LMFDB - Embedded newform 585.2.dc.a.164.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(164,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 6, 3]))

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

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

chi := DirichletCharacter("585.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.dc (of order $12$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$80$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			164.15
Character	$\chi$	$=$	585.164
Dual form			585.2.dc.a.239.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86715 + 0.500300i) q^{2} +(-0.305679 - 1.70486i) q^{3} +(1.50389 - 0.868268i) q^{4} +(-0.913957 - 2.04076i) q^{5} +(1.42369 + 3.03030i) q^{6} +(-2.65203 + 0.710610i) q^{7} +(0.360114 - 0.360114i) q^{8} +(-2.81312 + 1.04228i) q^{9} +O(q^{10})$	\(q+(-1.86715 + 0.500300i) q^{2} +(-0.305679 - 1.70486i) q^{3} +(1.50389 - 0.868268i) q^{4} +(-0.913957 - 2.04076i) q^{5} +(1.42369 + 3.03030i) q^{6} +(-2.65203 + 0.710610i) q^{7} +(0.360114 - 0.360114i) q^{8} +(-2.81312 + 1.04228i) q^{9} +(2.72748 + 3.35314i) q^{10} +(4.16840 - 1.11692i) q^{11} +(-1.93999 - 2.29851i) q^{12} +(-0.318701 - 3.59144i) q^{13} +(4.59622 - 2.65363i) q^{14} +(-3.19983 + 2.18199i) q^{15} +(-2.22876 + 3.86032i) q^{16} -5.70475i q^{17} +(4.73105 - 3.35350i) q^{18} +(-4.38738 - 4.38738i) q^{19} +(-3.14641 - 2.27550i) q^{20} +(2.02217 + 4.30414i) q^{21} +(-7.22423 + 4.17091i) q^{22} +(-3.12219 + 1.80260i) q^{23} +(-0.724024 - 0.503865i) q^{24} +(-3.32936 + 3.73033i) q^{25} +(2.39186 + 6.54630i) q^{26} +(2.63686 + 4.47738i) q^{27} +(-3.37135 + 3.37135i) q^{28} +(3.23630 + 1.86848i) q^{29} +(4.88291 - 5.67497i) q^{30} +(0.170221 - 0.635275i) q^{31} +(1.96647 - 7.33898i) q^{32} +(-3.17839 - 6.76514i) q^{33} +(2.85409 + 10.6516i) q^{34} +(3.87403 + 4.76268i) q^{35} +(-3.32563 + 4.01002i) q^{36} +(4.27633 + 4.27633i) q^{37} +(10.3869 + 5.99687i) q^{38} +(-6.02549 + 1.64117i) q^{39} +(-1.06403 - 0.405775i) q^{40} +(3.39412 + 0.909451i) q^{41} +(-5.92904 - 7.02476i) q^{42} +(-5.87686 + 10.1790i) q^{43} +(5.29901 - 5.29901i) q^{44} +(4.69812 + 4.78829i) q^{45} +(4.92775 - 4.92775i) q^{46} +(1.83506 + 6.84853i) q^{47} +(7.26260 + 2.61971i) q^{48} +(0.466138 - 0.269125i) q^{49} +(4.35013 - 8.63075i) q^{50} +(-9.72583 + 1.74383i) q^{51} +(-3.59762 - 5.12439i) q^{52} -13.5291 q^{53} +(-7.16345 - 7.04071i) q^{54} +(-6.08910 - 7.48588i) q^{55} +(-0.699133 + 1.21093i) q^{56} +(-6.13875 + 8.82101i) q^{57} +(-6.97746 - 1.86960i) q^{58} +(2.49384 - 9.30715i) q^{59} +(-2.91763 + 6.05977i) q^{60} +(-4.16347 + 7.21134i) q^{61} +1.27131i q^{62} +(6.71983 - 4.76320i) q^{63} +5.77176i q^{64} +(-7.03797 + 3.93281i) q^{65} +(9.31913 + 11.0414i) q^{66} +(1.24513 + 0.333632i) q^{67} +(-4.95326 - 8.57929i) q^{68} +(4.02757 + 4.77190i) q^{69} +(-9.61615 - 6.95445i) q^{70} +(-3.47485 + 3.47485i) q^{71} +(-0.637703 + 1.38838i) q^{72} +(4.18804 + 4.18804i) q^{73} +(-10.1240 - 5.84509i) q^{74} +(7.37741 + 4.53583i) q^{75} +(-10.4075 - 2.78869i) q^{76} +(-10.2611 + 5.92422i) q^{77} +(10.4294 - 6.07886i) q^{78} +(4.45129 - 7.70986i) q^{79} +(9.91496 + 1.02018i) q^{80} +(6.82729 - 5.86413i) q^{81} -6.79231 q^{82} +(-2.83175 + 0.758765i) q^{83} +(6.77825 + 4.71714i) q^{84} +(-11.6420 + 5.21390i) q^{85} +(5.88039 - 21.9459i) q^{86} +(2.19623 - 6.08861i) q^{87} +(1.09888 - 1.90332i) q^{88} +(-4.98237 - 4.98237i) q^{89} +(-11.1677 - 6.58997i) q^{90} +(3.39732 + 9.29814i) q^{91} +(-3.13028 + 5.42180i) q^{92} +(-1.13509 - 0.0960139i) q^{93} +(-6.85264 - 11.8691i) q^{94} +(-4.94369 + 12.9634i) q^{95} +(-13.1131 - 1.10920i) q^{96} +(-2.56400 - 9.56898i) q^{97} +(-0.735704 + 0.735704i) q^{98} +(-10.5621 + 7.48669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 6 q^{5} - 16 q^{9}+O(q^{10}) $ 320 * q - 6 * q^5 - 16 * q^9	$ 320 q - 6 q^{5} - 16 q^{9} - 24 q^{11} - 24 q^{14} - 14 q^{15} + 128 q^{16} - 16 q^{19} - 18 q^{20} - 16 q^{21} - 40 q^{24} - 24 q^{29} - 4 q^{31} + 4 q^{34} - 76 q^{39} + 12 q^{40} + 12 q^{41} - 20 q^{45} - 32 q^{46} - 108 q^{50} + 84 q^{54} - 16 q^{55} - 12 q^{59} + 32 q^{60} - 8 q^{61} - 56 q^{66} - 40 q^{70} - 72 q^{74} - 4 q^{76} + 16 q^{79} + 96 q^{84} - 16 q^{85} - 120 q^{86} - 16 q^{91} + 40 q^{94} + 108 q^{96} - 84 q^{99}+O(q^{100}) $ 320 * q - 6 * q^5 - 16 * q^9 - 24 * q^11 - 24 * q^14 - 14 * q^15 + 128 * q^16 - 16 * q^19 - 18 * q^20 - 16 * q^21 - 40 * q^24 - 24 * q^29 - 4 * q^31 + 4 * q^34 - 76 * q^39 + 12 * q^40 + 12 * q^41 - 20 * q^45 - 32 * q^46 - 108 * q^50 + 84 * q^54 - 16 * q^55 - 12 * q^59 + 32 * q^60 - 8 * q^61 - 56 * q^66 - 40 * q^70 - 72 * q^74 - 4 * q^76 + 16 * q^79 + 96 * q^84 - 16 * q^85 - 120 * q^86 - 16 * q^91 + 40 * q^94 + 108 * q^96 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.86715	+	0.500300i	−1.32027	+	0.353766i	−0.849080	−	0.528265i	$-0.822843\pi$
$2$	−1.86715	+	0.500300i	−1.32027	+	0.353766i	−0.471192	+	0.882031i	$0.656176\pi$
$3$	−0.305679	−	1.70486i	−0.176484	−	0.984304i
$3$	−0.305679	−	1.70486i	−0.176484	−	0.984304i
$4$	1.50389	−	0.868268i	0.751943	−	0.434134i
$5$	−0.913957	−	2.04076i	−0.408734	−	0.912654i
$5$	−0.913957	−	2.04076i	−0.408734	−	0.912654i
$6$	1.42369	+	3.03030i	0.581220	+	1.23711i
$7$	−2.65203	+	0.710610i	−1.00237	+	0.268585i	−0.722440	−	0.691434i	$-0.756979\pi$
$7$	−2.65203	+	0.710610i	−1.00237	+	0.268585i	−0.279935	+	0.960019i	$0.590313\pi$
$8$	0.360114	−	0.360114i	0.127319	−	0.127319i
$9$	−2.81312	+	1.04228i	−0.937707	+	0.347428i
$10$	2.72748	+	3.35314i	0.862506	+	1.06035i
$11$	4.16840	−	1.11692i	1.25682	−	0.336764i	0.431853	−	0.901944i	$-0.357860\pi$
$11$	4.16840	−	1.11692i	1.25682	−	0.336764i	0.824968	+	0.565180i	$0.191193\pi$
$12$	−1.93999	−	2.29851i	−0.560026	−	0.663522i
$13$	−0.318701	−	3.59144i	−0.0883917	−	0.996086i
$13$	−0.318701	−	3.59144i	−0.0883917	−	0.996086i
$14$	4.59622	−	2.65363i	1.22839	−	0.709212i
$15$	−3.19983	+	2.18199i	−0.826193	+	0.563387i
$16$	−2.22876	+	3.86032i	−0.557189	+	0.965080i
$17$		−	5.70475i		−	1.38361i	−0.722086	−	0.691803i	$-0.756817\pi$
$17$		−	5.70475i		−	1.38361i	0.722086	−	0.691803i	$-0.243183\pi$
$18$	4.73105	−	3.35350i	1.11512	−	0.790428i
$19$	−4.38738	−	4.38738i	−1.00653	−	1.00653i	−0.999979	−	0.00655523i	$-0.997913\pi$
$19$	−4.38738	−	4.38738i	−1.00653	−	1.00653i	−0.00655523	−	0.999979i	$-0.502087\pi$
$20$	−3.14641	−	2.27550i	−0.703559	−	0.508818i
$21$	2.02217	+	4.30414i	0.441273	+	0.939240i
$22$	−7.22423	+	4.17091i	−1.54021	+	0.889241i
$23$	−3.12219	+	1.80260i	−0.651022	+	0.375868i	−0.788848	−	0.614589i	$-0.789322\pi$
$23$	−3.12219	+	1.80260i	−0.651022	+	0.375868i	0.137826	+	0.990457i	$0.455989\pi$
$24$	−0.724024	−	0.503865i	−0.147791	−	0.102851i
$25$	−3.32936	+	3.73033i	−0.665873	+	0.746065i
$26$	2.39186	+	6.54630i	0.469082	+	1.28383i
$27$	2.63686	+	4.47738i	0.507464	+	0.861673i
$28$	−3.37135	+	3.37135i	−0.637126	+	0.637126i
$29$	3.23630	+	1.86848i	0.600967	+	0.346968i	0.769422	−	0.638741i	$-0.220544\pi$
$29$	3.23630	+	1.86848i	0.600967	+	0.346968i	−0.168455	+	0.985709i	$0.553878\pi$
$30$	4.88291	−	5.67497i	0.891492	−	1.03610i
$31$	0.170221	−	0.635275i	0.0305727	−	0.114099i	−0.948953	−	0.315417i	$-0.897856\pi$
$31$	0.170221	−	0.635275i	0.0305727	−	0.114099i	0.979526	+	0.201318i	$0.0645224\pi$
$32$	1.96647	−	7.33898i	0.347627	−	1.29736i
$33$	−3.17839	−	6.76514i	−0.553287	−	1.17766i
$34$	2.85409	+	10.6516i	0.489473	+	1.82674i
$35$	3.87403	+	4.76268i	0.654830	+	0.805041i
$36$	−3.32563	+	4.01002i	−0.554271	+	0.668336i
$37$	4.27633	+	4.27633i	0.703024	+	0.703024i	0.965059	−	0.262034i	$-0.0843933\pi$
$37$	4.27633	+	4.27633i	0.703024	+	0.703024i	−0.262034	+	0.965059i	$0.584393\pi$
$38$	10.3869	+	5.99687i	1.68498	+	0.972821i
$39$	−6.02549	+	1.64117i	−0.964851	+	0.262797i
$40$	−1.06403	−	0.405775i	−0.168238	−	0.0641587i
$41$	3.39412	+	0.909451i	0.530072	+	0.142032i	0.513921	−	0.857837i	$-0.328192\pi$
$41$	3.39412	+	0.909451i	0.530072	+	0.142032i	0.0161504	+	0.999870i	$0.494859\pi$
$42$	−5.92904	−	7.02476i	−0.914871	−	1.08394i
$43$	−5.87686	+	10.1790i	−0.896213	+	1.55229i	−0.0639170	+	0.997955i	$0.520359\pi$
$43$	−5.87686	+	10.1790i	−0.896213	+	1.55229i	−0.832296	+	0.554331i	$0.812974\pi$
$44$	5.29901	−	5.29901i	0.798856	−	0.798856i
$45$	4.69812	+	4.78829i	0.700354	+	0.713796i
$46$	4.92775	−	4.92775i	0.726557	−	0.726557i
$47$	1.83506	+	6.84853i	0.267671	+	0.998960i	0.960595	+	0.277950i	$0.0896551\pi$
$47$	1.83506	+	6.84853i	0.267671	+	0.998960i	−0.692925	+	0.721010i	$0.743678\pi$
$48$	7.26260	+	2.61971i	1.04827	+	0.378122i
$49$	0.466138	−	0.269125i	0.0665911	−	0.0384464i
$50$	4.35013	−	8.63075i	0.615201	−	1.22057i
$51$	−9.72583	+	1.74383i	−1.36189	+	0.244184i
$52$	−3.59762	−	5.12439i	−0.498900	−	0.710625i
$53$	−13.5291			−1.85836			−0.929181	−	0.369624i	$-0.879487\pi$
$53$	−13.5291			−1.85836			−0.929181	+	0.369624i	$0.879487\pi$
$54$	−7.16345	−	7.04071i	−0.974821	−	0.958119i
$55$	−6.08910	−	7.48588i	−0.821055	−	1.00940i
$56$	−0.699133	+	1.21093i	−0.0934256	+	0.161818i
$57$	−6.13875	+	8.82101i	−0.813098	+	1.16837i
$58$	−6.97746	−	1.86960i	−0.916185	−	0.245491i
$59$	2.49384	−	9.30715i	0.324671	−	1.21169i	−0.589972	−	0.807424i	$-0.700861\pi$
$59$	2.49384	−	9.30715i	0.324671	−	1.21169i	0.914643	−	0.404264i	$-0.132472\pi$
$60$	−2.91763	+	6.05977i	−0.376664	+	0.782313i
$61$	−4.16347	+	7.21134i	−0.533078	+	0.923318i	0.466176	+	0.884692i	$0.345631\pi$
$61$	−4.16347	+	7.21134i	−0.533078	+	0.923318i	−0.999254	+	0.0386258i	$0.987702\pi$
$62$			1.27131i			0.161457i
$63$	6.71983	−	4.76320i	0.846619	−	0.600107i
$64$			5.77176i			0.721470i
$65$	−7.03797	+	3.93281i	−0.872953	+	0.487805i
$66$	9.31913	+	11.0414i	1.14711	+	1.35910i
$67$	1.24513	+	0.333632i	0.152117	+	0.0407596i	0.334074	−	0.942547i	$-0.391576\pi$
$67$	1.24513	+	0.333632i	0.152117	+	0.0407596i	−0.181957	+	0.983307i	$0.558243\pi$
$68$	−4.95326	−	8.57929i	−0.600671	−	1.04039i
$69$	4.02757	+	4.77190i	0.484863	+	0.574469i
$70$	−9.61615	−	6.95445i	−1.14935	−	0.831216i
$71$	−3.47485	+	3.47485i	−0.412389	+	0.412389i	−0.882570	−	0.470181i	$-0.844189\pi$
$71$	−3.47485	+	3.47485i	−0.412389	+	0.412389i	0.470181	+	0.882570i	$0.344189\pi$
$72$	−0.637703	+	1.38838i	−0.0751540	+	0.163623i
$73$	4.18804	+	4.18804i	0.490173	+	0.490173i	0.908361	−	0.418187i	$-0.137334\pi$
$73$	4.18804	+	4.18804i	0.490173	+	0.490173i	−0.418187	+	0.908361i	$0.637334\pi$
$74$	−10.1240	−	5.84509i	−1.17689	−	0.679477i
$75$	7.37741	+	4.53583i	0.851870	+	0.523753i
$76$	−10.4075	−	2.78869i	−1.19383	−	0.319885i
$77$	−10.2611	+	5.92422i	−1.16936	+	0.675128i
$78$	10.4294	−	6.07886i	1.18090	−	0.688295i
$79$	4.45129	−	7.70986i	0.500809	−	0.867427i	−0.499191	−	0.866492i	$-0.666369\pi$
$79$	4.45129	−	7.70986i	0.500809	−	0.867427i	1.00000		0.000934328i	$-0.000297406\pi$
$80$	9.91496	+	1.02018i	1.10853	+	0.114060i
$81$	6.82729	−	5.86413i	0.758588	−	0.651571i
$82$	−6.79231			−0.750085
$83$	−2.83175	+	0.758765i	−0.310825	+	0.0832853i	−0.410859	−	0.911699i	$-0.634771\pi$
$83$	−2.83175	+	0.758765i	−0.310825	+	0.0832853i	0.100035	+	0.994984i	$0.468105\pi$
$84$	6.77825	+	4.71714i	0.739568	+	0.514683i
$85$	−11.6420	+	5.21390i	−1.26275	+	0.565527i
$86$	5.88039	−	21.9459i	0.634099	−	2.36649i
$87$	2.19623	−	6.08861i	0.235461	−	0.652768i
$88$	1.09888	−	1.90332i	0.117141	−	0.202894i
$89$	−4.98237	−	4.98237i	−0.528130	−	0.528130i	0.391885	−	0.920014i	$-0.371823\pi$
$89$	−4.98237	−	4.98237i	−0.528130	−	0.528130i	−0.920014	+	0.391885i	$0.871823\pi$
$90$	−11.1677	−	6.58997i	−1.17717	−	0.694644i
$91$	3.39732	+	9.29814i	0.356136	+	0.974710i
$92$	−3.13028	+	5.42180i	−0.326354	+	0.565262i
$93$	−1.13509	−	0.0960139i	−0.117703	−	0.00995618i
$94$	−6.85264	−	11.8691i	−0.706796	−	1.22421i
$95$	−4.94369	+	12.9634i	−0.507212	+	1.33002i
$96$	−13.1131	−	1.10920i	−1.33835	−	0.113207i
$97$	−2.56400	−	9.56898i	−0.260335	−	0.971583i	−0.965044	−	0.262087i	$-0.915589\pi$
$97$	−2.56400	−	9.56898i	−0.260335	−	0.971583i	0.704710	−	0.709496i	$-0.251077\pi$
$98$	−0.735704	+	0.735704i	−0.0743173	+	0.0743173i
$99$	−10.5621	+	7.48669i	−1.06153	+	0.752441i
$100$	−1.76806	+	8.50076i	−0.176806	+	0.850076i
$101$	0.698952	−	1.21062i	0.0695483	−	0.120461i	−0.829154	−	0.559020i	$-0.811178\pi$
$101$	0.698952	−	1.21062i	0.0695483	−	0.120461i	0.898703	+	0.438559i	$0.144511\pi$
$102$	17.2871	−	8.12181i	1.71168	−	0.804179i
$103$	4.16998	+	7.22261i	0.410880	+	0.711665i	0.994986	−	0.100012i	$-0.0318882\pi$
$103$	4.16998	+	7.22261i	0.410880	+	0.711665i	−0.584106	+	0.811677i	$0.698555\pi$
$104$	−1.40809	−	1.17856i	−0.138075	−	0.115567i
$105$	6.93552	−	8.06054i	0.676837	−	0.786628i
$106$	25.2608	−	6.76861i	2.45354	−	0.657425i
$107$	9.75919			0.943456			0.471728	−	0.881744i	$-0.343630\pi$
$107$	9.75919			0.943456			0.471728	+	0.881744i	$0.343630\pi$
$108$	7.85311	+	4.44396i	0.755666	+	0.427621i
$109$	−4.19307	−	4.19307i	−0.401623	−	0.401623i	0.477182	−	0.878805i	$-0.341658\pi$
$109$	−4.19307	−	4.19307i	−0.401623	−	0.401623i	−0.878805	+	0.477182i	$0.841658\pi$
$110$	15.1144	+	10.9308i	1.44111	+	1.04222i
$111$	5.98337	−	8.59775i	0.567917	−	0.816062i
$112$	3.16755	−	11.8215i	0.299306	−	1.11702i
$113$	−6.06358	−	10.5024i	−0.570413	−	0.987985i	−0.996523	−	0.0833134i	$-0.973450\pi$
$113$	−6.06358	−	10.5024i	−0.570413	−	0.987985i	0.426110	−	0.904671i	$-0.359884\pi$
$114$	7.04879	−	19.5413i	0.660180	−	1.83021i
$115$	6.53221	+	4.72413i	0.609132	+	0.440528i
$116$	6.48937			0.602523
$117$	4.63984	+	9.77097i	0.428953	+	0.903327i
$118$			18.6255i			1.71461i
$119$	4.05386	+	15.1292i	0.371616	+	1.38689i
$120$	−0.366539	+	1.93807i	−0.0334603	+	0.176920i
$121$	6.60180	−	3.81155i	0.600164	−	0.346505i
$122$	4.16597	−	15.5476i	0.377169	−	1.40762i
$123$	0.512979	−	6.06451i	0.0462537	−	0.546818i
$124$	−0.295596	−	1.10318i	−0.0265453	−	0.0990683i
$125$	10.6556	+	3.38506i	0.953064	+	0.302769i
$126$	−10.1639	+	12.2555i	−0.905471	+	1.09181i
$127$	−13.2277			−1.17377			−0.586884	−	0.809671i	$-0.699646\pi$
$127$	−13.2277			−1.17377			−0.586884	+	0.809671i	$0.699646\pi$
$128$	1.04534	+	3.90125i	0.0923956	+	0.344825i
$129$	19.1503	+	6.90773i	1.68609	+	0.608192i
$130$	11.1733	−	10.8642i	0.979966	−	0.952856i
$131$	−6.82784	+	3.94205i	−0.596551	+	0.344419i	−0.767683	−	0.640829i	$-0.778591\pi$
$131$	−6.82784	+	3.94205i	−0.596551	+	0.344419i	0.171133	+	0.985248i	$0.445257\pi$
$132$	−10.6539	−	7.41430i	−0.927303	−	0.645332i
$133$	14.7532	+	8.51776i	1.27926	+	0.738583i
$134$	−2.49176			−0.215255
$135$	6.72726	−	9.47333i	0.578991	−	0.815334i
$136$	−2.05436	−	2.05436i	−0.176160	−	0.176160i
$137$	−5.45954	−	20.3753i	−0.466440	−	1.74078i	−0.652072	−	0.758157i	$-0.726100\pi$
$137$	−5.45954	−	20.3753i	−0.466440	−	1.74078i	0.185632	−	0.982619i	$-0.440567\pi$
$138$	−9.90745	−	6.89483i	−0.843378	−	0.586927i
$139$	8.97123	+	15.5386i	0.760930	+	1.31797i	0.942372	+	0.334568i	$0.108590\pi$
$139$	8.97123	+	15.5386i	0.760930	+	1.31797i	−0.181442	+	0.983402i	$0.558076\pi$
$140$	9.96138	+	3.79883i	0.841890	+	0.321060i
$141$	11.1149	−	5.22198i	0.936041	−	0.439770i
$142$	4.74959	−	8.22653i	0.398577	−	0.690355i
$143$	−5.33983	−	14.6146i	−0.446539	−	1.22213i
$144$	2.24622	−	13.1825i	0.187185	−	1.09854i
$145$	0.855270	−	8.31222i	0.0710263	−	0.690292i
$146$	−9.91497	−	5.72441i	−0.820569	−	0.473756i
$147$	−0.601309	−	0.712435i	−0.0495952	−	0.0587607i
$148$	10.1441	+	2.71811i	0.833841	+	0.223427i
$149$	−3.50643	−	0.939545i	−0.287258	−	0.0769705i	0.112313	−	0.993673i	$-0.464174\pi$
$149$	−3.50643	−	0.939545i	−0.287258	−	0.0769705i	−0.399571	+	0.916702i	$0.630841\pi$
$150$	−16.0440	−	4.77814i	−1.30999	−	0.390133i
$151$	−2.39600	−	8.94201i	−0.194984	−	0.727690i	−0.992271	−	0.124090i	$-0.960399\pi$
$151$	−2.39600	−	8.94201i	−0.194984	−	0.727690i	0.797287	−	0.603600i	$-0.206268\pi$
$152$	−3.15991			−0.256303
$153$	5.94597	+	16.0482i	0.480703	+	1.29742i
$154$	16.1950	−	16.1950i	1.30503	−	1.30503i
$155$	−1.45202	+	0.233234i	−0.116629	+	0.0187338i
$156$	−7.63667	+	7.69988i	−0.611423	+	0.616483i
$157$	10.0422	−	5.79786i	0.801454	−	0.462720i	−0.0425250	−	0.999095i	$-0.513540\pi$
$157$	10.0422	−	5.79786i	0.801454	−	0.462720i	0.843979	+	0.536375i	$0.180207\pi$
$158$	−4.45396	+	16.6224i	−0.354338	+	1.32241i
$159$	4.13556	+	23.0652i	0.327971	+	1.82919i
$160$	−16.7743	+	2.69442i	−1.32613	+	0.213013i
$161$	6.99921	−	6.99921i	0.551615	−	0.551615i
$162$	−9.81373	+	14.3649i	−0.771039	+	1.12861i
$163$	7.76209	+	7.76209i	0.607974	+	0.607974i	0.942416	−	0.334442i	$-0.108548\pi$
$163$	7.76209	+	7.76209i	0.607974	+	0.607974i	−0.334442	+	0.942416i	$0.608548\pi$
$164$	5.89401	−	1.57929i	0.460245	−	0.123322i
$165$	−10.9011	+	12.6694i	−0.848648	+	0.986309i
$166$	4.90768	−	2.83345i	0.380910	−	0.219918i
$167$	10.3038	+	2.76089i	0.797330	+	0.213644i	0.634411	−	0.772996i	$-0.281243\pi$
$167$	10.3038	+	2.76089i	0.797330	+	0.213644i	0.162918	+	0.986640i	$0.447909\pi$
$168$	2.27819	+	0.821769i	0.175766	+	0.0634009i
$169$	−12.7969	+	2.28919i	−0.984374	+	0.176091i
$170$	19.1288	−	15.5596i	1.46711	−	1.19337i
$171$	16.9151	+	7.76934i	1.29353	+	0.594136i
$172$			20.4108i			1.55631i
$173$	0.497111	+	0.287007i	0.0377947	+	0.0218208i	0.518778	−	0.854909i	$-0.326387\pi$
$173$	0.497111	+	0.287007i	0.0377947	+	0.0218208i	−0.480984	+	0.876730i	$0.659720\pi$
$174$	−1.05456	+	12.4671i	−0.0799457	+	0.945129i
$175$	6.17878	−	12.2588i	0.467072	−	0.926680i
$176$	−4.97869	+	18.5807i	−0.375283	+	1.40057i
$177$	−16.6297	−	1.40666i	−1.24997	−	0.105731i
$178$	11.7955	+	6.81013i	0.884109	+	0.510441i
$179$	−11.0659			−0.827104			−0.413552	−	0.910481i	$-0.635712\pi$
$179$	−11.0659			−0.827104			−0.413552	+	0.910481i	$0.635712\pi$
$180$	11.2229	+	3.12181i	0.836509	+	0.232686i
$181$			9.43519i			0.701312i	0.936504	+	0.350656i	$0.114041\pi$
$181$			9.43519i			0.701312i	−0.936504	+	0.350656i	$0.885959\pi$
$182$	−10.9952	−	15.6613i	−0.815015	−	1.16089i
$183$	13.5670	+	4.89379i	1.00290	+	0.361760i
$184$	−0.475204	+	1.77348i	−0.0350325	+	0.130743i
$185$	4.81856	−	12.6353i	0.354268	−	0.928968i
$186$	2.16742	−	0.388614i	0.158923	−	0.0284946i
$187$	−6.37176	−	23.7797i	−0.465949	−	1.73895i
$188$	8.70608	+	8.70608i	0.634956	+	0.634956i
$189$	−10.1747	−	10.0004i	−0.740102	−	0.727421i
$190$	2.74498	−	26.6780i	0.199142	−	1.93542i
$191$	−1.66462	−	0.961070i	−0.120448	−	0.0695406i	0.438566	−	0.898699i	$-0.355487\pi$
$191$	−1.66462	−	0.961070i	−0.120448	−	0.0695406i	−0.559013	+	0.829159i	$0.688820\pi$
$192$	9.84006	−	1.76431i	0.710145	−	0.127328i
$193$	1.82755	−	6.82049i	0.131550	−	0.490950i	−0.868439	−	0.495797i	$-0.834876\pi$
$193$	1.82755	−	6.82049i	0.131550	−	0.490950i	0.999988	+	0.00484677i	$0.00154278\pi$
$194$	9.57473	+	16.5839i	0.687425	+	1.19066i
$195$	8.85627	+	10.7966i	0.634210	+	0.773160i
$196$	0.467345	−	0.809465i	0.0333818	−	0.0578189i
$197$	−2.08919	−	2.08919i	−0.148849	−	0.148849i	0.628755	−	0.777604i	$-0.283565\pi$
$197$	−2.08919	−	2.08919i	−0.148849	−	0.148849i	−0.777604	+	0.628755i	$0.783565\pi$
$198$	15.9754	−	19.2630i	1.13532	−	1.36896i
$199$			2.27253i			0.161095i	0.996751	+	0.0805475i	$0.0256669\pi$
$199$			2.27253i			0.161095i	−0.996751	+	0.0805475i	$0.974333\pi$
$200$	0.144391	+	2.54229i	0.0102100	+	0.179767i
$201$	0.188186	−	2.22476i	0.0132736	−	0.156923i
$202$	−0.699372	+	2.61009i	−0.0492076	+	0.183645i
$203$	−9.91055	−	2.65552i	−0.695584	−	0.186381i
$204$	−13.1124	+	11.0671i	−0.918053	+	0.774855i
$205$	−1.24611	−	7.75776i	−0.0870321	−	0.541825i
$206$	−11.3994	−	11.3994i	−0.794236	−	0.794236i
$207$	6.90429	−	8.32513i	0.479881	−	0.578637i
$208$	14.5744	+	6.77416i	1.01055	+	0.469703i
$209$	−23.1887	−	13.3880i	−1.60400	−	0.926068i
$210$	−8.91694	+	18.5201i	−0.615327	+	1.27801i
$211$	−8.85381	−	15.3353i	−0.609522	−	1.05572i	−0.991319	−	0.131477i	$-0.958028\pi$
$211$	−8.85381	−	15.3353i	−0.609522	−	1.05572i	0.381798	−	0.924246i	$-0.375305\pi$
$212$	−20.3462	+	11.7469i	−1.39738	+	0.806779i
$213$	6.98634	+	4.86196i	0.478696	+	0.333136i
$214$	−18.2218	+	4.88253i	−1.24562	+	0.333763i
$215$	26.1441	+	2.69005i	1.78301	+	0.183460i
$216$	2.56194	+	0.662796i	0.174318	+	0.0450976i
$217$			1.80573i			0.122581i
$218$	9.92687	+	5.73128i	0.672332	+	0.388171i
$219$	5.85985	−	8.42024i	0.395972	−	0.568987i
$220$	−15.6571	−	5.97092i	−1.05560	−	0.402559i
$221$	−20.4883	+	1.81811i	−1.37819	+	0.122299i
$222$	−6.87038	+	19.0467i	−0.461110	+	1.27833i
$223$	0.727345	+	2.71449i	0.0487066	+	0.181776i	0.985994	−	0.166783i	$-0.0533379\pi$
$223$	0.727345	+	2.71449i	0.0487066	+	0.181776i	−0.937287	+	0.348559i	$0.886671\pi$
$224$			20.8606i			1.39381i
$225$	5.47785	−	13.9640i	0.365190	−	0.930933i
$226$	16.5759	+	16.5759i	1.10262	+	1.10262i
$227$	−14.8613	+	3.98209i	−0.986382	+	0.264300i	−0.715730	−	0.698377i	$-0.753906\pi$
$227$	−14.8613	+	3.98209i	−0.986382	+	0.264300i	−0.270652	+	0.962677i	$0.587239\pi$
$228$	−1.57297	+	18.5959i	−0.104172	+	1.23154i
$229$	−23.7164	−	6.35478i	−1.56722	−	0.419936i	−0.632281	−	0.774739i	$-0.717881\pi$
$229$	−23.7164	−	6.35478i	−1.56722	−	0.419936i	−0.934941	+	0.354804i	$0.884548\pi$
$230$	−14.5601	−	5.55258i	−0.960063	−	0.366126i
$231$	13.2366	+	15.6828i	0.870903	+	1.03185i
$232$	1.83830	−	0.492572i	0.120690	−	0.0323389i
$233$		−	15.9464i		−	1.04468i	−0.852736	−	0.522341i	$-0.825059\pi$
$233$		−	15.9464i		−	1.04468i	0.852736	−	0.522341i	$-0.174941\pi$
$234$	−13.5517	−	15.9225i	−0.885901	−	1.04089i
$235$	12.2990	−	10.0042i	0.802299	−	0.652600i
$236$	−4.33065	−	16.1622i	−0.281901	−	1.05207i
$237$	−14.5049	−	5.23210i	−0.942196	−	0.339861i
$238$	−15.1383	−	26.2203i	−0.981270	−	1.69961i
$239$	22.0128	+	5.89833i	1.42389	+	0.381531i	0.886863	−	0.462032i	$-0.152880\pi$
$239$	22.0128	+	5.89833i	1.42389	+	0.381531i	0.537030	+	0.843563i	$0.319546\pi$
$240$	−1.29153	−	17.2155i	−0.0833678	−	1.11126i
$241$	−1.64059	−	6.12278i	−0.105680	−	0.394403i	0.892741	−	0.450569i	$-0.148779\pi$
$241$	−1.64059	−	6.12278i	−0.105680	−	0.394403i	−0.998421	+	0.0561663i	$0.982112\pi$
$242$	−10.4196	+	10.4196i	−0.669798	+	0.669798i
$243$	−12.0845	−	9.84706i	−0.775222	−	0.631689i
$244$			14.4600i			0.925709i
$245$	−0.975247	−	0.705304i	−0.0623063	−	0.0450602i
$246$	2.07627	+	11.5800i	0.132378	+	0.738312i
$247$	−14.3587	+	17.1553i	−0.913625	+	1.09156i
$248$	−0.167472	−	0.290070i	−0.0106345	−	0.0184195i
$249$	2.15920	+	4.59581i	0.136834	+	0.291248i
$250$	−21.5891	−	0.989416i	−1.36541	−	0.0625761i
$251$	−0.856146			−0.0540395			−0.0270197	−	0.999635i	$-0.508602\pi$
$251$	−0.856146			−0.0540395			−0.0270197	+	0.999635i	$0.508602\pi$
$252$	5.97012	−	12.9979i	0.376082	−	0.818792i
$253$	−11.0012	+	11.0012i	−0.691640	+	0.691640i
$254$	24.6980	−	6.61782i	1.54969	−	0.415239i
$255$	12.4477	+	18.2543i	0.779506	+	1.14313i
$256$	−9.67535	−	16.7582i	−0.604709	−	1.04739i
$257$	20.8316	−	12.0271i	1.29944	−	0.750231i	0.319131	−	0.947711i	$-0.396609\pi$
$257$	20.8316	−	12.0271i	1.29944	−	0.750231i	0.980307	+	0.197480i	$0.0632758\pi$
$258$	−39.2123	−	3.31685i	−2.44125	−	0.206498i
$259$	−14.3798	−	8.30217i	−0.893516	−	0.515872i
$260$	−7.16956	+	12.0253i	−0.444637	+	0.745780i
$261$	−11.0516	−	1.88312i	−0.684077	−	0.116562i
$262$	10.7764	−	10.7764i	0.665766	−	0.665766i
$263$	0.0832717	−	0.144231i	0.00513475	−	0.00889366i	−0.863447	−	0.504440i	$-0.831699\pi$
$263$	0.0832717	−	0.144231i	0.00513475	−	0.00889366i	0.868581	+	0.495547i	$0.165032\pi$
$264$	−3.58080	−	1.29164i	−0.220383	−	0.0794948i
$265$	12.3650	+	27.6096i	0.759576	+	1.69604i
$266$	−31.8078	−	8.52288i	−1.95026	−	0.522571i
$267$	−6.97125	+	10.0173i	−0.426634	+	0.613047i
$268$	2.16222	−	0.579364i	0.132078	−	0.0353903i
$269$		−	1.83214i		−	0.111708i	−0.998439	−	0.0558539i	$-0.982212\pi$
$269$		−	1.83214i		−	0.111708i	0.998439	−	0.0558539i	$-0.0177881\pi$
$270$	−7.82128	+	21.0537i	−0.475988	+	1.28129i
$271$	10.4998	−	10.4998i	0.637816	−	0.637816i	−0.312201	−	0.950016i	$-0.601066\pi$
$271$	10.4998	−	10.4998i	0.637816	−	0.637816i	0.950016	+	0.312201i	$0.101066\pi$
$272$	22.0222	+	12.7145i	1.33529	+	0.770930i
$273$	14.8136	−	8.63421i	0.896558	−	0.522566i
$274$	20.3875	+	35.3122i	1.23165	+	2.13329i
$275$	−9.71166	+	19.2681i	−0.585635	+	1.16191i
$276$	10.2003	+	3.67937i	0.613986	+	0.221472i
$277$	−12.7374	+	22.0619i	−0.765318	+	1.32557i	0.174760	+	0.984611i	$0.444085\pi$
$277$	−12.7374	+	22.0619i	−0.765318	+	1.32557i	−0.940078	+	0.340959i	$0.889248\pi$
$278$	−24.5246	−	24.5246i	−1.47089	−	1.47089i
$279$	0.183283	+	1.96452i	0.0109729	+	0.117613i
$280$	3.11020	+	0.320018i	0.185870	+	0.0191247i
$281$	−9.57841	+	2.56653i	−0.571400	+	0.153106i	−0.532939	−	0.846154i	$-0.678912\pi$
$281$	−9.57841	+	2.56653i	−0.571400	+	0.153106i	−0.0384615	+	0.999260i	$0.512246\pi$
$282$	−18.1405	+	15.3110i	−1.08025	+	0.911755i
$283$	9.01345	+	15.6118i	0.535794	+	0.928022i	0.999124	+	0.0418367i	$0.0133209\pi$
$283$	9.01345	+	15.6118i	0.535794	+	0.928022i	−0.463331	+	0.886186i	$0.653346\pi$
$284$	−2.20867	+	8.24289i	−0.131061	+	0.489125i
$285$	23.6121	+	4.46566i	1.39866	+	0.264523i
$286$	17.2819	+	24.6161i	1.02190	+	1.45558i
$287$	−9.64758			−0.569478
$288$	2.11737	+	22.6951i	0.124767	+	1.33732i
$289$	−15.5442			−0.914366
$290$	2.56169	+	15.9480i	0.150428	+	0.936500i
$291$	−15.5300	+	7.29631i	−0.910387	+	0.427717i
$292$	9.93468	+	2.66199i	0.581383	+	0.155781i
$293$	−16.6910	−	4.47235i	−0.975101	−	0.261278i	−0.264121	−	0.964490i	$-0.585082\pi$
$293$	−16.6910	−	4.47235i	−0.975101	−	0.261278i	−0.710980	+	0.703212i	$0.751748\pi$
$294$	1.47916	+	1.02939i	0.0862666	+	0.0600350i
$295$	−21.2729	+	3.41701i	−1.23855	+	0.198946i
$296$	3.07993			0.179017
$297$	15.9924	+	15.7184i	0.927973	+	0.912073i
$298$	7.01707			0.406488
$299$	7.46897	+	10.6387i	0.431941	+	0.615250i
$300$	15.0331	+	0.415791i	0.867937	+	0.0240057i
$301$	8.35232	−	31.1713i	0.481420	−	1.79668i
$302$	8.94738	+	15.4973i	0.514864	+	0.891770i
$303$	−2.27760	−	0.821556i	−0.130845	−	0.0471972i
$304$	26.7151	−	7.15829i	1.53222	−	0.410556i
$305$	18.5218	+	1.90577i	1.06056	+	0.109124i
$306$	−19.1309	−	26.9895i	−1.09364	−	1.54289i
$307$	−12.1533	−	12.1533i	−0.693623	−	0.693623i	0.269404	−	0.963027i	$-0.413173\pi$
$307$	−12.1533	−	12.1533i	−0.693623	−	0.693623i	−0.963027	+	0.269404i	$0.913173\pi$
$308$	−10.2876	+	17.8187i	−0.586192	+	1.01531i
$309$	11.0389	−	9.31704i	0.627980	−	0.530028i
$310$	2.59444	−	1.16193i	0.147354	−	0.0659929i
$311$	2.53814	+	4.39618i	0.143925	+	0.249285i	0.928971	−	0.370152i	$-0.120694\pi$
$311$	2.53814	+	4.39618i	0.143925	+	0.249285i	−0.785047	+	0.619437i	$0.787361\pi$
$312$	−1.57885	+	2.76087i	−0.0893850	+	0.156303i
$313$	−21.3536	−	12.3285i	−1.20698	−	0.696847i	−0.244878	−	0.969554i	$-0.578748\pi$
$313$	−21.3536	−	12.3285i	−1.20698	−	0.696847i	−0.962097	+	0.272707i	$0.912081\pi$
$314$	−15.8496	+	15.8496i	−0.894443	+	0.894443i
$315$	−15.8622	−	9.36017i	−0.893732	−	0.527386i
$316$		−	15.4596i		−	0.869673i
$317$	7.51828	−	2.01452i	0.422269	−	0.113147i	−0.0414260	−	0.999142i	$-0.513190\pi$
$317$	7.51828	−	2.01452i	0.422269	−	0.113147i	0.463695	+	0.885995i	$0.346523\pi$
$318$	−19.2613	−	40.9972i	−1.08012	−	2.29901i
$319$	15.5772	+	4.17389i	0.872154	+	0.233693i
$320$	11.7787	−	5.27514i	0.658452	−	0.294889i
$321$	−2.98318	−	16.6381i	−0.166505	−	0.928647i
$322$	−9.56685	+	16.5703i	−0.533140	+	0.923425i
$323$	−25.0289	+	25.0289i	−1.39265	+	1.39265i
$324$	5.17582	−	14.7469i	0.287546	−	0.819273i
$325$	14.4583	+	10.7684i	0.802003	+	0.597321i
$326$	−18.3763	−	10.6096i	−1.01777	−	0.587610i
$327$	−5.86688	+	8.43035i	−0.324439	+	0.466199i
$328$	1.54977	−	0.894762i	0.0855719	−	0.0494050i
$329$	−9.73327	−	16.8585i	−0.536612	−	0.929440i
$330$	14.0154	−	29.1094i	0.771524	−	1.60242i
$331$	−14.7788	+	3.95997i	−0.812317	+	0.217660i	−0.640985	−	0.767554i	$-0.721474\pi$
$331$	−14.7788	+	3.95997i	−0.812317	+	0.217660i	−0.171332	+	0.985213i	$0.554807\pi$
$332$	−3.59981	+	3.59981i	−0.197565	+	0.197565i
$333$	−16.4870	−	7.57269i	−0.903481	−	0.414981i
$334$	−20.6199			−1.12827
$335$	−0.457136	−	2.84593i	−0.0249760	−	0.155490i
$336$	−21.1223	−	1.78667i	−1.15231	−	0.0974708i
$337$	−9.15282	−	15.8531i	−0.498586	−	0.863576i	0.501413	−	0.865208i	$-0.332814\pi$
$337$	−9.15282	−	15.8531i	−0.498586	−	0.863576i	−0.999999	+	0.00163220i	$0.999480\pi$
$338$	22.7483	−	10.6765i	1.23735	−	0.580726i
$339$	−16.0517	+	13.5479i	−0.871808	+	0.735823i
$340$	−12.9812	+	17.9495i	−0.704003	+	0.973448i
$341$		−	2.83821i		−	0.153697i
$342$	−35.4700	−	6.04385i	−1.91800	−	0.326814i
$343$	12.5450	−	12.5450i	0.677366	−	0.677366i
$344$	1.54927	+	5.78194i	0.0835309	+	0.311741i
$345$	6.05724	−	12.5806i	0.326111	−	0.677317i
$346$	−1.07177	−	0.287180i	−0.0576187	−	0.0154389i
$347$	17.5779	+	30.4458i	0.943631	+	1.63442i	0.758470	+	0.651708i	$0.225947\pi$
$347$	17.5779	+	30.4458i	0.943631	+	1.63442i	0.185161	+	0.982708i	$0.440719\pi$
$348$	−1.98367	−	11.0635i	−0.106336	−	0.593066i
$349$	−6.78641	−	25.3272i	−0.363268	−	1.35574i	−0.869753	−	0.493487i	$-0.835722\pi$
$349$	−6.78641	−	25.3272i	−0.363268	−	1.35574i	0.506485	−	0.862249i	$-0.330945\pi$
$350$	−5.40359	+	25.9803i	−0.288834	+	1.38870i
$351$	15.2399	−	10.8971i	0.813444	−	0.581643i
$352$		−	32.7882i		−	1.74762i
$353$	−27.7816	+	7.44407i	−1.47867	+	0.396208i	−0.905894	−	0.423506i	$-0.860799\pi$
$353$	−27.7816	+	7.44407i	−1.47867	+	0.396208i	−0.572774	+	0.819713i	$0.694133\pi$
$354$	31.7539	−	5.69342i	1.68770	−	0.302602i
$355$	10.2672	+	3.91546i	0.544926	+	0.207811i
$356$	−11.8189	−	3.16688i	−0.626403	−	0.167844i
$357$	24.5540	−	11.5360i	1.29954	−	0.610548i
$358$	20.6616	−	5.53627i	1.09200	−	0.292601i
$359$	−0.369810	−	0.369810i	−0.0195178	−	0.0195178i	0.697281	−	0.716798i	$-0.254393\pi$
$359$	−0.369810	−	0.369810i	−0.0195178	−	0.0195178i	−0.716798	+	0.697281i	$0.754393\pi$
$360$	3.41618	+	0.0324725i	0.180049	+	0.00171145i
$361$			19.4982i			1.02622i
$362$	−4.72043	−	17.6169i	−0.248100	−	0.925923i
$363$	−8.51621	−	10.0901i	−0.446985	−	0.529591i
$364$	13.1825	+	11.0336i	0.690949	+	0.578315i
$365$	4.71908	−	12.3745i	0.247008	−	0.647709i
$366$	−27.7800	−	2.34983i	−1.45209	−	0.122828i
$367$	−10.2799	−	5.93511i	−0.536607	−	0.309810i	0.207096	−	0.978321i	$-0.433599\pi$
$367$	−10.2799	−	5.93511i	−0.536607	−	0.309810i	−0.743703	+	0.668510i	$0.766932\pi$
$368$		−	16.0702i		−	0.837718i
$369$	−10.4960	+	0.979235i	−0.546398	+	0.0509769i
$370$	−2.67550	+	26.0027i	−0.139093	+	1.35182i
$371$	35.8796	−	9.61391i	1.86278	−	0.499129i
$372$	−1.79041	+	0.841169i	−0.0928285	+	0.0436126i
$373$	20.6079	−	11.8980i	1.06704	−	0.616054i	0.139667	−	0.990199i	$-0.455397\pi$
$373$	20.6079	−	11.8980i	1.06704	−	0.616054i	0.927371	+	0.374144i	$0.122063\pi$
$374$	23.7940	+	41.2124i	1.23036	+	2.13104i
$375$	2.51388	−	19.2011i	0.129816	−	0.991538i
$376$	3.12708	+	1.80542i	0.161267	+	0.0931074i
$377$	5.67912	−	12.2185i	0.292490	−	0.629283i
$378$	24.0009	+	13.5818i	1.23447	+	0.698571i
$379$	−3.57979	−	3.57979i	−0.183882	−	0.183882i	0.609163	−	0.793045i	$-0.291505\pi$
$379$	−3.57979	−	3.57979i	−0.183882	−	0.183882i	−0.793045	+	0.609163i	$0.791505\pi$
$380$	3.82101	+	23.7880i	0.196013	+	1.22030i
$381$	4.04343	+	22.5514i	0.207151	+	1.15534i
$382$	3.58892	+	0.961647i	0.183625	+	0.0492021i
$383$	−2.94675	+	10.9974i	−0.150572	+	0.561942i	0.848872	+	0.528598i	$0.177282\pi$
$383$	−2.94675	+	10.9974i	−0.150572	+	0.561942i	−0.999444	+	0.0333436i	$0.989384\pi$
$384$	6.33156	−	2.97469i	0.323106	−	0.151801i
$385$	21.4680	+	15.5258i	1.09411	+	0.791269i
$386$			13.6492i			0.694725i
$387$	5.92290	−	34.7602i	0.301078	−	1.76696i
$388$	−12.1644	−	12.1644i	−0.617554	−	0.617554i
$389$	0.132903	−	0.230195i	0.00673846	−	0.0116713i	−0.862637	−	0.505824i	$-0.831188\pi$
$389$	0.132903	−	0.230195i	0.00673846	−	0.0116713i	0.869375	+	0.494153i	$0.164522\pi$
$390$	−21.9375	−	15.7280i	−1.11085	−	0.796420i
$391$	10.2834	+	17.8113i	0.520053	+	0.900758i
$392$	0.0709470	−	0.264778i	0.00358337	−	0.0133733i
$393$	8.80779	+	10.4355i	0.444294	+	0.526403i
$394$	4.94605	+	2.85560i	0.249179	+	0.143863i
$395$	−19.8022	−	2.03751i	−0.996358	−	0.102518i
$396$	−9.38369	+	20.4298i	−0.471548	+	1.02664i
$397$	6.59359	+	6.59359i	0.330923	+	0.330923i	0.852937	−	0.522014i	$-0.174819\pi$
$397$	6.59359	+	6.59359i	0.330923	+	0.330923i	−0.522014	+	0.852937i	$0.674819\pi$
$398$	−1.13695	−	4.24314i	−0.0569899	−	0.212689i
$399$	10.0119	−	27.7559i	0.501221	−	1.38953i
$400$	−6.97991	−	21.1664i	−0.348995	−	1.05832i
$401$	2.71759	−	10.1422i	0.135710	−	0.506476i	−0.864284	−	0.503004i	$-0.832228\pi$
$401$	2.71759	−	10.1422i	0.135710	−	0.506476i	0.999994	−	0.00347209i	$-0.00110520\pi$
$402$	0.761679	+	4.24811i	0.0379891	+	0.211877i
$403$	−2.33580	−	0.408877i	−0.116355	−	0.0203676i
$404$		−	2.42751i		−	0.120773i
$405$	−18.2071	−	8.57327i	−0.904719	−	0.426009i
$406$	19.8330			0.984296
$407$	22.6018	+	13.0492i	1.12033	+	0.646822i
$408$	−2.87443	+	4.13038i	−0.142305	+	0.204484i
$409$	0.238507	−	0.890119i	0.0117934	−	0.0440135i	−0.959778	−	0.280759i	$-0.909414\pi$
$409$	0.238507	−	0.890119i	0.0117934	−	0.0440135i	0.971572	+	0.236745i	$0.0760806\pi$
$410$	6.20788	+	13.8614i	0.306585	+	0.684568i
$411$	−33.0682	+	15.5361i	−1.63113	+	0.766337i
$412$	12.5423	+	7.24132i	0.617916	+	0.356754i
$413$			26.4550i			1.30177i
$414$	−8.72624	+	18.9985i	−0.428871	+	0.933724i
$415$	4.13655	+	5.08543i	0.203055	+	0.249634i
$416$	−26.9842	−	4.72353i	−1.32301	−	0.231590i
$417$	23.7489	−	20.0446i	1.16299	−	0.981587i
$418$	49.9948	+	13.3961i	2.44532	+	0.655223i
$419$	−10.8394	+	6.25812i	−0.529538	+	0.305729i	−0.740828	−	0.671694i	$-0.765567\pi$
$419$	−10.8394	+	6.25812i	−0.529538	+	0.305729i	0.211290	+	0.977423i	$0.432233\pi$
$420$	3.43151	−	18.1440i	0.167440	−	0.885337i
$421$	8.95672	−	2.39995i	0.436524	−	0.116966i	−0.0338630	−	0.999426i	$-0.510781\pi$
$421$	8.95672	−	2.39995i	0.436524	−	0.116966i	0.470387	+	0.882460i	$0.344114\pi$
$422$	24.2036	+	24.2036i	1.17821	+	1.17821i
$423$	−12.3003	−	17.3531i	−0.598063	−	0.843736i
$424$	−4.87201	+	4.87201i	−0.236606	+	0.236606i
$425$	21.2806	+	18.9932i	1.03226	+	0.921306i
$426$	−15.4770	−	5.58272i	−0.749861	−	0.270484i
$427$	5.91721	−	22.0833i	0.286354	−	1.06869i
$428$	14.6767	−	8.47359i	0.709425	−	0.409587i
$429$	−23.2836	+	13.5711i	−1.12414	+	0.655217i
$430$	−50.1607	+	8.05719i	−2.41896	+	0.388552i
$431$	5.04319	−	5.04319i	0.242922	−	0.242922i	−0.575136	−	0.818058i	$-0.695051\pi$
$431$	5.04319	−	5.04319i	0.242922	−	0.242922i	0.818058	+	0.575136i	$0.195051\pi$
$432$	−23.1611	+	0.200137i	−1.11434	+	0.00962912i
$433$	−25.1759			−1.20988			−0.604938	−	0.796273i	$-0.706802\pi$
$433$	−25.1759			−1.20988			−0.604938	+	0.796273i	$0.706802\pi$
$434$	−0.903408	−	3.37157i	−0.0433650	−	0.161840i
$435$	−14.4326	+	1.08275i	−0.691992	+	0.0519141i
$436$	−9.94660	−	2.66518i	−0.476356	−	0.127639i
$437$	21.6069	+	5.78956i	1.03360	+	0.276952i
$438$	−6.72854	+	18.6535i	−0.321502	+	0.891299i
$439$	9.68692	+	5.59274i	0.462331	+	0.266927i	0.713024	−	0.701140i	$-0.247325\pi$
$439$	9.68692	+	5.59274i	0.462331	+	0.266927i	−0.250693	+	0.968067i	$0.580658\pi$
$440$	−4.88854	−	0.502996i	−0.233052	−	0.0239794i
$441$	−1.03080	+	1.24293i	−0.0490856	+	0.0591870i
$442$	37.3450	−	13.6450i	1.77632	−	0.649025i
$443$	16.0589	−	27.8148i	0.762981	−	1.32152i	−0.178326	−	0.983971i	$-0.557068\pi$
$443$	16.0589	−	27.8148i	0.762981	−	1.32152i	0.941307	−	0.337550i	$-0.109598\pi$
$444$	1.53316	−	18.1252i	0.0727604	−	0.860184i
$445$	−5.61412	+	14.7215i	−0.266135	+	0.697864i
$446$	−2.71612	−	4.70446i	−0.128612	−	0.222763i
$447$	−0.529953	+	6.26518i	−0.0250659	+	0.296333i
$448$	−4.10147	−	15.3069i	−0.193776	−	0.723183i
$449$	12.4055	+	12.4055i	0.585454	+	0.585454i	0.936397	−	0.350943i	$-0.114139\pi$
$449$	12.4055	+	12.4055i	0.585454	+	0.585454i	−0.350943	+	0.936397i	$0.614139\pi$
$450$	−3.24176	+	28.8134i	−0.152818	+	1.35828i
$451$	15.1638			0.714037
$452$	−18.2378	−	10.5296i	−0.857836	−	0.495272i
$453$	−14.5125	+	6.81824i	−0.681856	+	0.320349i
$454$	25.7561	−	14.8703i	1.20879	−	0.697897i
$455$	15.8702	−	15.4312i	0.744008	−	0.723426i
$456$	0.965919	+	5.38722i	0.0452333	+	0.252279i
$457$	1.77886	+	6.63880i	0.0832117	+	0.310550i	0.994970	−	0.100178i	$-0.0319412\pi$
$457$	1.77886	+	6.63880i	0.0832117	+	0.310550i	−0.911758	+	0.410728i	$0.865275\pi$
$458$	47.4612			2.21772
$459$	25.5424	−	15.0427i	1.19222	−	0.702131i
$460$	13.9255	+	1.43284i	0.649280	+	0.0668065i
$461$	−2.88732	−	10.7756i	−0.134476	−	0.501871i	−0.999999	−	0.00100278i	$-0.999681\pi$
$461$	−2.88732	−	10.7756i	−0.134476	−	0.501871i	0.865524	−	0.500868i	$-0.166986\pi$
$462$	−32.5607	−	22.6598i	−1.51486	−	1.05423i
$463$	−6.42069	+	23.9623i	−0.298395	+	1.11362i	0.640089	+	0.768301i	$0.278898\pi$
$463$	−6.42069	+	23.9623i	−0.298395	+	1.11362i	−0.938484	+	0.345324i	$0.887769\pi$
$464$	−14.4259	+	8.32878i	−0.669704	+	0.386654i
$465$	0.841483	+	2.40419i	0.0390228	+	0.111492i
$466$	7.97799	+	29.7743i	0.369573	+	1.37927i
$467$		−	21.6050i		−	0.999758i	−0.866095	−	0.499879i	$-0.833378\pi$
$467$		−	21.6050i		−	0.999758i	0.866095	−	0.499879i	$-0.166622\pi$
$468$	15.4616	+	10.6658i	0.714713	+	0.493026i
$469$	−3.53921			−0.163426
$470$	−17.9590	+	24.8324i	−0.828385	+	1.14543i
$471$	−12.9543	−	15.3483i	−0.596901	−	0.707212i
$472$	−2.45356	−	4.24970i	−0.112934	−	0.195608i
$473$	−13.1280	+	48.9943i	−0.603625	+	2.25276i
$474$	29.7004	+	2.51227i	1.36419	+	0.115392i
$475$	30.9735	−	1.75917i	1.42116	−	0.0807161i
$476$	19.2327	+	19.2327i	0.881531	+	0.881531i
$477$	38.0589	−	14.1011i	1.74260	−	0.645647i
$478$	−44.0522			−2.01490
$479$	8.52440	−	2.28411i	0.389490	−	0.104363i	−0.0587592	−	0.998272i	$-0.518714\pi$
$479$	8.52440	−	2.28411i	0.389490	−	0.104363i	0.448249	+	0.893909i	$0.352048\pi$
$480$	9.72119	+	27.7743i	0.443710	+	1.26772i
$481$	13.9953	−	16.7210i	0.638131	−	0.762414i
$482$	6.12646	+	10.6113i	0.279053	+	0.483333i
$483$	−14.0722	−	9.79319i	−0.640308	−	0.445606i
$484$	6.61890	−	11.4643i	0.300859	−	0.521103i
$485$	−17.1846	+	13.9781i	−0.780311	+	0.634714i
$486$	27.4900	+	12.3400i	1.24697	+	0.559755i
$487$	−14.3077	+	14.3077i	−0.648345	+	0.648345i	−0.952593	−	0.304248i	$-0.901595\pi$
$487$	−14.3077	+	14.3077i	−0.648345	+	0.648345i	0.304248	+	0.952593i	$0.401595\pi$
$488$	1.09758	+	4.09622i	0.0496851	+	0.185427i
$489$	10.8606	−	15.6060i	0.491133	−	0.705728i
$490$	2.17379	+	0.828990i	0.0982020	+	0.0374500i
$491$	−21.6659	−	37.5265i	−0.977769	−	1.69355i	−0.670476	−	0.741931i	$-0.733910\pi$
$491$	−21.6659	−	37.5265i	−0.977769	−	1.69355i	−0.307293	−	0.951615i	$-0.599423\pi$
$492$	−4.49416	−	9.56572i	−0.202612	−	0.431256i
$493$	10.6592	−	18.4623i	0.480067	−	0.831501i
$494$	18.2271	−	39.2151i	0.820075	−	1.76437i
$495$	24.9318	+	14.7121i	1.12060	+	0.661260i
$496$	2.07298	+	2.07298i	0.0930797	+	0.0930797i
$497$	6.74616	−	11.6847i	0.302607	−	0.524130i
$498$	−6.33082	−	7.50080i	−0.283691	−	0.336119i
$499$	−5.43864	+	20.2973i	−0.243467	+	0.908631i	0.730681	+	0.682719i	$0.239203\pi$
$499$	−5.43864	+	20.2973i	−0.243467	+	0.908631i	−0.974148	+	0.225912i	$0.927464\pi$
$500$	18.9639	−	4.16116i	0.848092	−	0.186093i
$501$	1.55729	−	18.4105i	0.0695745	−	0.822519i
$502$	1.59855	−	0.428330i	0.0713468	−	0.0191173i
$503$	4.01093			0.178838			0.0894192	−	0.995994i	$-0.471499\pi$
$503$	4.01093			0.178838			0.0894192	+	0.995994i	$0.471499\pi$
$504$	0.704610	−	4.13520i	0.0313858	−	0.184196i
$505$	−3.10939	−	0.319935i	−0.138366	−	0.0142369i
$506$	15.0369	−	26.0448i	0.668474	−	1.15783i
$507$	7.81449	+	21.1171i	0.347054	+	0.937845i
$508$	−19.8929	+	11.4852i	−0.882606	+	0.509573i
$509$	−32.1898	−	8.62522i	−1.42679	−	0.382306i	−0.538900	−	0.842370i	$-0.681160\pi$
$509$	−32.1898	−	8.62522i	−1.42679	−	0.382306i	−0.887886	+	0.460064i	$0.847827\pi$
$510$	−32.3743	−	27.8558i	−1.43356	−	1.23347i
$511$	−14.0829	−	8.13077i	−0.622991	−	0.359684i
$512$	20.7376	+	20.7376i	0.916481	+	0.916481i
$513$	8.07506	−	31.2129i	0.356522	−	1.37808i
$514$	−32.8784	+	32.8784i	−1.45021	+	1.45021i
$515$	10.9284	−	15.1111i	0.481563	−	0.665873i
$516$	34.7976	−	6.23915i	1.53188	−	0.274663i
$517$	15.2985	+	26.4978i	0.672828	+	1.16537i
$518$	31.0027	+	8.30716i	1.36218	+	0.364995i
$519$	0.337352	−	0.935239i	0.0148081	−	0.0410524i
$520$	−1.11821	+	3.95073i	−0.0490367	+	0.173251i
$521$		−	8.38577i		−	0.367387i	−0.982984	−	0.183694i	$-0.941195\pi$
$521$		−	8.38577i		−	0.367387i	0.982984	−	0.183694i	$-0.0588055\pi$
$522$	21.5771	−	2.01306i	0.944403	−	0.0881094i
$523$		−	1.31582i		−	0.0575369i	−0.999586	−	0.0287685i	$-0.990841\pi$
$523$		−	1.31582i		−	0.0575369i	0.999586	−	0.0287685i	$-0.00915855\pi$
$524$	−6.84552	+	11.8568i	−0.299048	+	0.517966i
$525$	−22.7884	−	6.78671i	−0.994566	−	0.296196i
$526$	−0.0833218	+	0.310961i	−0.00363300	+	0.0135585i
$527$	−3.62409	−	0.971071i	−0.157868	−	0.0423005i
$528$	33.1995	+	2.80825i	1.44482	+	0.122213i
$529$	−5.00128	+	8.66247i	−0.217447	+	0.376629i
$530$	−36.9003	−	45.3649i	−1.60285	−	1.97052i
$531$	2.68520	+	28.7814i	0.116528	+	1.24901i
$532$	29.5828			1.28258
$533$	2.18453	−	12.4796i	0.0946224	−	0.540552i
$534$	8.00471	−	22.1914i	0.346398	−	0.960317i
$535$	−8.91948	−	19.9161i	−0.385623	−	0.861049i
$536$	0.568534	−	0.328243i	0.0245569	−	0.0141780i
$537$	3.38261	+	18.8658i	0.145971	+	0.814121i
$538$	0.916622	+	3.42088i	0.0395184	+	0.147485i
$539$	1.64246	−	1.64246i	0.0707457	−	0.0707457i
$540$	1.89164	−	20.0879i	0.0814032	−	0.864444i
$541$	9.35888	−	9.35888i	0.402370	−	0.402370i	−0.476698	−	0.879067i	$-0.658166\pi$
$541$	9.35888	−	9.35888i	0.402370	−	0.402370i	0.879067	+	0.476698i	$0.158166\pi$
$542$	−14.3516	+	24.8576i	−0.616453	+	1.06773i
$543$	16.0857	−	2.88414i	0.690304	−	0.123770i
$544$	−41.8671	−	11.2183i	−1.79504	−	0.480979i
$545$	−4.72474	+	12.3893i	−0.202386	+	0.530700i
$546$	−23.3394	+	23.5326i	−0.998835	+	1.00710i
$547$	34.0336	+	19.6493i	1.45517	+	0.840143i	0.998768	−	0.0496297i	$-0.0158041\pi$
$547$	34.0336	+	19.6493i	1.45517	+	0.840143i	0.456403	+	0.889773i	$0.349137\pi$
$548$	−25.9017	−	25.9017i	−1.10647	−	1.10647i
$549$	4.19608	−	24.6259i	0.179085	−	1.05101i
$550$	8.49324	−	40.8352i	0.362153	−	1.74122i
$551$	−6.00116	−	22.3966i	−0.255658	−	0.954128i
$552$	3.16881	+	0.268040i	0.134873	+	0.0114085i
$553$	−6.32626	+	23.6099i	−0.269020	+	1.00400i
$554$	12.7451	−	47.5653i	0.541487	−	2.02086i
$555$	−23.0144	−	4.35263i	−0.976909	−	0.184759i
$556$	26.9834	+	15.5789i	1.14435	+	0.660692i
$557$	−14.8483	+	14.8483i	−0.629142	+	0.629142i	−0.947852	−	0.318710i	$-0.896750\pi$
$557$	−14.8483	+	14.8483i	−0.629142	+	0.629142i	0.318710	+	0.947852i	$0.396750\pi$
$558$	−1.32507	−	3.57636i	−0.0560946	−	0.151399i
$559$	38.4303	+	17.8623i	1.62543	+	0.755496i
$560$	−27.0197	+	4.34012i	−1.14179	+	0.183403i
$561$	−38.5935	+	18.1319i	−1.62942	+	0.765531i
$562$	16.6003	−	9.58417i	0.700240	−	0.404284i
$563$	21.9880	−	12.6948i	0.926685	−	0.535022i	0.0409231	−	0.999162i	$-0.486970\pi$
$563$	21.9880	−	12.6948i	0.926685	−	0.535022i	0.885761	+	0.464141i	$0.153637\pi$
$564$	12.1814	−	17.5039i	0.512930	−	0.737049i
$565$	−15.8910	+	21.9730i	−0.668540	+	0.924413i
$566$	−24.6400	−	24.6400i	−1.03570	−	1.03570i
$567$	−13.9391	+	20.4034i	−0.585387	+	0.856863i
$568$			2.50268i			0.105010i
$569$	0.754546	−	1.30691i	0.0316322	−	0.0547886i	−0.849776	−	0.527144i	$-0.823263\pi$
$569$	0.754546	−	1.30691i	0.0316322	−	0.0547886i	0.881408	+	0.472355i	$0.156596\pi$
$570$	−46.3214	+	3.47509i	−1.94019	+	0.145555i
$571$	−28.7908	+	16.6224i	−1.20486	+	0.695624i	−0.961631	−	0.274346i	$-0.911539\pi$
$571$	−28.7908	+	16.6224i	−1.20486	+	0.695624i	−0.243225	+	0.969970i	$0.578205\pi$
$572$	−20.7199	−	17.3423i	−0.866342	−	0.725117i
$573$	−1.12965	+	3.13173i	−0.0471919	+	0.130830i
$574$	18.0134	−	4.82669i	0.751866	−	0.201462i
$575$	3.67064	−	17.6483i	0.153076	−	0.735985i
$576$	−6.01580	−	16.2366i	−0.250658	−	0.676527i
$577$	−2.16290	+	2.16290i	−0.0900425	+	0.0900425i	−0.750693	−	0.660651i	$-0.770280\pi$
$577$	−2.16290	+	2.16290i	−0.0900425	+	0.0900425i	0.660651	+	0.750693i	$0.270280\pi$
$578$	29.0233	−	7.77678i	1.20721	−	0.323471i
$579$	−12.1867	−	1.03083i	−0.506460	−	0.0428400i
$580$	−5.93101	−	13.2432i	−0.246272	−	0.549895i
$581$	6.97071	−	4.02454i	0.289194	−	0.166966i
$582$	25.3465	−	21.3930i	1.05065	−	0.886767i
$583$	−56.3947	+	15.1109i	−2.33563	+	0.625830i
$584$	3.01634			0.124817
$585$	15.6996	−	18.3990i	0.649097	−	0.760706i
$586$	33.4021			1.37983
$587$	8.59481	−	2.30297i	0.354746	−	0.0950538i	−0.0770452	−	0.997028i	$-0.524549\pi$
$587$	8.59481	−	2.30297i	0.354746	−	0.0950538i	0.431791	+	0.901974i	$0.357882\pi$
$588$	−1.52289	−	0.549323i	−0.0628027	−	0.0226537i
$589$	−3.53402	+	2.04037i	−0.145617	+	0.0840718i
$590$	38.0100	−	17.0229i	1.56485	−	0.700821i
$591$	−2.92317	+	4.20041i	−0.120243	+	0.172782i
$592$	−26.0389	+	6.97710i	−1.07019	+	0.286757i
$593$	−2.22524	+	2.22524i	−0.0913797	+	0.0913797i	−0.751319	−	0.659939i	$-0.770582\pi$
$593$	−2.22524	+	2.22524i	−0.0913797	+	0.0913797i	0.659939	+	0.751319i	$0.270582\pi$
$594$	−37.7240	−	21.3475i	−1.54784	−	0.875899i
$595$	27.1699	−	22.1004i	1.11386	−	0.906027i
$596$	−6.08904	+	1.63155i	−0.249417	+	0.0668311i
$597$	3.87435	−	0.694664i	0.158566	−	0.0284307i
$598$	−19.2682	−	16.1272i	−0.787935	−	0.659492i
$599$	−21.7861	+	12.5782i	−0.890155	+	0.513931i	−0.873993	−	0.485938i	$-0.838478\pi$
$599$	−21.7861	+	12.5782i	−0.890155	+	0.513931i	−0.0161617	+	0.999869i	$0.505145\pi$
$600$	4.29012	−	1.02329i	0.175143	−	0.0417758i
$601$	−2.82189	+	4.88765i	−0.115107	+	0.199372i	−0.917823	−	0.396991i	$-0.870054\pi$
$601$	−2.82189	+	4.88765i	−0.115107	+	0.199372i	0.802715	+	0.596362i	$0.203388\pi$
$602$			62.3800i			2.54242i
$603$	−3.85044	+	0.359232i	−0.156802	+	0.0146291i
$604$	−11.3674	−	11.3674i	−0.462532	−	0.462532i
$605$	−13.8122	−	9.98907i	−0.561546	−	0.406113i
$606$	4.66363	+	0.394483i	0.189447	+	0.0160248i
$607$	7.92254	−	4.57408i	0.321566	−	0.185656i	−0.330524	−	0.943797i	$-0.607226\pi$
$607$	7.92254	−	4.57408i	0.321566	−	0.185656i	0.652090	+	0.758141i	$0.273892\pi$
$608$	−40.8266	+	23.5712i	−1.65574	+	0.955940i
$609$	−1.49786	+	17.7079i	−0.0606962	+	0.717559i
$610$	−35.5364	+	5.70813i	−1.43883	+	0.231115i
$611$	24.0112	−	8.77313i	0.971390	−	0.354923i
$612$	22.8762	+	18.9719i	0.924714	+	0.766893i
$613$	−2.64652	+	2.64652i	−0.106892	+	0.106892i	−0.758530	−	0.651638i	$-0.774082\pi$
$613$	−2.64652	+	2.64652i	−0.106892	+	0.106892i	0.651638	+	0.758530i	$0.274082\pi$
$614$	28.7722	+	16.6116i	1.16115	+	0.670391i
$615$	−12.8450	+	4.49583i	−0.517961	+	0.181290i
$616$	−1.56175	+	5.82854i	−0.0629248	+	0.234838i
$617$	8.84475	−	33.0091i	0.356076	−	1.32889i	−0.523049	−	0.852303i	$-0.675205\pi$
$617$	8.84475	−	33.0091i	0.356076	−	1.32889i	0.879125	−	0.476592i	$-0.158128\pi$
$618$	−15.9499	+	22.9190i	−0.641599	+	0.921939i
$619$	−11.8626	−	44.2717i	−0.476797	−	1.77943i	−0.614455	−	0.788952i	$-0.710624\pi$
$619$	−11.8626	−	44.2717i	−0.476797	−	1.77943i	0.137658	−	0.990480i	$-0.456043\pi$
$620$	−1.98116	+	1.61150i	−0.0795651	+	0.0647192i
$621$	−16.3037	−	9.22604i	−0.654246	−	0.370228i
$622$	−6.93848	−	6.93848i	−0.278208	−	0.278208i
$623$	16.7539	+	9.67289i	0.671232	+	0.387536i
$624$	7.09392	−	26.9181i	0.283984	−	1.07759i
$625$	−2.83066	−	24.8392i	−0.113226	−	0.993569i
$626$	46.0382	+	12.3359i	1.84006	+	0.493042i
$627$	−15.7364	+	43.6261i	−0.628452	+	1.74226i
$628$	10.0682	−	17.4386i	0.401765	−	0.695878i
$629$	24.3954	−	24.3954i	0.972709	−	0.972709i
$630$	34.2999	+	9.54097i	1.36654	+	0.380121i
$631$	−22.2495	+	22.2495i	−0.885739	+	0.885739i	−0.994110	−	0.108371i	$-0.965436\pi$
$631$	−22.2495	+	22.2495i	−0.885739	+	0.885739i	0.108371	+	0.994110i	$0.465436\pi$
$632$	−1.17345	−	4.37939i	−0.0466775	−	0.174203i
$633$	−23.4381	+	19.7822i	−0.931581	+	0.786273i
$634$	−13.0299	+	7.52280i	−0.517482	+	0.298769i
$635$	12.0895	+	26.9945i	0.479759	+	1.07124i
$636$	26.2462	+	31.0967i	1.04073	+	1.23306i
$637$	−1.11510	−	1.58833i	−0.0441820	−	0.0629321i
$638$	−31.1731			−1.23415
$639$	6.15340	−	13.3970i	0.243425	−	0.529976i
$640$	7.00610	−	5.69885i	0.276940	−	0.225267i
$641$	−2.97522	+	5.15324i	−0.117514	+	0.203541i	−0.918782	−	0.394765i	$-0.870826\pi$
$641$	−2.97522	+	5.15324i	−0.117514	+	0.203541i	0.801268	+	0.598306i	$0.204159\pi$
$642$	13.8941	+	29.5733i	0.548355	+	1.16716i
$643$	−31.8448	−	8.53278i	−1.25584	−	0.336500i	−0.431248	−	0.902234i	$-0.641926\pi$
$643$	−31.8448	−	8.53278i	−1.25584	−	0.336500i	−0.824588	+	0.565733i	$0.808593\pi$
$644$	4.44882	−	16.6032i	0.175308	−	0.654258i
$645$	−3.40554	−	45.3944i	−0.134093	−	1.78740i
$646$	34.2107	−	59.2546i	1.34600	−	2.33134i
$647$		−	11.2018i		−	0.440387i	−0.975456	−	0.220194i	$-0.929331\pi$
$647$		−	11.2018i		−	0.440387i	0.975456	−	0.220194i	$-0.0706689\pi$
$648$	0.346846	−	4.57036i	0.0136254	−	0.179541i
$649$		−	41.5814i		−	1.63221i
$650$	−32.3832	−	12.8726i	−1.27017	−	0.504905i
$651$	3.07853	−	0.551975i	0.120657	−	0.0216336i
$652$	18.4129	+	4.93371i	0.721103	+	0.193219i
$653$	−3.65988	−	6.33910i	−0.143222	−	0.248068i	0.785486	−	0.618879i	$-0.212413\pi$
$653$	−3.65988	−	6.33910i	−0.143222	−	0.248068i	−0.928708	+	0.370811i	$0.879080\pi$
$654$	6.73661	−	18.6759i	0.263422	−	0.730285i
$655$	14.2851	+	10.3311i	0.558166	+	0.403669i
$656$	−11.0754	+	11.0754i	−0.432423	+	0.432423i
$657$	−16.1466	−	7.41635i	−0.629939	−	0.289339i
$658$	26.6078	+	26.6078i	1.03728	+	1.03728i
$659$	−16.2946	−	9.40770i	−0.634748	−	0.366472i	0.147841	−	0.989011i	$-0.452768\pi$
$659$	−16.2946	−	9.40770i	−0.634748	−	0.366472i	−0.782589	+	0.622539i	$0.786101\pi$
$660$	−5.39357	+	28.5183i	−0.209944	+	1.11008i
$661$	12.5294	+	3.35726i	0.487339	+	0.130582i	0.494118	−	0.869395i	$-0.335491\pi$
$661$	12.5294	+	3.35726i	0.487339	+	0.130582i	−0.00677886	+	0.999977i	$0.502158\pi$
$662$	25.6130	−	14.7877i	0.995479	−	0.574740i
$663$	9.36247	+	34.3740i	0.363608	+	1.33497i
$664$	−0.746510	+	1.29299i	−0.0289702	+	0.0501779i
$665$	3.89888	−	37.8925i	0.151192	−	1.46941i
$666$	34.5722	+	5.89087i	1.33965	+	0.228267i
$667$	−13.4725			−0.521657
$668$	17.8929	−	4.79438i	0.692296	−	0.185500i
$669$	4.40550	−	2.06979i	0.170327	−	0.0800226i
$670$	2.27736	+	5.08507i	0.0879821	+	0.196453i
$671$	−9.30053	+	34.7101i	−0.359043	+	1.33997i
$672$	35.5645	−	6.37666i	1.37193	−	0.245985i
$673$	2.22086	−	3.84664i	0.0856078	−	0.148277i	−0.820042	−	0.572303i	$-0.806050\pi$
$673$	2.22086	−	3.84664i	0.0856078	−	0.148277i	0.905650	+	0.424026i	$0.139383\pi$
$674$	25.0210	+	25.0210i	0.963773	+	0.963773i
$675$	−25.4812	−	5.07048i	−0.980771	−	0.195163i
$676$	−17.2574	+	14.5538i	−0.663745	+	0.559761i
$677$	2.83091	−	4.90328i	0.108801	−	0.188448i	−0.806484	−	0.591256i	$-0.798632\pi$
$677$	2.83091	−	4.90328i	0.108801	−	0.188448i	0.915285	+	0.402808i	$0.131966\pi$
$678$	23.1928	−	33.3267i	0.890715	−	1.27990i
$679$	13.5996	+	23.5553i	0.521906	+	0.903968i
$680$	−2.31485	+	6.07004i	−0.0887704	+	0.232775i
$681$	11.3317	+	24.1193i	0.434232	+	0.924255i
$682$	1.41996	+	5.29935i	0.0543729	+	0.202923i
$683$	9.53948	−	9.53948i	0.365018	−	0.365018i	−0.500639	−	0.865656i	$-0.666901\pi$
$683$	9.53948	−	9.53948i	0.365018	−	0.365018i	0.865656	+	0.500639i	$0.166901\pi$
$684$	32.1843	−	3.00267i	1.23060	−	0.114810i
$685$	−36.5912	+	29.7637i	−1.39808	+	1.13721i
$686$	−17.1471	+	29.6996i	−0.654678	+	1.13394i
$687$	−3.58443	+	42.3757i	−0.136755	+	1.61673i
$688$	−26.1962	−	45.3731i	−0.998720	−	1.72983i
$689$	4.31173	+	48.5889i	0.164264	+	1.85109i
$690$	−5.01568	+	26.5203i	−0.190944	+	1.00961i
$691$	9.42267	−	2.52480i	0.358455	−	0.0960478i	−0.0750971	−	0.997176i	$-0.523927\pi$
$691$	9.42267	−	2.52480i	0.358455	−	0.0960478i	0.433552	+	0.901128i	$0.357260\pi$
$692$	0.996797			0.0378926
$693$	22.6909	−	27.3605i	0.861955	−	1.03934i
$694$	−48.0525	−	48.0525i	−1.82405	−	1.82405i
$695$	23.5112	−	32.5097i	0.891832	−	1.23316i
$696$	−1.40170	−	2.98349i	−0.0531312	−	0.113089i
$697$	5.18819	−	19.3626i	0.196517	−	0.733411i
$698$	25.3425	+	43.8944i	0.959226	+	1.66143i
$699$	−27.1864	+	4.87448i	−1.02829	+	0.184370i
$700$	−1.35178	−	23.8007i	−0.0510925	−	0.899582i
$701$	−17.4583			−0.659391			−0.329695	−	0.944087i	$-0.606946\pi$
$701$	−17.4583			−0.659391			−0.329695	+	0.944087i	$0.606946\pi$
$702$	−23.0033	+	27.9710i	−0.868202	+	1.05570i
$703$		−	37.5238i		−	1.41524i
$704$	6.44659	+	24.0590i	0.242965	+	0.906758i
$705$	−20.8153	−	17.9101i	−0.783949	−	0.674532i
$706$	48.1481	−	27.7983i	1.81208	−	1.04620i
$707$	−0.993364	+	3.70729i	−0.0373593	+	0.139427i
$708$	−26.2306	+	12.3236i	−0.985805	+	0.463150i
$709$	0.0326216	+	0.121745i	0.00122513	+	0.00457224i	0.966536	−	0.256532i	$-0.0825800\pi$
$709$	0.0326216	+	0.121745i	0.00122513	+	0.00457224i	−0.965311	+	0.261104i	$0.915913\pi$
$710$	−21.1293	−	2.17405i	−0.792967	−	0.0815908i
$711$	−4.48616	+	26.3283i	−0.168244	+	0.987387i
$712$	−3.58844			−0.134482
$713$	0.613682	+	2.29029i	0.0229826	+	0.0857721i
$714$	−40.0746	+	33.8237i	−1.49975	+	1.26582i
$715$	−24.9445	+	24.2544i	−0.932870	+	0.907063i
$716$	−16.6418	+	9.60817i	−0.621934	+	0.359074i
$717$	3.32697	−	39.3319i	0.124248	−	1.46888i
$718$	0.875505	+	0.505473i	0.0326736	+	0.0188641i
$719$	−31.3120			−1.16774			−0.583870	−	0.811847i	$-0.698462\pi$
$719$	−31.3120			−1.16774			−0.583870	+	0.811847i	$0.698462\pi$
$720$	−28.9553	+	7.46430i	−1.07910	+	0.278178i
$721$	−16.1914	−	16.1914i	−0.602998	−	0.602998i
$722$	−9.75495	−	36.4060i	−0.363042	−	1.35489i
$723$	−9.93701	+	4.66860i	−0.369561	+	0.173627i
$724$	8.19228	+	14.1894i	0.304464	+	0.527346i
$725$	−17.7449	+	5.85161i	−0.659028	+	0.217323i
$726$	20.9491	+	14.5790i	0.777493	+	0.541076i
$727$	−16.0747	+	27.8422i	−0.596177	+	1.03261i	0.397203	+	0.917731i	$0.369981\pi$
$727$	−16.0747	+	27.8422i	−0.596177	+	1.03261i	−0.993380	+	0.114878i	$0.963352\pi$
$728$	4.57181	+	2.12497i	0.169442	+	0.0787565i
$729$	−13.0939	+	23.6125i	−0.484960	+	0.874537i
$730$	−2.62026	+	25.4659i	−0.0969804	+	0.942535i
$731$	58.0688	+	33.5261i	2.14775	+	1.24001i
$732$	24.6524	−	4.42013i	0.911179	−	0.163373i
$733$	46.9561	+	12.5818i	1.73436	+	0.464721i	0.981181	−	0.193091i	$-0.0618513\pi$
$733$	46.9561	+	12.5818i	1.73436	+	0.464721i	0.753182	+	0.657812i	$0.228518\pi$
$734$	22.1634	+	5.93868i	0.818068	+	0.219201i
$735$	−0.904335	+	1.87826i	−0.0333569	+	0.0692807i
$736$	7.08953	+	26.4585i	0.261323	+	0.975272i
$737$	5.56285			0.204910
$738$	19.1076	−	7.07951i	0.703360	−	0.260600i
$739$	−16.7699	+	16.7699i	−0.616892	+	0.616892i	−0.944733	−	0.327841i	$-0.893679\pi$
$739$	−16.7699	+	16.7699i	−0.616892	+	0.616892i	0.327841	+	0.944733i	$0.393679\pi$
$740$	−3.72429	−	23.1859i	−0.136908	−	0.852330i
$741$	33.6366	+	19.2357i	1.23567	+	0.706641i
$742$	−62.1826	+	35.9011i	−2.28280	+	1.31797i
$743$	−6.35670	+	23.7235i	−0.233205	+	0.870331i	0.745745	+	0.666231i	$0.232094\pi$
$743$	−6.35670	+	23.7235i	−0.233205	+	0.870331i	−0.978950	+	0.204100i	$0.934573\pi$
$744$	−0.443337	+	0.374186i	−0.0162535	+	0.0137183i
$745$	1.28734	+	8.01447i	0.0471647	+	0.293627i
$746$	−32.5254	+	32.5254i	−1.19084	+	1.19084i
$747$	7.17520	−	5.08598i	0.262527	−	0.186086i
$748$	−30.2296	−	30.2296i	−1.10530	−	1.10530i
$749$	−25.8817	+	6.93498i	−0.945696	+	0.253399i
$750$	4.91251	+	37.1089i	0.179380	+	1.35502i
$751$	−2.07588	+	1.19851i	−0.0757499	+	0.0437342i	−0.537397	−	0.843330i	$-0.680592\pi$
$751$	−2.07588	+	1.19851i	−0.0757499	+	0.0437342i	0.461647	+	0.887064i	$0.347259\pi$
$752$	−30.5274	−	8.17979i	−1.11322	−	0.298286i
$753$	0.261706	+	1.45961i	0.00953710	+	0.0531912i
$754$	−4.49085	+	25.6549i	−0.163547	+	0.934298i
$755$	−16.0586	+	13.0623i	−0.584432	+	0.475385i
$756$	−23.9846	−	6.20504i	−0.872313	−	0.225675i
$757$			33.9141i			1.23263i	0.787500	+	0.616315i	$0.211375\pi$
$757$			33.9141i			1.23263i	−0.787500	+	0.616315i	$0.788625\pi$
$758$	8.47497	+	4.89302i	0.307825	+	0.177723i
$759$	22.1184	+	15.3927i	0.802847	+	0.558720i
$760$	2.88802	+	6.44860i	0.104760	+	0.233915i
$761$	1.73420	−	6.47214i	0.0628648	−	0.234615i	−0.927344	−	0.374211i	$-0.877914\pi$
$761$	1.73420	−	6.47214i	0.0628648	−	0.234615i	0.990209	+	0.139596i	$0.0445804\pi$
$762$	−18.8322	−	40.0839i	−0.682217	−	1.45209i
$763$	14.0998	+	8.14052i	0.510447	+	0.294707i
$764$	−3.33787			−0.120760
$765$	27.3160	−	26.8016i	0.987612	−	0.969014i
$766$		−	22.0081i		−	0.795183i
$767$	−34.2208	−	5.99029i	−1.23564	−	0.216297i
$768$	−25.6129	+	21.6178i	−0.924225	+	0.780065i
$769$	−2.72783	+	10.1804i	−0.0983682	+	0.367115i	−0.997509	−	0.0705452i	$-0.977526\pi$
$769$	−2.72783	+	10.1804i	−0.0983682	+	0.367115i	0.899140	+	0.437660i	$0.144193\pi$
$770$	−47.8516	−	18.2485i	−1.72445	−	0.657630i
$771$	−26.8724	−	31.8385i	−0.967785	−	1.14664i
$772$	−3.17360	−	11.8440i	−0.114220	−	0.426276i
$773$	−16.0666	−	16.0666i	−0.577874	−	0.577874i	0.356443	−	0.934317i	$-0.383989\pi$
$773$	−16.0666	−	16.0666i	−0.577874	−	0.577874i	−0.934317	+	0.356443i	$0.883989\pi$
$774$	6.33161	+	67.8656i	0.227585	+	2.43938i
$775$	1.80305	+	2.75004i	0.0647676	+	0.0987845i
$776$	−4.36925	−	2.52259i	−0.156847	−	0.0905556i
$777$	−9.75846	+	27.0534i	−0.350083	+	0.970534i
$778$	−0.132983	+	0.496299i	−0.00476767	+	0.0177932i
$779$	−10.9012	−	18.8814i	−0.390575	−	0.676496i
$780$	22.6932	+	8.54722i	0.812545	+	0.306040i
$781$	−10.6035	+	18.3657i	−0.379422	+	0.657178i
$782$	−28.1116	−	28.1116i	−1.00527	−	1.00527i
$783$	0.167786	+	19.4171i	0.00599616	+	0.693911i
$784$			2.39925i			0.0856876i
$785$	−21.0102	−	15.1947i	−0.749885	−	0.542321i
$786$	−21.6663	−	15.0781i	−0.772813	−	0.537819i
$787$	3.09793	−	11.5616i	0.110429	−	0.412128i	−0.888475	−	0.458925i	$-0.848235\pi$
$787$	3.09793	−	11.5616i	0.110429	−	0.412128i	0.998904	+	0.0467971i	$0.0149014\pi$
$788$	−4.95589	−	1.32793i	−0.176546	−	0.0473054i
$789$	−0.271348	−	0.0978786i	−0.00966026	−	0.00348457i
$790$	37.9930	−	6.10272i	1.35173	−	0.217125i
$791$	23.5439	+	23.5439i	0.837126	+	0.837126i
$792$	−1.10749	+	6.49961i	−0.0393529	+	0.230953i
$793$	27.2260	+	12.6546i	0.966823	+	0.449378i
$794$	−15.6100	−	9.01242i	−0.553977	−	0.319839i
$795$	43.2908	−	29.5203i	1.53537	−	1.04698i
$796$	1.97316	+	3.41762i	0.0699369	+	0.121134i
$797$	−8.18273	+	4.72430i	−0.289847	+	0.167343i	−0.637873	−	0.770142i	$-0.720185\pi$
$797$	−8.18273	+	4.72430i	−0.289847	+	0.167343i	0.348026	+	0.937485i	$0.386852\pi$
$798$	−4.80736	+	56.8333i	−0.170179	+	2.01188i
$799$	39.0692	−	10.4686i	1.38217	−	0.370351i
$800$	20.8297	+	31.7697i	0.736441	+	1.12323i
$801$	19.2090	+	8.82296i	0.678718	+	0.311744i
$802$			20.2965i			0.716696i
$803$	22.1352	+	12.7797i	0.781133	+	0.450988i
$804$	−1.64868	−	3.50919i	−0.0581445	−	0.123759i
$805$	−20.6807	−	7.88670i	−0.728898	−	0.277970i
$806$	4.56584	−	0.405168i	0.160825	−	0.0142715i
$807$	−3.12356	+	0.560048i	−0.109954	+	0.0197146i
$808$	−0.184259	−	0.687663i	−0.00648220	−	0.0241919i
$809$		−	31.8281i		−	1.11902i	−0.828824	−	0.559509i	$-0.810990\pi$
$809$		−	31.8281i		−	1.11902i	0.828824	−	0.559509i	$-0.189010\pi$
$810$	38.2846	+	6.89852i	1.34518	+	0.242389i
$811$	28.7510	+	28.7510i	1.00958	+	1.00958i	0.999954	+	0.00962961i	$0.00306525\pi$
$811$	28.7510	+	28.7510i	1.00958	+	1.00958i	0.00962961	+	0.999954i	$0.496935\pi$
$812$	−17.2100	+	4.61141i	−0.603954	+	0.161829i
$813$	−21.1102	−	14.6911i	−0.740368	−	0.515240i
$814$	−48.7294	−	13.0570i	−1.70796	−	0.457647i
$815$	8.74631	−	22.9347i	0.306370	−	0.803369i
$816$	14.9448	−	41.4314i	0.523172	−	1.45039i
$817$	70.4433	−	18.8752i	2.46450	−	0.660360i
$818$			1.78131i			0.0622819i
$819$	−19.2484	−	22.6158i	−0.672592	−	0.790261i
$820$	−8.60982	−	10.5848i	−0.300668	−	0.369638i
$821$	−0.261502	−	0.975938i	−0.00912648	−	0.0340605i	0.961212	−	0.275809i	$-0.0889457\pi$
$821$	−0.261502	−	0.975938i	−0.00912648	−	0.0340605i	−0.970339	+	0.241749i	$0.922279\pi$
$822$	53.9704	−	45.5521i	1.88244	−	1.58881i
$823$	−3.43202	−	5.94443i	−0.119633	−	0.207210i	0.799990	−	0.600014i	$-0.204838\pi$
$823$	−3.43202	−	5.94443i	−0.119633	−	0.207210i	−0.919622	+	0.392804i	$0.871505\pi$
$824$	4.10262	+	1.09929i	0.142922	+	0.0382958i
$825$	35.8182	+	10.6672i	1.24703	+	0.371384i
$826$	−13.2355	−	49.3954i	−0.460520	−	1.71869i
$827$	−7.53747	+	7.53747i	−0.262103	+	0.262103i	−0.825908	−	0.563805i	$-0.809337\pi$
$827$	−7.53747	+	7.53747i	−0.262103	+	0.262103i	0.563805	+	0.825908i	$0.309337\pi$
$828$	3.15480	−	18.5148i	0.109637	−	0.643434i
$829$		−	30.6559i		−	1.06472i	−0.846517	−	0.532361i	$-0.821305\pi$
$829$		−	30.6559i		−	1.06472i	0.846517	−	0.532361i	$-0.178695\pi$
$830$	−10.2678	−	7.42572i	−0.356400	−	0.257751i
$831$	41.5061	+	14.9717i	1.43983	+	0.519364i
$832$	20.7289	−	1.83946i	0.718646	−	0.0637719i
$833$	−1.53529	−	2.65920i	−0.0531946	−	0.0921358i
$834$	−34.3144	+	49.3077i	−1.18821	+	1.70739i
$835$	−3.78291	−	23.5508i	−0.130913	−	0.815009i
$836$	−46.4976			−1.60815
$837$	3.29322	−	0.912986i	0.113830	−	0.0315574i
$838$	17.1078	−	17.1078i	0.590978	−	0.590978i
$839$	1.30473	−	0.349602i	0.0450444	−	0.0120696i	−0.236226	−	0.971698i	$-0.575911\pi$
$839$	1.30473	−	0.349602i	0.0450444	−	0.0120696i	0.281271	+	0.959628i	$0.409244\pi$
$840$	−0.405136	−	5.40029i	−0.0139785	−	0.186328i
$841$	−7.51756	−	13.0208i	−0.259226	−	0.448993i
$842$	−15.5228	+	8.96211i	−0.534952	+	0.308855i
$843$	7.30350	+	15.5454i	0.251546	+	0.535410i
$844$	−26.6302	−	15.3750i	−0.916651	−	0.529228i
$845$	16.3675	+	24.0230i	0.563058	+	0.826418i
$846$	31.6483	+	26.2469i	1.08809	+	0.902386i
$847$	−14.7997	+	14.7997i	−0.508523	+	0.508523i
$848$	30.1530	−	52.2266i	1.03546	−	1.79347i
$849$	23.8607	−	20.1389i	0.818897	−	0.691165i
$850$	−49.2363	−	24.8164i	−1.68879	−	0.851196i
$851$	−21.0600	−	5.64302i	−0.721929	−	0.193440i
$852$	14.7281	+	1.24581i	0.504578	+	0.0426807i
$853$	19.2515	−	5.15844i	0.659160	−	0.176621i	0.0862932	−	0.996270i	$-0.472498\pi$
$853$	19.2515	−	5.15844i	0.659160	−	0.176621i	0.572867	+	0.819648i	$0.305831\pi$
$854$			44.1932i			1.51226i
$855$	0.395623	−	41.6205i	0.0135300	−	1.42339i
$856$	3.51442	−	3.51442i	0.120120	−	0.120120i
$857$	41.8798	+	24.1793i	1.43059	+	0.825950i	0.997165	−	0.0752406i	$-0.0239725\pi$
$857$	41.8798	+	24.1793i	1.43059	+	0.825950i	0.433422	+	0.901191i	$0.357306\pi$
$858$	36.6844	−	36.9880i	1.25238	−	1.26275i
$859$	12.1450	+	21.0358i	0.414383	+	0.717733i	0.995363	−	0.0961847i	$-0.0306640\pi$
$859$	12.1450	+	21.0358i	0.414383	+	0.717733i	−0.580980	+	0.813918i	$0.697331\pi$
$860$	41.6534	−	18.6546i	1.42037	−	0.636116i
$861$	2.94906	+	16.4478i	0.100504	+	0.560540i
$862$	−6.89327	+	11.9395i	−0.234786	+	0.406661i
$863$	1.98375	+	1.98375i	0.0675275	+	0.0675275i	0.740064	−	0.672536i	$-0.234795\pi$
$863$	1.98375	+	1.98375i	0.0675275	+	0.0675275i	−0.672536	+	0.740064i	$0.734795\pi$
$864$	38.0448	−	10.5472i	1.29431	−	0.358824i
$865$	0.131373	−	1.27679i	0.00446683	−	0.0434123i
$866$	47.0071	−	12.5955i	1.59736	−	0.428013i
$867$	4.75155	+	26.5008i	0.161371	+	0.900014i
$868$	1.56786	+	2.71561i	0.0532166	+	0.0921739i
$869$	9.94347	−	37.1095i	0.337309	−	1.25885i
$870$	26.4061	−	9.24231i	0.895252	−	0.313344i
$871$	0.801394	−	4.57814i	0.0271542	−	0.155124i
$872$	−3.01996			−0.102269
$873$	17.1864	+	24.2463i	0.581672	+	0.820612i
$874$	−43.2398			−1.46261
$875$	−30.6644	−	1.40533i	−1.03665	−	0.0475089i
$876$	1.50150	−	17.7510i	0.0507311	−	0.599751i
$877$	6.51757	+	1.74638i	0.220083	+	0.0589710i	0.367175	−	0.930152i	$-0.380325\pi$
$877$	6.51757	+	1.74638i	0.220083	+	0.0589710i	−0.147093	+	0.989123i	$0.546992\pi$
$878$	−20.8849	−	5.59610i	−0.704833	−	0.188859i
$879$	−2.52264	+	29.8231i	−0.0850867	+	1.00591i
$880$	42.4690	−	6.82169i	1.43163	−	0.229959i
$881$	−10.2597			−0.345657			−0.172828	−	0.984952i	$-0.555291\pi$
$881$	−10.2597			−0.345657			−0.172828	+	0.984952i	$0.555291\pi$
$882$	1.30281	−	2.83644i	0.0438680	−	0.0955078i
$883$	−12.9441			−0.435604			−0.217802	−	0.975993i	$-0.569889\pi$
$883$	−12.9441			−0.435604			−0.217802	+	0.975993i	$0.569889\pi$
$884$	−29.2334	+	20.5235i	−0.983226	+	0.690282i
$885$	12.3282	+	35.2228i	0.414408	+	1.18400i
$886$	−16.0685	+	59.9686i	−0.539833	+	2.01468i
$887$	−15.3790	−	26.6372i	−0.516376	−	0.894389i	−0.999819	−	0.0190132i	$-0.993948\pi$
$887$	−15.3790	−	26.6372i	−0.516376	−	0.894389i	0.483444	−	0.875375i	$-0.339386\pi$
$888$	−0.941471	−	5.25086i	−0.0315937	−	0.176207i
$889$	35.0803	−	9.39974i	1.17656	−	0.315257i
$890$	3.11724	−	30.2959i	0.104490	−	1.01552i
$891$	21.9091	−	32.0696i	0.733984	−	1.07437i
$892$	3.45075	+	3.45075i	0.115540	+	0.115540i
$893$	21.9960	−	38.0982i	0.736068	−	1.27491i
$894$	−2.14497	−	11.9632i	−0.0717386	−	0.400108i
$895$	10.1138	+	22.5828i	0.338065	+	0.754859i
$896$	−5.54453	−	9.60342i	−0.185230	−	0.320828i
$897$	15.8544	−	15.9856i	0.529362	−	0.533743i
$898$	−29.3695	−	16.9565i	−0.980072	−	0.565845i
$899$	1.73789	−	1.73789i	0.0579618	−	0.0579618i
$900$	−3.88644	−	25.7565i	−0.129548	−	0.858550i
$901$			77.1801i			2.57124i
$902$	−28.3131	+	7.58647i	−0.942723	+	0.252602i
$903$	−55.6959	−	4.71115i	−1.85344	−	0.156777i
$904$	−5.96564	−	1.59849i	−0.198414	−	0.0531649i
$905$	19.2549	−	8.62336i	0.640055	−	0.286650i
$906$	23.6858	−	19.9913i	0.786907	−	0.664165i
$907$	18.0844	−	31.3231i	0.600482	−	1.04007i	−0.392266	−	0.919852i	$-0.628309\pi$
$907$	18.0844	−	31.3231i	0.600482	−	1.04007i	0.992748	−	0.120214i	$-0.0383579\pi$
$908$	−18.8922	+	18.8922i	−0.626961	+	0.626961i
$909$	−0.704427	+	4.13412i	−0.0233644	+	0.137120i
$910$	−21.9118	+	36.7522i	−0.726370	+	1.21832i
$911$	−38.6704	−	22.3264i	−1.28121	−	0.739705i	−0.304138	−	0.952628i	$-0.598368\pi$
$911$	−38.6704	−	22.3264i	−1.28121	−	0.739705i	−0.977069	+	0.212923i	$0.931702\pi$
$912$	−20.3701	−	43.3574i	−0.674523	−	1.43571i
$913$	−10.9564	+	6.32568i	−0.362604	+	0.209349i
$914$	−6.64279	−	11.5057i	−0.219724	−	0.380573i
$915$	−2.41266	−	32.1597i	−0.0797602	−	1.06317i
$916$	−41.1843	+	11.0353i	−1.36077	+	0.364617i
$917$	15.3064	−	15.3064i	0.505461	−	0.505461i
$918$	−40.1655	+	40.8657i	−1.32566	+	1.34877i
$919$	46.1793			1.52331			0.761657	−	0.647981i	$-0.224386\pi$
$919$	46.1793			1.52331			0.761657	+	0.647981i	$0.224386\pi$
$920$	4.05356	−	0.651114i	0.133642	−	0.0214666i
$921$	−17.0046	+	24.4346i	−0.560322	+	0.805148i
$922$	10.7821	+	18.6751i	0.355090	+	0.615033i
$923$	13.5872	+	11.3723i	0.447227	+	0.374323i
$924$	33.5232	+	12.0922i	1.10283	+	0.397804i
$925$	−30.1896	+	1.71464i	−0.992627	+	0.0563770i
$926$		−	47.9535i		−	1.57585i
$927$	−19.2586	−	15.9718i	−0.632537	−	0.524582i
$928$	20.0769	−	20.0769i	0.659055	−	0.659055i
$929$	3.41425	+	12.7422i	0.112018	+	0.418057i	0.999047	−	0.0436576i	$-0.0139011\pi$
$929$	3.41425	+	12.7422i	0.112018	+	0.418057i	−0.887028	+	0.461715i	$0.847234\pi$
$930$	−2.77399	−	4.06799i	−0.0909628	−	0.133395i
$931$	−3.22587	−	0.864370i	−0.105724	−	0.0283286i
$932$	−13.8458	−	23.9815i	−0.453533	−	0.785542i
$933$	6.71903	−	5.67100i	0.219971	−	0.185660i
$934$	10.8090	+	40.3396i	0.353680	+	1.31995i
$935$	−42.7051	+	34.7368i	−1.39661	+	1.13602i
$936$	5.18953	+	1.84779i	0.169625	+	0.0603969i
$937$		−	50.4598i		−	1.64845i	−0.566262	−	0.824225i	$-0.691611\pi$
$937$		−	50.4598i		−	1.64845i	0.566262	−	0.824225i	$-0.308389\pi$
$938$	6.60823	−	1.77067i	0.215766	−	0.0578144i
$939$	−14.4910	+	40.1735i	−0.472898	+	1.31101i
$940$	9.80999	−	25.7239i	0.319967	−	0.839023i
$941$	10.9342	+	2.92980i	0.356444	+	0.0955088i	0.432597	−	0.901587i	$-0.357597\pi$
$941$	10.9342	+	2.92980i	0.356444	+	0.0955088i	−0.0761535	+	0.997096i	$0.524264\pi$
$942$	31.8663	+	22.1765i	1.03826	+	0.722549i
$943$	−12.2365	+	3.27875i	−0.398474	+	0.106771i
$944$	30.3704	+	30.3704i	0.988472	+	0.988472i
$945$	−11.1091	+	29.9040i	−0.361379	+	0.972779i
$946$		−	98.0474i		−	3.18780i
$947$	−3.21958	−	12.0156i	−0.104622	−	0.390456i	0.893680	−	0.448705i	$-0.148115\pi$
$947$	−3.21958	−	12.0156i	−0.104622	−	0.390456i	−0.998302	+	0.0582496i	$0.981448\pi$
$948$	−26.3566	+	4.72569i	−0.856022	+	0.153483i
$949$	13.7064	−	16.3758i	0.444928	−	0.531582i
$950$	−56.9520	+	18.7807i	−1.84777	+	0.609326i
$951$	−5.73266	−	12.2019i	−0.185894	−	0.395672i
$952$	6.90808	+	3.98838i	0.223892	+	0.129264i
$953$		−	42.1762i		−	1.36622i	−0.730315	−	0.683110i	$-0.760627\pi$
$953$		−	42.1762i		−	1.36622i	0.730315	−	0.683110i	$-0.239373\pi$
$954$	−64.0068	+	45.3698i	−2.07230	+	1.46890i
$955$	−0.439915	+	4.27546i	−0.0142353	+	0.138351i
$956$	38.2261	−	10.2427i	1.23632	−	0.331271i
$957$	2.35430	−	27.8328i	0.0761036	−	0.899707i
$958$	−14.7736	+	8.52952i	−0.477312	+	0.275576i
$959$	28.9577	+	50.1563i	0.935094	+	1.61963i
$960$	−12.5939	−	18.4687i	−0.406467	−	0.596073i
$961$	26.4722	+	15.2837i	0.853942	+	0.493023i
$962$	−17.7657	+	38.2225i	−0.572791	+	1.23234i
$963$	−27.4538	+	10.1718i	−0.884685	+	0.327783i
$964$	−7.78348	−	7.78348i	−0.250689	−	0.250689i
$965$	−15.5893	+	2.50407i	−0.501836	+	0.0806087i
$966$	31.1744	+	11.2450i	1.00302	+	0.361801i
$967$	−45.2322	−	12.1199i	−1.45457	−	0.389751i	−0.556958	−	0.830540i	$-0.688032\pi$
$967$	−45.2322	−	12.1199i	−1.45457	−	0.389751i	−0.897610	+	0.440790i	$0.854698\pi$
$968$	1.00481	−	3.74999i	0.0322957	−	0.120529i
$969$	50.3217	+	35.0201i	1.61657	+	1.12501i
$970$	25.0928	−	34.6967i	0.805682	−	1.11404i
$971$		−	30.9429i		−	0.993006i	−0.868035	−	0.496503i	$-0.834617\pi$
$971$		−	30.9429i		−	0.993006i	0.868035	−	0.496503i	$-0.165383\pi$
$972$	−26.7236	−	4.31624i	−0.857160	−	0.138444i
$973$	−34.8339	−	34.8339i	−1.11672	−	1.11672i
$974$	19.5565	−	33.8728i	0.626629	−	1.08535i
$975$	13.9390	−	27.9411i	0.446404	−	0.894831i
$976$	−18.5587	−	32.1447i	−0.594050	−	1.02893i
$977$	13.5500	−	50.5694i	0.433503	−	1.61786i	−0.311119	−	0.950371i	$-0.600704\pi$
$977$	13.5500	−	50.5694i	0.433503	−	1.61786i	0.744622	−	0.667486i	$-0.232630\pi$
$978$	−12.4706	+	34.5723i	−0.398767	+	1.10550i
$979$	−26.3334	−	15.2036i	−0.841620	−	0.485910i
$980$	−2.07905	−	0.213920i	−0.0664129	−	0.00683343i
$981$	16.1660	+	7.42524i	0.516140	+	0.237070i
$982$	59.2280	+	59.2280i	1.89004	+	1.89004i
$983$	−4.41886	−	16.4914i	−0.140940	−	0.525995i	−0.999903	−	0.0139565i	$-0.995557\pi$
$983$	−4.41886	−	16.4914i	−0.140940	−	0.525995i	0.858963	−	0.512038i	$-0.171109\pi$
$984$	−1.99918	−	2.36864i	−0.0637315	−	0.0755095i
$985$	−2.35410	+	6.17296i	−0.0750078	+	0.196687i
$986$	−10.6656	+	39.8047i	−0.339663	+	1.26764i
$987$	−25.7662	+	21.7472i	−0.820148	+	0.692221i
$988$	−6.69852	+	38.2668i	−0.213108	+	1.21743i
$989$		−	42.3745i		−	1.34743i
$990$	−53.9118	−	14.9963i	−1.71343	−	0.476613i
$991$	−17.1097			−0.543508			−0.271754	−	0.962367i	$-0.587604\pi$
$991$	−17.1097			−0.543508			−0.271754	+	0.962367i	$0.587604\pi$
$992$	−4.32754	−	2.49850i	−0.137399	−	0.0793276i
$993$	11.2688	+	23.9854i	0.357604	+	0.761153i
$994$	−6.75022	+	25.1921i	−0.214104	+	0.799046i
$995$	4.63767	−	2.07699i	0.147024	−	0.0658450i
$996$	7.23758	+	5.03680i	0.229332	+	0.159597i
$997$	−33.6079	−	19.4035i	−1.06437	−	0.614516i	−0.137735	−	0.990469i	$-0.543982\pi$
$997$	−33.6079	−	19.4035i	−1.06437	−	0.614516i	−0.926639	+	0.375953i	$0.877315\pi$
$998$		−	40.6189i		−	1.28577i
$999$	−7.87067	+	30.4229i	−0.249017	+	0.962537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.dc.a.164.15	✓	320
5.4	even	2	inner	585.2.dc.a.164.66	yes	320
9.5	odd	6	inner	585.2.dc.a.554.15	yes	320
13.5	odd	4	inner	585.2.dc.a.434.66	yes	320
45.14	odd	6	inner	585.2.dc.a.554.66	yes	320
65.44	odd	4	inner	585.2.dc.a.434.15	yes	320
117.5	even	12	inner	585.2.dc.a.239.66	yes	320
585.239	even	12	inner	585.2.dc.a.239.15	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.dc.a.164.15	✓	320	1.1	even	1	trivial
585.2.dc.a.164.66	yes	320	5.4	even	2	inner
585.2.dc.a.239.15	yes	320	585.239	even	12	inner
585.2.dc.a.239.66	yes	320	117.5	even	12	inner
585.2.dc.a.434.15	yes	320	65.44	odd	4	inner
585.2.dc.a.434.66	yes	320	13.5	odd	4	inner
585.2.dc.a.554.15	yes	320	9.5	odd	6	inner
585.2.dc.a.554.66	yes	320	45.14	odd	6	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.dc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86715 + 0.500300i) q^{2} +(-0.305679 - 1.70486i) q^{3} +(1.50389 - 0.868268i) q^{4} +(-0.913957 - 2.04076i) q^{5} +(1.42369 + 3.03030i) q^{6} +(-2.65203 + 0.710610i) q^{7} +(0.360114 - 0.360114i) q^{8} +(-2.81312 + 1.04228i) q^{9} +O(q^{10})\)	\(q+(-1.86715 + 0.500300i) q^{2} +(-0.305679 - 1.70486i) q^{3} +(1.50389 - 0.868268i) q^{4} +(-0.913957 - 2.04076i) q^{5} +(1.42369 + 3.03030i) q^{6} +(-2.65203 + 0.710610i) q^{7} +(0.360114 - 0.360114i) q^{8} +(-2.81312 + 1.04228i) q^{9} +(2.72748 + 3.35314i) q^{10} +(4.16840 - 1.11692i) q^{11} +(-1.93999 - 2.29851i) q^{12} +(-0.318701 - 3.59144i) q^{13} +(4.59622 - 2.65363i) q^{14} +(-3.19983 + 2.18199i) q^{15} +(-2.22876 + 3.86032i) q^{16} -5.70475i q^{17} +(4.73105 - 3.35350i) q^{18} +(-4.38738 - 4.38738i) q^{19} +(-3.14641 - 2.27550i) q^{20} +(2.02217 + 4.30414i) q^{21} +(-7.22423 + 4.17091i) q^{22} +(-3.12219 + 1.80260i) q^{23} +(-0.724024 - 0.503865i) q^{24} +(-3.32936 + 3.73033i) q^{25} +(2.39186 + 6.54630i) q^{26} +(2.63686 + 4.47738i) q^{27} +(-3.37135 + 3.37135i) q^{28} +(3.23630 + 1.86848i) q^{29} +(4.88291 - 5.67497i) q^{30} +(0.170221 - 0.635275i) q^{31} +(1.96647 - 7.33898i) q^{32} +(-3.17839 - 6.76514i) q^{33} +(2.85409 + 10.6516i) q^{34} +(3.87403 + 4.76268i) q^{35} +(-3.32563 + 4.01002i) q^{36} +(4.27633 + 4.27633i) q^{37} +(10.3869 + 5.99687i) q^{38} +(-6.02549 + 1.64117i) q^{39} +(-1.06403 - 0.405775i) q^{40} +(3.39412 + 0.909451i) q^{41} +(-5.92904 - 7.02476i) q^{42} +(-5.87686 + 10.1790i) q^{43} +(5.29901 - 5.29901i) q^{44} +(4.69812 + 4.78829i) q^{45} +(4.92775 - 4.92775i) q^{46} +(1.83506 + 6.84853i) q^{47} +(7.26260 + 2.61971i) q^{48} +(0.466138 - 0.269125i) q^{49} +(4.35013 - 8.63075i) q^{50} +(-9.72583 + 1.74383i) q^{51} +(-3.59762 - 5.12439i) q^{52} -13.5291 q^{53} +(-7.16345 - 7.04071i) q^{54} +(-6.08910 - 7.48588i) q^{55} +(-0.699133 + 1.21093i) q^{56} +(-6.13875 + 8.82101i) q^{57} +(-6.97746 - 1.86960i) q^{58} +(2.49384 - 9.30715i) q^{59} +(-2.91763 + 6.05977i) q^{60} +(-4.16347 + 7.21134i) q^{61} +1.27131i q^{62} +(6.71983 - 4.76320i) q^{63} +5.77176i q^{64} +(-7.03797 + 3.93281i) q^{65} +(9.31913 + 11.0414i) q^{66} +(1.24513 + 0.333632i) q^{67} +(-4.95326 - 8.57929i) q^{68} +(4.02757 + 4.77190i) q^{69} +(-9.61615 - 6.95445i) q^{70} +(-3.47485 + 3.47485i) q^{71} +(-0.637703 + 1.38838i) q^{72} +(4.18804 + 4.18804i) q^{73} +(-10.1240 - 5.84509i) q^{74} +(7.37741 + 4.53583i) q^{75} +(-10.4075 - 2.78869i) q^{76} +(-10.2611 + 5.92422i) q^{77} +(10.4294 - 6.07886i) q^{78} +(4.45129 - 7.70986i) q^{79} +(9.91496 + 1.02018i) q^{80} +(6.82729 - 5.86413i) q^{81} -6.79231 q^{82} +(-2.83175 + 0.758765i) q^{83} +(6.77825 + 4.71714i) q^{84} +(-11.6420 + 5.21390i) q^{85} +(5.88039 - 21.9459i) q^{86} +(2.19623 - 6.08861i) q^{87} +(1.09888 - 1.90332i) q^{88} +(-4.98237 - 4.98237i) q^{89} +(-11.1677 - 6.58997i) q^{90} +(3.39732 + 9.29814i) q^{91} +(-3.13028 + 5.42180i) q^{92} +(-1.13509 - 0.0960139i) q^{93} +(-6.85264 - 11.8691i) q^{94} +(-4.94369 + 12.9634i) q^{95} +(-13.1131 - 1.10920i) q^{96} +(-2.56400 - 9.56898i) q^{97} +(-0.735704 + 0.735704i) q^{98} +(-10.5621 + 7.48669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 6 q^{5} - 16 q^{9}+O(q^{10}) \) 320 * q - 6 * q^5 - 16 * q^9	\( 320 q - 6 q^{5} - 16 q^{9} - 24 q^{11} - 24 q^{14} - 14 q^{15} + 128 q^{16} - 16 q^{19} - 18 q^{20} - 16 q^{21} - 40 q^{24} - 24 q^{29} - 4 q^{31} + 4 q^{34} - 76 q^{39} + 12 q^{40} + 12 q^{41} - 20 q^{45} - 32 q^{46} - 108 q^{50} + 84 q^{54} - 16 q^{55} - 12 q^{59} + 32 q^{60} - 8 q^{61} - 56 q^{66} - 40 q^{70} - 72 q^{74} - 4 q^{76} + 16 q^{79} + 96 q^{84} - 16 q^{85} - 120 q^{86} - 16 q^{91} + 40 q^{94} + 108 q^{96} - 84 q^{99}+O(q^{100}) \) 320 * q - 6 * q^5 - 16 * q^9 - 24 * q^11 - 24 * q^14 - 14 * q^15 + 128 * q^16 - 16 * q^19 - 18 * q^20 - 16 * q^21 - 40 * q^24 - 24 * q^29 - 4 * q^31 + 4 * q^34 - 76 * q^39 + 12 * q^40 + 12 * q^41 - 20 * q^45 - 32 * q^46 - 108 * q^50 + 84 * q^54 - 16 * q^55 - 12 * q^59 + 32 * q^60 - 8 * q^61 - 56 * q^66 - 40 * q^70 - 72 * q^74 - 4 * q^76 + 16 * q^79 + 96 * q^84 - 16 * q^85 - 120 * q^86 - 16 * q^91 + 40 * q^94 + 108 * q^96 - 84 * q^99

Introduction

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