LMFDB - Embedded newform 330.2.d.b.131.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [330,2,Mod(131,330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(330, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("330.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2051727616.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 37x^{4} + 36x^{2} + 4 $ x^8 + 11x^6 + 37x^4 + 36*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.4
Root			$-2.25619i$ of defining polynomial
Character	$\chi$	$=$	330.131
Dual form			330.2.d.b.131.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.0828988 + 1.73007i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(0.0828988 + 1.73007i) q^{6} +4.34658i q^{7} +1.00000 q^{8} +(-2.98626 + 0.286841i) q^{9} -1.00000i q^{10} +(1.20394 - 3.09039i) q^{11} +(0.0828988 + 1.73007i) q^{12} +4.51238i q^{13} +4.34658i q^{14} +(1.73007 - 0.0828988i) q^{15} +1.00000 q^{16} +2.72065 q^{17} +(-2.98626 + 0.286841i) q^{18} -3.97251i q^{19} -1.00000i q^{20} +(-7.51987 + 0.360326i) q^{21} +(1.20394 - 3.09039i) q^{22} -1.66840i q^{23} +(0.0828988 + 1.73007i) q^{24} -1.00000 q^{25} +4.51238i q^{26} +(-0.743810 - 5.14264i) q^{27} +4.34658i q^{28} -5.08606 q^{29} +(1.73007 - 0.0828988i) q^{30} +9.74541 q^{31} +1.00000 q^{32} +(5.44639 + 1.82671i) q^{33} +2.72065 q^{34} +4.34658 q^{35} +(-2.98626 + 0.286841i) q^{36} -5.60710 q^{37} -3.97251i q^{38} +(-7.80671 + 0.374071i) q^{39} -1.00000i q^{40} +2.92026 q^{41} +(-7.51987 + 0.360326i) q^{42} -3.25186i q^{43} +(1.20394 - 3.09039i) q^{44} +(0.286841 + 2.98626i) q^{45} -1.66840i q^{46} -9.25186i q^{47} +(0.0828988 + 1.73007i) q^{48} -11.8928 q^{49} -1.00000 q^{50} +(0.225539 + 4.70691i) q^{51} +4.51238i q^{52} +3.05225i q^{53} +(-0.743810 - 5.14264i) q^{54} +(-3.09039 - 1.20394i) q^{55} +4.34658i q^{56} +(6.87271 - 0.329316i) q^{57} -5.08606 q^{58} -5.43264i q^{59} +(1.73007 - 0.0828988i) q^{60} -11.5646i q^{61} +9.74541 q^{62} +(-1.24678 - 12.9800i) q^{63} +1.00000 q^{64} +4.51238 q^{65} +(5.44639 + 1.82671i) q^{66} +12.3529 q^{67} +2.72065 q^{68} +(2.88645 - 0.138309i) q^{69} +4.34658 q^{70} +3.60710i q^{71} +(-2.98626 + 0.286841i) q^{72} -1.36502i q^{73} -5.60710 q^{74} +(-0.0828988 - 1.73007i) q^{75} -3.97251i q^{76} +(13.4326 + 5.23303i) q^{77} +(-7.80671 + 0.374071i) q^{78} +1.07107i q^{79} -1.00000i q^{80} +(8.83544 - 1.71316i) q^{81} +2.92026 q^{82} -14.5887 q^{83} +(-7.51987 + 0.360326i) q^{84} -2.72065i q^{85} -3.25186i q^{86} +(-0.421628 - 8.79922i) q^{87} +(1.20394 - 3.09039i) q^{88} +3.75791i q^{89} +(0.286841 + 2.98626i) q^{90} -19.6134 q^{91} -1.66840i q^{92} +(0.807883 + 16.8602i) q^{93} -9.25186i q^{94} -3.97251 q^{95} +(0.0828988 + 1.73007i) q^{96} -12.7977 q^{97} -11.8928 q^{98} +(-2.70883 + 9.57404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 2 q^{3} + 8 q^{4} + 2 q^{6} + 8 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} + 4 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{21} + 6 q^{22} + 2 q^{24} - 8 q^{25} - 22 q^{27} - 4 q^{29} + 4 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 2 * q^3 + 8 * q^4 + 2 * q^6 + 8 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 + 4 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 - 8 * q^21 + 6 * q^22 + 2 * q^24 - 8 * q^25 - 22 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 2 * q^33 + 4 * q^34 + 2 * q^36 - 12 * q^37 - 8 * q^39 - 16 * q^41 - 8 * q^42 + 6 * q^44 + 2 * q^48 - 4 * q^49 - 8 * q^50 - 28 * q^51 - 22 * q^54 - 6 * q^55 + 14 * q^57 - 4 * q^58 + 4 * q^60 - 4 * q^62 + 14 * q^63 + 8 * q^64 + 4 * q^65 - 2 * q^66 - 12 * q^67 + 4 * q^68 + 8 * q^69 + 2 * q^72 - 12 * q^74 - 2 * q^75 + 36 * q^77 - 8 * q^78 + 2 * q^81 - 16 * q^82 - 72 * q^83 - 8 * q^84 - 22 * q^87 + 6 * q^88 - 48 * q^91 + 8 * q^93 + 20 * q^95 + 2 * q^96 - 8 * q^97 - 4 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.0828988	+	1.73007i	0.0478616	+	0.998854i
$3$	0.0828988	+	1.73007i	0.0478616	+	0.998854i
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.0828988	+	1.73007i	0.0338433	+	0.706296i
$7$			4.34658i			1.64285i	0.570314	+	0.821427i	$0.306822\pi$
$7$			4.34658i			1.64285i	−0.570314	+	0.821427i	$0.693178\pi$
$8$	1.00000			0.353553
$9$	−2.98626	+	0.286841i	−0.995419	+	0.0956136i
$10$		−	1.00000i		−	0.316228i
$11$	1.20394	−	3.09039i	0.363002	−	0.931788i
$11$	1.20394	−	3.09039i	0.363002	−	0.931788i
$12$	0.0828988	+	1.73007i	0.0239308	+	0.499427i
$13$			4.51238i			1.25151i	0.780020	+	0.625754i	$0.215209\pi$
$13$			4.51238i			1.25151i	−0.780020	+	0.625754i	$0.784791\pi$
$14$			4.34658i			1.16167i
$15$	1.73007	−	0.0828988i	0.446701	−	0.0214044i
$16$	1.00000			0.250000
$17$	2.72065			0.659855			0.329928	−	0.944006i	$-0.392976\pi$
$17$	2.72065			0.659855			0.329928	+	0.944006i	$0.392976\pi$
$18$	−2.98626	+	0.286841i	−0.703867	+	0.0676090i
$19$		−	3.97251i		−	0.911357i	−0.890145	−	0.455678i	$-0.849397\pi$
$19$		−	3.97251i		−	0.911357i	0.890145	−	0.455678i	$-0.150603\pi$
$20$		−	1.00000i		−	0.223607i
$21$	−7.51987	+	0.360326i	−1.64097	+	0.0786297i
$22$	1.20394	−	3.09039i	0.256681	−	0.658874i
$23$		−	1.66840i		−	0.347886i	−0.984756	−	0.173943i	$-0.944349\pi$
$23$		−	1.66840i		−	0.347886i	0.984756	−	0.173943i	$-0.0556509\pi$
$24$	0.0828988	+	1.73007i	0.0169216	+	0.353148i
$25$	−1.00000			−0.200000
$26$			4.51238i			0.884950i
$27$	−0.743810	−	5.14264i	−0.143146	−	0.989702i
$28$			4.34658i			0.821427i
$29$	−5.08606			−0.944458			−0.472229	−	0.881476i	$-0.656550\pi$
$29$	−5.08606			−0.944458			−0.472229	+	0.881476i	$0.656550\pi$
$30$	1.73007	−	0.0828988i	0.315865	−	0.0151352i
$31$	9.74541			1.75033			0.875164	−	0.483827i	$-0.160754\pi$
$31$	9.74541			1.75033			0.875164	+	0.483827i	$0.160754\pi$
$32$	1.00000			0.176777
$33$	5.44639	+	1.82671i	0.948094	+	0.317989i
$34$	2.72065			0.466588
$35$	4.34658			0.734706
$36$	−2.98626	+	0.286841i	−0.497709	+	0.0478068i
$37$	−5.60710			−0.921802			−0.460901	−	0.887452i	$-0.652474\pi$
$37$	−5.60710			−0.921802			−0.460901	+	0.887452i	$0.652474\pi$
$38$		−	3.97251i		−	0.644426i
$39$	−7.80671	+	0.374071i	−1.25007	+	0.0598993i
$40$		−	1.00000i		−	0.158114i
$41$	2.92026			0.456069			0.228034	−	0.973653i	$-0.426770\pi$
$41$	2.92026			0.456069			0.228034	+	0.973653i	$0.426770\pi$
$42$	−7.51987	+	0.360326i	−1.16034	+	0.0555996i
$43$		−	3.25186i		−	0.495904i	−0.968772	−	0.247952i	$-0.920243\pi$
$43$		−	3.25186i		−	0.495904i	0.968772	−	0.247952i	$-0.0797575\pi$
$44$	1.20394	−	3.09039i	0.181501	−	0.465894i
$45$	0.286841	+	2.98626i	0.0427597	+	0.445165i
$46$		−	1.66840i		−	0.245993i
$47$		−	9.25186i		−	1.34952i	−0.738036	−	0.674761i	$-0.764247\pi$
$47$		−	9.25186i		−	1.34952i	0.738036	−	0.674761i	$-0.235753\pi$
$48$	0.0828988	+	1.73007i	0.0119654	+	0.249713i
$49$	−11.8928			−1.69897
$50$	−1.00000			−0.141421
$51$	0.225539	+	4.70691i	0.0315817	+	0.659099i
$52$			4.51238i			0.625754i
$53$			3.05225i			0.419258i	0.977781	+	0.209629i	$0.0672257\pi$
$53$			3.05225i			0.419258i	−0.977781	+	0.209629i	$0.932774\pi$
$54$	−0.743810	−	5.14264i	−0.101220	−	0.699825i
$55$	−3.09039	−	1.20394i	−0.416708	−	0.162339i
$56$			4.34658i			0.580836i
$57$	6.87271	−	0.329316i	0.910312	−	0.0436190i
$58$	−5.08606			−0.667833
$59$		−	5.43264i		−	0.707270i	−0.935384	−	0.353635i	$-0.884946\pi$
$59$		−	5.43264i		−	0.707270i	0.935384	−	0.353635i	$-0.115054\pi$
$60$	1.73007	−	0.0828988i	0.223351	−	0.0107022i
$61$		−	11.5646i		−	1.48070i	−0.672222	−	0.740349i	$-0.734660\pi$
$61$		−	11.5646i		−	1.48070i	0.672222	−	0.740349i	$-0.265340\pi$
$62$	9.74541			1.23767
$63$	−1.24678	−	12.9800i	−0.157079	−	1.63533i
$64$	1.00000			0.125000
$65$	4.51238			0.559692
$66$	5.44639	+	1.82671i	0.670404	+	0.224852i
$67$	12.3529			1.50915			0.754574	−	0.656215i	$-0.227844\pi$
$67$	12.3529			1.50915			0.754574	+	0.656215i	$0.227844\pi$
$68$	2.72065			0.329928
$69$	2.88645	−	0.138309i	0.347488	−	0.0166504i
$70$	4.34658			0.519516
$71$			3.60710i			0.428084i	0.976824	+	0.214042i	$0.0686630\pi$
$71$			3.60710i			0.428084i	−0.976824	+	0.214042i	$0.931337\pi$
$72$	−2.98626	+	0.286841i	−0.351934	+	0.0338045i
$73$		−	1.36502i		−	0.159763i	−0.996804	−	0.0798816i	$-0.974546\pi$
$73$		−	1.36502i		−	0.159763i	0.996804	−	0.0798816i	$-0.0254542\pi$
$74$	−5.60710			−0.651812
$75$	−0.0828988	−	1.73007i	−0.00957233	−	0.199771i
$76$		−	3.97251i		−	0.455678i
$77$	13.4326	+	5.23303i	1.53079	+	0.596359i
$78$	−7.80671	+	0.374071i	−0.883936	+	0.0423552i
$79$			1.07107i			0.120505i	0.998183	+	0.0602526i	$0.0191906\pi$
$79$			1.07107i			0.120505i	−0.998183	+	0.0602526i	$0.980809\pi$
$80$		−	1.00000i		−	0.111803i
$81$	8.83544	−	1.71316i	0.981716	−	0.190351i
$82$	2.92026			0.322489
$83$	−14.5887			−1.60131			−0.800657	−	0.599123i	$-0.795516\pi$
$83$	−14.5887			−1.60131			−0.800657	+	0.599123i	$0.795516\pi$
$84$	−7.51987	+	0.360326i	−0.820485	+	0.0393148i
$85$		−	2.72065i		−	0.295096i
$86$		−	3.25186i		−	0.350657i
$87$	−0.421628	−	8.79922i	−0.0452033	−	0.943375i
$88$	1.20394	−	3.09039i	0.128341	−	0.329437i
$89$			3.75791i			0.398338i	0.979965	+	0.199169i	$0.0638243\pi$
$89$			3.75791i			0.398338i	−0.979965	+	0.199169i	$0.936176\pi$
$90$	0.286841	+	2.98626i	0.0302357	+	0.314779i
$91$	−19.6134			−2.05605
$92$		−	1.66840i		−	0.173943i
$93$	0.807883	+	16.8602i	0.0837735	+	1.74832i
$94$		−	9.25186i		−	0.954256i
$95$	−3.97251			−0.407571
$96$	0.0828988	+	1.73007i	0.00846082	+	0.176574i
$97$	−12.7977			−1.29941			−0.649703	−	0.760188i	$-0.725107\pi$
$97$	−12.7977			−1.29941			−0.649703	+	0.760188i	$0.725107\pi$
$98$	−11.8928			−1.20135
$99$	−2.70883	+	9.57404i	−0.272247	+	0.962227i
$100$	−1.00000			−0.100000
$101$	6.73948			0.670603			0.335302	−	0.942111i	$-0.391162\pi$
$101$	6.73948			0.670603			0.335302	+	0.942111i	$0.391162\pi$
$102$	0.225539	+	4.70691i	0.0223317	+	0.466053i
$103$	−5.25186			−0.517481			−0.258740	−	0.965947i	$-0.583307\pi$
$103$	−5.25186			−0.517481			−0.258740	+	0.965947i	$0.583307\pi$
$104$			4.51238i			0.442475i
$105$	0.360326	+	7.51987i	0.0351643	+	0.733864i
$106$			3.05225i			0.296461i
$107$	6.25707			0.604894			0.302447	−	0.953166i	$-0.402196\pi$
$107$	6.25707			0.604894			0.302447	+	0.953166i	$0.402196\pi$
$108$	−0.743810	−	5.14264i	−0.0715732	−	0.494851i
$109$			17.9168i			1.71612i	0.513550	+	0.858060i	$0.328330\pi$
$109$			17.9168i			1.71612i	−0.513550	+	0.858060i	$0.671670\pi$
$110$	−3.09039	−	1.20394i	−0.294657	−	0.114791i
$111$	−0.464822	−	9.70066i	−0.0441190	−	0.920746i
$112$			4.34658i			0.410713i
$113$		−	8.51238i		−	0.800777i	−0.916345	−	0.400389i	$-0.868875\pi$
$113$		−	8.51238i		−	0.800777i	0.916345	−	0.400389i	$-0.131125\pi$
$114$	6.87271	−	0.329316i	0.643688	−	0.0308433i
$115$	−1.66840			−0.155580
$116$	−5.08606			−0.472229
$117$	−1.29433	−	13.4751i	−0.119661	−	1.24578i
$118$		−	5.43264i		−	0.500115i
$119$			11.8255i			1.08405i
$120$	1.73007	−	0.0828988i	0.157933	−	0.00756759i
$121$	−8.10105	−	7.44131i	−0.736459	−	0.676482i
$122$		−	11.5646i		−	1.04701i
$123$	0.242086	+	5.05225i	0.0218282	+	0.455546i
$124$	9.74541			0.875164
$125$			1.00000i			0.0894427i
$126$	−1.24678	−	12.9800i	−0.111072	−	1.15635i
$127$			8.95024i			0.794205i	0.917774	+	0.397103i	$0.129984\pi$
$127$			8.95024i			0.794205i	−0.917774	+	0.397103i	$0.870016\pi$
$128$	1.00000			0.0883883
$129$	5.62593	−	0.269575i	0.495335	−	0.0237348i
$130$	4.51238			0.395762
$131$	−12.3379			−1.07797			−0.538985	−	0.842316i	$-0.681192\pi$
$131$	−12.3379			−1.07797			−0.538985	+	0.842316i	$0.681192\pi$
$132$	5.44639	+	1.82671i	0.474047	+	0.158995i
$133$	17.2668			1.49723
$134$	12.3529			1.06713
$135$	−5.14264	+	0.743810i	−0.442608	+	0.0640170i
$136$	2.72065			0.233294
$137$			20.9416i			1.78916i	0.446908	+	0.894580i	$0.352525\pi$
$137$			20.9416i			1.78916i	−0.446908	+	0.894580i	$0.647475\pi$
$138$	2.88645	−	0.138309i	0.245711	−	0.0117736i
$139$			15.5458i			1.31858i	0.751890	+	0.659289i	$0.229143\pi$
$139$			15.5458i			1.31858i	−0.751890	+	0.659289i	$0.770857\pi$
$140$	4.34658			0.367353
$141$	16.0063	−	0.766968i	1.34798	−	0.0645903i
$142$			3.60710i			0.302701i
$143$	13.9450	+	5.43264i	1.16614	+	0.454300i
$144$	−2.98626	+	0.286841i	−0.248855	+	0.0239034i
$145$			5.08606i			0.422374i
$146$		−	1.36502i		−	0.112970i
$147$	−0.985897	−	20.5753i	−0.0813154	−	1.69702i
$148$	−5.60710			−0.460901
$149$	−23.2882			−1.90784			−0.953920	−	0.300061i	$-0.902993\pi$
$149$	−23.2882			−1.90784			−0.953920	+	0.300061i	$0.902993\pi$
$150$	−0.0828988	−	1.73007i	−0.00676866	−	0.141259i
$151$			10.8440i			0.882470i	0.897392	+	0.441235i	$0.145460\pi$
$151$			10.8440i			0.882470i	−0.897392	+	0.441235i	$0.854540\pi$
$152$		−	3.97251i		−	0.322213i
$153$	−8.12456	+	0.780394i	−0.656832	+	0.0630911i
$154$	13.4326	+	5.23303i	1.08243	+	0.421690i
$155$		−	9.74541i		−	0.782770i
$156$	−7.80671	+	0.374071i	−0.625037	+	0.0299496i
$157$	11.0861			0.884764			0.442382	−	0.896827i	$-0.354134\pi$
$157$	11.0861			0.884764			0.442382	+	0.896827i	$0.354134\pi$
$158$			1.07107i			0.0852101i
$159$	−5.28059	+	0.253028i	−0.418778	+	0.0200664i
$160$		−	1.00000i		−	0.0790569i
$161$	7.25186			0.571527
$162$	8.83544	−	1.71316i	0.694178	−	0.134599i
$163$	4.16580			0.326290			0.163145	−	0.986602i	$-0.447836\pi$
$163$	4.16580			0.326290			0.163145	+	0.986602i	$0.447836\pi$
$164$	2.92026			0.228034
$165$	1.82671	−	5.44639i	0.142209	−	0.424001i
$166$	−14.5887			−1.13230
$167$	8.78828			0.680057			0.340029	−	0.940415i	$-0.389563\pi$
$167$	8.78828			0.680057			0.340029	+	0.940415i	$0.389563\pi$
$168$	−7.51987	+	0.360326i	−0.580171	+	0.0277998i
$169$	−7.36157			−0.566275
$170$		−	2.72065i		−	0.208665i
$171$	1.13948	+	11.8629i	0.0871381	+	0.907181i
$172$		−	3.25186i		−	0.247952i
$173$	2.66319			0.202479			0.101239	−	0.994862i	$-0.467719\pi$
$173$	2.66319			0.202479			0.101239	+	0.994862i	$0.467719\pi$
$174$	−0.421628	−	8.79922i	−0.0319636	−	0.667067i
$175$		−	4.34658i		−	0.328571i
$176$	1.20394	−	3.09039i	0.0907505	−	0.232947i
$177$	9.39883	−	0.450359i	0.706459	−	0.0338511i
$178$			3.75791i			0.281668i
$179$		−	11.2605i		−	0.841651i	−0.907142	−	0.420825i	$-0.861740\pi$
$179$		−	11.2605i		−	0.841651i	0.907142	−	0.420825i	$-0.138260\pi$
$180$	0.286841	+	2.98626i	0.0213798	+	0.222582i
$181$	−0.711272			−0.0528684			−0.0264342	−	0.999651i	$-0.508415\pi$
$181$	−0.711272			−0.0528684			−0.0264342	+	0.999651i	$0.508415\pi$
$182$	−19.6134			−1.45384
$183$	20.0076	−	0.958694i	1.47900	−	0.0708687i
$184$		−	1.66840i		−	0.122996i
$185$			5.60710i			0.412242i
$186$	0.807883	+	16.8602i	0.0592368	+	1.23625i
$187$	3.27551	−	8.40788i	0.239529	−	0.614845i
$188$		−	9.25186i		−	0.674761i
$189$	22.3529	−	3.23303i	1.62593	−	0.235168i
$190$	−3.97251			−0.288196
$191$			19.5852i			1.41714i	0.705642	+	0.708568i	$0.250659\pi$
$191$			19.5852i			1.41714i	−0.705642	+	0.708568i	$0.749341\pi$
$192$	0.0828988	+	1.73007i	0.00598270	+	0.124857i
$193$		−	8.82899i		−	0.635524i	−0.948170	−	0.317762i	$-0.897069\pi$
$193$		−	8.82899i		−	0.635524i	0.948170	−	0.317762i	$-0.102931\pi$
$194$	−12.7977			−0.918818
$195$	0.374071	+	7.80671i	0.0267878	+	0.559050i
$196$	−11.8928			−0.849484
$197$	−12.9502			−0.922666			−0.461333	−	0.887227i	$-0.652629\pi$
$197$	−12.9502			−0.922666			−0.461333	+	0.887227i	$0.652629\pi$
$198$	−2.70883	+	9.57404i	−0.192508	+	0.680397i
$199$	1.17485			0.0832830			0.0416415	−	0.999133i	$-0.486741\pi$
$199$	1.17485			0.0832830			0.0416415	+	0.999133i	$0.486741\pi$
$200$	−1.00000			−0.0707107
$201$	1.02404	+	21.3713i	0.0722303	+	1.50742i
$202$	6.73948			0.474188
$203$		−	22.1070i		−	1.55161i
$204$	0.225539	+	4.70691i	0.0157909	+	0.329549i
$205$		−	2.92026i		−	0.203960i
$206$	−5.25186			−0.365914
$207$	0.478566	+	4.98228i	0.0332627	+	0.346293i
$208$			4.51238i			0.312877i
$209$	−12.2766	−	4.78267i	−0.849191	−	0.330824i
$210$	0.360326	+	7.51987i	0.0248649	+	0.518921i
$211$		−	21.1498i		−	1.45602i	−0.685569	−	0.728008i	$-0.740446\pi$
$211$		−	21.1498i		−	1.45602i	0.685569	−	0.728008i	$-0.259554\pi$
$212$			3.05225i			0.209629i
$213$	−6.24053	+	0.299024i	−0.427594	+	0.0204888i
$214$	6.25707			0.427725
$215$	−3.25186			−0.221775
$216$	−0.743810	−	5.14264i	−0.0506099	−	0.349912i
$217$			42.3592i			2.87553i
$218$			17.9168i			1.21348i
$219$	2.36157	−	0.113158i	0.159580	−	0.00764652i
$220$	−3.09039	−	1.20394i	−0.208354	−	0.0811697i
$221$			12.2766i			0.825815i
$222$	−0.464822	−	9.70066i	−0.0311968	−	0.651065i
$223$	22.6382			1.51597			0.757983	−	0.652275i	$-0.226185\pi$
$223$	22.6382			1.51597			0.757983	+	0.652275i	$0.226185\pi$
$224$			4.34658i			0.290418i
$225$	2.98626	−	0.286841i	0.199084	−	0.0191227i
$226$		−	8.51238i		−	0.566235i
$227$	−23.5758			−1.56478			−0.782390	−	0.622789i	$-0.785999\pi$
$227$	−23.5758			−1.56478			−0.782390	+	0.622789i	$0.785999\pi$
$228$	6.87271	−	0.329316i	0.455156	−	0.0218095i
$229$	3.50893			0.231877			0.115938	−	0.993256i	$-0.463012\pi$
$229$	3.50893			0.231877			0.115938	+	0.993256i	$0.463012\pi$
$230$	−1.66840			−0.110011
$231$	−7.93994	+	23.6732i	−0.522410	+	1.55758i
$232$	−5.08606			−0.333916
$233$	−9.84991			−0.645289			−0.322644	−	0.946520i	$-0.604572\pi$
$233$	−9.84991			−0.645289			−0.322644	+	0.946520i	$0.604572\pi$
$234$	−1.29433	−	13.4751i	−0.0846133	−	0.880896i
$235$	−9.25186			−0.603525
$236$		−	5.43264i		−	0.353635i
$237$	−1.85303	+	0.0887907i	−0.120367	+	0.00576758i
$238$			11.8255i			0.766536i
$239$	24.1540			1.56239			0.781197	−	0.624285i	$-0.214610\pi$
$239$	24.1540			1.56239			0.781197	+	0.624285i	$0.214610\pi$
$240$	1.73007	−	0.0828988i	0.111675	−	0.00535109i
$241$			4.69316i			0.302313i	0.988510	+	0.151157i	$0.0482998\pi$
$241$			4.69316i			0.302313i	−0.988510	+	0.151157i	$0.951700\pi$
$242$	−8.10105	−	7.44131i	−0.520755	−	0.478345i
$243$	3.69633	+	15.1439i	0.237119	+	0.971481i
$244$		−	11.5646i		−	0.740349i
$245$			11.8928i			0.759801i
$246$	0.242086	+	5.05225i	0.0154349	+	0.322120i
$247$	17.9255			1.14057
$248$	9.74541			0.618834
$249$	−1.20938	−	25.2394i	−0.0766415	−	1.59948i
$250$			1.00000i			0.0632456i
$251$		−	10.5424i		−	0.665427i	−0.943028	−	0.332714i	$-0.892036\pi$
$251$		−	10.5424i		−	0.665427i	0.943028	−	0.332714i	$-0.107964\pi$
$252$	−1.24678	−	12.9800i	−0.0785395	−	0.817663i
$253$	−5.15603	−	2.00866i	−0.324157	−	0.126284i
$254$			8.95024i			0.561588i
$255$	4.70691	−	0.225539i	0.294758	−	0.0141238i
$256$	1.00000			0.0625000
$257$			11.0334i			0.688246i	0.938925	+	0.344123i	$0.111824\pi$
$257$			11.0334i			0.688246i	−0.938925	+	0.344123i	$0.888176\pi$
$258$	5.62593	−	0.269575i	0.350255	−	0.0167830i
$259$		−	24.3717i		−	1.51439i
$260$	4.51238			0.279846
$261$	15.1883	−	1.45889i	0.940131	−	0.0903030i
$262$	−12.3379			−0.762239
$263$	−30.8378			−1.90154			−0.950770	−	0.309897i	$-0.899705\pi$
$263$	−30.8378			−1.90154			−0.950770	+	0.309897i	$0.899705\pi$
$264$	5.44639	+	1.82671i	0.335202	+	0.112426i
$265$	3.05225			0.187498
$266$	17.2668			1.05870
$267$	−6.50144	+	0.311526i	−0.397882	+	0.0190651i
$268$	12.3529			0.754574
$269$		−	9.58345i		−	0.584313i	−0.956370	−	0.292157i	$-0.905627\pi$
$269$		−	9.58345i		−	0.584313i	0.956370	−	0.292157i	$-0.0943729\pi$
$270$	−5.14264	+	0.743810i	−0.312971	+	0.0452669i
$271$		−	21.3400i		−	1.29631i	−0.761507	−	0.648157i	$-0.775540\pi$
$271$		−	21.3400i		−	1.29631i	0.761507	−	0.648157i	$-0.224460\pi$
$272$	2.72065			0.164964
$273$	−1.62593	−	33.9325i	−0.0984057	−	2.05369i
$274$			20.9416i			1.26513i
$275$	−1.20394	+	3.09039i	−0.0726004	+	0.186358i
$276$	2.88645	−	0.138309i	0.173744	−	0.00832521i
$277$		−	7.43264i		−	0.446584i	−0.974752	−	0.223292i	$-0.928320\pi$
$277$		−	7.43264i		−	0.446584i	0.974752	−	0.223292i	$-0.0716804\pi$
$278$			15.5458i			0.932375i
$279$	−29.1023	+	2.79538i	−1.74231	+	0.167355i
$280$	4.34658			0.259758
$281$	−20.0300			−1.19489			−0.597444	−	0.801911i	$-0.703817\pi$
$281$	−20.0300			−1.19489			−0.597444	+	0.801911i	$0.703817\pi$
$282$	16.0063	−	0.766968i	0.953163	−	0.0456723i
$283$			5.98189i			0.355587i	0.984068	+	0.177793i	$0.0568958\pi$
$283$			5.98189i			0.355587i	−0.984068	+	0.177793i	$0.943104\pi$
$284$			3.60710i			0.214042i
$285$	−0.329316	−	6.87271i	−0.0195070	−	0.407104i
$286$	13.9450	+	5.43264i	0.824586	+	0.321239i
$287$			12.6932i			0.749254i
$288$	−2.98626	+	0.286841i	−0.175967	+	0.0169023i
$289$	−9.59805			−0.564591
$290$			5.08606i			0.298664i
$291$	−1.06091	−	22.1408i	−0.0621917	−	1.29792i
$292$		−	1.36502i		−	0.0798816i
$293$	22.9998			1.34366			0.671830	−	0.740705i	$-0.265509\pi$
$293$	22.9998			1.34366			0.671830	+	0.740705i	$0.265509\pi$
$294$	−0.985897	−	20.5753i	−0.0574987	−	1.19997i
$295$	−5.43264			−0.316301
$296$	−5.60710			−0.325906
$297$	−16.7883	−	3.89277i	−0.974155	−	0.225882i
$298$	−23.2882			−1.34905
$299$	7.52848			0.435383
$300$	−0.0828988	−	1.73007i	−0.00478616	−	0.0998854i
$301$	14.1345			0.814697
$302$			10.8440i			0.624001i
$303$	0.558695	+	11.6597i	0.0320962	+	0.669835i
$304$		−	3.97251i		−	0.227839i
$305$	−11.5646			−0.662189
$306$	−8.12456	+	0.780394i	−0.464450	+	0.0446122i
$307$		−	27.2645i		−	1.55607i	−0.628222	−	0.778034i	$-0.716217\pi$
$307$		−	27.2645i		−	1.55607i	0.628222	−	0.778034i	$-0.283783\pi$
$308$	13.4326	+	5.23303i	0.765396	+	0.298180i
$309$	−0.435373	−	9.08606i	−0.0247675	−	0.516888i
$310$		−	9.74541i		−	0.553502i
$311$		−	0.0613019i		−	0.00347611i	−0.999998	−	0.00173806i	$-0.999447\pi$
$311$		−	0.0613019i		−	0.00347611i	0.999998	−	0.00173806i	$-0.000553241\pi$
$312$	−7.80671	+	0.374071i	−0.441968	+	0.0211776i
$313$	−22.2766			−1.25915			−0.629574	−	0.776940i	$-0.716771\pi$
$313$	−22.2766			−1.25915			−0.629574	+	0.776940i	$0.716771\pi$
$314$	11.0861			0.625623
$315$	−12.9800	+	1.24678i	−0.731340	+	0.0702479i
$316$			1.07107i			0.0602526i
$317$			2.48169i			0.139385i	0.997569	+	0.0696927i	$0.0222019\pi$
$317$			2.48169i			0.139385i	−0.997569	+	0.0696927i	$0.977798\pi$
$318$	−5.28059	+	0.253028i	−0.296121	+	0.0141891i
$319$	−6.12332	+	15.7179i	−0.342840	+	0.880035i
$320$		−	1.00000i		−	0.0559017i
$321$	0.518704	+	10.8251i	0.0289512	+	0.604201i
$322$	7.25186			0.404130
$323$		−	10.8078i		−	0.601363i
$324$	8.83544	−	1.71316i	0.490858	−	0.0951755i
$325$		−	4.51238i		−	0.250302i
$326$	4.16580			0.230722
$327$	−30.9973	+	1.48528i	−1.71415	+	0.0821363i
$328$	2.92026			0.161245
$329$	40.2140			2.21707
$330$	1.82671	−	5.44639i	0.100557	−	0.299814i
$331$	−11.2519			−0.618458			−0.309229	−	0.950988i	$-0.600071\pi$
$331$	−11.2519			−0.618458			−0.309229	+	0.950988i	$0.600071\pi$
$332$	−14.5887			−0.800657
$333$	16.7442	−	1.60835i	0.917579	−	0.0881368i
$334$	8.78828			0.480873
$335$		−	12.3529i		−	0.674911i
$336$	−7.51987	+	0.360326i	−0.410243	+	0.0196574i
$337$			0.968917i			0.0527803i	0.999652	+	0.0263901i	$0.00840121\pi$
$337$			0.968917i			0.0527803i	−0.999652	+	0.0263901i	$0.991599\pi$
$338$	−7.36157			−0.400417
$339$	14.7270	−	0.705666i	0.799860	−	0.0383265i
$340$		−	2.72065i		−	0.147548i
$341$	11.7329	−	30.1171i	0.635373	−	1.63093i
$342$	1.13948	+	11.8629i	0.0616159	+	0.641474i
$343$		−	21.2668i		−	1.14830i
$344$		−	3.25186i		−	0.175328i
$345$	−0.138309	−	2.88645i	−0.00744629	−	0.155401i
$346$	2.66319			0.143174
$347$	1.59388			0.0855641			0.0427821	−	0.999084i	$-0.486378\pi$
$347$	1.59388			0.0855641			0.0427821	+	0.999084i	$0.486378\pi$
$348$	−0.421628	−	8.79922i	−0.0226016	−	0.471688i
$349$		−	18.9416i		−	1.01392i	−0.861970	−	0.506960i	$-0.830769\pi$
$349$		−	18.9416i		−	1.01392i	0.861970	−	0.506960i	$-0.169231\pi$
$350$		−	4.34658i		−	0.232335i
$351$	23.2055	−	3.35635i	1.23862	−	0.179149i
$352$	1.20394	−	3.09039i	0.0641703	−	0.164718i
$353$		−	0.806322i		−	0.0429162i	−0.999770	−	0.0214581i	$-0.993169\pi$
$353$		−	0.806322i		−	0.0429162i	0.999770	−	0.0214581i	$-0.00683085\pi$
$354$	9.39883	−	0.450359i	0.499542	−	0.0239363i
$355$	3.60710			0.191445
$356$			3.75791i			0.199169i
$357$	−20.4590	+	0.980323i	−1.08280	+	0.0518842i
$358$		−	11.2605i		−	0.595137i
$359$	−6.83531			−0.360754			−0.180377	−	0.983598i	$-0.557732\pi$
$359$	−6.83531			−0.360754			−0.180377	+	0.983598i	$0.557732\pi$
$360$	0.286841	+	2.98626i	0.0151178	+	0.157389i
$361$	3.21916			0.169429
$362$	−0.711272			−0.0373836
$363$	12.2024	−	14.6322i	0.640459	−	0.767992i
$364$	−19.6134			−1.02802
$365$	−1.36502			−0.0714482
$366$	20.0076	−	0.958694i	1.04581	−	0.0501117i
$367$	3.28873			0.171670			0.0858351	−	0.996309i	$-0.472644\pi$
$367$	3.28873			0.171670			0.0858351	+	0.996309i	$0.472644\pi$
$368$		−	1.66840i		−	0.0869716i
$369$	−8.72065	+	0.837650i	−0.453979	+	0.0436063i
$370$			5.60710i			0.291499i
$371$	−13.2668			−0.688780
$372$	0.807883	+	16.8602i	0.0418868	+	0.874161i
$373$			11.3650i			0.588458i	0.955735	+	0.294229i	$0.0950629\pi$
$373$			11.3650i			0.588458i	−0.955735	+	0.294229i	$0.904937\pi$
$374$	3.27551	−	8.40788i	0.169372	−	0.434761i
$375$	−1.73007	+	0.0828988i	−0.0893402	+	0.00428087i
$376$		−	9.25186i		−	0.477128i
$377$		−	22.9502i		−	1.18200i
$378$	22.3529	−	3.23303i	1.14971	−	0.166289i
$379$	26.1848			1.34502			0.672511	−	0.740087i	$-0.265216\pi$
$379$	26.1848			1.34502			0.672511	+	0.740087i	$0.265216\pi$
$380$	−3.97251			−0.203786
$381$	−15.4845	+	0.741964i	−0.793295	+	0.0380120i
$382$			19.5852i			1.00207i
$383$			18.7796i			0.959590i	0.877381	+	0.479795i	$0.159289\pi$
$383$			18.7796i			0.959590i	−0.877381	+	0.479795i	$0.840711\pi$
$384$	0.0828988	+	1.73007i	0.00423041	+	0.0882871i
$385$	5.23303	−	13.4326i	0.266700	−	0.684591i
$386$		−	8.82899i		−	0.449384i
$387$	0.932765	+	9.71088i	0.0474151	+	0.493632i
$388$	−12.7977			−0.649703
$389$		−	24.4661i		−	1.24048i	−0.784413	−	0.620239i	$-0.787035\pi$
$389$		−	24.4661i		−	1.24048i	0.784413	−	0.620239i	$-0.212965\pi$
$390$	0.374071	+	7.80671i	0.0189418	+	0.395308i
$391$		−	4.53915i		−	0.229555i
$392$	−11.8928			−0.600676
$393$	−1.02280	−	21.3454i	−0.0515934	−	1.07673i
$394$	−12.9502			−0.652424
$395$	1.07107			0.0538916
$396$	−2.70883	+	9.57404i	−0.136124	+	0.481114i
$397$	−34.0708			−1.70997			−0.854983	−	0.518656i	$-0.826433\pi$
$397$	−34.0708			−1.70997			−0.854983	+	0.518656i	$0.826433\pi$
$398$	1.17485			0.0588900
$399$	1.43140	+	29.8728i	0.0716597	+	1.49551i
$400$	−1.00000			−0.0500000
$401$		−	2.52416i		−	0.126051i	−0.998012	−	0.0630254i	$-0.979925\pi$
$401$		−	2.52416i		−	0.126051i	0.998012	−	0.0630254i	$-0.0200749\pi$
$402$	1.02404	+	21.3713i	0.0510745	+	1.06591i
$403$			43.9750i			2.19055i
$404$	6.73948			0.335302
$405$	−1.71316	−	8.83544i	−0.0851276	−	0.439037i
$406$		−	22.1070i		−	1.09715i
$407$	−6.75063	+	17.3281i	−0.334616	+	0.858924i
$408$	0.225539	+	4.70691i	0.0111658	+	0.233027i
$409$		−	1.07974i		−	0.0533895i	−0.999644	−	0.0266948i	$-0.991502\pi$
$409$		−	1.07974i		−	0.0533895i	0.999644	−	0.0266948i	$-0.00849822\pi$
$410$		−	2.92026i		−	0.144222i
$411$	−36.2303	+	1.73603i	−1.78711	+	0.0856321i
$412$	−5.25186			−0.258740
$413$	23.6134			1.16194
$414$	0.478566	+	4.98228i	0.0235203	+	0.244866i
$415$			14.5887i			0.716130i
$416$			4.51238i			0.221238i
$417$	−26.8953	+	1.28873i	−1.31707	+	0.0631093i
$418$	−12.2766	−	4.78267i	−0.600469	−	0.233928i
$419$		−	27.6897i		−	1.35273i	−0.736566	−	0.676366i	$-0.763554\pi$
$419$		−	27.6897i		−	1.35273i	0.736566	−	0.676366i	$-0.236446\pi$
$420$	0.360326	+	7.51987i	0.0175821	+	0.366932i
$421$	31.0847			1.51498			0.757488	−	0.652849i	$-0.226426\pi$
$421$	31.0847			1.51498			0.757488	+	0.652849i	$0.226426\pi$
$422$		−	21.1498i		−	1.02956i
$423$	2.65381	+	27.6284i	0.129033	+	1.34334i
$424$			3.05225i			0.148230i
$425$	−2.72065			−0.131971
$426$	−6.24053	+	0.299024i	−0.302354	+	0.0144878i
$427$	50.2666			2.43257
$428$	6.25707			0.302447
$429$	−8.24280	+	24.5762i	−0.397966	+	1.18655i
$430$	−3.25186			−0.156819
$431$	−2.86529			−0.138016			−0.0690080	−	0.997616i	$-0.521983\pi$
$431$	−2.86529			−0.138016			−0.0690080	+	0.997616i	$0.521983\pi$
$432$	−0.743810	−	5.14264i	−0.0357866	−	0.247425i
$433$	−14.8158			−0.712000			−0.356000	−	0.934486i	$-0.615860\pi$
$433$	−14.8158			−0.712000			−0.356000	+	0.934486i	$0.615860\pi$
$434$			42.3592i			2.03331i
$435$	−8.79922	+	0.421628i	−0.421890	+	0.0202155i
$436$			17.9168i			0.858060i
$437$	−6.62776			−0.317049
$438$	2.36157	−	0.113158i	0.112840	−	0.00540691i
$439$			11.3108i			0.539836i	0.962883	+	0.269918i	$0.0869966\pi$
$439$			11.3108i			0.539836i	−0.962883	+	0.269918i	$0.913003\pi$
$440$	−3.09039	−	1.20394i	−0.147329	−	0.0573957i
$441$	35.5149	−	3.41133i	1.69118	−	0.162444i
$442$			12.2766i			0.583939i
$443$			1.60476i			0.0762447i	0.999273	+	0.0381223i	$0.0121377\pi$
$443$			1.60476i			0.0762447i	−0.999273	+	0.0381223i	$0.987862\pi$
$444$	−0.464822	−	9.70066i	−0.0220595	−	0.460373i
$445$	3.75791			0.178142
$446$	22.6382			1.07195
$447$	−1.93056	−	40.2900i	−0.0913123	−	1.90565i
$448$			4.34658i			0.205357i
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$	2.98626	−	0.286841i	0.140773	−	0.0135218i
$451$	3.51583	−	9.02476i	0.165554	−	0.424959i
$452$		−	8.51238i		−	0.400389i
$453$	−18.7608	+	0.898952i	−0.881459	+	0.0422365i
$454$	−23.5758			−1.10647
$455$			19.6134i			0.919492i
$456$	6.87271	−	0.329316i	0.321844	−	0.0154217i
$457$			32.8716i			1.53767i	0.639448	+	0.768835i	$0.279163\pi$
$457$			32.8716i			1.53767i	−0.639448	+	0.768835i	$0.720837\pi$
$458$	3.50893			0.163962
$459$	−2.02365	−	13.9913i	−0.0944559	−	0.653060i
$460$	−1.66840			−0.0777898
$461$	−15.9387			−0.742339			−0.371170	−	0.928565i	$-0.621043\pi$
$461$	−15.9387			−0.742339			−0.371170	+	0.928565i	$0.621043\pi$
$462$	−7.93994	+	23.6732i	−0.369399	+	1.10138i
$463$	10.4842			0.487241			0.243620	−	0.969871i	$-0.421665\pi$
$463$	10.4842			0.487241			0.243620	+	0.969871i	$0.421665\pi$
$464$	−5.08606			−0.236114
$465$	16.8602	−	0.807883i	0.781873	−	0.0374647i
$466$	−9.84991			−0.456288
$467$			2.64436i			0.122367i	0.998127	+	0.0611833i	$0.0194874\pi$
$467$			2.64436i			0.122367i	−0.998127	+	0.0611833i	$0.980513\pi$
$468$	−1.29433	−	13.4751i	−0.0598306	−	0.622888i
$469$			53.6929i			2.47931i
$470$	−9.25186			−0.426756
$471$	0.919021	+	19.1796i	0.0423463	+	0.883750i
$472$		−	5.43264i		−	0.250058i
$473$	−10.0495	−	3.91505i	−0.462077	−	0.180014i
$474$	−1.85303	+	0.0887907i	−0.0851124	+	0.00407829i
$475$			3.97251i			0.182271i
$476$			11.8255i			0.542023i
$477$	−0.875509	−	9.11479i	−0.0400868	−	0.417338i
$478$	24.1540			1.10478
$479$	28.6082			1.30714			0.653571	−	0.756865i	$-0.273270\pi$
$479$	28.6082			1.30714			0.653571	+	0.756865i	$0.273270\pi$
$480$	1.73007	−	0.0828988i	0.0789663	−	0.00378379i
$481$		−	25.3014i		−	1.15364i
$482$			4.69316i			0.213768i
$483$	0.601170	+	12.5462i	0.0273542	+	0.570872i
$484$	−8.10105	−	7.44131i	−0.368229	−	0.338241i
$485$			12.7977i			0.581112i
$486$	3.69633	+	15.1439i	0.167669	+	0.686940i
$487$	−25.5584			−1.15816			−0.579082	−	0.815269i	$-0.696589\pi$
$487$	−25.5584			−1.15816			−0.579082	+	0.815269i	$0.696589\pi$
$488$		−	11.5646i		−	0.523506i
$489$	0.345340	+	7.20710i	0.0156168	+	0.325917i
$490$			11.8928i			0.537261i
$491$	30.0732			1.35718			0.678592	−	0.734516i	$-0.262591\pi$
$491$	30.0732			1.35718			0.678592	+	0.734516i	$0.262591\pi$
$492$	0.242086	+	5.05225i	0.0109141	+	0.227773i
$493$	−13.8374			−0.623205
$494$	17.9255			0.806505
$495$	9.57404	+	2.70883i	0.430321	+	0.121753i
$496$	9.74541			0.437582
$497$	−15.6786			−0.703280
$498$	−1.20938	−	25.2394i	−0.0541937	−	1.13100i
$499$	13.6503			0.611071			0.305536	−	0.952181i	$-0.401165\pi$
$499$	13.6503			0.611071			0.305536	+	0.952181i	$0.401165\pi$
$500$			1.00000i			0.0447214i
$501$	0.728538	+	15.2043i	0.0325487	+	0.679278i
$502$		−	10.5424i		−	0.470528i
$503$	22.0495			0.983139			0.491570	−	0.870838i	$-0.336423\pi$
$503$	22.0495			0.983139			0.491570	+	0.870838i	$0.336423\pi$
$504$	−1.24678	−	12.9800i	−0.0555358	−	0.578175i
$505$		−	6.73948i		−	0.299903i
$506$	−5.15603	−	2.00866i	−0.229213	−	0.0892959i
$507$	−0.610265	−	12.7360i	−0.0271028	−	0.565626i
$508$			8.95024i			0.397103i
$509$		−	17.7660i		−	0.787464i	−0.919225	−	0.393732i	$-0.871184\pi$
$509$		−	17.7660i		−	0.787464i	0.919225	−	0.393732i	$-0.128816\pi$
$510$	4.70691	−	0.225539i	0.208425	−	0.00998703i
$511$	5.93316			0.262467
$512$	1.00000			0.0441942
$513$	−20.4292	+	2.95479i	−0.901971	+	0.130457i
$514$			11.0334i			0.486663i
$515$			5.25186i			0.231425i
$516$	5.62593	−	0.269575i	0.247668	−	0.0118674i
$517$	−28.5919	−	11.1387i	−1.25747	−	0.489879i
$518$		−	24.3717i		−	1.07083i
$519$	0.220775	+	4.60749i	0.00969096	+	0.202247i
$520$	4.51238			0.197881
$521$			21.0074i			0.920352i	0.887828	+	0.460176i	$0.152214\pi$
$521$			21.0074i			0.920352i	−0.887828	+	0.460176i	$0.847786\pi$
$522$	15.1883	−	1.45889i	0.664773	−	0.0638538i
$523$		−	41.7779i		−	1.82682i	−0.407042	−	0.913409i	$-0.633440\pi$
$523$		−	41.7779i		−	1.82682i	0.407042	−	0.913409i	$-0.366560\pi$
$524$	−12.3379			−0.538985
$525$	7.51987	−	0.360326i	0.328194	−	0.0157259i
$526$	−30.8378			−1.34459
$527$	26.5139			1.15496
$528$	5.44639	+	1.82671i	0.237024	+	0.0794973i
$529$	20.2164			0.878975
$530$	3.05225			0.132581
$531$	1.55830	+	16.2233i	0.0676246	+	0.704030i
$532$	17.2668			0.748613
$533$			13.1773i			0.570774i
$534$	−6.50144	+	0.311526i	−0.281345	+	0.0134811i
$535$		−	6.25707i		−	0.270517i
$536$	12.3529			0.533564
$537$	19.4814	−	0.933483i	0.840686	−	0.0402828i
$538$		−	9.58345i		−	0.413172i
$539$	−14.3182	+	36.7533i	−0.616729	+	1.58308i
$540$	−5.14264	+	0.743810i	−0.221304	+	0.0320085i
$541$			6.18327i			0.265840i	0.991127	+	0.132920i	$0.0424353\pi$
$541$			6.18327i			0.265840i	−0.991127	+	0.132920i	$0.957565\pi$
$542$		−	21.3400i		−	0.916632i
$543$	−0.0589636	−	1.23055i	−0.00253037	−	0.0528078i
$544$	2.72065			0.116647
$545$	17.9168			0.767472
$546$	−1.62593	−	33.9325i	−0.0695833	−	1.45218i
$547$			21.2999i			0.910720i	0.890307	+	0.455360i	$0.150489\pi$
$547$			21.2999i			0.910720i	−0.890307	+	0.455360i	$0.849511\pi$
$548$			20.9416i			0.894580i
$549$	3.31721	+	34.5349i	0.141575	+	1.47392i
$550$	−1.20394	+	3.09039i	−0.0513363	+	0.131775i
$551$			20.2044i			0.860738i
$552$	2.88645	−	0.138309i	0.122855	−	0.00588681i
$553$	−4.65551			−0.197972
$554$		−	7.43264i		−	0.315783i
$555$	−9.70066	+	0.464822i	−0.411770	+	0.0197306i
$556$			15.5458i			0.659289i
$557$	5.87740			0.249033			0.124517	−	0.992218i	$-0.460262\pi$
$557$	5.87740			0.249033			0.124517	+	0.992218i	$0.460262\pi$
$558$	−29.1023	+	2.79538i	−1.23200	+	0.118338i
$559$	14.6736			0.620628
$560$	4.34658			0.183677
$561$	14.8177	+	4.96984i	0.625605	+	0.209827i
$562$	−20.0300			−0.844913
$563$	21.9442			0.924839			0.462420	−	0.886661i	$-0.346981\pi$
$563$	21.9442			0.924839			0.462420	+	0.886661i	$0.346981\pi$
$564$	16.0063	−	0.766968i	0.673988	−	0.0322952i
$565$	−8.51238			−0.358118
$566$			5.98189i			0.251438i
$567$	7.44639	+	38.4040i	0.312719	+	1.61282i
$568$			3.60710i			0.151351i
$569$	−15.7284			−0.659367			−0.329683	−	0.944092i	$-0.606942\pi$
$569$	−15.7284			−0.659367			−0.329683	+	0.944092i	$0.606942\pi$
$570$	−0.329316	−	6.87271i	−0.0137935	−	0.287866i
$571$			39.4633i			1.65149i	0.564044	+	0.825745i	$0.309245\pi$
$571$			39.4633i			1.65149i	−0.564044	+	0.825745i	$0.690755\pi$
$572$	13.9450	+	5.43264i	0.583071	+	0.227150i
$573$	−33.8837	+	1.62359i	−1.41551	+	0.0678265i
$574$			12.6932i			0.529802i
$575$			1.66840i			0.0695773i
$576$	−2.98626	+	0.286841i	−0.124427	+	0.0119517i
$577$	−12.1721			−0.506732			−0.253366	−	0.967370i	$-0.581538\pi$
$577$	−12.1721			−0.506732			−0.253366	+	0.967370i	$0.581538\pi$
$578$	−9.59805			−0.399226
$579$	15.2747	−	0.731912i	0.634796	−	0.0304172i
$580$			5.08606i			0.211187i
$581$		−	63.4108i		−	2.63072i
$582$	−1.06091	−	22.1408i	−0.0439762	−	0.917765i
$583$	9.43264	+	3.67473i	0.390660	+	0.152192i
$584$		−	1.36502i		−	0.0564848i
$585$	−13.4751	+	1.29433i	−0.557128	+	0.0535141i
$586$	22.9998			0.950111
$587$		−	3.76175i		−	0.155264i	−0.996982	−	0.0776321i	$-0.975264\pi$
$587$		−	3.76175i		−	0.155264i	0.996982	−	0.0776321i	$-0.0247359\pi$
$588$	−0.985897	−	20.5753i	−0.0406577	−	0.848510i
$589$		−	38.7138i		−	1.59517i
$590$	−5.43264			−0.223658
$591$	−1.07356	−	22.4048i	−0.0441603	−	0.921609i
$592$	−5.60710			−0.230451
$593$	19.5389			0.802367			0.401183	−	0.915998i	$-0.368599\pi$
$593$	19.5389			0.802367			0.401183	+	0.915998i	$0.368599\pi$
$594$	−16.7883	−	3.89277i	−0.688831	−	0.159722i
$595$	11.8255			0.484800
$596$	−23.2882			−0.953920
$597$	0.0973938	+	2.03257i	0.00398606	+	0.0831876i
$598$	7.52848			0.307862
$599$		−	33.4776i		−	1.36786i	−0.729549	−	0.683929i	$-0.760270\pi$
$599$		−	33.4776i		−	1.36786i	0.729549	−	0.683929i	$-0.239730\pi$
$600$	−0.0828988	−	1.73007i	−0.00338433	−	0.0706296i
$601$			22.9203i			0.934937i	0.884010	+	0.467469i	$0.154834\pi$
$601$			22.9203i			0.934937i	−0.884010	+	0.467469i	$0.845166\pi$
$602$	14.1345			0.576078
$603$	−36.8889	+	3.54332i	−1.50223	+	0.144295i
$604$			10.8440i			0.441235i
$605$	−7.44131	+	8.10105i	−0.302532	+	0.329354i
$606$	0.558695	+	11.6597i	0.0226954	+	0.473645i
$607$			7.21187i			0.292721i	0.989231	+	0.146360i	$0.0467559\pi$
$607$			7.21187i			0.292721i	−0.989231	+	0.146360i	$0.953244\pi$
$608$		−	3.97251i		−	0.161107i
$609$	38.2465	−	1.83264i	1.54983	−	0.0742624i
$610$	−11.5646			−0.468238
$611$	41.7479			1.68894
$612$	−8.12456	+	0.780394i	−0.328416	+	0.0315456i
$613$		−	10.9911i		−	0.443926i	−0.975055	−	0.221963i	$-0.928754\pi$
$613$		−	10.9911i		−	0.443926i	0.975055	−	0.221963i	$-0.0712464\pi$
$614$		−	27.2645i		−	1.10031i
$615$	5.05225	−	0.242086i	0.203726	−	0.00976186i
$616$	13.4326	+	5.23303i	0.541217	+	0.210845i
$617$			9.52449i			0.383442i	0.981450	+	0.191721i	$0.0614068\pi$
$617$			9.52449i			0.383442i	−0.981450	+	0.191721i	$0.938593\pi$
$618$	−0.435373	−	9.08606i	−0.0175133	−	0.365495i
$619$	20.5329			0.825287			0.412644	−	0.910893i	$-0.364605\pi$
$619$	20.5329			0.825287			0.412644	+	0.910893i	$0.364605\pi$
$620$		−	9.74541i		−	0.391385i
$621$	−8.58001	+	1.24098i	−0.344304	+	0.0497987i
$622$		−	0.0613019i		−	0.00245798i
$623$	−16.3341			−0.654411
$624$	−7.80671	+	0.374071i	−0.312519	+	0.0149748i
$625$	1.00000			0.0400000
$626$	−22.2766			−0.890353
$627$	7.25662	−	21.6358i	0.289802	−	0.864052i
$628$	11.0861			0.442382
$629$	−15.2550			−0.608256
$630$	−12.9800	+	1.24678i	−0.517136	+	0.0496728i
$631$	−29.6731			−1.18127			−0.590634	−	0.806940i	$-0.701122\pi$
$631$	−29.6731			−1.18127			−0.590634	+	0.806940i	$0.701122\pi$
$632$			1.07107i			0.0426050i
$633$	36.5906	−	1.75330i	1.45435	−	0.0696873i
$634$			2.48169i			0.0985604i
$635$	8.95024			0.355179
$636$	−5.28059	+	0.253028i	−0.209389	+	0.0100332i
$637$		−	53.6647i		−	2.12627i
$638$	−6.12332	+	15.7179i	−0.242425	+	0.622279i
$639$	−1.03466	−	10.7717i	−0.0409307	−	0.426123i
$640$		−	1.00000i		−	0.0395285i
$641$		−	19.0947i		−	0.754196i	−0.926173	−	0.377098i	$-0.876922\pi$
$641$		−	19.0947i		−	0.754196i	0.926173	−	0.377098i	$-0.123078\pi$
$642$	0.518704	+	10.8251i	0.0204716	+	0.427235i
$643$	22.0663			0.870209			0.435104	−	0.900380i	$-0.356711\pi$
$643$	22.0663			0.870209			0.435104	+	0.900380i	$0.356711\pi$
$644$	7.25186			0.285763
$645$	−0.269575	−	5.62593i	−0.0106145	−	0.221521i
$646$		−	10.8078i		−	0.425228i
$647$			18.5832i			0.730581i	0.930894	+	0.365291i	$0.119030\pi$
$647$			18.5832i			0.730581i	−0.930894	+	0.365291i	$0.880970\pi$
$648$	8.83544	−	1.71316i	0.347089	−	0.0672993i
$649$	−16.7890	−	6.54059i	−0.659026	−	0.256740i
$650$		−	4.51238i		−	0.176990i
$651$	−73.2843	+	3.51153i	−2.87224	+	0.137628i
$652$	4.16580			0.163145
$653$			31.2063i			1.22120i	0.791941	+	0.610598i	$0.209071\pi$
$653$			31.2063i			1.22120i	−0.791941	+	0.610598i	$0.790929\pi$
$654$	−30.9973	+	1.48528i	−1.21209	+	0.0580791i
$655$			12.3379i			0.482082i
$656$	2.92026			0.114017
$657$	0.391542	+	4.07629i	0.0152755	+	0.159031i
$658$	40.2140			1.56770
$659$	−26.6138			−1.03672			−0.518362	−	0.855161i	$-0.673458\pi$
$659$	−26.6138			−1.03672			−0.518362	+	0.855161i	$0.673458\pi$
$660$	1.82671	−	5.44639i	0.0711046	−	0.212000i
$661$	−4.07452			−0.158481			−0.0792403	−	0.996856i	$-0.525249\pi$
$661$	−4.07452			−0.158481			−0.0792403	+	0.996856i	$0.525249\pi$
$662$	−11.2519			−0.437316
$663$	−21.2394	+	1.01772i	−0.824868	+	0.0395248i
$664$	−14.5887			−0.566150
$665$		−	17.2668i		−	0.669580i
$666$	16.7442	−	1.60835i	0.648826	−	0.0623221i
$667$			8.48561i			0.328564i
$668$	8.78828			0.340029
$669$	1.87668	+	39.1656i	0.0725566	+	1.51423i
$670$		−	12.3529i		−	0.477234i
$671$	−35.7392	−	13.9231i	−1.37970	−	0.537497i
$672$	−7.51987	+	0.360326i	−0.290085	+	0.0138999i
$673$		−	0.828988i		−	0.0319551i	−0.999872	−	0.0159776i	$-0.994914\pi$
$673$		−	0.828988i		−	0.0319551i	0.999872	−	0.0159776i	$-0.00508603\pi$
$674$			0.968917i			0.0373213i
$675$	0.743810	+	5.14264i	0.0286293	+	0.197940i
$676$	−7.36157			−0.283137
$677$	6.51415			0.250359			0.125179	−	0.992134i	$-0.460049\pi$
$677$	6.51415			0.250359			0.125179	+	0.992134i	$0.460049\pi$
$678$	14.7270	−	0.705666i	0.565586	−	0.0271009i
$679$		−	55.6261i		−	2.13473i
$680$		−	2.72065i		−	0.104332i
$681$	−1.95440	−	40.7876i	−0.0748929	−	1.56299i
$682$	11.7329	−	30.1171i	0.449276	−	1.15325i
$683$			8.99407i			0.344148i	0.985084	+	0.172074i	$0.0550469\pi$
$683$			8.99407i			0.344148i	−0.985084	+	0.172074i	$0.944953\pi$
$684$	1.13948	+	11.8629i	0.0435690	+	0.453591i
$685$	20.9416			0.800136
$686$		−	21.2668i		−	0.811972i
$687$	0.290886	+	6.07068i	0.0110980	+	0.231611i
$688$		−	3.25186i		−	0.123976i
$689$	−13.7729			−0.524706
$690$	−0.138309	−	2.88645i	−0.00526532	−	0.109885i
$691$	−39.7848			−1.51348			−0.756742	−	0.653714i	$-0.773210\pi$
$691$	−39.7848			−1.51348			−0.756742	+	0.653714i	$0.773210\pi$
$692$	2.66319			0.101239
$693$	−41.6144	−	11.7741i	−1.58080	−	0.447263i
$694$	1.59388			0.0605030
$695$	15.5458			0.589686
$696$	−0.421628	−	8.79922i	−0.0159818	−	0.333534i
$697$	7.94502			0.300939
$698$		−	18.9416i		−	0.716949i
$699$	−0.816545	−	17.0410i	−0.0308846	−	0.644549i
$700$		−	4.34658i		−	0.164285i
$701$	−40.4528			−1.52788			−0.763941	−	0.645286i	$-0.776738\pi$
$701$	−40.4528			−1.52788			−0.763941	+	0.645286i	$0.776738\pi$
$702$	23.2055	−	3.35635i	0.875837	−	0.126677i
$703$			22.2743i			0.840090i
$704$	1.20394	−	3.09039i	0.0453753	−	0.116474i
$705$	−0.766968	−	16.0063i	−0.0288857	−	0.602833i
$706$		−	0.806322i		−	0.0303463i
$707$			29.2937i			1.10170i
$708$	9.39883	−	0.450359i	0.353230	−	0.0169255i
$709$	−31.3126			−1.17597			−0.587984	−	0.808872i	$-0.700078\pi$
$709$	−31.3126			−1.17597			−0.587984	+	0.808872i	$0.700078\pi$
$710$	3.60710			0.135372
$711$	−0.307228	−	3.19850i	−0.0115219	−	0.119953i
$712$			3.75791i			0.140834i
$713$		−	16.2593i		−	0.608915i
$714$	−20.4590	+	0.980323i	−0.765657	+	0.0366877i
$715$	5.43264	−	13.9450i	0.203169	−	0.521514i
$716$		−	11.2605i		−	0.420825i
$717$	2.00234	+	41.7880i	0.0747787	+	1.56060i
$718$	−6.83531			−0.255092
$719$			49.2324i			1.83606i	0.396513	+	0.918029i	$0.370220\pi$
$719$			49.2324i			1.83606i	−0.396513	+	0.918029i	$0.629780\pi$
$720$	0.286841	+	2.98626i	0.0106899	+	0.111291i
$721$		−	22.8276i		−	0.850145i
$722$	3.21916			0.119805
$723$	−8.11948	+	0.389058i	−0.301967	+	0.0144692i
$724$	−0.711272			−0.0264342
$725$	5.08606			0.188892
$726$	12.2024	−	14.6322i	0.452873	−	0.543053i
$727$	22.6682			0.840716			0.420358	−	0.907358i	$-0.361905\pi$
$727$	22.6682			0.840716			0.420358	+	0.907358i	$0.361905\pi$
$728$	−19.6134			−0.726922
$729$	−25.8935	+	7.65030i	−0.959018	+	0.283344i
$730$	−1.36502			−0.0505215
$731$		−	8.84718i		−	0.327225i
$732$	20.0076	−	0.958694i	0.739501	−	0.0354343i
$733$		−	0.210758i		−	0.00778452i	−0.999992	−	0.00389226i	$-0.998761\pi$
$733$		−	0.210758i		−	0.00778452i	0.999992	−	0.00389226i	$-0.00123895\pi$
$734$	3.28873			0.121389
$735$	−20.5753	+	0.985897i	−0.758931	+	0.0363653i
$736$		−	1.66840i		−	0.0614982i
$737$	14.8722	−	38.1753i	0.547824	−	1.40621i
$738$	−8.72065	+	0.837650i	−0.321012	+	0.0308343i
$739$		−	14.8053i		−	0.544623i	−0.962209	−	0.272312i	$-0.912212\pi$
$739$		−	14.8053i		−	0.544623i	0.962209	−	0.272312i	$-0.0877881\pi$
$740$			5.60710i			0.206121i
$741$	1.48600	+	31.0123i	0.0545896	+	1.13926i
$742$	−13.2668			−0.487041
$743$	−19.2717			−0.707009			−0.353504	−	0.935433i	$-0.615010\pi$
$743$	−19.2717			−0.707009			−0.353504	+	0.935433i	$0.615010\pi$
$744$	0.807883	+	16.8602i	0.0296184	+	0.618125i
$745$			23.2882i			0.853212i
$746$			11.3650i			0.416103i
$747$	43.5655	−	4.18462i	1.59398	−	0.153107i
$748$	3.27551	−	8.40788i	0.119764	−	0.307423i
$749$			27.1969i			0.993752i
$750$	−1.73007	+	0.0828988i	−0.0631731	+	0.00302704i
$751$	−24.6107			−0.898057			−0.449029	−	0.893517i	$-0.648230\pi$
$751$	−24.6107			−0.898057			−0.449029	+	0.893517i	$0.648230\pi$
$752$		−	9.25186i		−	0.337381i
$753$	18.2390	−	0.873948i	0.664665	−	0.0318484i
$754$		−	22.9502i		−	0.835798i
$755$	10.8440			0.394653
$756$	22.3529	−	3.23303i	0.812967	−	0.117584i
$757$	21.6166			0.785670			0.392835	−	0.919609i	$-0.371494\pi$
$757$	21.6166			0.785670			0.392835	+	0.919609i	$0.371494\pi$
$758$	26.1848			0.951074
$759$	3.04769	−	9.08678i	0.110624	−	0.329829i
$760$	−3.97251			−0.144098
$761$	34.6751			1.25697			0.628485	−	0.777822i	$-0.283675\pi$
$761$	34.6751			1.25697			0.628485	+	0.777822i	$0.283675\pi$
$762$	−15.4845	+	0.741964i	−0.560944	+	0.0268785i
$763$	−77.8769			−2.81933
$764$			19.5852i			0.708568i
$765$	0.780394	+	8.12456i	0.0282152	+	0.293744i
$766$			18.7796i			0.678533i
$767$	24.5141			0.885155
$768$	0.0828988	+	1.73007i	0.00299135	+	0.0624284i
$769$		−	16.8772i		−	0.608606i	−0.952575	−	0.304303i	$-0.901577\pi$
$769$		−	16.8772i		−	0.608606i	0.952575	−	0.304303i	$-0.0984235\pi$
$770$	5.23303	−	13.4326i	0.188585	−	0.484079i
$771$	−19.0885	+	0.914657i	−0.687457	+	0.0329406i
$772$		−	8.82899i		−	0.317762i
$773$			8.07701i			0.290510i	0.989394	+	0.145255i	$0.0464002\pi$
$773$			8.07701i			0.290510i	−0.989394	+	0.145255i	$0.953600\pi$
$774$	0.932765	+	9.71088i	0.0335276	+	0.349050i
$775$	−9.74541			−0.350066
$776$	−12.7977			−0.459409
$777$	42.1647	−	2.02039i	1.51265	−	0.0724810i
$778$		−	24.4661i		−	0.877151i
$779$		−	11.6008i		−	0.415641i
$780$	0.374071	+	7.80671i	0.0133939	+	0.279525i
$781$	11.1474	+	4.34274i	0.398884	+	0.155396i
$782$		−	4.53915i		−	0.162320i
$783$	3.78306	+	26.1558i	0.135196	+	0.934731i
$784$	−11.8928			−0.424742
$785$		−	11.0861i		−	0.395678i
$786$	−1.02280	−	21.3454i	−0.0364820	−	0.761366i
$787$		−	15.2992i		−	0.545356i	−0.962105	−	0.272678i	$-0.912091\pi$
$787$		−	15.2992i		−	0.545356i	0.962105	−	0.272678i	$-0.0879094\pi$
$788$	−12.9502			−0.461333
$789$	−2.55642	−	53.3514i	−0.0910108	−	1.89936i
$790$	1.07107			0.0381071
$791$	36.9998			1.31556
$792$	−2.70883	+	9.57404i	−0.0962540	+	0.340199i
$793$	52.1840			1.85311
$794$	−34.0708			−1.20913
$795$	0.253028	+	5.28059i	0.00897397	+	0.187283i
$796$	1.17485			0.0416415
$797$			4.37200i			0.154864i	0.996998	+	0.0774321i	$0.0246721\pi$
$797$			4.37200i			0.154864i	−0.996998	+	0.0774321i	$0.975328\pi$
$798$	1.43140	+	29.8728i	0.0506710	+	1.05748i
$799$		−	25.1711i		−	0.890489i
$800$	−1.00000			−0.0353553
$801$	−1.07792	−	11.2221i	−0.0380865	−	0.396513i
$802$		−	2.52416i		−	0.0891313i
$803$	−4.21844	−	1.64340i	−0.148865	−	0.0579944i
$804$	1.02404	+	21.3713i	0.0361151	+	0.753709i
$805$		−	7.25186i		−	0.255594i
$806$			43.9750i			1.54895i
$807$	16.5800	−	0.794457i	0.583644	−	0.0279662i
$808$	6.73948			0.237094
$809$	16.6459			0.585237			0.292619	−	0.956229i	$-0.405473\pi$
$809$	16.6459			0.585237			0.292619	+	0.956229i	$0.405473\pi$
$810$	−1.71316	−	8.83544i	−0.0601943	−	0.310446i
$811$			35.1018i			1.23259i	0.787515	+	0.616295i	$0.211367\pi$
$811$			35.1018i			1.23259i	−0.787515	+	0.616295i	$0.788633\pi$
$812$		−	22.1070i		−	0.775803i
$813$	36.9196	−	1.76906i	1.29483	−	0.0620437i
$814$	−6.75063	+	17.3281i	−0.236609	+	0.607351i
$815$		−	4.16580i		−	0.145922i
$816$	0.225539	+	4.70691i	0.00789544	+	0.164775i
$817$	−12.9180			−0.451945
$818$		−	1.07974i		−	0.0377521i
$819$	58.5707	−	5.62593i	2.04663	−	0.196586i
$820$		−	2.92026i		−	0.101980i
$821$	−4.78900			−0.167137			−0.0835686	−	0.996502i	$-0.526632\pi$
$821$	−4.78900			−0.167137			−0.0835686	+	0.996502i	$0.526632\pi$
$822$	−36.2303	+	1.73603i	−1.26368	+	0.0605510i
$823$	19.7053			0.686883			0.343441	−	0.939174i	$-0.388407\pi$
$823$	19.7053			0.686883			0.343441	+	0.939174i	$0.388407\pi$
$824$	−5.25186			−0.182957
$825$	−5.44639	−	1.82671i	−0.189619	−	0.0635978i
$826$	23.6134			0.821616
$827$	−49.7179			−1.72886			−0.864431	−	0.502752i	$-0.832321\pi$
$827$	−49.7179			−1.72886			−0.864431	+	0.502752i	$0.832321\pi$
$828$	0.478566	+	4.98228i	0.0166313	+	0.173146i
$829$	43.5766			1.51348			0.756738	−	0.653718i	$-0.226792\pi$
$829$	43.5766			1.51348			0.756738	+	0.653718i	$0.226792\pi$
$830$			14.5887i			0.506380i
$831$	12.8590	−	0.616157i	0.446072	−	0.0213743i
$832$			4.51238i			0.156439i
$833$	−32.3561			−1.12107
$834$	−26.8953	+	1.28873i	−0.931307	+	0.0446250i
$835$		−	8.78828i		−	0.304131i
$836$	−12.2766	−	4.78267i	−0.424596	−	0.165412i
$837$	−7.24874	−	50.1171i	−0.250553	−	1.73230i
$838$		−	27.6897i		−	0.956525i
$839$			5.89727i			0.203596i	0.994805	+	0.101798i	$0.0324596\pi$
$839$			5.89727i			0.203596i	−0.994805	+	0.101798i	$0.967540\pi$
$840$	0.360326	+	7.51987i	0.0124324	+	0.259460i
$841$	−3.13198			−0.107999
$842$	31.0847			1.07125
$843$	−1.66046	−	34.6532i	−0.0571893	−	1.19352i
$844$		−	21.1498i		−	0.728008i
$845$			7.36157i			0.253246i
$846$	2.65381	+	27.6284i	0.0912399	+	0.949884i
$847$	32.3442	−	35.2119i	1.11136	−	1.20989i
$848$			3.05225i			0.104815i
$849$	−10.3491	+	0.495892i	−0.355179	+	0.0170190i
$850$	−2.72065			−0.0933176
$851$			9.35492i			0.320682i
$852$	−6.24053	+	0.299024i	−0.213797	+	0.0102444i
$853$			25.2919i			0.865979i	0.901399	+	0.432990i	$0.142541\pi$
$853$			25.2919i			0.865979i	−0.901399	+	0.432990i	$0.857459\pi$
$854$	50.2666			1.72009
$855$	11.8629	−	1.13948i	0.405704	−	0.0389693i
$856$	6.25707			0.213862
$857$	25.0718			0.856436			0.428218	−	0.903675i	$-0.359142\pi$
$857$	25.0718			0.856436			0.428218	+	0.903675i	$0.359142\pi$
$858$	−8.24280	+	24.5762i	−0.281405	+	0.839016i
$859$	12.2263			0.417157			0.208578	−	0.978006i	$-0.433116\pi$
$859$	12.2263			0.417157			0.208578	+	0.978006i	$0.433116\pi$
$860$	−3.25186			−0.110887
$861$	−21.9600	+	1.05225i	−0.748395	+	0.0358605i
$862$	−2.86529			−0.0975920
$863$			16.5713i			0.564095i	0.959400	+	0.282048i	$0.0910136\pi$
$863$			16.5713i			0.564095i	−0.959400	+	0.282048i	$0.908986\pi$
$864$	−0.743810	−	5.14264i	−0.0253049	−	0.174956i
$865$		−	2.66319i		−	0.0905512i
$866$	−14.8158			−0.503460
$867$	−0.795667	−	16.6053i	−0.0270223	−	0.563944i
$868$			42.3592i			1.43777i
$869$	3.31004	+	1.28951i	0.112285	+	0.0437437i
$870$	−8.79922	+	0.421628i	−0.298322	+	0.0142945i
$871$			55.7410i			1.88871i
$872$			17.9168i			0.606740i
$873$	38.2171	−	3.67089i	1.29345	−	0.124241i
$874$	−6.62776			−0.224187
$875$	−4.34658			−0.146941
$876$	2.36157	−	0.113158i	0.0797900	−	0.00382326i
$877$			41.5248i			1.40219i	0.713067	+	0.701096i	$0.247306\pi$
$877$			41.5248i			1.40219i	−0.713067	+	0.701096i	$0.752694\pi$
$878$			11.3108i			0.381722i
$879$	1.90665	+	39.7911i	0.0643098	+	1.34212i
$880$	−3.09039	−	1.20394i	−0.104177	−	0.0405849i
$881$			18.8053i			0.633568i	0.948498	+	0.316784i	$0.102603\pi$
$881$			18.8053i			0.633568i	−0.948498	+	0.316784i	$0.897397\pi$
$882$	35.5149	−	3.41133i	1.19585	−	0.114866i
$883$	−12.9252			−0.434966			−0.217483	−	0.976064i	$-0.569785\pi$
$883$	−12.9252			−0.434966			−0.217483	+	0.976064i	$0.569785\pi$
$884$			12.2766i			0.412907i
$885$	−0.450359	−	9.39883i	−0.0151387	−	0.315938i
$886$			1.60476i			0.0539131i
$887$	43.1169			1.44772			0.723862	−	0.689945i	$-0.242365\pi$
$887$	43.1169			1.44772			0.723862	+	0.689945i	$0.242365\pi$
$888$	−0.464822	−	9.70066i	−0.0155984	−	0.325533i
$889$	−38.9029			−1.30476
$890$	3.75791			0.125966
$891$	5.34303	−	29.3675i	0.178998	−	0.983849i
$892$	22.6382			0.757983
$893$	−36.7531			−1.22990
$894$	−1.93056	−	40.2900i	−0.0645676	−	1.34750i
$895$	−11.2605			−0.376398
$896$			4.34658i			0.145209i
$897$	0.624101	+	13.0248i	0.0208381	+	0.434884i
$898$			4.00000i			0.133482i
$899$	−49.5658			−1.65311
$900$	2.98626	−	0.286841i	0.0995419	−	0.00956136i
$901$			8.30411i			0.276650i
$902$	3.51583	−	9.02476i	0.117064	−	0.300492i
$903$	1.17173	+	24.4536i	0.0389927	+	0.813764i
$904$		−	8.51238i		−	0.283118i
$905$			0.711272i			0.0236435i
$906$	−18.7608	+	0.898952i	−0.623286	+	0.0298657i
$907$	−16.4347			−0.545706			−0.272853	−	0.962056i	$-0.587967\pi$
$907$	−16.4347			−0.545706			−0.272853	+	0.962056i	$0.587967\pi$
$908$	−23.5758			−0.782390
$909$	−20.1258	+	1.93316i	−0.667531	+	0.0641188i
$910$			19.6134i			0.650179i
$911$			48.2030i			1.59704i	0.601971	+	0.798518i	$0.294382\pi$
$911$			48.2030i			1.59704i	−0.601971	+	0.798518i	$0.705618\pi$
$912$	6.87271	−	0.329316i	0.227578	−	0.0109048i
$913$	−17.5639	+	45.0847i	−0.581281	+	1.49209i
$914$			32.8716i			1.08730i
$915$	−0.958694	−	20.0076i	−0.0316934	−	0.661430i
$916$	3.50893			0.115938
$917$		−	53.6278i		−	1.77095i
$918$	−2.02365	−	13.9913i	−0.0667904	−	0.461783i
$919$			33.3400i			1.09979i	0.835235	+	0.549893i	$0.185331\pi$
$919$			33.3400i			1.09979i	−0.835235	+	0.549893i	$0.814669\pi$
$920$	−1.66840			−0.0550057
$921$	47.1694	−	2.26019i	1.55428	−	0.0744759i
$922$	−15.9387			−0.524913
$923$	−16.2766			−0.535751
$924$	−7.93994	+	23.6732i	−0.261205	+	0.778790i
$925$	5.60710			0.184360
$926$	10.4842			0.344531
$927$	15.6834	−	1.50645i	0.515110	−	0.0494782i
$928$	−5.08606			−0.166958
$929$		−	26.4142i		−	0.866622i	−0.901244	−	0.433311i	$-0.857345\pi$
$929$		−	26.4142i		−	0.866622i	0.901244	−	0.433311i	$-0.142655\pi$
$930$	16.8602	−	0.807883i	0.552868	−	0.0264915i
$931$			47.2442i			1.54837i
$932$	−9.84991			−0.322644
$933$	0.106056	−	0.00508185i	0.00347213	−	0.000166372i
$934$			2.64436i			0.0865262i
$935$	−8.40788	−	3.27551i	−0.274967	−	0.107121i
$936$	−1.29433	−	13.4751i	−0.0423066	−	0.440448i
$937$		−	36.8009i		−	1.20223i	−0.799162	−	0.601116i	$-0.794723\pi$
$937$		−	36.8009i		−	1.20223i	0.799162	−	0.601116i	$-0.205277\pi$
$938$			53.6929i			1.75314i
$939$	−1.84670	−	38.5400i	−0.0602649	−	1.25771i
$940$	−9.25186			−0.301762
$941$	−12.9934			−0.423574			−0.211787	−	0.977316i	$-0.567928\pi$
$941$	−12.9934			−0.423574			−0.211787	+	0.977316i	$0.567928\pi$
$942$	0.919021	+	19.1796i	0.0299433	+	0.624906i
$943$		−	4.87218i		−	0.158660i
$944$		−	5.43264i		−	0.176817i
$945$	−3.23303	−	22.3529i	−0.105171	−	0.727140i
$946$	−10.0495	−	3.91505i	−0.326738	−	0.127289i
$947$			6.36307i			0.206772i	0.994641	+	0.103386i	$0.0329677\pi$
$947$			6.36307i			0.206772i	−0.994641	+	0.103386i	$0.967032\pi$
$948$	−1.85303	+	0.0887907i	−0.0601836	+	0.00288379i
$949$	6.15947			0.199945
$950$			3.97251i			0.128885i
$951$	−4.29348	+	0.205729i	−0.139226	+	0.00667122i
$952$			11.8255i			0.383268i
$953$	−29.7400			−0.963372			−0.481686	−	0.876344i	$-0.659975\pi$
$953$	−29.7400			−0.963372			−0.481686	+	0.876344i	$0.659975\pi$
$954$	−0.875509	−	9.11479i	−0.0283456	−	0.295102i
$955$	19.5852			0.633763
$956$	24.1540			0.781197
$957$	−27.7007	−	9.29075i	−0.895435	−	0.300327i
$958$	28.6082			0.924289
$959$	−91.0243			−2.93933
$960$	1.73007	−	0.0828988i	0.0558376	−	0.00267555i
$961$	63.9730			2.06365
$962$		−	25.3014i		−	0.815749i
$963$	−18.6852	+	1.79478i	−0.602123	+	0.0578361i
$964$			4.69316i			0.151157i
$965$	−8.82899			−0.284215
$966$	0.601170	+	12.5462i	0.0193423	+	0.403667i
$967$		−	36.5418i		−	1.17510i	−0.809186	−	0.587552i	$-0.800092\pi$
$967$		−	36.5418i		−	1.17510i	0.809186	−	0.587552i	$-0.199908\pi$
$968$	−8.10105	−	7.44131i	−0.260378	−	0.239173i
$969$	18.6982	−	0.895955i	0.600674	−	0.0287822i
$970$			12.7977i			0.410908i
$971$		−	22.7040i		−	0.728607i	−0.931280	−	0.364304i	$-0.881307\pi$
$971$		−	22.7040i		−	0.728607i	0.931280	−	0.364304i	$-0.118693\pi$
$972$	3.69633	+	15.1439i	0.118560	+	0.485740i
$973$	−67.5711			−2.16623
$974$	−25.5584			−0.818946
$975$	7.80671	−	0.374071i	0.250015	−	0.0119799i
$976$		−	11.5646i		−	0.370175i
$977$			2.83708i			0.0907662i	0.998970	+	0.0453831i	$0.0144509\pi$
$977$			2.83708i			0.0907662i	−0.998970	+	0.0453831i	$0.985549\pi$
$978$	0.345340	+	7.20710i	0.0110427	+	0.230458i
$979$	11.6134	+	4.52431i	0.371167	+	0.144598i
$980$			11.8928i			0.379901i
$981$	−5.13927	−	53.5042i	−0.164084	−	1.70826i
$982$	30.0732			0.959673
$983$		−	35.3487i		−	1.12745i	−0.825963	−	0.563724i	$-0.809368\pi$
$983$		−	35.3487i		−	1.12745i	0.825963	−	0.563724i	$-0.190632\pi$
$984$	0.242086	+	5.05225i	0.00771743	+	0.161060i
$985$			12.9502i			0.412629i
$986$	−13.8374			−0.440673
$987$	3.33369	+	69.5728i	0.106112	+	2.21453i
$988$	17.9255			0.570285
$989$	−5.42542			−0.172518
$990$	9.57404	+	2.70883i	0.304283	+	0.0860922i
$991$	−20.0173			−0.635871			−0.317936	−	0.948112i	$-0.602990\pi$
$991$	−20.0173			−0.635871			−0.317936	+	0.948112i	$0.602990\pi$
$992$	9.74541			0.309417
$993$	−0.932765	−	19.4665i	−0.0296004	−	0.617749i
$994$	−15.6786			−0.497294
$995$		−	1.17485i		−	0.0372453i
$996$	−1.20938	−	25.2394i	−0.0383208	−	0.799740i
$997$		−	6.80711i		−	0.215583i	−0.994174	−	0.107792i	$-0.965622\pi$
$997$		−	6.80711i		−	0.215583i	0.994174	−	0.107792i	$-0.0343779\pi$
$998$	13.6503			0.432093
$999$	4.17062	+	28.8353i	0.131953	+	0.912309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.d.b.131.4	yes	8
3.2	odd	2		330.2.d.a.131.3	✓	8
4.3	odd	2		2640.2.f.a.1121.5		8
5.2	odd	4		1650.2.f.f.1649.8		8
5.3	odd	4		1650.2.f.d.1649.1		8
5.4	even	2		1650.2.d.c.1451.5		8
11.10	odd	2		330.2.d.a.131.4	yes	8
12.11	even	2		2640.2.f.b.1121.6		8
15.2	even	4		1650.2.f.c.1649.1		8
15.8	even	4		1650.2.f.e.1649.8		8
15.14	odd	2		1650.2.d.f.1451.6		8
33.32	even	2	inner	330.2.d.b.131.3	yes	8
44.43	even	2		2640.2.f.b.1121.5		8
55.32	even	4		1650.2.f.e.1649.4		8
55.43	even	4		1650.2.f.c.1649.5		8
55.54	odd	2		1650.2.d.f.1451.5		8
132.131	odd	2		2640.2.f.a.1121.6		8
165.32	odd	4		1650.2.f.d.1649.5		8
165.98	odd	4		1650.2.f.f.1649.4		8
165.164	even	2		1650.2.d.c.1451.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.3	✓	8	3.2	odd	2
330.2.d.a.131.4	yes	8	11.10	odd	2
330.2.d.b.131.3	yes	8	33.32	even	2	inner
330.2.d.b.131.4	yes	8	1.1	even	1	trivial
1650.2.d.c.1451.5		8	5.4	even	2
1650.2.d.c.1451.6		8	165.164	even	2
1650.2.d.f.1451.5		8	55.54	odd	2
1650.2.d.f.1451.6		8	15.14	odd	2
1650.2.f.c.1649.1		8	15.2	even	4
1650.2.f.c.1649.5		8	55.43	even	4
1650.2.f.d.1649.1		8	5.3	odd	4
1650.2.f.d.1649.5		8	165.32	odd	4
1650.2.f.e.1649.4		8	55.32	even	4
1650.2.f.e.1649.8		8	15.8	even	4
1650.2.f.f.1649.4		8	165.98	odd	4
1650.2.f.f.1649.8		8	5.2	odd	4
2640.2.f.a.1121.5		8	4.3	odd	2
2640.2.f.a.1121.6		8	132.131	odd	2
2640.2.f.b.1121.5		8	44.43	even	2
2640.2.f.b.1121.6		8	12.11	even	2

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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.0828988 + 1.73007i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(0.0828988 + 1.73007i) q^{6} +4.34658i q^{7} +1.00000 q^{8} +(-2.98626 + 0.286841i) q^{9} -1.00000i q^{10} +(1.20394 - 3.09039i) q^{11} +(0.0828988 + 1.73007i) q^{12} +4.51238i q^{13} +4.34658i q^{14} +(1.73007 - 0.0828988i) q^{15} +1.00000 q^{16} +2.72065 q^{17} +(-2.98626 + 0.286841i) q^{18} -3.97251i q^{19} -1.00000i q^{20} +(-7.51987 + 0.360326i) q^{21} +(1.20394 - 3.09039i) q^{22} -1.66840i q^{23} +(0.0828988 + 1.73007i) q^{24} -1.00000 q^{25} +4.51238i q^{26} +(-0.743810 - 5.14264i) q^{27} +4.34658i q^{28} -5.08606 q^{29} +(1.73007 - 0.0828988i) q^{30} +9.74541 q^{31} +1.00000 q^{32} +(5.44639 + 1.82671i) q^{33} +2.72065 q^{34} +4.34658 q^{35} +(-2.98626 + 0.286841i) q^{36} -5.60710 q^{37} -3.97251i q^{38} +(-7.80671 + 0.374071i) q^{39} -1.00000i q^{40} +2.92026 q^{41} +(-7.51987 + 0.360326i) q^{42} -3.25186i q^{43} +(1.20394 - 3.09039i) q^{44} +(0.286841 + 2.98626i) q^{45} -1.66840i q^{46} -9.25186i q^{47} +(0.0828988 + 1.73007i) q^{48} -11.8928 q^{49} -1.00000 q^{50} +(0.225539 + 4.70691i) q^{51} +4.51238i q^{52} +3.05225i q^{53} +(-0.743810 - 5.14264i) q^{54} +(-3.09039 - 1.20394i) q^{55} +4.34658i q^{56} +(6.87271 - 0.329316i) q^{57} -5.08606 q^{58} -5.43264i q^{59} +(1.73007 - 0.0828988i) q^{60} -11.5646i q^{61} +9.74541 q^{62} +(-1.24678 - 12.9800i) q^{63} +1.00000 q^{64} +4.51238 q^{65} +(5.44639 + 1.82671i) q^{66} +12.3529 q^{67} +2.72065 q^{68} +(2.88645 - 0.138309i) q^{69} +4.34658 q^{70} +3.60710i q^{71} +(-2.98626 + 0.286841i) q^{72} -1.36502i q^{73} -5.60710 q^{74} +(-0.0828988 - 1.73007i) q^{75} -3.97251i q^{76} +(13.4326 + 5.23303i) q^{77} +(-7.80671 + 0.374071i) q^{78} +1.07107i q^{79} -1.00000i q^{80} +(8.83544 - 1.71316i) q^{81} +2.92026 q^{82} -14.5887 q^{83} +(-7.51987 + 0.360326i) q^{84} -2.72065i q^{85} -3.25186i q^{86} +(-0.421628 - 8.79922i) q^{87} +(1.20394 - 3.09039i) q^{88} +3.75791i q^{89} +(0.286841 + 2.98626i) q^{90} -19.6134 q^{91} -1.66840i q^{92} +(0.807883 + 16.8602i) q^{93} -9.25186i q^{94} -3.97251 q^{95} +(0.0828988 + 1.73007i) q^{96} -12.7977 q^{97} -11.8928 q^{98} +(-2.70883 + 9.57404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 2 q^{3} + 8 q^{4} + 2 q^{6} + 8 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} + 4 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{21} + 6 q^{22} + 2 q^{24} - 8 q^{25} - 22 q^{27} - 4 q^{29} + 4 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 2 * q^3 + 8 * q^4 + 2 * q^6 + 8 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 + 4 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 - 8 * q^21 + 6 * q^22 + 2 * q^24 - 8 * q^25 - 22 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 2 * q^33 + 4 * q^34 + 2 * q^36 - 12 * q^37 - 8 * q^39 - 16 * q^41 - 8 * q^42 + 6 * q^44 + 2 * q^48 - 4 * q^49 - 8 * q^50 - 28 * q^51 - 22 * q^54 - 6 * q^55 + 14 * q^57 - 4 * q^58 + 4 * q^60 - 4 * q^62 + 14 * q^63 + 8 * q^64 + 4 * q^65 - 2 * q^66 - 12 * q^67 + 4 * q^68 + 8 * q^69 + 2 * q^72 - 12 * q^74 - 2 * q^75 + 36 * q^77 - 8 * q^78 + 2 * q^81 - 16 * q^82 - 72 * q^83 - 8 * q^84 - 22 * q^87 + 6 * q^88 - 48 * q^91 + 8 * q^93 + 20 * q^95 + 2 * q^96 - 8 * q^97 - 4 * q^98 - 6 * q^99

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