LMFDB - Embedded newform 560.2.t.a.43.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

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

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

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.11
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29547 - 0.567247i) q^{2} +0.154841i q^{3} +(1.35646 + 1.46970i) q^{4} +(-0.497515 - 2.18002i) q^{5} +(0.0878329 - 0.200591i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.923567 - 2.67339i) q^{8} +2.97602 q^{9} +O(q^{10})$	\(q+(-1.29547 - 0.567247i) q^{2} +0.154841i q^{3} +(1.35646 + 1.46970i) q^{4} +(-0.497515 - 2.18002i) q^{5} +(0.0878329 - 0.200591i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.923567 - 2.67339i) q^{8} +2.97602 q^{9} +(-0.592095 + 3.10635i) q^{10} +(0.532976 - 0.532976i) q^{11} +(-0.227569 + 0.210035i) q^{12} +0.714286 q^{13} +(-1.31714 + 0.514928i) q^{14} +(0.337555 - 0.0770356i) q^{15} +(-0.320025 + 3.98718i) q^{16} +(-3.64759 + 3.64759i) q^{17} +(-3.85534 - 1.68814i) q^{18} +(4.12435 - 4.12435i) q^{19} +(2.52911 - 3.68831i) q^{20} +(0.109489 + 0.109489i) q^{21} +(-0.992781 + 0.388123i) q^{22} +(-4.27023 - 4.27023i) q^{23} +(0.413950 - 0.143006i) q^{24} +(-4.50496 + 2.16918i) q^{25} +(-0.925333 - 0.405177i) q^{26} +0.925332i q^{27} +(1.99840 + 0.0800705i) q^{28} +(1.49715 + 1.49715i) q^{29} +(-0.480990 - 0.0916804i) q^{30} -6.38689i q^{31} +(2.67630 - 4.98372i) q^{32} +(0.0825263 + 0.0825263i) q^{33} +(6.79440 - 2.65624i) q^{34} +(-1.89330 - 1.18971i) q^{35} +(4.03686 + 4.37386i) q^{36} +10.5280 q^{37} +(-7.68249 + 3.00343i) q^{38} +0.110600i q^{39} +(-5.36855 + 3.34345i) q^{40} -5.41114i q^{41} +(-0.0797318 - 0.203946i) q^{42} +6.83831 q^{43} +(1.50627 + 0.0603525i) q^{44} +(-1.48062 - 6.48779i) q^{45} +(3.10966 + 7.95421i) q^{46} +(-8.90138 - 8.90138i) q^{47} +(-0.617377 - 0.0495529i) q^{48} -1.00000i q^{49} +(7.06648 - 0.254679i) q^{50} +(-0.564795 - 0.564795i) q^{51} +(0.968901 + 1.04978i) q^{52} -8.74882i q^{53} +(0.524892 - 1.19874i) q^{54} +(-1.42706 - 0.896733i) q^{55} +(-2.54343 - 1.23731i) q^{56} +(0.638618 + 0.638618i) q^{57} +(-1.09025 - 2.78876i) q^{58} +(5.47803 + 5.47803i) q^{59} +(0.571100 + 0.391609i) q^{60} +(-4.98993 + 4.98993i) q^{61} +(-3.62295 + 8.27400i) q^{62} +(2.10437 - 2.10437i) q^{63} +(-6.29405 + 4.93811i) q^{64} +(-0.355368 - 1.55716i) q^{65} +(-0.0600972 - 0.153723i) q^{66} -12.2829 q^{67} +(-10.3087 - 0.413041i) q^{68} +(0.661205 - 0.661205i) q^{69} +(1.77785 + 2.61520i) q^{70} +5.99986 q^{71} +(-2.74856 - 7.95608i) q^{72} +(4.26845 - 4.26845i) q^{73} +(-13.6387 - 5.97199i) q^{74} +(-0.335878 - 0.697551i) q^{75} +(11.6561 + 0.467029i) q^{76} -0.753741i q^{77} +(0.0627378 - 0.143279i) q^{78} -3.77156 q^{79} +(8.85134 - 1.28602i) q^{80} +8.78479 q^{81} +(-3.06945 + 7.00994i) q^{82} -11.6538i q^{83} +(-0.0123982 + 0.309433i) q^{84} +(9.76653 + 6.13707i) q^{85} +(-8.85879 - 3.87901i) q^{86} +(-0.231820 + 0.231820i) q^{87} +(-1.91709 - 0.932614i) q^{88} -5.69680 q^{89} +(-1.76209 + 9.24458i) q^{90} +(0.505076 - 0.505076i) q^{91} +(0.483547 - 12.0684i) q^{92} +0.988950 q^{93} +(6.48215 + 16.5807i) q^{94} +(-11.0431 - 6.93924i) q^{95} +(0.771682 + 0.414400i) q^{96} +(-7.66124 + 7.66124i) q^{97} +(-0.567247 + 1.29547i) q^{98} +(1.58615 - 1.58615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.29547	−	0.567247i	−0.916032	−	0.401104i
$2$	−1.29547	−	0.567247i	−0.916032	−	0.401104i
$3$			0.154841i			0.0893973i	0.999001	+	0.0446986i	$0.0142328\pi$
$3$			0.154841i			0.0893973i	−0.999001	+	0.0446986i	$0.985767\pi$
$4$	1.35646	+	1.46970i	0.678231	+	0.734849i
$5$	−0.497515	−	2.18002i	−0.222496	−	0.974934i
$5$	−0.497515	−	2.18002i	−0.222496	−	0.974934i
$6$	0.0878329	−	0.200591i	0.0358576	−	0.0818908i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−0.923567	−	2.67339i	−0.326530	−	0.945187i
$9$	2.97602			0.992008
$10$	−0.592095	+	3.10635i	−0.187237	+	0.982315i
$11$	0.532976	−	0.532976i	0.160698	−	0.160698i	−0.622178	−	0.782876i	$-0.713752\pi$
$11$	0.532976	−	0.532976i	0.160698	−	0.160698i	0.782876	+	0.622178i	$0.213752\pi$
$12$	−0.227569	+	0.210035i	−0.0656935	+	0.0606320i
$13$	0.714286			0.198107			0.0990536	−	0.995082i	$-0.468418\pi$
$13$	0.714286			0.198107			0.0990536	+	0.995082i	$0.468418\pi$
$14$	−1.31714	+	0.514928i	−0.352020	+	0.137620i
$15$	0.337555	−	0.0770356i	0.0871564	−	0.0198905i
$16$	−0.320025	+	3.98718i	−0.0800063	+	0.996794i
$17$	−3.64759	+	3.64759i	−0.884670	+	0.884670i	−0.994005	−	0.109335i	$-0.965128\pi$
$17$	−3.64759	+	3.64759i	−0.884670	+	0.884670i	0.109335	+	0.994005i	$0.465128\pi$
$18$	−3.85534	−	1.68814i	−0.908712	−	0.397899i
$19$	4.12435	−	4.12435i	0.946192	−	0.946192i	−0.0524327	−	0.998624i	$-0.516698\pi$
$19$	4.12435	−	4.12435i	0.946192	−	0.946192i	0.998624	+	0.0524327i	$0.0166975\pi$
$20$	2.52911	−	3.68831i	0.565526	−	0.824731i
$21$	0.109489	+	0.109489i	0.0238924	+	0.0238924i
$22$	−0.992781	+	0.388123i	−0.211662	+	0.0827480i
$23$	−4.27023	−	4.27023i	−0.890405	−	0.890405i	0.104156	−	0.994561i	$-0.466786\pi$
$23$	−4.27023	−	4.27023i	−0.890405	−	0.890405i	−0.994561	+	0.104156i	$0.966786\pi$
$24$	0.413950	−	0.143006i	0.0844971	−	0.0291909i
$25$	−4.50496	+	2.16918i	−0.900991	+	0.433837i
$26$	−0.925333	−	0.405177i	−0.181473	−	0.0794617i
$27$			0.925332i			0.178080i
$28$	1.99840	+	0.0800705i	0.377661	+	0.0151319i
$29$	1.49715	+	1.49715i	0.278014	+	0.278014i	0.832316	−	0.554302i	$-0.187015\pi$
$29$	1.49715	+	1.49715i	0.278014	+	0.278014i	−0.554302	+	0.832316i	$0.687015\pi$
$30$	−0.480990	−	0.0916804i	−0.0878163	−	0.0167385i
$31$		−	6.38689i		−	1.14712i	−0.819164	−	0.573560i	$-0.805562\pi$
$31$		−	6.38689i		−	1.14712i	0.819164	−	0.573560i	$-0.194438\pi$
$32$	2.67630	−	4.98372i	0.473107	−	0.881005i
$33$	0.0825263	+	0.0825263i	0.0143660	+	0.0143660i
$34$	6.79440	−	2.65624i	1.16523	−	0.455541i
$35$	−1.89330	−	1.18971i	−0.320026	−	0.201098i
$36$	4.03686	+	4.37386i	0.672810	+	0.728976i
$37$	10.5280			1.73080			0.865398	−	0.501085i	$-0.167066\pi$
$37$	10.5280			1.73080			0.865398	+	0.501085i	$0.167066\pi$
$38$	−7.68249	+	3.00343i	−1.24626	+	0.487221i
$39$			0.110600i			0.0177103i
$40$	−5.36855	+	3.34345i	−0.848843	+	0.528645i
$41$		−	5.41114i		−	0.845078i	−0.906345	−	0.422539i	$-0.861139\pi$
$41$		−	5.41114i		−	0.845078i	0.906345	−	0.422539i	$-0.138861\pi$
$42$	−0.0797318	−	0.203946i	−0.0123029	−	0.0314696i
$43$	6.83831			1.04283			0.521416	−	0.853303i	$-0.325404\pi$
$43$	6.83831			1.04283			0.521416	+	0.853303i	$0.325404\pi$
$44$	1.50627	+	0.0603525i	0.227079	+	0.00909848i
$45$	−1.48062	−	6.48779i	−0.220717	−	0.967142i
$46$	3.10966	+	7.95421i	0.458494	+	1.17278i
$47$	−8.90138	−	8.90138i	−1.29840	−	1.29840i	−0.929449	−	0.368950i	$-0.879717\pi$
$47$	−8.90138	−	8.90138i	−1.29840	−	1.29840i	−0.368950	−	0.929449i	$-0.620283\pi$
$48$	−0.617377	−	0.0495529i	−0.0891107	−	0.00715235i
$49$		−	1.00000i		−	0.142857i
$50$	7.06648	−	0.254679i	0.999351	−	0.0360171i
$51$	−0.564795	−	0.564795i	−0.0790871	−	0.0790871i
$52$	0.968901	+	1.04978i	0.134362	+	0.145579i
$53$		−	8.74882i		−	1.20174i	−0.799346	−	0.600872i	$-0.794820\pi$
$53$		−	8.74882i		−	1.20174i	0.799346	−	0.600872i	$-0.205180\pi$
$54$	0.524892	−	1.19874i	0.0714287	−	0.163127i
$55$	−1.42706	−	0.896733i	−0.192425	−	0.120915i
$56$	−2.54343	−	1.23731i	−0.339881	−	0.165343i
$57$	0.638618	+	0.638618i	0.0845870	+	0.0845870i
$58$	−1.09025	−	2.78876i	−0.143157	−	0.366183i
$59$	5.47803	+	5.47803i	0.713178	+	0.713178i	0.967199	−	0.254020i	$-0.0817530\pi$
$59$	5.47803	+	5.47803i	0.713178	+	0.713178i	−0.254020	+	0.967199i	$0.581753\pi$
$60$	0.571100	+	0.391609i	0.0737287	+	0.0505565i
$61$	−4.98993	+	4.98993i	−0.638896	+	0.638896i	−0.950283	−	0.311387i	$-0.899206\pi$
$61$	−4.98993	+	4.98993i	−0.638896	+	0.638896i	0.311387	+	0.950283i	$0.399206\pi$
$62$	−3.62295	+	8.27400i	−0.460115	+	1.05080i
$63$	2.10437	−	2.10437i	0.265125	−	0.265125i
$64$	−6.29405	+	4.93811i	−0.786756	+	0.617264i
$65$	−0.355368	−	1.55716i	−0.0440780	−	0.193141i
$66$	−0.0600972	−	0.153723i	−0.00739745	−	0.0189220i
$67$	−12.2829			−1.50059			−0.750297	−	0.661101i	$-0.770089\pi$
$67$	−12.2829			−1.50059			−0.750297	+	0.661101i	$0.770089\pi$
$68$	−10.3087	−	0.413041i	−1.25011	−	0.0500886i
$69$	0.661205	−	0.661205i	0.0795998	−	0.0795998i
$70$	1.77785	+	2.61520i	0.212493	+	0.312576i
$71$	5.99986			0.712053			0.356026	−	0.934476i	$-0.384131\pi$
$71$	5.99986			0.712053			0.356026	+	0.934476i	$0.384131\pi$
$72$	−2.74856	−	7.95608i	−0.323921	−	0.937633i
$73$	4.26845	−	4.26845i	0.499584	−	0.499584i	−0.411725	−	0.911308i	$-0.635073\pi$
$73$	4.26845	−	4.26845i	0.499584	−	0.499584i	0.911308	+	0.411725i	$0.135073\pi$
$74$	−13.6387	−	5.97199i	−1.58547	−	0.694230i
$75$	−0.335878	−	0.697551i	−0.0387838	−	0.0805462i
$76$	11.6561	+	0.467029i	1.33704	+	0.0535719i
$77$		−	0.753741i		−	0.0858968i
$78$	0.0627378	−	0.143279i	0.00710366	−	0.0162232i
$79$	−3.77156			−0.424334			−0.212167	−	0.977233i	$-0.568052\pi$
$79$	−3.77156			−0.424334			−0.212167	+	0.977233i	$0.568052\pi$
$80$	8.85134	−	1.28602i	0.989609	−	0.143781i
$81$	8.78479			0.976088
$82$	−3.06945	+	7.00994i	−0.338964	+	0.774119i
$83$		−	11.6538i		−	1.27917i	−0.768721	−	0.639585i	$-0.779106\pi$
$83$		−	11.6538i		−	1.27917i	0.768721	−	0.639585i	$-0.220894\pi$
$84$	−0.0123982	+	0.309433i	−0.00135275	+	0.0337619i
$85$	9.76653	+	6.13707i	1.05933	+	0.665659i
$86$	−8.85879	−	3.87901i	−0.955268	−	0.418284i
$87$	−0.231820	+	0.231820i	−0.0248537	+	0.0248537i
$88$	−1.91709	−	0.932614i	−0.204363	−	0.0994170i
$89$	−5.69680			−0.603860			−0.301930	−	0.953330i	$-0.597631\pi$
$89$	−5.69680			−0.603860			−0.301930	+	0.953330i	$0.597631\pi$
$90$	−1.76209	+	9.24458i	−0.185741	+	0.974464i
$91$	0.505076	−	0.505076i	0.0529464	−	0.0529464i
$92$	0.483547	−	12.0684i	0.0504133	−	1.25821i
$93$	0.988950			0.102549
$94$	6.48215	+	16.5807i	0.668582	+	1.71017i
$95$	−11.0431	−	6.93924i	−1.13300	−	0.711951i
$96$	0.771682	+	0.414400i	0.0787595	+	0.0422945i
$97$	−7.66124	+	7.66124i	−0.777881	+	0.777881i	−0.979470	−	0.201589i	$-0.935389\pi$
$97$	−7.66124	+	7.66124i	−0.777881	+	0.777881i	0.201589	+	0.979470i	$0.435389\pi$
$98$	−0.567247	+	1.29547i	−0.0573006	+	0.130862i
$99$	1.58615	−	1.58615i	0.159414	−	0.159414i
$100$	−9.29885	−	3.67851i	−0.929885	−	0.367851i
$101$	9.82665	+	9.82665i	0.977789	+	0.977789i	0.999759	−	0.0219700i	$-0.00699384\pi$
$101$	9.82665	+	9.82665i	0.977789	+	0.977789i	−0.0219700	+	0.999759i	$0.506994\pi$
$102$	0.411294	+	1.05205i	0.0407242	+	0.104168i
$103$	−2.77733	−	2.77733i	−0.273659	−	0.273659i	0.556912	−	0.830571i	$-0.311986\pi$
$103$	−2.77733	−	2.77733i	−0.273659	−	0.273659i	−0.830571	+	0.556912i	$0.811986\pi$
$104$	−0.659691	−	1.90957i	−0.0646880	−	0.187248i
$105$	0.184215	−	0.293160i	0.0179776	−	0.0286095i
$106$	−4.96274	+	11.3338i	−0.482024	+	1.10084i
$107$			12.8963i			1.24674i	0.781929	+	0.623368i	$0.214236\pi$
$107$			12.8963i			1.24674i	−0.781929	+	0.623368i	$0.785764\pi$
$108$	−1.35996	+	1.25518i	−0.130862	+	0.120779i
$109$	−5.13548	−	5.13548i	−0.491890	−	0.491890i	0.417011	−	0.908901i	$-0.363078\pi$
$109$	−5.13548	−	5.13548i	−0.491890	−	0.491890i	−0.908901	+	0.417011i	$0.863078\pi$
$110$	1.34004	+	1.97118i	0.127768	+	0.187945i
$111$			1.63017i			0.154728i
$112$	2.59307	+	3.04565i	0.245022	+	0.287787i
$113$	13.3973	+	13.3973i	1.26031	+	1.26031i	0.950944	+	0.309364i	$0.100116\pi$
$113$	13.3973	+	13.3973i	1.26031	+	1.26031i	0.309364	+	0.950944i	$0.399884\pi$
$114$	−0.465053	−	1.18956i	−0.0435562	−	0.111413i
$115$	−7.18468	+	11.4337i	−0.669974	+	1.06620i
$116$	−0.169533	+	4.23119i	−0.0157407	+	0.392856i
$117$	2.12573			0.196524
$118$	−3.98920	−	10.2040i	−0.367236	−	0.939354i
$119$			5.15847i			0.472876i
$120$	−0.517701	−	0.831271i	−0.0472594	−	0.0758843i
$121$			10.4319i			0.948352i
$122$	9.29481	−	3.63376i	0.841513	−	0.328985i
$123$	0.837864			0.0755477
$124$	9.38680	−	8.66357i	0.842960	−	0.778012i
$125$	6.97015	+	8.74169i	0.623429	+	0.781880i
$126$	−3.91983	+	1.53244i	−0.349206	+	0.136520i
$127$	3.68243	+	3.68243i	0.326763	+	0.326763i	0.851354	−	0.524591i	$-0.175782\pi$
$127$	3.68243	+	3.68243i	0.326763	+	0.326763i	−0.524591	+	0.851354i	$0.675782\pi$
$128$	10.9549	−	2.82687i	0.968281	−	0.249862i
$129$			1.05885i			0.0932264i
$130$	−0.422925	+	2.21882i	−0.0370930	+	0.194604i
$131$	−8.29158	−	8.29158i	−0.724439	−	0.724439i	0.245067	−	0.969506i	$-0.421190\pi$
$131$	−8.29158	−	8.29158i	−0.724439	−	0.724439i	−0.969506	+	0.245067i	$0.921190\pi$
$132$	−0.00934502	+	0.233233i	−0.000813379	+	0.0203003i
$133$		−	5.83272i		−	0.505761i
$134$	15.9121	+	6.96743i	1.37459	+	0.601895i
$135$	2.01724	−	0.460367i	0.173616	−	0.0396220i
$136$	13.1202	+	6.38264i	1.12505	+	0.547307i
$137$	13.0689	+	13.0689i	1.11655	+	1.11655i	0.992244	+	0.124305i	$0.0396700\pi$
$137$	13.0689	+	13.0689i	1.11655	+	1.11655i	0.124305	+	0.992244i	$0.460330\pi$
$138$	−1.23164	+	0.481502i	−0.104844	+	0.0409882i
$139$	3.05759	+	3.05759i	0.259341	+	0.259341i	0.824786	−	0.565445i	$-0.191295\pi$
$139$	3.05759	+	3.05759i	0.259341	+	0.259341i	−0.565445	+	0.824786i	$0.691295\pi$
$140$	−0.819678	−	4.39638i	−0.0692754	−	0.371562i
$141$	1.37830	−	1.37830i	0.116073	−	0.116073i
$142$	−7.77262	−	3.40341i	−0.652264	−	0.285608i
$143$	0.380697	−	0.380697i	0.0318355	−	0.0318355i
$144$	−0.952403	+	11.8659i	−0.0793669	+	0.988828i
$145$	2.51896	−	4.00868i	0.209188	−	0.332902i
$146$	−7.95089	+	3.10836i	−0.658020	+	0.257250i
$147$	0.154841			0.0127710
$148$	14.2809	+	15.4730i	1.17388	+	1.27187i
$149$	2.56097	−	2.56097i	0.209803	−	0.209803i	−0.594381	−	0.804184i	$-0.702603\pi$
$149$	2.56097	−	2.56097i	0.209803	−	0.209803i	0.804184	+	0.594381i	$0.202603\pi$
$150$	0.0394347	+	1.09418i	0.00321983	+	0.0893393i
$151$	11.3549			0.924048			0.462024	−	0.886867i	$-0.347123\pi$
$151$	11.3549			0.924048			0.462024	+	0.886867i	$0.347123\pi$
$152$	−14.8351	−	7.21690i	−1.20329	−	0.585368i
$153$	−10.8553	+	10.8553i	−0.877599	+	0.877599i
$154$	−0.427558	+	0.976446i	−0.0344536	+	0.0786843i
$155$	−13.9235	+	3.17758i	−1.11837	+	0.255229i
$156$	−0.162549	+	0.150025i	−0.0130144	+	0.0120116i
$157$			9.46863i			0.755679i	0.925871	+	0.377839i	$0.123333\pi$
$157$			9.46863i			0.755679i	−0.925871	+	0.377839i	$0.876667\pi$
$158$	4.88593	+	2.13941i	0.388704	+	0.170202i
$159$	1.35467			0.107433
$160$	−12.1961	−	3.35490i	−0.964186	−	0.265228i
$161$	−6.03902			−0.475941
$162$	−11.3804	−	4.98315i	−0.894128	−	0.391513i
$163$			9.76627i			0.764954i	0.923965	+	0.382477i	$0.124929\pi$
$163$			9.76627i			0.764954i	−0.923965	+	0.382477i	$0.875071\pi$
$164$	7.95274	−	7.34000i	0.621005	−	0.573158i
$165$	0.138851	−	0.220967i	0.0108095	−	0.0172023i
$166$	−6.61058	+	15.0971i	−0.513080	+	1.17176i
$167$	−6.24777	+	6.24777i	−0.483467	+	0.483467i	−0.906237	−	0.422770i	$-0.861058\pi$
$167$	−6.24777	+	6.24777i	−0.483467	+	0.483467i	0.422770	+	0.906237i	$0.361058\pi$
$168$	0.191586	−	0.393827i	0.0147812	−	0.0303844i
$169$	−12.4898			−0.960754
$170$	−9.17097	−	13.4904i	−0.703381	−	1.03467i
$171$	12.2742	−	12.2742i	0.938630	−	0.938630i
$172$	9.27590	+	10.0502i	0.707281	+	0.766324i
$173$	14.4934			1.10191			0.550955	−	0.834535i	$-0.314263\pi$
$173$	14.4934			1.10191			0.550955	+	0.834535i	$0.314263\pi$
$174$	0.431814	−	0.168816i	0.0327357	−	0.0127979i
$175$	−1.65164	+	4.71933i	−0.124852	+	0.356748i
$176$	1.95450	+	2.29563i	0.147326	+	0.173040i
$177$	−0.848221	+	0.848221i	−0.0637562	+	0.0637562i
$178$	7.38001	+	3.23150i	0.553155	+	0.242211i
$179$	−7.23232	+	7.23232i	−0.540569	+	0.540569i	−0.923696	−	0.383127i	$-0.874847\pi$
$179$	−7.23232	+	7.23232i	−0.540569	+	0.540569i	0.383127	+	0.923696i	$0.374847\pi$
$180$	7.52669	−	10.9765i	0.561006	−	0.818139i
$181$	10.3041	+	10.3041i	0.765898	+	0.765898i	0.977382	−	0.211484i	$-0.0678295\pi$
$181$	10.3041	+	10.3041i	0.765898	+	0.765898i	−0.211484	+	0.977382i	$0.567829\pi$
$182$	−0.940812	+	0.367806i	−0.0697376	+	0.0272636i
$183$	−0.772645	−	0.772645i	−0.0571155	−	0.0571155i
$184$	−7.47216	+	15.3598i	−0.550855	+	1.13234i
$185$	−5.23785	−	22.9513i	−0.385094	−	1.68741i
$186$	−1.28115	−	0.560979i	−0.0939385	−	0.0411330i
$187$			3.88815i			0.284330i
$188$	1.00796	−	25.1567i	0.0735133	−	1.83474i
$189$	0.654308	+	0.654308i	0.0475939	+	0.0475939i
$190$	10.3697	+	15.2537i	0.752296	+	1.10662i
$191$			5.29541i			0.383163i	0.981477	+	0.191581i	$0.0613616\pi$
$191$			5.29541i			0.383163i	−0.981477	+	0.191581i	$0.938638\pi$
$192$	−0.764620	−	0.974575i	−0.0551817	−	0.0703339i
$193$	−11.9014	−	11.9014i	−0.856681	−	0.856681i	0.134265	−	0.990945i	$-0.457133\pi$
$193$	−11.9014	−	11.9014i	−0.856681	−	0.856681i	−0.990945	+	0.134265i	$0.957133\pi$
$194$	14.2707	−	5.57905i	1.02458	−	0.400553i
$195$	0.241111	−	0.0550254i	0.0172663	−	0.00394045i
$196$	1.46970	−	1.35646i	0.104978	−	0.0968901i
$197$	−2.64138			−0.188190			−0.0940951	−	0.995563i	$-0.529996\pi$
$197$	−2.64138			−0.188190			−0.0940951	+	0.995563i	$0.529996\pi$
$198$	−2.95454	+	1.15506i	−0.209970	+	0.0820867i
$199$		−	13.6414i		−	0.967015i	−0.875340	−	0.483507i	$-0.839363\pi$
$199$		−	13.6414i		−	0.967015i	0.875340	−	0.483507i	$-0.160637\pi$
$200$	9.95971	+	10.0401i	0.704258	+	0.709944i
$201$		−	1.90189i		−	0.134149i
$202$	−7.15595	−	18.3042i	−0.503491	−	1.28788i
$203$	2.11729			0.148605
$204$	0.0639555	−	1.59620i	0.00447778	−	0.111756i
$205$	−11.7964	+	2.69212i	−0.823895	+	0.188026i
$206$	2.02250	+	5.17337i	0.140915	+	0.360446i
$207$	−12.7083	−	12.7083i	−0.883289	−	0.883289i
$208$	−0.228590	+	2.84798i	−0.0158498	+	0.197472i
$209$		−	4.39636i		−	0.304103i
$210$	−0.404939	+	0.275283i	−0.0279434	+	0.0189963i
$211$	4.31527	+	4.31527i	0.297075	+	0.297075i	0.839867	−	0.542792i	$-0.182633\pi$
$211$	4.31527	+	4.31527i	0.297075	+	0.297075i	−0.542792	+	0.839867i	$0.682633\pi$
$212$	12.8581	−	11.8674i	0.883100	−	0.815059i
$213$			0.929023i			0.0636556i
$214$	7.31541	−	16.7068i	0.500071	−	1.14205i
$215$	−3.40216	−	14.9076i	−0.232026	−	1.01669i
$216$	2.47377	−	0.854605i	0.168319	−	0.0581485i
$217$	−4.51621	−	4.51621i	−0.306581	−	0.306581i
$218$	3.73975	+	9.56593i	0.253288	+	0.647886i
$219$	0.660929	+	0.660929i	0.0446614	+	0.0446614i
$220$	−0.617825	−	3.31373i	−0.0416537	−	0.223412i
$221$	−2.60542	+	2.60542i	−0.175259	+	0.175259i
$222$	0.924707	−	2.11182i	0.0620623	−	0.141736i
$223$	0.246379	−	0.246379i	0.0164988	−	0.0164988i	−0.698809	−	0.715308i	$-0.746286\pi$
$223$	0.246379	−	0.246379i	0.0164988	−	0.0164988i	0.715308	+	0.698809i	$0.246286\pi$
$224$	−1.63159	−	5.41645i	−0.109015	−	0.361902i
$225$	−13.4069	+	6.45555i	−0.893791	+	0.430370i
$226$	−9.75613	−	24.9552i	−0.648968	−	1.66000i
$227$	12.5761			0.834704			0.417352	−	0.908745i	$-0.362958\pi$
$227$	12.5761			0.834704			0.417352	+	0.908745i	$0.362958\pi$
$228$	−0.0723150	+	1.80484i	−0.00478918	+	0.119528i
$229$	−0.647872	+	0.647872i	−0.0428126	+	0.0428126i	−0.728189	−	0.685376i	$-0.759638\pi$
$229$	−0.647872	+	0.647872i	−0.0428126	+	0.0428126i	0.685376	+	0.728189i	$0.259638\pi$
$230$	15.7932	−	10.7365i	1.04137	−	0.707941i
$231$	0.116710			0.00767894
$232$	2.61975	−	5.38519i	0.171995	−	0.353555i
$233$	0.622834	−	0.622834i	0.0408032	−	0.0408032i	−0.686411	−	0.727214i	$-0.740815\pi$
$233$	0.622834	−	0.622834i	0.0408032	−	0.0408032i	0.727214	+	0.686411i	$0.240815\pi$
$234$	−2.75381	−	1.20582i	−0.180022	−	0.0788266i
$235$	−14.9766	+	23.8337i	−0.976965	+	1.55474i
$236$	−0.620314	+	15.4818i	−0.0403790	+	1.00778i
$237$		−	0.583992i		−	0.0379343i
$238$	2.92613	−	6.68261i	0.189673	−	0.433170i
$239$	4.94078			0.319592			0.159796	−	0.987150i	$-0.448916\pi$
$239$	4.94078			0.319592			0.159796	+	0.987150i	$0.448916\pi$
$240$	0.199128	+	1.37055i	0.0128537	+	0.0884684i
$241$	−2.74731			−0.176970			−0.0884850	−	0.996078i	$-0.528203\pi$
$241$	−2.74731			−0.176970			−0.0884850	+	0.996078i	$0.528203\pi$
$242$	5.91745	−	13.5141i	0.380388	−	0.868721i
$243$			4.13624i			0.265340i
$244$	−14.1024	−	0.565044i	−0.902811	−	0.0361733i
$245$	−2.18002	+	0.497515i	−0.139276	+	0.0317851i
$246$	−1.08542	−	0.475276i	−0.0692041	−	0.0303025i
$247$	2.94597	−	2.94597i	0.187447	−	0.187447i
$248$	−17.0747	+	5.89872i	−1.08424	+	0.374569i
$249$	1.80448			0.114354
$250$	−4.07089	−	15.2783i	−0.257465	−	0.966288i
$251$	−5.35608	+	5.35608i	−0.338073	+	0.338073i	−0.855642	−	0.517569i	$-0.826837\pi$
$251$	−5.35608	+	5.35608i	−0.338073	+	0.338073i	0.517569	+	0.855642i	$0.326837\pi$
$252$	5.94728	+	0.238292i	0.374643	+	0.0150110i
$253$	−4.55186			−0.286173
$254$	−2.68161	−	6.85931i	−0.168259	−	0.430391i
$255$	−0.950269	+	1.51226i	−0.0595081	+	0.0947012i
$256$	−15.7952	−	2.55200i	−0.987198	−	0.159500i
$257$	−12.6062	+	12.6062i	−0.786356	+	0.786356i	−0.980895	−	0.194539i	$-0.937679\pi$
$257$	−12.6062	+	12.6062i	−0.786356	+	0.786356i	0.194539	+	0.980895i	$0.437679\pi$
$258$	0.600629	−	1.37170i	0.0373935	−	0.0853984i
$259$	7.44444	−	7.44444i	0.462575	−	0.462575i
$260$	1.80651	−	2.63451i	0.112035	−	0.163385i
$261$	4.45556	+	4.45556i	0.275792	+	0.275792i
$262$	6.03808	+	15.4448i	0.373034	+	0.954185i
$263$	7.07649	+	7.07649i	0.436355	+	0.436355i	0.890783	−	0.454428i	$-0.150156\pi$
$263$	7.07649	+	7.07649i	0.436355	+	0.436355i	−0.454428	+	0.890783i	$0.650156\pi$
$264$	0.144407	−	0.296844i	0.00888761	−	0.0182695i
$265$	−19.0726	+	4.35267i	−1.17162	+	0.267383i
$266$	−3.30859	+	7.55608i	−0.202863	+	0.463293i
$267$		−	0.882097i		−	0.0539835i
$268$	−16.6613	−	18.0521i	−1.01775	−	1.10271i
$269$	−20.5933	−	20.5933i	−1.25559	−	1.25559i	−0.953175	−	0.302418i	$-0.902206\pi$
$269$	−20.5933	−	20.5933i	−1.25559	−	1.25559i	−0.302418	−	0.953175i	$-0.597794\pi$
$270$	−2.87441	−	0.547884i	−0.174931	−	0.0333432i
$271$		−	16.9238i		−	1.02805i	−0.857775	−	0.514025i	$-0.828154\pi$
$271$		−	16.9238i		−	1.02805i	0.857775	−	0.514025i	$-0.171846\pi$
$272$	−13.3763	−	15.7109i	−0.811055	−	0.952613i
$273$	0.0782064	+	0.0782064i	0.00473326	+	0.00473326i
$274$	−9.51699	−	24.3435i	−0.574942	−	1.47065i
$275$	−1.24491	+	3.55716i	−0.0750709	+	0.214505i
$276$	1.86867	+	0.0748728i	0.112481	+	0.00450681i
$277$	24.6202			1.47928			0.739641	−	0.673001i	$-0.234995\pi$
$277$	24.6202			1.47928			0.739641	+	0.673001i	$0.234995\pi$
$278$	−2.22659	−	5.69541i	−0.133542	−	0.341588i
$279$		−	19.0075i		−	1.13795i
$280$	−1.43197	+	6.16031i	−0.0855765	+	0.368149i
$281$			13.9786i			0.833896i	0.908930	+	0.416948i	$0.136900\pi$
$281$			13.9786i			0.833896i	−0.908930	+	0.416948i	$0.863100\pi$
$282$	−2.56737	+	1.00370i	−0.152885	+	0.0597694i
$283$	8.51533			0.506184			0.253092	−	0.967442i	$-0.418553\pi$
$283$	8.51533			0.506184			0.253092	+	0.967442i	$0.418553\pi$
$284$	8.13858	+	8.81799i	0.482936	+	0.523251i
$285$	1.07448	−	1.70992i	0.0636465	−	0.101287i
$286$	−0.709129	+	0.277231i	−0.0419317	+	0.0163930i
$287$	−3.82625	−	3.82625i	−0.225857	−	0.225857i
$288$	7.96472	−	14.8317i	0.469326	−	0.873964i
$289$		−	9.60977i		−	0.565281i
$290$	−5.53714	+	3.76423i	−0.325152	+	0.221043i
$291$	−1.18627	−	1.18627i	−0.0695404	−	0.0695404i
$292$	12.0633	+	0.483345i	0.705952	+	0.0282856i
$293$		−	11.3616i		−	0.663750i	−0.943323	−	0.331875i	$-0.892319\pi$
$293$		−	11.3616i		−	0.663750i	0.943323	−	0.331875i	$-0.107681\pi$
$294$	−0.200591	−	0.0878329i	−0.0116987	−	0.00512252i
$295$	9.21680	−	14.6676i	0.536623	−	0.853981i
$296$	−9.72333	−	28.1455i	−0.565157	−	1.63593i
$297$	0.493179	+	0.493179i	0.0286172	+	0.0286172i
$298$	−4.77035	+	1.86494i	−0.276339	+	0.108033i
$299$	−3.05017	−	3.05017i	−0.176396	−	0.176396i
$300$	0.569583	−	1.43984i	0.0328849	−	0.0831292i
$301$	4.83541	−	4.83541i	0.278709	−	0.278709i
$302$	−14.7099	−	6.44103i	−0.846458	−	0.370640i
$303$	−1.52157	+	1.52157i	−0.0874117	+	0.0874117i
$304$	15.1246	+	17.7644i	0.867457	+	1.01886i
$305$	13.3607	+	8.39558i	0.765032	+	0.480729i
$306$	20.2203	−	7.90503i	1.15592	−	0.451901i
$307$	20.6029			1.17587			0.587935	−	0.808908i	$-0.299941\pi$
$307$	20.6029			1.17587			0.587935	+	0.808908i	$0.299941\pi$
$308$	1.10777	−	1.02242i	0.0631212	−	0.0582579i
$309$	0.430044	−	0.430044i	0.0244644	−	0.0244644i
$310$	19.8399	+	3.78165i	1.12683	+	0.214783i
$311$	−13.6874			−0.776140			−0.388070	−	0.921630i	$-0.626858\pi$
$311$	−13.6874			−0.776140			−0.388070	+	0.921630i	$0.626858\pi$
$312$	0.295678	−	0.102147i	0.0167395	−	0.00578293i
$313$	−0.317917	+	0.317917i	−0.0179697	+	0.0179697i	−0.716035	−	0.698065i	$-0.754045\pi$
$313$	−0.317917	+	0.317917i	−0.0179697	+	0.0179697i	0.698065	+	0.716035i	$0.254045\pi$
$314$	5.37105	−	12.2663i	0.303106	−	0.692226i
$315$	−5.63451	−	3.54060i	−0.317469	−	0.199490i
$316$	−5.11598	−	5.54306i	−0.287796	−	0.311822i
$317$			25.4141i			1.42740i	0.700454	+	0.713698i	$0.252981\pi$
$317$			25.4141i			1.42740i	−0.700454	+	0.713698i	$0.747019\pi$
$318$	−1.75493	−	0.768435i	−0.0984117	−	0.0430917i
$319$	1.59589			0.0893528
$320$	13.8966	+	11.2644i	0.776841	+	0.629697i
$321$	−1.99688			−0.111455
$322$	7.82334	+	3.42562i	0.435978	+	0.190902i
$323$			30.0879i			1.67413i
$324$	11.9162	+	12.9110i	0.662013	+	0.717278i
$325$	−3.21783	+	1.54942i	−0.178493	+	0.0859462i
$326$	5.53989	−	12.6519i	0.306826	−	0.700722i
$327$	0.795181	−	0.795181i	0.0439736	−	0.0439736i
$328$	−14.4661	+	4.99755i	−0.798756	+	0.275943i
$329$	−12.5884			−0.694024
$330$	−0.305219	+	0.207492i	−0.0168018	+	0.0114221i
$331$	−11.1549	+	11.1549i	−0.613129	+	0.613129i	−0.943760	−	0.330631i	$-0.892739\pi$
$331$	−11.1549	+	11.1549i	−0.613129	+	0.613129i	0.330631	+	0.943760i	$0.392739\pi$
$332$	17.1276	−	15.8079i	0.939997	−	0.867572i
$333$	31.3316			1.71696
$334$	11.6378	−	4.54974i	0.636792	−	0.248951i
$335$	6.11092	+	26.7769i	0.333875	+	1.46298i
$336$	−0.471591	+	0.401512i	−0.0257274	+	0.0219043i
$337$	3.39757	−	3.39757i	0.185078	−	0.185078i	−0.608487	−	0.793564i	$-0.708223\pi$
$337$	3.39757	−	3.39757i	0.185078	−	0.185078i	0.793564	+	0.608487i	$0.208223\pi$
$338$	16.1801	+	7.08480i	0.880081	+	0.385362i
$339$	−2.07444	+	2.07444i	−0.112668	+	0.112668i
$340$	4.22828	+	22.6786i	0.229311	+	1.22992i
$341$	−3.40406	−	3.40406i	−0.184340	−	0.184340i
$342$	−22.8633	+	8.93828i	−1.23630	+	0.483327i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−6.31563	−	18.2815i	−0.340516	−	0.985671i
$345$	−1.77040	−	1.11248i	−0.0953151	−	0.0598939i
$346$	−18.7757	−	8.22133i	−1.00939	−	0.441981i
$347$		−	19.1514i		−	1.02810i	−0.857760	−	0.514050i	$-0.828144\pi$
$347$		−	19.1514i		−	1.02810i	0.857760	−	0.514050i	$-0.171856\pi$
$348$	−0.655160	−	0.0262506i	−0.0351203	−	0.00140718i
$349$	−5.75121	−	5.75121i	−0.307855	−	0.307855i	0.536222	−	0.844077i	$-0.319851\pi$
$349$	−5.75121	−	5.75121i	−0.307855	−	0.307855i	−0.844077	+	0.536222i	$0.819851\pi$
$350$	4.81667	−	5.17684i	0.257462	−	0.276714i
$351$			0.660951i			0.0352790i
$352$	−1.22980	−	4.08260i	−0.0655485	−	0.217603i
$353$	18.3912	+	18.3912i	0.978867	+	0.978867i	0.999781	−	0.0209139i	$-0.00665757\pi$
$353$	18.3912	+	18.3912i	0.978867	+	0.978867i	−0.0209139	+	0.999781i	$0.506658\pi$
$354$	1.57999	−	0.617690i	0.0839757	−	0.0328299i
$355$	−2.98502	−	13.0798i	−0.158429	−	0.694204i
$356$	−7.72750	−	8.37258i	−0.409556	−	0.443746i
$357$	−0.798740			−0.0422738
$358$	13.4717	−	5.26671i	0.712003	−	0.278354i
$359$			19.6918i			1.03929i	0.854381	+	0.519646i	$0.173936\pi$
$359$			19.6918i			1.03929i	−0.854381	+	0.519646i	$0.826064\pi$
$360$	−15.9769	+	9.95017i	−0.842059	+	0.524420i
$361$		−	15.0206i		−	0.790558i
$362$	−7.50364	−	19.1936i	−0.394382	−	1.00879i
$363$	−1.61528			−0.0847801
$364$	1.42743	+	0.0571932i	0.0748175	+	0.00299774i
$365$	−11.4289	−	7.18167i	−0.598216	−	0.375906i
$366$	0.562654	+	1.43922i	0.0294104	+	0.0752290i
$367$	13.0711	+	13.0711i	0.682306	+	0.682306i	0.960519	−	0.278213i	$-0.0897421\pi$
$367$	13.0711	+	13.0711i	0.682306	+	0.682306i	−0.278213	+	0.960519i	$0.589742\pi$
$368$	18.3927	−	15.6596i	0.958788	−	0.816312i
$369$		−	16.1037i		−	0.838324i
$370$	−6.23359	+	32.7037i	−0.324069	+	1.70019i
$371$	−6.18635	−	6.18635i	−0.321179	−	0.321179i
$372$	1.34147	+	1.45346i	0.0695521	+	0.0753583i
$373$		−	7.55593i		−	0.391231i	−0.980681	−	0.195616i	$-0.937329\pi$
$373$		−	7.55593i		−	0.391231i	0.980681	−	0.195616i	$-0.0626705\pi$
$374$	2.20554	−	5.03696i	0.114046	−	0.260455i
$375$	−1.35357	+	1.07926i	−0.0698980	+	0.0557328i
$376$	−15.5759	+	32.0179i	−0.803263	+	1.65120i
$377$	1.06939	+	1.06939i	0.0550766	+	0.0550766i
$378$	−0.476479	−	1.21879i	−0.0245074	−	0.0626877i
$379$	19.8253	+	19.8253i	1.01836	+	1.01836i	0.999828	+	0.0185276i	$0.00589787\pi$
$379$	19.8253	+	19.8253i	1.01836	+	1.01836i	0.0185276	+	0.999828i	$0.494102\pi$
$380$	−4.78095	−	25.6428i	−0.245257	−	1.31545i
$381$	−0.570190	+	0.570190i	−0.0292117	+	0.0292117i
$382$	3.00381	−	6.86003i	0.153688	−	0.350989i
$383$	−24.1593	+	24.1593i	−1.23448	+	1.23448i	−0.272258	+	0.962224i	$0.587770\pi$
$383$	−24.1593	+	24.1593i	−1.23448	+	1.23448i	−0.962224	+	0.272258i	$0.912230\pi$
$384$	0.437715	+	1.69626i	0.0223370	+	0.0865617i
$385$	−1.64317	+	0.374998i	−0.0837437	+	0.0191117i
$386$	8.66681	+	22.1689i	0.441129	+	1.12837i
$387$	20.3510			1.03450
$388$	−21.6519	−	0.867534i	−1.09921	−	0.0440424i
$389$	11.6130	−	11.6130i	0.588803	−	0.588803i	−0.348505	−	0.937307i	$-0.613310\pi$
$389$	11.6130	−	11.6130i	0.588803	−	0.588803i	0.937307	+	0.348505i	$0.113310\pi$
$390$	−0.343564	−	0.0654860i	−0.0173970	−	0.00331601i
$391$	31.1521			1.57543
$392$	−2.67339	+	0.923567i	−0.135027	+	0.0466472i
$393$	1.28387	−	1.28387i	0.0647629	−	0.0647629i
$394$	3.42181	+	1.49831i	0.172388	+	0.0754839i
$395$	1.87641	+	8.22208i	0.0944125	+	0.413698i
$396$	4.48271	+	0.179610i	0.225265	+	0.00902576i
$397$			0.0333432i			0.00167345i	1.00000		0.000836723i	$0.000266337\pi$
$397$			0.0333432i			0.00167345i	−1.00000		0.000836723i	$0.999734\pi$
$398$	−7.73806	+	17.6720i	−0.387874	+	0.885817i
$399$	0.903142			0.0452136
$400$	−7.20722	−	18.6563i	−0.360361	−	0.932813i
$401$	−14.7164			−0.734900			−0.367450	−	0.930043i	$-0.619769\pi$
$401$	−14.7164			−0.734900			−0.367450	+	0.930043i	$0.619769\pi$
$402$	−1.07884	+	2.46383i	−0.0538078	+	0.122885i
$403$		−	4.56207i		−	0.227253i
$404$	−1.11274	+	27.7717i	−0.0553608	+	1.38169i
$405$	−4.37057	−	19.1510i	−0.217175	−	0.951621i
$406$	−2.74288	−	1.20103i	−0.136127	−	0.0596060i
$407$	5.61118	−	5.61118i	0.278136	−	0.278136i
$408$	−0.988292	+	2.03154i	−0.0489277	+	0.100576i
$409$	−8.39292			−0.415003			−0.207502	−	0.978235i	$-0.566533\pi$
$409$	−8.39292			−0.415003			−0.207502	+	0.978235i	$0.566533\pi$
$410$	16.8089	+	3.20391i	0.830132	+	0.158230i
$411$	−2.02359	+	2.02359i	−0.0998164	+	0.0998164i
$412$	0.314496	−	7.84919i	0.0154941	−	0.386702i
$413$	7.74710			0.381210
$414$	9.25442	+	23.6719i	0.454830	+	1.16341i
$415$	−25.4055	+	5.79794i	−1.24711	+	0.284610i
$416$	1.91164	−	3.55980i	0.0937259	−	0.174533i
$417$	−0.473439	+	0.473439i	−0.0231844	+	0.0231844i
$418$	−2.49382	+	5.69533i	−0.121977	+	0.278568i
$419$	23.3181	−	23.3181i	1.13917	−	1.13917i	0.150566	−	0.988600i	$-0.451890\pi$
$419$	23.3181	−	23.3181i	1.13917	−	1.13917i	0.988600	−	0.150566i	$-0.0481096\pi$
$420$	0.680738	−	0.126919i	0.0332166	−	0.00619303i
$421$	−9.42712	−	9.42712i	−0.459450	−	0.459450i	0.439025	−	0.898475i	$-0.355324\pi$
$421$	−9.42712	−	9.42712i	−0.459450	−	0.459450i	−0.898475	+	0.439025i	$0.855324\pi$
$422$	−3.14246	−	8.03811i	−0.152972	−	0.391289i
$423$	−26.4907	−	26.4907i	−1.28802	−	1.28802i
$424$	−23.3890	+	8.08012i	−1.13587	+	0.392405i
$425$	8.51993	−	24.3445i	0.413277	−	1.18088i
$426$	0.526986	−	1.20352i	0.0255325	−	0.0583106i
$427$			7.05683i			0.341504i
$428$	−18.9537	+	17.4934i	−0.916163	+	0.845575i
$429$	0.0589474	+	0.0589474i	0.00284601	+	0.00284601i
$430$	−4.04893	+	21.2422i	−0.195257	+	1.02439i
$431$		−	26.9200i		−	1.29669i	−0.761346	−	0.648346i	$-0.775461\pi$
$431$		−	26.9200i		−	1.29669i	0.761346	−	0.648346i	$-0.224539\pi$
$432$	−3.68946	−	0.296130i	−0.177509	−	0.0142475i
$433$	−6.40121	−	6.40121i	−0.307623	−	0.307623i	0.536364	−	0.843987i	$-0.319797\pi$
$433$	−6.40121	−	6.40121i	−0.307623	−	0.307623i	−0.843987	+	0.536364i	$0.819797\pi$
$434$	3.28879	+	8.41241i	0.157867	+	0.403808i
$435$	0.620706	+	0.390038i	0.0297606	+	0.0187009i
$436$	0.581526	−	14.5137i	0.0278500	−	0.695080i
$437$	−35.2239			−1.68499
$438$	−0.481301	−	1.23112i	−0.0229974	−	0.0588252i
$439$			41.6149i			1.98617i	0.117391	+	0.993086i	$0.462547\pi$
$439$			41.6149i			1.98617i	−0.117391	+	0.993086i	$0.537453\pi$
$440$	−1.07933	+	4.64328i	−0.0514552	+	0.221360i
$441$		−	2.97602i		−	0.141715i
$442$	4.85315	−	1.89731i	0.230841	−	0.0902460i
$443$	19.6696			0.934531			0.467266	−	0.884117i	$-0.345239\pi$
$443$	19.6696			0.934531			0.467266	+	0.884117i	$0.345239\pi$
$444$	−2.39585	+	2.21126i	−0.113702	+	0.104942i
$445$	2.83425	+	12.4191i	0.134356	+	0.588724i
$446$	−0.458933	+	0.179418i	−0.0217311	+	0.00849567i
$447$	0.396542	+	0.396542i	0.0187558	+	0.0187558i
$448$	−0.958793	+	7.94234i	−0.0452987	+	0.375240i
$449$			38.3988i			1.81215i	0.423115	+	0.906076i	$0.360937\pi$
$449$			38.3988i			1.81215i	−0.423115	+	0.906076i	$0.639063\pi$
$450$	21.0300	−	0.757931i	0.991364	−	0.0357292i
$451$	−2.88401	−	2.88401i	−0.135803	−	0.135803i
$452$	−1.51706	+	37.8628i	−0.0713566	+	1.78092i
$453$			1.75820i			0.0826074i
$454$	−16.2919	−	7.13374i	−0.764616	−	0.334803i
$455$	−1.35236	−	0.849792i	−0.0633996	−	0.0398389i
$456$	1.11747	−	2.29708i	0.0523303	−	0.107571i
$457$	15.3734	+	15.3734i	0.719139	+	0.719139i	0.968429	−	0.249290i	$-0.0801971\pi$
$457$	15.3734	+	15.3734i	0.719139	+	0.719139i	−0.249290	+	0.968429i	$0.580197\pi$
$458$	1.20680	−	0.471792i	0.0563900	−	0.0220454i
$459$	−3.37523	−	3.37523i	−0.157542	−	0.157542i
$460$	−26.5498	+	4.95005i	−1.23789	+	0.230797i
$461$	0.0147536	−	0.0147536i	0.000687144	−	0.000687144i	−0.706763	−	0.707450i	$-0.749845\pi$
$461$	0.0147536	−	0.0147536i	0.000687144	−	0.000687144i	0.707450	+	0.706763i	$0.249845\pi$
$462$	−0.151194	−	0.0662033i	−0.00703416	−	0.00308006i
$463$	4.33815	−	4.33815i	0.201611	−	0.201611i	−0.599079	−	0.800690i	$-0.704466\pi$
$463$	4.33815	−	4.33815i	0.201611	−	0.201611i	0.800690	+	0.599079i	$0.204466\pi$
$464$	−6.44854	+	5.49029i	−0.299366	+	0.254880i
$465$	−0.492018	−	2.15593i	−0.0228168	−	0.0999788i
$466$	−1.16016	+	0.453559i	−0.0537434	+	0.0210107i
$467$	−30.0927			−1.39252			−0.696262	−	0.717788i	$-0.745155\pi$
$467$	−30.0927			−1.39252			−0.696262	+	0.717788i	$0.745155\pi$
$468$	2.88347	+	3.12418i	0.133289	+	0.144415i
$469$	−8.68532	+	8.68532i	−0.401051	+	0.401051i
$470$	32.9213	−	22.3803i	1.51855	−	1.03233i
$471$	−1.46613			−0.0675556
$472$	9.58559	−	19.7042i	0.441213	−	0.906961i
$473$	3.64465	−	3.64465i	0.167581	−	0.167581i
$474$	−0.331268	+	0.756541i	−0.0152156	+	0.0347491i
$475$	−9.63355	+	27.5265i	−0.442018	+	1.26300i
$476$	−7.58139	+	6.99726i	−0.347492	+	0.320719i
$477$		−	26.0367i		−	1.19214i
$478$	−6.40061	−	2.80264i	−0.292757	−	0.128190i
$479$	−7.34763			−0.335722			−0.167861	−	0.985811i	$-0.553686\pi$
$479$	−7.34763			−0.335722			−0.167861	+	0.985811i	$0.553686\pi$
$480$	0.519475	−	1.88845i	0.0237107	−	0.0861956i
$481$	7.52002			0.342883
$482$	3.55905	+	1.55841i	0.162110	+	0.0709835i
$483$		−	0.935086i		−	0.0425479i
$484$	−15.3317	+	14.1504i	−0.696896	+	0.643202i
$485$	20.5132	+	12.8901i	0.931457	+	0.585307i
$486$	2.34627	−	5.35835i	0.106429	−	0.243060i
$487$	−18.7796	+	18.7796i	−0.850985	+	0.850985i	−0.990255	−	0.139269i	$-0.955525\pi$
$487$	−18.7796	+	18.7796i	−0.850985	+	0.850985i	0.139269	+	0.990255i	$0.455525\pi$
$488$	17.9486	+	8.73151i	0.812494	+	0.395257i
$489$	−1.51222			−0.0683848
$490$	3.10635	+	0.592095i	0.140331	+	0.0267481i
$491$	3.43339	−	3.43339i	0.154947	−	0.154947i	−0.625376	−	0.780323i	$-0.715055\pi$
$491$	3.43339	−	3.43339i	0.154947	−	0.154947i	0.780323	+	0.625376i	$0.215055\pi$
$492$	1.13653	+	1.23141i	0.0512387	+	0.0555161i
$493$	−10.9220			−0.491901
$494$	−5.48749	+	2.14531i	−0.246894	+	0.0965220i
$495$	−4.24697	−	2.66870i	−0.190887	−	0.119949i
$496$	25.4657	+	2.04397i	1.14344	+	0.0917768i
$497$	4.24255	−	4.24255i	0.190304	−	0.190304i
$498$	−2.33764	−	1.02359i	−0.104752	−	0.0458680i
$499$	12.9704	−	12.9704i	0.580634	−	0.580634i	−0.354444	−	0.935077i	$-0.615330\pi$
$499$	12.9704	−	12.9704i	0.580634	−	0.580634i	0.935077	+	0.354444i	$0.115330\pi$
$500$	−3.39291	+	22.1018i	−0.151735	+	0.988421i
$501$	−0.967409	−	0.967409i	−0.0432206	−	0.0432206i
$502$	9.97685	−	3.90040i	0.445288	−	0.174083i
$503$	11.7649	+	11.7649i	0.524571	+	0.524571i	0.918948	−	0.394378i	$-0.129040\pi$
$503$	11.7649	+	11.7649i	0.524571	+	0.524571i	−0.394378	+	0.918948i	$0.629040\pi$
$504$	−7.56932	−	3.68227i	−0.337164	−	0.164022i
$505$	16.5334	−	26.3112i	0.735725	−	1.17083i
$506$	5.89678	+	2.58203i	0.262144	+	0.114785i
$507$		−	1.93393i		−	0.0858888i
$508$	−0.416987	+	10.4071i	−0.0185008	+	0.461742i
$509$	−4.67666	−	4.67666i	−0.207289	−	0.207289i	0.595825	−	0.803114i	$-0.296825\pi$
$509$	−4.67666	−	4.67666i	−0.207289	−	0.207289i	−0.803114	+	0.595825i	$0.796825\pi$
$510$	2.08886	−	1.42004i	0.0924964	−	0.0628804i
$511$		−	6.03649i		−	0.267039i
$512$	19.0145	+	12.2658i	0.840329	+	0.542076i
$513$	3.81640	+	3.81640i	0.168498	+	0.168498i
$514$	23.4818	−	9.18010i	1.03574	−	0.404917i
$515$	−4.67287	+	7.43640i	−0.205911	+	0.327687i
$516$	−1.55619	+	1.43629i	−0.0685073	+	0.0632290i
$517$	−9.48843			−0.417301
$518$	−13.8668	+	5.42117i	−0.609274	+	0.238193i
$519$			2.24416i			0.0985079i
$520$	−3.83468	+	2.38818i	−0.168162	+	0.104728i
$521$		−	42.5118i		−	1.86247i	−0.364414	−	0.931237i	$-0.618731\pi$
$521$		−	42.5118i		−	1.86247i	0.364414	−	0.931237i	$-0.381269\pi$
$522$	−3.24462	−	8.29943i	−0.142013	−	0.363256i
$523$	26.4479			1.15649			0.578243	−	0.815864i	$-0.303738\pi$
$523$	26.4479			1.15649			0.578243	+	0.815864i	$0.303738\pi$
$524$	0.938912	−	23.4333i	0.0410166	−	1.02369i
$525$	−0.730744	−	0.255741i	−0.0318923	−	0.0111615i
$526$	−5.15323	−	13.1815i	−0.224691	−	0.574739i
$527$	23.2967	+	23.2967i	1.01482	+	1.01482i
$528$	−0.355458	+	0.302637i	−0.0154693	+	0.0131706i
$529$			13.4697i			0.585641i
$530$	27.1769	+	5.18014i	1.18049	+	0.225011i
$531$	16.3027	+	16.3027i	0.707479	+	0.707479i
$532$	8.57233	−	7.91186i	0.371658	−	0.343022i
$533$		−	3.86510i		−	0.167416i
$534$	−0.500367	+	1.14273i	−0.0216530	+	0.0494506i
$535$	28.1142	−	6.41612i	1.21548	−	0.277393i
$536$	11.3441	+	32.8370i	0.489989	+	1.41834i
$537$	−1.11986	−	1.11986i	−0.0483254	−	0.0483254i
$538$	14.9964	+	38.3593i	0.646540	+	1.65379i
$539$	−0.532976	−	0.532976i	−0.0229569	−	0.0229569i
$540$	3.41291	+	2.34026i	0.146868	+	0.100709i
$541$	−9.19763	+	9.19763i	−0.395437	+	0.395437i	−0.876620	−	0.481183i	$-0.840207\pi$
$541$	−9.19763	+	9.19763i	−0.395437	+	0.395437i	0.481183	+	0.876620i	$0.340207\pi$
$542$	−9.60000	+	21.9242i	−0.412355	+	0.941727i
$543$	−1.59549	+	1.59549i	−0.0684692	+	0.0684692i
$544$	8.41651	+	27.9406i	0.360855	+	1.19794i
$545$	−8.64046	+	13.7504i	−0.370117	+	0.589003i
$546$	−0.0569513	−	0.145676i	−0.00243729	−	0.00623436i
$547$	−19.5636			−0.836479			−0.418239	−	0.908337i	$-0.637353\pi$
$547$	−19.5636			−0.836479			−0.418239	+	0.908337i	$0.637353\pi$
$548$	−1.47988	+	36.9347i	−0.0632172	+	1.57777i
$549$	−14.8502	+	14.8502i	−0.633790	+	0.633790i
$550$	3.63052	−	3.90200i	0.154806	−	0.166382i
$551$	12.3496			0.526109
$552$	−2.37833	−	1.15699i	−0.101228	−	0.0492449i
$553$	−2.66690	+	2.66690i	−0.113408	+	0.113408i
$554$	−31.8946	−	13.9657i	−1.35507	−	0.593347i
$555$	3.55379	−	0.811032i	0.150850	−	0.0344264i
$556$	−0.346232	+	8.64123i	−0.0146835	+	0.366470i
$557$		−	1.81801i		−	0.0770314i	−0.999258	−	0.0385157i	$-0.987737\pi$
$557$		−	1.81801i		−	0.0770314i	0.999258	−	0.0385157i	$-0.0122630\pi$
$558$	−10.7820	+	24.6236i	−0.456437	+	1.04240i
$559$	4.88451			0.206593
$560$	5.34949	−	7.16819i	0.226057	−	0.302911i
$561$	−0.602044			−0.0254183
$562$	7.92934	−	18.1088i	0.334479	−	0.763875i
$563$			18.8145i			0.792937i	0.918048	+	0.396468i	$0.129764\pi$
$563$			18.8145i			0.792937i	−0.918048	+	0.396468i	$0.870236\pi$
$564$	3.89528	+	0.156074i	0.164021	+	0.00657189i
$565$	22.5409	−	35.8716i	0.948304	−	1.50913i
$566$	−11.0313	−	4.83030i	−0.463681	−	0.203032i
$567$	6.21179	−	6.21179i	0.260871	−	0.260871i
$568$	−5.54128	−	16.0400i	−0.232507	−	0.673023i
$569$	−13.6143			−0.570740			−0.285370	−	0.958417i	$-0.592117\pi$
$569$	−13.6143			−0.570740			−0.285370	+	0.958417i	$0.592117\pi$
$570$	−2.36189	+	1.60565i	−0.0989289	+	0.0672532i
$571$	22.0915	−	22.0915i	0.924499	−	0.924499i	−0.0728439	−	0.997343i	$-0.523207\pi$
$571$	22.0915	−	22.0915i	0.924499	−	0.924499i	0.997343	+	0.0728439i	$0.0232075\pi$
$572$	1.07591	+	0.0431089i	0.0449861	+	0.00180247i
$573$	−0.819946			−0.0342537
$574$	2.78635	+	7.12721i	0.116300	+	0.297484i
$575$	28.5001	+	9.97429i	1.18854	+	0.415957i
$576$	−18.7312	+	14.6959i	−0.780468	+	0.612331i
$577$	−11.0777	+	11.0777i	−0.461171	+	0.461171i	−0.899039	−	0.437868i	$-0.855734\pi$
$577$	−11.0777	+	11.0777i	−0.461171	+	0.461171i	0.437868	+	0.899039i	$0.355734\pi$
$578$	−5.45111	+	12.4491i	−0.226736	+	0.517815i
$579$	1.84282	−	1.84282i	0.0765849	−	0.0765849i
$580$	9.30842	−	1.73550i	0.386511	−	0.0720626i
$581$	−8.24047	−	8.24047i	−0.341872	−	0.341872i
$582$	0.863864	+	2.20968i	0.0358083	+	0.0915943i
$583$	−4.66291	−	4.66291i	−0.193118	−	0.193118i
$584$	−15.3534	−	7.46903i	−0.635329	−	0.309071i
$585$	−1.05758	−	4.63413i	−0.0437257	−	0.191598i
$586$	−6.44482	+	14.7185i	−0.266233	+	0.608016i
$587$		−	9.71916i		−	0.401153i	−0.979678	−	0.200576i	$-0.935719\pi$
$587$		−	9.71916i		−	0.401153i	0.979678	−	0.200576i	$-0.0642815\pi$
$588$	0.210035	+	0.227569i	0.00866171	+	0.00938479i
$589$	−26.3418	−	26.3418i	−1.08539	−	1.08539i
$590$	−20.2602	+	13.7732i	−0.834099	+	0.567032i
$591$		−	0.408992i		−	0.0168237i
$592$	−3.36923	+	41.9771i	−0.138475	+	1.72525i
$593$	−5.23368	−	5.23368i	−0.214922	−	0.214922i	0.591433	−	0.806354i	$-0.298563\pi$
$593$	−5.23368	−	5.23368i	−0.214922	−	0.214922i	−0.806354	+	0.591433i	$0.798563\pi$
$594$	−0.359142	−	0.918651i	−0.0147358	−	0.0376927i
$595$	11.2455	−	2.56642i	0.461023	−	0.105213i
$596$	7.23770	+	0.289996i	0.296468	+	0.0118787i
$597$	2.11225			0.0864485
$598$	2.22119	+	5.68158i	0.0908311	+	0.232337i
$599$		−	2.60416i		−	0.106403i	−0.998584	−	0.0532015i	$-0.983057\pi$
$599$		−	2.60416i		−	0.106403i	0.998584	−	0.0532015i	$-0.0169426\pi$
$600$	−1.55462	+	1.54217i	−0.0634671	+	0.0629587i
$601$		−	19.8463i		−	0.809546i	−0.914417	−	0.404773i	$-0.867351\pi$
$601$		−	19.8463i		−	0.809546i	0.914417	−	0.404773i	$-0.132649\pi$
$602$	−9.00699	+	3.52124i	−0.367097	+	0.143515i
$603$	−36.5542			−1.48860
$604$	15.4025	+	16.6883i	0.626718	+	0.679036i
$605$	22.7417	−	5.19002i	0.924580	−	0.211004i
$606$	2.83424	−	1.10803i	0.115133	−	0.0450107i
$607$	−7.15749	−	7.15749i	−0.290513	−	0.290513i	0.546770	−	0.837283i	$-0.315857\pi$
$607$	−7.15749	−	7.15749i	−0.290513	−	0.290513i	−0.837283	+	0.546770i	$0.815857\pi$
$608$	−9.51662	−	31.5926i	−0.385950	−	1.28125i
$609$			0.327843i			0.0132849i
$610$	−12.5460	−	18.4550i	−0.507972	−	0.747222i
$611$	−6.35813	−	6.35813i	−0.257222	−	0.257222i
$612$	−30.6788	−	1.22922i	−1.24012	−	0.0496883i
$613$		−	8.41056i		−	0.339699i	−0.985470	−	0.169850i	$-0.945672\pi$
$613$		−	8.41056i		−	0.339699i	0.985470	−	0.169850i	$-0.0543282\pi$
$614$	−26.6903	−	11.6869i	−1.07713	−	0.471646i
$615$	−0.416850	−	1.82656i	−0.0168090	−	0.0736540i
$616$	−2.01505	+	0.696131i	−0.0811885	+	0.0280479i
$617$	8.57529	+	8.57529i	0.345228	+	0.345228i	0.858329	−	0.513101i	$-0.171503\pi$
$617$	8.57529	+	8.57529i	0.345228	+	0.345228i	−0.513101	+	0.858329i	$0.671503\pi$
$618$	−0.801048	+	0.313166i	−0.0322229	+	0.0125974i
$619$	−10.1973	−	10.1973i	−0.409863	−	0.409863i	0.471828	−	0.881691i	$-0.343594\pi$
$619$	−10.1973	−	10.1973i	−0.409863	−	0.409863i	−0.881691	+	0.471828i	$0.843594\pi$
$620$	−23.5568	−	16.1531i	−0.946064	−	0.648726i
$621$	3.95138	−	3.95138i	0.158563	−	0.158563i
$622$	17.7315	+	7.76412i	0.710969	+	0.311313i
$623$	−4.02825	+	4.02825i	−0.161388	+	0.161388i
$624$	−0.440984	−	0.0353950i	−0.0176535	−	0.00141693i
$625$	15.5893	−	19.5442i	0.623571	−	0.781767i
$626$	0.592188	−	0.231513i	0.0236686	−	0.00925312i
$627$	0.680735			0.0271860
$628$	−13.9160	+	12.8438i	−0.555310	+	0.512524i
$629$	−38.4019	+	38.4019i	−1.53118	+	1.53118i
$630$	5.29092	+	7.78289i	0.210795	+	0.310078i
$631$	2.13934			0.0851659			0.0425829	−	0.999093i	$-0.486441\pi$
$631$	2.13934			0.0851659			0.0425829	+	0.999093i	$0.486441\pi$
$632$	3.48329	+	10.0829i	0.138558	+	0.401075i
$633$	−0.668179	+	0.668179i	−0.0265577	+	0.0265577i
$634$	14.4161	−	32.9230i	0.572535	−	1.30754i
$635$	6.19570	−	9.85983i	0.245869	−	0.391275i
$636$	1.83756	+	1.99096i	0.0728641	+	0.0789467i
$637$		−	0.714286i		−	0.0283010i
$638$	−2.06742	−	0.905265i	−0.0818500	−	0.0358398i
$639$	17.8557			0.706362
$640$	−11.6128	−	22.4754i	−0.459038	−	0.888417i
$641$	−7.05776			−0.278765			−0.139382	−	0.990239i	$-0.544512\pi$
$641$	−7.05776			−0.278765			−0.139382	+	0.990239i	$0.544512\pi$
$642$	2.58689	+	1.13272i	0.102096	+	0.0447050i
$643$		−	1.60854i		−	0.0634347i	−0.999497	−	0.0317173i	$-0.989902\pi$
$643$		−	1.60854i		−	0.0634347i	0.999497	−	0.0317173i	$-0.0100976\pi$
$644$	−8.19169	−	8.87553i	−0.322798	−	0.349745i
$645$	2.30831	−	0.526793i	0.0908895	−	0.0207425i
$646$	17.0673	−	38.9778i	0.671502	−	1.53356i
$647$	7.26354	−	7.26354i	0.285559	−	0.285559i	−0.549762	−	0.835321i	$-0.685282\pi$
$647$	7.26354	−	7.26354i	0.285559	−	0.285559i	0.835321	+	0.549762i	$0.185282\pi$
$648$	−8.11334	−	23.4852i	−0.318722	−	0.922586i
$649$	5.83931			0.229213
$650$	5.04749	−	0.181914i	0.197979	−	0.00713524i
$651$	0.699294	−	0.699294i	0.0274075	−	0.0274075i
$652$	−14.3535	+	13.2476i	−0.562125	+	0.518815i
$653$	36.5417			1.42999			0.714993	−	0.699131i	$-0.246430\pi$
$653$	36.5417			1.42999			0.714993	+	0.699131i	$0.246430\pi$
$654$	−1.48119	+	0.579066i	−0.0579193	+	0.0226433i
$655$	−13.9506	+	22.2010i	−0.545095	+	0.867464i
$656$	21.5752	+	1.73170i	0.842369	+	0.0676116i
$657$	12.7030	−	12.7030i	0.495591	−	0.495591i
$658$	16.3079	+	7.14076i	0.635748	+	0.278376i
$659$	14.7185	−	14.7185i	0.573352	−	0.573352i	−0.359712	−	0.933064i	$-0.617125\pi$
$659$	14.7185	−	14.7185i	0.573352	−	0.573352i	0.933064	+	0.359712i	$0.117125\pi$
$660$	0.513100	−	0.0956644i	0.0199724	−	0.00372373i
$661$	−18.8553	−	18.8553i	−0.733388	−	0.733388i	0.237902	−	0.971289i	$-0.423540\pi$
$661$	−18.8553	−	18.8553i	−0.733388	−	0.733388i	−0.971289	+	0.237902i	$0.923540\pi$
$662$	20.7784	−	8.12321i	0.807575	−	0.315718i
$663$	−0.403425	−	0.403425i	−0.0156677	−	0.0156677i
$664$	−31.1551	+	10.7631i	−1.20905	+	0.417687i
$665$	−12.7154	+	2.90187i	−0.493083	+	0.112530i
$666$	−40.5891	−	17.7728i	−1.57279	−	0.688682i
$667$		−	12.7864i		−	0.495090i
$668$	−17.6572	−	0.707478i	−0.683177	−	0.0273731i
$669$	0.0381495	+	0.0381495i	0.00147494	+	0.00147494i
$670$	7.27264	−	38.1550i	0.280967	−	1.47406i
$671$			5.31903i			0.205339i
$672$	0.838686	−	0.252637i	0.0323530	−	0.00974568i
$673$	−19.7669	−	19.7669i	−0.761959	−	0.761959i	0.214717	−	0.976676i	$-0.431117\pi$
$673$	−19.7669	−	19.7669i	−0.761959	−	0.761959i	−0.976676	+	0.214717i	$0.931117\pi$
$674$	−6.32870	+	2.47417i	−0.243772	+	0.0953016i
$675$	−2.00721	−	4.16858i	−0.0772577	−	0.160449i
$676$	−16.9419	−	18.3562i	−0.651612	−	0.706009i
$677$	−7.83333			−0.301059			−0.150530	−	0.988606i	$-0.548098\pi$
$677$	−7.83333			−0.301059			−0.150530	+	0.988606i	$0.548098\pi$
$678$	3.86409	−	1.51065i	0.148399	−	0.0580160i
$679$			10.8346i			0.415795i
$680$	7.38676	−	31.7778i	0.283269	−	1.21862i
$681$			1.94729i			0.0746203i
$682$	2.47890	+	6.34078i	0.0949219	+	0.242801i
$683$	0.0924181			0.00353628			0.00176814	−	0.999998i	$-0.499437\pi$
$683$	0.0924181			0.00353628			0.00176814	+	0.999998i	$0.499437\pi$
$684$	34.6888	+	1.38989i	1.32636	+	0.0531437i
$685$	21.9884	−	34.9923i	0.840134	−	1.33699i
$686$	0.514928	+	1.31714i	0.0196600	+	0.0502885i
$687$	−0.100317	−	0.100317i	−0.00382733	−	0.00382733i
$688$	−2.18843	+	27.2655i	−0.0834332	+	1.03949i
$689$		−	6.24916i		−	0.238074i
$690$	1.66244	+	2.44543i	0.0632880	+	0.0930961i
$691$	16.9407	+	16.9407i	0.644454	+	0.644454i	0.951647	−	0.307193i	$-0.0993897\pi$
$691$	16.9407	+	16.9407i	0.644454	+	0.644454i	−0.307193	+	0.951647i	$0.599390\pi$
$692$	19.6597	+	21.3009i	0.747350	+	0.809738i
$693$		−	2.24315i		−	0.0852103i
$694$	−10.8636	+	24.8100i	−0.412376	+	0.941774i
$695$	5.14440	−	8.18679i	0.195138	−	0.310543i
$696$	0.833847	+	0.405645i	0.0316069	+	0.0153759i
$697$	19.7376	+	19.7376i	0.747615	+	0.747615i
$698$	4.18813	+	10.7128i	0.158523	+	0.405487i
$699$	0.0964400	+	0.0964400i	0.00364769	+	0.00364769i
$700$	−9.17638	+	3.97418i	−0.346835	+	0.150210i
$701$	−28.2665	+	28.2665i	−1.06761	+	1.06761i	−0.0700677	+	0.997542i	$0.522322\pi$
$701$	−28.2665	+	28.2665i	−1.06761	+	1.06761i	−0.997542	+	0.0700677i	$0.977678\pi$
$702$	0.374923	−	0.856240i	0.0141505	−	0.0323167i
$703$	43.4213	−	43.4213i	1.63766	−	1.63766i
$704$	−0.722682	+	5.98647i	−0.0272371	+	0.225624i
$705$	−3.69043	−	2.31899i	−0.138990	−	0.0873380i
$706$	−13.3928	−	34.2576i	−0.504046	−	1.28930i
$707$	13.8970			0.522650
$708$	−2.39721	−	0.0960499i	−0.0900926	−	0.00360978i
$709$	−19.0496	+	19.0496i	−0.715422	+	0.715422i	−0.967664	−	0.252242i	$-0.918832\pi$
$709$	−19.0496	+	19.0496i	−0.715422	+	0.715422i	0.252242	+	0.967664i	$0.418832\pi$
$710$	−3.55249	+	18.6377i	−0.133323	+	0.699460i
$711$	−11.2243			−0.420943
$712$	5.26138	+	15.2298i	0.197179	+	0.570761i
$713$	−27.2735	+	27.2735i	−1.02140	+	1.02140i
$714$	1.03474	+	0.453083i	0.0387242	+	0.0169562i
$715$	−1.01933	−	0.640524i	−0.0381207	−	0.0239542i
$716$	−20.4397	−	0.818965i	−0.763867	−	0.0306061i
$717$			0.765033i			0.0285707i
$718$	11.1701	−	25.5100i	0.416865	−	0.952026i
$719$	−11.7405			−0.437848			−0.218924	−	0.975742i	$-0.570255\pi$
$719$	−11.7405			−0.437848			−0.218924	+	0.975742i	$0.570255\pi$
$720$	26.3418	−	3.82723i	0.981701	−	0.142632i
$721$	−3.92774			−0.146277
$722$	−8.52039	+	19.4587i	−0.317096	+	0.724176i
$723$		−	0.425396i		−	0.0158206i
$724$	−1.16680	+	29.1210i	−0.0433639	+	1.08228i
$725$	−9.99221	−	3.49701i	−0.371101	−	0.129876i
$726$	2.09254	+	0.916262i	0.0776613	+	0.0340057i
$727$	−13.7420	+	13.7420i	−0.509664	+	0.509664i	−0.914423	−	0.404759i	$-0.867355\pi$
$727$	−13.7420	+	13.7420i	−0.509664	+	0.509664i	0.404759	+	0.914423i	$0.367355\pi$
$728$	−1.81674	−	0.883795i	−0.0673328	−	0.0327556i
$729$	25.7139			0.952368
$730$	10.7320	+	15.7866i	0.397208	+	0.584289i
$731$	−24.9433	+	24.9433i	−0.922562	+	0.922562i
$732$	0.0874918	−	2.18362i	0.00323379	−	0.0807088i
$733$	47.3485			1.74886			0.874428	−	0.485155i	$-0.161237\pi$
$733$	47.3485			1.74886			0.874428	+	0.485155i	$0.161237\pi$
$734$	−9.51862	−	24.3477i	−0.351339	−	0.898691i
$735$	−0.0770356	−	0.337555i	−0.00284150	−	0.0124509i
$736$	−32.7100	+	9.85322i	−1.20571	+	0.363194i
$737$	−6.54648	+	6.54648i	−0.241143	+	0.241143i
$738$	−9.13477	+	20.8618i	−0.336255	+	0.767932i
$739$	−33.6796	+	33.6796i	−1.23892	+	1.23892i	−0.278481	+	0.960442i	$0.589831\pi$
$739$	−33.6796	+	33.6796i	−1.23892	+	1.23892i	−0.960442	+	0.278481i	$0.910169\pi$
$740$	26.6265	−	38.8306i	0.978810	−	1.42744i
$741$	0.456156	+	0.456156i	0.0167573	+	0.0167573i
$742$	4.50501	+	11.5234i	0.165384	+	0.423037i
$743$	−31.2125	−	31.2125i	−1.14508	−	1.14508i	−0.987508	−	0.157568i	$-0.949634\pi$
$743$	−31.2125	−	31.2125i	−1.14508	−	1.14508i	−0.157568	−	0.987508i	$-0.550366\pi$
$744$	−0.913362	−	2.64385i	−0.0334855	−	0.0969283i
$745$	−6.85708	−	4.30883i	−0.251224	−	0.157863i
$746$	−4.28608	+	9.78845i	−0.156925	+	0.358381i
$747$		−	34.6820i		−	1.26895i
$748$	−5.71441	+	5.27412i	−0.208939	+	0.192841i
$749$	9.11909	+	9.11909i	0.333204	+	0.333204i
$750$	2.36571	−	0.630339i	0.0863835	−	0.0230167i
$751$		−	13.1291i		−	0.479087i	−0.970886	−	0.239544i	$-0.923002\pi$
$751$		−	13.1291i		−	0.479087i	0.970886	−	0.239544i	$-0.0769978\pi$
$752$	38.3400	−	32.6427i	1.39812	−	1.19036i
$753$	−0.829340	−	0.829340i	−0.0302228	−	0.0302228i
$754$	−0.778753	−	1.99197i	−0.0283605	−	0.0725435i
$755$	−5.64923	−	24.7539i	−0.205597	−	0.900885i
$756$	−0.0740918	+	1.84918i	−0.00269469	+	0.0672540i
$757$	−35.3133			−1.28348			−0.641741	−	0.766921i	$-0.721788\pi$
$757$	−35.3133			−1.28348			−0.641741	+	0.766921i	$0.721788\pi$
$758$	−14.4371	−	36.9288i	−0.524380	−	1.34131i
$759$		−	0.704813i		−	0.0255831i
$760$	−8.35227	+	35.9314i	−0.302969	+	1.30337i
$761$			37.8915i			1.37356i	0.726863	+	0.686782i	$0.240977\pi$
$761$			37.8915i			1.37356i	−0.726863	+	0.686782i	$0.759023\pi$
$762$	1.06210	−	0.415223i	0.0384758	−	0.0150419i
$763$	−7.26267			−0.262926
$764$	−7.78266	+	7.18303i	−0.281567	+	0.259873i
$765$	29.0654	+	18.2641i	1.05086	+	0.660339i
$766$	45.0018	−	17.5932i	1.62598	−	0.635670i
$767$	3.91288	+	3.91288i	0.141286	+	0.141286i
$768$	0.395153	−	2.44573i	0.0142588	−	0.0882528i
$769$		−	24.7356i		−	0.891987i	−0.895036	−	0.445993i	$-0.852850\pi$
$769$		−	24.7356i		−	0.891987i	0.895036	−	0.445993i	$-0.147150\pi$
$770$	2.34139	+	0.446287i	0.0843777	+	0.0160831i
$771$	−1.95196	−	1.95196i	−0.0702981	−	0.0702981i
$772$	1.34768	−	33.6352i	0.0485039	−	1.21056i
$773$		−	6.68688i		−	0.240510i	−0.992743	−	0.120255i	$-0.961629\pi$
$773$		−	6.68688i		−	0.240510i	0.992743	−	0.120255i	$-0.0383713\pi$
$774$	−26.3640	−	11.5440i	−0.947634	−	0.414942i
$775$	13.8543	+	28.7727i	0.497663	+	1.03354i
$776$	27.5572	+	13.4058i	0.989244	+	0.481241i
$777$	1.15270	+	1.15270i	0.0413529	+	0.0413529i
$778$	−21.6317	+	8.45680i	−0.775533	+	0.303191i
$779$	−22.3174	−	22.3174i	−0.799606	−	0.799606i
$780$	0.407929	+	0.279721i	0.0146062	+	0.0100156i
$781$	3.19778	−	3.19778i	0.114426	−	0.114426i
$782$	−40.3564	−	17.6709i	−1.44314	−	0.631911i
$783$	−1.38536	+	1.38536i	−0.0495088	+	0.0495088i
$784$	3.98718	+	0.320025i	0.142399	+	0.0114295i
$785$	20.6418	−	4.71079i	0.736737	−	0.168135i
$786$	−2.39149	+	0.934940i	−0.0853015	+	0.0333482i
$787$	14.3180			0.510380			0.255190	−	0.966891i	$-0.417862\pi$
$787$	14.3180			0.510380			0.255190	+	0.966891i	$0.417862\pi$
$788$	−3.58292	−	3.88202i	−0.127636	−	0.138291i
$789$	−1.09573	+	1.09573i	−0.0390090	+	0.0390090i
$790$	2.23313	−	11.7158i	0.0794510	−	0.416830i
$791$	18.9466			0.673663
$792$	−5.70531	−	2.77548i	−0.202729	−	0.0986225i
$793$	−3.56424	+	3.56424i	−0.126570	+	0.126570i
$794$	0.0189138	−	0.0431949i	0.000671226	−	0.00153293i
$795$	−0.673971	−	2.95321i	−0.0239033	−	0.104740i
$796$	20.0488	−	18.5041i	0.710610	−	0.655859i
$797$			50.7482i			1.79759i	0.438366	+	0.898797i	$0.355558\pi$
$797$			50.7482i			1.79759i	−0.438366	+	0.898797i	$0.644442\pi$
$798$	−1.16999	−	0.512305i	−0.0414172	−	0.0181354i
$799$	64.9371			2.29731
$800$	−1.24600	+	28.2568i	−0.0440528	+	0.999029i
$801$	−16.9538			−0.599034
$802$	19.0645	+	8.34782i	0.673193	+	0.294772i
$803$		−	4.54996i		−	0.160564i
$804$	2.79521	−	2.57984i	0.0985793	−	0.0909840i
$805$	3.00450	+	13.1652i	0.105895	+	0.464011i
$806$	−2.58782	+	5.91000i	−0.0911520	+	0.208171i
$807$	3.18867	−	3.18867i	0.112247	−	0.112247i
$808$	17.1949	−	35.3461i	0.604915	−	1.24347i
$809$	54.9307			1.93126			0.965630	−	0.259921i	$-0.0836965\pi$
$809$	54.9307			1.93126			0.965630	+	0.259921i	$0.0836965\pi$
$810$	−5.20144	+	27.2887i	−0.182760	+	0.958826i
$811$	15.2249	−	15.2249i	0.534619	−	0.534619i	−0.387325	−	0.921943i	$-0.626601\pi$
$811$	15.2249	−	15.2249i	0.534619	−	0.534619i	0.921943	+	0.387325i	$0.126601\pi$
$812$	2.87203	+	3.11178i	0.100788	+	0.109202i
$813$	2.62050			0.0919049
$814$	−10.4520	+	4.08616i	−0.366343	+	0.143220i
$815$	21.2907	−	4.85887i	0.745779	−	0.170199i
$816$	2.43269	−	2.07119i	0.0851610	−	0.0725061i
$817$	28.2036	−	28.2036i	0.986719	−	0.986719i
$818$	10.8727	+	4.76086i	0.380156	+	0.166460i
$819$	1.50312	−	1.50312i	0.0525232	−	0.0525232i
$820$	−19.9579	−	13.6854i	−0.696962	−	0.477913i
$821$	8.32349	+	8.32349i	0.290492	+	0.290492i	0.837275	−	0.546783i	$-0.184148\pi$
$821$	8.32349	+	8.32349i	0.290492	+	0.290492i	−0.546783	+	0.837275i	$0.684148\pi$
$822$	3.76937	−	1.47362i	0.131472	−	0.0513983i
$823$	−36.4389	−	36.4389i	−1.27018	−	1.27018i	−0.945994	−	0.324185i	$-0.894910\pi$
$823$	−36.4389	−	36.4389i	−1.27018	−	1.27018i	−0.324185	−	0.945994i	$-0.605090\pi$
$824$	−4.85985	+	9.98995i	−0.169301	+	0.348016i
$825$	−0.550792	−	0.192763i	−0.0191761	−	0.00671114i
$826$	−10.0361	−	4.39452i	−0.349201	−	0.152905i
$827$		−	6.79561i		−	0.236306i	−0.992995	−	0.118153i	$-0.962303\pi$
$827$		−	6.79561i		−	0.236306i	0.992995	−	0.118153i	$-0.0376974\pi$
$828$	1.43905	−	35.9157i	0.0500104	−	1.24816i
$829$	−35.6065	−	35.6065i	−1.23667	−	1.23667i	−0.961355	−	0.275311i	$-0.911219\pi$
$829$	−35.6065	−	35.6065i	−1.23667	−	1.23667i	−0.275311	−	0.961355i	$-0.588781\pi$
$830$	36.2008	+	6.90015i	1.25655	+	0.239508i
$831$			3.81220i			0.132244i
$832$	−4.49575	+	3.52722i	−0.155862	+	0.122284i
$833$	3.64759	+	3.64759i	0.126381	+	0.126381i
$834$	0.881881	−	0.344767i	0.0305370	−	0.0119383i
$835$	16.7286	+	10.5119i	0.578918	+	0.363779i
$836$	6.46132	−	5.96349i	0.223470	−	0.206252i
$837$	5.90999			0.204279
$838$	−43.4350	+	16.9807i	−1.50044	+	0.586589i
$839$			46.6680i			1.61116i	0.592489	+	0.805578i	$0.298145\pi$
$839$			46.6680i			1.61116i	−0.592489	+	0.805578i	$0.701855\pi$
$840$	−0.953867	−	0.221727i	−0.0329115	−	0.00765031i
$841$		−	24.5171i		−	0.845416i
$842$	6.86500	+	17.5600i	0.236583	+	0.605158i
$843$	−2.16446			−0.0745480
$844$	−0.488647	+	12.1956i	−0.0168199	+	0.419791i
$845$	6.21386	+	27.2280i	0.213763	+	0.936671i
$846$	19.2910	+	49.3446i	0.663239	+	1.69650i
$847$	7.37645	+	7.37645i	0.253458	+	0.253458i
$848$	34.8831	+	2.79984i	1.19789	+	0.0961471i
$849$			1.31852i			0.0452515i
$850$	−24.8466	+	26.7046i	−0.852232	+	0.915959i
$851$	−44.9571	−	44.9571i	−1.54111	−	1.54111i
$852$	−1.36538	+	1.26018i	−0.0467773	+	0.0431732i
$853$		−	4.56823i		−	0.156413i	−0.996937	−	0.0782066i	$-0.975081\pi$
$853$		−	4.56823i		−	0.156413i	0.996937	−	0.0782066i	$-0.0249194\pi$
$854$	4.00297	−	9.14188i	0.136979	−	0.312829i
$855$	−32.8645	−	20.6513i	−1.12394	−	0.706261i
$856$	34.4770	−	11.9106i	1.17840	−	0.407097i
$857$	29.0856	+	29.0856i	0.993546	+	0.993546i	0.999979	−	0.00643293i	$-0.00204768\pi$
$857$	29.0856	+	29.0856i	0.993546	+	0.993546i	−0.00643293	+	0.999979i	$0.502048\pi$
$858$	−0.0429266	−	0.109802i	−0.00146549	−	0.00374858i
$859$	−6.06991	−	6.06991i	−0.207103	−	0.207103i	0.595932	−	0.803035i	$-0.296783\pi$
$859$	−6.06991	−	6.06991i	−0.207103	−	0.207103i	−0.803035	+	0.595932i	$0.796783\pi$
$860$	17.2948	−	25.2218i	0.589749	−	0.860056i
$861$	0.592459	−	0.592459i	0.0201910	−	0.0201910i
$862$	−15.2703	+	34.8740i	−0.520109	+	1.18781i
$863$	−29.3435	+	29.3435i	−0.998866	+	0.998866i	−0.999999	−	0.00113331i	$-0.999639\pi$
$863$	−29.3435	+	29.3435i	−0.998866	+	0.998866i	0.00113331	+	0.999999i	$0.499639\pi$
$864$	4.61159	+	2.47646i	0.156890	+	0.0842509i
$865$	−7.21067	−	31.5958i	−0.245170	−	1.07429i
$866$	4.66148	+	11.9236i	0.158404	+	0.405181i
$867$	1.48798			0.0505346
$868$	0.511402	−	12.7635i	0.0173581	−	0.433223i
$869$	−2.01015	+	2.01015i	−0.0681897	+	0.0681897i
$870$	−0.582855	−	0.857374i	−0.0197606	−	0.0290677i
$871$	−8.77350			−0.297279
$872$	−8.98620	+	18.4721i	−0.304311	+	0.625545i
$873$	−22.8000	+	22.8000i	−0.771664	+	0.771664i
$874$	45.6313	+	19.9807i	1.54350	+	0.675856i
$875$	11.1099	+	1.25267i	0.375585	+	0.0423479i
$876$	−0.0748415	+	1.86789i	−0.00252866	+	0.0631102i
$877$		−	31.4887i		−	1.06330i	−0.846964	−	0.531649i	$-0.821572\pi$
$877$		−	31.4887i		−	1.06330i	0.846964	−	0.531649i	$-0.178428\pi$
$878$	23.6059	−	53.9107i	0.796662	−	1.81940i
$879$	1.75923			0.0593374
$880$	4.03213	−	5.40296i	0.135923	−	0.182134i
$881$	24.9429			0.840349			0.420174	−	0.907443i	$-0.361969\pi$
$881$	24.9429			0.840349			0.420174	+	0.907443i	$0.361969\pi$
$882$	−1.68814	+	3.85534i	−0.0568427	+	0.129816i
$883$			46.9355i			1.57950i	0.613426	+	0.789752i	$0.289791\pi$
$883$			46.9355i			1.57950i	−0.613426	+	0.789752i	$0.710209\pi$
$884$	−7.36333	−	0.295029i	−0.247656	−	0.00992291i
$885$	2.27114	+	1.42714i	0.0763436	+	0.0479726i
$886$	−25.4813	−	11.1575i	−0.856061	−	0.374845i
$887$	−29.6494	+	29.6494i	−0.995528	+	0.995528i	−0.999990	−	0.00446210i	$-0.998580\pi$
$887$	−29.6494	+	29.6494i	−0.995528	+	0.995528i	0.00446210	+	0.999990i	$0.498580\pi$
$888$	4.35807	−	1.50557i	0.146247	−	0.0505235i
$889$	5.20774			0.174662
$890$	3.37305	−	17.6963i	0.113065	−	0.593181i
$891$	4.68208	−	4.68208i	0.156856	−	0.156856i
$892$	0.696306	+	0.0278992i	0.0233141	+	0.000934133i
$893$	−73.4249			−2.45707
$894$	−0.288769	−	0.738644i	−0.00965788	−	0.0247039i
$895$	19.3648	+	12.1684i	0.647293	+	0.406745i
$896$	5.74735	−	9.74515i	0.192006	−	0.325563i
$897$	0.472290	−	0.472290i	0.0157693	−	0.0157693i
$898$	21.7816	−	49.7443i	0.726862	−	1.65999i
$899$	9.56215	−	9.56215i	0.318915	−	0.318915i
$900$	−27.6736	−	10.9473i	−0.922453	−	0.364911i
$901$	31.9121	+	31.9121i	1.06315	+	1.06315i
$902$	2.10019	+	5.37207i	0.0699285	+	0.178870i
$903$	0.748719	+	0.748719i	0.0249158	+	0.0249158i
$904$	23.4429	−	48.1894i	0.779698	−	1.60275i
$905$	17.3367	−	27.5896i	0.576291	−	0.917109i
$906$	0.997333	−	2.27769i	0.0331342	−	0.0756710i
$907$		−	47.3082i		−	1.57084i	−0.618962	−	0.785421i	$-0.712447\pi$
$907$		−	47.3082i		−	1.57084i	0.618962	−	0.785421i	$-0.287553\pi$
$908$	17.0590	+	18.4830i	0.566122	+	0.613381i
$909$	29.2444	+	29.2444i	0.969974	+	0.969974i
$910$	1.26989	+	1.86800i	0.0420965	+	0.0619235i
$911$		−	8.48271i		−	0.281045i	−0.990078	−	0.140522i	$-0.955122\pi$
$911$		−	8.48271i		−	0.281045i	0.990078	−	0.140522i	$-0.0448782\pi$
$912$	−2.75066	+	2.34191i	−0.0910833	+	0.0775483i
$913$	−6.21119	−	6.21119i	−0.205560	−	0.205560i
$914$	−11.1952	−	28.6363i	−0.370305	−	0.947205i
$915$	−1.29998	+	2.06878i	−0.0429759	+	0.0683918i
$916$	−1.83099	−	0.0733630i	−0.0604976	−	0.00242398i
$917$	−11.7261			−0.387229
$918$	2.45790	+	6.28708i	0.0811228	+	0.207504i
$919$			39.8565i			1.31475i	0.753565	+	0.657373i	$0.228332\pi$
$919$			39.8565i			1.31475i	−0.753565	+	0.657373i	$0.771668\pi$
$920$	37.2022	+	8.64768i	1.22652	+	0.285106i
$921$			3.19017i			0.105120i
$922$	−0.0274817	+	0.0107438i	−0.000905062	+	0.000353830i
$923$	4.28562			0.141063
$924$	0.158312	+	0.171528i	0.00520809	+	0.00564286i
$925$	−47.4283	+	22.8372i	−1.55943	+	0.750883i
$926$	−8.08073	+	3.15912i	−0.265549	+	0.103815i
$927$	−8.26541	−	8.26541i	−0.271472	−	0.271472i
$928$	11.4682	−	3.45456i	0.376462	−	0.113401i
$929$		−	55.9271i		−	1.83491i	−0.397841	−	0.917455i	$-0.630240\pi$
$929$		−	55.9271i		−	1.83491i	0.397841	−	0.917455i	$-0.369760\pi$
$930$	−0.585553	+	3.07203i	−0.0192010	+	0.100736i
$931$	−4.12435	−	4.12435i	−0.135170	−	0.135170i
$932$	1.76023	+	0.0705277i	0.0576582	+	0.00231021i
$933$		−	2.11936i		−	0.0693848i
$934$	38.9841	+	17.0700i	1.27560	+	0.558548i
$935$	8.47624	−	1.93441i	0.277203	−	0.0632621i
$936$	−1.96326	−	5.68292i	−0.0641710	−	0.185752i
$937$	−17.6667	−	17.6667i	−0.577146	−	0.577146i	0.356970	−	0.934116i	$-0.383810\pi$
$937$	−17.6667	−	17.6667i	−0.577146	−	0.577146i	−0.934116	+	0.356970i	$0.883810\pi$
$938$	16.1782	−	6.32481i	0.528238	−	0.206512i
$939$	−0.0492265	−	0.0492265i	−0.00160645	−	0.00160645i
$940$	−55.3436	+	10.3185i	−1.80511	+	0.336551i
$941$	−9.57513	+	9.57513i	−0.312140	+	0.312140i	−0.845738	−	0.533598i	$-0.820840\pi$
$941$	−9.57513	+	9.57513i	−0.312140	+	0.312140i	0.533598	+	0.845738i	$0.320840\pi$
$942$	1.89932	+	0.831657i	0.0618831	+	0.0270969i
$943$	−23.1068	+	23.1068i	−0.752461	+	0.752461i
$944$	−23.5950	+	20.0888i	−0.767951	+	0.653834i
$945$	1.10088	−	1.75193i	0.0358115	−	0.0569904i
$946$	−6.78894	+	2.65410i	−0.220727	+	0.0862923i
$947$	−8.74305			−0.284111			−0.142055	−	0.989859i	$-0.545371\pi$
$947$	−8.74305			−0.284111			−0.142055	+	0.989859i	$0.545371\pi$
$948$	0.858291	−	0.792162i	0.0278760	−	0.0257282i
$949$	3.04889	−	3.04889i	0.0989712	−	0.0989712i
$950$	28.0943	−	30.1951i	0.911499	−	0.979657i
$951$	−3.93513			−0.127605
$952$	13.7906	−	4.76419i	0.446956	−	0.154408i
$953$	10.7519	−	10.7519i	0.348288	−	0.348288i	−0.511184	−	0.859471i	$-0.670793\pi$
$953$	10.7519	−	10.7519i	0.348288	−	0.348288i	0.859471	+	0.511184i	$0.170793\pi$
$954$	−14.7692	+	33.7297i	−0.478172	+	1.09204i
$955$	11.5441	−	2.63455i	0.373558	−	0.0852520i
$956$	6.70197	+	7.26145i	0.216757	+	0.234852i
$957$			0.247109i			0.00798790i
$958$	9.51860	+	4.16792i	0.307532	+	0.134659i
$959$	18.4822			0.596820
$960$	−1.74418	+	2.15175i	−0.0562932	+	0.0694475i
$961$	−9.79237			−0.315883
$962$	−9.74192	−	4.26571i	−0.314092	−	0.137532i
$963$			38.3798i			1.23677i
$964$	−3.72663	−	4.03772i	−0.120027	−	0.130046i
$965$	−20.0241	+	31.8664i	−0.644599	+	1.02581i
$966$	−0.530425	+	1.21137i	−0.0170661	+	0.0389752i
$967$	1.07843	−	1.07843i	0.0346799	−	0.0346799i	−0.689554	−	0.724234i	$-0.742193\pi$
$967$	1.07843	−	1.07843i	0.0346799	−	0.0346799i	0.724234	+	0.689554i	$0.242193\pi$
$968$	27.8885	−	9.63453i	0.896370	−	0.309666i
$969$	−4.65883			−0.149663
$970$	−19.2623	−	28.3347i	−0.618476	−	0.909772i
$971$	−20.9200	+	20.9200i	−0.671355	+	0.671355i	−0.958028	−	0.286673i	$-0.907451\pi$
$971$	−20.9200	+	20.9200i	−0.671355	+	0.671355i	0.286673	+	0.958028i	$0.407451\pi$
$972$	−6.07902	+	5.61065i	−0.194985	+	0.179962i
$973$	4.32408			0.138624
$974$	34.9810	−	13.6757i	1.12086	−	0.438196i
$975$	−0.239913	−	0.498251i	−0.00768336	−	0.0159568i
$976$	−18.2989	−	21.4927i	−0.585732	−	0.687963i
$977$	25.1908	−	25.1908i	0.805925	−	0.805925i	−0.178089	−	0.984014i	$-0.556992\pi$
$977$	25.1908	−	25.1908i	0.805925	−	0.805925i	0.984014	+	0.178089i	$0.0569916\pi$
$978$	1.95902	+	0.857800i	0.0626427	+	0.0274294i
$979$	−3.03626	+	3.03626i	−0.0970392	+	0.0970392i
$980$	−3.68831	−	2.52911i	−0.117819	−	0.0807894i
$981$	−15.2833	−	15.2833i	−0.487959	−	0.487959i
$982$	−6.39542	+	2.50026i	−0.204086	+	0.0797864i
$983$	20.7554	+	20.7554i	0.661995	+	0.661995i	0.955850	−	0.293855i	$-0.0949383\pi$
$983$	20.7554	+	20.7554i	0.661995	+	0.661995i	−0.293855	+	0.955850i	$0.594938\pi$
$984$	−0.773823	−	2.23994i	−0.0246686	−	0.0714067i
$985$	1.31412	+	5.75825i	0.0418715	+	0.183473i
$986$	14.1491	+	6.19546i	0.450598	+	0.197304i
$987$		−	1.94920i		−	0.0620438i
$988$	8.32577	+	0.333592i	0.264878	+	0.0106130i
$989$	−29.2012	−	29.2012i	−0.928543	−	0.928543i
$990$	3.98799	+	5.86629i	0.126746	+	0.186443i
$991$			3.64545i			0.115801i	0.998322	+	0.0579007i	$0.0184407\pi$
$991$			3.64545i			0.115801i	−0.998322	+	0.0579007i	$0.981559\pi$
$992$	−31.8305	−	17.0932i	−1.01062	−	0.542710i
$993$	−1.72723	−	1.72723i	−0.0548121	−	0.0548121i
$994$	−7.90264	+	3.08950i	−0.250657	+	0.0979930i
$995$	−29.7385	+	6.78681i	−0.942775	+	0.215156i
$996$	2.44771	+	2.65204i	0.0775586	+	0.0840332i
$997$	15.0851			0.477750			0.238875	−	0.971050i	$-0.423221\pi$
$997$	15.0851			0.477750			0.238875	+	0.971050i	$0.423221\pi$
$998$	−24.1601	+	9.44527i	−0.764774	+	0.298985i
$999$			9.74191i			0.308220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.11	✓	144
5.2	odd	4		560.2.bl.a.267.46	yes	144
16.3	odd	4		560.2.bl.a.323.46	yes	144
80.67	even	4	inner	560.2.t.a.547.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.11	✓	144	1.1	even	1	trivial
560.2.t.a.547.11	yes	144	80.67	even	4	inner
560.2.bl.a.267.46	yes	144	5.2	odd	4
560.2.bl.a.323.46	yes	144	16.3	odd	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29547 - 0.567247i) q^{2} +0.154841i q^{3} +(1.35646 + 1.46970i) q^{4} +(-0.497515 - 2.18002i) q^{5} +(0.0878329 - 0.200591i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.923567 - 2.67339i) q^{8} +2.97602 q^{9} +O(q^{10})\)	\(q+(-1.29547 - 0.567247i) q^{2} +0.154841i q^{3} +(1.35646 + 1.46970i) q^{4} +(-0.497515 - 2.18002i) q^{5} +(0.0878329 - 0.200591i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.923567 - 2.67339i) q^{8} +2.97602 q^{9} +(-0.592095 + 3.10635i) q^{10} +(0.532976 - 0.532976i) q^{11} +(-0.227569 + 0.210035i) q^{12} +0.714286 q^{13} +(-1.31714 + 0.514928i) q^{14} +(0.337555 - 0.0770356i) q^{15} +(-0.320025 + 3.98718i) q^{16} +(-3.64759 + 3.64759i) q^{17} +(-3.85534 - 1.68814i) q^{18} +(4.12435 - 4.12435i) q^{19} +(2.52911 - 3.68831i) q^{20} +(0.109489 + 0.109489i) q^{21} +(-0.992781 + 0.388123i) q^{22} +(-4.27023 - 4.27023i) q^{23} +(0.413950 - 0.143006i) q^{24} +(-4.50496 + 2.16918i) q^{25} +(-0.925333 - 0.405177i) q^{26} +0.925332i q^{27} +(1.99840 + 0.0800705i) q^{28} +(1.49715 + 1.49715i) q^{29} +(-0.480990 - 0.0916804i) q^{30} -6.38689i q^{31} +(2.67630 - 4.98372i) q^{32} +(0.0825263 + 0.0825263i) q^{33} +(6.79440 - 2.65624i) q^{34} +(-1.89330 - 1.18971i) q^{35} +(4.03686 + 4.37386i) q^{36} +10.5280 q^{37} +(-7.68249 + 3.00343i) q^{38} +0.110600i q^{39} +(-5.36855 + 3.34345i) q^{40} -5.41114i q^{41} +(-0.0797318 - 0.203946i) q^{42} +6.83831 q^{43} +(1.50627 + 0.0603525i) q^{44} +(-1.48062 - 6.48779i) q^{45} +(3.10966 + 7.95421i) q^{46} +(-8.90138 - 8.90138i) q^{47} +(-0.617377 - 0.0495529i) q^{48} -1.00000i q^{49} +(7.06648 - 0.254679i) q^{50} +(-0.564795 - 0.564795i) q^{51} +(0.968901 + 1.04978i) q^{52} -8.74882i q^{53} +(0.524892 - 1.19874i) q^{54} +(-1.42706 - 0.896733i) q^{55} +(-2.54343 - 1.23731i) q^{56} +(0.638618 + 0.638618i) q^{57} +(-1.09025 - 2.78876i) q^{58} +(5.47803 + 5.47803i) q^{59} +(0.571100 + 0.391609i) q^{60} +(-4.98993 + 4.98993i) q^{61} +(-3.62295 + 8.27400i) q^{62} +(2.10437 - 2.10437i) q^{63} +(-6.29405 + 4.93811i) q^{64} +(-0.355368 - 1.55716i) q^{65} +(-0.0600972 - 0.153723i) q^{66} -12.2829 q^{67} +(-10.3087 - 0.413041i) q^{68} +(0.661205 - 0.661205i) q^{69} +(1.77785 + 2.61520i) q^{70} +5.99986 q^{71} +(-2.74856 - 7.95608i) q^{72} +(4.26845 - 4.26845i) q^{73} +(-13.6387 - 5.97199i) q^{74} +(-0.335878 - 0.697551i) q^{75} +(11.6561 + 0.467029i) q^{76} -0.753741i q^{77} +(0.0627378 - 0.143279i) q^{78} -3.77156 q^{79} +(8.85134 - 1.28602i) q^{80} +8.78479 q^{81} +(-3.06945 + 7.00994i) q^{82} -11.6538i q^{83} +(-0.0123982 + 0.309433i) q^{84} +(9.76653 + 6.13707i) q^{85} +(-8.85879 - 3.87901i) q^{86} +(-0.231820 + 0.231820i) q^{87} +(-1.91709 - 0.932614i) q^{88} -5.69680 q^{89} +(-1.76209 + 9.24458i) q^{90} +(0.505076 - 0.505076i) q^{91} +(0.483547 - 12.0684i) q^{92} +0.988950 q^{93} +(6.48215 + 16.5807i) q^{94} +(-11.0431 - 6.93924i) q^{95} +(0.771682 + 0.414400i) q^{96} +(-7.66124 + 7.66124i) q^{97} +(-0.567247 + 1.29547i) q^{98} +(1.58615 - 1.58615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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