LMFDB - Embedded newform 880.2.s.b.67.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(67,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.16
Character	$\chi$	$=$	880.67
Dual form			880.2.s.b.683.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26665 - 0.628966i) q^{2} +2.88691i q^{3} +(1.20880 + 1.59336i) q^{4} +(1.59326 + 1.56892i) q^{5} +(1.81577 - 3.65670i) q^{6} +(2.03489 + 2.03489i) q^{7} +(-0.528960 - 2.77852i) q^{8} -5.33424 q^{9} +(-1.03131 - 2.98938i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-4.59988 + 3.48970i) q^{12} +2.19325 q^{13} +(-1.29761 - 3.85736i) q^{14} +(-4.52933 + 4.59961i) q^{15} +(-1.07759 + 3.85212i) q^{16} +(2.77969 + 2.77969i) q^{17} +(6.75662 + 3.35506i) q^{18} +(5.38125 + 5.38125i) q^{19} +(-0.573909 + 4.43516i) q^{20} +(-5.87453 + 5.87453i) q^{21} +(0.450910 + 1.34040i) q^{22} +(5.14513 - 5.14513i) q^{23} +(8.02135 - 1.52706i) q^{24} +(0.0769853 + 4.99941i) q^{25} +(-2.77807 - 1.37948i) q^{26} -6.73875i q^{27} +(-0.782529 + 5.70208i) q^{28} +(-4.94112 + 4.94112i) q^{29} +(8.63007 - 2.97730i) q^{30} -4.58689i q^{31} +(3.78778 - 4.20151i) q^{32} +(2.04135 - 2.04135i) q^{33} +(-1.77256 - 5.26923i) q^{34} +(0.0495406 + 6.43468i) q^{35} +(-6.44805 - 8.49937i) q^{36} -8.04518 q^{37} +(-3.43153 - 10.2008i) q^{38} +6.33170i q^{39} +(3.51651 - 5.25682i) q^{40} -6.14881i q^{41} +(11.1359 - 3.74609i) q^{42} -0.679540 q^{43} +(0.271923 - 1.98143i) q^{44} +(-8.49886 - 8.36900i) q^{45} +(-9.75319 + 3.28096i) q^{46} +(9.11033 - 9.11033i) q^{47} +(-11.1207 - 3.11091i) q^{48} +1.28152i q^{49} +(3.04694 - 6.38092i) q^{50} +(-8.02471 + 8.02471i) q^{51} +(2.65120 + 3.49463i) q^{52} -6.00375i q^{53} +(-4.23845 + 8.53563i) q^{54} +(-0.0172150 - 2.23600i) q^{55} +(4.57761 - 6.73035i) q^{56} +(-15.5352 + 15.5352i) q^{57} +(9.36646 - 3.15087i) q^{58} +(-1.68838 + 1.68838i) q^{59} +(-12.8039 - 1.65682i) q^{60} +(-2.50998 - 2.50998i) q^{61} +(-2.88500 + 5.80998i) q^{62} +(-10.8546 - 10.8546i) q^{63} +(-7.44040 + 2.93946i) q^{64} +(3.49442 + 3.44103i) q^{65} +(-3.86962 + 1.30174i) q^{66} +4.64277 q^{67} +(-1.06895 + 7.78914i) q^{68} +(14.8535 + 14.8535i) q^{69} +(3.98445 - 8.18165i) q^{70} -13.8082 q^{71} +(2.82160 + 14.8213i) q^{72} +(-0.596207 - 0.596207i) q^{73} +(10.1904 + 5.06015i) q^{74} +(-14.4328 + 0.222250i) q^{75} +(-2.06940 + 15.0791i) q^{76} -2.87776i q^{77} +(3.98243 - 8.02005i) q^{78} +13.0360 q^{79} +(-7.76055 + 4.44679i) q^{80} +3.45142 q^{81} +(-3.86739 + 7.78838i) q^{82} -7.30691i q^{83} +(-16.4614 - 2.25909i) q^{84} +(0.0676733 + 8.78989i) q^{85} +(0.860740 + 0.427408i) q^{86} +(-14.2646 - 14.2646i) q^{87} +(-1.59068 + 2.33875i) q^{88} -2.80835 q^{89} +(5.50127 + 15.9461i) q^{90} +(4.46300 + 4.46300i) q^{91} +(14.4175 + 1.97859i) q^{92} +13.2419 q^{93} +(-17.2697 + 5.80950i) q^{94} +(0.131010 + 17.0165i) q^{95} +(12.1294 + 10.9350i) q^{96} +(-12.0829 - 12.0829i) q^{97} +(0.806032 - 1.62324i) q^{98} +(3.77188 + 3.77188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 8 q^{5} - 4 q^{7} + 12 q^{8} - 240 q^{9} + 16 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 8 q^{17} - 12 q^{18} - 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{25} + 8 q^{26} + 36 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 236 * q + 8 * q^5 - 4 * q^7 + 12 * q^8 - 240 * q^9 + 16 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 + 8 * q^17 - 12 * q^18 - 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 - 12 * q^25 + 8 * q^26 + 36 * q^28 - 8 * q^29 + 40 * q^32 - 4 * q^33 + 44 * q^34 - 12 * q^35 - 32 * q^36 + 4 * q^37 - 44 * q^38 - 40 * q^40 - 60 * q^42 - 16 * q^43 - 40 * q^46 + 48 * q^47 - 112 * q^48 - 28 * q^51 + 108 * q^52 - 24 * q^56 + 16 * q^57 - 28 * q^58 - 8 * q^59 + 100 * q^60 - 24 * q^61 + 36 * q^62 + 24 * q^63 - 32 * q^65 - 4 * q^66 - 56 * q^67 - 36 * q^68 - 48 * q^69 + 164 * q^70 - 4 * q^71 + 12 * q^72 - 8 * q^73 - 72 * q^75 - 24 * q^76 + 152 * q^78 - 40 * q^79 - 24 * q^80 + 244 * q^81 + 40 * q^82 + 104 * q^84 - 24 * q^85 + 72 * q^86 - 140 * q^87 + 32 * q^88 - 36 * q^89 + 72 * q^90 + 12 * q^91 + 12 * q^93 + 16 * q^94 + 36 * q^95 + 72 * q^96 + 20 * q^97 - 64 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.26665	−	0.628966i	−0.895657	−	0.444746i
$2$	−1.26665	−	0.628966i	−0.895657	−	0.444746i
$3$			2.88691i			1.66676i	0.552702	+	0.833379i	$0.313597\pi$
$3$			2.88691i			1.66676i	−0.552702	+	0.833379i	$0.686403\pi$
$4$	1.20880	+	1.59336i	0.604401	+	0.796680i
$5$	1.59326	+	1.56892i	0.712530	+	0.701642i
$5$	1.59326	+	1.56892i	0.712530	+	0.701642i
$6$	1.81577	−	3.65670i	0.741284	−	1.49284i
$7$	2.03489	+	2.03489i	0.769114	+	0.769114i	0.977951	−	0.208836i	$-0.0669675\pi$
$7$	2.03489	+	2.03489i	0.769114	+	0.769114i	−0.208836	+	0.977951i	$0.566968\pi$
$8$	−0.528960	−	2.77852i	−0.187016	−	0.982357i
$9$	−5.33424			−1.77808
$10$	−1.03131	−	2.98938i	−0.326129	−	0.945325i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	−4.59988	+	3.48970i	−1.32787	+	1.00739i
$13$	2.19325			0.608297			0.304148	−	0.952625i	$-0.401628\pi$
$13$	2.19325			0.608297			0.304148	+	0.952625i	$0.401628\pi$
$14$	−1.29761	−	3.85736i	−0.346802	−	1.03092i
$15$	−4.52933	+	4.59961i	−1.16947	+	1.18761i
$16$	−1.07759	+	3.85212i	−0.269398	+	0.963029i
$17$	2.77969	+	2.77969i	0.674174	+	0.674174i	0.958676	−	0.284502i	$-0.0918281\pi$
$17$	2.77969	+	2.77969i	0.674174	+	0.674174i	−0.284502	+	0.958676i	$0.591828\pi$
$18$	6.75662	+	3.35506i	1.59255	+	0.790795i
$19$	5.38125	+	5.38125i	1.23454	+	1.23454i	0.962200	+	0.272343i	$0.0877986\pi$
$19$	5.38125	+	5.38125i	1.23454	+	1.23454i	0.272343	+	0.962200i	$0.412201\pi$
$20$	−0.573909	+	4.43516i	−0.128330	+	0.991732i
$21$	−5.87453	+	5.87453i	−1.28193	+	1.28193i
$22$	0.450910	+	1.34040i	0.0961344	+	0.285775i
$23$	5.14513	−	5.14513i	1.07283	−	1.07283i	0.0757030	−	0.997130i	$-0.475880\pi$
$23$	5.14513	−	5.14513i	1.07283	−	1.07283i	0.997130	−	0.0757030i	$-0.0241201\pi$
$24$	8.02135	−	1.52706i	1.63735	−	0.311710i
$25$	0.0769853	+	4.99941i	0.0153971	+	0.999881i
$26$	−2.77807	−	1.37948i	−0.544825	−	0.270538i
$27$		−	6.73875i		−	1.29687i
$28$	−0.782529	+	5.70208i	−0.147884	+	1.07759i
$29$	−4.94112	+	4.94112i	−0.917543	+	0.917543i	−0.996850	−	0.0793075i	$-0.974729\pi$
$29$	−4.94112	+	4.94112i	−0.917543	+	0.917543i	0.0793075	+	0.996850i	$0.474729\pi$
$30$	8.63007	−	2.97730i	1.57563	−	0.543578i
$31$		−	4.58689i		−	0.823830i	−0.911222	−	0.411915i	$-0.864860\pi$
$31$		−	4.58689i		−	0.823830i	0.911222	−	0.411915i	$-0.135140\pi$
$32$	3.78778	−	4.20151i	0.669591	−	0.742730i
$33$	2.04135	−	2.04135i	0.355354	−	0.355354i
$34$	−1.77256	−	5.26923i	−0.303992	−	0.903665i
$35$	0.0495406	+	6.43468i	0.00837388	+	1.08766i
$36$	−6.44805	−	8.49937i	−1.07467	−	1.41656i
$37$	−8.04518			−1.32262			−0.661310	−	0.750113i	$-0.729999\pi$
$37$	−8.04518			−1.32262			−0.661310	+	0.750113i	$0.729999\pi$
$38$	−3.43153	−	10.2008i	−0.556668	−	1.65479i
$39$			6.33170i			1.01388i
$40$	3.51651	−	5.25682i	0.556009	−	0.831177i
$41$		−	6.14881i		−	0.960282i	−0.877191	−	0.480141i	$-0.840585\pi$
$41$		−	6.14881i		−	0.960282i	0.877191	−	0.480141i	$-0.159415\pi$
$42$	11.1359	−	3.74609i	1.71830	−	0.578034i
$43$	−0.679540			−0.103629			−0.0518145	−	0.998657i	$-0.516500\pi$
$43$	−0.679540			−0.103629			−0.0518145	+	0.998657i	$0.516500\pi$
$44$	0.271923	−	1.98143i	0.0409939	−	0.298712i
$45$	−8.49886	−	8.36900i	−1.26694	−	1.24758i
$46$	−9.75319	+	3.28096i	−1.43803	+	0.483752i
$47$	9.11033	−	9.11033i	1.32888	−	1.32888i	0.422528	−	0.906350i	$-0.361143\pi$
$47$	9.11033	−	9.11033i	1.32888	−	1.32888i	0.906350	−	0.422528i	$-0.138857\pi$
$48$	−11.1207	−	3.11091i	−1.60514	−	0.449021i
$49$			1.28152i			0.183074i
$50$	3.04694	−	6.38092i	0.430903	−	0.902398i
$51$	−8.02471	+	8.02471i	−1.12368	+	1.12368i
$52$	2.65120	+	3.49463i	0.367656	+	0.484618i
$53$		−	6.00375i		−	0.824678i	−0.911031	−	0.412339i	$-0.864712\pi$
$53$		−	6.00375i		−	0.824678i	0.911031	−	0.412339i	$-0.135288\pi$
$54$	−4.23845	+	8.53563i	−0.576779	+	1.16155i
$55$	−0.0172150	−	2.23600i	−0.00232126	−	0.301502i
$56$	4.57761	−	6.73035i	0.611708	−	0.899381i
$57$	−15.5352	+	15.5352i	−2.05768	+	2.05768i
$58$	9.36646	−	3.15087i	1.22988	−	0.413729i
$59$	−1.68838	+	1.68838i	−0.219808	+	0.219808i	−0.808418	−	0.588609i	$-0.799676\pi$
$59$	−1.68838	+	1.68838i	−0.219808	+	0.219808i	0.588609	+	0.808418i	$0.299676\pi$
$60$	−12.8039	−	1.65682i	−1.65298	−	0.213895i
$61$	−2.50998	−	2.50998i	−0.321371	−	0.321371i	0.527922	−	0.849293i	$-0.322971\pi$
$61$	−2.50998	−	2.50998i	−0.321371	−	0.321371i	−0.849293	+	0.527922i	$0.822971\pi$
$62$	−2.88500	+	5.80998i	−0.366395	+	0.737869i
$63$	−10.8546	−	10.8546i	−1.36755	−	1.36755i
$64$	−7.44040	+	2.93946i	−0.930050	+	0.367432i
$65$	3.49442	+	3.44103i	0.433430	+	0.426807i
$66$	−3.86962	+	1.30174i	−0.476317	+	0.160233i
$67$	4.64277			0.567204			0.283602	−	0.958942i	$-0.408471\pi$
$67$	4.64277			0.567204			0.283602	+	0.958942i	$0.408471\pi$
$68$	−1.06895	+	7.78914i	−0.129629	+	0.944572i
$69$	14.8535	+	14.8535i	1.78815	+	1.78815i
$70$	3.98445	−	8.18165i	0.476233	−	0.977894i
$71$	−13.8082			−1.63874			−0.819369	−	0.573267i	$-0.805676\pi$
$71$	−13.8082			−1.63874			−0.819369	+	0.573267i	$0.805676\pi$
$72$	2.82160	+	14.8213i	0.332529	+	1.74671i
$73$	−0.596207	−	0.596207i	−0.0697807	−	0.0697807i	0.671355	−	0.741136i	$-0.265713\pi$
$73$	−0.596207	−	0.596207i	−0.0697807	−	0.0697807i	−0.741136	+	0.671355i	$0.765713\pi$
$74$	10.1904	+	5.06015i	1.18461	+	0.588230i
$75$	−14.4328	+	0.222250i	−1.66656	+	0.0256632i
$76$	−2.06940	+	15.0791i	−0.237376	+	1.72970i
$77$		−	2.87776i		−	0.327952i
$78$	3.98243	−	8.02005i	0.450921	−	0.908092i
$79$	13.0360			1.46667			0.733335	−	0.679868i	$-0.237963\pi$
$79$	13.0360			1.46667			0.733335	+	0.679868i	$0.237963\pi$
$80$	−7.76055	+	4.44679i	−0.867655	+	0.497166i
$81$	3.45142			0.383492
$82$	−3.86739	+	7.78838i	−0.427082	+	0.860083i
$83$		−	7.30691i		−	0.802037i	−0.916070	−	0.401019i	$-0.868656\pi$
$83$		−	7.30691i		−	0.802037i	0.916070	−	0.401019i	$-0.131344\pi$
$84$	−16.4614	−	2.25909i	−1.79608	−	0.246487i
$85$	0.0676733	+	8.78989i	0.00734020	+	0.953398i
$86$	0.860740	+	0.427408i	0.0928159	+	0.0460886i
$87$	−14.2646	−	14.2646i	−1.52932	−	1.52932i
$88$	−1.59068	+	2.33875i	−0.169567	+	0.249311i
$89$	−2.80835			−0.297684			−0.148842	−	0.988861i	$-0.547555\pi$
$89$	−2.80835			−0.297684			−0.148842	+	0.988861i	$0.547555\pi$
$90$	5.50127	+	15.9461i	0.579884	+	1.68086i
$91$	4.46300	+	4.46300i	0.467850	+	0.467850i
$92$	14.4175	+	1.97859i	1.50313	+	0.206283i
$93$	13.2419			1.37312
$94$	−17.2697	+	5.80950i	−1.78123	+	0.599205i
$95$	0.131010	+	17.0165i	0.0134413	+	1.74586i
$96$	12.1294	+	10.9350i	1.23795	+	1.11605i
$97$	−12.0829	−	12.0829i	−1.22684	−	1.22684i	−0.965154	−	0.261681i	$-0.915723\pi$
$97$	−12.0829	−	12.0829i	−1.22684	−	1.22684i	−0.261681	−	0.965154i	$-0.584277\pi$
$98$	0.806032	−	1.62324i	0.0814216	−	0.163972i
$99$	3.77188	+	3.77188i	0.379088	+	0.379088i
$100$	−7.87279	+	6.16596i	−0.787279	+	0.616596i
$101$	0.524124	−	0.524124i	0.0521523	−	0.0521523i	−0.680550	−	0.732702i	$-0.738259\pi$
$101$	0.524124	−	0.524124i	0.0521523	−	0.0521523i	0.732702	+	0.680550i	$0.238259\pi$
$102$	15.2118	−	5.11723i	1.50619	−	0.506681i
$103$	2.31333	−	2.31333i	0.227940	−	0.227940i	−0.583892	−	0.811831i	$-0.698471\pi$
$103$	2.31333	−	2.31333i	0.227940	−	0.227940i	0.811831	+	0.583892i	$0.198471\pi$
$104$	−1.16014	−	6.09399i	−0.113761	−	0.597565i
$105$	−18.5763	+	0.143019i	−1.81287	+	0.0139572i
$106$	−3.77615	+	7.60464i	−0.366772	+	0.738628i
$107$		−	18.9750i		−	1.83438i	−0.398453	−	0.917189i	$-0.630453\pi$
$107$		−	18.9750i		−	1.83438i	0.398453	−	0.917189i	$-0.369547\pi$
$108$	10.7373	−	8.14582i	1.03319	−	0.783832i
$109$	1.36317	−	1.36317i	0.130568	−	0.130568i	−0.638803	−	0.769371i	$-0.720570\pi$
$109$	1.36317	−	1.36317i	0.130568	−	0.130568i	0.769371	+	0.638803i	$0.220570\pi$
$110$	−1.38456	+	2.84306i	−0.132013	+	0.271075i
$111$		−	23.2257i		−	2.20449i
$112$	−10.0314	+	5.64584i	−0.947877	+	0.533482i
$113$	−6.32229	+	6.32229i	−0.594751	+	0.594751i	−0.938911	−	0.344160i	$-0.888164\pi$
$113$	−6.32229	+	6.32229i	−0.594751	+	0.594751i	0.344160	+	0.938911i	$0.388164\pi$
$114$	29.4487	−	9.90653i	2.75813	−	0.927831i
$115$	16.2698	−	0.125261i	1.51717	−	0.0116807i
$116$	−13.8458	−	1.90014i	−1.28555	−	0.176424i
$117$	−11.6993			−1.08160
$118$	3.20052	−	1.07665i	0.294631	−	0.0991137i
$119$			11.3127i			1.03703i
$120$	15.1760	+	10.1518i	1.38537	+	0.926732i
$121$			1.00000i			0.0909091i
$122$	1.60058	+	4.75797i	0.144909	+	0.430766i
$123$	17.7510			1.60056
$124$	7.30857	−	5.54465i	0.656329	−	0.497924i
$125$	−7.72101	+	8.08616i	−0.690588	+	0.723248i
$126$	6.92178	+	20.5761i	0.616642	+	1.83307i
$127$	−2.33436	+	2.33436i	−0.207141	+	0.207141i	−0.803051	−	0.595910i	$-0.796792\pi$
$127$	−2.33436	+	2.33436i	−0.207141	+	0.207141i	0.595910	+	0.803051i	$0.296792\pi$
$128$	11.2732	+	0.956496i	0.996420	+	0.0845431i
$129$		−	1.96177i		−	0.172724i
$130$	−2.26192	−	6.55645i	−0.198383	−	0.575038i
$131$	0.725080	−	0.725080i	0.0633505	−	0.0633505i	−0.674722	−	0.738072i	$-0.735736\pi$
$131$	0.725080	−	0.725080i	0.0633505	−	0.0633505i	0.738072	+	0.674722i	$0.235736\pi$
$132$	5.72020	+	0.785016i	0.497880	+	0.0683269i
$133$			21.9005i			1.89901i
$134$	−5.88076	−	2.92014i	−0.508020	−	0.252262i
$135$	10.5726	−	10.7366i	0.909940	−	0.924060i
$136$	6.25309	−	9.19378i	0.536198	−	0.788361i
$137$	1.64092	−	1.64092i	0.140193	−	0.140193i	−0.633527	−	0.773720i	$-0.718394\pi$
$137$	1.64092	−	1.64092i	0.140193	−	0.140193i	0.773720	+	0.633527i	$0.218394\pi$
$138$	−9.47184	−	28.1566i	−0.806297	−	2.39685i
$139$	2.53960	−	2.53960i	0.215406	−	0.215406i	−0.591153	−	0.806559i	$-0.701327\pi$
$139$	2.53960	−	2.53960i	0.215406	−	0.215406i	0.806559	+	0.591153i	$0.201327\pi$
$140$	−10.1929	+	7.85720i	−0.861456	+	0.664055i
$141$	26.3007	+	26.3007i	2.21492	+	2.21492i
$142$	17.4902	+	8.68492i	1.46775	+	0.728823i
$143$	−1.55086	−	1.55086i	−0.129689	−	0.129689i
$144$	5.74813	−	20.5481i	0.479011	−	1.71234i
$145$	−15.6247	+	0.120295i	−1.29756	+	0.00998992i
$146$	0.380191	+	1.13018i	0.0314649	+	0.0935343i
$147$	−3.69963			−0.305140
$148$	−9.72504	−	12.8189i	−0.799393	−	1.05370i
$149$	7.85861	+	7.85861i	0.643803	+	0.643803i	0.951488	−	0.307685i	$-0.0995544\pi$
$149$	7.85861	+	7.85861i	0.643803	+	0.643803i	−0.307685	+	0.951488i	$0.599554\pi$
$150$	18.4211	+	8.79625i	1.50408	+	0.718211i
$151$	−15.0986			−1.22871			−0.614355	−	0.789030i	$-0.710584\pi$
$151$	−15.0986			−1.22871			−0.614355	+	0.789030i	$0.710584\pi$
$152$	12.1055	−	17.7984i	0.981883	−	1.44364i
$153$	−14.8275	−	14.8275i	−1.19874	−	1.19874i
$154$	−1.81002	+	3.64512i	−0.145855	+	0.293732i
$155$	7.19646	−	7.30813i	0.578034	−	0.587003i
$156$	−10.0887	+	7.65378i	−0.807741	+	0.612793i
$157$			1.15418i			0.0921136i	0.998939	+	0.0460568i	$0.0146655\pi$
$157$			1.15418i			0.0921136i	−0.998939	+	0.0460568i	$0.985334\pi$
$158$	−16.5121	−	8.19923i	−1.31363	−	0.652296i
$159$	17.3323			1.37454
$160$	12.6268	−	0.751401i	0.998234	−	0.0594035i
$161$	20.9395			1.65026
$162$	−4.37175	−	2.17083i	−0.343477	−	0.170556i
$163$			21.3513i			1.67236i	0.548454	+	0.836181i	$0.315216\pi$
$163$			21.3513i			1.67236i	−0.548454	+	0.836181i	$0.684784\pi$
$164$	9.79726	−	7.43270i	0.765038	−	0.580396i
$165$	6.45513	−	0.0496980i	0.502531	−	0.00386899i
$166$	−4.59580	+	9.25529i	−0.356703	+	0.718350i
$167$	11.6057	+	11.6057i	0.898074	+	0.898074i	0.995266	−	0.0971918i	$-0.0309860\pi$
$167$	11.6057	+	11.6057i	0.898074	+	0.898074i	−0.0971918	+	0.995266i	$0.530986\pi$
$168$	19.4299	+	13.2151i	1.49905	+	1.01957i
$169$	−8.18967			−0.629975
$170$	5.44283	−	11.1763i	0.417446	−	0.857181i
$171$	−28.7049	−	28.7049i	−2.19512	−	2.19512i
$172$	−0.821431	−	1.08275i	−0.0626335	−	0.0825591i
$173$	12.7552			0.969762			0.484881	−	0.874580i	$-0.338863\pi$
$173$	12.7552			0.969762			0.484881	+	0.874580i	$0.338863\pi$
$174$	9.09627	+	27.0401i	0.689587	+	2.04991i
$175$	−10.0166	+	10.3299i	−0.757181	+	0.780865i
$176$	3.48583	−	1.96189i	0.262754	−	0.147883i
$177$	−4.87419	−	4.87419i	−0.366367	−	0.366367i
$178$	3.55719	+	1.76635i	0.266623	+	0.132394i
$179$	−17.4256	−	17.4256i	−1.30245	−	1.30245i	−0.926737	−	0.375710i	$-0.877399\pi$
$179$	−17.4256	−	17.4256i	−1.30245	−	1.30245i	−0.375710	−	0.926737i	$-0.622601\pi$
$180$	3.06137	−	23.6582i	0.228181	−	1.76338i
$181$	−0.610576	+	0.610576i	−0.0453838	+	0.0453838i	−0.729434	−	0.684051i	$-0.760217\pi$
$181$	−0.610576	+	0.610576i	−0.0453838	+	0.0453838i	0.684051	+	0.729434i	$0.260217\pi$
$182$	−2.84598	−	8.46014i	−0.210958	−	0.627107i
$183$	7.24610	−	7.24610i	0.535647	−	0.535647i
$184$	−17.0174	−	11.5743i	−1.25454	−	0.853269i
$185$	−12.8181	−	12.6222i	−0.942406	−	0.928005i
$186$	−16.7729	−	8.32873i	−1.22985	−	0.610692i
$187$		−	3.93108i		−	0.287469i
$188$	25.5286	+	3.50344i	1.86187	+	0.255514i
$189$	13.7126	−	13.7126i	0.997444	−	0.997444i
$190$	10.5369	−	21.6363i	0.764424	−	1.56967i
$191$		−	16.2113i		−	1.17301i	−0.809947	−	0.586503i	$-0.800504\pi$
$191$		−	16.2113i		−	1.17301i	0.809947	−	0.586503i	$-0.199496\pi$
$192$	−8.48595	−	21.4798i	−0.612421	−	1.55017i
$193$	−0.407460	+	0.407460i	−0.0293296	+	0.0293296i	−0.721619	−	0.692290i	$-0.756602\pi$
$193$	−0.407460	+	0.407460i	−0.0293296	+	0.0293296i	0.692290	+	0.721619i	$0.256602\pi$
$194$	7.70509	+	22.9046i	0.553193	+	1.64445i
$195$	−9.93393	+	10.0881i	−0.711383	+	0.722422i
$196$	−2.04192	+	1.54910i	−0.145852	+	0.110650i
$197$	16.0366			1.14256			0.571279	−	0.820756i	$-0.306448\pi$
$197$	16.0366			1.14256			0.571279	+	0.820756i	$0.306448\pi$
$198$	−2.40527	−	7.15004i	−0.170935	−	0.508131i
$199$			2.39691i			0.169913i	0.996385	+	0.0849563i	$0.0270751\pi$
$199$			2.39691i			0.169913i	−0.996385	+	0.0849563i	$0.972925\pi$
$200$	13.8503	−	2.85839i	0.979361	−	0.202119i
$201$			13.4032i			0.945392i
$202$	−0.993538	+	0.334225i	−0.0699051	+	0.0235160i
$203$	−20.1092			−1.41139
$204$	−22.4866	−	3.08596i	−1.57437	−	0.216060i
$205$	9.64698	−	9.79668i	0.673774	−	0.684230i
$206$	−4.38519	+	1.47517i	−0.305531	+	0.102780i
$207$	−27.4454	+	27.4454i	−1.90758	+	1.90758i
$208$	−2.36342	+	8.44864i	−0.163874	+	0.585808i
$209$		−	7.61024i		−	0.526411i
$210$	23.6197	+	11.5027i	1.62991	+	0.793764i
$211$	−4.98933	+	4.98933i	−0.343480	+	0.343480i	−0.857674	−	0.514194i	$-0.828091\pi$
$211$	−4.98933	+	4.98933i	−0.343480	+	0.343480i	0.514194	+	0.857674i	$0.328091\pi$
$212$	9.56613	−	7.25735i	0.657004	−	0.498437i
$213$		−	39.8632i		−	2.73138i
$214$	−11.9346	+	24.0346i	−0.815833	+	1.64297i
$215$	−1.08269	−	1.06614i	−0.0738387	−	0.0727104i
$216$	−18.7238	+	3.56453i	−1.27399	+	0.242536i
$217$	9.33380	−	9.33380i	0.633619	−	0.633619i
$218$	−2.58405	+	0.869270i	−0.175014	+	0.0588744i
$219$	1.72119	−	1.72119i	0.116308	−	0.116308i
$220$	3.54195	−	2.73032i	0.238798	−	0.184078i
$221$	6.09654	+	6.09654i	0.410098	+	0.410098i
$222$	−14.6082	+	29.4188i	−0.980437	+	1.97446i
$223$	12.5512	+	12.5512i	0.840493	+	0.840493i	0.988923	−	0.148430i	$-0.0474220\pi$
$223$	12.5512	+	12.5512i	0.840493	+	0.840493i	−0.148430	+	0.988923i	$0.547422\pi$
$224$	16.2573	−	0.841899i	1.08624	−	0.0562517i
$225$	−0.410659	−	26.6681i	−0.0273772	−	1.77787i
$226$	11.9846	−	4.03162i	0.797206	−	0.268179i
$227$	−1.36237			−0.0904234			−0.0452117	−	0.998977i	$-0.514396\pi$
$227$	−1.36237			−0.0904234			−0.0452117	+	0.998977i	$0.514396\pi$
$228$	−43.5321	−	5.97416i	−2.88298	−	0.395648i
$229$	5.92599	+	5.92599i	0.391601	+	0.391601i	0.875258	−	0.483657i	$-0.160692\pi$
$229$	5.92599	+	5.92599i	0.391601	+	0.391601i	−0.483657	+	0.875258i	$0.660692\pi$
$230$	−20.6870	−	10.0745i	−1.36406	−	0.664294i
$231$	8.30784			0.546616
$232$	16.3427	+	11.1154i	1.07295	+	0.729759i
$233$	−3.54716	−	3.54716i	−0.232382	−	0.232382i	0.581304	−	0.813686i	$-0.302543\pi$
$233$	−3.54716	−	3.54716i	−0.232382	−	0.232382i	−0.813686	+	0.581304i	$0.802543\pi$
$234$	14.8189	+	7.35847i	0.968743	+	0.481038i
$235$	28.8085	−	0.221797i	1.87926	−	0.0144684i
$236$	−4.73111	−	0.649277i	−0.307969	−	0.0422643i
$237$			37.6339i			2.44458i
$238$	7.11531	−	14.3292i	0.461217	−	0.928826i
$239$	−13.3983			−0.866665			−0.433332	−	0.901234i	$-0.642662\pi$
$239$	−13.3983			−0.866665			−0.433332	+	0.901234i	$0.642662\pi$
$240$	−12.8375	−	22.4040i	−0.828655	−	1.44617i
$241$	−1.52804			−0.0984299			−0.0492149	−	0.998788i	$-0.515672\pi$
$241$	−1.52804			−0.0984299			−0.0492149	+	0.998788i	$0.515672\pi$
$242$	0.628966	−	1.26665i	0.0404315	−	0.0814233i
$243$		−	10.2523i		−	0.657685i
$244$	0.965231	−	7.03338i	0.0617926	−	0.450266i
$245$	−2.01060	+	2.04180i	−0.128453	+	0.130446i
$246$	−22.4844	−	11.1648i	−1.43355	−	0.711842i
$247$	11.8024	+	11.8024i	0.750969	+	0.750969i
$248$	−12.7448	+	2.42628i	−0.809295	+	0.154069i
$249$	21.0944			1.33680
$250$	14.8657	−	5.38608i	0.940192	−	0.340646i
$251$	11.1274	+	11.1274i	0.702356	+	0.702356i	0.964916	−	0.262560i	$-0.0845666\pi$
$251$	11.1274	+	11.1274i	0.702356	+	0.702356i	−0.262560	+	0.964916i	$0.584567\pi$
$252$	4.17420	−	30.4163i	0.262950	−	1.91605i
$253$	−7.27631			−0.457458
$254$	4.42506	−	1.48859i	0.277653	−	0.0934021i
$255$	−25.3756	+	0.195367i	−1.58908	+	0.0122343i
$256$	−13.6776	−	8.30201i	−0.854850	−	0.518876i
$257$	−11.0066	−	11.0066i	−0.686570	−	0.686570i	0.274902	−	0.961472i	$-0.411355\pi$
$257$	−11.0066	−	11.0066i	−0.686570	−	0.686570i	−0.961472	+	0.274902i	$0.911355\pi$
$258$	−1.23389	+	2.48488i	−0.0768185	+	0.154702i
$259$	−16.3710	−	16.3710i	−1.01725	−	1.01725i
$260$	−1.25872	+	9.72739i	−0.0780628	+	0.603267i
$261$	26.3571	−	26.3571i	1.63147	−	1.63147i
$262$	−1.37447	+	0.462371i	−0.0849152	+	0.0285654i
$263$	12.6552	−	12.6552i	0.780356	−	0.780356i	−0.199535	−	0.979891i	$-0.563943\pi$
$263$	12.6552	−	12.6552i	0.780356	−	0.780356i	0.979891	+	0.199535i	$0.0639431\pi$
$264$	−6.75175	−	4.59216i	−0.415541	−	0.282628i
$265$	9.41939	−	9.56556i	0.578629	−	0.587607i
$266$	13.7746	−	27.7402i	0.844578	−	1.70086i
$267$		−	8.10744i		−	0.496167i
$268$	5.61219	+	7.39760i	0.342819	+	0.451880i
$269$	7.55422	−	7.55422i	0.460589	−	0.460589i	−0.438259	−	0.898849i	$-0.644405\pi$
$269$	7.55422	−	7.55422i	0.460589	−	0.460589i	0.898849	+	0.438259i	$0.144405\pi$
$270$	−20.1447	+	6.94975i	−1.22597	+	0.422948i
$271$			17.0423i			1.03525i	0.855608	+	0.517624i	$0.173183\pi$
$271$			17.0423i			1.03525i	−0.855608	+	0.517624i	$0.826817\pi$
$272$	−13.7031	+	7.71232i	−0.830870	+	0.467628i
$273$	−12.8843	+	12.8843i	−0.779793	+	0.779793i
$274$	−3.11055	+	1.04639i	−0.187915	+	0.0632145i
$275$	3.48068	−	3.58955i	0.209893	−	0.216458i
$276$	−5.71202	+	41.6220i	−0.343823	+	2.50535i
$277$	13.6507			0.820193			0.410097	−	0.912042i	$-0.365495\pi$
$277$	13.6507			0.820193			0.410097	+	0.912042i	$0.365495\pi$
$278$	−4.81412	+	1.61946i	−0.288731	+	0.0971290i
$279$			24.4676i			1.46484i
$280$	17.8527	−	3.54134i	1.06690	−	0.211636i
$281$		−	4.61742i		−	0.275452i	−0.990470	−	0.137726i	$-0.956021\pi$
$281$		−	4.61742i		−	0.275452i	0.990470	−	0.137726i	$-0.0439794\pi$
$282$	−16.7715	−	49.8560i	−0.998729	−	2.96888i
$283$	−9.94355			−0.591083			−0.295541	−	0.955330i	$-0.595500\pi$
$283$	−9.94355			−0.591083			−0.295541	+	0.955330i	$0.595500\pi$
$284$	−16.6915	−	22.0015i	−0.990456	−	1.30555i
$285$	−49.1251	+	0.378214i	−2.90992	+	0.0224034i
$286$	0.988957	+	2.93983i	0.0584783	+	0.173836i
$287$	12.5121	−	12.5121i	0.738567	−	0.738567i
$288$	−20.2049	+	22.4119i	−1.19059	+	1.32063i
$289$		−	1.54664i		−	0.0909791i
$290$	19.8667	+	9.67505i	1.16661	+	0.568139i
$291$	34.8823	−	34.8823i	2.04484	−	2.04484i
$292$	0.229275	−	1.67067i	0.0134173	−	0.0977685i
$293$			21.2206i			1.23972i	0.784711	+	0.619862i	$0.212811\pi$
$293$			21.2206i			1.23972i	−0.784711	+	0.619862i	$0.787189\pi$
$294$	4.68614	+	2.32694i	0.273301	+	0.135710i
$295$	−5.33896	+	0.0411046i	−0.310846	+	0.00239320i
$296$	4.25558	+	22.3537i	0.247351	+	1.29928i
$297$	−4.76502	+	4.76502i	−0.276494	+	0.276494i
$298$	−5.01131	−	14.8969i	−0.290297	−	0.862955i
$299$	11.2845	−	11.2845i	0.652601	−	0.652601i
$300$	−17.8006	−	22.7280i	−1.02772	−	1.31220i
$301$	−1.38279	−	1.38279i	−0.0797025	−	0.0797025i
$302$	19.1247	+	9.49654i	1.10050	+	0.546464i
$303$	1.51310	+	1.51310i	0.0869252	+	0.0869252i
$304$	−26.5280	+	14.9304i	−1.52148	+	0.856318i
$305$	−0.0611071	−	7.93703i	−0.00349898	−	0.454473i
$306$	9.45528	+	28.1073i	0.540522	+	1.60679i
$307$	8.19084			0.467476			0.233738	−	0.972300i	$-0.424904\pi$
$307$	8.19084			0.467476			0.233738	+	0.972300i	$0.424904\pi$
$308$	4.58531	−	3.47865i	0.261272	−	0.198214i
$309$	6.67838	+	6.67838i	0.379920	+	0.379920i
$310$	−13.7120	+	4.73051i	−0.778787	+	0.268675i
$311$	6.31498			0.358090			0.179045	−	0.983841i	$-0.442699\pi$
$311$	6.31498			0.358090			0.179045	+	0.983841i	$0.442699\pi$
$312$	17.5928	−	3.34922i	0.995996	−	0.189612i
$313$	−3.09169	−	3.09169i	−0.174753	−	0.174753i	0.614311	−	0.789064i	$-0.289434\pi$
$313$	−3.09169	−	3.09169i	−0.174753	−	0.174753i	−0.789064	+	0.614311i	$0.789434\pi$
$314$	0.725940	−	1.46194i	0.0409672	−	0.0825022i
$315$	−0.264261	−	34.3242i	−0.0148894	−	1.93395i
$316$	15.7580	+	20.7711i	0.886457	+	1.16847i
$317$		−	10.2677i		−	0.576693i	−0.957526	−	0.288347i	$-0.906894\pi$
$317$		−	10.2677i		−	0.576693i	0.957526	−	0.288347i	$-0.0931056\pi$
$318$	−21.9539	−	10.9014i	−1.23111	−	0.611321i
$319$	6.98780			0.391242
$320$	−16.4663	−	6.99005i	−0.920494	−	0.390756i
$321$	54.7790			3.05746
$322$	−26.5230	−	13.1702i	−1.47807	−	0.733949i
$323$			29.9164i			1.66459i
$324$	4.17209	+	5.49936i	0.231783	+	0.305520i
$325$	0.168848	+	10.9649i	0.00936599	+	0.608225i
$326$	13.4292	−	27.0446i	0.743776	−	1.49786i
$327$	3.93535	+	3.93535i	0.217625	+	0.217625i
$328$	−17.0846	+	3.25248i	−0.943340	+	0.179588i
$329$	37.0769			2.04412
$330$	−8.20765	−	3.99711i	−0.451816	−	0.220034i
$331$	10.0350	+	10.0350i	0.551573	+	0.551573i	0.926895	−	0.375321i	$-0.122468\pi$
$331$	10.0350	+	10.0350i	0.551573	+	0.551573i	−0.375321	+	0.926895i	$0.622468\pi$
$332$	11.6425	−	8.83261i	0.638967	−	0.484753i
$333$	42.9150			2.35172
$334$	−7.40075	−	21.9999i	−0.404951	−	1.20378i
$335$	7.39716	+	7.28413i	0.404150	+	0.397974i
$336$	−16.2990	−	28.9597i	−0.889185	−	1.57988i
$337$	9.25202	+	9.25202i	0.503989	+	0.503989i	0.912675	−	0.408686i	$-0.134013\pi$
$337$	9.25202	+	9.25202i	0.503989	+	0.503989i	−0.408686	+	0.912675i	$0.634013\pi$
$338$	10.3734	+	5.15103i	0.564241	+	0.280179i
$339$	−18.2519	−	18.2519i	−0.991306	−	0.991306i
$340$	−13.9237	+	10.7331i	−0.755116	+	0.582083i
$341$	−3.24342	+	3.24342i	−0.175641	+	0.175641i
$342$	18.3046	+	54.4135i	0.989802	+	2.94234i
$343$	11.6365	−	11.6365i	0.628309	−	0.628309i
$344$	0.359450	+	1.88812i	0.0193802	+	0.101801i
$345$	0.361618	+	46.9696i	0.0194689	+	2.52876i
$346$	−16.1564	−	8.02260i	−0.868573	−	0.431298i
$347$			25.4494i			1.36620i	0.730326	+	0.683099i	$0.239368\pi$
$347$			25.4494i			1.36620i	−0.730326	+	0.683099i	$0.760632\pi$
$348$	5.48553	−	39.9716i	0.294055	−	2.14270i
$349$	−15.1714	+	15.1714i	−0.812106	+	0.812106i	−0.984949	−	0.172843i	$-0.944705\pi$
$349$	−15.1714	+	15.1714i	−0.812106	+	0.812106i	0.172843	+	0.984949i	$0.444705\pi$
$350$	19.1846	−	6.78426i	1.02546	−	0.362634i
$351$		−	14.7797i		−	0.788884i
$352$	−5.64928	+	0.292553i	−0.301108	+	0.0155931i
$353$	−16.9001	+	16.9001i	−0.899503	+	0.899503i	−0.995392	−	0.0958888i	$-0.969431\pi$
$353$	−16.9001	+	16.9001i	−0.899503	+	0.899503i	0.0958888	+	0.995392i	$0.469431\pi$
$354$	3.10819	+	9.23960i	0.165199	+	0.491079i
$355$	−22.0002	−	21.6640i	−1.16765	−	1.14981i
$356$	−3.39474	−	4.47471i	−0.179921	−	0.237159i
$357$	−32.6587			−1.72848
$358$	11.1120	+	33.0322i	0.587287	+	1.74580i
$359$			23.5838i			1.24471i	0.782737	+	0.622353i	$0.213823\pi$
$359$			23.5838i			1.24471i	−0.782737	+	0.622353i	$0.786177\pi$
$360$	−18.7579	+	28.0412i	−0.988628	+	1.47790i
$361$			38.9157i			2.04820i
$362$	1.15742	−	0.389354i	0.0608325	−	0.0204640i
$363$	−2.88691			−0.151523
$364$	−1.71628	+	12.5061i	−0.0899574	+	0.655496i
$365$	−0.0145150	−	1.88532i	−0.000759751	−	0.0986819i
$366$	−13.7358	+	4.62072i	−0.717983	+	0.241529i
$367$	9.55980	−	9.55980i	0.499018	−	0.499018i	−0.412115	−	0.911132i	$-0.635210\pi$
$367$	9.55980	−	9.55980i	0.499018	−	0.499018i	0.911132	+	0.412115i	$0.135210\pi$
$368$	14.2753	+	25.3640i	0.744151	+	1.32219i
$369$			32.7992i			1.70746i
$370$	8.29708	+	24.0501i	0.431345	+	1.25031i
$371$	12.2169	−	12.2169i	0.634272	−	0.634272i
$372$	16.0069	+	21.0992i	0.829919	+	1.09394i
$373$			22.3552i			1.15751i	0.815503	+	0.578753i	$0.196460\pi$
$373$			22.3552i			1.15751i	−0.815503	+	0.578753i	$0.803540\pi$
$374$	−2.47251	+	4.97930i	−0.127851	+	0.257473i
$375$	−23.3440	−	22.2898i	−1.20548	−	1.15104i
$376$	−30.1323	−	20.4943i	−1.55395	−	1.05691i
$377$	−10.8371	+	10.8371i	−0.558138	+	0.558138i
$378$	−25.9938	+	8.74429i	−1.33698	+	0.449758i
$379$	−20.3991	+	20.3991i	−1.04783	+	1.04783i	−0.0490364	+	0.998797i	$0.515615\pi$
$379$	−20.3991	+	20.3991i	−1.04783	+	1.04783i	−0.998797	+	0.0490364i	$0.984385\pi$
$380$	−26.9550	+	20.7783i	−1.38276	+	1.06591i
$381$	−6.73910	−	6.73910i	−0.345254	−	0.345254i
$382$	−10.1963	+	20.5340i	−0.521690	+	1.05061i
$383$	−14.3315	−	14.3315i	−0.732306	−	0.732306i	0.238770	−	0.971076i	$-0.423256\pi$
$383$	−14.3315	−	14.3315i	−0.732306	−	0.732306i	−0.971076	+	0.238770i	$0.923256\pi$
$384$	−2.76132	+	32.5447i	−0.140913	+	1.66079i
$385$	4.51498	−	4.58504i	0.230105	−	0.233675i
$386$	0.772387	−	0.259830i	0.0393135	−	0.0132250i
$387$	3.62483			0.184261
$388$	4.64657	−	33.8583i	0.235894	−	1.71890i
$389$	6.36393	+	6.36393i	0.322664	+	0.322664i	0.849788	−	0.527124i	$-0.176730\pi$
$389$	6.36393	+	6.36393i	0.322664	+	0.322664i	−0.527124	+	0.849788i	$0.676730\pi$
$390$	18.9279	−	6.52995i	0.958450	−	0.330657i
$391$	28.6037			1.44655
$392$	3.56073	−	0.677873i	0.179844	−	0.0342378i
$393$	2.09324	+	2.09324i	0.105590	+	0.105590i
$394$	−20.3127	−	10.0865i	−1.02334	−	0.508148i
$395$	20.7699	+	20.4525i	1.04505	+	1.02908i
$396$	−1.45050	+	10.5694i	−0.0728905	+	0.531133i
$397$		−	9.10601i		−	0.457017i	−0.973542	−	0.228509i	$-0.926615\pi$
$397$		−	9.10601i		−	0.457017i	0.973542	−	0.228509i	$-0.0733850\pi$
$398$	1.50758	−	3.03605i	0.0755680	−	0.152183i
$399$	−63.2246			−3.16519
$400$	−19.3413	−	5.09076i	−0.967063	−	0.254538i
$401$	−21.5540			−1.07636			−0.538178	−	0.842831i	$-0.680887\pi$
$401$	−21.5540			−1.07636			−0.538178	+	0.842831i	$0.680887\pi$
$402$	8.43019	−	16.9772i	0.420460	−	0.846747i
$403$		−	10.0602i		−	0.501133i
$404$	1.46868	+	0.201555i	0.0730696	+	0.0100278i
$405$	5.49903	+	5.41501i	0.273249	+	0.269074i
$406$	25.4713	+	12.6480i	1.26412	+	0.627711i
$407$	5.68880	+	5.68880i	0.281983	+	0.281983i
$408$	26.5416	+	18.0521i	1.31401	+	0.893713i
$409$	11.7008			0.578565			0.289283	−	0.957244i	$-0.406583\pi$
$409$	11.7008			0.578565			0.289283	+	0.957244i	$0.406583\pi$
$410$	−18.3811	+	6.34133i	−0.907779	+	0.313176i
$411$	4.73718	+	4.73718i	0.233668	+	0.233668i
$412$	6.48234	+	0.889608i	0.319362	+	0.0438279i
$413$	−6.87131			−0.338115
$414$	52.0259	−	17.5015i	2.55693	−	0.860150i
$415$	11.4639	−	11.6418i	0.562743	−	0.571475i
$416$	8.30753	−	9.21495i	0.407310	−	0.451800i
$417$	7.33161	+	7.33161i	0.359030	+	0.359030i
$418$	−4.78658	+	9.63950i	−0.234119	+	0.471484i
$419$	−1.33956	−	1.33956i	−0.0654416	−	0.0654416i	0.673629	−	0.739070i	$-0.264735\pi$
$419$	−1.33956	−	1.33956i	−0.0654416	−	0.0654416i	−0.739070	+	0.673629i	$0.764735\pi$
$420$	−22.6830	−	29.4259i	−1.10682	−	1.43584i
$421$	23.0615	−	23.0615i	1.12395	−	1.12395i	0.132804	−	0.991142i	$-0.457602\pi$
$421$	23.0615	−	23.0615i	1.12395	−	1.12395i	0.991142	−	0.132804i	$-0.0423982\pi$
$422$	9.45786	−	3.18161i	0.460401	−	0.154879i
$423$	−48.5967	+	48.5967i	−2.36285	+	2.36285i
$424$	−16.6816	+	3.17574i	−0.810128	+	0.154228i
$425$	−13.6828	+	14.1108i	−0.663714	+	0.684474i
$426$	−25.0726	+	50.4927i	−1.21477	+	2.44638i
$427$		−	10.2151i		−	0.494341i
$428$	30.2339	−	22.9370i	1.46141	−	1.10870i
$429$	4.47719	−	4.47719i	0.216161	−	0.216161i
$430$	0.700818	+	2.03141i	0.0337964	+	0.0979631i
$431$		−	8.28421i		−	0.399036i	−0.979894	−	0.199518i	$-0.936062\pi$
$431$		−	8.28421i		−	0.399036i	0.979894	−	0.199518i	$-0.0639377\pi$
$432$	25.9584	+	7.26161i	1.24893	+	0.349375i
$433$	6.57616	−	6.57616i	0.316030	−	0.316030i	−0.531210	−	0.847240i	$-0.678263\pi$
$433$	6.57616	−	6.57616i	0.316030	−	0.316030i	0.847240	+	0.531210i	$0.178263\pi$
$434$	−17.6933	+	5.95201i	−0.849305	+	0.285706i
$435$	−0.347280	−	45.1072i	−0.0166508	−	2.16272i
$436$	3.81982	+	0.524216i	0.182936	+	0.0251054i
$437$	55.3744			2.64892
$438$	−3.26272	+	1.09758i	−0.155899	+	0.0524443i
$439$		−	4.45338i		−	0.212548i	−0.994337	−	0.106274i	$-0.966108\pi$
$439$		−	4.45338i		−	0.212548i	0.994337	−	0.106274i	$-0.0338921\pi$
$440$	−6.20368	+	1.23059i	−0.295749	+	0.0586660i
$441$		−	6.83594i		−	0.325521i
$442$	−3.88767	−	11.5567i	−0.184917	−	0.549696i
$443$	40.8004			1.93848			0.969242	−	0.246109i	$-0.0791521\pi$
$443$	40.8004			1.93848			0.969242	+	0.246109i	$0.0791521\pi$
$444$	37.0069	−	28.0753i	1.75627	−	1.33239i
$445$	−4.47444	−	4.40607i	−0.212109	−	0.208868i
$446$	−8.00371	−	23.7923i	−0.378987	−	1.12660i
$447$	−22.6871	+	22.6871i	−1.07306	+	1.07306i
$448$	−21.1218	−	9.15890i	−0.997913	−	0.432717i
$449$		−	2.09129i		−	0.0986940i	−0.998782	−	0.0493470i	$-0.984286\pi$
$449$		−	2.09129i		−	0.0986940i	0.998782	−	0.0493470i	$-0.0157140\pi$
$450$	−16.2531	+	34.0374i	−0.766181	+	1.60454i
$451$	−4.34786	+	4.34786i	−0.204733	+	0.204733i
$452$	−17.7161	−	2.43128i	−0.833295	−	0.114358i
$453$		−	43.5884i		−	2.04796i
$454$	1.72564	+	0.856882i	0.0809883	+	0.0402155i
$455$	0.108655	+	14.1128i	0.00509381	+	0.661620i
$456$	51.3824	+	34.9474i	2.40620	+	1.63656i
$457$	−2.89540	+	2.89540i	−0.135441	+	0.135441i	−0.771577	−	0.636136i	$-0.780532\pi$
$457$	−2.89540	+	2.89540i	−0.135441	+	0.135441i	0.636136	+	0.771577i	$0.280532\pi$
$458$	−3.77891	−	11.2334i	−0.176577	−	0.524903i
$459$	18.7316	−	18.7316i	0.874318	−	0.874318i
$460$	19.8666	+	25.7723i	0.926286	+	1.20164i
$461$	−25.8045	−	25.8045i	−1.20183	−	1.20183i	−0.973608	−	0.228227i	$-0.926707\pi$
$461$	−25.8045	−	25.8045i	−1.20183	−	1.20183i	−0.228227	−	0.973608i	$-0.573293\pi$
$462$	−10.5231	−	5.22535i	−0.489580	−	0.243105i
$463$	−5.84979	−	5.84979i	−0.271863	−	0.271863i	0.557987	−	0.829850i	$-0.311574\pi$
$463$	−5.84979	−	5.84979i	−0.271863	−	0.271863i	−0.829850	+	0.557987i	$0.811574\pi$
$464$	−13.7093	−	24.3583i	−0.636436	−	1.13080i
$465$	21.0979	+	20.7755i	0.978392	+	0.963442i
$466$	2.26196	+	6.72405i	0.104783	+	0.311486i
$467$	0.750391			0.0347240			0.0173620	−	0.999849i	$-0.494473\pi$
$467$	0.750391			0.0347240			0.0173620	+	0.999849i	$0.494473\pi$
$468$	−14.1422	−	18.6412i	−0.653721	−	0.861690i
$469$	9.44750	+	9.44750i	0.436245	+	0.436245i
$470$	−36.6298	−	17.8387i	−1.68961	−	0.822836i
$471$	−3.33201			−0.153531
$472$	5.58428	+	3.79811i	0.257038	+	0.174822i
$473$	0.480508	+	0.480508i	0.0220938	+	0.0220938i
$474$	23.6704	−	47.6689i	1.08722	−	2.18951i
$475$	−26.4888	+	27.3173i	−1.21539	+	1.25341i
$476$	−18.0252	+	13.6748i	−0.826184	+	0.626785i
$477$			32.0254i			1.46634i
$478$	16.9710	+	8.42709i	0.776234	+	0.385446i
$479$	7.83800			0.358127			0.179064	−	0.983837i	$-0.442693\pi$
$479$	7.83800			0.358127			0.179064	+	0.983837i	$0.442693\pi$
$480$	2.16923	+	36.4523i	0.0990112	+	1.66381i
$481$	−17.6451			−0.804545
$482$	1.93549	+	0.961087i	0.0881594	+	0.0437763i
$483$			60.4504i			2.75059i
$484$	−1.59336	+	1.20880i	−0.0724254	+	0.0549456i
$485$	−0.294167	−	38.2085i	−0.0133574	−	1.73496i
$486$	−6.44835	+	12.9861i	−0.292503	+	0.589060i
$487$	4.01808	+	4.01808i	0.182077	+	0.182077i	0.792260	−	0.610183i	$-0.208904\pi$
$487$	4.01808	+	4.01808i	0.182077	+	0.182077i	−0.610183	+	0.792260i	$0.708904\pi$
$488$	−5.64637	+	8.30174i	−0.255599	+	0.375802i
$489$	−61.6392			−2.78742
$490$	3.83095	−	1.32165i	0.173065	−	0.0597059i
$491$	−13.3956	−	13.3956i	−0.604537	−	0.604537i	0.336976	−	0.941513i	$-0.390596\pi$
$491$	−13.3956	−	13.3956i	−0.604537	−	0.604537i	−0.941513	+	0.336976i	$0.890596\pi$
$492$	21.4575	+	28.2838i	0.967380	+	1.27513i
$493$	−27.4696			−1.23717
$494$	−7.52620	−	22.3728i	−0.338620	−	1.00660i
$495$	0.0918288	+	11.9274i	0.00412740	+	0.536096i
$496$	17.6692	+	4.94279i	0.793372	+	0.221938i
$497$	−28.0982	−	28.0982i	−1.26038	−	1.26038i
$498$	−26.7192	−	13.2677i	−1.19732	−	0.594538i
$499$	20.1431	+	20.1431i	0.901728	+	0.901728i	0.995586	−	0.0938578i	$-0.0299199\pi$
$499$	20.1431	+	20.1431i	0.901728	+	0.901728i	−0.0938578	+	0.995586i	$0.529920\pi$
$500$	−22.2173	−	2.52777i	−0.993590	−	0.113045i
$501$	−33.5045	+	33.5045i	−1.49687	+	1.49687i
$502$	−7.09577	−	21.0933i	−0.316700	−	0.941440i
$503$	−4.51777	+	4.51777i	−0.201437	+	0.201437i	−0.800616	−	0.599178i	$-0.795494\pi$
$503$	−4.51777	+	4.51777i	−0.201437	+	0.201437i	0.599178	+	0.800616i	$0.295494\pi$
$504$	−24.4181	+	35.9014i	−1.08767	+	1.59917i
$505$	1.65738	−	0.0127601i	0.0737523	−	0.000567818i
$506$	9.21654	+	4.57655i	0.409725	+	0.203453i
$507$		−	23.6428i		−	1.05002i
$508$	−6.54127	−	0.897695i	−0.290222	−	0.0398288i
$509$	−16.1092	+	16.1092i	−0.714026	+	0.714026i	−0.967375	−	0.253349i	$-0.918468\pi$
$509$	−16.1092	+	16.1092i	−0.714026	+	0.714026i	0.253349	+	0.967375i	$0.418468\pi$
$510$	32.2649	+	15.7129i	1.42871	+	0.695781i
$511$		−	2.42643i		−	0.107339i
$512$	12.1030	+	19.1185i	0.534884	+	0.844926i
$513$	36.2629	−	36.2629i	1.60105	−	1.60105i
$514$	7.01870	+	20.8642i	0.309582	+	0.920281i
$515$	7.31519	−	0.0563196i	0.322346	−	0.00248174i
$516$	3.12581	−	2.37140i	0.137606	−	0.104395i
$517$	−12.8839			−0.566635
$518$	10.4395	+	31.0332i	0.458687	+	1.36352i
$519$			36.8232i			1.61636i
$520$	7.71256	−	11.5295i	0.338218	−	0.505602i
$521$			4.16709i			0.182563i	0.995825	+	0.0912817i	$0.0290964\pi$
$521$			4.16709i			0.182563i	−0.995825	+	0.0912817i	$0.970904\pi$
$522$	−49.9630	+	16.8075i	−2.18682	+	0.735645i
$523$	32.0597			1.40187			0.700936	−	0.713224i	$-0.252766\pi$
$523$	32.0597			1.40187			0.700936	+	0.713224i	$0.252766\pi$
$524$	2.03179	+	0.278834i	0.0887592	+	0.0121809i
$525$	−29.8214	−	28.9169i	−1.30151	−	1.26204i
$526$	−23.9895	+	8.07004i	−1.04599	+	0.351870i
$527$	12.7501	−	12.7501i	0.555405	−	0.555405i
$528$	5.66379	+	10.0633i	0.246485	+	0.437948i
$529$		−	29.9447i		−	1.30194i
$530$	−17.9475	+	6.19173i	−0.779589	+	0.268952i
$531$	9.00622	−	9.00622i	0.390837	−	0.390837i
$532$	−34.8953	+	26.4733i	−1.51290	+	1.14776i
$533$		−	13.4858i		−	0.584137i
$534$	−5.09931	+	10.2693i	−0.220669	+	0.444395i
$535$	29.7702	−	30.2321i	1.28708	−	1.30705i
$536$	−2.45584	−	12.9000i	−0.106076	−	0.557197i
$537$	50.3060	−	50.3060i	2.17086	−	2.17086i
$538$	−14.3199	+	4.81720i	−0.617375	+	0.207684i
$539$	0.906171	−	0.906171i	0.0390316	−	0.0390316i
$540$	29.8874	+	3.86743i	1.28615	+	0.166428i
$541$	1.01291	+	1.01291i	0.0435485	+	0.0435485i	0.728546	−	0.684997i	$-0.240197\pi$
$541$	1.01291	+	1.01291i	0.0435485	+	0.0435485i	−0.684997	+	0.728546i	$0.740197\pi$
$542$	10.7191	−	21.5867i	0.460423	−	0.927227i
$543$	−1.76268	−	1.76268i	−0.0756437	−	0.0756437i
$544$	22.2078	−	1.15005i	0.952150	−	0.0493079i
$545$	4.31059	−	0.0331872i	0.184645	−	0.00142158i
$546$	24.4237	−	8.21610i	1.04524	−	0.351617i
$547$	0.542595			0.0231997			0.0115998	−	0.999933i	$-0.496308\pi$
$547$	0.542595			0.0231997			0.0115998	+	0.999933i	$0.496308\pi$
$548$	4.59812	+	0.631026i	0.196422	+	0.0269561i
$549$	13.3889	+	13.3889i	0.571423	+	0.571423i
$550$	−6.66651	+	2.35748i	−0.284261	+	0.100523i
$551$	−53.1788			−2.26549
$552$	33.4139	−	49.1278i	1.42219	−	2.09102i
$553$	26.5269	+	26.5269i	1.12804	+	1.12804i
$554$	−17.2907	−	8.58585i	−0.734612	−	0.364778i
$555$	36.4393	−	37.0047i	1.54676	−	1.57076i
$556$	7.11639	+	0.976622i	0.301802	+	0.0414180i
$557$			14.5708i			0.617386i	0.951162	+	0.308693i	$0.0998916\pi$
$557$			14.5708i			0.617386i	−0.951162	+	0.308693i	$0.900108\pi$
$558$	15.3893	−	30.9919i	0.651480	−	1.31199i
$559$	−1.49040			−0.0630372
$560$	−24.8405	−	6.74312i	−1.04970	−	0.284949i
$561$	11.3487			0.479141
$562$	−2.90420	+	5.84865i	−0.122506	+	0.246711i
$563$			39.0332i			1.64505i	0.568726	+	0.822527i	$0.307437\pi$
$563$			39.0332i			1.64505i	−0.568726	+	0.822527i	$0.692563\pi$
$564$	−10.1141	+	73.6988i	−0.425881	+	3.10328i
$565$	−19.9923	+	0.153920i	−0.841080	+	0.00647547i
$566$	12.5950	+	6.25416i	0.529407	+	0.262882i
$567$	7.02325	+	7.02325i	0.294949	+	0.294949i
$568$	7.30402	+	38.3666i	0.306470	+	1.60983i
$569$	−4.02290			−0.168649			−0.0843244	−	0.996438i	$-0.526873\pi$
$569$	−4.02290			−0.168649			−0.0843244	+	0.996438i	$0.526873\pi$
$570$	62.4622	+	30.4190i	2.61625	+	1.27411i
$571$	−31.4970	−	31.4970i	−1.31811	−	1.31811i	−0.915274	−	0.402833i	$-0.868026\pi$
$571$	−31.4970	−	31.4970i	−1.31811	−	1.31811i	−0.402833	−	0.915274i	$-0.631974\pi$
$572$	0.596393	−	4.34576i	0.0249365	−	0.181705i
$573$	46.8005			1.95512
$574$	−23.7182	+	7.97877i	−0.989977	+	0.333027i
$575$	26.1187	+	25.3265i	1.08922	+	1.05619i
$576$	39.6889	−	15.6798i	1.65370	−	0.653325i
$577$	−14.7579	−	14.7579i	−0.614381	−	0.614381i	0.329704	−	0.944085i	$-0.393051\pi$
$577$	−14.7579	−	14.7579i	−0.614381	−	0.614381i	−0.944085	+	0.329704i	$0.893051\pi$
$578$	−0.972787	+	1.95906i	−0.0404626	+	0.0814860i
$579$	−1.17630	−	1.17630i	−0.0488853	−	0.0488853i
$580$	−19.0789	−	24.7504i	−0.792208	−	1.02770i
$581$	14.8687	−	14.8687i	0.616859	−	0.616859i
$582$	−66.1235	+	22.2439i	−2.74091	+	0.922039i
$583$	−4.24529	+	4.24529i	−0.175822	+	0.175822i
$584$	−1.34121	+	1.97195i	−0.0554995	+	0.0815997i
$585$	−18.6401	−	18.3553i	−0.770673	−	0.758897i
$586$	13.3471	−	26.8791i	0.551362	−	1.11037i
$587$		−	10.0263i		−	0.413829i	−0.978359	−	0.206914i	$-0.933658\pi$
$587$		−	10.0263i		−	0.413829i	0.978359	−	0.206914i	$-0.0663422\pi$
$588$	−4.47212	−	5.89484i	−0.184427	−	0.243099i
$589$	24.6832	−	24.6832i	1.01705	−	1.01705i
$590$	6.78845	+	3.30596i	0.279476	+	0.136104i
$591$			46.2961i			1.90437i
$592$	8.66941	−	30.9910i	0.356311	−	1.27372i
$593$	8.00919	−	8.00919i	0.328898	−	0.328898i	−0.523269	−	0.852167i	$-0.675288\pi$
$593$	8.00919	−	8.00919i	0.328898	−	0.328898i	0.852167	+	0.523269i	$0.175288\pi$
$594$	9.03264	−	3.03857i	0.370614	−	0.124674i
$595$	−17.7487	+	18.0241i	−0.727626	+	0.738917i
$596$	−3.02208	+	22.0211i	−0.123789	+	0.902020i
$597$	−6.91967			−0.283203
$598$	−21.3911	+	7.19596i	−0.874749	+	0.294265i
$599$			37.5624i			1.53476i	0.641193	+	0.767380i	$0.278440\pi$
$599$			37.5624i			1.53476i	−0.641193	+	0.767380i	$0.721560\pi$
$600$	8.25192	+	39.9844i	0.336883	+	1.63236i
$601$		−	19.6343i		−	0.800901i	−0.916318	−	0.400451i	$-0.868854\pi$
$601$		−	19.6343i		−	0.800901i	0.916318	−	0.400451i	$-0.131146\pi$
$602$	0.881781	+	2.62123i	0.0359387	+	0.106833i
$603$	−24.7656			−1.00854
$604$	−18.2513	−	24.0576i	−0.742634	−	0.978889i
$605$	−1.56892	+	1.59326i	−0.0637856	+	0.0647754i
$606$	−0.964878	−	2.86825i	−0.0391955	−	0.116515i
$607$	19.0803	−	19.0803i	0.774444	−	0.774444i	−0.204436	−	0.978880i	$-0.565536\pi$
$607$	19.0803	−	19.0803i	0.774444	−	0.774444i	0.978880	+	0.204436i	$0.0655359\pi$
$608$	42.9924	−	2.22640i	1.74357	−	0.0902924i
$609$		−	58.0535i		−	2.35245i
$610$	−4.91472	+	10.0919i	−0.198991	+	0.408608i
$611$	19.9812	−	19.9812i	0.808352	−	0.808352i
$612$	5.70203	−	41.5492i	0.230491	−	1.67953i
$613$		−	2.52577i		−	0.102015i	−0.998698	−	0.0510075i	$-0.983757\pi$
$613$		−	2.52577i		−	0.102015i	0.998698	−	0.0510075i	$-0.0162433\pi$
$614$	−10.3749	−	5.15176i	−0.418698	−	0.207908i
$615$	28.2821	+	27.8500i	1.14044	+	1.12302i
$616$	−7.99594	+	1.52222i	−0.322165	+	0.0613321i
$617$	−11.9830	+	11.9830i	−0.482417	+	0.482417i	−0.905903	−	0.423486i	$-0.860806\pi$
$617$	−11.9830	+	11.9830i	−0.482417	+	0.482417i	0.423486	+	0.905903i	$0.360806\pi$
$618$	−4.25870	−	12.6597i	−0.171310	−	0.509246i
$619$	22.6167	−	22.6167i	0.909044	−	0.909044i	−0.0871513	−	0.996195i	$-0.527776\pi$
$619$	22.6167	−	22.6167i	0.909044	−	0.909044i	0.996195	+	0.0871513i	$0.0277764\pi$
$620$	20.3436	+	2.63246i	0.817018	+	0.105722i
$621$	−34.6717	−	34.6717i	−1.39133	−	1.39133i
$622$	−7.99887	−	3.97191i	−0.320726	−	0.159259i
$623$	−5.71466	−	5.71466i	−0.228953	−	0.228953i
$624$	−24.3904	−	6.82298i	−0.976399	−	0.273138i
$625$	−24.9881	+	0.769762i	−0.999526	+	0.0307905i
$626$	1.97152	+	5.86066i	0.0787978	+	0.234239i
$627$	21.9701			0.877400
$628$	−1.83902	+	1.39518i	−0.0733851	+	0.0556736i
$629$	−22.3631	−	22.3631i	−0.891676	−	0.891676i
$630$	−21.2540	+	43.6429i	−0.846780	+	1.73878i
$631$	−1.80470			−0.0718440			−0.0359220	−	0.999355i	$-0.511437\pi$
$631$	−1.80470			−0.0718440			−0.0359220	+	0.999355i	$0.511437\pi$
$632$	−6.89555	−	36.2210i	−0.274290	−	1.44079i
$633$	−14.4037	−	14.4037i	−0.572498	−	0.572498i
$634$	−6.45806	+	13.0056i	−0.256482	+	0.516519i
$635$	−7.38169	+	0.0568315i	−0.292933	+	0.00225529i
$636$	20.9513	+	27.6165i	0.830773	+	1.09507i
$637$			2.81069i			0.111363i
$638$	−8.85109	−	4.39509i	−0.350418	−	0.174003i
$639$	73.6566			2.91381
$640$	16.4605	+	19.2107i	0.650660	+	0.759369i
$641$	−15.3147			−0.604896			−0.302448	−	0.953166i	$-0.597804\pi$
$641$	−15.3147			−0.604896			−0.302448	+	0.953166i	$0.597804\pi$
$642$	−69.3858	−	34.4541i	−2.73844	−	1.35980i
$643$			4.11917i			0.162444i	0.996696	+	0.0812220i	$0.0258823\pi$
$643$			4.11917i			0.162444i	−0.996696	+	0.0812220i	$0.974118\pi$
$644$	25.3117	+	33.3641i	0.997422	+	1.31473i
$645$	3.07786	−	3.12562i	0.121191	−	0.123071i
$646$	18.8164	−	37.8936i	0.740322	−	1.49090i
$647$	−7.42125	−	7.42125i	−0.291759	−	0.291759i	0.546016	−	0.837775i	$-0.316144\pi$
$647$	−7.42125	−	7.42125i	−0.291759	−	0.291759i	−0.837775	+	0.546016i	$0.816144\pi$
$648$	−1.82567	−	9.58987i	−0.0717190	−	0.376726i
$649$	2.38773			0.0937265
$650$	6.68270	−	13.9949i	0.262117	−	0.548926i
$651$	26.9458	+	26.9458i	1.05609	+	1.05609i
$652$	−34.0203	+	25.8095i	−1.33234	+	1.01078i
$653$	−13.5489			−0.530209			−0.265105	−	0.964220i	$-0.585406\pi$
$653$	−13.5489			−0.530209			−0.265105	+	0.964220i	$0.585406\pi$
$654$	−2.50950	−	7.45990i	−0.0981294	−	0.291705i
$655$	2.29284	−	0.0176525i	0.0895885	−	0.000689741i
$656$	23.6859	+	6.62590i	0.924780	+	0.258698i
$657$	3.18031	+	3.18031i	0.124076	+	0.124076i
$658$	−46.9635	−	23.3201i	−1.83083	−	0.909114i
$659$	−35.3966	−	35.3966i	−1.37886	−	1.37886i	−0.846555	−	0.532302i	$-0.821327\pi$
$659$	−35.3966	−	35.3966i	−1.37886	−	1.37886i	−0.532302	−	0.846555i	$-0.678673\pi$
$660$	7.88217	+	10.2253i	0.306813	+	0.398018i
$661$	12.0773	−	12.0773i	0.469751	−	0.469751i	−0.432083	−	0.901834i	$-0.642221\pi$
$661$	12.0773	−	12.0773i	0.469751	−	0.469751i	0.901834	+	0.432083i	$0.142221\pi$
$662$	−6.39915	−	19.0225i	−0.248710	−	0.739330i
$663$	−17.6002	+	17.6002i	−0.683534	+	0.683534i
$664$	−20.3024	+	3.86507i	−0.787887	+	0.149994i
$665$	−34.3600	+	34.8932i	−1.33243	+	1.35310i
$666$	−54.3582	−	26.9921i	−2.10634	−	1.04592i
$667$			50.8454i			1.96874i
$668$	−4.46304	+	32.5210i	−0.172680	+	1.25827i
$669$	−36.2343	+	36.2343i	−1.40090	+	1.40090i
$670$	−4.78814	−	13.8790i	−0.184982	−	0.536192i
$671$			3.54965i			0.137033i
$672$	2.43048	+	46.9333i	0.0937580	+	1.81049i
$673$	−13.8155	+	13.8155i	−0.532550	+	0.532550i	−0.921331	−	0.388780i	$-0.872897\pi$
$673$	−13.8155	+	13.8155i	−0.532550	+	0.532550i	0.388780	+	0.921331i	$0.372897\pi$
$674$	−5.89986	−	17.5383i	−0.227254	−	0.675549i
$675$	33.6898	−	0.518785i	1.29672	−	0.0199680i
$676$	−9.89970	−	13.0491i	−0.380758	−	0.501888i
$677$	−44.6474			−1.71594			−0.857969	−	0.513701i	$-0.828274\pi$
$677$	−44.6474			−1.71594			−0.857969	+	0.513701i	$0.828274\pi$
$678$	11.6389	+	34.5986i	0.446990	+	1.32875i
$679$		−	49.1748i		−	1.88715i
$680$	24.3871	−	4.83754i	0.935204	−	0.185511i
$681$		−	3.93302i		−	0.150714i
$682$	6.14828	−	2.06828i	0.235430	−	0.0791984i
$683$	−9.43457			−0.361004			−0.180502	−	0.983575i	$-0.557772\pi$
$683$	−9.43457			−0.361004			−0.180502	+	0.983575i	$0.557772\pi$
$684$	11.0387	−	80.4358i	0.422074	−	3.07554i
$685$	5.18888	−	0.0399492i	0.198257	−	0.00152638i
$686$	−22.0582	+	7.42037i	−0.842188	+	0.283311i
$687$	−17.1078	+	17.1078i	−0.652704	+	0.652704i
$688$	0.732266	−	2.61767i	0.0279174	−	0.0997977i
$689$		−	13.1677i		−	0.501649i
$690$	29.0842	−	59.7214i	1.10722	−	2.27356i
$691$	4.51027	−	4.51027i	0.171579	−	0.171579i	−0.616094	−	0.787673i	$-0.711286\pi$
$691$	4.51027	−	4.51027i	0.171579	−	0.171579i	0.787673	+	0.616094i	$0.211286\pi$
$692$	15.4186	+	20.3237i	0.586125	+	0.772590i
$693$			15.3507i			0.583124i
$694$	16.0068	−	32.2355i	0.607611	−	1.22364i
$695$	8.03070	−	0.0618283i	0.304622	−	0.00234528i
$696$	−32.0890	+	47.1798i	−1.21633	+	1.78835i
$697$	17.0918	−	17.0918i	0.647397	−	0.647397i
$698$	28.7591	−	9.67455i	1.08855	−	0.366187i
$699$	10.2403	−	10.2403i	0.387325	−	0.387325i
$700$	−28.5673	−	3.47321i	−1.07974	−	0.131275i
$701$	4.22544	+	4.22544i	0.159593	+	0.159593i	0.782386	−	0.622793i	$-0.214002\pi$
$701$	4.22544	+	4.22544i	0.159593	+	0.159593i	−0.622793	+	0.782386i	$0.714002\pi$
$702$	−9.29595	+	18.7207i	−0.350853	+	0.706569i
$703$	−43.2931	−	43.2931i	−1.63283	−	1.63283i
$704$	7.33967	+	3.18265i	0.276624	+	0.119951i
$705$	0.640307	+	83.1676i	0.0241153	+	3.13227i
$706$	32.0362	−	10.7769i	1.20570	−	0.405595i
$707$	2.13306			0.0802222
$708$	1.87440	−	13.6583i	0.0704444	−	0.513310i
$709$	−10.7723	−	10.7723i	−0.404563	−	0.404563i	0.475275	−	0.879837i	$-0.342349\pi$
$709$	−10.7723	−	10.7723i	−0.404563	−	0.404563i	−0.879837	+	0.475275i	$0.842349\pi$
$710$	14.2406	+	41.2781i	0.534440	+	1.54914i
$711$	−69.5374			−2.60786
$712$	1.48550	+	7.80306i	0.0556716	+	0.292432i
$713$	−23.6001	−	23.6001i	−0.883832	−	0.883832i
$714$	41.3672	+	20.5412i	1.54813	+	0.768737i
$715$	−0.0377566	−	4.90410i	−0.00141202	−	0.183403i
$716$	6.70112	−	48.8292i	0.250432	−	1.82483i
$717$		−	38.6797i		−	1.44452i
$718$	14.8334	−	29.8724i	0.553579	−	1.11483i
$719$	−10.0503			−0.374815			−0.187407	−	0.982282i	$-0.560008\pi$
$719$	−10.0503			−0.374815			−0.187407	+	0.982282i	$0.560008\pi$
$720$	41.3966	−	23.7203i	1.54276	−	0.884002i
$721$	9.41474			0.350623
$722$	24.4767	−	49.2926i	0.910927	−	1.83448i
$723$		−	4.41132i		−	0.164059i
$724$	−1.71093	−	0.234801i	−0.0635863	−	0.00872632i
$725$	−25.0831	−	24.3223i	−0.931561	−	0.903306i
$726$	3.65670	+	1.81577i	0.135713	+	0.0673895i
$727$	33.2216	+	33.2216i	1.23212	+	1.23212i	0.963148	+	0.268971i	$0.0866837\pi$
$727$	33.2216	+	33.2216i	1.23212	+	1.23212i	0.268971	+	0.963148i	$0.413316\pi$
$728$	10.0398	−	14.7613i	0.372100	−	0.547091i
$729$	39.9517			1.47969
$730$	−1.16741	+	2.39716i	−0.0432079	+	0.0887230i
$731$	−1.88891	−	1.88891i	−0.0698639	−	0.0698639i
$732$	20.3047	+	2.78654i	0.750485	+	0.102993i
$733$	−36.6003			−1.35186			−0.675932	−	0.736964i	$-0.736259\pi$
$733$	−36.6003			−1.35186			−0.675932	+	0.736964i	$0.736259\pi$
$734$	−18.1217	+	6.09613i	−0.668885	+	0.225012i
$735$	−5.89449	−	5.80442i	−0.217422	−	0.214099i
$736$	−2.12871	−	41.1059i	−0.0784652	−	1.51519i
$737$	−3.28293	−	3.28293i	−0.120928	−	0.120928i
$738$	20.6296	−	41.5451i	0.759386	−	1.52930i
$739$	−6.50981	−	6.50981i	−0.239467	−	0.239467i	0.577162	−	0.816629i	$-0.304160\pi$
$739$	−6.50981	−	6.50981i	−0.239467	−	0.239467i	−0.816629	+	0.577162i	$0.804160\pi$
$740$	4.61721	−	35.6816i	0.169732	−	1.31168i
$741$	−34.0725	+	34.0725i	−1.25168	+	1.25168i
$742$	−23.1586	+	7.79054i	−0.850180	+	0.286000i
$743$	−11.9317	+	11.9317i	−0.437730	+	0.437730i	−0.891248	−	0.453517i	$-0.850169\pi$
$743$	−11.9317	+	11.9317i	−0.437730	+	0.437730i	0.453517	+	0.891248i	$0.350169\pi$
$744$	−7.00446	−	36.7930i	−0.256796	−	1.34890i
$745$	0.191323	+	24.8504i	0.00700953	+	0.910448i
$746$	14.0606	−	28.3161i	0.514796	−	1.03673i
$747$			38.9768i			1.42609i
$748$	6.26362	−	4.75190i	0.229021	−	0.173747i
$749$	38.6119	−	38.6119i	1.41085	−	1.41085i
$750$	15.5491	+	42.9160i	0.567774	+	1.56707i
$751$			16.6966i			0.609267i	0.952470	+	0.304633i	$0.0985340\pi$
$751$			16.6966i			0.609267i	−0.952470	+	0.304633i	$0.901466\pi$
$752$	25.2768	+	44.9112i	0.921751	+	1.63774i
$753$	−32.1238	+	32.1238i	−1.17066	+	1.17066i
$754$	20.5430	−	6.91063i	0.748130	−	0.251670i
$755$	−24.0561	−	23.6886i	−0.875493	−	0.862115i
$756$	38.4249	+	5.27327i	1.39750	+	0.191787i
$757$	−22.8516			−0.830556			−0.415278	−	0.909694i	$-0.636316\pi$
$757$	−22.8516			−0.830556			−0.415278	+	0.909694i	$0.636316\pi$
$758$	38.6689	−	13.0082i	1.40452	−	0.472479i
$759$		−	21.0060i		−	0.762471i
$760$	47.2115	−	9.36507i	1.71254	−	0.339707i
$761$		−	47.4653i		−	1.72061i	−0.509776	−	0.860307i	$-0.670272\pi$
$761$		−	47.4653i		−	1.72061i	0.509776	−	0.860307i	$-0.329728\pi$
$762$	4.29741	+	12.7747i	0.155679	+	0.462780i
$763$	5.54779			0.200843
$764$	25.8304	−	19.5962i	0.934511	−	0.708967i
$765$	−0.360986	−	46.8874i	−0.0130515	−	1.69522i
$766$	9.13897	+	27.1671i	0.330204	+	0.981585i
$767$	−3.70303	+	3.70303i	−0.133709	+	0.133709i
$768$	23.9671	−	39.4860i	0.864840	−	1.42483i
$769$		−	44.4374i		−	1.60245i	−0.598360	−	0.801227i	$-0.704181\pi$
$769$		−	44.4374i		−	1.60245i	0.598360	−	0.801227i	$-0.295819\pi$
$770$	−8.60273	+	2.96787i	−0.310021	+	0.106955i
$771$	31.7749	−	31.7749i	1.14435	−	1.14435i
$772$	−1.14177	−	0.156691i	−0.0410931	−	0.00563945i
$773$		−	1.71747i		−	0.0617731i	−0.999523	−	0.0308865i	$-0.990167\pi$
$773$		−	1.71747i		−	0.0617731i	0.999523	−	0.0308865i	$-0.00983305\pi$
$774$	−4.59140	−	2.27990i	−0.165034	−	0.0819493i
$775$	22.9317	−	0.353123i	0.823732	−	0.0126846i
$776$	−27.1813	+	39.9641i	−0.975753	+	1.43463i
$777$	47.2617	−	47.2617i	1.69550	−	1.69550i
$778$	−4.05817	−	12.0636i	−0.145493	−	0.432500i
$779$	33.0883	−	33.0883i	1.18551	−	1.18551i
$780$	−28.0821	−	3.63382i	−1.00550	−	0.130112i
$781$	9.76391	+	9.76391i	0.349380	+	0.349380i
$782$	−36.2309	−	17.9908i	−1.29561	−	0.643349i
$783$	33.2970	+	33.2970i	1.18994	+	1.18994i
$784$	−4.93656	−	1.38095i	−0.176306	−	0.0493198i
$785$	−1.81082	+	1.83891i	−0.0646308	+	0.0656337i
$786$	−1.33482	−	3.96798i	−0.0476116	−	0.141533i
$787$	−50.0936			−1.78564			−0.892822	−	0.450410i	$-0.851278\pi$
$787$	−50.0936			−1.78564			−0.892822	+	0.450410i	$0.851278\pi$
$788$	19.3850	+	25.5520i	0.690563	+	0.910252i
$789$	36.5345	+	36.5345i	1.30066	+	1.30066i
$790$	−13.4442	−	38.9697i	−0.478324	−	1.38648i
$791$	−25.7303			−0.914864
$792$	8.48509	−	12.4754i	0.301504	−	0.443295i
$793$	−5.50501	−	5.50501i	−0.195489	−	0.195489i
$794$	−5.72737	+	11.5341i	−0.203257	+	0.409331i
$795$	27.6149	+	27.1929i	0.979399	+	0.964434i
$796$	−3.81915	+	2.89740i	−0.135366	+	0.102695i
$797$			22.7211i			0.804821i	0.915459	+	0.402410i	$0.131828\pi$
$797$			22.7211i			0.804821i	−0.915459	+	0.402410i	$0.868172\pi$
$798$	80.0835	+	39.7662i	2.83492	+	1.40771i
$799$	50.6478			1.79179
$800$	21.2967	+	18.6132i	0.752951	+	0.658076i
$801$	14.9804			0.529306
$802$	27.3014	+	13.5567i	0.964045	+	0.478705i
$803$			0.843164i			0.0297546i
$804$	−21.3562	+	16.2019i	−0.753175	+	0.571396i
$805$	33.3622	+	32.8524i	1.17586	+	1.15789i
$806$	−6.32751	+	12.7427i	−0.222877	+	0.448843i
$807$	21.8084	+	21.8084i	0.767690	+	0.767690i
$808$	−1.73353	−	1.17905i	−0.0609855	−	0.0414789i
$809$	−5.59179			−0.196597			−0.0982984	−	0.995157i	$-0.531340\pi$
$809$	−5.59179			−0.196597			−0.0982984	+	0.995157i	$0.531340\pi$
$810$	−3.55949	−	10.3176i	−0.125068	−	0.362524i
$811$	21.2116	+	21.2116i	0.744840	+	0.744840i	0.973505	−	0.228665i	$-0.0734361\pi$
$811$	21.2116	+	21.2116i	0.744840	+	0.744840i	−0.228665	+	0.973505i	$0.573436\pi$
$812$	−24.3081	−	32.0412i	−0.853047	−	1.12443i
$813$	−49.1997			−1.72551
$814$	−3.62765	−	10.7838i	−0.127149	−	0.377971i
$815$	−33.4984	+	34.0182i	−1.17340	+	1.19161i
$816$	−22.2648	−	39.5595i	−0.779423	−	1.38486i
$817$	−3.65678	−	3.65678i	−0.127934	−	0.127934i
$818$	−14.8208	−	7.35938i	−0.518196	−	0.257315i
$819$	−23.8068	−	23.8068i	−0.831875	−	0.831875i
$820$	27.2709	+	3.52886i	0.952342	+	0.123233i
$821$	19.0547	−	19.0547i	0.665012	−	0.665012i	−0.291545	−	0.956557i	$-0.594169\pi$
$821$	19.0547	−	19.0547i	0.665012	−	0.665012i	0.956557	+	0.291545i	$0.0941693\pi$
$822$	−3.02082	−	8.97987i	−0.105363	−	0.313209i
$823$	32.6560	−	32.6560i	1.13832	−	1.13832i	0.149563	−	0.988752i	$-0.452213\pi$
$823$	32.6560	−	32.6560i	1.13832	−	1.13832i	0.988752	−	0.149563i	$-0.0477868\pi$
$824$	−7.65132	−	5.20399i	−0.266546	−	0.181290i
$825$	10.3627	+	10.0484i	0.360783	+	0.349840i
$826$	8.70354	+	4.32182i	0.302835	+	0.150375i
$827$			53.5541i			1.86226i	0.364691	+	0.931129i	$0.381175\pi$
$827$			53.5541i			1.86226i	−0.364691	+	0.931129i	$0.618825\pi$
$828$	−76.9064	−	10.5543i	−2.67268	−	0.366787i
$829$	−28.2992	+	28.2992i	−0.982873	+	0.982873i	−0.999856	−	0.0169823i	$-0.994594\pi$
$829$	−28.2992	+	28.2992i	−0.982873	+	0.982873i	0.0169823	+	0.999856i	$0.494594\pi$
$830$	−21.8431	+	7.53570i	−0.758186	+	0.261568i
$831$			39.4084i			1.36706i
$832$	−16.3186	+	6.44696i	−0.565747	+	0.223508i
$833$	−3.56223	+	3.56223i	−0.123424	+	0.123424i
$834$	−4.67525	−	13.8979i	−0.161890	−	0.481245i
$835$	0.282547	+	36.6993i	0.00977795	+	1.27003i
$836$	12.1258	−	9.19928i	0.419381	−	0.318164i
$837$	−30.9099			−1.06840
$838$	0.854213	+	2.53928i	0.0295083	+	0.0877181i
$839$			48.5389i			1.67575i	0.545864	+	0.837874i	$0.316202\pi$
$839$			48.5389i			1.67575i	−0.545864	+	0.837874i	$0.683798\pi$
$840$	10.2235	+	51.5392i	0.352745	+	1.77827i
$841$		−	19.8293i		−	0.683769i
$842$	−43.7157	+	14.7059i	−1.50654	+	0.506799i
$843$	13.3301			0.459112
$844$	−13.9809	−	1.91868i	−0.481243	−	0.0660437i
$845$	−13.0483	−	12.8489i	−0.448876	−	0.442017i
$846$	92.1207	−	30.9893i	3.16717	−	1.06543i
$847$	−2.03489	+	2.03489i	−0.0699195	+	0.0699195i
$848$	23.1271	+	6.46958i	0.794189	+	0.222166i
$849$		−	28.7061i		−	0.985192i
$850$	26.2065	−	9.26742i	0.898877	−	0.317870i
$851$	−41.3935	+	41.3935i	−1.41895	+	1.41895i
$852$	63.5164	−	48.1867i	2.17603	−	1.65085i
$853$		−	9.48412i		−	0.324730i	−0.986731	−	0.162365i	$-0.948088\pi$
$853$		−	9.48412i		−	0.324730i	0.986731	−	0.162365i	$-0.0519122\pi$
$854$	−6.42493	+	12.9389i	−0.219857	+	0.442760i
$855$	−0.698839	−	90.7702i	−0.0238998	−	3.10427i
$856$	−52.7224	+	10.0370i	−1.80201	+	0.343058i
$857$	−3.31296	+	3.31296i	−0.113169	+	0.113169i	−0.761423	−	0.648255i	$-0.775499\pi$
$857$	−3.31296	+	3.31296i	−0.113169	+	0.113169i	0.648255	+	0.761423i	$0.275499\pi$
$858$	−8.48703	+	2.85503i	−0.289742	+	0.0974691i
$859$	−5.25110	+	5.25110i	−0.179165	+	0.179165i	−0.790992	−	0.611827i	$-0.790435\pi$
$859$	−5.25110	+	5.25110i	−0.179165	+	0.179165i	0.611827	+	0.790992i	$0.290435\pi$
$860$	0.389995	−	3.01387i	0.0132987	−	0.102772i
$861$	36.1213	+	36.1213i	1.23101	+	1.23101i
$862$	−5.21049	+	10.4932i	−0.177470	+	0.357400i
$863$	24.7549	+	24.7549i	0.842667	+	0.842667i	0.989205	−	0.146538i	$-0.0468130\pi$
$863$	24.7549	+	24.7549i	0.842667	+	0.842667i	−0.146538	+	0.989205i	$0.546813\pi$
$864$	−28.3129	−	25.5249i	−0.963226	−	0.868375i
$865$	20.3224	+	20.0119i	0.690984	+	0.680426i
$866$	−12.4659	+	4.19351i	−0.423608	+	0.142501i
$867$	4.46502			0.151640
$868$	26.1548	+	3.58937i	0.887752	+	0.121831i
$869$	−9.21787	−	9.21787i	−0.312695	−	0.312695i
$870$	−27.9310	+	57.3534i	−0.946950	+	1.94446i
$871$	10.1827			0.345029
$872$	−4.50866	−	3.06654i	−0.152683	−	0.103846i
$873$	64.4533	+	64.4533i	2.18141	+	2.18141i
$874$	−70.1400	−	34.8287i	−2.37252	−	1.17810i
$875$	−32.1658	+	0.743050i	−1.08740	+	0.0251197i
$876$	4.82307	+	0.661897i	0.162956	+	0.0223634i
$877$		−	16.8803i		−	0.570007i	−0.958526	−	0.285004i	$-0.908005\pi$
$877$		−	16.8803i		−	0.570007i	0.958526	−	0.285004i	$-0.0919948\pi$
$878$	−2.80102	+	5.64087i	−0.0945299	+	0.190370i
$879$	−61.2621			−2.06632
$880$	8.63189	+	2.34318i	0.290981	+	0.0789886i
$881$	−27.6748			−0.932388			−0.466194	−	0.884683i	$-0.654375\pi$
$881$	−27.6748			−0.932388			−0.466194	+	0.884683i	$0.654375\pi$
$882$	−4.29957	+	8.65874i	−0.144774	+	0.291555i
$883$		−	32.4805i		−	1.09306i	−0.837440	−	0.546529i	$-0.815949\pi$
$883$		−	32.4805i		−	1.09306i	0.837440	−	0.546529i	$-0.184051\pi$
$884$	−2.34447	+	17.0835i	−0.0788530	+	0.574581i
$885$	−0.118665	−	15.4131i	−0.00398889	−	0.518105i
$886$	−51.6798	−	25.6621i	−1.73622	−	0.862134i
$887$	11.8026	+	11.8026i	0.396292	+	0.396292i	0.876923	−	0.480631i	$-0.159592\pi$
$887$	11.8026	+	11.8026i	0.396292	+	0.396292i	−0.480631	+	0.876923i	$0.659592\pi$
$888$	−64.5332	+	12.2855i	−2.16559	+	0.412274i
$889$	−9.50033			−0.318631
$890$	2.89628	+	8.39521i	0.0970835	+	0.281408i
$891$	−2.44053	−	2.44053i	−0.0817607	−	0.0817607i
$892$	−4.82666	+	35.1706i	−0.161609	+	1.17760i
$893$	98.0499			3.28111
$894$	43.0060	−	14.4672i	1.43834	−	0.483855i
$895$	−0.424236	−	55.1028i	−0.0141806	−	1.84188i
$896$	20.9933	+	24.8860i	0.701338	+	0.831384i
$897$	32.5774	+	32.5774i	1.08773	+	1.08773i
$898$	−1.31535	+	2.64893i	−0.0438938	+	0.0883960i
$899$	22.6644	+	22.6644i	0.755899	+	0.755899i
$900$	41.9954	−	32.8908i	1.39985	−	1.09636i
$901$	16.6886	−	16.6886i	0.555976	−	0.555976i
$902$	8.24188	−	2.77256i	0.274425	−	0.0923162i
$903$	3.99198	−	3.99198i	0.132845	−	0.132845i
$904$	20.9109	+	14.2224i	0.695486	+	0.473030i
$905$	−1.93075	+	0.0148649i	−0.0641804	+	0.000494124i
$906$	−27.4156	+	55.2113i	−0.910824	+	1.83427i
$907$			21.4125i			0.710991i	0.934678	+	0.355496i	$0.115688\pi$
$907$			21.4125i			0.710991i	−0.934678	+	0.355496i	$0.884312\pi$
$908$	−1.64683	−	2.17074i	−0.0546520	−	0.0720385i
$909$	−2.79581	+	2.79581i	−0.0927310	+	0.0927310i
$910$	8.73887	−	17.9444i	0.289691	−	0.594850i
$911$			17.0306i			0.564250i	0.959378	+	0.282125i	$0.0910394\pi$
$911$			17.0306i			0.564250i	−0.959378	+	0.282125i	$0.908961\pi$
$912$	−43.1027	−	76.5839i	−1.42727	−	2.53595i
$913$	−5.16676	+	5.16676i	−0.170995	+	0.170995i
$914$	5.48857	−	1.84635i	0.181546	−	0.0610718i
$915$	22.9135	−	0.176411i	0.757497	−	0.00583196i
$916$	−2.27888	+	16.6056i	−0.0752964	+	0.548665i
$917$	2.95091			0.0974476
$918$	−35.5080	+	11.9449i	−1.17194	+	0.394239i
$919$		−	20.5526i		−	0.677968i	−0.940792	−	0.338984i	$-0.889917\pi$
$919$		−	20.5526i		−	0.677968i	0.940792	−	0.338984i	$-0.110083\pi$
$920$	−8.95414	−	45.1399i	−0.295209	−	1.48822i
$921$			23.6462i			0.779169i
$922$	16.4551	+	48.9154i	0.541920	+	1.61094i
$923$	−30.2849			−0.996839
$924$	10.0425	+	13.2374i	0.330375	+	0.435478i
$925$	−0.619361	−	40.2211i	−0.0203645	−	1.32246i
$926$	3.73032	+	11.0890i	0.122586	+	0.364406i
$927$	−12.3399	+	12.3399i	−0.405295	+	0.405295i
$928$	2.04430	+	39.4761i	0.0671075	+	1.29586i
$929$			43.3429i			1.42203i	0.703175	+	0.711016i	$0.251765\pi$
$929$			43.3429i			1.42203i	−0.703175	+	0.711016i	$0.748235\pi$
$930$	−13.6566	−	39.5852i	−0.447816	−	1.29805i
$931$	−6.89618	+	6.89618i	−0.226013	+	0.226013i
$932$	1.36408	−	9.93971i	0.0446821	−	0.325586i
$933$			18.2308i			0.596849i
$934$	−0.950483	−	0.471971i	−0.0311007	−	0.0154434i
$935$	6.16754	−	6.26324i	0.201700	−	0.204830i
$936$	6.18847	+	32.5068i	0.202276	+	1.06252i
$937$	12.0305	−	12.0305i	0.393020	−	0.393020i	−0.482743	−	0.875762i	$-0.660359\pi$
$937$	12.0305	−	12.0305i	0.393020	−	0.393020i	0.875762	+	0.482743i	$0.160359\pi$
$938$	−6.02451	−	17.9088i	−0.196707	−	0.584744i
$939$	8.92543	−	8.92543i	0.291270	−	0.291270i
$940$	35.1772	+	45.6342i	1.14735	+	1.48842i
$941$	40.5927	+	40.5927i	1.32328	+	1.32328i	0.911101	+	0.412183i	$0.135234\pi$
$941$	40.5927	+	40.5927i	1.32328	+	1.32328i	0.412183	+	0.911101i	$0.364766\pi$
$942$	4.22049	+	2.09572i	0.137511	+	0.0682824i
$943$	−31.6364	−	31.6364i	−1.03022	−	1.03022i
$944$	−4.68445	−	8.32321i	−0.152466	−	0.270897i
$945$	43.3617	−	0.333841i	1.41056	−	0.0108599i
$946$	−0.306412	−	0.910858i	−0.00996231	−	0.0296145i
$947$	−13.0546			−0.424218			−0.212109	−	0.977246i	$-0.568033\pi$
$947$	−13.0546			−0.424218			−0.212109	+	0.977246i	$0.568033\pi$
$948$	−59.9643	+	45.4919i	−1.94755	+	1.47751i
$949$	−1.30763	−	1.30763i	−0.0424474	−	0.0424474i
$950$	50.7337	−	17.9409i	1.64602	−	0.582081i
$951$	29.6420			0.961208
$952$	31.4326	−	5.98397i	1.01874	−	0.193942i
$953$	−12.1743	−	12.1743i	−0.394365	−	0.394365i	0.481875	−	0.876240i	$-0.339956\pi$
$953$	−12.1743	−	12.1743i	−0.394365	−	0.394365i	−0.876240	+	0.481875i	$0.839956\pi$
$954$	20.1429	−	40.5650i	0.652151	−	1.31334i
$955$	25.4342	−	25.8289i	0.823031	−	0.835802i
$956$	−16.1959	−	21.3483i	−0.523814	−	0.690455i
$957$			20.1731i			0.652105i
$958$	−9.92800	−	4.92984i	−0.320759	−	0.159276i
$959$	6.67816			0.215649
$960$	20.1796	−	47.5367i	0.651295	−	1.53424i
$961$	9.96044			0.321305
$962$	22.3501	+	11.0981i	0.720596	+	0.357819i
$963$			101.217i			3.26167i
$964$	−1.84710	−	2.43472i	−0.0594912	−	0.0784171i
$965$	−1.28846	+	0.00991986i	−0.0414771	+	0.000319332i
$966$	38.0213	−	76.5695i	1.22331	−	2.46358i
$967$	−12.5620	−	12.5620i	−0.403967	−	0.403967i	0.475661	−	0.879629i	$-0.342209\pi$
$967$	−12.5620	−	12.5620i	−0.403967	−	0.403967i	−0.879629	+	0.475661i	$0.842209\pi$
$968$	2.77852	−	0.528960i	0.0893052	−	0.0170014i
$969$	−86.3660			−2.77447
$970$	−23.6592	+	48.5817i	−0.759652	+	1.55987i
$971$	4.66895	+	4.66895i	0.149834	+	0.149834i	0.778044	−	0.628210i	$-0.216212\pi$
$971$	4.66895	+	4.66895i	0.149834	+	0.149834i	−0.628210	+	0.778044i	$0.716212\pi$
$972$	16.3356	−	12.3930i	0.523965	−	0.397506i
$973$	10.3356			0.331344
$974$	−2.56226	−	7.61674i	−0.0821003	−	0.244056i
$975$	−31.6548	+	0.487448i	−1.01376	+	0.0156108i
$976$	12.3735	−	6.96401i	0.396066	−	0.222913i
$977$	−36.3053	−	36.3053i	−1.16151	−	1.16151i	−0.984145	−	0.177365i	$-0.943243\pi$
$977$	−36.3053	−	36.3053i	−1.16151	−	1.16151i	−0.177365	−	0.984145i	$-0.556757\pi$
$978$	78.0753	+	38.7690i	2.49657	+	1.23970i
$979$	1.98580	+	1.98580i	0.0634665	+	0.0634665i
$980$	−5.68374	−	0.735476i	−0.181560	−	0.0234939i
$981$	−7.27148	+	7.27148i	−0.232160	+	0.232160i
$982$	8.54218	+	25.3930i	0.272592	+	0.810323i
$983$	20.8985	−	20.8985i	0.666557	−	0.666557i	−0.290360	−	0.956917i	$-0.593775\pi$
$983$	20.8985	−	20.8985i	0.666557	−	0.666557i	0.956917	+	0.290360i	$0.0937751\pi$
$984$	−9.38960	−	49.3217i	−0.299330	−	1.57232i
$985$	25.5505	+	25.1601i	0.814106	+	0.801666i
$986$	34.7943	+	17.2774i	1.10808	+	0.550225i
$987$			107.038i			3.40705i
$988$	−4.53869	+	33.0723i	−0.144395	+	1.05217i
$989$	−3.49632	+	3.49632i	−0.111177	+	0.111177i
$990$	7.38560	−	15.1656i	0.234730	−	0.481993i
$991$		−	10.1712i		−	0.323099i	−0.986865	−	0.161550i	$-0.948351\pi$
$991$		−	10.1712i		−	0.323099i	0.986865	−	0.161550i	$-0.0516492\pi$
$992$	−19.2719	−	17.3741i	−0.611883	−	0.551629i
$993$	−28.9701	+	28.9701i	−0.919339	+	0.919339i
$994$	17.9178	+	53.2634i	0.568317	+	1.68941i
$995$	−3.76056	+	3.81892i	−0.119218	+	0.121068i
$996$	25.4989	+	33.6109i	0.807965	+	1.06500i
$997$	54.2218			1.71722			0.858610	−	0.512629i	$-0.171328\pi$
$997$	54.2218			1.71722			0.858610	+	0.512629i	$0.171328\pi$
$998$	−12.8449	−	38.1835i	−0.406598	−	1.20868i
$999$			54.2145i			1.71527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.s.b.67.16	✓	236
5.3	odd	4		880.2.bk.b.243.45	yes	236
16.11	odd	4		880.2.bk.b.507.45	yes	236
80.43	even	4	inner	880.2.s.b.683.16	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.16	✓	236	1.1	even	1	trivial
880.2.s.b.683.16	yes	236	80.43	even	4	inner
880.2.bk.b.243.45	yes	236	5.3	odd	4
880.2.bk.b.507.45	yes	236	16.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26665 - 0.628966i) q^{2} +2.88691i q^{3} +(1.20880 + 1.59336i) q^{4} +(1.59326 + 1.56892i) q^{5} +(1.81577 - 3.65670i) q^{6} +(2.03489 + 2.03489i) q^{7} +(-0.528960 - 2.77852i) q^{8} -5.33424 q^{9} +(-1.03131 - 2.98938i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-4.59988 + 3.48970i) q^{12} +2.19325 q^{13} +(-1.29761 - 3.85736i) q^{14} +(-4.52933 + 4.59961i) q^{15} +(-1.07759 + 3.85212i) q^{16} +(2.77969 + 2.77969i) q^{17} +(6.75662 + 3.35506i) q^{18} +(5.38125 + 5.38125i) q^{19} +(-0.573909 + 4.43516i) q^{20} +(-5.87453 + 5.87453i) q^{21} +(0.450910 + 1.34040i) q^{22} +(5.14513 - 5.14513i) q^{23} +(8.02135 - 1.52706i) q^{24} +(0.0769853 + 4.99941i) q^{25} +(-2.77807 - 1.37948i) q^{26} -6.73875i q^{27} +(-0.782529 + 5.70208i) q^{28} +(-4.94112 + 4.94112i) q^{29} +(8.63007 - 2.97730i) q^{30} -4.58689i q^{31} +(3.78778 - 4.20151i) q^{32} +(2.04135 - 2.04135i) q^{33} +(-1.77256 - 5.26923i) q^{34} +(0.0495406 + 6.43468i) q^{35} +(-6.44805 - 8.49937i) q^{36} -8.04518 q^{37} +(-3.43153 - 10.2008i) q^{38} +6.33170i q^{39} +(3.51651 - 5.25682i) q^{40} -6.14881i q^{41} +(11.1359 - 3.74609i) q^{42} -0.679540 q^{43} +(0.271923 - 1.98143i) q^{44} +(-8.49886 - 8.36900i) q^{45} +(-9.75319 + 3.28096i) q^{46} +(9.11033 - 9.11033i) q^{47} +(-11.1207 - 3.11091i) q^{48} +1.28152i q^{49} +(3.04694 - 6.38092i) q^{50} +(-8.02471 + 8.02471i) q^{51} +(2.65120 + 3.49463i) q^{52} -6.00375i q^{53} +(-4.23845 + 8.53563i) q^{54} +(-0.0172150 - 2.23600i) q^{55} +(4.57761 - 6.73035i) q^{56} +(-15.5352 + 15.5352i) q^{57} +(9.36646 - 3.15087i) q^{58} +(-1.68838 + 1.68838i) q^{59} +(-12.8039 - 1.65682i) q^{60} +(-2.50998 - 2.50998i) q^{61} +(-2.88500 + 5.80998i) q^{62} +(-10.8546 - 10.8546i) q^{63} +(-7.44040 + 2.93946i) q^{64} +(3.49442 + 3.44103i) q^{65} +(-3.86962 + 1.30174i) q^{66} +4.64277 q^{67} +(-1.06895 + 7.78914i) q^{68} +(14.8535 + 14.8535i) q^{69} +(3.98445 - 8.18165i) q^{70} -13.8082 q^{71} +(2.82160 + 14.8213i) q^{72} +(-0.596207 - 0.596207i) q^{73} +(10.1904 + 5.06015i) q^{74} +(-14.4328 + 0.222250i) q^{75} +(-2.06940 + 15.0791i) q^{76} -2.87776i q^{77} +(3.98243 - 8.02005i) q^{78} +13.0360 q^{79} +(-7.76055 + 4.44679i) q^{80} +3.45142 q^{81} +(-3.86739 + 7.78838i) q^{82} -7.30691i q^{83} +(-16.4614 - 2.25909i) q^{84} +(0.0676733 + 8.78989i) q^{85} +(0.860740 + 0.427408i) q^{86} +(-14.2646 - 14.2646i) q^{87} +(-1.59068 + 2.33875i) q^{88} -2.80835 q^{89} +(5.50127 + 15.9461i) q^{90} +(4.46300 + 4.46300i) q^{91} +(14.4175 + 1.97859i) q^{92} +13.2419 q^{93} +(-17.2697 + 5.80950i) q^{94} +(0.131010 + 17.0165i) q^{95} +(12.1294 + 10.9350i) q^{96} +(-12.0829 - 12.0829i) q^{97} +(0.806032 - 1.62324i) q^{98} +(3.77188 + 3.77188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 8 q^{5} - 4 q^{7} + 12 q^{8} - 240 q^{9} + 16 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 8 q^{17} - 12 q^{18} - 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{25} + 8 q^{26} + 36 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 236 * q + 8 * q^5 - 4 * q^7 + 12 * q^8 - 240 * q^9 + 16 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 + 8 * q^17 - 12 * q^18 - 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 - 12 * q^25 + 8 * q^26 + 36 * q^28 - 8 * q^29 + 40 * q^32 - 4 * q^33 + 44 * q^34 - 12 * q^35 - 32 * q^36 + 4 * q^37 - 44 * q^38 - 40 * q^40 - 60 * q^42 - 16 * q^43 - 40 * q^46 + 48 * q^47 - 112 * q^48 - 28 * q^51 + 108 * q^52 - 24 * q^56 + 16 * q^57 - 28 * q^58 - 8 * q^59 + 100 * q^60 - 24 * q^61 + 36 * q^62 + 24 * q^63 - 32 * q^65 - 4 * q^66 - 56 * q^67 - 36 * q^68 - 48 * q^69 + 164 * q^70 - 4 * q^71 + 12 * q^72 - 8 * q^73 - 72 * q^75 - 24 * q^76 + 152 * q^78 - 40 * q^79 - 24 * q^80 + 244 * q^81 + 40 * q^82 + 104 * q^84 - 24 * q^85 + 72 * q^86 - 140 * q^87 + 32 * q^88 - 36 * q^89 + 72 * q^90 + 12 * q^91 + 12 * q^93 + 16 * q^94 + 36 * q^95 + 72 * q^96 + 20 * q^97 - 64 * q^98 - 8 * q^99

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