LMFDB - Embedded newform 546.2.i.k.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.21870000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 24x^{4} - 43x^{3} + 138x^{2} - 117x + 73 $ x^6 - 3x^5 + 24x^4 - 43x^3 + 138x^2 - 117*x + 73
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.500000 - 0.679547i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.2.i.k.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.90280 - 3.29575i) q^{5} +1.00000 q^{6} +(-2.64411 + 0.0932392i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.90280 - 3.29575i) q^{5} +1.00000 q^{6} +(-2.64411 + 0.0932392i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.90280 - 3.29575i) q^{10} +(-2.64411 + 4.57973i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.40280 - 2.24325i) q^{14} -3.80560 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.07981 + 5.33439i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.74131 - 4.74808i) q^{19} +3.80560 q^{20} +(-1.24131 + 2.33648i) q^{21} -5.28822 q^{22} +(-3.14411 - 5.44575i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.74131 + 8.21218i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.24131 - 2.33648i) q^{28} -3.00000 q^{29} +(-1.90280 - 3.29575i) q^{30} +(4.24131 - 7.34616i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.64411 + 4.57973i) q^{33} -6.15962 q^{34} +(5.33851 + 8.53690i) q^{35} +1.00000 q^{36} +(-0.661495 - 1.14574i) q^{37} +(2.74131 - 4.74808i) q^{38} +(0.500000 - 0.866025i) q^{39} +(1.90280 + 3.29575i) q^{40} +5.32299 q^{41} +(-2.64411 + 0.0932392i) q^{42} +1.61121 q^{43} +(-2.64411 - 4.57973i) q^{44} +(-1.90280 + 3.29575i) q^{45} +(3.14411 - 5.44575i) q^{46} +(-3.54691 - 6.14343i) q^{47} -1.00000 q^{48} +(6.98261 - 0.493069i) q^{49} -9.48261 q^{50} +(3.07981 + 5.33439i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(0.177010 - 0.306590i) q^{53} +(-0.500000 - 0.866025i) q^{54} +20.1248 q^{55} +(2.64411 - 0.0932392i) q^{56} -5.48261 q^{57} +(-1.50000 - 2.59808i) q^{58} +(0.838505 - 1.45233i) q^{59} +(1.90280 - 3.29575i) q^{60} +(4.88541 + 8.46179i) q^{61} +8.48261 q^{62} +(1.40280 + 2.24325i) q^{63} +1.00000 q^{64} +(-1.90280 - 3.29575i) q^{65} +(-2.64411 + 4.57973i) q^{66} +(4.22392 - 7.31604i) q^{67} +(-3.07981 - 5.33439i) q^{68} -6.28822 q^{69} +(-4.72392 + 8.89173i) q^{70} -15.4826 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.855892 + 1.48245i) q^{73} +(0.661495 - 1.14574i) q^{74} +(4.74131 + 8.21218i) q^{75} +5.48261 q^{76} +(6.56430 - 12.3558i) q^{77} +1.00000 q^{78} +(-1.43570 - 2.48671i) q^{79} +(-1.90280 + 3.29575i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.66149 + 4.60984i) q^{82} -7.44784 q^{83} +(-1.40280 - 2.24325i) q^{84} +23.4411 q^{85} +(0.805603 + 1.39535i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(2.64411 - 4.57973i) q^{88} +(-5.33851 - 9.24656i) q^{89} -3.80560 q^{90} +(-2.64411 + 0.0932392i) q^{91} +6.28822 q^{92} +(-4.24131 - 7.34616i) q^{93} +(3.54691 - 6.14343i) q^{94} +(-10.4323 + 18.0693i) q^{95} +(-0.500000 - 0.866025i) q^{96} -3.15962 q^{97} +(3.91832 + 5.80059i) q^{98} +5.28822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 6 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} + 6 q^{22} - 3 q^{24} - 18 q^{25} + 3 q^{26} - 6 q^{27} - 3 q^{28} - 18 q^{29} - 3 q^{30} + 15 q^{31} + 3 q^{32} - 3 q^{33} - 12 q^{34} + 30 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 36 q^{41} + 3 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{47} - 6 q^{48} + 21 q^{49} - 36 q^{50} + 6 q^{51} - 3 q^{52} - 3 q^{53} - 3 q^{54} + 54 q^{55} - 3 q^{56} - 12 q^{57} - 9 q^{58} + 3 q^{59} + 3 q^{60} + 30 q^{62} + 6 q^{64} - 3 q^{65} + 3 q^{66} - 6 q^{67} - 6 q^{68} + 3 q^{70} - 72 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} + 18 q^{75} + 12 q^{76} + 33 q^{77} + 6 q^{78} - 15 q^{79} - 3 q^{80} - 3 q^{81} + 18 q^{82} + 18 q^{83} - 48 q^{85} - 12 q^{86} - 9 q^{87} - 3 q^{88} - 30 q^{89} - 6 q^{90} + 3 q^{91} - 15 q^{93} - 6 q^{94} - 6 q^{95} - 3 q^{96} + 6 q^{97} + 9 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 6 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 + 6 * q^22 - 3 * q^24 - 18 * q^25 + 3 * q^26 - 6 * q^27 - 3 * q^28 - 18 * q^29 - 3 * q^30 + 15 * q^31 + 3 * q^32 - 3 * q^33 - 12 * q^34 + 30 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 36 * q^41 + 3 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^47 - 6 * q^48 + 21 * q^49 - 36 * q^50 + 6 * q^51 - 3 * q^52 - 3 * q^53 - 3 * q^54 + 54 * q^55 - 3 * q^56 - 12 * q^57 - 9 * q^58 + 3 * q^59 + 3 * q^60 + 30 * q^62 + 6 * q^64 - 3 * q^65 + 3 * q^66 - 6 * q^67 - 6 * q^68 + 3 * q^70 - 72 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 + 18 * q^75 + 12 * q^76 + 33 * q^77 + 6 * q^78 - 15 * q^79 - 3 * q^80 - 3 * q^81 + 18 * q^82 + 18 * q^83 - 48 * q^85 - 12 * q^86 - 9 * q^87 - 3 * q^88 - 30 * q^89 - 6 * q^90 + 3 * q^91 - 15 * q^93 - 6 * q^94 - 6 * q^95 - 3 * q^96 + 6 * q^97 + 9 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.90280	−	3.29575i	−0.850959	−	1.47390i	−0.880344	−	0.474335i	$-0.842688\pi$
$5$	−1.90280	−	3.29575i	−0.850959	−	1.47390i	0.0293855	−	0.999568i	$-0.490645\pi$
$6$	1.00000			0.408248
$7$	−2.64411	+	0.0932392i	−0.999379	+	0.0352411i
$7$	−2.64411	+	0.0932392i	−0.999379	+	0.0352411i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.90280	−	3.29575i	0.601719	−	1.04221i
$11$	−2.64411	+	4.57973i	−0.797229	+	1.38084i	0.124186	+	0.992259i	$0.460368\pi$
$11$	−2.64411	+	4.57973i	−0.797229	+	1.38084i	−0.921414	+	0.388581i	$0.872965\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−1.40280	−	2.24325i	−0.374914	−	0.599532i
$15$	−3.80560			−0.982602
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.07981	+	5.33439i	−0.746964	+	1.29378i	0.202308	+	0.979322i	$0.435156\pi$
$17$	−3.07981	+	5.33439i	−0.746964	+	1.29378i	−0.949272	+	0.314458i	$0.898177\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.74131	−	4.74808i	−0.628899	−	1.08928i	−0.987773	−	0.155899i	$-0.950173\pi$
$19$	−2.74131	−	4.74808i	−0.628899	−	1.08928i	0.358874	−	0.933386i	$-0.383161\pi$
$20$	3.80560			0.850959
$21$	−1.24131	+	2.33648i	−0.270875	+	0.509863i
$22$	−5.28822			−1.12745
$23$	−3.14411	−	5.44575i	−0.655592	−	1.13552i	−0.981745	−	0.190201i	$-0.939086\pi$
$23$	−3.14411	−	5.44575i	−0.655592	−	1.13552i	0.326153	−	0.945317i	$-0.394247\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.74131	+	8.21218i	−0.948261	+	1.64244i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	1.24131	−	2.33648i	0.234585	−	0.441554i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	−1.90280	−	3.29575i	−0.347402	−	0.601719i
$31$	4.24131	−	7.34616i	0.761761	−	1.31941i	−0.180181	−	0.983633i	$-0.557668\pi$
$31$	4.24131	−	7.34616i	0.761761	−	1.31941i	0.941942	−	0.335775i	$-0.108998\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.64411	+	4.57973i	0.460280	+	0.797229i
$34$	−6.15962			−1.05637
$35$	5.33851	+	8.53690i	0.902372	+	1.44300i
$36$	1.00000			0.166667
$37$	−0.661495	−	1.14574i	−0.108749	−	0.188359i	0.806515	−	0.591214i	$-0.201351\pi$
$37$	−0.661495	−	1.14574i	−0.108749	−	0.188359i	−0.915264	+	0.402855i	$0.868018\pi$
$38$	2.74131	−	4.74808i	0.444699	−	0.770241i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	1.90280	+	3.29575i	0.300859	+	0.521104i
$41$	5.32299			0.831311			0.415656	−	0.909522i	$-0.363552\pi$
$41$	5.32299			0.831311			0.415656	+	0.909522i	$0.363552\pi$
$42$	−2.64411	+	0.0932392i	−0.407995	+	0.0143871i
$43$	1.61121			0.245707			0.122853	−	0.992425i	$-0.460796\pi$
$43$	1.61121			0.245707			0.122853	+	0.992425i	$0.460796\pi$
$44$	−2.64411	−	4.57973i	−0.398614	−	0.690420i
$45$	−1.90280	+	3.29575i	−0.283653	+	0.491301i
$46$	3.14411	−	5.44575i	0.463573	−	0.802933i
$47$	−3.54691	−	6.14343i	−0.517370	−	0.896111i	−0.999796	−	0.0201745i	$-0.993578\pi$
$47$	−3.54691	−	6.14343i	−0.517370	−	0.896111i	0.482427	−	0.875936i	$-0.339756\pi$
$48$	−1.00000			−0.144338
$49$	6.98261	−	0.493069i	0.997516	−	0.0704384i
$50$	−9.48261			−1.34104
$51$	3.07981	+	5.33439i	0.431260	+	0.746964i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	0.177010	−	0.306590i	0.0243142	−	0.0421134i	−0.853612	−	0.520909i	$-0.825593\pi$
$53$	0.177010	−	0.306590i	0.0243142	−	0.0421134i	0.877926	+	0.478795i	$0.158926\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	20.1248			2.71363
$56$	2.64411	−	0.0932392i	0.353334	−	0.0124596i
$57$	−5.48261			−0.726190
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	0.838505	−	1.45233i	0.109164	−	0.189078i	−0.806268	−	0.591551i	$-0.798516\pi$
$59$	0.838505	−	1.45233i	0.109164	−	0.189078i	0.915432	+	0.402473i	$0.131849\pi$
$60$	1.90280	−	3.29575i	0.245651	−	0.425479i
$61$	4.88541	+	8.46179i	0.625513	+	1.08342i	0.988441	+	0.151604i	$0.0484437\pi$
$61$	4.88541	+	8.46179i	0.625513	+	1.08342i	−0.362928	+	0.931817i	$0.618223\pi$
$62$	8.48261			1.07729
$63$	1.40280	+	2.24325i	0.176736	+	0.282622i
$64$	1.00000			0.125000
$65$	−1.90280	−	3.29575i	−0.236013	−	0.408787i
$66$	−2.64411	+	4.57973i	−0.325467	+	0.563726i
$67$	4.22392	−	7.31604i	0.516034	−	0.893797i	−0.483793	−	0.875183i	$-0.660741\pi$
$67$	4.22392	−	7.31604i	0.516034	−	0.893797i	0.999827	−	0.0186144i	$-0.00592548\pi$
$68$	−3.07981	−	5.33439i	−0.373482	−	0.646890i
$69$	−6.28822			−0.757012
$70$	−4.72392	+	8.89173i	−0.564616	+	1.06277i
$71$	−15.4826			−1.83745			−0.918724	−	0.394900i	$-0.870779\pi$
$71$	−15.4826			−1.83745			−0.918724	+	0.394900i	$0.870779\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−0.855892	+	1.48245i	−0.100175	+	0.173507i	−0.911756	−	0.410731i	$-0.865273\pi$
$73$	−0.855892	+	1.48245i	−0.100175	+	0.173507i	0.811582	+	0.584239i	$0.198607\pi$
$74$	0.661495	−	1.14574i	0.0768972	−	0.133190i
$75$	4.74131	+	8.21218i	0.547479	+	0.948261i
$76$	5.48261			0.628899
$77$	6.56430	−	12.3558i	0.748071	−	1.40808i
$78$	1.00000			0.113228
$79$	−1.43570	−	2.48671i	−0.161529	−	0.279777i	0.773888	−	0.633322i	$-0.218309\pi$
$79$	−1.43570	−	2.48671i	−0.161529	−	0.279777i	−0.935417	+	0.353546i	$0.884976\pi$
$80$	−1.90280	+	3.29575i	−0.212740	+	0.368476i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.66149	+	4.60984i	0.293913	+	0.509072i
$83$	−7.44784			−0.817507			−0.408753	−	0.912645i	$-0.634036\pi$
$83$	−7.44784			−0.817507			−0.408753	+	0.912645i	$0.634036\pi$
$84$	−1.40280	−	2.24325i	−0.153058	−	0.244758i
$85$	23.4411			2.54254
$86$	0.805603	+	1.39535i	0.0868704	+	0.150464i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	2.64411	−	4.57973i	0.281863	−	0.488201i
$89$	−5.33851	−	9.24656i	−0.565880	−	0.980134i	−0.996967	−	0.0778231i	$-0.975203\pi$
$89$	−5.33851	−	9.24656i	−0.565880	−	0.980134i	0.431087	−	0.902310i	$-0.358130\pi$
$90$	−3.80560			−0.401146
$91$	−2.64411	+	0.0932392i	−0.277178	+	0.00977412i
$92$	6.28822			0.655592
$93$	−4.24131	−	7.34616i	−0.439803	−	0.761761i
$94$	3.54691	−	6.14343i	0.365836	−	0.633646i
$95$	−10.4323	+	18.0693i	−1.07033	+	1.85387i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−3.15962			−0.320811			−0.160406	−	0.987051i	$-0.551280\pi$
$97$	−3.15962			−0.320811			−0.160406	+	0.987051i	$0.551280\pi$
$98$	3.91832	+	5.80059i	0.395810	+	0.585948i
$99$	5.28822			0.531486
$100$	−4.74131	−	8.21218i	−0.474131	−	0.821218i
$101$	2.48261	−	4.30001i	0.247029	−	0.427867i	−0.715671	−	0.698438i	$-0.753879\pi$
$101$	2.48261	−	4.30001i	0.247029	−	0.427867i	0.962700	+	0.270570i	$0.0872123\pi$
$102$	−3.07981	+	5.33439i	−0.304947	+	0.528183i
$103$	2.80560	+	4.85945i	0.276444	+	0.478816i	0.970498	−	0.241107i	$-0.0775105\pi$
$103$	2.80560	+	4.85945i	0.276444	+	0.478816i	−0.694054	+	0.719923i	$0.744177\pi$
$104$	−1.00000			−0.0980581
$105$	10.0624	−	0.354831i	0.981992	−	0.0346280i
$106$	0.354020			0.0343855
$107$	8.52952	+	14.7736i	0.824580	+	1.42821i	0.902240	+	0.431235i	$0.141922\pi$
$107$	8.52952	+	14.7736i	0.824580	+	1.42821i	−0.0776598	+	0.996980i	$0.524745\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$	10.0624	+	17.4286i	0.959415	+	1.66175i
$111$	−1.32299			−0.125573
$112$	1.40280	+	2.24325i	0.132552	+	0.211967i
$113$	−5.45158			−0.512842			−0.256421	−	0.966565i	$-0.582543\pi$
$113$	−5.45158			−0.512842			−0.256421	+	0.966565i	$0.582543\pi$
$114$	−2.74131	−	4.74808i	−0.256747	−	0.444699i
$115$	−11.9652	+	20.7244i	−1.11576	+	1.93256i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	1.67701			0.154381
$119$	7.64598	−	14.3919i	0.700906	−	1.31930i
$120$	3.80560			0.347402
$121$	−8.48261	−	14.6923i	−0.771147	−	1.33567i
$122$	−4.88541	+	8.46179i	−0.442305	+	0.766094i
$123$	2.66149	−	4.60984i	0.239979	−	0.415656i
$124$	4.24131	+	7.34616i	0.380881	+	0.659704i
$125$	17.0590			1.52581
$126$	−1.24131	+	2.33648i	−0.110584	+	0.208151i
$127$	−10.1248			−0.898435			−0.449218	−	0.893422i	$-0.648297\pi$
$127$	−10.1248			−0.898435			−0.449218	+	0.893422i	$0.648297\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.805603	−	1.39535i	0.0709294	−	0.122853i
$130$	1.90280	−	3.29575i	0.166887	−	0.289056i
$131$	−5.03139	−	8.71463i	−0.439595	−	0.761401i	0.558063	−	0.829798i	$-0.311545\pi$
$131$	−5.03139	−	8.71463i	−0.439595	−	0.761401i	−0.997658	+	0.0683977i	$0.978211\pi$
$132$	−5.28822			−0.460280
$133$	7.69102	+	12.2988i	0.666896	+	1.06645i
$134$	8.44784			0.729782
$135$	1.90280	+	3.29575i	0.163767	+	0.283653i
$136$	3.07981	−	5.33439i	0.264092	−	0.457420i
$137$	3.33851	−	5.78246i	0.285228	−	0.494029i	−0.687437	−	0.726244i	$-0.741264\pi$
$137$	3.33851	−	5.78246i	0.285228	−	0.494029i	0.972664	+	0.232215i	$0.0745974\pi$
$138$	−3.14411	−	5.44575i	−0.267644	−	0.463573i
$139$	−12.2882			−1.04227			−0.521136	−	0.853473i	$-0.674492\pi$
$139$	−12.2882			−1.04227			−0.521136	+	0.853473i	$0.674492\pi$
$140$	−10.0624	+	0.354831i	−0.850430	+	0.0299887i
$141$	−7.09382			−0.597407
$142$	−7.74131	−	13.4083i	−0.649636	−	1.12520i
$143$	−2.64411	+	4.57973i	−0.221111	+	0.382976i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	5.70840	+	9.88725i	0.474057	+	0.821091i
$146$	−1.71178			−0.141668
$147$	3.06430	−	6.29365i	0.252739	−	0.519092i
$148$	1.32299			0.108749
$149$	9.14411	+	15.8381i	0.749115	+	1.29750i	0.948248	+	0.317532i	$0.102854\pi$
$149$	9.14411	+	15.8381i	0.749115	+	1.29750i	−0.199133	+	0.979972i	$0.563813\pi$
$150$	−4.74131	+	8.21218i	−0.387126	+	0.670522i
$151$	7.64411	−	13.2400i	0.622069	−	1.07745i	−0.367031	−	0.930209i	$-0.619626\pi$
$151$	7.64411	−	13.2400i	0.622069	−	1.07745i	0.989100	−	0.147246i	$-0.0470409\pi$
$152$	2.74131	+	4.74808i	0.222349	+	0.385120i
$153$	6.15962			0.497976
$154$	13.9826	−	0.493069i	1.12675	−	0.0397326i
$155$	−32.2815			−2.59291
$156$	0.500000	+	0.866025i	0.0400320	+	0.0693375i
$157$	−5.20840	+	9.02122i	−0.415676	+	0.719972i	−0.995499	−	0.0947705i	$-0.969788\pi$
$157$	−5.20840	+	9.02122i	−0.415676	+	0.719972i	0.579823	+	0.814742i	$0.303122\pi$
$158$	1.43570	−	2.48671i	0.114218	−	0.197832i
$159$	−0.177010	−	0.306590i	−0.0140378	−	0.0243142i
$160$	−3.80560			−0.300859
$161$	8.82112	+	14.1060i	0.695201	+	1.11171i
$162$	−1.00000			−0.0785674
$163$	4.86990	+	8.43491i	0.381440	+	0.660673i	0.991268	−	0.131860i	$-0.0420950\pi$
$163$	4.86990	+	8.43491i	0.381440	+	0.660673i	−0.609828	+	0.792533i	$0.708762\pi$
$164$	−2.66149	+	4.60984i	−0.207828	+	0.359968i
$165$	10.0624	−	17.4286i	0.783359	−	1.35682i
$166$	−3.72392	−	6.45002i	−0.289032	−	0.500618i
$167$	−8.70502			−0.673615			−0.336808	−	0.941574i	$-0.609347\pi$
$167$	−8.70502			−0.673615			−0.336808	+	0.941574i	$0.609347\pi$
$168$	1.24131	−	2.33648i	0.0957689	−	0.180264i
$169$	1.00000			0.0769231
$170$	11.7205	+	20.3006i	0.898924	+	1.55698i
$171$	−2.74131	+	4.74808i	−0.209633	+	0.363095i
$172$	−0.805603	+	1.39535i	−0.0614266	+	0.106394i
$173$	6.02952	+	10.4434i	0.458416	+	0.794000i	0.998877	−	0.0473689i	$-0.0150836\pi$
$173$	6.02952	+	10.4434i	0.458416	+	0.794000i	−0.540461	+	0.841369i	$0.681750\pi$
$174$	−3.00000			−0.227429
$175$	11.7708	−	22.1560i	0.889791	−	1.67483i
$176$	5.28822			0.398614
$177$	−0.838505	−	1.45233i	−0.0630259	−	0.109164i
$178$	5.33851	−	9.24656i	0.400138	−	0.693059i
$179$	2.12859	−	3.68683i	0.159098	−	0.275567i	−0.775445	−	0.631415i	$-0.782475\pi$
$179$	2.12859	−	3.68683i	0.159098	−	0.275567i	0.934544	+	0.355848i	$0.115808\pi$
$180$	−1.90280	−	3.29575i	−0.141826	−	0.245651i
$181$	12.1596			0.903818			0.451909	−	0.892064i	$-0.350743\pi$
$181$	12.1596			0.903818			0.451909	+	0.892064i	$0.350743\pi$
$182$	−1.40280	−	2.24325i	−0.103983	−	0.166280i
$183$	9.77083			0.722280
$184$	3.14411	+	5.44575i	0.231787	+	0.401466i
$185$	−2.51739	+	4.36024i	−0.185082	+	0.320571i
$186$	4.24131	−	7.34616i	0.310988	−	0.538646i
$187$	−16.2867	−	28.2094i	−1.19100	−	2.06288i
$188$	7.09382			0.517370
$189$	2.64411	−	0.0932392i	0.192331	−	0.00678215i
$190$	−20.8646			−1.51368
$191$	12.0938	+	20.9471i	0.875078	+	1.51568i	0.856680	+	0.515849i	$0.172523\pi$
$191$	12.0938	+	20.9471i	0.875078	+	1.51568i	0.0183984	+	0.999831i	$0.494143\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−0.774209	+	1.34097i	−0.0557288	+	0.0965250i	−0.892544	−	0.450960i	$-0.851082\pi$
$193$	−0.774209	+	1.34097i	−0.0557288	+	0.0965250i	0.836815	+	0.547485i	$0.184415\pi$
$194$	−1.57981	−	2.73631i	−0.113424	−	0.196456i
$195$	−3.80560			−0.272525
$196$	−3.06430	+	6.29365i	−0.218878	+	0.449547i
$197$	−18.2882			−1.30298			−0.651491	−	0.758657i	$-0.725856\pi$
$197$	−18.2882			−1.30298			−0.651491	+	0.758657i	$0.725856\pi$
$198$	2.64411	+	4.57973i	0.187909	+	0.325467i
$199$	13.1093	−	22.7060i	0.929296	−	1.60959i	0.144794	−	0.989462i	$-0.453748\pi$
$199$	13.1093	−	22.7060i	0.929296	−	1.60959i	0.784502	−	0.620126i	$-0.212919\pi$
$200$	4.74131	−	8.21218i	0.335261	−	0.580689i
$201$	−4.22392	−	7.31604i	−0.297932	−	0.516034i
$202$	4.96523			0.349352
$203$	7.93232	−	0.279717i	0.556740	−	0.0196323i
$204$	−6.15962			−0.431260
$205$	−10.1286	−	17.5432i	−0.707412	−	1.22527i
$206$	−2.80560	+	4.85945i	−0.195476	+	0.338574i
$207$	−3.14411	+	5.44575i	−0.218531	+	0.378506i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	28.9932			2.00550
$210$	5.33851	+	8.53690i	0.368392	+	0.589102i
$211$	−9.89942			−0.681504			−0.340752	−	0.940153i	$-0.610682\pi$
$211$	−9.89942			−0.681504			−0.340752	+	0.940153i	$0.610682\pi$
$212$	0.177010	+	0.306590i	0.0121571	+	0.0210567i
$213$	−7.74131	+	13.4083i	−0.530426	+	0.918724i
$214$	−8.52952	+	14.7736i	−0.583066	+	1.00990i
$215$	−3.06580	−	5.31013i	−0.209086	−	0.362148i
$216$	1.00000			0.0680414
$217$	−10.5295	+	19.8195i	−0.714791	+	1.34543i
$218$	−4.00000			−0.270914
$219$	0.855892	+	1.48245i	0.0578358	+	0.100175i
$220$	−10.0624	+	17.4286i	−0.678409	+	1.17504i
$221$	−3.07981	+	5.33439i	−0.207171	+	0.358830i
$222$	−0.661495	−	1.14574i	−0.0443966	−	0.0768972i
$223$	2.96897			0.198817			0.0994085	−	0.995047i	$-0.468305\pi$
$223$	2.96897			0.198817			0.0994085	+	0.995047i	$0.468305\pi$
$224$	−1.24131	+	2.33648i	−0.0829383	+	0.156113i
$225$	9.48261			0.632174
$226$	−2.72579	−	4.72121i	−0.181317	−	0.314050i
$227$	−9.20653	+	15.9462i	−0.611059	+	1.05839i	0.380003	+	0.924985i	$0.375923\pi$
$227$	−9.20653	+	15.9462i	−0.611059	+	1.05839i	−0.991062	+	0.133400i	$0.957410\pi$
$228$	2.74131	−	4.74808i	0.181547	−	0.314449i
$229$	0.711784	+	1.23285i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$229$	0.711784	+	1.23285i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$230$	−23.9305			−1.57793
$231$	−7.41832	−	11.8628i	−0.488089	−	0.780513i
$232$	3.00000			0.196960
$233$	−5.36803	−	9.29770i	−0.351671	−	0.609112i	0.634871	−	0.772618i	$-0.281053\pi$
$233$	−5.36803	−	9.29770i	−0.351671	−	0.609112i	−0.986542	+	0.163506i	$0.947720\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−13.4981	+	23.3794i	−0.880521	+	1.52511i
$236$	0.838505	+	1.45233i	0.0545820	+	0.0945388i
$237$	−2.87141			−0.186518
$238$	16.2867	−	0.574318i	1.05571	−	0.0372275i
$239$	2.12859			0.137687			0.0688436	−	0.997627i	$-0.478069\pi$
$239$	2.12859			0.137687			0.0688436	+	0.997627i	$0.478069\pi$
$240$	1.90280	+	3.29575i	0.122825	+	0.212740i
$241$	−9.36990	+	16.2291i	−0.603568	+	1.04541i	0.388708	+	0.921361i	$0.372922\pi$
$241$	−9.36990	+	16.2291i	−0.603568	+	1.04541i	−0.992276	+	0.124050i	$0.960412\pi$
$242$	8.48261	−	14.6923i	0.545283	−	0.944458i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−9.77083			−0.625513
$245$	−14.9116	−	22.0747i	−0.952664	−	1.41030i
$246$	5.32299			0.339381
$247$	−2.74131	−	4.74808i	−0.174425	−	0.302113i
$248$	−4.24131	+	7.34616i	−0.269323	+	0.466482i
$249$	−3.72392	+	6.45002i	−0.235994	+	0.408753i
$250$	8.52952	+	14.7736i	0.539454	+	0.934362i
$251$	−7.77457			−0.490727			−0.245363	−	0.969431i	$-0.578907\pi$
$251$	−7.77457			−0.490727			−0.245363	+	0.969431i	$0.578907\pi$
$252$	−2.64411	+	0.0932392i	−0.166563	+	0.00587351i
$253$	33.2534			2.09063
$254$	−5.06242	−	8.76838i	−0.317645	−	0.550177i
$255$	11.7205	−	20.3006i	0.733969	−	1.27127i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.28822	−	5.69536i	−0.205113	−	0.355267i	0.745056	−	0.667002i	$-0.232423\pi$
$257$	−3.28822	−	5.69536i	−0.205113	−	0.355267i	−0.950169	+	0.311736i	$0.899090\pi$
$258$	1.61121			0.100309
$259$	1.85589	+	2.96779i	0.115320	+	0.184410i
$260$	3.80560			0.236013
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	5.03139	−	8.71463i	0.310841	−	0.538392i
$263$	10.2379	−	17.7326i	0.631298	−	1.09344i	−0.355989	−	0.934490i	$-0.615856\pi$
$263$	10.2379	−	17.7326i	0.631298	−	1.09344i	0.987287	−	0.158949i	$-0.0508107\pi$
$264$	−2.64411	−	4.57973i	−0.162734	−	0.281863i
$265$	−1.34726			−0.0827615
$266$	−6.80560	+	12.8100i	−0.417278	+	0.785434i
$267$	−10.6770			−0.653422
$268$	4.22392	+	7.31604i	0.258017	+	0.446898i
$269$	12.0764	−	20.9170i	0.736313	−	1.27533i	−0.217832	−	0.975986i	$-0.569898\pi$
$269$	12.0764	−	20.9170i	0.736313	−	1.27533i	0.954145	−	0.299345i	$-0.0967682\pi$
$270$	−1.90280	+	3.29575i	−0.115801	+	0.200573i
$271$	−15.2205	−	26.3627i	−0.924582	−	1.60142i	−0.792232	−	0.610220i	$-0.791081\pi$
$271$	−15.2205	−	26.3627i	−0.924582	−	1.60142i	−0.132350	−	0.991203i	$-0.542252\pi$
$272$	6.15962			0.373482
$273$	−1.24131	+	2.33648i	−0.0751273	+	0.141410i
$274$	6.67701			0.403373
$275$	−25.0731	−	43.4278i	−1.51196	−	2.61879i
$276$	3.14411	−	5.44575i	0.189253	−	0.327796i
$277$	4.56242	−	7.90235i	0.274130	−	0.474806i	−0.695786	−	0.718250i	$-0.744944\pi$
$277$	4.56242	−	7.90235i	0.274130	−	0.474806i	0.969915	+	0.243443i	$0.0782770\pi$
$278$	−6.14411	−	10.6419i	−0.368499	−	0.638259i
$279$	−8.48261			−0.507841
$280$	−5.33851	−	8.53690i	−0.319037	−	0.510177i
$281$	−6.70804			−0.400168			−0.200084	−	0.979779i	$-0.564122\pi$
$281$	−6.70804			−0.400168			−0.200084	+	0.979779i	$0.564122\pi$
$282$	−3.54691	−	6.14343i	−0.211215	−	0.365836i
$283$	−13.4323	+	23.2655i	−0.798469	+	1.38299i	0.122144	+	0.992512i	$0.461023\pi$
$283$	−13.4323	+	23.2655i	−0.798469	+	1.38299i	−0.920613	+	0.390476i	$0.872310\pi$
$284$	7.74131	−	13.4083i	0.459362	−	0.795638i
$285$	10.4323	+	18.0693i	0.617958	+	1.07033i
$286$	−5.28822			−0.312699
$287$	−14.0746	+	0.496311i	−0.830795	+	0.0292963i
$288$	−1.00000			−0.0589256
$289$	−10.4705	−	18.1354i	−0.615910	−	1.06679i
$290$	−5.70840	+	9.88725i	−0.335209	+	0.580599i
$291$	−1.57981	+	2.73631i	−0.0926102	+	0.160406i
$292$	−0.855892	−	1.48245i	−0.0500873	−	0.0867537i
$293$	9.80560			0.572849			0.286425	−	0.958103i	$-0.407533\pi$
$293$	9.80560			0.572849			0.286425	+	0.958103i	$0.407533\pi$
$294$	6.98261	−	0.493069i	0.407234	−	0.0287564i
$295$	−6.38203			−0.371576
$296$	0.661495	+	1.14574i	0.0384486	+	0.0665950i
$297$	2.64411	−	4.57973i	0.153427	−	0.265743i
$298$	−9.14411	+	15.8381i	−0.529704	+	0.917474i
$299$	−3.14411	−	5.44575i	−0.181828	−	0.314936i
$300$	−9.48261			−0.547479
$301$	−4.26020	+	0.150227i	−0.245554	+	0.00865897i
$302$	15.2882			0.879738
$303$	−2.48261	−	4.30001i	−0.142622	−	0.247029i
$304$	−2.74131	+	4.74808i	−0.157225	+	0.272321i
$305$	18.5919	−	32.2022i	1.06457	−	1.84389i
$306$	3.07981	+	5.33439i	0.176061	+	0.304947i
$307$	20.5174			1.17099			0.585495	−	0.810676i	$-0.300900\pi$
$307$	20.5174			1.17099			0.585495	+	0.810676i	$0.300900\pi$
$308$	7.41832	+	11.8628i	0.422698	+	0.675944i
$309$	5.61121			0.319210
$310$	−16.1407	−	27.9566i	−0.916732	−	1.58783i
$311$	11.2727	−	19.5249i	0.639216	−	1.10715i	−0.346389	−	0.938091i	$-0.612592\pi$
$311$	11.2727	−	19.5249i	0.639216	−	1.10715i	0.985605	−	0.169064i	$-0.0540744\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	−16.0469	−	27.7941i	−0.907025	−	1.57101i	−0.818176	−	0.574968i	$-0.805014\pi$
$313$	−16.0469	−	27.7941i	−0.907025	−	1.57101i	−0.0888492	−	0.996045i	$-0.528319\pi$
$314$	−10.4168			−0.587855
$315$	4.72392	−	8.89173i	0.266163	−	0.500992i
$316$	2.87141			0.161529
$317$	−15.7239	−	27.2346i	−0.883143	−	1.52965i	−0.847827	−	0.530273i	$-0.822089\pi$
$317$	−15.7239	−	27.2346i	−0.883143	−	1.52965i	−0.0353163	−	0.999376i	$-0.511244\pi$
$318$	0.177010	−	0.306590i	0.00992623	−	0.0171927i
$319$	7.93232	−	13.7392i	0.444125	−	0.769247i
$320$	−1.90280	−	3.29575i	−0.106370	−	0.184238i
$321$	17.0590			0.952143
$322$	−7.80560	+	14.6923i	−0.434989	+	0.818771i
$323$	33.7708			1.87906
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−4.74131	+	8.21218i	−0.263000	+	0.455530i
$326$	−4.86990	+	8.43491i	−0.269719	+	0.467167i
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−5.32299			−0.293913
$329$	9.95122	+	15.9132i	0.548628	+	0.877322i
$330$	20.1248			1.10784
$331$	−8.44784	−	14.6321i	−0.464335	−	0.804252i	0.534836	−	0.844956i	$-0.320373\pi$
$331$	−8.44784	−	14.6321i	−0.464335	−	0.804252i	−0.999171	+	0.0407037i	$0.987040\pi$
$332$	3.72392	−	6.45002i	0.204377	−	0.353991i
$333$	−0.661495	+	1.14574i	−0.0362497	+	0.0627863i
$334$	−4.35251	−	7.53877i	−0.238159	−	0.412503i
$335$	−32.1491			−1.75649
$336$	2.64411	−	0.0932392i	0.144248	−	0.00508661i
$337$	−7.25719			−0.395324			−0.197662	−	0.980270i	$-0.563335\pi$
$337$	−7.25719			−0.395324			−0.197662	+	0.980270i	$0.563335\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	−2.72579	+	4.72121i	−0.148045	+	0.256421i
$340$	−11.7205	+	20.3006i	−0.635635	+	1.10095i
$341$	22.4289	+	38.8481i	1.21460	+	2.10374i
$342$	−5.48261			−0.296466
$343$	−18.4168	+	1.95478i	−0.994414	+	0.105548i
$344$	−1.61121			−0.0868704
$345$	11.9652	+	20.7244i	0.644186	+	1.11576i
$346$	−6.02952	+	10.4434i	−0.324149	+	0.561443i
$347$	−4.01552	+	6.95508i	−0.215564	+	0.373368i	−0.953447	−	0.301561i	$-0.902492\pi$
$347$	−4.01552	+	6.95508i	−0.215564	+	0.373368i	0.737883	+	0.674929i	$0.235826\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−9.25344			−0.495325			−0.247663	−	0.968846i	$-0.579662\pi$
$349$	−9.25344			−0.495325			−0.247663	+	0.968846i	$0.579662\pi$
$350$	25.0731	−	0.884151i	1.34021	−	0.0472598i
$351$	−1.00000			−0.0533761
$352$	2.64411	+	4.57973i	0.140931	+	0.244100i
$353$	−6.35402	+	11.0055i	−0.338190	+	0.585763i	−0.984092	−	0.177657i	$-0.943148\pi$
$353$	−6.35402	+	11.0055i	−0.338190	+	0.585763i	0.645902	+	0.763420i	$0.276481\pi$
$354$	0.838505	−	1.45233i	0.0445660	−	0.0771906i
$355$	29.4603	+	51.0268i	1.56359	+	2.70822i
$356$	10.6770			0.565880
$357$	−8.64073	−	13.8175i	−0.457316	−	0.731302i
$358$	4.25719			0.224999
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$	1.90280	−	3.29575i	0.100286	−	0.173701i
$361$	−5.52952	+	9.57741i	−0.291027	+	0.504074i
$362$	6.07981	+	10.5305i	0.319548	+	0.553473i
$363$	−16.9652			−0.890443
$364$	1.24131	−	2.33648i	0.0650621	−	0.122465i
$365$	6.51437			0.340978
$366$	4.88541	+	8.46179i	0.255365	+	0.442305i
$367$	−13.5295	+	23.4338i	−0.706235	+	1.22324i	0.260009	+	0.965606i	$0.416275\pi$
$367$	−13.5295	+	23.4338i	−0.706235	+	1.22324i	−0.966244	+	0.257629i	$0.917059\pi$
$368$	−3.14411	+	5.44575i	−0.163898	+	0.283880i
$369$	−2.66149	−	4.60984i	−0.138552	−	0.239979i
$370$	−5.03477			−0.261745
$371$	−0.439448	+	0.827163i	−0.0228150	+	0.0429441i
$372$	8.48261			0.439803
$373$	−1.85438	−	3.21189i	−0.0960164	−	0.166305i	0.814016	−	0.580842i	$-0.197277\pi$
$373$	−1.85438	−	3.21189i	−0.0960164	−	0.166305i	−0.910032	+	0.414537i	$0.863943\pi$
$374$	16.2867	−	28.2094i	0.842166	−	1.45867i
$375$	8.52952	−	14.7736i	0.440463	−	0.762904i
$376$	3.54691	+	6.14343i	0.182918	+	0.316823i
$377$	−3.00000			−0.154508
$378$	1.40280	+	2.24325i	0.0721523	+	0.115380i
$379$	−19.2224			−0.987389			−0.493694	−	0.869635i	$-0.664354\pi$
$379$	−19.2224			−0.987389			−0.493694	+	0.869635i	$0.664354\pi$
$380$	−10.4323	−	18.0693i	−0.535167	−	0.926936i
$381$	−5.06242	+	8.76838i	−0.259356	+	0.449218i
$382$	−12.0938	+	20.9471i	−0.618774	+	1.07175i
$383$	−12.6112	−	21.8432i	−0.644403	−	1.11614i	−0.984439	−	0.175726i	$-0.943773\pi$
$383$	−12.6112	−	21.8432i	−0.644403	−	1.11614i	0.340037	−	0.940412i	$-0.389561\pi$
$384$	1.00000			0.0510310
$385$	−53.2123	+	1.87642i	−2.71195	+	0.0956314i
$386$	−1.54842			−0.0788124
$387$	−0.805603	−	1.39535i	−0.0409511	−	0.0709294i
$388$	1.57981	−	2.73631i	0.0802028	−	0.138915i
$389$	−9.06430	+	15.6998i	−0.459578	+	0.796013i	−0.998939	−	0.0460624i	$-0.985333\pi$
$389$	−9.06430	+	15.6998i	−0.459578	+	0.796013i	0.539360	+	0.842075i	$0.318666\pi$
$390$	−1.90280	−	3.29575i	−0.0963521	−	0.166887i
$391$	38.7330			1.95881
$392$	−6.98261	+	0.493069i	−0.352675	+	0.0249037i
$393$	−10.0628			−0.507601
$394$	−9.14411	−	15.8381i	−0.460673	−	0.797910i
$395$	−5.46372	+	9.46344i	−0.274909	+	0.476157i
$396$	−2.64411	+	4.57973i	−0.132871	+	0.230140i
$397$	7.30373	+	12.6504i	0.366564	+	0.634907i	0.989026	−	0.147743i	$-0.0472008\pi$
$397$	7.30373	+	12.6504i	0.366564	+	0.634907i	−0.622462	+	0.782650i	$0.713868\pi$
$398$	26.2187			1.31422
$399$	14.4966	−	0.511194i	0.725739	−	0.0255917i
$400$	9.48261			0.474131
$401$	10.6267	+	18.4060i	0.530673	+	0.919153i	0.999359	+	0.0357881i	$0.0113941\pi$
$401$	10.6267	+	18.4060i	0.530673	+	0.919153i	−0.468686	+	0.883365i	$0.655273\pi$
$402$	4.22392	−	7.31604i	0.210670	−	0.364891i
$403$	4.24131	−	7.34616i	0.211275	−	0.365938i
$404$	2.48261	+	4.30001i	0.123515	+	0.213934i
$405$	3.80560			0.189102
$406$	4.20840	+	6.72974i	0.208860	+	0.333991i
$407$	6.99626			0.346792
$408$	−3.07981	−	5.33439i	−0.152473	−	0.264092i
$409$	7.99662	−	13.8506i	0.395407	−	0.684866i	−0.597746	−	0.801686i	$-0.703937\pi$
$409$	7.99662	−	13.8506i	0.395407	−	0.684866i	0.993153	+	0.116820i	$0.0372701\pi$
$410$	10.1286	−	17.5432i	0.500216	−	0.866399i
$411$	−3.33851	−	5.78246i	−0.164676	−	0.285228i
$412$	−5.61121			−0.276444
$413$	−2.08168	+	3.91831i	−0.102433	+	0.192807i
$414$	−6.28822			−0.309049
$415$	14.1718	+	24.5462i	0.695664	+	1.20493i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−6.14411	+	10.6419i	−0.300878	+	0.521136i
$418$	14.4966	+	25.1089i	0.709053	+	1.22812i
$419$	−5.61121			−0.274125			−0.137063	−	0.990562i	$-0.543766\pi$
$419$	−5.61121			−0.274125			−0.137063	+	0.990562i	$0.543766\pi$
$420$	−4.72392	+	8.89173i	−0.230504	+	0.433872i
$421$	17.5802			0.856805			0.428403	−	0.903588i	$-0.359076\pi$
$421$	17.5802			0.856805			0.428403	+	0.903588i	$0.359076\pi$
$422$	−4.94971	−	8.57315i	−0.240948	−	0.417334i
$423$	−3.54691	+	6.14343i	−0.172457	+	0.298704i
$424$	−0.177010	+	0.306590i	−0.00859637	+	0.0148893i
$425$	−29.2047	−	50.5840i	−1.41663	−	2.45368i
$426$	−15.4826			−0.750135
$427$	−13.7065	−	21.9184i	−0.663306	−	1.06070i
$428$	−17.0590			−0.824580
$429$	2.64411	+	4.57973i	0.127659	+	0.221111i
$430$	3.06580	−	5.31013i	0.147846	−	0.256077i
$431$	−8.61121	+	14.9150i	−0.414787	+	0.718432i	−0.995406	−	0.0957430i	$-0.969477\pi$
$431$	−8.61121	+	14.9150i	−0.414787	+	0.718432i	0.580619	+	0.814175i	$0.302811\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	35.0243			1.68316			0.841580	−	0.540133i	$-0.181626\pi$
$433$	35.0243			1.68316			0.841580	+	0.540133i	$0.181626\pi$
$434$	−22.4289	+	0.790912i	−1.07662	+	0.0379650i
$435$	11.4168			0.547394
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	−17.2379	+	29.8570i	−0.824602	+	1.42825i
$438$	−0.855892	+	1.48245i	−0.0408961	+	0.0708341i
$439$	7.25682	+	12.5692i	0.346349	+	0.599894i	0.985598	−	0.169106i	$-0.0540879\pi$
$439$	7.25682	+	12.5692i	0.346349	+	0.599894i	−0.639249	+	0.769000i	$0.720755\pi$
$440$	−20.1248			−0.959415
$441$	−3.91832	−	5.80059i	−0.186587	−	0.276218i
$442$	−6.15962			−0.292983
$443$	−5.19102	−	8.99111i	−0.246633	−	0.427180i	0.715957	−	0.698145i	$-0.245991\pi$
$443$	−5.19102	−	8.99111i	−0.246633	−	0.427180i	−0.962589	+	0.270964i	$0.912657\pi$
$444$	0.661495	−	1.14574i	0.0313932	−	0.0543746i
$445$	−20.3162	+	35.1887i	−0.963082	+	1.66811i
$446$	1.48448	+	2.57120i	0.0702924	+	0.121750i
$447$	18.2882			0.865003
$448$	−2.64411	+	0.0932392i	−0.124922	+	0.00440514i
$449$	31.0833			1.46691			0.733456	−	0.679737i	$-0.237906\pi$
$449$	31.0833			1.46691			0.733456	+	0.679737i	$0.237906\pi$
$450$	4.74131	+	8.21218i	0.223507	+	0.387126i
$451$	−14.0746	+	24.3779i	−0.662745	+	1.14791i
$452$	2.72579	−	4.72121i	0.128210	−	0.222067i
$453$	−7.64411	−	13.2400i	−0.359152	−	0.622069i
$454$	−18.4131			−0.864168
$455$	5.33851	+	8.53690i	0.250273	+	0.400216i
$456$	5.48261			0.256747
$457$	−2.70840	−	4.69109i	−0.126694	−	0.219440i	0.795700	−	0.605691i	$-0.207103\pi$
$457$	−2.70840	−	4.69109i	−0.126694	−	0.219440i	−0.922394	+	0.386251i	$0.873770\pi$
$458$	−0.711784	+	1.23285i	−0.0332595	+	0.0576071i
$459$	3.07981	−	5.33439i	0.143753	−	0.248988i
$460$	−11.9652	−	20.7244i	−0.557882	−	0.966279i
$461$	9.54166			0.444399			0.222200	−	0.975001i	$-0.428676\pi$
$461$	9.54166			0.444399			0.222200	+	0.975001i	$0.428676\pi$
$462$	6.56430	−	12.3558i	0.305399	−	0.574845i
$463$	−27.2224			−1.26513			−0.632566	−	0.774506i	$-0.717998\pi$
$463$	−27.2224			−1.26513			−0.632566	+	0.774506i	$0.717998\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	−16.1407	+	27.9566i	−0.748508	+	1.29645i
$466$	5.36803	−	9.29770i	0.248669	−	0.430707i
$467$	−6.53290	−	11.3153i	−0.302307	−	0.523610i	0.674351	−	0.738411i	$-0.264423\pi$
$467$	−6.53290	−	11.3153i	−0.302307	−	0.523610i	−0.976658	+	0.214800i	$0.931090\pi$
$468$	1.00000			0.0462250
$469$	−10.4864	+	19.7382i	−0.484215	+	0.911427i
$470$	−26.9963			−1.24524
$471$	5.20840	+	9.02122i	0.239991	+	0.415676i
$472$	−0.838505	+	1.45233i	−0.0385953	+	0.0668491i
$473$	−4.26020	+	7.37889i	−0.195884	+	0.339282i
$474$	−1.43570	−	2.48671i	−0.0659441	−	0.114218i
$475$	51.9895			2.38544
$476$	8.64073	+	13.8175i	0.396047	+	0.633326i
$477$	−0.354020			−0.0162095
$478$	1.06430	+	1.84342i	0.0486798	+	0.0843159i
$479$	12.6060	−	21.8342i	0.575981	−	0.997628i	−0.419954	−	0.907546i	$-0.637954\pi$
$479$	12.6060	−	21.8342i	0.575981	−	0.997628i	0.995934	−	0.0900823i	$-0.0287130\pi$
$480$	−1.90280	+	3.29575i	−0.0868506	+	0.150430i
$481$	−0.661495	−	1.14574i	−0.0301616	−	0.0522414i
$482$	−18.7398			−0.853574
$483$	16.6267	−	0.586308i	0.756542	−	0.0266779i
$484$	16.9652			0.771147
$485$	6.01214	+	10.4133i	0.272997	+	0.472845i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−6.96710	+	12.0674i	−0.315709	+	0.546825i	−0.979588	−	0.201016i	$-0.935576\pi$
$487$	−6.96710	+	12.0674i	−0.315709	+	0.546825i	0.663879	+	0.747840i	$0.268909\pi$
$488$	−4.88541	−	8.46179i	−0.221152	−	0.383047i
$489$	9.73980			0.440449
$490$	11.6615	−	23.9511i	0.526813	−	1.08200i
$491$	−12.3510			−0.557393			−0.278697	−	0.960379i	$-0.589902\pi$
$491$	−12.3510			−0.557393			−0.278697	+	0.960379i	$0.589902\pi$
$492$	2.66149	+	4.60984i	0.119989	+	0.207828i
$493$	9.23943	−	16.0032i	0.416123	−	0.720747i
$494$	2.74131	−	4.74808i	0.123337	−	0.213626i
$495$	−10.0624	−	17.4286i	−0.452272	−	0.783359i
$496$	−8.48261			−0.380881
$497$	40.9377	−	1.44359i	1.83631	−	0.0647537i
$498$	−7.44784			−0.333746
$499$	17.3820	+	30.1066i	0.778127	+	1.34776i	0.933020	+	0.359824i	$0.117163\pi$
$499$	17.3820	+	30.1066i	0.778127	+	1.34776i	−0.154894	+	0.987931i	$0.549503\pi$
$500$	−8.52952	+	14.7736i	−0.381452	+	0.660694i
$501$	−4.35251	+	7.53877i	−0.194456	+	0.336808i
$502$	−3.88729	−	6.73298i	−0.173498	−	0.300507i
$503$	−5.68075			−0.253292			−0.126646	−	0.991948i	$-0.540421\pi$
$503$	−5.68075			−0.253292			−0.126646	+	0.991948i	$0.540421\pi$
$504$	−1.40280	−	2.24325i	−0.0624857	−	0.0999221i
$505$	−18.8957			−0.840847
$506$	16.6267	+	28.7983i	0.739148	+	1.28024i
$507$	0.500000	−	0.866025i	0.0222058	−	0.0384615i
$508$	5.06242	−	8.76838i	0.224609	−	0.389034i
$509$	4.69289	+	8.12832i	0.208009	+	0.360282i	0.951087	−	0.308923i	$-0.0999684\pi$
$509$	4.69289	+	8.12832i	0.208009	+	0.360282i	−0.743078	+	0.669204i	$0.766635\pi$
$510$	23.4411			1.03799
$511$	2.12485	−	3.99956i	0.0939978	−	0.176930i
$512$	−1.00000			−0.0441942
$513$	2.74131	+	4.74808i	0.121032	+	0.209633i
$514$	3.28822	−	5.69536i	0.145037	−	0.251211i
$515$	10.6770	−	18.4931i	0.470485	−	0.814904i
$516$	0.805603	+	1.39535i	0.0354647	+	0.0614266i
$517$	37.5136			1.64985
$518$	−1.64224	+	3.09114i	−0.0721557	+	0.135817i
$519$	12.0590			0.529333
$520$	1.90280	+	3.29575i	0.0834434	+	0.144528i
$521$	21.0243	−	36.4151i	0.921090	−	1.59537i	0.123358	−	0.992362i	$-0.460634\pi$
$521$	21.0243	−	36.4151i	0.921090	−	1.59537i	0.797732	−	0.603012i	$-0.206033\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−10.4168	−	18.0424i	−0.455495	−	0.788941i	0.543221	−	0.839590i	$-0.317204\pi$
$523$	−10.4168	−	18.0424i	−0.455495	−	0.788941i	−0.998717	+	0.0506487i	$0.983871\pi$
$524$	10.0628			0.439595
$525$	−13.3022	−	21.2718i	−0.580557	−	0.928379i
$526$	20.4759			0.892790
$527$	26.1248	+	45.2496i	1.13802	+	1.97110i
$528$	2.64411	−	4.57973i	0.115070	−	0.199307i
$529$	−8.27083	+	14.3255i	−0.359601	+	0.622848i
$530$	−0.673630	−	1.16676i	−0.0292606	−	0.0506809i
$531$	−1.67701			−0.0727760
$532$	−14.4966	+	0.511194i	−0.628508	+	0.0221631i
$533$	5.32299			0.230564
$534$	−5.33851	−	9.24656i	−0.231020	−	0.400138i
$535$	32.4600	−	56.2223i	1.40337	−	2.43070i
$536$	−4.22392	+	7.31604i	−0.182446	+	0.316005i
$537$	−2.12859	−	3.68683i	−0.0918556	−	0.159098i
$538$	24.1529			1.04130
$539$	−16.2047	+	33.2822i	−0.697984	+	1.43357i
$540$	−3.80560			−0.163767
$541$	−8.01552	−	13.8833i	−0.344614	−	0.596889i	0.640670	−	0.767817i	$-0.278657\pi$
$541$	−8.01552	−	13.8833i	−0.344614	−	0.596889i	−0.985284	+	0.170928i	$0.945323\pi$
$542$	15.2205	−	26.3627i	0.653778	−	1.13238i
$543$	6.07981	−	10.5305i	0.260910	−	0.451909i
$544$	3.07981	+	5.33439i	0.132046	+	0.228710i
$545$	15.2224			0.652056
$546$	−2.64411	+	0.0932392i	−0.113157	+	0.00399027i
$547$	23.2534			0.994245			0.497123	−	0.867680i	$-0.334390\pi$
$547$	23.2534			0.994245			0.497123	+	0.867680i	$0.334390\pi$
$548$	3.33851	+	5.78246i	0.142614	+	0.247014i
$549$	4.88541	−	8.46179i	0.208504	−	0.361140i
$550$	25.0731	−	43.4278i	1.06912	−	1.85177i
$551$	8.22392	+	14.2442i	0.350351	+	0.606825i
$552$	6.28822			0.267644
$553$	4.02801	+	6.44127i	0.171289	+	0.273911i
$554$	9.12485			0.387678
$555$	2.51739	+	4.36024i	0.106857	+	0.185082i
$556$	6.14411	−	10.6419i	0.260568	−	0.451317i
$557$	−17.5295	+	30.3620i	−0.742750	+	1.28648i	0.208489	+	0.978025i	$0.433145\pi$
$557$	−17.5295	+	30.3620i	−0.742750	+	1.28648i	−0.951239	+	0.308456i	$0.900188\pi$
$558$	−4.24131	−	7.34616i	−0.179549	−	0.310988i
$559$	1.61121			0.0681467
$560$	4.72392	−	8.89173i	0.199622	−	0.375744i
$561$	−32.5734			−1.37525
$562$	−3.35402	−	5.80933i	−0.141481	−	0.245052i
$563$	13.7587	−	23.8308i	0.579860	−	1.00435i	−0.415635	−	0.909531i	$-0.636441\pi$
$563$	13.7587	−	23.8308i	0.579860	−	1.00435i	0.995495	−	0.0948152i	$-0.0302260\pi$
$564$	3.54691	−	6.14343i	0.149352	−	0.258685i
$565$	10.3733	+	17.9670i	0.436407	+	0.755879i
$566$	−26.8646			−1.12921
$567$	1.24131	−	2.33648i	0.0521300	−	0.0981231i
$568$	15.4826			0.649636
$569$	9.01401	+	15.6127i	0.377887	+	0.654519i	0.990755	−	0.135666i	$-0.0433175\pi$
$569$	9.01401	+	15.6127i	0.377887	+	0.654519i	−0.612868	+	0.790185i	$0.709984\pi$
$570$	−10.4323	+	18.0693i	−0.436962	+	0.756840i
$571$	−2.64598	+	4.58297i	−0.110731	+	0.191791i	−0.916065	−	0.401030i	$-0.868652\pi$
$571$	−2.64598	+	4.58297i	−0.110731	+	0.191791i	0.805334	+	0.592821i	$0.201986\pi$
$572$	−2.64411	−	4.57973i	−0.110556	−	0.191488i
$573$	24.1876			1.01045
$574$	−7.46710	−	11.9408i	−0.311671	−	0.498398i
$575$	59.6287			2.48669
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	4.08168	−	7.06968i	0.169923	−	0.294315i	−0.768470	−	0.639886i	$-0.778982\pi$
$577$	4.08168	−	7.06968i	0.169923	−	0.294315i	0.938392	+	0.345571i	$0.112315\pi$
$578$	10.4705	−	18.1354i	0.435514	−	0.754333i
$579$	0.774209	+	1.34097i	0.0321750	+	0.0557288i
$580$	−11.4168			−0.474057
$581$	19.6929	−	0.694430i	0.816999	−	0.0288098i
$582$	−3.15962			−0.130971
$583$	0.936068	+	1.62132i	0.0387680	+	0.0671481i
$584$	0.855892	−	1.48245i	0.0354171	−	0.0613442i
$585$	−1.90280	+	3.29575i	−0.0786712	+	0.136262i
$586$	4.90280	+	8.49190i	0.202533	+	0.350797i
$587$	14.4546			0.596605			0.298303	−	0.954471i	$-0.403580\pi$
$587$	14.4546			0.596605			0.298303	+	0.954471i	$0.403580\pi$
$588$	3.91832	+	5.80059i	0.161589	+	0.239212i
$589$	−46.5069			−1.91628
$590$	−3.19102	−	5.52700i	−0.131372	−	0.227543i
$591$	−9.14411	+	15.8381i	−0.376138	+	0.651491i
$592$	−0.661495	+	1.14574i	−0.0271873	+	0.0470897i
$593$	−1.98448	−	3.43723i	−0.0814930	−	0.141150i	0.822398	−	0.568912i	$-0.192636\pi$
$593$	−1.98448	−	3.43723i	−0.0814930	−	0.141150i	−0.903891	+	0.427762i	$0.859302\pi$
$594$	5.28822			0.216978
$595$	−61.9807	+	2.18563i	−2.54096	+	0.0896019i
$596$	−18.2882			−0.749115
$597$	−13.1093	−	22.7060i	−0.536529	−	0.929296i
$598$	3.14411	−	5.44575i	0.128572	−	0.222693i
$599$	10.6267	−	18.4060i	0.434196	−	0.752050i	−0.563034	−	0.826434i	$-0.690366\pi$
$599$	10.6267	−	18.4060i	0.434196	−	0.752050i	0.997230	+	0.0743844i	$0.0236992\pi$
$600$	−4.74131	−	8.21218i	−0.193563	−	0.335261i
$601$	−27.2497			−1.11154			−0.555769	−	0.831337i	$-0.687576\pi$
$601$	−27.2497			−1.11154			−0.555769	+	0.831337i	$0.687576\pi$
$602$	−2.26020	−	3.61433i	−0.0921189	−	0.147309i
$603$	−8.44784			−0.344023
$604$	7.64411	+	13.2400i	0.311034	+	0.538727i
$605$	−32.2815	+	55.9131i	−1.31243	+	2.27319i
$606$	2.48261	−	4.30001i	0.100849	−	0.174676i
$607$	4.96185	+	8.59417i	0.201395	+	0.348827i	0.948978	−	0.315342i	$-0.102119\pi$
$607$	4.96185	+	8.59417i	0.201395	+	0.348827i	−0.747583	+	0.664168i	$0.768786\pi$
$608$	−5.48261			−0.222349
$609$	3.72392	−	7.00945i	0.150901	−	0.284037i
$610$	37.1839			1.50553
$611$	−3.54691	−	6.14343i	−0.143493	−	0.248536i
$612$	−3.07981	+	5.33439i	−0.124494	+	0.215630i
$613$	4.93420	−	8.54628i	0.199290	−	0.345181i	−0.749008	−	0.662561i	$-0.769470\pi$
$613$	4.93420	−	8.54628i	0.199290	−	0.345181i	0.948299	+	0.317380i	$0.102803\pi$
$614$	10.2587	+	17.7686i	0.414007	+	0.717081i
$615$	−20.2572			−0.816849
$616$	−6.56430	+	12.3558i	−0.264483	+	0.497831i
$617$	−41.9865			−1.69031			−0.845156	−	0.534520i	$-0.820493\pi$
$617$	−41.9865			−1.69031			−0.845156	+	0.534520i	$0.820493\pi$
$618$	2.80560	+	4.85945i	0.112858	+	0.195476i
$619$	12.5174	−	21.6808i	0.503116	−	0.871423i	−0.496877	−	0.867821i	$-0.665520\pi$
$619$	12.5174	−	21.6808i	0.503116	−	0.871423i	0.999994	−	0.00360210i	$-0.00114659\pi$
$620$	16.1407	−	27.9566i	0.648227	−	1.12276i
$621$	3.14411	+	5.44575i	0.126169	+	0.218531i
$622$	22.5454			0.903988
$623$	14.9777	+	23.9511i	0.600070	+	0.959583i
$624$	−1.00000			−0.0400320
$625$	−8.75344	−	15.1614i	−0.350138	−	0.606456i
$626$	16.0469	−	27.7941i	0.641363	−	1.11087i
$627$	14.4966	−	25.1089i	0.578939	−	1.00275i
$628$	−5.20840	−	9.02122i	−0.207838	−	0.359986i
$629$	8.14912			0.324927
$630$	10.0624	−	0.354831i	0.400897	−	0.0141368i
$631$	−4.55216			−0.181219			−0.0906093	−	0.995887i	$-0.528881\pi$
$631$	−4.55216			−0.181219			−0.0906093	+	0.995887i	$0.528881\pi$
$632$	1.43570	+	2.48671i	0.0571092	+	0.0989161i
$633$	−4.94971	+	8.57315i	−0.196733	+	0.340752i
$634$	15.7239	−	27.2346i	0.624477	−	1.08163i
$635$	19.2656	+	33.3690i	0.764531	+	1.32421i
$636$	0.354020			0.0140378
$637$	6.98261	−	0.493069i	0.276661	−	0.0195361i
$638$	15.8646			0.628087
$639$	7.74131	+	13.4083i	0.306241	+	0.530426i
$640$	1.90280	−	3.29575i	0.0752148	−	0.130276i
$641$	−16.5764	+	28.7112i	−0.654730	+	1.13403i	0.327232	+	0.944944i	$0.393884\pi$
$641$	−16.5764	+	28.7112i	−0.654730	+	1.13403i	−0.981961	+	0.189081i	$0.939449\pi$
$642$	8.52952	+	14.7736i	0.336633	+	0.583066i
$643$	−42.0590			−1.65865			−0.829323	−	0.558769i	$-0.811274\pi$
$643$	−42.0590			−1.65865			−0.829323	+	0.558769i	$0.811274\pi$
$644$	−16.6267	+	0.586308i	−0.655185	+	0.0231038i
$645$	−6.13161			−0.241432
$646$	16.8854	+	29.2464i	0.664348	+	1.15068i
$647$	8.12859	−	14.0791i	0.319568	−	0.553508i	−0.660830	−	0.750536i	$-0.729796\pi$
$647$	8.12859	−	14.0791i	0.319568	−	0.553508i	0.980398	+	0.197028i	$0.0631289\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	4.43420	+	7.68025i	0.174057	+	0.301476i
$650$	−9.48261			−0.371939
$651$	11.8994	+	19.0286i	0.466375	+	0.745789i
$652$	−9.73980			−0.381440
$653$	−15.4947	−	26.8377i	−0.606356	−	1.05024i	−0.991836	−	0.127523i	$-0.959297\pi$
$653$	−15.4947	−	26.8377i	−0.606356	−	1.05024i	0.385479	−	0.922717i	$-0.374036\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	−19.1475	+	33.1644i	−0.748154	+	1.29584i
$656$	−2.66149	−	4.60984i	−0.103914	−	0.179984i
$657$	1.71178			0.0667831
$658$	−8.80560	+	16.5746i	−0.343278	+	0.646145i
$659$	3.25344			0.126736			0.0633680	−	0.997990i	$-0.479816\pi$
$659$	3.25344			0.126736			0.0633680	+	0.997990i	$0.479816\pi$
$660$	10.0624	+	17.4286i	0.391679	+	0.678409i
$661$	2.43607	−	4.21939i	0.0947520	−	0.164115i	−0.814753	−	0.579808i	$-0.803128\pi$
$661$	2.43607	−	4.21939i	0.0947520	−	0.164115i	0.909505	+	0.415693i	$0.136461\pi$
$662$	8.44784	−	14.6321i	0.328335	−	0.568692i
$663$	3.07981	+	5.33439i	0.119610	+	0.207171i
$664$	7.44784			0.289032
$665$	25.8994	−	48.7499i	1.00434	−	1.89044i
$666$	−1.32299			−0.0512648
$667$	9.43232	+	16.3373i	0.365221	+	0.632581i
$668$	4.35251	−	7.53877i	0.168404	−	0.291684i
$669$	1.48448	−	2.57120i	0.0573935	−	0.0994085i
$670$	−16.0746	−	27.8420i	−0.621014	−	1.07563i
$671$	−51.6703			−1.99471
$672$	1.40280	+	2.24325i	0.0541142	+	0.0865351i
$673$	16.8714			0.650345			0.325172	−	0.945655i	$-0.394578\pi$
$673$	16.8714			0.650345			0.325172	+	0.945655i	$0.394578\pi$
$674$	−3.62859	−	6.28491i	−0.139768	−	0.242086i
$675$	4.74131	−	8.21218i	0.182493	−	0.316087i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−15.3994	−	26.6726i	−0.591848	−	1.02511i	−0.993983	−	0.109530i	$-0.965065\pi$
$677$	−15.3994	−	26.6726i	−0.591848	−	1.02511i	0.402136	−	0.915580i	$-0.368268\pi$
$678$	−5.45158			−0.209367
$679$	8.35438	−	0.294601i	0.320612	−	0.0113057i
$680$	−23.4411			−0.898924
$681$	9.20653	+	15.9462i	0.352795	+	0.611059i
$682$	−22.4289	+	38.8481i	−0.858849	+	1.48757i
$683$	−18.1718	+	31.4744i	−0.695323	+	1.20433i	0.274749	+	0.961516i	$0.411405\pi$
$683$	−18.1718	+	31.4744i	−0.695323	+	1.20433i	−0.970072	+	0.242819i	$0.921928\pi$
$684$	−2.74131	−	4.74808i	−0.104816	−	0.181547i
$685$	−25.4100			−0.970868
$686$	−10.9013	−	14.9720i	−0.416213	−	0.571635i
$687$	1.42357			0.0543125
$688$	−0.805603	−	1.39535i	−0.0307133	−	0.0531970i
$689$	0.177010	−	0.306590i	0.00674355	−	0.0116802i
$690$	−11.9652	+	20.7244i	−0.455508	+	0.788964i
$691$	−19.4774	−	33.7358i	−0.740954	−	1.28337i	−0.952061	−	0.305907i	$-0.901040\pi$
$691$	−19.4774	−	33.7358i	−0.740954	−	1.28337i	0.211108	−	0.977463i	$-0.432293\pi$
$692$	−12.0590			−0.458416
$693$	−13.9826	+	0.493069i	−0.531156	+	0.0187301i
$694$	−8.03103			−0.304854
$695$	23.3820	+	40.4989i	0.886931	+	1.53621i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	−16.3938	+	28.3949i	−0.620960	+	1.07553i
$698$	−4.62672	−	8.01372i	−0.175124	−	0.303324i
$699$	−10.7361			−0.406075
$700$	13.3022	+	21.2718i	0.502777	+	0.803999i
$701$	40.7323			1.53844			0.769219	−	0.638985i	$-0.220645\pi$
$701$	40.7323			1.53844			0.769219	+	0.638985i	$0.220645\pi$
$702$	−0.500000	−	0.866025i	−0.0188713	−	0.0326860i
$703$	−3.62672	+	6.28166i	−0.136784	+	0.236917i
$704$	−2.64411	+	4.57973i	−0.0996536	+	0.172605i
$705$	13.4981	+	23.3794i	0.508369	+	0.880521i
$706$	−12.7080			−0.478273
$707$	−6.16337	+	11.6012i	−0.231797	+	0.436307i
$708$	1.67701			0.0630259
$709$	11.5609	+	20.0241i	0.434179	+	0.752021i	0.997228	−	0.0744029i	$-0.0237051\pi$
$709$	11.5609	+	20.0241i	0.434179	+	0.752021i	−0.563049	+	0.826424i	$0.690372\pi$
$710$	−29.4603	+	51.0268i	−1.10563	+	1.91500i
$711$	−1.43570	+	2.48671i	−0.0538431	+	0.0932590i
$712$	5.33851	+	9.24656i	0.200069	+	0.346530i
$713$	−53.3405			−1.99762
$714$	7.64598	−	14.3919i	0.286144	−	0.538602i
$715$	20.1248			0.752627
$716$	2.12859	+	3.68683i	0.0795492	+	0.137783i
$717$	1.06430	−	1.84342i	0.0397469	−	0.0688436i
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	13.1876	+	22.8417i	0.491816	+	0.851850i	0.999956	−	0.00942457i	$-0.00299998\pi$
$719$	13.1876	+	22.8417i	0.491816	+	0.851850i	−0.508140	+	0.861275i	$0.669667\pi$
$720$	3.80560			0.141826
$721$	−7.87141	−	12.5873i	−0.293147	−	0.468776i
$722$	−11.0590			−0.411575
$723$	9.36990	+	16.2291i	0.348470	+	0.603568i
$724$	−6.07981	+	10.5305i	−0.225954	+	0.391365i
$725$	14.2239	−	24.6366i	0.528263	−	0.914979i
$726$	−8.48261	−	14.6923i	−0.314819	−	0.545283i
$727$	−6.73980			−0.249965			−0.124983	−	0.992159i	$-0.539888\pi$
$727$	−6.73980			−0.249965			−0.124983	+	0.992159i	$0.539888\pi$
$728$	2.64411	−	0.0932392i	0.0979972	−	0.00345567i
$729$	1.00000			0.0370370
$730$	3.25719	+	5.64161i	0.120554	+	0.208805i
$731$	−4.96221	+	8.59480i	−0.183534	+	0.317890i
$732$	−4.88541	+	8.46179i	−0.180570	+	0.312757i
$733$	−11.9807	−	20.7513i	−0.442519	−	0.766465i	0.555357	−	0.831612i	$-0.312582\pi$
$733$	−11.9807	−	20.7513i	−0.442519	−	0.766465i	−0.997876	+	0.0651471i	$0.979248\pi$
$734$	−27.0590			−0.998768
$735$	−26.5731	+	1.87642i	−0.980162	+	0.0692129i
$736$	−6.28822			−0.231787
$737$	22.3370	+	38.6888i	0.822794	+	1.42512i
$738$	2.66149	−	4.60984i	0.0979710	−	0.169691i
$739$	−2.96897	+	5.14241i	−0.109215	+	0.189166i	−0.915453	−	0.402426i	$-0.868167\pi$
$739$	−2.96897	+	5.14241i	−0.109215	+	0.189166i	0.806237	+	0.591592i	$0.201500\pi$
$740$	−2.51739	−	4.36024i	−0.0925410	−	0.160286i
$741$	−5.48261			−0.201409
$742$	−0.936068	+	0.0330085i	−0.0343641	+	0.00121178i
$743$	−22.3783			−0.820980			−0.410490	−	0.911865i	$-0.634642\pi$
$743$	−22.3783			−0.820980			−0.410490	+	0.911865i	$0.634642\pi$
$744$	4.24131	+	7.34616i	0.155494	+	0.269323i
$745$	34.7988	−	60.2734i	1.27493	−	2.20825i
$746$	1.85438	−	3.21189i	0.0678938	−	0.117596i
$747$	3.72392	+	6.45002i	0.136251	+	0.235994i
$748$	32.5734			1.19100
$749$	−23.9305	−	38.2676i	−0.874400	−	1.39827i
$750$	17.0590			0.622908
$751$	−20.6233	−	35.7207i	−0.752556	−	1.30347i	−0.946580	−	0.322469i	$-0.895487\pi$
$751$	−20.6233	−	35.7207i	−0.752556	−	1.30347i	0.194024	−	0.980997i	$-0.437846\pi$
$752$	−3.54691	+	6.14343i	−0.129342	+	0.224028i
$753$	−3.88729	+	6.73298i	−0.141661	+	0.245363i
$754$	−1.50000	−	2.59808i	−0.0546268	−	0.0946164i
$755$	−58.1809			−2.11742
$756$	−1.24131	+	2.33648i	−0.0451459	+	0.0849771i
$757$	−41.9585			−1.52501			−0.762503	−	0.646984i	$-0.776030\pi$
$757$	−41.9585			−1.52501			−0.762503	+	0.646984i	$0.776030\pi$
$758$	−9.61121	−	16.6471i	−0.349095	−	0.604650i
$759$	16.6267	−	28.7983i	0.603512	−	1.04531i
$760$	10.4323	−	18.0693i	0.378420	−	0.655443i
$761$	−9.58018	−	16.5934i	−0.347281	−	0.601508i	0.638484	−	0.769635i	$-0.279562\pi$
$761$	−9.58018	−	16.5934i	−0.347281	−	0.601508i	−0.985765	+	0.168126i	$0.946228\pi$
$762$	−10.1248			−0.366785
$763$	4.96523	−	9.34594i	0.179753	−	0.338346i
$764$	−24.1876			−0.875078
$765$	−11.7205	−	20.3006i	−0.423757	−	0.733969i
$766$	12.6112	−	21.8432i	0.455661	−	0.789229i
$767$	0.838505	−	1.45233i	0.0302767	−	0.0524407i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	31.7981			1.14667			0.573335	−	0.819321i	$-0.305649\pi$
$769$	31.7981			1.14667			0.573335	+	0.819321i	$0.305649\pi$
$770$	−28.2312	−	45.1450i	−1.01738	−	1.62691i
$771$	−6.57643			−0.236844
$772$	−0.774209	−	1.34097i	−0.0278644	−	0.0482625i
$773$	25.1876	−	43.6263i	0.905936	−	1.56913i	0.0862810	−	0.996271i	$-0.472502\pi$
$773$	25.1876	−	43.6263i	0.905936	−	1.56913i	0.819655	−	0.572857i	$-0.194165\pi$
$774$	0.805603	−	1.39535i	0.0289568	−	0.0501546i
$775$	40.2187	+	69.6608i	1.44470	+	2.50229i
$776$	3.15962			0.113424
$777$	3.49813	−	0.123354i	0.125495	−	0.00442532i
$778$	−18.1286			−0.649942
$779$	−14.5919	−	25.2740i	−0.522811	−	0.905535i
$780$	1.90280	−	3.29575i	0.0681312	−	0.118007i
$781$	40.9377	−	70.9062i	1.46487	−	2.53722i
$782$	19.3665	+	33.5438i	0.692545	+	1.19952i
$783$	3.00000			0.107211
$784$	−3.91832	−	5.80059i	−0.139940	−	0.207164i
$785$	39.6422			1.41489
$786$	−5.03139	−	8.71463i	−0.179464	−	0.310841i
$787$	11.0295	−	19.1037i	0.393160	−	0.680973i	−0.599704	−	0.800222i	$-0.704715\pi$
$787$	11.0295	−	19.1037i	0.393160	−	0.680973i	0.992864	+	0.119248i	$0.0380485\pi$
$788$	9.14411	−	15.8381i	0.325745	−	0.564208i
$789$	−10.2379	−	17.7326i	−0.364480	−	0.631298i
$790$	−10.9274			−0.388781
$791$	14.4146	−	0.508301i	0.512523	−	0.0180731i
$792$	−5.28822			−0.187909
$793$	4.88541	+	8.46179i	0.173486	+	0.300487i
$794$	−7.30373	+	12.6504i	−0.259200	+	0.448947i
$795$	−0.673630	+	1.16676i	−0.0238912	+	0.0413808i
$796$	13.1093	+	22.7060i	0.464648	+	0.804794i
$797$	−52.5312			−1.86075			−0.930374	−	0.366611i	$-0.880518\pi$
$797$	−52.5312			−1.86075			−0.930374	+	0.366611i	$0.880518\pi$
$798$	7.69102	+	12.2988i	0.272259	+	0.435374i
$799$	43.6952			1.54583
$800$	4.74131	+	8.21218i	0.167630	+	0.290345i
$801$	−5.33851	+	9.24656i	−0.188627	+	0.326711i
$802$	−10.6267	+	18.4060i	−0.375243	+	0.649939i
$803$	−4.52614	−	7.83951i	−0.159724	−	0.276650i
$804$	8.44784			0.297932
$805$	29.7050	−	55.9131i	1.04696	−	1.97068i
$806$	8.48261			0.298787
$807$	−12.0764	−	20.9170i	−0.425111	−	0.736313i
$808$	−2.48261	+	4.30001i	−0.0873380	+	0.151274i
$809$	23.4929	−	40.6909i	0.825966	−	1.43061i	−0.0752136	−	0.997167i	$-0.523964\pi$
$809$	23.4929	−	40.6909i	0.825966	−	1.43061i	0.901179	−	0.433447i	$-0.142703\pi$
$810$	1.90280	+	3.29575i	0.0668576	+	0.115801i
$811$	1.81236			0.0636407			0.0318203	−	0.999494i	$-0.489870\pi$
$811$	1.81236			0.0636407			0.0318203	+	0.999494i	$0.489870\pi$
$812$	−3.72392	+	7.00945i	−0.130684	+	0.245984i
$813$	−30.4411			−1.06762
$814$	3.49813	+	6.05894i	0.122609	+	0.212366i
$815$	18.5329	−	32.0999i	0.649179	−	1.12441i
$816$	3.07981	−	5.33439i	0.107815	−	0.186741i
$817$	−4.41681	−	7.65014i	−0.154525	−	0.267644i
$818$	15.9932			0.559191
$819$	1.40280	+	2.24325i	0.0490178	+	0.0783853i
$820$	20.2572			0.707412
$821$	17.5761	+	30.4426i	0.613409	+	1.06246i	0.990661	+	0.136345i	$0.0435356\pi$
$821$	17.5761	+	30.4426i	0.613409	+	1.06246i	−0.377252	+	0.926110i	$0.623131\pi$
$822$	3.33851	−	5.78246i	0.116444	−	0.201686i
$823$	−17.3385	+	30.0312i	−0.604382	+	1.04682i	0.387766	+	0.921758i	$0.373247\pi$
$823$	−17.3385	+	30.0312i	−0.604382	+	1.04682i	−0.992149	+	0.125063i	$0.960087\pi$
$824$	−2.80560	−	4.85945i	−0.0977378	−	0.169287i
$825$	−50.1461			−1.74586
$826$	−4.43420	+	0.156363i	−0.154285	+	0.00544056i
$827$	19.4138			0.675084			0.337542	−	0.941311i	$-0.390405\pi$
$827$	19.4138			0.675084			0.337542	+	0.941311i	$0.390405\pi$
$828$	−3.14411	−	5.44575i	−0.109265	−	0.189253i
$829$	−20.9482	+	36.2834i	−0.727561	+	1.26017i	0.230350	+	0.973108i	$0.426013\pi$
$829$	−20.9482	+	36.2834i	−0.727561	+	1.26017i	−0.957911	+	0.287065i	$0.907320\pi$
$830$	−14.1718	+	24.5462i	−0.491909	+	0.852011i
$831$	−4.56242	−	7.90235i	−0.158269	−	0.274130i
$832$	1.00000			0.0346688
$833$	−18.8749	+	38.7665i	−0.653977	+	1.34318i
$834$	−12.2882			−0.425506
$835$	16.5639	+	28.6896i	0.573219	+	0.992844i
$836$	−14.4966	+	25.1089i	−0.501376	+	0.868409i
$837$	−4.24131	+	7.34616i	−0.146601	+	0.253920i
$838$	−2.80560	−	4.85945i	−0.0969179	−	0.167867i
$839$	15.9895			0.552019			0.276009	−	0.961155i	$-0.410988\pi$
$839$	15.9895			0.552019			0.276009	+	0.961155i	$0.410988\pi$
$840$	−10.0624	+	0.354831i	−0.347187	+	0.0122428i
$841$	−20.0000			−0.689655
$842$	8.79009	+	15.2249i	0.302926	+	0.524684i
$843$	−3.35402	+	5.80933i	−0.115519	+	0.200084i
$844$	4.94971	−	8.57315i	0.170376	−	0.295100i
$845$	−1.90280	−	3.29575i	−0.0654584	−	0.113377i
$846$	−7.09382			−0.243891
$847$	23.7988	+	38.0572i	0.817738	+	1.30766i
$848$	−0.354020			−0.0121571
$849$	13.4323	+	23.2655i	0.460996	+	0.798469i
$850$	29.2047	−	50.5840i	1.00171	−	1.73502i
$851$	−4.15962	+	7.20468i	−0.142590	+	0.246973i
$852$	−7.74131	−	13.4083i	−0.265213	−	0.459362i
$853$	−44.2747			−1.51594			−0.757968	−	0.652291i	$-0.773808\pi$
$853$	−44.2747			−1.51594			−0.757968	+	0.652291i	$0.773808\pi$
$854$	12.1286	−	22.8294i	0.415032	−	0.781206i
$855$	20.8646			0.713556
$856$	−8.52952	−	14.7736i	−0.291533	−	0.504950i
$857$	−11.9164	+	20.6399i	−0.407058	+	0.705045i	−0.994559	−	0.104179i	$-0.966779\pi$
$857$	−11.9164	+	20.6399i	−0.407058	+	0.705045i	0.587501	+	0.809224i	$0.300112\pi$
$858$	−2.64411	+	4.57973i	−0.0902684	+	0.156349i
$859$	7.32299	+	12.6838i	0.249857	+	0.432765i	0.963486	−	0.267759i	$-0.0862830\pi$
$859$	7.32299	+	12.6838i	0.249857	+	0.432765i	−0.713629	+	0.700524i	$0.752950\pi$
$860$	6.13161			0.209086
$861$	−6.60746	+	12.4371i	−0.225182	+	0.423855i
$862$	−17.2224			−0.586598
$863$	10.5764	+	18.3189i	0.360026	+	0.623583i	0.987965	−	0.154680i	$-0.0494345\pi$
$863$	10.5764	+	18.3189i	0.360026	+	0.623583i	−0.627939	+	0.778263i	$0.716101\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	22.9460	−	39.7436i	0.780186	−	1.35132i
$866$	17.5121	+	30.3319i	0.595087	+	1.03072i
$867$	−20.9410			−0.711192
$868$	−11.8994	−	19.0286i	−0.403893	−	0.645872i
$869$	15.1846			0.515103
$870$	5.70840	+	9.88725i	0.193533	+	0.335209i
$871$	4.22392	−	7.31604i	0.143122	−	0.247895i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	1.57981	+	2.73631i	0.0534685	+	0.0926102i
$874$	−34.4759			−1.16616
$875$	−45.1060	+	1.59057i	−1.52486	+	0.0537711i
$876$	−1.71178			−0.0578358
$877$	−3.11308	−	5.39201i	−0.105121	−	0.182075i	0.808667	−	0.588267i	$-0.200190\pi$
$877$	−3.11308	−	5.39201i	−0.105121	−	0.182075i	−0.913788	+	0.406192i	$0.866856\pi$
$878$	−7.25682	+	12.5692i	−0.244906	+	0.424189i
$879$	4.90280	−	8.49190i	0.165367	−	0.286425i
$880$	−10.0624	−	17.4286i	−0.339204	−	0.587519i
$881$	46.9517			1.58184			0.790922	−	0.611918i	$-0.209602\pi$
$881$	46.9517			1.58184			0.790922	+	0.611918i	$0.209602\pi$
$882$	3.06430	−	6.29365i	0.103180	−	0.211918i
$883$	−29.1143			−0.979776			−0.489888	−	0.871785i	$-0.662962\pi$
$883$	−29.1143			−0.979776			−0.489888	+	0.871785i	$0.662962\pi$
$884$	−3.07981	−	5.33439i	−0.103585	−	0.179415i
$885$	−3.19102	+	5.52700i	−0.107265	+	0.185788i
$886$	5.19102	−	8.99111i	0.174396	−	0.302062i
$887$	−21.8019	−	37.7619i	−0.732035	−	1.26792i	−0.956012	−	0.293327i	$-0.905238\pi$
$887$	−21.8019	−	37.7619i	−0.732035	−	1.26792i	0.223977	−	0.974594i	$-0.428096\pi$
$888$	1.32299			0.0443966
$889$	26.7712	−	0.944032i	0.897877	−	0.0316618i
$890$	−40.6325			−1.36200
$891$	−2.64411	−	4.57973i	−0.0885809	−	0.153427i
$892$	−1.48448	+	2.57120i	−0.0497042	+	0.0860903i
$893$	−19.4463	+	33.6820i	−0.650747	+	1.12713i
$894$	9.14411	+	15.8381i	0.305825	+	0.529704i
$895$	−16.2012			−0.541545
$896$	−1.40280	−	2.24325i	−0.0468643	−	0.0749416i
$897$	−6.28822			−0.209957
$898$	15.5417	+	26.9189i	0.518632	+	0.898297i
$899$	−12.7239	+	22.0385i	−0.424366	+	0.735024i
$900$	−4.74131	+	8.21218i	−0.158044	+	0.273739i
$901$	1.09032	+	1.88848i	0.0363237	+	0.0629144i
$902$	−28.1491			−0.937263
$903$	−2.00000	+	3.76456i	−0.0665558	+	0.125277i
$904$	5.45158			0.181317
$905$	−23.1373	−	40.0751i	−0.769111	−	1.33214i
$906$	7.64411	−	13.2400i	0.253958	−	0.439869i
$907$	−1.23793	+	2.14415i	−0.0411047	+	0.0711954i	−0.885846	−	0.463980i	$-0.846421\pi$
$907$	−1.23793	+	2.14415i	−0.0411047	+	0.0711954i	0.844741	+	0.535175i	$0.179754\pi$
$908$	−9.20653	−	15.9462i	−0.305530	−	0.529193i
$909$	−4.96523			−0.164686
$910$	−4.72392	+	8.89173i	−0.156596	+	0.294758i
$911$	46.0000			1.52405			0.762024	−	0.647549i	$-0.224206\pi$
$911$	46.0000			1.52405			0.762024	+	0.647549i	$0.224206\pi$
$912$	2.74131	+	4.74808i	0.0907737	+	0.157225i
$913$	19.6929	−	34.1091i	0.651740	−	1.12885i
$914$	2.70840	−	4.69109i	0.0895861	−	0.155168i
$915$	−18.5919	−	32.2022i	−0.614631	−	1.06457i
$916$	−1.42357			−0.0470360
$917$	14.1161	+	22.5733i	0.466154	+	0.745436i
$918$	6.15962			0.203298
$919$	−17.7708	−	30.7800i	−0.586206	−	1.01534i	−0.994724	−	0.102588i	$-0.967288\pi$
$919$	−17.7708	−	30.7800i	−0.586206	−	1.01534i	0.408518	−	0.912750i	$-0.366046\pi$
$920$	11.9652	−	20.7244i	0.394482	−	0.683263i
$921$	10.2587	−	17.7686i	0.338035	−	0.585495i
$922$	4.77083	+	8.26332i	0.157119	+	0.272138i
$923$	−15.4826			−0.509616
$924$	13.9826	−	0.493069i	0.459994	−	0.0162208i
$925$	12.5454			0.412490
$926$	−13.6112	−	23.5753i	−0.447292	−	0.774732i
$927$	2.80560	−	4.85945i	0.0921481	−	0.159605i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−7.09382	−	12.2869i	−0.232741	−	0.403119i	0.725873	−	0.687829i	$-0.241436\pi$
$929$	−7.09382	−	12.2869i	−0.232741	−	0.403119i	−0.958614	+	0.284710i	$0.908103\pi$
$930$	−32.2815			−1.05855
$931$	−21.4826	−	31.8024i	−0.704064	−	1.04228i
$932$	10.7361			0.351671
$933$	−11.2727	−	19.5249i	−0.369052	−	0.639216i
$934$	6.53290	−	11.3153i	0.213763	−	0.370249i
$935$	−61.9807	+	107.354i	−2.02699	+	3.51084i
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	−2.09683			−0.0685006			−0.0342503	−	0.999413i	$-0.510904\pi$
$937$	−2.09683			−0.0685006			−0.0342503	+	0.999413i	$0.510904\pi$
$938$	−22.3370	+	0.787669i	−0.729329	+	0.0257183i
$939$	−32.0938			−1.04734
$940$	−13.4981	−	23.3794i	−0.440260	−	0.762553i
$941$	3.95309	−	6.84695i	0.128867	−	0.223204i	−0.794371	−	0.607433i	$-0.792199\pi$
$941$	3.95309	−	6.84695i	0.128867	−	0.223204i	0.923238	+	0.384229i	$0.125533\pi$
$942$	−5.20840	+	9.02122i	−0.169699	+	0.293927i
$943$	−16.7361	−	28.9877i	−0.545001	−	0.943969i
$944$	−1.67701			−0.0545820
$945$	−5.33851	−	8.53690i	−0.173662	−	0.277705i
$946$	−8.52040			−0.277022
$947$	18.4271	+	31.9166i	0.598799	+	1.03715i	0.992999	+	0.118126i	$0.0376887\pi$
$947$	18.4271	+	31.9166i	0.598799	+	1.03715i	−0.394199	+	0.919025i	$0.628978\pi$
$948$	1.43570	−	2.48671i	0.0466295	−	0.0807646i
$949$	−0.855892	+	1.48245i	−0.0277834	+	0.0481223i
$950$	25.9947	+	45.0242i	0.843381	+	1.46078i
$951$	−31.4478			−1.01977
$952$	−7.64598	+	14.3919i	−0.247808	+	0.466443i
$953$	21.6527			0.701401			0.350701	−	0.936488i	$-0.385944\pi$
$953$	21.6527			0.701401			0.350701	+	0.936488i	$0.385944\pi$
$954$	−0.177010	−	0.306590i	−0.00573091	−	0.00992623i
$955$	46.0243	−	79.7164i	1.48931	−	2.57956i
$956$	−1.06430	+	1.84342i	−0.0344218	+	0.0596203i
$957$	−7.93232	−	13.7392i	−0.256416	−	0.444125i
$958$	25.2119			0.814560
$959$	−8.28822	+	15.6007i	−0.267640	+	0.503774i
$960$	−3.80560			−0.122825
$961$	−20.4774	−	35.4678i	−0.660560	−	1.14412i
$962$	0.661495	−	1.14574i	0.0213275	−	0.0369402i
$963$	8.52952	−	14.7736i	0.274860	−	0.476072i
$964$	−9.36990	−	16.2291i	−0.301784	−	0.522705i
$965$	5.89266			0.189691
$966$	8.82112	+	14.1060i	0.283815	+	0.453853i
$967$	7.21867			0.232137			0.116068	−	0.993241i	$-0.462971\pi$
$967$	7.21867			0.232137			0.116068	+	0.993241i	$0.462971\pi$
$968$	8.48261	+	14.6923i	0.272642	+	0.472229i
$969$	16.8854	−	29.2464i	0.542438	−	0.939530i
$970$	−6.01214	+	10.4133i	−0.193038	+	0.334352i
$971$	13.8991	+	24.0739i	0.446042	+	0.772567i	0.998124	−	0.0612223i	$-0.0194999\pi$
$971$	13.8991	+	24.0739i	0.446042	+	0.772567i	−0.552082	+	0.833790i	$0.686167\pi$
$972$	−1.00000			−0.0320750
$973$	32.4914	−	1.14574i	1.04163	−	0.0367308i
$974$	−13.9342			−0.446480
$975$	4.74131	+	8.21218i	0.151843	+	0.263000i
$976$	4.88541	−	8.46179i	0.156378	−	0.270855i
$977$	3.28822	−	5.69536i	0.105199	−	0.182211i	−0.808620	−	0.588331i	$-0.799785\pi$
$977$	3.28822	−	5.69536i	0.105199	−	0.182211i	0.913820	+	0.406120i	$0.133119\pi$
$978$	4.86990	+	8.43491i	0.155722	+	0.269719i
$979$	56.4623			1.80454
$980$	26.5731	−	1.87642i	0.848845	−	0.0599402i
$981$	4.00000			0.127710
$982$	−6.17550	−	10.6963i	−0.197068	−	0.341332i
$983$	−5.22392	+	9.04809i	−0.166617	+	0.288589i	−0.937228	−	0.348716i	$-0.886618\pi$
$983$	−5.22392	+	9.04809i	−0.166617	+	0.288589i	0.770611	+	0.637306i	$0.219951\pi$
$984$	−2.66149	+	4.60984i	−0.0848454	+	0.146956i
$985$	34.7988	+	60.2734i	1.10878	+	1.92047i
$986$	18.4789			0.588487
$987$	18.7568	−	0.661422i	0.597036	−	0.0210533i
$988$	5.48261			0.174425
$989$	−5.06580	−	8.77423i	−0.161083	−	0.279004i
$990$	10.0624	−	17.4286i	0.319805	−	0.553918i
$991$	−5.49475	+	9.51718i	−0.174546	+	0.302323i	−0.940004	−	0.341163i	$-0.889179\pi$
$991$	−5.49475	+	9.51718i	−0.174546	+	0.302323i	0.765458	+	0.643486i	$0.222513\pi$
$992$	−4.24131	−	7.34616i	−0.134662	−	0.233241i
$993$	−16.8957			−0.536168
$994$	21.7190	+	34.7313i	0.688886	+	1.10161i
$995$	−99.7778			−3.16317
$996$	−3.72392	−	6.45002i	−0.117997	−	0.204377i
$997$	−22.1078	+	38.2919i	−0.700162	+	1.21272i	0.268247	+	0.963350i	$0.413556\pi$
$997$	−22.1078	+	38.2919i	−0.700162	+	1.21272i	−0.968409	+	0.249366i	$0.919778\pi$
$998$	−17.3820	+	30.1066i	−0.550219	+	0.953007i
$999$	0.661495	+	1.14574i	0.0209288	+	0.0362497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.k.235.1	yes	6
3.2	odd	2		1638.2.j.q.235.3		6
7.2	even	3	inner	546.2.i.k.79.1	✓	6
7.3	odd	6		3822.2.a.bw.1.1		3
7.4	even	3		3822.2.a.bv.1.3		3
21.2	odd	6		1638.2.j.q.1171.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.k.79.1	✓	6	7.2	even	3	inner
546.2.i.k.235.1	yes	6	1.1	even	1	trivial
1638.2.j.q.235.3		6	3.2	odd	2
1638.2.j.q.1171.3		6	21.2	odd	6
3822.2.a.bv.1.3		3	7.4	even	3
3822.2.a.bw.1.1		3	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.90280 - 3.29575i) q^{5} +1.00000 q^{6} +(-2.64411 + 0.0932392i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.90280 - 3.29575i) q^{5} +1.00000 q^{6} +(-2.64411 + 0.0932392i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.90280 - 3.29575i) q^{10} +(-2.64411 + 4.57973i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.40280 - 2.24325i) q^{14} -3.80560 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.07981 + 5.33439i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.74131 - 4.74808i) q^{19} +3.80560 q^{20} +(-1.24131 + 2.33648i) q^{21} -5.28822 q^{22} +(-3.14411 - 5.44575i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.74131 + 8.21218i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.24131 - 2.33648i) q^{28} -3.00000 q^{29} +(-1.90280 - 3.29575i) q^{30} +(4.24131 - 7.34616i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.64411 + 4.57973i) q^{33} -6.15962 q^{34} +(5.33851 + 8.53690i) q^{35} +1.00000 q^{36} +(-0.661495 - 1.14574i) q^{37} +(2.74131 - 4.74808i) q^{38} +(0.500000 - 0.866025i) q^{39} +(1.90280 + 3.29575i) q^{40} +5.32299 q^{41} +(-2.64411 + 0.0932392i) q^{42} +1.61121 q^{43} +(-2.64411 - 4.57973i) q^{44} +(-1.90280 + 3.29575i) q^{45} +(3.14411 - 5.44575i) q^{46} +(-3.54691 - 6.14343i) q^{47} -1.00000 q^{48} +(6.98261 - 0.493069i) q^{49} -9.48261 q^{50} +(3.07981 + 5.33439i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(0.177010 - 0.306590i) q^{53} +(-0.500000 - 0.866025i) q^{54} +20.1248 q^{55} +(2.64411 - 0.0932392i) q^{56} -5.48261 q^{57} +(-1.50000 - 2.59808i) q^{58} +(0.838505 - 1.45233i) q^{59} +(1.90280 - 3.29575i) q^{60} +(4.88541 + 8.46179i) q^{61} +8.48261 q^{62} +(1.40280 + 2.24325i) q^{63} +1.00000 q^{64} +(-1.90280 - 3.29575i) q^{65} +(-2.64411 + 4.57973i) q^{66} +(4.22392 - 7.31604i) q^{67} +(-3.07981 - 5.33439i) q^{68} -6.28822 q^{69} +(-4.72392 + 8.89173i) q^{70} -15.4826 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.855892 + 1.48245i) q^{73} +(0.661495 - 1.14574i) q^{74} +(4.74131 + 8.21218i) q^{75} +5.48261 q^{76} +(6.56430 - 12.3558i) q^{77} +1.00000 q^{78} +(-1.43570 - 2.48671i) q^{79} +(-1.90280 + 3.29575i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.66149 + 4.60984i) q^{82} -7.44784 q^{83} +(-1.40280 - 2.24325i) q^{84} +23.4411 q^{85} +(0.805603 + 1.39535i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(2.64411 - 4.57973i) q^{88} +(-5.33851 - 9.24656i) q^{89} -3.80560 q^{90} +(-2.64411 + 0.0932392i) q^{91} +6.28822 q^{92} +(-4.24131 - 7.34616i) q^{93} +(3.54691 - 6.14343i) q^{94} +(-10.4323 + 18.0693i) q^{95} +(-0.500000 - 0.866025i) q^{96} -3.15962 q^{97} +(3.91832 + 5.80059i) q^{98} +5.28822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 6 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} + 6 q^{22} - 3 q^{24} - 18 q^{25} + 3 q^{26} - 6 q^{27} - 3 q^{28} - 18 q^{29} - 3 q^{30} + 15 q^{31} + 3 q^{32} - 3 q^{33} - 12 q^{34} + 30 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 36 q^{41} + 3 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{47} - 6 q^{48} + 21 q^{49} - 36 q^{50} + 6 q^{51} - 3 q^{52} - 3 q^{53} - 3 q^{54} + 54 q^{55} - 3 q^{56} - 12 q^{57} - 9 q^{58} + 3 q^{59} + 3 q^{60} + 30 q^{62} + 6 q^{64} - 3 q^{65} + 3 q^{66} - 6 q^{67} - 6 q^{68} + 3 q^{70} - 72 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} + 18 q^{75} + 12 q^{76} + 33 q^{77} + 6 q^{78} - 15 q^{79} - 3 q^{80} - 3 q^{81} + 18 q^{82} + 18 q^{83} - 48 q^{85} - 12 q^{86} - 9 q^{87} - 3 q^{88} - 30 q^{89} - 6 q^{90} + 3 q^{91} - 15 q^{93} - 6 q^{94} - 6 q^{95} - 3 q^{96} + 6 q^{97} + 9 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 6 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 + 6 * q^22 - 3 * q^24 - 18 * q^25 + 3 * q^26 - 6 * q^27 - 3 * q^28 - 18 * q^29 - 3 * q^30 + 15 * q^31 + 3 * q^32 - 3 * q^33 - 12 * q^34 + 30 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 36 * q^41 + 3 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^47 - 6 * q^48 + 21 * q^49 - 36 * q^50 + 6 * q^51 - 3 * q^52 - 3 * q^53 - 3 * q^54 + 54 * q^55 - 3 * q^56 - 12 * q^57 - 9 * q^58 + 3 * q^59 + 3 * q^60 + 30 * q^62 + 6 * q^64 - 3 * q^65 + 3 * q^66 - 6 * q^67 - 6 * q^68 + 3 * q^70 - 72 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 + 18 * q^75 + 12 * q^76 + 33 * q^77 + 6 * q^78 - 15 * q^79 - 3 * q^80 - 3 * q^81 + 18 * q^82 + 18 * q^83 - 48 * q^85 - 12 * q^86 - 9 * q^87 - 3 * q^88 - 30 * q^89 - 6 * q^90 + 3 * q^91 - 15 * q^93 - 6 * q^94 - 6 * q^95 - 3 * q^96 + 6 * q^97 + 9 * q^98 - 6 * q^99

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