0530084i	0.733114	−	0.680106i	$-0.238066\pi$
$587$	1.28429	+	1.28429i	0.0530084	+	0.0530084i	−0.680106	+	0.733114i	$0.738066\pi$
$588$	37.9408	+	24.5492i	1.56465	+	1.01239i
$589$	3.85439			0.158817
$590$	−5.69151	−	29.0266i	−0.234316	−	1.19501i
$591$	55.1106	+	31.8181i	2.26695	+	1.30882i
$592$	6.85311	−	14.6872i	0.281661	−	0.603642i
$593$	−21.5831	−	5.78316i	−0.886310	−	0.237486i	−0.213182	−	0.977012i	$-0.568383\pi$
$593$	−21.5831	−	5.78316i	−0.886310	−	0.237486i	−0.673128	+	0.739526i	$0.735050\pi$
$594$	40.9450	−	28.6663i	1.67999	−	1.17619i
$595$	−22.7354	−	30.0088i	−0.932059	−	1.23024i
$596$	11.2071	+	4.08058i	0.459059	+	0.167147i
$597$	73.4694	+	19.6861i	3.00690	+	0.805698i
$598$	2.79049	−	3.32516i	0.114112	−	0.135976i
$599$	3.39981	−	5.88865i	0.138913	−	0.240604i	−0.788173	−	0.615454i	$-0.788973\pi$
$599$	3.39981	−	5.88865i	0.138913	−	0.240604i	0.927085	+	0.374851i	$0.122306\pi$
$600$	40.6069	−	20.8548i	1.65777	−	0.851395i
$601$	7.47373			0.304860			0.152430	−	0.988314i	$-0.451290\pi$
$601$	7.47373			0.304860			0.152430	+	0.988314i	$0.451290\pi$
$602$	−9.01302	+	20.2891i	−0.367343	+	0.826921i
$603$	34.9613	−	34.9613i	1.42374	−	1.42374i
$604$	−21.9471	+	3.86712i	−0.893013	+	0.157351i
$605$	−6.82645	+	8.45927i	−0.277535	+	0.343918i
$606$	−6.25399	−	71.5334i	−0.254051	−	2.90584i
$607$	−8.52009	−	2.28295i	−0.345820	−	0.0926622i	0.0817285	−	0.996655i	$-0.473956\pi$
$607$	−8.52009	−	2.28295i	−0.345820	−	0.0926622i	−0.427548	+	0.903992i	$0.640623\pi$
$608$	−2.47037	−	2.94589i	−0.100187	−	0.119471i
$609$	−8.98145	−	31.2167i	−0.363947	−	1.26496i
$610$	−3.82437	−	1.30984i	−0.154844	−	0.0530339i
$611$	0.532732	+	0.922719i	0.0215520	+	0.0373292i
$612$	−8.24140	+	94.0684i	−0.333139	+	3.80249i
$613$	−32.3792	+	8.67598i	−1.30778	+	0.350420i	−0.844388	−	0.535732i	$-0.820036\pi$
$613$	−32.3792	+	8.67598i	−1.30778	+	0.350420i	−0.463396	+	0.886151i	$0.653369\pi$
$614$	−1.53204	−	0.714516i	−0.0618282	−	0.0288355i
$615$	−5.58529	+	4.07245i	−0.225221	+	0.164217i
$616$	−9.56064	−	15.8859i	−0.385209	−	0.640063i
$617$	−21.5127	−	21.5127i	−0.866069	−	0.866069i	0.125966	−	0.992035i	$-0.459797\pi$
$617$	−21.5127	−	21.5127i	−0.866069	−	0.866069i	−0.992035	+	0.125966i	$0.959797\pi$
$618$	51.9839	−	18.9170i	2.09110	−	0.760954i
$619$	36.6246	+	21.1452i	1.47207	+	0.849898i	0.999507	−	0.0314006i	$-0.00999677\pi$
$619$	36.6246	+	21.1452i	1.47207	+	0.849898i	0.472560	+	0.881299i	$0.343330\pi$
$620$	−13.0970	−	21.7194i	−0.525987	−	0.872272i
$621$	32.0098	−	18.4809i	1.28451	−	0.741612i
$622$	−15.0740	−	2.65889i	−0.604411	−	0.106612i
$623$	8.13616	−	4.89860i	0.325968	−	0.196258i
$624$	11.7144	+	9.83441i	0.468952	+	0.393691i
$625$	2.44439	−	24.8802i	0.0977756	−	0.995208i
$626$	11.6540	−	1.01889i	0.465789	−	0.0407229i
$627$	−5.25022	+	1.40679i	−0.209674	+	0.0561818i
$628$	4.83023	+	3.38303i	0.192747	+	0.134998i
$629$	25.7851			1.02812
$630$	−59.0839	−	19.0324i	−2.35396	−	0.758268i
$631$			21.0485i			0.837927i	0.908003	+	0.418964i	$0.137607\pi$
$631$			21.0485i			0.837927i	−0.908003	+	0.418964i	$0.862393\pi$
$632$	−39.6775	−	0.00721080i	−1.57828	−	0.000286830i
$633$	13.2708	+	49.5272i	0.527466	+	1.96853i
$634$	8.96665	−	0.783933i	0.356111	−	0.0311340i
$635$	16.4061	+	7.27113i	0.651056	+	0.288546i
$636$	−16.7075	−	6.08333i	−0.662496	−	0.241220i
$637$	6.07472	+	5.64449i	0.240689	+	0.223643i
$638$	−2.31507	+	13.1248i	−0.0916544	+	0.519614i
$639$	−3.61299	−	6.25788i	−0.142928	−	0.247558i
$640$	−8.20584	+	23.9304i	−0.324364	+	0.945932i
$641$	−22.9707	+	39.7864i	−0.907287	+	1.57147i	−0.0894699	+	0.995990i	$0.528517\pi$
$641$	−22.9707	+	39.7864i	−0.907287	+	1.57147i	−0.817817	+	0.575478i	$0.804816\pi$
$642$	−30.4664	+	11.0868i	−1.20241	+	0.437560i
$643$	24.1897	−	24.1897i	0.953950	−	0.953950i	−0.0450358	−	0.998985i	$-0.514340\pi$
$643$	24.1897	−	24.1897i	0.953950	−	0.953950i	0.998985	+	0.0450358i	$0.0143402\pi$
$644$	−6.02001	−	12.3187i	−0.237221	−	0.485424i
$645$	6.62771	−	42.3103i	0.260966	−	1.66597i
$646$	2.58531	−	5.54333i	0.101717	−	0.218099i
$647$	−1.99992	−	7.46379i	−0.0786248	−	0.293432i	0.915406	−	0.402532i	$-0.131870\pi$
$647$	−1.99992	−	7.46379i	−0.0786248	−	0.293432i	−0.994031	+	0.109100i	$0.965203\pi$
$648$	33.6296	+	58.2727i	1.32110	+	2.28917i
$649$	20.0705	−	11.5877i	0.787836	−	0.454857i
$650$	8.00228	−	2.47574i	0.313875	−	0.0971065i
$651$	−11.6751	+	47.0053i	−0.457584	+	1.84228i
$652$	−22.8515	+	10.6525i	−0.894934	+	0.417183i
$653$	−8.32230	+	31.0593i	−0.325677	+	1.21544i	0.587953	+	0.808895i	$0.299934\pi$
$653$	−8.32230	+	31.0593i	−0.325677	+	1.21544i	−0.913630	+	0.406547i	$0.866733\pi$
$654$	−83.6610	+	7.31428i	−3.27140	+	0.286011i
$655$	6.64107	−	8.22956i	0.259488	−	0.321555i
$656$	0.666114	−	3.77237i	0.0260074	−	0.147286i
$657$	8.91473	+	8.91473i	0.347797	+	0.347797i
$658$	3.34658	−	0.354560i	0.130463	−	0.0138222i
$659$		−	26.5566i		−	1.03450i	−0.855835	−	0.517250i	$-0.826956\pi$
$659$		−	26.5566i		−	1.03450i	0.855835	−	0.517250i	$-0.173044\pi$
$660$	25.7671	+	24.8047i	1.00298	+	0.965521i
$661$	−24.3850	−	14.0787i	−0.948465	−	0.547596i	−0.0558611	−	0.998439i	$-0.517790\pi$
$661$	−24.3850	−	14.0787i	−0.948465	−	0.547596i	−0.892604	+	0.450842i	$0.851124\pi$
$662$	−13.2556	−	11.1241i	−0.515193	−	0.432352i
$663$	−6.29807	+	23.5047i	−0.244597	+	0.912847i
$664$	10.5934	+	39.5637i	0.411102	+	1.53537i
$665$	3.17482	+	2.46722i	0.123114	+	0.0956748i
$666$	34.8265	−	24.3827i	1.34950	−	0.944809i
$667$	−2.55079	+	9.51968i	−0.0987670	+	0.368603i
$668$	1.24158	−	14.1716i	0.0480383	−	0.548315i
$669$	24.0211	−	41.6057i	0.928709	−	1.60857i
$670$	17.4903	+	11.7558i	0.675709	+	0.454165i
$671$		−	3.16727i		−	0.122271i
$672$	43.4087	−	21.2036i	1.67453	−	0.817947i
$673$	−0.208368	+	0.208368i	−0.00803201	+	0.00803201i	−0.711111	−	0.703079i	$-0.751808\pi$
$673$	−0.208368	+	0.208368i	−0.00803201	+	0.00803201i	0.703079	+	0.711111i	$0.251808\pi$
$674$	11.9477	+	5.57218i	0.460208	+	0.214632i
$675$	71.2382	+	3.49104i	2.74196	+	0.134370i
$676$	−14.9063	−	17.7690i	−0.573318	−	0.683421i
$677$	−26.2296	−	7.02820i	−1.00808	−	0.270116i	−0.283256	−	0.959044i	$-0.591415\pi$
$677$	−26.2296	−	7.02820i	−1.00808	−	0.270116i	−0.724829	+	0.688929i	$0.758081\pi$
$678$	42.7119	+	7.53392i	1.64034	+	0.289338i
$679$	3.60817	+	3.47815i	0.138469	+	0.133479i
$680$	−40.0212	+	4.26772i	−1.53474	+	0.163660i
$681$	6.58586	+	11.4070i	0.252371	+	0.437119i
$682$	12.7742	−	15.2218i	0.489148	−	0.582872i
$683$	7.00457	+	26.1414i	0.268022	+	1.00027i	0.960374	+	0.278713i	$0.0899079\pi$
$683$	7.00457	+	26.1414i	0.268022	+	1.00027i	−0.692352	+	0.721560i	$0.743425\pi$
$684$	−1.74999	−	9.93175i	−0.0669127	−	0.379750i
$685$	−0.690665	−	0.947235i	−0.0263890	−	0.0361920i
$686$	24.0826	−	10.2970i	0.919477	−	0.393143i
$687$	35.5846	−	35.5846i	1.35764	−	1.35764i
$688$	13.6084	+	19.4449i	0.518817	+	0.741329i
$689$	−2.82557	−	1.63134i	−0.107646	−	0.0621492i
$690$	17.3846	+	19.9328i	0.661821	+	0.758827i
$691$	−18.4600	−	31.9737i	−0.702252	−	1.21634i	−0.967674	−	0.252204i	$-0.918845\pi$
$691$	−18.4600	−	31.9737i	−0.702252	−	1.21634i	0.265422	−	0.964132i	$-0.414489\pi$
$692$	10.8366	+	23.2466i	0.411947	+	0.883702i
$693$	−0.892264	−	48.6266i	−0.0338943	−	1.84717i
$694$	0.679558	−	0.475770i	0.0257957	−	0.0180600i
$695$	24.5649	−	9.47743i	0.931799	−	0.359500i
$696$	−33.5410	−	8.99380i	−1.27137	−	0.340909i
$697$	5.88683	−	1.57737i	0.222979	−	0.0597472i
$698$	16.1696	−	5.88415i	0.612029	−	0.222718i
$699$			25.8527i			0.977840i
$700$	3.11492	−	26.2735i	0.117733	−	0.993045i
$701$		−	32.7053i		−	1.23526i	−0.786468	−	0.617631i	$-0.788093\pi$
$701$		−	32.7053i		−	1.23526i	0.786468	−	0.617631i	$-0.211907\pi$
$702$	8.17214	+	22.4570i	0.308438	+	0.847585i
$703$	−2.65995	+	0.712732i	−0.100322	+	0.0268812i
$704$	−19.8212	−	0.00720442i	−0.747038	−	0.000271527i
$705$	−6.05664	+	2.33673i	−0.228106	+	0.0880062i
$706$	21.1054	+	30.1456i	0.794314	+	1.13454i
$707$	−36.4177	−	20.1441i	−1.36963	−	0.757598i
$708$	25.5136	+	54.7314i	0.958859	+	2.05693i
$709$	5.19917	+	9.00523i	0.195259	+	0.338199i	0.946985	−	0.321277i	$-0.104112\pi$
$709$	5.19917	+	9.00523i	0.195259	+	0.338199i	−0.751726	+	0.659475i	$0.770779\pi$
$710$	2.32113	−	2.02440i	0.0871104	−	0.0759745i
$711$	−90.1339	−	52.0388i	−3.38028	−	1.95161i
$712$	0.00184511	−	10.1527i	6.91485e−5	−	0.380490i
$713$	10.3909	−	10.3909i	0.389142	−	0.389142i
$714$	59.7713	+	48.3194i	2.23689	+	1.80831i
$715$	3.86664	+	5.30302i	0.144604	+	0.198322i
$716$	23.1204	−	4.07386i	0.864049	−	0.152247i
$717$	−16.8117	−	62.7422i	−0.627845	−	2.34315i
$718$	35.6878	+	29.9493i	1.33186	+	1.11770i
$719$	23.3347	+	40.4169i	0.870239	+	1.50730i	0.861750	+	0.507334i	$0.169369\pi$
$719$	23.3347	+	40.4169i	0.870239	+	1.50730i	0.00848907	+	0.999964i	$0.497298\pi$
$720$	−50.0188	+	43.6086i	−1.86409	+	1.62520i
$721$	7.72867	−	31.1165i	0.287831	−	1.15884i
$722$	4.55407	−	25.8183i	0.169485	−	0.960856i
$723$	−81.2162	−	21.7618i	−3.02046	−	0.809330i
$724$	−30.2759	−	36.0903i	−1.12519	−	1.34128i
$725$	−14.0897	+	12.7733i	−0.523278	+	0.474388i
$726$	9.37966	−	20.1116i	0.348112	−	0.746410i
$727$	−10.4956	+	10.4956i	−0.389261	+	0.389261i	−0.874424	−	0.485163i	$-0.838760\pi$
$727$	−10.4956	+	10.4956i	−0.389261	+	0.389261i	0.485163	+	0.874424i	$0.338760\pi$
$728$	8.51970	−	2.44955i	0.315761	−	0.0907865i
$729$			38.3481i			1.42030i
$730$	−2.99758	+	4.45982i	−0.110945	+	0.165065i
$731$	−18.8796	+	32.7004i	−0.698287	+	1.20947i
$732$	8.22117	+	0.720263i	0.303863	+	0.0266217i
$733$	−4.24134	+	15.8289i	−0.156658	+	0.584654i	0.842300	+	0.539009i	$0.181201\pi$
$733$	−4.24134	+	15.8289i	−0.156658	+	0.584654i	−0.998958	+	0.0456452i	$0.985466\pi$
$734$	19.8664	+	28.3758i	0.733282	+	1.04737i
$735$	−39.7051	+	31.2445i	−1.46454	+	1.15247i
$736$	−14.6015	−	1.28192i	−0.538217	−	0.0472521i
$737$	−4.27346	+	15.9488i	−0.157415	+	0.587481i
$738$	6.45943	−	7.69710i	0.237775	−	0.283334i
$739$	−17.4130	−	10.0534i	−0.640548	−	0.369820i	0.144278	−	0.989537i	$-0.453914\pi$
$739$	−17.4130	−	10.0534i	−0.640548	−	0.369820i	−0.784825	+	0.619717i	$0.787247\pi$
$740$	13.0546	+	12.5670i	0.479896	+	0.461971i
$741$		−	2.59879i		−	0.0954691i
$742$	−8.33212	+	6.06426i	−0.305882	+	0.222626i
$743$	13.0655	+	13.0655i	0.479326	+	0.479326i	0.904916	−	0.425590i	$-0.139934\pi$
$743$	13.0655	+	13.0655i	0.479326	+	0.479326i	−0.425590	+	0.904916i	$0.639934\pi$
$744$	36.6056	+	36.6190i	1.34203	+	1.34252i
$745$	−8.37414	+	10.3772i	−0.306805	+	0.380190i
$746$	3.27333	+	37.4405i	0.119845	+	1.37079i
$747$	−27.8062	+	103.774i	−1.01738	+	3.79690i
$748$	−13.3236	−	28.5815i	−0.487158	−	1.04504i
$749$	−4.52957	+	18.2366i	−0.165507	+	0.666349i
$750$	7.35716	+	50.5042i	0.268645	+	1.84415i
$751$	2.69156	−	1.55397i	0.0982165	−	0.0567053i	−0.450087	−	0.892985i	$-0.648607\pi$
$751$	2.69156	−	1.55397i	0.0982165	−	0.0567053i	0.548304	+	0.836279i	$0.315274\pi$
$752$	1.52123	−	3.26023i	0.0554736	−	0.118888i
$753$	5.28618	+	19.7283i	0.192639	+	0.718939i
$754$	−5.77492	−	2.69332i	−0.210310	−	0.0980848i
$755$	3.85589	−	24.6154i	0.140330	−	0.895846i
$756$	75.3021	+	5.20716i	2.73871	+	0.189383i
$757$	−33.5021	+	33.5021i	−1.21766	+	1.21766i	−0.249204	+	0.968451i	$0.580169\pi$
$757$	−33.5021	+	33.5021i	−1.21766	+	1.21766i	−0.968451	+	0.249204i	$0.919831\pi$
$758$	−13.4543	−	36.9725i	−0.488684	−	1.34290i
$759$	−10.3613	+	17.9464i	−0.376092	+	0.651411i
$760$	4.01056	−	1.54649i	0.145478	−	0.0560969i
$761$	−8.47733	−	14.6832i	−0.307303	−	0.532264i	0.670469	−	0.741938i	$-0.266093\pi$
$761$	−8.47733	−	14.6832i	−0.307303	−	0.532264i	−0.977771	+	0.209674i	$0.932760\pi$
$762$	−36.0780	−	6.36378i	−1.30697	−	0.230535i
$763$	−23.5593	+	42.5919i	−0.852905	+	1.54193i
$764$	0.634335	−	1.74216i	0.0229494	−	0.0630292i
$765$	−96.5199	−	42.7773i	−3.48968	−	1.54662i
$766$	2.14009	+	24.4784i	0.0773246	+	0.884442i
$767$	2.86789	+	10.7031i	0.103553	+	0.386467i
$768$	4.52619	−	51.4474i	0.163325	−	1.85645i
$769$		−	40.7180i		−	1.46833i	−0.678972	−	0.734164i	$-0.737574\pi$
$769$		−	40.7180i		−	1.46833i	0.678972	−	0.734164i	$-0.262426\pi$
$770$	20.2655	−	4.36119i	0.730319	−	0.157166i
$771$	−16.3828			−0.590011
$772$	−28.8731	−	20.2223i	−1.03916	−	0.727818i
$773$	32.7546	−	8.77656i	1.17810	−	0.315671i	0.383927	−	0.923363i	$-0.374571\pi$
$773$	32.7546	−	8.77656i	1.17810	−	0.315671i	0.794172	+	0.607692i	$0.207905\pi$
$774$	5.42220	+	62.0193i	0.194897	+	2.22924i
$775$	27.7165	−	5.98970i	0.995605	−	0.215156i
$776$	5.17535	−	1.38572i	0.185784	−	0.0497446i
$777$	−0.634844	−	34.5977i	−0.0227749	−	1.24119i
$778$	5.84723	−	33.1495i	0.209633	−	1.18847i
$779$	−0.563675	+	0.325438i	−0.0201958	+	0.0116600i
$780$	−14.6441	+	8.83053i	−0.524345	+	0.316184i
$781$	2.08982	+	1.20656i	0.0747795	+	0.0431740i
$782$	−7.97441	−	21.9136i	−0.285164	−	0.783630i
$783$	−38.3653	−	38.3653i	−1.37106	−	1.37106i
$784$	3.85399	−	27.7335i	0.137642	−	0.990482i
$785$	−5.32741	+	3.88442i	−0.190143	+	0.138641i
$786$	−9.12495	+	19.5654i	−0.325476	+	0.697876i
$787$	−29.7565	+	7.97322i	−1.06070	+	0.284215i	−0.746668	−	0.665196i	$-0.768348\pi$
$787$	−29.7565	+	7.97322i	−1.06070	+	0.284215i	−0.314036	+	0.949411i	$0.601681\pi$
$788$	3.44123	−	39.2786i	0.122589	−	1.39924i
$789$	−19.4647	−	33.7139i	−0.692963	−	1.20025i
$790$	14.3738	−	41.9675i	0.511397	−	1.49314i
$791$	17.4456	−	18.0978i	0.620295	−	0.643485i
$792$	−45.0223	−	26.0046i	−1.59980	−	0.924032i
$793$	1.46274	+	0.391941i	0.0519435	+	0.0139182i
$794$	10.5171	−	0.919485i	0.373238	−	0.0326313i
$795$	12.4842	−	15.4703i	0.442768	−	0.548674i
$796$	−8.17800	−	46.4126i	−0.289861	−	1.64505i
$797$	−5.09246	+	5.09246i	−0.180384	+	0.180384i	−0.791523	−	0.611139i	$-0.790712\pi$
$797$	−5.09246	+	5.09246i	−0.180384	+	0.180384i	0.611139	+	0.791523i	$0.290712\pi$
$798$	−7.50152	−	3.33240i	−0.265551	−	0.117966i
$799$	5.72370			0.202490
$800$	−22.3420	−	17.3446i	−0.789910	−	0.613223i
$801$	13.3158	−	23.0636i	0.470490	−	0.814913i
$802$	13.1209	+	11.0111i	0.463316	+	0.388816i
$803$	−4.06675	−	1.08968i	−0.143513	−	0.0384541i
$804$	−40.4258	−	14.7193i	−1.42571	−	0.519111i
$805$	15.2102	−	1.90759i	0.536087	−	0.0672336i
$806$	5.44911	+	7.78314i	0.191937	+	0.274149i
$807$	31.3013	+	8.38717i	1.10186	+	0.295242i
$808$	−38.5346	+	22.2386i	−1.35564	+	0.782352i
$809$	−6.85811	−	3.95953i	−0.241118	−	0.139210i	0.374572	−	0.927198i	$-0.377790\pi$
$809$	−6.85811	−	3.95953i	−0.241118	−	0.139210i	−0.615691	+	0.787988i	$0.711123\pi$
$810$	−73.8162	+	14.4738i	−2.59364	+	0.508558i
$811$	40.2831			1.41453			0.707266	−	0.706948i	$-0.249928\pi$
$811$	40.2831			1.41453			0.707266	+	0.706948i	$0.249928\pi$
$812$	−15.1795	+	13.2159i	−0.532695	+	0.463788i
$813$	33.4238	+	33.4238i	1.17222	+	1.17222i
$814$	−6.00085	+	12.8668i	−0.210330	+	0.450982i
$815$	−2.99405	−	28.0289i	−0.104877	−	0.981810i
$816$	77.2178	−	28.0838i	2.70316	−	0.983130i
$817$	1.04371	−	3.89518i	0.0365148	−	0.136275i
$818$	−6.48415	−	1.14374i	−0.226713	−	0.0399898i
$819$	22.5676	+	5.60532i	0.788577	+	0.195866i
$820$	3.74917	+	2.07048i	0.130927	+	0.0723043i
$821$	−13.6970	+	7.90794i	−0.478027	+	0.275989i	−0.719594	−	0.694395i	$-0.755672\pi$
$821$	−13.6970	+	7.90794i	−0.478027	+	0.275989i	0.241567	+	0.970384i	$0.422339\pi$
$822$	1.83323	+	1.53845i	0.0639411	+	0.0536595i
$823$	−9.90021	+	2.65275i	−0.345099	+	0.0924691i	−0.427206	−	0.904154i	$-0.640502\pi$
$823$	−9.90021	+	2.65275i	−0.345099	+	0.0924691i	0.0821062	+	0.996624i	$0.473835\pi$
$824$	−24.2321	−	24.2409i	−0.844166	−	0.844473i
$825$	−35.5675	+	18.2749i	−1.23830	+	0.636250i
$826$	34.5724	+	5.44620i	1.20293	+	0.189497i
$827$	18.6181	+	18.6181i	0.647416	+	0.647416i	0.952368	−	0.304952i	$-0.0986403\pi$
$827$	18.6181	+	18.6181i	0.647416	+	0.647416i	−0.304952	+	0.952368i	$0.598640\pi$
$828$	−31.4923	−	22.0569i	−1.09443	−	0.766529i
$829$	−16.4972	+	28.5740i	−0.572972	+	0.992416i	0.423287	+	0.905996i	$0.360876\pi$
$829$	−16.4972	+	28.5740i	−0.572972	+	0.992416i	−0.996259	+	0.0864204i	$0.972457\pi$
$830$	−45.6854	−	3.11952i	−1.58576	−	0.108280i
$831$	−28.1882	+	16.2745i	−0.977837	+	0.564555i
$832$	2.45614	−	9.15312i	0.0851512	−	0.317327i
$833$	42.5767	−	13.1003i	1.47519	−	0.453898i
$834$	−44.0329	+	30.8282i	−1.52473	+	1.06749i
$835$	14.5409	+	6.44449i	0.503209	+	0.223021i
$836$	2.16447	+	2.58014i	0.0748596	+	0.0892361i
$837$	20.9382	+	78.1424i	0.723730	+	2.70100i
$838$	−14.3001	−	39.2965i	−0.493988	−	1.35748i
$839$	46.3593			1.60050			0.800251	−	0.599666i	$-0.204700\pi$
$839$	46.3593			1.60050			0.800251	+	0.599666i	$0.204700\pi$
$840$	6.71164	+	53.5942i	0.231574	+	1.84918i
$841$	−14.5329			−0.501136
$842$	9.43576	+	25.9294i	0.325178	+	0.893587i
$843$	−22.3909	−	83.5641i	−0.771185	−	2.87810i
$844$	24.3394	−	20.4182i	0.837798	−	0.702823i
$845$	24.1928	−	9.33390i	0.832259	−	0.321096i
$846$	7.73068	−	5.41238i	0.265786	−	0.186082i
$847$	−6.63412	−	11.0187i	−0.227951	−	0.378607i
$848$	0.957522	+	10.9752i	0.0328814	+	0.376888i
$849$	−1.16662	+	0.673547i	−0.0400382	+	0.0231161i
$850$	9.97632	−	43.8790i	0.342185	−	1.50504i
$851$	−5.24943	+	9.09228i	−0.179948	+	0.311679i
$852$	−3.60705	+	5.15008i	−0.123576	+	0.176439i
$853$	−12.1510	−	12.1510i	−0.416041	−	0.416041i	0.467795	−	0.883837i	$-0.345048\pi$
$853$	−12.1510	−	12.1510i	−0.416041	−	0.416041i	−0.883837	+	0.467795i	$0.845048\pi$
$854$	3.00701	−	3.71968i	0.102898	−	0.127285i
$855$	11.1393	+	1.74491i	0.380954	+	0.0596748i
$856$	14.2018	+	14.2070i	0.485408	+	0.485585i
$857$	44.1259	−	11.8235i	1.50731	−	0.403883i	0.591769	−	0.806107i	$-0.298430\pi$
$857$	44.1259	−	11.8235i	1.50731	−	0.403883i	0.915541	+	0.402225i	$0.131763\pi$
$858$	−10.2632	−	8.61288i	−0.350379	−	0.294039i
$859$	16.6199	−	9.59551i	0.567064	−	0.327395i	−0.188912	−	0.981994i	$-0.560496\pi$
$859$	16.6199	−	9.59551i	0.567064	−	0.327395i	0.755976	+	0.654599i	$0.227163\pi$
$860$	−25.4957	+	7.35427i	−0.869396	+	0.250779i
$861$	−2.26140	−	7.85993i	−0.0770685	−	0.267866i
$862$	−40.8487	−	7.20528i	−1.39131	−	0.245413i
$863$	13.5525	−	50.5786i	0.461332	−	1.72171i	−0.207441	−	0.978247i	$-0.566514\pi$
$863$	13.5525	−	50.5786i	0.461332	−	1.72171i	0.668773	−	0.743466i	$-0.266820\pi$
$864$	46.3039	−	66.0863i	1.57529	−	2.24830i
$865$	−28.5135	+	3.04581i	−0.969487	+	0.103561i
$866$	−11.5289	+	24.7198i	−0.391767	+	0.840013i
$867$	53.6327	+	53.6327i	1.82146	+	1.82146i
$868$	29.4537	−	5.74884i	0.999723	−	0.195128i
$869$	34.7567			1.17904
$870$	21.6578	−	32.2226i	0.734268	−	1.09245i
$871$	−6.83680	−	3.94723i	−0.231656	−	0.133747i
$872$	26.0089	+	45.0677i	0.880773	+	1.52618i
$873$	13.5748	+	3.63735i	0.459436	+	0.123106i
$874$	1.42835	+	2.04015i	0.0483146	+	0.0690092i
$875$	26.6638	+	12.8078i	0.901401	+	0.432984i
$876$	3.75326	−	10.3081i	0.126811	−	0.348279i
$877$	15.5988	+	4.17969i	0.526735	+	0.141138i	0.512380	−	0.858759i	$-0.328764\pi$
$877$	15.5988	+	4.17969i	0.526735	+	0.141138i	0.0143549	+	0.999897i	$0.495431\pi$
$878$	−6.31539	−	5.29990i	−0.213134	−	0.178863i
$879$	−43.8122	+	75.8849i	−1.47775	+	2.55953i
$880$	7.18435	−	20.9639i	0.242184	−	0.706692i
$881$	−49.7235			−1.67523			−0.837613	−	0.546264i	$-0.816050\pi$
$881$	−49.7235			−1.67523			−0.837613	+	0.546264i	$0.816050\pi$
$882$	45.1182	−	57.9547i	1.51921	−	1.95144i
$883$	−39.0926	+	39.0926i	−1.31557	+	1.31557i	−0.398330	+	0.917242i	$0.630410\pi$
$883$	−39.0926	+	39.0926i	−1.31557	+	1.31557i	−0.917242	+	0.398330i	$0.869590\pi$
$884$	14.8486	−	2.61635i	0.499411	−	0.0879972i
$885$	−67.1316	+	7.17102i	−2.25661	+	0.241051i
$886$	−27.7396	+	2.42521i	−0.931931	+	0.0814765i
$887$	12.4497	+	3.33589i	0.418020	+	0.112008i	0.461697	−	0.887038i	$-0.347241\pi$
$887$	12.4497	+	3.33589i	0.418020	+	0.112008i	−0.0436773	+	0.999046i	$0.513907\pi$
$888$	−32.0333	−	18.5022i	−1.07497	−	0.620893i
$889$	−14.7360	+	15.2869i	−0.494231	+	0.512707i
$890$	10.7387	+	3.67799i	0.359963	+	0.123287i
$891$	−29.4682	−	51.0404i	−0.987221	−	1.70992i
$892$	−29.6534	−	2.59796i	−0.992869	−	0.0869860i
$893$	−0.590448	+	0.158210i	−0.0197586	+	0.00529430i
$894$	11.5062	−	24.6713i	0.384825	−	0.825130i
$895$	−4.06203	+	25.9314i	−0.135779	+	0.866789i
$896$	−23.2714	−	18.8267i	−0.777442	−	0.628955i
$897$	−7.00598	−	7.00598i	−0.233923	−	0.233923i
$898$	−7.61347	−	20.9218i	−0.254065	−	0.698169i
$899$	−18.6810	−	10.7855i	−0.623046	−	0.359716i
$900$	−28.0179	−	68.6985i	−0.933929	−	2.28995i
$901$	−15.1790	+	8.76361i	−0.505686	+	0.291958i
$902$	−0.582902	+	3.30463i	−0.0194085	+	0.110032i
$903$	44.3413	+	24.5270i	1.47558	+	0.816206i
$904$	−6.95049	−	25.9585i	−0.231170	−	0.863365i
$905$	49.1378	−	18.9579i	1.63339	−	0.630184i
$906$	4.43010	+	50.6716i	0.147180	+	1.68345i
$907$	−24.3312	+	6.51953i	−0.807905	+	0.216477i	−0.639052	−	0.769164i	$-0.720673\pi$
$907$	−24.3312	+	6.51953i	−0.807905	+	0.216477i	−0.168853	+	0.985641i	$0.554006\pi$
$908$	4.68189	−	6.68471i	0.155374	−	0.221840i
$909$	−116.705			−3.87085
$910$	−0.493667	+	9.89891i	−0.0163649	+	0.328146i
$911$			53.5648i			1.77468i	0.461116	+	0.887340i	$0.347449\pi$
$911$			53.5648i			1.77468i	−0.461116	+	0.887340i	$0.652551\pi$
$912$	−7.18940	+	5.03147i	−0.238065	+	0.166609i
$913$	−9.28587	−	34.6553i	−0.307318	−	1.14692i
$914$	0.291206	+	3.33083i	0.00963225	+	0.110174i
$915$	−3.73855	+	8.43542i	−0.123593	+	0.278866i
$916$	−29.2992	−	10.6681i	−0.968074	−	0.352483i
$917$	6.45397	+	10.7195i	0.213129	+	0.353989i
$918$	126.427	+	22.3005i	4.17273	+	0.736025i
$919$	−5.91387	−	10.2431i	−0.195081	−	0.337890i	0.751846	−	0.659338i	$-0.229164\pi$
$919$	−5.91387	−	10.2431i	−0.195081	−	0.337890i	−0.946927	+	0.321449i	$0.895830\pi$
$920$	6.64279	−	14.9810i	0.219006	−	0.493909i
$921$	−1.92921	+	3.34149i	−0.0635697	+	0.110106i
$922$	6.77844	+	18.6271i	0.223236	+	0.613451i
$923$	−0.815832	+	0.815832i	−0.0268534	+	0.0268534i
$924$	−38.0218	+	18.5808i	−1.25082	+	0.611265i
$925$	−18.0198	+	9.25873i	−0.592488	+	0.304425i
$926$	−12.3071	−	5.73980i	−0.404436	−	0.188622i
$927$	−23.2699	−	86.8446i	−0.764285	−	2.85235i
$928$	3.72983	+	21.1904i	0.122438	+	0.695610i
$929$	−47.3135	+	27.3165i	−1.55231	+	0.896224i	−0.554353	+	0.832282i	$0.687034\pi$
$929$	−47.3135	+	27.3165i	−1.55231	+	0.896224i	−0.997954	+	0.0639427i	$0.979633\pi$
$930$	−51.9888	+	25.4620i	−1.70478	+	0.834933i
$931$	−4.03004	+	2.52828i	−0.132079	+	0.0828609i
$932$	14.5184	−	6.76790i	0.475566	−	0.221690i
$933$	−9.04232	+	33.7464i	−0.296032	+	1.10481i
$934$	3.85686	+	44.1149i	0.126200	+	1.44348i
$935$	35.0571	−	3.74481i	1.14649	−	0.122468i
$936$	17.5811	−	17.5747i	0.574655	−	0.574446i
$937$	36.1144	+	36.1144i	1.17981	+	1.17981i	0.979793	+	0.200015i	$0.0640990\pi$
$937$	36.1144	+	36.1144i	1.17981	+	1.17981i	0.200015	+	0.979793i	$0.435901\pi$
$938$	−20.1606	+	14.6732i	−0.658266	+	0.479097i
$939$		−	26.7013i		−	0.871365i
$940$	2.89781	+	2.78957i	0.0945162	+	0.0909858i
$941$	−38.0916	−	21.9922i	−1.24175	−	0.716924i	−0.272299	−	0.962213i	$-0.587784\pi$
$941$	−38.0916	−	21.9922i	−1.24175	−	0.716924i	−0.969450	+	0.245288i	$0.921117\pi$
$942$	8.65250	−	10.3104i	0.281914	−	0.335930i
$943$	−0.642254	+	2.39692i	−0.0209147	+	0.0780546i
$944$	24.0570	−	28.6559i	0.782988	−	0.932670i
$945$	−32.7729	+	77.7678i	−1.06610	+	2.52979i
$946$	−11.9238	−	17.0312i	−0.387677	−	0.553731i
$947$	3.62153	−	13.5157i	0.117684	−	0.439203i	−0.881790	−	0.471643i	$-0.843661\pi$
$947$	3.62153	−	13.5157i	0.117684	−	0.439203i	0.999474	+	0.0324401i	$0.0103278\pi$
$948$	−7.90394	+	90.2165i	−0.256708	+	2.93010i
$949$	1.00650	−	1.74330i	0.0326723	−	0.0565900i
$950$	0.183726	+	4.80224i	0.00596087	+	0.155805i
$951$		−	20.5441i		−	0.666187i
$952$	11.4879	−	46.2158i	0.372326	−	1.49786i
$953$	−7.62036	+	7.62036i	−0.246848	+	0.246848i	−0.819676	−	0.572828i	$-0.805846\pi$
$953$	−7.62036	+	7.62036i	−0.246848	+	0.246848i	0.572828	+	0.819676i	$0.305846\pi$
$954$	−12.2145	+	26.1899i	−0.395459	+	0.847930i
$955$	1.61315	+	1.30178i	0.0522004	+	0.0421246i
$956$	−30.8337	+	25.8662i	−0.997235	+	0.836573i
$957$	29.3826	+	7.87306i	0.949806	+	0.254500i
$958$	0.191575	−	1.08609i	0.00618949	−	0.0350899i
$959$	1.33300	−	0.383522i	0.0430448	−	0.0123846i
$960$	52.7813	+	23.4155i	1.70351	+	0.755731i
$961$	0.581578	+	1.00732i	0.0187606	+	0.0324943i
$962$	−5.19970	−	4.36360i	−0.167645	−	0.140688i
$963$	13.6379	+	50.8974i	0.439475	+	1.64014i
$964$	9.04030	+	51.3064i	0.291168	+	1.65247i
$965$	31.8450	−	23.2194i	1.02513	−	0.747460i
$966$	−29.2067	+	11.2393i	−0.939711	+	0.361620i
$967$	−1.97282	+	1.97282i	−0.0634417	+	0.0634417i	−0.738116	−	0.674674i	$-0.764284\pi$
$967$	−1.97282	+	1.97282i	−0.0634417	+	0.0634417i	0.674674	+	0.738116i	$0.264284\pi$
$968$	−13.7497	−	0.00249882i	−0.441934	−	8.03150e-5i
$969$	−12.0904	−	6.98039i	−0.388399	−	0.224243i
$970$	−0.408066	+	5.97613i	−0.0131022	+	0.191882i
$971$	−10.2184	−	17.6987i	−0.327923	−	0.567979i	0.654177	−	0.756342i	$-0.273015\pi$
$971$	−10.2184	−	17.6987i	−0.327923	−	0.567979i	−0.982099	+	0.188363i	$0.939682\pi$
$972$	61.6109	−	28.7206i	1.97617	−	0.921213i
$973$	0.571554	+	31.1485i	0.0183232	+	0.998576i
$974$	−29.8041	−	42.5702i	−0.954985	−	1.36404i
$975$	−4.03851	−	18.6876i	−0.129336	−	0.598483i
$976$	−1.74771	−	4.80541i	−0.0559428	−	0.153817i
$977$	−4.05294	+	1.08598i	−0.129665	+	0.0347437i	−0.323068	−	0.946376i	$-0.604714\pi$
$977$	−4.05294	+	1.08598i	−0.129665	+	0.0347437i	0.193403	+	0.981119i	$0.438048\pi$
$978$	19.6787	+	54.0770i	0.629256	+	1.72919i
$979$			8.89360i			0.284241i
$980$	27.9406	+	14.1182i	0.892529	+	0.450991i
$981$			136.490i			4.35781i
$982$	−22.5120	+	8.19215i	−0.718386	+	0.261422i
$983$	−17.1102	+	4.58467i	−0.545731	+	0.146228i	−0.521143	−	0.853469i	$-0.674494\pi$
$983$	−17.1102	+	4.58467i	−0.545731	+	0.146228i	−0.0245883	+	0.999698i	$0.507827\pi$
$984$	−8.44515	−	2.26452i	−0.269221	−	0.0721901i
$985$	40.3022	+	17.8618i	1.28414	+	0.569125i
$986$	−28.0417	+	19.6324i	−0.893028	+	0.625224i
$987$	−0.140921	−	7.67989i	−0.00448555	−	0.244454i
$988$	−1.45943	+	0.680330i	−0.0464308	+	0.0216442i
$989$	−7.68715	−	13.3145i	−0.244437	−	0.423378i
$990$	43.8086	−	38.2082i	1.39233	−	1.21434i
$991$	8.43961	+	4.87261i	0.268093	+	0.154784i	0.628021	−	0.778197i	$-0.283865\pi$
$991$	8.43961	+	4.87261i	0.268093	+	0.154784i	−0.359928	+	0.932980i	$0.617199\pi$
$992$	10.9816	−	30.1434i	0.348667	−	0.957054i
$993$	−27.9290	+	27.9290i	−0.886299	+	0.886299i
$994$	1.30880	+	3.40106i	0.0415126	+	0.107875i
$995$	52.0555	+	8.15425i	1.65027	+	0.258507i
$996$	92.0652	−	16.2221i	2.91720	−	0.514016i
$997$	15.9489	+	59.5220i	0.505105	+	1.88508i	0.463815	+	0.885932i	$0.346480\pi$
$997$	15.9489	+	59.5220i	0.505105	+	1.88508i	0.0412903	+	0.999147i	$0.486853\pi$
$998$	13.4236	−	15.9957i	0.424917	−	0.506334i
$999$	−28.8993	−	50.0551i	−0.914334	−	1.58367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.5	✓	176
5.3	odd	4	inner	280.2.br.a.123.28	yes	176
7.2	even	3	inner	280.2.br.a.107.36	yes	176
8.3	odd	2	inner	280.2.br.a.67.33	yes	176
35.23	odd	12	inner	280.2.br.a.163.33	yes	176
40.3	even	4	inner	280.2.br.a.123.36	yes	176
56.51	odd	6	inner	280.2.br.a.107.28	yes	176
280.163	even	12	inner	280.2.br.a.163.5	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.5	✓	176	1.1	even	1	trivial
280.2.br.a.67.33	yes	176	8.3	odd	2	inner
280.2.br.a.107.28	yes	176	56.51	odd	6	inner
280.2.br.a.107.36	yes	176	7.2	even	3	inner
280.2.br.a.123.28	yes	176	5.3	odd	4	inner
280.2.br.a.123.36	yes	176	40.3	even	4	inner
280.2.br.a.163.5	yes	176	280.163	even	12	inner
280.2.br.a.163.33	yes	176	35.23	odd	12	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32896 + 0.483609i) q^{2} +(0.835437 + 3.11790i) q^{3} +(1.53224 - 1.28539i) q^{4} +(0.804876 + 2.08619i) q^{5} +(-2.61810 - 3.73952i) q^{6} +(-2.64531 + 0.0485395i) q^{7} +(-1.41466 + 2.44923i) q^{8} +(-6.42524 + 3.70961i) q^{9} +O(q^{10})\)	\(q+(-1.32896 + 0.483609i) q^{2} +(0.835437 + 3.11790i) q^{3} +(1.53224 - 1.28539i) q^{4} +(0.804876 + 2.08619i) q^{5} +(-2.61810 - 3.73952i) q^{6} +(-2.64531 + 0.0485395i) q^{7} +(-1.41466 + 2.44923i) q^{8} +(-6.42524 + 3.70961i) q^{9} +(-2.07854 - 2.38320i) q^{10} +(1.23882 - 2.14570i) q^{11} +(5.28780 + 3.70352i) q^{12} +(0.837650 + 0.837650i) q^{13} +(3.49202 - 1.34380i) q^{14} +(-5.83209 + 4.25240i) q^{15} +(0.695547 - 3.93906i) q^{16} +(6.14695 - 1.64707i) q^{17} +(6.74485 - 8.03721i) q^{18} +(-0.588582 + 0.339818i) q^{19} +(3.91483 + 2.16197i) q^{20} +(-2.36133 - 8.20723i) q^{21} +(-0.608659 + 3.45065i) q^{22} +(-0.670633 + 2.50284i) q^{23} +(-8.81831 - 2.36458i) q^{24} +(-3.70435 + 3.35824i) q^{25} +(-1.51829 - 0.708105i) q^{26} +(-10.0867 - 10.0867i) q^{27} +(-3.99086 + 3.47462i) q^{28} +3.80356 q^{29} +(5.69408 - 8.47170i) q^{30} +(-4.91145 - 2.83563i) q^{31} +(0.980615 + 5.57121i) q^{32} +(7.72504 + 2.06992i) q^{33} +(-7.37248 + 5.16160i) q^{34} +(-2.23041 - 5.47953i) q^{35} +(-5.07674 + 13.9430i) q^{36} +(3.91379 + 1.04870i) q^{37} +(0.617860 - 0.736247i) q^{38} +(-1.91190 + 3.31151i) q^{39} +(-6.24818 - 0.979912i) q^{40} +0.957683 q^{41} +(7.10719 + 9.76509i) q^{42} +(-4.19558 + 4.19558i) q^{43} +(-0.859886 - 4.88011i) q^{44} +(-12.9105 - 10.4185i) q^{45} +(-0.319153 - 3.65048i) q^{46} +(0.868770 + 0.232786i) q^{47} +(12.8627 - 1.12220i) q^{48} +(6.99529 - 0.256804i) q^{49} +(3.29884 - 6.25441i) q^{50} +(10.2708 + 17.7895i) q^{51} +(2.36019 + 0.206778i) q^{52} +(-2.66036 + 0.712842i) q^{53} +(18.2828 + 8.52675i) q^{54} +(5.47344 + 0.857389i) q^{55} +(3.62332 - 6.54764i) q^{56} +(-1.55124 - 1.55124i) q^{57} +(-5.05476 + 1.83943i) q^{58} +(8.10063 + 4.67690i) q^{59} +(-3.47020 + 14.0122i) q^{60} +(1.10707 - 0.639170i) q^{61} +(7.89844 + 1.39320i) q^{62} +(16.8167 - 10.1249i) q^{63} +(-3.99748 - 6.92966i) q^{64} +(-1.07329 + 2.42170i) q^{65} +(-11.2673 + 0.985070i) q^{66} +(-6.43707 + 1.72481i) q^{67} +(7.30150 - 10.4249i) q^{68} -8.36385 q^{69} +(5.61406 + 6.20341i) q^{70} +0.973953i q^{71} +(0.00381367 - 20.9847i) q^{72} +(-0.439806 - 1.64138i) q^{73} +(-5.70841 + 0.499073i) q^{74} +(-13.5654 - 8.74417i) q^{75} +(-0.465053 + 1.27724i) q^{76} +(-3.17291 + 5.73618i) q^{77} +(0.939355 - 5.32546i) q^{78} +(7.01405 + 12.1487i) q^{79} +(8.77745 - 1.71942i) q^{80} +(11.8936 - 20.6003i) q^{81} +(-1.27272 + 0.463144i) q^{82} +(10.2393 - 10.2393i) q^{83} +(-14.1676 - 9.54026i) q^{84} +(8.38363 + 11.4980i) q^{85} +(3.54672 - 7.60476i) q^{86} +(3.17763 + 11.8591i) q^{87} +(3.50282 + 6.06961i) q^{88} +(-3.10863 + 1.79477i) q^{89} +(22.1959 + 7.60206i) q^{90} +(-2.25650 - 2.17518i) q^{91} +(2.18955 + 4.69698i) q^{92} +(4.73798 - 17.6824i) q^{93} +(-1.26713 + 0.110783i) q^{94} +(-1.18266 - 0.954381i) q^{95} +(-16.5512 + 7.71185i) q^{96} +(-1.33941 - 1.33941i) q^{97} +(-9.17223 + 3.72427i) q^{98} +18.3822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

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