LMFDB - Embedded newform 731.2.m.b.87.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.1
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95693 - 1.95693i) q^{2} +(-2.36371 + 0.979079i) q^{3} +5.65912i q^{4} +(0.741144 + 1.78928i) q^{5} +(6.54158 + 2.70961i) q^{6} +(-1.36877 + 3.30450i) q^{7} +(7.16062 - 7.16062i) q^{8} +(2.50719 - 2.50719i) q^{9} +O(q^{10})$	\(q+(-1.95693 - 1.95693i) q^{2} +(-2.36371 + 0.979079i) q^{3} +5.65912i q^{4} +(0.741144 + 1.78928i) q^{5} +(6.54158 + 2.70961i) q^{6} +(-1.36877 + 3.30450i) q^{7} +(7.16062 - 7.16062i) q^{8} +(2.50719 - 2.50719i) q^{9} +(2.05112 - 4.95185i) q^{10} +(2.44670 + 1.01346i) q^{11} +(-5.54072 - 13.3765i) q^{12} -4.23014i q^{13} +(9.14525 - 3.78809i) q^{14} +(-3.50369 - 3.50369i) q^{15} -16.7074 q^{16} +(3.31537 - 2.45118i) q^{17} -9.81277 q^{18} +(3.89847 + 3.89847i) q^{19} +(-10.1257 + 4.19422i) q^{20} -9.15101i q^{21} +(-2.80475 - 6.77126i) q^{22} +(6.60529 + 2.73600i) q^{23} +(-9.91478 + 23.9364i) q^{24} +(0.883306 - 0.883306i) q^{25} +(-8.27807 + 8.27807i) q^{26} +(-0.534285 + 1.28988i) q^{27} +(-18.7006 - 7.74603i) q^{28} +(2.00354 + 4.83696i) q^{29} +13.7129i q^{30} +(2.40145 - 0.994712i) q^{31} +(18.3738 + 18.3738i) q^{32} -6.77552 q^{33} +(-11.2847 - 1.69115i) q^{34} -6.92714 q^{35} +(14.1885 + 14.1885i) q^{36} +(6.44396 - 2.66918i) q^{37} -15.2580i q^{38} +(4.14164 + 9.99880i) q^{39} +(18.1194 + 7.50530i) q^{40} +(-1.46389 + 3.53415i) q^{41} +(-17.9078 + 17.9078i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-5.73526 + 13.8461i) q^{44} +(6.34425 + 2.62787i) q^{45} +(-7.57191 - 18.2802i) q^{46} +6.09285i q^{47} +(39.4913 - 16.3578i) q^{48} +(-4.09646 - 4.09646i) q^{49} -3.45713 q^{50} +(-5.43666 + 9.03989i) q^{51} +23.9388 q^{52} +(-6.86761 - 6.86761i) q^{53} +(3.56975 - 1.47864i) q^{54} +5.12894i q^{55} +(13.8610 + 33.4635i) q^{56} +(-13.0317 - 5.39792i) q^{57} +(5.54481 - 13.3863i) q^{58} +(3.57697 - 3.57697i) q^{59} +(19.8278 - 19.8278i) q^{60} +(-3.10756 + 7.50230i) q^{61} +(-6.64603 - 2.75288i) q^{62} +(4.85325 + 11.7168i) q^{63} -38.4977i q^{64} +(7.56890 - 3.13514i) q^{65} +(13.2592 + 13.2592i) q^{66} +7.69445 q^{67} +(13.8715 + 18.7621i) q^{68} -18.2917 q^{69} +(13.5559 + 13.5559i) q^{70} +(12.1130 - 5.01739i) q^{71} -35.9060i q^{72} +(-1.92117 - 4.63813i) q^{73} +(-17.8337 - 7.38697i) q^{74} +(-1.22305 + 2.95270i) q^{75} +(-22.0619 + 22.0619i) q^{76} +(-6.69793 + 6.69793i) q^{77} +(11.4620 - 27.6718i) q^{78} +(-8.86103 - 3.67036i) q^{79} +(-12.3826 - 29.8941i) q^{80} +7.06511i q^{81} +(9.78081 - 4.05134i) q^{82} +(-2.41038 - 2.41038i) q^{83} +51.7866 q^{84} +(6.84302 + 4.11545i) q^{85} -2.76751 q^{86} +(-9.47154 - 9.47154i) q^{87} +(24.7768 - 10.2629i) q^{88} +7.39289i q^{89} +(-7.27267 - 17.5578i) q^{90} +(13.9785 + 5.79009i) q^{91} +(-15.4833 + 37.3801i) q^{92} +(-4.70241 + 4.70241i) q^{93} +(11.9233 - 11.9233i) q^{94} +(-4.08612 + 9.86477i) q^{95} +(-61.4198 - 25.4409i) q^{96} +(1.16669 + 2.81664i) q^{97} +16.0330i q^{98} +(8.67526 - 3.59341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.95693	−	1.95693i	−1.38376	−	1.38376i	−0.837841	−	0.545914i	$-0.816182\pi$
$2$	−1.95693	−	1.95693i	−1.38376	−	1.38376i	−0.545914	−	0.837841i	$-0.683818\pi$
$3$	−2.36371	+	0.979079i	−1.36469	+	0.565272i	−0.940342	−	0.340230i	$-0.889495\pi$
$3$	−2.36371	+	0.979079i	−1.36469	+	0.565272i	−0.424344	+	0.905501i	$0.639495\pi$
$4$			5.65912i			2.82956i
$5$	0.741144	+	1.78928i	0.331450	+	0.800190i	0.998478	+	0.0551576i	$0.0175661\pi$
$5$	0.741144	+	1.78928i	0.331450	+	0.800190i	−0.667028	+	0.745033i	$0.732434\pi$
$6$	6.54158	+	2.70961i	2.67059	+	1.10619i
$7$	−1.36877	+	3.30450i	−0.517347	+	1.24898i	0.422181	+	0.906512i	$0.361265\pi$
$7$	−1.36877	+	3.30450i	−0.517347	+	1.24898i	−0.939528	+	0.342473i	$0.888735\pi$
$8$	7.16062	−	7.16062i	2.53166	−	2.53166i
$9$	2.50719	−	2.50719i	0.835730	−	0.835730i
$10$	2.05112	−	4.95185i	0.648622	−	1.56591i
$11$	2.44670	+	1.01346i	0.737707	+	0.305568i	0.719715	−	0.694270i	$-0.244273\pi$
$11$	2.44670	+	1.01346i	0.737707	+	0.305568i	0.0179922	+	0.999838i	$0.494273\pi$
$12$	−5.54072	−	13.3765i	−1.59947	−	3.86146i
$13$		−	4.23014i		−	1.17323i	−0.809866	−	0.586615i	$-0.800460\pi$
$13$		−	4.23014i		−	1.17323i	0.809866	−	0.586615i	$-0.199540\pi$
$14$	9.14525	−	3.78809i	2.44417	−	1.01241i
$15$	−3.50369	−	3.50369i	−0.904650	−	0.904650i
$16$	−16.7074			−4.17684
$17$	3.31537	−	2.45118i	0.804096	−	0.594500i
$17$	3.31537	−	2.45118i	0.804096	−	0.594500i
$18$	−9.81277			−2.31289
$19$	3.89847	+	3.89847i	0.894369	+	0.894369i	0.994931	−	0.100561i	$-0.0320639\pi$
$19$	3.89847	+	3.89847i	0.894369	+	0.894369i	−0.100561	+	0.994931i	$0.532064\pi$
$20$	−10.1257	+	4.19422i	−2.26418	+	0.937856i
$21$		−	9.15101i		−	1.99691i
$22$	−2.80475	−	6.77126i	−0.597974	−	1.44364i
$23$	6.60529	+	2.73600i	1.37730	+	0.570496i	0.943758	−	0.330638i	$-0.107264\pi$
$23$	6.60529	+	2.73600i	1.37730	+	0.570496i	0.433541	+	0.901134i	$0.357264\pi$
$24$	−9.91478	+	23.9364i	−2.02385	+	4.88600i
$25$	0.883306	−	0.883306i	0.176661	−	0.176661i
$26$	−8.27807	+	8.27807i	−1.62346	+	1.62346i
$27$	−0.534285	+	1.28988i	−0.102823	+	0.248237i
$28$	−18.7006	−	7.74603i	−3.53408	−	1.46386i
$29$	2.00354	+	4.83696i	0.372047	+	0.898201i	0.993403	+	0.114673i	$0.0365820\pi$
$29$	2.00354	+	4.83696i	0.372047	+	0.898201i	−0.621356	+	0.783528i	$0.713418\pi$
$30$			13.7129i			2.50363i
$31$	2.40145	−	0.994712i	0.431313	−	0.178656i	−0.156455	−	0.987685i	$-0.550007\pi$
$31$	2.40145	−	0.994712i	0.431313	−	0.178656i	0.587768	+	0.809029i	$0.300007\pi$
$32$	18.3738	+	18.3738i	3.24806	+	3.24806i
$33$	−6.77552			−1.17947
$34$	−11.2847	−	1.69115i	−1.93531	−	0.290030i
$35$	−6.92714			−1.17090
$36$	14.1885	+	14.1885i	2.36475	+	2.36475i
$37$	6.44396	−	2.66918i	1.05938	−	0.438810i	0.216149	−	0.976360i	$-0.430650\pi$
$37$	6.44396	−	2.66918i	1.05938	−	0.438810i	0.843231	+	0.537551i	$0.180650\pi$
$38$		−	15.2580i		−	2.47518i
$39$	4.14164	+	9.99880i	0.663193	+	1.60109i
$40$	18.1194	+	7.50530i	2.86493	+	1.18669i
$41$	−1.46389	+	3.53415i	−0.228622	+	0.551942i	−0.996010	−	0.0892408i	$-0.971556\pi$
$41$	−1.46389	+	3.53415i	−0.228622	+	0.551942i	0.767388	+	0.641183i	$0.221556\pi$
$42$	−17.9078	+	17.9078i	−2.76324	+	2.76324i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	−5.73526	+	13.8461i	−0.864623	+	2.08738i
$45$	6.34425	+	2.62787i	0.945745	+	0.391740i
$46$	−7.57191	−	18.2802i	−1.11642	−	2.69527i
$47$			6.09285i			0.888733i	0.895845	+	0.444367i	$0.146571\pi$
$47$			6.09285i			0.888733i	−0.895845	+	0.444367i	$0.853429\pi$
$48$	39.4913	−	16.3578i	5.70008	−	2.36105i
$49$	−4.09646	−	4.09646i	−0.585209	−	0.585209i
$50$	−3.45713			−0.488912
$51$	−5.43666	+	9.03989i	−0.761285	+	1.26584i
$52$	23.9388			3.31972
$53$	−6.86761	−	6.86761i	−0.943339	−	0.943339i	0.0551396	−	0.998479i	$-0.482440\pi$
$53$	−6.86761	−	6.86761i	−0.943339	−	0.943339i	−0.998479	+	0.0551396i	$0.982440\pi$
$54$	3.56975	−	1.47864i	0.485781	−	0.201217i
$55$			5.12894i			0.691586i
$56$	13.8610	+	33.4635i	1.85226	+	4.47175i
$57$	−13.0317	−	5.39792i	−1.72610	−	0.714972i
$58$	5.54481	−	13.3863i	0.728069	−	1.75771i
$59$	3.57697	−	3.57697i	0.465681	−	0.465681i	−0.434831	−	0.900512i	$-0.643192\pi$
$59$	3.57697	−	3.57697i	0.465681	−	0.465681i	0.900512	+	0.434831i	$0.143192\pi$
$60$	19.8278	−	19.8278i	2.55976	−	2.55976i
$61$	−3.10756	+	7.50230i	−0.397882	+	0.960572i	0.590286	+	0.807194i	$0.299015\pi$
$61$	−3.10756	+	7.50230i	−0.397882	+	0.960572i	−0.988168	+	0.153377i	$0.950985\pi$
$62$	−6.64603	−	2.75288i	−0.844047	−	0.349616i
$63$	4.85325	+	11.7168i	0.611452	+	1.47618i
$64$		−	38.4977i		−	4.81221i
$65$	7.56890	−	3.13514i	0.938807	−	0.388866i
$66$	13.2592	+	13.2592i	1.63209	+	1.63209i
$67$	7.69445			0.940027			0.470013	−	0.882659i	$-0.344249\pi$
$67$	7.69445			0.940027			0.470013	+	0.882659i	$0.344249\pi$
$68$	13.8715	+	18.7621i	1.68217	+	2.27524i
$69$	−18.2917			−2.20207
$70$	13.5559	+	13.5559i	1.62024	+	1.62024i
$71$	12.1130	−	5.01739i	1.43755	−	0.595454i	0.478350	−	0.878169i	$-0.341235\pi$
$71$	12.1130	−	5.01739i	1.43755	−	0.595454i	0.959204	+	0.282715i	$0.0912350\pi$
$72$		−	35.9060i		−	4.23157i
$73$	−1.92117	−	4.63813i	−0.224856	−	0.542852i	0.770681	−	0.637222i	$-0.219916\pi$
$73$	−1.92117	−	4.63813i	−0.224856	−	0.542852i	−0.995537	+	0.0943699i	$0.969916\pi$
$74$	−17.8337	−	7.38697i	−2.07313	−	0.858718i
$75$	−1.22305	+	2.95270i	−0.141226	+	0.340949i
$76$	−22.0619	+	22.0619i	−2.53067	+	2.53067i
$77$	−6.69793	+	6.69793i	−0.763300	+	0.763300i
$78$	11.4620	−	27.6718i	1.29782	−	3.13321i
$79$	−8.86103	−	3.67036i	−0.996944	−	0.412948i	−0.176268	−	0.984342i	$-0.556403\pi$
$79$	−8.86103	−	3.67036i	−0.996944	−	0.412948i	−0.820676	+	0.571394i	$0.806403\pi$
$80$	−12.3826	−	29.8941i	−1.38441	−	3.34227i
$81$			7.06511i			0.785012i
$82$	9.78081	−	4.05134i	1.08011	−	0.447396i
$83$	−2.41038	−	2.41038i	−0.264574	−	0.264574i	0.562336	−	0.826909i	$-0.309903\pi$
$83$	−2.41038	−	2.41038i	−0.264574	−	0.264574i	−0.826909	+	0.562336i	$0.809903\pi$
$84$	51.7866			5.65038
$85$	6.84302	+	4.11545i	0.742230	+	0.446383i
$86$	−2.76751			−0.298428
$87$	−9.47154	−	9.47154i	−1.01546	−	1.01546i
$88$	24.7768	−	10.2629i	2.64122	−	1.09403i
$89$			7.39289i			0.783645i	0.920041	+	0.391823i	$0.128155\pi$
$89$			7.39289i			0.783645i	−0.920041	+	0.391823i	$0.871845\pi$
$90$	−7.27267	−	17.5578i	−0.766607	−	1.85075i
$91$	13.9785	+	5.79009i	1.46535	+	0.606966i
$92$	−15.4833	+	37.3801i	−1.61425	+	3.89715i
$93$	−4.70241	+	4.70241i	−0.487618	+	0.487618i
$94$	11.9233	−	11.9233i	1.22979	−	1.22979i
$95$	−4.08612	+	9.86477i	−0.419227	+	1.01210i
$96$	−61.4198	−	25.4409i	−6.26863	−	2.59655i
$97$	1.16669	+	2.81664i	0.118460	+	0.285987i	0.971976	−	0.235079i	$-0.0755347\pi$
$97$	1.16669	+	2.81664i	0.118460	+	0.285987i	−0.853517	+	0.521065i	$0.825535\pi$
$98$			16.0330i			1.61957i
$99$	8.67526	−	3.59341i	0.871896	−	0.361151i
$100$	4.99873	+	4.99873i	0.499873	+	0.499873i
$101$	6.00114			0.597136			0.298568	−	0.954388i	$-0.403491\pi$
$101$	6.00114			0.597136			0.298568	+	0.954388i	$0.403491\pi$
$102$	28.3295	−	7.05126i	2.80504	−	0.698178i
$103$	−10.7669			−1.06089			−0.530445	−	0.847720i	$-0.677975\pi$
$103$	−10.7669			−1.06089			−0.530445	+	0.847720i	$0.677975\pi$
$104$	−30.2904	−	30.2904i	−2.97022	−	2.97022i
$105$	16.3737	−	6.78221i	1.59791	−	0.661876i
$106$			26.8788i			2.61070i
$107$	4.13324	+	9.97852i	0.399575	+	0.964660i	0.987767	+	0.155938i	$0.0498402\pi$
$107$	4.13324	+	9.97852i	0.399575	+	0.964660i	−0.588191	+	0.808722i	$0.700160\pi$
$108$	−7.29956	−	3.02358i	−0.702401	−	0.290944i
$109$	1.69563	−	4.09361i	0.162412	−	0.392097i	−0.821633	−	0.570017i	$-0.806937\pi$
$109$	1.69563	−	4.09361i	0.162412	−	0.392097i	0.984045	+	0.177920i	$0.0569368\pi$
$110$	10.0370	−	10.0370i	0.956986	−	0.956986i
$111$	−12.6183	+	12.6183i	−1.19768	+	1.19768i
$112$	22.8685	−	55.2095i	2.16087	−	5.21681i
$113$	2.05033	+	0.849274i	0.192879	+	0.0798930i	0.477032	−	0.878886i	$-0.341713\pi$
$113$	2.05033	+	0.849274i	0.192879	+	0.0798930i	−0.284153	+	0.958779i	$0.591713\pi$
$114$	14.9388	+	36.0655i	1.39915	+	3.37784i
$115$			13.8465i			1.29119i
$116$	−27.3729	+	11.3382i	−2.54151	+	1.05273i
$117$	−10.6058	−	10.6058i	−0.980503	−	0.980503i
$118$	−13.9997			−1.28878
$119$	3.56197	+	14.3108i	0.326525	+	1.31187i
$120$	−50.1772			−4.58053
$121$	−2.81894	−	2.81894i	−0.256267	−	0.256267i
$122$	20.7627	−	8.60020i	1.87977	−	0.778625i
$123$		−	9.78697i		−	0.882461i
$124$	5.62919	+	13.5901i	0.505516	+	1.22042i
$125$	11.1815	+	4.63154i	1.00011	+	0.414258i
$126$	13.4314	−	32.4263i	1.19657	−	2.88877i
$127$	5.56446	−	5.56446i	0.493766	−	0.493766i	−0.415725	−	0.909491i	$-0.636472\pi$
$127$	5.56446	−	5.56446i	0.493766	−	0.493766i	0.909491	+	0.415725i	$0.136472\pi$
$128$	−38.5895	+	38.5895i	−3.41086	+	3.41086i
$129$	−0.979079	+	2.36371i	−0.0862031	+	0.208113i
$130$	−20.9470	−	8.67654i	−1.83717	−	0.760983i
$131$	−4.73985	−	11.4430i	−0.414122	−	0.999780i	−0.984019	−	0.178064i	$-0.943017\pi$
$131$	−4.73985	−	11.4430i	−0.414122	−	0.999780i	0.569897	−	0.821716i	$-0.306983\pi$
$132$		−	38.3435i		−	3.33737i
$133$	−18.2186	+	7.54639i	−1.57975	+	0.654355i
$134$	−15.0575	−	15.0575i	−1.30077	−	1.30077i
$135$	−2.70393			−0.232717
$136$	6.18811	−	41.2921i	0.530626	−	3.54077i
$137$	−10.9004			−0.931281			−0.465641	−	0.884974i	$-0.654176\pi$
$137$	−10.9004			−0.931281			−0.465641	+	0.884974i	$0.654176\pi$
$138$	35.7955	+	35.7955i	3.04712	+	3.04712i
$139$	4.27255	−	1.76975i	0.362393	−	0.150108i	−0.194055	−	0.980991i	$-0.562164\pi$
$139$	4.27255	−	1.76975i	0.362393	−	0.150108i	0.556448	+	0.830883i	$0.312164\pi$
$140$		−	39.2015i		−	3.31313i
$141$	−5.96538	−	14.4017i	−0.502376	−	1.21284i
$142$	−33.5230	−	13.8857i	−2.81319	−	1.16526i
$143$	4.28706	−	10.3499i	0.358502	−	0.865499i
$144$	−41.8885	+	41.8885i	−3.49071	+	3.49071i
$145$	−7.16977	+	7.16977i	−0.595417	+	0.595417i
$146$	−5.31687	+	12.8361i	−0.440027	+	1.06232i
$147$	13.6936	+	5.67208i	1.12943	+	0.467825i
$148$	15.1052	+	36.4671i	1.24164	+	2.99758i
$149$			8.61092i			0.705434i	0.935730	+	0.352717i	$0.114742\pi$
$149$			8.61092i			0.705434i	−0.935730	+	0.352717i	$0.885258\pi$
$150$	8.17164	−	3.38480i	0.667211	−	0.276368i
$151$	12.9014	+	12.9014i	1.04990	+	1.04990i	0.998688	+	0.0512098i	$0.0163077\pi$
$151$	12.9014	+	12.9014i	1.04990	+	1.04990i	0.0512098	+	0.998688i	$0.483692\pi$
$152$	55.8308			4.52848
$153$	2.16668	−	14.4579i	0.175166	−	1.16885i
$154$	26.2147			2.11244
$155$	3.55964	+	3.55964i	0.285917	+	0.285917i
$156$	−56.5844	+	23.4380i	−4.53038	+	1.87654i
$157$		−	10.0874i		−	0.805061i	−0.915407	−	0.402530i	$-0.868131\pi$
$157$		−	10.0874i		−	0.805061i	0.915407	−	0.402530i	$-0.131869\pi$
$158$	10.1578	+	24.5230i	0.808108	+	1.95095i
$159$	22.9569	+	9.50908i	1.82060	+	0.754119i
$160$	−19.2583	+	46.4936i	−1.52250	+	3.67564i
$161$	−18.0823	+	18.0823i	−1.42508	+	1.42508i
$162$	13.8259	−	13.8259i	1.08626	−	1.08626i
$163$	−9.07605	+	21.9115i	−0.710891	+	1.71624i	−0.0131282	+	0.999914i	$0.504179\pi$
$163$	−9.07605	+	21.9115i	−0.710891	+	1.71624i	−0.697763	+	0.716329i	$0.745821\pi$
$164$	−20.0002	−	8.28435i	−1.56175	−	0.646899i
$165$	−5.02164	−	12.1233i	−0.390934	−	0.943798i
$166$			9.43387i			0.732210i
$167$	−4.20419	+	1.74143i	−0.325330	+	0.134756i	−0.539370	−	0.842069i	$-0.681338\pi$
$167$	−4.20419	+	1.74143i	−0.325330	+	0.134756i	0.214040	+	0.976825i	$0.431338\pi$
$168$	−65.5269	−	65.5269i	−5.05551	−	5.05551i
$169$	−4.89407			−0.376467
$170$	−5.33766	−	21.4449i	−0.409380	−	1.64475i
$171$	19.5484			1.49490
$172$	4.00160	+	4.00160i	0.305119	+	0.305119i
$173$	6.77175	−	2.80495i	0.514846	−	0.213256i	−0.110105	−	0.993920i	$-0.535119\pi$
$173$	6.77175	−	2.80495i	0.514846	−	0.213256i	0.624951	+	0.780664i	$0.285119\pi$
$174$			37.0702i			2.81028i
$175$	1.70985	+	4.12793i	0.129252	+	0.312042i
$176$	−40.8778	−	16.9322i	−3.08128	−	1.27631i
$177$	−4.95276	+	11.9570i	−0.372272	+	0.898745i
$178$	14.4673	−	14.4673i	1.08437	−	1.08437i
$179$	−8.27269	+	8.27269i	−0.618330	+	0.618330i	−0.945103	−	0.326773i	$-0.894039\pi$
$179$	−8.27269	+	8.27269i	−0.618330	+	0.618330i	0.326773	+	0.945103i	$0.394039\pi$
$180$	−14.8714	+	35.9029i	−1.10845	+	2.67604i
$181$	−5.21744	−	2.16113i	−0.387809	−	0.160636i	0.180255	−	0.983620i	$-0.442308\pi$
$181$	−5.21744	−	2.16113i	−0.387809	−	0.160636i	−0.568064	+	0.822984i	$0.692308\pi$
$182$	−16.0241	−	38.6857i	−1.18779	−	2.86757i
$183$		−	20.7758i		−	1.53579i
$184$	66.8894	−	27.7065i	4.93115	−	2.04255i
$185$	9.55180	+	9.55180i	0.702263	+	0.702263i
$186$	18.4045			1.34949
$187$	10.5959	−	2.63733i	0.774847	−	0.192860i
$188$	−34.4801			−2.51472
$189$	−3.53109	−	3.53109i	−0.256849	−	0.256849i
$190$	27.3009	−	11.3084i	1.98061	−	0.820397i
$191$			19.3730i			1.40178i	0.713270	+	0.700889i	$0.247213\pi$
$191$			19.3730i			1.40178i	−0.713270	+	0.700889i	$0.752787\pi$
$192$	37.6923	+	90.9973i	2.72021	+	6.56716i
$193$	−23.9649	−	9.92660i	−1.72503	−	0.714532i	−0.999657	−	0.0261800i	$-0.991666\pi$
$193$	−23.9649	−	9.92660i	−1.72503	−	0.714532i	−0.725376	−	0.688352i	$-0.758334\pi$
$194$	3.22883	−	7.79509i	0.231817	−	0.559655i
$195$	−14.8211	+	14.8211i	−1.06136	+	1.06136i
$196$	23.1824	−	23.1824i	1.65588	−	1.65588i
$197$	−2.62221	+	6.33058i	−0.186825	+	0.451035i	−0.989345	−	0.145590i	$-0.953492\pi$
$197$	−2.62221	+	6.33058i	−0.186825	+	0.451035i	0.802520	+	0.596625i	$0.203492\pi$
$198$	−24.0089	−	9.94480i	−1.70624	−	0.706746i
$199$	−8.12100	−	19.6058i	−0.575682	−	1.38982i	−0.896654	−	0.442731i	$-0.854010\pi$
$199$	−8.12100	−	19.6058i	−0.575682	−	1.38982i	0.320972	−	0.947089i	$-0.395990\pi$
$200$		−	12.6500i		−	0.894493i
$201$	−18.1874	+	7.53348i	−1.28284	+	0.531370i
$202$	−11.7438	−	11.7438i	−0.826290	−	0.826290i
$203$	−18.7261			−1.31432
$204$	−51.1578	−	30.7667i	−3.58176	−	2.15410i
$205$	−7.40854			−0.517435
$206$	21.0699	+	21.0699i	1.46801	+	1.46801i
$207$	23.4204	−	9.70104i	1.62783	−	0.674269i
$208$			70.6745i			4.90039i
$209$	5.58744	+	13.4893i	0.386492	+	0.933073i
$210$	−45.3144	−	18.7699i	−3.12699	−	1.29524i
$211$	2.89550	−	6.99036i	0.199334	−	0.481236i	−0.792328	−	0.610095i	$-0.791131\pi$
$211$	2.89550	−	6.99036i	0.199334	−	0.481236i	0.991663	+	0.128859i	$0.0411314\pi$
$212$	38.8646	−	38.8646i	2.66923	−	2.66923i
$213$	−23.7193	+	23.7193i	−1.62522	+	1.62522i
$214$	11.4388	−	27.6157i	0.781939	−	1.88777i
$215$	1.78928	+	0.741144i	0.122028	+	0.0505456i
$216$	5.41051	+	13.0621i	0.368138	+	0.888765i
$217$			9.29712i			0.631130i
$218$	−11.3291	+	4.69267i	−0.767304	+	0.317828i
$219$	9.08218	+	9.08218i	0.613717	+	0.613717i
$220$	−29.0253			−1.95688
$221$	−10.3689	−	14.0245i	−0.697485	−	0.943389i
$222$	49.3861			3.31458
$223$	−17.5348	−	17.5348i	−1.17421	−	1.17421i	−0.981195	−	0.193019i	$-0.938172\pi$
$223$	−17.5348	−	17.5348i	−1.17421	−	1.17421i	−0.193019	−	0.981195i	$-0.561828\pi$
$224$	−85.8659	+	35.5668i	−5.73716	+	2.37641i
$225$		−	4.42923i		−	0.295282i
$226$	−2.35037	−	5.67431i	−0.156345	−	0.377449i
$227$	0.764800	+	0.316791i	0.0507616	+	0.0210261i	0.407920	−	0.913018i	$-0.366254\pi$
$227$	0.764800	+	0.316791i	0.0507616	+	0.0210261i	−0.357158	+	0.934044i	$0.616254\pi$
$228$	30.5475	−	73.7481i	2.02305	−	4.88409i
$229$	13.4671	−	13.4671i	0.889928	−	0.889928i	−0.104588	−	0.994516i	$-0.533352\pi$
$229$	13.4671	−	13.4671i	0.889928	−	0.889928i	0.994516	+	0.104588i	$0.0333524\pi$
$230$	27.0965	−	27.0965i	1.78669	−	1.78669i
$231$	9.27414	−	22.3897i	0.610193	−	1.47314i
$232$	48.9822	+	20.2891i	3.21584	+	1.33204i
$233$	0.0267958	+	0.0646907i	0.00175545	+	0.00423803i	0.924755	−	0.380563i	$-0.124270\pi$
$233$	0.0267958	+	0.0646907i	0.00175545	+	0.00423803i	−0.922999	+	0.384801i	$0.874270\pi$
$234$			41.5094i			2.71355i
$235$	−10.9018	+	4.51568i	−0.711156	+	0.294570i
$236$	20.2425	+	20.2425i	1.31767	+	1.31767i
$237$	24.5384			1.59394
$238$	21.0346	−	34.9756i	1.36347	−	2.26713i
$239$	10.2289			0.661650			0.330825	−	0.943692i	$-0.392673\pi$
$239$	10.2289			0.661650			0.330825	+	0.943692i	$0.392673\pi$
$240$	58.5375	+	58.5375i	3.77858	+	3.77858i
$241$	−6.25432	+	2.59062i	−0.402876	+	0.166877i	−0.574914	−	0.818214i	$-0.694965\pi$
$241$	−6.25432	+	2.59062i	−0.402876	+	0.166877i	0.172039	+	0.985090i	$0.444965\pi$
$242$			11.0329i			0.709222i
$243$	−8.52015	−	20.5695i	−0.546568	−	1.31953i
$244$	−42.4564	−	17.5860i	−2.71799	−	1.12583i
$245$	4.29365	−	10.3658i	0.274311	−	0.662246i
$246$	−19.1524	+	19.1524i	−1.22111	+	1.22111i
$247$	16.4911	−	16.4911i	1.04930	−	1.04930i
$248$	10.0731	−	24.3186i	0.639642	−	1.54423i
$249$	8.05738	+	3.33748i	0.510616	+	0.211504i
$250$	−12.8178	−	30.9450i	−0.810672	−	1.95714i
$251$			5.73348i			0.361894i	0.983493	+	0.180947i	$0.0579162\pi$
$251$			5.73348i			0.361894i	−0.983493	+	0.180947i	$0.942084\pi$
$252$	−66.3066	+	27.4651i	−4.17693	+	1.73014i
$253$	13.3883	+	13.3883i	0.841717	+	0.841717i
$254$	−21.7785			−1.36650
$255$	−20.2042	−	3.02785i	−1.26524	−	0.189611i
$256$	74.0381			4.62738
$257$	4.06395	+	4.06395i	0.253502	+	0.253502i	0.822405	−	0.568903i	$-0.192632\pi$
$257$	4.06395	+	4.06395i	0.253502	+	0.253502i	−0.568903	+	0.822405i	$0.692632\pi$
$258$	6.54158	−	2.70961i	0.407261	−	0.168693i
$259$			24.9476i			1.55017i
$260$	17.7421	+	42.8333i	1.10032	+	2.65641i
$261$	17.1504	+	7.10394i	1.06158	+	0.439723i
$262$	−13.1176	+	31.6686i	−0.810407	+	1.95650i
$263$	15.1564	−	15.1564i	0.934581	−	0.934581i	−0.0634069	−	0.997988i	$-0.520197\pi$
$263$	15.1564	−	15.1564i	0.934581	−	0.934581i	0.997988	+	0.0634069i	$0.0201966\pi$
$264$	−48.5169	+	48.5169i	−2.98601	+	2.98601i
$265$	7.19819	−	17.3780i	0.442181	−	1.06752i
$266$	50.4202	+	20.8847i	3.09146	+	1.28052i
$267$	−7.23823	−	17.4746i	−0.442972	−	1.06943i
$268$			43.5438i			2.65986i
$269$	11.2409	−	4.65615i	0.685372	−	0.283890i	−0.0126988	−	0.999919i	$-0.504042\pi$
$269$	11.2409	−	4.65615i	0.685372	−	0.283890i	0.698070	+	0.716029i	$0.254042\pi$
$270$	5.29139	+	5.29139i	0.322024	+	0.322024i
$271$	−17.4884			−1.06235			−0.531173	−	0.847263i	$-0.678249\pi$
$271$	−17.4884			−1.06235			−0.531173	+	0.847263i	$0.678249\pi$
$272$	−55.3911	+	40.9528i	−3.35858	+	2.48313i
$273$	−38.7100			−2.34284
$274$	21.3312	+	21.3312i	1.28867	+	1.28867i
$275$	3.05637	−	1.26599i	0.184306	−	0.0763422i
$276$		−	103.515i		−	6.23087i
$277$	−2.89966	−	7.00040i	−0.174224	−	0.420614i	0.812513	−	0.582943i	$-0.198099\pi$
$277$	−2.89966	−	7.00040i	−0.174224	−	0.420614i	−0.986737	+	0.162330i	$0.948099\pi$
$278$	−11.8243	−	4.89779i	−0.709176	−	0.293750i
$279$	3.52695	−	8.51481i	0.211153	−	0.509769i
$280$	−49.6026	+	49.6026i	−2.96432	+	2.96432i
$281$	5.96669	−	5.96669i	0.355943	−	0.355943i	−0.506372	−	0.862315i	$-0.669014\pi$
$281$	5.96669	−	5.96669i	0.355943	−	0.355943i	0.862315	+	0.506372i	$0.169014\pi$
$282$	−16.5093	+	39.8569i	−0.983112	+	2.37344i
$283$	8.13841	+	3.37104i	0.483778	+	0.200387i	0.611223	−	0.791458i	$-0.290678\pi$
$283$	8.13841	+	3.37104i	0.483778	+	0.200387i	−0.127445	+	0.991846i	$0.540678\pi$
$284$	28.3940	+	68.5491i	1.68487	+	4.06764i
$285$		−	27.3181i		−	1.61818i
$286$	−28.6434	+	11.8645i	−1.69372	+	0.701561i
$287$	−9.67489	−	9.67489i	−0.571091	−	0.571091i
$288$	92.1333			5.42901
$289$	4.98338	−	16.2532i	0.293140	−	0.956069i
$290$	28.0614			1.64782
$291$	−5.51543	−	5.51543i	−0.323320	−	0.323320i
$292$	26.2477	−	10.8722i	1.53603	−	0.636244i
$293$		−	20.6380i		−	1.20569i	−0.797860	−	0.602843i	$-0.794034\pi$
$293$		−	20.6380i		−	1.20569i	0.797860	−	0.602843i	$-0.205966\pi$
$294$	−15.6975	−	37.8972i	−0.915499	−	2.21021i
$295$	9.05124	+	3.74915i	0.526984	+	0.218284i
$296$	27.0298	−	65.2557i	1.57107	−	3.79291i
$297$	−2.61446	+	2.61446i	−0.151707	+	0.151707i
$298$	16.8509	−	16.8509i	0.976148	−	0.976148i
$299$	11.5737	−	27.9413i	0.669322	−	1.61589i
$300$	−16.7097	−	6.92138i	−0.964734	−	0.399606i
$301$	1.36877	+	3.30450i	0.0788946	+	0.190468i
$302$		−	50.4940i		−	2.90560i
$303$	−14.1849	+	5.87559i	−0.814903	+	0.337544i
$304$	−65.1331	−	65.1331i	−3.73564	−	3.73564i
$305$	−15.7269			−0.900518
$306$	−32.5330	+	24.0529i	−1.85979	+	1.37501i
$307$	−12.9924			−0.741517			−0.370759	−	0.928729i	$-0.620902\pi$
$307$	−12.9924			−0.741517			−0.370759	+	0.928729i	$0.620902\pi$
$308$	−37.9044	−	37.9044i	−2.15980	−	2.15980i
$309$	25.4497	−	10.5416i	1.44778	−	0.599691i
$310$		−	13.9319i		−	0.791278i
$311$	−3.78838	−	9.14596i	−0.214819	−	0.518620i	0.779333	−	0.626610i	$-0.215558\pi$
$311$	−3.78838	−	9.14596i	−0.214819	−	0.518620i	−0.994152	+	0.107991i	$0.965558\pi$
$312$	101.254	+	41.9409i	5.73240	+	2.37444i
$313$	−5.57339	+	13.4554i	−0.315027	+	0.760542i	0.684477	+	0.729035i	$0.260031\pi$
$313$	−5.57339	+	13.4554i	−0.315027	+	0.760542i	−0.999504	+	0.0315073i	$0.989969\pi$
$314$	−19.7403	+	19.7403i	−1.11401	+	1.11401i
$315$	−17.3676	+	17.3676i	−0.978556	+	0.978556i
$316$	20.7710	−	50.1456i	1.16846	−	2.82091i
$317$	21.8411	+	9.04686i	1.22672	+	0.508122i	0.899539	−	0.436841i	$-0.143903\pi$
$317$	21.8411	+	9.04686i	1.22672	+	0.508122i	0.327177	+	0.944963i	$0.393903\pi$
$318$	−26.3165	−	63.5336i	−1.47575	−	3.56279i
$319$			13.8651i			0.776295i
$320$	68.8832	−	28.5323i	3.85069	−	1.59501i
$321$	−19.5395	−	19.5395i	−1.09059	−	1.09059i
$322$	70.7712			3.94393
$323$	22.4807	+	3.36900i	1.25086	+	0.187456i
$324$	−39.9823			−2.22124
$325$	−3.73651	−	3.73651i	−0.207264	−	0.207264i
$326$	60.6404	−	25.1181i	3.35856	−	1.39116i
$327$			11.3362i			0.626896i
$328$	14.8243	+	35.7891i	0.818537	+	1.97612i
$329$	−20.1338	−	8.33971i	−1.11001	−	0.459783i
$330$	−13.8974	+	33.5514i	−0.765029	+	1.84694i
$331$	−16.2091	+	16.2091i	−0.890935	+	0.890935i	−0.994611	−	0.103676i	$-0.966940\pi$
$331$	−16.2091	+	16.2091i	−0.890935	+	0.890935i	0.103676	+	0.994611i	$0.466940\pi$
$332$	13.6406	−	13.6406i	0.748626	−	0.748626i
$333$	9.46410	−	22.8484i	0.518629	−	1.25208i
$334$	11.6351	+	4.81943i	0.636646	+	0.263707i
$335$	5.70270	+	13.7675i	0.311572	+	0.752200i
$336$			152.889i			8.34079i
$337$	7.40092	−	3.06556i	0.403154	−	0.166992i	−0.171887	−	0.985117i	$-0.554986\pi$
$337$	7.40092	−	3.06556i	0.403154	−	0.166992i	0.575040	+	0.818125i	$0.304986\pi$
$338$	9.57734	+	9.57734i	0.520939	+	0.520939i
$339$	−5.67788			−0.308380
$340$	−23.2898	+	38.7255i	−1.26307	+	2.10018i
$341$	6.88371			0.372774
$342$	−38.2547	−	38.2547i	−2.06858	−	2.06858i
$343$	−3.98762	+	1.65173i	−0.215311	+	0.0891849i
$344$		−	10.1266i		−	0.545992i
$345$	−13.5568	−	32.7290i	−0.729874	−	1.76207i
$346$	−18.7409	−	7.76273i	−1.00752	−	0.417327i
$347$	−0.118365	+	0.285759i	−0.00635417	+	0.0153403i	−0.927025	−	0.375000i	$-0.877643\pi$
$347$	−0.118365	+	0.285759i	−0.00635417	+	0.0153403i	0.920671	+	0.390340i	$0.127643\pi$
$348$	53.6005	−	53.6005i	2.87329	−	2.87329i
$349$	15.0089	−	15.0089i	0.803406	−	0.803406i	−0.180221	−	0.983626i	$-0.557681\pi$
$349$	15.0089	−	15.0089i	0.803406	−	0.803406i	0.983626	+	0.180221i	$0.0576812\pi$
$350$	4.73202	−	11.4241i	0.252937	−	0.610644i
$351$	5.45636	+	2.26010i	0.291239	+	0.120635i
$352$	26.3341	+	63.5762i	1.40361	+	3.38862i
$353$			3.75774i			0.200004i	0.994987	+	0.100002i	$0.0318850\pi$
$353$			3.75774i			0.200004i	−0.994987	+	0.100002i	$0.968115\pi$
$354$	33.0912	−	13.7068i	1.75878	−	0.728510i
$355$	17.9550	+	17.9550i	0.952954	+	0.952954i
$356$	−41.8372			−2.21737
$357$	−22.4308	−	30.3390i	−1.18716	−	1.60571i
$358$	32.3781			1.71124
$359$	−6.79433	−	6.79433i	−0.358591	−	0.358591i	0.504702	−	0.863293i	$-0.331602\pi$
$359$	−6.79433	−	6.79433i	−0.358591	−	0.358591i	−0.863293	+	0.504702i	$0.831602\pi$
$360$	64.2460	−	26.6115i	3.38606	−	1.40255i
$361$			11.3961i			0.599793i
$362$	5.98096	+	14.4393i	0.314352	+	0.758914i
$363$	9.42311	+	3.90318i	0.494585	+	0.204864i
$364$	−32.7668	+	79.1060i	−1.71745	+	4.14628i
$365$	6.87504	−	6.87504i	0.359856	−	0.359856i
$366$	−40.6567	+	40.6567i	−2.12516	+	2.12516i
$367$	−11.7053	+	28.2592i	−0.611014	+	1.47512i	0.250874	+	0.968020i	$0.419282\pi$
$367$	−11.7053	+	28.2592i	−0.611014	+	1.47512i	−0.861888	+	0.507098i	$0.830718\pi$
$368$	−110.357	−	45.7114i	−5.75276	−	2.38287i
$369$	5.19053	+	12.5311i	0.270208	+	0.652340i
$370$		−	37.3843i		−	1.94352i
$371$	32.0942	−	13.2939i	1.66625	−	0.690183i
$372$	−26.6115	−	26.6115i	−1.37974	−	1.37974i
$373$	−5.11570			−0.264881			−0.132440	−	0.991191i	$-0.542281\pi$
$373$	−5.11570			−0.264881			−0.132440	+	0.991191i	$0.542281\pi$
$374$	−25.8964	−	15.5743i	−1.33907	−	0.805327i
$375$	−30.9645			−1.59900
$376$	43.6286	+	43.6286i	2.24997	+	2.24997i
$377$	20.4610	−	8.47523i	1.05380	−	0.436497i
$378$			13.8202i			0.710832i
$379$	8.77692	+	21.1894i	0.450840	+	1.08842i	0.972003	+	0.234967i	$0.0754982\pi$
$379$	8.77692	+	21.1894i	0.450840	+	1.08842i	−0.521163	+	0.853457i	$0.674502\pi$
$380$	−55.8259	−	23.1238i	−2.86381	−	1.18623i
$381$	−7.70470	+	18.6008i	−0.394724	+	0.952948i
$382$	37.9114	−	37.9114i	1.93972	−	1.93972i
$383$	−7.90310	+	7.90310i	−0.403830	+	0.403830i	−0.879580	−	0.475751i	$-0.842177\pi$
$383$	−7.90310	+	7.90310i	−0.403830	+	0.403830i	0.475751	+	0.879580i	$0.342177\pi$
$384$	53.4320	−	128.996i	2.72669	−	6.58282i
$385$	−16.9486	−	7.02034i	−0.863781	−	0.357790i
$386$	27.4720	+	66.3232i	1.39829	+	3.37576i
$387$		−	3.54570i		−	0.180238i
$388$	−15.9397	+	6.60245i	−0.809216	+	0.335188i
$389$	−7.63230	−	7.63230i	−0.386973	−	0.386973i	0.486633	−	0.873606i	$-0.338225\pi$
$389$	−7.63230	−	7.63230i	−0.386973	−	0.386973i	−0.873606	+	0.486633i	$0.838225\pi$
$390$	58.0076			2.93733
$391$	28.6054	−	7.11993i	1.44664	−	0.360070i
$392$	−58.6664			−2.96310
$393$	22.4072	+	22.4072i	1.13029	+	1.13029i
$394$	17.5199	−	7.25700i	0.882642	−	0.365602i
$395$		−	18.5751i		−	0.934616i
$396$	20.3355	+	49.0943i	1.02190	+	2.46708i
$397$	2.36041	+	0.977713i	0.118465	+	0.0490700i	0.441129	−	0.897444i	$-0.354578\pi$
$397$	2.36041	+	0.977713i	0.118465	+	0.0490700i	−0.322663	+	0.946514i	$0.604578\pi$
$398$	−22.4749	+	54.2593i	−1.12657	+	2.71977i
$399$	35.6749	−	35.6749i	1.78598	−	1.78598i
$400$	−14.7577	+	14.7577i	−0.737886	+	0.737886i
$401$	−10.1512	+	24.5072i	−0.506926	+	1.22383i	0.438718	+	0.898625i	$0.355433\pi$
$401$	−10.1512	+	24.5072i	−0.506926	+	1.22383i	−0.945644	+	0.325204i	$0.894567\pi$
$402$	50.3339	+	20.8490i	2.51043	+	1.03985i
$403$	−4.20777	−	10.1585i	−0.209604	−	0.506029i
$404$			33.9611i			1.68963i
$405$	−12.6415	+	5.23626i	−0.628159	+	0.260192i
$406$	36.6457	+	36.6457i	1.81869	+	1.81869i
$407$	18.4715			0.915599
$408$	25.8014	+	103.661i	1.27736	+	5.13199i
$409$	−9.81406			−0.485274			−0.242637	−	0.970117i	$-0.578012\pi$
$409$	−9.81406			−0.485274			−0.242637	+	0.970117i	$0.578012\pi$
$410$	14.4980	+	14.4980i	0.716004	+	0.716004i
$411$	25.7653	−	10.6723i	1.27091	−	0.526427i
$412$		−	60.9309i		−	3.00185i
$413$	6.92405	+	16.7161i	0.340710	+	0.822548i
$414$	−64.8162	−	26.8477i	−3.18554	−	1.31949i
$415$	2.52641	−	6.09928i	0.124016	−	0.299402i
$416$	77.7238	−	77.7238i	3.81072	−	3.81072i
$417$	−8.36632	+	8.36632i	−0.409701	+	0.409701i
$418$	15.4633	−	37.3317i	0.756335	−	1.82596i
$419$	2.10888	+	0.873526i	0.103025	+	0.0426746i	0.433601	−	0.901105i	$-0.357243\pi$
$419$	2.10888	+	0.873526i	0.103025	+	0.0426746i	−0.330575	+	0.943780i	$0.607243\pi$
$420$	38.3813	+	92.6607i	1.87282	+	4.52138i
$421$		−	11.0770i		−	0.539862i	−0.962880	−	0.269931i	$-0.912999\pi$
$421$		−	11.0770i		−	0.539862i	0.962880	−	0.269931i	$-0.0870009\pi$
$422$	−19.3459	+	8.01333i	−0.941743	+	0.390083i
$423$	15.2759	+	15.2759i	0.742741	+	0.742741i
$424$	−98.3527			−4.77643
$425$	0.763342	−	5.09364i	0.0370275	−	0.247078i
$426$	92.8337			4.49781
$427$	−20.5379	−	20.5379i	−0.993897	−	0.993897i
$428$	−56.4696	+	23.3905i	−2.72956	+	1.13062i
$429$			28.6614i			1.38379i
$430$	−2.05112	−	4.95185i	−0.0989140	−	0.238799i
$431$	20.8865	+	8.65148i	1.00607	+	0.416727i	0.824019	−	0.566562i	$-0.191727\pi$
$431$	20.8865	+	8.65148i	1.00607	+	0.416727i	0.182049	+	0.983289i	$0.441727\pi$
$432$	8.92648	−	21.5504i	0.429476	−	1.03685i
$433$	2.06892	−	2.06892i	0.0994259	−	0.0994259i	−0.655644	−	0.755070i	$-0.727603\pi$
$433$	2.06892	−	2.06892i	0.0994259	−	0.0994259i	0.755070	+	0.655644i	$0.227603\pi$
$434$	18.1938	−	18.1938i	0.873329	−	0.873329i
$435$	9.92746	−	23.9670i	0.475985	−	1.14913i
$436$	23.1662	+	9.59576i	1.10946	+	0.459554i
$437$	15.0843	+	36.4167i	0.721580	+	1.74205i
$438$		−	35.5463i		−	1.69847i
$439$	−37.3256	+	15.4608i	−1.78145	+	0.737903i	−0.789132	+	0.614223i	$0.789469\pi$
$439$	−37.3256	+	15.4608i	−1.78145	+	0.737903i	−0.992322	+	0.123679i	$0.960531\pi$
$440$	36.7264	+	36.7264i	1.75086	+	1.75086i
$441$	−20.5412			−0.978154
$442$	−7.15380	+	47.7359i	−0.340272	+	2.27057i
$443$	−32.6240			−1.55001			−0.775006	−	0.631953i	$-0.782253\pi$
$443$	−32.6240			−1.55001			−0.775006	+	0.631953i	$0.782253\pi$
$444$	−71.4084	−	71.4084i	−3.38889	−	3.38889i
$445$	−13.2280	+	5.47920i	−0.627065	+	0.259739i
$446$			68.6284i			3.24965i
$447$	−8.43077	−	20.3537i	−0.398762	−	0.962696i
$448$	127.216	+	52.6945i	6.01038	+	2.48958i
$449$	5.52173	−	13.3306i	0.260586	−	0.629111i	−0.738389	−	0.674375i	$-0.764413\pi$
$449$	5.52173	−	13.3306i	0.260586	−	0.629111i	0.998975	+	0.0452641i	$0.0144129\pi$
$450$	−8.66768	+	8.66768i	−0.408598	+	0.408598i
$451$	−7.16341	+	7.16341i	−0.337312	+	0.337312i
$452$	−4.80614	+	11.6030i	−0.226062	+	0.545761i
$453$	−43.1265	−	17.8636i	−2.02626	−	0.839304i
$454$	−0.876721	−	2.11659i	−0.0411466	−	0.0993366i
$455$			29.3028i			1.37373i
$456$	−131.968	+	54.6628i	−6.17995	+	2.55982i
$457$	−19.5705	−	19.5705i	−0.915471	−	0.915471i	0.0812246	−	0.996696i	$-0.474117\pi$
$457$	−19.5705	−	19.5705i	−0.915471	−	0.915471i	−0.996696	+	0.0812246i	$0.974117\pi$
$458$	−52.7080			−2.46288
$459$	1.39038	+	5.58605i	0.0648972	+	0.260735i
$460$	−78.3589			−3.65350
$461$	17.8736	+	17.8736i	0.832455	+	0.832455i	0.987852	−	0.155397i	$-0.0496658\pi$
$461$	17.8736	+	17.8736i	0.832455	+	0.832455i	−0.155397	+	0.987852i	$0.549666\pi$
$462$	−61.9639	+	25.6663i	−2.88282	+	1.19410i
$463$			37.6760i			1.75095i	0.483260	+	0.875477i	$0.339453\pi$
$463$			37.6760i			1.75095i	−0.483260	+	0.875477i	$0.660547\pi$
$464$	−33.4738	−	80.8129i	−1.55398	−	3.75164i
$465$	−11.8991	−	4.92877i	−0.551807	−	0.228566i
$466$	0.0741576	−	0.179032i	0.00343528	−	0.00829351i
$467$	−15.8475	+	15.8475i	−0.733337	+	0.733337i	−0.971279	−	0.237942i	$-0.923527\pi$
$467$	−15.8475	+	15.8475i	−0.733337	+	0.733337i	0.237942	+	0.971279i	$0.423527\pi$
$468$	60.0192	−	60.0192i	2.77439	−	2.77439i
$469$	−10.5319	+	25.4263i	−0.486320	+	1.17408i
$470$	30.1709	+	12.4972i	1.39168	+	0.576452i
$471$	9.87634	+	23.8436i	0.455078	+	1.09866i
$472$		−	51.2266i		−	2.35789i
$473$	2.44670	−	1.01346i	0.112499	−	0.0465987i
$474$	−48.0199	−	48.0199i	−2.20563	−	2.20563i
$475$	6.88708			0.316001
$476$	−80.9863	+	20.1576i	−3.71200	+	0.923921i
$477$	−34.4368			−1.57675
$478$	−20.0171	−	20.0171i	−0.915562	−	0.915562i
$479$	−9.50951	+	3.93897i	−0.434500	+	0.179976i	−0.589203	−	0.807985i	$-0.700558\pi$
$479$	−9.50951	+	3.93897i	−0.434500	+	0.179976i	0.154702	+	0.987961i	$0.450558\pi$
$480$		−	128.752i		−	5.87672i
$481$	−11.2910	−	27.2588i	−0.514824	−	1.24290i
$482$	17.3089	+	7.16958i	0.788398	+	0.326565i
$483$	25.0372	−	60.4451i	1.13923	−	2.75035i
$484$	15.9527	−	15.9527i	0.725123	−	0.725123i
$485$	−4.17508	+	4.17508i	−0.189580	+	0.189580i
$486$	−23.5796	+	56.9262i	−1.06959	+	2.58223i
$487$	18.8543	+	7.80971i	0.854370	+	0.353892i	0.766503	−	0.642241i	$-0.221995\pi$
$487$	18.8543	+	7.80971i	0.854370	+	0.353892i	0.0878670	+	0.996132i	$0.471995\pi$
$488$	31.4691	+	75.9732i	1.42454	+	3.43914i
$489$		−	60.6786i		−	2.74398i
$490$	−28.6874	+	11.8827i	−1.29597	+	0.536807i
$491$	−16.6092	−	16.6092i	−0.749562	−	0.749562i	0.224835	−	0.974397i	$-0.427816\pi$
$491$	−16.6092	−	16.6092i	−0.749562	−	0.749562i	−0.974397	+	0.224835i	$0.927816\pi$
$492$	55.3856			2.49697
$493$	18.4988	+	11.1253i	0.833142	+	0.501058i
$494$	−64.5435			−2.90395
$495$	12.8592	+	12.8592i	0.577979	+	0.577979i
$496$	−40.1218	+	16.6190i	−1.80152	+	0.746216i
$497$			46.8953i			2.10354i
$498$	−9.23650	−	22.2989i	−0.413898	−	0.999237i
$499$	18.2050	+	7.54075i	0.814967	+	0.337570i	0.750934	−	0.660377i	$-0.229604\pi$
$499$	18.2050	+	7.54075i	0.814967	+	0.337570i	0.0640330	+	0.997948i	$0.479604\pi$
$500$	−26.2104	+	63.2776i	−1.17217	+	2.82986i
$501$	8.23246	−	8.23246i	0.367799	−	0.367799i
$502$	11.2200	−	11.2200i	0.500773	−	0.500773i
$503$	−7.32077	+	17.6739i	−0.326417	+	0.788040i	0.672436	+	0.740155i	$0.265248\pi$
$503$	−7.32077	+	17.6739i	−0.326417	+	0.788040i	−0.998853	+	0.0478846i	$0.984752\pi$
$504$	118.652	+	49.1471i	5.28517	+	2.18919i
$505$	4.44771	+	10.7377i	0.197920	+	0.477822i
$506$		−	52.3999i		−	2.32946i
$507$	11.5682	−	4.79169i	0.513760	−	0.212806i
$508$	31.4899	+	31.4899i	1.39714	+	1.39714i
$509$	31.7766			1.40847			0.704236	−	0.709966i	$-0.251290\pi$
$509$	31.7766			1.40847			0.704236	+	0.709966i	$0.251290\pi$
$510$	33.6129	+	45.4635i	1.48841	+	2.01316i
$511$	17.9564			0.794342
$512$	−67.7081	−	67.7081i	−2.99230	−	2.99230i
$513$	−7.11143	+	2.94565i	−0.313977	+	0.130054i
$514$		−	15.9057i		−	0.701570i
$515$	−7.97979	−	19.2649i	−0.351631	−	0.848913i
$516$	−13.3765	−	5.54072i	−0.588867	−	0.243917i
$517$	−6.17483	+	14.9074i	−0.271569	+	0.655625i
$518$	48.8205	−	48.8205i	2.14505	−	2.14505i
$519$	−13.2601	+	13.2601i	−0.582056	+	0.582056i
$520$	31.7485	−	76.6476i	1.39226	−	3.36122i
$521$	−22.5983	−	9.36054i	−0.990051	−	0.410092i	−0.171911	−	0.985112i	$-0.554994\pi$
$521$	−22.5983	−	9.36054i	−0.990051	−	0.410092i	−0.818139	+	0.575020i	$0.804994\pi$
$522$	−19.6602	−	47.4640i	−0.860505	−	2.07744i
$523$			6.57913i			0.287685i	0.989601	+	0.143843i	$0.0459459\pi$
$523$			6.57913i			0.287685i	−0.989601	+	0.143843i	$0.954054\pi$
$524$	64.7573	−	26.8233i	2.82894	−	1.17178i
$525$	−8.08314	−	8.08314i	−0.352777	−	0.352777i
$526$	−59.3197			−2.58646
$527$	5.52347	−	9.18423i	0.240606	−	0.400071i
$528$	113.201			4.92645
$529$	19.8807	+	19.8807i	0.864379	+	0.864379i
$530$	−48.0937	+	19.9211i	−2.08906	+	0.865316i
$531$		−	17.9363i		−	0.778368i
$532$	−42.7059	−	103.101i	−1.85154	−	4.47000i
$533$	14.9500	+	6.19248i	0.647555	+	0.268226i
$534$	−20.0319	+	48.3612i	−0.866864	+	2.09279i
$535$	−14.7910	+	14.7910i	−0.639473	+	0.639473i
$536$	55.0970	−	55.0970i	2.37983	−	2.37983i
$537$	11.4546	−	27.6538i	0.494302	−	1.19335i
$538$	−31.1094	−	12.8859i	−1.34122	−	0.555552i
$539$	−5.87122	−	14.1744i	−0.252892	−	0.610534i
$540$		−	15.3019i		−	0.658488i
$541$	23.9872	−	9.93583i	1.03129	−	0.427175i	0.198113	−	0.980179i	$-0.436519\pi$
$541$	23.9872	−	9.93583i	1.03129	−	0.427175i	0.833178	+	0.553004i	$0.186519\pi$
$542$	34.2236	+	34.2236i	1.47003	+	1.47003i
$543$	14.4484			0.620041
$544$	105.954	+	15.8784i	4.54273	+	0.680782i
$545$	8.58132			0.367583
$546$	75.7527	+	75.7527i	3.24191	+	3.24191i
$547$	−10.1574	+	4.20735i	−0.434301	+	0.179893i	−0.589113	−	0.808051i	$-0.700523\pi$
$547$	−10.1574	+	4.20735i	−0.434301	+	0.179893i	0.154812	+	0.987944i	$0.450523\pi$
$548$		−	61.6864i		−	2.63511i
$549$	11.0185	+	26.6009i	0.470257	+	1.13530i
$550$	−8.45855	−	3.50365i	−0.360674	−	0.149396i
$551$	−11.0460	+	26.6674i	−0.470576	+	1.13607i
$552$	−130.980	+	130.980i	−5.57488	+	5.57488i
$553$	24.2574	−	24.2574i	1.03153	−	1.03153i
$554$	−8.02485	+	19.3737i	−0.340943	+	0.823109i
$555$	−31.9296	−	13.2257i	−1.35534	−	0.561399i
$556$	10.0152	+	24.1788i	0.424739	+	1.02541i
$557$		−	39.3119i		−	1.66570i	−0.553499	−	0.832850i	$-0.686708\pi$
$557$		−	39.3119i		−	1.66570i	0.553499	−	0.832850i	$-0.313292\pi$
$558$	−23.5648	+	9.76088i	−0.997579	+	0.413211i
$559$	−2.99116	−	2.99116i	−0.126513	−	0.126513i
$560$	115.734			4.89066
$561$	−22.4634	+	16.6081i	−0.948405	+	0.701193i
$562$	−23.3527			−0.985076
$563$	−2.71744	−	2.71744i	−0.114526	−	0.114526i	0.647521	−	0.762047i	$-0.275806\pi$
$563$	−2.71744	−	2.71744i	−0.114526	−	0.114526i	−0.762047	+	0.647521i	$0.775806\pi$
$564$	81.5009	−	33.7588i	3.43181	−	1.42150i
$565$			4.29805i			0.180820i
$566$	−9.32939	−	22.5231i	−0.392143	−	0.946718i
$567$	−23.3467	−	9.67051i	−0.980468	−	0.406123i
$568$	50.8093	−	122.665i	2.13191	−	5.14689i
$569$	28.6905	−	28.6905i	1.20277	−	1.20277i	0.229445	−	0.973322i	$-0.426309\pi$
$569$	28.6905	−	28.6905i	1.20277	−	1.20277i	0.973322	−	0.229445i	$-0.0736911\pi$
$570$	−53.4594	+	53.4594i	−2.23917	+	2.23917i
$571$	15.6964	−	37.8945i	0.656875	−	1.58584i	−0.145728	−	0.989325i	$-0.546553\pi$
$571$	15.6964	−	37.8945i	0.656875	−	1.58584i	0.802604	−	0.596513i	$-0.203447\pi$
$572$	58.5711	+	24.2609i	2.44898	+	1.01440i
$573$	−18.9677	−	45.7920i	−0.792385	−	1.91299i
$574$			37.8661i			1.58050i
$575$	8.25122	−	3.41777i	0.344100	−	0.142531i
$576$	−96.5210	−	96.5210i	−4.02171	−	4.02171i
$577$	−7.50414			−0.312402			−0.156201	−	0.987725i	$-0.549925\pi$
$577$	−7.50414			−0.312402			−0.156201	+	0.987725i	$0.549925\pi$
$578$	−41.5584	+	22.0542i	−1.72860	+	0.917332i
$579$	66.3650			2.75803
$580$	−40.5746	−	40.5746i	−1.68477	−	1.68477i
$581$	11.2644	−	4.66585i	0.467325	−	0.193572i
$582$			21.5866i			0.894793i
$583$	−9.84295	−	23.7630i	−0.407653	−	0.984162i
$584$	−46.9686	−	19.4551i	−1.94358	−	0.805056i
$585$	11.1163	−	26.8371i	0.459601	−	1.10958i
$586$	−40.3871	+	40.3871i	−1.66838	+	1.66838i
$587$	−11.1068	+	11.1068i	−0.458426	+	0.458426i	−0.898139	−	0.439712i	$-0.855080\pi$
$587$	−11.1068	+	11.1068i	−0.458426	+	0.458426i	0.439712	+	0.898139i	$0.355080\pi$
$588$	−32.0989	+	77.4937i	−1.32374	+	3.19579i
$589$	13.2398	+	5.48411i	0.545537	+	0.225969i
$590$	−10.3758	−	25.0494i	−0.427165	−	1.03127i
$591$		−	17.5310i		−	0.721128i
$592$	−107.662	+	44.5949i	−4.42486	+	1.83284i
$593$	15.5600	+	15.5600i	0.638974	+	0.638974i	0.950302	−	0.311328i	$-0.100774\pi$
$593$	15.5600	+	15.5600i	0.638974	+	0.638974i	−0.311328	+	0.950302i	$0.600774\pi$
$594$	10.2326			0.419850
$595$	−22.9660	+	16.9797i	−0.941516	+	0.696100i
$596$	−48.7302			−1.99607
$597$	38.3913	+	38.3913i	1.57125	+	1.57125i
$598$	−77.3278	+	32.0302i	−3.16217	+	1.30981i
$599$			33.7657i			1.37963i	0.723985	+	0.689815i	$0.242308\pi$
$599$			33.7657i			1.37963i	−0.723985	+	0.689815i	$0.757692\pi$
$600$	12.3854	+	29.9010i	0.505631	+	1.22070i
$601$	−29.9757	−	12.4164i	−1.22274	−	0.506474i	−0.324457	−	0.945900i	$-0.605182\pi$
$601$	−29.9757	−	12.4164i	−1.22274	−	0.506474i	−0.898278	+	0.439427i	$0.855182\pi$
$602$	3.78809	−	9.14525i	0.154391	−	0.372733i
$603$	19.2914	−	19.2914i	0.785608	−	0.785608i
$604$	−73.0103	+	73.0103i	−2.97075	+	2.97075i
$605$	2.95463	−	7.13311i	0.120123	−	0.290002i
$606$	39.2569	+	16.2608i	1.59470	+	0.660548i
$607$	−9.22693	−	22.2758i	−0.374510	−	0.904146i	−0.992974	−	0.118333i	$-0.962245\pi$
$607$	−9.22693	−	22.2758i	−0.374510	−	0.904146i	0.618464	−	0.785813i	$-0.287755\pi$
$608$			143.259i			5.80994i
$609$	44.2631	−	18.3344i	1.79363	−	0.742946i
$610$	30.7763	+	30.7763i	1.24610	+	1.24610i
$611$	25.7736			1.04269
$612$	81.8187	+	12.2615i	3.30732	+	0.495642i
$613$	−33.4225			−1.34992			−0.674960	−	0.737854i	$-0.735839\pi$
$613$	−33.4225			−1.34992			−0.674960	+	0.737854i	$0.735839\pi$
$614$	25.4252	+	25.4252i	1.02608	+	1.02608i
$615$	17.5116	−	7.25355i	0.706137	−	0.292491i
$616$			95.9227i			3.86483i
$617$	7.32122	+	17.6750i	0.294741	+	0.711568i	0.999997	+	0.00261470i	$0.000832286\pi$
$617$	7.32122	+	17.6750i	0.294741	+	0.711568i	−0.705255	+	0.708953i	$0.749168\pi$
$618$	−70.4322	−	29.1740i	−2.83320	−	1.17355i
$619$	1.37608	−	3.32214i	0.0553092	−	0.133528i	−0.893809	−	0.448447i	$-0.851977\pi$
$619$	1.37608	−	3.32214i	0.0553092	−	0.133528i	0.949119	+	0.314919i	$0.101977\pi$
$620$	−20.1444	+	20.1444i	−0.809018	+	0.809018i
$621$	−7.05821	+	7.05821i	−0.283236	+	0.283236i
$622$	−10.4844	+	25.3115i	−0.420385	+	1.01490i
$623$	−24.4298	−	10.1192i	−0.978761	−	0.405416i
$624$	−69.1959	−	167.054i	−2.77005	−	6.68750i
$625$			17.1936i			0.687745i
$626$	37.2379	−	15.4244i	1.48832	−	0.616484i
$627$	−26.4142	−	26.4142i	−1.05488	−	1.05488i
$628$	57.0857			2.27797
$629$	14.8215	−	24.6446i	0.590971	−	0.982646i
$630$	67.9744			2.70816
$631$	10.4006	+	10.4006i	0.414041	+	0.414041i	0.883144	−	0.469103i	$-0.155423\pi$
$631$	10.4006	+	10.4006i	0.414041	+	0.414041i	−0.469103	+	0.883144i	$0.655423\pi$
$632$	−89.7325	+	37.1684i	−3.56937	+	1.47848i
$633$			19.3581i			0.769414i
$634$	−25.0373	−	60.4454i	−0.994358	−	2.40059i
$635$	14.0804	+	5.83231i	0.558765	+	0.231448i
$636$	−53.8130	+	129.916i	−2.13382	+	5.15151i
$637$	−17.3286	+	17.3286i	−0.686585	+	0.686585i
$638$	27.1329	−	27.1329i	1.07420	−	1.07420i
$639$	17.7902	−	42.9492i	0.703768	−	1.69905i
$640$	−97.6478	−	40.4470i	−3.85987	−	1.59881i
$641$	10.1593	+	24.5267i	0.401268	+	0.968746i	0.987359	+	0.158501i	$0.0506661\pi$
$641$	10.1593	+	24.5267i	0.401268	+	0.968746i	−0.586091	+	0.810245i	$0.699334\pi$
$642$			76.4748i			3.01822i
$643$	22.8583	−	9.46822i	0.901444	−	0.373390i	0.116669	−	0.993171i	$-0.462778\pi$
$643$	22.8583	−	9.46822i	0.901444	−	0.373390i	0.784775	+	0.619781i	$0.212778\pi$
$644$	−102.330	−	102.330i	−4.03235	−	4.03235i
$645$	−4.95497			−0.195102
$646$	−37.4002	−	50.5860i	−1.47149	−	1.99028i
$647$	19.8761			0.781410			0.390705	−	0.920516i	$-0.372231\pi$
$647$	19.8761			0.781410			0.390705	+	0.920516i	$0.372231\pi$
$648$	50.5905	+	50.5905i	1.98738	+	1.98738i
$649$	12.3768	−	5.12666i	0.485834	−	0.201239i
$650$			14.6241i			0.573606i
$651$	−9.10262	−	21.9757i	−0.356760	−	0.861294i
$652$	−124.000	−	51.3624i	−4.85621	−	2.01151i
$653$	−5.24318	+	12.6582i	−0.205181	+	0.495352i	−0.992653	−	0.121000i	$-0.961390\pi$
$653$	−5.24318	+	12.6582i	−0.205181	+	0.495352i	0.787471	+	0.616352i	$0.211390\pi$
$654$	22.1842	−	22.1842i	0.867470	−	0.867470i
$655$	16.9618	−	16.9618i	0.662753	−	0.662753i
$656$	24.4578	−	59.0464i	0.954917	−	2.30537i
$657$	−16.4454	−	6.81191i	−0.641597	−	0.265758i
$658$	23.0802	+	55.7206i	0.899761	+	2.17222i
$659$		−	0.686657i		−	0.0267484i	−0.999911	−	0.0133742i	$-0.995743\pi$
$659$		−	0.686657i		−	0.0267484i	0.999911	−	0.0133742i	$-0.00425726\pi$
$660$	68.6072	−	28.4180i	2.67053	−	1.10617i
$661$	−11.9310	−	11.9310i	−0.464063	−	0.464063i	0.435922	−	0.899984i	$-0.356422\pi$
$661$	−11.9310	−	11.9310i	−0.464063	−	0.464063i	−0.899984	+	0.435922i	$0.856422\pi$
$662$	63.4402			2.46567
$663$	38.2400	+	22.9978i	1.48512	+	0.893162i
$664$	−34.5196			−1.33962
$665$	−27.0052	−	27.0052i	−1.04722	−	1.04722i
$666$	−63.2331	+	26.1920i	−2.45023	+	1.01492i
$667$			37.4312i			1.44934i
$668$	−9.85496	−	23.7920i	−0.381300	−	0.920539i
$669$	58.6149	+	24.2791i	2.26618	+	0.938684i
$670$	15.7823	−	38.1018i	0.609722	−	1.47200i
$671$	−15.2065	+	15.2065i	−0.587040	+	0.587040i
$672$	168.139	−	168.139i	6.48610	−	6.48610i
$673$	9.77625	−	23.6019i	0.376847	−	0.909788i	−0.615707	−	0.787976i	$-0.711129\pi$
$673$	9.77625	−	23.6019i	0.376847	−	0.909788i	0.992553	−	0.121813i	$-0.0388707\pi$
$674$	−20.4821	−	8.48397i	−0.788942	−	0.326790i
$675$	0.667420	+	1.61129i	0.0256890	+	0.0620187i
$676$		−	27.6961i		−	1.06524i
$677$	13.0653	−	5.41183i	0.502141	−	0.207993i	−0.117211	−	0.993107i	$-0.537395\pi$
$677$	13.0653	−	5.41183i	0.502141	−	0.207993i	0.619352	+	0.785114i	$0.287395\pi$
$678$	11.1112	+	11.1112i	0.426723	+	0.426723i
$679$	−10.9045			−0.418478
$680$	78.4694	−	19.5311i	3.00916	−	0.748985i
$681$	−2.11793			−0.0811591
$682$	−13.4709	−	13.4709i	−0.515828	−	0.515828i
$683$	36.9834	−	15.3190i	1.41513	−	0.586166i	0.461498	−	0.887141i	$-0.347312\pi$
$683$	36.9834	−	15.3190i	1.41513	−	0.586166i	0.953632	+	0.300975i	$0.0973120\pi$
$684$			110.627i			4.22991i
$685$	−8.07874	−	19.5038i	−0.308673	−	0.745202i
$686$	11.0358	+	4.57117i	0.421348	+	0.174528i
$687$	−18.6468	+	45.0175i	−0.711421	+	1.71752i
$688$	−11.8139	+	11.8139i	−0.450400	+	0.450400i
$689$	−29.0510	+	29.0510i	−1.10675	+	1.10675i
$690$	−37.5186	+	90.5779i	−1.42831	+	3.44824i
$691$	−38.8998	−	16.1128i	−1.47982	−	0.612960i	−0.510743	−	0.859733i	$-0.670630\pi$
$691$	−38.8998	−	16.1128i	−1.47982	−	0.612960i	−0.969073	+	0.246773i	$0.920630\pi$
$692$	15.8735	+	38.3221i	0.603421	+	1.45679i
$693$			33.5860i			1.27583i
$694$	0.790840	−	0.327577i	0.0300199	−	0.0124346i
$695$	6.33314	+	6.33314i	0.240230	+	0.240230i
$696$	−135.644			−5.14158
$697$	3.80951	+	15.3053i	0.144295	+	0.579730i
$698$	−58.7424			−2.22343
$699$	−0.126675	−	0.126675i	−0.00479127	−	0.00479127i
$700$	−23.3604	+	9.67621i	−0.882942	+	0.365727i
$701$		−	21.0803i		−	0.796194i	−0.917343	−	0.398097i	$-0.869671\pi$
$701$		−	21.0803i		−	0.796194i	0.917343	−	0.398097i	$-0.130329\pi$
$702$	−6.25485	−	15.1005i	−0.236074	−	0.569933i
$703$	35.5272	+	14.7159i	1.33994	+	0.555019i
$704$	39.0157	−	94.1922i	1.47046	−	3.55000i
$705$	21.3475	−	21.3475i	0.803992	−	0.803992i
$706$	7.35361	−	7.35361i	0.276757	−	0.276757i
$707$	−8.21418	+	19.8308i	−0.308926	+	0.745813i
$708$	−67.6662	−	28.0283i	−2.54305	−	1.05337i
$709$	2.53783	+	6.12687i	0.0953102	+	0.230099i	0.964343	−	0.264655i	$-0.0852581\pi$
$709$	2.53783	+	6.12687i	0.0953102	+	0.230099i	−0.869033	+	0.494754i	$0.835258\pi$
$710$		−	70.2733i		−	2.63731i
$711$	−31.4186	+	13.0140i	−1.17829	+	0.488063i
$712$	52.9377	+	52.9377i	1.98392	+	1.98392i
$713$	18.5838			0.695968
$714$	−15.4757	+	103.267i	−0.579165	+	3.86466i
$715$	21.6961			0.811389
$716$	−46.8161	−	46.8161i	−1.74960	−	1.74960i
$717$	−24.1780	+	10.0149i	−0.902945	+	0.374012i
$718$			26.5920i			0.992404i
$719$	−4.03537	−	9.74225i	−0.150494	−	0.363325i	0.830596	−	0.556875i	$-0.188000\pi$
$719$	−4.03537	−	9.74225i	−0.150494	−	0.363325i	−0.981090	+	0.193550i	$0.938000\pi$
$720$	−105.996	−	43.9049i	−3.95023	−	1.63624i
$721$	14.7373	−	35.5791i	0.548847	−	1.32503i
$722$	22.3013	−	22.3013i	0.829967	−	0.829967i
$723$	12.2469	−	12.2469i	0.455469	−	0.455469i
$724$	12.2301	−	29.5261i	0.454528	−	1.09733i
$725$	6.04225	+	2.50278i	0.224404	+	0.0929511i
$726$	−10.8021	−	26.0786i	−0.400903	−	0.967866i
$727$			37.1507i			1.37784i	0.724835	+	0.688922i	$0.241916\pi$
$727$			37.1507i			1.37784i	−0.724835	+	0.688922i	$0.758084\pi$
$728$	141.555	−	58.6342i	5.24639	−	2.17313i
$729$	25.2909	+	25.2909i	0.936700	+	0.936700i
$730$	−26.9079			−0.995905
$731$	0.611073	−	4.07757i	0.0226013	−	0.150814i
$732$	117.573			4.34561
$733$	−23.0544	−	23.0544i	−0.851534	−	0.851534i	0.138788	−	0.990322i	$-0.455679\pi$
$733$	−23.0544	−	23.0544i	−0.851534	−	0.851534i	−0.990322	+	0.138788i	$0.955679\pi$
$734$	78.2076	−	32.3947i	2.88670	−	1.19571i
$735$			28.7055i			1.05882i
$736$	71.0937	+	171.635i	2.62055	+	6.32656i
$737$	18.8260	+	7.79798i	0.693464	+	0.287242i
$738$	14.3649	−	34.6798i	0.528777	−	1.27658i
$739$	−2.00382	+	2.00382i	−0.0737118	+	0.0737118i	−0.743002	−	0.669290i	$-0.766599\pi$
$739$	−2.00382	+	2.00382i	−0.0737118	+	0.0737118i	0.669290	+	0.743002i	$0.266599\pi$
$740$	−54.0548	+	54.0548i	−1.98709	+	1.98709i
$741$	−22.8340	+	55.1260i	−0.838826	+	2.02511i
$742$	−88.8211	−	36.7909i	−3.26073	−	1.35064i
$743$	−1.28518	−	3.10271i	−0.0471488	−	0.113827i	0.898550	−	0.438870i	$-0.144621\pi$
$743$	−1.28518	−	3.10271i	−0.0471488	−	0.113827i	−0.945699	+	0.325043i	$0.894621\pi$
$744$			67.3444i			2.46896i
$745$	−15.4073	+	6.38193i	−0.564482	+	0.233816i
$746$	10.0110	+	10.0110i	0.366530	+	0.366530i
$747$	−12.0866			−0.442224
$748$	14.9249	+	59.9633i	0.545710	+	2.19248i
$749$	−38.6315			−1.41157
$750$	60.5953	+	60.5953i	2.21263	+	2.21263i
$751$	−13.9449	+	5.77616i	−0.508856	+	0.210775i	−0.622314	−	0.782768i	$-0.713807\pi$
$751$	−13.9449	+	5.77616i	−0.508856	+	0.210775i	0.113458	+	0.993543i	$0.463807\pi$
$752$		−	101.795i		−	3.71210i
$753$	−5.61353	−	13.5523i	−0.204568	−	0.493872i
$754$	−56.6261	−	23.4553i	−2.06220	−	0.854191i
$755$	−13.5224	+	32.6459i	−0.492130	+	1.18811i
$756$	19.9829	−	19.9829i	0.726769	−	0.726769i
$757$	32.0883	−	32.0883i	1.16627	−	1.16627i	0.183193	−	0.983077i	$-0.441357\pi$
$757$	32.0883	−	32.0883i	1.16627	−	1.16627i	0.983077	−	0.183193i	$-0.0586432\pi$
$758$	24.2902	−	58.6418i	0.882260	−	2.12996i
$759$	−44.7543	−	18.5378i	−1.62448	−	0.672881i
$760$	41.3787	+	99.8970i	1.50096	+	3.62365i
$761$		−	32.8169i		−	1.18961i	−0.803870	−	0.594805i	$-0.797229\pi$
$761$		−	32.8169i		−	1.18961i	0.803870	−	0.594805i	$-0.202771\pi$
$762$	51.4779	−	21.3228i	1.86485	−	0.772445i
$763$	11.2064	+	11.2064i	0.405700	+	0.405700i
$764$	−109.634			−3.96641
$765$	27.4750	−	6.83855i	0.993359	−	0.247248i
$766$	30.9316			1.11760
$767$	−15.1311	−	15.1311i	−0.546351	−	0.546351i
$768$	−175.004	+	72.4892i	−6.31493	+	2.61573i
$769$			26.7427i			0.964366i	0.876071	+	0.482183i	$0.160156\pi$
$769$			26.7427i			0.964366i	−0.876071	+	0.482183i	$0.839844\pi$
$770$	19.4289	+	46.9054i	0.700168	+	1.69035i
$771$	−13.5849	−	5.62706i	−0.489249	−	0.202653i
$772$	56.1758	−	135.620i	2.02181	−	4.88108i
$773$	26.6597	−	26.6597i	0.958881	−	0.958881i	−0.0403063	−	0.999187i	$-0.512833\pi$
$773$	26.6597	−	26.6597i	0.958881	−	0.958881i	0.999187	+	0.0403063i	$0.0128334\pi$
$774$	−6.93867	+	6.93867i	−0.249405	+	0.249405i
$775$	1.24258	−	2.99985i	0.0446347	−	0.107758i
$776$	28.5231	+	11.8147i	1.02392	+	0.424122i
$777$	−24.4256	−	58.9687i	−0.876265	−	2.11549i
$778$			29.8717i			1.07095i
$779$	−19.4847	+	8.07083i	−0.698112	+	0.289168i
$780$	−83.8744	−	83.8744i	−3.00318	−	3.00318i
$781$	34.7219			1.24245
$782$	−69.9119	−	42.0456i	−2.50004	−	1.50355i
$783$	−7.30954			−0.261222
$784$	68.4411	+	68.4411i	2.44433	+	2.44433i
$785$	18.0491	−	7.47620i	0.644202	−	0.266837i
$786$		−	87.6985i		−	3.12810i
$787$	4.44642	+	10.7346i	0.158498	+	0.382648i	0.983101	−	0.183064i	$-0.0586015\pi$
$787$	4.44642	+	10.7346i	0.158498	+	0.382648i	−0.824603	+	0.565712i	$0.808602\pi$
$788$	−35.8255	−	14.8394i	−1.27623	−	0.528632i
$789$	−20.9859	+	50.6644i	−0.747118	+	1.80370i
$790$	−36.3501	+	36.3501i	−1.29328	+	1.29328i
$791$	−5.61286	+	5.61286i	−0.199570	+	0.199570i
$792$	36.3892	−	87.8512i	1.29303	−	3.12166i
$793$	31.7358	+	13.1454i	1.12697	+	0.466807i
$794$	−2.70583	−	6.53245i	−0.0960264	−	0.231828i
$795$			48.1240i			1.70678i
$796$	110.952	−	45.9577i	3.93258	−	1.62893i
$797$	21.2467	+	21.2467i	0.752597	+	0.752597i	0.974963	−	0.222366i	$-0.0713780\pi$
$797$	21.2467	+	21.2467i	0.752597	+	0.752597i	−0.222366	+	0.974963i	$0.571378\pi$
$798$	−139.626			−4.94272
$799$	14.9347	+	20.2001i	0.528352	+	0.714627i
$800$	32.4594			1.14761
$801$	18.5354	+	18.5354i	0.654916	+	0.654916i
$802$	67.8238	−	28.0935i	2.39494	−	0.992017i
$803$		−	13.2951i		−	0.469174i
$804$	−42.6328	−	102.925i	−1.50354	−	3.62987i
$805$	−45.7558	−	18.9527i	−1.61268	−	0.667993i
$806$	−11.6450	+	28.1136i	−0.410179	+	0.990260i
$807$	−22.0115	+	22.0115i	−0.774842	+	0.774842i
$808$	42.9719	−	42.9719i	1.51174	−	1.51174i
$809$	2.35575	−	5.68728i	0.0828237	−	0.199954i	−0.877042	−	0.480413i	$-0.840487\pi$
$809$	2.35575	−	5.68728i	0.0828237	−	0.199954i	0.959866	+	0.280459i	$0.0904867\pi$
$810$	34.9854	+	14.4914i	1.22926	+	0.509176i
$811$	−14.1459	−	34.1511i	−0.496729	−	1.19921i	−0.951235	−	0.308466i	$-0.900185\pi$
$811$	−14.1459	−	34.1511i	−0.496729	−	1.19921i	0.454507	−	0.890743i	$-0.349815\pi$
$812$		−	105.973i		−	3.71894i
$813$	41.3375	−	17.1226i	1.44977	−	0.600514i
$814$	−36.1474	−	36.1474i	−1.26696	−	1.26696i
$815$	−45.9325			−1.60895
$816$	90.8323	−	151.033i	3.17976	−	5.28720i
$817$	5.51326			0.192885
$818$	19.2054	+	19.2054i	0.671501	+	0.671501i
$819$	49.5636	−	20.5299i	1.73189	−	0.717374i
$820$		−	41.9258i		−	1.46411i
$821$	−3.96723	−	9.57773i	−0.138457	−	0.334265i	0.839408	−	0.543502i	$-0.182902\pi$
$821$	−3.96723	−	9.57773i	−0.138457	−	0.334265i	−0.977865	+	0.209237i	$0.932902\pi$
$822$	−71.3056	−	29.5358i	−2.48707	−	1.03018i
$823$	−10.8996	+	26.3141i	−0.379938	+	0.917251i	0.612039	+	0.790828i	$0.290350\pi$
$823$	−10.8996	+	26.3141i	−0.379938	+	0.917251i	−0.991976	+	0.126423i	$0.959650\pi$
$824$	−77.0973	+	77.0973i	−2.68581	+	2.68581i
$825$	−5.98486	+	5.98486i	−0.208366	+	0.208366i
$826$	19.1624	−	46.2621i	0.666745	−	1.60966i
$827$	13.2805	+	5.50096i	0.461808	+	0.191287i	0.601443	−	0.798916i	$-0.294593\pi$
$827$	13.2805	+	5.50096i	0.461808	+	0.191287i	−0.139635	+	0.990203i	$0.544593\pi$
$828$	54.8993	+	132.539i	1.90788	+	4.60604i
$829$			16.5255i			0.573956i	0.957937	+	0.286978i	$0.0926506\pi$
$829$			16.5255i			0.573956i	−0.957937	+	0.286978i	$0.907349\pi$
$830$	−16.8798	+	6.99185i	−0.585907	+	0.242691i
$831$	13.7079	+	13.7079i	0.475522	+	0.475522i
$832$	−162.851			−5.64583
$833$	−23.6225	−	3.54011i	−0.818471	−	0.122658i
$834$	32.7445			1.13385
$835$	−6.23181	−	6.23181i	−0.215661	−	0.215661i
$836$	−76.3374	+	31.6200i	−2.64019	+	1.09360i
$837$			3.62903i			0.125438i
$838$	−2.41749	−	5.83635i	−0.0835109	−	0.201613i
$839$	−22.4936	−	9.31716i	−0.776566	−	0.321664i	−0.0410369	−	0.999158i	$-0.513066\pi$
$839$	−22.4936	−	9.31716i	−0.776566	−	0.321664i	−0.735529	+	0.677494i	$0.763066\pi$
$840$	68.6811	−	165.811i	2.36972	−	5.72101i
$841$	1.12405	−	1.12405i	0.0387604	−	0.0387604i
$842$	−21.6769	+	21.6769i	−0.747037	+	0.747037i
$843$	−8.26164	+	19.9454i	−0.284546	+	0.686955i
$844$	39.5592	+	16.3860i	1.36169	+	0.564028i
$845$	−3.62721	−	8.75687i	−0.124780	−	0.301245i
$846$		−	59.7877i		−	2.05554i
$847$	13.1737	−	5.45672i	0.452653	−	0.187495i
$848$	114.740	+	114.740i	3.94018	+	3.94018i
$849$	−22.5373			−0.773479
$850$	−11.4617	+	8.47406i	−0.393132	+	0.290658i
$851$	49.8671			1.70942
$852$	−134.230	−	134.230i	−4.59865	−	4.59865i
$853$	−1.03252	+	0.427685i	−0.0353529	+	0.0146437i	−0.400290	−	0.916389i	$-0.631091\pi$
$853$	−1.03252	+	0.427685i	−0.0353529	+	0.0146437i	0.364937	+	0.931032i	$0.381091\pi$
$854$			80.3821i			2.75062i
$855$	14.4882	+	34.9775i	0.495485	+	1.19621i
$856$	101.049	+	41.8558i	3.45378	+	1.43060i
$857$	−15.6798	+	37.8543i	−0.535611	+	1.29308i	0.392149	+	0.919902i	$0.371732\pi$
$857$	−15.6798	+	37.8543i	−0.535611	+	1.29308i	−0.927760	+	0.373177i	$0.878268\pi$
$858$	56.0882	−	56.0882i	1.91482	−	1.91482i
$859$	6.67913	−	6.67913i	0.227889	−	0.227889i	−0.583921	−	0.811810i	$-0.698482\pi$
$859$	6.67913	−	6.67913i	0.227889	−	0.227889i	0.811810	+	0.583921i	$0.198482\pi$
$860$	−4.19422	+	10.1257i	−0.143022	+	0.345285i
$861$	32.3411	+	13.3961i	1.10218	+	0.456538i
$862$	−23.9431	−	57.8037i	−0.815504	−	1.96880i
$863$		−	14.7844i		−	0.503268i	−0.967822	−	0.251634i	$-0.919032\pi$
$863$		−	14.7844i		−	0.503268i	0.967822	−	0.251634i	$-0.0809679\pi$
$864$	−33.5168	+	13.8831i	−1.14027	+	0.472314i
$865$	10.0377	+	10.0377i	0.341291	+	0.341291i
$866$	−8.09744			−0.275162
$867$	4.13389	+	43.2969i	0.140394	+	1.47044i
$868$	−52.6135			−1.78582
$869$	−17.9605	−	17.9605i	−0.609269	−	0.609269i
$870$	−66.3289	+	27.4743i	−2.24876	+	0.931467i
$871$		−	32.5486i		−	1.10287i
$872$	−17.1710	−	41.4545i	−0.581484	−	1.40383i
$873$	9.98698	+	4.13674i	0.338008	+	0.140007i
$874$	41.7459	−	100.784i	1.41208	−	3.40906i
$875$	−30.6099	+	30.6099i	−1.03480	+	1.03480i
$876$	−51.3971	+	51.3971i	−1.73655	+	1.73655i
$877$	2.25131	−	5.43515i	0.0760215	−	0.183532i	−0.881300	−	0.472557i	$-0.843331\pi$
$877$	2.25131	−	5.43515i	0.0760215	−	0.183532i	0.957322	+	0.289025i	$0.0933311\pi$
$878$	103.299	+	42.7879i	3.48617	+	1.44402i
$879$	20.2063	+	48.7822i	0.681540	+	1.64538i
$880$		−	85.6911i		−	2.88865i
$881$	6.26454	−	2.59486i	0.211058	−	0.0874229i	−0.274650	−	0.961544i	$-0.588562\pi$
$881$	6.26454	−	2.59486i	0.211058	−	0.0874229i	0.485708	+	0.874121i	$0.338562\pi$
$882$	40.1977	+	40.1977i	1.35353	+	1.35353i
$883$	13.4686			0.453253			0.226626	−	0.973982i	$-0.427230\pi$
$883$	13.4686			0.453253			0.226626	+	0.973982i	$0.427230\pi$
$884$	79.3662	−	58.6785i	2.66937	−	1.97357i
$885$	−25.0652			−0.842557
$886$	63.8427	+	63.8427i	2.14484	+	2.14484i
$887$	−48.7436	+	20.1903i	−1.63665	+	0.677923i	−0.995953	−	0.0898701i	$-0.971355\pi$
$887$	−48.7436	+	20.1903i	−1.63665	+	0.677923i	−0.640698	+	0.767793i	$0.721355\pi$
$888$			180.710i			6.06421i
$889$	10.7713	+	26.0042i	0.361258	+	0.872154i
$890$	36.6085	+	15.1637i	1.22712	+	0.508290i
$891$	−7.16017	+	17.2862i	−0.239875	+	0.579109i
$892$	99.2312	−	99.2312i	3.32251	−	3.32251i
$893$	−23.7528	+	23.7528i	−0.794856	+	0.794856i
$894$	−23.3323	+	56.3291i	−0.780347	+	1.88393i
$895$	−20.9334	−	8.67091i	−0.699727	−	0.289836i
$896$	−74.6990	−	180.339i	−2.49552	−	6.02471i
$897$			77.3765i			2.58353i
$898$	−36.8927	+	15.2814i	−1.23112	+	0.509948i
$899$	9.62277	+	9.62277i	0.320937	+	0.320937i
$900$	25.0655			0.835518
$901$	−39.6025	−	5.93490i	−1.31935	−	0.197720i
$902$	28.0365			0.933514
$903$	−6.47074	−	6.47074i	−0.215333	−	0.215333i
$904$	20.7629	−	8.60029i	0.690565	−	0.286042i
$905$		−	10.9372i		−	0.363564i
$906$	49.4376	+	119.353i	1.64245	+	3.96524i
$907$	33.8932	+	14.0390i	1.12540	+	0.466158i	0.866217	−	0.499669i	$-0.166545\pi$
$907$	33.8932	+	14.0390i	1.12540	+	0.466158i	0.259188	+	0.965827i	$0.416545\pi$
$908$	−1.79275	+	4.32809i	−0.0594947	+	0.143633i
$909$	15.0460	−	15.0460i	0.499044	−	0.499044i
$910$	57.3433	−	57.3433i	1.90091	−	1.90091i
$911$	21.6326	−	52.2256i	0.716719	−	1.73031i	0.0342316	−	0.999414i	$-0.489102\pi$
$911$	21.6326	−	52.2256i	0.716719	−	1.73031i	0.682487	−	0.730898i	$-0.260898\pi$
$912$	217.726	+	90.1850i	7.20962	+	2.98632i
$913$	−3.45466	−	8.34028i	−0.114332	−	0.276023i
$914$			76.5962i			2.53358i
$915$	37.1737	−	15.3978i	1.22892	−	0.509037i
$916$	76.2116	+	76.2116i	2.51810	+	2.51810i
$917$	44.3012			1.46295
$918$	8.21063	−	13.6524i	0.270991	−	0.450595i
$919$	−1.05478			−0.0347939			−0.0173970	−	0.999849i	$-0.505538\pi$
$919$	−1.05478			−0.0347939			−0.0173970	+	0.999849i	$0.505538\pi$
$920$	99.1494	+	99.1494i	3.26886	+	3.26886i
$921$	30.7103	−	12.7206i	1.01194	−	0.419159i
$922$		−	69.9545i		−	2.30383i
$923$	−21.2243	−	51.2399i	−0.698605	−	1.68658i
$924$	126.706	+	52.4834i	4.16833	+	1.72658i
$925$	3.33429	−	8.04969i	0.109631	−	0.264672i
$926$	73.7292	−	73.7292i	2.42289	−	2.42289i
$927$	−26.9945	+	26.9945i	−0.886617	+	0.886617i
$928$	−52.0609	+	125.686i	−1.70898	+	4.12585i
$929$	−30.2212	−	12.5180i	−0.991527	−	0.410704i	−0.172844	−	0.984949i	$-0.555296\pi$
$929$	−30.2212	−	12.5180i	−0.991527	−	0.410704i	−0.818683	+	0.574245i	$0.805296\pi$
$930$	13.6404	+	32.9309i	0.447287	+	1.07985i
$931$		−	31.9399i		−	1.04679i
$932$	−0.366092	+	0.151640i	−0.0119917	+	0.00496715i
$933$	17.9092	+	17.9092i	0.586322	+	0.586322i
$934$	62.0250			2.02952
$935$	12.5720	+	17.0043i	0.411148	+	0.556102i
$936$	−151.888			−4.96460
$937$	17.4920	+	17.4920i	0.571437	+	0.571437i	0.932530	−	0.361093i	$-0.117596\pi$
$937$	17.4920	+	17.4920i	0.571437	+	0.571437i	−0.361093	+	0.932530i	$0.617596\pi$
$938$	70.3677	−	29.1472i	2.29759	−	0.951691i
$939$		−	37.2613i		−	1.21598i
$940$	−25.5547	−	61.6946i	−0.833504	−	2.01226i
$941$	6.62150	+	2.74272i	0.215855	+	0.0894100i	0.487991	−	0.872849i	$-0.337730\pi$
$941$	6.62150	+	2.74272i	0.215855	+	0.0894100i	−0.272136	+	0.962259i	$0.587730\pi$
$942$	27.3329	−	65.9874i	0.890553	−	2.14999i
$943$	−19.3389	+	19.3389i	−0.629761	+	0.629761i
$944$	−59.7617	+	59.7617i	−1.94508	+	1.94508i
$945$	3.70106	−	8.93515i	0.120396	−	0.290661i
$946$	−6.77126	−	2.80475i	−0.220153	−	0.0911902i
$947$	−19.8562	−	47.9371i	−0.645240	−	1.55775i	−0.819520	−	0.573050i	$-0.805760\pi$
$947$	−19.8562	−	47.9371i	−0.645240	−	1.55775i	0.174281	−	0.984696i	$-0.444240\pi$
$948$			138.866i			4.51015i
$949$	−19.6199	+	8.12684i	−0.636889	+	0.263808i
$950$	−13.4775	−	13.4775i	−0.437268	−	0.437268i
$951$	−60.4834			−1.96131
$952$	127.980	+	76.9681i	4.14785	+	2.49455i
$953$	−10.8410			−0.351173			−0.175586	−	0.984464i	$-0.556182\pi$
$953$	−10.8410			−0.351173			−0.175586	+	0.984464i	$0.556182\pi$
$954$	67.3903	+	67.3903i	2.18184	+	2.18184i
$955$	−34.6637	+	14.3582i	−1.12169	+	0.464619i
$956$			57.8863i			1.87218i
$957$	−13.5750	−	32.7730i	−0.438817	−	1.05940i
$958$	26.3177	+	10.9011i	0.850285	+	0.352200i
$959$	14.9201	−	36.0203i	0.481795	−	1.16316i
$960$	−134.884	+	134.884i	−4.35337	+	4.35337i
$961$	−17.1428	+	17.1428i	−0.552994	+	0.552994i
$962$	−31.2479	+	75.4391i	−1.00747	+	2.43226i
$963$	35.3809	+	14.6552i	1.14013	+	0.472258i
$964$	−14.6606	−	35.3939i	−0.472187	−	1.13996i
$965$		−	50.2370i		−	1.61719i
$966$	−167.282	+	69.2906i	−5.38222	+	2.22939i
$967$	−12.1810	−	12.1810i	−0.391715	−	0.391715i	0.483583	−	0.875298i	$-0.339335\pi$
$967$	−12.1810	−	12.1810i	−0.391715	−	0.391715i	−0.875298	+	0.483583i	$0.839335\pi$
$968$	−40.3707			−1.29756
$969$	−56.4363	+	14.0471i	−1.81300	+	0.451257i
$970$	16.3406			0.524666
$971$	−41.4803	−	41.4803i	−1.33117	−	1.33117i	−0.904328	−	0.426837i	$-0.859628\pi$
$971$	−41.4803	−	41.4803i	−1.33117	−	1.33117i	−0.426837	−	0.904328i	$-0.640372\pi$
$972$	116.405	−	48.2165i	3.73369	−	1.54655i
$973$			16.5410i			0.530281i
$974$	−21.6135	−	52.1795i	−0.692540	−	1.67194i
$975$	12.4903	+	5.17367i	0.400011	+	0.165690i
$976$	51.9191	−	125.344i	1.66189	−	4.01215i
$977$	−21.4259	+	21.4259i	−0.685476	+	0.685476i	−0.961229	−	0.275753i	$-0.911073\pi$
$977$	−21.4259	+	21.4259i	−0.685476	+	0.685476i	0.275753	+	0.961229i	$0.411073\pi$
$978$	−118.743	+	118.743i	−3.79700	+	3.79700i
$979$	−7.49237	+	18.0882i	−0.239457	+	0.578100i
$980$	58.6612	+	24.2983i	1.87386	+	0.776180i
$981$	−6.01219	−	14.5147i	−0.191955	−	0.463419i
$982$			65.0059i			2.07442i
$983$	−21.6860	+	8.98265i	−0.691677	+	0.286502i	−0.700699	−	0.713457i	$-0.747128\pi$
$983$	−21.6860	+	8.98265i	−0.691677	+	0.286502i	0.00902182	+	0.999959i	$0.497128\pi$
$984$	−70.0807	−	70.0807i	−2.23409	−	2.23409i
$985$	−13.2706			−0.422837
$986$	−14.4293	−	57.9721i	−0.459523	−	1.84621i
$987$	55.7557			1.77472
$988$	93.3248	+	93.3248i	2.96906	+	2.96906i
$989$	6.60529	−	2.73600i	0.210036	−	0.0869998i
$990$		−	50.3291i		−	1.59956i
$991$	2.39853	+	5.79056i	0.0761917	+	0.183943i	0.957386	−	0.288811i	$-0.0932599\pi$
$991$	2.39853	+	5.79056i	0.0761917	+	0.183943i	−0.881194	+	0.472754i	$0.843260\pi$
$992$	62.4004	+	25.8471i	1.98122	+	0.820647i
$993$	22.4436	−	54.1837i	0.712227	−	1.71947i
$994$	91.7705	−	91.7705i	2.91078	−	2.91078i
$995$	29.0615	−	29.0615i	0.921310	−	0.921310i
$996$	−18.8872	+	45.5977i	−0.598463	+	1.44482i
$997$	24.0517	+	9.96253i	0.761724	+	0.315517i	0.729515	−	0.683965i	$-0.239746\pi$
$997$	24.0517	+	9.96253i	0.761724	+	0.315517i	0.0322091	+	0.999481i	$0.489746\pi$
$998$	−20.8691	−	50.3825i	−0.660600	−	1.59483i
$999$			9.73801i			0.308097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.1	✓	116
17.9	even	8	inner	731.2.m.b.689.1	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.1	✓	116	1.1	even	1	trivial
731.2.m.b.689.1	yes	116	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95693 - 1.95693i) q^{2} +(-2.36371 + 0.979079i) q^{3} +5.65912i q^{4} +(0.741144 + 1.78928i) q^{5} +(6.54158 + 2.70961i) q^{6} +(-1.36877 + 3.30450i) q^{7} +(7.16062 - 7.16062i) q^{8} +(2.50719 - 2.50719i) q^{9} +O(q^{10})\)	\(q+(-1.95693 - 1.95693i) q^{2} +(-2.36371 + 0.979079i) q^{3} +5.65912i q^{4} +(0.741144 + 1.78928i) q^{5} +(6.54158 + 2.70961i) q^{6} +(-1.36877 + 3.30450i) q^{7} +(7.16062 - 7.16062i) q^{8} +(2.50719 - 2.50719i) q^{9} +(2.05112 - 4.95185i) q^{10} +(2.44670 + 1.01346i) q^{11} +(-5.54072 - 13.3765i) q^{12} -4.23014i q^{13} +(9.14525 - 3.78809i) q^{14} +(-3.50369 - 3.50369i) q^{15} -16.7074 q^{16} +(3.31537 - 2.45118i) q^{17} -9.81277 q^{18} +(3.89847 + 3.89847i) q^{19} +(-10.1257 + 4.19422i) q^{20} -9.15101i q^{21} +(-2.80475 - 6.77126i) q^{22} +(6.60529 + 2.73600i) q^{23} +(-9.91478 + 23.9364i) q^{24} +(0.883306 - 0.883306i) q^{25} +(-8.27807 + 8.27807i) q^{26} +(-0.534285 + 1.28988i) q^{27} +(-18.7006 - 7.74603i) q^{28} +(2.00354 + 4.83696i) q^{29} +13.7129i q^{30} +(2.40145 - 0.994712i) q^{31} +(18.3738 + 18.3738i) q^{32} -6.77552 q^{33} +(-11.2847 - 1.69115i) q^{34} -6.92714 q^{35} +(14.1885 + 14.1885i) q^{36} +(6.44396 - 2.66918i) q^{37} -15.2580i q^{38} +(4.14164 + 9.99880i) q^{39} +(18.1194 + 7.50530i) q^{40} +(-1.46389 + 3.53415i) q^{41} +(-17.9078 + 17.9078i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-5.73526 + 13.8461i) q^{44} +(6.34425 + 2.62787i) q^{45} +(-7.57191 - 18.2802i) q^{46} +6.09285i q^{47} +(39.4913 - 16.3578i) q^{48} +(-4.09646 - 4.09646i) q^{49} -3.45713 q^{50} +(-5.43666 + 9.03989i) q^{51} +23.9388 q^{52} +(-6.86761 - 6.86761i) q^{53} +(3.56975 - 1.47864i) q^{54} +5.12894i q^{55} +(13.8610 + 33.4635i) q^{56} +(-13.0317 - 5.39792i) q^{57} +(5.54481 - 13.3863i) q^{58} +(3.57697 - 3.57697i) q^{59} +(19.8278 - 19.8278i) q^{60} +(-3.10756 + 7.50230i) q^{61} +(-6.64603 - 2.75288i) q^{62} +(4.85325 + 11.7168i) q^{63} -38.4977i q^{64} +(7.56890 - 3.13514i) q^{65} +(13.2592 + 13.2592i) q^{66} +7.69445 q^{67} +(13.8715 + 18.7621i) q^{68} -18.2917 q^{69} +(13.5559 + 13.5559i) q^{70} +(12.1130 - 5.01739i) q^{71} -35.9060i q^{72} +(-1.92117 - 4.63813i) q^{73} +(-17.8337 - 7.38697i) q^{74} +(-1.22305 + 2.95270i) q^{75} +(-22.0619 + 22.0619i) q^{76} +(-6.69793 + 6.69793i) q^{77} +(11.4620 - 27.6718i) q^{78} +(-8.86103 - 3.67036i) q^{79} +(-12.3826 - 29.8941i) q^{80} +7.06511i q^{81} +(9.78081 - 4.05134i) q^{82} +(-2.41038 - 2.41038i) q^{83} +51.7866 q^{84} +(6.84302 + 4.11545i) q^{85} -2.76751 q^{86} +(-9.47154 - 9.47154i) q^{87} +(24.7768 - 10.2629i) q^{88} +7.39289i q^{89} +(-7.27267 - 17.5578i) q^{90} +(13.9785 + 5.79009i) q^{91} +(-15.4833 + 37.3801i) q^{92} +(-4.70241 + 4.70241i) q^{93} +(11.9233 - 11.9233i) q^{94} +(-4.08612 + 9.86477i) q^{95} +(-61.4198 - 25.4409i) q^{96} +(1.16669 + 2.81664i) q^{97} +16.0330i q^{98} +(8.67526 - 3.59341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Introduction

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