LMFDB - Embedded newform 980.2.x.j.263.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,4,0,0,0,0,0,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.1
Character	$\chi$	$=$	980.263
Dual form			980.2.x.j.667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34206 + 0.445955i) q^{2} +(-0.815107 - 3.04202i) q^{3} +(1.60225 - 1.19700i) q^{4} +(0.727838 + 2.11430i) q^{5} +(2.45053 + 3.71907i) q^{6} +(-1.61650 + 2.32097i) q^{8} +(-5.99142 + 3.45915i) q^{9} +(-1.91968 - 2.51293i) q^{10} +(3.44275 + 1.98767i) q^{11} +(-4.94729 - 3.89839i) q^{12} +(-2.52606 - 2.52606i) q^{13} +(5.83847 - 3.93748i) q^{15} +(1.13440 - 3.83577i) q^{16} +(-0.277420 - 1.03535i) q^{17} +(6.49821 - 7.31428i) q^{18} +(0.658126 + 1.13991i) q^{19} +(3.69698 + 2.51641i) q^{20} +(-5.50679 - 1.13226i) q^{22} +(5.02084 + 1.34533i) q^{23} +(8.37807 + 3.02560i) q^{24} +(-3.94050 + 3.07773i) q^{25} +(4.51663 + 2.26361i) q^{26} +(8.72570 + 8.72570i) q^{27} +4.50936i q^{29} +(-6.07964 + 7.88803i) q^{30} +(2.23010 + 1.28755i) q^{31} +(0.188156 + 5.65372i) q^{32} +(3.24033 - 12.0931i) q^{33} +(0.834032 + 1.26578i) q^{34} +(-5.45915 + 12.7141i) q^{36} +(7.29473 + 1.95462i) q^{37} +(-1.39159 - 1.23633i) q^{38} +(-5.62531 + 9.74333i) q^{39} +(-6.08378 - 1.72848i) q^{40} +11.3180 q^{41} +(1.77452 - 1.77452i) q^{43} +(7.89537 - 0.936217i) q^{44} +(-11.6744 - 10.1499i) q^{45} +(-7.33822 + 0.433557i) q^{46} +(1.76949 - 6.60383i) q^{47} +(-12.5932 - 0.324292i) q^{48} +(3.91586 - 5.88779i) q^{50} +(-2.92342 + 1.68784i) q^{51} +(-7.07105 - 1.02369i) q^{52} +(-8.08454 + 2.16624i) q^{53} +(-15.6017 - 7.81913i) q^{54} +(-1.69676 + 8.72570i) q^{55} +(2.93118 - 2.93118i) q^{57} +(-2.01097 - 6.05182i) q^{58} +(4.17259 - 7.22714i) q^{59} +(4.64153 - 13.2974i) q^{60} +(0.673601 + 1.16671i) q^{61} +(-3.56712 - 0.733444i) q^{62} +(-2.77382 - 7.50373i) q^{64} +(3.50228 - 7.17940i) q^{65} +(1.04426 + 17.6747i) q^{66} +(5.32697 - 1.42736i) q^{67} +(-1.68380 - 1.32681i) q^{68} -16.3701i q^{69} +3.47330i q^{71} +(1.65657 - 19.4976i) q^{72} +(2.33220 - 0.624911i) q^{73} +(-10.6616 + 0.629911i) q^{74} +(12.5745 + 9.47841i) q^{75} +(2.41895 + 1.03864i) q^{76} +(3.20442 - 15.5848i) q^{78} +(-1.72570 - 2.98900i) q^{79} +(8.93562 - 0.393371i) q^{80} +(9.05394 - 15.6819i) q^{81} +(-15.1894 + 5.04730i) q^{82} +(8.37751 - 8.37751i) q^{83} +(1.98711 - 1.34011i) q^{85} +(-1.59015 + 3.17286i) q^{86} +(13.7176 - 3.67561i) q^{87} +(-10.1785 + 4.77744i) q^{88} +(8.15730 - 4.70962i) q^{89} +(20.1942 + 8.41554i) q^{90} +(9.65498 - 3.85438i) q^{92} +(2.09898 - 7.83352i) q^{93} +(0.570251 + 9.65185i) q^{94} +(-1.93109 + 2.22114i) q^{95} +(17.0454 - 5.18076i) q^{96} +(-9.04418 + 9.04418i) q^{97} -27.5026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) $ 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.34206	+	0.445955i	−0.948979	+	0.315338i
$2$	−1.34206	+	0.445955i	−0.948979	+	0.315338i
$3$	−0.815107	−	3.04202i	−0.470602	−	1.75631i	−0.637613	−	0.770357i	$-0.720078\pi$
$3$	−0.815107	−	3.04202i	−0.470602	−	1.75631i	0.167011	−	0.985955i	$-0.446588\pi$
$4$	1.60225	−	1.19700i	0.801124	−	0.598499i
$5$	0.727838	+	2.11430i	0.325499	+	0.945542i
$5$	0.727838	+	2.11430i	0.325499	+	0.945542i
$6$	2.45053	+	3.71907i	1.00042	+	1.51830i
$7$		0			0
$7$		0			0
$8$	−1.61650	+	2.32097i	−0.571521	+	0.820588i
$9$	−5.99142	+	3.45915i	−1.99714	+	1.15305i
$10$	−1.91968	−	2.51293i	−0.607057	−	0.794658i
$11$	3.44275	+	1.98767i	1.03803	+	0.599306i	0.919274	−	0.393618i	$-0.128777\pi$
$11$	3.44275	+	1.98767i	1.03803	+	0.599306i	0.118754	+	0.992924i	$0.462110\pi$
$12$	−4.94729	−	3.89839i	−1.42816	−	1.12537i
$13$	−2.52606	−	2.52606i	−0.700602	−	0.700602i	0.263937	−	0.964540i	$-0.414979\pi$
$13$	−2.52606	−	2.52606i	−0.700602	−	0.700602i	−0.964540	+	0.263937i	$0.914979\pi$
$14$		0			0
$15$	5.83847	−	3.93748i	1.50749	−	1.01665i
$16$	1.13440	−	3.83577i	0.283599	−	0.958943i
$17$	−0.277420	−	1.03535i	−0.0672843	−	0.251108i	0.924089	−	0.382177i	$-0.124826\pi$
$17$	−0.277420	−	1.03535i	−0.0672843	−	0.251108i	−0.991373	+	0.131069i	$0.958159\pi$
$18$	6.49821	−	7.31428i	1.53164	−	1.72399i
$19$	0.658126	+	1.13991i	0.150984	+	0.261513i	0.931590	−	0.363512i	$-0.118422\pi$
$19$	0.658126	+	1.13991i	0.150984	+	0.261513i	−0.780605	+	0.625024i	$0.785089\pi$
$20$	3.69698	+	2.51641i	0.826671	+	0.562686i
$21$		0			0
$22$	−5.50679	−	1.13226i	−1.17405	−	0.241399i
$23$	5.02084	+	1.34533i	1.04692	+	0.280521i	0.740977	−	0.671530i	$-0.234363\pi$
$23$	5.02084	+	1.34533i	1.04692	+	0.280521i	0.305940	+	0.952051i	$0.401029\pi$
$24$	8.37807	+	3.02560i	1.71017	+	0.617598i
$25$	−3.94050	+	3.07773i	−0.788101	+	0.615546i
$26$	4.51663	+	2.26361i	0.885784	+	0.443931i
$27$	8.72570	+	8.72570i	1.67926	+	1.67926i
$28$		0			0
$29$			4.50936i			0.837366i	0.908132	+	0.418683i	$0.137508\pi$
$29$			4.50936i			0.837366i	−0.908132	+	0.418683i	$0.862492\pi$
$30$	−6.07964	+	7.88803i	−1.10998	+	1.44015i
$31$	2.23010	+	1.28755i	0.400539	+	0.231251i	0.686716	−	0.726925i	$-0.259051\pi$
$31$	2.23010	+	1.28755i	0.400539	+	0.231251i	−0.286178	+	0.958177i	$0.592385\pi$
$32$	0.188156	+	5.65372i	0.0332615	+	0.999447i
$33$	3.24033	−	12.0931i	0.564069	−	2.10513i
$34$	0.834032	+	1.26578i	0.143035	+	0.217079i
$35$		0			0
$36$	−5.45915	+	12.7141i	−0.909858	+	2.11902i
$37$	7.29473	+	1.95462i	1.19925	+	0.321337i	0.802534	−	0.596606i	$-0.203485\pi$
$37$	7.29473	+	1.95462i	1.19925	+	0.321337i	0.396712	+	0.917943i	$0.370151\pi$
$38$	−1.39159	−	1.23633i	−0.225746	−	0.200559i
$39$	−5.62531	+	9.74333i	−0.900771	+	1.56018i
$40$	−6.08378	−	1.72848i	−0.961930	−	0.273297i
$41$	11.3180			1.76757			0.883784	−	0.467894i	$-0.154987\pi$
$41$	11.3180			1.76757			0.883784	+	0.467894i	$0.154987\pi$
$42$		0			0
$43$	1.77452	−	1.77452i	0.270611	−	0.270611i	−0.558735	−	0.829346i	$-0.688713\pi$
$43$	1.77452	−	1.77452i	0.270611	−	0.270611i	0.829346	+	0.558735i	$0.188713\pi$
$44$	7.89537	−	0.936217i	1.19027	−	0.141140i
$45$	−11.6744	−	10.1499i	−1.74032	−	1.51306i
$46$	−7.33822	+	0.433557i	−1.08196	+	0.0639245i
$47$	1.76949	−	6.60383i	0.258107	−	0.963268i	−0.708229	−	0.705983i	$-0.750505\pi$
$47$	1.76949	−	6.60383i	0.258107	−	0.963268i	0.966336	−	0.257285i	$-0.0828279\pi$
$48$	−12.5932	−	0.324292i	−1.81766	−	0.0468075i
$49$		0			0
$50$	3.91586	−	5.88779i	0.553786	−	0.832659i
$51$	−2.92342	+	1.68784i	−0.409360	+	0.236344i
$52$	−7.07105	−	1.02369i	−0.980579	−	0.141960i
$53$	−8.08454	+	2.16624i	−1.11050	+	0.297557i	−0.767032	−	0.641609i	$-0.778267\pi$
$53$	−8.08454	+	2.16624i	−1.11050	+	0.297557i	−0.343465	+	0.939166i	$0.611601\pi$
$54$	−15.6017	−	7.81913i	−2.12312	−	1.06405i
$55$	−1.69676	+	8.72570i	−0.228792	+	1.17657i
$56$		0			0
$57$	2.93118	−	2.93118i	0.388244	−	0.388244i
$58$	−2.01097	−	6.05182i	−0.264053	−	0.794643i
$59$	4.17259	−	7.22714i	0.543225	−	0.940893i	−0.455491	−	0.890240i	$-0.650536\pi$
$59$	4.17259	−	7.22714i	0.543225	−	0.940893i	0.998716	−	0.0506532i	$-0.0161303\pi$
$60$	4.64153	−	13.2974i	0.599218	−	1.71669i
$61$	0.673601	+	1.16671i	0.0862458	+	0.149382i	0.905921	−	0.423446i	$-0.139180\pi$
$61$	0.673601	+	1.16671i	0.0862458	+	0.149382i	−0.819676	+	0.572828i	$0.805846\pi$
$62$	−3.56712	−	0.733444i	−0.453025	−	0.0931475i
$63$		0			0
$64$	−2.77382	−	7.50373i	−0.346728	−	0.937966i
$65$	3.50228	−	7.17940i	0.434404	−	0.890495i
$66$	1.04426	+	17.6747i	0.128539	+	2.17560i
$67$	5.32697	−	1.42736i	0.650793	−	0.174379i	0.0817054	−	0.996657i	$-0.473963\pi$
$67$	5.32697	−	1.42736i	0.650793	−	0.174379i	0.569087	+	0.822277i	$0.307297\pi$
$68$	−1.68380	−	1.32681i	−0.204191	−	0.160899i
$69$		−	16.3701i		−	1.97073i
$70$		0			0
$71$			3.47330i			0.412205i	0.978530	+	0.206102i	$0.0660780\pi$
$71$			3.47330i			0.412205i	−0.978530	+	0.206102i	$0.933922\pi$
$72$	1.65657	−	19.4976i	0.195229	−	2.29782i
$73$	2.33220	−	0.624911i	0.272963	−	0.0731403i	−0.119741	−	0.992805i	$-0.538206\pi$
$73$	2.33220	−	0.624911i	0.272963	−	0.0731403i	0.392704	+	0.919665i	$0.371540\pi$
$74$	−10.6616	+	0.629911i	−1.23939	+	0.0732256i
$75$	12.5745	+	9.47841i	1.45197	+	1.09447i
$76$	2.41895	+	1.03864i	0.277472	+	0.119140i
$77$		0			0
$78$	3.20442	−	15.5848i	0.362829	−	1.76463i
$79$	−1.72570	−	2.98900i	−0.194157	−	0.336289i	0.752467	−	0.658630i	$-0.228864\pi$
$79$	−1.72570	−	2.98900i	−0.194157	−	0.336289i	−0.946624	+	0.322341i	$0.895530\pi$
$80$	8.93562	−	0.393371i	0.999032	−	0.0439802i
$81$	9.05394	−	15.6819i	1.00599	−	1.74243i
$82$	−15.1894	+	5.04730i	−1.67739	+	0.557382i
$83$	8.37751	−	8.37751i	0.919551	−	0.919551i	−0.0774458	−	0.996997i	$-0.524676\pi$
$83$	8.37751	−	8.37751i	0.919551	−	0.919551i	0.996997	+	0.0774458i	$0.0246765\pi$
$84$		0			0
$85$	1.98711	−	1.34011i	0.215533	−	0.145356i
$86$	−1.59015	+	3.17286i	−0.171470	+	0.342138i
$87$	13.7176	−	3.67561i	1.47068	−	0.394066i
$88$	−10.1785	+	4.77744i	−1.08504	+	0.509277i
$89$	8.15730	−	4.70962i	0.864672	−	0.499219i	−0.000902138	−	1.00000i	$-0.500287\pi$
$89$	8.15730	−	4.70962i	0.864672	−	0.499219i	0.865574	+	0.500781i	$0.166954\pi$
$90$	20.1942	+	8.41554i	2.12866	+	0.887076i
$91$		0			0
$92$	9.65498	−	3.85438i	1.00660	−	0.401846i
$93$	2.09898	−	7.83352i	0.217655	−	0.812298i
$94$	0.570251	+	9.65185i	0.0588169	+	0.995512i
$95$	−1.93109	+	2.22114i	−0.198126	+	0.227884i
$96$	17.0454	−	5.18076i	1.73969	−	0.528759i
$97$	−9.04418	+	9.04418i	−0.918298	+	0.918298i	−0.996906	−	0.0786079i	$-0.974952\pi$
$97$	−9.04418	+	9.04418i	−0.918298	+	0.918298i	0.0786079	+	0.996906i	$0.474952\pi$
$98$		0			0
$99$	−27.5026			−2.76411
$100$	−2.62963	+	9.64806i	−0.262963	+	0.964806i
$101$	−5.13644	+	8.89658i	−0.511095	+	0.885242i	0.488822	+	0.872383i	$0.337427\pi$
$101$	−5.13644	+	8.89658i	−0.511095	+	0.885242i	−0.999917	+	0.0128590i	$0.995907\pi$
$102$	3.17070	−	3.56889i	0.313946	−	0.353373i
$103$	−4.03745	−	1.08183i	−0.397821	−	0.106596i	0.0543611	−	0.998521i	$-0.482688\pi$
$103$	−4.03745	−	1.08183i	−0.397821	−	0.106596i	−0.452183	+	0.891925i	$0.649354\pi$
$104$	9.94629	−	1.77953i	0.975314	−	0.174497i
$105$		0			0
$106$	9.88388	−	6.51257i	0.960007	−	0.632557i
$107$	4.11801	−	15.3686i	0.398104	−	1.48574i	−0.418326	−	0.908297i	$-0.637383\pi$
$107$	4.11801	−	15.3686i	0.398104	−	1.48574i	0.816429	−	0.577446i	$-0.195950\pi$
$108$	24.4254	+	3.53609i	2.35033	+	0.340261i
$109$	2.58551	+	1.49274i	0.247647	+	0.142979i	0.618686	−	0.785638i	$-0.287665\pi$
$109$	2.58551	+	1.49274i	0.247647	+	0.142979i	−0.371040	+	0.928617i	$0.620999\pi$
$110$	−1.61411	−	12.4671i	−0.153899	−	1.18869i
$111$		−	23.7839i		−	2.25747i
$112$		0			0
$113$	−0.407307	−	0.407307i	−0.0383162	−	0.0383162i	0.687689	−	0.726005i	$-0.258625\pi$
$113$	−0.407307	−	0.407307i	−0.0383162	−	0.0383162i	−0.726005	+	0.687689i	$0.758625\pi$
$114$	−2.62664	+	5.24099i	−0.246008	+	0.490864i
$115$	0.809931	+	11.5947i	0.0755265	+	1.08121i
$116$	5.39769	+	7.22511i	0.501163	+	0.670834i
$117$	23.8727	+	6.39666i	2.20703	+	0.591371i
$118$	−2.37688	+	11.5600i	−0.218810	+	1.06419i
$119$		0			0
$120$	−0.299139	+	19.9159i	−0.0273076	+	1.81806i
$121$	2.40168	+	4.15983i	0.218334	+	0.378166i
$122$	−1.42431	−	1.26540i	−0.128951	−	0.114564i
$123$	−9.22535	−	34.4295i	−0.831822	−	3.10440i
$124$	5.11438	−	0.606452i	0.459284	−	0.0544610i
$125$	−9.37529	−	6.09130i	−0.838551	−	0.544823i
$126$		0			0
$127$	10.3756	+	10.3756i	0.920687	+	0.920687i	0.997078	−	0.0763907i	$-0.0243396\pi$
$127$	10.3756	+	10.3756i	0.920687	+	0.920687i	−0.0763907	+	0.997078i	$0.524340\pi$
$128$	7.06896	+	8.83345i	0.624814	+	0.780774i
$129$	−6.84453	−	3.95169i	−0.602627	−	0.347927i
$130$	−1.49857	+	11.1970i	−0.131433	+	0.982045i
$131$	−8.53900	+	4.92999i	−0.746056	+	0.430736i	−0.824267	−	0.566201i	$-0.808412\pi$
$131$	−8.53900	+	4.92999i	−0.746056	+	0.430736i	0.0782112	+	0.996937i	$0.475079\pi$
$132$	−9.28357	−	23.2548i	−0.808031	−	2.02407i
$133$		0			0
$134$	−6.51257	+	4.29119i	−0.562600	+	0.370702i
$135$	−12.0978	+	24.7996i	−1.04121	+	2.13441i
$136$	2.85146	+	1.02976i	0.244511	+	0.0883010i
$137$	4.17809	+	15.5929i	0.356958	+	1.33219i	0.878002	+	0.478657i	$0.158876\pi$
$137$	4.17809	+	15.5929i	0.356958	+	1.33219i	−0.521044	+	0.853530i	$0.674457\pi$
$138$	7.30032	+	21.9696i	0.621445	+	1.87018i
$139$	−9.10621			−0.772379			−0.386189	−	0.922420i	$-0.626209\pi$
$139$	−9.10621			−0.772379			−0.386189	+	0.922420i	$0.626209\pi$
$140$		0			0
$141$	−21.5313			−1.81326
$142$	−1.54894	−	4.66137i	−0.129984	−	0.391174i
$143$	−3.67561	−	13.7176i	−0.307370	−	1.14712i
$144$	6.47185	+	26.9057i	0.539321	+	2.24215i
$145$	−9.53412	+	3.28208i	−0.791765	+	0.272562i
$146$	−2.85127	+	1.87872i	−0.235973	+	0.155484i
$147$		0			0
$148$	14.0276	−	5.59999i	1.15306	−	0.460316i
$149$	−1.70973	+	0.987112i	−0.140066	+	0.0808674i	−0.568396	−	0.822755i	$-0.692436\pi$
$149$	−1.70973	+	0.987112i	−0.140066	+	0.0808674i	0.428329	+	0.903623i	$0.359102\pi$
$150$	−21.1026	−	7.11295i	−1.72302	−	0.580770i
$151$	7.47376	+	4.31498i	0.608206	+	0.351148i	0.772263	−	0.635303i	$-0.219125\pi$
$151$	7.47376	+	4.31498i	0.608206	+	0.351148i	−0.164057	+	0.986451i	$0.552458\pi$
$152$	−3.70956	−	0.315174i	−0.300885	−	0.0255640i
$153$	5.24355	+	5.24355i	0.423916	+	0.423916i
$154$		0			0
$155$	−1.09911	+	5.65223i	−0.0882827	+	0.453998i
$156$	2.64959	+	22.3447i	0.212137	+	1.78901i
$157$	−4.10320	−	15.3134i	−0.327471	−	1.22214i	−0.911804	−	0.410625i	$-0.865311\pi$
$157$	−4.10320	−	15.3134i	−0.327471	−	1.22214i	0.584333	−	0.811514i	$-0.301356\pi$
$158$	3.64896	+	3.24184i	0.290295	+	0.257907i
$159$	13.1795	+	22.8276i	1.04520	+	1.81035i
$160$	−11.8167	+	4.51281i	−0.934193	+	0.356769i
$161$		0			0
$162$	−5.15751	+	25.0837i	−0.405212	+	1.97076i
$163$	−6.72849	−	1.80289i	−0.527016	−	0.141213i	−0.0145060	−	0.999895i	$-0.504618\pi$
$163$	−6.72849	−	1.80289i	−0.527016	−	0.141213i	−0.512510	+	0.858681i	$0.671284\pi$
$164$	18.1342	−	13.5476i	1.41604	−	1.05789i
$165$	27.9268	−	1.95078i	2.17410	−	0.151868i
$166$	−7.50712	+	14.9791i	−0.582665	+	1.16260i
$167$	11.9207	+	11.9207i	0.922449	+	0.922449i	0.997202	−	0.0747528i	$-0.0238168\pi$
$167$	11.9207	+	11.9207i	0.922449	+	0.922449i	−0.0747528	+	0.997202i	$0.523817\pi$
$168$		0			0
$169$		−	0.238064i		−	0.0183127i
$170$	−2.06919	+	2.68467i	−0.158700	+	0.205905i
$171$	−7.88621	−	4.55310i	−0.603073	−	0.348185i
$172$	0.719123	−	4.96730i	0.0548327	−	0.378753i
$173$	−0.0573054	+	0.213867i	−0.00435685	+	0.0162600i	−0.968070	−	0.250680i	$-0.919346\pi$
$173$	−0.0573054	+	0.213867i	−0.00435685	+	0.0162600i	0.963713	+	0.266940i	$0.0860125\pi$
$174$	−16.7706	+	11.0503i	−1.27138	+	0.837721i
$175$		0			0
$176$	11.5297	−	10.9508i	0.869083	−	0.825447i
$177$	−25.3862	−	6.80222i	−1.90814	−	0.511286i
$178$	−8.84730	+	9.95838i	−0.663133	+	0.746412i
$179$	10.2023	−	17.6708i	0.762553	−	1.32078i	−0.178978	−	0.983853i	$-0.557279\pi$
$179$	10.2023	−	17.6708i	0.762553	−	1.32078i	0.941531	−	0.336927i	$-0.109388\pi$
$180$	−30.8548	−	2.28844i	−2.29978	−	0.170570i
$181$	13.1697			0.978898			0.489449	−	0.872032i	$-0.337198\pi$
$181$	13.1697			0.978898			0.489449	+	0.872032i	$0.337198\pi$
$182$		0			0
$183$	3.00010	−	3.00010i	0.221774	−	0.221774i
$184$	−11.2387	+	9.47849i	−0.828526	+	0.698764i
$185$	1.17674	+	16.8459i	0.0865158	+	1.23853i
$186$	0.676436	+	11.4491i	0.0495987	+	0.839489i
$187$	1.10284	−	4.11586i	0.0806477	−	0.300981i
$188$	−5.06960	−	12.6991i	−0.369739	−	0.926174i
$189$		0			0
$190$	1.60111	−	3.84208i	0.116157	−	0.278734i
$191$	10.4817	−	6.05163i	0.758431	−	0.437880i	−0.0703012	−	0.997526i	$-0.522396\pi$
$191$	10.4817	−	6.05163i	0.758431	−	0.437880i	0.828732	+	0.559646i	$0.189063\pi$
$192$	−20.5655	+	14.5544i	−1.48419	+	1.05037i
$193$	−0.678188	+	0.181720i	−0.0488170	+	0.0130805i	−0.283145	−	0.959077i	$-0.591378\pi$
$193$	−0.678188	+	0.181720i	−0.0488170	+	0.0130805i	0.234328	+	0.972158i	$0.424711\pi$
$194$	8.10453	−	16.1711i	0.581871	−	1.16102i
$195$	−24.6946	−	4.80202i	−1.76842	−	0.343880i
$196$		0			0
$197$	−1.16924	+	1.16924i	−0.0833051	+	0.0833051i	−0.747531	−	0.664226i	$-0.768761\pi$
$197$	−1.16924	+	1.16924i	−0.0833051	+	0.0833051i	0.664226	+	0.747531i	$0.268761\pi$
$198$	36.9101	−	12.2649i	2.62309	−	0.871630i
$199$	−8.72570	+	15.1133i	−0.618548	+	1.07136i	0.371203	+	0.928552i	$0.378946\pi$
$199$	−8.72570	+	15.1133i	−0.618548	+	1.07136i	−0.989751	+	0.142805i	$0.954388\pi$
$200$	−0.773487	−	14.1210i	−0.0546938	−	0.998503i
$201$	−8.68410	−	15.0413i	−0.612529	−	1.06093i
$202$	2.92593	−	14.2304i	0.205868	−	1.00124i
$203$		0			0
$204$	−2.66370	+	6.20365i	−0.186497	+	0.434343i
$205$	8.23764	+	23.9295i	0.575342	+	1.67131i
$206$	5.90094	−	0.348640i	0.411138	−	0.0242909i
$207$	−34.7356	+	9.30738i	−2.41429	+	0.646907i
$208$	−12.5549	+	6.82383i	−0.870528	+	0.473148i
$209$			5.23255i			0.361943i
$210$		0			0
$211$			6.32503i			0.435433i	0.976012	+	0.217717i	$0.0698608\pi$
$211$			6.32503i			0.435433i	−0.976012	+	0.217717i	$0.930139\pi$
$212$	−10.3604	+	13.1480i	−0.711558	+	0.903010i
$213$	10.5658	−	2.83111i	0.723960	−	0.193984i
$214$	1.32711	+	22.4621i	0.0907190	+	1.53548i
$215$	5.04341	+	2.46029i	0.343958	+	0.167791i
$216$	−34.3572	+	6.14697i	−2.33771	+	0.418248i
$217$		0			0
$218$	−4.13560	−	0.850329i	−0.280098	−	0.0575916i
$219$	−3.80199	−	6.58523i	−0.256914	−	0.444989i
$220$	7.72599	+	16.0117i	0.520886	+	1.07951i
$221$	−1.91456	+	3.31612i	−0.128788	+	0.223067i
$222$	10.6066	+	31.9195i	0.711867	+	2.14229i
$223$	1.13429	−	1.13429i	0.0759578	−	0.0759578i	−0.668107	−	0.744065i	$-0.732895\pi$
$223$	1.13429	−	1.13429i	0.0759578	−	0.0759578i	0.744065	+	0.668107i	$0.232895\pi$
$224$		0			0
$225$	12.9629	−	32.0707i	0.864191	−	2.13805i
$226$	0.728271	+	0.364990i	0.0484439	+	0.0242788i
$227$	−4.84005	+	1.29689i	−0.321246	+	0.0860775i	−0.415838	−	0.909439i	$-0.636512\pi$
$227$	−4.84005	+	1.29689i	−0.321246	+	0.0860775i	0.0945927	+	0.995516i	$0.469845\pi$
$228$	1.18786	−	8.20509i	0.0786681	−	0.543395i
$229$	8.93604	−	5.15923i	0.590510	−	0.340931i	−0.174789	−	0.984606i	$-0.555924\pi$
$229$	8.93604	−	5.15923i	0.590510	−	0.340931i	0.765299	+	0.643675i	$0.222591\pi$
$230$	−6.25770	−	15.1996i	−0.412621	−	1.00223i
$231$		0			0
$232$	−10.4661	−	7.28940i	−0.687132	−	0.478572i
$233$	−3.30639	+	12.3396i	−0.216609	+	0.808395i	0.768985	+	0.639267i	$0.220762\pi$
$233$	−3.30639	+	12.3396i	−0.216609	+	0.808395i	−0.985594	+	0.169129i	$0.945905\pi$
$234$	−34.8912	+	2.06144i	−2.28091	+	0.134761i
$235$	15.2504	−	1.06529i	0.994824	−	0.0694919i
$236$	−1.96534	−	16.5742i	−0.127933	−	1.07889i
$237$	−7.68598	+	7.68598i	−0.499258	+	0.499258i
$238$		0			0
$239$	19.1256			1.23713			0.618565	−	0.785733i	$-0.287714\pi$
$239$	19.1256			1.23713			0.618565	+	0.785733i	$0.287714\pi$
$240$	−8.48013	−	26.8617i	−0.547390	−	1.73391i
$241$	7.07911	−	12.2614i	0.456006	−	0.789825i	−0.542740	−	0.839901i	$-0.682613\pi$
$241$	7.07911	−	12.2614i	0.456006	−	0.789825i	0.998745	+	0.0500757i	$0.0159463\pi$
$242$	−5.07829	−	4.51169i	−0.326445	−	0.290023i
$243$	−19.3260	−	5.17838i	−1.23976	−	0.332193i
$244$	2.47583	+	1.06306i	0.158499	+	0.0680556i
$245$		0			0
$246$	27.7350	+	42.0923i	1.76832	+	2.68371i
$247$	1.21701	−	4.54193i	0.0774363	−	0.288996i
$248$	−6.59335	+	3.09468i	−0.418678	+	0.196512i
$249$	−32.3131	−	18.6560i	−2.04776	−	1.18227i
$250$	15.2986	+	3.99393i	0.967571	+	0.252599i
$251$			8.70910i			0.549714i	0.961485	+	0.274857i	$0.0886305\pi$
$251$			8.70910i			0.549714i	−0.961485	+	0.274857i	$0.911370\pi$
$252$		0			0
$253$	14.6114	+	14.6114i	0.918611	+	0.918611i
$254$	−18.5518	−	9.29764i	−1.16404	−	0.583386i
$255$	−5.69636	−	4.95250i	−0.356720	−	0.310138i
$256$	−13.4263	−	8.70257i	−0.839143	−	0.543911i
$257$	−5.76635	−	1.54509i	−0.359695	−	0.0963799i	0.0744458	−	0.997225i	$-0.476281\pi$
$257$	−5.76635	−	1.54509i	−0.359695	−	0.0963799i	−0.434141	+	0.900845i	$0.642948\pi$
$258$	10.9480	+	2.25105i	0.681596	+	0.140144i
$259$		0			0
$260$	−2.98220	−	15.6954i	−0.184949	−	0.973387i
$261$	−15.5985	−	27.0174i	−0.965524	−	1.67234i
$262$	9.26129	−	10.4244i	0.572164	−	0.644019i
$263$	4.09029	+	15.2652i	0.252218	+	0.941292i	0.969617	+	0.244629i	$0.0786661\pi$
$263$	4.09029	+	15.2652i	0.252218	+	0.941292i	−0.717398	+	0.696663i	$0.754667\pi$
$264$	22.8297	+	27.0692i	1.40507	+	1.66600i
$265$	−10.4643	−	15.5164i	−0.642818	−	0.953167i
$266$		0			0
$267$	−20.9758	−	20.9758i	−1.28370	−	1.28370i
$268$	6.82658	−	8.66334i	0.417000	−	0.529198i
$269$	−6.92467	−	3.99796i	−0.422205	−	0.243760i	0.273815	−	0.961782i	$-0.411714\pi$
$269$	−6.92467	−	3.99796i	−0.422205	−	0.243760i	−0.696020	+	0.718022i	$0.745048\pi$
$270$	5.17648	−	38.6776i	0.315030	−	2.35385i
$271$	−26.0319	+	15.0295i	−1.58133	+	0.912980i	−0.586662	+	0.809832i	$0.699558\pi$
$271$	−26.0319	+	15.0295i	−1.58133	+	0.912980i	−0.994666	+	0.103148i	$0.967108\pi$
$272$	−4.28606	−	0.110372i	−0.259880	−	0.00669229i
$273$		0			0
$274$	−12.5610	−	19.0633i	−0.758835	−	1.15166i
$275$	−19.6837	+	2.76343i	−1.18697	+	0.166641i
$276$	−19.5949	−	26.2289i	−1.17948	−	1.57880i
$277$	−0.639600	−	2.38702i	−0.0384299	−	0.143422i	0.944045	−	0.329816i	$-0.106987\pi$
$277$	−0.639600	−	2.38702i	−0.0384299	−	0.143422i	−0.982475	+	0.186394i	$0.940320\pi$
$278$	12.2211	−	4.06096i	0.732971	−	0.243560i
$279$	−17.8153			−1.06657
$280$		0			0
$281$	−2.85110			−0.170082			−0.0850411	−	0.996377i	$-0.527102\pi$
$281$	−2.85110			−0.170082			−0.0850411	+	0.996377i	$0.527102\pi$
$282$	28.8963	−	9.60201i	1.72075	−	0.571791i
$283$	2.23944	+	8.35771i	0.133121	+	0.496814i	0.999999	−	0.00170684i	$-0.000543303\pi$
$283$	2.23944	+	8.35771i	0.133121	+	0.496814i	−0.866878	+	0.498521i	$0.833877\pi$
$284$	4.15753	+	5.56508i	0.246704	+	0.330227i
$285$	8.33080	+	4.06396i	0.493474	+	0.240728i
$286$	11.0503	+	16.7706i	0.653418	+	0.991667i
$287$		0			0
$288$	−20.6844	−	33.2230i	−1.21884	−	1.95768i
$289$	13.7275	−	7.92555i	0.807497	−	0.466209i
$290$	11.3317	−	8.65654i	0.665420	−	0.508329i
$291$	34.8846	+	20.1406i	2.04497	+	1.18066i
$292$	2.98875	−	3.79290i	0.174903	−	0.221963i
$293$	16.5266	+	16.5266i	0.965497	+	0.965497i	0.999424	−	0.0339277i	$-0.0108016\pi$
$293$	16.5266	+	16.5266i	0.965497	+	0.965497i	−0.0339277	+	0.999424i	$0.510802\pi$
$294$		0			0
$295$	18.3173	+	3.56191i	1.06647	+	0.207382i
$296$	−16.3286	+	13.7712i	−0.949079	+	0.800436i
$297$	12.6966	+	47.3842i	0.736729	+	2.74951i
$298$	1.85435	−	2.08723i	0.107420	−	0.120910i
$299$	−9.28454	−	16.0813i	−0.536939	−	0.930006i
$300$	31.4930	+	0.135178i	1.81825	+	0.00780451i
$301$		0			0
$302$	−11.9545	−	2.45799i	−0.687905	−	0.141442i
$303$	31.2503	+	8.37350i	1.79528	+	0.481045i
$304$	5.11900	−	1.23131i	0.293595	−	0.0706207i
$305$	−1.97650	+	2.27337i	−0.113174	+	0.130173i
$306$	−9.37555	−	4.69877i	−0.535964	−	0.268611i
$307$	−15.0259	−	15.0259i	−0.857575	−	0.857575i	0.133477	−	0.991052i	$-0.457386\pi$
$307$	−15.0259	−	15.0259i	−0.857575	−	0.857575i	−0.991052	+	0.133477i	$0.957386\pi$
$308$		0			0
$309$			13.1638i			0.748863i
$310$	−1.04557	−	8.07579i	−0.0593844	−	0.458674i
$311$	−24.3986	−	14.0866i	−1.38352	−	0.798776i	−0.390945	−	0.920414i	$-0.627852\pi$
$311$	−24.3986	−	14.0866i	−1.38352	−	0.798776i	−0.992574	+	0.121638i	$0.961185\pi$
$312$	−13.5206	−	28.8063i	−0.765456	−	1.63084i
$313$	−6.64347	+	24.7938i	−0.375511	+	1.40143i	0.477085	+	0.878857i	$0.341693\pi$
$313$	−6.64347	+	24.7938i	−0.375511	+	1.40143i	−0.852597	+	0.522570i	$0.824973\pi$
$314$	12.3358	+	18.7216i	0.696150	+	1.05652i
$315$		0			0
$316$	−6.34283	−	2.72346i	−0.356812	−	0.153207i
$317$	25.4060	+	6.80753i	1.42695	+	0.382349i	0.887942	−	0.459955i	$-0.152134\pi$
$317$	25.4060	+	6.80753i	1.42695	+	0.382349i	0.539003	+	0.842304i	$0.318801\pi$
$318$	−27.8678	−	24.7585i	−1.56275	−	1.38839i
$319$	−8.96312	+	15.5246i	−0.501838	+	0.869209i
$320$	13.8462	−	11.3262i	0.774027	−	0.633153i
$321$	−50.1083			−2.79678
$322$		0			0
$323$	0.997621	−	0.997621i	0.0555091	−	0.0555091i
$324$	−4.26451	−	35.9638i	−0.236917	−	1.99799i
$325$	17.7285	+	2.17941i	0.983398	+	0.120892i
$326$	9.83404	−	0.581015i	0.544657	−	0.0321794i
$327$	2.43349	−	9.08191i	0.134572	−	0.502231i
$328$	−18.2955	+	26.2687i	−1.01020	+	1.45044i
$329$		0			0
$330$	−36.6095	+	15.0722i	−2.01528	+	0.829695i
$331$	14.8975	−	8.60110i	0.818843	−	0.472759i	−0.0311741	−	0.999514i	$-0.509925\pi$
$331$	14.8975	−	8.60110i	0.818843	−	0.472759i	0.850017	+	0.526755i	$0.176591\pi$
$332$	3.39499	−	23.4507i	0.186324	−	1.28702i
$333$	−50.4671	+	13.5226i	−2.76558	+	0.741034i
$334$	−21.3143	−	10.6822i	−1.16627	−	0.584502i
$335$	6.89503	+	10.2239i	0.376715	+	0.558592i
$336$		0			0
$337$	−12.9038	+	12.9038i	−0.702913	+	0.702913i	−0.965035	−	0.262121i	$-0.915578\pi$
$337$	−12.9038	+	12.9038i	−0.702913	+	0.702913i	0.262121	+	0.965035i	$0.415578\pi$
$338$	0.106166	+	0.319497i	0.00577468	+	0.0173783i
$339$	−0.907038	+	1.57104i	−0.0492635	+	0.0853270i
$340$	1.57973	−	4.52576i	0.0856732	−	0.245444i
$341$	5.11846	+	8.86543i	0.277180	+	0.480090i
$342$	12.6142	+	2.59364i	0.682100	+	0.140248i
$343$		0			0
$344$	1.25009	+	6.98711i	0.0674002	+	0.376720i
$345$	34.6112	−	11.9148i	1.86340	−	0.641469i
$346$	−0.0184677	−	0.312578i	−0.000992831	−	0.0168043i
$347$	−18.2417	+	4.88784i	−0.979264	+	0.262393i	−0.712735	−	0.701434i	$-0.752544\pi$
$347$	−18.2417	+	4.88784i	−0.979264	+	0.262393i	−0.266529	+	0.963827i	$0.585877\pi$
$348$	17.5792	−	22.3091i	0.942346	−	1.19589i
$349$			22.9263i			1.22721i	0.789611	+	0.613607i	$0.210282\pi$
$349$			22.9263i			1.22721i	−0.789611	+	0.613607i	$0.789718\pi$
$350$		0			0
$351$		−	44.0832i		−	2.35299i
$352$	−10.5900	+	19.8383i	−0.564448	+	1.05739i
$353$	−28.9021	+	7.74430i	−1.53830	+	0.412188i	−0.925718	−	0.378215i	$-0.876538\pi$
$353$	−28.9021	+	7.74430i	−1.53830	+	0.412188i	−0.612587	+	0.790403i	$0.709871\pi$
$354$	37.1033	−	2.19214i	1.97202	−	0.116511i
$355$	−7.34358	+	2.52800i	−0.389757	+	0.134172i
$356$	7.43261	−	17.3102i	0.393928	−	0.917441i
$357$		0			0
$358$	−5.81164	+	28.2651i	−0.307155	+	1.49385i
$359$	−4.27518	−	7.40483i	−0.225635	−	0.390812i	0.730875	−	0.682512i	$-0.239112\pi$
$359$	−4.27518	−	7.40483i	−0.225635	−	0.390812i	−0.956510	+	0.291700i	$0.905779\pi$
$360$	42.4295	−	10.6886i	2.23623	−	0.563341i
$361$	8.63374	−	14.9541i	0.454407	−	0.787057i
$362$	−17.6746	+	5.87311i	−0.928954	+	0.308684i
$363$	10.6967	−	10.6967i	0.561429	−	0.561429i
$364$		0			0
$365$	3.01871	+	4.47613i	0.158007	+	0.234291i
$366$	−2.68841	+	5.36423i	−0.140525	+	0.280393i
$367$	−5.06713	+	1.35773i	−0.264502	+	0.0708731i	−0.388633	−	0.921393i	$-0.627052\pi$
$367$	−5.06713	+	1.35773i	−0.264502	+	0.0708731i	0.124131	+	0.992266i	$0.460386\pi$
$368$	10.8560	−	17.7326i	0.565908	−	0.924378i
$369$	−67.8106	+	39.1505i	−3.53008	+	2.03809i
$370$	−9.09176	−	22.0834i	−0.472658	−	1.14806i
$371$		0			0
$372$	−6.01360	−	15.0637i	−0.311791	−	0.781017i
$373$	−0.799311	+	2.98307i	−0.0413867	+	0.154457i	−0.983527	−	0.180762i	$-0.942144\pi$
$373$	−0.799311	+	2.98307i	−0.0413867	+	0.154457i	0.942140	+	0.335219i	$0.108810\pi$
$374$	0.355410	+	6.01554i	0.0183778	+	0.311056i
$375$	−10.8880	+	33.4849i	−0.562254	+	1.72915i
$376$	12.4669	+	14.7821i	0.642932	+	0.762327i
$377$	11.3909	−	11.3909i	0.586661	−	0.586661i
$378$		0			0
$379$	−17.0070			−0.873589			−0.436794	−	0.899561i	$-0.643886\pi$
$379$	−17.0070			−0.873589			−0.436794	+	0.899561i	$0.643886\pi$
$380$	−0.435391	+	5.87033i	−0.0223351	+	0.301142i
$381$	23.1056	−	40.0201i	1.18374	−	2.05029i
$382$	−11.3683	+	12.7960i	−0.581655	+	0.654701i
$383$	26.3270	+	7.05430i	1.34525	+	0.360458i	0.858379	−	0.513017i	$-0.171472\pi$
$383$	26.3270	+	7.05430i	1.34525	+	0.360458i	0.486869	+	0.873475i	$0.338139\pi$
$384$	21.1096	−	28.7041i	1.07724	−	1.46480i
$385$		0			0
$386$	0.829130	−	0.546320i	0.0422016	−	0.0278070i
$387$	−4.49355	+	16.7702i	−0.228420	+	0.852475i
$388$	−3.66516	+	25.3169i	−0.186070	+	1.28527i
$389$	10.9526	+	6.32350i	0.555320	+	0.320614i	0.751265	−	0.660001i	$-0.229444\pi$
$389$	10.9526	+	6.32350i	0.555320	+	0.320614i	−0.195945	+	0.980615i	$0.562777\pi$
$390$	35.2831	−	4.56810i	1.78663	−	0.231315i
$391$		−	5.57153i		−	0.281764i
$392$		0			0
$393$	21.9573	+	21.9573i	1.10760	+	1.10760i
$394$	1.04776	−	2.09062i	0.0527856	−	0.105324i
$395$	5.06361	−	5.82416i	0.254778	−	0.293045i
$396$	−44.0659	+	32.9205i	−2.21440	+	1.65432i
$397$	−11.7173	−	3.13965i	−0.588076	−	0.157574i	−0.0475022	−	0.998871i	$-0.515126\pi$
$397$	−11.7173	−	3.13965i	−0.588076	−	0.157574i	−0.540574	+	0.841297i	$0.681793\pi$
$398$	4.97053	−	24.1743i	0.249150	−	1.21175i
$399$		0			0
$400$	7.33539	+	18.6062i	0.366769	+	0.930312i
$401$	7.12839	+	12.3467i	0.355975	+	0.616566i	0.987284	−	0.158965i	$-0.0508156\pi$
$401$	7.12839	+	12.3467i	0.355975	+	0.616566i	−0.631310	+	0.775531i	$0.717482\pi$
$402$	18.3623	+	16.3136i	0.915829	+	0.813648i
$403$	−2.38094	−	8.88580i	−0.118603	−	0.442633i
$404$	2.41932	+	20.4028i	0.120366	+	1.01508i
$405$	39.7459	+	7.72884i	1.97499	+	0.384049i
$406$		0			0
$407$	21.2288	+	21.2288i	1.05227	+	1.05227i
$408$	0.808298	−	9.51357i	0.0400167	−	0.470992i
$409$	25.8941	+	14.9499i	1.28038	+	0.739227i	0.976918	−	0.213617i	$-0.0685243\pi$
$409$	25.8941	+	14.9499i	1.28038	+	0.739227i	0.303461	+	0.952844i	$0.401858\pi$
$410$	−21.7269	−	28.4412i	−1.07302	−	1.40461i
$411$	44.0282	−	25.4197i	2.17175	−	1.25386i
$412$	−7.76394	+	3.09945i	−0.382502	+	0.152699i
$413$		0			0
$414$	42.4666	−	27.9816i	2.08712	−	1.37522i
$415$	23.8100	+	11.6151i	1.16879	+	0.570161i
$416$	13.8063	−	14.7569i	0.676912	−	0.723518i
$417$	7.42253	+	27.7013i	0.363483	+	1.35654i
$418$	−2.33348	−	7.02239i	−0.114134	−	0.343477i
$419$	37.6505			1.83935			0.919674	−	0.392684i	$-0.128453\pi$
$419$	37.6505			1.83935			0.919674	+	0.392684i	$0.128453\pi$
$420$		0			0
$421$	−8.37171			−0.408012			−0.204006	−	0.978970i	$-0.565396\pi$
$421$	−8.37171			−0.408012			−0.204006	+	0.978970i	$0.565396\pi$
$422$	−2.82068	−	8.48857i	−0.137309	−	0.413217i
$423$	12.2419	+	45.6872i	0.595219	+	2.22139i
$424$	8.04090	−	22.2657i	0.390500	−	1.08132i
$425$	4.27969	+	3.22596i	0.207596	+	0.156482i
$426$	−12.9174	+	8.51141i	−0.625852	+	0.412379i
$427$		0			0
$428$	−11.7981	−	29.5536i	−0.570285	−	1.42853i
$429$	−38.7331	+	22.3626i	−1.87005	+	1.07967i
$430$	−7.86574	−	1.05272i	−0.379320	−	0.0507668i
$431$	4.31232	+	2.48972i	0.207717	+	0.119925i	0.600250	−	0.799812i	$-0.295068\pi$
$431$	4.31232	+	2.48972i	0.207717	+	0.119925i	−0.392533	+	0.919738i	$0.628401\pi$
$432$	43.3682	−	23.5714i	2.08655	−	1.13408i
$433$	−2.70541	−	2.70541i	−0.130014	−	0.130014i	0.639106	−	0.769119i	$-0.279305\pi$
$433$	−2.70541	−	2.70541i	−0.130014	−	0.130014i	−0.769119	+	0.639106i	$0.779305\pi$
$434$		0			0
$435$	17.7555	+	26.3277i	0.851310	+	1.26232i
$436$	5.92943	−	0.703100i	0.283968	−	0.0336724i
$437$	1.77079	+	6.60868i	0.0847084	+	0.316136i
$438$	8.03921	+	7.14226i	0.384128	+	0.341270i
$439$	−18.7676	−	32.5065i	−0.895731	−	1.55145i	−0.832898	−	0.553427i	$-0.813320\pi$
$439$	−18.7676	−	32.5065i	−0.895731	−	1.55145i	−0.0628330	−	0.998024i	$-0.520014\pi$
$440$	−17.5093	−	18.0433i	−0.834722	−	0.860179i
$441$		0			0
$442$	1.09062	−	5.30425i	0.0518754	−	0.252297i
$443$	12.2588	+	3.28474i	0.582433	+	0.156063i	0.537993	−	0.842950i	$-0.319183\pi$
$443$	12.2588	+	3.28474i	0.582433	+	0.156063i	0.0444406	+	0.999012i	$0.485849\pi$
$444$	−28.4693	−	38.1078i	−1.35109	−	1.80851i
$445$	15.8947	+	13.8191i	0.753482	+	0.655089i
$446$	−1.01644	+	2.02813i	−0.0481300	+	0.0960347i
$447$	4.39643	+	4.39643i	0.207944	+	0.207944i
$448$		0			0
$449$			25.1638i			1.18755i	0.804630	+	0.593777i	$0.202364\pi$
$449$			25.1638i			1.18755i	−0.804630	+	0.593777i	$0.797636\pi$
$450$	−3.09483	+	48.8217i	−0.145892	+	2.30148i
$451$	38.9649	+	22.4964i	1.83479	+	1.05931i
$452$	−1.14015	−	0.165062i	−0.0536283	−	0.00776384i
$453$	7.03434	−	26.2525i	0.330502	−	1.23345i
$454$	5.91729	−	3.89895i	0.277712	−	0.182987i
$455$		0			0
$456$	2.06492	+	11.5414i	0.0966987	+	0.540478i
$457$	−26.2723	−	7.03963i	−1.22896	−	0.329300i	−0.414788	−	0.909918i	$-0.636144\pi$
$457$	−26.2723	−	7.03963i	−1.22896	−	0.329300i	−0.814176	+	0.580618i	$0.802811\pi$
$458$	−9.69192	+	10.9091i	−0.452874	+	0.509747i
$459$	6.61343	−	11.4548i	0.308689	−	0.534664i
$460$	15.1766	+	17.6081i	0.707611	+	0.820983i
$461$	20.0052			0.931737			0.465868	−	0.884854i	$-0.345742\pi$
$461$	20.0052			0.931737			0.465868	+	0.884854i	$0.345742\pi$
$462$		0			0
$463$	−10.1515	+	10.1515i	−0.471781	+	0.471781i	−0.902491	−	0.430710i	$-0.858263\pi$
$463$	−10.1515	+	10.1515i	−0.471781	+	0.471781i	0.430710	+	0.902491i	$0.358263\pi$
$464$	17.2969	+	5.11540i	0.802987	+	0.237476i
$465$	18.0901	−	1.26366i	0.838908	−	0.0586006i
$466$	−1.06554	−	18.0350i	−0.0493604	−	0.835455i
$467$	1.07000	−	3.99329i	0.0495137	−	0.184787i	−0.936740	−	0.350026i	$-0.886173\pi$
$467$	1.07000	−	3.99329i	0.0495137	−	0.184787i	0.986254	+	0.165239i	$0.0528394\pi$
$468$	45.9067	−	18.3265i	2.12204	−	0.847141i
$469$		0			0
$470$	−19.9918	+	8.23066i	−0.922154	+	0.379652i
$471$	−43.2390	+	24.9640i	−1.99235	+	1.15028i
$472$	10.0290	+	21.3672i	0.461621	+	0.983504i
$473$	9.63636	−	2.58206i	0.443080	−	0.118723i
$474$	6.88744	−	13.7426i	0.316351	−	0.631221i
$475$	−6.10167	−	2.46627i	−0.279964	−	0.113160i
$476$		0			0
$477$	40.9445	−	40.9445i	1.87472	−	1.87472i
$478$	−25.6677	+	8.52915i	−1.17401	+	0.390114i
$479$	−4.66449	+	8.07913i	−0.213126	+	0.369145i	−0.952691	−	0.303940i	$-0.901698\pi$
$479$	−4.66449	+	8.07913i	−0.213126	+	0.369145i	0.739565	+	0.673085i	$0.235031\pi$
$480$	23.3600	+	32.2682i	1.06623	+	1.47284i
$481$	−13.4894	−	23.3644i	−0.615065	−	1.06532i
$482$	−4.03256	+	19.6125i	−0.183678	+	0.893324i
$483$		0			0
$484$	8.82738	+	3.79027i	0.401245	+	0.172285i
$485$	−25.7048	−	12.5394i	−1.16719	−	0.569384i
$486$	28.2459	−	1.66883i	1.28126	−	0.0756995i
$487$	28.0071	−	7.50448i	1.26912	−	0.340061i	0.439429	−	0.898278i	$-0.355181\pi$
$487$	28.0071	−	7.50448i	1.26912	−	0.340061i	0.829695	+	0.558217i	$0.188514\pi$
$488$	−3.79678	−	0.322585i	−0.171872	−	0.0146027i
$489$			21.9378i			0.992060i
$490$		0			0
$491$		−	28.1818i		−	1.27183i	−0.771760	−	0.635914i	$-0.780623\pi$
$491$		−	28.1818i		−	1.27183i	0.771760	−	0.635914i	$-0.219377\pi$
$492$	−55.9933	−	44.1218i	−2.52437	−	1.98917i
$493$	4.66874	−	1.25099i	0.210270	−	0.0563416i
$494$	0.392203	+	6.63828i	0.0176460	+	0.298670i
$495$	−20.0174	−	58.1486i	−0.899716	−	2.61359i
$496$	7.46858	−	7.09358i	0.335349	−	0.318511i
$497$		0			0
$498$	51.6859	+	10.6272i	2.31610	+	0.476218i
$499$	−15.5368	−	26.9104i	−0.695521	−	1.20468i	−0.970005	−	0.243085i	$-0.921840\pi$
$499$	−15.5368	−	26.9104i	−0.695521	−	1.20468i	0.274484	−	0.961592i	$-0.411493\pi$
$500$	−22.3128	+	1.46241i	−0.997859	+	0.0654011i
$501$	26.5463	−	45.9796i	1.18600	−	2.05422i
$502$	−3.88387	−	11.6881i	−0.173346	−	0.521667i
$503$	−28.6110	+	28.6110i	−1.27570	+	1.27570i	−0.332654	+	0.943049i	$0.607944\pi$
$503$	−28.6110	+	28.6110i	−1.27570	+	1.27570i	−0.943049	+	0.332654i	$0.892056\pi$
$504$		0			0
$505$	−22.5485	−	4.38469i	−1.00340	−	0.195116i
$506$	−26.1254	−	13.0933i	−1.16142	−	0.582070i
$507$	−0.724197	+	0.194048i	−0.0321627	+	0.00861798i
$508$	29.0439	+	4.20473i	1.28861	+	0.186555i
$509$	10.6109	−	6.12618i	0.470318	−	0.271538i	−0.246055	−	0.969256i	$-0.579134\pi$
$509$	10.6109	−	6.12618i	0.470318	−	0.271538i	0.716373	+	0.697718i	$0.245801\pi$
$510$	9.85345	+	4.10623i	0.436318	+	0.181827i
$511$		0			0
$512$	21.8998	+	5.69184i	0.967845	+	0.251546i
$513$	−4.20388	+	15.6891i	−0.185606	+	0.692690i
$514$	8.42782	−	0.497933i	0.371735	−	0.0219629i
$515$	−0.651297	−	9.32376i	−0.0286996	−	0.410854i
$516$	−15.6968	+	1.86129i	−0.691013	+	0.0819389i
$517$	19.2182	−	19.2182i	0.845214	−	0.845214i
$518$		0			0
$519$	0.697297			0.0306080
$520$	11.0017	+	19.7342i	0.482458	+	0.865403i
$521$	−17.7836	+	30.8021i	−0.779115	+	1.34947i	0.153338	+	0.988174i	$0.450998\pi$
$521$	−17.7836	+	30.8021i	−0.779115	+	1.34947i	−0.932453	+	0.361292i	$0.882336\pi$
$522$	32.9827	+	29.3028i	1.44361	+	1.28255i
$523$	−11.0942	−	2.97269i	−0.485118	−	0.129987i	0.00796695	−	0.999968i	$-0.497464\pi$
$523$	−11.0942	−	2.97269i	−0.485118	−	0.129987i	−0.493085	+	0.869981i	$0.664131\pi$
$524$	−7.78040	+	18.1202i	−0.339889	+	0.791586i
$525$		0			0
$526$	−12.2970	−	18.6627i	−0.536175	−	0.813733i
$527$	0.714386	−	2.66612i	0.0311191	−	0.116138i
$528$	−42.7105	−	26.1475i	−1.85873	−	1.13792i
$529$	3.48031	+	2.00936i	0.151318	+	0.0873633i
$530$	20.9634	+	16.1574i	0.910591	+	0.701831i
$531$			57.7344i			2.50546i
$532$		0			0
$533$	−28.5898	−	28.5898i	−1.23836	−	1.23836i
$534$	37.5051	+	18.7965i	1.62300	+	0.813405i
$535$	35.4911	−	2.47918i	1.53441	−	0.107184i
$536$	−5.29821	+	14.6711i	−0.228848	+	0.633694i
$537$	−62.0710	−	16.6319i	−2.67856	−	0.717718i
$538$	11.0762	+	2.27741i	0.477530	+	0.0981860i
$539$		0			0
$540$	10.3014	+	54.2162i	0.443300	+	2.33309i
$541$	−6.42555	−	11.1294i	−0.276256	−	0.478489i	0.694195	−	0.719787i	$-0.255760\pi$
$541$	−6.42555	−	11.1294i	−0.276256	−	0.478489i	−0.970451	+	0.241297i	$0.922427\pi$
$542$	28.2339	−	31.7796i	1.21275	−	1.36505i
$543$	−10.7347	−	40.0626i	−0.460672	−	1.71925i
$544$	5.80136	−	1.76326i	0.248731	−	0.0755993i
$545$	−1.27427	+	6.55300i	−0.0545838	+	0.280700i
$546$		0			0
$547$	−1.19674	−	1.19674i	−0.0511688	−	0.0511688i	0.681059	−	0.732228i	$-0.261520\pi$
$547$	−1.19674	−	1.19674i	−0.0511688	−	0.0511688i	−0.732228	+	0.681059i	$0.761520\pi$
$548$	25.3589	+	19.9824i	1.08328	+	0.853608i
$549$	−8.07165	−	4.66017i	−0.344490	−	0.198891i
$550$	25.1843	−	12.4867i	1.07386	−	0.532436i
$551$	−5.14025	+	2.96772i	−0.218982	+	0.126429i
$552$	37.9945	+	26.4623i	1.61715	+	1.12631i
$553$		0			0
$554$	1.92289	+	2.91829i	0.0816956	+	0.123986i
$555$	50.2863	−	17.3109i	2.13454	−	0.734805i
$556$	−14.5904	+	10.9001i	−0.618771	+	0.462267i
$557$	−4.30105	−	16.0517i	−0.182241	−	0.680133i	−0.995204	−	0.0978181i	$-0.968814\pi$
$557$	−4.30105	−	16.0517i	−0.182241	−	0.680133i	0.812963	−	0.582315i	$-0.197853\pi$
$558$	23.9092	−	7.94483i	1.01216	−	0.336332i
$559$	−8.96505			−0.379181
$560$		0			0
$561$	−13.4195			−0.566570
$562$	3.82634	−	1.27146i	0.161404	−	0.0536334i
$563$	−9.63625	−	35.9630i	−0.406119	−	1.51566i	−0.801982	−	0.597349i	$-0.796221\pi$
$563$	−9.63625	−	35.9630i	−0.406119	−	1.51566i	0.395862	−	0.918310i	$-0.370446\pi$
$564$	−34.4985	+	25.7729i	−1.45265	+	1.08524i
$565$	0.564715	−	1.15762i	0.0237577	−	0.0487015i
$566$	−6.73263	−	10.2179i	−0.282993	−	0.429488i
$567$		0			0
$568$	−8.06143	−	5.61460i	−0.338250	−	0.235583i
$569$	−14.2519	+	8.22834i	−0.597471	+	0.344950i	−0.768046	−	0.640395i	$-0.778771\pi$
$569$	−14.2519	+	8.22834i	−0.597471	+	0.344950i	0.170575	+	0.985345i	$0.445437\pi$
$570$	−12.9928	−	1.73891i	−0.544208	−	0.0728348i
$571$	−38.7542	−	22.3748i	−1.62181	−	0.936355i	−0.986434	−	0.164156i	$-0.947510\pi$
$571$	−38.7542	−	22.3748i	−1.62181	−	0.936355i	−0.635380	−	0.772199i	$-0.719157\pi$
$572$	−22.3091	−	17.5792i	−0.932791	−	0.735025i
$573$	−26.9529	−	26.9529i	−1.12597	−	1.12597i
$574$		0			0
$575$	−23.9252	+	10.1515i	−0.997749	+	0.423347i
$576$	42.5756	+	35.3629i	1.77398	+	1.47345i
$577$	−3.54445	−	13.2280i	−0.147557	−	0.550691i	−0.999628	−	0.0272648i	$-0.991320\pi$
$577$	−3.54445	−	13.2280i	−0.147557	−	0.550691i	0.852071	−	0.523426i	$-0.175346\pi$
$578$	−14.8886	+	16.7584i	−0.619285	+	0.697057i
$579$	1.10559	+	1.91494i	0.0459468	+	0.0795822i
$580$	−11.3474	+	16.6710i	−0.471174	+	0.692226i
$581$		0			0
$582$	−55.7990	−	11.4729i	−2.31294	−	0.475569i
$583$	−32.1388	−	8.61157i	−1.33105	−	0.356655i
$584$	−2.31961	+	6.42314i	−0.0959862	+	0.265792i
$585$	3.85099	+	55.1296i	0.159219	+	2.27933i
$586$	−29.5499	−	14.8096i	−1.22069	−	0.611779i
$587$	−24.5126	−	24.5126i	−1.01175	−	1.01175i	−0.999930	−	0.0118150i	$-0.996239\pi$
$587$	−24.5126	−	24.5126i	−1.01175	−	1.01175i	−0.0118150	−	0.999930i	$-0.503761\pi$
$588$		0			0
$589$			3.38948i			0.139661i
$590$	−26.1713	+	3.38840i	−1.07746	+	0.139498i
$591$	4.50992	+	2.60380i	0.185513	+	0.107106i
$592$	15.7726	−	25.7636i	0.648249	−	1.05888i
$593$	−11.8464	+	44.2116i	−0.486475	+	1.81555i	0.0868479	+	0.996222i	$0.472321\pi$
$593$	−11.8464	+	44.2116i	−0.486475	+	1.81555i	−0.573323	+	0.819329i	$0.694346\pi$
$594$	−38.1708	−	57.9303i	−1.56617	−	2.37691i
$595$		0			0
$596$	−1.55784	+	3.62814i	−0.0638115	+	0.148614i
$597$	53.0875	+	14.2248i	2.17273	+	0.582180i
$598$	19.6320	+	17.4416i	0.802810	+	0.713239i
$599$	15.6035	−	27.0260i	0.637540	−	1.10425i	−0.348430	−	0.937335i	$-0.613285\pi$
$599$	15.6035	−	27.0260i	0.637540	−	1.10425i	0.985971	−	0.166918i	$-0.0533815\pi$
$600$	−42.3258	+	13.8631i	−1.72794	+	0.565957i
$601$	−3.84939			−0.157020			−0.0785099	−	0.996913i	$-0.525016\pi$
$601$	−3.84939			−0.157020			−0.0785099	+	0.996913i	$0.525016\pi$
$602$		0			0
$603$	−26.9786	+	26.9786i	−1.09866	+	1.09866i
$604$	17.1398	−	2.03241i	0.697410	−	0.0826974i
$605$	−7.04708	+	8.10554i	−0.286504	+	0.329537i
$606$	−45.6740	+	2.69851i	−1.85538	+	0.109620i
$607$	1.49094	−	5.56425i	0.0605152	−	0.225846i	−0.929045	−	0.369967i	$-0.879369\pi$
$607$	1.49094	−	5.56425i	0.0605152	−	0.225846i	0.989560	+	0.144121i	$0.0460356\pi$
$608$	−6.32089	+	3.93534i	−0.256346	+	0.159599i
$609$		0			0
$610$	1.63876	−	3.93243i	0.0663515	−	0.159219i
$611$	−21.1515	+	12.2118i	−0.855698	+	0.494038i
$612$	14.6780	+	2.12495i	0.593322	+	0.0858961i
$613$	−19.6676	+	5.26991i	−0.794366	+	0.212850i	−0.633109	−	0.774063i	$-0.718222\pi$
$613$	−19.6676	+	5.26991i	−0.794366	+	0.212850i	−0.161257	+	0.986912i	$0.551555\pi$
$614$	26.8666	+	13.4648i	1.08425	+	0.543395i
$615$	66.0796	−	44.5642i	2.66459	−	1.79700i
$616$		0			0
$617$	−5.54965	+	5.54965i	−0.223420	+	0.223420i	−0.809937	−	0.586517i	$-0.800499\pi$
$617$	−5.54965	+	5.54965i	−0.223420	+	0.223420i	0.586517	+	0.809937i	$0.300499\pi$
$618$	−5.87047	−	17.6666i	−0.236145	−	0.710655i
$619$	−2.52112	+	4.36671i	−0.101332	+	0.175513i	−0.912234	−	0.409670i	$-0.865644\pi$
$619$	−2.52112	+	4.36671i	−0.101332	+	0.175513i	0.810901	+	0.585183i	$0.198977\pi$
$620$	5.00466	+	10.3719i	0.200992	+	0.416546i
$621$	32.0714	+	55.5492i	1.28698	+	2.22911i
$622$	39.0264	+	8.02430i	1.56482	+	0.321745i
$623$		0			0
$624$	30.9919	+	32.6302i	1.24067	+	1.30625i
$625$	6.05513	−	24.2556i	0.242205	−	0.970225i
$626$	−2.14098	−	36.2374i	−0.0855707	−	1.44834i
$627$	15.9175	−	4.26509i	0.635685	−	0.170331i
$628$	−24.9044	−	19.6243i	−0.993793	−	0.783094i
$629$		−	8.09482i		−	0.322762i
$630$		0			0
$631$			22.4036i			0.891874i	0.895064	+	0.445937i	$0.147130\pi$
$631$			22.4036i			0.891874i	−0.895064	+	0.445937i	$0.852870\pi$
$632$	9.72700	+	0.826432i	0.386919	+	0.0328737i
$633$	19.2409	−	5.15558i	0.764756	−	0.204916i
$634$	−37.1323	+	2.19385i	−1.47471	+	0.0871289i
$635$	−14.3854	+	29.4889i	−0.570866	+	1.17023i
$636$	48.4414	+	20.7996i	1.92083	+	0.824759i
$637$		0			0
$638$	5.10577	−	24.8321i	0.202139	−	0.983111i
$639$	−12.0146	−	20.8100i	−0.475292	−	0.823230i
$640$	−13.5315	+	21.3752i	−0.534878	+	0.844929i
$641$	21.5598	−	37.3426i	0.851559	−	1.47494i	−0.0282413	−	0.999601i	$-0.508991\pi$
$641$	21.5598	−	37.3426i	0.851559	−	1.47494i	0.879801	−	0.475343i	$-0.157676\pi$
$642$	67.2484	−	22.3461i	2.65408	−	0.881930i
$643$	−1.10922	+	1.10922i	−0.0437432	+	0.0437432i	−0.728640	−	0.684897i	$-0.759847\pi$
$643$	−1.10922	+	1.10922i	−0.0437432	+	0.0437432i	0.684897	+	0.728640i	$0.259847\pi$
$644$		0			0
$645$	3.37334	−	17.3476i	0.132825	−	0.683060i
$646$	−0.893973	+	1.78376i	−0.0351729	+	0.0701811i
$647$	−32.5679	+	8.72654i	−1.28038	+	0.343076i	−0.833997	−	0.551769i	$-0.813953\pi$
$647$	−32.5679	+	8.72654i	−1.28038	+	0.343076i	−0.446378	+	0.894844i	$0.647286\pi$
$648$	21.7615	+	46.3638i	0.854871	+	1.82134i
$649$	28.7304	−	16.5875i	1.12777	−	0.651116i
$650$	−24.7646	+	4.98120i	−0.971347	+	0.195379i
$651$		0			0
$652$	−12.9388	+	5.16530i	−0.506721	+	0.202289i
$653$	9.95952	−	37.1694i	0.389746	−	1.45455i	−0.440801	−	0.897605i	$-0.645306\pi$
$653$	9.95952	−	37.1694i	0.389746	−	1.45455i	0.830547	−	0.556948i	$-0.188028\pi$
$654$	0.784236	+	13.2737i	0.0306661	+	0.519042i
$655$	−16.6385	−	14.4657i	−0.650119	−	0.565223i
$656$	12.8391	−	43.4131i	0.501281	−	1.69500i
$657$	−11.8115	+	11.8115i	−0.460811	+	0.460811i
$658$		0			0
$659$	12.4757			0.485985			0.242993	−	0.970028i	$-0.421871\pi$
$659$	12.4757			0.485985			0.242993	+	0.970028i	$0.421871\pi$
$660$	42.4106	−	36.5539i	1.65083	−	1.42286i
$661$	−3.31297	+	5.73823i	−0.128859	+	0.223191i	−0.923235	−	0.384236i	$-0.874465\pi$
$661$	−3.31297	+	5.73823i	−0.128859	+	0.223191i	0.794376	+	0.607427i	$0.207798\pi$
$662$	−16.1577	+	18.1868i	−0.627986	+	0.706851i
$663$	11.6483	+	3.12115i	0.452382	+	0.121215i
$664$	5.90168	+	32.9862i	0.229030	+	1.28011i
$665$		0			0
$666$	61.6993	−	40.6542i	2.39080	−	1.57532i
$667$	−6.06657	+	22.6407i	−0.234898	+	0.876653i
$668$	33.3689	+	4.83086i	1.29108	+	0.186912i
$669$	−4.37511	−	2.52597i	−0.169151	−	0.0976596i
$670$	−13.8129	−	10.6462i	−0.533640	−	0.411299i
$671$			5.35559i			0.206750i
$672$		0			0
$673$	−27.7823	−	27.7823i	−1.07093	−	1.07093i	−0.997285	−	0.0736433i	$-0.976537\pi$
$673$	−27.7823	−	27.7823i	−1.07093	−	1.07093i	−0.0736433	−	0.997285i	$-0.523463\pi$
$674$	11.5631	−	23.0721i	0.445395	−	0.888706i
$675$	−61.2390	−	7.52828i	−2.35709	−	0.289764i
$676$	−0.284962	−	0.381438i	−0.0109601	−	0.0146707i
$677$	17.0379	+	4.56530i	0.654821	+	0.175459i	0.570908	−	0.821014i	$-0.306591\pi$
$677$	17.0379	+	4.56530i	0.654821	+	0.175459i	0.0839136	+	0.996473i	$0.473258\pi$
$678$	0.516687	−	2.51292i	0.0198433	−	0.0965082i
$679$		0			0
$680$	−0.101812	+	6.77833i	−0.00390429	+	0.259937i
$681$	7.89032	+	13.6664i	0.302358	+	0.523699i
$682$	−10.8229	−	9.61533i	−0.414429	−	0.368190i
$683$	−1.40860	−	5.25698i	−0.0538987	−	0.201153i	0.933726	−	0.357989i	$-0.116537\pi$
$683$	−1.40860	−	5.25698i	−0.0538987	−	0.201153i	−0.987625	+	0.156836i	$0.949871\pi$
$684$	−18.0857	+	2.14457i	−0.691524	+	0.0819996i
$685$	−29.9269	+	20.1828i	−1.14345	+	0.771145i
$686$		0			0
$687$	−22.9783	−	22.9783i	−0.876677	−	0.876677i
$688$	−4.79363	−	8.81964i	−0.182756	−	0.336246i
$689$	25.8941	+	14.9499i	0.986485	+	0.569547i
$690$	−41.1368	+	31.4254i	−1.56605	+	1.19634i
$691$	32.0466	−	18.5021i	1.21911	−	0.703854i	0.254384	−	0.967103i	$-0.418127\pi$
$691$	32.0466	−	18.5021i	1.21911	−	0.703854i	0.964728	+	0.263249i	$0.0847941\pi$
$692$	0.164180	+	0.411262i	0.00624120	+	0.0156338i
$693$		0			0
$694$	22.3016	−	14.6947i	0.846559	−	0.557805i
$695$	−6.62785	−	19.2532i	−0.251409	−	0.730317i
$696$	−13.6435	+	37.7797i	−0.517156	+	1.43204i
$697$	−3.13983	−	11.7180i	−0.118930	−	0.443851i
$698$	−10.2241	−	30.7684i	−0.386987	−	1.16460i
$699$	40.2324			1.52173
$700$		0			0
$701$	−29.4765			−1.11331			−0.556656	−	0.830743i	$-0.687916\pi$
$701$	−29.4765			−1.11331			−0.556656	+	0.830743i	$0.687916\pi$
$702$	19.6591	+	59.1623i	0.741987	+	2.23294i
$703$	2.57277	+	9.60170i	0.0970338	+	0.362135i
$704$	5.36536	−	31.3469i	0.202215	−	1.18143i
$705$	−15.6713	−	45.5236i	−0.590216	−	1.71452i
$706$	35.3348	−	23.2824i	1.32984	−	0.876244i
$707$		0			0
$708$	−48.8172	+	19.4884i	−1.83466	+	0.732419i
$709$	15.6918	−	9.05966i	0.589318	−	0.340243i	−0.175510	−	0.984478i	$-0.556157\pi$
$709$	15.6918	−	9.05966i	0.589318	−	0.340243i	0.764828	+	0.644235i	$0.222824\pi$
$710$	8.72815	−	6.66763i	0.327562	−	0.250232i
$711$	20.6788	+	11.9389i	0.775515	+	0.447744i
$712$	−2.25542	+	26.5460i	−0.0845254	+	0.994853i
$713$	9.46481	+	9.46481i	0.354460	+	0.354460i
$714$		0			0
$715$	26.3277	−	17.7555i	0.984602	−	0.664017i
$716$	−4.80539	−	40.5251i	−0.179586	−	1.51450i
$717$	−15.5894	−	58.1804i	−0.582197	−	2.17279i
$718$	9.03977	+	8.03118i	0.337361	+	0.299721i
$719$	4.66449	+	8.07913i	0.173956	+	0.301301i	0.939799	−	0.341726i	$-0.111012\pi$
$719$	4.66449	+	8.07913i	0.173956	+	0.301301i	−0.765843	+	0.643027i	$0.777678\pi$
$720$	−52.1763	+	33.2664i	−1.94449	+	1.23977i
$721$		0			0
$722$	−4.91814	+	23.9195i	−0.183034	+	0.890193i
$723$	−43.0696	−	11.5405i	−1.60178	−	0.429195i
$724$	21.1012	−	15.7641i	0.784218	−	0.585869i
$725$	−13.8786	−	17.7691i	−0.515438	−	0.659929i
$726$	−9.58532	+	19.1258i	−0.355745	+	0.709824i
$727$	−11.9373	−	11.9373i	−0.442729	−	0.442729i	0.450199	−	0.892928i	$-0.351353\pi$
$727$	−11.9373	−	11.9373i	−0.442729	−	0.442729i	−0.892928	+	0.450199i	$0.851353\pi$
$728$		0			0
$729$			8.68729i			0.321751i
$730$	−6.04744	−	4.66102i	−0.223826	−	0.172512i
$731$	−2.32952	−	1.34495i	−0.0861605	−	0.0497448i
$732$	1.21579	−	8.39802i	0.0449370	−	0.310400i
$733$	−11.7409	+	43.8178i	−0.433662	+	1.61845i	0.310587	+	0.950545i	$0.399474\pi$
$733$	−11.7409	+	43.8178i	−0.433662	+	1.61845i	−0.744249	+	0.667903i	$0.767192\pi$
$734$	6.19490	−	4.08187i	0.228658	−	0.150665i
$735$		0			0
$736$	−6.66142	+	28.6396i	−0.245543	+	1.05567i
$737$	21.1765	+	5.67423i	0.780047	+	0.209013i
$738$	73.5465	−	82.7828i	2.70728	−	3.04728i
$739$	−11.9877	+	20.7633i	−0.440975	+	0.763792i	−0.997762	−	0.0668636i	$-0.978701\pi$
$739$	−11.9877	+	20.7633i	−0.440975	+	0.763792i	0.556787	+	0.830656i	$0.312034\pi$
$740$	22.0499	+	25.5827i	0.810570	+	0.940439i
$741$	−14.8087			−0.544009
$742$		0			0
$743$	−26.3785	+	26.3785i	−0.967733	+	0.967733i	−0.999495	−	0.0317628i	$-0.989888\pi$
$743$	−26.3785	+	26.3785i	−0.967733	+	0.967733i	0.0317628	+	0.999495i	$0.489888\pi$
$744$	14.7884	+	17.5346i	0.542167	+	0.642850i
$745$	−3.33145	−	2.89642i	−0.122055	−	0.106116i
$746$	−0.257592	−	4.35991i	−0.00943113	−	0.159628i
$747$	−21.2141	+	79.1721i	−0.776184	+	2.89676i
$748$	−3.15964	−	7.91472i	−0.115528	−	0.289391i
$749$		0			0
$750$	−0.320402	−	49.7943i	−0.0116994	−	1.81823i
$751$	45.3197	−	26.1653i	1.65374	−	0.954786i	0.678223	−	0.734857i	$-0.262751\pi$
$751$	45.3197	−	26.1653i	1.65374	−	0.954786i	0.975516	−	0.219930i	$-0.0705828\pi$
$752$	−23.3235	−	14.2787i	−0.850520	−	0.520692i
$753$	26.4933	−	7.09885i	0.965468	−	0.258696i
$754$	−10.2074	+	20.3671i	−0.371733	+	0.741726i
$755$	−3.68346	+	18.9424i	−0.134055	+	0.689383i
$756$		0			0
$757$	23.8139	−	23.8139i	0.865530	−	0.865530i	−0.126444	−	0.991974i	$-0.540356\pi$
$757$	23.8139	−	23.8139i	0.865530	−	0.865530i	0.991974	+	0.126444i	$0.0403563\pi$
$758$	22.8243	−	7.58434i	0.829018	−	0.275476i
$759$	32.5383	−	56.3581i	1.18107	−	2.04567i
$760$	−2.03358	−	8.07250i	−0.0737659	−	0.292820i
$761$	−9.43544	−	16.3427i	−0.342034	−	0.592421i	0.642776	−	0.766054i	$-0.277783\pi$
$761$	−9.43544	−	16.3427i	−0.342034	−	0.592421i	−0.984810	+	0.173633i	$0.944449\pi$
$762$	−13.1619	+	64.0134i	−0.476807	+	2.31896i
$763$		0			0
$764$	9.55054	−	22.2428i	0.345526	−	0.804716i
$765$	−7.26997	+	14.9029i	−0.262846	+	0.538815i
$766$	−38.4783	+	2.27338i	−1.39028	+	0.0821405i
$767$	−28.7964	+	7.71597i	−1.03978	+	0.278607i
$768$	−15.5295	+	47.9366i	−0.560374	+	1.72976i
$769$		−	12.2463i		−	0.441614i	−0.975318	−	0.220807i	$-0.929131\pi$
$769$		−	12.2463i		−	0.441614i	0.975318	−	0.220807i	$-0.0708691\pi$
$770$		0			0
$771$			18.8008i			0.677093i
$772$	−0.869107	+	1.10295i	−0.0312798	+	0.0396960i
$773$	−4.15790	+	1.11411i	−0.149549	+	0.0400716i	−0.332817	−	0.942991i	$-0.607999\pi$
$773$	−4.15790	+	1.11411i	−0.149549	+	0.0400716i	0.183268	+	0.983063i	$0.441332\pi$
$774$	−1.44813	−	24.5105i	−0.0520519	−	0.881011i
$775$	−12.7505	+	1.79006i	−0.458011	+	0.0643010i
$776$	−6.37133	−	35.6113i	−0.228718	−	1.27837i
$777$		0			0
$778$	−17.5191	−	3.60213i	−0.628089	−	0.129143i
$779$	7.44864	+	12.9014i	0.266875	+	0.462242i
$780$	−45.3149	+	21.8654i	−1.62253	+	0.782905i
$781$	−6.90378	+	11.9577i	−0.247037	+	0.427880i
$782$	2.48465	+	7.47732i	0.0888509	+	0.267388i
$783$	−39.3473	+	39.3473i	−1.40616	+	1.40616i
$784$		0			0
$785$	29.3905	−	19.8210i	1.04899	−	0.707443i
$786$	−39.2601	−	19.6761i	−1.40036	−	0.701822i
$787$	−4.08160	+	1.09366i	−0.145493	+	0.0389848i	−0.330831	−	0.943690i	$-0.607329\pi$
$787$	−4.08160	+	1.09366i	−0.145493	+	0.0389848i	0.185337	+	0.982675i	$0.440662\pi$
$788$	−0.473836	+	3.27300i	−0.0168797	+	0.116596i
$789$	43.1030	−	24.8855i	1.53451	−	0.885948i
$790$	−4.19835	+	10.0745i	−0.149371	+	0.358435i
$791$		0			0
$792$	44.4581	−	63.8327i	1.57975	−	2.26820i
$793$	1.24563	−	4.64874i	0.0442334	−	0.165081i
$794$	17.1255	−	1.01181i	0.607761	−	0.0359078i
$795$	−38.6718	+	44.4802i	−1.37155	+	1.57755i
$796$	4.10991	+	34.6600i	0.145672	+	1.22849i
$797$	35.3989	−	35.3989i	1.25389	−	1.25389i	0.299933	−	0.953960i	$-0.403036\pi$
$797$	35.3989	−	35.3989i	1.25389	−	1.25389i	0.953960	−	0.299933i	$-0.0969644\pi$
$798$		0			0
$799$	−7.32815			−0.259251
$800$	−18.1421	−	21.6994i	−0.641419	−	0.767191i
$801$	−32.5825	+	56.4346i	−1.15125	+	1.99402i
$802$	−15.0728	−	13.3911i	−0.532239	−	0.472856i
$803$	9.27129	+	2.48424i	0.327177	+	0.0876668i
$804$	−31.9185	−	13.7050i	−1.12568	−	0.483340i
$805$		0			0
$806$	7.15804	+	10.8635i	0.252131	+	0.382650i
$807$	−6.51753	+	24.3238i	−0.229428	+	0.856237i
$808$	−12.3456	−	26.3029i	−0.434318	−	0.925333i
$809$	−25.0379	−	14.4556i	−0.880284	−	0.508232i	−0.00953207	−	0.999955i	$-0.503034\pi$
$809$	−25.0379	−	14.4556i	−0.880284	−	0.508232i	−0.870752	+	0.491722i	$0.836368\pi$
$810$	−56.7881	+	7.35235i	−1.99533	+	0.258335i
$811$			23.9566i			0.841229i	0.907240	+	0.420614i	$0.138185\pi$
$811$			23.9566i			0.841229i	−0.907240	+	0.420614i	$0.861815\pi$
$812$		0			0
$813$	66.9390	+	66.9390i	2.34765	+	2.34765i
$814$	−37.9574	−	19.0232i	−1.33041	−	0.666763i
$815$	−1.08540	−	15.5382i	−0.0380199	−	0.544281i
$816$	3.15784	+	13.1282i	0.110547	+	0.459580i
$817$	3.19064	+	0.854928i	0.111626	+	0.0299102i
$818$	−41.4184	−	8.51612i	−1.44816	−	0.297759i
$819$		0			0
$820$	41.8423	+	28.4806i	1.46120	+	0.994586i
$821$	−17.8387	−	30.8975i	−0.622574	−	1.07833i	−0.989005	−	0.147885i	$-0.952754\pi$
$821$	−17.8387	−	30.8975i	−0.622574	−	1.07833i	0.366430	−	0.930445i	$-0.380580\pi$
$822$	−47.7524	+	53.7493i	−1.66556	+	1.87472i
$823$	3.41164	+	12.7324i	0.118922	+	0.443824i	0.999550	−	0.0299839i	$-0.00954561\pi$
$823$	3.41164	+	12.7324i	0.118922	+	0.443824i	−0.880628	+	0.473808i	$0.842879\pi$
$824$	9.03745	−	7.62202i	0.314835	−	0.265526i
$825$	24.4507	+	57.6257i	0.851265	+	2.00627i
$826$		0			0
$827$	6.42266	+	6.42266i	0.223338	+	0.223338i	0.809902	−	0.586565i	$-0.199520\pi$
$827$	6.42266	+	6.42266i	0.223338	+	0.223338i	−0.586565	+	0.809902i	$0.699520\pi$
$828$	−44.5141	+	56.4911i	−1.54697	+	1.96320i
$829$	−16.2271	−	9.36870i	−0.563589	−	0.325388i	0.190996	−	0.981591i	$-0.438828\pi$
$829$	−16.2271	−	9.36870i	−0.563589	−	0.325388i	−0.754585	+	0.656202i	$0.772162\pi$
$830$	−37.1342	−	4.96992i	−1.28895	−	0.172508i
$831$	−6.74002	+	3.89135i	−0.233809	+	0.134990i
$832$	−11.9480	+	25.9617i	−0.414223	+	0.900059i
$833$		0			0
$834$	−22.3150	−	33.8666i	−0.772706	−	1.17271i
$835$	−16.5275	+	33.8802i	−0.571958	+	1.17247i
$836$	6.26335	+	8.38384i	0.216622	+	0.289961i
$837$	8.22443	+	30.6940i	0.284278	+	1.06094i
$838$	−50.5292	+	16.7904i	−1.74550	+	0.580016i
$839$	−50.3921			−1.73973			−0.869864	−	0.493291i	$-0.835794\pi$
$839$	−50.3921			−1.73973			−0.869864	+	0.493291i	$0.835794\pi$
$840$		0			0
$841$	8.66571			0.298818
$842$	11.2353	−	3.73341i	0.387195	−	0.128662i
$843$	2.32395	+	8.67309i	0.0800410	+	0.298717i
$844$	7.57104	+	10.1343i	0.260606	+	0.348836i
$845$	0.503339	−	0.173272i	0.0173154	−	0.00596075i
$846$	−36.8038	−	55.8557i	−1.26534	−	1.92036i
$847$		0			0
$848$	−0.861844	+	33.4678i	−0.0295958	+	1.14929i
$849$	23.5989	−	13.6249i	0.809914	−	0.467604i
$850$	−7.18224	−	2.42088i	−0.246349	−	0.0830355i
$851$	33.9960	+	19.6276i	1.16537	+	0.672826i
$852$	13.5403	−	17.1834i	0.463882	−	0.588694i
$853$	−12.0652	−	12.0652i	−0.413104	−	0.413104i	0.469714	−	0.882818i	$-0.344357\pi$
$853$	−12.0652	−	12.0652i	−0.413104	−	0.413104i	−0.882818	+	0.469714i	$0.844357\pi$
$854$		0			0
$855$	3.88673	−	19.9877i	0.132923	−	0.683565i
$856$	29.0134	+	34.4013i	0.991658	+	1.17581i
$857$	−5.32241	−	19.8635i	−0.181810	−	0.678525i	−0.995291	−	0.0969329i	$-0.969097\pi$
$857$	−5.32241	−	19.8635i	−0.181810	−	0.678525i	0.813481	−	0.581592i	$-0.197570\pi$
$858$	42.0094	−	47.2851i	1.43418	−	1.61429i
$859$	−21.8383	−	37.8250i	−0.745112	−	1.29057i	−0.950142	−	0.311816i	$-0.899063\pi$
$859$	−21.8383	−	37.8250i	−0.745112	−	1.29057i	0.205030	−	0.978756i	$-0.434271\pi$
$860$	11.0258	−	2.09495i	0.375975	−	0.0714372i
$861$		0			0
$862$	−6.89769	−	1.41825i	−0.234936	−	0.0483057i
$863$	24.6545	+	6.60616i	0.839250	+	0.224876i	0.652745	−	0.757578i	$-0.273617\pi$
$863$	24.6545	+	6.60616i	0.839250	+	0.224876i	0.186505	+	0.982454i	$0.440284\pi$
$864$	−47.6909	+	50.9745i	−1.62248	+	1.73419i
$865$	−0.493887	+	0.0344997i	−0.0167927	+	0.00117302i
$866$	4.83731	+	2.42433i	0.164378	+	0.0823820i
$867$	−35.2990	−	35.2990i	−1.19882	−	1.19882i
$868$		0			0
$869$		−	13.7205i		−	0.465437i
$870$	−35.5699	−	27.4152i	−1.20593	−	0.929464i
$871$	−17.0618	−	9.85064i	−0.578117	−	0.333776i
$872$	−7.64410	+	3.58786i	−0.258862	+	0.121500i
$873$	22.9023	−	85.4726i	0.775126	−	2.89281i
$874$	−5.32368	−	8.07955i	−0.180076	−	0.273295i
$875$		0			0
$876$	−13.9742	−	6.00021i	−0.472145	−	0.202728i
$877$	−49.9561	−	13.3857i	−1.68690	−	0.452002i	−0.717310	−	0.696754i	$-0.754627\pi$
$877$	−49.9561	−	13.3857i	−1.68690	−	0.452002i	−0.969586	+	0.244751i	$0.921294\pi$
$878$	39.6837	+	35.2561i	1.33926	+	1.18984i
$879$	36.8034	−	63.7454i	1.24135	−	2.15008i
$880$	31.5450	+	16.4068i	1.06338	+	0.553073i
$881$	29.9298			1.00836			0.504181	−	0.863598i	$-0.331795\pi$
$881$	29.9298			1.00836			0.504181	+	0.863598i	$0.331795\pi$
$882$		0			0
$883$	22.0057	−	22.0057i	0.740550	−	0.740550i	−0.232134	−	0.972684i	$-0.574571\pi$
$883$	22.0057	−	22.0057i	0.740550	−	0.740550i	0.972684	+	0.232134i	$0.0745707\pi$
$884$	0.901783	+	7.60498i	0.0303302	+	0.255783i
$885$	−4.09515	−	58.6249i	−0.137657	−	1.97065i
$886$	−17.9169	+	1.05857i	−0.601930	+	0.0355632i
$887$	−12.4757	+	46.5601i	−0.418894	+	1.56333i	0.358011	+	0.933717i	$0.383455\pi$
$887$	−12.4757	+	46.5601i	−0.418894	+	1.56333i	−0.776905	+	0.629618i	$0.783212\pi$
$888$	55.2019	+	38.4469i	1.85245	+	1.29019i
$889$		0			0
$890$	−27.4944	−	11.4577i	−0.921613	−	0.384064i
$891$	62.3408	−	35.9925i	2.08850	−	1.20579i
$892$	0.459672	−	3.17516i	0.0153910	−	0.106312i
$893$	8.69230	−	2.32910i	0.290877	−	0.0779402i
$894$	−7.86088	−	3.93966i	−0.262907	−	0.131762i
$895$	44.7870	+	8.70910i	1.49706	+	0.291113i
$896$		0			0
$897$	−41.3518	+	41.3518i	−1.38070	+	1.38070i
$898$	−11.2219	−	33.7713i	−0.374481	−	1.12696i
$899$	−5.80603	+	10.0563i	−0.193642	+	0.335398i
$900$	−17.6189	−	66.9018i	−0.587295	−	2.23006i
$901$	4.48563	+	7.76933i	0.149438	+	0.258834i
$902$	−62.3256	−	12.8149i	−2.07522	−	0.426689i
$903$		0			0
$904$	1.60376	−	0.286935i	0.0533404	−	0.00954330i
$905$	9.58543	+	27.8447i	0.318630	+	0.925589i
$906$	2.26694	+	38.3694i	0.0753141	+	1.27474i
$907$	−7.78619	+	2.08630i	−0.258536	+	0.0692745i	−0.385759	−	0.922600i	$-0.626060\pi$
$907$	−7.78619	+	2.08630i	−0.258536	+	0.0692745i	0.127223	+	0.991874i	$0.459394\pi$
$908$	−6.20259	+	7.87147i	−0.205840	+	0.261224i
$909$		−	71.0708i		−	2.35727i
$910$		0			0
$911$		−	15.9014i		−	0.526836i	−0.964682	−	0.263418i	$-0.915150\pi$
$911$		−	15.9014i		−	0.526836i	0.964682	−	0.263418i	$-0.0848498\pi$
$912$	−7.91821	−	14.5684i	−0.262198	−	0.482410i
$913$	45.4934	−	12.1899i	1.50561	−	0.403427i
$914$	38.3983	−	2.26865i	1.27010	−	0.0750402i
$915$	8.52670	+	4.15952i	0.281884	+	0.137509i
$916$	8.14218	−	18.9628i	0.269025	−	0.626548i
$917$		0			0
$918$	−3.76729	+	18.3223i	−0.124339	+	0.604727i
$919$	22.6796	+	39.2823i	0.748132	+	1.29580i	0.948717	+	0.316127i	$0.102382\pi$
$919$	22.6796	+	39.2823i	0.748132	+	1.29580i	−0.200585	+	0.979676i	$0.564284\pi$
$920$	−28.2203	−	16.8631i	−0.930395	−	0.555960i
$921$	−33.4614	+	57.9569i	−1.10259	+	1.90975i
$922$	−26.8482	+	8.92144i	−0.884199	+	0.293812i
$923$	8.77375	−	8.77375i	0.288792	−	0.288792i
$924$		0			0
$925$	−34.7607	+	14.7490i	−1.14292	+	0.484946i
$926$	9.09682	−	18.1511i	0.298940	−	0.596481i
$927$	27.9322	−	7.48442i	0.917415	−	0.245821i
$928$	−25.4947	+	0.848461i	−0.836903	+	0.0278521i
$929$	33.4187	−	19.2943i	1.09643	−	0.633025i	0.161150	−	0.986930i	$-0.448480\pi$
$929$	33.4187	−	19.2943i	1.09643	−	0.633025i	0.935281	+	0.353905i	$0.115146\pi$
$930$	−23.7145	+	9.76328i	−0.777628	+	0.320150i
$931$		0			0
$932$	9.47283	+	23.7289i	0.310293	+	0.777265i
$933$	−22.9641	+	85.7032i	−0.751811	+	2.80580i
$934$	0.344827	+	5.83641i	0.0112831	+	0.190973i
$935$	9.50483	−	0.663945i	0.310841	−	0.0217133i
$936$	−53.4367	+	45.0676i	−1.74663	+	1.47308i
$937$	−15.2293	+	15.2293i	−0.497519	+	0.497519i	−0.910665	−	0.413146i	$-0.864430\pi$
$937$	−15.2293	+	15.2293i	−0.497519	+	0.497519i	0.413146	+	0.910665i	$0.364430\pi$
$938$		0			0
$939$	80.8383			2.63806
$940$	23.1597	−	19.9615i	0.755387	−	0.651072i
$941$	−23.7077	+	41.0629i	−0.772848	+	1.33861i	0.163148	+	0.986602i	$0.447835\pi$
$941$	−23.7077	+	41.0629i	−0.772848	+	1.33861i	−0.935996	+	0.352010i	$0.885498\pi$
$942$	46.8965	−	52.7859i	1.52797	−	1.71986i
$943$	56.8256	+	15.2264i	1.85050	+	0.495839i
$944$	−22.9883	−	24.2035i	−0.748205	−	0.787758i
$945$		0			0
$946$	−11.7811	+	7.76266i	−0.383036	+	0.252386i
$947$	−9.12616	+	34.0593i	−0.296560	+	1.10678i	0.643410	+	0.765522i	$0.277519\pi$
$947$	−9.12616	+	34.0593i	−0.296560	+	1.10678i	−0.939970	+	0.341257i	$0.889147\pi$
$948$	−3.11475	+	21.5149i	−0.101162	+	0.698773i
$949$	−7.46983	−	4.31271i	−0.242481	−	0.139996i
$950$	9.28866	+	0.588812i	0.301364	+	0.0191036i
$951$		−	82.8346i		−	2.68610i
$952$		0			0
$953$	34.4409	+	34.4409i	1.11565	+	1.11565i	0.992372	+	0.123279i	$0.0393409\pi$
$953$	34.4409	+	34.4409i	1.11565	+	1.11565i	0.123279	+	0.992372i	$0.460659\pi$
$954$	−36.6905	+	73.2093i	−1.18790	+	2.37024i
$955$	20.4239	+	17.7569i	0.660903	+	0.574599i
$956$	30.6439	−	22.8933i	0.991095	−	0.740421i
$957$	54.5320	+	14.6118i	1.76277	+	0.472332i
$958$	2.65709	−	12.9228i	0.0858467	−	0.417518i
$959$		0			0
$960$	−45.7406	−	32.8884i	−1.47627	−	1.06147i
$961$	−12.1844	−	21.1040i	−0.393046	−	0.680775i
$962$	28.5231	+	25.3407i	0.919621	+	0.817017i
$963$	28.4896	+	106.325i	0.918065	+	3.42627i
$964$	−3.33435	−	28.1195i	−0.107392	−	0.905667i
$965$	−0.877821	−	1.30163i	−0.0282581	−	0.0419009i
$966$		0			0
$967$	−28.3737	−	28.3737i	−0.912437	−	0.912437i	0.0840261	−	0.996464i	$-0.473222\pi$
$967$	−28.3737	−	28.3737i	−0.912437	−	0.912437i	−0.996464	+	0.0840261i	$0.973222\pi$
$968$	−13.5372	−	1.15015i	−0.435101	−	0.0369674i
$969$	−3.84795	−	2.22162i	−0.123614	−	0.0713686i
$970$	40.0894	+	5.36542i	1.28719	+	0.172273i
$971$	6.28643	−	3.62947i	0.201741	−	0.116475i	−0.395726	−	0.918369i	$-0.629507\pi$
$971$	6.28643	−	3.62947i	0.201741	−	0.116475i	0.597467	+	0.801893i	$0.296174\pi$
$972$	−37.1635	+	14.8361i	−1.19202	+	0.475867i
$973$		0			0
$974$	−34.2406	+	22.5614i	−1.09714	+	0.722913i
$975$	−7.82079	−	55.7068i	−0.250466	−	1.78405i
$976$	5.23937	−	1.26027i	0.167708	−	0.0403402i
$977$	3.08533	+	11.5146i	0.0987084	+	0.368385i	0.997556	−	0.0698774i	$-0.0222608\pi$
$977$	3.08533	+	11.5146i	0.0987084	+	0.368385i	−0.898847	+	0.438262i	$0.855594\pi$
$978$	−9.78326	−	29.4418i	−0.312834	−	0.941444i
$979$	37.4447			1.19674
$980$		0			0
$981$	−20.6545			−0.659446
$982$	12.5678	+	37.8217i	0.401056	+	1.20694i
$983$	−4.89406	−	18.2649i	−0.156096	−	0.582560i	−0.999009	−	0.0445091i	$-0.985828\pi$
$983$	−4.89406	−	18.2649i	−0.156096	−	0.582560i	0.842913	−	0.538050i	$-0.180839\pi$
$984$	94.8227	+	34.2436i	3.02284	+	1.09165i
$985$	−3.32315	−	1.62111i	−0.105884	−	0.0516528i
$986$	−5.70785	+	3.76095i	−0.181775	+	0.119773i
$987$		0			0
$988$	−3.48673	−	8.73406i	−0.110928	−	0.277867i
$989$	11.2969	−	6.52224i	0.359219	−	0.207395i
$990$	52.7963	+	69.1120i	1.67798	+	2.19652i
$991$	−19.1208	−	11.0394i	−0.607392	−	0.350678i	0.164552	−	0.986368i	$-0.447382\pi$
$991$	−19.1208	−	11.0394i	−0.607392	−	0.350678i	−0.771944	+	0.635690i	$0.780716\pi$
$992$	−6.85985	+	12.8507i	−0.217801	+	0.408009i
$993$	−38.3078	−	38.3078i	−1.21566	−	1.21566i
$994$		0			0
$995$	−38.3050	−	7.44864i	−1.21435	−	0.236138i
$996$	−74.1048	+	8.78719i	−2.34810	+	0.278433i
$997$	−7.72606	−	28.8340i	−0.244687	−	0.913183i	−0.973541	−	0.228514i	$-0.926613\pi$
$997$	−7.72606	−	28.8340i	−0.244687	−	0.913183i	0.728854	−	0.684669i	$-0.240053\pi$
$998$	32.8521	+	29.1867i	1.03992	+	0.923890i
$999$	46.5962	+	80.7070i	1.47424	+	2.55346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.j.263.1		64
4.3	odd	2	inner	980.2.x.j.263.4		64
5.2	odd	4	inner	980.2.x.j.67.7		64
7.2	even	3	inner	980.2.x.j.863.14		64
7.3	odd	6		980.2.k.i.883.12	yes	32
7.4	even	3		980.2.k.i.883.11	yes	32
7.5	odd	6	inner	980.2.x.j.863.13		64
7.6	odd	2	inner	980.2.x.j.263.2		64
20.7	even	4	inner	980.2.x.j.67.14		64
28.3	even	6		980.2.k.i.883.15	yes	32
28.11	odd	6		980.2.k.i.883.16	yes	32
28.19	even	6	inner	980.2.x.j.863.8		64
28.23	odd	6	inner	980.2.x.j.863.7		64
28.27	even	2	inner	980.2.x.j.263.3		64
35.2	odd	12	inner	980.2.x.j.667.4		64
35.12	even	12	inner	980.2.x.j.667.3		64
35.17	even	12		980.2.k.i.687.15	yes	32
35.27	even	4	inner	980.2.x.j.67.8		64
35.32	odd	12		980.2.k.i.687.16	yes	32
140.27	odd	4	inner	980.2.x.j.67.13		64
140.47	odd	12	inner	980.2.x.j.667.2		64
140.67	even	12		980.2.k.i.687.11	✓	32
140.87	odd	12		980.2.k.i.687.12	yes	32
140.107	even	12	inner	980.2.x.j.667.1		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.i.687.11	✓	32	140.67	even	12
980.2.k.i.687.12	yes	32	140.87	odd	12
980.2.k.i.687.15	yes	32	35.17	even	12
980.2.k.i.687.16	yes	32	35.32	odd	12
980.2.k.i.883.11	yes	32	7.4	even	3
980.2.k.i.883.12	yes	32	7.3	odd	6
980.2.k.i.883.15	yes	32	28.3	even	6
980.2.k.i.883.16	yes	32	28.11	odd	6
980.2.x.j.67.7		64	5.2	odd	4	inner
980.2.x.j.67.8		64	35.27	even	4	inner
980.2.x.j.67.13		64	140.27	odd	4	inner
980.2.x.j.67.14		64	20.7	even	4	inner
980.2.x.j.263.1		64	1.1	even	1	trivial
980.2.x.j.263.2		64	7.6	odd	2	inner
980.2.x.j.263.3		64	28.27	even	2	inner
980.2.x.j.263.4		64	4.3	odd	2	inner
980.2.x.j.667.1		64	140.107	even	12	inner
980.2.x.j.667.2		64	140.47	odd	12	inner
980.2.x.j.667.3		64	35.12	even	12	inner
980.2.x.j.667.4		64	35.2	odd	12	inner
980.2.x.j.863.7		64	28.23	odd	6	inner
980.2.x.j.863.8		64	28.19	even	6	inner
980.2.x.j.863.13		64	7.5	odd	6	inner
980.2.x.j.863.14		64	7.2	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34206 + 0.445955i) q^{2} +(-0.815107 - 3.04202i) q^{3} +(1.60225 - 1.19700i) q^{4} +(0.727838 + 2.11430i) q^{5} +(2.45053 + 3.71907i) q^{6} +(-1.61650 + 2.32097i) q^{8} +(-5.99142 + 3.45915i) q^{9} +(-1.91968 - 2.51293i) q^{10} +(3.44275 + 1.98767i) q^{11} +(-4.94729 - 3.89839i) q^{12} +(-2.52606 - 2.52606i) q^{13} +(5.83847 - 3.93748i) q^{15} +(1.13440 - 3.83577i) q^{16} +(-0.277420 - 1.03535i) q^{17} +(6.49821 - 7.31428i) q^{18} +(0.658126 + 1.13991i) q^{19} +(3.69698 + 2.51641i) q^{20} +(-5.50679 - 1.13226i) q^{22} +(5.02084 + 1.34533i) q^{23} +(8.37807 + 3.02560i) q^{24} +(-3.94050 + 3.07773i) q^{25} +(4.51663 + 2.26361i) q^{26} +(8.72570 + 8.72570i) q^{27} +4.50936i q^{29} +(-6.07964 + 7.88803i) q^{30} +(2.23010 + 1.28755i) q^{31} +(0.188156 + 5.65372i) q^{32} +(3.24033 - 12.0931i) q^{33} +(0.834032 + 1.26578i) q^{34} +(-5.45915 + 12.7141i) q^{36} +(7.29473 + 1.95462i) q^{37} +(-1.39159 - 1.23633i) q^{38} +(-5.62531 + 9.74333i) q^{39} +(-6.08378 - 1.72848i) q^{40} +11.3180 q^{41} +(1.77452 - 1.77452i) q^{43} +(7.89537 - 0.936217i) q^{44} +(-11.6744 - 10.1499i) q^{45} +(-7.33822 + 0.433557i) q^{46} +(1.76949 - 6.60383i) q^{47} +(-12.5932 - 0.324292i) q^{48} +(3.91586 - 5.88779i) q^{50} +(-2.92342 + 1.68784i) q^{51} +(-7.07105 - 1.02369i) q^{52} +(-8.08454 + 2.16624i) q^{53} +(-15.6017 - 7.81913i) q^{54} +(-1.69676 + 8.72570i) q^{55} +(2.93118 - 2.93118i) q^{57} +(-2.01097 - 6.05182i) q^{58} +(4.17259 - 7.22714i) q^{59} +(4.64153 - 13.2974i) q^{60} +(0.673601 + 1.16671i) q^{61} +(-3.56712 - 0.733444i) q^{62} +(-2.77382 - 7.50373i) q^{64} +(3.50228 - 7.17940i) q^{65} +(1.04426 + 17.6747i) q^{66} +(5.32697 - 1.42736i) q^{67} +(-1.68380 - 1.32681i) q^{68} -16.3701i q^{69} +3.47330i q^{71} +(1.65657 - 19.4976i) q^{72} +(2.33220 - 0.624911i) q^{73} +(-10.6616 + 0.629911i) q^{74} +(12.5745 + 9.47841i) q^{75} +(2.41895 + 1.03864i) q^{76} +(3.20442 - 15.5848i) q^{78} +(-1.72570 - 2.98900i) q^{79} +(8.93562 - 0.393371i) q^{80} +(9.05394 - 15.6819i) q^{81} +(-15.1894 + 5.04730i) q^{82} +(8.37751 - 8.37751i) q^{83} +(1.98711 - 1.34011i) q^{85} +(-1.59015 + 3.17286i) q^{86} +(13.7176 - 3.67561i) q^{87} +(-10.1785 + 4.77744i) q^{88} +(8.15730 - 4.70962i) q^{89} +(20.1942 + 8.41554i) q^{90} +(9.65498 - 3.85438i) q^{92} +(2.09898 - 7.83352i) q^{93} +(0.570251 + 9.65185i) q^{94} +(-1.93109 + 2.22114i) q^{95} +(17.0454 - 5.18076i) q^{96} +(-9.04418 + 9.04418i) q^{97} -27.5026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) \) 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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