LMFDB - Embedded newform 240.2.bc.d.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	240.43
Dual form			240.2.bc.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40680 + 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 - 0.406803i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.144584 - 1.40680i) q^{6} +(2.10278 - 2.10278i) q^{7} +(-2.69597 + 0.855416i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.40680 + 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 - 0.406803i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.144584 - 1.40680i) q^{6} +(2.10278 - 2.10278i) q^{7} +(-2.69597 + 0.855416i) q^{8} -1.00000 q^{9} +(-2.95819 - 1.11763i) q^{10} +(2.10278 - 2.10278i) q^{11} +(0.406803 + 1.95819i) q^{12} +(-2.65416 + 3.26222i) q^{14} +(-1.00000 + 2.00000i) q^{15} +(3.66902 - 1.59320i) q^{16} +(-4.62721 + 4.62721i) q^{17} +(1.40680 - 0.144584i) q^{18} +(3.52444 - 3.52444i) q^{19} +(4.32318 + 1.14458i) q^{20} +(2.10278 + 2.10278i) q^{21} +(-2.65416 + 3.26222i) q^{22} +(3.52444 + 3.52444i) q^{23} +(-0.855416 - 2.69597i) q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(3.26222 - 4.97305i) q^{28} +(1.00000 + 1.00000i) q^{29} +(1.11763 - 2.95819i) q^{30} +4.20555i q^{31} +(-4.93124 + 2.77180i) q^{32} +(2.10278 + 2.10278i) q^{33} +(5.84056 - 7.17860i) q^{34} +(6.30833 - 2.10278i) q^{35} +(-1.95819 + 0.406803i) q^{36} -7.25443 q^{37} +(-4.44861 + 5.46777i) q^{38} +(-6.24736 - 0.985140i) q^{40} -4.00000i q^{41} +(-3.26222 - 2.65416i) q^{42} -3.04888 q^{43} +(3.26222 - 4.97305i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(-5.46777 - 4.44861i) q^{46} +(-4.68111 - 4.68111i) q^{47} +(1.59320 + 3.66902i) q^{48} -1.84333i q^{49} +(-4.79875 - 5.19346i) q^{50} +(-4.62721 - 4.62721i) q^{51} -3.15667i q^{53} +(0.144584 + 1.40680i) q^{54} +(6.30833 - 2.10278i) q^{55} +(-3.87028 + 7.46777i) q^{56} +(3.52444 + 3.52444i) q^{57} +(-1.55139 - 1.26222i) q^{58} +(-5.15165 - 5.15165i) q^{59} +(-1.14458 + 4.32318i) q^{60} +(-6.62721 + 6.62721i) q^{61} +(-0.608056 - 5.91638i) q^{62} +(-2.10278 + 2.10278i) q^{63} +(6.53653 - 4.61235i) q^{64} +(-3.26222 - 2.65416i) q^{66} +7.45998 q^{67} +(-7.17860 + 10.9433i) q^{68} +(-3.52444 + 3.52444i) q^{69} +(-8.57054 + 3.87028i) q^{70} -12.4111 q^{71} +(2.69597 - 0.855416i) q^{72} +(10.2544 - 10.2544i) q^{73} +(10.2056 - 1.04888i) q^{74} +(-4.00000 + 3.00000i) q^{75} +(5.46777 - 8.33527i) q^{76} -8.84333i q^{77} -12.4111 q^{79} +(8.93124 + 0.482629i) q^{80} +1.00000 q^{81} +(0.578337 + 5.62721i) q^{82} -16.4111i q^{83} +(4.97305 + 3.26222i) q^{84} +(-13.8816 + 4.62721i) q^{85} +(4.28917 - 0.440820i) q^{86} +(-1.00000 + 1.00000i) q^{87} +(-3.87028 + 7.46777i) q^{88} +13.2544 q^{89} +(2.95819 + 1.11763i) q^{90} +(8.33527 + 5.46777i) q^{92} -4.20555 q^{93} +(7.26222 + 5.90859i) q^{94} +(10.5733 - 3.52444i) q^{95} +(-2.77180 - 4.93124i) q^{96} +(-11.4111 + 11.4111i) q^{97} +(0.266516 + 2.59320i) q^{98} +(-2.10278 + 2.10278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.40680	+	0.144584i	−0.994760	+	0.102237i
$2$	−1.40680	+	0.144584i	−0.994760	+	0.102237i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.95819	−	0.406803i	0.979095	−	0.203402i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−0.144584	−	1.40680i	−0.0590263	−	0.574325i
$7$	2.10278	−	2.10278i	0.794774	−	0.794774i	−0.187492	−	0.982266i	$-0.560036\pi$
$7$	2.10278	−	2.10278i	0.794774	−	0.794774i	0.982266	+	0.187492i	$0.0600358\pi$
$8$	−2.69597	+	0.855416i	−0.953170	+	0.302435i
$9$	−1.00000			−0.333333
$10$	−2.95819	−	1.11763i	−0.935462	−	0.353427i
$11$	2.10278	−	2.10278i	0.634011	−	0.634011i	−0.315061	−	0.949071i	$-0.602025\pi$
$11$	2.10278	−	2.10278i	0.634011	−	0.634011i	0.949071	+	0.315061i	$0.102025\pi$
$12$	0.406803	+	1.95819i	0.117434	+	0.565281i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.65416	+	3.26222i	−0.709355	+	0.871865i
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	3.66902	−	1.59320i	0.917256	−	0.398299i
$17$	−4.62721	+	4.62721i	−1.12226	+	1.12226i	−0.130864	+	0.991400i	$0.541775\pi$
$17$	−4.62721	+	4.62721i	−1.12226	+	1.12226i	−0.991400	+	0.130864i	$0.958225\pi$
$18$	1.40680	−	0.144584i	0.331587	−	0.0340788i
$19$	3.52444	−	3.52444i	0.808562	−	0.808562i	−0.175855	−	0.984416i	$-0.556269\pi$
$19$	3.52444	−	3.52444i	0.808562	−	0.808562i	0.984416	+	0.175855i	$0.0562689\pi$
$20$	4.32318	+	1.14458i	0.966694	+	0.255937i
$21$	2.10278	+	2.10278i	0.458863	+	0.458863i
$22$	−2.65416	+	3.26222i	−0.565869	+	0.695507i
$23$	3.52444	+	3.52444i	0.734896	+	0.734896i	0.971585	−	0.236689i	$-0.0760623\pi$
$23$	3.52444	+	3.52444i	0.734896	+	0.734896i	−0.236689	+	0.971585i	$0.576062\pi$
$24$	−0.855416	−	2.69597i	−0.174611	−	0.550313i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	3.26222	−	4.97305i	0.616501	−	0.939818i
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	0.793832	−	0.608137i	$-0.208083\pi$
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	−0.608137	+	0.793832i	$0.708083\pi$
$30$	1.11763	−	2.95819i	0.204051	−	0.540089i
$31$			4.20555i			0.755339i	0.925940	+	0.377670i	$0.123274\pi$
$31$			4.20555i			0.755339i	−0.925940	+	0.377670i	$0.876726\pi$
$32$	−4.93124	+	2.77180i	−0.871729	+	0.489989i
$33$	2.10278	+	2.10278i	0.366046	+	0.366046i
$34$	5.84056	−	7.17860i	1.00165	−	1.23112i
$35$	6.30833	−	2.10278i	1.06630	−	0.355434i
$36$	−1.95819	+	0.406803i	−0.326365	+	0.0678005i
$37$	−7.25443			−1.19262			−0.596310	−	0.802754i	$-0.703367\pi$
$37$	−7.25443			−1.19262			−0.596310	+	0.802754i	$0.703367\pi$
$38$	−4.44861	+	5.46777i	−0.721660	+	0.886989i
$39$		0			0
$40$	−6.24736	−	0.985140i	−0.987794	−	0.155764i
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$	−3.26222	−	2.65416i	−0.503371	−	0.409546i
$43$	−3.04888			−0.464949			−0.232475	−	0.972602i	$-0.574682\pi$
$43$	−3.04888			−0.464949			−0.232475	+	0.972602i	$0.574682\pi$
$44$	3.26222	−	4.97305i	0.491798	−	0.749716i
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	−5.46777	−	4.44861i	−0.806179	−	0.655912i
$47$	−4.68111	−	4.68111i	−0.682810	−	0.682810i	0.277822	−	0.960633i	$-0.410387\pi$
$47$	−4.68111	−	4.68111i	−0.682810	−	0.682810i	−0.960633	+	0.277822i	$0.910387\pi$
$48$	1.59320	+	3.66902i	0.229958	+	0.529578i
$49$		−	1.84333i		−	0.263332i
$50$	−4.79875	−	5.19346i	−0.678645	−	0.734466i
$51$	−4.62721	−	4.62721i	−0.647939	−	0.647939i
$52$		0			0
$53$		−	3.15667i		−	0.433603i	−0.976216	−	0.216801i	$-0.930438\pi$
$53$		−	3.15667i		−	0.433603i	0.976216	−	0.216801i	$-0.0695624\pi$
$54$	0.144584	+	1.40680i	0.0196754	+	0.191442i
$55$	6.30833	−	2.10278i	0.850614	−	0.283538i
$56$	−3.87028	+	7.46777i	−0.517187	+	0.997923i
$57$	3.52444	+	3.52444i	0.466823	+	0.466823i
$58$	−1.55139	−	1.26222i	−0.203707	−	0.165737i
$59$	−5.15165	−	5.15165i	−0.670688	−	0.670688i	0.287187	−	0.957875i	$-0.407280\pi$
$59$	−5.15165	−	5.15165i	−0.670688	−	0.670688i	−0.957875	+	0.287187i	$0.907280\pi$
$60$	−1.14458	+	4.32318i	−0.147765	+	0.558121i
$61$	−6.62721	+	6.62721i	−0.848528	+	0.848528i	−0.989949	−	0.141422i	$-0.954833\pi$
$61$	−6.62721	+	6.62721i	−0.848528	+	0.848528i	0.141422	+	0.989949i	$0.454833\pi$
$62$	−0.608056	−	5.91638i	−0.0772232	−	0.751381i
$63$	−2.10278	+	2.10278i	−0.264925	+	0.264925i
$64$	6.53653	−	4.61235i	0.817066	−	0.576544i
$65$		0			0
$66$	−3.26222	−	2.65416i	−0.401551	−	0.326705i
$67$	7.45998			0.911381			0.455691	−	0.890138i	$-0.349392\pi$
$67$	7.45998			0.911381			0.455691	+	0.890138i	$0.349392\pi$
$68$	−7.17860	+	10.9433i	−0.870533	+	1.32707i
$69$	−3.52444	+	3.52444i	−0.424292	+	0.424292i
$70$	−8.57054	+	3.87028i	−1.02438	+	0.462586i
$71$	−12.4111			−1.47293			−0.736463	−	0.676477i	$-0.763506\pi$
$71$	−12.4111			−1.47293			−0.736463	+	0.676477i	$0.763506\pi$
$72$	2.69597	−	0.855416i	0.317723	−	0.100812i
$73$	10.2544	−	10.2544i	1.20019	−	1.20019i	0.226081	−	0.974108i	$-0.427408\pi$
$73$	10.2544	−	10.2544i	1.20019	−	1.20019i	0.974108	−	0.226081i	$-0.0725915\pi$
$74$	10.2056	−	1.04888i	1.18637	−	0.121929i
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	5.46777	−	8.33527i	0.627196	−	0.956122i
$77$		−	8.84333i		−	1.00779i
$78$		0			0
$79$	−12.4111			−1.39636			−0.698179	−	0.715923i	$-0.746006\pi$
$79$	−12.4111			−1.39636			−0.698179	+	0.715923i	$0.746006\pi$
$80$	8.93124	+	0.482629i	0.998543	+	0.0539595i
$81$	1.00000			0.111111
$82$	0.578337	+	5.62721i	0.0638666	+	0.621422i
$83$		−	16.4111i		−	1.80135i	−0.434491	−	0.900676i	$-0.643072\pi$
$83$		−	16.4111i		−	1.80135i	0.434491	−	0.900676i	$-0.356928\pi$
$84$	4.97305	+	3.26222i	0.542604	+	0.355937i
$85$	−13.8816	+	4.62721i	−1.50568	+	0.501892i
$86$	4.28917	−	0.440820i	0.462513	−	0.0475348i
$87$	−1.00000	+	1.00000i	−0.107211	+	0.107211i
$88$	−3.87028	+	7.46777i	−0.412573	+	0.796067i
$89$	13.2544			1.40497			0.702483	−	0.711700i	$-0.252075\pi$
$89$	13.2544			1.40497			0.702483	+	0.711700i	$0.252075\pi$
$90$	2.95819	+	1.11763i	0.311821	+	0.117809i
$91$		0			0
$92$	8.33527	+	5.46777i	0.869012	+	0.570054i
$93$	−4.20555			−0.436095
$94$	7.26222	+	5.90859i	0.749041	+	0.609424i
$95$	10.5733	−	3.52444i	1.08480	−	0.361600i
$96$	−2.77180	−	4.93124i	−0.282895	−	0.503293i
$97$	−11.4111	+	11.4111i	−1.15862	+	1.15862i	−0.173849	+	0.984772i	$0.555621\pi$
$97$	−11.4111	+	11.4111i	−1.15862	+	1.15862i	−0.984772	+	0.173849i	$0.944379\pi$
$98$	0.266516	+	2.59320i	0.0269222	+	0.261952i
$99$	−2.10278	+	2.10278i	−0.211337	+	0.211337i
$100$	7.50179	+	6.61235i	0.750179	+	0.661235i
$101$	6.25443	+	6.25443i	0.622339	+	0.622339i	0.946129	−	0.323790i	$-0.104957\pi$
$101$	6.25443	+	6.25443i	0.622339	+	0.622339i	−0.323790	+	0.946129i	$0.604957\pi$
$102$	7.17860	+	5.84056i	0.710787	+	0.578301i
$103$	9.15165	+	9.15165i	0.901739	+	0.901739i	0.995587	−	0.0938476i	$-0.0299166\pi$
$103$	9.15165	+	9.15165i	0.901739	+	0.901739i	−0.0938476	+	0.995587i	$0.529917\pi$
$104$		0			0
$105$	2.10278	+	6.30833i	0.205210	+	0.615629i
$106$	0.456405	+	4.44082i	0.0443300	+	0.431331i
$107$		−	14.0978i		−	1.36288i	−0.731873	−	0.681441i	$-0.761354\pi$
$107$		−	14.0978i		−	1.36288i	0.731873	−	0.681441i	$-0.238646\pi$
$108$	−0.406803	−	1.95819i	−0.0391447	−	0.188427i
$109$	−9.78389	−	9.78389i	−0.937126	−	0.937126i	0.0610107	−	0.998137i	$-0.480568\pi$
$109$	−9.78389	−	9.78389i	−0.937126	−	0.937126i	−0.998137	+	0.0610107i	$0.980568\pi$
$110$	−8.57054	+	3.87028i	−0.817169	+	0.369016i
$111$		−	7.25443i		−	0.688560i
$112$	4.36499	−	11.0653i	0.412453	−	1.04557i
$113$	6.62721	+	6.62721i	0.623436	+	0.623436i	0.946408	−	0.322973i	$-0.104682\pi$
$113$	6.62721	+	6.62721i	0.623436	+	0.623436i	−0.322973	+	0.946408i	$0.604682\pi$
$114$	−5.46777	−	4.44861i	−0.512103	−	0.416651i
$115$	3.52444	+	10.5733i	0.328656	+	0.985967i
$116$	2.36499	+	1.55139i	0.219584	+	0.144043i
$117$		0			0
$118$	7.99221	+	6.50251i	0.735742	+	0.598605i
$119$			19.4600i			1.78389i
$120$	0.985140	−	6.24736i	0.0899306	−	0.570303i
$121$			2.15667i			0.196061i
$122$	8.36499	−	10.2814i	0.757331	−	0.930832i
$123$	4.00000			0.360668
$124$	1.71083	+	8.23527i	0.153637	+	0.739549i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	2.65416	−	3.26222i	0.236452	−	0.290622i
$127$	−1.89722	−	1.89722i	−0.168351	−	0.168351i	0.617903	−	0.786254i	$-0.287982\pi$
$127$	−1.89722	−	1.89722i	−0.168351	−	0.168351i	−0.786254	+	0.617903i	$0.787982\pi$
$128$	−8.52873	+	7.43375i	−0.753841	+	0.657057i
$129$		−	3.04888i		−	0.268439i
$130$		0			0
$131$	−5.35720	−	5.35720i	−0.468061	−	0.468061i	0.433225	−	0.901286i	$-0.357376\pi$
$131$	−5.35720	−	5.35720i	−0.468061	−	0.468061i	−0.901286	+	0.433225i	$0.857376\pi$
$132$	4.97305	+	3.26222i	0.432848	+	0.283940i
$133$		−	14.8222i		−	1.28525i
$134$	−10.4947	+	1.07860i	−0.906606	+	0.0931764i
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	8.51664	−	16.4330i	0.730296	−	1.40912i
$137$	−11.7839	−	11.7839i	−1.00677	−	1.00677i	−0.999977	−	0.00678847i	$-0.997839\pi$
$137$	−11.7839	−	11.7839i	−1.00677	−	1.00677i	−0.00678847	−	0.999977i	$-0.502161\pi$
$138$	4.44861	−	5.46777i	0.378691	−	0.465447i
$139$	3.72999	+	3.72999i	0.316373	+	0.316373i	0.847372	−	0.530999i	$-0.178183\pi$
$139$	3.72999	+	3.72999i	0.316373	+	0.316373i	−0.530999	+	0.847372i	$0.678183\pi$
$140$	11.4975	−	6.68388i	0.971715	−	0.564891i
$141$	4.68111	−	4.68111i	0.394221	−	0.394221i
$142$	17.4600	−	1.79445i	1.46521	−	0.150587i
$143$		0			0
$144$	−3.66902	+	1.59320i	−0.305752	+	0.132766i
$145$	1.00000	+	3.00000i	0.0830455	+	0.249136i
$146$	−12.9433	+	15.9086i	−1.07120	+	1.31660i
$147$	1.84333			0.152035
$148$	−14.2056	+	2.95112i	−1.16769	+	0.242581i
$149$	8.25443	−	8.25443i	0.676229	−	0.676229i	−0.282916	−	0.959145i	$-0.591302\pi$
$149$	8.25443	−	8.25443i	0.676229	−	0.676229i	0.959145	+	0.282916i	$0.0913017\pi$
$150$	5.19346	−	4.79875i	0.424044	−	0.391816i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−6.48693	+	12.5166i	−0.526159	+	1.01523i
$153$	4.62721	−	4.62721i	0.374088	−	0.374088i
$154$	1.27861	+	12.4408i	0.103033	+	1.00251i
$155$	−4.20555	+	8.41110i	−0.337798	+	0.675596i
$156$		0			0
$157$		−	8.50885i		−	0.679080i	−0.940592	−	0.339540i	$-0.889729\pi$
$157$		−	8.50885i		−	0.679080i	0.940592	−	0.339540i	$-0.110271\pi$
$158$	17.4600	−	1.79445i	1.38904	−	0.142759i
$159$	3.15667			0.250341
$160$	−12.6343	+	0.612353i	−0.998828	+	0.0484108i
$161$	14.8222			1.16815
$162$	−1.40680	+	0.144584i	−0.110529	+	0.0113596i
$163$			0.411100i			0.0321999i	0.999870	+	0.0160999i	$0.00512499\pi$
$163$			0.411100i			0.0321999i	−0.999870	+	0.0160999i	$0.994875\pi$
$164$	−1.62721	−	7.83276i	−0.127064	−	0.611636i
$165$	2.10278	+	6.30833i	0.163701	+	0.491102i
$166$	2.37279	+	23.0872i	0.184164	+	1.79191i
$167$	−10.7789	+	10.7789i	−0.834094	+	0.834094i	−0.988074	−	0.153980i	$-0.950791\pi$
$167$	−10.7789	+	10.7789i	−0.834094	+	0.834094i	0.153980	+	0.988074i	$0.450791\pi$
$168$	−7.46777	−	3.87028i	−0.576151	−	0.298598i
$169$	−13.0000			−1.00000
$170$	18.8597	−	8.51664i	1.44647	−	0.653197i
$171$	−3.52444	+	3.52444i	−0.269521	+	0.269521i
$172$	−5.97028	+	1.24029i	−0.455230	+	0.0945714i
$173$	−18.5089			−1.40720			−0.703601	−	0.710595i	$-0.748426\pi$
$173$	−18.5089			−1.40720			−0.703601	+	0.710595i	$0.748426\pi$
$174$	1.26222	−	1.55139i	0.0956886	−	0.117610i
$175$	14.7194	+	2.10278i	1.11268	+	0.158955i
$176$	4.36499	−	11.0653i	0.329024	−	0.834076i
$177$	5.15165	−	5.15165i	0.387222	−	0.387222i
$178$	−18.6464	+	1.91638i	−1.39760	+	0.143639i
$179$	−9.35720	+	9.35720i	−0.699390	+	0.699390i	−0.964279	−	0.264889i	$-0.914665\pi$
$179$	−9.35720	+	9.35720i	−0.699390	+	0.699390i	0.264889	+	0.964279i	$0.414665\pi$
$180$	−4.32318	−	1.14458i	−0.322231	−	0.0853123i
$181$	4.62721	+	4.62721i	0.343938	+	0.343938i	0.857846	−	0.513908i	$-0.171803\pi$
$181$	4.62721	+	4.62721i	0.343938	+	0.343938i	−0.513908	+	0.857846i	$0.671803\pi$
$182$		0			0
$183$	−6.62721	−	6.62721i	−0.489898	−	0.489898i
$184$	−12.5166	−	6.48693i	−0.922739	−	0.478223i
$185$	−14.5089	−	7.25443i	−1.06671	−	0.533356i
$186$	5.91638	−	0.608056i	0.433810	−	0.0445849i
$187$			19.4600i			1.42305i
$188$	−11.0708	−	7.26222i	−0.807421	−	0.529652i
$189$	−2.10278	−	2.10278i	−0.152954	−	0.152954i
$190$	−14.3650	+	6.48693i	−1.04215	+	0.470611i
$191$			19.0489i			1.37833i	0.724605	+	0.689164i	$0.242022\pi$
$191$			19.0489i			1.37833i	−0.724605	+	0.689164i	$0.757978\pi$
$192$	4.61235	+	6.53653i	0.332868	+	0.471733i
$193$	−7.41110	−	7.41110i	−0.533463	−	0.533463i	0.388138	−	0.921601i	$-0.373118\pi$
$193$	−7.41110	−	7.41110i	−0.533463	−	0.533463i	−0.921601	+	0.388138i	$0.873118\pi$
$194$	14.4033	−	17.7030i	1.03410	−	1.27100i
$195$		0			0
$196$	−0.749871	−	3.60958i	−0.0535622	−	0.257827i
$197$	15.6655			1.11612			0.558061	−	0.829800i	$-0.311545\pi$
$197$	15.6655			1.11612			0.558061	+	0.829800i	$0.311545\pi$
$198$	2.65416	−	3.26222i	0.188623	−	0.231836i
$199$		−	7.79445i		−	0.552534i	−0.961081	−	0.276267i	$-0.910903\pi$
$199$		−	7.79445i		−	0.552534i	0.961081	−	0.276267i	$-0.0890974\pi$
$200$	−11.5096	−	8.21764i	−0.813850	−	0.581075i
$201$			7.45998i			0.526186i
$202$	−9.70304	−	7.89446i	−0.682703	−	0.555452i
$203$	4.20555			0.295172
$204$	−10.9433	−	7.17860i	−0.766186	−	0.502603i
$205$	4.00000	−	8.00000i	0.279372	−	0.558744i
$206$	−14.1978	−	11.5514i	−0.989205	−	0.804823i
$207$	−3.52444	−	3.52444i	−0.244965	−	0.244965i
$208$		0			0
$209$		−	14.8222i		−	1.02527i
$210$	−3.87028	−	8.57054i	−0.267074	−	0.591424i
$211$	−6.57331	−	6.57331i	−0.452526	−	0.452526i	0.443666	−	0.896192i	$-0.353678\pi$
$211$	−6.57331	−	6.57331i	−0.452526	−	0.452526i	−0.896192	+	0.443666i	$0.853678\pi$
$212$	−1.28415	−	6.18137i	−0.0881955	−	0.424538i
$213$		−	12.4111i		−	0.850395i
$214$	2.03831	+	19.8328i	0.139336	+	1.35574i
$215$	−6.09775	−	3.04888i	−0.415863	−	0.207932i
$216$	0.855416	+	2.69597i	0.0582037	+	0.183438i
$217$	8.84333	+	8.84333i	0.600324	+	0.600324i
$218$	15.1786	+	12.3494i	1.02802	+	0.836407i
$219$	10.2544	+	10.2544i	0.692930	+	0.692930i
$220$	11.4975	−	6.68388i	0.775161	−	0.450627i
$221$		0			0
$222$	1.04888	+	10.2056i	0.0703959	+	0.684952i
$223$	−1.35720	+	1.35720i	−0.0908849	+	0.0908849i	−0.751088	−	0.660203i	$-0.770470\pi$
$223$	−1.35720	+	1.35720i	−0.0908849	+	0.0908849i	0.660203	+	0.751088i	$0.270470\pi$
$224$	−4.54082	+	16.1978i	−0.303397	+	1.08226i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−10.2814	−	8.36499i	−0.683907	−	0.556431i
$227$	12.2056			0.810111			0.405055	−	0.914292i	$-0.367252\pi$
$227$	12.2056			0.810111			0.405055	+	0.914292i	$0.367252\pi$
$228$	8.33527	+	5.46777i	0.552017	+	0.362112i
$229$	−9.78389	+	9.78389i	−0.646537	+	0.646537i	−0.952155	−	0.305617i	$-0.901137\pi$
$229$	−9.78389	+	9.78389i	−0.646537	+	0.646537i	0.305617	+	0.952155i	$0.401137\pi$
$230$	−6.48693	−	14.3650i	−0.427735	−	0.947200i
$231$	8.84333			0.581848
$232$	−3.55139	−	1.84056i	−0.233160	−	0.120838i
$233$	−7.78389	+	7.78389i	−0.509939	+	0.509939i	−0.914508	−	0.404568i	$-0.867422\pi$
$233$	−7.78389	+	7.78389i	−0.509939	+	0.509939i	0.404568	+	0.914508i	$0.367422\pi$
$234$		0			0
$235$	−4.68111	−	14.0433i	−0.305362	−	0.916086i
$236$	−12.1836	−	7.99221i	−0.793086	−	0.520248i
$237$		−	12.4111i		−	0.806188i
$238$	−2.81361	−	27.3764i	−0.182379	−	1.77455i
$239$	−4.41110			−0.285330			−0.142665	−	0.989771i	$-0.545567\pi$
$239$	−4.41110			−0.285330			−0.142665	+	0.989771i	$0.545567\pi$
$240$	−0.482629	+	8.93124i	−0.0311536	+	0.576509i
$241$	18.8222			1.21244			0.606222	−	0.795295i	$-0.292684\pi$
$241$	18.8222			1.21244			0.606222	+	0.795295i	$0.292684\pi$
$242$	−0.311821	−	3.03402i	−0.0200446	−	0.195034i
$243$			1.00000i			0.0641500i
$244$	−10.2814	+	15.6733i	−0.658198	+	1.00338i
$245$	1.84333	−	3.68665i	0.117766	−	0.235532i
$246$	−5.62721	+	0.578337i	−0.358778	+	0.0368734i
$247$		0			0
$248$	−3.59749	−	11.3380i	−0.228441	−	0.719967i
$249$	16.4111			1.04001
$250$	−4.40403	−	15.1857i	−0.278536	−	0.960426i
$251$	−1.89722	+	1.89722i	−0.119752	+	0.119752i	−0.764443	−	0.644691i	$-0.776986\pi$
$251$	−1.89722	+	1.89722i	−0.119752	+	0.119752i	0.644691	+	0.764443i	$0.276986\pi$
$252$	−3.26222	+	4.97305i	−0.205500	+	0.313273i
$253$	14.8222			0.931864
$254$	2.94333	+	2.39471i	0.184681	+	0.150258i
$255$	−4.62721	−	13.8816i	−0.289767	−	0.869302i
$256$	10.9234	−	11.6909i	0.682716	−	0.730684i
$257$	4.52946	−	4.52946i	0.282540	−	0.282540i	−0.551581	−	0.834121i	$-0.685975\pi$
$257$	4.52946	−	4.52946i	0.282540	−	0.282540i	0.834121	+	0.551581i	$0.185975\pi$
$258$	0.440820	+	4.28917i	0.0274442	+	0.267032i
$259$	−15.2544	+	15.2544i	−0.947864	+	0.947864i
$260$		0			0
$261$	−1.00000	−	1.00000i	−0.0618984	−	0.0618984i
$262$	8.31109	+	6.76196i	0.513461	+	0.417755i
$263$	−0.0644618	−	0.0644618i	−0.00397489	−	0.00397489i	0.705117	−	0.709091i	$-0.250895\pi$
$263$	−0.0644618	−	0.0644618i	−0.00397489	−	0.00397489i	−0.709091	+	0.705117i	$0.750895\pi$
$264$	−7.46777	−	3.87028i	−0.459609	−	0.238199i
$265$	3.15667	−	6.31335i	0.193913	−	0.387826i
$266$	2.14306	+	20.8519i	0.131399	+	1.27851i
$267$			13.2544i			0.811158i
$268$	14.6081	−	3.03474i	0.892329	−	0.185376i
$269$	12.6655	+	12.6655i	0.772231	+	0.772231i	0.978496	−	0.206265i	$-0.0661310\pi$
$269$	12.6655	+	12.6655i	0.772231	+	0.772231i	−0.206265	+	0.978496i	$0.566131\pi$
$270$	−1.11763	+	2.95819i	−0.0680171	+	0.180030i
$271$			7.79445i			0.473479i	0.971573	+	0.236740i	$0.0760788\pi$
$271$			7.79445i			0.473479i	−0.971573	+	0.236740i	$0.923921\pi$
$272$	−9.60529	+	24.3494i	−0.582406	+	1.47640i
$273$		0			0
$274$	18.2814	+	14.8738i	1.10442	+	0.898562i
$275$	14.7194	+	2.10278i	0.887615	+	0.126802i
$276$	−5.46777	+	8.33527i	−0.329121	+	0.501725i
$277$	17.5678			1.05555			0.527773	−	0.849386i	$-0.323027\pi$
$277$	17.5678			1.05555			0.527773	+	0.849386i	$0.323027\pi$
$278$	−5.78666	−	4.70806i	−0.347061	−	0.282371i
$279$		−	4.20555i		−	0.251780i
$280$	−15.2083	+	11.0653i	−0.908871	+	0.661276i
$281$			19.2544i			1.14862i	0.818637	+	0.574311i	$0.194730\pi$
$281$			19.2544i			1.14862i	−0.818637	+	0.574311i	$0.805270\pi$
$282$	−5.90859	+	7.26222i	−0.351851	+	0.432459i
$283$	17.3622			1.03208			0.516039	−	0.856565i	$-0.327406\pi$
$283$	17.3622			1.03208			0.516039	+	0.856565i	$0.327406\pi$
$284$	−24.3033	+	5.04888i	−1.44214	+	0.299596i
$285$	3.52444	+	10.5733i	0.208770	+	0.626309i
$286$		0			0
$287$	−8.41110	−	8.41110i	−0.496492	−	0.496492i
$288$	4.93124	−	2.77180i	0.290576	−	0.163330i
$289$		−	25.8222i		−	1.51895i
$290$	−1.84056	−	4.07583i	−0.108081	−	0.239341i
$291$	−11.4111	−	11.4111i	−0.668931	−	0.668931i
$292$	15.9086	−	24.2517i	0.930980	−	1.41922i
$293$			4.31335i			0.251989i	0.992031	+	0.125994i	$0.0402121\pi$
$293$			4.31335i			0.251989i	−0.992031	+	0.125994i	$0.959788\pi$
$294$	−2.59320	+	0.266516i	−0.151238	+	0.0155435i
$295$	−5.15165	−	15.4550i	−0.299941	−	0.899822i
$296$	19.5577	−	6.20555i	1.13677	−	0.360690i
$297$	−2.10278	−	2.10278i	−0.122015	−	0.122015i
$298$	−10.4189	+	12.8058i	−0.603550	+	0.741821i
$299$		0			0
$300$	−6.61235	+	7.50179i	−0.381764	+	0.433116i
$301$	−6.41110	+	6.41110i	−0.369530	+	0.369530i
$302$		0			0
$303$	−6.25443	+	6.25443i	−0.359307	+	0.359307i
$304$	7.31612	−	18.5464i	0.419608	−	1.06371i
$305$	−19.8816	+	6.62721i	−1.13842	+	0.379473i
$306$	−5.84056	+	7.17860i	−0.333882	+	0.410373i
$307$	19.0489			1.08718			0.543588	−	0.839352i	$-0.317065\pi$
$307$	19.0489			1.08718			0.543588	+	0.839352i	$0.317065\pi$
$308$	−3.59749	−	17.3169i	−0.204986	−	0.986723i
$309$	−9.15165	+	9.15165i	−0.520619	+	0.520619i
$310$	4.70027	−	12.4408i	0.266957	−	0.706591i
$311$	18.0978			1.02623			0.513115	−	0.858320i	$-0.328492\pi$
$311$	18.0978			1.02623			0.513115	+	0.858320i	$0.328492\pi$
$312$		0			0
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	−0.617220	−	0.786790i	$-0.711741\pi$
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	0.786790	+	0.617220i	$0.211741\pi$
$314$	1.23025	+	11.9703i	0.0694268	+	0.675522i
$315$	−6.30833	+	2.10278i	−0.355434	+	0.118478i
$316$	−24.3033	+	5.04888i	−1.36717	+	0.284021i
$317$			11.1567i			0.626621i	0.949651	+	0.313311i	$0.101438\pi$
$317$			11.1567i			0.626621i	−0.949651	+	0.313311i	$0.898562\pi$
$318$	−4.44082	+	0.456405i	−0.249029	+	0.0255939i
$319$	4.20555			0.235466
$320$	17.6854	−	2.68818i	0.988644	−	0.150274i
$321$	14.0978			0.786860
$322$	−20.8519	+	2.14306i	−1.16203	+	0.119428i
$323$			32.6167i			1.81484i
$324$	1.95819	−	0.406803i	0.108788	−	0.0226002i
$325$		0			0
$326$	−0.0594386	−	0.578337i	−0.00329200	−	0.0320311i
$327$	9.78389	−	9.78389i	0.541050	−	0.541050i
$328$	3.42166	+	10.7839i	0.188930	+	0.595441i
$329$	−19.6867			−1.08536
$330$	−3.87028	−	8.57054i	−0.213052	−	0.471793i
$331$	6.57331	−	6.57331i	0.361302	−	0.361302i	−0.502990	−	0.864292i	$-0.667767\pi$
$331$	6.57331	−	6.57331i	0.361302	−	0.361302i	0.864292	+	0.502990i	$0.167767\pi$
$332$	−6.67609	−	32.1361i	−0.366398	−	1.76370i
$333$	7.25443			0.397540
$334$	13.6053	−	16.7222i	0.744448	−	0.914998i
$335$	14.9200	+	7.45998i	0.815164	+	0.407582i
$336$	11.0653	+	4.36499i	0.603660	+	0.238130i
$337$	−23.4111	+	23.4111i	−1.27528	+	1.27528i	−0.332007	+	0.943277i	$0.607726\pi$
$337$	−23.4111	+	23.4111i	−1.27528	+	1.27528i	−0.943277	+	0.332007i	$0.892274\pi$
$338$	18.2884	−	1.87960i	0.994760	−	0.102237i
$339$	−6.62721	+	6.62721i	−0.359941	+	0.359941i
$340$	−25.3005	+	14.7081i	−1.37211	+	0.797657i
$341$	8.84333	+	8.84333i	0.478893	+	0.478893i
$342$	4.44861	−	5.46777i	0.240553	−	0.295663i
$343$	10.8433	+	10.8433i	0.585485	+	0.585485i
$344$	8.21968	−	2.60806i	0.443176	−	0.140617i
$345$	−10.5733	+	3.52444i	−0.569248	+	0.189749i
$346$	26.0383	−	2.67609i	1.39983	−	0.143867i
$347$		−	18.5089i		−	0.993607i	−0.867863	−	0.496804i	$-0.834507\pi$
$347$		−	18.5089i		−	0.993607i	0.867863	−	0.496804i	$-0.165493\pi$
$348$	−1.55139	+	2.36499i	−0.0831631	+	0.126777i
$349$	13.4705	+	13.4705i	0.721061	+	0.721061i	0.968821	−	0.247760i	$-0.0796945\pi$
$349$	13.4705	+	13.4705i	0.721061	+	0.721061i	−0.247760	+	0.968821i	$0.579694\pi$
$350$	−21.0114	−	0.829993i	−1.12310	−	0.0443650i
$351$		0			0
$352$	−4.54082	+	16.1978i	−0.242027	+	0.863343i
$353$	−4.62721	−	4.62721i	−0.246282	−	0.246282i	0.573161	−	0.819443i	$-0.305717\pi$
$353$	−4.62721	−	4.62721i	−0.246282	−	0.246282i	−0.819443	+	0.573161i	$0.805717\pi$
$354$	−6.50251	+	7.99221i	−0.345605	+	0.424781i
$355$	−24.8222	−	12.4111i	−1.31743	−	0.658713i
$356$	25.9547	−	5.39194i	1.37560	−	0.285772i
$357$	−19.4600			−1.02993
$358$	11.8108	−	14.5166i	0.624222	−	0.767229i
$359$		−	5.14663i		−	0.271629i	−0.990734	−	0.135814i	$-0.956635\pi$
$359$		−	5.14663i		−	0.271629i	0.990734	−	0.135814i	$-0.0433651\pi$
$360$	6.24736	+	0.985140i	0.329265	+	0.0519215i
$361$		−	5.84333i		−	0.307543i
$362$	−7.17860	−	5.84056i	−0.377299	−	0.306973i
$363$	−2.15667			−0.113196
$364$		0			0
$365$	30.7633	−	10.2544i	1.61022	−	0.536741i
$366$	10.2814	+	8.36499i	0.537416	+	0.437245i
$367$	11.2594	+	11.2594i	0.587738	+	0.587738i	0.937018	−	0.349280i	$-0.113574\pi$
$367$	11.2594	+	11.2594i	0.587738	+	0.587738i	−0.349280	+	0.937018i	$0.613574\pi$
$368$	18.5464	+	7.31612i	0.966796	+	0.381379i
$369$			4.00000i			0.208232i
$370$	21.4600	+	8.10780i	1.11565	+	0.421504i
$371$	−6.63778	−	6.63778i	−0.344616	−	0.344616i
$372$	−8.23527	+	1.71083i	−0.426979	+	0.0887025i
$373$		−	3.68665i		−	0.190888i	−0.995435	−	0.0954438i	$-0.969573\pi$
$373$		−	3.68665i		−	0.190888i	0.995435	−	0.0954438i	$-0.0304270\pi$
$374$	−2.81361	−	27.3764i	−0.145488	−	1.41560i
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	16.6244	+	8.61585i	0.857340	+	0.444329i
$377$		0			0
$378$	3.26222	+	2.65416i	0.167790	+	0.136515i
$379$	−13.0922	−	13.0922i	−0.672502	−	0.672502i	0.285790	−	0.958292i	$-0.407744\pi$
$379$	−13.0922	−	13.0922i	−0.672502	−	0.672502i	−0.958292	+	0.285790i	$0.907744\pi$
$380$	19.2708	−	11.2028i	0.988572	−	0.574691i
$381$	1.89722	−	1.89722i	0.0971978	−	0.0971978i
$382$	−2.75417	−	26.7980i	−0.140915	−	1.37111i
$383$	−8.47556	+	8.47556i	−0.433081	+	0.433081i	−0.889675	−	0.456594i	$-0.849069\pi$
$383$	−8.47556	+	8.47556i	−0.433081	+	0.433081i	0.456594	+	0.889675i	$0.349069\pi$
$384$	−7.43375	−	8.52873i	−0.379352	−	0.435230i
$385$	8.84333	−	17.6867i	0.450698	−	0.901395i
$386$	11.4975	+	9.35443i	0.585207	+	0.476128i
$387$	3.04888			0.154983
$388$	−17.7030	+	26.9872i	−0.898736	+	1.37007i
$389$	0.254426	−	0.254426i	0.0128999	−	0.0128999i	−0.700627	−	0.713527i	$-0.747096\pi$
$389$	0.254426	−	0.254426i	0.0128999	−	0.0128999i	0.713527	+	0.700627i	$0.247096\pi$
$390$		0			0
$391$	−32.6167			−1.64949
$392$	1.57681	+	4.96955i	0.0796409	+	0.251000i
$393$	5.35720	−	5.35720i	0.270235	−	0.270235i
$394$	−22.0383	+	2.26499i	−1.11027	+	0.114108i
$395$	−24.8222	−	12.4111i	−1.24894	−	0.624470i
$396$	−3.26222	+	4.97305i	−0.163933	+	0.249905i
$397$		−	17.2544i		−	0.865975i	−0.901400	−	0.432987i	$-0.857459\pi$
$397$		−	17.2544i		−	0.865975i	0.901400	−	0.432987i	$-0.142541\pi$
$398$	1.12695	+	10.9653i	0.0564891	+	0.549639i
$399$	14.8222			0.742038
$400$	17.3799	+	9.89650i	0.868993	+	0.494825i
$401$	−7.56777			−0.377917			−0.188958	−	0.981985i	$-0.560511\pi$
$401$	−7.56777			−0.377917			−0.188958	+	0.981985i	$0.560511\pi$
$402$	−1.07860	−	10.4947i	−0.0537954	−	0.523429i
$403$		0			0
$404$	14.7917	+	9.70304i	0.735914	+	0.482744i
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	−5.91638	+	0.608056i	−0.293625	+	0.0301773i
$407$	−15.2544	+	15.2544i	−0.756134	+	0.756134i
$408$	16.4330	+	8.51664i	0.813556	+	0.421637i
$409$	−3.35218			−0.165755			−0.0828773	−	0.996560i	$-0.526411\pi$
$409$	−3.35218			−0.165755			−0.0828773	+	0.996560i	$0.526411\pi$
$410$	−4.47054	+	11.8328i	−0.220784	+	0.584379i
$411$	11.7839	−	11.7839i	0.581256	−	0.581256i
$412$	21.6436	+	14.1978i	1.06630	+	0.699473i
$413$	−21.6655			−1.06609
$414$	5.46777	+	4.44861i	0.268726	+	0.218637i
$415$	16.4111	−	32.8222i	0.805589	−	1.61118i
$416$		0			0
$417$	−3.72999	+	3.72999i	−0.182658	+	0.182658i
$418$	2.14306	+	20.8519i	0.104820	+	1.01990i
$419$	−0.946101	+	0.946101i	−0.0462201	+	0.0462201i	−0.729839	−	0.683619i	$-0.760405\pi$
$419$	−0.946101	+	0.946101i	−0.0462201	+	0.0462201i	0.683619	+	0.729839i	$0.260405\pi$
$420$	6.68388	+	11.4975i	0.326140	+	0.561020i
$421$	−19.7839	−	19.7839i	−0.964208	−	0.964208i	0.0351736	−	0.999381i	$-0.488802\pi$
$421$	−19.7839	−	19.7839i	−0.964208	−	0.964208i	−0.999381	+	0.0351736i	$0.988802\pi$
$422$	10.1978	+	8.29696i	0.496419	+	0.403890i
$423$	4.68111	+	4.68111i	0.227603	+	0.227603i
$424$	2.70027	+	8.51030i	0.131137	+	0.413297i
$425$	−32.3905	−	4.62721i	−1.57117	−	0.224453i
$426$	1.79445	+	17.4600i	0.0869414	+	0.845939i
$427$			27.8711i			1.34878i
$428$	−5.73501	−	27.6061i	−0.277212	−	1.33439i
$429$		0			0
$430$	9.01916	+	3.40753i	0.434942	+	0.164326i
$431$		−	8.54002i		−	0.411358i	−0.978619	−	0.205679i	$-0.934060\pi$
$431$		−	8.54002i		−	0.411358i	0.978619	−	0.205679i	$-0.0659404\pi$
$432$	−1.59320	−	3.66902i	−0.0766527	−	0.176526i
$433$	−0.156674	−	0.156674i	−0.00752928	−	0.00752928i	0.703332	−	0.710861i	$-0.251695\pi$
$433$	−0.156674	−	0.156674i	−0.00752928	−	0.00752928i	−0.710861	+	0.703332i	$0.751695\pi$
$434$	−13.7194	−	11.1622i	−0.658553	−	0.535803i
$435$	−3.00000	+	1.00000i	−0.143839	+	0.0479463i
$436$	−23.1388	−	15.1786i	−1.10815	−	0.726923i
$437$	24.8433			1.18842
$438$	−15.9086	−	12.9433i	−0.760142	−	0.618456i
$439$		−	22.3033i		−	1.06448i	−0.846594	−	0.532239i	$-0.821351\pi$
$439$		−	22.3033i		−	1.06448i	0.846594	−	0.532239i	$-0.178649\pi$
$440$	−15.2083	+	11.0653i	−0.725028	+	0.527516i
$441$			1.84333i			0.0877774i
$442$		0			0
$443$	11.1255			0.528589			0.264294	−	0.964442i	$-0.414861\pi$
$443$	11.1255			0.528589			0.264294	+	0.964442i	$0.414861\pi$
$444$	−2.95112	−	14.2056i	−0.140054	−	0.674166i
$445$	26.5089	+	13.2544i	1.25664	+	0.628320i
$446$	1.71308	−	2.10554i	0.0811169	−	0.0997004i
$447$	8.25443	+	8.25443i	0.390421	+	0.390421i
$448$	4.04611	−	23.4436i	0.191161	−	1.10761i
$449$			17.7633i			0.838301i	0.907917	+	0.419150i	$0.137672\pi$
$449$			17.7633i			0.838301i	−0.907917	+	0.419150i	$0.862328\pi$
$450$	4.79875	+	5.19346i	0.226215	+	0.244822i
$451$	−8.41110	−	8.41110i	−0.396063	−	0.396063i
$452$	15.6733	+	10.2814i	0.737211	+	0.483595i
$453$		0			0
$454$	−17.1708	+	1.76473i	−0.805866	+	0.0828229i
$455$		0			0
$456$	−12.5166	−	6.48693i	−0.586146	−	0.303778i
$457$	3.41110	+	3.41110i	0.159565	+	0.159565i	0.782374	−	0.622809i	$-0.214009\pi$
$457$	3.41110	+	3.41110i	0.159565	+	0.159565i	−0.622809	+	0.782374i	$0.714009\pi$
$458$	12.3494	−	15.1786i	0.577050	−	0.709249i
$459$	4.62721	+	4.62721i	0.215980	+	0.215980i
$460$	11.2028	+	19.2708i	0.522332	+	0.898506i
$461$	−3.84333	+	3.84333i	−0.179002	+	0.179002i	−0.790920	−	0.611919i	$-0.790398\pi$
$461$	−3.84333	+	3.84333i	−0.179002	+	0.179002i	0.611919	+	0.790920i	$0.290398\pi$
$462$	−12.4408	+	1.27861i	−0.578799	+	0.0594861i
$463$	−21.3572	+	21.3572i	−0.992553	+	0.992553i	−0.999972	−	0.00741917i	$-0.997638\pi$
$463$	−21.3572	+	21.3572i	−0.992553	+	0.992553i	0.00741917	+	0.999972i	$0.497638\pi$
$464$	5.26222	+	2.07583i	0.244292	+	0.0963678i
$465$	−8.41110	−	4.20555i	−0.390055	−	0.195028i
$466$	9.82497	−	12.0758i	0.455133	−	0.559402i
$467$	6.30330			0.291682			0.145841	−	0.989308i	$-0.453411\pi$
$467$	6.30330			0.291682			0.145841	+	0.989308i	$0.453411\pi$
$468$		0			0
$469$	15.6867	−	15.6867i	0.724342	−	0.724342i
$470$	8.61585	+	19.0794i	0.397419	+	0.880067i
$471$	8.50885			0.392067
$472$	18.2955	+	9.48190i	0.842119	+	0.436440i
$473$	−6.41110	+	6.41110i	−0.294783	+	0.294783i
$474$	1.79445	+	17.4600i	0.0824218	+	0.801963i
$475$	24.6711	+	3.52444i	1.13199	+	0.161712i
$476$	7.91638	+	38.1063i	0.362847	+	1.74660i
$477$			3.15667i			0.144534i
$478$	6.20555	−	0.637776i	0.283835	−	0.0291712i
$479$	28.4111			1.29814			0.649068	−	0.760730i	$-0.275159\pi$
$479$	28.4111			1.29814			0.649068	+	0.760730i	$0.275159\pi$
$480$	−0.612353	−	12.6343i	−0.0279500	−	0.576673i
$481$		0			0
$482$	−26.4791	+	2.72139i	−1.20609	+	0.123956i
$483$			14.8222i			0.674433i
$484$	0.877342	+	4.22318i	0.0398792	+	0.191963i
$485$	−34.2333	+	11.4111i	−1.55445	+	0.518151i
$486$	−0.144584	−	1.40680i	−0.00655848	−	0.0638139i
$487$	22.9250	−	22.9250i	1.03883	−	1.03883i	0.0396148	−	0.999215i	$-0.487387\pi$
$487$	22.9250	−	22.9250i	1.03883	−	1.03883i	0.999215	−	0.0396148i	$-0.0126131\pi$
$488$	12.1978	−	23.5358i	0.552167	−	1.06542i
$489$	−0.411100			−0.0185906
$490$	−2.06016	+	5.45291i	−0.0930688	+	0.246337i
$491$	6.84835	−	6.84835i	0.309062	−	0.309062i	−0.535484	−	0.844545i	$-0.679871\pi$
$491$	6.84835	−	6.84835i	0.309062	−	0.309062i	0.844545	+	0.535484i	$0.179871\pi$
$492$	7.83276	−	1.62721i	0.353128	−	0.0733604i
$493$	−9.25443			−0.416798
$494$		0			0
$495$	−6.30833	+	2.10278i	−0.283538	+	0.0945127i
$496$	6.70027	+	15.4303i	0.300851	+	0.692839i
$497$	−26.0978	+	26.0978i	−1.17064	+	1.17064i
$498$	−23.0872	+	2.37279i	−1.03456	+	0.106327i
$499$	3.52444	−	3.52444i	0.157776	−	0.157776i	−0.623805	−	0.781580i	$-0.714414\pi$
$499$	3.52444	−	3.52444i	0.157776	−	0.157776i	0.781580	+	0.623805i	$0.214414\pi$
$500$	8.39122	+	20.7265i	0.375267	+	0.926917i
$501$	−10.7789	−	10.7789i	−0.481564	−	0.481564i
$502$	2.39471	−	2.94333i	0.106881	−	0.131367i
$503$	−27.3955	−	27.3955i	−1.22151	−	1.22151i	−0.967097	−	0.254409i	$-0.918119\pi$
$503$	−27.3955	−	27.3955i	−1.22151	−	1.22151i	−0.254409	−	0.967097i	$-0.581881\pi$
$504$	3.87028	−	7.46777i	0.172396	−	0.332641i
$505$	6.25443	+	18.7633i	0.278318	+	0.834955i
$506$	−20.8519	+	2.14306i	−0.926981	+	0.0952705i
$507$		−	13.0000i		−	0.577350i
$508$	−4.48693	−	2.94333i	−0.199075	−	0.130589i
$509$	25.8222	+	25.8222i	1.14455	+	1.14455i	0.987608	+	0.156941i	$0.0501632\pi$
$509$	25.8222	+	25.8222i	1.14455	+	1.14455i	0.156941	+	0.987608i	$0.449837\pi$
$510$	8.51664	+	18.8597i	0.377123	+	0.835122i
$511$		−	43.1255i		−	1.90776i
$512$	−13.6768	+	18.0262i	−0.604436	+	0.796654i
$513$	−3.52444	−	3.52444i	−0.155608	−	0.155608i
$514$	−5.71717	+	7.02695i	−0.252174	+	0.309945i
$515$	9.15165	+	27.4550i	0.403270	+	1.20981i
$516$	−1.24029	−	5.97028i	−0.0546008	−	0.262827i
$517$	−19.6867			−0.865818
$518$	19.2544	−	23.6655i	0.845991	−	1.03980i
$519$		−	18.5089i		−	0.812448i
$520$		0			0
$521$		−	41.7633i		−	1.82968i	−0.403814	−	0.914841i	$-0.632316\pi$
$521$		−	41.7633i		−	1.82968i	0.403814	−	0.914841i	$-0.367684\pi$
$522$	1.55139	+	1.26222i	0.0679024	+	0.0552458i
$523$	−15.4600			−0.676018			−0.338009	−	0.941143i	$-0.609753\pi$
$523$	−15.4600			−0.676018			−0.338009	+	0.941143i	$0.609753\pi$
$524$	−12.6697	−	8.31109i	−0.553481	−	0.363072i
$525$	−2.10278	+	14.7194i	−0.0917726	+	0.642408i
$526$	0.100005	+	0.0813650i	0.00436044	+	0.00354768i
$527$	−19.4600	−	19.4600i	−0.847690	−	0.847690i
$528$	11.0653	+	4.36499i	0.481554	+	0.189962i
$529$			1.84333i			0.0801446i
$530$	−3.52801	+	9.33804i	−0.153247	+	0.405619i
$531$	5.15165	+	5.15165i	0.223563	+	0.223563i
$532$	−6.02972	−	29.0247i	−0.261421	−	1.25838i
$533$		0			0
$534$	−1.91638	−	18.6464i	−0.0829299	−	0.806907i
$535$	14.0978	−	28.1955i	0.609499	−	1.21900i
$536$	−20.1119	+	6.38138i	−0.868701	+	0.275634i
$537$	−9.35720	−	9.35720i	−0.403793	−	0.403793i
$538$	−19.6491	−	15.9867i	−0.847135	−	0.689234i
$539$	−3.87610	−	3.87610i	−0.166955	−	0.166955i
$540$	1.14458	−	4.32318i	0.0492551	−	0.186040i
$541$	−23.9794	+	23.9794i	−1.03095	+	1.03095i	−0.0314492	+	0.999505i	$0.510012\pi$
$541$	−23.9794	+	23.9794i	−1.03095	+	1.03095i	−0.999505	+	0.0314492i	$0.989988\pi$
$542$	−1.12695	−	10.9653i	−0.0484069	−	0.470998i
$543$	−4.62721	+	4.62721i	−0.198573	+	0.198573i
$544$	9.99221	−	35.6436i	0.428412	−	1.52821i
$545$	−9.78389	−	29.3517i	−0.419096	−	1.25729i
$546$		0			0
$547$	−20.9511			−0.895805			−0.447903	−	0.894082i	$-0.647829\pi$
$547$	−20.9511			−0.895805			−0.447903	+	0.894082i	$0.647829\pi$
$548$	−27.8688	−	18.2814i	−1.19050	−	0.780942i
$549$	6.62721	−	6.62721i	0.282843	−	0.282843i
$550$	−21.0114	−	0.829993i	−0.895928	−	0.0353910i
$551$	7.04888			0.300292
$552$	6.48693	−	12.5166i	0.276102	−	0.532744i
$553$	−26.0978	+	26.0978i	−1.10979	+	1.10979i
$554$	−24.7144	+	2.54002i	−1.05001	+	0.107915i
$555$	7.25443	−	14.5089i	0.307933	−	0.615866i
$556$	8.82140	+	5.78666i	0.374111	+	0.245409i
$557$			6.82220i			0.289066i	0.989500	+	0.144533i	$0.0461680\pi$
$557$			6.82220i			0.289066i	−0.989500	+	0.144533i	$0.953832\pi$
$558$	0.608056	+	5.91638i	0.0257411	+	0.250460i
$559$		0			0
$560$	19.7953	−	17.7655i	0.836502	−	0.750731i
$561$	−19.4600			−0.821601
$562$	−2.78389	−	27.0872i	−0.117431	−	1.14260i
$563$		−	26.5089i		−	1.11721i	−0.829432	−	0.558607i	$-0.811336\pi$
$563$		−	26.5089i		−	1.11721i	0.829432	−	0.558607i	$-0.188664\pi$
$564$	7.26222	−	11.0708i	0.305795	−	0.466165i
$565$	6.62721	+	19.8816i	0.278809	+	0.836427i
$566$	−24.4252	+	2.51030i	−1.02667	+	0.105516i
$567$	2.10278	−	2.10278i	0.0883083	−	0.0883083i
$568$	33.4600	−	10.6167i	1.40395	−	0.445465i
$569$	6.74557			0.282789			0.141395	−	0.989953i	$-0.454841\pi$
$569$	6.74557			0.282789			0.141395	+	0.989953i	$0.454841\pi$
$570$	−6.48693	−	14.3650i	−0.271707	−	0.601683i
$571$	−12.2700	+	12.2700i	−0.513484	+	0.513484i	−0.915592	−	0.402108i	$-0.868278\pi$
$571$	−12.2700	+	12.2700i	−0.513484	+	0.513484i	0.402108	+	0.915592i	$0.368278\pi$
$572$		0			0
$573$	−19.0489			−0.795778
$574$	13.0489	+	10.6167i	0.544650	+	0.443130i
$575$	−3.52444	+	24.6711i	−0.146979	+	1.02885i
$576$	−6.53653	+	4.61235i	−0.272355	+	0.192181i
$577$	29.4111	−	29.4111i	1.22440	−	1.22440i	0.258348	−	0.966052i	$-0.416822\pi$
$577$	29.4111	−	29.4111i	1.22440	−	1.22440i	0.966052	−	0.258348i	$-0.0831782\pi$
$578$	3.73348	+	36.3268i	0.155292	+	1.51099i
$579$	7.41110	−	7.41110i	0.307995	−	0.307995i
$580$	3.17860	+	5.46777i	0.131984	+	0.227037i
$581$	−34.5089	−	34.5089i	−1.43167	−	1.43167i
$582$	17.7030	+	14.4033i	0.733815	+	0.597036i
$583$	−6.63778	−	6.63778i	−0.274909	−	0.274909i
$584$	−18.8738	+	36.4174i	−0.781005	+	1.50696i
$585$		0			0
$586$	−0.623642	−	6.06803i	−0.0257624	−	0.250668i
$587$			24.4111i			1.00755i	0.863834	+	0.503777i	$0.168057\pi$
$587$			24.4111i			1.00755i	−0.863834	+	0.503777i	$0.831943\pi$
$588$	3.60958	−	0.749871i	0.148857	−	0.0309242i
$589$	14.8222	+	14.8222i	0.610738	+	0.610738i
$590$	9.48190	+	20.9972i	0.390364	+	0.864442i
$591$			15.6655i			0.644394i
$592$	−26.6167	+	11.5577i	−1.09394	+	0.475020i
$593$	16.1950	+	16.1950i	0.665048	+	0.665048i	0.956566	−	0.291517i	$-0.0941600\pi$
$593$	16.1950	+	16.1950i	0.665048	+	0.665048i	−0.291517	+	0.956566i	$0.594160\pi$
$594$	3.26222	+	2.65416i	0.133850	+	0.108902i
$595$	−19.4600	+	38.9200i	−0.797781	+	1.59556i
$596$	12.8058	−	19.5217i	0.524547	−	0.799639i
$597$	7.79445			0.319006
$598$		0			0
$599$		−	13.1466i		−	0.537157i	−0.963258	−	0.268578i	$-0.913446\pi$
$599$		−	13.1466i		−	0.537157i	0.963258	−	0.268578i	$-0.0865538\pi$
$600$	8.21764	−	11.5096i	0.335484	−	0.469877i
$601$			4.62670i			0.188727i	0.995538	+	0.0943634i	$0.0300816\pi$
$601$			4.62670i			0.188727i	−0.995538	+	0.0943634i	$0.969918\pi$
$602$	8.09221	−	9.94610i	0.329814	−	0.405373i
$603$	−7.45998			−0.303794
$604$		0			0
$605$	−2.15667	+	4.31335i	−0.0876813	+	0.175363i
$606$	7.89446	−	9.70304i	0.320690	−	0.394159i
$607$	−23.2494	−	23.2494i	−0.943664	−	0.943664i	0.0548315	−	0.998496i	$-0.482538\pi$
$607$	−23.2494	−	23.2494i	−0.943664	−	0.943664i	−0.998496	+	0.0548315i	$0.982538\pi$
$608$	−7.61083	+	27.1489i	−0.308660	+	1.10103i
$609$			4.20555i			0.170417i
$610$	27.0114	−	12.1978i	1.09366	−	0.493873i
$611$		0			0
$612$	7.17860	−	10.9433i	0.290178	−	0.442358i
$613$			25.2544i			1.02002i	0.860169	+	0.510008i	$0.170358\pi$
$613$			25.2544i			1.02002i	−0.860169	+	0.510008i	$0.829642\pi$
$614$	−26.7980	+	2.75417i	−1.08148	+	0.111149i
$615$	8.00000	+	4.00000i	0.322591	+	0.161296i
$616$	7.56472	+	23.8414i	0.304791	+	0.960596i
$617$	22.7250	+	22.7250i	0.914873	+	0.914873i	0.996651	−	0.0817779i	$-0.0260598\pi$
$617$	22.7250	+	22.7250i	0.914873	+	0.914873i	−0.0817779	+	0.996651i	$0.526060\pi$
$618$	11.5514	−	14.1978i	0.464665	−	0.571118i
$619$	3.72999	+	3.72999i	0.149921	+	0.149921i	0.778083	−	0.628162i	$-0.216192\pi$
$619$	3.72999	+	3.72999i	0.149921	+	0.149921i	−0.628162	+	0.778083i	$0.716192\pi$
$620$	−4.81361	+	18.1814i	−0.193319	+	0.730181i
$621$	3.52444	−	3.52444i	0.141431	−	0.141431i
$622$	−25.4600	+	2.61665i	−1.02085	+	0.104918i
$623$	27.8711	−	27.8711i	1.11663	−	1.11663i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−3.78666	+	4.65416i	−0.151345	+	0.186018i
$627$	14.8222			0.591942
$628$	−3.46143	−	16.6620i	−0.138126	−	0.664884i
$629$	33.5678	−	33.5678i	1.33843	−	1.33843i
$630$	8.57054	−	3.87028i	0.341459	−	0.154195i
$631$	−16.6066			−0.661098			−0.330549	−	0.943789i	$-0.607234\pi$
$631$	−16.6066			−0.661098			−0.330549	+	0.943789i	$0.607234\pi$
$632$	33.4600	−	10.6167i	1.33097	−	0.422308i
$633$	6.57331	−	6.57331i	0.261266	−	0.261266i
$634$	−1.61308	−	15.6952i	−0.0640636	−	0.623338i
$635$	−1.89722	−	5.69167i	−0.0752891	−	0.225867i
$636$	6.18137	−	1.28415i	0.245107	−	0.0509197i
$637$		0			0
$638$	−5.91638	+	0.608056i	−0.234232	+	0.0240732i
$639$	12.4111			0.490976
$640$	−24.4912	+	6.33877i	−0.968101	+	0.250562i
$641$	1.17780			0.0465203			0.0232601	−	0.999729i	$-0.492595\pi$
$641$	1.17780			0.0465203			0.0232601	+	0.999729i	$0.492595\pi$
$642$	−19.8328	+	2.03831i	−0.782737	+	0.0804458i
$643$		−	20.6066i		−	0.812645i	−0.913730	−	0.406323i	$-0.866811\pi$
$643$		−	20.6066i		−	0.812645i	0.913730	−	0.406323i	$-0.133189\pi$
$644$	29.0247	−	6.02972i	1.14373	−	0.237604i
$645$	3.04888	−	6.09775i	0.120049	−	0.240099i
$646$	−4.71585	−	45.8852i	−0.185543	−	1.80533i
$647$	24.5522	−	24.5522i	0.965246	−	0.965246i	−0.0341699	−	0.999416i	$-0.510879\pi$
$647$	24.5522	−	24.5522i	0.965246	−	0.965246i	0.999416	+	0.0341699i	$0.0108787\pi$
$648$	−2.69597	+	0.855416i	−0.105908	+	0.0336039i
$649$	−21.6655			−0.850446
$650$		0			0
$651$	−8.84333	+	8.84333i	−0.346597	+	0.346597i
$652$	0.167237	+	0.805013i	0.00654950	+	0.0315267i
$653$	9.15667			0.358328			0.179164	−	0.983819i	$-0.442661\pi$
$653$	9.15667			0.358328			0.179164	+	0.983819i	$0.442661\pi$
$654$	−12.3494	+	15.1786i	−0.482900	+	0.593530i
$655$	−5.35720	−	16.0716i	−0.209323	−	0.627969i
$656$	−6.37279	−	14.6761i	−0.248816	−	0.573005i
$657$	−10.2544	+	10.2544i	−0.400063	+	0.400063i
$658$	27.6952	−	2.84638i	1.07967	−	0.110963i
$659$	−16.2005	+	16.2005i	−0.631083	+	0.631083i	−0.948340	−	0.317257i	$-0.897238\pi$
$659$	−16.2005	+	16.2005i	−0.631083	+	0.631083i	0.317257	+	0.948340i	$0.397238\pi$
$660$	6.68388	+	11.4975i	0.260170	+	0.447539i
$661$	30.7250	+	30.7250i	1.19506	+	1.19506i	0.975627	+	0.219436i	$0.0704216\pi$
$661$	30.7250	+	30.7250i	1.19506	+	1.19506i	0.219436	+	0.975627i	$0.429578\pi$
$662$	−8.29696	+	10.1978i	−0.322471	+	0.396347i
$663$		0			0
$664$	14.0383	+	44.2439i	0.544792	+	1.71699i
$665$	14.8222	−	29.6444i	0.574780	−	1.14956i
$666$	−10.2056	+	1.04888i	−0.395457	+	0.0406431i
$667$			7.04888i			0.272934i
$668$	−16.7222	+	25.4919i	−0.647001	+	0.986313i
$669$	−1.35720	−	1.35720i	−0.0524724	−	0.0524724i
$670$	−22.0680	−	8.33753i	−0.852562	−	0.322107i
$671$			27.8711i			1.07595i
$672$	−16.1978	−	4.54082i	−0.624842	−	0.175166i
$673$	36.3311	+	36.3311i	1.40046	+	1.40046i	0.798609	+	0.601850i	$0.205569\pi$
$673$	36.3311	+	36.3311i	1.40046	+	1.40046i	0.601850	+	0.798609i	$0.294431\pi$
$674$	29.5499	−	36.3197i	1.13822	−	1.39898i
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	−25.4565	+	5.28844i	−0.979095	+	0.203402i
$677$	7.66553			0.294610			0.147305	−	0.989091i	$-0.452940\pi$
$677$	7.66553			0.294610			0.147305	+	0.989091i	$0.452940\pi$
$678$	8.36499	−	10.2814i	0.321256	−	0.394854i
$679$			47.9900i			1.84169i
$680$	33.4663	−	24.3494i	1.28337	−	0.933757i
$681$			12.2056i			0.467718i
$682$	−13.7194	−	11.1622i	−0.525344	−	0.427423i
$683$	21.8922			0.837682			0.418841	−	0.908060i	$-0.362436\pi$
$683$	21.8922			0.837682			0.418841	+	0.908060i	$0.362436\pi$
$684$	−5.46777	+	8.33527i	−0.209065	+	0.318707i
$685$	−11.7839	−	35.3517i	−0.450239	−	1.35072i
$686$	−16.8222	−	13.6867i	−0.642275	−	0.522559i
$687$	−9.78389	−	9.78389i	−0.373279	−	0.373279i
$688$	−11.1864	+	4.85746i	−0.426477	+	0.185189i
$689$		0			0
$690$	14.3650	−	6.48693i	0.546866	−	0.246953i
$691$	30.7789	+	30.7789i	1.17088	+	1.17088i	0.981999	+	0.188884i	$0.0604869\pi$
$691$	30.7789	+	30.7789i	1.17088	+	1.17088i	0.188884	+	0.981999i	$0.439513\pi$
$692$	−36.2439	+	7.52946i	−1.37778	+	0.286227i
$693$			8.84333i			0.335930i
$694$	2.67609	+	26.0383i	0.101583	+	0.988401i
$695$	3.72999	+	11.1900i	0.141487	+	0.424460i
$696$	1.84056	−	3.55139i	0.0697661	−	0.134615i
$697$	18.5089	+	18.5089i	0.701073	+	0.701073i
$698$	−20.8980	−	17.0028i	−0.791002	−	0.643564i
$699$	−7.78389	−	7.78389i	−0.294414	−	0.294414i
$700$	29.6789	−	1.87028i	1.12176	−	0.0706898i
$701$	22.6655	−	22.6655i	0.856065	−	0.856065i	−0.134807	−	0.990872i	$-0.543041\pi$
$701$	22.6655	−	22.6655i	0.856065	−	0.856065i	0.990872	+	0.134807i	$0.0430414\pi$
$702$		0			0
$703$	−25.5678	+	25.5678i	−0.964307	+	0.964307i
$704$	4.04611	−	23.4436i	0.152493	−	0.883564i
$705$	14.0433	−	4.68111i	0.528903	−	0.176301i
$706$	7.17860	+	5.84056i	0.270170	+	0.219812i
$707$	26.3033			0.989237
$708$	7.99221	−	12.1836i	0.300366	−	0.457889i
$709$	−13.3728	+	13.3728i	−0.502226	+	0.502226i	−0.912129	−	0.409903i	$-0.865562\pi$
$709$	−13.3728	+	13.3728i	−0.502226	+	0.502226i	0.409903	+	0.912129i	$0.365562\pi$
$710$	36.7144	+	13.8711i	1.37787	+	0.520572i
$711$	12.4111			0.465453
$712$	−35.7336	+	11.3380i	−1.33917	+	0.424911i
$713$	−14.8222	+	14.8222i	−0.555096	+	0.555096i
$714$	27.3764	−	2.81361i	1.02453	−	0.105297i
$715$		0			0
$716$	−14.5166	+	22.1297i	−0.542512	+	0.827027i
$717$		−	4.41110i		−	0.164736i
$718$	0.744121	+	7.24029i	0.0277704	+	0.270205i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	−8.93124	−	0.482629i	−0.332848	−	0.0179865i
$721$	38.4877			1.43336
$722$	0.844853	+	8.22041i	0.0314422	+	0.305932i
$723$			18.8222i			0.700005i
$724$	10.9433	+	7.17860i	0.406706	+	0.266791i
$725$	−1.00000	+	7.00000i	−0.0371391	+	0.259973i
$726$	3.03402	−	0.311821i	0.112603	−	0.0115728i
$727$	−30.9149	+	30.9149i	−1.14657	+	1.14657i	−0.159349	+	0.987222i	$0.550939\pi$
$727$	−30.9149	+	30.9149i	−1.14657	+	1.14657i	−0.987222	+	0.159349i	$0.949061\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−41.7953	+	18.8738i	−1.54691	+	0.698552i
$731$	14.1078	−	14.1078i	0.521796	−	0.521796i
$732$	−15.6733	−	10.2814i	−0.579303	−	0.380011i
$733$	29.7633			1.09933			0.549666	−	0.835385i	$-0.314755\pi$
$733$	29.7633			1.09933			0.549666	+	0.835385i	$0.314755\pi$
$734$	−17.4678	−	14.2119i	−0.644747	−	0.524570i
$735$	3.68665	+	1.84333i	0.135984	+	0.0679921i
$736$	−27.1489	−	7.61083i	−1.00072	−	0.280539i
$737$	15.6867	−	15.6867i	0.577825	−	0.577825i
$738$	−0.578337	−	5.62721i	−0.0212889	−	0.207141i
$739$	31.9355	−	31.9355i	1.17477	−	1.17477i	0.193709	−	0.981059i	$-0.437948\pi$
$739$	31.9355	−	31.9355i	1.17477	−	1.17477i	0.981059	−	0.193709i	$-0.0620517\pi$
$740$	−31.3622	−	8.30330i	−1.15290	−	0.305235i
$741$		0			0
$742$	10.2978	+	8.37833i	0.378043	+	0.307578i
$743$	22.7789	+	22.7789i	0.835675	+	0.835675i	0.988286	−	0.152611i	$-0.0487681\pi$
$743$	22.7789	+	22.7789i	0.835675	+	0.835675i	−0.152611	+	0.988286i	$0.548768\pi$
$744$	11.3380	−	3.59749i	0.415673	−	0.131891i
$745$	24.7633	−	8.25443i	0.907256	−	0.302419i
$746$	0.533032	+	5.18639i	0.0195157	+	0.189887i
$747$			16.4111i			0.600451i
$748$	7.91638	+	38.1063i	0.289452	+	1.39331i
$749$	−29.6444	−	29.6444i	−1.08318	−	1.08318i
$750$	15.1857	−	4.40403i	0.554502	−	0.160813i
$751$			34.7144i			1.26675i	0.773846	+	0.633373i	$0.218330\pi$
$751$			34.7144i			1.26675i	−0.773846	+	0.633373i	$0.781670\pi$
$752$	−24.6330	−	9.71717i	−0.898274	−	0.354349i
$753$	−1.89722	−	1.89722i	−0.0691387	−	0.0691387i
$754$		0			0
$755$		0			0
$756$	−4.97305	−	3.26222i	−0.180868	−	0.118646i
$757$	3.05892			0.111178			0.0555892	−	0.998454i	$-0.482296\pi$
$757$	3.05892			0.111178			0.0555892	+	0.998454i	$0.482296\pi$
$758$	20.3111	+	16.5252i	0.737732	+	0.600224i
$759$			14.8222i			0.538012i
$760$	−25.4905	+	18.5464i	−0.924637	+	0.672747i
$761$		−	20.0766i		−	0.727777i	−0.931442	−	0.363889i	$-0.881449\pi$
$761$		−	20.0766i		−	0.727777i	0.931442	−	0.363889i	$-0.118551\pi$
$762$	−2.39471	+	2.94333i	−0.0867513	+	0.106626i
$763$	−41.1466			−1.48961
$764$	7.74914	+	37.3013i	0.280354	+	1.34951i
$765$	13.8816	−	4.62721i	0.501892	−	0.167297i
$766$	10.6980	−	13.1489i	0.386535	−	0.475088i
$767$		0			0
$768$	11.6909	+	10.9234i	0.421861	+	0.394166i
$769$		−	27.6655i		−	0.997644i	−0.866704	−	0.498822i	$-0.833766\pi$
$769$		−	27.6655i		−	0.997644i	0.866704	−	0.498822i	$-0.166234\pi$
$770$	−9.88361	+	26.1602i	−0.356181	+	0.942750i
$771$	4.52946	+	4.52946i	0.163125	+	0.163125i
$772$	−17.5272	−	11.4975i	−0.630818	−	0.413804i
$773$			17.0388i			0.612844i	0.951896	+	0.306422i	$0.0991319\pi$
$773$			17.0388i			0.612844i	−0.951896	+	0.306422i	$0.900868\pi$
$774$	−4.28917	+	0.440820i	−0.154171	+	0.0158449i
$775$	−16.8222	+	12.6167i	−0.604271	+	0.453203i
$776$	21.0028	−	40.5252i	0.753955	−	1.45477i
$777$	−15.2544	−	15.2544i	−0.547249	−	0.547249i
$778$	−0.321141	+	0.394713i	−0.0115135	+	0.0141512i
$779$	−14.0978	−	14.0978i	−0.505104	−	0.505104i
$780$		0			0
$781$	−26.0978	+	26.0978i	−0.933851	+	0.933851i
$782$	45.8852	−	4.71585i	1.64085	−	0.168639i
$783$	1.00000	−	1.00000i	0.0357371	−	0.0357371i
$784$	−2.93678	−	6.76320i	−0.104885	−	0.241543i
$785$	8.50885	−	17.0177i	0.303694	−	0.607388i
$786$	−6.76196	+	8.31109i	−0.241191	+	0.296447i
$787$	−14.3799			−0.512589			−0.256295	−	0.966599i	$-0.582502\pi$
$787$	−14.3799			−0.512589			−0.256295	+	0.966599i	$0.582502\pi$
$788$	30.6761	−	6.37279i	1.09279	−	0.227021i
$789$	0.0644618	−	0.0644618i	0.00229490	−	0.00229490i
$790$	36.7144	+	13.8711i	1.30624	+	0.493511i
$791$	27.8711			0.990981
$792$	3.87028	−	7.46777i	0.137524	−	0.265356i
$793$		0			0
$794$	2.49472	+	24.2736i	0.0885343	+	0.861437i
$795$	6.31335	+	3.15667i	0.223911	+	0.111956i
$796$	−3.17081	−	15.2630i	−0.112386	−	0.540983i
$797$			6.52998i			0.231304i	0.993290	+	0.115652i	$0.0368957\pi$
$797$			6.52998i			0.231304i	−0.993290	+	0.115652i	$0.963104\pi$
$798$	−20.8519	+	2.14306i	−0.738150	+	0.0758634i
$799$	43.3210			1.53259
$800$	−25.8809	−	11.4096i	−0.915028	−	0.403389i
$801$	−13.2544			−0.468322
$802$	10.6464	−	1.09418i	0.375936	−	0.0386369i
$803$		−	43.1255i		−	1.52187i
$804$	3.03474	+	14.6081i	0.107027	+	0.515186i
$805$	29.6444	+	14.8222i	1.04483	+	0.522414i
$806$		0			0
$807$	−12.6655	+	12.6655i	−0.445848	+	0.445848i
$808$	−22.2119	−	11.5116i	−0.781412	−	0.404977i
$809$	43.8399			1.54133			0.770664	−	0.637241i	$-0.219924\pi$
$809$	43.8399			1.54133			0.770664	+	0.637241i	$0.219924\pi$
$810$	−2.95819	−	1.11763i	−0.103940	−	0.0392697i
$811$	26.5733	−	26.5733i	0.933115	−	0.933115i	−0.0647841	−	0.997899i	$-0.520636\pi$
$811$	26.5733	−	26.5733i	0.933115	−	0.933115i	0.997899	+	0.0647841i	$0.0206359\pi$
$812$	8.23527	−	1.71083i	0.289001	−	0.0600384i
$813$	−7.79445			−0.273363
$814$	19.2544	−	23.6655i	0.674867	−	0.829476i
$815$	−0.411100	+	0.822200i	−0.0144002	+	0.0288004i
$816$	−24.3494	−	9.60529i	−0.852400	−	0.336252i
$817$	−10.7456	+	10.7456i	−0.375940	+	0.375940i
$818$	4.71585	−	0.484672i	0.164886	−	0.0169462i
$819$		0			0
$820$	4.57834	−	17.2927i	0.159882	−	0.603889i
$821$	−14.7633	−	14.7633i	−0.515242	−	0.515242i	0.400886	−	0.916128i	$-0.368702\pi$
$821$	−14.7633	−	14.7633i	−0.515242	−	0.515242i	−0.916128	+	0.400886i	$0.868702\pi$
$822$	−14.8738	+	18.2814i	−0.518785	+	0.637636i
$823$	18.0927	+	18.0927i	0.630673	+	0.630673i	0.948237	−	0.317564i	$-0.102865\pi$
$823$	18.0927	+	18.0927i	0.630673	+	0.630673i	−0.317564	+	0.948237i	$0.602865\pi$
$824$	−32.5011	−	16.8441i	−1.13223	−	0.586793i
$825$	−2.10278	+	14.7194i	−0.0732092	+	0.512465i
$826$	30.4791	−	3.13249i	1.06050	−	0.108993i
$827$			6.31335i			0.219537i	0.993957	+	0.109768i	$0.0350109\pi$
$827$			6.31335i			0.219537i	−0.993957	+	0.109768i	$0.964989\pi$
$828$	−8.33527	−	5.46777i	−0.289671	−	0.190018i
$829$	−24.2927	−	24.2927i	−0.843722	−	0.843722i	0.145619	−	0.989341i	$-0.453483\pi$
$829$	−24.2927	−	24.2927i	−0.843722	−	0.843722i	−0.989341	+	0.145619i	$0.953483\pi$
$830$	−18.3416	+	48.5472i	−0.636647	+	1.68510i
$831$			17.5678i			0.609419i
$832$		0			0
$833$	8.52946	+	8.52946i	0.295528	+	0.295528i
$834$	4.70806	−	5.78666i	0.163027	−	0.200376i
$835$	−32.3366	+	10.7789i	−1.11905	+	0.373018i
$836$	−6.02972	−	29.0247i	−0.208542	−	1.00384i
$837$	4.20555			0.145365
$838$	1.19419	−	1.46777i	0.0412525	−	0.0507032i
$839$		−	19.2645i		−	0.665083i	−0.943089	−	0.332542i	$-0.892094\pi$
$839$		−	19.2645i		−	0.665083i	0.943089	−	0.332542i	$-0.107906\pi$
$840$	−11.0653	−	15.2083i	−0.381788	−	0.524737i
$841$		−	27.0000i		−	0.931034i
$842$	30.6925	+	24.9716i	1.05773	+	0.860578i
$843$	−19.2544			−0.663158
$844$	−15.5458	−	10.1978i	−0.535110	−	0.351021i
$845$	−26.0000	−	13.0000i	−0.894427	−	0.447214i
$846$	−7.26222	−	5.90859i	−0.249680	−	0.203141i
$847$	4.53500	+	4.53500i	0.155824	+	0.155824i
$848$	−5.02920	−	11.5819i	−0.172704	−	0.397724i
$849$			17.3622i			0.595870i
$850$	46.2361	+	1.82642i	1.58588	+	0.0626458i
$851$	−25.5678	−	25.5678i	−0.876452	−	0.876452i
$852$	−5.04888	−	24.3033i	−0.172972	−	0.832617i
$853$		−	45.2544i		−	1.54948i	−0.632279	−	0.774741i	$-0.717880\pi$
$853$		−	45.2544i		−	1.54948i	0.632279	−	0.774741i	$-0.282120\pi$
$854$	−4.02972	−	39.2091i	−0.137894	−	1.34171i
$855$	−10.5733	+	3.52444i	−0.361600	+	0.120533i
$856$	12.0594	+	38.0071i	0.412183	+	1.29906i
$857$	17.0383	+	17.0383i	0.582018	+	0.582018i	0.935457	−	0.353440i	$-0.114988\pi$
$857$	17.0383	+	17.0383i	0.582018	+	0.582018i	−0.353440	+	0.935457i	$0.614988\pi$
$858$		0			0
$859$	−11.3088	−	11.3088i	−0.385853	−	0.385853i	0.487353	−	0.873205i	$-0.337963\pi$
$859$	−11.3088	−	11.3088i	−0.385853	−	0.385853i	−0.873205	+	0.487353i	$0.837963\pi$
$860$	−13.1809	−	3.48970i	−0.449463	−	0.118998i
$861$	8.41110	−	8.41110i	0.286650	−	0.286650i
$862$	1.23475	+	12.0141i	0.0420559	+	0.409203i
$863$	0.681112	−	0.681112i	0.0231853	−	0.0231853i	−0.695419	−	0.718604i	$-0.744781\pi$
$863$	0.681112	−	0.681112i	0.0231853	−	0.0231853i	0.718604	+	0.695419i	$0.244781\pi$
$864$	2.77180	+	4.93124i	0.0942985	+	0.167764i
$865$	−37.0177	−	18.5089i	−1.25864	−	0.629320i
$866$	0.243062	+	0.197757i	0.00825960	+	0.00672006i
$867$	25.8222			0.876968
$868$	20.9144	+	13.7194i	0.709881	+	0.465668i
$869$	−26.0978	+	26.0978i	−0.885306	+	0.885306i
$870$	4.07583	−	1.84056i	0.138183	−	0.0624007i
$871$		0			0
$872$	34.7464	+	18.0078i	1.17666	+	0.609821i
$873$	11.4111	−	11.4111i	0.386207	−	0.386207i
$874$	−34.9497	+	3.59195i	−1.18219	+	0.121500i
$875$	27.3361	+	18.9250i	0.924128	+	0.639781i
$876$	24.2517	+	15.9086i	0.819388	+	0.537501i
$877$		−	32.5089i		−	1.09775i	−0.835906	−	0.548873i	$-0.815057\pi$
$877$		−	32.5089i		−	1.09775i	0.835906	−	0.548873i	$-0.184943\pi$
$878$	3.22471	+	31.3764i	0.108829	+	1.05890i
$879$	−4.31335			−0.145486
$880$	19.7953	−	17.7655i	0.667298	−	0.598876i
$881$	−1.05892			−0.0356760			−0.0178380	−	0.999841i	$-0.505678\pi$
$881$	−1.05892			−0.0356760			−0.0178380	+	0.999841i	$0.505678\pi$
$882$	−0.266516	−	2.59320i	−0.00897406	−	0.0873175i
$883$		−	23.7422i		−	0.798987i	−0.916736	−	0.399494i	$-0.869186\pi$
$883$		−	23.7422i		−	0.798987i	0.916736	−	0.399494i	$-0.130814\pi$
$884$		0			0
$885$	15.4550	−	5.15165i	0.519513	−	0.173171i
$886$	−15.6514	+	1.60857i	−0.525819	+	0.0540411i
$887$	−11.5244	+	11.5244i	−0.386953	+	0.386953i	−0.873599	−	0.486646i	$-0.838220\pi$
$887$	−11.5244	+	11.5244i	−0.386953	+	0.386953i	0.486646	+	0.873599i	$0.338220\pi$
$888$	6.20555	+	19.5577i	0.208245	+	0.656314i
$889$	−7.97887			−0.267603
$890$	−39.2091	−	14.8136i	−1.31429	−	0.496553i
$891$	2.10278	−	2.10278i	0.0704456	−	0.0704456i
$892$	−2.10554	+	3.20977i	−0.0704989	+	0.107471i
$893$	−32.9966			−1.10419
$894$	−12.8058	−	10.4189i	−0.428290	−	0.348460i
$895$	−28.0716	+	9.35720i	−0.938330	+	0.312777i
$896$	−2.30250	+	33.5655i	−0.0769212	+	1.12135i
$897$		0			0
$898$	−2.56829	−	24.9894i	−0.0857050	−	0.833908i
$899$	−4.20555	+	4.20555i	−0.140263	+	0.140263i
$900$	−7.50179	−	6.61235i	−0.250060	−	0.220412i
$901$	14.6066	+	14.6066i	0.486617	+	0.486617i
$902$	13.0489	+	10.6167i	0.434480	+	0.353496i
$903$	−6.41110	−	6.41110i	−0.213348	−	0.213348i
$904$	−23.5358	−	12.1978i	−0.782789	−	0.405691i
$905$	4.62721	+	13.8816i	0.153814	+	0.461441i
$906$		0			0
$907$		−	26.5089i		−	0.880212i	−0.897946	−	0.440106i	$-0.854941\pi$
$907$		−	26.5089i		−	0.880212i	0.897946	−	0.440106i	$-0.145059\pi$
$908$	23.9008	−	4.96526i	0.793176	−	0.164778i
$909$	−6.25443	−	6.25443i	−0.207446	−	0.207446i
$910$		0			0
$911$			1.77332i			0.0587529i	0.999568	+	0.0293764i	$0.00935215\pi$
$911$			1.77332i			0.0587529i	−0.999568	+	0.0293764i	$0.990648\pi$
$912$	18.5464	+	7.31612i	0.614131	+	0.242261i
$913$	−34.5089	−	34.5089i	−1.14208	−	1.14208i
$914$	−5.29194	−	4.30556i	−0.175042	−	0.142415i
$915$	−6.62721	−	19.8816i	−0.219089	−	0.657267i
$916$	−15.1786	+	23.1388i	−0.501515	+	0.764529i
$917$	−22.5300			−0.744005
$918$	−7.17860	−	5.84056i	−0.236929	−	0.192767i
$919$			19.1255i			0.630892i	0.948944	+	0.315446i	$0.102154\pi$
$919$			19.1255i			0.630892i	−0.948944	+	0.315446i	$0.897846\pi$
$920$	−18.5464	−	25.4905i	−0.611456	−	0.840397i
$921$			19.0489i			0.627682i
$922$	4.85112	−	5.96249i	0.159763	−	0.196364i
$923$		0			0
$924$	17.3169	−	3.59749i	0.569685	−	0.118349i
$925$	−21.7633	−	29.0177i	−0.715572	−	0.954096i
$926$	26.9575	−	33.1333i	0.885877	−	1.08883i
$927$	−9.15165	−	9.15165i	−0.300580	−	0.300580i
$928$	−7.70304	−	2.15944i	−0.252865	−	0.0708872i
$929$		−	14.6277i		−	0.479920i	−0.970783	−	0.239960i	$-0.922866\pi$
$929$		−	14.6277i		−	0.479920i	0.970783	−	0.239960i	$-0.0771344\pi$
$930$	12.4408	+	4.70027i	0.407951	+	0.154128i
$931$	−6.49669	−	6.49669i	−0.212920	−	0.212920i
$932$	−12.0758	+	18.4088i	−0.395557	+	0.603002i
$933$			18.0978i			0.592494i
$934$	−8.86751	+	0.911358i	−0.290154	+	0.0298206i
$935$	−19.4600	+	38.9200i	−0.636409	+	1.27282i
$936$		0			0
$937$	−3.31335	−	3.31335i	−0.108242	−	0.108242i	0.650911	−	0.759154i	$-0.274387\pi$
$937$	−3.31335	−	3.31335i	−0.108242	−	0.108242i	−0.759154	+	0.650911i	$0.774387\pi$
$938$	−19.8000	+	24.3361i	−0.646493	+	0.794601i
$939$	3.00000	+	3.00000i	0.0979013	+	0.0979013i
$940$	−14.8794	−	25.5952i	−0.485312	−	0.834825i
$941$	−13.4111	+	13.4111i	−0.437189	+	0.437189i	−0.891065	−	0.453876i	$-0.850041\pi$
$941$	−13.4111	+	13.4111i	−0.437189	+	0.437189i	0.453876	+	0.891065i	$0.350041\pi$
$942$	−11.9703	+	1.23025i	−0.390013	+	0.0400836i
$943$	14.0978	−	14.0978i	0.459086	−	0.459086i
$944$	−27.1091	−	10.6939i	−0.882327	−	0.348058i
$945$	−2.10278	−	6.30833i	−0.0684033	−	0.205210i
$946$	8.09221	−	9.94610i	0.263101	−	0.323376i
$947$	−14.9300			−0.485160			−0.242580	−	0.970131i	$-0.577994\pi$
$947$	−14.9300			−0.485160			−0.242580	+	0.970131i	$0.577994\pi$
$948$	−5.04888	−	24.3033i	−0.163980	−	0.789335i
$949$		0			0
$950$	−35.2169	−	1.39114i	−1.14259	−	0.0451346i
$951$	−11.1567			−0.361780
$952$	−16.6464	−	52.4635i	−0.539512	−	1.70035i
$953$	24.6272	−	24.6272i	0.797754	−	0.797754i	−0.184987	−	0.982741i	$-0.559224\pi$
$953$	24.6272	−	24.6272i	0.797754	−	0.797754i	0.982741	+	0.184987i	$0.0592244\pi$
$954$	−0.456405	−	4.44082i	−0.0147767	−	0.143777i
$955$	−19.0489	+	38.0978i	−0.616407	+	1.23281i
$956$	−8.63778	+	1.79445i	−0.279366	+	0.0580367i
$957$			4.20555i			0.135946i
$958$	−39.9688	+	4.10780i	−1.29133	+	0.132717i
$959$	−49.5577			−1.60030
$960$	2.68818	+	17.6854i	0.0867606	+	0.570794i
$961$	13.3133			0.429463
$962$		0			0
$963$			14.0978i			0.454294i
$964$	36.8575	−	7.65693i	1.18710	−	0.246613i
$965$	−7.41110	−	22.2333i	−0.238572	−	0.715715i
$966$	−2.14306	−	20.8519i	−0.0689517	−	0.670900i
$967$	−32.2872	+	32.2872i	−1.03829	+	1.03829i	−0.0390491	+	0.999237i	$0.512433\pi$
$967$	−32.2872	+	32.2872i	−1.03829	+	1.03829i	−0.999237	+	0.0390491i	$0.987567\pi$
$968$	−1.84485	−	5.81433i	−0.0592958	−	0.186880i
$969$	−32.6167			−1.04780
$970$	46.5097	−	21.0028i	1.49333	−	0.674358i
$971$	−27.2494	+	27.2494i	−0.874475	+	0.874475i	−0.992956	−	0.118481i	$-0.962197\pi$
$971$	−27.2494	+	27.2494i	−0.874475	+	0.874475i	0.118481	+	0.992956i	$0.462197\pi$
$972$	0.406803	+	1.95819i	0.0130482	+	0.0628090i
$973$	15.6867			0.502891
$974$	−28.9363	+	35.5655i	−0.927180	+	1.13959i
$975$		0			0
$976$	−13.7569	+	34.8738i	−0.440349	+	1.11628i
$977$	−10.5295	+	10.5295i	−0.336867	+	0.336867i	−0.855187	−	0.518320i	$-0.826558\pi$
$977$	−10.5295	+	10.5295i	−0.336867	+	0.336867i	0.518320	+	0.855187i	$0.326558\pi$
$978$	0.578337	−	0.0594386i	0.0184932	−	0.00190064i
$979$	27.8711	−	27.8711i	0.890763	−	0.890763i
$980$	2.10984	−	7.96904i	0.0673964	−	0.254562i
$981$	9.78389	+	9.78389i	0.312375	+	0.312375i
$982$	−8.64412	+	10.6244i	−0.275845	+	0.339040i
$983$	9.62219	+	9.62219i	0.306900	+	0.306900i	0.843706	−	0.536806i	$-0.180369\pi$
$983$	9.62219	+	9.62219i	0.306900	+	0.306900i	−0.536806	+	0.843706i	$0.680369\pi$
$984$	−10.7839	+	3.42166i	−0.343778	+	0.109079i
$985$	31.3311	+	15.6655i	0.998290	+	0.499145i
$986$	13.0192	−	1.33804i	0.414614	−	0.0426120i
$987$		−	19.6867i		−	0.626633i
$988$		0			0
$989$	−10.7456	−	10.7456i	−0.341689	−	0.341689i
$990$	8.57054	−	3.87028i	0.272390	−	0.123005i
$991$		−	4.01005i		−	0.127383i	−0.997970	−	0.0636917i	$-0.979713\pi$
$991$		−	4.01005i		−	0.127383i	0.997970	−	0.0636917i	$-0.0202874\pi$
$992$	−11.6569	−	20.7386i	−0.370108	−	0.658451i
$993$	6.57331	+	6.57331i	0.208598	+	0.208598i
$994$	32.9411	−	40.4877i	1.04483	−	1.28419i
$995$	7.79445	−	15.5889i	0.247101	−	0.494201i
$996$	32.1361	−	6.67609i	1.01827	−	0.211540i
$997$	−2.31335			−0.0732645			−0.0366322	−	0.999329i	$-0.511663\pi$
$997$	−2.31335			−0.0732645			−0.0366322	+	0.999329i	$0.511663\pi$
$998$	−4.44861	+	5.46777i	−0.140818	+	0.173079i
$999$			7.25443i			0.229520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.d.43.1	yes	6
3.2	odd	2		720.2.bd.e.523.3		6
4.3	odd	2		960.2.bc.d.463.1		6
5.2	odd	4		240.2.y.d.187.2	yes	6
8.3	odd	2		1920.2.bc.h.1183.1		6
8.5	even	2		1920.2.bc.g.1183.3		6
15.2	even	4		720.2.z.e.667.2		6
16.3	odd	4		240.2.y.d.163.2	✓	6
16.5	even	4		1920.2.y.h.223.1		6
16.11	odd	4		1920.2.y.g.223.3		6
16.13	even	4		960.2.y.d.943.1		6
20.7	even	4		960.2.y.d.847.1		6
40.27	even	4		1920.2.y.h.1567.1		6
40.37	odd	4		1920.2.y.g.1567.3		6
48.35	even	4		720.2.z.e.163.2		6
80.27	even	4		1920.2.bc.g.607.3		6
80.37	odd	4		1920.2.bc.h.607.1		6
80.67	even	4	inner	240.2.bc.d.67.1	yes	6
80.77	odd	4		960.2.bc.d.367.1		6
240.227	odd	4		720.2.bd.e.307.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.2	✓	6	16.3	odd	4
240.2.y.d.187.2	yes	6	5.2	odd	4
240.2.bc.d.43.1	yes	6	1.1	even	1	trivial
240.2.bc.d.67.1	yes	6	80.67	even	4	inner
720.2.z.e.163.2		6	48.35	even	4
720.2.z.e.667.2		6	15.2	even	4
720.2.bd.e.307.3		6	240.227	odd	4
720.2.bd.e.523.3		6	3.2	odd	2
960.2.y.d.847.1		6	20.7	even	4
960.2.y.d.943.1		6	16.13	even	4
960.2.bc.d.367.1		6	80.77	odd	4
960.2.bc.d.463.1		6	4.3	odd	2
1920.2.y.g.223.3		6	16.11	odd	4
1920.2.y.g.1567.3		6	40.37	odd	4
1920.2.y.h.223.1		6	16.5	even	4
1920.2.y.h.1567.1		6	40.27	even	4
1920.2.bc.g.607.3		6	80.27	even	4
1920.2.bc.g.1183.3		6	8.5	even	2
1920.2.bc.h.607.1		6	80.37	odd	4
1920.2.bc.h.1183.1		6	8.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40680 + 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 - 0.406803i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.144584 - 1.40680i) q^{6} +(2.10278 - 2.10278i) q^{7} +(-2.69597 + 0.855416i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.40680 + 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 - 0.406803i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.144584 - 1.40680i) q^{6} +(2.10278 - 2.10278i) q^{7} +(-2.69597 + 0.855416i) q^{8} -1.00000 q^{9} +(-2.95819 - 1.11763i) q^{10} +(2.10278 - 2.10278i) q^{11} +(0.406803 + 1.95819i) q^{12} +(-2.65416 + 3.26222i) q^{14} +(-1.00000 + 2.00000i) q^{15} +(3.66902 - 1.59320i) q^{16} +(-4.62721 + 4.62721i) q^{17} +(1.40680 - 0.144584i) q^{18} +(3.52444 - 3.52444i) q^{19} +(4.32318 + 1.14458i) q^{20} +(2.10278 + 2.10278i) q^{21} +(-2.65416 + 3.26222i) q^{22} +(3.52444 + 3.52444i) q^{23} +(-0.855416 - 2.69597i) q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(3.26222 - 4.97305i) q^{28} +(1.00000 + 1.00000i) q^{29} +(1.11763 - 2.95819i) q^{30} +4.20555i q^{31} +(-4.93124 + 2.77180i) q^{32} +(2.10278 + 2.10278i) q^{33} +(5.84056 - 7.17860i) q^{34} +(6.30833 - 2.10278i) q^{35} +(-1.95819 + 0.406803i) q^{36} -7.25443 q^{37} +(-4.44861 + 5.46777i) q^{38} +(-6.24736 - 0.985140i) q^{40} -4.00000i q^{41} +(-3.26222 - 2.65416i) q^{42} -3.04888 q^{43} +(3.26222 - 4.97305i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(-5.46777 - 4.44861i) q^{46} +(-4.68111 - 4.68111i) q^{47} +(1.59320 + 3.66902i) q^{48} -1.84333i q^{49} +(-4.79875 - 5.19346i) q^{50} +(-4.62721 - 4.62721i) q^{51} -3.15667i q^{53} +(0.144584 + 1.40680i) q^{54} +(6.30833 - 2.10278i) q^{55} +(-3.87028 + 7.46777i) q^{56} +(3.52444 + 3.52444i) q^{57} +(-1.55139 - 1.26222i) q^{58} +(-5.15165 - 5.15165i) q^{59} +(-1.14458 + 4.32318i) q^{60} +(-6.62721 + 6.62721i) q^{61} +(-0.608056 - 5.91638i) q^{62} +(-2.10278 + 2.10278i) q^{63} +(6.53653 - 4.61235i) q^{64} +(-3.26222 - 2.65416i) q^{66} +7.45998 q^{67} +(-7.17860 + 10.9433i) q^{68} +(-3.52444 + 3.52444i) q^{69} +(-8.57054 + 3.87028i) q^{70} -12.4111 q^{71} +(2.69597 - 0.855416i) q^{72} +(10.2544 - 10.2544i) q^{73} +(10.2056 - 1.04888i) q^{74} +(-4.00000 + 3.00000i) q^{75} +(5.46777 - 8.33527i) q^{76} -8.84333i q^{77} -12.4111 q^{79} +(8.93124 + 0.482629i) q^{80} +1.00000 q^{81} +(0.578337 + 5.62721i) q^{82} -16.4111i q^{83} +(4.97305 + 3.26222i) q^{84} +(-13.8816 + 4.62721i) q^{85} +(4.28917 - 0.440820i) q^{86} +(-1.00000 + 1.00000i) q^{87} +(-3.87028 + 7.46777i) q^{88} +13.2544 q^{89} +(2.95819 + 1.11763i) q^{90} +(8.33527 + 5.46777i) q^{92} -4.20555 q^{93} +(7.26222 + 5.90859i) q^{94} +(10.5733 - 3.52444i) q^{95} +(-2.77180 - 4.93124i) q^{96} +(-11.4111 + 11.4111i) q^{97} +(0.266516 + 2.59320i) q^{98} +(-2.10278 + 2.10278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

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