LMFDB - Embedded newform 336.2.w.a.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.3
Root			$-0.603113 + 1.27916i$ of defining polynomial
Character	$\chi$	$=$	336.253
Dual form			336.2.w.a.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19435 - 0.757321i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.852931 + 1.80901i) q^{4} +(-0.894131 + 0.894131i) q^{5} +(-0.309024 - 1.38004i) q^{6} -1.00000i q^{7} +(0.351303 - 2.80653i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.19435 - 0.757321i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.852931 + 1.80901i) q^{4} +(-0.894131 + 0.894131i) q^{5} +(-0.309024 - 1.38004i) q^{6} -1.00000i q^{7} +(0.351303 - 2.80653i) q^{8} +1.00000i q^{9} +(1.74505 - 0.390759i) q^{10} +(2.02397 - 2.02397i) q^{11} +(-0.676048 + 1.88227i) q^{12} +(3.23067 + 3.23067i) q^{13} +(-0.757321 + 1.19435i) q^{14} -1.26449 q^{15} +(-2.54502 + 3.08592i) q^{16} +0.119728 q^{17} +(0.757321 - 1.19435i) q^{18} +(4.85319 + 4.85319i) q^{19} +(-2.38012 - 0.854858i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-3.95012 + 0.884529i) q^{22} +9.33278i q^{23} +(2.23292 - 1.73610i) q^{24} +3.40106i q^{25} +(-1.41189 - 6.30519i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.80901 - 0.852931i) q^{28} +(-5.18402 - 5.18402i) q^{29} +(1.51024 + 0.957626i) q^{30} +0.957732 q^{31} +(5.37666 - 1.75826i) q^{32} +2.86233 q^{33} +(-0.142997 - 0.0906728i) q^{34} +(0.894131 + 0.894131i) q^{35} +(-1.80901 + 0.852931i) q^{36} +(0.136949 - 0.136949i) q^{37} +(-2.12097 - 9.47182i) q^{38} +4.56885i q^{39} +(2.19529 + 2.82351i) q^{40} -3.36970i q^{41} +(-1.38004 + 0.309024i) q^{42} +(8.82429 - 8.82429i) q^{43} +(5.38769 + 1.93507i) q^{44} +(-0.894131 - 0.894131i) q^{45} +(7.06790 - 11.1466i) q^{46} +3.50414 q^{47} +(-3.98167 + 0.382473i) q^{48} -1.00000 q^{49} +(2.57569 - 4.06205i) q^{50} +(0.0846608 + 0.0846608i) q^{51} +(-3.08877 + 8.59984i) q^{52} +(-5.46741 + 5.46741i) q^{53} +(1.38004 - 0.309024i) q^{54} +3.61939i q^{55} +(-2.80653 - 0.351303i) q^{56} +6.86345i q^{57} +(2.26555 + 10.1175i) q^{58} +(5.48985 - 5.48985i) q^{59} +(-1.07852 - 2.28748i) q^{60} +(-8.06921 - 8.06921i) q^{61} +(-1.14386 - 0.725310i) q^{62} +1.00000 q^{63} +(-7.75317 - 1.97188i) q^{64} -5.77728 q^{65} +(-3.41861 - 2.16770i) q^{66} +(-8.09022 - 8.09022i) q^{67} +(0.102120 + 0.216590i) q^{68} +(-6.59927 + 6.59927i) q^{69} +(-0.390759 - 1.74505i) q^{70} -3.42115i q^{71} +(2.80653 + 0.351303i) q^{72} -2.48540i q^{73} +(-0.267279 + 0.0598504i) q^{74} +(-2.40491 + 2.40491i) q^{75} +(-4.64002 + 12.9189i) q^{76} +(-2.02397 - 2.02397i) q^{77} +(3.46009 - 5.45680i) q^{78} -6.89542 q^{79} +(-0.483635 - 5.03479i) q^{80} -1.00000 q^{81} +(-2.55194 + 4.02459i) q^{82} +(11.1660 + 11.1660i) q^{83} +(1.88227 + 0.676048i) q^{84} +(-0.107053 + 0.107053i) q^{85} +(-17.2221 + 3.85645i) q^{86} -7.33131i q^{87} +(-4.96930 - 6.39135i) q^{88} -3.31067i q^{89} +(0.390759 + 1.74505i) q^{90} +(3.23067 - 3.23067i) q^{91} +(-16.8831 + 7.96021i) q^{92} +(0.677219 + 0.677219i) q^{93} +(-4.18516 - 2.65376i) q^{94} -8.67878 q^{95} +(5.04515 + 2.55860i) q^{96} -5.52833 q^{97} +(1.19435 + 0.757321i) q^{98} +(2.02397 + 2.02397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4}+O(q^{10}) $ 20 * q + 4 * q^4	$ 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−1.19435	−	0.757321i	−0.844531	−	0.535507i
$2$	−1.19435	−	0.757321i	−0.844531	−	0.535507i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	0.852931	+	1.80901i	0.426465	+	0.904504i
$5$	−0.894131	+	0.894131i	−0.399867	+	0.399867i	−0.878186	−	0.478319i	$-0.841246\pi$
$5$	−0.894131	+	0.894131i	−0.399867	+	0.399867i	0.478319	+	0.878186i	$0.341246\pi$
$6$	−0.309024	−	1.38004i	−0.126159	−	0.563398i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.351303	−	2.80653i	0.124204	−	0.992257i
$9$			1.00000i			0.333333i
$10$	1.74505	−	0.390759i	0.551832	−	0.123569i
$11$	2.02397	−	2.02397i	0.610250	−	0.610250i	−0.332761	−	0.943011i	$-0.607980\pi$
$11$	2.02397	−	2.02397i	0.610250	−	0.610250i	0.943011	+	0.332761i	$0.107980\pi$
$12$	−0.676048	+	1.88227i	−0.195158	+	0.543366i
$13$	3.23067	+	3.23067i	0.896026	+	0.896026i	0.995082	−	0.0990557i	$-0.0315822\pi$
$13$	3.23067	+	3.23067i	0.896026	+	0.896026i	−0.0990557	+	0.995082i	$0.531582\pi$
$14$	−0.757321	+	1.19435i	−0.202402	+	0.319203i
$15$	−1.26449			−0.326490
$16$	−2.54502	+	3.08592i	−0.636254	+	0.771479i
$17$	0.119728			0.0290384			0.0145192	−	0.999895i	$-0.495378\pi$
$17$	0.119728			0.0290384			0.0145192	+	0.999895i	$0.495378\pi$
$18$	0.757321	−	1.19435i	0.178502	−	0.281510i
$19$	4.85319	+	4.85319i	1.11340	+	1.11340i	0.992688	+	0.120711i	$0.0385174\pi$
$19$	4.85319	+	4.85319i	1.11340	+	1.11340i	0.120711	+	0.992688i	$0.461483\pi$
$20$	−2.38012	−	0.854858i	−0.532211	−	0.191152i
$21$	0.707107	−	0.707107i	0.154303	−	0.154303i
$22$	−3.95012	+	0.884529i	−0.842168	+	0.188582i
$23$			9.33278i			1.94602i	0.230767	+	0.973009i	$0.425877\pi$
$23$			9.33278i			1.94602i	−0.230767	+	0.973009i	$0.574123\pi$
$24$	2.23292	−	1.73610i	0.455793	−	0.354381i
$25$			3.40106i			0.680212i
$26$	−1.41189	−	6.30519i	−0.276894	−	1.23655i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.80901	−	0.852931i	0.341870	−	0.161189i
$29$	−5.18402	−	5.18402i	−0.962648	−	0.962648i	0.0366787	−	0.999327i	$-0.488322\pi$
$29$	−5.18402	−	5.18402i	−0.962648	−	0.962648i	−0.999327	+	0.0366787i	$0.988322\pi$
$30$	1.51024	+	0.957626i	0.275731	+	0.174838i
$31$	0.957732			0.172014			0.0860069	−	0.996295i	$-0.472589\pi$
$31$	0.957732			0.172014			0.0860069	+	0.996295i	$0.472589\pi$
$32$	5.37666	−	1.75826i	0.950469	−	0.310820i
$33$	2.86233			0.498267
$34$	−0.142997	−	0.0906728i	−0.0245238	−	0.0155503i
$35$	0.894131	+	0.894131i	0.151136	+	0.151136i
$36$	−1.80901	+	0.852931i	−0.301501	+	0.142155i
$37$	0.136949	−	0.136949i	0.0225143	−	0.0225143i	−0.695760	−	0.718274i	$-0.744932\pi$
$37$	0.136949	−	0.136949i	0.0225143	−	0.0225143i	0.718274	+	0.695760i	$0.244932\pi$
$38$	−2.12097	−	9.47182i	−0.344067	−	1.53653i
$39$			4.56885i			0.731602i
$40$	2.19529	+	2.82351i	0.347106	+	0.446436i
$41$		−	3.36970i		−	0.526258i	−0.964761	−	0.263129i	$-0.915245\pi$
$41$		−	3.36970i		−	0.526258i	0.964761	−	0.263129i	$-0.0847546\pi$
$42$	−1.38004	+	0.309024i	−0.212944	+	0.0476835i
$43$	8.82429	−	8.82429i	1.34569	−	1.34569i	0.455409	−	0.890282i	$-0.349493\pi$
$43$	8.82429	−	8.82429i	1.34569	−	1.34569i	0.890282	−	0.455409i	$-0.150507\pi$
$44$	5.38769	+	1.93507i	0.812224	+	0.291723i
$45$	−0.894131	−	0.894131i	−0.133289	−	0.133289i
$46$	7.06790	−	11.1466i	1.04211	−	1.64347i
$47$	3.50414			0.511132			0.255566	−	0.966792i	$-0.417738\pi$
$47$	3.50414			0.511132			0.255566	+	0.966792i	$0.417738\pi$
$48$	−3.98167	+	0.382473i	−0.574705	+	0.0552053i
$49$	−1.00000			−0.142857
$50$	2.57569	−	4.06205i	0.364258	−	0.574460i
$51$	0.0846608	+	0.0846608i	0.0118549	+	0.0118549i
$52$	−3.08877	+	8.59984i	−0.428335	+	1.19258i
$53$	−5.46741	+	5.46741i	−0.751006	+	0.751006i	−0.974667	−	0.223661i	$-0.928199\pi$
$53$	−5.46741	+	5.46741i	−0.751006	+	0.751006i	0.223661	+	0.974667i	$0.428199\pi$
$54$	1.38004	−	0.309024i	0.187799	−	0.0420529i
$55$			3.61939i			0.488038i
$56$	−2.80653	−	0.351303i	−0.375038	−	0.0469449i
$57$			6.86345i			0.909086i
$58$	2.26555	+	10.1175i	0.297482	+	1.32849i
$59$	5.48985	−	5.48985i	0.714718	−	0.714718i	−0.252801	−	0.967518i	$-0.581352\pi$
$59$	5.48985	−	5.48985i	0.714718	−	0.714718i	0.967518	+	0.252801i	$0.0813517\pi$
$60$	−1.07852	−	2.28748i	−0.139237	−	0.295312i
$61$	−8.06921	−	8.06921i	−1.03316	−	1.03316i	−0.999431	−	0.0337247i	$-0.989263\pi$
$61$	−8.06921	−	8.06921i	−1.03316	−	1.03316i	−0.0337247	−	0.999431i	$-0.510737\pi$
$62$	−1.14386	−	0.725310i	−0.145271	−	0.0921145i
$63$	1.00000			0.125988
$64$	−7.75317	−	1.97188i	−0.969147	−	0.246485i
$65$	−5.77728			−0.716583
$66$	−3.41861	−	2.16770i	−0.420802	−	0.266825i
$67$	−8.09022	−	8.09022i	−0.988378	−	0.988378i	0.0115550	−	0.999933i	$-0.496322\pi$
$67$	−8.09022	−	8.09022i	−0.988378	−	0.988378i	−0.999933	+	0.0115550i	$0.996322\pi$
$68$	0.102120	+	0.216590i	0.0123839	+	0.0262653i
$69$	−6.59927	+	6.59927i	−0.794459	+	0.794459i
$70$	−0.390759	−	1.74505i	−0.0467046	−	0.208573i
$71$		−	3.42115i		−	0.406016i	−0.979177	−	0.203008i	$-0.934928\pi$
$71$		−	3.42115i		−	0.406016i	0.979177	−	0.203008i	$-0.0650717\pi$
$72$	2.80653	+	0.351303i	0.330752	+	0.0414015i
$73$		−	2.48540i		−	0.290894i	−0.989366	−	0.145447i	$-0.953538\pi$
$73$		−	2.48540i		−	0.290894i	0.989366	−	0.145447i	$-0.0464620\pi$
$74$	−0.267279	+	0.0598504i	−0.0310706	+	0.00695746i
$75$	−2.40491	+	2.40491i	−0.277695	+	0.277695i
$76$	−4.64002	+	12.9189i	−0.532247	+	1.48190i
$77$	−2.02397	−	2.02397i	−0.230653	−	0.230653i
$78$	3.46009	−	5.45680i	0.391778	−	0.617861i
$79$	−6.89542			−0.775795			−0.387898	−	0.921703i	$-0.626799\pi$
$79$	−6.89542			−0.775795			−0.387898	+	0.921703i	$0.626799\pi$
$80$	−0.483635	−	5.03479i	−0.0540720	−	0.562907i
$81$	−1.00000			−0.111111
$82$	−2.55194	+	4.02459i	−0.281815	+	0.444442i
$83$	11.1660	+	11.1660i	1.22563	+	1.22563i	0.965600	+	0.260032i	$0.0837333\pi$
$83$	11.1660	+	11.1660i	1.22563	+	1.22563i	0.260032	+	0.965600i	$0.416267\pi$
$84$	1.88227	+	0.676048i	0.205373	+	0.0737629i
$85$	−0.107053	+	0.107053i	−0.0116115	+	0.0116115i
$86$	−17.2221	+	3.85645i	−1.85710	+	0.415852i
$87$		−	7.33131i		−	0.785999i
$88$	−4.96930	−	6.39135i	−0.529729	−	0.681321i
$89$		−	3.31067i		−	0.350930i	−0.984486	−	0.175465i	$-0.943857\pi$
$89$		−	3.31067i		−	0.350930i	0.984486	−	0.175465i	$-0.0561429\pi$
$90$	0.390759	+	1.74505i	0.0411896	+	0.183944i
$91$	3.23067	−	3.23067i	0.338666	−	0.338666i
$92$	−16.8831	+	7.96021i	−1.76018	+	0.829909i
$93$	0.677219	+	0.677219i	0.0702243	+	0.0702243i
$94$	−4.18516	−	2.65376i	−0.431667	−	0.273714i
$95$	−8.67878			−0.890424
$96$	5.04515	+	2.55860i	0.514919	+	0.261136i
$97$	−5.52833			−0.561317			−0.280659	−	0.959808i	$-0.590553\pi$
$97$	−5.52833			−0.561317			−0.280659	+	0.959808i	$0.590553\pi$
$98$	1.19435	+	0.757321i	0.120647	+	0.0765009i
$99$	2.02397	+	2.02397i	0.203417	+	0.203417i
$100$	−6.15254	+	2.90087i	−0.615254	+	0.290087i
$101$	3.93841	−	3.93841i	0.391887	−	0.391887i	−0.483473	−	0.875359i	$-0.660625\pi$
$101$	3.93841	−	3.93841i	0.391887	−	0.391887i	0.875359	+	0.483473i	$0.160625\pi$
$102$	−0.0369990	−	0.165230i	−0.00366345	−	0.0163602i
$103$			3.09565i			0.305024i	0.988302	+	0.152512i	$0.0487362\pi$
$103$			3.09565i			0.305024i	−0.988302	+	0.152512i	$0.951264\pi$
$104$	10.2019	−	7.93201i	1.00038	−	0.777797i
$105$			1.26449i			0.123402i
$106$	10.6706	−	2.38940i	1.03642	−	0.232079i
$107$	−0.776589	+	0.776589i	−0.0750757	+	0.0750757i	−0.743648	−	0.668572i	$-0.766906\pi$
$107$	−0.776589	+	0.776589i	−0.0750757	+	0.0750757i	0.668572	+	0.743648i	$0.266906\pi$
$108$	−1.88227	−	0.676048i	−0.181122	−	0.0650528i
$109$	−7.63298	−	7.63298i	−0.731107	−	0.731107i	0.239732	−	0.970839i	$-0.422940\pi$
$109$	−7.63298	−	7.63298i	−0.731107	−	0.731107i	−0.970839	+	0.239732i	$0.922940\pi$
$110$	2.74104	−	4.32281i	0.261348	−	0.412164i
$111$	0.193675			0.0183828
$112$	3.08592	+	2.54502i	0.291592	+	0.240482i
$113$	−1.64790			−0.155022			−0.0775109	−	0.996992i	$-0.524697\pi$
$113$	−1.64790			−0.155022			−0.0775109	+	0.996992i	$0.524697\pi$
$114$	5.19783	−	8.19734i	0.486822	−	0.767751i
$115$	−8.34472	−	8.34472i	−0.778149	−	0.778149i
$116$	4.95632	−	13.7995i	0.460183	−	1.28126i
$117$	−3.23067	+	3.23067i	−0.298675	+	0.298675i
$118$	−10.7144	+	2.39921i	−0.986337	+	0.220865i
$119$		−	0.119728i		−	0.0109755i
$120$	−0.444220	+	3.54883i	−0.0405516	+	0.323962i
$121$			2.80708i			0.255189i
$122$	3.52646	+	15.7484i	0.319270	+	1.42579i
$123$	2.38274	−	2.38274i	0.214844	−	0.214844i
$124$	0.816879	+	1.73254i	0.0733579	+	0.155587i
$125$	−7.51165	−	7.51165i	−0.671862	−	0.671862i
$126$	−1.19435	−	0.757321i	−0.106401	−	0.0674675i
$127$	11.9725			1.06239			0.531195	−	0.847250i	$-0.321743\pi$
$127$	11.9725			1.06239			0.531195	+	0.847250i	$0.321743\pi$
$128$	7.76663	+	8.22675i	0.686480	+	0.727149i
$129$	12.4794			1.09875
$130$	6.90008	+	4.37525i	0.605177	+	0.383735i
$131$	−3.95526	−	3.95526i	−0.345573	−	0.345573i	0.512885	−	0.858458i	$-0.328577\pi$
$131$	−3.95526	−	3.95526i	−0.345573	−	0.345573i	−0.858458	+	0.512885i	$0.828577\pi$
$132$	2.44137	+	5.17797i	0.212494	+	0.450685i
$133$	4.85319	−	4.85319i	0.420825	−	0.420825i
$134$	3.53564	+	15.7894i	0.305433	+	1.36400i
$135$		−	1.26449i		−	0.108830i
$136$	0.0420610	−	0.336021i	0.00360670	−	0.0288135i
$137$			6.13628i			0.524258i	0.965033	+	0.262129i	$0.0844245\pi$
$137$			6.13628i			0.524258i	−0.965033	+	0.262129i	$0.915575\pi$
$138$	12.8796	−	2.88406i	1.09638	−	0.245507i
$139$	9.98810	−	9.98810i	0.847179	−	0.847179i	−0.142601	−	0.989780i	$-0.545547\pi$
$139$	9.98810	−	9.98810i	0.847179	−	0.847179i	0.989780	+	0.142601i	$0.0455465\pi$
$140$	−0.854858	+	2.38012i	−0.0722487	+	0.201157i
$141$	2.47780	+	2.47780i	0.208669	+	0.208669i
$142$	−2.59091	+	4.08604i	−0.217424	+	0.342893i
$143$	13.0776			1.09360
$144$	−3.08592	−	2.54502i	−0.257160	−	0.212085i
$145$	9.27038			0.769863
$146$	−1.88224	+	2.96843i	−0.155776	+	0.245669i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	0.364550	+	0.130934i	0.0299658	+	0.0107627i
$149$	−8.39975	+	8.39975i	−0.688134	+	0.688134i	−0.961819	−	0.273685i	$-0.911757\pi$
$149$	−8.39975	+	8.39975i	−0.688134	+	0.688134i	0.273685	+	0.961819i	$0.411757\pi$
$150$	4.69359	−	1.05101i	0.383230	−	0.0858147i
$151$			0.310686i			0.0252833i	0.999920	+	0.0126416i	$0.00402406\pi$
$151$			0.310686i			0.0252833i	−0.999920	+	0.0126416i	$0.995976\pi$
$152$	15.3255	−	11.9157i	1.24307	−	0.966488i
$153$			0.119728i			0.00967947i
$154$	0.884529	+	3.95012i	0.0712774	+	0.318310i
$155$	−0.856338	+	0.856338i	−0.0687827	+	0.0687827i
$156$	−8.26509	+	3.89692i	−0.661737	+	0.312003i
$157$	5.62609	+	5.62609i	0.449011	+	0.449011i	0.895026	−	0.446015i	$-0.147157\pi$
$157$	5.62609	+	5.62609i	0.449011	+	0.449011i	−0.446015	+	0.895026i	$0.647157\pi$
$158$	8.23552	+	5.22204i	0.655183	+	0.415443i
$159$	−7.73208			−0.613194
$160$	−3.23532	+	6.37956i	−0.255775	+	0.504348i
$161$	9.33278			0.735526
$162$	1.19435	+	0.757321i	0.0938368	+	0.0595007i
$163$	−10.6342	−	10.6342i	−0.832934	−	0.832934i	0.154983	−	0.987917i	$-0.450468\pi$
$163$	−10.6342	−	10.6342i	−0.832934	−	0.832934i	−0.987917	+	0.154983i	$0.950468\pi$
$164$	6.09581	−	2.87412i	0.476003	−	0.224431i
$165$	−2.55929	+	2.55929i	−0.199241	+	0.199241i
$166$	−4.87986	−	21.7924i	−0.378750	−	1.69142i
$167$			16.4161i			1.27031i	0.772383	+	0.635157i	$0.219065\pi$
$167$			16.4161i			1.27031i	−0.772383	+	0.635157i	$0.780935\pi$
$168$	−1.73610	−	2.23292i	−0.133943	−	0.172274i
$169$			7.87443i			0.605726i
$170$	0.208932	−	0.0467849i	0.0160243	−	0.00358824i
$171$	−4.85319	+	4.85319i	−0.371133	+	0.371133i
$172$	23.4897	+	8.43670i	1.79107	+	0.643292i
$173$	−14.0510	−	14.0510i	−1.06828	−	1.06828i	−0.997491	−	0.0707873i	$-0.977449\pi$
$173$	−14.0510	−	14.0510i	−1.06828	−	1.06828i	−0.0707873	−	0.997491i	$-0.522551\pi$
$174$	−5.55215	+	8.75613i	−0.420908	+	0.663801i
$175$	3.40106			0.257096
$176$	1.09476	+	11.3968i	0.0825210	+	0.859070i
$177$	7.76382			0.583565
$178$	−2.50724	+	3.95409i	−0.187925	+	0.296371i
$179$	9.72673	+	9.72673i	0.727010	+	0.727010i	0.970023	−	0.243013i	$-0.0781358\pi$
$179$	9.72673	+	9.72673i	0.727010	+	0.727010i	−0.243013	+	0.970023i	$0.578136\pi$
$180$	0.854858	−	2.38012i	0.0637173	−	0.177404i
$181$	16.3503	−	16.3503i	1.21531	−	1.21531i	0.246047	−	0.969258i	$-0.420868\pi$
$181$	16.3503	−	16.3503i	1.21531	−	1.21531i	0.969258	−	0.246047i	$-0.0791319\pi$
$182$	−6.30519	+	1.41189i	−0.467372	+	0.104656i
$183$		−	11.4116i		−	0.843568i
$184$	26.1927	+	3.27863i	1.93095	+	0.241704i
$185$			0.244901i			0.0180055i
$186$	−0.295963	−	1.32171i	−0.0217010	−	0.0969122i
$187$	0.242327	−	0.242327i	0.0177207	−	0.0177207i
$188$	2.98879	+	6.33902i	0.217980	+	0.462321i
$189$	0.707107	+	0.707107i	0.0514344	+	0.0514344i
$190$	10.3655	+	6.57262i	0.751990	+	0.476828i
$191$	−3.56107			−0.257670			−0.128835	−	0.991666i	$-0.541124\pi$
$191$	−3.56107			−0.257670			−0.128835	+	0.991666i	$0.541124\pi$
$192$	−4.08799	−	6.87665i	−0.295025	−	0.496280i
$193$	−3.87386			−0.278846			−0.139423	−	0.990233i	$-0.544525\pi$
$193$	−3.87386			−0.278846			−0.139423	+	0.990233i	$0.544525\pi$
$194$	6.60275	+	4.18672i	0.474050	+	0.300589i
$195$	−4.08515	−	4.08515i	−0.292544	−	0.292544i
$196$	−0.852931	−	1.80901i	−0.0609236	−	0.129215i
$197$	−2.00899	+	2.00899i	−0.143135	+	0.143135i	−0.775043	−	0.631908i	$-0.782272\pi$
$197$	−2.00899	+	2.00899i	−0.143135	+	0.143135i	0.631908	+	0.775043i	$0.282272\pi$
$198$	−0.884529	−	3.95012i	−0.0628608	−	0.280723i
$199$		−	3.24060i		−	0.229720i	−0.993382	−	0.114860i	$-0.963358\pi$
$199$		−	3.24060i		−	0.229720i	0.993382	−	0.114860i	$-0.0366419\pi$
$200$	9.54516	+	1.19480i	0.674945	+	0.0844854i
$201$		−	11.4413i		−	0.807007i
$202$	−7.68647	+	1.72119i	−0.540818	+	0.121103i
$203$	−5.18402	+	5.18402i	−0.363847	+	0.363847i
$204$	−0.0809422	+	0.225362i	−0.00566709	+	0.0157785i
$205$	3.01295	+	3.01295i	0.210434	+	0.210434i
$206$	2.34440	−	3.69729i	0.163342	−	0.257602i
$207$	−9.33278			−0.648673
$208$	−18.1917	+	1.74747i	−1.26137	+	0.121165i
$209$	19.6454			1.35890
$210$	0.957626	−	1.51024i	0.0660825	−	0.104217i
$211$	−15.4495	−	15.4495i	−1.06358	−	1.06358i	−0.997836	−	0.0657479i	$-0.979057\pi$
$211$	−15.4495	−	15.4495i	−1.06358	−	1.06358i	−0.0657479	−	0.997836i	$-0.520943\pi$
$212$	−14.5539	−	5.22726i	−0.999566	−	0.359010i
$213$	2.41912	−	2.41912i	0.165755	−	0.165755i
$214$	1.51564	−	0.339390i	0.103607	−	0.0232002i
$215$			15.7801i			1.07620i
$216$	1.73610	+	2.23292i	0.118127	+	0.151931i
$217$		−	0.957732i		−	0.0650151i
$218$	3.33582	+	14.8970i	0.225930	+	1.00896i
$219$	1.75744	−	1.75744i	0.118757	−	0.118757i
$220$	−6.54750	+	3.08709i	−0.441433	+	0.208131i
$221$	0.386803	+	0.386803i	0.0260192	+	0.0260192i
$222$	−0.231315	−	0.146674i	−0.0155249	−	0.00984413i
$223$	−28.2506			−1.89180			−0.945901	−	0.324454i	$-0.894819\pi$
$223$	−28.2506			−1.89180			−0.945901	+	0.324454i	$0.894819\pi$
$224$	−1.75826	−	5.37666i	−0.117479	−	0.359243i
$225$	−3.40106			−0.226737
$226$	1.96817	+	1.24799i	0.130921	+	0.0830152i
$227$	2.00765	+	2.00765i	0.133252	+	0.133252i	0.770587	−	0.637335i	$-0.219963\pi$
$227$	2.00765	+	2.00765i	0.133252	+	0.133252i	−0.637335	+	0.770587i	$0.719963\pi$
$228$	−12.4160	+	5.85405i	−0.822272	+	0.387694i
$229$	10.0493	−	10.0493i	0.664075	−	0.664075i	−0.292263	−	0.956338i	$-0.594408\pi$
$229$	10.0493	−	10.0493i	0.664075	−	0.664075i	0.956338	+	0.292263i	$0.0944083\pi$
$230$	3.64687	+	16.2861i	0.240467	+	1.07388i
$231$		−	2.86233i		−	0.188327i
$232$	−16.3702	+	12.7279i	−1.07476	+	0.835629i
$233$		−	8.71002i		−	0.570613i	−0.958436	−	0.285306i	$-0.907905\pi$
$233$		−	8.71002i		−	0.570613i	0.958436	−	0.285306i	$-0.0920953\pi$
$234$	6.30519	−	1.41189i	0.412183	−	0.0922980i
$235$	−3.13316	+	3.13316i	−0.204385	+	0.204385i
$236$	14.6136	+	5.24872i	0.951267	+	0.341663i
$237$	−4.87580	−	4.87580i	−0.316717	−	0.316717i
$238$	−0.0906728	+	0.142997i	−0.00587744	+	0.00926914i
$239$	−14.0831			−0.910962			−0.455481	−	0.890246i	$-0.650533\pi$
$239$	−14.0831			−0.910962			−0.455481	+	0.890246i	$0.650533\pi$
$240$	3.21815	−	3.90212i	0.207731	−	0.251881i
$241$	1.02384			0.0659515			0.0329757	−	0.999456i	$-0.489502\pi$
$241$	1.02384			0.0659515			0.0329757	+	0.999456i	$0.489502\pi$
$242$	2.12586	−	3.35263i	0.136656	−	0.215515i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	7.71478	−	21.4797i	0.493888	−	1.37510i
$245$	0.894131	−	0.894131i	0.0571239	−	0.0571239i
$246$	−4.65031	+	1.04132i	−0.296493	+	0.0663921i
$247$			31.3581i			1.99527i
$248$	0.336454	−	2.68790i	0.0213649	−	0.170682i
$249$			15.7912i			1.00072i
$250$	3.28279	+	14.6602i	0.207622	+	0.927195i
$251$	16.8358	−	16.8358i	1.06266	−	1.06266i	0.0647626	−	0.997901i	$-0.479371\pi$
$251$	16.8358	−	16.8358i	1.06266	−	1.06266i	0.997901	−	0.0647626i	$-0.0206290\pi$
$252$	0.852931	+	1.80901i	0.0537296	+	0.113957i
$253$	18.8893	+	18.8893i	1.18756	+	1.18756i
$254$	−14.2994	−	9.06704i	−0.897221	−	0.568917i
$255$	−0.151396			−0.00948076
$256$	−3.04577	−	15.7074i	−0.190360	−	0.981714i
$257$	−18.0887			−1.12834			−0.564171	−	0.825658i	$-0.690804\pi$
$257$	−18.0887			−1.12834			−0.564171	+	0.825658i	$0.690804\pi$
$258$	−14.9048	−	9.45093i	−0.927930	−	0.588389i
$259$	−0.136949	−	0.136949i	−0.00850960	−	0.00850960i
$260$	−4.92762	−	10.4511i	−0.305598	−	0.648152i
$261$	5.18402	−	5.18402i	0.320883	−	0.320883i
$262$	1.72856	+	7.71936i	0.106791	+	0.476904i
$263$		−	7.95967i		−	0.490814i	−0.969420	−	0.245407i	$-0.921078\pi$
$263$		−	7.95967i		−	0.490814i	0.969420	−	0.245407i	$-0.0789217\pi$
$264$	1.00554	−	8.03319i	0.0618870	−	0.494409i
$265$		−	9.77716i		−	0.600606i
$266$	−9.47182	+	2.12097i	−0.580754	+	0.130045i
$267$	2.34100	−	2.34100i	0.143267	−	0.143267i
$268$	7.73488	−	21.5357i	0.472483	−	1.31550i
$269$	−5.18208	−	5.18208i	−0.315957	−	0.315957i	0.531255	−	0.847212i	$-0.321721\pi$
$269$	−5.18208	−	5.18208i	−0.315957	−	0.315957i	−0.847212	+	0.531255i	$0.821721\pi$
$270$	−0.957626	+	1.51024i	−0.0582792	+	0.0919104i
$271$	12.3595			0.750787			0.375394	−	0.926865i	$-0.377507\pi$
$271$	12.3595			0.750787			0.375394	+	0.926865i	$0.377507\pi$
$272$	−0.304711	+	0.369472i	−0.0184758	+	0.0224025i
$273$	4.56885			0.276520
$274$	4.64713	−	7.32885i	0.280743	−	0.442752i
$275$	6.88365	+	6.88365i	0.415100	+	0.415100i
$276$	−17.5668	−	6.30941i	−1.05740	−	0.379782i
$277$	−9.03949	+	9.03949i	−0.543130	+	0.543130i	−0.924445	−	0.381315i	$-0.875471\pi$
$277$	−9.03949	+	9.03949i	−0.543130	+	0.543130i	0.381315	+	0.924445i	$0.375471\pi$
$278$	−19.4934	+	4.36506i	−1.16914	+	0.261799i
$279$			0.957732i			0.0573379i
$280$	2.82351	−	2.19529i	0.168737	−	0.131194i
$281$			28.8938i			1.72366i	0.507200	+	0.861828i	$0.330681\pi$
$281$			28.8938i			1.72366i	−0.507200	+	0.861828i	$0.669319\pi$
$282$	−1.08287	−	4.83585i	−0.0644837	−	0.287971i
$283$	−6.61846	+	6.61846i	−0.393427	+	0.393427i	−0.875907	−	0.482480i	$-0.839736\pi$
$283$	−6.61846	+	6.61846i	−0.393427	+	0.393427i	0.482480	+	0.875907i	$0.339736\pi$
$284$	6.18888	−	2.91800i	0.367243	−	0.173152i
$285$	−6.13682	−	6.13682i	−0.363514	−	0.363514i
$286$	−15.6191	−	9.90390i	−0.923579	−	0.585630i
$287$	−3.36970			−0.198907
$288$	1.75826	+	5.37666i	0.103607	+	0.316823i
$289$	−16.9857			−0.999157
$290$	−11.0721	−	7.02065i	−0.650174	−	0.412267i
$291$	−3.90912	−	3.90912i	−0.229157	−	0.229157i
$292$	4.49610	−	2.11987i	0.263115	−	0.124056i
$293$	13.1240	−	13.1240i	0.766712	−	0.766712i	−0.210814	−	0.977526i	$-0.567612\pi$
$293$	13.1240	−	13.1240i	0.766712	−	0.766712i	0.977526	+	0.210814i	$0.0676115\pi$
$294$	0.309024	+	1.38004i	0.0180227	+	0.0804854i
$295$			9.81729i			0.571585i
$296$	−0.336240	−	0.432462i	−0.0195436	−	0.0251363i
$297$			2.86233i			0.166089i
$298$	16.3935	−	3.67091i	0.949651	−	0.212650i
$299$	−30.1511	+	30.1511i	−1.74368	+	1.74368i
$300$	−6.40173	−	2.29928i	−0.369604	−	0.132749i
$301$	−8.82429	−	8.82429i	−0.508623	−	0.508623i
$302$	0.235289	−	0.371067i	0.0135394	−	0.0213525i
$303$	5.56976			0.319974
$304$	−27.3280	+	2.62509i	−1.56737	+	0.150559i
$305$	14.4298			0.826251
$306$	0.0906728	−	0.142997i	0.00518342	−	0.00817461i
$307$	7.54597	+	7.54597i	0.430671	+	0.430671i	0.888857	−	0.458185i	$-0.151500\pi$
$307$	7.54597	+	7.54597i	0.430671	+	0.430671i	−0.458185	+	0.888857i	$0.651500\pi$
$308$	1.93507	−	5.38769i	0.110261	−	0.306992i
$309$	−2.18896	+	2.18896i	−0.124525	+	0.124525i
$310$	1.67129	−	0.374242i	0.0949227	−	0.0212555i
$311$		−	32.5271i		−	1.84444i	−0.386665	−	0.922220i	$-0.626373\pi$
$311$		−	32.5271i		−	1.84444i	0.386665	−	0.922220i	$-0.373627\pi$
$312$	12.8226	+	1.60505i	0.725937	+	0.0908683i
$313$			10.5957i			0.598907i	0.954111	+	0.299453i	$0.0968043\pi$
$313$			10.5957i			0.598907i	−0.954111	+	0.299453i	$0.903196\pi$
$314$	−2.45875	−	10.9803i	−0.138755	−	0.619652i
$315$	−0.894131	+	0.894131i	−0.0503786	+	0.0503786i
$316$	−5.88131	−	12.4739i	−0.330850	−	0.701710i
$317$	11.5297	+	11.5297i	0.647571	+	0.647571i	0.952405	−	0.304834i	$-0.0986011\pi$
$317$	11.5297	+	11.5297i	0.647571	+	0.647571i	−0.304834	+	0.952405i	$0.598601\pi$
$318$	9.23479	+	5.85567i	0.517861	+	0.328369i
$319$	−20.9846			−1.17491
$320$	8.69547	−	5.16923i	0.486092	−	0.288969i
$321$	−1.09826			−0.0612991
$322$	−11.1466	−	7.06790i	−0.621174	−	0.393879i
$323$	0.581065	+	0.581065i	0.0323313	+	0.0323313i
$324$	−0.852931	−	1.80901i	−0.0473850	−	0.100500i
$325$	−10.9877	+	10.9877i	−0.609488	+	0.609488i
$326$	4.64742	+	20.7544i	0.257397	+	1.14948i
$327$		−	10.7947i		−	0.596946i
$328$	−9.45714	−	1.18379i	−0.522183	−	0.0653636i
$329$		−	3.50414i		−	0.193190i
$330$	4.99489	−	1.11848i	0.274960	−	0.0615703i
$331$	−2.46209	+	2.46209i	−0.135328	+	0.135328i	−0.771526	−	0.636198i	$-0.780506\pi$
$331$	−2.46209	+	2.46209i	−0.135328	+	0.135328i	0.636198	+	0.771526i	$0.280506\pi$
$332$	−10.6756	+	29.7233i	−0.585899	+	1.63128i
$333$	0.136949	+	0.136949i	0.00750476	+	0.00750476i
$334$	12.4322	−	19.6065i	0.680262	−	1.07282i
$335$	14.4674			0.790440
$336$	0.382473	+	3.98167i	0.0208656	+	0.217218i
$337$	16.9229			0.921850			0.460925	−	0.887439i	$-0.347518\pi$
$337$	16.9229			0.921850			0.460925	+	0.887439i	$0.347518\pi$
$338$	5.96347	−	9.40481i	0.324370	−	0.511554i
$339$	−1.16524	−	1.16524i	−0.0632874	−	0.0632874i
$340$	−0.284968	−	0.102351i	−0.0154546	−	0.00555075i
$341$	1.93842	−	1.93842i	0.104971	−	0.104971i
$342$	9.47182	−	2.12097i	0.512177	−	0.114689i
$343$			1.00000i			0.0539949i
$344$	−21.6656	−	27.8656i	−1.16813	−	1.50241i
$345$		−	11.8012i		−	0.635356i
$346$	6.14067	+	27.4229i	0.330124	+	1.47426i
$347$	−23.6687	+	23.6687i	−1.27060	+	1.27060i	−0.324832	+	0.945772i	$0.605308\pi$
$347$	−23.6687	+	23.6687i	−1.27060	+	1.27060i	−0.945772	+	0.324832i	$0.894692\pi$
$348$	13.2624	−	6.25310i	0.710939	−	0.335201i
$349$	16.1446	+	16.1446i	0.864201	+	0.864201i	0.991823	−	0.127622i	$-0.0407343\pi$
$349$	16.1446	+	16.1446i	0.864201	+	0.864201i	−0.127622	+	0.991823i	$0.540734\pi$
$350$	−4.06205	−	2.57569i	−0.217126	−	0.137677i
$351$	−4.56885			−0.243867
$352$	7.32354	−	14.4409i	0.390346	−	0.769702i
$353$	33.5199			1.78409			0.892043	−	0.451950i	$-0.149271\pi$
$353$	33.5199			1.78409			0.892043	+	0.451950i	$0.149271\pi$
$354$	−9.27270	−	5.87970i	−0.492838	−	0.312503i
$355$	3.05895	+	3.05895i	0.162352	+	0.162352i
$356$	5.98902	−	2.82377i	0.317418	−	0.149660i
$357$	0.0846608	−	0.0846608i	0.00448072	−	0.00448072i
$358$	−4.25084	−	18.9833i	−0.224664	−	1.00330i
$359$		−	16.0137i		−	0.845170i	−0.906323	−	0.422585i	$-0.861123\pi$
$359$		−	16.0137i		−	0.845170i	0.906323	−	0.422585i	$-0.138877\pi$
$360$	−2.82351	+	2.19529i	−0.148812	+	0.115702i
$361$			28.1069i			1.47931i
$362$	−31.9103	+	7.14550i	−1.67717	+	0.375559i
$363$	−1.98491	+	1.98491i	−0.104181	+	0.104181i
$364$	8.59984	+	3.08877i	0.450754	+	0.161895i
$365$	2.22227	+	2.22227i	0.116319	+	0.116319i
$366$	−8.64222	+	13.6294i	−0.451736	+	0.712420i
$367$	11.1537			0.582220			0.291110	−	0.956690i	$-0.405976\pi$
$367$	11.1537			0.582220			0.291110	+	0.956690i	$0.405976\pi$
$368$	−28.8002	−	23.7521i	−1.50131	−	1.23816i
$369$	3.36970			0.175419
$370$	0.185468	−	0.292496i	0.00964204	−	0.0152062i
$371$	5.46741	+	5.46741i	0.283854	+	0.283854i
$372$	−0.647473	+	1.80271i	−0.0335699	+	0.0934664i
$373$	17.3690	−	17.3690i	0.899331	−	0.899331i	−0.0960455	−	0.995377i	$-0.530619\pi$
$373$	17.3690	−	17.3690i	0.899331	−	0.899331i	0.995377	+	0.0960455i	$0.0306194\pi$
$374$	−0.472941	+	0.105903i	−0.0244552	+	0.00547613i
$375$		−	10.6231i		−	0.548573i
$376$	1.23102	−	9.83446i	0.0634848	−	0.507174i
$377$		−	33.4957i		−	1.72512i
$378$	−0.309024	−	1.38004i	−0.0158945	−	0.0709815i
$379$	25.7851	−	25.7851i	1.32449	−	1.32449i	0.414394	−	0.910098i	$-0.363994\pi$
$379$	25.7851	−	25.7851i	1.32449	−	1.32449i	0.910098	−	0.414394i	$-0.136006\pi$
$380$	−7.40240	−	15.7000i	−0.379735	−	0.805392i
$381$	8.46586	+	8.46586i	0.433719	+	0.433719i
$382$	4.25316	+	2.69687i	0.217611	+	0.137984i
$383$	4.93117			0.251971			0.125986	−	0.992032i	$-0.459791\pi$
$383$	4.93117			0.251971			0.125986	+	0.992032i	$0.459791\pi$
$384$	−0.325353	+	11.3090i	−0.0166031	+	0.577111i
$385$	3.61939			0.184461
$386$	4.62673	+	2.93375i	0.235494	+	0.149324i
$387$	8.82429	+	8.82429i	0.448564	+	0.448564i
$388$	−4.71529	−	10.0008i	−0.239382	−	0.507713i
$389$	9.90961	−	9.90961i	0.502437	−	0.502437i	−0.409757	−	0.912195i	$-0.634387\pi$
$389$	9.90961	−	9.90961i	0.502437	−	0.502437i	0.912195	+	0.409757i	$0.134387\pi$
$390$	1.78532	+	7.97286i	0.0904032	+	0.403722i
$391$			1.11740i			0.0565093i
$392$	−0.351303	+	2.80653i	−0.0177435	+	0.141751i
$393$		−	5.59359i		−	0.282159i
$394$	3.92089	−	0.877983i	0.197531	−	0.0442322i
$395$	6.16540	−	6.16540i	0.310215	−	0.310215i
$396$	−1.93507	+	5.38769i	−0.0972410	+	0.270741i
$397$	23.1340	+	23.1340i	1.16106	+	1.16106i	0.984244	+	0.176816i	$0.0565798\pi$
$397$	23.1340	+	23.1340i	1.16106	+	1.16106i	0.176816	+	0.984244i	$0.443420\pi$
$398$	−2.45417	+	3.87040i	−0.123016	+	0.194005i
$399$	6.86345			0.343602
$400$	−10.4954	−	8.65576i	−0.524770	−	0.432788i
$401$	−25.3078			−1.26381			−0.631905	−	0.775046i	$-0.717727\pi$
$401$	−25.3078			−1.26381			−0.631905	+	0.775046i	$0.717727\pi$
$402$	−8.66474	+	13.6649i	−0.432158	+	0.681543i
$403$	3.09411	+	3.09411i	0.154129	+	0.154129i
$404$	10.4838	+	3.76542i	0.521589	+	0.187337i
$405$	0.894131	−	0.894131i	0.0444297	−	0.0444297i
$406$	10.1175	−	2.26555i	0.502122	−	0.112438i
$407$		−	0.554362i		−	0.0274787i
$408$	0.267344	−	0.207861i	0.0132355	−	0.0102907i
$409$			11.8729i			0.587077i	0.955947	+	0.293538i	$0.0948328\pi$
$409$			11.8729i			0.587077i	−0.955947	+	0.293538i	$0.905167\pi$
$410$	−1.31674	−	5.88028i	−0.0650291	−	0.290406i
$411$	−4.33900	+	4.33900i	−0.214027	+	0.214027i
$412$	−5.60006	+	2.64038i	−0.275895	+	0.130082i
$413$	−5.48985	−	5.48985i	−0.270138	−	0.270138i
$414$	11.1466	+	7.06790i	0.547824	+	0.347368i
$415$	−19.9678			−0.980181
$416$	23.0506	+	11.6899i	1.13015	+	0.573142i
$417$	14.1253			0.691719
$418$	−23.4635	−	14.8779i	−1.14764	−	0.727702i
$419$	−20.7205	−	20.7205i	−1.01226	−	1.01226i	−0.999924	−	0.0123379i	$-0.996073\pi$
$419$	−20.7205	−	20.7205i	−1.01226	−	1.01226i	−0.0123379	−	0.999924i	$-0.503927\pi$
$420$	−2.28748	+	1.07852i	−0.111617	+	0.0526266i
$421$	−7.56576	+	7.56576i	−0.368733	+	0.368733i	−0.867015	−	0.498282i	$-0.833964\pi$
$421$	−7.56576	+	7.56576i	−0.368733	+	0.368733i	0.498282	+	0.867015i	$0.333964\pi$
$422$	6.75182	+	30.1522i	0.328674	+	1.46779i
$423$			3.50414i			0.170377i
$424$	13.4237	+	17.2651i	0.651913	+	0.838469i
$425$			0.407204i			0.0197523i
$426$	−4.72131	+	1.05722i	−0.228748	+	0.0512224i
$427$	−8.06921	+	8.06921i	−0.390496	+	0.390496i
$428$	−2.06723	−	0.742479i	−0.0999234	−	0.0358891i
$429$	9.24723	+	9.24723i	0.446460	+	0.446460i
$430$	11.9506	−	18.8470i	0.576310	−	0.908881i
$431$	10.9428			0.527098			0.263549	−	0.964646i	$-0.415107\pi$
$431$	10.9428			0.527098			0.263549	+	0.964646i	$0.415107\pi$
$432$	−0.382473	−	3.98167i	−0.0184018	−	0.191568i
$433$	−30.4908			−1.46529			−0.732647	−	0.680609i	$-0.761715\pi$
$433$	−30.4908			−1.46529			−0.732647	+	0.680609i	$0.761715\pi$
$434$	−0.725310	+	1.14386i	−0.0348160	+	0.0549073i
$435$	6.55515	+	6.55515i	0.314295	+	0.314295i
$436$	7.29772	−	20.3185i	0.349497	−	0.973081i
$437$	−45.2937	+	45.2937i	−2.16669	+	2.16669i
$438$	−3.42994	+	0.768049i	−0.163889	+	0.0366988i
$439$			29.1948i			1.39339i	0.717366	+	0.696696i	$0.245347\pi$
$439$			29.1948i			1.39339i	−0.717366	+	0.696696i	$0.754653\pi$
$440$	10.1579	+	1.27150i	0.484259	+	0.0606165i
$441$		−	1.00000i		−	0.0476190i
$442$	−0.169043	−	0.754911i	−0.00804056	−	0.0359074i
$443$	11.6570	−	11.6570i	0.553843	−	0.553843i	−0.373705	−	0.927548i	$-0.621913\pi$
$443$	11.6570	−	11.6570i	0.553843	−	0.553843i	0.927548	+	0.373705i	$0.121913\pi$
$444$	0.165192	+	0.350360i	0.00783964	+	0.0166273i
$445$	2.96017	+	2.96017i	0.140325	+	0.140325i
$446$	33.7411	+	21.3948i	1.59769	+	1.01307i
$447$	−11.8790			−0.561859
$448$	−1.97188	+	7.75317i	−0.0931627	+	0.366303i
$449$	−8.71500			−0.411286			−0.205643	−	0.978627i	$-0.565929\pi$
$449$	−8.71500			−0.411286			−0.205643	+	0.978627i	$0.565929\pi$
$450$	4.06205	+	2.57569i	0.191487	+	0.121419i
$451$	−6.82017	−	6.82017i	−0.321149	−	0.321149i
$452$	−1.40555	−	2.98107i	−0.0661115	−	0.140218i
$453$	−0.219688	+	0.219688i	−0.0103219	+	0.0103219i
$454$	−0.877397	−	3.91827i	−0.0411783	−	0.183893i
$455$			5.77728i			0.270843i
$456$	19.2624	+	2.41115i	0.902047	+	0.112913i
$457$		−	31.7466i		−	1.48504i	−0.669822	−	0.742522i	$-0.733630\pi$
$457$		−	31.7466i		−	1.48504i	0.669822	−	0.742522i	$-0.266370\pi$
$458$	−19.6128	+	4.39180i	−0.916448	+	0.205215i
$459$	−0.0846608	+	0.0846608i	−0.00395163	+	0.00395163i
$460$	7.97819	−	22.2131i	0.371985	−	1.03569i
$461$	12.5034	+	12.5034i	0.582340	+	0.582340i	0.935546	−	0.353206i	$-0.114908\pi$
$461$	12.5034	+	12.5034i	0.582340	+	0.582340i	−0.353206	+	0.935546i	$0.614908\pi$
$462$	−2.16770	+	3.41861i	−0.100851	+	0.159048i
$463$	4.11446			0.191215			0.0956077	−	0.995419i	$-0.469521\pi$
$463$	4.11446			0.191215			0.0956077	+	0.995419i	$0.469521\pi$
$464$	29.1909	−	2.80403i	1.35515	−	0.130174i
$465$	−1.21104			−0.0561608
$466$	−6.59628	+	10.4028i	−0.305567	+	0.481900i
$467$	10.9183	+	10.9183i	0.505238	+	0.505238i	0.913061	−	0.407823i	$-0.133712\pi$
$467$	10.9183	+	10.9183i	0.505238	+	0.505238i	−0.407823	+	0.913061i	$0.633712\pi$
$468$	−8.59984	−	3.08877i	−0.397528	−	0.142778i
$469$	−8.09022	+	8.09022i	−0.373572	+	0.373572i
$470$	6.11489	−	1.36927i	0.282059	−	0.0631599i
$471$			7.95649i			0.366616i
$472$	−13.4788	−	17.3360i	−0.620412	−	0.797955i
$473$		−	35.7202i		−	1.64242i
$474$	2.13085	+	9.51593i	0.0978733	+	0.437081i
$475$	−16.5060	+	16.5060i	−0.757347	+	0.757347i
$476$	0.216590	−	0.102120i	0.00992737	−	0.00468066i
$477$	−5.46741	−	5.46741i	−0.250335	−	0.250335i
$478$	16.8201	+	10.6654i	0.769335	+	0.487826i
$479$	26.7048			1.22018			0.610088	−	0.792334i	$-0.291134\pi$
$479$	26.7048			1.22018			0.610088	+	0.792334i	$0.291134\pi$
$480$	−6.79875	+	2.22331i	−0.310319	+	0.101480i
$481$	0.884874			0.0403468
$482$	−1.22282	−	0.775377i	−0.0556981	−	0.0353174i
$483$	6.59927	+	6.59927i	0.300277	+	0.300277i
$484$	−5.07804	+	2.39425i	−0.230820	+	0.108829i
$485$	4.94305	−	4.94305i	0.224452	−	0.224452i
$486$	0.309024	+	1.38004i	0.0140176	+	0.0625998i
$487$		−	17.7727i		−	0.805359i	−0.915341	−	0.402680i	$-0.868079\pi$
$487$		−	17.7727i		−	0.805359i	0.915341	−	0.402680i	$-0.131921\pi$
$488$	−25.4812	+	19.8117i	−1.15348	+	0.896833i
$489$		−	15.0390i		−	0.680088i
$490$	−1.74505	+	0.390759i	−0.0788332	+	0.0176527i
$491$	12.1323	−	12.1323i	0.547521	−	0.547521i	−0.378202	−	0.925723i	$-0.623457\pi$
$491$	12.1323	−	12.1323i	0.547521	−	0.547521i	0.925723	+	0.378202i	$0.123457\pi$
$492$	6.34270	+	2.27808i	0.285951	+	0.102704i
$493$	−0.620674	−	0.620674i	−0.0279538	−	0.0279538i
$494$	23.7481	−	37.4525i	1.06848	−	1.68507i
$495$	−3.61939			−0.162679
$496$	−2.43744	+	2.95548i	−0.109445	+	0.132705i
$497$	−3.42115			−0.153459
$498$	11.9590	−	18.8601i	0.535895	−	0.845143i
$499$	−13.2987	−	13.2987i	−0.595331	−	0.595331i	0.343736	−	0.939067i	$-0.388308\pi$
$499$	−13.2987	−	13.2987i	−0.595331	−	0.595331i	−0.939067	+	0.343736i	$0.888308\pi$
$500$	7.18171	−	19.9955i	0.321176	−	0.894228i
$501$	−11.6079	+	11.6079i	−0.518604	+	0.518604i
$502$	−32.8578	+	7.35767i	−1.46652	+	0.328389i
$503$			9.05699i			0.403831i	0.979403	+	0.201916i	$0.0647167\pi$
$503$			9.05699i			0.403831i	−0.979403	+	0.201916i	$0.935283\pi$
$504$	0.351303	−	2.80653i	0.0156483	−	0.125013i
$505$			7.04291i			0.313405i
$506$	−8.25511	−	36.8656i	−0.366984	−	1.63887i
$507$	−5.56807	+	5.56807i	−0.247286	+	0.247286i
$508$	10.2117	+	21.6584i	0.453073	+	0.960936i
$509$	−5.57709	−	5.57709i	−0.247200	−	0.247200i	0.572620	−	0.819821i	$-0.305927\pi$
$509$	−5.57709	−	5.57709i	−0.247200	−	0.247200i	−0.819821	+	0.572620i	$0.805927\pi$
$510$	0.180819	+	0.114655i	0.00800680	+	0.00507701i
$511$	−2.48540			−0.109948
$512$	−8.25786	+	21.0667i	−0.364949	+	0.931027i
$513$	−6.86345			−0.303029
$514$	21.6042	+	13.6989i	0.952920	+	0.604235i
$515$	−2.76792	−	2.76792i	−0.121969	−	0.121969i
$516$	10.6441	+	22.5754i	0.468580	+	0.993826i
$517$	7.09228	−	7.09228i	0.311918	−	0.311918i
$518$	0.0598504	+	0.267279i	0.00262967	+	0.0117436i
$519$		−	19.8711i		−	0.872246i
$520$	−2.02958	+	16.2141i	−0.0890028	+	0.711035i
$521$			27.4233i			1.20144i	0.799461	+	0.600718i	$0.205118\pi$
$521$			27.4233i			1.20144i	−0.799461	+	0.600718i	$0.794882\pi$
$522$	−10.1175	+	2.26555i	−0.442830	+	0.0991606i
$523$	−8.04026	+	8.04026i	−0.351576	+	0.351576i	−0.860696	−	0.509120i	$-0.829971\pi$
$523$	−8.04026	+	8.04026i	−0.351576	+	0.351576i	0.509120	+	0.860696i	$0.329971\pi$
$524$	3.78154	−	10.5287i	0.165197	−	0.459947i
$525$	2.40491	+	2.40491i	0.104959	+	0.104959i
$526$	−6.02802	+	9.50661i	−0.262834	+	0.414508i
$527$	0.114668			0.00499500
$528$	−7.28467	+	8.83290i	−0.317025	+	0.384403i
$529$	−64.1007			−2.78699
$530$	−7.40444	+	11.6773i	−0.321628	+	0.507230i
$531$	5.48985	+	5.48985i	0.238239	+	0.238239i
$532$	12.9189	+	4.64002i	0.560105	+	0.201171i
$533$	10.8864	−	10.8864i	0.471541	−	0.471541i
$534$	−4.56885	+	1.02308i	−0.197713	+	0.0442729i
$535$		−	1.38874i		−	0.0600406i
$536$	−25.5475	+	19.8633i	−1.10349	+	0.857964i
$537$			13.7557i			0.593601i
$538$	2.26471	+	10.1137i	0.0976385	+	0.436033i
$539$	−2.02397	+	2.02397i	−0.0871786	+	0.0871786i
$540$	2.28748	−	1.07852i	0.0984373	−	0.0464123i
$541$	22.3119	+	22.3119i	0.959265	+	0.959265i	0.999202	−	0.0399372i	$-0.0127158\pi$
$541$	22.3119	+	22.3119i	0.959265	+	0.959265i	−0.0399372	+	0.999202i	$0.512716\pi$
$542$	−14.7616	−	9.36012i	−0.634063	−	0.402052i
$543$	23.1228			0.992293
$544$	0.643739	−	0.210514i	0.0276001	−	0.00902571i
$545$	13.6498			0.584692
$546$	−5.45680	−	3.46009i	−0.233529	−	0.148078i
$547$	−2.44272	−	2.44272i	−0.104443	−	0.104443i	0.652954	−	0.757397i	$-0.273529\pi$
$547$	−2.44272	−	2.44272i	−0.104443	−	0.104443i	−0.757397	+	0.652954i	$0.773529\pi$
$548$	−11.1006	+	5.23382i	−0.474193	+	0.223578i
$549$	8.06921	−	8.06921i	0.344385	−	0.344385i
$550$	−3.00834	−	13.4346i	−0.128276	−	0.572853i
$551$		−	50.3181i		−	2.14362i
$552$	16.2027	+	20.8394i	0.689632	+	0.886982i
$553$			6.89542i			0.293223i
$554$	17.6421	−	3.95050i	0.749540	−	0.167841i
$555$	−0.173171	+	0.173171i	−0.00735070	+	0.00735070i
$556$	26.5877	+	9.54939i	1.12757	+	0.404984i
$557$	1.16381	+	1.16381i	0.0493120	+	0.0493120i	0.731333	−	0.682021i	$-0.238899\pi$
$557$	1.16381	+	1.16381i	0.0493120	+	0.0493120i	−0.682021	+	0.731333i	$0.738899\pi$
$558$	0.725310	−	1.14386i	0.0307048	−	0.0484236i
$559$	57.0167			2.41155
$560$	−5.03479	+	0.483635i	−0.212759	+	0.0204373i
$561$	0.342702			0.0144689
$562$	21.8818	−	34.5092i	0.923029	−	1.45568i
$563$	6.27044	+	6.27044i	0.264267	+	0.264267i	0.826785	−	0.562518i	$-0.190167\pi$
$563$	6.27044	+	6.27044i	0.264267	+	0.264267i	−0.562518	+	0.826785i	$0.690167\pi$
$564$	−2.36897	+	6.59576i	−0.0997516	+	0.277732i
$565$	1.47344	−	1.47344i	0.0619882	−	0.0619882i
$566$	12.9170	−	2.89244i	0.542943	−	0.121578i
$567$			1.00000i			0.0419961i
$568$	−9.60154	−	1.20186i	−0.402872	−	0.0504289i
$569$		−	33.1529i		−	1.38984i	−0.719086	−	0.694921i	$-0.755439\pi$
$569$		−	33.1529i		−	1.38984i	0.719086	−	0.694921i	$-0.244561\pi$
$570$	2.68195	+	11.9770i	0.112335	+	0.501663i
$571$	−1.59895	+	1.59895i	−0.0669141	+	0.0669141i	−0.739772	−	0.672858i	$-0.765067\pi$
$571$	−1.59895	+	1.59895i	−0.0669141	+	0.0669141i	0.672858	+	0.739772i	$0.265067\pi$
$572$	11.1543	+	23.6574i	0.466383	+	0.989166i
$573$	−2.51806	−	2.51806i	−0.105193	−	0.105193i
$574$	4.02459	+	2.55194i	0.167983	+	0.106516i
$575$	−31.7413			−1.32371
$576$	1.97188	−	7.75317i	0.0821618	−	0.323049i
$577$	−35.4434			−1.47553			−0.737763	−	0.675059i	$-0.764118\pi$
$577$	−35.4434			−1.47553			−0.737763	+	0.675059i	$0.764118\pi$
$578$	20.2868	+	12.8636i	0.843819	+	0.535055i
$579$	−2.73923	−	2.73923i	−0.113839	−	0.113839i
$580$	7.90700	+	16.7702i	0.328320	+	0.696344i
$581$	11.1660	−	11.1660i	0.463245	−	0.463245i
$582$	1.70839	+	7.62931i	0.0708150	+	0.316245i
$583$			22.1318i			0.916603i
$584$	−6.97533	−	0.873128i	−0.288641	−	0.0361303i
$585$		−	5.77728i		−	0.238861i
$586$	−25.6137	+	5.73553i	−1.05809	+	0.236933i
$587$	−6.93808	+	6.93808i	−0.286365	+	0.286365i	−0.835641	−	0.549276i	$-0.814904\pi$
$587$	−6.93808	+	6.93808i	−0.286365	+	0.286365i	0.549276	+	0.835641i	$0.314904\pi$
$588$	0.676048	−	1.88227i	0.0278798	−	0.0776237i
$589$	4.64806	+	4.64806i	0.191520	+	0.191520i
$590$	7.43484	−	11.7253i	0.306087	−	0.482721i
$591$	−2.84114			−0.116869
$592$	0.0740756	+	0.771151i	0.00304449	+	0.0316941i
$593$	1.28186			0.0526398			0.0263199	−	0.999654i	$-0.491621\pi$
$593$	1.28186			0.0526398			0.0263199	+	0.999654i	$0.491621\pi$
$594$	2.16770	−	3.41861i	0.0889418	−	0.140267i
$595$	0.107053	+	0.107053i	0.00438874	+	0.00438874i
$596$	−22.3596	−	8.03081i	−0.915886	−	0.328955i
$597$	2.29145	−	2.29145i	0.0937827	−	0.0937827i
$598$	58.8449	−	13.1768i	2.40635	−	0.538841i
$599$		−	4.29013i		−	0.175290i	−0.996152	−	0.0876450i	$-0.972066\pi$
$599$		−	4.29013i		−	0.175290i	0.996152	−	0.0876450i	$-0.0279341\pi$
$600$	5.90460	+	7.59430i	0.241054	+	0.310036i
$601$		−	1.23806i		−	0.0505017i	−0.999681	−	0.0252509i	$-0.991962\pi$
$601$		−	1.23806i		−	0.0505017i	0.999681	−	0.0252509i	$-0.00803845\pi$
$602$	3.85645	+	17.2221i	0.157177	+	0.701920i
$603$	8.09022	−	8.09022i	0.329459	−	0.329459i
$604$	−0.562033	+	0.264994i	−0.0228688	+	0.0107824i
$605$	−2.50990	−	2.50990i	−0.102042	−	0.102042i
$606$	−6.65222	−	4.21809i	−0.270228	−	0.171348i
$607$	27.4249			1.11314			0.556571	−	0.830800i	$-0.312117\pi$
$607$	27.4249			1.11314			0.556571	+	0.830800i	$0.312117\pi$
$608$	34.6272	+	17.5608i	1.40432	+	0.712184i
$609$	−7.33131			−0.297080
$610$	−17.2342	−	10.9280i	−0.697794	−	0.442463i
$611$	11.3207	+	11.3207i	0.457987	+	0.457987i
$612$	−0.216590	+	0.102120i	−0.00875512	+	0.00412796i
$613$	1.60492	−	1.60492i	0.0648222	−	0.0648222i	−0.673953	−	0.738775i	$-0.735405\pi$
$613$	1.60492	−	1.60492i	0.0648222	−	0.0648222i	0.738775	+	0.673953i	$0.235405\pi$
$614$	−3.29779	−	14.7272i	−0.133088	−	0.594343i
$615$			4.26096i			0.171818i
$616$	−6.39135	+	4.96930i	−0.257515	+	0.200219i
$617$		−	26.8011i		−	1.07897i	−0.841994	−	0.539486i	$-0.818619\pi$
$617$		−	26.8011i		−	1.07897i	0.841994	−	0.539486i	$-0.181381\pi$
$618$	4.27212	−	0.956633i	0.171850	−	0.0384814i
$619$	−33.4026	+	33.4026i	−1.34256	+	1.34256i	−0.449066	+	0.893499i	$0.648243\pi$
$619$	−33.4026	+	33.4026i	−1.34256	+	1.34256i	−0.893499	+	0.449066i	$0.851757\pi$
$620$	−2.27952	−	0.818724i	−0.0915476	−	0.0328808i
$621$	−6.59927	−	6.59927i	−0.264820	−	0.264820i
$622$	−24.6334	+	38.8486i	−0.987710	+	1.55769i
$623$	−3.31067			−0.132639
$624$	−14.0991	−	11.6278i	−0.564416	−	0.465485i
$625$	−3.57252			−0.142901
$626$	8.02437	−	12.6550i	0.320718	−	0.505795i
$627$	13.8914	+	13.8914i	0.554770	+	0.554770i
$628$	−5.37897	+	14.9763i	−0.214644	+	0.597620i
$629$	0.0163967	−	0.0163967i	0.000653779	−	0.000653779i
$630$	1.74505	−	0.390759i	0.0695243	−	0.0155682i
$631$		−	32.2658i		−	1.28448i	−0.766503	−	0.642241i	$-0.778005\pi$
$631$		−	32.2658i		−	1.28448i	0.766503	−	0.642241i	$-0.221995\pi$
$632$	−2.42238	+	19.3522i	−0.0963572	+	0.769788i
$633$		−	21.8488i		−	0.868413i
$634$	−5.03877	−	22.5021i	−0.200115	−	0.893672i
$635$	−10.7050	+	10.7050i	−0.424815	+	0.424815i
$636$	−6.59493	−	13.9874i	−0.261506	−	0.554636i
$637$	−3.23067	−	3.23067i	−0.128004	−	0.128004i
$638$	25.0629	+	15.8921i	0.992250	+	0.629173i
$639$	3.42115			0.135339
$640$	−14.3002	−	0.411406i	−0.565264	−	0.0162623i
$641$	16.5808			0.654904			0.327452	−	0.944868i	$-0.393810\pi$
$641$	16.5808			0.654904			0.327452	+	0.944868i	$0.393810\pi$
$642$	1.31171	+	0.831737i	0.0517690	+	0.0328260i
$643$	21.3939	+	21.3939i	0.843692	+	0.843692i	0.989337	−	0.145645i	$-0.0465258\pi$
$643$	21.3939	+	21.3939i	0.843692	+	0.843692i	−0.145645	+	0.989337i	$0.546526\pi$
$644$	7.96021	+	16.8831i	0.313676	+	0.665286i
$645$	−11.1582	+	11.1582i	−0.439355	+	0.439355i
$646$	−0.253941	−	1.13405i	−0.00999117	−	0.0446184i
$647$		−	42.6361i		−	1.67620i	−0.545517	−	0.838100i	$-0.683667\pi$
$647$		−	42.6361i		−	1.67620i	0.545517	−	0.838100i	$-0.316333\pi$
$648$	−0.351303	+	2.80653i	−0.0138005	+	0.110251i
$649$		−	22.2226i		−	0.872313i
$650$	21.4443	−	4.80192i	0.841116	−	0.188347i
$651$	0.677219	−	0.677219i	0.0265423	−	0.0265423i
$652$	10.1671	−	28.3076i	0.398174	−	1.10861i
$653$	−4.48193	−	4.48193i	−0.175391	−	0.175391i	0.613952	−	0.789343i	$-0.289579\pi$
$653$	−4.48193	−	4.48193i	−0.175391	−	0.175391i	−0.789343	+	0.613952i	$0.789579\pi$
$654$	−8.17502	+	12.8926i	−0.319669	+	0.504140i
$655$	7.07305			0.276367
$656$	10.3986	+	8.57594i	0.405997	+	0.334834i
$657$	2.48540			0.0969646
$658$	−2.65376	+	4.18516i	−0.103454	+	0.163155i
$659$	−24.7529	−	24.7529i	−0.964238	−	0.964238i	0.0351443	−	0.999382i	$-0.488811\pi$
$659$	−24.7529	−	24.7529i	−0.964238	−	0.964238i	−0.999382	+	0.0351443i	$0.988811\pi$
$660$	−6.81268	−	2.44688i	−0.265183	−	0.0952448i
$661$	34.2858	−	34.2858i	1.33356	−	1.33356i	0.431404	−	0.902159i	$-0.358018\pi$
$661$	34.2858	−	34.2858i	1.33356	−	1.33356i	0.902159	−	0.431404i	$-0.141982\pi$
$662$	4.80517	−	1.07600i	0.186758	−	0.0418198i
$663$			0.547022i			0.0212446i
$664$	35.2604	−	27.4151i	1.36837	−	1.06391i
$665$			8.67878i			0.336548i
$666$	−0.0598504	−	0.267279i	−0.00231915	−	0.0103569i
$667$	48.3813	−	48.3813i	1.87333	−	1.87333i
$668$	−29.6968	+	14.0018i	−1.14900	+	0.541745i
$669$	−19.9762	−	19.9762i	−0.772325	−	0.772325i
$670$	−17.2791	−	10.9565i	−0.667552	−	0.423286i
$671$	−32.6637			−1.26097
$672$	2.55860	−	5.04515i	0.0987000	−	0.194621i
$673$	−18.8904			−0.728172			−0.364086	−	0.931365i	$-0.618619\pi$
$673$	−18.8904			−0.728172			−0.364086	+	0.931365i	$0.618619\pi$
$674$	−20.2118	−	12.8161i	−0.778531	−	0.493657i
$675$	−2.40491	−	2.40491i	−0.0925651	−	0.0925651i
$676$	−14.2449	+	6.71635i	−0.547881	+	0.258321i
$677$	−15.3312	+	15.3312i	−0.589227	+	0.589227i	−0.937422	−	0.348195i	$-0.886795\pi$
$677$	−15.3312	+	15.3312i	−0.589227	+	0.589227i	0.348195	+	0.937422i	$0.386795\pi$
$678$	0.509243	+	2.27417i	0.0195574	+	0.0873390i
$679$			5.52833i			0.212158i
$680$	0.262839	+	0.338055i	0.0100794	+	0.0129638i
$681$			2.83925i			0.108800i
$682$	−3.78316	+	0.847142i	−0.144864	+	0.0324387i
$683$	−2.13282	+	2.13282i	−0.0816102	+	0.0816102i	−0.746734	−	0.665123i	$-0.768379\pi$
$683$	−2.13282	+	2.13282i	−0.0816102	+	0.0816102i	0.665123	+	0.746734i	$0.268379\pi$
$684$	−12.9189	−	4.64002i	−0.493966	−	0.177416i
$685$	−5.48664	−	5.48664i	−0.209634	−	0.209634i
$686$	0.757321	−	1.19435i	0.0289146	−	0.0456004i
$687$	14.2118			0.542215
$688$	4.77305	+	49.6890i	0.181971	+	1.89437i
$689$	−35.3268			−1.34584
$690$	−8.93731	+	14.0948i	−0.340237	+	0.536578i
$691$	17.0497	+	17.0497i	0.648602	+	0.648602i	0.952655	−	0.304053i	$-0.0983401\pi$
$691$	17.0497	+	17.0497i	0.648602	+	0.648602i	−0.304053	+	0.952655i	$0.598340\pi$
$692$	13.4338	−	37.4029i	0.510678	−	1.42185i
$693$	2.02397	−	2.02397i	0.0768843	−	0.0768843i
$694$	46.1935	−	10.3439i	1.75348	−	0.392648i
$695$			17.8613i			0.677519i
$696$	−20.5755	−	2.57551i	−0.779913	−	0.0976246i
$697$		−	0.403449i		−	0.0152817i
$698$	−7.05563	−	31.5089i	−0.267059	−	1.19263i
$699$	6.15892	−	6.15892i	0.232952	−	0.232952i
$700$	2.90087	+	6.15254i	0.109643	+	0.232544i
$701$	34.0605	+	34.0605i	1.28645	+	1.28645i	0.936930	+	0.349518i	$0.113655\pi$
$701$	34.0605	+	34.0605i	1.28645	+	1.28645i	0.349518	+	0.936930i	$0.386345\pi$
$702$	5.45680	+	3.46009i	0.205954	+	0.130593i
$703$	1.32928			0.0501347
$704$	−19.6832	+	11.7012i	−0.741840	+	0.441004i
$705$	−4.43096			−0.166880
$706$	−40.0345	−	25.3853i	−1.50672	−	0.955390i
$707$	−3.93841	−	3.93841i	−0.148119	−	0.148119i
$708$	6.62200	+	14.0448i	0.248870	+	0.527836i
$709$	−7.04022	+	7.04022i	−0.264401	+	0.264401i	−0.826839	−	0.562438i	$-0.809863\pi$
$709$	−7.04022	+	7.04022i	−0.264401	+	0.264401i	0.562438	+	0.826839i	$0.309863\pi$
$710$	−1.33684	−	5.97006i	−0.0501709	−	0.224052i
$711$		−	6.89542i		−	0.258598i
$712$	−9.29147	−	1.16305i	−0.348213	−	0.0435871i
$713$			8.93830i			0.334742i
$714$	−0.165230	+	0.0369990i	−0.00618357	+	0.00138465i
$715$	−11.6930	+	11.6930i	−0.437295	+	0.437295i
$716$	−9.29950	+	25.8920i	−0.347539	+	0.967628i
$717$	−9.95827	−	9.95827i	−0.371898	−	0.371898i
$718$	−12.1275	+	19.1259i	−0.452594	+	0.713772i
$719$	−27.4221			−1.02267			−0.511335	−	0.859381i	$-0.670849\pi$
$719$	−27.4221			−1.02267			−0.511335	+	0.859381i	$0.670849\pi$
$720$	5.03479	−	0.483635i	0.187636	−	0.0180240i
$721$	3.09565			0.115288
$722$	21.2860	−	33.5694i	0.792182	−	1.24933i
$723$	0.723966	+	0.723966i	0.0269246	+	0.0269246i
$724$	43.5234	+	15.6321i	1.61753	+	0.580963i
$725$	17.6312	−	17.6312i	0.654805	−	0.654805i
$726$	3.87388	−	0.867458i	0.143773	−	0.0321944i
$727$			1.52531i			0.0565706i	0.999600	+	0.0282853i	$0.00900469\pi$
$727$			1.52531i			0.0565706i	−0.999600	+	0.0282853i	$0.990995\pi$
$728$	−7.93201	−	10.2019i	−0.293980	−	0.378107i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.971191	−	4.33713i	−0.0359454	−	0.160525i
$731$	1.05652	−	1.05652i	0.0390767	−	0.0390767i
$732$	20.6436	−	9.73329i	0.763011	−	0.359753i
$733$	−20.5365	−	20.5365i	−0.758532	−	0.758532i	0.217523	−	0.976055i	$-0.430202\pi$
$733$	−20.5365	−	20.5365i	−0.758532	−	0.758532i	−0.976055	+	0.217523i	$0.930202\pi$
$734$	−13.3214	−	8.44694i	−0.491703	−	0.311782i
$735$	1.26449			0.0466415
$736$	16.4095	+	50.1792i	0.604861	+	1.84963i
$737$	−32.7488			−1.20632
$738$	−4.02459	−	2.55194i	−0.148147	−	0.0939383i
$739$	−10.9539	−	10.9539i	−0.402947	−	0.402947i	0.476324	−	0.879270i	$-0.341969\pi$
$739$	−10.9539	−	10.9539i	−0.402947	−	0.402947i	−0.879270	+	0.476324i	$0.841969\pi$
$740$	−0.443027	+	0.208883i	−0.0162860	+	0.00767870i
$741$	−22.1735	+	22.1735i	−0.814565	+	0.814565i
$742$	−2.38940	−	10.6706i	−0.0877177	−	0.391729i
$743$		−	34.0256i		−	1.24828i	−0.781314	−	0.624138i	$-0.785450\pi$
$743$		−	34.0256i		−	1.24828i	0.781314	−	0.624138i	$-0.214550\pi$
$744$	2.13854	−	1.66272i	0.0784027	−	0.0609584i
$745$		−	15.0209i		−	0.550325i
$746$	−33.8985	+	7.59070i	−1.24111	+	0.277915i
$747$	−11.1660	+	11.1660i	−0.408544	+	0.408544i
$748$	0.645059	+	0.231683i	0.0235857	+	0.00847117i
$749$	0.776589	+	0.776589i	0.0283759	+	0.0283759i
$750$	−8.04507	+	12.6876i	−0.293764	+	0.463287i
$751$	−3.00646			−0.109707			−0.0548537	−	0.998494i	$-0.517469\pi$
$751$	−3.00646			−0.109707			−0.0548537	+	0.998494i	$0.517469\pi$
$752$	−8.91810	+	10.8135i	−0.325210	+	0.394327i
$753$	23.8094			0.867661
$754$	−25.3670	+	40.0055i	−0.923811	+	1.45691i
$755$	−0.277794	−	0.277794i	−0.0101100	−	0.0101100i
$756$	−0.676048	+	1.88227i	−0.0245876	+	0.0684577i
$757$	−17.3543	+	17.3543i	−0.630751	+	0.630751i	−0.948257	−	0.317505i	$-0.897155\pi$
$757$	−17.3543	+	17.3543i	−0.630751	+	0.630751i	0.317505	+	0.948257i	$0.397155\pi$
$758$	−50.3240	+	11.2688i	−1.82785	+	0.409300i
$759$			26.7135i			0.969637i
$760$	−3.04888	+	24.3572i	−0.110595	+	0.883529i
$761$			17.6334i			0.639212i	0.947551	+	0.319606i	$0.103551\pi$
$761$			17.6334i			0.639212i	−0.947551	+	0.319606i	$0.896449\pi$
$762$	−3.69980	−	16.5225i	−0.134030	−	0.598548i
$763$	−7.63298	+	7.63298i	−0.276332	+	0.276332i
$764$	−3.03735	−	6.44201i	−0.109887	−	0.233064i
$765$	−0.107053	−	0.107053i	−0.00387050	−	0.00387050i
$766$	−5.88953	−	3.73448i	−0.212797	−	0.134932i
$767$	35.4718			1.28081
$768$	8.95315	−	13.2605i	0.323069	−	0.478498i
$769$	−49.0940			−1.77037			−0.885187	−	0.465235i	$-0.845970\pi$
$769$	−49.0940			−1.77037			−0.885187	+	0.465235i	$0.845970\pi$
$770$	−4.32281	−	2.74104i	−0.155783	−	0.0987802i
$771$	−12.7906	−	12.7906i	−0.460644	−	0.460644i
$772$	−3.30413	−	7.00784i	−0.118918	−	0.252218i
$773$	−7.85287	+	7.85287i	−0.282448	+	0.282448i	−0.834085	−	0.551637i	$-0.814004\pi$
$773$	−7.85287	+	7.85287i	−0.282448	+	0.282448i	0.551637	+	0.834085i	$0.314004\pi$
$774$	−3.85645	−	17.2221i	−0.138617	−	0.619035i
$775$			3.25730i			0.117006i
$776$	−1.94212	+	15.5154i	−0.0697181	+	0.556971i
$777$		−	0.193675i		−	0.00694806i
$778$	−19.3403	+	4.33076i	−0.693382	+	0.155265i
$779$	16.3538	−	16.3538i	0.585935	−	0.585935i
$780$	3.90572	−	10.8744i	0.139847	−	0.389367i
$781$	−6.92430	−	6.92430i	−0.247771	−	0.247771i
$782$	0.846229	−	1.33456i	0.0302611	−	0.0477238i
$783$	7.33131			0.262000
$784$	2.54502	−	3.08592i	0.0908935	−	0.110211i
$785$	−10.0609			−0.359090
$786$	−4.23614	+	6.68069i	−0.151098	+	0.238292i
$787$	7.65872	+	7.65872i	0.273004	+	0.273004i	0.830308	−	0.557304i	$-0.188164\pi$
$787$	7.65872	+	7.65872i	0.273004	+	0.273004i	−0.557304	+	0.830308i	$0.688164\pi$
$788$	−5.34782	−	1.92075i	−0.190508	−	0.0684239i
$789$	5.62834	−	5.62834i	0.200374	−	0.200374i
$790$	−12.0328	+	2.69445i	−0.428109	+	0.0958641i
$791$			1.64790i			0.0585928i
$792$	6.39135	−	4.96930i	0.227107	−	0.176576i
$793$		−	52.1378i		−	1.85147i
$794$	−10.1102	−	45.1498i	−0.358796	−	1.60231i
$795$	6.91349	−	6.91349i	0.245196	−	0.245196i
$796$	5.86226	−	2.76400i	0.207782	−	0.0979675i
$797$	−14.1964	−	14.1964i	−0.502862	−	0.502862i	0.409464	−	0.912326i	$-0.365716\pi$
$797$	−14.1964	−	14.1964i	−0.502862	−	0.502862i	−0.912326	+	0.409464i	$0.865716\pi$
$798$	−8.19734	−	5.19783i	−0.290183	−	0.184001i
$799$	0.419545			0.0148424
$800$	5.97996	+	18.2864i	0.211423	+	0.646520i
$801$	3.31067			0.116977
$802$	30.2263	+	19.1661i	1.06733	+	0.676778i
$803$	−5.03037	−	5.03037i	−0.177518	−	0.177518i
$804$	20.6974	−	9.75864i	0.729941	−	0.344161i
$805$	−8.34472	+	8.34472i	−0.294113	+	0.294113i
$806$	−1.35221	−	6.03868i	−0.0476296	−	0.212704i
$807$		−	7.32857i		−	0.257978i
$808$	−9.66968	−	12.4368i	−0.340178	−	0.437526i
$809$			39.3970i			1.38513i	0.721357	+	0.692563i	$0.243519\pi$
$809$			39.3970i			1.38513i	−0.721357	+	0.692563i	$0.756481\pi$
$810$	−1.74505	+	0.390759i	−0.0613147	+	0.0137299i
$811$	−13.5619	+	13.5619i	−0.476222	+	0.476222i	−0.903921	−	0.427699i	$-0.859324\pi$
$811$	−13.5619	+	13.5619i	−0.476222	+	0.476222i	0.427699	+	0.903921i	$0.359324\pi$
$812$	−13.7995	−	4.95632i	−0.484269	−	0.173933i
$813$	8.73950	+	8.73950i	0.306508	+	0.306508i
$814$	−0.419830	+	0.662100i	−0.0147150	+	0.0232066i
$815$	19.0167			0.666126
$816$	−0.476719	+	0.0457929i	−0.0166885	+	0.00160307i
$817$	85.6519			2.99658
$818$	8.99159	−	14.1804i	0.314383	−	0.495805i
$819$	3.23067	+	3.23067i	0.112889	+	0.112889i
$820$	−2.88061	+	8.02029i	−0.100595	+	0.280081i
$821$	5.06432	−	5.06432i	0.176746	−	0.176746i	−0.613190	−	0.789936i	$-0.710114\pi$
$821$	5.06432	−	5.06432i	0.176746	−	0.176746i	0.789936	+	0.613190i	$0.210114\pi$
$822$	8.46830	−	1.89626i	0.295366	−	0.0661397i
$823$			17.1851i			0.599035i	0.954091	+	0.299518i	$0.0968257\pi$
$823$			17.1851i			0.599035i	−0.954091	+	0.299518i	$0.903174\pi$
$824$	8.68803	+	1.08751i	0.302662	+	0.0378853i
$825$			9.73495i			0.338927i
$826$	2.39921	+	10.7144i	0.0834792	+	0.372800i
$827$	−15.6454	+	15.6454i	−0.544044	+	0.544044i	−0.924712	−	0.380668i	$-0.875694\pi$
$827$	−15.6454	+	15.6454i	−0.544044	+	0.544044i	0.380668	+	0.924712i	$0.375694\pi$
$828$	−7.96021	−	16.8831i	−0.276636	−	0.586727i
$829$	−34.8216	−	34.8216i	−1.20941	−	1.20941i	−0.971219	−	0.238186i	$-0.923447\pi$
$829$	−34.8216	−	34.8216i	−1.20941	−	1.20941i	−0.238186	−	0.971219i	$-0.576553\pi$
$830$	23.8485	+	15.1220i	0.827793	+	0.524893i
$831$	−12.7838			−0.443464
$832$	−18.6774	−	31.4184i	−0.647523	−	1.08924i
$833$	−0.119728			−0.00414834
$834$	−16.8705	−	10.6974i	−0.584178	−	0.370420i
$835$	−14.6781	−	14.6781i	−0.507957	−	0.507957i
$836$	16.7562	+	35.5387i	0.579525	+	1.22913i
$837$	−0.677219	+	0.677219i	−0.0234081	+	0.0234081i
$838$	9.05540	+	40.4395i	0.312814	+	1.39696i
$839$			35.3335i			1.21985i	0.792460	+	0.609923i	$0.208800\pi$
$839$			35.3335i			1.21985i	−0.792460	+	0.609923i	$0.791200\pi$
$840$	3.54883	+	0.444220i	0.122446	+	0.0153270i
$841$			24.7481i			0.853384i
$842$	14.7659	−	3.30644i	0.508865	−	0.113947i
$843$	−20.4310	+	20.4310i	−0.703680	+	0.703680i
$844$	14.7709	−	41.1255i	0.508434	−	1.41560i
$845$	−7.04077	−	7.04077i	−0.242210	−	0.242210i
$846$	2.65376	−	4.18516i	0.0912381	−	0.143889i
$847$	2.80708			0.0964525
$848$	−2.95732	−	30.7866i	−0.101555	−	1.05722i
$849$	−9.35991			−0.321231
$850$	0.308384	−	0.486342i	0.0105775	−	0.0166814i
$851$	1.27811	+	1.27811i	0.0438132	+	0.0438132i
$852$	6.43954	+	2.31286i	0.220615	+	0.0792373i
$853$	6.94647	−	6.94647i	0.237843	−	0.237843i	−0.578114	−	0.815956i	$-0.696211\pi$
$853$	6.94647	−	6.94647i	0.237843	−	0.237843i	0.815956	+	0.578114i	$0.196211\pi$
$854$	15.7484	−	3.52646i	0.538899	−	0.120673i
$855$		−	8.67878i		−	0.296808i
$856$	1.90670	+	2.45234i	0.0651696	+	0.0838191i
$857$			54.3462i			1.85643i	0.372041	+	0.928216i	$0.378658\pi$
$857$			54.3462i			1.85643i	−0.372041	+	0.928216i	$0.621342\pi$
$858$	−4.04129	−	18.0475i	−0.137967	−	0.616132i
$859$	4.78678	−	4.78678i	0.163323	−	0.163323i	−0.620714	−	0.784037i	$-0.713157\pi$
$859$	4.78678	−	4.78678i	0.163323	−	0.163323i	0.784037	+	0.620714i	$0.213157\pi$
$860$	−28.5464	+	13.4594i	−0.973424	+	0.458960i
$861$	−2.38274	−	2.38274i	−0.0812034	−	0.0812034i
$862$	−13.0696	−	8.28724i	−0.445151	−	0.282265i
$863$	6.00992			0.204580			0.102290	−	0.994755i	$-0.467383\pi$
$863$	6.00992			0.204580			0.102290	+	0.994755i	$0.467383\pi$
$864$	−2.55860	+	5.04515i	−0.0870452	+	0.171640i
$865$	25.1269			0.854340
$866$	36.4166	+	23.0913i	1.23749	+	0.784674i
$867$	−12.0107	−	12.0107i	−0.407904	−	0.407904i
$868$	1.73254	−	0.816879i	0.0588064	−	0.0277267i
$869$	−13.9561	+	13.9561i	−0.473429	+	0.473429i
$870$	−2.86478	−	12.7935i	−0.0971250	−	0.433740i
$871$		−	52.2737i		−	1.77123i
$872$	−24.1036	+	18.7407i	−0.816252	+	0.634639i
$873$		−	5.52833i		−	0.187106i
$874$	88.3984	−	19.7946i	2.99012	−	0.669561i
$875$	−7.51165	+	7.51165i	−0.253940	+	0.253940i
$876$	4.67820	+	1.68025i	0.158062	+	0.0567704i
$877$	−8.29062	−	8.29062i	−0.279954	−	0.279954i	0.553136	−	0.833091i	$-0.313431\pi$
$877$	−8.29062	−	8.29062i	−0.279954	−	0.279954i	−0.833091	+	0.553136i	$0.813431\pi$
$878$	22.1098	−	34.8687i	0.746171	−	1.17676i
$879$	18.5601			0.626018
$880$	−11.1691	−	9.21141i	−0.376511	−	0.310517i
$881$	−27.6859			−0.932762			−0.466381	−	0.884584i	$-0.654442\pi$
$881$	−27.6859			−0.932762			−0.466381	+	0.884584i	$0.654442\pi$
$882$	−0.757321	+	1.19435i	−0.0255003	+	0.0402158i
$883$	33.1342	+	33.1342i	1.11505	+	1.11505i	0.992456	+	0.122599i	$0.0391228\pi$
$883$	33.1342	+	33.1342i	1.11505	+	1.11505i	0.122599	+	0.992456i	$0.460877\pi$
$884$	−0.369813	+	1.02965i	−0.0124382	+	0.0346307i
$885$	−6.94187	+	6.94187i	−0.233348	+	0.233348i
$886$	−22.7507	+	5.09444i	−0.764324	+	0.171151i
$887$		−	37.8556i		−	1.27107i	−0.772073	−	0.635534i	$-0.780780\pi$
$887$		−	37.8556i		−	1.27107i	0.772073	−	0.635534i	$-0.219220\pi$
$888$	0.0680387	−	0.543554i	0.00228323	−	0.0182405i
$889$		−	11.9725i		−	0.401546i
$890$	−1.29367	−	5.77727i	−0.0433640	−	0.193654i
$891$	−2.02397	+	2.02397i	−0.0678056	+	0.0678056i
$892$	−24.0958	−	51.1056i	−0.806788	−	1.71114i
$893$	17.0063	+	17.0063i	0.569093	+	0.569093i
$894$	14.1877	+	8.99624i	0.474508	+	0.300879i
$895$	−17.3939			−0.581415
$896$	8.22675	−	7.76663i	0.274836	−	0.259465i
$897$	−42.6401			−1.42371
$898$	10.4087	+	6.60005i	0.347344	+	0.220247i
$899$	−4.96490	−	4.96490i	−0.165589	−	0.165589i
$900$	−2.90087	−	6.15254i	−0.0966957	−	0.205085i
$901$	−0.654604	+	0.654604i	−0.0218080	+	0.0218080i
$902$	2.98060	+	13.3107i	0.0992430	+	0.443198i
$903$		−	12.4794i		−	0.415289i
$904$	−0.578914	+	4.62489i	−0.0192544	+	0.153821i
$905$			29.2385i			0.971922i
$906$	0.428758	−	0.0960096i	0.0142445	−	0.00318970i
$907$	10.8409	−	10.8409i	0.359965	−	0.359965i	−0.503835	−	0.863800i	$-0.668078\pi$
$907$	10.8409	−	10.8409i	0.359965	−	0.359965i	0.863800	+	0.503835i	$0.168078\pi$
$908$	−1.91947	+	5.34424i	−0.0636998	+	0.177355i
$909$	3.93841	+	3.93841i	0.130629	+	0.130629i
$910$	4.37525	−	6.90008i	0.145038	−	0.228735i
$911$	33.9443			1.12463			0.562313	−	0.826925i	$-0.309912\pi$
$911$	33.9443			1.12463			0.562313	+	0.826925i	$0.309912\pi$
$912$	−21.1800	−	17.4676i	−0.701341	−	0.578410i
$913$	45.1995			1.49588
$914$	−24.0424	+	37.9165i	−0.795250	+	1.25417i
$915$	10.2034	+	10.2034i	0.337315	+	0.337315i
$916$	26.7505	+	9.60788i	0.883863	+	0.317453i
$917$	−3.95526	+	3.95526i	−0.130614	+	0.130614i
$918$	0.165230	−	0.0369990i	0.00545339	−	0.00122115i
$919$			40.1474i			1.32434i	0.749353	+	0.662171i	$0.230365\pi$
$919$			40.1474i			1.32434i	−0.749353	+	0.662171i	$0.769635\pi$
$920$	−26.3512	+	20.4881i	−0.868773	+	0.675474i
$921$			10.6716i			0.351642i
$922$	−5.46431	−	24.4024i	−0.179957	−	0.803651i
$923$	11.0526	−	11.0526i	0.363801	−	0.363801i
$924$	5.17797	−	2.44137i	0.170343	−	0.0803151i
$925$	0.465772	+	0.465772i	0.0153145	+	0.0153145i
$926$	−4.91410	−	3.11597i	−0.161487	−	0.102397i
$927$	−3.09565			−0.101675
$928$	−36.9876	−	18.7579i	−1.21418	−	0.615757i
$929$	34.8692			1.14402			0.572011	−	0.820246i	$-0.306164\pi$
$929$	34.8692			1.14402			0.572011	+	0.820246i	$0.306164\pi$
$930$	1.44641	+	0.917149i	0.0474296	+	0.0300745i
$931$	−4.85319	−	4.85319i	−0.159057	−	0.159057i
$932$	15.7565	−	7.42905i	0.516121	−	0.243347i
$933$	23.0001	−	23.0001i	0.752990	−	0.752990i
$934$	−4.77158	−	21.3089i	−0.156131	−	0.697248i
$935$			0.433344i			0.0141719i
$936$	7.93201	+	10.2019i	0.259266	+	0.333459i
$937$			45.3449i			1.48135i	0.671862	+	0.740676i	$0.265495\pi$
$937$			45.3449i			1.48135i	−0.671862	+	0.740676i	$0.734505\pi$
$938$	15.7894	−	3.53564i	0.515543	−	0.115443i
$939$	−7.49232	+	7.49232i	−0.244503	+	0.244503i
$940$	−8.34028	−	2.99554i	−0.272030	−	0.0977038i
$941$	3.55463	+	3.55463i	0.115878	+	0.115878i	0.762668	−	0.646790i	$-0.223889\pi$
$941$	3.55463	+	3.55463i	0.115878	+	0.115878i	−0.646790	+	0.762668i	$0.723889\pi$
$942$	6.02561	−	9.50281i	0.196325	−	0.309618i
$943$	31.4486			1.02411
$944$	2.96946	+	30.9130i	0.0966476	+	1.00613i
$945$	−1.26449			−0.0411339
$946$	−27.0516	+	42.6623i	−0.879525	+	1.38707i
$947$	−0.315602	−	0.315602i	−0.0102557	−	0.0102557i	0.701960	−	0.712216i	$-0.252308\pi$
$947$	−0.315602	−	0.315602i	−0.0102557	−	0.0102557i	−0.712216	+	0.701960i	$0.752308\pi$
$948$	4.66164	−	12.9791i	0.151403	−	0.421541i
$949$	8.02950	−	8.02950i	0.260648	−	0.260648i
$950$	32.2142	−	7.21356i	1.04517	−	0.234039i
$951$			16.3054i			0.528739i
$952$	−0.336021	−	0.0420610i	−0.0108905	−	0.00136320i
$953$		−	15.8425i		−	0.513189i	−0.966519	−	0.256594i	$-0.917400\pi$
$953$		−	15.8425i		−	0.513189i	0.966519	−	0.256594i	$-0.0826005\pi$
$954$	2.38940	+	10.6706i	0.0773598	+	0.345472i
$955$	3.18407	−	3.18407i	0.103034	−	0.103034i
$956$	−12.0119	−	25.4765i	−0.388494	−	0.823968i
$957$	−14.8384	−	14.8384i	−0.479656	−	0.479656i
$958$	−31.8949	−	20.2241i	−1.03048	−	0.653412i
$959$	6.13628			0.198151
$960$	9.80382	+	2.49343i	0.316417	+	0.0804751i
$961$	−30.0827			−0.970411
$962$	−1.05685	−	0.670133i	−0.0340741	−	0.0216060i
$963$	−0.776589	−	0.776589i	−0.0250252	−	0.0250252i
$964$	0.873266	+	1.85214i	0.0281260	+	0.0596533i
$965$	3.46374	−	3.46374i	0.111502	−	0.111502i
$966$	−2.88406	−	12.8796i	−0.0927930	−	0.414394i
$967$			18.3606i			0.590436i	0.955430	+	0.295218i	$0.0953922\pi$
$967$			18.3606i			0.590436i	−0.955430	+	0.295218i	$0.904608\pi$
$968$	7.87815	+	0.986138i	0.253213	+	0.0316957i
$969$			0.821750i			0.0263984i
$970$	−9.64720	+	2.16025i	−0.309753	+	0.0693613i
$971$	16.5118	−	16.5118i	0.529888	−	0.529888i	−0.390651	−	0.920539i	$-0.627750\pi$
$971$	16.5118	−	16.5118i	0.529888	−	0.529888i	0.920539	+	0.390651i	$0.127750\pi$
$972$	0.676048	−	1.88227i	0.0216843	−	0.0603740i
$973$	−9.98810	−	9.98810i	−0.320204	−	0.320204i
$974$	−13.4597	+	21.2268i	−0.431275	+	0.680151i
$975$	−15.5390			−0.497645
$976$	45.4372	−	4.36463i	1.45441	−	0.139708i
$977$	39.3211			1.25799			0.628997	−	0.777408i	$-0.283466\pi$
$977$	39.3211			1.25799			0.628997	+	0.777408i	$0.283466\pi$
$978$	−11.3894	+	17.9618i	−0.364191	+	0.574355i
$979$	−6.70069	−	6.70069i	−0.214155	−	0.214155i
$980$	2.38012	+	0.854858i	0.0760302	+	0.0273074i
$981$	7.63298	−	7.63298i	0.243702	−	0.243702i
$982$	−23.6781	+	5.30212i	−0.755600	+	0.169197i
$983$			51.1394i			1.63109i	0.578692	+	0.815547i	$0.303564\pi$
$983$			51.1394i			1.63109i	−0.578692	+	0.815547i	$0.696436\pi$
$984$	−5.85015	−	7.52427i	−0.186496	−	0.239865i
$985$		−	3.59260i		−	0.114470i
$986$	0.271251	+	1.21135i	0.00863840	+	0.0385773i
$987$	2.47780	−	2.47780i	0.0788693	−	0.0788693i
$988$	−56.7271	+	26.7463i	−1.80473	+	0.850913i
$989$	82.3551	+	82.3551i	2.61874	+	2.61874i
$990$	4.32281	+	2.74104i	0.137388	+	0.0871159i
$991$	27.1183			0.861442			0.430721	−	0.902485i	$-0.358259\pi$
$991$	27.1183			0.861442			0.430721	+	0.902485i	$0.358259\pi$
$992$	5.14940	−	1.68394i	0.163494	−	0.0534653i
$993$	−3.48191			−0.110495
$994$	4.08604	+	2.59091i	0.129601	+	0.0821785i
$995$	2.89752	+	2.89752i	0.0918574	+	0.0918574i
$996$	−28.5663	+	13.4688i	−0.905159	+	0.426774i
$997$	8.87789	−	8.87789i	0.281166	−	0.281166i	−0.552408	−	0.833574i	$-0.686291\pi$
$997$	8.87789	−	8.87789i	0.281166	−	0.281166i	0.833574	+	0.552408i	$0.186291\pi$
$998$	5.81188	+	25.9546i	0.183972	+	0.821579i
$999$			0.193675i			0.00612761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.a.253.3	yes	20
4.3	odd	2		1344.2.w.a.337.2		20
8.3	odd	2		2688.2.w.b.673.9		20
8.5	even	2		2688.2.w.a.673.4		20
16.3	odd	4		2688.2.w.b.2017.9		20
16.5	even	4	inner	336.2.w.a.85.3	✓	20
16.11	odd	4		1344.2.w.a.1009.2		20
16.13	even	4		2688.2.w.a.2017.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.3	✓	20	16.5	even	4	inner
336.2.w.a.253.3	yes	20	1.1	even	1	trivial
1344.2.w.a.337.2		20	4.3	odd	2
1344.2.w.a.1009.2		20	16.11	odd	4
2688.2.w.a.673.4		20	8.5	even	2
2688.2.w.a.2017.4		20	16.13	even	4
2688.2.w.b.673.9		20	8.3	odd	2
2688.2.w.b.2017.9		20	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19435 - 0.757321i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.852931 + 1.80901i) q^{4} +(-0.894131 + 0.894131i) q^{5} +(-0.309024 - 1.38004i) q^{6} -1.00000i q^{7} +(0.351303 - 2.80653i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.19435 - 0.757321i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.852931 + 1.80901i) q^{4} +(-0.894131 + 0.894131i) q^{5} +(-0.309024 - 1.38004i) q^{6} -1.00000i q^{7} +(0.351303 - 2.80653i) q^{8} +1.00000i q^{9} +(1.74505 - 0.390759i) q^{10} +(2.02397 - 2.02397i) q^{11} +(-0.676048 + 1.88227i) q^{12} +(3.23067 + 3.23067i) q^{13} +(-0.757321 + 1.19435i) q^{14} -1.26449 q^{15} +(-2.54502 + 3.08592i) q^{16} +0.119728 q^{17} +(0.757321 - 1.19435i) q^{18} +(4.85319 + 4.85319i) q^{19} +(-2.38012 - 0.854858i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-3.95012 + 0.884529i) q^{22} +9.33278i q^{23} +(2.23292 - 1.73610i) q^{24} +3.40106i q^{25} +(-1.41189 - 6.30519i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.80901 - 0.852931i) q^{28} +(-5.18402 - 5.18402i) q^{29} +(1.51024 + 0.957626i) q^{30} +0.957732 q^{31} +(5.37666 - 1.75826i) q^{32} +2.86233 q^{33} +(-0.142997 - 0.0906728i) q^{34} +(0.894131 + 0.894131i) q^{35} +(-1.80901 + 0.852931i) q^{36} +(0.136949 - 0.136949i) q^{37} +(-2.12097 - 9.47182i) q^{38} +4.56885i q^{39} +(2.19529 + 2.82351i) q^{40} -3.36970i q^{41} +(-1.38004 + 0.309024i) q^{42} +(8.82429 - 8.82429i) q^{43} +(5.38769 + 1.93507i) q^{44} +(-0.894131 - 0.894131i) q^{45} +(7.06790 - 11.1466i) q^{46} +3.50414 q^{47} +(-3.98167 + 0.382473i) q^{48} -1.00000 q^{49} +(2.57569 - 4.06205i) q^{50} +(0.0846608 + 0.0846608i) q^{51} +(-3.08877 + 8.59984i) q^{52} +(-5.46741 + 5.46741i) q^{53} +(1.38004 - 0.309024i) q^{54} +3.61939i q^{55} +(-2.80653 - 0.351303i) q^{56} +6.86345i q^{57} +(2.26555 + 10.1175i) q^{58} +(5.48985 - 5.48985i) q^{59} +(-1.07852 - 2.28748i) q^{60} +(-8.06921 - 8.06921i) q^{61} +(-1.14386 - 0.725310i) q^{62} +1.00000 q^{63} +(-7.75317 - 1.97188i) q^{64} -5.77728 q^{65} +(-3.41861 - 2.16770i) q^{66} +(-8.09022 - 8.09022i) q^{67} +(0.102120 + 0.216590i) q^{68} +(-6.59927 + 6.59927i) q^{69} +(-0.390759 - 1.74505i) q^{70} -3.42115i q^{71} +(2.80653 + 0.351303i) q^{72} -2.48540i q^{73} +(-0.267279 + 0.0598504i) q^{74} +(-2.40491 + 2.40491i) q^{75} +(-4.64002 + 12.9189i) q^{76} +(-2.02397 - 2.02397i) q^{77} +(3.46009 - 5.45680i) q^{78} -6.89542 q^{79} +(-0.483635 - 5.03479i) q^{80} -1.00000 q^{81} +(-2.55194 + 4.02459i) q^{82} +(11.1660 + 11.1660i) q^{83} +(1.88227 + 0.676048i) q^{84} +(-0.107053 + 0.107053i) q^{85} +(-17.2221 + 3.85645i) q^{86} -7.33131i q^{87} +(-4.96930 - 6.39135i) q^{88} -3.31067i q^{89} +(0.390759 + 1.74505i) q^{90} +(3.23067 - 3.23067i) q^{91} +(-16.8831 + 7.96021i) q^{92} +(0.677219 + 0.677219i) q^{93} +(-4.18516 - 2.65376i) q^{94} -8.67878 q^{95} +(5.04515 + 2.55860i) q^{96} -5.52833 q^{97} +(1.19435 + 0.757321i) q^{98} +(2.02397 + 2.02397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4}+O(q^{10}) \) 20 * q + 4 * q^4	\( 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Introduction

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