LMFDB - Embedded newform 273.2.i.e.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 8x^{7} + 41x^{6} - 40x^{5} + 59x^{4} - 10x^{3} + 18x^{2} - 4x + 4 $ x^10 - x^9 + 7x^8 - 8x^7 + 41x^6 - 40x^5 + 59x^4 - 10x^3 + 18x^2 - 4x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$1.08681 + 1.88241i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.e.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.660777 + 1.14450i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.126747 + 0.219533i) q^{4} +(-1.01284 + 1.75429i) q^{5} -1.32155 q^{6} +(-2.38540 - 1.14450i) q^{7} -2.97812 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.660777 + 1.14450i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.126747 + 0.219533i) q^{4} +(-1.01284 + 1.75429i) q^{5} -1.32155 q^{6} +(-2.38540 - 1.14450i) q^{7} -2.97812 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.33853 - 2.31839i) q^{10} +(0.0340296 + 0.0589410i) q^{11} +(-0.126747 + 0.219533i) q^{12} -1.00000 q^{13} +(2.88609 - 1.97383i) q^{14} -2.02568 q^{15} +(1.71438 - 2.96939i) q^{16} +(3.02309 + 5.23614i) q^{17} +(-0.660777 - 1.14450i) q^{18} +(2.67362 - 4.63084i) q^{19} -0.513501 q^{20} +(-0.201533 - 2.63806i) q^{21} -0.0899440 q^{22} +(-2.77658 + 4.80918i) q^{23} +(-1.48906 - 2.57912i) q^{24} +(0.448301 + 0.776481i) q^{25} +(0.660777 - 1.14450i) q^{26} -1.00000 q^{27} +(-0.0510876 - 0.668736i) q^{28} -2.38258 q^{29} +(1.33853 - 2.31839i) q^{30} +(1.58763 + 2.74985i) q^{31} +(-0.712476 - 1.23404i) q^{32} +(-0.0340296 + 0.0589410i) q^{33} -7.99035 q^{34} +(4.42382 - 3.02549i) q^{35} -0.253495 q^{36} +(-2.64724 + 4.58515i) q^{37} +(3.53333 + 6.11991i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(3.01636 - 5.22449i) q^{40} -2.36912 q^{41} +(3.15243 + 1.51252i) q^{42} -0.103923 q^{43} +(-0.00862633 + 0.0149412i) q^{44} +(-1.01284 - 1.75429i) q^{45} +(-3.66940 - 6.35559i) q^{46} +(2.03077 - 3.51740i) q^{47} +3.42875 q^{48} +(4.38024 + 5.46017i) q^{49} -1.18491 q^{50} +(-3.02309 + 5.23614i) q^{51} +(-0.126747 - 0.219533i) q^{52} +(3.97984 + 6.89328i) q^{53} +(0.660777 - 1.14450i) q^{54} -0.137867 q^{55} +(7.10399 + 3.40845i) q^{56} +5.34724 q^{57} +(1.57435 - 2.72686i) q^{58} +(3.44149 + 5.96083i) q^{59} +(-0.256750 - 0.444704i) q^{60} +(4.02309 - 6.96819i) q^{61} -4.19627 q^{62} +(2.18386 - 1.49357i) q^{63} +8.74065 q^{64} +(1.01284 - 1.75429i) q^{65} +(-0.0449720 - 0.0778938i) q^{66} +(2.33370 + 4.04209i) q^{67} +(-0.766337 + 1.32733i) q^{68} -5.55316 q^{69} +(0.539515 + 7.06223i) q^{70} +0.522494 q^{71} +(1.48906 - 2.57912i) q^{72} +(3.43806 + 5.95489i) q^{73} +(-3.49847 - 6.05952i) q^{74} +(-0.448301 + 0.776481i) q^{75} +1.35550 q^{76} +(-0.0137162 - 0.179545i) q^{77} +1.32155 q^{78} +(-5.86681 + 10.1616i) q^{79} +(3.47278 + 6.01504i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.56546 - 2.71146i) q^{82} +12.8208 q^{83} +(0.553598 - 0.378611i) q^{84} -12.2476 q^{85} +(0.0686701 - 0.118940i) q^{86} +(-1.19129 - 2.06337i) q^{87} +(-0.101344 - 0.175533i) q^{88} +(2.48975 - 4.31238i) q^{89} +2.67705 q^{90} +(2.38540 + 1.14450i) q^{91} -1.40770 q^{92} +(-1.58763 + 2.74985i) q^{93} +(2.68378 + 4.64844i) q^{94} +(5.41591 + 9.38063i) q^{95} +(0.712476 - 1.23404i) q^{96} -5.09702 q^{97} +(-9.14353 + 1.40523i) q^{98} -0.0680592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.660777	+	1.14450i	−0.467240	+	0.809283i	−0.999299	−	0.0374236i	$-0.988085\pi$
$2$	−0.660777	+	1.14450i	−0.467240	+	0.809283i	0.532060	+	0.846707i	$0.321418\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.126747	+	0.219533i	0.0633737	+	0.109766i
$5$	−1.01284	+	1.75429i	−0.452957	+	0.784544i	−0.998568	−	0.0534942i	$-0.982964\pi$
$5$	−1.01284	+	1.75429i	−0.452957	+	0.784544i	0.545611	+	0.838038i	$0.316297\pi$
$6$	−1.32155			−0.539522
$7$	−2.38540	−	1.14450i	−0.901596	−	0.432580i
$7$	−2.38540	−	1.14450i	−0.901596	−	0.432580i
$8$	−2.97812			−1.05292
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.33853	−	2.31839i	−0.423279	−	0.733141i
$11$	0.0340296	+	0.0589410i	0.0102603	+	0.0177714i	0.871110	−	0.491088i	$-0.163401\pi$
$11$	0.0340296	+	0.0589410i	0.0102603	+	0.0177714i	−0.860850	+	0.508859i	$0.830067\pi$
$12$	−0.126747	+	0.219533i	−0.0365888	+	0.0633737i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.88609	−	1.97383i	0.771341	−	0.527527i
$15$	−2.02568			−0.523029
$16$	1.71438	−	2.96939i	0.428594	−	0.742346i
$17$	3.02309	+	5.23614i	0.733206	+	1.26995i	0.955506	+	0.294972i	$0.0953104\pi$
$17$	3.02309	+	5.23614i	0.733206	+	1.26995i	−0.222299	+	0.974978i	$0.571356\pi$
$18$	−0.660777	−	1.14450i	−0.155747	−	0.269761i
$19$	2.67362	−	4.63084i	0.613370	−	1.06239i	−0.377298	−	0.926092i	$-0.623147\pi$
$19$	2.67362	−	4.63084i	0.613370	−	1.06239i	0.990668	−	0.136297i	$-0.0435200\pi$
$20$	−0.513501			−0.114822
$21$	−0.201533	−	2.63806i	−0.0439781	−	0.575673i
$22$	−0.0899440			−0.0191761
$23$	−2.77658	+	4.80918i	−0.578957	+	1.00278i	0.416642	+	0.909071i	$0.363207\pi$
$23$	−2.77658	+	4.80918i	−0.578957	+	1.00278i	−0.995599	+	0.0937129i	$0.970126\pi$
$24$	−1.48906	−	2.57912i	−0.303953	−	0.526461i
$25$	0.448301	+	0.776481i	0.0896603	+	0.155296i
$26$	0.660777	−	1.14450i	0.129589	−	0.224455i
$27$	−1.00000			−0.192450
$28$	−0.0510876	−	0.668736i	−0.00965465	−	0.126379i
$29$	−2.38258			−0.442433			−0.221217	−	0.975225i	$-0.571003\pi$
$29$	−2.38258			−0.442433			−0.221217	+	0.975225i	$0.571003\pi$
$30$	1.33853	−	2.31839i	0.244380	−	0.423279i
$31$	1.58763	+	2.74985i	0.285146	+	0.493888i	0.972645	−	0.232298i	$-0.0746244\pi$
$31$	1.58763	+	2.74985i	0.285146	+	0.493888i	−0.687498	+	0.726186i	$0.741291\pi$
$32$	−0.712476	−	1.23404i	−0.125949	−	0.218150i
$33$	−0.0340296	+	0.0589410i	−0.00592380	+	0.0102603i
$34$	−7.99035			−1.37033
$35$	4.42382	−	3.02549i	0.747762	−	0.511401i
$36$	−0.253495			−0.0422491
$37$	−2.64724	+	4.58515i	−0.435203	+	0.753794i	−0.997312	−	0.0732691i	$-0.976657\pi$
$37$	−2.64724	+	4.58515i	−0.435203	+	0.753794i	0.562109	+	0.827063i	$0.309990\pi$
$38$	3.53333	+	6.11991i	0.573182	+	0.992781i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	3.01636	−	5.22449i	0.476929	−	0.826064i
$41$	−2.36912			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$41$	−2.36912			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$42$	3.15243	+	1.51252i	0.486431	+	0.233387i
$43$	−0.103923			−0.0158482			−0.00792408	−	0.999969i	$-0.502522\pi$
$43$	−0.103923			−0.0158482			−0.00792408	+	0.999969i	$0.502522\pi$
$44$	−0.00862633	+	0.0149412i	−0.00130047	+	0.00225248i
$45$	−1.01284	−	1.75429i	−0.150986	−	0.261515i
$46$	−3.66940	−	6.35559i	−0.541024	−	0.937081i
$47$	2.03077	−	3.51740i	0.296219	−	0.513066i	−0.679049	−	0.734093i	$-0.737608\pi$
$47$	2.03077	−	3.51740i	0.296219	−	0.513066i	0.975268	+	0.221027i	$0.0709409\pi$
$48$	3.42875			0.494898
$49$	4.38024	+	5.46017i	0.625749	+	0.780025i
$50$	−1.18491			−0.167571
$51$	−3.02309	+	5.23614i	−0.423317	+	0.733206i
$52$	−0.126747	−	0.219533i	−0.0175767	−	0.0304437i
$53$	3.97984	+	6.89328i	0.546673	+	0.946865i	0.998500	+	0.0547594i	$0.0174392\pi$
$53$	3.97984	+	6.89328i	0.546673	+	0.946865i	−0.451827	+	0.892106i	$0.649227\pi$
$54$	0.660777	−	1.14450i	0.0899204	−	0.155747i
$55$	−0.137867			−0.0185899
$56$	7.10399	+	3.40845i	0.949310	+	0.455473i
$57$	5.34724			0.708259
$58$	1.57435	−	2.72686i	0.206722	−	0.358054i
$59$	3.44149	+	5.96083i	0.448044	+	0.776034i	0.998259	−	0.0589887i	$-0.0187876\pi$
$59$	3.44149	+	5.96083i	0.448044	+	0.776034i	−0.550215	+	0.835023i	$0.685454\pi$
$60$	−0.256750	−	0.444704i	−0.0331463	−	0.0574111i
$61$	4.02309	−	6.96819i	0.515104	−	0.892186i	−0.484743	−	0.874657i	$-0.661087\pi$
$61$	4.02309	−	6.96819i	0.515104	−	0.892186i	0.999846	−	0.0175288i	$-0.00557987\pi$
$62$	−4.19627			−0.532927
$63$	2.18386	−	1.49357i	0.275141	−	0.188172i
$64$	8.74065			1.09258
$65$	1.01284	−	1.75429i	0.125628	−	0.217593i
$66$	−0.0449720	−	0.0778938i	−0.00553567	−	0.00958806i
$67$	2.33370	+	4.04209i	0.285107	+	0.493819i	0.972635	−	0.232338i	$-0.0746376\pi$
$67$	2.33370	+	4.04209i	0.285107	+	0.493819i	−0.687528	+	0.726158i	$0.741304\pi$
$68$	−0.766337	+	1.32733i	−0.0929320	+	0.160963i
$69$	−5.55316			−0.668522
$70$	0.539515	+	7.06223i	0.0644843	+	0.844098i
$71$	0.522494			0.0620087			0.0310043	−	0.999519i	$-0.490129\pi$
$71$	0.522494			0.0620087			0.0310043	+	0.999519i	$0.490129\pi$
$72$	1.48906	−	2.57912i	0.175487	−	0.303953i
$73$	3.43806	+	5.95489i	0.402394	+	0.696967i	0.994014	−	0.109250i	$-0.0348448\pi$
$73$	3.43806	+	5.95489i	0.402394	+	0.696967i	−0.591620	+	0.806217i	$0.701512\pi$
$74$	−3.49847	−	6.05952i	−0.406689	−	0.704405i
$75$	−0.448301	+	0.776481i	−0.0517654	+	0.0896603i
$76$	1.35550			0.155486
$77$	−0.0137162	−	0.179545i	−0.00156311	−	0.0204610i
$78$	1.32155			0.149637
$79$	−5.86681	+	10.1616i	−0.660067	+	1.14327i	0.320530	+	0.947238i	$0.396139\pi$
$79$	−5.86681	+	10.1616i	−0.660067	+	1.14327i	−0.980598	+	0.196032i	$0.937194\pi$
$80$	3.47278	+	6.01504i	0.388269	+	0.672502i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.56546	−	2.71146i	0.172876	−	0.299431i
$83$	12.8208			1.40726			0.703631	−	0.710565i	$-0.251561\pi$
$83$	12.8208			1.40726			0.703631	+	0.710565i	$0.251561\pi$
$84$	0.553598	−	0.378611i	0.0604025	−	0.0413099i
$85$	−12.2476			−1.32844
$86$	0.0686701	−	0.118940i	0.00740489	−	0.0128256i
$87$	−1.19129	−	2.06337i	−0.127719	−	0.221217i
$88$	−0.101344	−	0.175533i	−0.0108033	−	0.0187119i
$89$	2.48975	−	4.31238i	0.263913	−	0.457112i	−0.703365	−	0.710829i	$-0.748320\pi$
$89$	2.48975	−	4.31238i	0.263913	−	0.457112i	0.967278	+	0.253717i	$0.0816533\pi$
$90$	2.67705			0.282186
$91$	2.38540	+	1.14450i	0.250058	+	0.119976i
$92$	−1.40770			−0.146763
$93$	−1.58763	+	2.74985i	−0.164629	+	0.285146i
$94$	2.68378	+	4.64844i	0.276811	+	0.479450i
$95$	5.41591	+	9.38063i	0.555660	+	0.962432i
$96$	0.712476	−	1.23404i	0.0727167	−	0.125949i
$97$	−5.09702			−0.517524			−0.258762	−	0.965941i	$-0.583314\pi$
$97$	−5.09702			−0.517524			−0.258762	+	0.965941i	$0.583314\pi$
$98$	−9.14353	+	1.40523i	−0.923636	+	0.141950i
$99$	−0.0680592			−0.00684021
$100$	−0.113642	+	0.196834i	−0.0113642	+	0.0196834i
$101$	−9.57632	−	16.5867i	−0.952879	−	1.65044i	−0.739149	−	0.673542i	$-0.764772\pi$
$101$	−9.57632	−	16.5867i	−0.952879	−	1.65044i	−0.213731	−	0.976893i	$-0.568561\pi$
$102$	−3.99517	−	6.91984i	−0.395581	−	0.685167i
$103$	8.29993	−	14.3759i	0.817817	−	1.41650i	−0.0894710	−	0.995989i	$-0.528518\pi$
$103$	8.29993	−	14.3759i	0.817817	−	1.41650i	0.907288	−	0.420511i	$-0.138149\pi$
$104$	2.97812			0.292028
$105$	4.83206	+	2.31839i	0.471561	+	0.226252i
$106$	−10.5191			−1.02171
$107$	6.45363	−	11.1780i	0.623896	−	1.08062i	−0.364857	−	0.931064i	$-0.618882\pi$
$107$	6.45363	−	11.1780i	0.623896	−	1.08062i	0.988753	−	0.149556i	$-0.0477846\pi$
$108$	−0.126747	−	0.219533i	−0.0121963	−	0.0211246i
$109$	10.1572	+	17.5927i	0.972879	+	1.68508i	0.686764	+	0.726880i	$0.259030\pi$
$109$	10.1572	+	17.5927i	0.972879	+	1.68508i	0.286114	+	0.958195i	$0.407636\pi$
$110$	0.0910990	−	0.157788i	0.00868595	−	0.0150445i
$111$	−5.29448			−0.502529
$112$	−7.48793	+	5.12106i	−0.707543	+	0.483895i
$113$	−8.38961			−0.789228			−0.394614	−	0.918847i	$-0.629122\pi$
$113$	−8.38961			−0.789228			−0.394614	+	0.918847i	$0.629122\pi$
$114$	−3.53333	+	6.11991i	−0.330927	+	0.573182i
$115$	−5.62448	−	9.74188i	−0.524485	−	0.908435i
$116$	−0.301985	−	0.523054i	−0.0280386	−	0.0485643i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−9.09623			−0.837376
$119$	−1.21850	−	15.9502i	−0.111700	−	1.46215i
$120$	6.03272			0.550710
$121$	5.49768	−	9.52227i	0.499789	−	0.865661i
$122$	5.31673	+	9.20884i	0.481354	+	0.833729i
$123$	−1.18456	−	2.05172i	−0.106808	−	0.184997i
$124$	−0.402455	+	0.697073i	−0.0361416	+	0.0625990i
$125$	−11.9447			−1.06836
$126$	0.266337	+	3.48634i	0.0237272	+	0.310588i
$127$	−10.0551			−0.892245			−0.446122	−	0.894972i	$-0.647195\pi$
$127$	−10.0551			−0.892245			−0.446122	+	0.894972i	$0.647195\pi$
$128$	−4.35067	+	7.53558i	−0.384549	+	0.666058i
$129$	−0.0519616	−	0.0900002i	−0.00457497	−	0.00792408i
$130$	1.33853	+	2.31839i	0.117396	+	0.203337i
$131$	3.61657	−	6.26408i	0.315981	−	0.547295i	−0.663665	−	0.748030i	$-0.731000\pi$
$131$	3.61657	−	6.26408i	0.315981	−	0.547295i	0.979646	+	0.200735i	$0.0643331\pi$
$132$	−0.0172527			−0.00150165
$133$	−11.6776	+	7.98645i	−1.01258	+	0.692513i
$134$	−6.16822			−0.532853
$135$	1.01284	−	1.75429i	0.0871716	−	0.150986i
$136$	−9.00310	−	15.5938i	−0.772010	−	1.33716i
$137$	−10.3196	−	17.8740i	−0.881660	−	1.52708i	−0.849494	−	0.527597i	$-0.823093\pi$
$137$	−10.3196	−	17.8740i	−0.881660	−	1.52708i	−0.0321656	−	0.999483i	$-0.510240\pi$
$138$	3.66940	−	6.35559i	0.312360	−	0.541024i
$139$	15.2921			1.29706			0.648528	−	0.761191i	$-0.275385\pi$
$139$	15.2921			1.29706			0.648528	+	0.761191i	$0.275385\pi$
$140$	1.22490	+	0.587701i	0.103523	+	0.0496698i
$141$	4.06155			0.342044
$142$	−0.345252	+	0.597994i	−0.0289729	+	0.0501826i
$143$	−0.0340296	−	0.0589410i	−0.00284570	−	0.00492890i
$144$	1.71438	+	2.96939i	0.142865	+	0.247449i
$145$	2.41317	−	4.17974i	0.200403	−	0.347108i
$146$	−9.08715			−0.752058
$147$	−2.53853	+	6.52349i	−0.209374	+	0.538048i
$148$	−1.34212			−0.110322
$149$	−4.34204	+	7.52064i	−0.355714	+	0.616115i	−0.987240	−	0.159240i	$-0.949096\pi$
$149$	−4.34204	+	7.52064i	−0.355714	+	0.616115i	0.631526	+	0.775355i	$0.282429\pi$
$150$	−0.592455	−	1.02616i	−0.0483737	−	0.0837857i
$151$	−6.76571	−	11.7185i	−0.550585	−	0.953642i	−0.998232	−	0.0594314i	$-0.981071\pi$
$151$	−6.76571	−	11.7185i	−0.550585	−	0.953642i	0.447647	−	0.894210i	$-0.352262\pi$
$152$	−7.96235	+	13.7912i	−0.645832	+	1.11861i
$153$	−6.04617			−0.488804
$154$	0.214552	+	0.102941i	0.0172891	+	0.00829521i
$155$	−6.43207			−0.516636
$156$	0.126747	−	0.219533i	0.0101479	−	0.0175767i
$157$	10.4540	+	18.1068i	0.834317	+	1.44508i	0.894585	+	0.446897i	$0.147471\pi$
$157$	10.4540	+	18.1068i	0.834317	+	1.44508i	−0.0602683	+	0.998182i	$0.519196\pi$
$158$	−7.75330	−	13.4291i	−0.616820	−	1.06836i
$159$	−3.97984	+	6.89328i	−0.315622	+	0.546673i
$160$	2.88650			0.228198
$161$	12.1274	−	8.29401i	0.955770	−	0.653660i
$162$	1.32155			0.103831
$163$	−11.4332	+	19.8029i	−0.895520	+	1.55109i	−0.0623595	+	0.998054i	$0.519863\pi$
$163$	−11.4332	+	19.8029i	−0.895520	+	1.55109i	−0.833160	+	0.553032i	$0.813471\pi$
$164$	−0.300280	−	0.520101i	−0.0234479	−	0.0406130i
$165$	−0.0689333	−	0.119396i	−0.00536645	−	0.00929496i
$166$	−8.47167	+	14.6734i	−0.657529	+	1.13887i
$167$	12.7013			0.982859			0.491430	−	0.870917i	$-0.336474\pi$
$167$	12.7013			0.982859			0.491430	+	0.870917i	$0.336474\pi$
$168$	0.600189	+	7.85646i	0.0463056	+	0.606139i
$169$	1.00000			0.0769231
$170$	8.09296	−	14.0174i	0.620702	−	1.07509i
$171$	2.67362	+	4.63084i	0.204457	+	0.354130i
$172$	−0.0131720	−	0.0228146i	−0.00100436	−	0.00173960i
$173$	−7.29648	+	12.6379i	−0.554741	+	0.960840i	0.443183	+	0.896431i	$0.353849\pi$
$173$	−7.29648	+	12.6379i	−0.554741	+	0.960840i	−0.997924	+	0.0644083i	$0.979484\pi$
$174$	3.14870			0.238703
$175$	−0.180695	−	2.36530i	−0.0136593	−	0.178800i
$176$	0.233358			0.0175900
$177$	−3.44149	+	5.96083i	−0.258678	+	0.448044i
$178$	3.29035	+	5.69905i	0.246622	+	0.427162i
$179$	−3.14344	−	5.44459i	−0.234951	−	0.406948i	0.724307	−	0.689478i	$-0.242160\pi$
$179$	−3.14344	−	5.44459i	−0.234951	−	0.406948i	−0.959259	+	0.282530i	$0.908826\pi$
$180$	0.256750	−	0.444704i	0.0191370	−	0.0331463i
$181$	15.1782			1.12819			0.564093	−	0.825711i	$-0.309226\pi$
$181$	15.1782			1.12819			0.564093	+	0.825711i	$0.309226\pi$
$182$	−2.88609	+	1.97383i	−0.213932	+	0.146310i
$183$	8.04617			0.594790
$184$	8.26898	−	14.3223i	0.609597	−	1.05585i
$185$	−5.36247	−	9.28807i	−0.394256	−	0.682872i
$186$	−2.09814	−	3.63408i	−0.153843	−	0.266464i
$187$	−0.205749	+	0.356368i	−0.0150459	+	0.0260602i
$188$	1.02958			0.0750900
$189$	2.38540	+	1.14450i	0.173512	+	0.0832501i
$190$	−14.3148			−1.03851
$191$	10.4729	−	18.1396i	0.757794	−	1.31254i	−0.186179	−	0.982516i	$-0.559611\pi$
$191$	10.4729	−	18.1396i	0.757794	−	1.31254i	0.943973	−	0.330022i	$-0.107056\pi$
$192$	4.37033	+	7.56963i	0.315401	+	0.546291i
$193$	−1.61417	−	2.79582i	−0.116190	−	0.201248i	0.802065	−	0.597237i	$-0.203735\pi$
$193$	−1.61417	−	2.79582i	−0.116190	−	0.201248i	−0.918255	+	0.395990i	$0.870402\pi$
$194$	3.36799	−	5.83353i	0.241808	−	0.418823i
$195$	2.02568			0.145062
$196$	−0.643503	+	1.65367i	−0.0459645	+	0.118119i
$197$	−11.2173			−0.799199			−0.399599	−	0.916690i	$-0.630851\pi$
$197$	−11.2173			−0.799199			−0.399599	+	0.916690i	$0.630851\pi$
$198$	0.0449720	−	0.0778938i	0.00319602	−	0.00553567i
$199$	−7.68057	−	13.3031i	−0.544461	−	0.943034i	−0.998641	−	0.0521242i	$-0.983401\pi$
$199$	−7.68057	−	13.3031i	−0.544461	−	0.943034i	0.454179	−	0.890910i	$-0.349932\pi$
$200$	−1.33509	−	2.31245i	−0.0944054	−	0.163515i
$201$	−2.33370	+	4.04209i	−0.164606	+	0.285107i
$202$	25.3112			1.78089
$203$	5.68339	+	2.72686i	0.398896	+	0.191388i
$204$	−1.53267			−0.107309
$205$	2.39955	−	4.15614i	0.167592	−	0.290277i
$206$	10.9688	+	18.9985i	0.764233	+	1.32369i
$207$	−2.77658	−	4.80918i	−0.192986	−	0.334261i
$208$	−1.71438	+	2.96939i	−0.118871	+	0.205890i
$209$	0.363929			0.0251735
$210$	−5.84632	+	3.99835i	−0.403434	+	0.275912i
$211$	17.9977			1.23902			0.619508	−	0.784991i	$-0.287332\pi$
$211$	17.9977			1.23902			0.619508	+	0.784991i	$0.287332\pi$
$212$	−1.00887	+	1.74741i	−0.0692894	+	0.120013i
$213$	0.261247	+	0.452493i	0.0179004	+	0.0310043i
$214$	8.52883	+	14.7724i	0.583019	+	1.00982i
$215$	0.105258	−	0.182312i	0.00717853	−	0.0124336i
$216$	2.97812			0.202635
$217$	−0.639919	−	8.37653i	−0.0434406	−	0.568636i
$218$	−26.8465			−1.81827
$219$	−3.43806	+	5.95489i	−0.232322	+	0.402394i
$220$	−0.0174742	−	0.0302662i	−0.00117811	−	0.00204055i
$221$	−3.02309	−	5.23614i	−0.203355	−	0.352221i
$222$	3.49847	−	6.05952i	0.234802	−	0.406689i
$223$	2.97864			0.199465			0.0997323	−	0.995014i	$-0.468201\pi$
$223$	2.97864			0.199465			0.0997323	+	0.995014i	$0.468201\pi$
$224$	0.287175	+	3.75911i	0.0191877	+	0.251166i
$225$	−0.896603			−0.0597735
$226$	5.54366	−	9.60191i	0.368759	−	0.638709i
$227$	5.92556	+	10.2634i	0.393293	+	0.681204i	0.992882	−	0.119105i	$-0.0380024\pi$
$227$	5.92556	+	10.2634i	0.393293	+	0.681204i	−0.599588	+	0.800309i	$0.704669\pi$
$228$	0.677749	+	1.17390i	0.0448850	+	0.0777431i
$229$	−3.22309	+	5.58255i	−0.212988	+	0.368905i	−0.952648	−	0.304075i	$-0.901653\pi$
$229$	−3.22309	+	5.58255i	−0.212988	+	0.368905i	0.739661	+	0.672980i	$0.234986\pi$
$230$	14.8661			0.980242
$231$	0.148632	−	0.101651i	0.00977928	−	0.00668814i
$232$	7.09559			0.465848
$233$	−3.57765	+	6.19666i	−0.234379	+	0.405957i	−0.959092	−	0.283094i	$-0.908639\pi$
$233$	−3.57765	+	6.19666i	−0.234379	+	0.405957i	0.724713	+	0.689051i	$0.241972\pi$
$234$	0.660777	+	1.14450i	0.0431963	+	0.0748183i
$235$	4.11371	+	7.12515i	0.268349	+	0.464794i
$236$	−0.872400	+	1.51104i	−0.0567884	+	0.0983604i
$237$	−11.7336			−0.762180
$238$	19.0602	+	9.14495i	1.23549	+	0.592779i
$239$	0.280704			0.0181573			0.00907863	−	0.999959i	$-0.497110\pi$
$239$	0.280704			0.0181573			0.00907863	+	0.999959i	$0.497110\pi$
$240$	−3.47278	+	6.01504i	−0.224167	+	0.388269i
$241$	−3.65975	−	6.33887i	−0.235745	−	0.408323i	0.723744	−	0.690069i	$-0.242420\pi$
$241$	−3.65975	−	6.33887i	−0.235745	−	0.408323i	−0.959489	+	0.281746i	$0.909086\pi$
$242$	7.26549	+	12.5842i	0.467043	+	0.808943i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.03966			0.130576
$245$	−14.0152	+	2.15394i	−0.895401	+	0.137610i
$246$	3.13092			0.199620
$247$	−2.67362	+	4.63084i	−0.170118	+	0.294654i
$248$	−4.72814	−	8.18938i	−0.300237	−	0.520026i
$249$	6.41038	+	11.1031i	0.406242	+	0.703631i
$250$	7.89275	−	13.6707i	0.499182	−	0.864608i
$251$	0.159014			0.0100369			0.00501843	−	0.999987i	$-0.498403\pi$
$251$	0.159014			0.0100369			0.00501843	+	0.999987i	$0.498403\pi$
$252$	0.604686	+	0.290125i	0.0380916	+	0.0182761i
$253$	−0.377944			−0.0237611
$254$	6.64417	−	11.5080i	0.416892	−	0.722079i
$255$	−6.12382	−	10.6068i	−0.383489	−	0.664222i
$256$	2.99100	+	5.18057i	0.186938	+	0.323786i
$257$	1.46621	−	2.53955i	0.0914598	−	0.158413i	−0.816666	−	0.577111i	$-0.804180\pi$
$257$	1.46621	−	2.53955i	0.0914598	−	0.158413i	0.908126	+	0.418698i	$0.137513\pi$
$258$	0.137340			0.00855043
$259$	11.5624	−	7.90764i	0.718454	−	0.491357i
$260$	0.513501			0.0318459
$261$	1.19129	−	2.06337i	0.0737389	−	0.127719i
$262$	4.77949	+	8.27832i	0.295278	+	0.511436i
$263$	2.82887	+	4.89975i	0.174436	+	0.302132i	0.939966	−	0.341268i	$-0.110857\pi$
$263$	2.82887	+	4.89975i	0.174436	+	0.302132i	−0.765530	+	0.643400i	$0.777523\pi$
$264$	0.101344	−	0.175533i	0.00623730	−	0.0108033i
$265$	−16.1238			−0.990477
$266$	−1.42417	−	18.6423i	−0.0873213	−	1.14303i
$267$	4.97951			0.304741
$268$	−0.591581	+	1.02465i	−0.0361365	+	0.0625903i
$269$	14.4515	+	25.0307i	0.881123	+	1.52615i	0.850094	+	0.526631i	$0.176545\pi$
$269$	14.4515	+	25.0307i	0.881123	+	1.52615i	0.0310290	+	0.999518i	$0.490122\pi$
$270$	1.33853	+	2.31839i	0.0814601	+	0.141093i
$271$	7.17368	−	12.4252i	0.435770	−	0.754776i	−0.561588	−	0.827417i	$-0.689809\pi$
$271$	7.17368	−	12.4252i	0.435770	−	0.754776i	0.997358	+	0.0726408i	$0.0231427\pi$
$272$	20.7308			1.25699
$273$	0.201533	+	2.63806i	0.0121973	+	0.159663i
$274$	27.2757			1.64779
$275$	−0.0305111	+	0.0528467i	−0.00183989	+	0.00318678i
$276$	−0.703849	−	1.21910i	−0.0423667	−	0.0733814i
$277$	−7.79055	−	13.4936i	−0.468089	−	0.810754i	0.531246	−	0.847218i	$-0.321724\pi$
$277$	−7.79055	−	13.4936i	−0.468089	−	0.810754i	−0.999335	+	0.0364636i	$0.988391\pi$
$278$	−10.1046	+	17.5018i	−0.606036	+	1.04969i
$279$	−3.17526			−0.190098
$280$	−13.1746	+	9.01026i	−0.787336	+	0.538466i
$281$	−11.6351			−0.694093			−0.347047	−	0.937848i	$-0.612815\pi$
$281$	−11.6351			−0.694093			−0.347047	+	0.937848i	$0.612815\pi$
$282$	−2.68378	+	4.64844i	−0.159817	+	0.276811i
$283$	−14.9871	−	25.9584i	−0.890890	−	1.54307i	−0.838810	−	0.544424i	$-0.816748\pi$
$283$	−14.9871	−	25.9584i	−0.890890	−	1.54307i	−0.0520799	−	0.998643i	$-0.516585\pi$
$284$	0.0662248	+	0.114705i	0.00392972	+	0.00680647i
$285$	−5.41591	+	9.38063i	−0.320811	+	0.555660i
$286$	0.0899440			0.00531850
$287$	5.65130	+	2.71146i	0.333586	+	0.160052i
$288$	1.42495			0.0839660
$289$	−9.77811	+	16.9362i	−0.575183	+	0.996246i
$290$	3.18914	+	5.52375i	0.187273	+	0.324366i
$291$	−2.54851	−	4.41415i	−0.149396	−	0.258762i
$292$	−0.871530	+	1.50953i	−0.0510024	+	0.0883388i
$293$	3.83767			0.224199			0.112100	−	0.993697i	$-0.464242\pi$
$293$	3.83767			0.224199			0.112100	+	0.993697i	$0.464242\pi$
$294$	−5.78873	−	7.21591i	−0.337605	−	0.420841i
$295$	−13.9427			−0.811778
$296$	7.88378	−	13.6551i	0.458235	−	0.793687i
$297$	−0.0340296	−	0.0589410i	−0.00197460	−	0.00342011i
$298$	−5.73825	−	9.93893i	−0.332408	−	0.575747i
$299$	2.77658	−	4.80918i	0.160574	−	0.278122i
$300$	−0.227284			−0.0131223
$301$	0.247898	+	0.118940i	0.0142886	+	0.00685560i
$302$	17.8825			1.02902
$303$	9.57632	−	16.5867i	0.550145	−	0.952879i
$304$	−9.16717	−	15.8780i	−0.525773	−	0.910666i
$305$	8.14950	+	14.1154i	0.466639	+	0.808243i
$306$	3.99517	−	6.91984i	0.228389	−	0.395581i
$307$	0.566409			0.0323266			0.0161633	−	0.999869i	$-0.494855\pi$
$307$	0.566409			0.0323266			0.0161633	+	0.999869i	$0.494855\pi$
$308$	0.0376775	−	0.0257680i	0.00214687	−	0.00146827i
$309$	16.5999			0.944333
$310$	4.25016	−	7.36150i	0.241393	−	0.418105i
$311$	−10.1522	−	17.5842i	−0.575680	−	0.997106i	−0.995967	−	0.0897156i	$-0.971404\pi$
$311$	−10.1522	−	17.5842i	−0.575680	−	0.997106i	0.420288	−	0.907391i	$-0.361929\pi$
$312$	1.48906	+	2.57912i	0.0843013	+	0.146014i
$313$	−6.42436	+	11.1273i	−0.363126	+	0.628953i	−0.988474	−	0.151393i	$-0.951624\pi$
$313$	−6.42436	+	11.1273i	−0.363126	+	0.628953i	0.625347	+	0.780346i	$0.284957\pi$
$314$	−27.6310			−1.55930
$315$	0.408243	+	5.34389i	0.0230019	+	0.301094i
$316$	−2.97441			−0.167324
$317$	16.6311	−	28.8059i	0.934094	−	1.61790i	0.157853	−	0.987463i	$-0.449543\pi$
$317$	16.6311	−	28.8059i	0.934094	−	1.61790i	0.776241	−	0.630436i	$-0.217124\pi$
$318$	−5.25957	−	9.10985i	−0.294942	−	0.510855i
$319$	−0.0810782	−	0.140431i	−0.00453951	−	0.00786265i
$320$	−8.85290	+	15.3337i	−0.494892	+	0.857178i
$321$	12.9073			0.720413
$322$	1.47901	+	19.3602i	0.0824222	+	1.07890i
$323$	32.3303			1.79891
$324$	0.126747	−	0.219533i	0.00704152	−	0.0121963i
$325$	−0.448301	−	0.776481i	−0.0248673	−	0.0430714i
$326$	−15.1096	−	26.1706i	−0.836845	−	1.44946i
$327$	−10.1572	+	17.5927i	−0.561692	+	0.972879i
$328$	7.05552			0.389576
$329$	−8.86987	+	6.06619i	−0.489012	+	0.334440i
$330$	0.182198			0.0100297
$331$	−14.8151	+	25.6605i	−0.814312	+	1.41043i	0.0955088	+	0.995429i	$0.469552\pi$
$331$	−14.8151	+	25.6605i	−0.814312	+	1.41043i	−0.909821	+	0.415001i	$0.863781\pi$
$332$	1.62500	+	2.81458i	0.0891834	+	0.154470i
$333$	−2.64724	−	4.58515i	−0.145068	−	0.251265i
$334$	−8.39275	+	14.5367i	−0.459231	+	0.795412i
$335$	−9.45467			−0.516564
$336$	−8.17893	−	3.92420i	−0.446197	−	0.214083i
$337$	23.6462			1.28809			0.644044	−	0.764988i	$-0.277255\pi$
$337$	23.6462			1.28809			0.644044	+	0.764988i	$0.277255\pi$
$338$	−0.660777	+	1.14450i	−0.0359415	+	0.0622526i
$339$	−4.19481	−	7.26562i	−0.227831	−	0.394614i
$340$	−1.55236	−	2.68876i	−0.0841884	−	0.145819i
$341$	−0.108053	+	0.187153i	−0.00585138	+	0.0101349i
$342$	−7.06666			−0.382121
$343$	−4.19946	−	18.0379i	−0.226749	−	0.973953i
$344$	0.309496			0.0166869
$345$	5.62448	−	9.74188i	0.302812	−	0.524485i
$346$	−9.64269	−	16.7016i	−0.518394	−	0.897885i
$347$	1.00326	+	1.73769i	0.0538576	+	0.0932841i	0.891697	−	0.452632i	$-0.149515\pi$
$347$	1.00326	+	1.73769i	0.0538576	+	0.0932841i	−0.837840	+	0.545916i	$0.816182\pi$
$348$	0.301985	−	0.523054i	0.0161881	−	0.0280386i
$349$	−26.7671			−1.43281			−0.716406	−	0.697684i	$-0.754214\pi$
$349$	−26.7671			−1.43281			−0.716406	+	0.697684i	$0.754214\pi$
$350$	2.82648	+	1.35613i	0.151082	+	0.0724881i
$351$	1.00000			0.0533761
$352$	0.0484905	−	0.0839881i	0.00258455	−	0.00447658i
$353$	6.89228	+	11.9378i	0.366839	+	0.635384i	0.989069	−	0.147450i	$-0.0471066\pi$
$353$	6.89228	+	11.9378i	0.366839	+	0.635384i	−0.622230	+	0.782834i	$0.713773\pi$
$354$	−4.54811	−	7.87756i	−0.241729	−	0.418688i
$355$	−0.529204	+	0.916609i	−0.0280872	+	0.0486485i
$356$	1.26228			0.0669007
$357$	13.2040	−	9.03036i	0.698831	−	0.477937i
$358$	8.30844			0.439115
$359$	0.198871	−	0.344454i	0.0104960	−	0.0181796i	−0.860730	−	0.509062i	$-0.829992\pi$
$359$	0.198871	−	0.344454i	0.0104960	−	0.0181796i	0.871226	+	0.490883i	$0.163326\pi$
$360$	3.01636	+	5.22449i	0.158976	+	0.275355i
$361$	−4.79648	−	8.30775i	−0.252446	−	0.437250i
$362$	−10.0294	+	17.3714i	−0.527133	+	0.913022i
$363$	10.9954			0.577107
$364$	0.0510876	+	0.668736i	0.00267772	+	0.0350513i
$365$	−13.9288			−0.729068
$366$	−5.31673	+	9.20884i	−0.277910	+	0.481354i
$367$	−8.37214	−	14.5010i	−0.437022	−	0.756944i	0.560436	−	0.828198i	$-0.310634\pi$
$367$	−8.37214	−	14.5010i	−0.437022	−	0.756944i	−0.997458	+	0.0712531i	$0.977300\pi$
$368$	9.52021	+	16.4895i	0.496275	+	0.859574i
$369$	1.18456	−	2.05172i	0.0616658	−	0.106808i
$370$	14.1736			0.736849
$371$	−1.60414	−	20.9981i	−0.0832827	−	1.09017i
$372$	−0.804911			−0.0417327
$373$	−5.21292	+	9.02903i	−0.269915	+	0.467506i	−0.968840	−	0.247689i	$-0.920329\pi$
$373$	−5.21292	+	9.02903i	−0.269915	+	0.467506i	0.698925	+	0.715195i	$0.253662\pi$
$374$	−0.271908	−	0.470959i	−0.0140601	−	0.0243527i
$375$	−5.97233	−	10.3444i	−0.308410	−	0.534181i
$376$	−6.04788	+	10.4752i	−0.311896	+	0.540219i
$377$	2.38258			0.122709
$378$	−2.88609	+	1.97383i	−0.148445	+	0.101523i
$379$	25.6729			1.31873			0.659365	−	0.751823i	$-0.270825\pi$
$379$	25.6729			1.31873			0.659365	+	0.751823i	$0.270825\pi$
$380$	−1.37290	+	2.37794i	−0.0704285	+	0.121986i
$381$	−5.02755	−	8.70796i	−0.257569	−	0.446122i
$382$	13.8405	+	23.9725i	0.708143	+	1.22654i
$383$	−3.40247	+	5.89326i	−0.173858	+	0.301131i	−0.939766	−	0.341820i	$-0.888957\pi$
$383$	−3.40247	+	5.89326i	−0.173858	+	0.301131i	0.765907	+	0.642951i	$0.222290\pi$
$384$	−8.70134			−0.444038
$385$	0.328866	+	0.157788i	0.0167606	+	0.00804163i
$386$	4.26642			0.217155
$387$	0.0519616	−	0.0900002i	0.00264136	−	0.00457497i
$388$	−0.646034	−	1.11896i	−0.0327974	−	0.0568068i
$389$	18.3785	+	31.8325i	0.931827	+	1.61397i	0.780197	+	0.625534i	$0.215119\pi$
$389$	18.3785	+	31.8325i	0.931827	+	1.61397i	0.151630	+	0.988437i	$0.451548\pi$
$390$	−1.33853	+	2.31839i	−0.0677789	+	0.117396i
$391$	−33.5754			−1.69798
$392$	−13.0449	−	16.2610i	−0.658865	−	0.821306i
$393$	7.23314			0.364863
$394$	7.41213	−	12.8382i	0.373418	−	0.646778i
$395$	−11.8843	−	20.5842i	−0.597964	−	1.03570i
$396$	−0.00862633	−	0.0149412i	−0.000433490	−	0.000750826i
$397$	−11.3499	+	19.6586i	−0.569635	+	0.986637i	0.426967	+	0.904267i	$0.359582\pi$
$397$	−11.3499	+	19.6586i	−0.569635	+	0.986637i	−0.996602	+	0.0823697i	$0.973751\pi$
$398$	20.3006			1.01758
$399$	−12.7553	−	6.11991i	−0.638563	−	0.306379i
$400$	3.07423			0.153711
$401$	−8.73572	+	15.1307i	−0.436241	+	0.755592i	−0.997396	−	0.0721191i	$-0.977024\pi$
$401$	−8.73572	+	15.1307i	−0.436241	+	0.755592i	0.561155	+	0.827711i	$0.310357\pi$
$402$	−3.08411	−	5.34183i	−0.153821	−	0.266426i
$403$	−1.58763	−	2.74985i	−0.0790854	−	0.136980i
$404$	2.42755	−	4.20463i	0.120775	−	0.209188i
$405$	2.02568			0.100657
$406$	−6.87634	+	4.70279i	−0.341267	+	0.233396i
$407$	−0.360338			−0.0178613
$408$	9.00310	−	15.5938i	0.445720	−	0.772010i
$409$	15.2027	+	26.3319i	0.751726	+	1.30203i	0.946986	+	0.321276i	$0.104112\pi$
$409$	15.2027	+	26.3319i	0.751726	+	1.30203i	−0.195260	+	0.980752i	$0.562555\pi$
$410$	3.17113	+	5.49256i	0.156611	+	0.271258i
$411$	10.3196	−	17.8740i	0.509027	−	0.881660i
$412$	4.20798			0.207312
$413$	−1.38715	−	18.1577i	−0.0682571	−	0.893484i
$414$	7.33881			0.360683
$415$	−12.9854	+	22.4914i	−0.637429	+	1.10406i
$416$	0.712476	+	1.23404i	0.0349320	+	0.0605040i
$417$	7.64603	+	13.2433i	0.374428	+	0.648528i
$418$	−0.240476	+	0.416516i	−0.0117621	+	0.0203725i
$419$	−26.1442			−1.27723			−0.638615	−	0.769526i	$-0.720492\pi$
$419$	−26.1442			−1.27723			−0.638615	+	0.769526i	$0.720492\pi$
$420$	0.103487	+	1.35465i	0.00504967	+	0.0661000i
$421$	−22.0532			−1.07481			−0.537404	−	0.843325i	$-0.680595\pi$
$421$	−22.0532			−1.07481			−0.537404	+	0.843325i	$0.680595\pi$
$422$	−11.8925	+	20.5984i	−0.578917	+	1.00271i
$423$	2.03077	+	3.51740i	0.0987396	+	0.171022i
$424$	−11.8524	−	20.5290i	−0.575604	−	0.996976i
$425$	−2.71051	+	4.69474i	−0.131479	+	0.227728i
$426$	−0.690504			−0.0334550
$427$	−17.5718	+	12.0175i	−0.850357	+	0.581567i
$428$	3.27193			0.158154
$429$	0.0340296	−	0.0589410i	0.00164297	−	0.00284570i
$430$	0.139104	+	0.240935i	0.00670819	+	0.0116189i
$431$	11.9912	+	20.7694i	0.577597	+	1.00043i	0.995754	+	0.0920524i	$0.0293427\pi$
$431$	11.9912	+	20.7694i	0.577597	+	1.00043i	−0.418157	+	0.908375i	$0.637324\pi$
$432$	−1.71438	+	2.96939i	−0.0824829	+	0.142865i
$433$	−21.7131			−1.04347			−0.521733	−	0.853109i	$-0.674714\pi$
$433$	−21.7131			−1.04347			−0.521733	+	0.853109i	$0.674714\pi$
$434$	10.0098	+	4.80263i	0.480485	+	0.230534i
$435$	4.82635			0.231406
$436$	−2.57479	+	4.45966i	−0.123310	+	0.213579i
$437$	14.8470	+	25.7158i	0.710231	+	1.23016i
$438$	−4.54358	−	7.86971i	−0.217101	−	0.376029i
$439$	−4.56494	+	7.90671i	−0.217873	+	0.377367i	−0.954157	−	0.299305i	$-0.903245\pi$
$439$	−4.56494	+	7.90671i	−0.217873	+	0.377367i	0.736285	+	0.676672i	$0.236578\pi$
$440$	0.410582			0.0195737
$441$	−6.91877	+	1.06332i	−0.329465	+	0.0506341i
$442$	7.99035			0.380062
$443$	−2.23701	+	3.87461i	−0.106283	+	0.184088i	−0.914262	−	0.405124i	$-0.867228\pi$
$443$	−2.23701	+	3.87461i	−0.106283	+	0.184088i	0.807978	+	0.589212i	$0.200562\pi$
$444$	−0.671061	−	1.16231i	−0.0318471	−	0.0551609i
$445$	5.04346	+	8.73552i	0.239083	+	0.414104i
$446$	−1.96822	+	3.40905i	−0.0931978	+	0.161423i
$447$	−8.68409			−0.410743
$448$	−20.8499	−	10.0037i	−0.985066	−	0.472629i
$449$	−18.9055			−0.892207			−0.446103	−	0.894981i	$-0.647189\pi$
$449$	−18.9055			−0.892207			−0.446103	+	0.894981i	$0.647189\pi$
$450$	0.592455	−	1.02616i	0.0279286	−	0.0483737i
$451$	−0.0806204	−	0.139639i	−0.00379626	−	0.00657532i
$452$	−1.06336	−	1.84180i	−0.0500163	−	0.0866308i
$453$	6.76571	−	11.7185i	0.317881	−	0.550585i
$454$	−15.6619			−0.735049
$455$	−4.42382	+	3.02549i	−0.207392	+	0.141837i
$456$	−15.9247			−0.745742
$457$	12.9644	−	22.4550i	0.606449	−	1.05040i	−0.385371	−	0.922762i	$-0.625927\pi$
$457$	12.9644	−	22.4550i	0.606449	−	1.05040i	0.991821	−	0.127639i	$-0.0407400\pi$
$458$	−4.25949	−	7.37764i	−0.199033	−	0.344735i
$459$	−3.02309	−	5.23614i	−0.141106	−	0.244402i
$460$	1.42578	−	2.46952i	0.0664772	−	0.115142i
$461$	30.8552			1.43707			0.718535	−	0.695491i	$-0.244813\pi$
$461$	30.8552			1.43707			0.718535	+	0.695491i	$0.244813\pi$
$462$	0.0181267	+	0.237278i	0.000843330	+	0.0110392i
$463$	33.5654			1.55992			0.779958	−	0.625832i	$-0.215240\pi$
$463$	33.5654			1.55992			0.779958	+	0.625832i	$0.215240\pi$
$464$	−4.08463	+	7.07479i	−0.189624	+	0.328439i
$465$	−3.21603	−	5.57033i	−0.149140	−	0.258318i
$466$	−4.72805	−	8.18923i	−0.219023	−	0.379359i
$467$	0.000783656	−	0.00135733i	3.62633e−5	−	6.28099e-5i	−0.866007	−	0.500031i	$-0.833322\pi$
$467$	0.000783656	−	0.00135733i	3.62633e−5	−	6.28099e-5i	0.866044	+	0.499969i	$0.166655\pi$
$468$	0.253495			0.0117178
$469$	−0.940636	−	12.3129i	−0.0434345	−	0.568557i
$470$	−10.8730			−0.501533
$471$	−10.4540	+	18.1068i	−0.481693	+	0.834317i
$472$	−10.2491	−	17.7520i	−0.471755	−	0.817104i
$473$	−0.00353647	−	0.00612535i	−0.000162607	−	0.000281644i
$474$	7.75330	−	13.4291i	0.356121	−	0.616820i
$475$	4.79435			0.219980
$476$	3.34715	−	2.28915i	0.153416	−	0.104923i
$477$	−7.95968			−0.364449
$478$	−0.185483	+	0.321266i	−0.00848380	+	0.0146944i
$479$	5.72799	+	9.92116i	0.261718	+	0.453309i	0.966699	−	0.255917i	$-0.0823775\pi$
$479$	5.72799	+	9.92116i	0.261718	+	0.453309i	−0.704980	+	0.709227i	$0.749044\pi$
$480$	1.44325	+	2.49978i	0.0658751	+	0.114099i
$481$	2.64724	−	4.58515i	0.120704	−	0.209065i
$482$	9.67311			0.440598
$483$	13.2465	+	6.35559i	0.602737	+	0.289189i
$484$	2.78727			0.126694
$485$	5.16247	−	8.94167i	0.234416	−	0.406020i
$486$	0.660777	+	1.14450i	0.0299735	+	0.0519155i
$487$	−7.77754	−	13.4711i	−0.352434	−	0.610434i	0.634241	−	0.773135i	$-0.281313\pi$
$487$	−7.77754	−	13.4711i	−0.352434	−	0.610434i	−0.986675	+	0.162701i	$0.947979\pi$
$488$	−11.9812	+	20.7521i	−0.542364	+	0.939402i
$489$	−22.8665			−1.03406
$490$	6.79577	−	17.4637i	0.307001	−	0.788930i
$491$	27.2263			1.22871			0.614354	−	0.789031i	$-0.289417\pi$
$491$	27.2263			1.22871			0.614354	+	0.789031i	$0.289417\pi$
$492$	0.300280	−	0.520101i	0.0135377	−	0.0234479i
$493$	−7.20274	−	12.4755i	−0.324395	−	0.561868i
$494$	−3.53333	−	6.11991i	−0.158972	−	0.275348i
$495$	0.0689333	−	0.119396i	0.00309832	−	0.00536645i
$496$	10.8872			0.488848
$497$	−1.24636	−	0.597994i	−0.0559067	−	0.0268237i
$498$	−16.9433			−0.759249
$499$	14.5108	−	25.1334i	0.649592	−	1.12513i	−0.333628	−	0.942705i	$-0.608273\pi$
$499$	14.5108	−	25.1334i	0.649592	−	1.12513i	0.983220	−	0.182422i	$-0.0583937\pi$
$500$	−1.51395	−	2.62225i	−0.0677061	−	0.117270i
$501$	6.35067	+	10.9997i	0.283727	+	0.491430i
$502$	−0.105073	+	0.181991i	−0.00468962	+	0.00812266i
$503$	1.79018			0.0798202			0.0399101	−	0.999203i	$-0.487293\pi$
$503$	1.79018			0.0798202			0.0399101	+	0.999203i	$0.487293\pi$
$504$	−6.50380	+	4.44801i	−0.289702	+	0.198130i
$505$	38.7972			1.72645
$506$	0.249737	−	0.432557i	0.0111022	−	0.0192295i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−1.27446	−	2.20742i	−0.0565449	−	0.0979386i
$509$	10.3013	−	17.8424i	0.456598	−	0.790851i	−0.542180	−	0.840262i	$-0.682401\pi$
$509$	10.3013	−	17.8424i	0.456598	−	0.790851i	0.998779	+	0.0494108i	$0.0157343\pi$
$510$	16.1859			0.716725
$511$	−1.38576	−	18.1396i	−0.0613026	−	0.802450i
$512$	−25.3082			−1.11848
$513$	−2.67362	+	4.63084i	−0.118043	+	0.204457i
$514$	1.93768	+	3.35616i	0.0854674	+	0.148034i
$515$	16.8130	+	29.1210i	0.740871	+	1.28323i
$516$	0.0131720	−	0.0228146i	0.000579865	−	0.00100436i
$517$	0.276426			0.0121572
$518$	1.41011	+	18.4584i	0.0619569	+	0.811014i
$519$	−14.5930			−0.640560
$520$	−3.01636	+	5.22449i	−0.132276	+	0.229109i
$521$	−18.2678	−	31.6408i	−0.800327	−	1.38621i	−0.919401	−	0.393321i	$-0.871326\pi$
$521$	−18.2678	−	31.6408i	−0.800327	−	1.38621i	0.119074	−	0.992885i	$-0.462007\pi$
$522$	1.57435	+	2.72686i	0.0689075	+	0.119351i
$523$	5.48336	−	9.49745i	0.239770	−	0.415295i	−0.720878	−	0.693062i	$-0.756261\pi$
$523$	5.48336	−	9.49745i	0.239770	−	0.415295i	0.960648	+	0.277767i	$0.0895945\pi$
$524$	1.83356			0.0800995
$525$	1.95806	−	1.33913i	0.0854567	−	0.0584446i
$526$	−7.47702			−0.326014
$527$	−9.59908	+	16.6261i	−0.418142	+	0.724244i
$528$	0.116679	+	0.202094i	0.00507781	+	0.00879502i
$529$	−3.91882	−	6.78759i	−0.170383	−	0.295113i
$530$	10.6542	−	18.4537i	0.462790	−	0.801576i
$531$	−6.88298			−0.298696
$532$	−3.23340	−	1.55137i	−0.140186	−	0.0672602i
$533$	2.36912			0.102618
$534$	−3.29035	+	5.69905i	−0.142387	+	0.246622i
$535$	13.0730	+	22.6431i	0.565196	+	0.978948i
$536$	−6.95002	−	12.0378i	−0.300195	−	0.519954i
$537$	3.14344	−	5.44459i	0.135649	−	0.234951i
$538$	−38.1969			−1.64678
$539$	−0.172770	+	0.443984i	−0.00744174	+	0.0191237i
$540$	0.513501			0.0220975
$541$	3.16154	−	5.47595i	0.135925	−	0.235429i	−0.790025	−	0.613074i	$-0.789933\pi$
$541$	3.16154	−	5.47595i	0.135925	−	0.235429i	0.925951	+	0.377645i	$0.123266\pi$
$542$	9.48041	+	16.4206i	0.407219	+	0.705323i
$543$	7.58909	+	13.1447i	0.325679	+	0.564093i
$544$	4.30775	−	7.46124i	0.184693	−	0.319898i
$545$	−41.1504			−1.76269
$546$	−3.15243	−	1.51252i	−0.134912	−	0.0647298i
$547$	−9.45925			−0.404448			−0.202224	−	0.979339i	$-0.564817\pi$
$547$	−9.45925			−0.404448			−0.202224	+	0.979339i	$0.564817\pi$
$548$	2.61596	−	4.53097i	0.111748	−	0.193553i
$549$	4.02309	+	6.96819i	0.171701	+	0.297395i
$550$	−0.0403220	−	0.0698398i	−0.00171934	−	0.00297798i
$551$	−6.37010	+	11.0333i	−0.271375	+	0.470036i
$552$	16.5380			0.703902
$553$	25.6246	−	17.5249i	1.08967	−	0.745235i
$554$	20.5913			0.874840
$555$	5.36247	−	9.28807i	0.227624	−	0.394256i
$556$	1.93823	+	3.35711i	0.0821993	+	0.142373i
$557$	9.45981	+	16.3849i	0.400825	+	0.694250i	0.993826	−	0.110952i	$-0.0353901\pi$
$557$	9.45981	+	16.3849i	0.400825	+	0.694250i	−0.593001	+	0.805202i	$0.702057\pi$
$558$	2.09814	−	3.63408i	0.0888212	−	0.153843i
$559$	0.103923			0.00439549
$560$	−1.39976	−	18.3229i	−0.0591507	−	0.774282i
$561$	−0.411498			−0.0173735
$562$	7.68822	−	13.3164i	0.324308	−	0.561718i
$563$	8.02802	+	13.9049i	0.338341	+	0.586023i	0.984121	−	0.177500i	$-0.0568011\pi$
$563$	8.02802	+	13.9049i	0.338341	+	0.586023i	−0.645780	+	0.763523i	$0.723468\pi$
$564$	0.514791	+	0.891644i	0.0216766	+	0.0375450i
$565$	8.49735	−	14.7178i	0.357486	−	0.619185i
$566$	39.6125			1.66504
$567$	0.201533	+	2.63806i	0.00846360	+	0.110788i
$568$	−1.55605			−0.0652903
$569$	9.94178	−	17.2197i	0.416781	−	0.721886i	−0.578833	−	0.815446i	$-0.696492\pi$
$569$	9.94178	−	17.2197i	0.416781	−	0.721886i	0.995614	+	0.0935605i	$0.0298249\pi$
$570$	−7.15742	−	12.3970i	−0.299791	−	0.519254i
$571$	1.47226	+	2.55003i	0.0616123	+	0.106716i	0.895186	−	0.445692i	$-0.147042\pi$
$571$	1.47226	+	2.55003i	0.0616123	+	0.106716i	−0.833574	+	0.552408i	$0.813709\pi$
$572$	0.00862633	−	0.0149412i	0.000360685	−	0.000624725i
$573$	20.9458			0.875025
$574$	−6.83751	+	4.67624i	−0.285392	+	0.195182i
$575$	−4.97898			−0.207638
$576$	−4.37033	+	7.56963i	−0.182097	+	0.315401i
$577$	14.0130	+	24.2712i	0.583367	+	1.01042i	0.995077	+	0.0991065i	$0.0315985\pi$
$577$	14.0130	+	24.2712i	0.583367	+	1.01042i	−0.411710	+	0.911315i	$0.635068\pi$
$578$	−12.9223	−	22.3821i	−0.537497	−	0.930972i
$579$	1.61417	−	2.79582i	0.0670825	−	0.116190i
$580$	1.22345			0.0508012
$581$	−30.5826	−	14.6734i	−1.26878	−	0.608754i
$582$	6.73598			0.279215
$583$	−0.270865	+	0.469152i	−0.0112181	+	0.0194303i
$584$	−10.2389	−	17.7343i	−0.423690	−	0.733852i
$585$	1.01284	+	1.75429i	0.0418759	+	0.0725311i
$586$	−2.53584	+	4.39221i	−0.104755	+	0.181441i
$587$	20.3286			0.839051			0.419525	−	0.907744i	$-0.362197\pi$
$587$	20.3286			0.839051			0.419525	+	0.907744i	$0.362197\pi$
$588$	−1.75387	+	0.269545i	−0.0723285	+	0.0111158i
$589$	16.9789			0.699601
$590$	9.21304	−	15.9575i	0.379295	−	0.656958i
$591$	−5.60864	−	9.71446i	−0.230709	−	0.399599i
$592$	9.07672	+	15.7213i	0.373051	+	0.646143i
$593$	−1.48961	+	2.58008i	−0.0611710	+	0.105951i	−0.894989	−	0.446088i	$-0.852817\pi$
$593$	−1.48961	+	2.58008i	−0.0611710	+	0.105951i	0.833818	+	0.552039i	$0.186150\pi$
$594$	0.0899440			0.00369045
$595$	29.2155	+	14.0174i	1.19772	+	0.574658i
$596$	−2.20137			−0.0901717
$597$	7.68057	−	13.3031i	0.314345	−	0.544461i
$598$	3.66940	+	6.35559i	0.150053	+	0.259900i
$599$	21.8949	+	37.9230i	0.894600	+	1.54949i	0.834299	+	0.551312i	$0.185873\pi$
$599$	21.8949	+	37.9230i	0.894600	+	1.54949i	0.0603006	+	0.998180i	$0.480794\pi$
$600$	1.33509	−	2.31245i	0.0545050	−	0.0944054i
$601$	30.8592			1.25877			0.629387	−	0.777092i	$-0.283306\pi$
$601$	30.8592			1.25877			0.629387	+	0.777092i	$0.283306\pi$
$602$	−0.299932	+	0.205127i	−0.0122243	+	0.00836034i
$603$	−4.66740			−0.190071
$604$	1.71507	−	2.97059i	0.0697853	−	0.120872i
$605$	11.1366	+	19.2891i	0.452766	+	0.784214i
$606$	12.6556	+	21.9202i	0.514099	+	0.890446i
$607$	−4.48448	+	7.76734i	−0.182019	+	0.315267i	−0.942568	−	0.334014i	$-0.891597\pi$
$607$	−4.48448	+	7.76734i	−0.182019	+	0.315267i	0.760549	+	0.649281i	$0.224930\pi$
$608$	−7.61955			−0.309014
$609$	0.480168	+	6.28539i	0.0194574	+	0.254697i
$610$	−21.5400			−0.872130
$611$	−2.03077	+	3.51740i	−0.0821563	+	0.142299i
$612$	−0.766337	−	1.32733i	−0.0309773	−	0.0536543i
$613$	−10.8671	−	18.8223i	−0.438916	−	0.760225i	0.558690	−	0.829377i	$-0.311304\pi$
$613$	−10.8671	−	18.8223i	−0.438916	−	0.760225i	−0.997606	+	0.0691515i	$0.977971\pi$
$614$	−0.374270	+	0.648254i	−0.0151043	+	0.0261614i
$615$	4.79910			0.193518
$616$	0.0408484	+	0.534705i	0.00164583	+	0.0215439i
$617$	16.2684			0.654941			0.327471	−	0.944861i	$-0.393804\pi$
$617$	16.2684			0.654941			0.327471	+	0.944861i	$0.393804\pi$
$618$	−10.9688	+	18.9985i	−0.441230	+	0.764233i
$619$	21.4463	+	37.1461i	0.862000	+	1.49303i	0.869995	+	0.493060i	$0.164122\pi$
$619$	21.4463	+	37.1461i	0.862000	+	1.49303i	−0.00799528	+	0.999968i	$0.502545\pi$
$620$	−0.815248	−	1.41205i	−0.0327411	−	0.0567093i
$621$	2.77658	−	4.80918i	0.111420	−	0.192986i
$622$	26.8334			1.07592
$623$	−10.8746	+	7.43722i	−0.435681	+	0.297966i
$624$	−3.42875			−0.137260
$625$	9.85654	−	17.0720i	0.394262	−	0.682881i
$626$	−8.49014	−	14.7053i	−0.339334	−	0.587744i
$627$	0.181964	+	0.315172i	0.00726696	+	0.0125867i
$628$	−2.65003	+	4.58998i	−0.105748	+	0.183160i
$629$	−32.0113			−1.27637
$630$	−6.38583	−	3.06388i	−0.254418	−	0.122068i
$631$	−29.3809			−1.16963			−0.584817	−	0.811165i	$-0.698834\pi$
$631$	−29.3809			−1.16963			−0.584817	+	0.811165i	$0.698834\pi$
$632$	17.4720	−	30.2624i	0.695000	−	1.20378i
$633$	8.99887	+	15.5865i	0.357673	+	0.619508i
$634$	21.9789	+	38.0685i	0.872892	+	1.51189i
$635$	10.1842	−	17.6396i	0.404148	−	0.700006i
$636$	−2.01774			−0.0800085
$637$	−4.38024	−	5.46017i	−0.173552	−	0.216340i
$638$	0.214298			0.00848415
$639$	−0.261247	+	0.452493i	−0.0103348	+	0.0179004i
$640$	−8.81309	−	15.2647i	−0.348368	−	0.603391i
$641$	17.2397	+	29.8601i	0.680928	+	1.17940i	0.974698	+	0.223525i	$0.0717565\pi$
$641$	17.2397	+	29.8601i	0.680928	+	1.17940i	−0.293770	+	0.955876i	$0.594910\pi$
$642$	−8.52883	+	14.7724i	−0.336606	+	0.583019i
$643$	13.2947			0.524291			0.262146	−	0.965028i	$-0.415570\pi$
$643$	13.2947			0.524291			0.262146	+	0.965028i	$0.415570\pi$
$644$	3.35792	+	1.61111i	0.132321	+	0.0634866i
$645$	0.210516			0.00828905
$646$	−21.3631	+	37.0021i	−0.840522	+	1.45583i
$647$	−14.8803	−	25.7734i	−0.585003	−	1.01326i	−0.994875	−	0.101112i	$-0.967760\pi$
$647$	−14.8803	−	25.7734i	−0.585003	−	1.01326i	0.409872	−	0.912143i	$-0.365573\pi$
$648$	1.48906	+	2.57912i	0.0584957	+	0.101318i
$649$	−0.234225	+	0.405690i	−0.00919414	+	0.0159247i
$650$	1.18491			0.0464760
$651$	6.93433	−	4.74245i	0.271778	−	0.185871i
$652$	−5.79653			−0.227010
$653$	6.33274	−	10.9686i	0.247819	−	0.429235i	−0.715101	−	0.699021i	$-0.753619\pi$
$653$	6.33274	−	10.9686i	0.247819	−	0.429235i	0.962920	+	0.269785i	$0.0869528\pi$
$654$	−13.4232	−	23.2497i	−0.524890	−	0.909136i
$655$	7.32602	+	12.6890i	0.286251	+	0.495802i
$656$	−4.06157	+	7.03484i	−0.158578	+	0.274664i
$657$	−6.87611			−0.268263
$658$	−1.08174	−	14.1600i	−0.0421706	−	0.552013i
$659$	−40.5989			−1.58151			−0.790755	−	0.612133i	$-0.790312\pi$
$659$	−40.5989			−1.58151			−0.790755	+	0.612133i	$0.790312\pi$
$660$	0.0174742	−	0.0302662i	0.000680183	−	0.00117811i
$661$	−1.54989	−	2.68449i	−0.0602838	−	0.104415i	0.834308	−	0.551298i	$-0.185867\pi$
$661$	−1.54989	−	2.68449i	−0.0602838	−	0.104415i	−0.894592	+	0.446883i	$0.852534\pi$
$662$	−19.5790	−	33.9118i	−0.760958	−	1.31802i
$663$	3.02309	−	5.23614i	0.117407	−	0.203355i
$664$	−38.1817			−1.48174
$665$	−2.18297	−	28.5750i	−0.0846520	−	1.10809i
$666$	6.99694			0.271126
$667$	6.61542	−	11.4582i	0.256150	−	0.443665i
$668$	1.60986	+	2.78836i	0.0622874	+	0.107885i
$669$	1.48932	+	2.57958i	0.0575805	+	0.0997323i
$670$	6.24743	−	10.8209i	0.241359	−	0.418047i
$671$	0.547617			0.0211405
$672$	−3.11190	+	2.12826i	−0.120044	+	0.0820993i
$673$	33.8836			1.30612			0.653058	−	0.757308i	$-0.273486\pi$
$673$	33.8836			1.30612			0.653058	+	0.757308i	$0.273486\pi$
$674$	−15.6248	+	27.0630i	−0.601847	+	1.04243i
$675$	−0.448301	−	0.776481i	−0.0172551	−	0.0298868i
$676$	0.126747	+	0.219533i	0.00487490	+	0.00844358i
$677$	−13.6504	+	23.6431i	−0.524627	+	0.908680i	0.474962	+	0.880006i	$0.342462\pi$
$677$	−13.6504	+	23.6431i	−0.524627	+	0.908680i	−0.999589	+	0.0286738i	$0.990872\pi$
$678$	11.0873			0.425806
$679$	12.1584	+	5.83353i	0.466597	+	0.223870i
$680$	36.4749			1.39875
$681$	−5.92556	+	10.2634i	−0.227068	+	0.393293i
$682$	−0.142798	−	0.247333i	−0.00546800	−	0.00947086i
$683$	4.82769	+	8.36180i	0.184726	+	0.319955i	0.943484	−	0.331417i	$-0.107527\pi$
$683$	4.82769	+	8.36180i	0.184726	+	0.319955i	−0.758758	+	0.651373i	$0.774193\pi$
$684$	−0.677749	+	1.17390i	−0.0259144	+	0.0448850i
$685$	41.8084			1.59742
$686$	23.4192	+	7.11273i	0.894150	+	0.271565i
$687$	−6.44618			−0.245937
$688$	−0.178164	+	0.308588i	−0.00679242	+	0.0117648i
$689$	−3.97984	−	6.89328i	−0.151620	−	0.262613i
$690$	7.43305	+	12.8744i	0.282971	+	0.490121i
$691$	−24.4938	+	42.4245i	−0.931788	+	1.61390i	−0.151524	+	0.988454i	$0.548418\pi$
$691$	−24.4938	+	42.4245i	−0.931788	+	1.61390i	−0.780264	+	0.625450i	$0.784915\pi$
$692$	−3.69924			−0.140624
$693$	0.162348	+	0.0778938i	0.00616710	+	0.00295894i
$694$	−2.65171			−0.100658
$695$	−15.4885	+	26.8268i	−0.587510	+	1.01760i
$696$	3.54779	+	6.14496i	0.134479	+	0.232924i
$697$	−7.16207	−	12.4051i	−0.271283	−	0.469875i
$698$	17.6871	−	30.6350i	0.669467	−	1.15955i
$699$	−7.15529			−0.270638
$700$	0.496358	−	0.339464i	0.0187606	−	0.0128305i
$701$	11.7557			0.444007			0.222004	−	0.975046i	$-0.428740\pi$
$701$	11.7557			0.444007			0.222004	+	0.975046i	$0.428740\pi$
$702$	−0.660777	+	1.14450i	−0.0249394	+	0.0431963i
$703$	14.1554	+	24.5179i	0.533881	+	0.924710i
$704$	0.297441	+	0.515183i	0.0112102	+	0.0194167i
$705$	−4.11371	+	7.12515i	−0.154931	+	0.268349i
$706$	−18.2170			−0.685608
$707$	3.85989	+	50.5259i	0.145166	+	1.90022i
$708$	−1.74480			−0.0655736
$709$	20.3879	−	35.3129i	0.765684	−	1.32620i	−0.174200	−	0.984710i	$-0.555734\pi$
$709$	20.3879	−	35.3129i	0.765684	−	1.32620i	0.939884	−	0.341493i	$-0.110933\pi$
$710$	−0.699372	−	1.21135i	−0.0262470	−	0.0454611i
$711$	−5.86681	−	10.1616i	−0.220022	−	0.381090i
$712$	−7.41478	+	12.8428i	−0.277881	+	0.481303i
$713$	−17.6327			−0.660350
$714$	1.61032	+	21.0790i	0.0602647	+	0.788864i
$715$	0.137867			0.00515592
$716$	0.796845	−	1.38018i	0.0297795	−	0.0515796i
$717$	0.140352	+	0.243097i	0.00524155	+	0.00907863i
$718$	0.262818	+	0.455215i	0.00980830	+	0.0169885i
$719$	7.31366	−	12.6676i	0.272754	−	0.472423i	−0.696812	−	0.717253i	$-0.745399\pi$
$719$	7.31366	−	12.6676i	0.272754	−	0.472423i	0.969566	+	0.244830i	$0.0787323\pi$
$720$	−6.94557			−0.258846
$721$	−36.2519	+	24.7930i	−1.35009	+	0.923339i
$722$	12.6776			0.471812
$723$	3.65975	−	6.33887i	0.136108	−	0.235745i
$724$	1.92380	+	3.33211i	0.0714973	+	0.123837i
$725$	−1.06811	−	1.85003i	−0.0396687	−	0.0687082i
$726$	−7.26549	+	12.5842i	−0.269648	+	0.467043i
$727$	−49.8840			−1.85009			−0.925047	−	0.379852i	$-0.875975\pi$
$727$	−49.8840			−1.85009			−0.925047	+	0.379852i	$0.875975\pi$
$728$	−7.10399	−	3.40845i	−0.263291	−	0.126326i
$729$	1.00000			0.0370370
$730$	9.20385	−	15.9415i	0.340650	−	0.590023i
$731$	−0.314169	−	0.544157i	−0.0116200	−	0.0201264i
$732$	1.01983	+	1.76640i	0.0376941	+	0.0652880i
$733$	3.33680	−	5.77950i	0.123247	−	0.213471i	−0.797799	−	0.602923i	$-0.794002\pi$
$733$	3.33680	−	5.77950i	0.123247	−	0.213471i	0.921046	+	0.389453i	$0.127336\pi$
$734$	22.1285			0.816777
$735$	−8.87299	−	11.0606i	−0.327285	−	0.407976i
$736$	7.91299			0.291677
$737$	−0.158830	+	0.275101i	−0.00585057	+	0.0101335i
$738$	1.56546	+	2.71146i	0.0576255	+	0.0998102i
$739$	−11.2868	−	19.5494i	−0.415193	−	0.719135i	0.580256	−	0.814434i	$-0.302952\pi$
$739$	−11.2868	−	19.5494i	−0.415193	−	0.719135i	−0.995449	+	0.0952994i	$0.969619\pi$
$740$	1.35936	−	2.35448i	0.0499710	−	0.0865523i
$741$	−5.34724			−0.196436
$742$	25.0923	+	12.0392i	0.921169	+	0.441971i
$743$	−22.6974			−0.832686			−0.416343	−	0.909208i	$-0.636688\pi$
$743$	−22.6974			−0.832686			−0.416343	+	0.909208i	$0.636688\pi$
$744$	4.72814	−	8.18938i	0.173342	−	0.300237i
$745$	−8.79561	−	15.2344i	−0.322246	−	0.558147i
$746$	−6.88915	−	11.9324i	−0.252230	−	0.436875i
$747$	−6.41038	+	11.1031i	−0.234544	+	0.406242i
$748$	−0.104313			−0.00381405
$749$	−28.1877	+	19.2778i	−1.02996	+	0.704397i
$750$	15.7855			0.576405
$751$	−15.5491	+	26.9318i	−0.567395	+	0.982756i	0.429428	+	0.903101i	$0.358715\pi$
$751$	−15.5491	+	26.9318i	−0.567395	+	0.982756i	−0.996822	+	0.0796552i	$0.974618\pi$
$752$	−6.96302	−	12.0603i	−0.253915	−	0.439794i
$753$	0.0795069	+	0.137710i	0.00289739	+	0.00501843i
$754$	−1.57435	+	2.72686i	−0.0573345	+	0.0993063i
$755$	27.4104			0.997565
$756$	0.0510876	+	0.668736i	0.00185804	+	0.0243217i
$757$	−16.9262			−0.615192			−0.307596	−	0.951517i	$-0.599525\pi$
$757$	−16.9262			−0.615192			−0.307596	+	0.951517i	$0.599525\pi$
$758$	−16.9641	+	29.3827i	−0.616164	+	1.06723i
$759$	−0.188972	−	0.327309i	−0.00685925	−	0.0118806i
$760$	−16.1292	−	27.9366i	−0.585068	−	1.01337i
$761$	18.2025	−	31.5276i	0.659840	−	1.14288i	−0.320817	−	0.947141i	$-0.603958\pi$
$761$	18.2025	−	31.5276i	0.659840	−	1.14288i	0.980657	−	0.195735i	$-0.0627092\pi$
$762$	13.2883			0.481386
$763$	−4.09401	−	53.5904i	−0.148213	−	1.94010i
$764$	5.30966			0.192097
$765$	6.12382	−	10.6068i	0.221407	−	0.383489i
$766$	−4.49655	−	7.78826i	−0.162467	−	0.281401i
$767$	−3.44149	−	5.96083i	−0.124265	−	0.215233i
$768$	−2.99100	+	5.18057i	−0.107929	+	0.186938i
$769$	−9.82130			−0.354165			−0.177083	−	0.984196i	$-0.556666\pi$
$769$	−9.82130			−0.354165			−0.177083	+	0.984196i	$0.556666\pi$
$770$	−0.397896	+	0.272125i	−0.0143392	+	0.00980669i
$771$	2.93243			0.105609
$772$	0.409183	−	0.708726i	0.0147268	−	0.0255076i
$773$	−4.70186	−	8.14386i	−0.169114	−	0.292914i	0.768994	−	0.639255i	$-0.220757\pi$
$773$	−4.70186	−	8.14386i	−0.169114	−	0.292914i	−0.938109	+	0.346341i	$0.887424\pi$
$774$	0.0686701	+	0.118940i	0.00246830	+	0.00427522i
$775$	−1.42347	+	2.46553i	−0.0511326	+	0.0885643i
$776$	15.1795			0.544912
$777$	12.6294	+	6.05952i	0.453078	+	0.217384i
$778$	−48.5764			−1.74155
$779$	−6.33413	+	10.9710i	−0.226944	+	0.393078i
$780$	0.256750	+	0.444704i	0.00919313	+	0.0159230i
$781$	0.0177803	+	0.0307964i	0.000636228	+	0.00110198i
$782$	22.1859	−	38.4270i	0.793364	−	1.37415i
$783$	2.38258			0.0851463
$784$	23.7227	−	3.64584i	0.847240	−	0.130209i
$785$	−42.3529			−1.51164
$786$	−4.77949	+	8.27832i	−0.170479	+	0.295278i
$787$	−1.58282	−	2.74152i	−0.0564214	−	0.0977247i	0.836435	−	0.548066i	$-0.184636\pi$
$787$	−1.58282	−	2.74152i	−0.0564214	−	0.0977247i	−0.892857	+	0.450341i	$0.851302\pi$
$788$	−1.42176	−	2.46256i	−0.0506482	−	0.0877252i
$789$	−2.82887	+	4.89975i	−0.100711	+	0.174436i
$790$	31.4115			1.11757
$791$	20.0126	+	9.60191i	0.711565	+	0.341405i
$792$	0.202688			0.00720221
$793$	−4.02309	+	6.96819i	−0.142864	+	0.247448i
$794$	−14.9995	−	25.9799i	−0.532313	−	0.921992i
$795$	−8.06190	−	13.9636i	−0.285926	−	0.495238i
$796$	1.94698	−	3.37228i	0.0690090	−	0.119527i
$797$	−31.1127			−1.10207			−0.551035	−	0.834482i	$-0.685767\pi$
$797$	−31.1127			−1.10207			−0.551035	+	0.834482i	$0.685767\pi$
$798$	15.4326	−	10.5545i	0.546309	−	0.373626i
$799$	24.5568			0.868758
$800$	0.638808	−	1.10645i	0.0225853	−	0.0391188i
$801$	2.48975	+	4.31238i	0.0879712	+	0.152371i
$802$	−11.5447	−	19.9961i	−0.407658	−	0.706085i
$803$	−0.233992	+	0.405285i	−0.00825738	+	0.0143022i
$804$	−1.18316			−0.0417269
$805$	2.26704	+	29.6755i	0.0799026	+	1.04592i
$806$	4.19627			0.147807
$807$	−14.4515	+	25.0307i	−0.508717	+	0.881123i
$808$	28.5194	+	49.3970i	1.00331	+	1.73778i
$809$	−25.2971	−	43.8158i	−0.889397	−	1.54048i	−0.840590	−	0.541673i	$-0.817791\pi$
$809$	−25.2971	−	43.8158i	−0.889397	−	1.54048i	−0.0488074	−	0.998808i	$-0.515542\pi$
$810$	−1.33853	+	2.31839i	−0.0470310	+	0.0814601i
$811$	0.221250			0.00776913			0.00388456	−	0.999992i	$-0.498764\pi$
$811$	0.221250			0.00776913			0.00388456	+	0.999992i	$0.498764\pi$
$812$	0.121720	+	1.59331i	0.00427154	+	0.0559144i
$813$	14.3474			0.503184
$814$	0.238103	−	0.412407i	0.00834551	−	0.0144548i
$815$	−23.1601	−	40.1145i	−0.811263	−	1.40515i
$816$	10.3654	+	17.9534i	0.362862	+	0.628495i
$817$	−0.277851	+	0.481253i	−0.00972079	+	0.0168369i
$818$	−40.1824			−1.40495
$819$	−2.18386	+	1.49357i	−0.0763104	+	0.0521894i
$820$	1.21655			0.0424836
$821$	0.875179	−	1.51585i	0.0305440	−	0.0529037i	−0.850349	−	0.526219i	$-0.823609\pi$
$821$	0.875179	−	1.51585i	0.0305440	−	0.0529037i	0.880893	+	0.473315i	$0.156943\pi$
$822$	13.6379	+	23.6215i	0.475675	+	0.823894i
$823$	−6.42236	−	11.1239i	−0.223869	−	0.387753i	0.732110	−	0.681186i	$-0.238536\pi$
$823$	−6.42236	−	11.1239i	−0.223869	−	0.387753i	−0.955980	+	0.293433i	$0.905202\pi$
$824$	−24.7182	+	42.8131i	−0.861098	+	1.49147i
$825$	−0.0610221			−0.00212452
$826$	21.6981	+	10.4106i	0.754974	+	0.362232i
$827$	−12.4757			−0.433823			−0.216911	−	0.976191i	$-0.569598\pi$
$827$	−12.4757			−0.433823			−0.216911	+	0.976191i	$0.569598\pi$
$828$	0.703849	−	1.21910i	0.0244605	−	0.0423667i
$829$	1.72429	+	2.98656i	0.0598871	+	0.103728i	0.894415	−	0.447239i	$-0.147593\pi$
$829$	1.72429	+	2.98656i	0.0598871	+	0.103728i	−0.834527	+	0.550966i	$0.814259\pi$
$830$	−17.1609	−	29.7236i	−0.595665	−	1.03172i
$831$	7.79055	−	13.4936i	0.270251	−	0.468089i
$832$	−8.74065			−0.303028
$833$	−15.3484	+	39.4421i	−0.531790	+	1.36659i
$834$	−20.2093			−0.699791
$835$	−12.8645	+	22.2819i	−0.445193	+	0.771097i
$836$	0.0461271	+	0.0798944i	0.00159534	+	0.00276321i
$837$	−1.58763	−	2.74985i	−0.0548764	−	0.0950488i
$838$	17.2755	−	29.9221i	0.596773	−	1.03364i
$839$	17.4568			0.602675			0.301338	−	0.953518i	$-0.402567\pi$
$839$	17.4568			0.602675			0.301338	+	0.953518i	$0.402567\pi$
$840$	−14.3904	−	6.90445i	−0.496517	−	0.238226i
$841$	−23.3233			−0.804253
$842$	14.5723	−	25.2399i	0.502193	−	0.869824i
$843$	−5.81756	−	10.0763i	−0.200367	−	0.347047i
$844$	2.28117	+	3.95110i	0.0785210	+	0.136002i
$845$	−1.01284	+	1.75429i	−0.0348428	+	0.0603496i
$846$	−5.36756			−0.184540
$847$	−24.0124	+	16.4223i	−0.825076	+	0.564277i
$848$	27.2917			0.937202
$849$	14.9871	−	25.9584i	0.514356	−	0.890890i
$850$	−3.58208	−	6.20435i	−0.122864	−	0.212808i
$851$	−14.7005	−	25.4621i	−0.503928	−	0.872829i
$852$	−0.0662248	+	0.114705i	−0.00226882	+	0.00392972i
$853$	31.5211			1.07926			0.539632	−	0.841901i	$-0.318564\pi$
$853$	31.5211			1.07926			0.539632	+	0.841901i	$0.318564\pi$
$854$	−2.14299	−	28.0517i	−0.0733317	−	0.959911i
$855$	−10.8318			−0.370440
$856$	−19.2197	+	33.2894i	−0.656915	+	1.13781i
$857$	−3.92650	−	6.80090i	−0.134127	−	0.232314i	0.791137	−	0.611639i	$-0.209490\pi$
$857$	−3.92650	−	6.80090i	−0.134127	−	0.232314i	−0.925264	+	0.379325i	$0.876156\pi$
$858$	0.0449720	+	0.0778938i	0.00153532	+	0.00265925i
$859$	−2.68877	+	4.65709i	−0.0917398	+	0.158898i	−0.908243	−	0.418443i	$-0.862576\pi$
$859$	−2.68877	+	4.65709i	−0.0917398	+	0.158898i	0.816503	+	0.577340i	$0.195909\pi$
$860$	0.0533647			0.00181972
$861$	0.477457	+	6.24990i	0.0162717	+	0.212996i
$862$	−31.6941			−1.07951
$863$	26.8672	−	46.5354i	0.914570	−	1.58408i	0.107041	−	0.994255i	$-0.465862\pi$
$863$	26.8672	−	46.5354i	0.914570	−	1.58408i	0.807529	−	0.589828i	$-0.200804\pi$
$864$	0.712476	+	1.23404i	0.0242389	+	0.0419830i
$865$	−14.7804	−	25.6003i	−0.502547	−	0.870438i
$866$	14.3475	−	24.8507i	0.487549	−	0.844460i
$867$	−19.5562			−0.664164
$868$	1.75782	−	1.20219i	0.0596642	−	0.0408049i
$869$	−0.798581			−0.0270900
$870$	−3.18914	+	5.52375i	−0.108122	+	0.187273i
$871$	−2.33370	−	4.04209i	−0.0790744	−	0.136961i
$872$	−30.2492	−	52.3931i	−1.02437	−	1.77425i
$873$	2.54851	−	4.41415i	0.0862539	−	0.149396i
$874$	−39.2423			−1.32739
$875$	28.4928	+	13.6707i	0.963231	+	0.462152i
$876$	−1.74306			−0.0588925
$877$	14.4436	−	25.0171i	0.487727	−	0.844768i	−0.512174	−	0.858882i	$-0.671160\pi$
$877$	14.4436	−	25.0171i	0.487727	−	0.844768i	0.999900	+	0.0141144i	$0.00449289\pi$
$878$	−6.03282	−	10.4491i	−0.203598	−	0.352642i
$879$	1.91884	+	3.32352i	0.0647207	+	0.112100i
$880$	−0.236355	+	0.409379i	−0.00796753	+	0.0138002i
$881$	−30.9653			−1.04325			−0.521623	−	0.853176i	$-0.674673\pi$
$881$	−30.9653			−1.04325			−0.521623	+	0.853176i	$0.674673\pi$
$882$	3.35480	−	8.62114i	0.112962	−	0.290289i
$883$	6.60585			0.222305			0.111152	−	0.993803i	$-0.464546\pi$
$883$	6.60585			0.222305			0.111152	+	0.993803i	$0.464546\pi$
$884$	0.766337	−	1.32733i	0.0257747	−	0.0446431i
$885$	−6.97137	−	12.0748i	−0.234340	−	0.405889i
$886$	−2.95633	−	5.12051i	−0.0993197	−	0.172027i
$887$	12.6969	−	21.9917i	0.426321	−	0.738410i	−0.570222	−	0.821491i	$-0.693143\pi$
$887$	12.6969	−	21.9917i	0.426321	−	0.738410i	0.996543	+	0.0830809i	$0.0264760\pi$
$888$	15.7676			0.529125
$889$	23.9854	+	11.5080i	0.804444	+	0.385967i
$890$	−13.3304			−0.446836
$891$	0.0340296	−	0.0589410i	0.00114004	−	0.00197460i
$892$	0.377535	+	0.653910i	0.0126408	+	0.0218945i
$893$	−10.8590	−	18.8084i	−0.363384	−	0.629399i
$894$	5.73825	−	9.93893i	0.191916	−	0.332408i
$895$	12.7352			0.425691
$896$	19.0025	−	12.9960i	0.634831	−	0.434167i
$897$	5.55316			0.185415
$898$	12.4923	−	21.6374i	0.416875	−	0.722048i
$899$	−3.78264	−	6.55173i	−0.126158	−	0.218513i
$900$	−0.113642	−	0.196834i	−0.00378807	−	0.00656113i
$901$	−24.0628	+	41.6780i	−0.801648	+	1.38850i
$902$	0.213088			0.00709507
$903$	0.0209440	+	0.274156i	0.000696972	+	0.00912335i
$904$	24.9852			0.830997
$905$	−15.3731	+	26.6270i	−0.511019	+	0.885112i
$906$	8.94125	+	15.4867i	0.297053	+	0.514511i
$907$	1.26656	+	2.19375i	0.0420556	+	0.0728424i	0.886287	−	0.463136i	$-0.153276\pi$
$907$	1.26656	+	2.19375i	0.0420556	+	0.0728424i	−0.844231	+	0.535979i	$0.819943\pi$
$908$	−1.50210	+	2.60171i	−0.0498489	+	0.0863408i
$909$	19.1526			0.635253
$910$	−0.539515	−	7.06223i	−0.0178847	−	0.234111i
$911$	−49.8354			−1.65112			−0.825560	−	0.564314i	$-0.809141\pi$
$911$	−49.8354			−1.65112			−0.825560	+	0.564314i	$0.809141\pi$
$912$	9.16717	−	15.8780i	0.303555	−	0.525773i
$913$	0.436286	+	0.755669i	0.0144390	+	0.0250090i
$914$	17.1332	+	29.6755i	0.566715	+	0.981579i
$915$	−8.14950	+	14.1154i	−0.269414	+	0.466639i
$916$	−1.63407			−0.0539913
$917$	−15.7962	+	10.8032i	−0.521636	+	0.356752i
$918$	7.99035			0.263721
$919$	−23.5577	+	40.8032i	−0.777098	+	1.34597i	0.156509	+	0.987677i	$0.449976\pi$
$919$	−23.5577	+	40.8032i	−0.777098	+	1.34597i	−0.933608	+	0.358297i	$0.883357\pi$
$920$	16.7503	+	29.0125i	0.552243	+	0.956512i
$921$	0.283204	+	0.490524i	0.00933190	+	0.0161633i
$922$	−20.3884	+	35.3138i	−0.671457	+	1.16300i
$923$	−0.522494			−0.0171981
$924$	0.0411545	+	0.0197457i	0.00135388	+	0.000649585i
$925$	−4.74704			−0.156082
$926$	−22.1792	+	38.4156i	−0.728855	+	1.26241i
$927$	8.29993	+	14.3759i	0.272606	+	0.472167i
$928$	1.69753	+	2.94020i	0.0557241	+	0.0965169i
$929$	20.5362	−	35.5698i	0.673771	−	1.16701i	−0.303055	−	0.952973i	$-0.598007\pi$
$929$	20.5362	−	35.5698i	0.673771	−	1.16701i	0.976826	−	0.214033i	$-0.0686600\pi$
$930$	8.50032			0.278737
$931$	36.9963	−	5.68580i	1.21250	−	0.186345i
$932$	−1.81383			−0.0594140
$933$	10.1522	−	17.5842i	0.332369	−	0.575680i
$934$	0.00103564	+	0.00179379i	3.38873e−5	+	5.86945e-5i
$935$	−0.416783	−	0.721889i	−0.0136302	−	0.0236083i
$936$	−1.48906	+	2.57912i	−0.0486714	+	0.0843013i
$937$	15.0742			0.492451			0.246226	−	0.969213i	$-0.420810\pi$
$937$	15.0742			0.492451			0.246226	+	0.969213i	$0.420810\pi$
$938$	14.7137	+	7.05952i	0.480418	+	0.230502i
$939$	−12.8487			−0.419302
$940$	−1.04280	+	1.80619i	−0.0340125	+	0.0589114i
$941$	20.2690	+	35.1069i	0.660749	+	1.14445i	0.980419	+	0.196922i	$0.0630945\pi$
$941$	20.2690	+	35.1069i	0.660749	+	1.14445i	−0.319670	+	0.947529i	$0.603572\pi$
$942$	−13.8155	−	23.9291i	−0.450133	−	0.779652i
$943$	6.57806	−	11.3935i	0.214211	−	0.371025i
$944$	23.6000			0.768115
$945$	−4.42382	+	3.02549i	−0.143907	+	0.0984192i
$946$	0.00934727			0.000303906
$947$	4.52470	−	7.83702i	0.147033	−	0.254669i	−0.783096	−	0.621900i	$-0.786361\pi$
$947$	4.52470	−	7.83702i	0.147033	−	0.254669i	0.930130	+	0.367231i	$0.119694\pi$
$948$	−1.48721	−	2.57592i	−0.0483022	−	0.0836618i
$949$	−3.43806	−	5.95489i	−0.111604	−	0.193304i
$950$	−3.16800	+	5.48713i	−0.102783	+	0.178026i
$951$	33.2621			1.07860
$952$	3.62885	+	47.5015i	0.117612	+	1.53953i
$953$	−19.6398			−0.636195			−0.318098	−	0.948058i	$-0.603044\pi$
$953$	−19.6398			−0.636195			−0.318098	+	0.948058i	$0.603044\pi$
$954$	5.25957	−	9.10985i	0.170285	−	0.294942i
$955$	21.2148	+	36.7452i	0.686496	+	1.18905i
$956$	0.0355786	+	0.0616239i	0.00115069	+	0.00199306i
$957$	0.0810782	−	0.140431i	0.00262088	−	0.00453951i
$958$	−15.1397			−0.489141
$959$	4.15947	+	54.4474i	0.134316	+	1.75820i
$960$	−17.7058			−0.571452
$961$	10.4589	−	18.1153i	0.337383	−	0.584365i
$962$	3.49847	+	6.05952i	0.112795	+	0.195367i
$963$	6.45363	+	11.1780i	0.207965	+	0.360207i
$964$	0.927728	−	1.60687i	0.0298801	−	0.0517538i
$965$	6.53959			0.210517
$966$	−16.0270	+	10.9610i	−0.515659	+	0.352664i
$967$	−51.6182			−1.65993			−0.829964	−	0.557816i	$-0.811639\pi$
$967$	−51.6182			−1.65993			−0.829964	+	0.557816i	$0.811639\pi$
$968$	−16.3727	+	28.3584i	−0.526240	+	0.911474i
$969$	16.1652	+	27.9989i	0.519300	+	0.899454i
$970$	6.82249	+	11.8169i	0.219057	+	0.379418i
$971$	7.53294	−	13.0474i	0.241743	−	0.418712i	−0.719468	−	0.694526i	$-0.755614\pi$
$971$	7.53294	−	13.0474i	0.241743	−	0.418712i	0.961211	+	0.275814i	$0.0889474\pi$
$972$	0.253495			0.00813085
$973$	−36.4777	−	17.5018i	−1.16942	−	0.561081i
$974$	20.5569			0.658685
$975$	0.448301	−	0.776481i	0.0143571	−	0.0248673i
$976$	−13.7942	−	23.8922i	−0.441540	−	0.764770i
$977$	4.84086	+	8.38461i	0.154873	+	0.268248i	0.933013	−	0.359843i	$-0.117170\pi$
$977$	4.84086	+	8.38461i	0.154873	+	0.268248i	−0.778140	+	0.628091i	$0.783837\pi$
$978$	15.1096	−	26.1706i	0.483153	−	0.836845i
$979$	0.338902			0.0108313
$980$	−2.24926	−	2.80380i	−0.0718499	−	0.0895641i
$981$	−20.3143			−0.648586
$982$	−17.9905	+	31.1605i	−0.574101	+	0.994372i
$983$	1.43537	+	2.48614i	0.0457812	+	0.0792954i	0.888008	−	0.459828i	$-0.152089\pi$
$983$	1.43537	+	2.48614i	0.0457812	+	0.0792954i	−0.842227	+	0.539123i	$0.818756\pi$
$984$	3.52776	+	6.11026i	0.112461	+	0.194788i
$985$	11.3613	−	19.6784i	0.362002	−	0.627007i
$986$	19.0376			0.606281
$987$	−9.68841	−	4.64844i	−0.308385	−	0.147961i
$988$	−1.35550			−0.0431241
$989$	0.288552	−	0.499786i	0.00917541	−	0.0158923i
$990$	0.0910990	+	0.157788i	0.00289532	+	0.00501484i
$991$	20.5526	+	35.5982i	0.652876	+	1.13081i	0.982422	+	0.186675i	$0.0597711\pi$
$991$	20.5526	+	35.5982i	0.652876	+	1.13081i	−0.329546	+	0.944140i	$0.606896\pi$
$992$	2.26229	−	3.91840i	0.0718278	−	0.124409i
$993$	−29.6302			−0.940287
$994$	1.50797	−	1.03131i	0.0478298	−	0.0327113i
$995$	31.1168			0.986470
$996$	−1.62500	+	2.81458i	−0.0514901	+	0.0891834i
$997$	−7.90644	−	13.6944i	−0.250399	−	0.433705i	0.713236	−	0.700924i	$-0.247229\pi$
$997$	−7.90644	−	13.6944i	−0.250399	−	0.433705i	−0.963636	+	0.267219i	$0.913895\pi$
$998$	19.1768	+	33.2152i	0.607031	+	1.05141i
$999$	2.64724	−	4.58515i	0.0837549	−	0.145068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.e.79.2	✓	10
3.2	odd	2		819.2.j.g.352.4		10
7.2	even	3		1911.2.a.t.1.4		5
7.4	even	3	inner	273.2.i.e.235.2	yes	10
7.5	odd	6		1911.2.a.u.1.4		5
21.2	odd	6		5733.2.a.bq.1.2		5
21.5	even	6		5733.2.a.bp.1.2		5
21.11	odd	6		819.2.j.g.235.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.2	✓	10	1.1	even	1	trivial
273.2.i.e.235.2	yes	10	7.4	even	3	inner
819.2.j.g.235.4		10	21.11	odd	6
819.2.j.g.352.4		10	3.2	odd	2
1911.2.a.t.1.4		5	7.2	even	3
1911.2.a.u.1.4		5	7.5	odd	6
5733.2.a.bp.1.2		5	21.5	even	6
5733.2.a.bq.1.2		5	21.2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.660777 + 1.14450i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.126747 + 0.219533i) q^{4} +(-1.01284 + 1.75429i) q^{5} -1.32155 q^{6} +(-2.38540 - 1.14450i) q^{7} -2.97812 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.660777 + 1.14450i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.126747 + 0.219533i) q^{4} +(-1.01284 + 1.75429i) q^{5} -1.32155 q^{6} +(-2.38540 - 1.14450i) q^{7} -2.97812 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.33853 - 2.31839i) q^{10} +(0.0340296 + 0.0589410i) q^{11} +(-0.126747 + 0.219533i) q^{12} -1.00000 q^{13} +(2.88609 - 1.97383i) q^{14} -2.02568 q^{15} +(1.71438 - 2.96939i) q^{16} +(3.02309 + 5.23614i) q^{17} +(-0.660777 - 1.14450i) q^{18} +(2.67362 - 4.63084i) q^{19} -0.513501 q^{20} +(-0.201533 - 2.63806i) q^{21} -0.0899440 q^{22} +(-2.77658 + 4.80918i) q^{23} +(-1.48906 - 2.57912i) q^{24} +(0.448301 + 0.776481i) q^{25} +(0.660777 - 1.14450i) q^{26} -1.00000 q^{27} +(-0.0510876 - 0.668736i) q^{28} -2.38258 q^{29} +(1.33853 - 2.31839i) q^{30} +(1.58763 + 2.74985i) q^{31} +(-0.712476 - 1.23404i) q^{32} +(-0.0340296 + 0.0589410i) q^{33} -7.99035 q^{34} +(4.42382 - 3.02549i) q^{35} -0.253495 q^{36} +(-2.64724 + 4.58515i) q^{37} +(3.53333 + 6.11991i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(3.01636 - 5.22449i) q^{40} -2.36912 q^{41} +(3.15243 + 1.51252i) q^{42} -0.103923 q^{43} +(-0.00862633 + 0.0149412i) q^{44} +(-1.01284 - 1.75429i) q^{45} +(-3.66940 - 6.35559i) q^{46} +(2.03077 - 3.51740i) q^{47} +3.42875 q^{48} +(4.38024 + 5.46017i) q^{49} -1.18491 q^{50} +(-3.02309 + 5.23614i) q^{51} +(-0.126747 - 0.219533i) q^{52} +(3.97984 + 6.89328i) q^{53} +(0.660777 - 1.14450i) q^{54} -0.137867 q^{55} +(7.10399 + 3.40845i) q^{56} +5.34724 q^{57} +(1.57435 - 2.72686i) q^{58} +(3.44149 + 5.96083i) q^{59} +(-0.256750 - 0.444704i) q^{60} +(4.02309 - 6.96819i) q^{61} -4.19627 q^{62} +(2.18386 - 1.49357i) q^{63} +8.74065 q^{64} +(1.01284 - 1.75429i) q^{65} +(-0.0449720 - 0.0778938i) q^{66} +(2.33370 + 4.04209i) q^{67} +(-0.766337 + 1.32733i) q^{68} -5.55316 q^{69} +(0.539515 + 7.06223i) q^{70} +0.522494 q^{71} +(1.48906 - 2.57912i) q^{72} +(3.43806 + 5.95489i) q^{73} +(-3.49847 - 6.05952i) q^{74} +(-0.448301 + 0.776481i) q^{75} +1.35550 q^{76} +(-0.0137162 - 0.179545i) q^{77} +1.32155 q^{78} +(-5.86681 + 10.1616i) q^{79} +(3.47278 + 6.01504i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.56546 - 2.71146i) q^{82} +12.8208 q^{83} +(0.553598 - 0.378611i) q^{84} -12.2476 q^{85} +(0.0686701 - 0.118940i) q^{86} +(-1.19129 - 2.06337i) q^{87} +(-0.101344 - 0.175533i) q^{88} +(2.48975 - 4.31238i) q^{89} +2.67705 q^{90} +(2.38540 + 1.14450i) q^{91} -1.40770 q^{92} +(-1.58763 + 2.74985i) q^{93} +(2.68378 + 4.64844i) q^{94} +(5.41591 + 9.38063i) q^{95} +(0.712476 - 1.23404i) q^{96} -5.09702 q^{97} +(-9.14353 + 1.40523i) q^{98} -0.0680592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Introduction

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