LMFDB - Embedded newform 546.2.bb.a.341.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.4
Character	$\chi$	$=$	546.341
Dual form			546.2.bb.a.269.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.45489 - 0.939845i) q^{3} -1.00000 q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.939845 + 1.45489i) q^{6} +(-1.67305 - 2.04961i) q^{7} +1.00000i q^{8} +(1.23338 + 2.73473i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.45489 - 0.939845i) q^{3} -1.00000 q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.939845 + 1.45489i) q^{6} +(-1.67305 - 2.04961i) q^{7} +1.00000i q^{8} +(1.23338 + 2.73473i) q^{9} +(1.53584 + 0.886718i) q^{10} +(-0.773984 - 0.446860i) q^{11} +(1.45489 + 0.939845i) q^{12} +(-1.84344 + 3.09866i) q^{13} +(-2.04961 + 1.67305i) q^{14} +(2.73352 - 1.40109i) q^{15} +1.00000 q^{16} +7.49940 q^{17} +(2.73473 - 1.23338i) q^{18} +(-0.697770 + 0.402858i) q^{19} +(0.886718 - 1.53584i) q^{20} +(0.507788 + 4.55436i) q^{21} +(-0.446860 + 0.773984i) q^{22} +5.45295i q^{23} +(0.939845 - 1.45489i) q^{24} +(0.927464 + 1.60641i) q^{25} +(3.09866 + 1.84344i) q^{26} +(0.775795 - 5.13791i) q^{27} +(1.67305 + 2.04961i) q^{28} +(7.62822 - 4.40416i) q^{29} +(-1.40109 - 2.73352i) q^{30} +(-8.20495 + 4.73713i) q^{31} -1.00000i q^{32} +(0.706079 + 1.37756i) q^{33} -7.49940i q^{34} +(4.63139 - 0.752120i) q^{35} +(-1.23338 - 2.73473i) q^{36} +3.69465 q^{37} +(0.402858 + 0.697770i) q^{38} +(5.59426 - 2.77565i) q^{39} +(-1.53584 - 0.886718i) q^{40} +(3.47099 + 6.01193i) q^{41} +(4.55436 - 0.507788i) q^{42} +(1.93884 - 3.35816i) q^{43} +(0.773984 + 0.446860i) q^{44} +(-5.29377 - 0.530658i) q^{45} +5.45295 q^{46} +(-4.19126 + 7.25948i) q^{47} +(-1.45489 - 0.939845i) q^{48} +(-1.40178 + 6.85821i) q^{49} +(1.60641 - 0.927464i) q^{50} +(-10.9108 - 7.04827i) q^{51} +(1.84344 - 3.09866i) q^{52} +(2.72420 - 1.57281i) q^{53} +(-5.13791 - 0.775795i) q^{54} +(1.37261 - 0.792477i) q^{55} +(2.04961 - 1.67305i) q^{56} +(1.39380 + 0.0696839i) q^{57} +(-4.40416 - 7.62822i) q^{58} +3.34899 q^{59} +(-2.73352 + 1.40109i) q^{60} +(-7.11088 + 4.10547i) q^{61} +(4.73713 + 8.20495i) q^{62} +(3.54161 - 7.10331i) q^{63} -1.00000 q^{64} +(-3.12443 - 5.57887i) q^{65} +(1.37756 - 0.706079i) q^{66} +(3.99370 - 6.91729i) q^{67} -7.49940 q^{68} +(5.12492 - 7.93341i) q^{69} +(-0.752120 - 4.63139i) q^{70} +(-1.97967 - 1.14296i) q^{71} +(-2.73473 + 1.23338i) q^{72} +(-7.54968 + 4.35881i) q^{73} -3.69465i q^{74} +(0.160427 - 3.20882i) q^{75} +(0.697770 - 0.402858i) q^{76} +(0.379030 + 2.33398i) q^{77} +(-2.77565 - 5.59426i) q^{78} +(-6.40376 + 11.0916i) q^{79} +(-0.886718 + 1.53584i) q^{80} +(-5.95753 + 6.74595i) q^{81} +(6.01193 - 3.47099i) q^{82} +13.8340 q^{83} +(-0.507788 - 4.55436i) q^{84} +(-6.64985 + 11.5179i) q^{85} +(-3.35816 - 1.93884i) q^{86} +(-15.2374 - 0.761805i) q^{87} +(0.446860 - 0.773984i) q^{88} -15.5163 q^{89} +(-0.530658 + 5.29377i) q^{90} +(9.43523 - 1.40589i) q^{91} -5.45295i q^{92} +(16.3894 + 0.819400i) q^{93} +(7.25948 + 4.19126i) q^{94} -1.42888i q^{95} +(-0.939845 + 1.45489i) q^{96} +(4.24795 + 2.45256i) q^{97} +(6.85821 + 1.40178i) q^{98} +(0.267424 - 2.66779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.45489	−	0.939845i	−0.839978	−	0.542620i
$3$	−1.45489	−	0.939845i	−0.839978	−	0.542620i
$4$	−1.00000			−0.500000
$5$	−0.886718	+	1.53584i	−0.396552	+	0.686848i	−0.993298	−	0.115582i	$-0.963127\pi$
$5$	−0.886718	+	1.53584i	−0.396552	+	0.686848i	0.596746	+	0.802430i	$0.296460\pi$
$6$	−0.939845	+	1.45489i	−0.383690	+	0.593954i
$7$	−1.67305	−	2.04961i	−0.632355	−	0.774679i
$7$	−1.67305	−	2.04961i	−0.632355	−	0.774679i
$8$			1.00000i			0.353553i
$9$	1.23338	+	2.73473i	0.411128	+	0.911578i
$10$	1.53584	+	0.886718i	0.485675	+	0.280405i
$11$	−0.773984	−	0.446860i	−0.233365	−	0.134733i	0.378758	−	0.925496i	$-0.376351\pi$
$11$	−0.773984	−	0.446860i	−0.233365	−	0.134733i	−0.612123	+	0.790762i	$0.709684\pi$
$12$	1.45489	+	0.939845i	0.419989	+	0.271310i
$13$	−1.84344	+	3.09866i	−0.511280	+	0.859414i
$13$	−1.84344	+	3.09866i	−0.511280	+	0.859414i
$14$	−2.04961	+	1.67305i	−0.547781	+	0.447142i
$15$	2.73352	−	1.40109i	0.705793	−	0.361761i
$16$	1.00000			0.250000
$17$	7.49940			1.81887			0.909436	−	0.415844i	$-0.136514\pi$
$17$	7.49940			1.81887			0.909436	+	0.415844i	$0.136514\pi$
$18$	2.73473	−	1.23338i	0.644583	−	0.290711i
$19$	−0.697770	+	0.402858i	−0.160079	+	0.0924219i	−0.577900	−	0.816108i	$-0.696128\pi$
$19$	−0.697770	+	0.402858i	−0.160079	+	0.0924219i	0.417820	+	0.908530i	$0.362794\pi$
$20$	0.886718	−	1.53584i	0.198276	−	0.343424i
$21$	0.507788	+	4.55436i	0.110808	+	0.993842i
$22$	−0.446860	+	0.773984i	−0.0952709	+	0.165014i
$23$			5.45295i			1.13702i	0.822677	+	0.568509i	$0.192480\pi$
$23$			5.45295i			1.13702i	−0.822677	+	0.568509i	$0.807520\pi$
$24$	0.939845	−	1.45489i	0.191845	−	0.296977i
$25$	0.927464	+	1.60641i	0.185493	+	0.321283i
$26$	3.09866	+	1.84344i	0.607698	+	0.361529i
$27$	0.775795	−	5.13791i	0.149302	−	0.988792i
$28$	1.67305	+	2.04961i	0.316177	+	0.387339i
$29$	7.62822	−	4.40416i	1.41653	−	0.817832i	0.420534	−	0.907277i	$-0.361843\pi$
$29$	7.62822	−	4.40416i	1.41653	−	0.817832i	0.995992	+	0.0894452i	$0.0285094\pi$
$30$	−1.40109	−	2.73352i	−0.255804	−	0.499071i
$31$	−8.20495	+	4.73713i	−1.47365	+	0.850813i	−0.999560	−	0.0296621i	$-0.990557\pi$
$31$	−8.20495	+	4.73713i	−1.47365	+	0.850813i	−0.474092	+	0.880475i	$0.657224\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.706079	+	1.37756i	0.122913	+	0.239802i
$34$		−	7.49940i		−	1.28614i
$35$	4.63139	−	0.752120i	0.782849	−	0.127131i
$36$	−1.23338	−	2.73473i	−0.205564	−	0.455789i
$37$	3.69465			0.607397			0.303699	−	0.952768i	$-0.401778\pi$
$37$	3.69465			0.607397			0.303699	+	0.952768i	$0.401778\pi$
$38$	0.402858	+	0.697770i	0.0653521	+	0.113193i
$39$	5.59426	−	2.77565i	0.895799	−	0.444459i
$40$	−1.53584	−	0.886718i	−0.242838	−	0.140202i
$41$	3.47099	+	6.01193i	0.542078	+	0.938906i	0.998785	+	0.0492887i	$0.0156954\pi$
$41$	3.47099	+	6.01193i	0.542078	+	0.938906i	−0.456707	+	0.889617i	$0.650971\pi$
$42$	4.55436	−	0.507788i	0.702752	−	0.0783534i
$43$	1.93884	−	3.35816i	0.295670	−	0.512115i	−0.679471	−	0.733703i	$-0.737791\pi$
$43$	1.93884	−	3.35816i	0.295670	−	0.512115i	0.975140	+	0.221588i	$0.0711239\pi$
$44$	0.773984	+	0.446860i	0.116682	+	0.0673667i
$45$	−5.29377	−	0.530658i	−0.789149	−	0.0791058i
$46$	5.45295			0.803993
$47$	−4.19126	+	7.25948i	−0.611358	+	1.05890i	0.379653	+	0.925129i	$0.376043\pi$
$47$	−4.19126	+	7.25948i	−0.611358	+	1.05890i	−0.991012	+	0.133775i	$0.957290\pi$
$48$	−1.45489	−	0.939845i	−0.209995	−	0.135655i
$49$	−1.40178	+	6.85821i	−0.200255	+	0.979744i
$50$	1.60641	−	0.927464i	0.227181	−	0.131163i
$51$	−10.9108	−	7.04827i	−1.52781	−	0.986956i
$52$	1.84344	−	3.09866i	0.255640	−	0.429707i
$53$	2.72420	−	1.57281i	0.374197	−	0.216043i	−0.301093	−	0.953595i	$-0.597352\pi$
$53$	2.72420	−	1.57281i	0.374197	−	0.216043i	0.675290	+	0.737552i	$0.264018\pi$
$54$	−5.13791	−	0.775795i	−0.699181	−	0.105572i
$55$	1.37261	−	0.792477i	0.185083	−	0.106858i
$56$	2.04961	−	1.67305i	0.273890	−	0.223571i
$57$	1.39380	+	0.0696839i	0.184613	+	0.00922986i
$58$	−4.40416	−	7.62822i	−0.578294	−	1.00163i
$59$	3.34899			0.436002			0.218001	−	0.975949i	$-0.430046\pi$
$59$	3.34899			0.436002			0.218001	+	0.975949i	$0.430046\pi$
$60$	−2.73352	+	1.40109i	−0.352896	+	0.180880i
$61$	−7.11088	+	4.10547i	−0.910455	+	0.525652i	−0.880578	−	0.473902i	$-0.842845\pi$
$61$	−7.11088	+	4.10547i	−0.910455	+	0.525652i	−0.0298776	+	0.999554i	$0.509512\pi$
$62$	4.73713	+	8.20495i	0.601616	+	1.04203i
$63$	3.54161	−	7.10331i	0.446202	−	0.894933i
$64$	−1.00000			−0.125000
$65$	−3.12443	−	5.57887i	−0.387538	−	0.691974i
$66$	1.37756	−	0.706079i	0.169565	−	0.0869123i
$67$	3.99370	−	6.91729i	0.487908	−	0.845082i	−0.511995	−	0.858988i	$-0.671093\pi$
$67$	3.99370	−	6.91729i	0.487908	−	0.845082i	0.999903	+	0.0139067i	$0.00442678\pi$
$68$	−7.49940			−0.909436
$69$	5.12492	−	7.93341i	0.616968	−	0.955070i
$70$	−0.752120	−	4.63139i	−0.0898955	−	0.553558i
$71$	−1.97967	−	1.14296i	−0.234943	−	0.135645i	0.377907	−	0.925843i	$-0.376644\pi$
$71$	−1.97967	−	1.14296i	−0.234943	−	0.135645i	−0.612850	+	0.790199i	$0.709977\pi$
$72$	−2.73473	+	1.23338i	−0.322291	+	0.145356i
$73$	−7.54968	+	4.35881i	−0.883624	+	0.510160i	−0.871851	−	0.489770i	$-0.837081\pi$
$73$	−7.54968	+	4.35881i	−0.883624	+	0.510160i	−0.0117722	+	0.999931i	$0.503747\pi$
$74$		−	3.69465i		−	0.429495i
$75$	0.160427	−	3.20882i	0.0185245	−	0.370523i
$76$	0.697770	−	0.402858i	0.0800397	−	0.0462109i
$77$	0.379030	+	2.33398i	0.0431944	+	0.265982i
$78$	−2.77565	−	5.59426i	−0.314280	−	0.633426i
$79$	−6.40376	+	11.0916i	−0.720479	+	1.24791i	0.240329	+	0.970692i	$0.422745\pi$
$79$	−6.40376	+	11.0916i	−0.720479	+	1.24791i	−0.960808	+	0.277215i	$0.910589\pi$
$80$	−0.886718	+	1.53584i	−0.0991380	+	0.171712i
$81$	−5.95753	+	6.74595i	−0.661948	+	0.749550i
$82$	6.01193	−	3.47099i	0.663907	−	0.383307i
$83$	13.8340			1.51847			0.759237	−	0.650814i	$-0.225572\pi$
$83$	13.8340			1.51847			0.759237	+	0.650814i	$0.225572\pi$
$84$	−0.507788	−	4.55436i	−0.0554042	−	0.496921i
$85$	−6.64985	+	11.5179i	−0.721277	+	1.24929i
$86$	−3.35816	−	1.93884i	−0.362120	−	0.209070i
$87$	−15.2374	−	0.761805i	−1.63362	−	0.0816740i
$88$	0.446860	−	0.773984i	0.0476354	−	0.0825070i
$89$	−15.5163			−1.64473			−0.822363	−	0.568963i	$-0.807345\pi$
$89$	−15.5163			−1.64473			−0.822363	+	0.568963i	$0.807345\pi$
$90$	−0.530658	+	5.29377i	−0.0559363	+	0.558013i
$91$	9.43523	−	1.40589i	0.989080	−	0.147377i
$92$		−	5.45295i		−	0.568509i
$93$	16.3894	+	0.819400i	1.69950	+	0.0849678i
$94$	7.25948	+	4.19126i	0.748758	+	0.432296i
$95$		−	1.42888i		−	0.146600i
$96$	−0.939845	+	1.45489i	−0.0959225	+	0.148489i
$97$	4.24795	+	2.45256i	0.431314	+	0.249019i	0.699906	−	0.714235i	$-0.253225\pi$
$97$	4.24795	+	2.45256i	0.431314	+	0.249019i	−0.268592	+	0.963254i	$0.586558\pi$
$98$	6.85821	+	1.40178i	0.692784	+	0.141601i
$99$	0.267424	−	2.66779i	0.0268771	−	0.268123i
$100$	−0.927464	−	1.60641i	−0.0927464	−	0.160641i
$101$	−8.31852	+	14.4081i	−0.827724	+	1.43366i	0.0720963	+	0.997398i	$0.477031\pi$
$101$	−8.31852	+	14.4081i	−0.827724	+	1.43366i	−0.899820	+	0.436262i	$0.856302\pi$
$102$	−7.04827	+	10.9108i	−0.697883	+	1.08033i
$103$	7.46308	+	4.30881i	0.735359	+	0.424560i	0.820379	−	0.571820i	$-0.193762\pi$
$103$	7.46308	+	4.30881i	0.735359	+	0.424560i	−0.0850206	+	0.996379i	$0.527096\pi$
$104$	−3.09866	−	1.84344i	−0.303849	−	0.180765i
$105$	−7.44502	−	3.25855i	−0.726560	−	0.318001i
$106$	−1.57281	−	2.72420i	−0.152765	−	0.264597i
$107$			16.3289i			1.57857i	0.614027	+	0.789285i	$0.289549\pi$
$107$			16.3289i			1.57857i	−0.614027	+	0.789285i	$0.710451\pi$
$108$	−0.775795	+	5.13791i	−0.0746509	+	0.494396i
$109$	−0.641659	−	1.11139i	−0.0614598	−	0.106452i	0.833658	−	0.552281i	$-0.186242\pi$
$109$	−0.641659	−	1.11139i	−0.0614598	−	0.106452i	−0.895118	+	0.445829i	$0.852909\pi$
$110$	−0.792477	−	1.37261i	−0.0755597	−	0.130873i
$111$	−5.37530	−	3.47240i	−0.510201	−	0.329586i
$112$	−1.67305	−	2.04961i	−0.158089	−	0.193670i
$113$	−0.274369	−	0.158407i	−0.0258105	−	0.0149017i	0.487039	−	0.873380i	$-0.338077\pi$
$113$	−0.274369	−	0.158407i	−0.0258105	−	0.0149017i	−0.512850	+	0.858478i	$0.671410\pi$
$114$	0.0696839	−	1.39380i	0.00652650	−	0.130541i
$115$	−8.37485	−	4.83522i	−0.780959	−	0.450887i
$116$	−7.62822	+	4.40416i	−0.708263	+	0.408916i
$117$	−10.7477	−	1.21949i	−0.993624	−	0.112742i
$118$		−	3.34899i		−	0.308300i
$119$	−12.5469	−	15.3708i	−1.15017	−	1.40904i
$120$	1.40109	+	2.73352i	0.127902	+	0.249535i
$121$	−5.10063	−	8.83455i	−0.463694	−	0.803141i
$122$	4.10547	+	7.11088i	0.371692	+	0.643789i
$123$	0.600391	−	12.0089i	0.0541354	−	1.08280i
$124$	8.20495	−	4.73713i	0.736826	−	0.425407i
$125$	−12.1568			−1.08733
$126$	−7.10331	−	3.54161i	−0.632813	−	0.315512i
$127$	2.45373	+	4.24999i	0.217733	+	0.377125i	0.954115	−	0.299442i	$-0.0968003\pi$
$127$	2.45373	+	4.24999i	0.217733	+	0.377125i	−0.736381	+	0.676567i	$0.763467\pi$
$128$			1.00000i			0.0883883i
$129$	−5.97694	+	3.06354i	−0.526240	+	0.269729i
$130$	−5.57887	+	3.12443i	−0.489300	+	0.274031i
$131$	−2.64301	+	4.57783i	−0.230921	+	0.399967i	−0.958079	−	0.286503i	$-0.907507\pi$
$131$	−2.64301	+	4.57783i	−0.230921	+	0.399967i	0.727158	+	0.686470i	$0.240841\pi$
$132$	−0.706079	−	1.37756i	−0.0614563	−	0.119901i
$133$	1.99311	+	0.756152i	0.172824	+	0.0655667i
$134$	−6.91729	−	3.99370i	−0.597563	−	0.345003i
$135$	7.20310	+	5.74737i	0.619944	+	0.494655i
$136$			7.49940i			0.643068i
$137$			0.404382i			0.0345487i	0.999851	+	0.0172743i	$0.00549886\pi$
$137$			0.404382i			0.0345487i	−0.999851	+	0.0172743i	$0.994501\pi$
$138$	−7.93341	−	5.12492i	−0.675337	−	0.436262i
$139$	−3.91193	−	2.25855i	−0.331806	−	0.191568i	0.324837	−	0.945770i	$-0.394691\pi$
$139$	−3.91193	−	2.25855i	−0.331806	−	0.191568i	−0.656642	+	0.754202i	$0.728024\pi$
$140$	−4.63139	+	0.752120i	−0.391424	+	0.0635657i
$141$	12.9206	−	6.62257i	1.08811	−	0.557721i
$142$	−1.14296	+	1.97967i	−0.0959152	+	0.166130i
$143$	2.81147	−	1.57455i	0.235107	−	0.131671i
$144$	1.23338	+	2.73473i	0.102782	+	0.227894i
$145$			15.6210i			1.29725i
$146$	4.35881	+	7.54968i	0.360738	+	0.624816i
$147$	8.48508	−	8.66045i	0.699838	−	0.714302i
$148$	−3.69465			−0.303699
$149$	2.37853	−	1.37324i	0.194857	−	0.112500i	−0.399398	−	0.916778i	$-0.630781\pi$
$149$	2.37853	−	1.37324i	0.194857	−	0.112500i	0.594254	+	0.804277i	$0.297447\pi$
$150$	−3.20882	−	0.160427i	−0.261999	−	0.0130988i
$151$	7.11941	+	12.3312i	0.579369	+	1.00350i	0.995552	+	0.0942159i	$0.0300344\pi$
$151$	7.11941	+	12.3312i	0.579369	+	1.00350i	−0.416183	+	0.909281i	$0.636632\pi$
$152$	−0.402858	−	0.697770i	−0.0326761	−	0.0565966i
$153$	9.24963	+	20.5089i	0.747788	+	1.65804i
$154$	2.33398	−	0.379030i	0.188078	−	0.0305431i
$155$		−	16.8020i		−	1.34957i
$156$	−5.59426	+	2.77565i	−0.447900	+	0.222230i
$157$	19.0276	−	10.9856i	1.51857	−	0.876747i	0.518810	−	0.854889i	$-0.326375\pi$
$157$	19.0276	−	10.9856i	1.51857	−	0.876747i	0.999761	−	0.0218580i	$-0.00695817\pi$
$158$	11.0916	+	6.40376i	0.882403	+	0.509456i
$159$	−5.44159	−	0.272056i	−0.431546	−	0.0215754i
$160$	1.53584	+	0.886718i	0.121419	+	0.0701012i
$161$	11.1764	−	9.12307i	0.880824	−	0.718999i
$162$	6.74595	+	5.95753i	0.530012	+	0.468068i
$163$	−2.74658	−	4.75722i	−0.215129	−	0.372614i	0.738183	−	0.674600i	$-0.235684\pi$
$163$	−2.74658	−	4.75722i	−0.215129	−	0.372614i	−0.953312	+	0.301986i	$0.902351\pi$
$164$	−3.47099	−	6.01193i	−0.271039	−	0.469453i
$165$	−2.74180	−	0.137078i	−0.213449	−	0.0106715i
$166$		−	13.8340i		−	1.07372i
$167$	2.92252	+	5.06195i	0.226151	+	0.391706i	0.956664	−	0.291193i	$-0.0940522\pi$
$167$	2.92252	+	5.06195i	0.226151	+	0.391706i	−0.730513	+	0.682899i	$0.760719\pi$
$168$	−4.55436	+	0.507788i	−0.351376	+	0.0391767i
$169$	−6.20342	−	11.4244i	−0.477186	−	0.878802i
$170$	11.5179	+	6.64985i	0.883381	+	0.510020i
$171$	−1.96233	−	1.41134i	−0.150063	−	0.107928i
$172$	−1.93884	+	3.35816i	−0.147835	+	0.256058i
$173$	−7.29361	−	12.6329i	−0.554523	−	0.960462i	−0.997940	−	0.0641469i	$-0.979567\pi$
$173$	−7.29361	−	12.6329i	−0.554523	−	0.960462i	0.443417	−	0.896315i	$-0.353766\pi$
$174$	−0.761805	+	15.2374i	−0.0577523	+	1.15515i
$175$	1.74082	−	4.58856i	0.131594	−	0.346862i
$176$	−0.773984	−	0.446860i	−0.0583412	−	0.0336833i
$177$	−4.87240	−	3.14753i	−0.366232	−	0.236583i
$178$			15.5163i			1.16300i
$179$	8.38489	+	4.84102i	0.626716	+	0.361835i	0.779479	−	0.626428i	$-0.215484\pi$
$179$	8.38489	+	4.84102i	0.626716	+	0.361835i	−0.152763	+	0.988263i	$0.548817\pi$
$180$	5.29377	+	0.530658i	0.394575	+	0.0395529i
$181$		−	16.1898i		−	1.20338i	−0.798731	−	0.601688i	$-0.794495\pi$
$181$		−	16.1898i		−	1.20338i	0.798731	−	0.601688i	$-0.205505\pi$
$182$	−1.40589	−	9.43523i	−0.104212	−	0.699385i
$183$	14.2040	+	0.710140i	1.04999	+	0.0524950i
$184$	−5.45295			−0.401996
$185$	−3.27611	+	5.67440i	−0.240865	+	0.417190i
$186$	0.819400	−	16.3894i	0.0600813	−	1.20173i
$187$	−5.80442	−	3.35118i	−0.424461	−	0.245063i
$188$	4.19126	−	7.25948i	0.305679	−	0.529452i
$189$	−11.8287	+	7.00593i	−0.860408	+	0.509606i
$190$	−1.42888			−0.103662
$191$	13.6786	−	7.89736i	0.989751	−	0.571433i	0.0845509	−	0.996419i	$-0.473054\pi$
$191$	13.6786	−	7.89736i	0.989751	−	0.571433i	0.905200	+	0.424986i	$0.139721\pi$
$192$	1.45489	+	0.939845i	0.104997	+	0.0678275i
$193$	0.799689	−	1.38510i	0.0575629	−	0.0997018i	−0.835808	−	0.549022i	$-0.815000\pi$
$193$	0.799689	−	1.38510i	0.0575629	−	0.0997018i	0.893371	+	0.449320i	$0.148334\pi$
$194$	2.45256	−	4.24795i	0.176083	−	0.304985i
$195$	−0.697584	+	11.0531i	−0.0499550	+	0.791529i
$196$	1.40178	−	6.85821i	0.100127	−	0.489872i
$197$	3.83872	−	2.21629i	0.273498	−	0.157904i	−0.356978	−	0.934113i	$-0.616193\pi$
$197$	3.83872	−	2.21629i	0.273498	−	0.157904i	0.630476	+	0.776209i	$0.282860\pi$
$198$	−2.66779	−	0.267424i	−0.189592	−	0.0190050i
$199$		−	12.3701i		−	0.876891i	−0.898758	−	0.438446i	$-0.855529\pi$
$199$		−	12.3701i		−	0.876891i	0.898758	−	0.438446i	$-0.144471\pi$
$200$	−1.60641	+	0.927464i	−0.113591	+	0.0655816i
$201$	−12.3116	+	6.31041i	−0.868390	+	0.445102i
$202$	14.4081	+	8.31852i	1.01375	+	0.585289i
$203$	−21.7892	−	8.26647i	−1.52930	−	0.580193i
$204$	10.9108	+	7.04827i	0.763906	+	0.493478i
$205$	−12.3112			−0.859848
$206$	4.30881	−	7.46308i	0.300209	−	0.519977i
$207$	−14.9124	+	6.72557i	−1.03648	+	0.467459i
$208$	−1.84344	+	3.09866i	−0.127820	+	0.214854i
$209$	0.720084			0.0498092
$210$	−3.25855	+	7.44502i	−0.224861	+	0.513755i
$211$	−9.95733	−	17.2466i	−0.685491	−	1.18731i	−0.973282	−	0.229612i	$-0.926254\pi$
$211$	−9.95733	−	17.2466i	−0.685491	−	1.18731i	0.287791	−	0.957693i	$-0.407079\pi$
$212$	−2.72420	+	1.57281i	−0.187098	+	0.108021i
$213$	1.80598	+	3.52346i	0.123744	+	0.241423i
$214$	16.3289			1.11622
$215$	3.43840	+	5.95548i	0.234497	+	0.406161i
$216$	5.13791	+	0.775795i	0.349591	+	0.0527862i
$217$	23.4366	+	8.89145i	1.59098	+	0.603591i
$218$	−1.11139	+	0.641659i	−0.0752726	+	0.0434587i
$219$	15.0805	+	0.753961i	1.01905	+	0.0509480i
$220$	−1.37261	+	0.792477i	−0.0925414	+	0.0534288i
$221$	−13.8247	+	23.2381i	−0.929952	+	1.56316i
$222$	−3.47240	+	5.37530i	−0.233052	+	0.360766i
$223$	−6.77255	+	3.91013i	−0.453523	+	0.261842i	−0.709317	−	0.704890i	$-0.750997\pi$
$223$	−6.77255	+	3.91013i	−0.453523	+	0.261842i	0.255794	+	0.966731i	$0.417663\pi$
$224$	−2.04961	+	1.67305i	−0.136945	+	0.111786i
$225$	−3.24920	+	4.51769i	−0.216613	+	0.301179i
$226$	−0.158407	+	0.274369i	−0.0105371	+	0.0182508i
$227$	22.6931			1.50620			0.753098	−	0.657909i	$-0.228559\pi$
$227$	22.6931			1.50620			0.753098	+	0.657909i	$0.228559\pi$
$228$	−1.39380	−	0.0696839i	−0.0923066	−	0.00461493i
$229$	2.94903	+	1.70262i	0.194877	+	0.112513i	0.594264	−	0.804270i	$-0.297443\pi$
$229$	2.94903	+	1.70262i	0.194877	+	0.112513i	−0.399386	+	0.916783i	$0.630777\pi$
$230$	−4.83522	+	8.37485i	−0.318825	+	0.552221i
$231$	1.64214	−	3.75191i	0.108045	−	0.246857i
$232$	4.40416	+	7.62822i	0.289147	+	0.500817i
$233$	−5.66985	−	3.27349i	−0.371444	−	0.214453i	0.302645	−	0.953103i	$-0.402130\pi$
$233$	−5.66985	−	3.27349i	−0.371444	−	0.214453i	−0.674089	+	0.738650i	$0.735464\pi$
$234$	−1.21949	+	10.7477i	−0.0797208	+	0.702598i
$235$	−7.43293	−	12.8742i	−0.484871	−	0.839821i
$236$	−3.34899			−0.218001
$237$	19.7412	−	10.1185i	1.28233	−	0.657268i
$238$	−15.3708	+	12.5469i	−0.996343	+	0.813295i
$239$		−	2.75097i		−	0.177946i	−0.996034	−	0.0889729i	$-0.971642\pi$
$239$		−	2.75097i		−	0.177946i	0.996034	−	0.0889729i	$-0.0283584\pi$
$240$	2.73352	−	1.40109i	0.176448	−	0.0904402i
$241$		−	6.12961i		−	0.394843i	−0.980319	−	0.197421i	$-0.936743\pi$
$241$		−	6.12961i		−	0.394843i	0.980319	−	0.197421i	$-0.0632567\pi$
$242$	−8.83455	+	5.10063i	−0.567907	+	0.327881i
$243$	15.0077	−	4.21542i	0.962743	−	0.270419i
$244$	7.11088	−	4.10547i	0.455228	−	0.262826i
$245$	−9.29012	−	8.23421i	−0.593524	−	0.526064i
$246$	−12.0089	−	0.600391i	−0.765657	−	0.0382795i
$247$	0.0379805	−	2.90480i	0.00241664	−	0.184828i
$248$	−4.73713	−	8.20495i	−0.300808	−	0.521015i
$249$	−20.1268	−	13.0018i	−1.27549	−	0.823954i
$250$			12.1568i			0.768862i
$251$	−6.30342	+	10.9178i	−0.397868	+	0.689128i	−0.993463	−	0.114157i	$-0.963583\pi$
$251$	−6.30342	+	10.9178i	−0.397868	+	0.689128i	0.595594	+	0.803285i	$0.296917\pi$
$252$	−3.54161	+	7.10331i	−0.223101	+	0.447466i
$253$	2.43670	−	4.22049i	0.153194	−	0.265340i
$254$	4.24999	−	2.45373i	0.266668	−	0.153961i
$255$	20.4998	−	10.5074i	1.28375	−	0.657997i
$256$	1.00000			0.0625000
$257$	27.2662			1.70082			0.850411	−	0.526120i	$-0.176354\pi$
$257$	27.2662			1.70082			0.850411	+	0.526120i	$0.176354\pi$
$258$	3.06354	+	5.97694i	0.190727	+	0.372108i
$259$	−6.18135	−	7.57259i	−0.384091	−	0.470538i
$260$	3.12443	+	5.57887i	0.193769	+	0.345987i
$261$	21.4527	+	15.4291i	1.32789	+	0.955040i
$262$	4.57783	+	2.64301i	0.282819	+	0.163286i
$263$	−0.487124	−	0.281241i	−0.0300374	−	0.0173421i	0.484906	−	0.874566i	$-0.338854\pi$
$263$	−0.487124	−	0.281241i	−0.0300374	−	0.0173421i	−0.514943	+	0.857224i	$0.672187\pi$
$264$	−1.37756	+	0.706079i	−0.0847827	+	0.0434562i
$265$			5.57857i			0.342689i
$266$	0.756152	−	1.99311i	0.0463627	−	0.122205i
$267$	22.5745	+	14.5829i	1.38153	+	0.892461i
$268$	−3.99370	+	6.91729i	−0.243954	+	0.422541i
$269$	−3.93196			−0.239736			−0.119868	−	0.992790i	$-0.538247\pi$
$269$	−3.93196			−0.239736			−0.119868	+	0.992790i	$0.538247\pi$
$270$	5.74737	−	7.20310i	0.349774	−	0.438367i
$271$			0.877195i			0.0532858i	0.999645	+	0.0266429i	$0.00848170\pi$
$271$			0.877195i			0.0532858i	−0.999645	+	0.0266429i	$0.991518\pi$
$272$	7.49940			0.454718
$273$	−15.0485	−	6.82224i	−0.910776	−	0.412901i
$274$	0.404382			0.0244296
$275$		−	1.65779i		−	0.0999683i
$276$	−5.12492	+	7.93341i	−0.308484	+	0.477535i
$277$	−12.6070			−0.757482			−0.378741	−	0.925503i	$-0.623643\pi$
$277$	−12.6070			−0.757482			−0.378741	+	0.925503i	$0.623643\pi$
$278$	−2.25855	+	3.91193i	−0.135459	+	0.234622i
$279$	−23.0746	−	16.5956i	−1.38144	−	0.993556i
$280$	0.752120	+	4.63139i	0.0449477	+	0.276779i
$281$			6.37716i			0.380429i	0.981743	+	0.190215i	$0.0609184\pi$
$281$			6.37716i			0.380429i	−0.981743	+	0.190215i	$0.939082\pi$
$282$	−6.62257	−	12.9206i	−0.394368	−	0.769410i
$283$	0.658885	+	0.380407i	0.0391666	+	0.0226129i	0.519455	−	0.854498i	$-0.326135\pi$
$283$	0.658885	+	0.380407i	0.0391666	+	0.0226129i	−0.480289	+	0.877110i	$0.659468\pi$
$284$	1.97967	+	1.14296i	0.117472	+	0.0678223i
$285$	−1.34293	+	2.07886i	−0.0795483	+	0.123141i
$286$	−1.57455	−	2.81147i	−0.0931053	−	0.166245i
$287$	6.51495	−	17.1725i	0.384565	−	1.01366i
$288$	2.73473	−	1.23338i	0.161146	−	0.0726778i
$289$	39.2410			2.30829
$290$	15.6210			0.917295
$291$	−3.87526	−	7.56061i	−0.227172	−	0.443211i
$292$	7.54968	−	4.35881i	0.441812	−	0.255080i
$293$	−6.35235	+	11.0026i	−0.371108	+	0.642778i	−0.989736	−	0.142906i	$-0.954355\pi$
$293$	−6.35235	+	11.0026i	−0.371108	+	0.642778i	0.618628	+	0.785684i	$0.287689\pi$
$294$	−8.66045	−	8.48508i	−0.505088	−	0.494860i
$295$	−2.96961	+	5.14352i	−0.172897	+	0.299467i
$296$			3.69465i			0.214747i
$297$	−2.89638	+	3.62999i	−0.168065	+	0.210633i
$298$	−1.37324	−	2.37853i	−0.0795499	−	0.137784i
$299$	−16.8968	−	10.0522i	−0.977169	−	0.581334i
$300$	−0.160427	+	3.20882i	−0.00926227	+	0.185261i
$301$	−10.1267	+	1.64453i	−0.583693	+	0.0947893i
$302$	12.3312	−	7.11941i	0.709579	−	0.409676i
$303$	25.6439	−	13.1440i	1.47320	−	0.755104i
$304$	−0.697770	+	0.402858i	−0.0400199	+	0.0231055i
$305$		−	14.5616i		−	0.833793i
$306$	20.5089	−	9.24963i	1.17241	−	0.528766i
$307$		−	2.90418i		−	0.165750i	−0.996560	−	0.0828751i	$-0.973590\pi$
$307$		−	2.90418i		−	0.165750i	0.996560	−	0.0828751i	$-0.0264102\pi$
$308$	−0.379030	−	2.33398i	−0.0215972	−	0.132991i
$309$	−6.80831	−	13.2830i	−0.387311	−	0.755641i
$310$	−16.8020			−0.954288
$311$	9.08284	+	15.7319i	0.515040	+	0.892076i	0.999848	+	0.0174552i	$0.00555643\pi$
$311$	9.08284	+	15.7319i	0.515040	+	0.892076i	−0.484807	+	0.874621i	$0.661110\pi$
$312$	2.77565	+	5.59426i	0.157140	+	0.316713i
$313$	2.78744	+	1.60933i	0.157556	+	0.0909648i	0.576705	−	0.816953i	$-0.304338\pi$
$313$	2.78744	+	1.60933i	0.157556	+	0.0909648i	−0.419149	+	0.907917i	$0.637672\pi$
$314$	−10.9856	−	19.0276i	−0.619954	−	1.07379i
$315$	7.76913	+	11.7380i	0.437741	+	0.661360i
$316$	6.40376	−	11.0916i	0.360240	−	0.623953i
$317$	0.947773	+	0.547197i	0.0532322	+	0.0307336i	0.526380	−	0.850249i	$-0.323549\pi$
$317$	0.947773	+	0.547197i	0.0532322	+	0.0307336i	−0.473148	+	0.880983i	$0.656882\pi$
$318$	−0.272056	+	5.44159i	−0.0152561	+	0.305149i
$319$	−7.87217			−0.440757
$320$	0.886718	−	1.53584i	0.0495690	−	0.0858561i
$321$	15.3466	−	23.7566i	0.856563	−	1.32596i
$322$	−9.12307	−	11.1764i	−0.508409	−	0.622836i
$323$	−5.23286	+	3.02119i	−0.291164	+	0.168104i
$324$	5.95753	−	6.74595i	0.330974	−	0.374775i
$325$	−6.68747	−	0.0874392i	−0.370954	−	0.00485025i
$326$	−4.75722	+	2.74658i	−0.263478	+	0.152119i
$327$	−0.110990	+	2.22000i	−0.00613778	+	0.122766i
$328$	−6.01193	+	3.47099i	−0.331953	+	0.191653i
$329$	21.8913	−	3.55506i	1.20691	−	0.195997i
$330$	−0.137078	+	2.74180i	−0.00754589	+	0.150931i
$331$	10.8134	+	18.7294i	0.594360	+	1.02946i	0.993637	+	0.112632i	$0.0359281\pi$
$331$	10.8134	+	18.7294i	0.594360	+	1.02946i	−0.399276	+	0.916831i	$0.630739\pi$
$332$	−13.8340			−0.759237
$333$	4.55692	+	10.1039i	0.249718	+	0.553690i
$334$	5.06195	−	2.92252i	0.276978	−	0.159913i
$335$	7.08257	+	12.2674i	0.386962	+	0.670238i
$336$	0.507788	+	4.55436i	0.0277021	+	0.248460i
$337$	16.9544			0.923564			0.461782	−	0.886993i	$-0.347210\pi$
$337$	16.9544			0.923564			0.461782	+	0.886993i	$0.347210\pi$
$338$	−11.4244	+	6.20342i	−0.621407	+	0.337422i
$339$	0.250298	+	0.488329i	0.0135943	+	0.0265224i
$340$	6.64985	−	11.5179i	0.360639	−	0.624645i
$341$	8.46733			0.458532
$342$	−1.41134	+	1.96233i	−0.0763164	+	0.106110i
$343$	16.4019	−	8.60105i	0.885619	−	0.464413i
$344$	3.35816	+	1.93884i	0.181060	+	0.104535i
$345$	7.64009	+	14.9058i	0.411329	+	0.802499i
$346$	−12.6329	+	7.29361i	−0.679149	+	0.392107i
$347$			22.1793i			1.19065i	0.803486	+	0.595324i	$0.202976\pi$
$347$			22.1793i			1.19065i	−0.803486	+	0.595324i	$0.797024\pi$
$348$	15.2374	+	0.761805i	0.816811	+	0.0408370i
$349$	−9.10947	+	5.25936i	−0.487619	+	0.281527i	−0.723586	−	0.690234i	$-0.757508\pi$
$349$	−9.10947	+	5.25936i	−0.487619	+	0.281527i	0.235967	+	0.971761i	$0.424174\pi$
$350$	−4.58856	−	1.74082i	−0.245269	−	0.0930509i
$351$	14.4905	+	11.8754i	0.773447	+	0.633861i
$352$	−0.446860	+	0.773984i	−0.0238177	+	0.0412535i
$353$	12.5837	−	21.7956i	0.669762	−	1.16006i	−0.308209	−	0.951319i	$-0.599729\pi$
$353$	12.5837	−	21.7956i	0.669762	−	1.16006i	0.977971	−	0.208743i	$-0.0669372\pi$
$354$	−3.14753	+	4.87240i	−0.167290	+	0.258965i
$355$	3.51081	−	2.02697i	0.186335	−	0.107580i
$356$	15.5163			0.822363
$357$	3.80810	+	34.1549i	0.201546	+	1.80767i
$358$	4.84102	−	8.38489i	0.255856	−	0.443155i
$359$	−20.7408	−	11.9747i	−1.09466	−	0.632002i	−0.159846	−	0.987142i	$-0.551100\pi$
$359$	−20.7408	−	11.9747i	−1.09466	−	0.632002i	−0.934813	+	0.355140i	$0.884433\pi$
$360$	0.530658	−	5.29377i	0.0279681	−	0.279006i
$361$	−9.17541	+	15.8923i	−0.482916	+	0.836436i
$362$	−16.1898			−0.850915
$363$	−0.882277	+	17.6471i	−0.0463075	+	0.926231i
$364$	−9.43523	+	1.40589i	−0.494540	+	0.0736887i
$365$		−	15.4601i		−	0.809221i
$366$	0.710140	−	14.2040i	0.0371196	−	0.742456i
$367$	−12.3837	−	7.14973i	−0.646423	−	0.373213i	0.140661	−	0.990058i	$-0.455077\pi$
$367$	−12.3837	−	7.14973i	−0.646423	−	0.373213i	−0.787085	+	0.616845i	$0.788411\pi$
$368$			5.45295i			0.284254i
$369$	−12.1600	+	16.9072i	−0.633023	+	0.880156i
$370$	5.67440	+	3.27611i	0.294998	+	0.170317i
$371$	−7.78138	−	2.95213i	−0.403989	−	0.153267i
$372$	−16.3894	−	0.819400i	−0.849752	−	0.0424839i
$373$	−2.68705	−	4.65411i	−0.139130	−	0.240981i	0.788037	−	0.615627i	$-0.211097\pi$
$373$	−2.68705	−	4.65411i	−0.139130	−	0.240981i	−0.927168	+	0.374647i	$0.877764\pi$
$374$	−3.35118	+	5.80442i	−0.173285	+	0.300139i
$375$	17.6867	+	11.4255i	0.913338	+	0.590009i
$376$	−7.25948	−	4.19126i	−0.374379	−	0.216148i
$377$	−0.415214	+	31.7561i	−0.0213846	+	1.63552i
$378$	7.00593	+	11.8287i	0.360346	+	0.608400i
$379$	9.34507	+	16.1861i	0.480024	+	0.831426i	0.999737	−	0.0229149i	$-0.00729466\pi$
$379$	9.34507	+	16.1861i	0.480024	+	0.831426i	−0.519714	+	0.854341i	$0.673961\pi$
$380$			1.42888i			0.0733002i
$381$	0.424432	−	8.48937i	0.0217443	−	0.434924i
$382$	−7.89736	−	13.6786i	−0.404064	−	0.699859i
$383$	−16.4074	−	28.4184i	−0.838379	−	1.45211i	−0.891250	−	0.453513i	$-0.850171\pi$
$383$	−16.4074	−	28.4184i	−0.838379	−	1.45211i	0.0528709	−	0.998601i	$-0.483163\pi$
$384$	0.939845	−	1.45489i	0.0479613	−	0.0742443i
$385$	−3.92072	−	1.48746i	−0.199818	−	0.0758078i
$386$	−1.38510	−	0.799689i	−0.0704998	−	0.0407031i
$387$	11.5750	+	1.16030i	0.588391	+	0.0589814i
$388$	−4.24795	−	2.45256i	−0.215657	−	0.124510i
$389$	7.54767	−	4.35765i	0.382682	−	0.220941i	−0.296303	−	0.955094i	$-0.595754\pi$
$389$	7.54767	−	4.35765i	0.382682	−	0.220941i	0.678984	+	0.734153i	$0.262420\pi$
$390$	11.0531	+	0.697584i	0.559696	+	0.0353235i
$391$			40.8938i			2.06809i
$392$	−6.85821	−	1.40178i	−0.346392	−	0.0708007i
$393$	8.14774	−	4.17620i	0.410999	−	0.210661i
$394$	−2.21629	−	3.83872i	−0.111655	−	0.193392i
$395$	−11.3566	−	19.6703i	−0.571415	−	0.989720i
$396$	−0.267424	+	2.66779i	−0.0134386	+	0.134061i
$397$	−33.7920	+	19.5098i	−1.69597	+	0.979170i	−0.746464	+	0.665426i	$0.768250\pi$
$397$	−33.7920	+	19.5098i	−1.69597	+	0.979170i	−0.949508	+	0.313744i	$0.898417\pi$
$398$	−12.3701			−0.620056
$399$	−2.18908	−	2.97333i	−0.109591	−	0.148852i
$400$	0.927464	+	1.60641i	0.0463732	+	0.0803207i
$401$			7.14319i			0.356714i	0.983966	+	0.178357i	$0.0570782\pi$
$401$			7.14319i			0.356714i	−0.983966	+	0.178357i	$0.942922\pi$
$402$	6.31041	+	12.3116i	0.314734	+	0.614045i
$403$	0.446605	−	34.1570i	0.0222470	−	1.70148i
$404$	8.31852	−	14.4081i	0.413862	−	0.716830i
$405$	−5.07804	−	15.1316i	−0.252330	−	0.751894i
$406$	−8.26647	+	21.7892i	−0.410258	+	1.08138i
$407$	−2.85960	−	1.65099i	−0.141745	−	0.0818367i
$408$	7.04827	−	10.9108i	0.348942	−	0.540163i
$409$			14.9068i			0.737095i	0.929609	+	0.368548i	$0.120145\pi$
$409$			14.9068i			0.737095i	−0.929609	+	0.368548i	$0.879855\pi$
$410$			12.3112i			0.608004i
$411$	0.380056	−	0.588329i	0.0187468	−	0.0290201i
$412$	−7.46308	−	4.30881i	−0.367679	−	0.212280i
$413$	−5.60304	−	6.86412i	−0.275708	−	0.337761i
$414$	6.72557	+	14.9124i	0.330544	+	0.732902i
$415$	−12.2668	+	21.2468i	−0.602154	+	1.04296i
$416$	3.09866	+	1.84344i	0.151924	+	0.0903823i
$417$	3.56872	+	6.96255i	0.174761	+	0.340957i
$418$		−	0.720084i		−	0.0352205i
$419$	−10.6067	−	18.3714i	−0.518172	−	0.897500i	−0.999777	−	0.0211116i	$-0.993279\pi$
$419$	−10.6067	−	18.3714i	−0.518172	−	0.897500i	0.481605	−	0.876388i	$-0.340054\pi$
$420$	7.44502	+	3.25855i	0.363280	+	0.159001i
$421$	1.98956			0.0969651			0.0484825	−	0.998824i	$-0.484561\pi$
$421$	1.98956			0.0969651			0.0484825	+	0.998824i	$0.484561\pi$
$422$	−17.2466	+	9.95733i	−0.839551	+	0.484715i
$423$	−25.0222	−	2.50827i	−1.21662	−	0.121956i
$424$	1.57281	+	2.72420i	0.0763826	+	0.132299i
$425$	6.95542	+	12.0471i	0.337388	+	0.584373i
$426$	3.52346	−	1.80598i	0.170712	−	0.0875001i
$427$	20.3115	+	7.70585i	0.982942	+	0.372912i
$428$		−	16.3289i		−	0.789285i
$429$	−5.57020	−	0.351546i	−0.268932	−	0.0169728i
$430$	5.95548	−	3.43840i	0.287199	−	0.165814i
$431$	12.5888	+	7.26815i	0.606381	+	0.350094i	0.771548	−	0.636171i	$-0.219483\pi$
$431$	12.5888	+	7.26815i	0.606381	+	0.350094i	−0.165167	+	0.986266i	$0.552816\pi$
$432$	0.775795	−	5.13791i	0.0373255	−	0.247198i
$433$	−1.17784	−	0.680025i	−0.0566033	−	0.0326799i	0.471431	−	0.881903i	$-0.343738\pi$
$433$	−1.17784	−	0.680025i	−0.0566033	−	0.0326799i	−0.528035	+	0.849223i	$0.677071\pi$
$434$	8.89145	−	23.4366i	0.426803	−	1.12499i
$435$	14.6813	−	22.7267i	0.703914	−	1.08966i
$436$	0.641659	+	1.11139i	0.0307299	+	0.0532258i
$437$	−2.19676	−	3.80490i	−0.105085	−	0.182013i
$438$	0.753961	−	15.0805i	0.0360257	−	0.720576i
$439$			29.8566i			1.42498i	0.701684	+	0.712488i	$0.252432\pi$
$439$			29.8566i			1.42498i	−0.701684	+	0.712488i	$0.747568\pi$
$440$	0.792477	+	1.37261i	0.0377799	+	0.0654366i
$441$	−20.4843	+	4.62529i	−0.975443	+	0.220252i
$442$	23.2381	+	13.8247i	1.10532	+	0.657575i
$443$	31.3793	+	18.1168i	1.49087	+	0.860757i	0.999945	−	0.0104432i	$-0.00332424\pi$
$443$	31.3793	+	18.1168i	1.49087	+	0.860757i	0.490929	+	0.871200i	$0.336658\pi$
$444$	5.37530	+	3.47240i	0.255100	+	0.164793i
$445$	13.7586	−	23.8306i	0.652220	−	1.12968i
$446$	3.91013	+	6.77255i	0.185150	+	0.320690i
$447$	−4.75112	−	0.237535i	−0.224720	−	0.0112350i
$448$	1.67305	+	2.04961i	0.0790444	+	0.0968349i
$449$	−28.3824	−	16.3866i	−1.33945	−	0.773331i	−0.352723	−	0.935728i	$-0.614744\pi$
$449$	−28.3824	−	16.3866i	−1.33945	−	0.773331i	−0.986726	+	0.162397i	$0.948078\pi$
$450$	4.51769	+	3.24920i	0.212966	+	0.153169i
$451$		−	6.20419i		−	0.292144i
$452$	0.274369	+	0.158407i	0.0129052	+	0.00745085i
$453$	1.23147	−	24.6316i	0.0578596	−	1.15729i
$454$		−	22.6931i		−	1.06504i
$455$	−6.20716	+	15.7376i	−0.290996	+	0.737791i
$456$	−0.0696839	+	1.39380i	−0.00326325	+	0.0652706i
$457$	−10.8965			−0.509718			−0.254859	−	0.966978i	$-0.582029\pi$
$457$	−10.8965			−0.509718			−0.254859	+	0.966978i	$0.582029\pi$
$458$	1.70262	−	2.94903i	0.0795584	−	0.137799i
$459$	5.81800	−	38.5313i	0.271561	−	1.79849i
$460$	8.37485	+	4.83522i	0.390479	+	0.225443i
$461$	16.4579	−	28.5059i	0.766520	−	1.32765i	−0.172919	−	0.984936i	$-0.555320\pi$
$461$	16.4579	−	28.5059i	0.766520	−	1.32765i	0.939439	−	0.342715i	$-0.111347\pi$
$462$	−3.75191	−	1.64214i	−0.174555	−	0.0763992i
$463$	−9.98781			−0.464173			−0.232086	−	0.972695i	$-0.574555\pi$
$463$	−9.98781			−0.464173			−0.232086	+	0.972695i	$0.574555\pi$
$464$	7.62822	−	4.40416i	0.354131	−	0.204458i
$465$	−15.7913	+	24.4449i	−0.732302	+	1.13361i
$466$	−3.27349	+	5.66985i	−0.151641	+	0.262651i
$467$	10.4424	−	18.0868i	0.483217	−	0.836956i	−0.516597	−	0.856228i	$-0.672802\pi$
$467$	10.4424	−	18.0868i	0.483217	−	0.836956i	0.999814	+	0.0192723i	$0.00613493\pi$
$468$	10.7477	+	1.21949i	0.496812	+	0.0563711i
$469$	−20.8594	+	3.38748i	−0.963198	+	0.156419i
$470$	−12.8742	+	7.43293i	−0.593843	+	0.342855i
$471$	−38.0078	−	1.90023i	−1.75131	−	0.0875578i
$472$			3.34899i			0.154150i
$473$	−3.00126	+	1.73278i	−0.137998	+	0.0796732i
$474$	−10.1185	−	19.7412i	−0.464759	−	0.906741i
$475$	−1.29431	−	0.747272i	−0.0593872	−	0.0342872i
$476$	12.5469	+	15.3708i	0.575086	+	0.704521i
$477$	7.66120	+	5.51006i	0.350782	+	0.252289i
$478$	−2.75097			−0.125827
$479$	5.93024	−	10.2715i	0.270960	−	0.469316i	−0.698148	−	0.715953i	$-0.745992\pi$
$479$	5.93024	−	10.2715i	0.270960	−	0.469316i	0.969108	+	0.246637i	$0.0793256\pi$
$480$	−1.40109	−	2.73352i	−0.0639509	−	0.124768i
$481$	−6.81089	+	11.4485i	−0.310550	+	0.522006i
$482$	−6.12961			−0.279196
$483$	−24.8347	+	2.76894i	−1.13002	+	0.125991i
$484$	5.10063	+	8.83455i	0.231847	+	0.401571i
$485$	−7.53347	+	4.34945i	−0.342077	+	0.197498i
$486$	−4.21542	−	15.0077i	−0.191215	−	0.680762i
$487$	−18.9879			−0.860422			−0.430211	−	0.902728i	$-0.641561\pi$
$487$	−18.9879			−0.860422			−0.430211	+	0.902728i	$0.641561\pi$
$488$	−4.10547	−	7.11088i	−0.185846	−	0.321895i
$489$	−0.475088	+	9.50257i	−0.0214842	+	0.429721i
$490$	−8.23421	+	9.29012i	−0.371983	+	0.419685i
$491$	−22.5331	+	13.0095i	−1.01691	+	0.587111i	−0.913206	−	0.407498i	$-0.866401\pi$
$491$	−22.5331	+	13.0095i	−1.01691	+	0.587111i	−0.103699	+	0.994609i	$0.533068\pi$
$492$	−0.600391	+	12.0089i	−0.0270677	+	0.541401i
$493$	57.2071	−	33.0285i	2.57648	−	1.48753i
$494$	−2.90480	−	0.0379805i	−0.130693	−	0.00170882i
$495$	3.86017	+	2.77630i	0.173502	+	0.124785i
$496$	−8.20495	+	4.73713i	−0.368413	+	0.212703i
$497$	0.969467	+	5.96978i	0.0434866	+	0.267781i
$498$	−13.0018	+	20.1268i	−0.582624	+	0.901905i
$499$	−5.42439	+	9.39532i	−0.242829	+	0.420592i	−0.961519	−	0.274738i	$-0.911409\pi$
$499$	−5.42439	+	9.39532i	−0.242829	+	0.420592i	0.718690	+	0.695331i	$0.244742\pi$
$500$	12.1568			0.543667
$501$	0.505520	−	10.1113i	0.0225850	−	0.451739i
$502$	10.9178	+	6.30342i	0.487287	+	0.281335i
$503$	−4.86978	+	8.43471i	−0.217133	+	0.376085i	−0.953930	−	0.300029i	$-0.903004\pi$
$503$	−4.86978	+	8.43471i	−0.217133	+	0.376085i	0.736797	+	0.676114i	$0.236337\pi$
$504$	7.10331	+	3.54161i	0.316406	+	0.157756i
$505$	−14.7524	−	25.5518i	−0.656471	−	1.13704i
$506$	−4.22049	−	2.43670i	−0.187624	−	0.108325i
$507$	−1.71193	+	22.4515i	−0.0760293	+	0.997106i
$508$	−2.45373	−	4.24999i	−0.108867	−	0.188563i
$509$	−11.4969			−0.509590			−0.254795	−	0.966995i	$-0.582008\pi$
$509$	−11.4969			−0.509590			−0.254795	+	0.966995i	$0.582008\pi$
$510$	−10.5074	−	20.4998i	−0.465274	−	0.907746i
$511$	21.5649	+	8.18136i	0.953974	+	0.361922i
$512$		−	1.00000i		−	0.0441942i
$513$	1.52852	+	3.89762i	0.0674858	+	0.172084i
$514$		−	27.2662i		−	1.20266i
$515$	−13.2353	+	7.64139i	−0.583216	+	0.336720i
$516$	5.97694	−	3.06354i	0.263120	−	0.134865i
$517$	6.48794	−	3.74581i	0.285339	−	0.164741i
$518$	−7.57259	+	6.18135i	−0.332721	+	0.271593i
$519$	−1.26161	+	25.2343i	−0.0553783	+	1.10766i
$520$	5.57887	−	3.12443i	0.244650	−	0.137016i
$521$	1.77397	+	3.07261i	0.0777191	+	0.134613i	0.902265	−	0.431181i	$-0.141903\pi$
$521$	1.77397	+	3.07261i	0.0777191	+	0.134613i	−0.824546	+	0.565794i	$0.808570\pi$
$522$	15.4291	−	21.4527i	0.675316	−	0.938960i
$523$		−	11.9115i		−	0.520854i	−0.965494	−	0.260427i	$-0.916137\pi$
$523$		−	11.9115i		−	0.520854i	0.965494	−	0.260427i	$-0.0838634\pi$
$524$	2.64301	−	4.57783i	0.115461	−	0.199984i
$525$	−6.84523	+	5.03972i	−0.298750	+	0.219951i
$526$	−0.281241	+	0.487124i	−0.0122627	+	0.0212396i
$527$	−61.5322	+	35.5256i	−2.68038	+	1.54752i
$528$	0.706079	+	1.37756i	0.0307281	+	0.0599504i
$529$	−6.73462			−0.292809
$530$	5.57857			0.242318
$531$	4.13059	+	9.15860i	0.179252	+	0.397449i
$532$	−1.99311	−	0.756152i	−0.0864121	−	0.0327833i
$533$	−25.0275	−	0.327237i	−1.08406	−	0.0141742i
$534$	14.5829	−	22.5745i	0.631065	−	0.976893i
$535$	−25.0785	−	14.4791i	−1.08424	−	0.625985i
$536$	6.91729	+	3.99370i	0.298781	+	0.172502i
$537$	−7.64925	−	14.9236i	−0.330089	−	0.644002i
$538$			3.93196i			0.169519i
$539$	4.14962	−	4.68174i	0.178737	−	0.201657i
$540$	−7.20310	−	5.74737i	−0.309972	−	0.247328i
$541$	8.93957	−	15.4838i	0.384342	−	0.665700i	−0.607336	−	0.794445i	$-0.707762\pi$
$541$	8.93957	−	15.4838i	0.384342	−	0.665700i	0.991678	+	0.128745i	$0.0410950\pi$
$542$	0.877195			0.0376788
$543$	−15.2159	+	23.5543i	−0.652975	+	1.01081i
$544$		−	7.49940i		−	0.321534i
$545$	2.27588			0.0974881
$546$	−6.82224	+	15.0485i	−0.291965	+	0.644016i
$547$	−37.3187			−1.59563			−0.797817	−	0.602899i	$-0.794012\pi$
$547$	−37.3187			−1.59563			−0.797817	+	0.602899i	$0.794012\pi$
$548$		−	0.404382i		−	0.0172743i
$549$	−19.9978	−	14.3828i	−0.853486	−	0.613841i
$550$	−1.65779			−0.0706882
$551$	−3.54850	+	6.14618i	−0.151171	+	0.261836i
$552$	7.93341	+	5.12492i	0.337668	+	0.218131i
$553$	33.4473	−	5.43171i	1.42233	−	0.230980i
$554$			12.6070i			0.535621i
$555$	10.0994	−	5.17656i	0.428697	−	0.219733i
$556$	3.91193	+	2.25855i	0.165903	+	0.0957840i
$557$	−2.21001	−	1.27595i	−0.0936410	−	0.0540637i	0.452448	−	0.891791i	$-0.350551\pi$
$557$	−2.21001	−	1.27595i	−0.0936410	−	0.0540637i	−0.546089	+	0.837727i	$0.683884\pi$
$558$	−16.5956	+	23.0746i	−0.702550	+	0.976827i
$559$	6.83168	+	12.1984i	0.288949	+	0.515937i
$560$	4.63139	−	0.752120i	0.195712	−	0.0317829i
$561$	5.29517	+	10.3308i	0.223562	+	0.436168i
$562$	6.37716			0.269004
$563$	4.19756			0.176906			0.0884529	−	0.996080i	$-0.471808\pi$
$563$	4.19756			0.176906			0.0884529	+	0.996080i	$0.471808\pi$
$564$	−12.9206	+	6.62257i	−0.544055	+	0.278861i
$565$	0.486576	−	0.280925i	0.0204704	−	0.0118186i
$566$	0.380407	−	0.658885i	0.0159897	−	0.0276950i
$567$	23.7938	+	0.924278i	0.999246	+	0.0388160i
$568$	1.14296	−	1.97967i	0.0479576	−	0.0830650i
$569$		−	37.1060i		−	1.55556i	−0.628534	−	0.777782i	$-0.716345\pi$
$569$		−	37.1060i		−	1.55556i	0.628534	−	0.777782i	$-0.283655\pi$
$570$	2.07886	+	1.34293i	0.0870740	+	0.0562491i
$571$	2.55983	+	4.43376i	0.107126	+	0.185547i	0.914605	−	0.404349i	$-0.132502\pi$
$571$	2.55983	+	4.43376i	0.107126	+	0.185547i	−0.807479	+	0.589896i	$0.799169\pi$
$572$	−2.81147	+	1.57455i	−0.117553	+	0.0658354i
$573$	−27.3231	−	1.36604i	−1.14144	−	0.0570670i
$574$	−17.1725	−	6.51495i	−0.716764	−	0.271929i
$575$	−8.75969	+	5.05741i	−0.365304	+	0.210909i
$576$	−1.23338	−	2.73473i	−0.0513909	−	0.113947i
$577$	−4.55577	+	2.63028i	−0.189659	+	0.109500i	−0.591823	−	0.806068i	$-0.701592\pi$
$577$	−4.55577	+	2.63028i	−0.189659	+	0.109500i	0.402164	+	0.915568i	$0.368258\pi$
$578$		−	39.2410i		−	1.63221i
$579$	−2.46524	+	1.26358i	−0.102452	+	0.0525126i
$580$		−	15.6210i		−	0.648626i
$581$	−23.1450	−	28.3542i	−0.960215	−	1.17633i
$582$	−7.56061	+	3.87526i	−0.313397	+	0.160635i
$583$	−2.81131			−0.116433
$584$	−4.35881	−	7.54968i	−0.180369	−	0.312408i
$585$	11.4031	−	15.4254i	0.471461	−	0.637761i
$586$	11.0026	+	6.35235i	0.454513	+	0.262413i
$587$	−13.2127	−	22.8850i	−0.545346	−	0.944567i	−0.998585	−	0.0531780i	$-0.983065\pi$
$587$	−13.2127	−	22.8850i	−0.545346	−	0.944567i	0.453239	−	0.891389i	$-0.350268\pi$
$588$	−8.48508	+	8.66045i	−0.349919	+	0.357151i
$589$	3.81678	−	6.61085i	0.157268	−	0.272395i
$590$	5.14352	+	2.96961i	0.211755	+	0.122257i
$591$	−7.66787	−	0.383360i	−0.315414	−	0.0157693i
$592$	3.69465			0.151849
$593$	−11.1153	+	19.2523i	−0.456451	+	0.790596i	−0.998770	−	0.0495766i	$-0.984213\pi$
$593$	−11.1153	+	19.2523i	−0.456451	+	0.790596i	0.542320	+	0.840172i	$0.317546\pi$
$594$	3.62999	+	2.89638i	0.148940	+	0.118840i
$595$	34.7327	−	5.64045i	1.42390	−	0.231236i
$596$	−2.37853	+	1.37324i	−0.0974283	+	0.0562502i
$597$	−11.6260	+	17.9970i	−0.475819	+	0.736570i
$598$	−10.0522	+	16.8968i	−0.411065	+	0.690963i
$599$	15.9688	−	9.21958i	0.652467	−	0.376702i	−0.136934	−	0.990580i	$-0.543725\pi$
$599$	15.9688	−	9.21958i	0.652467	−	0.376702i	0.789401	+	0.613878i	$0.210391\pi$
$600$	3.20882	+	0.160427i	0.131000	+	0.00654941i
$601$	16.9272	−	9.77294i	0.690476	−	0.398646i	−0.113314	−	0.993559i	$-0.536147\pi$
$601$	16.9272	−	9.77294i	0.690476	−	0.398646i	0.803790	+	0.594913i	$0.202813\pi$
$602$	1.64453	+	10.1267i	0.0670262	+	0.412733i
$603$	23.8427	+	2.39004i	0.970950	+	0.0973299i
$604$	−7.11941	−	12.3312i	−0.289685	−	0.501748i
$605$	18.0913			0.735515
$606$	−13.1440	−	25.6439i	−0.533939	−	1.04171i
$607$	6.81702	−	3.93581i	0.276694	−	0.159750i	−0.355232	−	0.934778i	$-0.615598\pi$
$607$	6.81702	−	3.93581i	0.276694	−	0.159750i	0.631926	+	0.775029i	$0.282265\pi$
$608$	0.402858	+	0.697770i	0.0163380	+	0.0282983i
$609$	23.9316	+	32.5053i	0.969758	+	1.31718i
$610$	−14.5616			−0.589581
$611$	−14.7683	−	26.3698i	−0.597462	−	1.06681i
$612$	−9.24963	−	20.5089i	−0.373894	−	0.829022i
$613$	−12.1960	+	21.1240i	−0.492591	+	0.853192i	−0.999964	−	0.00853454i	$-0.997283\pi$
$613$	−12.1960	+	21.1240i	−0.492591	+	0.853192i	0.507373	+	0.861727i	$0.330617\pi$
$614$	−2.90418			−0.117203
$615$	17.9113	+	11.5706i	0.722254	+	0.466571i
$616$	−2.33398	+	0.379030i	−0.0940389	+	0.0152715i
$617$	3.90089	+	2.25218i	0.157044	+	0.0906694i	0.576462	−	0.817124i	$-0.304433\pi$
$617$	3.90089	+	2.25218i	0.157044	+	0.0906694i	−0.419419	+	0.907793i	$0.637766\pi$
$618$	−13.2830	+	6.80831i	−0.534319	+	0.273870i
$619$	4.81682	−	2.78099i	0.193604	−	0.111777i	−0.400065	−	0.916487i	$-0.631012\pi$
$619$	4.81682	−	2.78099i	0.193604	−	0.111777i	0.593669	+	0.804710i	$0.297679\pi$
$620$			16.8020i			0.674784i
$621$	28.0168	+	4.23037i	1.12427	+	0.169759i
$622$	15.7319	−	9.08284i	0.630793	−	0.364189i
$623$	25.9596	+	31.8024i	1.04005	+	1.27413i
$624$	5.59426	−	2.77565i	0.223950	−	0.111115i
$625$	6.14230	−	10.6388i	0.245692	−	0.425551i
$626$	1.60933	−	2.78744i	0.0643218	−	0.111409i
$627$	−1.04764	−	0.676767i	−0.0418387	−	0.0270275i
$628$	−19.0276	+	10.9856i	−0.759286	+	0.438374i
$629$	27.7077			1.10478
$630$	11.7380	−	7.76913i	0.467652	−	0.309529i
$631$	−17.4066	+	30.1491i	−0.692944	+	1.20021i	0.277924	+	0.960603i	$0.410354\pi$
$631$	−17.4066	+	30.1491i	−0.692944	+	1.20021i	−0.970869	+	0.239612i	$0.922980\pi$
$632$	−11.0916	−	6.40376i	−0.441202	−	0.254728i
$633$	−1.72236	+	34.4502i	−0.0684576	+	1.36927i
$634$	0.547197	−	0.947773i	0.0217320	−	0.0376409i
$635$	−8.70306			−0.345371
$636$	5.44159	+	0.272056i	0.215773	+	0.0107877i
$637$	−18.6672	−	16.9864i	−0.739620	−	0.673025i
$638$			7.87217i			0.311662i
$639$	0.684008	−	6.82357i	0.0270589	−	0.269936i
$640$	−1.53584	−	0.886718i	−0.0607094	−	0.0350506i
$641$			15.1407i			0.598023i	0.954250	+	0.299011i	$0.0966568\pi$
$641$			15.1407i			0.598023i	−0.954250	+	0.299011i	$0.903343\pi$
$642$	−23.7566	−	15.3466i	−0.937599	−	0.605682i
$643$	−17.4033	−	10.0478i	−0.686317	−	0.396246i	0.115914	−	0.993259i	$-0.463020\pi$
$643$	−17.4033	−	10.0478i	−0.686317	−	0.396246i	−0.802231	+	0.597014i	$0.796354\pi$
$644$	−11.1764	+	9.12307i	−0.440412	+	0.359499i
$645$	0.594754	−	11.8961i	0.0234184	−	0.468409i
$646$	3.02119	+	5.23286i	0.118867	+	0.205884i
$647$	11.0262	−	19.0980i	0.433486	−	0.750820i	−0.563684	−	0.825990i	$-0.690617\pi$
$647$	11.0262	−	19.0980i	0.433486	−	0.750820i	0.997171	+	0.0751699i	$0.0239499\pi$
$648$	−6.74595	−	5.95753i	−0.265006	−	0.234034i
$649$	−2.59207	−	1.49653i	−0.101748	−	0.0587440i
$650$	−0.0874392	+	6.68747i	−0.00342965	+	0.262304i
$651$	−25.7409	−	34.9628i	−1.00887	−	1.37030i
$652$	2.74658	+	4.75722i	0.107564	+	0.186307i
$653$			35.0539i			1.37176i	0.727713	+	0.685882i	$0.240583\pi$
$653$			35.0539i			1.37176i	−0.727713	+	0.685882i	$0.759417\pi$
$654$	2.22000	+	0.110990i	0.0868089	+	0.00434007i
$655$	−4.68721	−	8.11849i	−0.183145	−	0.317216i
$656$	3.47099	+	6.01193i	0.135519	+	0.234726i
$657$	−21.2318	−	15.2703i	−0.828333	−	0.595751i
$658$	−3.55506	−	21.8913i	−0.138590	−	0.853411i
$659$	−6.09325	−	3.51794i	−0.237359	−	0.137039i	0.376603	−	0.926375i	$-0.377092\pi$
$659$	−6.09325	−	3.51794i	−0.237359	−	0.137039i	−0.613962	+	0.789335i	$0.710425\pi$
$660$	2.74180	+	0.137078i	0.106724	+	0.00533575i
$661$	28.3125	+	16.3462i	1.10123	+	0.635795i	0.936544	−	0.350551i	$-0.114006\pi$
$661$	28.3125	+	16.3462i	1.10123	+	0.635795i	0.164686	+	0.986346i	$0.447339\pi$
$662$	18.7294	−	10.8134i	0.727940	−	0.420276i
$663$	41.9536	−	20.8157i	1.62934	−	0.808414i
$664$			13.8340i			0.536862i
$665$	−2.92865	+	2.39060i	−0.113568	+	0.0927035i
$666$	10.1039	−	4.55692i	0.391518	−	0.176577i
$667$	24.0156	+	41.5963i	0.929889	+	1.61061i
$668$	−2.92252	−	5.06195i	−0.113076	−	0.195853i
$669$	13.5282	+	0.676351i	0.523030	+	0.0261493i
$670$	12.2674	−	7.08257i	0.473930	−	0.273623i
$671$	7.33828			0.283291
$672$	4.55436	−	0.507788i	0.175688	−	0.0195883i
$673$	−11.4876	−	19.8971i	−0.442814	−	0.766976i	0.555083	−	0.831795i	$-0.312686\pi$
$673$	−11.4876	−	19.8971i	−0.442814	−	0.766976i	−0.997897	+	0.0648191i	$0.979353\pi$
$674$		−	16.9544i		−	0.653058i
$675$	8.97314	−	3.51898i	0.345376	−	0.135446i
$676$	6.20342	+	11.4244i	0.238593	+	0.439401i
$677$	−0.619754	+	1.07345i	−0.0238191	+	0.0412559i	−0.877689	−	0.479230i	$-0.840916\pi$
$677$	−0.619754	+	1.07345i	−0.0238191	+	0.0412559i	0.853870	+	0.520486i	$0.174249\pi$
$678$	0.488329	−	0.250298i	0.0187542	−	0.00961262i
$679$	−2.08028	−	12.8099i	−0.0798336	−	0.491599i
$680$	−11.5179	−	6.64985i	−0.441690	−	0.255010i
$681$	−33.0159	−	21.3280i	−1.26517	−	0.817291i
$682$		−	8.46733i		−	0.324231i
$683$			2.26076i			0.0865056i	0.999064	+	0.0432528i	$0.0137721\pi$
$683$			2.26076i			0.0865056i	−0.999064	+	0.0432528i	$0.986228\pi$
$684$	1.96233	+	1.41134i	0.0750314	+	0.0539638i
$685$	−0.621066	−	0.358572i	−0.0237297	−	0.0137003i
$686$	−8.60105	−	16.4019i	−0.328389	−	0.626227i
$687$	−2.69030	−	5.24875i	−0.102641	−	0.200252i
$688$	1.93884	−	3.35816i	0.0739174	−	0.128029i
$689$	−0.148281	+	11.3408i	−0.00564907	+	0.432049i
$690$	14.9058	−	7.64009i	0.567452	−	0.290853i
$691$		−	46.3884i		−	1.76470i	−0.470595	−	0.882349i	$-0.655961\pi$
$691$		−	46.3884i		−	1.76470i	0.470595	−	0.882349i	$-0.344039\pi$
$692$	7.29361	+	12.6329i	0.277262	+	0.480231i
$693$	−5.91534	+	3.91524i	−0.224705	+	0.148728i
$694$	22.1793			0.841915
$695$	6.93755	−	4.00540i	0.263156	−	0.151933i
$696$	0.761805	−	15.2374i	0.0288761	−	0.577573i
$697$	26.0303	+	45.0859i	0.985970	+	1.70775i
$698$	5.25936	+	9.10947i	0.199070	+	0.344799i
$699$	5.17241	+	10.0913i	0.195638	+	0.381689i
$700$	−1.74082	+	4.58856i	−0.0657969	+	0.173431i
$701$			41.1479i			1.55413i	0.629418	+	0.777067i	$0.283293\pi$
$701$			41.1479i			1.55413i	−0.629418	+	0.777067i	$0.716707\pi$
$702$	11.8754	−	14.4905i	0.448208	−	0.546909i
$703$	−2.57802	+	1.48842i	−0.0972318	+	0.0561368i
$704$	0.773984	+	0.446860i	0.0291706	+	0.0168417i
$705$	−1.28570	+	25.7163i	−0.0484224	+	0.968532i
$706$	−21.7956	−	12.5837i	−0.820288	−	0.473593i
$707$	43.4483	−	7.05582i	1.63404	−	0.265362i
$708$	4.87240	+	3.14753i	0.183116	+	0.118292i
$709$	−1.61596	−	2.79892i	−0.0606885	−	0.105116i	0.834085	−	0.551636i	$-0.185996\pi$
$709$	−1.61596	−	2.79892i	−0.0606885	−	0.105116i	−0.894773	+	0.446521i	$0.852663\pi$
$710$	−2.02697	−	3.51081i	−0.0760707	−	0.131758i
$711$	−38.2309	−	3.83234i	−1.43377	−	0.143724i
$712$		−	15.5163i		−	0.581499i
$713$	−25.8313	−	44.7411i	−0.967390	−	1.67557i
$714$	34.1549	−	3.80810i	1.27822	−	0.142515i
$715$	−0.0747129	+	5.71415i	−0.00279410	+	0.213697i
$716$	−8.38489	−	4.84102i	−0.313358	−	0.180917i
$717$	−2.58549	+	4.00235i	−0.0965569	+	0.149471i
$718$	−11.9747	+	20.7408i	−0.446893	+	0.774041i
$719$	11.6854	+	20.2397i	0.435791	+	0.754813i	0.997360	−	0.0726175i	$-0.0231352\pi$
$719$	11.6854	+	20.2397i	0.435791	+	0.754813i	−0.561569	+	0.827430i	$0.689802\pi$
$720$	−5.29377	−	0.530658i	−0.197287	−	0.0197765i
$721$	−3.65476	−	22.5052i	−0.136110	−	0.838139i
$722$	15.8923	+	9.17541i	0.591449	+	0.341473i
$723$	−5.76088	+	8.91788i	−0.214250	+	0.331659i
$724$			16.1898i			0.601688i
$725$	14.1498	+	8.16940i	0.525511	+	0.303404i
$726$	17.6471	+	0.882277i	0.654944	+	0.0327444i
$727$			34.2889i			1.27171i	0.771810	+	0.635853i	$0.219351\pi$
$727$			34.2889i			1.27171i	−0.771810	+	0.635853i	$0.780649\pi$
$728$	1.40589	+	9.43523i	0.0521058	+	0.349693i
$729$	−25.7963	−	7.97194i	−0.955418	−	0.295257i
$730$	−15.4601			−0.572205
$731$	14.5401	−	25.1842i	0.537785	−	0.931472i
$732$	−14.2040	−	0.710140i	−0.524996	−	0.0262475i
$733$	19.4049	+	11.2034i	0.716736	+	0.413808i	0.813550	−	0.581495i	$-0.197532\pi$
$733$	19.4049	+	11.2034i	0.716736	+	0.413808i	−0.0968139	+	0.995303i	$0.530865\pi$
$734$	−7.14973	+	12.3837i	−0.263901	+	0.457090i
$735$	5.77719	+	20.7111i	0.213095	+	0.763940i
$736$	5.45295			0.200998
$737$	−6.18212	+	3.56925i	−0.227721	+	0.131475i
$738$	16.9072	+	12.1600i	0.622364	+	0.447615i
$739$	2.39445	−	4.14731i	0.0880814	−	0.152561i	−0.818619	−	0.574337i	$-0.805260\pi$
$739$	2.39445	−	4.14731i	0.0880814	−	0.152561i	0.906700	+	0.421776i	$0.138593\pi$
$740$	3.27611	−	5.67440i	0.120432	−	0.208595i
$741$	−2.78532	+	4.19045i	−0.102321	+	0.153940i
$742$	−2.95213	+	7.78138i	−0.108376	+	0.285663i
$743$	37.6419	−	21.7325i	1.38095	−	0.797289i	0.388674	−	0.921375i	$-0.372933\pi$
$743$	37.6419	−	21.7325i	1.38095	−	0.797289i	0.992272	+	0.124086i	$0.0395998\pi$
$744$	−0.819400	+	16.3894i	−0.0300407	+	0.600865i
$745$			4.87072i			0.178449i
$746$	−4.65411	+	2.68705i	−0.170399	+	0.0983799i
$747$	17.0626	+	37.8322i	0.624287	+	1.38421i
$748$	5.80442	+	3.35118i	0.212230	+	0.122531i
$749$	33.4677	−	27.3191i	1.22288	−	0.998216i
$750$	11.4255	−	17.6867i	0.417200	−	0.645827i
$751$	27.6481			1.00889			0.504447	−	0.863442i	$-0.331696\pi$
$751$	27.6481			1.00889			0.504447	+	0.863442i	$0.331696\pi$
$752$	−4.19126	+	7.25948i	−0.152840	+	0.264726i
$753$	19.4318	−	9.95997i	0.708136	−	0.362962i
$754$	31.7561	+	0.415214i	1.15649	+	0.0151212i
$755$	−25.2516			−0.919000
$756$	11.8287	−	7.00593i	0.430204	−	0.254803i
$757$	−12.4453	−	21.5558i	−0.452330	−	0.783459i	0.546200	−	0.837655i	$-0.316074\pi$
$757$	−12.4453	−	21.5558i	−0.452330	−	0.783459i	−0.998530	+	0.0541956i	$0.982741\pi$
$758$	16.1861	−	9.34507i	0.587907	−	0.339428i
$759$	−7.51173	+	3.85021i	−0.272659	+	0.139754i
$760$	1.42888			0.0518311
$761$	17.5767	+	30.4438i	0.637156	+	1.10359i	0.986054	+	0.166425i	$0.0532224\pi$
$761$	17.5767	+	30.4438i	0.637156	+	1.10359i	−0.348899	+	0.937160i	$0.613444\pi$
$762$	−8.48937	−	0.424432i	−0.307537	−	0.0153755i
$763$	−1.20438	+	3.17456i	−0.0436013	+	0.114927i
$764$	−13.6786	+	7.89736i	−0.494875	+	0.285716i
$765$	−39.7001	−	3.97962i	−1.43536	−	0.143883i
$766$	−28.4184	+	16.4074i	−1.02680	+	0.592823i
$767$	−6.17368	+	10.3774i	−0.222919	+	0.374706i
$768$	−1.45489	−	0.939845i	−0.0524987	−	0.0339137i
$769$	21.8138	−	12.5942i	0.786626	−	0.454159i	−0.0521474	−	0.998639i	$-0.516607\pi$
$769$	21.8138	−	12.5942i	0.786626	−	0.454159i	0.838773	+	0.544481i	$0.183273\pi$
$770$	−1.48746	+	3.92072i	−0.0536042	+	0.141293i
$771$	−39.6692	−	25.6260i	−1.42865	−	0.922899i
$772$	−0.799689	+	1.38510i	−0.0287814	+	0.0498509i
$773$	47.2270			1.69864			0.849318	−	0.527881i	$-0.177013\pi$
$773$	47.2270			1.69864			0.849318	+	0.527881i	$0.177013\pi$
$774$	1.16030	−	11.5750i	0.0417061	−	0.416055i
$775$	−15.2196	−	8.78703i	−0.546704	−	0.315640i
$776$	−2.45256	+	4.24795i	−0.0880417	+	0.152493i
$777$	1.87610	+	16.8268i	0.0673047	+	0.603657i
$778$	−4.35765	−	7.54767i	−0.156229	−	0.270597i
$779$	−4.84391	−	2.79663i	−0.173551	−	0.100200i
$780$	0.697584	−	11.0531i	0.0249775	−	0.395765i
$781$	1.02149	+	1.76927i	0.0365517	+	0.0633094i
$782$	40.8938			1.46236
$783$	−16.7102	−	42.6099i	−0.597175	−	1.52275i
$784$	−1.40178	+	6.85821i	−0.0500637	+	0.244936i
$785$			38.9645i			1.39070i
$786$	−4.17620	−	8.14774i	−0.148960	−	0.290620i
$787$		−	27.1391i		−	0.967403i	−0.875233	−	0.483701i	$-0.839292\pi$
$787$		−	27.1391i		−	0.967403i	0.875233	−	0.483701i	$-0.160708\pi$
$788$	−3.83872	+	2.21629i	−0.136749	+	0.0789520i
$789$	0.444387	+	0.866995i	0.0158206	+	0.0308658i
$790$	−19.6703	+	11.3566i	−0.699838	+	0.404051i
$791$	0.134362	+	0.827373i	0.00477736	+	0.0294180i
$792$	2.66779	+	0.267424i	0.0947958	+	0.00950251i
$793$	0.387054	−	29.6024i	0.0137447	−	1.05121i
$794$	19.5098	+	33.7920i	0.692378	+	1.19923i
$795$	5.24299	−	8.11618i	0.185950	−	0.287851i
$796$			12.3701i			0.438446i
$797$	−16.0179	+	27.7438i	−0.567382	+	0.982735i	0.429441	+	0.903095i	$0.358711\pi$
$797$	−16.0179	+	27.7438i	−0.567382	+	0.982735i	−0.996824	+	0.0796404i	$0.974623\pi$
$798$	−2.97333	+	2.18908i	−0.105255	+	0.0774925i
$799$	−31.4319	+	54.4417i	−1.11198	+	1.92601i
$800$	1.60641	−	0.927464i	0.0567953	−	0.0327908i
$801$	−19.1376	−	42.4330i	−0.676192	−	1.49930i
$802$	7.14319			0.252235
$803$	7.79111			0.274942
$804$	12.3116	−	6.31041i	0.434195	−	0.222551i
$805$	4.10127	+	25.2547i	0.144551	+	0.890113i
$806$	−34.1570	−	0.446605i	−1.20313	−	0.0157310i
$807$	5.72055	+	3.69543i	0.201373	+	0.130085i
$808$	−14.4081	−	8.31852i	−0.506875	−	0.292644i
$809$	29.2986	+	16.9155i	1.03008	+	0.594719i	0.917009	−	0.398868i	$-0.130597\pi$
$809$	29.2986	+	16.9155i	1.03008	+	0.594719i	0.113075	+	0.993586i	$0.463930\pi$
$810$	−15.1316	+	5.07804i	−0.531669	+	0.178424i
$811$		−	23.0154i		−	0.808181i	−0.914719	−	0.404090i	$-0.867588\pi$
$811$		−	23.0154i		−	0.808181i	0.914719	−	0.404090i	$-0.132412\pi$
$812$	21.7892	+	8.26647i	0.764652	+	0.290096i
$813$	0.824428	−	1.27622i	0.0289139	−	0.0447589i
$814$	−1.65099	+	2.85960i	−0.0578673	+	0.100229i
$815$	9.74177			0.341239
$816$	−10.9108	−	7.04827i	−0.381953	−	0.246739i
$817$			3.12430i			0.109305i
$818$	14.9068			0.521205
$819$	15.4820	+	24.0688i	0.540984	+	0.841033i
$820$	12.3112			0.429924
$821$		−	3.89844i		−	0.136056i	−0.997683	−	0.0680282i	$-0.978329\pi$
$821$		−	3.89844i		−	0.136056i	0.997683	−	0.0680282i	$-0.0216708\pi$
$822$	−0.588329	−	0.380056i	−0.0205203	−	0.0132560i
$823$	−4.39494			−0.153198			−0.0765989	−	0.997062i	$-0.524406\pi$
$823$	−4.39494			−0.153198			−0.0765989	+	0.997062i	$0.524406\pi$
$824$	−4.30881	+	7.46308i	−0.150104	+	0.259989i
$825$	−1.55806	+	2.41189i	−0.0542448	+	0.0839712i
$826$	−6.86412	+	5.60304i	−0.238833	+	0.194955i
$827$			48.0745i			1.67171i	0.548948	+	0.835856i	$0.315028\pi$
$827$			48.0745i			1.67171i	−0.548948	+	0.835856i	$0.684972\pi$
$828$	14.9124	−	6.72557i	0.518240	−	0.233730i
$829$	5.36318	+	3.09643i	0.186271	+	0.107543i	0.590236	−	0.807231i	$-0.299035\pi$
$829$	5.36318	+	3.09643i	0.186271	+	0.107543i	−0.403965	+	0.914775i	$0.632368\pi$
$830$	21.2468	+	12.2668i	0.737485	+	0.425787i
$831$	18.3418	+	11.8486i	0.636269	+	0.411025i
$832$	1.84344	−	3.09866i	0.0639100	−	0.107427i
$833$	−10.5125	+	51.4324i	−0.364237	+	1.78203i
$834$	6.96255	−	3.56872i	0.241093	−	0.123575i
$835$	−10.3658			−0.358723
$836$	−0.720084			−0.0249046
$837$	17.9736	+	45.8313i	0.621258	+	1.58416i
$838$	−18.3714	+	10.6067i	−0.634628	+	0.366403i
$839$	27.1029	−	46.9435i	0.935695	−	1.62067i	0.162305	−	0.986741i	$-0.448107\pi$
$839$	27.1029	−	46.9435i	0.935695	−	1.62067i	0.773390	−	0.633930i	$-0.218559\pi$
$840$	3.25855	−	7.44502i	0.112431	−	0.256878i
$841$	24.2932	−	42.0771i	0.837697	−	1.45093i
$842$		−	1.98956i		−	0.0685647i
$843$	5.99354	−	9.27803i	0.206428	−	0.319552i
$844$	9.95733	+	17.2466i	0.342745	+	0.593653i
$845$	23.0468	+	0.602780i	0.792833	+	0.0207363i
$846$	−2.50827	+	25.0222i	−0.0862361	+	0.860280i
$847$	−9.57374	+	25.2350i	−0.328958	+	0.867084i
$848$	2.72420	−	1.57281i	0.0935492	−	0.0540107i
$849$	−0.601078	−	1.17270i	−0.0206289	−	0.0402469i
$850$	12.0471	−	6.95542i	0.413214	−	0.238569i
$851$			20.1467i			0.690622i
$852$	−1.80598	−	3.52346i	−0.0618719	−	0.120712i
$853$			15.5780i			0.533381i	0.963782	+	0.266690i	$0.0859301\pi$
$853$			15.5780i			0.533381i	−0.963782	+	0.266690i	$0.914070\pi$
$854$	7.70585	−	20.3115i	0.263689	−	0.695045i
$855$	3.90762	−	1.76236i	0.133638	−	0.0602715i
$856$	−16.3289			−0.558109
$857$	−14.2172	−	24.6250i	−0.485652	−	0.841173i	0.514213	−	0.857663i	$-0.328084\pi$
$857$	−14.2172	−	24.6250i	−0.485652	−	0.841173i	−0.999864	+	0.0164897i	$0.994751\pi$
$858$	−0.351546	+	5.57020i	−0.0120016	+	0.190163i
$859$	−23.4649	−	13.5474i	−0.800610	−	0.462233i	0.0430741	−	0.999072i	$-0.486285\pi$
$859$	−23.4649	−	13.5474i	−0.800610	−	0.462233i	−0.843685	+	0.536839i	$0.819618\pi$
$860$	−3.43840	−	5.95548i	−0.117248	−	0.203080i
$861$	−25.6179	+	18.8609i	−0.873057	+	0.642778i
$862$	7.26815	−	12.5888i	0.247554	−	0.428776i
$863$	11.4245	+	6.59595i	0.388895	+	0.224529i	0.681681	−	0.731649i	$-0.261249\pi$
$863$	11.4245	+	6.59595i	0.388895	+	0.224529i	−0.292786	+	0.956178i	$0.594582\pi$
$864$	−5.13791	−	0.775795i	−0.174795	−	0.0263931i
$865$	25.8695			0.879589
$866$	−0.680025	+	1.17784i	−0.0231082	+	0.0400246i
$867$	−57.0912	−	36.8805i	−1.93892	−	1.25253i
$868$	−23.4366	−	8.89145i	−0.795489	−	0.301795i
$869$	9.91281	−	5.72317i	0.336269	−	0.194145i
$870$	−22.7267	−	14.6813i	−0.770508	−	0.497743i
$871$	14.0722	+	25.1268i	0.476818	+	0.851388i
$872$	1.11139	−	0.641659i	0.0376363	−	0.0217293i
$873$	−1.46774	+	14.6420i	−0.0496754	+	0.495555i
$874$	−3.80490	+	2.19676i	−0.128703	+	0.0743066i
$875$	20.3389	+	24.9166i	0.687581	+	0.842335i
$876$	−15.0805	−	0.753961i	−0.509524	−	0.0254740i
$877$	1.79895	+	3.11587i	0.0607462	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$877$	1.79895	+	3.11587i	0.0607462	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$878$	29.8566			1.00761
$879$	19.5827	−	10.0373i	0.660507	−	0.338549i
$880$	1.37261	−	0.792477i	0.0462707	−	0.0267144i
$881$	−10.4378	−	18.0787i	−0.351657	−	0.609088i	0.634883	−	0.772609i	$-0.281048\pi$
$881$	−10.4378	−	18.0787i	−0.351657	−	0.609088i	−0.986540	+	0.163520i	$0.947715\pi$
$882$	4.62529	+	20.4843i	0.155742	+	0.689742i
$883$	29.7344			1.00064			0.500321	−	0.865840i	$-0.333215\pi$
$883$	29.7344			1.00064			0.500321	+	0.865840i	$0.333215\pi$
$884$	13.8247	−	23.2381i	0.464976	−	0.781582i
$885$	9.15455	−	4.69225i	0.307727	−	0.157728i
$886$	18.1168	−	31.3793i	0.608647	−	1.05421i
$887$	−2.77630			−0.0932190			−0.0466095	−	0.998913i	$-0.514842\pi$
$887$	−2.77630			−0.0932190			−0.0466095	+	0.998913i	$0.514842\pi$
$888$	3.47240	−	5.37530i	0.116526	−	0.180383i
$889$	4.60558	−	12.1396i	0.154466	−	0.407150i
$890$	−23.8306	−	13.7586i	−0.798803	−	0.461189i
$891$	7.62553	−	2.55907i	0.255465	−	0.0857321i
$892$	6.77255	−	3.91013i	0.226762	−	0.130921i
$893$		−	6.75393i		−	0.226012i
$894$	−0.237535	+	4.75112i	−0.00794437	+	0.158901i
$895$	−14.8701	+	8.58523i	−0.497051	+	0.286973i
$896$	2.04961	−	1.67305i	0.0684726	−	0.0558928i
$897$	15.1354	+	30.5052i	0.505358	+	1.01854i
$898$	−16.3866	+	28.3824i	−0.546828	+	0.947133i
$899$	−41.7261	+	72.2718i	−1.39164	+	2.41040i
$900$	3.24920	−	4.51769i	0.108307	−	0.150590i
$901$	20.4298	−	11.7952i	0.680616	−	0.392954i
$902$	−6.20419			−0.206577
$903$	16.2788	+	7.12492i	0.541724	+	0.237102i
$904$	0.158407	−	0.274369i	0.00526855	−	0.00912539i
$905$	24.8649	+	14.3557i	0.826537	+	0.477201i
$906$	−24.6316	−	1.23147i	−0.818330	−	0.0409129i
$907$	14.1441	−	24.4983i	0.469647	−	0.813453i	−0.529751	−	0.848153i	$-0.677714\pi$
$907$	14.1441	−	24.4983i	0.469647	−	0.813453i	0.999398	+	0.0347008i	$0.0110478\pi$
$908$	−22.6931			−0.753098
$909$	−49.6622	−	4.97824i	−1.64719	−	0.165118i
$910$	15.7376	+	6.20716i	0.521697	+	0.205765i
$911$		−	12.5281i		−	0.415076i	−0.978227	−	0.207538i	$-0.933455\pi$
$911$		−	12.5281i		−	0.415076i	0.978227	−	0.207538i	$-0.0665451\pi$
$912$	1.39380	+	0.0696839i	0.0461533	+	0.00230746i
$913$	−10.7073	−	6.18184i	−0.354359	−	0.204589i
$914$			10.8965i			0.360425i
$915$	−13.6856	+	21.1854i	−0.452433	+	0.700368i
$916$	−2.94903	−	1.70262i	−0.0974387	−	0.0562563i
$917$	13.8047	−	2.24182i	0.455870	−	0.0740315i
$918$	−38.5313	−	5.81800i	−1.27172	−	0.192023i
$919$	−22.4099	−	38.8151i	−0.739235	−	1.28039i	−0.952840	−	0.303472i	$-0.901854\pi$
$919$	−22.4099	−	38.8151i	−0.739235	−	1.28039i	0.213606	−	0.976920i	$-0.431479\pi$
$920$	4.83522	−	8.37485i	0.159413	−	0.276111i
$921$	−2.72948	+	4.22524i	−0.0899393	+	0.139227i
$922$	−28.5059	−	16.4579i	−0.938791	−	0.542011i
$923$	7.19106	−	4.02733i	0.236697	−	0.132561i
$924$	−1.64214	+	3.75191i	−0.0540224	+	0.123429i
$925$	3.42666	+	5.93515i	0.112668	+	0.195146i
$926$			9.98781i			0.328220i
$927$	−2.57862	+	25.7239i	−0.0846929	+	0.844885i
$928$	−4.40416	−	7.62822i	−0.144574	−	0.250409i
$929$	−21.9801	−	38.0706i	−0.721143	−	1.24906i	−0.960542	−	0.278135i	$-0.910284\pi$
$929$	−21.9801	−	38.0706i	−0.721143	−	1.24906i	0.239399	−	0.970921i	$-0.423050\pi$
$930$	24.4449	+	15.7913i	0.801581	+	0.517816i
$931$	−1.78476	−	5.35017i	−0.0584931	−	0.175345i
$932$	5.66985	+	3.27349i	0.185722	+	0.107227i
$933$	1.57109	−	31.4246i	0.0514353	−	1.02880i
$934$	−18.0868	−	10.4424i	−0.591817	−	0.341686i
$935$	10.2938	−	5.94310i	0.336642	−	0.194360i
$936$	1.21949	−	10.7477i	0.0398604	−	0.351299i
$937$		−	32.4932i		−	1.06151i	−0.847527	−	0.530753i	$-0.821909\pi$
$937$		−	32.4932i		−	1.06151i	0.847527	−	0.530753i	$-0.178091\pi$
$938$	3.38748	+	20.8594i	0.110605	+	0.681084i
$939$	−2.54289	−	4.96116i	−0.0829840	−	0.161901i
$940$	7.43293	+	12.8742i	0.242435	+	0.419910i
$941$	−26.4431	−	45.8008i	−0.862021	−	1.49306i	−0.869975	−	0.493095i	$-0.835865\pi$
$941$	−26.4431	−	45.8008i	−0.862021	−	1.49306i	0.00795494	−	0.999968i	$-0.497468\pi$
$942$	−1.90023	+	38.0078i	−0.0619127	+	1.23836i
$943$	−32.7827	+	18.9271i	−1.06755	+	0.616352i
$944$	3.34899			0.109000
$945$	−0.271310	−	24.3792i	−0.00882571	−	0.793055i
$946$	1.73278	+	3.00126i	0.0563374	+	0.0975793i
$947$		−	6.42050i		−	0.208638i	−0.994544	−	0.104319i	$-0.966734\pi$
$947$		−	6.42050i		−	0.208638i	0.994544	−	0.104319i	$-0.0332663\pi$
$948$	−19.7412	+	10.1185i	−0.641163	+	0.328634i
$949$	0.410939	−	31.4292i	0.0133396	−	1.02023i
$950$	−0.747272	+	1.29431i	−0.0242447	+	0.0419931i
$951$	−0.864620	−	1.68687i	−0.0280372	−	0.0547004i
$952$	15.3708	−	12.5469i	0.498171	−	0.406647i
$953$	−30.0111	−	17.3269i	−0.972155	−	0.561274i	−0.0722625	−	0.997386i	$-0.523022\pi$
$953$	−30.0111	−	17.3269i	−0.972155	−	0.561274i	−0.899893	+	0.436112i	$0.856355\pi$
$954$	5.51006	−	7.66120i	0.178395	−	0.248041i
$955$			28.0109i			0.906412i
$956$			2.75097i			0.0889729i
$957$	11.4531	+	7.39862i	0.370226	+	0.239163i
$958$	−10.2715	−	5.93024i	−0.331857	−	0.191597i
$959$	0.828824	−	0.676552i	0.0267641	−	0.0218470i
$960$	−2.73352	+	1.40109i	−0.0882241	+	0.0452201i
$961$	29.3808	−	50.8890i	0.947766	−	1.64158i
$962$	11.4485	+	6.81089i	0.369114	+	0.219592i
$963$	−44.6551	+	20.1397i	−1.43899	+	0.648994i
$964$			6.12961i			0.197421i
$965$	1.41820	+	2.45639i	0.0456534	+	0.0790739i
$966$	2.76894	+	24.8347i	0.0890892	+	0.799042i
$967$	51.5097			1.65644			0.828220	−	0.560404i	$-0.189354\pi$
$967$	51.5097			1.65644			0.828220	+	0.560404i	$0.189354\pi$
$968$	8.83455	−	5.10063i	0.283953	−	0.163941i
$969$	10.4527	+	0.522588i	0.335788	+	0.0167879i
$970$	4.34945	+	7.53347i	0.139652	+	0.241885i
$971$	15.4438	+	26.7494i	0.495614	+	0.858428i	0.999987	−	0.00505724i	$-0.00160978\pi$
$971$	15.4438	+	26.7494i	0.495614	+	0.858428i	−0.504373	+	0.863486i	$0.668276\pi$
$972$	−15.0077	+	4.21542i	−0.481371	+	0.135210i
$973$	1.91572	+	11.7966i	0.0614152	+	0.378182i
$974$			18.9879i			0.608410i
$975$	9.64732	+	6.41240i	0.308961	+	0.205361i
$976$	−7.11088	+	4.10547i	−0.227614	+	0.131413i
$977$	48.2996	+	27.8858i	1.54524	+	0.892146i	0.998495	+	0.0548486i	$0.0174676\pi$
$977$	48.2996	+	27.8858i	1.54524	+	0.892146i	0.546748	+	0.837297i	$0.315866\pi$
$978$	9.50257	+	0.475088i	0.303859	+	0.0151916i
$979$	12.0094	+	6.93362i	0.383822	+	0.221599i
$980$	9.29012	+	8.23421i	0.296762	+	0.263032i
$981$	2.24793	−	3.12553i	0.0717710	−	0.0997906i
$982$	13.0095	+	22.5331i	0.415150	+	0.719061i
$983$	−4.09336	−	7.08990i	−0.130558	−	0.226133i	0.793334	−	0.608787i	$-0.208343\pi$
$983$	−4.09336	−	7.08990i	−0.130558	−	0.226133i	−0.923892	+	0.382654i	$0.875010\pi$
$984$	12.0089	+	0.600391i	0.382829	+	0.0191398i
$985$			7.86088i			0.250469i
$986$	−33.0285	−	57.2071i	−1.05184	−	1.82185i
$987$	−35.1905	−	15.4022i	−1.12013	−	0.490258i
$988$	−0.0379805	+	2.90480i	−0.00120832	+	0.0924140i
$989$	18.3119	+	10.5724i	0.582284	+	0.336182i
$990$	2.77630	−	3.86017i	0.0882365	−	0.122684i
$991$	−25.1642	+	43.5856i	−0.799366	+	1.38454i	0.120664	+	0.992693i	$0.461498\pi$
$991$	−25.1642	+	43.5856i	−0.799366	+	1.38454i	−0.920030	+	0.391848i	$0.871836\pi$
$992$	4.73713	+	8.20495i	0.150404	+	0.260507i
$993$	1.87044	−	37.4121i	0.0593568	−	1.18724i
$994$	5.96978	−	0.969467i	0.189350	−	0.0307496i
$995$	18.9985	+	10.9688i	0.602291	+	0.347733i
$996$	20.1268	+	13.0018i	0.637743	+	0.411977i
$997$			32.8316i			1.03979i	0.854231	+	0.519894i	$0.174029\pi$
$997$			32.8316i			1.03979i	−0.854231	+	0.519894i	$0.825971\pi$
$998$	9.39532	+	5.42439i	0.297404	+	0.171706i
$999$	2.86630	−	18.9828i	0.0906856	−	0.600589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.341.4	yes	76
3.2	odd	2	inner	546.2.bb.a.341.22	yes	76
7.3	odd	6		546.2.u.a.185.29	yes	76
13.9	even	3		546.2.u.a.425.10	yes	76
21.17	even	6		546.2.u.a.185.10	✓	76
39.35	odd	6		546.2.u.a.425.29	yes	76
91.87	odd	6	inner	546.2.bb.a.269.3	yes	76
273.269	even	6	inner	546.2.bb.a.269.23	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.10	✓	76	21.17	even	6
546.2.u.a.185.29	yes	76	7.3	odd	6
546.2.u.a.425.10	yes	76	13.9	even	3
546.2.u.a.425.29	yes	76	39.35	odd	6
546.2.bb.a.269.3	yes	76	91.87	odd	6	inner
546.2.bb.a.269.23	yes	76	273.269	even	6	inner
546.2.bb.a.341.4	yes	76	1.1	even	1	trivial
546.2.bb.a.341.22	yes	76	3.2	odd	2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.45489 - 0.939845i) q^{3} -1.00000 q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.939845 + 1.45489i) q^{6} +(-1.67305 - 2.04961i) q^{7} +1.00000i q^{8} +(1.23338 + 2.73473i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.45489 - 0.939845i) q^{3} -1.00000 q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.939845 + 1.45489i) q^{6} +(-1.67305 - 2.04961i) q^{7} +1.00000i q^{8} +(1.23338 + 2.73473i) q^{9} +(1.53584 + 0.886718i) q^{10} +(-0.773984 - 0.446860i) q^{11} +(1.45489 + 0.939845i) q^{12} +(-1.84344 + 3.09866i) q^{13} +(-2.04961 + 1.67305i) q^{14} +(2.73352 - 1.40109i) q^{15} +1.00000 q^{16} +7.49940 q^{17} +(2.73473 - 1.23338i) q^{18} +(-0.697770 + 0.402858i) q^{19} +(0.886718 - 1.53584i) q^{20} +(0.507788 + 4.55436i) q^{21} +(-0.446860 + 0.773984i) q^{22} +5.45295i q^{23} +(0.939845 - 1.45489i) q^{24} +(0.927464 + 1.60641i) q^{25} +(3.09866 + 1.84344i) q^{26} +(0.775795 - 5.13791i) q^{27} +(1.67305 + 2.04961i) q^{28} +(7.62822 - 4.40416i) q^{29} +(-1.40109 - 2.73352i) q^{30} +(-8.20495 + 4.73713i) q^{31} -1.00000i q^{32} +(0.706079 + 1.37756i) q^{33} -7.49940i q^{34} +(4.63139 - 0.752120i) q^{35} +(-1.23338 - 2.73473i) q^{36} +3.69465 q^{37} +(0.402858 + 0.697770i) q^{38} +(5.59426 - 2.77565i) q^{39} +(-1.53584 - 0.886718i) q^{40} +(3.47099 + 6.01193i) q^{41} +(4.55436 - 0.507788i) q^{42} +(1.93884 - 3.35816i) q^{43} +(0.773984 + 0.446860i) q^{44} +(-5.29377 - 0.530658i) q^{45} +5.45295 q^{46} +(-4.19126 + 7.25948i) q^{47} +(-1.45489 - 0.939845i) q^{48} +(-1.40178 + 6.85821i) q^{49} +(1.60641 - 0.927464i) q^{50} +(-10.9108 - 7.04827i) q^{51} +(1.84344 - 3.09866i) q^{52} +(2.72420 - 1.57281i) q^{53} +(-5.13791 - 0.775795i) q^{54} +(1.37261 - 0.792477i) q^{55} +(2.04961 - 1.67305i) q^{56} +(1.39380 + 0.0696839i) q^{57} +(-4.40416 - 7.62822i) q^{58} +3.34899 q^{59} +(-2.73352 + 1.40109i) q^{60} +(-7.11088 + 4.10547i) q^{61} +(4.73713 + 8.20495i) q^{62} +(3.54161 - 7.10331i) q^{63} -1.00000 q^{64} +(-3.12443 - 5.57887i) q^{65} +(1.37756 - 0.706079i) q^{66} +(3.99370 - 6.91729i) q^{67} -7.49940 q^{68} +(5.12492 - 7.93341i) q^{69} +(-0.752120 - 4.63139i) q^{70} +(-1.97967 - 1.14296i) q^{71} +(-2.73473 + 1.23338i) q^{72} +(-7.54968 + 4.35881i) q^{73} -3.69465i q^{74} +(0.160427 - 3.20882i) q^{75} +(0.697770 - 0.402858i) q^{76} +(0.379030 + 2.33398i) q^{77} +(-2.77565 - 5.59426i) q^{78} +(-6.40376 + 11.0916i) q^{79} +(-0.886718 + 1.53584i) q^{80} +(-5.95753 + 6.74595i) q^{81} +(6.01193 - 3.47099i) q^{82} +13.8340 q^{83} +(-0.507788 - 4.55436i) q^{84} +(-6.64985 + 11.5179i) q^{85} +(-3.35816 - 1.93884i) q^{86} +(-15.2374 - 0.761805i) q^{87} +(0.446860 - 0.773984i) q^{88} -15.5163 q^{89} +(-0.530658 + 5.29377i) q^{90} +(9.43523 - 1.40589i) q^{91} -5.45295i q^{92} +(16.3894 + 0.819400i) q^{93} +(7.25948 + 4.19126i) q^{94} -1.42888i q^{95} +(-0.939845 + 1.45489i) q^{96} +(4.24795 + 2.45256i) q^{97} +(6.85821 + 1.40178i) q^{98} +(0.267424 - 2.66779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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