LMFDB - Embedded newform 390.2.l.c.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(53,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("390.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.l (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:	$3.11416567883$
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} + 2 x^{18} - 12 x^{17} + 6 x^{16} - 24 x^{15} + 72 x^{14} - 112 x^{13} + 189 x^{12} + \cdots + 59049 $ x^20 + 2x^18 - 12x^17 + 6x^16 - 24x^15 + 72x^14 - 112x^13 + 189x^12 - 356x^11 + 908x^10 - 1068x^9 + 1701x^8 - 3024x^7 + 5832x^6 - 5832x^5 + 4374x^4 - 26244x^3 + 13122*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Root			$-0.807075 + 1.53252i$ of defining polynomial
Character	$\chi$	$=$	390.53
Dual form			390.2.l.c.287.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.807075 + 1.53252i) q^{3} +1.00000i q^{4} +(-2.02552 + 0.947239i) q^{5} +(1.65435 - 0.512970i) q^{6} +(-1.59729 + 1.59729i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.69726 - 2.47372i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.807075 + 1.53252i) q^{3} +1.00000i q^{4} +(-2.02552 + 0.947239i) q^{5} +(1.65435 - 0.512970i) q^{6} +(-1.59729 + 1.59729i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.69726 - 2.47372i) q^{9} +(2.10206 + 0.762461i) q^{10} -2.58997i q^{11} +(-1.53252 - 0.807075i) q^{12} +(0.707107 + 0.707107i) q^{13} +2.25891 q^{14} +(0.183080 - 3.86865i) q^{15} -1.00000 q^{16} +(-0.155426 - 0.155426i) q^{17} +(-0.549041 + 2.94933i) q^{18} -6.77461i q^{19} +(-0.947239 - 2.02552i) q^{20} +(-1.15876 - 3.73703i) q^{21} +(-1.83139 + 1.83139i) q^{22} +(1.81338 - 1.81338i) q^{23} +(0.512970 + 1.65435i) q^{24} +(3.20547 - 3.83731i) q^{25} -1.00000i q^{26} +(5.16086 - 0.604615i) q^{27} +(-1.59729 - 1.59729i) q^{28} -0.890831 q^{29} +(-2.86501 + 2.60609i) q^{30} -9.39662 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.96919 + 2.09030i) q^{33} +0.219806i q^{34} +(1.72233 - 4.74837i) q^{35} +(2.47372 - 1.69726i) q^{36} +(-2.88699 + 2.88699i) q^{37} +(-4.79037 + 4.79037i) q^{38} +(-1.65435 + 0.512970i) q^{39} +(-0.762461 + 2.10206i) q^{40} -2.11082i q^{41} +(-1.82311 + 3.46184i) q^{42} +(-4.38869 - 4.38869i) q^{43} +2.58997 q^{44} +(5.78105 + 3.40287i) q^{45} -2.56451 q^{46} +(-3.71800 - 3.71800i) q^{47} +(0.807075 - 1.53252i) q^{48} +1.89731i q^{49} +(-4.98000 + 0.446773i) q^{50} +(0.363635 - 0.112754i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(-2.24202 + 2.24202i) q^{53} +(-4.07680 - 3.22175i) q^{54} +(2.45332 + 5.24604i) q^{55} +2.25891i q^{56} +(10.3823 + 5.46761i) q^{57} +(0.629912 + 0.629912i) q^{58} +2.75114 q^{59} +(3.86865 + 0.183080i) q^{60} -2.28989 q^{61} +(6.64441 + 6.64441i) q^{62} +(6.66228 + 1.24024i) q^{63} -1.00000i q^{64} +(-2.10206 - 0.762461i) q^{65} +(-1.32858 - 4.28471i) q^{66} +(-10.9926 + 10.9926i) q^{67} +(0.155426 - 0.155426i) q^{68} +(1.31552 + 4.24259i) q^{69} +(-4.57548 + 2.13973i) q^{70} -9.60806i q^{71} +(-2.94933 - 0.549041i) q^{72} +(-1.65186 - 1.65186i) q^{73} +4.08282 q^{74} +(3.29371 + 8.00946i) q^{75} +6.77461 q^{76} +(4.13694 + 4.13694i) q^{77} +(1.53252 + 0.807075i) q^{78} -12.1165i q^{79} +(2.02552 - 0.947239i) q^{80} +(-3.23861 + 8.39711i) q^{81} +(-1.49257 + 1.49257i) q^{82} +(-5.93928 + 5.93928i) q^{83} +(3.73703 - 1.15876i) q^{84} +(0.462045 + 0.167593i) q^{85} +6.20654i q^{86} +(0.718967 - 1.36522i) q^{87} +(-1.83139 - 1.83139i) q^{88} +6.43585 q^{89} +(-1.68163 - 6.49401i) q^{90} -2.25891 q^{91} +(1.81338 + 1.81338i) q^{92} +(7.58377 - 14.4005i) q^{93} +5.25805i q^{94} +(6.41718 + 13.7221i) q^{95} +(-1.65435 + 0.512970i) q^{96} +(8.84860 - 8.84860i) q^{97} +(1.34160 - 1.34160i) q^{98} +(-6.40687 + 4.39585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q - 4 * q^7 - 4 * q^9	$ 20 q - 4 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} + 16 q^{14} + 4 q^{15} - 20 q^{16} - 12 q^{17} + 8 q^{18} - 16 q^{21} + 4 q^{22} - 16 q^{23} - 4 q^{24} + 32 q^{25} + 36 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{30} - 8 q^{31} + 36 q^{33} + 20 q^{35} - 4 q^{36} - 16 q^{37} - 24 q^{38} - 8 q^{40} + 4 q^{42} - 20 q^{43} - 16 q^{44} + 24 q^{45} - 40 q^{46} - 16 q^{47} + 12 q^{51} - 32 q^{53} - 28 q^{54} - 4 q^{55} + 16 q^{57} + 28 q^{58} - 16 q^{60} + 24 q^{61} - 40 q^{62} + 36 q^{63} + 8 q^{65} + 12 q^{68} - 72 q^{69} + 20 q^{70} + 8 q^{72} + 28 q^{73} + 48 q^{74} - 52 q^{75} + 16 q^{76} - 8 q^{77} + 4 q^{78} - 16 q^{81} - 112 q^{83} - 8 q^{85} + 4 q^{87} + 4 q^{88} + 88 q^{89} - 4 q^{90} - 16 q^{91} - 16 q^{92} + 40 q^{93} + 8 q^{95} + 36 q^{97} - 40 q^{99}+O(q^{100}) $ 20 * q - 4 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 + 16 * q^14 + 4 * q^15 - 20 * q^16 - 12 * q^17 + 8 * q^18 - 16 * q^21 + 4 * q^22 - 16 * q^23 - 4 * q^24 + 32 * q^25 + 36 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^30 - 8 * q^31 + 36 * q^33 + 20 * q^35 - 4 * q^36 - 16 * q^37 - 24 * q^38 - 8 * q^40 + 4 * q^42 - 20 * q^43 - 16 * q^44 + 24 * q^45 - 40 * q^46 - 16 * q^47 + 12 * q^51 - 32 * q^53 - 28 * q^54 - 4 * q^55 + 16 * q^57 + 28 * q^58 - 16 * q^60 + 24 * q^61 - 40 * q^62 + 36 * q^63 + 8 * q^65 + 12 * q^68 - 72 * q^69 + 20 * q^70 + 8 * q^72 + 28 * q^73 + 48 * q^74 - 52 * q^75 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 16 * q^81 - 112 * q^83 - 8 * q^85 + 4 * q^87 + 4 * q^88 + 88 * q^89 - 4 * q^90 - 16 * q^91 - 16 * q^92 + 40 * q^93 + 8 * q^95 + 36 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.807075	+	1.53252i	−0.465965	+	0.884803i
$3$	−0.807075	+	1.53252i	−0.465965	+	0.884803i
$4$			1.00000i			0.500000i
$5$	−2.02552	+	0.947239i	−0.905841	+	0.423618i
$5$	−2.02552	+	0.947239i	−0.905841	+	0.423618i
$6$	1.65435	−	0.512970i	0.675384	−	0.209419i
$7$	−1.59729	+	1.59729i	−0.603720	+	0.603720i	−0.941298	−	0.337578i	$-0.890392\pi$
$7$	−1.59729	+	1.59729i	−0.603720	+	0.603720i	0.337578	+	0.941298i	$0.390392\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.69726	−	2.47372i	−0.565754	−	0.824574i
$10$	2.10206	+	0.762461i	0.664730	+	0.241111i
$11$		−	2.58997i		−	0.780905i	−0.920623	−	0.390453i	$-0.872319\pi$
$11$		−	2.58997i		−	0.780905i	0.920623	−	0.390453i	$-0.127681\pi$
$12$	−1.53252	−	0.807075i	−0.442402	−	0.232982i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	2.25891			0.603720
$15$	0.183080	−	3.86865i	0.0472710	−	0.998882i
$16$	−1.00000			−0.250000
$17$	−0.155426	−	0.155426i	−0.0376964	−	0.0376964i	0.688007	−	0.725704i	$-0.258486\pi$
$17$	−0.155426	−	0.155426i	−0.0376964	−	0.0376964i	−0.725704	+	0.688007i	$0.758486\pi$
$18$	−0.549041	+	2.94933i	−0.129410	+	0.695164i
$19$		−	6.77461i		−	1.55420i	−0.629376	−	0.777101i	$-0.716689\pi$
$19$		−	6.77461i		−	1.55420i	0.629376	−	0.777101i	$-0.283311\pi$
$20$	−0.947239	−	2.02552i	−0.211809	−	0.452920i
$21$	−1.15876	−	3.73703i	−0.252861	−	0.815486i
$22$	−1.83139	+	1.83139i	−0.390453	+	0.390453i
$23$	1.81338	−	1.81338i	0.378116	−	0.378116i	−0.492306	−	0.870422i	$-0.663846\pi$
$23$	1.81338	−	1.81338i	0.378116	−	0.378116i	0.870422	+	0.492306i	$0.163846\pi$
$24$	0.512970	+	1.65435i	0.104710	+	0.337692i
$25$	3.20547	−	3.83731i	0.641095	−	0.767462i
$26$		−	1.00000i		−	0.196116i
$27$	5.16086	−	0.604615i	0.993207	−	0.116358i
$28$	−1.59729	−	1.59729i	−0.301860	−	0.301860i
$29$	−0.890831			−0.165423			−0.0827115	−	0.996574i	$-0.526358\pi$
$29$	−0.890831			−0.165423			−0.0827115	+	0.996574i	$0.526358\pi$
$30$	−2.86501	+	2.60609i	−0.523077	+	0.475806i
$31$	−9.39662			−1.68768			−0.843841	−	0.536593i	$-0.819711\pi$
$31$	−9.39662			−1.68768			−0.843841	+	0.536593i	$0.819711\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.96919	+	2.09030i	0.690947	+	0.363874i
$34$			0.219806i			0.0376964i
$35$	1.72233	−	4.74837i	0.291127	−	0.802621i
$36$	2.47372	−	1.69726i	0.412287	−	0.282877i
$37$	−2.88699	+	2.88699i	−0.474618	+	0.474618i	−0.903405	−	0.428788i	$-0.858941\pi$
$37$	−2.88699	+	2.88699i	−0.474618	+	0.474618i	0.428788	+	0.903405i	$0.358941\pi$
$38$	−4.79037	+	4.79037i	−0.777101	+	0.777101i
$39$	−1.65435	+	0.512970i	−0.264907	+	0.0821410i
$40$	−0.762461	+	2.10206i	−0.120556	+	0.332365i
$41$		−	2.11082i		−	0.329654i	−0.986322	−	0.164827i	$-0.947293\pi$
$41$		−	2.11082i		−	0.329654i	0.986322	−	0.164827i	$-0.0527067\pi$
$42$	−1.82311	+	3.46184i	−0.281312	+	0.534174i
$43$	−4.38869	−	4.38869i	−0.669269	−	0.669269i	0.288278	−	0.957547i	$-0.406917\pi$
$43$	−4.38869	−	4.38869i	−0.669269	−	0.669269i	−0.957547	+	0.288278i	$0.906917\pi$
$44$	2.58997			0.390453
$45$	5.78105	+	3.40287i	0.861788	+	0.507269i
$46$	−2.56451			−0.378116
$47$	−3.71800	−	3.71800i	−0.542326	−	0.542326i	0.381884	−	0.924210i	$-0.375275\pi$
$47$	−3.71800	−	3.71800i	−0.542326	−	0.542326i	−0.924210	+	0.381884i	$0.875275\pi$
$48$	0.807075	−	1.53252i	0.116491	−	0.221201i
$49$			1.89731i			0.271044i
$50$	−4.98000	+	0.446773i	−0.704278	+	0.0631833i
$51$	0.363635	−	0.112754i	0.0509191	−	0.0157887i
$52$	−0.707107	+	0.707107i	−0.0980581	+	0.0980581i
$53$	−2.24202	+	2.24202i	−0.307965	+	0.307965i	−0.844120	−	0.536155i	$-0.819876\pi$
$53$	−2.24202	+	2.24202i	−0.307965	+	0.307965i	0.536155	+	0.844120i	$0.319876\pi$
$54$	−4.07680	−	3.22175i	−0.554783	−	0.438425i
$55$	2.45332	+	5.24604i	0.330806	+	0.707376i
$56$			2.25891i			0.301860i
$57$	10.3823	+	5.46761i	1.37516	+	0.724203i
$58$	0.629912	+	0.629912i	0.0827115	+	0.0827115i
$59$	2.75114			0.358169			0.179084	−	0.983834i	$-0.442687\pi$
$59$	2.75114			0.358169			0.179084	+	0.983834i	$0.442687\pi$
$60$	3.86865	+	0.183080i	0.499441	+	0.0236355i
$61$	−2.28989			−0.293191			−0.146595	−	0.989197i	$-0.546831\pi$
$61$	−2.28989			−0.293191			−0.146595	+	0.989197i	$0.546831\pi$
$62$	6.64441	+	6.64441i	0.843841	+	0.843841i
$63$	6.66228	+	1.24024i	0.839369	+	0.156255i
$64$		−	1.00000i		−	0.125000i
$65$	−2.10206	−	0.762461i	−0.260728	−	0.0945716i
$66$	−1.32858	−	4.28471i	−0.163537	−	0.527411i
$67$	−10.9926	+	10.9926i	−1.34295	+	1.34295i	−0.449850	+	0.893104i	$0.648523\pi$
$67$	−10.9926	+	10.9926i	−1.34295	+	1.34295i	−0.893104	+	0.449850i	$0.851477\pi$
$68$	0.155426	−	0.155426i	0.0188482	−	0.0188482i
$69$	1.31552	+	4.24259i	0.158370	+	0.510747i
$70$	−4.57548	+	2.13973i	−0.546874	+	0.255747i
$71$		−	9.60806i		−	1.14027i	−0.821552	−	0.570134i	$-0.806891\pi$
$71$		−	9.60806i		−	1.14027i	0.821552	−	0.570134i	$-0.193109\pi$
$72$	−2.94933	−	0.549041i	−0.347582	−	0.0647052i
$73$	−1.65186	−	1.65186i	−0.193336	−	0.193336i	0.603800	−	0.797136i	$-0.293653\pi$
$73$	−1.65186	−	1.65186i	−0.193336	−	0.193336i	−0.797136	+	0.603800i	$0.793653\pi$
$74$	4.08282			0.474618
$75$	3.29371	+	8.00946i	0.380325	+	0.924853i
$76$	6.77461			0.777101
$77$	4.13694	+	4.13694i	0.471448	+	0.471448i
$78$	1.53252	+	0.807075i	0.173524	+	0.0913832i
$79$		−	12.1165i		−	1.36321i	−0.731721	−	0.681605i	$-0.761282\pi$
$79$		−	12.1165i		−	1.36321i	0.731721	−	0.681605i	$-0.238718\pi$
$80$	2.02552	−	0.947239i	0.226460	−	0.105905i
$81$	−3.23861	+	8.39711i	−0.359846	+	0.933012i
$82$	−1.49257	+	1.49257i	−0.164827	+	0.164827i
$83$	−5.93928	+	5.93928i	−0.651921	+	0.651921i	−0.953455	−	0.301534i	$-0.902501\pi$
$83$	−5.93928	+	5.93928i	−0.651921	+	0.651921i	0.301534	+	0.953455i	$0.402501\pi$
$84$	3.73703	−	1.15876i	0.407743	−	0.126431i
$85$	0.462045	+	0.167593i	0.0501158	+	0.0181780i
$86$			6.20654i			0.669269i
$87$	0.718967	−	1.36522i	0.0770813	−	0.146367i
$88$	−1.83139	−	1.83139i	−0.195226	−	0.195226i
$89$	6.43585			0.682199			0.341099	−	0.940027i	$-0.389201\pi$
$89$	6.43585			0.682199			0.341099	+	0.940027i	$0.389201\pi$
$90$	−1.68163	−	6.49401i	−0.177259	−	0.684528i
$91$	−2.25891			−0.236798
$92$	1.81338	+	1.81338i	0.189058	+	0.189058i
$93$	7.58377	−	14.4005i	0.786400	−	1.49327i
$94$			5.25805i			0.542326i
$95$	6.41718	+	13.7221i	0.658388	+	1.40786i
$96$	−1.65435	+	0.512970i	−0.168846	+	0.0523548i
$97$	8.84860	−	8.84860i	0.898439	−	0.898439i	−0.0968592	−	0.995298i	$-0.530880\pi$
$97$	8.84860	−	8.84860i	0.898439	−	0.898439i	0.995298	+	0.0968592i	$0.0308796\pi$
$98$	1.34160	−	1.34160i	0.135522	−	0.135522i
$99$	−6.40687	+	4.39585i	−0.643914	+	0.441800i
$100$	3.83731	+	3.20547i	0.383731	+	0.320547i
$101$			16.1955i			1.61151i	0.592246	+	0.805757i	$0.298241\pi$
$101$			16.1955i			1.61151i	−0.592246	+	0.805757i	$0.701759\pi$
$102$	−0.336858	−	0.177400i	−0.0333539	−	0.0175652i
$103$	11.4202	+	11.4202i	1.12526	+	1.12526i	0.990937	+	0.134326i	$0.0428869\pi$
$103$	11.4202	+	11.4202i	1.12526	+	1.12526i	0.134326	+	0.990937i	$0.457113\pi$
$104$	1.00000			0.0980581
$105$	5.88694	+	6.47181i	0.574507	+	0.631584i
$106$	3.17070			0.307965
$107$	−10.0756	−	10.0756i	−0.974043	−	0.974043i	0.0256290	−	0.999672i	$-0.491841\pi$
$107$	−10.0756	−	10.0756i	−0.974043	−	0.974043i	−0.999672	+	0.0256290i	$0.991841\pi$
$108$	0.604615	+	5.16086i	0.0581791	+	0.496604i
$109$		−	9.17905i		−	0.879194i	−0.898195	−	0.439597i	$-0.855121\pi$
$109$		−	9.17905i		−	0.879194i	0.898195	−	0.439597i	$-0.144879\pi$
$110$	1.97475	−	5.44427i	0.188285	−	0.519091i
$111$	−2.09436	−	6.75439i	−0.198788	−	0.641098i
$112$	1.59729	−	1.59729i	0.150930	−	0.150930i
$113$	7.84170	−	7.84170i	0.737685	−	0.737685i	−0.234444	−	0.972130i	$-0.575327\pi$
$113$	7.84170	−	7.84170i	0.737685	−	0.737685i	0.972130	+	0.234444i	$0.0753271\pi$
$114$	−3.47517	−	11.2075i	−0.325480	−	1.04968i
$115$	−1.95534	+	5.39075i	−0.182336	+	0.502690i
$116$		−	0.890831i		−	0.0827115i
$117$	0.549041	−	2.94933i	0.0507589	−	0.272666i
$118$	−1.94535	−	1.94535i	−0.179084	−	0.179084i
$119$	0.496523			0.0455161
$120$	−2.60609	−	2.86501i	−0.237903	−	0.261538i
$121$	4.29206			0.390187
$122$	1.61920	+	1.61920i	0.146595	+	0.146595i
$123$	3.23488	+	1.70359i	0.291679	+	0.153607i
$124$		−	9.39662i		−	0.843841i
$125$	−2.85791	+	10.8089i	−0.255619	+	0.966778i
$126$	−3.83397	−	5.58793i	−0.341557	−	0.497812i
$127$	−8.05797	+	8.05797i	−0.715029	+	0.715029i	−0.967583	−	0.252554i	$-0.918729\pi$
$127$	−8.05797	+	8.05797i	−0.715029	+	0.715029i	0.252554	+	0.967583i	$0.418729\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.2678	−	3.18377i	0.904027	−	0.280315i
$130$	0.947239	+	2.02552i	0.0830784	+	0.177650i
$131$			14.2078i			1.24134i	0.784071	+	0.620671i	$0.213140\pi$
$131$			14.2078i			1.24134i	−0.784071	+	0.620671i	$0.786860\pi$
$132$	−2.09030	+	3.96919i	−0.181937	+	0.345474i
$133$	10.8210	+	10.8210i	0.938303	+	0.938303i
$134$	15.5458			1.34295
$135$	−9.88071	+	6.11323i	−0.850396	+	0.526143i
$136$	−0.219806			−0.0188482
$137$	−10.9549	−	10.9549i	−0.935939	−	0.935939i	0.0621288	−	0.998068i	$-0.480211\pi$
$137$	−10.9549	−	10.9549i	−0.935939	−	0.935939i	−0.998068	+	0.0621288i	$0.980211\pi$
$138$	2.06975	−	3.93017i	0.176189	−	0.334558i
$139$		−	15.0559i		−	1.27703i	−0.769611	−	0.638513i	$-0.779550\pi$
$139$		−	15.0559i		−	1.27703i	0.769611	−	0.638513i	$-0.220450\pi$
$140$	4.74837	+	1.72233i	0.401311	+	0.145564i
$141$	8.69863	−	2.69722i	0.732557	−	0.227147i
$142$	−6.79393	+	6.79393i	−0.570134	+	0.570134i
$143$	1.83139	−	1.83139i	0.153148	−	0.153148i
$144$	1.69726	+	2.47372i	0.141438	+	0.206144i
$145$	1.80440	−	0.843830i	0.149847	−	0.0700763i
$146$			2.33609i			0.193336i
$147$	−2.90767	−	1.53127i	−0.239821	−	0.126297i
$148$	−2.88699	−	2.88699i	−0.237309	−	0.237309i
$149$	−15.7204			−1.28787			−0.643934	−	0.765081i	$-0.722699\pi$
$149$	−15.7204			−1.28787			−0.643934	+	0.765081i	$0.722699\pi$
$150$	3.33454	−	7.99255i	0.272264	−	0.652589i
$151$	−14.3294			−1.16611			−0.583056	−	0.812432i	$-0.698143\pi$
$151$	−14.3294			−1.16611			−0.583056	+	0.812432i	$0.698143\pi$
$152$	−4.79037	−	4.79037i	−0.388550	−	0.388550i
$153$	−0.120683	+	0.648280i	−0.00975661	+	0.0524104i
$154$		−	5.85052i		−	0.471448i
$155$	19.0330	−	8.90085i	1.52877	−	0.714933i
$156$	−0.512970	−	1.65435i	−0.0410705	−	0.132454i
$157$	−9.89671	+	9.89671i	−0.789843	+	0.789843i	−0.981468	−	0.191625i	$-0.938624\pi$
$157$	−9.89671	+	9.89671i	−0.789843	+	0.789843i	0.191625	+	0.981468i	$0.438624\pi$
$158$	−8.56764	+	8.56764i	−0.681605	+	0.681605i
$159$	−1.62647	−	5.24543i	−0.128988	−	0.415990i
$160$	−2.10206	−	0.762461i	−0.166182	−	0.0602778i
$161$			5.79300i			0.456553i
$162$	8.22769	−	3.64761i	0.646429	−	0.286583i
$163$	−9.12788	−	9.12788i	−0.714951	−	0.714951i	0.252616	−	0.967567i	$-0.418709\pi$
$163$	−9.12788	−	9.12788i	−0.714951	−	0.714951i	−0.967567	+	0.252616i	$0.918709\pi$
$164$	2.11082			0.164827
$165$	−10.0197	−	0.474171i	−0.780032	−	0.0369141i
$166$	8.39941			0.651921
$167$	−13.1748	−	13.1748i	−1.01950	−	1.01950i	−0.999806	−	0.0196916i	$-0.993732\pi$
$167$	−13.1748	−	13.1748i	−1.01950	−	1.01950i	−0.0196916	−	0.999806i	$-0.506268\pi$
$168$	−3.46184	−	1.82311i	−0.267087	−	0.140656i
$169$			1.00000i			0.0769231i
$170$	−0.208209	−	0.445222i	−0.0159689	−	0.0341469i
$171$	−16.7585	+	11.4983i	−1.28155	+	0.879295i
$172$	4.38869	−	4.38869i	0.334634	−	0.334634i
$173$	−11.0567	+	11.0567i	−0.840628	+	0.840628i	−0.988941	−	0.148312i	$-0.952616\pi$
$173$	−11.0567	+	11.0567i	−0.840628	+	0.840628i	0.148312	+	0.988941i	$0.452616\pi$
$174$	−1.47374	+	0.456970i	−0.111724	+	0.0346428i
$175$	1.00922	+	11.2494i	0.0762900	+	0.850374i
$176$			2.58997i			0.195226i
$177$	−2.22038	+	4.21620i	−0.166894	+	0.316909i
$178$	−4.55083	−	4.55083i	−0.341099	−	0.341099i
$179$	−11.4964			−0.859281			−0.429641	−	0.903000i	$-0.641360\pi$
$179$	−11.4964			−0.859281			−0.429641	+	0.903000i	$0.641360\pi$
$180$	−3.40287	+	5.78105i	−0.253635	+	0.430894i
$181$	17.6773			1.31394			0.656970	−	0.753917i	$-0.271838\pi$
$181$	17.6773			1.31394			0.656970	+	0.753917i	$0.271838\pi$
$182$	1.59729	+	1.59729i	0.118399	+	0.118399i
$183$	1.84811	−	3.50931i	0.136616	−	0.259416i
$184$		−	2.56451i		−	0.189058i
$185$	3.11299	−	8.58232i	0.228871	−	0.630985i
$186$	−15.5453	+	4.82019i	−1.13983	+	0.353433i
$187$	−0.402549	+	0.402549i	−0.0294373	+	0.0294373i
$188$	3.71800	−	3.71800i	0.271163	−	0.271163i
$189$	−7.27765	+	9.20915i	−0.529371	+	0.669867i
$190$	5.16537	−	14.2406i	0.374735	−	1.03312i
$191$		−	18.0153i		−	1.30354i	−0.758416	−	0.651771i	$-0.774026\pi$
$191$		−	18.0153i		−	1.30354i	0.758416	−	0.651771i	$-0.225974\pi$
$192$	1.53252	+	0.807075i	0.110600	+	0.0582456i
$193$	3.58559	+	3.58559i	0.258097	+	0.258097i	0.824280	−	0.566183i	$-0.191580\pi$
$193$	3.58559	+	3.58559i	0.258097	+	0.258097i	−0.566183	+	0.824280i	$0.691580\pi$
$194$	−12.5138			−0.898439
$195$	2.86501	−	2.60609i	0.205167	−	0.186626i
$196$	−1.89731			−0.135522
$197$	−11.8377	−	11.8377i	−0.843398	−	0.843398i	0.145901	−	0.989299i	$-0.453392\pi$
$197$	−11.8377	−	11.8377i	−0.843398	−	0.843398i	−0.989299	+	0.145901i	$0.953392\pi$
$198$	7.63868	+	1.42200i	0.542857	+	0.101057i
$199$			6.88147i			0.487814i	0.969799	+	0.243907i	$0.0784292\pi$
$199$			6.88147i			0.487814i	−0.969799	+	0.243907i	$0.921571\pi$
$200$	−0.446773	−	4.98000i	−0.0315916	−	0.352139i
$201$	−7.97454	−	25.7182i	−0.562481	−	1.81402i
$202$	11.4520	−	11.4520i	0.805757	−	0.805757i
$203$	1.42292	−	1.42292i	0.0998692	−	0.0998692i
$204$	0.112754	+	0.363635i	0.00789435	+	0.0254595i
$205$	1.99945	+	4.27551i	0.139648	+	0.298614i
$206$		−	16.1506i		−	1.12526i
$207$	−7.56358	−	1.40802i	−0.525705	−	0.0978643i
$208$	−0.707107	−	0.707107i	−0.0490290	−	0.0490290i
$209$	−17.5460			−1.21368
$210$	0.413561	−	8.73895i	0.0285384	−	0.603045i
$211$	−7.30339			−0.502786			−0.251393	−	0.967885i	$-0.580889\pi$
$211$	−7.30339			−0.502786			−0.251393	+	0.967885i	$0.580889\pi$
$212$	−2.24202	−	2.24202i	−0.153983	−	0.153983i
$213$	14.7246	+	7.75442i	1.00891	+	0.531324i
$214$			14.2490i			0.974043i
$215$	13.0465	+	4.73224i	0.889765	+	0.322736i
$216$	3.22175	−	4.07680i	0.219212	−	0.277391i
$217$	15.0092	−	15.0092i	1.01889	−	1.01889i
$218$	−6.49057	+	6.49057i	−0.439597	+	0.439597i
$219$	3.86470	−	1.19834i	0.261152	−	0.0809765i
$220$	−5.24604	+	2.45332i	−0.353688	+	0.165403i
$221$		−	0.219806i		−	0.0147857i
$222$	−3.29514	+	6.25701i	−0.221155	+	0.419943i
$223$	16.1979	+	16.1979i	1.08469	+	1.08469i	0.996065	+	0.0886232i	$0.0282467\pi$
$223$	16.1979	+	16.1979i	1.08469	+	1.08469i	0.0886232	+	0.996065i	$0.471753\pi$
$224$	−2.25891			−0.150930
$225$	−14.9330	−	1.41654i	−0.995531	−	0.0944362i
$226$	−11.0898			−0.737685
$227$	−17.2226	−	17.2226i	−1.14310	−	1.14310i	−0.987879	−	0.155223i	$-0.950390\pi$
$227$	−17.2226	−	17.2226i	−1.14310	−	1.14310i	−0.155223	−	0.987879i	$-0.549610\pi$
$228$	−5.46761	+	10.3823i	−0.362102	+	0.687581i
$229$			23.5974i			1.55936i	0.626177	+	0.779681i	$0.284619\pi$
$229$			23.5974i			1.55936i	−0.626177	+	0.779681i	$0.715381\pi$
$230$	5.19447	−	2.42920i	0.342513	−	0.160177i
$231$	−9.67878	+	3.00114i	−0.636817	+	0.197461i
$232$	−0.629912	+	0.629912i	−0.0413558	+	0.0413558i
$233$	−7.44530	+	7.44530i	−0.487758	+	0.487758i	−0.907598	−	0.419840i	$-0.862086\pi$
$233$	−7.44530	+	7.44530i	−0.487758	+	0.487758i	0.419840	+	0.907598i	$0.362086\pi$
$234$	−2.47372	+	1.69726i	−0.161712	+	0.110953i
$235$	11.0527	+	4.00905i	0.721000	+	0.261522i
$236$			2.75114i			0.179084i
$237$	18.5688	+	9.77889i	1.20617	+	0.635207i
$238$	−0.351094	−	0.351094i	−0.0227581	−	0.0227581i
$239$	19.2221			1.24337			0.621687	−	0.783266i	$-0.286448\pi$
$239$	19.2221			1.24337			0.621687	+	0.783266i	$0.286448\pi$
$240$	−0.183080	+	3.86865i	−0.0118177	+	0.249721i
$241$	16.0808			1.03586			0.517928	−	0.855424i	$-0.326704\pi$
$241$	16.0808			1.03586			0.517928	+	0.855424i	$0.326704\pi$
$242$	−3.03494	−	3.03494i	−0.195094	−	0.195094i
$243$	−10.2550	−	11.7403i	−0.657857	−	0.753143i
$244$		−	2.28989i		−	0.146595i
$245$	−1.79721	−	3.84304i	−0.114819	−	0.245523i
$246$	−1.08279	−	3.49202i	−0.0690360	−	0.222643i
$247$	4.79037	−	4.79037i	0.304804	−	0.304804i
$248$	−6.64441	+	6.64441i	−0.421921	+	0.421921i
$249$	−4.30865	−	13.8955i	−0.273050	−	0.880594i
$250$	9.66389	−	5.62220i	0.611198	−	0.355579i
$251$			25.4480i			1.60626i	0.595801	+	0.803132i	$0.296835\pi$
$251$			25.4480i			1.60626i	−0.595801	+	0.803132i	$0.703165\pi$
$252$	−1.24024	+	6.66228i	−0.0781276	+	0.419684i
$253$	−4.69660	−	4.69660i	−0.295273	−	0.295273i
$254$	11.3957			0.715029
$255$	−0.629746	+	0.572835i	−0.0394362	+	0.0358723i
$256$	1.00000			0.0625000
$257$	12.1316	+	12.1316i	0.756749	+	0.756749i	0.975729	−	0.218980i	$-0.0702731\pi$
$257$	12.1316	+	12.1316i	0.756749	+	0.756749i	−0.218980	+	0.975729i	$0.570273\pi$
$258$	−9.51167	−	5.00914i	−0.592171	−	0.311856i
$259$		−	9.22273i		−	0.573073i
$260$	0.762461	−	2.10206i	0.0472858	−	0.130364i
$261$	1.51197	+	2.20367i	0.0935887	+	0.136404i
$262$	10.0464	−	10.0464i	0.620671	−	0.620671i
$263$	3.81582	−	3.81582i	0.235294	−	0.235294i	−0.579604	−	0.814898i	$-0.696793\pi$
$263$	3.81582	−	3.81582i	0.235294	−	0.235294i	0.814898	+	0.579604i	$0.196793\pi$
$264$	4.28471	−	1.32858i	0.263705	−	0.0817683i
$265$	2.41753	−	6.66499i	0.148508	−	0.409427i
$266$		−	15.3033i		−	0.938303i
$267$	−5.19421	+	9.86310i	−0.317881	+	0.603612i
$268$	−10.9926	−	10.9926i	−0.671477	−	0.671477i
$269$	−2.98732			−0.182140			−0.0910701	−	0.995844i	$-0.529029\pi$
$269$	−2.98732			−0.182140			−0.0910701	+	0.995844i	$0.529029\pi$
$270$	11.3094	+	2.66401i	0.688270	+	0.162127i
$271$	17.9161			1.08832			0.544162	−	0.838980i	$-0.316848\pi$
$271$	17.9161			1.08832			0.544162	+	0.838980i	$0.316848\pi$
$272$	0.155426	+	0.155426i	0.00942410	+	0.00942410i
$273$	1.82311	−	3.46184i	0.110340	−	0.209520i
$274$			15.4926i			0.935939i
$275$	−9.93851	−	8.30208i	−0.599315	−	0.500634i
$276$	−4.24259	+	1.31552i	−0.255374	+	0.0791848i
$277$	11.8188	−	11.8188i	0.710120	−	0.710120i	−0.256440	−	0.966560i	$-0.582550\pi$
$277$	11.8188	−	11.8188i	0.710120	−	0.710120i	0.966560	+	0.256440i	$0.0825496\pi$
$278$	−10.6461	+	10.6461i	−0.638513	+	0.638513i
$279$	15.9485	+	23.2446i	0.954812	+	1.39162i
$280$	−2.13973	−	4.57548i	−0.127873	−	0.273437i
$281$			0.763857i			0.0455679i	0.999740	+	0.0227839i	$0.00725298\pi$
$281$			0.763857i			0.0455679i	−0.999740	+	0.0227839i	$0.992747\pi$
$282$	−8.05808	−	4.24364i	−0.479852	−	0.252705i
$283$	−3.73216	−	3.73216i	−0.221854	−	0.221854i	0.587425	−	0.809279i	$-0.300142\pi$
$283$	−3.73216	−	3.73216i	−0.221854	−	0.221854i	−0.809279	+	0.587425i	$0.800142\pi$
$284$	9.60806			0.570134
$285$	−26.2086	−	1.24029i	−1.55246	−	0.0734686i
$286$	−2.58997			−0.153148
$287$	3.37160	+	3.37160i	0.199019	+	0.199019i
$288$	0.549041	−	2.94933i	0.0323526	−	0.173791i
$289$		−	16.9517i		−	0.997158i
$290$	−1.87258	−	0.679223i	−0.109962	−	0.0398854i
$291$	6.41921	+	20.7022i	0.376301	+	1.21358i
$292$	1.65186	−	1.65186i	0.0966680	−	0.0966680i
$293$	22.4543	−	22.4543i	1.31180	−	1.31180i	0.391704	−	0.920091i	$-0.371886\pi$
$293$	22.4543	−	22.4543i	1.31180	−	1.31180i	0.920091	−	0.391704i	$-0.128114\pi$
$294$	0.973263	+	3.13881i	0.0567619	+	0.183059i
$295$	−5.57250	+	2.60599i	−0.324444	+	0.151727i
$296$			4.08282i			0.237309i
$297$	−1.56593	−	13.3665i	−0.0908647	−	0.775601i
$298$	11.1160	+	11.1160i	0.643934	+	0.643934i
$299$	2.56451			0.148309
$300$	−8.00946	+	3.29371i	−0.462426	+	0.190162i
$301$	14.0200			0.808102
$302$	10.1324	+	10.1324i	0.583056	+	0.583056i
$303$	−24.8200	−	13.0710i	−1.42587	−	0.750909i
$304$			6.77461i			0.388550i
$305$	4.63822	−	2.16908i	0.265584	−	0.124201i
$306$	0.543739	−	0.373068i	0.0310835	−	0.0213269i
$307$	4.92117	−	4.92117i	0.280866	−	0.280866i	−0.552588	−	0.833454i	$-0.686360\pi$
$307$	4.92117	−	4.92117i	0.280866	−	0.280866i	0.833454	+	0.552588i	$0.186360\pi$
$308$	−4.13694	+	4.13694i	−0.235724	+	0.235724i
$309$	−26.7186	+	8.28476i	−1.51997	+	0.471304i
$310$	−19.7522	−	7.16455i	−1.12185	−	0.406919i
$311$		−	2.99483i		−	0.169821i	−0.996389	−	0.0849107i	$-0.972940\pi$
$311$		−	2.99483i		−	0.169821i	0.996389	−	0.0849107i	$-0.0270605\pi$
$312$	−0.807075	+	1.53252i	−0.0456916	+	0.0867621i
$313$	−22.8829	−	22.8829i	−1.29342	−	1.29342i	−0.932659	−	0.360759i	$-0.882518\pi$
$313$	−22.8829	−	22.8829i	−1.29342	−	1.29342i	−0.360759	−	0.932659i	$-0.617482\pi$
$314$	13.9961			0.789843
$315$	−14.6694	+	3.79865i	−0.826527	+	0.214030i
$316$	12.1165			0.681605
$317$	14.7717	+	14.7717i	0.829659	+	0.829659i	0.987469	−	0.157810i	$-0.0504435\pi$
$317$	14.7717	+	14.7717i	0.829659	+	0.829659i	−0.157810	+	0.987469i	$0.550444\pi$
$318$	−2.55899	+	4.85917i	−0.143501	+	0.272489i
$319$			2.30722i			0.129180i
$320$	0.947239	+	2.02552i	0.0529523	+	0.113230i
$321$	23.5728	−	7.30932i	1.31571	−	0.407967i
$322$	4.09627	−	4.09627i	0.228276	−	0.228276i
$323$	−1.05295	+	1.05295i	−0.0585878	+	0.0585878i
$324$	−8.39711	−	3.23861i	−0.466506	−	0.179923i
$325$	4.98000	−	0.446773i	0.276241	−	0.0247825i
$326$			12.9088i			0.714951i
$327$	14.0671	+	7.40818i	0.777914	+	0.409673i
$328$	−1.49257	−	1.49257i	−0.0824136	−	0.0824136i
$329$	11.8775			0.654826
$330$	6.74971	+	7.42028i	0.371559	+	0.408473i
$331$	−0.111775			−0.00614372			−0.00307186	−	0.999995i	$-0.500978\pi$
$331$	−0.111775			−0.00614372			−0.00307186	+	0.999995i	$0.500978\pi$
$332$	−5.93928	−	5.93928i	−0.325960	−	0.325960i
$333$	12.0416	+	2.24164i	0.659874	+	0.122841i
$334$			18.6320i			1.01950i
$335$	11.8531	−	32.6782i	0.647603	−	1.78540i
$336$	1.15876	+	3.73703i	0.0632153	+	0.203871i
$337$	−8.54851	+	8.54851i	−0.465667	+	0.465667i	−0.900508	−	0.434840i	$-0.856805\pi$
$337$	−8.54851	+	8.54851i	−0.465667	+	0.465667i	0.434840	+	0.900508i	$0.356805\pi$
$338$	0.707107	−	0.707107i	0.0384615	−	0.0384615i
$339$	5.68876	+	18.3464i	0.308971	+	0.996442i
$340$	−0.167593	+	0.462045i	−0.00908902	+	0.0250579i
$341$			24.3370i			1.31792i
$342$	19.9806	+	3.71954i	1.08043	+	0.201130i
$343$	−14.2116	−	14.2116i	−0.767355	−	0.767355i
$344$	−6.20654			−0.334634
$345$	−6.68335	−	7.34734i	−0.359820	−	0.395567i
$346$	15.6366			0.840628
$347$	6.09851	+	6.09851i	0.327385	+	0.327385i	0.851591	−	0.524206i	$-0.175638\pi$
$347$	6.09851	+	6.09851i	0.327385	+	0.327385i	−0.524206	+	0.851591i	$0.675638\pi$
$348$	1.36522	+	0.718967i	0.0731834	+	0.0385407i
$349$			4.89335i			0.261935i	0.991387	+	0.130967i	$0.0418083\pi$
$349$			4.89335i			0.261935i	−0.991387	+	0.130967i	$0.958192\pi$
$350$	7.24089	−	8.66815i	0.387042	−	0.463332i
$351$	4.07680	+	3.22175i	0.217604	+	0.171964i
$352$	1.83139	−	1.83139i	0.0976132	−	0.0976132i
$353$	8.68950	−	8.68950i	0.462495	−	0.462495i	−0.436977	−	0.899473i	$-0.643951\pi$
$353$	8.68950	−	8.68950i	0.462495	−	0.462495i	0.899473	+	0.436977i	$0.143951\pi$
$354$	4.55135	−	1.41126i	0.241901	−	0.0750074i
$355$	9.10114	+	19.4613i	0.483038	+	1.03290i
$356$			6.43585i			0.341099i
$357$	−0.400731	+	0.760933i	−0.0212089	+	0.0402728i
$358$	8.12918	+	8.12918i	0.429641	+	0.429641i
$359$	31.8464			1.68079			0.840394	−	0.541975i	$-0.182323\pi$
$359$	31.8464			1.68079			0.840394	+	0.541975i	$0.182323\pi$
$360$	6.49401	−	1.68163i	0.342264	−	0.0886296i
$361$	−26.8953			−1.41554
$362$	−12.4997	−	12.4997i	−0.656970	−	0.656970i
$363$	−3.46401	+	6.57768i	−0.181813	+	0.345239i
$364$		−	2.25891i		−	0.118399i
$365$	4.91059	+	1.78117i	0.257032	+	0.0932309i
$366$	−3.78827	+	1.17465i	−0.198016	+	0.0613997i
$367$	14.9797	−	14.9797i	0.781935	−	0.781935i	−0.198222	−	0.980157i	$-0.563517\pi$
$367$	14.9797	−	14.9797i	0.781935	−	0.781935i	0.980157	+	0.198222i	$0.0635167\pi$
$368$	−1.81338	+	1.81338i	−0.0945290	+	0.0945290i
$369$	−5.22158	+	3.58261i	−0.271825	+	0.186503i
$370$	−8.26983	+	3.86740i	−0.429928	+	0.201057i
$371$		−	7.16233i		−	0.371850i
$372$	14.4005	+	7.58377i	0.746633	+	0.393200i
$373$	16.2983	+	16.2983i	0.843893	+	0.843893i	0.989363	−	0.145470i	$-0.0464693\pi$
$373$	16.2983	+	16.2983i	0.843893	+	0.843893i	−0.145470	+	0.989363i	$0.546469\pi$
$374$	0.569291			0.0294373
$375$	−14.2584	−	13.1034i	−0.736298	−	0.676657i
$376$	−5.25805			−0.271163
$377$	−0.629912	−	0.629912i	−0.0324421	−	0.0324421i
$378$	11.6579	−	1.36577i	0.599619	−	0.0702478i
$379$			6.82263i			0.350455i	0.984528	+	0.175228i	$0.0560661\pi$
$379$			6.82263i			0.350455i	−0.984528	+	0.175228i	$0.943934\pi$
$380$	−13.7221	+	6.41718i	−0.703930	+	0.329194i
$381$	−5.84565	−	18.8524i	−0.299482	−	0.965838i
$382$	−12.7388	+	12.7388i	−0.651771	+	0.651771i
$383$	−15.1912	+	15.1912i	−0.776235	+	0.776235i	−0.979188	−	0.202953i	$-0.934946\pi$
$383$	−15.1912	+	15.1912i	−0.776235	+	0.776235i	0.202953	+	0.979188i	$0.434946\pi$
$384$	−0.512970	−	1.65435i	−0.0261774	−	0.0844230i
$385$	−12.2981	−	4.46079i	−0.626771	−	0.227343i
$386$		−	5.07079i		−	0.258097i
$387$	−3.40765	+	18.3051i	−0.173220	+	0.930503i
$388$	8.84860	+	8.84860i	0.449219	+	0.449219i
$389$	−2.88396			−0.146222			−0.0731112	−	0.997324i	$-0.523293\pi$
$389$	−2.88396			−0.146222			−0.0731112	+	0.997324i	$0.523293\pi$
$390$	−3.86865	−	0.183080i	−0.195897	−	0.00927060i
$391$	−0.563694			−0.0285072
$392$	1.34160	+	1.34160i	0.0677610	+	0.0677610i
$393$	−21.7738	−	11.4668i	−1.09834	−	0.578422i
$394$			16.7410i			0.843398i
$395$	11.4772	+	24.5422i	0.577480	+	1.23485i
$396$	−4.39585	−	6.40687i	−0.220900	−	0.321957i
$397$	−26.9155	+	26.9155i	−1.35085	+	1.35085i	−0.466137	+	0.884712i	$0.654355\pi$
$397$	−26.9155	+	26.9155i	−1.35085	+	1.35085i	−0.884712	+	0.466137i	$0.845645\pi$
$398$	4.86593	−	4.86593i	0.243907	−	0.243907i
$399$	−25.3169	+	7.85012i	−1.26743	+	0.392997i
$400$	−3.20547	+	3.83731i	−0.160274	+	0.191865i
$401$			29.6662i			1.48146i	0.671803	+	0.740729i	$0.265520\pi$
$401$			29.6662i			1.48146i	−0.671803	+	0.740729i	$0.734480\pi$
$402$	−12.5466	+	23.8243i	−0.625769	+	1.18825i
$403$	−6.64441	−	6.64441i	−0.330982	−	0.330982i
$404$	−16.1955			−0.805757
$405$	−1.39420	−	20.0763i	−0.0692782	−	0.997597i
$406$	−2.01231			−0.0998692
$407$	7.47721	+	7.47721i	0.370631	+	0.370631i
$408$	0.177400	−	0.336858i	0.00878260	−	0.0166769i
$409$			3.05276i			0.150949i	0.997148	+	0.0754747i	$0.0240472\pi$
$409$			3.05276i			0.150949i	−0.997148	+	0.0754747i	$0.975953\pi$
$410$	1.60942	−	4.43707i	0.0794834	−	0.219131i
$411$	25.6300	−	7.94722i	1.26424	−	0.392007i
$412$	−11.4202	+	11.4202i	−0.562632	+	0.562632i
$413$	−4.39438	+	4.39438i	−0.216234	+	0.216234i
$414$	4.35264	+	6.34388i	0.213921	+	0.311785i
$415$	6.40422	−	17.6561i	0.314371	−	0.866702i
$416$			1.00000i			0.0490290i
$417$	23.0736	+	12.1513i	1.12992	+	0.595049i
$418$	12.4069	+	12.4069i	0.606842	+	0.606842i
$419$	6.17929			0.301878			0.150939	−	0.988543i	$-0.451770\pi$
$419$	6.17929			0.301878			0.150939	+	0.988543i	$0.451770\pi$
$420$	−6.47181	+	5.88694i	−0.315792	+	0.287253i
$421$	2.65347			0.129322			0.0646610	−	0.997907i	$-0.479403\pi$
$421$	2.65347			0.129322			0.0646610	+	0.997907i	$0.479403\pi$
$422$	5.16428	+	5.16428i	0.251393	+	0.251393i
$423$	−2.88688	+	15.5077i	−0.140365	+	0.754011i
$424$			3.17070i			0.153983i
$425$	−1.09463	+	0.0982034i	−0.0530975	+	0.00476357i
$426$	−4.92865	−	15.8951i	−0.238794	−	0.770118i
$427$	3.65763	−	3.65763i	0.177005	−	0.177005i
$428$	10.0756	−	10.0756i	0.487021	−	0.487021i
$429$	1.32858	+	4.28471i	0.0641443	+	0.206868i
$430$	−5.87908	−	12.5715i	−0.283514	−	0.606251i
$431$			35.9248i			1.73043i	0.501397	+	0.865217i	$0.332820\pi$
$431$			35.9248i			1.73043i	−0.501397	+	0.865217i	$0.667180\pi$
$432$	−5.16086	+	0.604615i	−0.248302	+	0.0290895i
$433$	−8.25075	−	8.25075i	−0.396506	−	0.396506i	0.480493	−	0.876999i	$-0.340458\pi$
$433$	−8.25075	−	8.25075i	−0.396506	−	0.396506i	−0.876999	+	0.480493i	$0.840458\pi$
$434$	−21.2261			−1.01889
$435$	−0.163093	+	3.44632i	−0.00781971	+	0.165238i
$436$	9.17905			0.439597
$437$	−12.2849	−	12.2849i	−0.587669	−	0.587669i
$438$	−3.58011	−	1.88540i	−0.171064	−	0.0900877i
$439$			5.36829i			0.256215i	0.991760	+	0.128107i	$0.0408902\pi$
$439$			5.36829i			0.256215i	−0.991760	+	0.128107i	$0.959110\pi$
$440$	5.44427	+	1.97475i	0.259545	+	0.0941425i
$441$	4.69342	−	3.22023i	0.223496	−	0.153344i
$442$	−0.155426	+	0.155426i	−0.00739287	+	0.00739287i
$443$	11.3450	−	11.3450i	0.539018	−	0.539018i	−0.384223	−	0.923241i	$-0.625530\pi$
$443$	11.3450	−	11.3450i	0.539018	−	0.539018i	0.923241	+	0.384223i	$0.125530\pi$
$444$	6.75439	−	2.09436i	0.320549	−	0.0993941i
$445$	−13.0360	+	6.09629i	−0.617964	+	0.288992i
$446$		−	22.9072i		−	1.08469i
$447$	12.6876	−	24.0920i	0.600102	−	1.13951i
$448$	1.59729	+	1.59729i	0.0754650	+	0.0754650i
$449$	−16.0281			−0.756412			−0.378206	−	0.925721i	$-0.623459\pi$
$449$	−16.0281			−0.756412			−0.378206	+	0.925721i	$0.623459\pi$
$450$	9.55755	+	11.5608i	0.450547	+	0.544984i
$451$	−5.46696			−0.257429
$452$	7.84170	+	7.84170i	0.368843	+	0.368843i
$453$	11.5649	−	21.9602i	0.543367	−	1.03178i
$454$			24.3564i			1.14310i
$455$	4.57548	−	2.13973i	0.214502	−	0.100312i
$456$	11.2075	−	3.47517i	0.524842	−	0.162740i
$457$	0.963319	−	0.963319i	0.0450621	−	0.0450621i	−0.684217	−	0.729279i	$-0.739856\pi$
$457$	0.963319	−	0.963319i	0.0450621	−	0.0450621i	0.729279	+	0.684217i	$0.239856\pi$
$458$	16.6859	−	16.6859i	0.779681	−	0.779681i
$459$	−0.896106	−	0.708160i	−0.0418266	−	0.0330541i
$460$	−5.39075	−	1.95534i	−0.251345	−	0.0911680i
$461$		−	17.4655i		−	0.813447i	−0.913551	−	0.406724i	$-0.866671\pi$
$461$		−	17.4655i		−	0.813447i	0.913551	−	0.406724i	$-0.133329\pi$
$462$	8.96606	+	4.72180i	0.417139	+	0.219678i
$463$	−0.256369	−	0.256369i	−0.0119145	−	0.0119145i	0.701124	−	0.713039i	$-0.252682\pi$
$463$	−0.256369	−	0.256369i	−0.0119145	−	0.0119145i	−0.713039	+	0.701124i	$0.752682\pi$
$464$	0.890831			0.0413558
$465$	−1.72033	+	36.3523i	−0.0797784	+	1.68580i
$466$	10.5292			0.487758
$467$	−17.7653	−	17.7653i	−0.822079	−	0.822079i	0.164327	−	0.986406i	$-0.447455\pi$
$467$	−17.7653	−	17.7653i	−0.822079	−	0.822079i	−0.986406	+	0.164327i	$0.947455\pi$
$468$	2.94933	+	0.549041i	0.136333	+	0.0253794i
$469$		−	35.1167i		−	1.62154i
$470$	−4.98063	−	10.6503i	−0.229739	−	0.491261i
$471$	−7.17956	−	23.1543i	−0.330817	−	1.06690i
$472$	1.94535	−	1.94535i	0.0895421	−	0.0895421i
$473$	−11.3666	+	11.3666i	−0.522635	+	0.522635i
$474$	−6.21539	−	20.0448i	−0.285482	−	0.920690i
$475$	−25.9963	−	21.7158i	−1.19279	−	0.996391i
$476$			0.496523i			0.0227581i
$477$	9.35144	+	1.74084i	0.428173	+	0.0797078i
$478$	−13.5921	−	13.5921i	−0.621687	−	0.621687i
$479$	21.2442			0.970671			0.485336	−	0.874328i	$-0.338697\pi$
$479$	21.2442			0.970671			0.485336	+	0.874328i	$0.338697\pi$
$480$	2.86501	−	2.60609i	0.130769	−	0.118951i
$481$	−4.08282			−0.186160
$482$	−11.3708	−	11.3708i	−0.517928	−	0.517928i
$483$	−8.87792	−	4.67539i	−0.403959	−	0.212737i
$484$			4.29206i			0.195094i
$485$	−9.54128	+	26.3048i	−0.433247	+	1.19444i
$486$	−1.05032	+	15.5530i	−0.0476433	+	0.705500i
$487$	10.4620	−	10.4620i	0.474077	−	0.474077i	−0.429154	−	0.903231i	$-0.641188\pi$
$487$	10.4620	−	10.4620i	0.474077	−	0.474077i	0.903231	+	0.429154i	$0.141188\pi$
$488$	−1.61920	+	1.61920i	−0.0732976	+	0.0732976i
$489$	21.3556	−	6.62182i	0.965733	−	0.299449i
$490$	−1.44662	+	3.98826i	−0.0653518	+	0.180171i
$491$		−	16.1195i		−	0.727462i	−0.931504	−	0.363731i	$-0.881503\pi$
$491$		−	16.1195i		−	0.727462i	0.931504	−	0.363731i	$-0.118497\pi$
$492$	−1.70359	+	3.23488i	−0.0768037	+	0.145840i
$493$	0.138458	+	0.138458i	0.00623586	+	0.00623586i
$494$	−6.77461			−0.304804
$495$	8.81332	−	14.9727i	0.396129	−	0.672974i
$496$	9.39662			0.421921
$497$	15.3469	+	15.3469i	0.688402	+	0.688402i
$498$	−6.77895	+	12.8723i	−0.303772	+	0.576822i
$499$			0.297723i			0.0133279i	0.999978	+	0.00666395i	$0.00212122\pi$
$499$			0.297723i			0.0133279i	−0.999978	+	0.00666395i	$0.997879\pi$
$500$	−10.8089	−	2.85791i	−0.483389	−	0.127810i
$501$	30.8238	−	9.55766i	1.37710	−	0.427005i
$502$	17.9945	−	17.9945i	0.803132	−	0.803132i
$503$	−7.46751	+	7.46751i	−0.332960	+	0.332960i	−0.853709	−	0.520750i	$-0.825653\pi$
$503$	−7.46751	+	7.46751i	−0.332960	+	0.332960i	0.520750	+	0.853709i	$0.325653\pi$
$504$	5.58793	−	3.83397i	0.248906	−	0.170778i
$505$	−15.3410	−	32.8044i	−0.682667	−	1.45978i
$506$			6.64200i			0.295273i
$507$	−1.53252	−	0.807075i	−0.0680618	−	0.0358434i
$508$	−8.05797	−	8.05797i	−0.357514	−	0.357514i
$509$	−9.67667			−0.428911			−0.214456	−	0.976734i	$-0.568798\pi$
$509$	−9.67667			−0.428911			−0.214456	+	0.976734i	$0.568798\pi$
$510$	0.850353	+	0.0402420i	0.0376543	+	0.00178195i
$511$	5.27702			0.233442
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.09603	−	34.9628i	−0.180844	−	1.54364i
$514$		−	17.1567i		−	0.756749i
$515$	−33.9494	−	12.3142i	−1.49599	−	0.542627i
$516$	3.18377	+	10.2678i	0.140158	+	0.452013i
$517$	−9.62951	+	9.62951i	−0.423505	+	0.423505i
$518$	−6.52145	+	6.52145i	−0.286536	+	0.286536i
$519$	−8.02111	−	25.8683i	−0.352088	−	1.13549i
$520$	−2.02552	+	0.947239i	−0.0888250	+	0.0415392i
$521$		−	24.0972i		−	1.05572i	−0.849332	−	0.527860i	$-0.822995\pi$
$521$		−	24.0972i		−	1.05572i	0.849332	−	0.527860i	$-0.177005\pi$
$522$	0.489103	−	2.62735i	0.0214075	−	0.114996i
$523$	2.67631	+	2.67631i	0.117027	+	0.117027i	0.763195	−	0.646168i	$-0.223630\pi$
$523$	2.67631	+	2.67631i	0.117027	+	0.117027i	−0.646168	+	0.763195i	$0.723630\pi$
$524$	−14.2078			−0.620671
$525$	−18.0545	−	7.53244i	−0.787962	−	0.328743i
$526$	−5.39638			−0.235294
$527$	1.46048	+	1.46048i	0.0636195	+	0.0636195i
$528$	−3.96919	−	2.09030i	−0.172737	−	0.0909686i
$529$			16.4233i			0.714056i
$530$	−6.42232	+	3.00341i	−0.278968	+	0.130460i
$531$	−4.66941	−	6.80557i	−0.202635	−	0.295337i
$532$	−10.8210	+	10.8210i	−0.469151	+	0.469151i
$533$	1.49257	−	1.49257i	0.0646506	−	0.0646506i
$534$	10.6471	−	3.30140i	0.460746	−	0.142866i
$535$	29.9523	+	10.8643i	1.29495	+	0.469705i
$536$			15.5458i			0.671477i
$537$	9.27845	−	17.6185i	0.400395	−	0.760295i
$538$	2.11235	+	2.11235i	0.0910701	+	0.0910701i
$539$	4.91397			0.211660
$540$	−6.11323	−	9.88071i	−0.263071	−	0.425198i
$541$	−31.9887			−1.37530			−0.687650	−	0.726042i	$-0.741358\pi$
$541$	−31.9887			−1.37530			−0.687650	+	0.726042i	$0.741358\pi$
$542$	−12.6686	−	12.6686i	−0.544162	−	0.544162i
$543$	−14.2669	+	27.0908i	−0.612250	+	1.16258i
$544$		−	0.219806i		−	0.00942410i
$545$	8.69476	+	18.5924i	0.372443	+	0.796410i
$546$	−3.73703	+	1.15876i	−0.159930	+	0.0495902i
$547$	6.13891	−	6.13891i	0.262481	−	0.262481i	−0.563580	−	0.826061i	$-0.690576\pi$
$547$	6.13891	−	6.13891i	0.262481	−	0.262481i	0.826061	+	0.563580i	$0.190576\pi$
$548$	10.9549	−	10.9549i	0.467970	−	0.467970i
$549$	3.88654	+	5.66456i	0.165874	+	0.241757i
$550$	1.15713	+	12.8980i	0.0493402	+	0.549975i
$551$			6.03503i			0.257101i
$552$	3.93017	+	2.06975i	0.167279	+	0.0880944i
$553$	19.3536	+	19.3536i	0.822997	+	0.822997i
$554$	−16.7142			−0.710120
$555$	10.6402	+	11.6973i	0.451652	+	0.496523i
$556$	15.0559			0.638513
$557$	6.14058	+	6.14058i	0.260185	+	0.260185i	0.825129	−	0.564944i	$-0.191102\pi$
$557$	6.14058	+	6.14058i	0.260185	+	0.260185i	−0.564944	+	0.825129i	$0.691102\pi$
$558$	5.15913	−	27.7137i	0.218403	−	1.17322i
$559$		−	6.20654i		−	0.262509i
$560$	−1.72233	+	4.74837i	−0.0727818	+	0.200655i
$561$	−0.292029	−	0.941804i	−0.0123295	−	0.0397630i
$562$	0.540129	−	0.540129i	0.0227839	−	0.0227839i
$563$	24.9348	−	24.9348i	1.05088	−	1.05088i	0.0522422	−	0.998634i	$-0.483363\pi$
$563$	24.9348	−	24.9348i	1.05088	−	1.05088i	0.998634	−	0.0522422i	$-0.0166368\pi$
$564$	2.69722	+	8.69863i	0.113574	+	0.366278i
$565$	−8.45557	+	23.3115i	−0.355728	+	0.980722i
$566$			5.27807i			0.221854i
$567$	−8.23963	−	18.5857i	−0.346032	−	0.780524i
$568$	−6.79393	−	6.79393i	−0.285067	−	0.285067i
$569$	−5.56111			−0.233134			−0.116567	−	0.993183i	$-0.537189\pi$
$569$	−5.56111			−0.233134			−0.116567	+	0.993183i	$0.537189\pi$
$570$	17.6553	+	19.4093i	0.739498	+	0.812966i
$571$	33.8131			1.41503			0.707517	−	0.706697i	$-0.249815\pi$
$571$	33.8131			1.41503			0.707517	+	0.706697i	$0.249815\pi$
$572$	1.83139	+	1.83139i	0.0765741	+	0.0765741i
$573$	27.6089	+	14.5397i	1.15338	+	0.607405i
$574$		−	4.76816i		−	0.199019i
$575$	−1.14575	−	12.7713i	−0.0477812	−	0.532598i
$576$	−2.47372	+	1.69726i	−0.103072	+	0.0707192i
$577$	0.174550	−	0.174550i	0.00726661	−	0.00726661i	−0.703464	−	0.710731i	$-0.748364\pi$
$577$	0.174550	−	0.174550i	0.00726661	−	0.00726661i	0.710731	+	0.703464i	$0.248364\pi$
$578$	−11.9867	+	11.9867i	−0.498579	+	0.498579i
$579$	−8.38885	+	2.60117i	−0.348629	+	0.108101i
$580$	0.843830	+	1.80440i	0.0350381	+	0.0749235i
$581$		−	18.9736i		−	0.787156i
$582$	10.0996	−	19.1777i	0.418641	−	0.794942i
$583$	5.80677	+	5.80677i	0.240492	+	0.240492i
$584$	−2.33609			−0.0966680
$585$	1.68163	+	6.49401i	0.0695267	+	0.268494i
$586$	−31.7552			−1.31180
$587$	6.55064	+	6.55064i	0.270374	+	0.270374i	0.829251	−	0.558877i	$-0.188768\pi$
$587$	6.55064	+	6.55064i	0.270374	+	0.270374i	−0.558877	+	0.829251i	$0.688768\pi$
$588$	1.53127	−	2.90767i	0.0631485	−	0.119910i
$589$			63.6584i			2.62300i
$590$	5.78307	+	2.09764i	0.238085	+	0.0863584i
$591$	27.6954	−	8.58762i	1.13924	−	0.353248i
$592$	2.88699	−	2.88699i	0.118654	−	0.118654i
$593$	−17.9410	+	17.9410i	−0.736747	+	0.736747i	−0.971947	−	0.235200i	$-0.924425\pi$
$593$	−17.9410	+	17.9410i	−0.736747	+	0.736747i	0.235200	+	0.971947i	$0.424425\pi$
$594$	−8.34423	+	10.5588i	−0.342368	+	0.433233i
$595$	−1.00572	+	0.470326i	−0.0412304	+	0.0192815i
$596$		−	15.7204i		−	0.643934i
$597$	−10.5460	−	5.55386i	−0.431620	−	0.227304i
$598$	−1.81338	−	1.81338i	−0.0741547	−	0.0741547i
$599$	−41.6634			−1.70232			−0.851161	−	0.524905i	$-0.824101\pi$
$599$	−41.6634			−1.70232			−0.851161	+	0.524905i	$0.824101\pi$
$600$	7.99255	+	3.33454i	0.326294	+	0.136132i
$601$	−22.6630			−0.924444			−0.462222	−	0.886764i	$-0.652948\pi$
$601$	−22.6630			−0.924444			−0.462222	+	0.886764i	$0.652948\pi$
$602$	−9.91367	−	9.91367i	−0.404051	−	0.404051i
$603$	45.8498	+	8.53530i	1.86715	+	0.347584i
$604$		−	14.3294i		−	0.583056i
$605$	−8.69365	+	4.06561i	−0.353447	+	0.165290i
$606$	8.30782	+	26.7930i	0.337482	+	1.08839i
$607$	11.2274	−	11.2274i	0.455706	−	0.455706i	−0.441537	−	0.897243i	$-0.645567\pi$
$607$	11.2274	−	11.2274i	0.455706	−	0.455706i	0.897243	+	0.441537i	$0.145567\pi$
$608$	4.79037	−	4.79037i	0.194275	−	0.194275i
$609$	1.03226	+	3.32906i	0.0418291	+	0.134900i
$610$	−4.81349	−	1.74595i	−0.194892	−	0.0706915i
$611$		−	5.25805i		−	0.212718i
$612$	−0.648280	−	0.120683i	−0.0262052	−	0.00487830i
$613$	6.53782	+	6.53782i	0.264060	+	0.264060i	0.826701	−	0.562641i	$-0.190215\pi$
$613$	6.53782	+	6.53782i	0.264060	+	0.264060i	−0.562641	+	0.826701i	$0.690215\pi$
$614$	−6.95958			−0.280866
$615$	−8.16603	−	0.386448i	−0.329286	−	0.0155831i
$616$	5.85052			0.235724
$617$	22.7714	+	22.7714i	0.916744	+	0.916744i	0.996791	−	0.0800471i	$-0.0255071\pi$
$617$	22.7714	+	22.7714i	0.916744	+	0.916744i	−0.0800471	+	0.996791i	$0.525507\pi$
$618$	24.7511	+	13.0347i	0.995636	+	0.524333i
$619$		−	5.97955i		−	0.240338i	−0.992753	−	0.120169i	$-0.961656\pi$
$619$		−	5.97955i		−	0.240338i	0.992753	−	0.120169i	$-0.0383437\pi$
$620$	8.90085	+	19.0330i	0.357467	+	0.764386i
$621$	8.26220	−	10.4550i	0.331551	−	0.419545i
$622$	−2.11767	+	2.11767i	−0.0849107	+	0.0849107i
$623$	−10.2799	+	10.2799i	−0.411857	+	0.411857i
$624$	1.65435	−	0.512970i	0.0662269	−	0.0205352i
$625$	−4.44986	−	24.6008i	−0.177994	−	0.984031i
$626$			32.3613i			1.29342i
$627$	14.1610	−	26.8897i	0.565534	−	1.07387i
$628$	−9.89671	−	9.89671i	−0.394922	−	0.394922i
$629$	0.897427			0.0357828
$630$	13.0589	+	7.68678i	0.520278	+	0.306249i
$631$	−13.0508			−0.519544			−0.259772	−	0.965670i	$-0.583647\pi$
$631$	−13.0508			−0.519544			−0.259772	+	0.965670i	$0.583647\pi$
$632$	−8.56764	−	8.56764i	−0.340802	−	0.340802i
$633$	5.89438	−	11.1926i	0.234281	−	0.444867i
$634$		−	20.8903i		−	0.829659i
$635$	8.68876	−	23.9544i	0.344803	−	0.950602i
$636$	5.24543	−	1.62647i	0.207995	−	0.0644939i
$637$	−1.34160	+	1.34160i	−0.0531561	+	0.0531561i
$638$	1.63145	−	1.63145i	0.0645899	−	0.0645899i
$639$	−23.7677	+	16.3074i	−0.940235	+	0.645111i
$640$	0.762461	−	2.10206i	0.0301389	−	0.0830912i
$641$		−	24.2560i		−	0.958055i	−0.877800	−	0.479027i	$-0.840989\pi$
$641$		−	24.2560i		−	0.958055i	0.877800	−	0.479027i	$-0.159011\pi$
$642$	−21.8370	−	11.5000i	−0.861836	−	0.453870i
$643$	−13.2221	−	13.2221i	−0.521429	−	0.521429i	0.396574	−	0.918003i	$-0.370199\pi$
$643$	−13.2221	−	13.2221i	−0.521429	−	0.521429i	−0.918003	+	0.396574i	$0.870199\pi$
$644$	−5.79300			−0.228276
$645$	−17.7818	+	16.1748i	−0.700157	+	0.636883i
$646$	1.48910			0.0585878
$647$	−8.17921	−	8.17921i	−0.321558	−	0.321558i	0.527807	−	0.849365i	$-0.323015\pi$
$647$	−8.17921	−	8.17921i	−0.321558	−	0.321558i	−0.849365	+	0.527807i	$0.823015\pi$
$648$	3.64761	+	8.22769i	0.143292	+	0.323214i
$649$		−	7.12538i		−	0.279696i
$650$	−3.83731	−	3.20547i	−0.150512	−	0.125729i
$651$	10.8884	+	35.1154i	0.426749	+	1.37628i
$652$	9.12788	−	9.12788i	0.357476	−	0.357476i
$653$	12.1320	−	12.1320i	0.474763	−	0.474763i	−0.428689	−	0.903452i	$-0.641024\pi$
$653$	12.1320	−	12.1320i	0.474763	−	0.474763i	0.903452	+	0.428689i	$0.141024\pi$
$654$	−4.70858	−	15.1853i	−0.184120	−	0.593793i
$655$	−13.4582	−	28.7782i	−0.525855	−	1.12446i
$656$			2.11082i			0.0824136i
$657$	−1.28261	+	6.88989i	−0.0500393	+	0.268800i
$658$	−8.39864	−	8.39864i	−0.327413	−	0.327413i
$659$	13.1366			0.511731			0.255865	−	0.966712i	$-0.417640\pi$
$659$	13.1366			0.511731			0.255865	+	0.966712i	$0.417640\pi$
$660$	0.474171	−	10.0197i	0.0184571	−	0.390016i
$661$	−34.2832			−1.33346			−0.666731	−	0.745298i	$-0.732307\pi$
$661$	−34.2832			−1.33346			−0.666731	+	0.745298i	$0.732307\pi$
$662$	0.0790370	+	0.0790370i	0.00307186	+	0.00307186i
$663$	0.336858	+	0.177400i	0.0130825	+	0.00688964i
$664$			8.39941i			0.325960i
$665$	−32.1684	−	11.6681i	−1.24744	−	0.452471i
$666$	−6.92960	−	10.0998i	−0.268517	−	0.391358i
$667$	−1.61542	+	1.61542i	−0.0625491	+	0.0625491i
$668$	13.1748	−	13.1748i	0.509749	−	0.509749i
$669$	−37.8965	+	11.7507i	−1.46516	+	0.454309i
$670$	−31.4884	+	14.7256i	−1.21650	+	0.568900i
$671$			5.93075i			0.228954i
$672$	1.82311	−	3.46184i	0.0703281	−	0.133543i
$673$	0.645929	+	0.645929i	0.0248987	+	0.0248987i	0.719447	−	0.694548i	$-0.244396\pi$
$673$	0.645929	+	0.645929i	0.0248987	+	0.0248987i	−0.694548	+	0.719447i	$0.744396\pi$
$674$	12.0894			0.465667
$675$	14.2229	−	21.7419i	0.547440	−	0.836845i
$676$	−1.00000			−0.0384615
$677$	10.5020	+	10.5020i	0.403624	+	0.403624i	0.879508	−	0.475884i	$-0.157872\pi$
$677$	10.5020	+	10.5020i	0.403624	+	0.403624i	−0.475884	+	0.879508i	$0.657872\pi$
$678$	8.95033	−	16.9954i	0.343735	−	0.652706i
$679$			28.2676i			1.08481i
$680$	0.445222	−	0.208209i	0.0170735	−	0.00798444i
$681$	40.2939	−	12.4941i	1.54407	−	0.478775i
$682$	17.2088	−	17.2088i	0.658960	−	0.658960i
$683$	−19.5328	+	19.5328i	−0.747401	+	0.747401i	−0.973990	−	0.226590i	$-0.927242\pi$
$683$	−19.5328	+	19.5328i	−0.747401	+	0.747401i	0.226590	+	0.973990i	$0.427242\pi$
$684$	−11.4983	−	16.7585i	−0.439648	−	0.640777i
$685$	32.5663	+	11.8125i	1.24429	+	0.451331i
$686$			20.0983i			0.767355i
$687$	−36.1636	−	19.0449i	−1.37973	−	0.726608i
$688$	4.38869	+	4.38869i	0.167317	+	0.167317i
$689$	−3.17070			−0.120794
$690$	−0.469509	+	9.92120i	−0.0178739	+	0.377693i
$691$	7.28568			0.277160			0.138580	−	0.990351i	$-0.455746\pi$
$691$	7.28568			0.277160			0.138580	+	0.990351i	$0.455746\pi$
$692$	−11.0567	−	11.0567i	−0.420314	−	0.420314i
$693$	3.21218	−	17.2551i	0.122021	−	0.655468i
$694$		−	8.62460i		−	0.327385i
$695$	14.2616	+	30.4961i	0.540972	+	1.15678i
$696$	−0.456970	−	1.47374i	−0.0173214	−	0.0558621i
$697$	−0.328077	+	0.328077i	−0.0124268	+	0.0124268i
$698$	3.46012	−	3.46012i	0.130967	−	0.130967i
$699$	−5.40119	−	17.4190i	−0.204292	−	0.658848i
$700$	−11.2494	+	1.00922i	−0.425187	+	0.0381450i
$701$		−	16.4241i		−	0.620330i	−0.950683	−	0.310165i	$-0.899616\pi$
$701$		−	16.4241i		−	0.620330i	0.950683	−	0.310165i	$-0.100384\pi$
$702$	−0.604615	−	5.16086i	−0.0228197	−	0.194784i
$703$	19.5582	+	19.5582i	0.737652	+	0.737652i
$704$	−2.58997			−0.0976132
$705$	−15.0643	+	13.7030i	−0.567356	+	0.516083i
$706$	−12.2888			−0.462495
$707$	−25.8690	−	25.8690i	−0.972903	−	0.972903i
$708$	−4.21620	−	2.22038i	−0.158454	−	0.0834470i
$709$		−	25.9013i		−	0.972742i	−0.873752	−	0.486371i	$-0.838320\pi$
$709$		−	25.9013i		−	0.972742i	0.873752	−	0.486371i	$-0.161680\pi$
$710$	7.32577	−	20.1967i	0.274931	−	0.757969i
$711$	−29.9728	+	20.5648i	−1.12407	+	0.771241i
$712$	4.55083	−	4.55083i	0.170550	−	0.170550i
$713$	−17.0396	+	17.0396i	−0.638140	+	0.638140i
$714$	0.821420	−	0.254701i	0.0307409	−	0.00953196i
$715$	−1.97475	+	5.44427i	−0.0738515	+	0.203604i
$716$		−	11.4964i		−	0.429641i
$717$	−15.5137	+	29.4583i	−0.579368	+	1.10014i
$718$	−22.5188	−	22.5188i	−0.840394	−	0.840394i
$719$	7.92976			0.295730			0.147865	−	0.989008i	$-0.452760\pi$
$719$	7.92976			0.295730			0.147865	+	0.989008i	$0.452760\pi$
$720$	−5.78105	−	3.40287i	−0.215447	−	0.126817i
$721$	−36.4827			−1.35869
$722$	19.0179	+	19.0179i	0.707772	+	0.707772i
$723$	−12.9784	+	24.6442i	−0.482672	+	0.916529i
$724$			17.6773i			0.656970i
$725$	−2.85554	+	3.41839i	−0.106052	+	0.126956i
$726$	7.10055	−	2.20170i	0.263526	−	0.0817127i
$727$	−13.1739	+	13.1739i	−0.488594	+	0.488594i	−0.907862	−	0.419268i	$-0.862287\pi$
$727$	−13.1739	+	13.1739i	−0.488594	+	0.488594i	0.419268	+	0.907862i	$0.362287\pi$
$728$	−1.59729	+	1.59729i	−0.0591996	+	0.0591996i
$729$	26.2689	−	6.24066i	0.972922	−	0.231136i
$730$	−2.21283	−	4.73180i	−0.0819007	−	0.175132i
$731$			1.36423i			0.0504580i
$732$	3.50931	+	1.84811i	0.129708	+	0.0683082i
$733$	−4.39131	−	4.39131i	−0.162197	−	0.162197i	0.621342	−	0.783539i	$-0.286588\pi$
$733$	−4.39131	−	4.39131i	−0.162197	−	0.162197i	−0.783539	+	0.621342i	$0.786588\pi$
$734$	−21.1845			−0.781935
$735$	7.34003	+	0.347359i	0.270741	+	0.0128125i
$736$	2.56451			0.0945290
$737$	28.4704	+	28.4704i	1.04872	+	1.04872i
$738$	6.22550	+	1.15893i	0.229164	+	0.0426607i
$739$		−	13.4115i		−	0.493350i	−0.969098	−	0.246675i	$-0.920662\pi$
$739$		−	13.4115i		−	0.493350i	0.969098	−	0.246675i	$-0.0793380\pi$
$740$	8.58232	+	3.11299i	0.315492	+	0.114436i
$741$	3.47517	+	11.2075i	0.127664	+	0.411720i
$742$	−5.06453	+	5.06453i	−0.185925	+	0.185925i
$743$	6.99293	−	6.99293i	0.256546	−	0.256546i	−0.567102	−	0.823648i	$-0.691935\pi$
$743$	6.99293	−	6.99293i	0.256546	−	0.256546i	0.823648	+	0.567102i	$0.191935\pi$
$744$	−4.82019	−	15.5453i	−0.176717	−	0.569917i
$745$	31.8421	−	14.8910i	1.16660	−	0.545565i
$746$		−	23.0492i		−	0.843893i
$747$	24.7727	+	4.61163i	0.906384	+	0.168731i
$748$	−0.402549	−	0.402549i	−0.0147187	−	0.0147187i
$749$	32.1873			1.17610
$750$	0.816675	+	19.3477i	0.0298207	+	0.706478i
$751$	−11.5511			−0.421507			−0.210754	−	0.977539i	$-0.567592\pi$
$751$	−11.5511			−0.421507			−0.210754	+	0.977539i	$0.567592\pi$
$752$	3.71800	+	3.71800i	0.135581	+	0.135581i
$753$	−38.9997	−	20.5384i	−1.42123	−	0.748462i
$754$			0.890831i			0.0324421i
$755$	29.0245	−	13.5734i	1.05631	−	0.493986i
$756$	−9.20915	−	7.27765i	−0.334933	−	0.264686i
$757$	−5.58355	+	5.58355i	−0.202938	+	0.202938i	−0.801257	−	0.598320i	$-0.795835\pi$
$757$	−5.58355	+	5.58355i	−0.202938	+	0.202938i	0.598320	+	0.801257i	$0.295835\pi$
$758$	4.82433	−	4.82433i	0.175228	−	0.175228i
$759$	10.9882	−	3.40715i	0.398845	−	0.123672i
$760$	14.2406	+	5.16537i	0.516562	+	0.187368i
$761$			37.4923i			1.35909i	0.733632	+	0.679547i	$0.237824\pi$
$761$			37.4923i			1.35909i	−0.733632	+	0.679547i	$0.762176\pi$
$762$	−9.19717	+	17.4642i	−0.333178	+	0.632660i
$763$	14.6616	+	14.6616i	0.530787	+	0.530787i
$764$	18.0153			0.651771
$765$	−0.369632	−	1.42742i	−0.0133641	−	0.0516085i
$766$	21.4836			0.776235
$767$	1.94535	+	1.94535i	0.0702426	+	0.0702426i
$768$	−0.807075	+	1.53252i	−0.0291228	+	0.0553002i
$769$			25.0653i			0.903880i	0.892048	+	0.451940i	$0.149268\pi$
$769$			25.0653i			0.903880i	−0.892048	+	0.451940i	$0.850732\pi$
$770$	5.54184	+	11.8503i	0.199714	+	0.427057i
$771$	−28.3831	+	8.80087i	−1.02219	+	0.316956i
$772$	−3.58559	+	3.58559i	−0.129048	+	0.129048i
$773$	2.54918	−	2.54918i	0.0916877	−	0.0916877i	−0.659775	−	0.751463i	$-0.729349\pi$
$773$	2.54918	−	2.54918i	0.0916877	−	0.0916877i	0.751463	+	0.659775i	$0.229349\pi$
$774$	15.3533	−	10.5341i	0.551862	−	0.378641i
$775$	−30.1206	+	36.0577i	−1.08196	+	1.29523i
$776$		−	12.5138i		−	0.449219i
$777$	14.1341	+	7.44343i	0.507056	+	0.267032i
$778$	2.03926	+	2.03926i	0.0731112	+	0.0731112i
$779$	−14.3000			−0.512350
$780$	2.60609	+	2.86501i	0.0933131	+	0.102584i
$781$	−24.8846			−0.890441
$782$	0.398592	+	0.398592i	0.0142536	+	0.0142536i
$783$	−4.59745	+	0.538609i	−0.164299	+	0.0192483i
$784$		−	1.89731i		−	0.0677610i
$785$	10.6714	−	29.4205i	0.380880	−	1.05006i
$786$	7.28818	+	23.5046i	0.259961	+	0.838382i
$787$	−32.8392	+	32.8392i	−1.17059	+	1.17059i	−0.188522	+	0.982069i	$0.560370\pi$
$787$	−32.8392	+	32.8392i	−1.17059	+	1.17059i	−0.982069	+	0.188522i	$0.939630\pi$
$788$	11.8377	−	11.8377i	0.421699	−	0.421699i
$789$	2.76819	+	8.92749i	0.0985500	+	0.317827i
$790$	9.23833	−	25.4695i	0.328685	−	0.906165i
$791$			25.0510i			0.890711i
$792$	−1.42200	+	7.63868i	−0.0505286	+	0.271429i
$793$	−1.61920	−	1.61920i	−0.0574994	−	0.0574994i
$794$	38.0643			1.35085
$795$	8.26314	+	9.08407i	0.293063	+	0.322179i
$796$	−6.88147			−0.243907
$797$	5.07364	+	5.07364i	0.179717	+	0.179717i	0.791233	−	0.611515i	$-0.209440\pi$
$797$	5.07364	+	5.07364i	0.179717	+	0.179717i	−0.611515	+	0.791233i	$0.709440\pi$
$798$	23.4526	+	12.3509i	0.830213	+	0.437216i
$799$			1.15575i			0.0408875i
$800$	4.98000	−	0.446773i	0.176070	−	0.0157958i
$801$	−10.9233	−	15.9205i	−0.385957	−	0.562524i
$802$	20.9772	−	20.9772i	0.740729	−	0.740729i
$803$	−4.27828	+	4.27828i	−0.150977	+	0.150977i
$804$	25.7182	−	7.97454i	0.907010	−	0.281240i
$805$	−5.48736	−	11.7339i	−0.193404	−	0.413564i
$806$			9.39662i			0.330982i
$807$	2.41099	−	4.57814i	0.0848709	−	0.161158i
$808$	11.4520	+	11.4520i	0.402879	+	0.402879i
$809$	−15.3637			−0.540159			−0.270079	−	0.962838i	$-0.587050\pi$
$809$	−15.3637			−0.540159			−0.270079	+	0.962838i	$0.587050\pi$
$810$	−13.2102	+	15.1819i	−0.464160	+	0.533438i
$811$	34.1631			1.19963			0.599815	−	0.800139i	$-0.295241\pi$
$811$	34.1631			1.19963			0.599815	+	0.800139i	$0.295241\pi$
$812$	1.42292	+	1.42292i	0.0499346	+	0.0499346i
$813$	−14.4596	+	27.4568i	−0.507120	+	0.962952i
$814$		−	10.5744i		−	0.370631i
$815$	27.1350	+	9.84243i	0.950498	+	0.344765i
$816$	−0.363635	+	0.112754i	−0.0127298	+	0.00394718i
$817$	−29.7316	+	29.7316i	−1.04018	+	1.04018i
$818$	2.15863	−	2.15863i	0.0754747	−	0.0754747i
$819$	3.83397	+	5.58793i	0.133970	+	0.195258i
$820$	−4.27551	+	1.99945i	−0.149307	+	0.0698238i
$821$		−	30.8200i		−	1.07563i	−0.843064	−	0.537813i	$-0.819251\pi$
$821$		−	30.8200i		−	1.07563i	0.843064	−	0.537813i	$-0.180749\pi$
$822$	−23.7427	−	12.5036i	−0.828122	−	0.436115i
$823$	−7.53031	−	7.53031i	−0.262490	−	0.262490i	0.563575	−	0.826065i	$-0.309426\pi$
$823$	−7.53031	−	7.53031i	−0.262490	−	0.262490i	−0.826065	+	0.563575i	$0.809426\pi$
$824$	16.1506			0.562632
$825$	20.7443	−	8.53061i	0.722223	−	0.296998i
$826$	6.21460			0.216234
$827$	4.04738	+	4.04738i	0.140741	+	0.140741i	0.773967	−	0.633226i	$-0.218270\pi$
$827$	4.04738	+	4.04738i	0.140741	+	0.140741i	−0.633226	+	0.773967i	$0.718270\pi$
$828$	1.40802	−	7.56358i	0.0489321	−	0.262853i
$829$		−	6.31884i		−	0.219462i	−0.993961	−	0.109731i	$-0.965001\pi$
$829$		−	6.31884i		−	0.219462i	0.993961	−	0.109731i	$-0.0349990\pi$
$830$	−17.0132	+	7.95626i	−0.590537	+	0.276166i
$831$	8.57391	+	27.6511i	0.297426	+	0.959208i
$832$	0.707107	−	0.707107i	0.0245145	−	0.0245145i
$833$	0.294892	−	0.294892i	0.0102174	−	0.0102174i
$834$	−7.72324	−	24.9077i	−0.267434	−	0.862483i
$835$	39.1656	+	14.2062i	1.35538	+	0.491625i
$836$		−	17.5460i		−	0.606842i
$837$	−48.4946	+	5.68133i	−1.67622	+	0.196376i
$838$	−4.36942	−	4.36942i	−0.150939	−	0.150939i
$839$	35.0294			1.20935			0.604675	−	0.796472i	$-0.293303\pi$
$839$	35.0294			1.20935			0.604675	+	0.796472i	$0.293303\pi$
$840$	8.73895	+	0.413561i	0.301523	+	0.0142692i
$841$	−28.2064			−0.972635
$842$	−1.87628	−	1.87628i	−0.0646610	−	0.0646610i
$843$	−1.17063	−	0.616490i	−0.0403186	−	0.0212330i
$844$		−	7.30339i		−	0.251393i
$845$	−0.947239	−	2.02552i	−0.0325860	−	0.0696801i
$846$	13.0069	−	8.92428i	0.447188	−	0.306823i
$847$	−6.85567	+	6.85567i	−0.235564	+	0.235564i
$848$	2.24202	−	2.24202i	0.0769913	−	0.0769913i
$849$	8.73175	−	2.70749i	0.299673	−	0.0929209i
$850$	0.843463	+	0.704582i	0.0289305	+	0.0241670i
$851$			10.4704i			0.358921i
$852$	−7.75442	+	14.7246i	−0.265662	+	0.504456i
$853$	10.5775	+	10.5775i	0.362167	+	0.362167i	0.864610	−	0.502443i	$-0.167565\pi$
$853$	10.5775	+	10.5775i	0.362167	+	0.362167i	−0.502443	+	0.864610i	$0.667565\pi$
$854$	−5.17267			−0.177005
$855$	23.0531	−	39.1643i	0.788399	−	1.33939i
$856$	−14.2490			−0.487021
$857$	16.4306	+	16.4306i	0.561257	+	0.561257i	0.929665	−	0.368407i	$-0.120097\pi$
$857$	16.4306	+	16.4306i	0.561257	+	0.561257i	−0.368407	+	0.929665i	$0.620097\pi$
$858$	2.09030	−	3.96919i	0.0713616	−	0.135506i
$859$			26.0435i			0.888591i	0.895880	+	0.444296i	$0.146546\pi$
$859$			26.0435i			0.888591i	−0.895880	+	0.444296i	$0.853454\pi$
$860$	−4.73224	+	13.0465i	−0.161368	+	0.444883i
$861$	−7.88818	+	2.44592i	−0.268829	+	0.0833568i
$862$	25.4026	−	25.4026i	0.865217	−	0.865217i
$863$	−18.9471	+	18.9471i	−0.644966	+	0.644966i	−0.951772	−	0.306806i	$-0.900740\pi$
$863$	−18.9471	+	18.9471i	−0.644966	+	0.644966i	0.306806	+	0.951772i	$0.400740\pi$
$864$	4.07680	+	3.22175i	0.138696	+	0.109606i
$865$	11.9223	−	32.8690i	0.405370	−	1.11758i
$866$			11.6683i			0.396506i
$867$	25.9789	+	13.6813i	0.882289	+	0.464640i
$868$	15.0092	+	15.0092i	0.509444	+	0.509444i
$869$	−31.3813			−1.06454
$870$	2.55224	−	2.32159i	0.0865289	−	0.0787092i
$871$	−15.5458			−0.526750
$872$	−6.49057	−	6.49057i	−0.219798	−	0.219798i
$873$	−36.9074	−	6.87060i	−1.24912	−	0.232535i
$874$			17.3735i			0.587669i
$875$	−12.7001	−	21.8299i	−0.429341	−	0.737985i
$876$	1.19834	+	3.86470i	0.0404883	+	0.130576i
$877$	20.9293	−	20.9293i	0.706733	−	0.706733i	−0.259114	−	0.965847i	$-0.583431\pi$
$877$	20.9293	−	20.9293i	0.706733	−	0.706733i	0.965847	+	0.259114i	$0.0834305\pi$
$878$	3.79596	−	3.79596i	0.128107	−	0.128107i
$879$	16.2895	+	52.5341i	0.549430	+	1.77193i
$880$	−2.45332	−	5.24604i	−0.0827014	−	0.176844i
$881$		−	50.6327i		−	1.70586i	−0.522027	−	0.852929i	$-0.674824\pi$
$881$		−	50.6327i		−	1.70586i	0.522027	−	0.852929i	$-0.325176\pi$
$882$	−5.59579	−	1.04170i	−0.188420	−	0.0350759i
$883$	12.6846	+	12.6846i	0.426870	+	0.426870i	0.887561	−	0.460690i	$-0.152398\pi$
$883$	12.6846	+	12.6846i	0.426870	+	0.426870i	−0.460690	+	0.887561i	$0.652398\pi$
$884$	0.219806			0.00739287
$885$	0.503679	−	10.6432i	0.0169310	−	0.357768i
$886$	−16.0443			−0.539018
$887$	1.82891	+	1.82891i	0.0614087	+	0.0614087i	0.737144	−	0.675735i	$-0.236174\pi$
$887$	1.82891	+	1.82891i	0.0614087	+	0.0614087i	−0.675735	+	0.737144i	$0.736174\pi$
$888$	−6.25701	−	3.29514i	−0.209972	−	0.110578i
$889$		−	25.7419i		−	0.863355i
$890$	13.5285	+	4.90708i	0.453478	+	0.164486i
$891$	21.7483	+	8.38790i	0.728594	+	0.281005i
$892$	−16.1979	+	16.1979i	−0.542344	+	0.542344i
$893$	−25.1880	+	25.1880i	−0.842884	+	0.842884i
$894$	−26.0071	+	8.06412i	−0.869806	+	0.269705i
$895$	23.2862	−	10.8898i	0.778372	−	0.364007i
$896$		−	2.25891i		−	0.0754650i
$897$	−2.06975	+	3.93017i	−0.0691069	+	0.131225i
$898$	11.3336	+	11.3336i	0.378206	+	0.378206i
$899$	8.37079			0.279182
$900$	1.41654	−	14.9330i	0.0472181	−	0.497765i
$901$	0.696938			0.0232184
$902$	3.86572	+	3.86572i	0.128714	+	0.128714i
$903$	−11.3152	+	21.4861i	−0.376547	+	0.715011i
$904$		−	11.0898i		−	0.368843i
$905$	−35.8057	+	16.7446i	−1.19022	+	0.556609i
$906$	−23.7058	+	7.35057i	−0.787573	+	0.244206i
$907$	17.4232	−	17.4232i	0.578527	−	0.578527i	−0.355970	−	0.934497i	$-0.615850\pi$
$907$	17.4232	−	17.4232i	0.578527	−	0.578527i	0.934497	+	0.355970i	$0.115850\pi$
$908$	17.2226	−	17.2226i	0.571551	−	0.571551i
$909$	40.0632	−	27.4880i	1.32881	−	0.911720i
$910$	−4.74837	−	1.72233i	−0.157407	−	0.0570948i
$911$		−	14.2063i		−	0.470675i	−0.971914	−	0.235337i	$-0.924380\pi$
$911$		−	14.2063i		−	0.470675i	0.971914	−	0.235337i	$-0.0756195\pi$
$912$	−10.3823	−	5.46761i	−0.343791	−	0.181051i
$913$	15.3826	+	15.3826i	0.509088	+	0.509088i
$914$	−1.36234			−0.0450621
$915$	−0.419232	+	8.85880i	−0.0138594	+	0.292863i
$916$	−23.5974			−0.779681
$917$	−22.6940	−	22.6940i	−0.749423	−	0.749423i
$918$	0.132898	+	1.13439i	0.00438628	+	0.0374403i
$919$		−	43.6851i		−	1.44104i	−0.693435	−	0.720519i	$-0.743904\pi$
$919$		−	43.6851i		−	1.44104i	0.693435	−	0.720519i	$-0.256096\pi$
$920$	2.42920	+	5.19447i	0.0800885	+	0.171257i
$921$	3.57006	+	11.5136i	0.117637	+	0.379384i
$922$	−12.3499	+	12.3499i	−0.406724	+	0.406724i
$923$	6.79393	−	6.79393i	0.223625	−	0.223625i
$924$	−3.00114	−	9.67878i	−0.0987303	−	0.318409i
$925$	1.82409	+	20.3324i	0.0599758	+	0.668526i
$926$			0.362561i			0.0119145i
$927$	8.86733	−	47.6334i	0.291241	−	1.56448i
$928$	−0.629912	−	0.629912i	−0.0206779	−	0.0206779i
$929$	56.7945			1.86337			0.931683	−	0.363271i	$-0.118340\pi$
$929$	56.7945			1.86337			0.931683	+	0.363271i	$0.118340\pi$
$930$	26.9214	−	24.4885i	0.882787	−	0.803009i
$931$	12.8535			0.421257
$932$	−7.44530	−	7.44530i	−0.243879	−	0.243879i
$933$	4.58965	+	2.41705i	0.150259	+	0.0791308i
$934$			25.1239i			0.822079i
$935$	0.434062	−	1.19668i	0.0141953	−	0.0391357i
$936$	−1.69726	−	2.47372i	−0.0554767	−	0.0808562i
$937$	−26.3475	+	26.3475i	−0.860735	+	0.860735i	−0.991423	−	0.130689i	$-0.958281\pi$
$937$	−26.3475	+	26.3475i	−0.860735	+	0.860735i	0.130689	+	0.991423i	$0.458281\pi$
$938$	−24.8312	+	24.8312i	−0.810768	+	0.810768i
$939$	53.5368	−	16.6004i	1.74711	−	0.541733i
$940$	−4.00905	+	11.0527i	−0.130761	+	0.360500i
$941$		−	52.6644i		−	1.71681i	−0.512973	−	0.858405i	$-0.671456\pi$
$941$		−	52.6644i		−	1.71681i	0.512973	−	0.858405i	$-0.328544\pi$
$942$	−11.2959	+	21.4493i	−0.368039	+	0.698856i
$943$	−3.82772	−	3.82772i	−0.124648	−	0.124648i
$944$	−2.75114			−0.0895421
$945$	6.01778	−	25.5470i	0.195758	−	0.831044i
$946$	16.0748			0.522635
$947$	42.2920	+	42.2920i	1.37431	+	1.37431i	0.853950	+	0.520356i	$0.174201\pi$
$947$	42.2920	+	42.2920i	1.37431	+	1.37431i	0.520356	+	0.853950i	$0.325799\pi$
$948$	−9.77889	+	18.5688i	−0.317604	+	0.603086i
$949$		−	2.33609i		−	0.0758326i
$950$	3.02671	+	33.7375i	0.0981996	+	1.09459i
$951$	−34.5598	+	10.7161i	−1.12068	+	0.347493i
$952$	0.351094	−	0.351094i	0.0113790	−	0.0113790i
$953$	4.65373	−	4.65373i	0.150749	−	0.150749i	−0.627704	−	0.778452i	$-0.716005\pi$
$953$	4.65373	−	4.65373i	0.150749	−	0.150749i	0.778452	+	0.627704i	$0.216005\pi$
$954$	−5.38150	−	7.84343i	−0.174233	−	0.253940i
$955$	17.0648	+	36.4904i	0.552205	+	1.18080i
$956$			19.2221i			0.621687i
$957$	−3.53588	−	1.86210i	−0.114299	−	0.0601932i
$958$	−15.0219	−	15.0219i	−0.485336	−	0.485336i
$959$	34.9963			1.13009
$960$	−3.86865	−	0.183080i	−0.124860	−	0.00590887i
$961$	57.2964			1.84827
$962$	2.88699	+	2.88699i	0.0930802	+	0.0930802i
$963$	−7.82330	+	42.0251i	−0.252102	+	1.35424i
$964$			16.0808i			0.517928i
$965$	−10.6591	−	3.86628i	−0.343129	−	0.124460i
$966$	2.97164	+	9.58363i	0.0956109	+	0.308348i
$967$	−21.6611	+	21.6611i	−0.696575	+	0.696575i	−0.963670	−	0.267095i	$-0.913936\pi$
$967$	−21.6611	+	21.6611i	−0.696575	+	0.696575i	0.267095	+	0.963670i	$0.413936\pi$
$968$	3.03494	−	3.03494i	0.0975468	−	0.0975468i
$969$	−0.763864	−	2.46349i	−0.0245388	−	0.0791385i
$970$	25.3470	−	11.8536i	0.813843	−	0.380595i
$971$			34.7889i			1.11643i	0.829697	+	0.558215i	$0.188513\pi$
$971$			34.7889i			1.11643i	−0.829697	+	0.558215i	$0.811487\pi$
$972$	11.7403	−	10.2550i	0.376572	−	0.328928i
$973$	24.0487	+	24.0487i	0.770967	+	0.770967i
$974$	−14.7955			−0.474077
$975$	−3.33454	+	7.99255i	−0.106791	+	0.255966i
$976$	2.28989			0.0732976
$977$	−23.2379	−	23.2379i	−0.743445	−	0.743445i	0.229794	−	0.973239i	$-0.426195\pi$
$977$	−23.2379	−	23.2379i	−0.743445	−	0.743445i	−0.973239	+	0.229794i	$0.926195\pi$
$978$	−19.7830	−	10.4183i	−0.632591	−	0.333142i
$979$		−	16.6687i		−	0.532733i
$980$	3.84304	−	1.79721i	0.122761	−	0.0574096i
$981$	−22.7064	+	15.5792i	−0.724961	+	0.497407i
$982$	−11.3982	+	11.3982i	−0.363731	+	0.363731i
$983$	−6.01349	+	6.01349i	−0.191801	+	0.191801i	−0.796474	−	0.604673i	$-0.793304\pi$
$983$	−6.01349	+	6.01349i	−0.191801	+	0.191801i	0.604673	+	0.796474i	$0.293304\pi$
$984$	3.49202	−	1.08279i	0.111322	−	0.0345180i
$985$	35.1905	+	12.7643i	1.12126	+	0.406705i
$986$		−	0.195810i		−	0.00623586i
$987$	−9.58601	+	18.2025i	−0.305126	+	0.579392i
$988$	4.79037	+	4.79037i	0.152402	+	0.152402i
$989$	−15.9167			−0.506122
$990$	−16.8193	+	4.35536i	−0.534552	+	0.138423i
$991$	−23.6719			−0.751961			−0.375981	−	0.926628i	$-0.622694\pi$
$991$	−23.6719			−0.751961			−0.375981	+	0.926628i	$0.622694\pi$
$992$	−6.64441	−	6.64441i	−0.210960	−	0.210960i
$993$	0.0902109	−	0.171298i	0.00286276	−	0.00543598i
$994$		−	21.7038i		−	0.688402i
$995$	−6.51840	−	13.9386i	−0.206647	−	0.441882i
$996$	13.8955	−	4.30865i	0.440297	−	0.136525i
$997$	17.4439	−	17.4439i	0.552453	−	0.552453i	−0.374695	−	0.927148i	$-0.622253\pi$
$997$	17.4439	−	17.4439i	0.552453	−	0.552453i	0.927148	+	0.374695i	$0.122253\pi$
$998$	0.210522	−	0.210522i	0.00666395	−	0.00666395i
$999$	−13.1538	+	16.6448i	−0.416168	+	0.526619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.l.c.53.3	✓	20
3.2	odd	2		390.2.l.d.53.9	yes	20
5.2	odd	4		390.2.l.d.287.9	yes	20
15.2	even	4	inner	390.2.l.c.287.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.l.c.53.3	✓	20	1.1	even	1	trivial
390.2.l.c.287.3	yes	20	15.2	even	4	inner
390.2.l.d.53.9	yes	20	3.2	odd	2
390.2.l.d.287.9	yes	20	5.2	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.807075 + 1.53252i) q^{3} +1.00000i q^{4} +(-2.02552 + 0.947239i) q^{5} +(1.65435 - 0.512970i) q^{6} +(-1.59729 + 1.59729i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.69726 - 2.47372i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.807075 + 1.53252i) q^{3} +1.00000i q^{4} +(-2.02552 + 0.947239i) q^{5} +(1.65435 - 0.512970i) q^{6} +(-1.59729 + 1.59729i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.69726 - 2.47372i) q^{9} +(2.10206 + 0.762461i) q^{10} -2.58997i q^{11} +(-1.53252 - 0.807075i) q^{12} +(0.707107 + 0.707107i) q^{13} +2.25891 q^{14} +(0.183080 - 3.86865i) q^{15} -1.00000 q^{16} +(-0.155426 - 0.155426i) q^{17} +(-0.549041 + 2.94933i) q^{18} -6.77461i q^{19} +(-0.947239 - 2.02552i) q^{20} +(-1.15876 - 3.73703i) q^{21} +(-1.83139 + 1.83139i) q^{22} +(1.81338 - 1.81338i) q^{23} +(0.512970 + 1.65435i) q^{24} +(3.20547 - 3.83731i) q^{25} -1.00000i q^{26} +(5.16086 - 0.604615i) q^{27} +(-1.59729 - 1.59729i) q^{28} -0.890831 q^{29} +(-2.86501 + 2.60609i) q^{30} -9.39662 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.96919 + 2.09030i) q^{33} +0.219806i q^{34} +(1.72233 - 4.74837i) q^{35} +(2.47372 - 1.69726i) q^{36} +(-2.88699 + 2.88699i) q^{37} +(-4.79037 + 4.79037i) q^{38} +(-1.65435 + 0.512970i) q^{39} +(-0.762461 + 2.10206i) q^{40} -2.11082i q^{41} +(-1.82311 + 3.46184i) q^{42} +(-4.38869 - 4.38869i) q^{43} +2.58997 q^{44} +(5.78105 + 3.40287i) q^{45} -2.56451 q^{46} +(-3.71800 - 3.71800i) q^{47} +(0.807075 - 1.53252i) q^{48} +1.89731i q^{49} +(-4.98000 + 0.446773i) q^{50} +(0.363635 - 0.112754i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(-2.24202 + 2.24202i) q^{53} +(-4.07680 - 3.22175i) q^{54} +(2.45332 + 5.24604i) q^{55} +2.25891i q^{56} +(10.3823 + 5.46761i) q^{57} +(0.629912 + 0.629912i) q^{58} +2.75114 q^{59} +(3.86865 + 0.183080i) q^{60} -2.28989 q^{61} +(6.64441 + 6.64441i) q^{62} +(6.66228 + 1.24024i) q^{63} -1.00000i q^{64} +(-2.10206 - 0.762461i) q^{65} +(-1.32858 - 4.28471i) q^{66} +(-10.9926 + 10.9926i) q^{67} +(0.155426 - 0.155426i) q^{68} +(1.31552 + 4.24259i) q^{69} +(-4.57548 + 2.13973i) q^{70} -9.60806i q^{71} +(-2.94933 - 0.549041i) q^{72} +(-1.65186 - 1.65186i) q^{73} +4.08282 q^{74} +(3.29371 + 8.00946i) q^{75} +6.77461 q^{76} +(4.13694 + 4.13694i) q^{77} +(1.53252 + 0.807075i) q^{78} -12.1165i q^{79} +(2.02552 - 0.947239i) q^{80} +(-3.23861 + 8.39711i) q^{81} +(-1.49257 + 1.49257i) q^{82} +(-5.93928 + 5.93928i) q^{83} +(3.73703 - 1.15876i) q^{84} +(0.462045 + 0.167593i) q^{85} +6.20654i q^{86} +(0.718967 - 1.36522i) q^{87} +(-1.83139 - 1.83139i) q^{88} +6.43585 q^{89} +(-1.68163 - 6.49401i) q^{90} -2.25891 q^{91} +(1.81338 + 1.81338i) q^{92} +(7.58377 - 14.4005i) q^{93} +5.25805i q^{94} +(6.41718 + 13.7221i) q^{95} +(-1.65435 + 0.512970i) q^{96} +(8.84860 - 8.84860i) q^{97} +(1.34160 - 1.34160i) q^{98} +(-6.40687 + 4.39585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q - 4 * q^7 - 4 * q^9	\( 20 q - 4 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} + 16 q^{14} + 4 q^{15} - 20 q^{16} - 12 q^{17} + 8 q^{18} - 16 q^{21} + 4 q^{22} - 16 q^{23} - 4 q^{24} + 32 q^{25} + 36 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{30} - 8 q^{31} + 36 q^{33} + 20 q^{35} - 4 q^{36} - 16 q^{37} - 24 q^{38} - 8 q^{40} + 4 q^{42} - 20 q^{43} - 16 q^{44} + 24 q^{45} - 40 q^{46} - 16 q^{47} + 12 q^{51} - 32 q^{53} - 28 q^{54} - 4 q^{55} + 16 q^{57} + 28 q^{58} - 16 q^{60} + 24 q^{61} - 40 q^{62} + 36 q^{63} + 8 q^{65} + 12 q^{68} - 72 q^{69} + 20 q^{70} + 8 q^{72} + 28 q^{73} + 48 q^{74} - 52 q^{75} + 16 q^{76} - 8 q^{77} + 4 q^{78} - 16 q^{81} - 112 q^{83} - 8 q^{85} + 4 q^{87} + 4 q^{88} + 88 q^{89} - 4 q^{90} - 16 q^{91} - 16 q^{92} + 40 q^{93} + 8 q^{95} + 36 q^{97} - 40 q^{99}+O(q^{100}) \) 20 * q - 4 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 + 16 * q^14 + 4 * q^15 - 20 * q^16 - 12 * q^17 + 8 * q^18 - 16 * q^21 + 4 * q^22 - 16 * q^23 - 4 * q^24 + 32 * q^25 + 36 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^30 - 8 * q^31 + 36 * q^33 + 20 * q^35 - 4 * q^36 - 16 * q^37 - 24 * q^38 - 8 * q^40 + 4 * q^42 - 20 * q^43 - 16 * q^44 + 24 * q^45 - 40 * q^46 - 16 * q^47 + 12 * q^51 - 32 * q^53 - 28 * q^54 - 4 * q^55 + 16 * q^57 + 28 * q^58 - 16 * q^60 + 24 * q^61 - 40 * q^62 + 36 * q^63 + 8 * q^65 + 12 * q^68 - 72 * q^69 + 20 * q^70 + 8 * q^72 + 28 * q^73 + 48 * q^74 - 52 * q^75 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 16 * q^81 - 112 * q^83 - 8 * q^85 + 4 * q^87 + 4 * q^88 + 88 * q^89 - 4 * q^90 - 16 * q^91 - 16 * q^92 + 40 * q^93 + 8 * q^95 + 36 * q^97 - 40 * q^99

Introduction

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