LMFDB - Embedded newform 1218.2.i.a.697.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-3,-3,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			697.3
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	1218.697
Dual form			1218.2.i.a.1045.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.900969 + 1.56052i) q^{5} +1.00000 q^{6} +(-2.37047 - 1.17511i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.900969 - 1.56052i) q^{10} +(0.376510 - 0.652135i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.29590 q^{13} +(0.167563 + 2.64044i) q^{14} -1.80194 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.96950 - 3.41127i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.955927 - 1.65571i) q^{19} -1.80194 q^{20} +(2.20291 - 1.46533i) q^{21} -0.753020 q^{22} +(2.29105 + 3.96822i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.876510 - 1.51816i) q^{25} +(-1.14795 - 1.98831i) q^{26} +1.00000 q^{27} +(2.20291 - 1.46533i) q^{28} -1.00000 q^{29} +(0.900969 + 1.56052i) q^{30} +(0.634375 - 1.09877i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.376510 + 0.652135i) q^{33} -3.93900 q^{34} +(-0.301938 - 4.75791i) q^{35} +1.00000 q^{36} +(6.05980 + 10.4959i) q^{37} +(-0.955927 + 1.65571i) q^{38} +(-1.14795 + 1.98831i) q^{39} +(0.900969 + 1.56052i) q^{40} +5.03684 q^{41} +(-2.37047 - 1.17511i) q^{42} -1.17629 q^{43} +(0.376510 + 0.652135i) q^{44} +(0.900969 - 1.56052i) q^{45} +(2.29105 - 3.96822i) q^{46} +(-0.222521 - 0.385418i) q^{47} +1.00000 q^{48} +(4.23825 + 5.57111i) q^{49} -1.75302 q^{50} +(1.96950 + 3.41127i) q^{51} +(-1.14795 + 1.98831i) q^{52} +(5.15883 - 8.93536i) q^{53} +(-0.500000 - 0.866025i) q^{54} +1.35690 q^{55} +(-2.37047 - 1.17511i) q^{56} +1.91185 q^{57} +(0.500000 + 0.866025i) q^{58} +(-5.24698 + 9.08804i) q^{59} +(0.900969 - 1.56052i) q^{60} +(4.78501 + 8.28788i) q^{61} -1.26875 q^{62} +(0.167563 + 2.64044i) q^{63} +1.00000 q^{64} +(2.06853 + 3.58280i) q^{65} +(0.376510 - 0.652135i) q^{66} +(1.20895 - 2.09396i) q^{67} +(1.96950 + 3.41127i) q^{68} -4.58211 q^{69} +(-3.96950 + 2.64044i) q^{70} +11.5308 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.89493 + 5.01416i) q^{73} +(6.05980 - 10.4959i) q^{74} +(0.876510 + 1.51816i) q^{75} +1.91185 q^{76} +(-1.65883 + 1.10343i) q^{77} +2.29590 q^{78} +(7.40850 + 12.8319i) q^{79} +(0.900969 - 1.56052i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.51842 - 4.36203i) q^{82} -1.64310 q^{83} +(0.167563 + 2.64044i) q^{84} +7.09783 q^{85} +(0.588146 + 1.01870i) q^{86} +(0.500000 - 0.866025i) q^{87} +(0.376510 - 0.652135i) q^{88} +(0.711636 + 1.23259i) q^{89} -1.80194 q^{90} +(-5.44235 - 2.69792i) q^{91} -4.58211 q^{92} +(0.634375 + 1.09877i) q^{93} +(-0.222521 + 0.385418i) q^{94} +(1.72252 - 2.98349i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.53319 q^{97} +(2.70560 - 6.45599i) q^{98} -0.753020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} + 6 q^{6} + 6 q^{8} - 3 q^{9} + q^{10} + 7 q^{11} - 3 q^{12} - 14 q^{13} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} - 14 q^{22} + 8 q^{23}+ \cdots - 14 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 + 6 * q^6 + 6 * q^8 - 3 * q^9 + q^10 + 7 * q^11 - 3 * q^12 - 14 * q^13 - 2 * q^15 - 3 * q^16 + 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 - 14 * q^22 + 8 * q^23 - 3 * q^24 + 10 * q^25 + 7 * q^26 + 6 * q^27 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 + 7 * q^33 - 4 * q^34 + 7 * q^35 + 6 * q^36 + 15 * q^37 - 2 * q^38 + 7 * q^39 + q^40 - 26 * q^41 - 22 * q^43 + 7 * q^44 + q^45 + 8 * q^46 - q^47 + 6 * q^48 - 20 * q^50 + 2 * q^51 + 7 * q^52 + 14 * q^53 - 3 * q^54 + 4 * q^57 + 3 * q^58 - 22 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 6 * q^64 + 7 * q^65 + 7 * q^66 + 13 * q^67 + 2 * q^68 - 16 * q^69 - 14 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 15 * q^74 + 10 * q^75 + 4 * q^76 + 7 * q^77 - 14 * q^78 + 15 * q^79 + q^80 - 3 * q^81 + 13 * q^82 - 18 * q^83 + 6 * q^85 + 11 * q^86 + 3 * q^87 + 7 * q^88 + 7 * q^89 - 2 * q^90 - 35 * q^91 - 16 * q^92 - 4 * q^93 - q^94 + 10 * q^95 - 3 * q^96 - 34 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−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
$5$	0.900969	+	1.56052i	0.402926	+	0.697887i	0.994078	−	0.108673i	$-0.0346600\pi$
$5$	0.900969	+	1.56052i	0.402926	+	0.697887i	−0.591152	+	0.806560i	$0.701327\pi$
$6$	1.00000			0.408248
$7$	−2.37047	−	1.17511i	−0.895953	−	0.444148i
$7$	−2.37047	−	1.17511i	−0.895953	−	0.444148i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.900969	−	1.56052i	0.284911	−	0.493481i
$11$	0.376510	−	0.652135i	0.113522	−	0.196626i	−0.803666	−	0.595081i	$-0.797120\pi$
$11$	0.376510	−	0.652135i	0.113522	−	0.196626i	0.917188	+	0.398455i	$0.130453\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.29590			0.636767			0.318384	−	0.947962i	$-0.396860\pi$
$13$	2.29590			0.636767			0.318384	+	0.947962i	$0.396860\pi$
$14$	0.167563	+	2.64044i	0.0447830	+	0.705687i
$15$	−1.80194			−0.465258
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.96950	−	3.41127i	0.477674	−	0.827356i	−0.521998	−	0.852946i	$-0.674813\pi$
$17$	1.96950	−	3.41127i	0.477674	−	0.827356i	0.999673	+	0.0255907i	$0.00814667\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.955927	−	1.65571i	−0.219305	−	0.379847i	0.735291	−	0.677752i	$-0.237046\pi$
$19$	−0.955927	−	1.65571i	−0.219305	−	0.379847i	−0.954596	+	0.297905i	$0.903712\pi$
$20$	−1.80194			−0.402926
$21$	2.20291	−	1.46533i	0.480714	−	0.319762i
$22$	−0.753020			−0.160544
$23$	2.29105	+	3.96822i	0.477717	+	0.827431i	0.999674	−	0.0255413i	$-0.00813092\pi$
$23$	2.29105	+	3.96822i	0.477717	+	0.827431i	−0.521956	+	0.852972i	$0.674798\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	0.876510	−	1.51816i	0.175302	−	0.303632i
$26$	−1.14795	−	1.98831i	−0.225131	−	0.389939i
$27$	1.00000			0.192450
$28$	2.20291	−	1.46533i	0.416310	−	0.276922i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	0.900969	+	1.56052i	0.164494	+	0.284911i
$31$	0.634375	−	1.09877i	0.113937	−	0.197345i	−0.803417	−	0.595416i	$-0.796987\pi$
$31$	0.634375	−	1.09877i	0.113937	−	0.197345i	0.917354	+	0.398072i	$0.130320\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.376510	+	0.652135i	0.0655420	+	0.113522i
$34$	−3.93900			−0.675533
$35$	−0.301938	−	4.75791i	−0.0510368	−	0.804233i
$36$	1.00000			0.166667
$37$	6.05980	+	10.4959i	0.996225	+	1.72551i	0.573287	+	0.819354i	$0.305668\pi$
$37$	6.05980	+	10.4959i	0.996225	+	1.72551i	0.422938	+	0.906159i	$0.360999\pi$
$38$	−0.955927	+	1.65571i	−0.155072	+	0.268592i
$39$	−1.14795	+	1.98831i	−0.183819	+	0.318384i
$40$	0.900969	+	1.56052i	0.142456	+	0.246740i
$41$	5.03684			0.786622			0.393311	−	0.919406i	$-0.371330\pi$
$41$	5.03684			0.786622			0.393311	+	0.919406i	$0.371330\pi$
$42$	−2.37047	−	1.17511i	−0.365771	−	0.181323i
$43$	−1.17629			−0.179383			−0.0896914	−	0.995970i	$-0.528588\pi$
$43$	−1.17629			−0.179383			−0.0896914	+	0.995970i	$0.528588\pi$
$44$	0.376510	+	0.652135i	0.0567610	+	0.0983130i
$45$	0.900969	−	1.56052i	0.134309	−	0.232629i
$46$	2.29105	−	3.96822i	0.337797	−	0.585082i
$47$	−0.222521	−	0.385418i	−0.0324580	−	0.0562189i	0.849340	−	0.527846i	$-0.177000\pi$
$47$	−0.222521	−	0.385418i	−0.0324580	−	0.0562189i	−0.881798	+	0.471627i	$0.843667\pi$
$48$	1.00000			0.144338
$49$	4.23825	+	5.57111i	0.605464	+	0.795872i
$50$	−1.75302			−0.247915
$51$	1.96950	+	3.41127i	0.275785	+	0.477674i
$52$	−1.14795	+	1.98831i	−0.159192	+	0.275728i
$53$	5.15883	−	8.93536i	0.708620	−	1.22737i	−0.256749	−	0.966478i	$-0.582651\pi$
$53$	5.15883	−	8.93536i	0.708620	−	1.22737i	0.965369	−	0.260888i	$-0.0840154\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.35690			0.182964
$56$	−2.37047	−	1.17511i	−0.316767	−	0.157030i
$57$	1.91185			0.253231
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−5.24698	+	9.08804i	−0.683099	+	1.18316i	0.290932	+	0.956744i	$0.406035\pi$
$59$	−5.24698	+	9.08804i	−0.683099	+	1.18316i	−0.974030	+	0.226418i	$0.927299\pi$
$60$	0.900969	−	1.56052i	0.116315	−	0.201463i
$61$	4.78501	+	8.28788i	0.612658	+	1.06115i	0.990791	+	0.135403i	$0.0432330\pi$
$61$	4.78501	+	8.28788i	0.612658	+	1.06115i	−0.378133	+	0.925751i	$0.623434\pi$
$62$	−1.26875			−0.161131
$63$	0.167563	+	2.64044i	0.0211109	+	0.332664i
$64$	1.00000			0.125000
$65$	2.06853	+	3.58280i	0.256570	+	0.444392i
$66$	0.376510	−	0.652135i	0.0463452	−	0.0802722i
$67$	1.20895	−	2.09396i	0.147696	−	0.255818i	−0.782679	−	0.622425i	$-0.786147\pi$
$67$	1.20895	−	2.09396i	0.147696	−	0.255818i	0.930376	+	0.366608i	$0.119481\pi$
$68$	1.96950	+	3.41127i	0.238837	+	0.413678i
$69$	−4.58211			−0.551621
$70$	−3.96950	+	2.64044i	−0.474446	+	0.315593i
$71$	11.5308			1.36845			0.684227	−	0.729269i	$-0.260140\pi$
$71$	11.5308			1.36845			0.684227	+	0.729269i	$0.260140\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−2.89493	+	5.01416i	−0.338826	+	0.586863i	−0.984212	−	0.176993i	$-0.943363\pi$
$73$	−2.89493	+	5.01416i	−0.338826	+	0.586863i	0.645386	+	0.763856i	$0.276696\pi$
$74$	6.05980	−	10.4959i	0.704438	−	1.22012i
$75$	0.876510	+	1.51816i	0.101211	+	0.175302i
$76$	1.91185			0.219305
$77$	−1.65883	+	1.10343i	−0.189042	+	0.125747i
$78$	2.29590			0.259959
$79$	7.40850	+	12.8319i	0.833522	+	1.44370i	0.895229	+	0.445607i	$0.147012\pi$
$79$	7.40850	+	12.8319i	0.833522	+	1.44370i	−0.0617070	+	0.998094i	$0.519654\pi$
$80$	0.900969	−	1.56052i	0.100731	−	0.174472i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.51842	−	4.36203i	−0.278113	−	0.481705i
$83$	−1.64310			−0.180354			−0.0901771	−	0.995926i	$-0.528743\pi$
$83$	−1.64310			−0.180354			−0.0901771	+	0.995926i	$0.528743\pi$
$84$	0.167563	+	2.64044i	0.0182826	+	0.288096i
$85$	7.09783			0.769868
$86$	0.588146	+	1.01870i	0.0634214	+	0.109849i
$87$	0.500000	−	0.866025i	0.0536056	−	0.0928477i
$88$	0.376510	−	0.652135i	0.0401361	−	0.0695178i
$89$	0.711636	+	1.23259i	0.0754332	+	0.130654i	0.901275	−	0.433248i	$-0.142633\pi$
$89$	0.711636	+	1.23259i	0.0754332	+	0.130654i	−0.825841	+	0.563903i	$0.809299\pi$
$90$	−1.80194			−0.189941
$91$	−5.44235	−	2.69792i	−0.570514	−	0.282819i
$92$	−4.58211			−0.477717
$93$	0.634375	+	1.09877i	0.0657816	+	0.113937i
$94$	−0.222521	+	0.385418i	−0.0229513	+	0.0397528i
$95$	1.72252	−	2.98349i	0.176727	−	0.306100i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−4.53319			−0.460275			−0.230138	−	0.973158i	$-0.573918\pi$
$97$	−4.53319			−0.460275			−0.230138	+	0.973158i	$0.573918\pi$
$98$	2.70560	−	6.45599i	0.273306	−	0.652153i
$99$	−0.753020			−0.0756814
$100$	0.876510	+	1.51816i	0.0876510	+	0.151816i
$101$	6.44116	−	11.1564i	0.640919	−	1.11010i	−0.344309	−	0.938856i	$-0.611887\pi$
$101$	6.44116	−	11.1564i	0.640919	−	1.11010i	0.985228	−	0.171248i	$-0.0547799\pi$
$102$	1.96950	−	3.41127i	0.195010	−	0.337767i
$103$	5.18598	+	8.98238i	0.510990	+	0.885060i	0.999919	+	0.0127368i	$0.00405437\pi$
$103$	5.18598	+	8.98238i	0.510990	+	0.885060i	−0.488929	+	0.872324i	$0.662612\pi$
$104$	2.29590			0.225131
$105$	4.27144	+	2.11747i	0.416850	+	0.206644i
$106$	−10.3177			−1.00214
$107$	−5.51842	−	9.55818i	−0.533486	−	0.924024i	−0.999235	−	0.0391075i	$-0.987549\pi$
$107$	−5.51842	−	9.55818i	−0.533486	−	0.924024i	0.465749	−	0.884917i	$-0.345785\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.58426	−	11.4043i	0.630658	−	1.09233i	−0.356760	−	0.934196i	$-0.616118\pi$
$109$	6.58426	−	11.4043i	0.630658	−	1.09233i	0.987417	−	0.158135i	$-0.0505482\pi$
$110$	−0.678448	−	1.17511i	−0.0646875	−	0.112042i
$111$	−12.1196			−1.15034
$112$	0.167563	+	2.64044i	0.0158332	+	0.249498i
$113$	10.2349			0.962818			0.481409	−	0.876496i	$-0.340125\pi$
$113$	10.2349			0.962818			0.481409	+	0.876496i	$0.340125\pi$
$114$	−0.955927	−	1.65571i	−0.0895308	−	0.155072i
$115$	−4.12833	+	7.15048i	−0.384969	+	0.666786i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−1.14795	−	1.98831i	−0.106128	−	0.183819i
$118$	10.4940			0.966047
$119$	−8.67725	+	5.77195i	−0.795442	+	0.529114i
$120$	−1.80194			−0.164494
$121$	5.21648	+	9.03521i	0.474225	+	0.821383i
$122$	4.78501	−	8.28788i	0.433215	−	0.750350i
$123$	−2.51842	+	4.36203i	−0.227078	+	0.393311i
$124$	0.634375	+	1.09877i	0.0569686	+	0.0986724i
$125$	12.1685			1.08839
$126$	2.20291	−	1.46533i	0.196251	−	0.130542i
$127$	−0.807315			−0.0716376			−0.0358188	−	0.999358i	$-0.511404\pi$
$127$	−0.807315			−0.0716376			−0.0358188	+	0.999358i	$0.511404\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.588146	−	1.01870i	0.0517834	−	0.0896914i
$130$	2.06853	−	3.58280i	0.181422	−	0.314233i
$131$	−10.6664	−	18.4747i	−0.931925	−	1.61414i	−0.780028	−	0.625745i	$-0.784795\pi$
$131$	−10.6664	−	18.4747i	−0.931925	−	1.61414i	−0.151897	−	0.988396i	$-0.548538\pi$
$132$	−0.753020			−0.0655420
$133$	0.320356	+	5.04814i	0.0277784	+	0.437729i
$134$	−2.41789			−0.208874
$135$	0.900969	+	1.56052i	0.0775431	+	0.134309i
$136$	1.96950	−	3.41127i	0.168883	−	0.292514i
$137$	6.55765	−	11.3582i	0.560258	−	0.970395i	−0.437216	−	0.899357i	$-0.644035\pi$
$137$	6.55765	−	11.3582i	0.560258	−	0.970395i	0.997474	−	0.0710380i	$-0.0226312\pi$
$138$	2.29105	+	3.96822i	0.195027	+	0.337797i
$139$	6.48858			0.550354			0.275177	−	0.961394i	$-0.411263\pi$
$139$	6.48858			0.550354			0.275177	+	0.961394i	$0.411263\pi$
$140$	4.27144	+	2.11747i	0.361002	+	0.178959i
$141$	0.445042			0.0374793
$142$	−5.76540	−	9.98596i	−0.483821	−	0.838003i
$143$	0.864429	−	1.49723i	0.0722872	−	0.125205i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.900969	−	1.56052i	−0.0748214	−	0.129594i
$146$	5.78986			0.479172
$147$	−6.94385	+	0.884879i	−0.572719	+	0.0729836i
$148$	−12.1196			−0.996225
$149$	−10.2289	−	17.7169i	−0.837981	−	1.45143i	−0.891580	−	0.452863i	$-0.850403\pi$
$149$	−10.2289	−	17.7169i	−0.837981	−	1.45143i	0.0535997	−	0.998563i	$-0.482930\pi$
$150$	0.876510	−	1.51816i	0.0715668	−	0.123957i
$151$	6.87531	−	11.9084i	0.559505	−	0.969091i	−0.438033	−	0.898959i	$-0.644325\pi$
$151$	6.87531	−	11.9084i	0.559505	−	0.969091i	0.997538	−	0.0701322i	$-0.0223421\pi$
$152$	−0.955927	−	1.65571i	−0.0775359	−	0.134296i
$153$	−3.93900			−0.318449
$154$	1.78501	+	0.884879i	0.143840	+	0.0713056i
$155$	2.28621			0.183633
$156$	−1.14795	−	1.98831i	−0.0919094	−	0.159192i
$157$	0.928780	−	1.60869i	0.0741247	−	0.128388i	−0.826581	−	0.562818i	$-0.809717\pi$
$157$	0.928780	−	1.60869i	0.0741247	−	0.128388i	0.900705	+	0.434431i	$0.143050\pi$
$158$	7.40850	−	12.8319i	0.589389	−	1.02085i
$159$	5.15883	+	8.93536i	0.409122	+	0.708620i
$160$	−1.80194			−0.142456
$161$	−0.767790	−	12.0988i	−0.0605104	−	0.953517i
$162$	1.00000			0.0785674
$163$	9.37263	+	16.2339i	0.734121	+	1.27153i	0.955108	+	0.296258i	$0.0957387\pi$
$163$	9.37263	+	16.2339i	0.734121	+	1.27153i	−0.220987	+	0.975277i	$0.570928\pi$
$164$	−2.51842	+	4.36203i	−0.196655	+	0.340617i
$165$	−0.678448	+	1.17511i	−0.0528171	+	0.0914819i
$166$	0.821552	+	1.42297i	0.0637648	+	0.110444i
$167$	0.105604			0.00817191			0.00408596	−	0.999992i	$-0.498699\pi$
$167$	0.105604			0.00817191			0.00408596	+	0.999992i	$0.498699\pi$
$168$	2.20291	−	1.46533i	0.169958	−	0.113053i
$169$	−7.72886			−0.594527
$170$	−3.54892	−	6.14691i	−0.272190	−	0.471446i
$171$	−0.955927	+	1.65571i	−0.0731016	+	0.126616i
$172$	0.588146	−	1.01870i	0.0448457	−	0.0776751i
$173$	5.24578	+	9.08596i	0.398830	+	0.690793i	0.993582	−	0.113116i	$-0.0360832\pi$
$173$	5.24578	+	9.08596i	0.398830	+	0.690793i	−0.594752	+	0.803909i	$0.702750\pi$
$174$	−1.00000			−0.0758098
$175$	−3.86174	+	2.56876i	−0.291920	+	0.194180i
$176$	−0.753020			−0.0567610
$177$	−5.24698	−	9.08804i	−0.394387	−	0.683099i
$178$	0.711636	−	1.23259i	0.0533394	−	0.0923865i
$179$	8.68114	−	15.0362i	0.648859	−	1.12386i	−0.334537	−	0.942383i	$-0.608580\pi$
$179$	8.68114	−	15.0362i	0.648859	−	1.12386i	0.983396	−	0.181474i	$-0.0580867\pi$
$180$	0.900969	+	1.56052i	0.0671543	+	0.116315i
$181$	−13.5985			−1.01077			−0.505384	−	0.862894i	$-0.668649\pi$
$181$	−13.5985			−1.01077			−0.505384	+	0.862894i	$0.668649\pi$
$182$	0.384707	+	6.06218i	0.0285164	+	0.449359i
$183$	−9.57002			−0.707437
$184$	2.29105	+	3.96822i	0.168899	+	0.292541i
$185$	−10.9194	+	18.9129i	−0.802809	+	1.39051i
$186$	0.634375	−	1.09877i	0.0465146	−	0.0805657i
$187$	−1.48307	−	2.56876i	−0.108453	−	0.187846i
$188$	0.445042			0.0324580
$189$	−2.37047	−	1.17511i	−0.172426	−	0.0854764i
$190$	−3.44504			−0.249930
$191$	−1.49880	−	2.59600i	−0.108450	−	0.187840i	0.806693	−	0.590971i	$-0.201255\pi$
$191$	−1.49880	−	2.59600i	−0.108450	−	0.187840i	−0.915142	+	0.403131i	$0.867922\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−11.3339	+	19.6309i	−0.815834	+	1.41307i	0.0928934	+	0.995676i	$0.470388\pi$
$193$	−11.3339	+	19.6309i	−0.815834	+	1.41307i	−0.908727	+	0.417390i	$0.862945\pi$
$194$	2.26659	+	3.92586i	0.162732	+	0.281860i
$195$	−4.13706			−0.296261
$196$	−6.94385	+	0.884879i	−0.495989	+	0.0632056i
$197$	1.85086			0.131868			0.0659340	−	0.997824i	$-0.478997\pi$
$197$	1.85086			0.131868			0.0659340	+	0.997824i	$0.478997\pi$
$198$	0.376510	+	0.652135i	0.0267574	+	0.0463452i
$199$	2.94773	−	5.10562i	0.208959	−	0.361928i	−0.742428	−	0.669926i	$-0.766326\pi$
$199$	2.94773	−	5.10562i	0.208959	−	0.361928i	0.951387	+	0.307998i	$0.0996591\pi$
$200$	0.876510	−	1.51816i	0.0619786	−	0.107350i
$201$	1.20895	+	2.09396i	0.0852726	+	0.147696i
$202$	−12.8823			−0.906396
$203$	2.37047	+	1.17511i	0.166374	+	0.0824763i
$204$	−3.93900			−0.275785
$205$	4.53803	+	7.86010i	0.316950	+	0.548973i
$206$	5.18598	−	8.98238i	0.361324	−	0.625832i
$207$	2.29105	−	3.96822i	0.159239	−	0.275810i
$208$	−1.14795	−	1.98831i	−0.0795959	−	0.137864i
$209$	−1.43967			−0.0995837
$210$	−0.301938	−	4.75791i	−0.0208357	−	0.328327i
$211$	−10.8334			−0.745802			−0.372901	−	0.927871i	$-0.621637\pi$
$211$	−10.8334			−0.745802			−0.372901	+	0.927871i	$0.621637\pi$
$212$	5.15883	+	8.93536i	0.354310	+	0.613683i
$213$	−5.76540	+	9.98596i	−0.395039	+	0.684227i
$214$	−5.51842	+	9.55818i	−0.377231	+	0.653384i
$215$	−1.05980	−	1.83563i	−0.0722779	−	0.125189i
$216$	1.00000			0.0680414
$217$	−2.79494	+	1.85914i	−0.189733	+	0.126207i
$218$	−13.1685			−0.891885
$219$	−2.89493	−	5.01416i	−0.195621	−	0.338826i
$220$	−0.678448	+	1.17511i	−0.0457410	+	0.0792257i
$221$	4.52177	−	7.83194i	0.304167	−	0.526833i
$222$	6.05980	+	10.4959i	0.406707	+	0.704438i
$223$	−6.33944			−0.424520			−0.212260	−	0.977213i	$-0.568082\pi$
$223$	−6.33944			−0.424520			−0.212260	+	0.977213i	$0.568082\pi$
$224$	2.20291	−	1.46533i	0.147188	−	0.0979067i
$225$	−1.75302			−0.116868
$226$	−5.11745	−	8.86368i	−0.340408	−	0.589603i
$227$	−12.9852	+	22.4911i	−0.861860	+	1.49279i	0.00827158	+	0.999966i	$0.497367\pi$
$227$	−12.9852	+	22.4911i	−0.861860	+	1.49279i	−0.870132	+	0.492819i	$0.835966\pi$
$228$	−0.955927	+	1.65571i	−0.0633078	+	0.109652i
$229$	−1.23878	−	2.14563i	−0.0818611	−	0.141788i	0.822188	−	0.569216i	$-0.192753\pi$
$229$	−1.23878	−	2.14563i	−0.0818611	−	0.141788i	−0.904049	+	0.427428i	$0.859420\pi$
$230$	8.25667			0.544429
$231$	−0.126178	−	1.98831i	−0.00830192	−	0.130821i
$232$	−1.00000			−0.0656532
$233$	0.551606	+	0.955409i	0.0361369	+	0.0625909i	0.883528	−	0.468378i	$-0.155161\pi$
$233$	0.551606	+	0.955409i	0.0361369	+	0.0625909i	−0.847391	+	0.530969i	$0.821828\pi$
$234$	−1.14795	+	1.98831i	−0.0750437	+	0.129980i
$235$	0.400969	−	0.694498i	0.0261563	−	0.0453041i
$236$	−5.24698	−	9.08804i	−0.341549	−	0.591581i
$237$	−14.8170			−0.962468
$238$	9.33728	+	4.62874i	0.605246	+	0.300037i
$239$	−6.30798			−0.408029			−0.204015	−	0.978968i	$-0.565399\pi$
$239$	−6.30798			−0.408029			−0.204015	+	0.978968i	$0.565399\pi$
$240$	0.900969	+	1.56052i	0.0581573	+	0.100731i
$241$	5.33728	−	9.24444i	0.343805	−	0.595487i	−0.641331	−	0.767264i	$-0.721618\pi$
$241$	5.33728	−	9.24444i	0.343805	−	0.595487i	0.985136	+	0.171777i	$0.0549509\pi$
$242$	5.21648	−	9.03521i	0.335328	−	0.580805i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−9.57002			−0.612658
$245$	−4.87531	+	11.6333i	−0.311472	+	0.743223i
$246$	5.03684			0.321137
$247$	−2.19471	−	3.80135i	−0.139646	−	0.241874i
$248$	0.634375	−	1.09877i	0.0402828	−	0.0697719i
$249$	0.821552	−	1.42297i	0.0520637	−	0.0901771i
$250$	−6.08426	−	10.5382i	−0.384802	−	0.666497i
$251$	−25.2597			−1.59438			−0.797188	−	0.603732i	$-0.793680\pi$
$251$	−25.2597			−1.59438			−0.797188	+	0.603732i	$0.793680\pi$
$252$	−2.37047	−	1.17511i	−0.149326	−	0.0740247i
$253$	3.45042			0.216926
$254$	0.403657	+	0.699155i	0.0253277	+	0.0438689i
$255$	−3.54892	+	6.14691i	−0.222242	+	0.384934i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.6283	+	20.1409i	0.725356	+	1.25635i	0.958827	+	0.283989i	$0.0916580\pi$
$257$	11.6283	+	20.1409i	0.725356	+	1.25635i	−0.233472	+	0.972364i	$0.575009\pi$
$258$	−1.17629			−0.0732327
$259$	−2.03079	−	32.0011i	−0.126187	−	1.98845i
$260$	−4.13706			−0.256570
$261$	0.500000	+	0.866025i	0.0309492	+	0.0536056i
$262$	−10.6664	+	18.4747i	−0.658970	+	1.14137i
$263$	−3.04288	+	5.27042i	−0.187632	+	0.324988i	−0.944460	−	0.328626i	$-0.893415\pi$
$263$	−3.04288	+	5.27042i	−0.187632	+	0.324988i	0.756828	+	0.653614i	$0.226748\pi$
$264$	0.376510	+	0.652135i	0.0231726	+	0.0401361i
$265$	18.5918			1.14208
$266$	4.21164	−	2.80150i	0.258232	−	0.171771i
$267$	−1.42327			−0.0871028
$268$	1.20895	+	2.09396i	0.0738482	+	0.127909i
$269$	−5.23341	+	9.06453i	−0.319086	+	0.552674i	−0.980298	−	0.197526i	$-0.936709\pi$
$269$	−5.23341	+	9.06453i	−0.319086	+	0.552674i	0.661211	+	0.750200i	$0.270043\pi$
$270$	0.900969	−	1.56052i	0.0548312	−	0.0949705i
$271$	−8.07002	−	13.9777i	−0.490219	−	0.849084i	0.509718	−	0.860342i	$-0.329750\pi$
$271$	−8.07002	−	13.9777i	−0.490219	−	0.849084i	−0.999937	+	0.0112575i	$0.996417\pi$
$272$	−3.93900			−0.238837
$273$	5.05765	−	3.36425i	0.306103	−	0.203614i
$274$	−13.1153			−0.792324
$275$	−0.660030	−	1.14321i	−0.0398013	−	0.0689379i
$276$	2.29105	−	3.96822i	0.137905	−	0.238859i
$277$	−3.52661	+	6.10828i	−0.211894	+	0.367011i	−0.952307	−	0.305141i	$-0.901296\pi$
$277$	−3.52661	+	6.10828i	−0.211894	+	0.367011i	0.740413	+	0.672152i	$0.234630\pi$
$278$	−3.24429	−	5.61928i	−0.194580	−	0.337022i
$279$	−1.26875			−0.0759581
$280$	−0.301938	−	4.75791i	−0.0180442	−	0.284339i
$281$	9.47219			0.565063			0.282532	−	0.959258i	$-0.408826\pi$
$281$	9.47219			0.565063			0.282532	+	0.959258i	$0.408826\pi$
$282$	−0.222521	−	0.385418i	−0.0132509	−	0.0229513i
$283$	5.08911	−	8.81459i	0.302516	−	0.523973i	−0.674189	−	0.738559i	$-0.735507\pi$
$283$	5.08911	−	8.81459i	0.302516	−	0.523973i	0.976705	+	0.214586i	$0.0688401\pi$
$284$	−5.76540	+	9.98596i	−0.342113	+	0.592558i
$285$	1.72252	+	2.98349i	0.102033	+	0.176727i
$286$	−1.72886			−0.102229
$287$	−11.9397	−	5.91882i	−0.704776	−	0.349377i
$288$	1.00000			0.0589256
$289$	0.742135	+	1.28542i	0.0436550	+	0.0756127i
$290$	−0.900969	+	1.56052i	−0.0529067	+	0.0916371i
$291$	2.26659	−	3.92586i	0.132870	−	0.230138i
$292$	−2.89493	−	5.01416i	−0.169413	−	0.293432i
$293$	−4.03444			−0.235695			−0.117847	−	0.993032i	$-0.537599\pi$
$293$	−4.03444			−0.235695			−0.117847	+	0.993032i	$0.537599\pi$
$294$	4.23825	+	5.57111i	0.247180	+	0.324914i
$295$	−18.9095			−1.10095
$296$	6.05980	+	10.4959i	0.352219	+	0.610061i
$297$	0.376510	−	0.652135i	0.0218473	−	0.0378407i
$298$	−10.2289	+	17.7169i	−0.592542	+	1.02631i
$299$	5.26002	+	9.11062i	0.304195	+	0.526881i
$300$	−1.75302			−0.101211
$301$	2.78836	+	1.38227i	0.160719	+	0.0796726i
$302$	−13.7506			−0.791260
$303$	6.44116	+	11.1564i	0.370035	+	0.640919i
$304$	−0.955927	+	1.65571i	−0.0548262	+	0.0949617i
$305$	−8.62229	+	14.9343i	−0.493711	+	0.855133i
$306$	1.96950	+	3.41127i	0.112589	+	0.195010i
$307$	13.8726			0.791753			0.395876	−	0.918304i	$-0.370441\pi$
$307$	13.8726			0.791753			0.395876	+	0.918304i	$0.370441\pi$
$308$	−0.126178	−	1.98831i	−0.00718967	−	0.113294i
$309$	−10.3720			−0.590040
$310$	−1.14310	−	1.97991i	−0.0649240	−	0.112452i
$311$	5.83124	−	10.1000i	0.330659	−	0.572719i	−0.651982	−	0.758234i	$-0.726062\pi$
$311$	5.83124	−	10.1000i	0.330659	−	0.572719i	0.982641	+	0.185516i	$0.0593956\pi$
$312$	−1.14795	+	1.98831i	−0.0649898	+	0.112566i
$313$	16.2310	+	28.1129i	0.917431	+	1.58904i	0.803302	+	0.595571i	$0.203074\pi$
$313$	16.2310	+	28.1129i	0.917431	+	1.58904i	0.114129	+	0.993466i	$0.463592\pi$
$314$	−1.85756			−0.104828
$315$	−3.96950	+	2.64044i	−0.223656	+	0.148772i
$316$	−14.8170			−0.833522
$317$	4.61625	+	7.99558i	0.259275	+	0.449077i	0.966048	−	0.258363i	$-0.0831832\pi$
$317$	4.61625	+	7.99558i	0.259275	+	0.449077i	−0.706773	+	0.707440i	$0.749850\pi$
$318$	5.15883	−	8.93536i	0.289293	−	0.501070i
$319$	−0.376510	+	0.652135i	−0.0210805	+	0.0365125i
$320$	0.900969	+	1.56052i	0.0503657	+	0.0872359i
$321$	11.0368			0.616016
$322$	−10.0939	+	6.71431i	−0.562514	+	0.374174i
$323$	−7.53079			−0.419025
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.01238	−	3.48554i	0.111627	−	0.193343i
$326$	9.37263	−	16.2339i	0.519102	−	0.899111i
$327$	6.58426	+	11.4043i	0.364110	+	0.630658i
$328$	5.03684			0.278113
$329$	0.0745725	+	1.17511i	0.00411131	+	0.0647857i
$330$	1.35690			0.0746947
$331$	−3.12833	−	5.41843i	−0.171949	−	0.297824i	0.767152	−	0.641465i	$-0.221673\pi$
$331$	−3.12833	−	5.41843i	−0.171949	−	0.297824i	−0.939101	+	0.343641i	$0.888340\pi$
$332$	0.821552	−	1.42297i	0.0450885	−	0.0780956i
$333$	6.05980	−	10.4959i	0.332075	−	0.575171i
$334$	−0.0528022	−	0.0914561i	−0.00288921	−	0.00500425i
$335$	4.35690			0.238043
$336$	−2.37047	−	1.17511i	−0.129320	−	0.0641073i
$337$	17.4741			0.951875			0.475938	−	0.879479i	$-0.342109\pi$
$337$	17.4741			0.951875			0.475938	+	0.879479i	$0.342109\pi$
$338$	3.86443	+	6.69339i	0.210197	+	0.364072i
$339$	−5.11745	+	8.86368i	−0.277942	+	0.481409i
$340$	−3.54892	+	6.14691i	−0.192467	+	0.333363i
$341$	−0.477697	−	0.827396i	−0.0258688	−	0.0448060i
$342$	1.91185			0.103381
$343$	−3.50000	−	18.1865i	−0.188982	−	0.981981i
$344$	−1.17629			−0.0634214
$345$	−4.12833	−	7.15048i	−0.222262	−	0.384969i
$346$	5.24578	−	9.08596i	0.282015	−	0.488464i
$347$	7.87651	−	13.6425i	0.422833	−	0.732369i	−0.573382	−	0.819288i	$-0.694369\pi$
$347$	7.87651	−	13.6425i	0.422833	−	0.732369i	0.996215	+	0.0869194i	$0.0277023\pi$
$348$	0.500000	+	0.866025i	0.0268028	+	0.0464238i
$349$	0.845478			0.0452574			0.0226287	−	0.999744i	$-0.492796\pi$
$349$	0.845478			0.0452574			0.0226287	+	0.999744i	$0.492796\pi$
$350$	4.15548	+	2.05999i	0.222120	+	0.110111i
$351$	2.29590			0.122546
$352$	0.376510	+	0.652135i	0.0200681	+	0.0347589i
$353$	−11.9206	+	20.6471i	−0.634469	+	1.09893i	0.352159	+	0.935940i	$0.385448\pi$
$353$	−11.9206	+	20.6471i	−0.634469	+	1.09893i	−0.986627	+	0.162992i	$0.947886\pi$
$354$	−5.24698	+	9.08804i	−0.278874	+	0.483024i
$355$	10.3889	+	17.9941i	0.551385	+	0.955027i
$356$	−1.42327			−0.0754332
$357$	−0.660030	−	10.4007i	−0.0349325	−	0.550463i
$358$	−17.3623			−0.917625
$359$	7.50096	+	12.9920i	0.395885	+	0.685694i	0.993214	−	0.116303i	$-0.0371044\pi$
$359$	7.50096	+	12.9920i	0.395885	+	0.685694i	−0.597328	+	0.801997i	$0.703771\pi$
$360$	0.900969	−	1.56052i	0.0474852	−	0.0822468i
$361$	7.67241	−	13.2890i	0.403811	−	0.699421i
$362$	6.79925	+	11.7766i	0.357361	+	0.618967i
$363$	−10.4330			−0.547588
$364$	5.05765	−	3.36425i	0.265093	−	0.176335i
$365$	−10.4330			−0.546086
$366$	4.78501	+	8.28788i	0.250117	+	0.433215i
$367$	−11.6833	+	20.2361i	−0.609863	+	1.05631i	0.381400	+	0.924410i	$0.375442\pi$
$367$	−11.6833	+	20.2361i	−0.609863	+	1.05631i	−0.991263	+	0.131903i	$0.957891\pi$
$368$	2.29105	−	3.96822i	0.119429	−	0.206858i
$369$	−2.51842	−	4.36203i	−0.131104	−	0.227078i
$370$	21.8388			1.13534
$371$	−22.7289	+	15.1188i	−1.18002	+	0.784930i
$372$	−1.26875			−0.0657816
$373$	−11.2017	−	19.4019i	−0.580003	−	1.00459i	−0.995478	−	0.0949896i	$-0.969718\pi$
$373$	−11.2017	−	19.4019i	−0.580003	−	1.00459i	0.415476	−	0.909604i	$-0.363615\pi$
$374$	−1.48307	+	2.56876i	−0.0766879	+	0.132827i
$375$	−6.08426	+	10.5382i	−0.314190	+	0.544193i
$376$	−0.222521	−	0.385418i	−0.0114756	−	0.0198764i
$377$	−2.29590			−0.118245
$378$	0.167563	+	2.64044i	0.00861850	+	0.135810i
$379$	−6.57912			−0.337947			−0.168973	−	0.985621i	$-0.554045\pi$
$379$	−6.57912			−0.337947			−0.168973	+	0.985621i	$0.554045\pi$
$380$	1.72252	+	2.98349i	0.0883635	+	0.153050i
$381$	0.403657	−	0.699155i	0.0206800	−	0.0358188i
$382$	−1.49880	+	2.59600i	−0.0766855	+	0.132823i
$383$	−10.9276	−	18.9271i	−0.558373	−	0.967131i	−0.997632	−	0.0687707i	$-0.978092\pi$
$383$	−10.9276	−	18.9271i	−0.558373	−	0.967131i	0.439259	−	0.898360i	$-0.355241\pi$
$384$	1.00000			0.0510310
$385$	−3.21648	−	1.59450i	−0.163927	−	0.0812631i
$386$	22.6679			1.15376
$387$	0.588146	+	1.01870i	0.0298971	+	0.0517834i
$388$	2.26659	−	3.92586i	0.115069	−	0.199305i
$389$	12.3197	−	21.3383i	0.624633	−	1.08190i	−0.363979	−	0.931407i	$-0.618582\pi$
$389$	12.3197	−	21.3383i	0.624633	−	1.08190i	0.988612	−	0.150489i	$-0.0480848\pi$
$390$	2.06853	+	3.58280i	0.104744	+	0.181422i
$391$	18.0489			0.912773
$392$	4.23825	+	5.57111i	0.214064	+	0.281383i
$393$	21.3327			1.07609
$394$	−0.925428	−	1.60289i	−0.0466224	−	0.0807523i
$395$	−13.3497	+	23.1223i	−0.671694	+	1.16341i
$396$	0.376510	−	0.652135i	0.0189203	−	0.0327710i
$397$	−8.68694	−	15.0462i	−0.435985	−	0.755148i	0.561390	−	0.827551i	$-0.310267\pi$
$397$	−8.68694	−	15.0462i	−0.435985	−	0.755148i	−0.997375	+	0.0724028i	$0.976933\pi$
$398$	−5.89546			−0.295513
$399$	−4.53199	−	2.24663i	−0.226883	−	0.112472i
$400$	−1.75302			−0.0876510
$401$	−1.07069	−	1.85449i	−0.0534676	−	0.0926086i	0.838053	−	0.545589i	$-0.183694\pi$
$401$	−1.07069	−	1.85449i	−0.0534676	−	0.0926086i	−0.891520	+	0.452981i	$0.850361\pi$
$402$	1.20895	−	2.09396i	0.0602968	−	0.104437i
$403$	1.45646	−	2.52266i	0.0725514	−	0.125663i
$404$	6.44116	+	11.1564i	0.320460	+	0.555052i
$405$	−1.80194			−0.0895390
$406$	−0.167563	−	2.64044i	−0.00831600	−	0.131043i
$407$	9.12631			0.452374
$408$	1.96950	+	3.41127i	0.0975048	+	0.168883i
$409$	4.04288	−	7.00247i	0.199907	−	0.346250i	−0.748591	−	0.663032i	$-0.769269\pi$
$409$	4.04288	−	7.00247i	0.199907	−	0.346250i	0.948498	+	0.316783i	$0.102603\pi$
$410$	4.53803	−	7.86010i	0.224117	−	0.388183i
$411$	6.55765	+	11.3582i	0.323465	+	0.560258i
$412$	−10.3720			−0.510990
$413$	23.1172	−	15.3772i	1.13752	−	0.756660i
$414$	−4.58211			−0.225198
$415$	−1.48039	−	2.56410i	−0.0726693	−	0.125867i
$416$	−1.14795	+	1.98831i	−0.0562828	+	0.0974847i
$417$	−3.24429	+	5.61928i	−0.158874	+	0.275177i
$418$	0.719833	+	1.24679i	0.0352082	+	0.0609823i
$419$	−19.4534			−0.950361			−0.475180	−	0.879888i	$-0.657617\pi$
$419$	−19.4534			−0.950361			−0.475180	+	0.879888i	$0.657617\pi$
$420$	−3.96950	+	2.64044i	−0.193692	+	0.128840i
$421$	−35.3986			−1.72522			−0.862612	−	0.505866i	$-0.831173\pi$
$421$	−35.3986			−1.72522			−0.862612	+	0.505866i	$0.831173\pi$
$422$	5.41670	+	9.38200i	0.263681	+	0.456708i
$423$	−0.222521	+	0.385418i	−0.0108193	+	0.0187396i
$424$	5.15883	−	8.93536i	0.250535	−	0.433940i
$425$	−3.45257	−	5.98003i	−0.167474	−	0.290074i
$426$	11.5308			0.558669
$427$	−1.60358	−	25.2691i	−0.0776027	−	1.22286i
$428$	11.0368			0.533486
$429$	0.864429	+	1.49723i	0.0417350	+	0.0722872i
$430$	−1.05980	+	1.83563i	−0.0511082	+	0.0885220i
$431$	16.1664	−	28.0010i	0.778706	−	1.34876i	−0.153981	−	0.988074i	$-0.549209\pi$
$431$	16.1664	−	28.0010i	0.778706	−	1.34876i	0.932688	−	0.360685i	$-0.117457\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−18.8877			−0.907684			−0.453842	−	0.891082i	$-0.649947\pi$
$433$	−18.8877			−0.907684			−0.453842	+	0.891082i	$0.649947\pi$
$434$	3.00753	+	1.49092i	0.144366	+	0.0715663i
$435$	1.80194			0.0863963
$436$	6.58426	+	11.4043i	0.315329	+	0.546166i
$437$	4.38016	−	7.58666i	0.209531	−	0.362919i
$438$	−2.89493	+	5.01416i	−0.138325	+	0.239586i
$439$	−12.7419	−	22.0696i	−0.608138	−	1.05333i	−0.991547	−	0.129747i	$-0.958584\pi$
$439$	−12.7419	−	22.0696i	−0.608138	−	1.05333i	0.383410	−	0.923578i	$-0.374750\pi$
$440$	1.35690			0.0646875
$441$	2.70560	−	6.45599i	0.128838	−	0.307428i
$442$	−9.04354			−0.430157
$443$	−13.6020	−	23.5594i	−0.646251	−	1.11934i	−0.984011	−	0.178108i	$-0.943002\pi$
$443$	−13.6020	−	23.5594i	−0.646251	−	1.11934i	0.337760	−	0.941232i	$-0.390331\pi$
$444$	6.05980	−	10.4959i	0.287585	−	0.498113i
$445$	−1.28232	+	2.22105i	−0.0607880	+	0.105288i
$446$	3.16972	+	5.49011i	0.150091	+	0.259964i
$447$	20.4577			0.967617
$448$	−2.37047	−	1.17511i	−0.111994	−	0.0555186i
$449$	23.5429			1.11106			0.555529	−	0.831497i	$-0.312516\pi$
$449$	23.5429			1.11106			0.555529	+	0.831497i	$0.312516\pi$
$450$	0.876510	+	1.51816i	0.0413191	+	0.0715668i
$451$	1.89642	−	3.28470i	0.0892989	−	0.154670i
$452$	−5.11745	+	8.86368i	−0.240705	+	0.416913i
$453$	6.87531	+	11.9084i	0.323030	+	0.559505i
$454$	25.9705			1.21885
$455$	−0.693218	−	10.9237i	−0.0324986	−	0.512109i
$456$	1.91185			0.0895308
$457$	−8.68449	−	15.0420i	−0.406243	−	0.703634i	0.588222	−	0.808699i	$-0.299828\pi$
$457$	−8.68449	−	15.0420i	−0.406243	−	0.703634i	−0.994465	+	0.105066i	$0.966495\pi$
$458$	−1.23878	+	2.14563i	−0.0578845	+	0.100259i
$459$	1.96950	−	3.41127i	0.0919284	−	0.159225i
$460$	−4.12833	−	7.15048i	−0.192485	−	0.333393i
$461$	5.38942			0.251010			0.125505	−	0.992093i	$-0.459945\pi$
$461$	5.38942			0.251010			0.125505	+	0.992093i	$0.459945\pi$
$462$	−1.65883	+	1.10343i	−0.0771759	+	0.0513360i
$463$	0.00298391			0.000138674			6.93369e−5	−	1.00000i	$-0.499978\pi$
$463$	0.00298391			0.000138674			6.93369e−5		1.00000i	$0.499978\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	−1.14310	+	1.97991i	−0.0530102	+	0.0918163i
$466$	0.551606	−	0.955409i	0.0255526	−	0.0442585i
$467$	3.10723	+	5.38188i	0.143785	+	0.249044i	0.928919	−	0.370283i	$-0.120739\pi$
$467$	3.10723	+	5.38188i	0.143785	+	0.249044i	−0.785134	+	0.619326i	$0.787406\pi$
$468$	2.29590			0.106128
$469$	−5.32640	+	3.54302i	−0.245950	+	0.163602i
$470$	−0.801938			−0.0369906
$471$	0.928780	+	1.60869i	0.0427959	+	0.0741247i
$472$	−5.24698	+	9.08804i	−0.241512	+	0.418311i
$473$	−0.442886	+	0.767101i	−0.0203639	+	0.0352713i
$474$	7.40850	+	12.8319i	0.340284	+	0.589389i
$475$	−3.35152			−0.153778
$476$	−0.660030	−	10.4007i	−0.0302524	−	0.476715i
$477$	−10.3177			−0.472414
$478$	3.15399	+	5.46287i	0.144260	+	0.249866i
$479$	−4.66099	+	8.07307i	−0.212966	+	0.368868i	−0.952641	−	0.304096i	$-0.901646\pi$
$479$	−4.66099	+	8.07307i	−0.212966	+	0.368868i	0.739675	+	0.672964i	$0.234979\pi$
$480$	0.900969	−	1.56052i	0.0411234	−	0.0712278i
$481$	13.9127	+	24.0975i	0.634364	+	1.09875i
$482$	−10.6746			−0.486213
$483$	10.8617	+	5.38446i	0.494226	+	0.245001i
$484$	−10.4330			−0.474225
$485$	−4.08426	−	7.07415i	−0.185457	−	0.321221i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−4.96399	+	8.59789i	−0.224940	+	0.389607i	−0.956301	−	0.292383i	$-0.905552\pi$
$487$	−4.96399	+	8.59789i	−0.224940	+	0.389607i	0.731361	+	0.681990i	$0.238885\pi$
$488$	4.78501	+	8.28788i	0.216607	+	0.375175i
$489$	−18.7453			−0.847690
$490$	12.5124	−	1.59450i	0.565252	−	0.0720320i
$491$	−25.9409			−1.17070			−0.585349	−	0.810782i	$-0.699042\pi$
$491$	−25.9409			−1.17070			−0.585349	+	0.810782i	$0.699042\pi$
$492$	−2.51842	−	4.36203i	−0.113539	−	0.196655i
$493$	−1.96950	+	3.41127i	−0.0887018	+	0.153636i
$494$	−2.19471	+	3.80135i	−0.0987447	+	0.171031i
$495$	−0.678448	−	1.17511i	−0.0304940	−	0.0528171i
$496$	−1.26875			−0.0569686
$497$	−27.3334	−	13.5499i	−1.22607	−	0.607797i
$498$	−1.64310			−0.0736293
$499$	13.5884	+	23.5359i	0.608302	+	1.05361i	0.991520	+	0.129952i	$0.0414824\pi$
$499$	13.5884	+	23.5359i	0.608302	+	1.05361i	−0.383218	+	0.923658i	$0.625184\pi$
$500$	−6.08426	+	10.5382i	−0.272096	+	0.471285i
$501$	−0.0528022	+	0.0914561i	−0.00235903	+	0.00408596i
$502$	12.6298	+	21.8755i	0.563697	+	0.976351i
$503$	−10.7681			−0.480125			−0.240063	−	0.970757i	$-0.577168\pi$
$503$	−10.7681			−0.480125			−0.240063	+	0.970757i	$0.577168\pi$
$504$	0.167563	+	2.64044i	0.00746384	+	0.117615i
$505$	23.2131			1.03297
$506$	−1.72521	−	2.98815i	−0.0766949	−	0.132839i
$507$	3.86443	−	6.69339i	0.171625	−	0.297264i
$508$	0.403657	−	0.699155i	0.0179094	−	0.0310200i
$509$	0.711636	+	1.23259i	0.0315427	+	0.0546336i	0.881366	−	0.472434i	$-0.156625\pi$
$509$	0.711636	+	1.23259i	0.0315427	+	0.0546336i	−0.849823	+	0.527068i	$0.823291\pi$
$510$	7.09783			0.314297
$511$	12.7545	−	8.48407i	0.564226	−	0.375313i
$512$	1.00000			0.0441942
$513$	−0.955927	−	1.65571i	−0.0422052	−	0.0731016i
$514$	11.6283	−	20.1409i	0.512904	−	0.888375i
$515$	−9.34481	+	16.1857i	−0.411782	+	0.713227i
$516$	0.588146	+	1.01870i	0.0258917	+	0.0448457i
$517$	−0.335126			−0.0147388
$518$	−26.6984	+	17.7593i	−1.17306	+	0.780297i
$519$	−10.4916			−0.460529
$520$	2.06853	+	3.58280i	0.0907111	+	0.157116i
$521$	5.08911	−	8.81459i	0.222958	−	0.386174i	−0.732747	−	0.680501i	$-0.761762\pi$
$521$	5.08911	−	8.81459i	0.222958	−	0.386174i	0.955705	+	0.294327i	$0.0950955\pi$
$522$	0.500000	−	0.866025i	0.0218844	−	0.0379049i
$523$	10.2463	+	17.7471i	0.448040	+	0.776028i	0.998258	−	0.0589926i	$-0.0187888\pi$
$523$	10.2463	+	17.7471i	0.448040	+	0.776028i	−0.550218	+	0.835021i	$0.685456\pi$
$524$	21.3327			0.931925
$525$	−0.293741	−	4.62874i	−0.0128199	−	0.202015i
$526$	6.08575			0.265351
$527$	−2.49880	−	4.32805i	−0.108850	−	0.188533i
$528$	0.376510	−	0.652135i	0.0163855	−	0.0283805i
$529$	1.00216	−	1.73578i	0.0435720	−	0.0754689i
$530$	−9.29590	−	16.1010i	−0.403788	−	0.699381i
$531$	10.4940			0.455399
$532$	−4.53199	−	2.24663i	−0.196487	−	0.0974038i
$533$	11.5641			0.500895
$534$	0.711636	+	1.23259i	0.0307955	+	0.0533394i
$535$	9.94385	−	17.2232i	0.429910	−	0.744626i
$536$	1.20895	−	2.09396i	0.0522186	−	0.0904452i
$537$	8.68114	+	15.0362i	0.374619	+	0.648859i
$538$	10.4668			0.451256
$539$	5.22886	−	0.666332i	0.225223	−	0.0287009i
$540$	−1.80194			−0.0775431
$541$	−14.9306	−	25.8605i	−0.641915	−	1.11183i	−0.985005	−	0.172527i	$-0.944807\pi$
$541$	−14.9306	−	25.8605i	−0.641915	−	1.11183i	0.343090	−	0.939303i	$-0.388527\pi$
$542$	−8.07002	+	13.9777i	−0.346637	+	0.600393i
$543$	6.79925	−	11.7766i	0.291784	−	0.505384i
$544$	1.96950	+	3.41127i	0.0844416	+	0.146257i
$545$	23.7289			1.01643
$546$	−5.44235	−	2.69792i	−0.232911	−	0.115460i
$547$	−5.83579			−0.249520			−0.124760	−	0.992187i	$-0.539816\pi$
$547$	−5.83579			−0.249520			−0.124760	+	0.992187i	$0.539816\pi$
$548$	6.55765	+	11.3582i	0.280129	+	0.485197i
$549$	4.78501	−	8.28788i	0.204219	−	0.353718i
$550$	−0.660030	+	1.14321i	−0.0281438	+	0.0487465i
$551$	0.955927	+	1.65571i	0.0407239	+	0.0705358i
$552$	−4.58211			−0.195027
$553$	−2.48278	−	39.1234i	−0.105578	−	1.66370i
$554$	7.05323			0.299663
$555$	−10.9194	−	18.9129i	−0.463502	−	0.802809i
$556$	−3.24429	+	5.61928i	−0.137589	+	0.238310i
$557$	0.460771	−	0.798079i	0.0195235	−	0.0338157i	−0.856099	−	0.516813i	$-0.827118\pi$
$557$	0.460771	−	0.798079i	0.0195235	−	0.0338157i	0.875622	+	0.482997i	$0.160452\pi$
$558$	0.634375	+	1.09877i	0.0268552	+	0.0465146i
$559$	−2.70065			−0.114225
$560$	−3.96950	+	2.64044i	−0.167742	+	0.111579i
$561$	2.96615			0.125231
$562$	−4.73609	−	8.20316i	−0.199780	−	0.346029i
$563$	−2.12684	+	3.68380i	−0.0896357	+	0.155254i	−0.907357	−	0.420361i	$-0.861904\pi$
$563$	−2.12684	+	3.68380i	−0.0896357	+	0.155254i	0.817721	+	0.575614i	$0.195237\pi$
$564$	−0.222521	+	0.385418i	−0.00936982	+	0.0162290i
$565$	9.22132	+	15.9718i	0.387944	+	0.671939i
$566$	−10.1782			−0.427822
$567$	2.20291	−	1.46533i	0.0925134	−	0.0615382i
$568$	11.5308			0.483821
$569$	4.07487	+	7.05788i	0.170827	+	0.295882i	0.938709	−	0.344710i	$-0.112023\pi$
$569$	4.07487	+	7.05788i	0.170827	+	0.295882i	−0.767882	+	0.640591i	$0.778689\pi$
$570$	1.72252	−	2.98349i	0.0721485	−	0.124965i
$571$	18.9049	−	32.7443i	0.791146	−	1.37030i	−0.134112	−	0.990966i	$-0.542818\pi$
$571$	18.9049	−	32.7443i	0.791146	−	1.37030i	0.925258	−	0.379339i	$-0.123849\pi$
$572$	0.864429	+	1.49723i	0.0361436	+	0.0626025i
$573$	2.99761			0.125227
$574$	0.843986	+	13.2995i	0.0352273	+	0.555109i
$575$	8.03252			0.334979
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−9.42692	+	16.3279i	−0.392448	+	0.679740i	−0.992772	−	0.120017i	$-0.961705\pi$
$577$	−9.42692	+	16.3279i	−0.392448	+	0.679740i	0.600324	+	0.799757i	$0.295038\pi$
$578$	0.742135	−	1.28542i	0.0308688	−	0.0534663i
$579$	−11.3339	−	19.6309i	−0.471022	−	0.815834i
$580$	1.80194			0.0748214
$581$	3.89493	+	1.93082i	0.161589	+	0.0801040i
$582$	−4.53319			−0.187907
$583$	−3.88471	−	6.72851i	−0.160888	−	0.278666i
$584$	−2.89493	+	5.01416i	−0.119793	+	0.207488i
$585$	2.06853	−	3.58280i	0.0855233	−	0.148131i
$586$	2.01722	+	3.49393i	0.0833306	+	0.144333i
$587$	40.9191			1.68891			0.844457	−	0.535623i	$-0.179923\pi$
$587$	40.9191			1.68891			0.844457	+	0.535623i	$0.179923\pi$
$588$	2.70560	−	6.45599i	0.111577	−	0.266240i
$589$	−2.42566			−0.0999478
$590$	9.45473	+	16.3761i	0.389245	+	0.674192i
$591$	−0.925428	+	1.60289i	−0.0380670	+	0.0659340i
$592$	6.05980	−	10.4959i	0.249056	−	0.431378i
$593$	−5.23072	−	9.05987i	−0.214800	−	0.372044i	0.738411	−	0.674351i	$-0.235577\pi$
$593$	−5.23072	−	9.05987i	−0.214800	−	0.372044i	−0.953211	+	0.302307i	$0.902243\pi$
$594$	−0.753020			−0.0308968
$595$	−16.8252	−	8.34071i	−0.689766	−	0.341936i
$596$	20.4577			0.837981
$597$	2.94773	+	5.10562i	0.120643	+	0.208959i
$598$	5.26002	−	9.11062i	0.215098	−	0.372561i
$599$	0.776815	−	1.34548i	0.0317398	−	0.0549750i	−0.849719	−	0.527236i	$-0.823229\pi$
$599$	0.776815	−	1.34548i	0.0317398	−	0.0549750i	0.881459	+	0.472261i	$0.156562\pi$
$600$	0.876510	+	1.51816i	0.0357834	+	0.0619786i
$601$	19.6775			0.802664			0.401332	−	0.915933i	$-0.368547\pi$
$601$	19.6775			0.802664			0.401332	+	0.915933i	$0.368547\pi$
$602$	−0.197103	−	3.10593i	−0.00803331	−	0.126588i
$603$	−2.41789			−0.0984643
$604$	6.87531	+	11.9084i	0.279753	+	0.484546i
$605$	−9.39977	+	16.2809i	−0.382155	+	0.661912i
$606$	6.44116	−	11.1564i	0.261654	−	0.453198i
$607$	−1.93176	−	3.34591i	−0.0784079	−	0.135806i	0.824155	−	0.566364i	$-0.191650\pi$
$607$	−1.93176	−	3.34591i	−0.0784079	−	0.135806i	−0.902563	+	0.430557i	$0.858317\pi$
$608$	1.91185			0.0775359
$609$	−2.20291	+	1.46533i	−0.0892663	+	0.0593783i
$610$	17.2446			0.698213
$611$	−0.510885	−	0.884879i	−0.0206682	−	0.0357984i
$612$	1.96950	−	3.41127i	0.0796123	−	0.137893i
$613$	−10.7959	+	18.6990i	−0.436042	+	0.755247i	−0.997380	−	0.0723395i	$-0.976953\pi$
$613$	−10.7959	+	18.6990i	−0.436042	+	0.755247i	0.561338	+	0.827587i	$0.310287\pi$
$614$	−6.93631	−	12.0140i	−0.279927	−	0.484847i
$615$	−9.07606			−0.365982
$616$	−1.65883	+	1.10343i	−0.0668363	+	0.0444583i
$617$	−37.9493			−1.52778			−0.763890	−	0.645346i	$-0.776713\pi$
$617$	−37.9493			−1.52778			−0.763890	+	0.645346i	$0.776713\pi$
$618$	5.18598	+	8.98238i	0.208611	+	0.361324i
$619$	−13.9514	+	24.1645i	−0.560753	+	0.971253i	0.436678	+	0.899618i	$0.356155\pi$
$619$	−13.9514	+	24.1645i	−0.560753	+	0.971253i	−0.997431	+	0.0716351i	$0.977178\pi$
$620$	−1.14310	+	1.97991i	−0.0459082	+	0.0795153i
$621$	2.29105	+	3.96822i	0.0919368	+	0.159239i
$622$	−11.6625			−0.467623
$623$	−0.238487	−	3.75806i	−0.00955480	−	0.150564i
$624$	2.29590			0.0919094
$625$	6.58091	+	11.3985i	0.263236	+	0.455939i
$626$	16.2310	−	28.1129i	0.648722	−	1.12362i
$627$	0.719833	−	1.24679i	0.0287473	−	0.0497919i
$628$	0.928780	+	1.60869i	0.0370624	+	0.0641939i
$629$	47.7391			1.90348
$630$	4.27144	+	2.11747i	0.170178	+	0.0843620i
$631$	16.4969			0.656733			0.328366	−	0.944550i	$-0.393502\pi$
$631$	16.4969			0.656733			0.328366	+	0.944550i	$0.393502\pi$
$632$	7.40850	+	12.8319i	0.294694	+	0.510426i
$633$	5.41670	−	9.38200i	0.215294	−	0.372901i
$634$	4.61625	−	7.99558i	0.183335	−	0.317545i
$635$	−0.727365	−	1.25983i	−0.0288646	−	0.0499950i
$636$	−10.3177			−0.409122
$637$	9.73059	+	12.7907i	0.385540	+	0.506785i
$638$	0.753020			0.0298124
$639$	−5.76540	−	9.98596i	−0.228076	−	0.395039i
$640$	0.900969	−	1.56052i	0.0356139	−	0.0616851i
$641$	−11.0133	+	19.0757i	−0.435001	+	0.753443i	−0.997296	−	0.0734935i	$-0.976585\pi$
$641$	−11.0133	+	19.0757i	−0.435001	+	0.753443i	0.562295	+	0.826937i	$0.309919\pi$
$642$	−5.51842	−	9.55818i	−0.217795	−	0.377231i
$643$	31.9041			1.25817			0.629087	−	0.777335i	$-0.283429\pi$
$643$	31.9041			1.25817			0.629087	+	0.777335i	$0.283429\pi$
$644$	10.8617	+	5.38446i	0.428013	+	0.212177i
$645$	2.11960			0.0834594
$646$	3.76540	+	6.52186i	0.148148	+	0.256599i
$647$	−16.4088	+	28.4209i	−0.645096	+	1.11734i	0.339183	+	0.940720i	$0.389849\pi$
$647$	−16.4088	+	28.4209i	−0.645096	+	1.11734i	−0.984279	+	0.176619i	$0.943484\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	3.95108	+	6.84348i	0.155094	+	0.268630i
$650$	−4.02475			−0.157864
$651$	−0.212595	−	3.35006i	−0.00833227	−	0.131299i
$652$	−18.7453			−0.734121
$653$	−7.85354	−	13.6027i	−0.307333	−	0.532316i	0.670445	−	0.741959i	$-0.266103\pi$
$653$	−7.85354	−	13.6027i	−0.307333	−	0.532316i	−0.977778	+	0.209643i	$0.932770\pi$
$654$	6.58426	−	11.4043i	0.257465	−	0.445942i
$655$	19.2201	−	33.2902i	0.750993	−	1.30076i
$656$	−2.51842	−	4.36203i	−0.0983277	−	0.170309i
$657$	5.78986			0.225884
$658$	0.980386	−	0.652135i	0.0382194	−	0.0254229i
$659$	7.05323			0.274755			0.137377	−	0.990519i	$-0.456133\pi$
$659$	7.05323			0.274755			0.137377	+	0.990519i	$0.456133\pi$
$660$	−0.678448	−	1.17511i	−0.0264086	−	0.0457410i
$661$	10.6528	−	18.4512i	0.414346	−	0.717668i	−0.581014	−	0.813894i	$-0.697344\pi$
$661$	10.6528	−	18.4512i	0.414346	−	0.717668i	0.995360	+	0.0962260i	$0.0306771\pi$
$662$	−3.12833	+	5.41843i	−0.121586	+	0.210593i
$663$	4.52177	+	7.83194i	0.175611	+	0.304167i
$664$	−1.64310			−0.0637648
$665$	−7.58911	+	5.04814i	−0.294293	+	0.195758i
$666$	−12.1196			−0.469625
$667$	−2.29105	−	3.96822i	−0.0887099	−	0.153650i
$668$	−0.0528022	+	0.0914561i	−0.00204298	+	0.00353854i
$669$	3.16972	−	5.49011i	0.122548	−	0.212260i
$670$	−2.17845	−	3.77318i	−0.0841608	−	0.145771i
$671$	7.20642			0.278201
$672$	0.167563	+	2.64044i	0.00646388	+	0.101857i
$673$	36.6896			1.41428			0.707141	−	0.707073i	$-0.249985\pi$
$673$	36.6896			1.41428			0.707141	+	0.707073i	$0.249985\pi$
$674$	−8.73705	−	15.1330i	−0.336539	−	0.582902i
$675$	0.876510	−	1.51816i	0.0337369	−	0.0584340i
$676$	3.86443	−	6.69339i	0.148632	−	0.257438i
$677$	−13.3333	−	23.0939i	−0.512439	−	0.887570i	−0.999896	−	0.0144234i	$-0.995409\pi$
$677$	−13.3333	−	23.0939i	−0.512439	−	0.887570i	0.487457	−	0.873147i	$-0.337925\pi$
$678$	10.2349			0.393069
$679$	10.7458	+	5.32698i	0.412385	+	0.204431i
$680$	7.09783			0.272190
$681$	−12.9852	−	22.4911i	−0.497595	−	0.861860i
$682$	−0.477697	+	0.827396i	−0.0182920	+	0.0316826i
$683$	3.83459	−	6.64171i	0.146727	−	0.254138i	−0.783289	−	0.621658i	$-0.786460\pi$
$683$	3.83459	−	6.64171i	0.146727	−	0.254138i	0.930016	+	0.367520i	$0.119793\pi$
$684$	−0.955927	−	1.65571i	−0.0365508	−	0.0633078i
$685$	23.6329			0.902968
$686$	−14.0000	+	12.1244i	−0.534522	+	0.462910i
$687$	2.47757			0.0945250
$688$	0.588146	+	1.01870i	0.0224229	+	0.0388375i
$689$	11.8442	−	20.5147i	0.451226	−	0.781547i
$690$	−4.12833	+	7.15048i	−0.157163	+	0.272214i
$691$	−9.54706	−	16.5360i	−0.363187	−	0.629059i	0.625296	−	0.780387i	$-0.284978\pi$
$691$	−9.54706	−	16.5360i	−0.363187	−	0.629059i	−0.988483	+	0.151329i	$0.951645\pi$
$692$	−10.4916			−0.398830
$693$	1.78501	+	0.884879i	0.0678070	+	0.0336138i
$694$	−15.7530			−0.597976
$695$	5.84601	+	10.1256i	0.221752	+	0.384085i
$696$	0.500000	−	0.866025i	0.0189525	−	0.0328266i
$697$	9.92005	−	17.1820i	0.375749	−	0.650816i
$698$	−0.422739	−	0.732206i	−0.0160009	−	0.0277144i
$699$	−1.10321			−0.0417273
$700$	−0.293741	−	4.62874i	−0.0111024	−	0.174950i
$701$	8.33034			0.314633			0.157316	−	0.987548i	$-0.449716\pi$
$701$	8.33034			0.314633			0.157316	+	0.987548i	$0.449716\pi$
$702$	−1.14795	−	1.98831i	−0.0433265	−	0.0750437i
$703$	11.5855	−	20.0666i	0.436954	−	0.756826i
$704$	0.376510	−	0.652135i	0.0141903	−	0.0245783i
$705$	0.400969	+	0.694498i	0.0151014	+	0.0261563i
$706$	23.8412			0.897274
$707$	−28.3785	+	18.8769i	−1.06728	+	0.709938i
$708$	10.4940			0.394387
$709$	−0.0346798	−	0.0600672i	−0.00130243	−	0.00225587i	0.865373	−	0.501128i	$-0.167081\pi$
$709$	−0.0346798	−	0.0600672i	−0.00130243	−	0.00225587i	−0.866676	+	0.498872i	$0.833748\pi$
$710$	10.3889	−	17.9941i	0.389888	−	0.675306i
$711$	7.40850	−	12.8319i	0.277841	−	0.481234i
$712$	0.711636	+	1.23259i	0.0266697	+	0.0461932i
$713$	5.81355			0.217719
$714$	−8.67725	+	5.77195i	−0.324738	+	0.216010i
$715$	3.11529			0.116505
$716$	8.68114	+	15.0362i	0.324429	+	0.561928i
$717$	3.15399	−	5.46287i	0.117788	−	0.204015i
$718$	7.50096	−	12.9920i	0.279933	−	0.484859i
$719$	13.8104	+	23.9204i	0.515042	+	0.892079i	0.999848	+	0.0174571i	$0.00555706\pi$
$719$	13.8104	+	23.9204i	0.515042	+	0.892079i	−0.484805	+	0.874622i	$0.661110\pi$
$720$	−1.80194			−0.0671543
$721$	−1.73795	−	27.3865i	−0.0647248	−	1.01993i
$722$	−15.3448			−0.571075
$723$	5.33728	+	9.24444i	0.198496	+	0.343805i
$724$	6.79925	−	11.7766i	0.252692	−	0.437676i
$725$	−0.876510	+	1.51816i	−0.0325528	+	0.0563831i
$726$	5.21648	+	9.03521i	0.193602	+	0.335328i
$727$	34.4722			1.27850			0.639251	−	0.768998i	$-0.279244\pi$
$727$	34.4722			1.27850			0.639251	+	0.768998i	$0.279244\pi$
$728$	−5.44235	−	2.69792i	−0.201707	−	0.0999917i
$729$	1.00000			0.0370370
$730$	5.21648	+	9.03521i	0.193071	+	0.334408i
$731$	−2.31671	+	4.01266i	−0.0856865	+	0.148413i
$732$	4.78501	−	8.28788i	0.176859	−	0.306329i
$733$	14.4535	+	25.0343i	0.533853	+	0.924661i	0.999218	+	0.0395422i	$0.0125899\pi$
$733$	14.4535	+	25.0343i	0.533853	+	0.924661i	−0.465364	+	0.885119i	$0.654077\pi$
$734$	23.3666			0.862476
$735$	−7.63706	−	10.0388i	−0.281697	−	0.370286i
$736$	−4.58211			−0.168899
$737$	−0.910362	−	1.57679i	−0.0335336	−	0.0580819i
$738$	−2.51842	+	4.36203i	−0.0927042	+	0.160568i
$739$	−25.1417	+	43.5467i	−0.924851	+	1.60189i	−0.133051	+	0.991109i	$0.542477\pi$
$739$	−25.1417	+	43.5467i	−0.924851	+	1.60189i	−0.791800	+	0.610780i	$0.790856\pi$
$740$	−10.9194	−	18.9129i	−0.401405	−	0.695253i
$741$	4.38942			0.161249
$742$	24.4577	+	12.1244i	0.897871	+	0.445099i
$743$	38.3903			1.40840			0.704201	−	0.710000i	$-0.251305\pi$
$743$	38.3903			1.40840			0.704201	+	0.710000i	$0.251305\pi$
$744$	0.634375	+	1.09877i	0.0232573	+	0.0402828i
$745$	18.4318	−	31.9248i	0.675288	−	1.16963i
$746$	−11.2017	+	19.4019i	−0.410124	+	0.710355i
$747$	0.821552	+	1.42297i	0.0300590	+	0.0520637i
$748$	2.96615			0.108453
$749$	1.84936	+	29.1421i	0.0675743	+	1.06483i
$750$	12.1685			0.444332
$751$	4.13156	+	7.15606i	0.150763	+	0.261128i	0.931508	−	0.363721i	$-0.118494\pi$
$751$	4.13156	+	7.15606i	0.150763	+	0.261128i	−0.780745	+	0.624849i	$0.785160\pi$
$752$	−0.222521	+	0.385418i	−0.00811450	+	0.0140547i
$753$	12.6298	−	21.8755i	0.460256	−	0.797188i
$754$	1.14795	+	1.98831i	0.0418058	+	0.0724098i
$755$	24.7778			0.901756
$756$	2.20291	−	1.46533i	0.0801189	−	0.0532937i
$757$	−8.29829			−0.301606			−0.150803	−	0.988564i	$-0.548186\pi$
$757$	−8.29829			−0.301606			−0.150803	+	0.988564i	$0.548186\pi$
$758$	3.28956	+	5.69769i	0.119482	+	0.206949i
$759$	−1.72521	+	2.98815i	−0.0626211	+	0.108463i
$760$	1.72252	−	2.98349i	0.0624824	−	0.108223i
$761$	−7.13222	−	12.3534i	−0.258543	−	0.447809i	0.707309	−	0.706904i	$-0.249909\pi$
$761$	−7.13222	−	12.3534i	−0.258543	−	0.447809i	−0.965852	+	0.259095i	$0.916576\pi$
$762$	−0.807315			−0.0292459
$763$	−29.0090	+	19.2963i	−1.05020	+	0.698572i
$764$	2.99761			0.108450
$765$	−3.54892	−	6.14691i	−0.128311	−	0.222242i
$766$	−10.9276	+	18.9271i	−0.394830	+	0.683865i
$767$	−12.0465	+	20.8652i	−0.434975	+	0.753398i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−9.71917			−0.350482			−0.175241	−	0.984526i	$-0.556070\pi$
$769$	−9.71917			−0.350482			−0.175241	+	0.984526i	$0.556070\pi$
$770$	0.227365	+	3.58280i	0.00819368	+	0.129115i
$771$	−23.2567			−0.837568
$772$	−11.3339	−	19.6309i	−0.407917	−	0.706533i
$773$	−11.7935	+	20.4269i	−0.424183	+	0.734706i	−0.996344	−	0.0854351i	$-0.972772\pi$
$773$	−11.7935	+	20.4269i	−0.424183	+	0.734706i	0.572161	+	0.820141i	$0.306105\pi$
$774$	0.588146	−	1.01870i	0.0211405	−	0.0366164i
$775$	−1.11207	−	1.92617i	−0.0399468	−	0.0691899i
$776$	−4.53319			−0.162732
$777$	28.7292	+	14.2418i	1.03065	+	0.510923i
$778$	−24.6394			−0.883365
$779$	−4.81485	−	8.33956i	−0.172510	−	0.298796i
$780$	2.06853	−	3.58280i	0.0740653	−	0.128285i
$781$	4.34146	−	7.51963i	0.155350	−	0.269074i
$782$	−9.02446	−	15.6308i	−0.322714	−	0.558957i
$783$	−1.00000			−0.0357371
$784$	2.70560	−	6.45599i	0.0966284	−	0.230571i
$785$	3.34721			0.119467
$786$	−10.6664	−	18.4747i	−0.380457	−	0.658970i
$787$	−12.9306	+	22.3964i	−0.460925	+	0.798345i	−0.999007	−	0.0445468i	$-0.985816\pi$
$787$	−12.9306	+	22.3964i	−0.460925	+	0.798345i	0.538082	+	0.842892i	$0.319149\pi$
$788$	−0.925428	+	1.60289i	−0.0329670	+	0.0571005i
$789$	−3.04288	−	5.27042i	−0.108329	−	0.187632i
$790$	26.6993			0.949919
$791$	−24.2615	−	12.0271i	−0.862640	−	0.427634i
$792$	−0.753020			−0.0267574
$793$	10.9859	+	19.0281i	0.390121	+	0.675709i
$794$	−8.68694	+	15.0462i	−0.308288	+	0.533970i
$795$	−9.29590	+	16.1010i	−0.329691	+	0.571042i
$796$	2.94773	+	5.10562i	0.104480	+	0.180964i
$797$	−19.3588			−0.685724			−0.342862	−	0.939386i	$-0.611396\pi$
$797$	−19.3588			−0.685724			−0.342862	+	0.939386i	$0.611396\pi$
$798$	0.320356	+	5.04814i	0.0113405	+	0.178702i
$799$	−1.75302			−0.0620174
$800$	0.876510	+	1.51816i	0.0309893	+	0.0536751i
$801$	0.711636	−	1.23259i	0.0251444	−	0.0435514i
$802$	−1.07069	+	1.85449i	−0.0378073	+	0.0654842i
$803$	2.17994	+	3.77577i	0.0769284	+	0.133244i
$804$	−2.41789			−0.0852726
$805$	18.1887	−	12.0988i	0.641066	−	0.426426i
$806$	−2.91292			−0.102603
$807$	−5.23341	−	9.06453i	−0.184225	−	0.319086i
$808$	6.44116	−	11.1564i	0.226599	−	0.392481i
$809$	17.3361	−	30.0270i	0.609504	−	1.05569i	−0.381818	−	0.924238i	$-0.624702\pi$
$809$	17.3361	−	30.0270i	0.609504	−	1.05569i	0.991322	−	0.131455i	$-0.0419648\pi$
$810$	0.900969	+	1.56052i	0.0316568	+	0.0548312i
$811$	−41.6795			−1.46356			−0.731782	−	0.681539i	$-0.761311\pi$
$811$	−41.6795			−1.46356			−0.731782	+	0.681539i	$0.761311\pi$
$812$	−2.20291	+	1.46533i	−0.0773069	+	0.0514231i
$813$	16.1400			0.566056
$814$	−4.56315	−	7.90362i	−0.159938	−	0.277022i
$815$	−16.8889	+	29.2524i	−0.591592	+	1.02467i
$816$	1.96950	−	3.41127i	0.0689463	−	0.119419i
$817$	1.12445	+	1.94760i	0.0393395	+	0.0681380i
$818$	−8.08575			−0.282712
$819$	0.384707	+	6.06218i	0.0134427	+	0.211830i
$820$	−9.07606			−0.316950
$821$	14.1597	+	24.5253i	0.494176	+	0.855937i	0.999977	−	0.00671244i	$-0.00213665\pi$
$821$	14.1597	+	24.5253i	0.494176	+	0.855937i	−0.505802	+	0.862650i	$0.668803\pi$
$822$	6.55765	−	11.3582i	0.228724	−	0.396162i
$823$	−19.0896	+	33.0642i	−0.665423	+	1.15255i	0.313748	+	0.949506i	$0.398415\pi$
$823$	−19.0896	+	33.0642i	−0.665423	+	1.15255i	−0.979170	+	0.203040i	$0.934918\pi$
$824$	5.18598	+	8.98238i	0.180662	+	0.312916i
$825$	1.32006			0.0459586
$826$	−24.8756	−	12.3315i	−0.865533	−	0.429068i
$827$	14.6009			0.507723			0.253861	−	0.967241i	$-0.418299\pi$
$827$	14.6009			0.507723			0.253861	+	0.967241i	$0.418299\pi$
$828$	2.29105	+	3.96822i	0.0796196	+	0.137905i
$829$	−15.1204	+	26.1894i	−0.525154	+	0.909594i	0.474417	+	0.880301i	$0.342659\pi$
$829$	−15.1204	+	26.1894i	−0.525154	+	0.909594i	−0.999571	+	0.0292935i	$0.990674\pi$
$830$	−1.48039	+	2.56410i	−0.0513849	+	0.0890013i
$831$	−3.52661	−	6.10828i	−0.122337	−	0.211894i
$832$	2.29590			0.0795959
$833$	27.3518	−	3.48554i	0.947684	−	0.120767i
$834$	6.48858			0.224681
$835$	0.0951463	+	0.164798i	0.00329267	+	0.00570308i
$836$	0.719833	−	1.24679i	0.0248959	−	0.0431210i
$837$	0.634375	−	1.09877i	0.0219272	−	0.0379790i
$838$	9.72670	+	16.8471i	0.336003	+	0.581975i
$839$	−39.1473			−1.35152			−0.675758	−	0.737123i	$-0.736184\pi$
$839$	−39.1473			−1.35152			−0.675758	+	0.737123i	$0.736184\pi$
$840$	4.27144	+	2.11747i	0.147379	+	0.0730596i
$841$	1.00000			0.0344828
$842$	17.6993	+	30.6561i	0.609959	+	1.05648i
$843$	−4.73609	+	8.20316i	−0.163120	+	0.282532i
$844$	5.41670	−	9.38200i	0.186450	−	0.322942i
$845$	−6.96346	−	12.0611i	−0.239550	−	0.414913i
$846$	0.445042			0.0153009
$847$	−1.74818	−	27.5476i	−0.0600680	−	0.946547i
$848$	−10.3177			−0.354310
$849$	5.08911	+	8.81459i	0.174658	+	0.302516i
$850$	−3.45257	+	5.98003i	−0.118422	+	0.205113i
$851$	−27.7667	+	48.0933i	−0.951829	+	1.64862i
$852$	−5.76540	−	9.98596i	−0.197519	−	0.342113i
$853$	−48.2838			−1.65321			−0.826603	−	0.562785i	$-0.809730\pi$
$853$	−48.2838			−1.65321			−0.826603	+	0.562785i	$0.809730\pi$
$854$	−21.0819	+	14.0233i	−0.721407	+	0.479867i
$855$	−3.44504			−0.117818
$856$	−5.51842	−	9.55818i	−0.188616	−	0.326692i
$857$	4.66852	−	8.08612i	0.159474	−	0.276217i	−0.775205	−	0.631709i	$-0.782354\pi$
$857$	4.66852	−	8.08612i	0.159474	−	0.276217i	0.934679	+	0.355493i	$0.115687\pi$
$858$	0.864429	−	1.49723i	0.0295111	−	0.0511147i
$859$	6.50202	+	11.2618i	0.221846	+	0.384249i	0.955369	−	0.295416i	$-0.0954584\pi$
$859$	6.50202	+	11.2618i	0.221846	+	0.384249i	−0.733522	+	0.679665i	$0.762125\pi$
$860$	2.11960			0.0722779
$861$	11.0957	−	7.38064i	0.378140	−	0.251532i
$862$	−32.3327			−1.10126
$863$	−1.04556	−	1.81097i	−0.0355914	−	0.0616462i	0.847681	−	0.530506i	$-0.177998\pi$
$863$	−1.04556	−	1.81097i	−0.0355914	−	0.0616462i	−0.883272	+	0.468860i	$0.844665\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−9.45257	+	16.3723i	−0.321397	+	0.556676i
$866$	9.44385	+	16.3572i	0.320915	+	0.555841i
$867$	−1.48427			−0.0504085
$868$	−0.212595	−	3.35006i	−0.00721595	−	0.113708i
$869$	11.1575			0.378492
$870$	−0.900969	−	1.56052i	−0.0305457	−	0.0529067i
$871$	2.77562	−	4.80751i	0.0940482	−	0.162896i
$872$	6.58426	−	11.4043i	0.222971	−	0.386197i
$873$	2.26659	+	3.92586i	0.0767126	+	0.132870i
$874$	−8.76032			−0.296322
$875$	−28.8451	−	14.2993i	−0.975143	−	0.483405i
$876$	5.78986			0.195621
$877$	16.2192	+	28.0924i	0.547682	+	0.948614i	0.998433	+	0.0559637i	$0.0178231\pi$
$877$	16.2192	+	28.0924i	0.547682	+	0.948614i	−0.450750	+	0.892650i	$0.648844\pi$
$878$	−12.7419	+	22.0696i	−0.430018	+	0.744813i
$879$	2.01722	−	3.49393i	0.0680392	−	0.117847i
$880$	−0.678448	−	1.17511i	−0.0228705	−	0.0396128i
$881$	−9.62001			−0.324106			−0.162053	−	0.986782i	$-0.551812\pi$
$881$	−9.62001			−0.324106			−0.162053	+	0.986782i	$0.551812\pi$
$882$	−6.94385	+	0.884879i	−0.233811	+	0.0297954i
$883$	21.7616			0.732338			0.366169	−	0.930548i	$-0.380669\pi$
$883$	21.7616			0.732338			0.366169	+	0.930548i	$0.380669\pi$
$884$	4.52177	+	7.83194i	0.152084	+	0.263417i
$885$	9.45473	−	16.3761i	0.317817	−	0.550476i
$886$	−13.6020	+	23.5594i	−0.456969	+	0.791493i
$887$	−1.48158	−	2.56618i	−0.0497467	−	0.0861637i	0.840080	−	0.542463i	$-0.182508\pi$
$887$	−1.48158	−	2.56618i	−0.0497467	−	0.0861637i	−0.889826	+	0.456299i	$0.849175\pi$
$888$	−12.1196			−0.406707
$889$	1.91371	+	0.948680i	0.0641839	+	0.0318177i
$890$	2.56465			0.0859672
$891$	0.376510	+	0.652135i	0.0126136	+	0.0218473i
$892$	3.16972	−	5.49011i	0.106130	−	0.183823i
$893$	−0.425428	+	0.736862i	−0.0142364	+	0.0246582i
$894$	−10.2289	−	17.7169i	−0.342104	−	0.592542i
$895$	31.2857			1.04577
$896$	0.167563	+	2.64044i	0.00559788	+	0.0882109i
$897$	−10.5200			−0.351254
$898$	−11.7714	−	20.3887i	−0.392818	−	0.680381i
$899$	−0.634375	+	1.09877i	−0.0211576	+	0.0366460i
$900$	0.876510	−	1.51816i	0.0292170	−	0.0506053i
$901$	−20.3207	−	35.1964i	−0.676979	−	1.17256i
$902$	−3.79284			−0.126288
$903$	−2.59126	+	1.72366i	−0.0862318	+	0.0573598i
$904$	10.2349			0.340408
$905$	−12.2518	−	21.2208i	−0.407264	−	0.705403i
$906$	6.87531	−	11.9084i	0.228417	−	0.395630i
$907$	−14.4285	+	24.9910i	−0.479092	+	0.829812i	−0.999713	−	0.0239766i	$-0.992367\pi$
$907$	−14.4285	+	24.9910i	−0.479092	+	0.829812i	0.520621	+	0.853788i	$0.325701\pi$
$908$	−12.9852	−	22.4911i	−0.430930	−	0.746393i
$909$	−12.8823			−0.427279
$910$	−9.11356	+	6.06218i	−0.302112	+	0.200959i
$911$	46.2567			1.53255			0.766276	−	0.642512i	$-0.222108\pi$
$911$	46.2567			1.53255			0.766276	+	0.642512i	$0.222108\pi$
$912$	−0.955927	−	1.65571i	−0.0316539	−	0.0548262i
$913$	−0.618645	+	1.07153i	−0.0204742	+	0.0354623i
$914$	−8.68449	+	15.0420i	−0.287257	+	0.497544i
$915$	−8.62229	−	14.9343i	−0.285044	−	0.493711i
$916$	2.47757			0.0818611
$917$	3.57457	+	56.3278i	0.118043	+	1.86011i
$918$	−3.93900			−0.130006
$919$	−22.5227	−	39.0105i	−0.742956	−	1.28684i	−0.951144	−	0.308749i	$-0.900090\pi$
$919$	−22.5227	−	39.0105i	−0.742956	−	1.28684i	0.208187	−	0.978089i	$-0.433244\pi$
$920$	−4.12833	+	7.15048i	−0.136107	+	0.235744i
$921$	−6.93631	+	12.0140i	−0.228559	+	0.395876i
$922$	−2.69471	−	4.66737i	−0.0887455	−	0.153712i
$923$	26.4735			0.871386
$924$	1.78501	+	0.884879i	0.0587226	+	0.0291104i
$925$	21.2459			0.698561
$926$	−0.00149195	−	0.00258414i	−4.90286e−5	−	8.49200e-5i
$927$	5.18598	−	8.98238i	0.170330	−	0.295020i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	−21.1843	−	36.6922i	−0.695033	−	1.20383i	−0.970170	−	0.242427i	$-0.922057\pi$
$929$	−21.1843	−	36.6922i	−0.695033	−	1.20383i	0.275137	−	0.961405i	$-0.411277\pi$
$930$	2.28621			0.0749677
$931$	5.17270	−	12.3429i	0.169528	−	0.404522i
$932$	−1.10321			−0.0361369
$933$	5.83124	+	10.1000i	0.190906	+	0.330659i
$934$	3.10723	−	5.38188i	0.101672	−	0.176100i
$935$	2.67241	−	4.62874i	0.0873971	−	0.151376i
$936$	−1.14795	−	1.98831i	−0.0375219	−	0.0649898i
$937$	27.8237			0.908961			0.454480	−	0.890757i	$-0.349825\pi$
$937$	27.8237			0.908961			0.454480	+	0.890757i	$0.349825\pi$
$938$	5.73155	+	2.84128i	0.187142	+	0.0927712i
$939$	−32.4620			−1.05936
$940$	0.400969	+	0.694498i	0.0130782	+	0.0226520i
$941$	−12.8790	+	22.3070i	−0.419842	+	0.727188i	−0.995923	−	0.0902046i	$-0.971248\pi$
$941$	−12.8790	+	22.3070i	−0.419842	+	0.727188i	0.576081	+	0.817393i	$0.304581\pi$
$942$	0.928780	−	1.60869i	0.0302613	−	0.0524141i
$943$	11.5397	+	19.9873i	0.375783	+	0.650875i
$944$	10.4940			0.341549
$945$	−0.301938	−	4.75791i	−0.00982204	−	0.154775i
$946$	0.885772			0.0287989
$947$	−3.07056	−	5.31836i	−0.0997797	−	0.172823i	0.811814	−	0.583917i	$-0.198480\pi$
$947$	−3.07056	−	5.31836i	−0.0997797	−	0.172823i	−0.911593	+	0.411093i	$0.865147\pi$
$948$	7.40850	−	12.8319i	0.240617	−	0.416761i
$949$	−6.64646	+	11.5120i	−0.215753	+	0.373695i
$950$	1.67576	+	2.90250i	0.0543688	+	0.0941696i
$951$	−9.23251			−0.299384
$952$	−8.67725	+	5.77195i	−0.281231	+	0.187070i
$953$	−18.9506			−0.613870			−0.306935	−	0.951730i	$-0.599303\pi$
$953$	−18.9506			−0.613870			−0.306935	+	0.951730i	$0.599303\pi$
$954$	5.15883	+	8.93536i	0.167023	+	0.289293i
$955$	2.70075	−	4.67784i	0.0873942	−	0.151371i
$956$	3.15399	−	5.46287i	0.102007	−	0.176682i
$957$	−0.376510	−	0.652135i	−0.0121708	−	0.0210805i
$958$	9.32198			0.301179
$959$	−28.8918	+	19.2183i	−0.932964	+	0.620591i
$960$	−1.80194			−0.0581573
$961$	14.6951	+	25.4527i	0.474037	+	0.821056i
$962$	13.9127	−	24.0975i	0.448563	−	0.776934i
$963$	−5.51842	+	9.55818i	−0.177829	+	0.308008i
$964$	5.33728	+	9.24444i	0.171902	+	0.297743i
$965$	−40.8461			−1.31488
$966$	−0.767790	−	12.0988i	−0.0247033	−	0.389272i
$967$	−49.7415			−1.59958			−0.799790	−	0.600280i	$-0.795056\pi$
$967$	−49.7415			−1.59958			−0.799790	+	0.600280i	$0.795056\pi$
$968$	5.21648	+	9.03521i	0.167664	+	0.290403i
$969$	3.76540	−	6.52186i	0.120962	−	0.209512i
$970$	−4.08426	+	7.07415i	−0.131138	+	0.227137i
$971$	26.3442	+	45.6294i	0.845424	+	1.46432i	0.885252	+	0.465111i	$0.153986\pi$
$971$	26.3442	+	45.6294i	0.845424	+	1.46432i	−0.0398285	+	0.999207i	$0.512681\pi$
$972$	1.00000			0.0320750
$973$	−15.3810	−	7.62477i	−0.493092	−	0.244439i
$974$	9.92798			0.318113
$975$	2.01238	+	3.48554i	0.0644476	+	0.111627i
$976$	4.78501	−	8.28788i	0.153164	−	0.265289i
$977$	−13.4172	+	23.2393i	−0.429255	+	0.743492i	−0.996807	−	0.0798457i	$-0.974557\pi$
$977$	−13.4172	+	23.2393i	−0.429255	+	0.743492i	0.567552	+	0.823338i	$0.307891\pi$
$978$	9.37263	+	16.2339i	0.299704	+	0.519102i
$979$	1.07175			0.0342534
$980$	−7.63706	−	10.0388i	−0.243957	−	0.320677i
$981$	−13.1685			−0.420439
$982$	12.9705	+	22.4655i	0.413904	+	0.716903i
$983$	−4.84117	+	8.38515i	−0.154409	+	0.267445i	−0.932844	−	0.360281i	$-0.882681\pi$
$983$	−4.84117	+	8.38515i	−0.154409	+	0.267445i	0.778435	+	0.627726i	$0.216014\pi$
$984$	−2.51842	+	4.36203i	−0.0802842	+	0.139056i
$985$	1.66756	+	2.88830i	0.0531330	+	0.0920290i
$986$	3.93900			0.125443
$987$	−1.05496	−	0.522971i	−0.0335797	−	0.0166464i
$988$	4.38942			0.139646
$989$	−2.69495	−	4.66778i	−0.0856943	−	0.148427i
$990$	−0.678448	+	1.17511i	−0.0215625	+	0.0373473i
$991$	14.7793	−	25.5984i	0.469479	−	0.813161i	−0.529912	−	0.848052i	$-0.677775\pi$
$991$	14.7793	−	25.5984i	0.469479	−	0.813161i	0.999391	+	0.0348912i	$0.0111085\pi$
$992$	0.634375	+	1.09877i	0.0201414	+	0.0348860i
$993$	6.25667			0.198549
$994$	1.93213	+	30.4464i	0.0612835	+	0.965700i
$995$	10.6233			0.336780
$996$	0.821552	+	1.42297i	0.0260319	+	0.0450885i
$997$	−9.40677	+	16.2930i	−0.297915	+	0.516005i	−0.975659	−	0.219294i	$-0.929625\pi$
$997$	−9.40677	+	16.2930i	−0.297915	+	0.516005i	0.677743	+	0.735298i	$0.262958\pi$
$998$	13.5884	−	23.5359i	0.430135	−	0.745015i
$999$	6.05980	+	10.4959i	0.191724	+	0.332075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.a.697.3	✓	6
7.2	even	3	inner	1218.2.i.a.1045.3	yes	6
7.3	odd	6		8526.2.a.bz.1.3		3
7.4	even	3		8526.2.a.cb.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.a.697.3	✓	6	1.1	even	1	trivial
1218.2.i.a.1045.3	yes	6	7.2	even	3	inner
8526.2.a.bz.1.3		3	7.3	odd	6
8526.2.a.cb.1.1		3	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.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} +(0.900969 + 1.56052i) q^{5} +1.00000 q^{6} +(-2.37047 - 1.17511i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.900969 - 1.56052i) q^{10} +(0.376510 - 0.652135i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.29590 q^{13} +(0.167563 + 2.64044i) q^{14} -1.80194 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.96950 - 3.41127i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.955927 - 1.65571i) q^{19} -1.80194 q^{20} +(2.20291 - 1.46533i) q^{21} -0.753020 q^{22} +(2.29105 + 3.96822i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.876510 - 1.51816i) q^{25} +(-1.14795 - 1.98831i) q^{26} +1.00000 q^{27} +(2.20291 - 1.46533i) q^{28} -1.00000 q^{29} +(0.900969 + 1.56052i) q^{30} +(0.634375 - 1.09877i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.376510 + 0.652135i) q^{33} -3.93900 q^{34} +(-0.301938 - 4.75791i) q^{35} +1.00000 q^{36} +(6.05980 + 10.4959i) q^{37} +(-0.955927 + 1.65571i) q^{38} +(-1.14795 + 1.98831i) q^{39} +(0.900969 + 1.56052i) q^{40} +5.03684 q^{41} +(-2.37047 - 1.17511i) q^{42} -1.17629 q^{43} +(0.376510 + 0.652135i) q^{44} +(0.900969 - 1.56052i) q^{45} +(2.29105 - 3.96822i) q^{46} +(-0.222521 - 0.385418i) q^{47} +1.00000 q^{48} +(4.23825 + 5.57111i) q^{49} -1.75302 q^{50} +(1.96950 + 3.41127i) q^{51} +(-1.14795 + 1.98831i) q^{52} +(5.15883 - 8.93536i) q^{53} +(-0.500000 - 0.866025i) q^{54} +1.35690 q^{55} +(-2.37047 - 1.17511i) q^{56} +1.91185 q^{57} +(0.500000 + 0.866025i) q^{58} +(-5.24698 + 9.08804i) q^{59} +(0.900969 - 1.56052i) q^{60} +(4.78501 + 8.28788i) q^{61} -1.26875 q^{62} +(0.167563 + 2.64044i) q^{63} +1.00000 q^{64} +(2.06853 + 3.58280i) q^{65} +(0.376510 - 0.652135i) q^{66} +(1.20895 - 2.09396i) q^{67} +(1.96950 + 3.41127i) q^{68} -4.58211 q^{69} +(-3.96950 + 2.64044i) q^{70} +11.5308 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.89493 + 5.01416i) q^{73} +(6.05980 - 10.4959i) q^{74} +(0.876510 + 1.51816i) q^{75} +1.91185 q^{76} +(-1.65883 + 1.10343i) q^{77} +2.29590 q^{78} +(7.40850 + 12.8319i) q^{79} +(0.900969 - 1.56052i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.51842 - 4.36203i) q^{82} -1.64310 q^{83} +(0.167563 + 2.64044i) q^{84} +7.09783 q^{85} +(0.588146 + 1.01870i) q^{86} +(0.500000 - 0.866025i) q^{87} +(0.376510 - 0.652135i) q^{88} +(0.711636 + 1.23259i) q^{89} -1.80194 q^{90} +(-5.44235 - 2.69792i) q^{91} -4.58211 q^{92} +(0.634375 + 1.09877i) q^{93} +(-0.222521 + 0.385418i) q^{94} +(1.72252 - 2.98349i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.53319 q^{97} +(2.70560 - 6.45599i) q^{98} -0.753020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} + 6 q^{6} + 6 q^{8} - 3 q^{9} + q^{10} + 7 q^{11} - 3 q^{12} - 14 q^{13} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} - 14 q^{22} + 8 q^{23}+ \cdots - 14 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 + 6 * q^6 + 6 * q^8 - 3 * q^9 + q^10 + 7 * q^11 - 3 * q^12 - 14 * q^13 - 2 * q^15 - 3 * q^16 + 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 - 14 * q^22 + 8 * q^23 - 3 * q^24 + 10 * q^25 + 7 * q^26 + 6 * q^27 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 + 7 * q^33 - 4 * q^34 + 7 * q^35 + 6 * q^36 + 15 * q^37 - 2 * q^38 + 7 * q^39 + q^40 - 26 * q^41 - 22 * q^43 + 7 * q^44 + q^45 + 8 * q^46 - q^47 + 6 * q^48 - 20 * q^50 + 2 * q^51 + 7 * q^52 + 14 * q^53 - 3 * q^54 + 4 * q^57 + 3 * q^58 - 22 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 6 * q^64 + 7 * q^65 + 7 * q^66 + 13 * q^67 + 2 * q^68 - 16 * q^69 - 14 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 15 * q^74 + 10 * q^75 + 4 * q^76 + 7 * q^77 - 14 * q^78 + 15 * q^79 + q^80 - 3 * q^81 + 13 * q^82 - 18 * q^83 + 6 * q^85 + 11 * q^86 + 3 * q^87 + 7 * q^88 + 7 * q^89 - 2 * q^90 - 35 * q^91 - 16 * q^92 - 4 * q^93 - q^94 + 10 * q^95 - 3 * q^96 - 34 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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