LMFDB - Embedded newform 84.2.n.a.23.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,2,Mod(11,84)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951145 - 1.04658i) q^{2} +(-0.420559 + 1.68022i) q^{3} +(-0.190646 - 1.99089i) q^{4} +(2.36229 + 1.36387i) q^{5} +(1.35846 + 2.03828i) q^{6} +(-1.89768 - 1.84359i) q^{7} +(-2.26495 - 1.69410i) q^{8} +(-2.64626 - 1.41326i) q^{9} +(3.67427 - 1.17508i) q^{10} +(1.02012 + 1.76690i) q^{11} +(3.42531 + 0.516960i) q^{12} -4.44055 q^{13} +(-3.73442 + 0.232547i) q^{14} +(-3.28508 + 3.39557i) q^{15} +(-3.92731 + 0.759113i) q^{16} +(-0.571980 + 0.330233i) q^{17} +(-3.99606 + 1.42530i) q^{18} +(2.54543 + 1.46961i) q^{19} +(2.26495 - 4.96308i) q^{20} +(3.89571 - 2.41318i) q^{21} +(2.81949 + 0.612946i) q^{22} +(0.521208 - 0.902759i) q^{23} +(3.79901 - 3.09315i) q^{24} +(1.22028 + 2.11358i) q^{25} +(-4.22361 + 4.64738i) q^{26} +(3.48749 - 3.85193i) q^{27} +(-3.30860 + 4.12955i) q^{28} +2.06727i q^{29} +(0.429143 + 6.66777i) q^{30} +(2.68812 - 1.55199i) q^{31} +(-2.94097 + 4.83226i) q^{32} +(-3.39781 + 0.970941i) q^{33} +(-0.198422 + 0.912721i) q^{34} +(-1.96845 - 6.94327i) q^{35} +(-2.30915 + 5.53785i) q^{36} +(4.76004 - 8.24463i) q^{37} +(3.95913 - 1.26618i) q^{38} +(1.86751 - 7.46109i) q^{39} +(-3.03995 - 7.09106i) q^{40} +7.85889i q^{41} +(1.17982 - 6.37244i) q^{42} +0.530567i q^{43} +(3.32324 - 2.36781i) q^{44} +(-4.32373 - 6.94768i) q^{45} +(-0.449062 - 1.40414i) q^{46} +(-0.521208 + 0.902759i) q^{47} +(0.376190 - 6.91798i) q^{48} +(0.202367 + 6.99707i) q^{49} +(3.37268 + 0.733208i) q^{50} +(-0.314312 - 1.09993i) q^{51} +(0.846575 + 8.84066i) q^{52} +(9.16829 - 5.29332i) q^{53} +(-0.714234 - 7.31368i) q^{54} +5.56526i q^{55} +(1.17493 + 7.39050i) q^{56} +(-3.53976 + 3.65883i) q^{57} +(2.16356 + 1.96627i) q^{58} +(1.74375 + 3.02026i) q^{59} +(7.38651 + 5.89288i) q^{60} +(0.0992110 - 0.171839i) q^{61} +(0.932518 - 4.28949i) q^{62} +(2.41628 + 7.56053i) q^{63} +(2.26004 + 7.67413i) q^{64} +(-10.4899 - 6.05633i) q^{65} +(-2.21564 + 4.47957i) q^{66} +(-4.12631 + 2.38233i) q^{67} +(0.766504 + 1.07579i) q^{68} +(1.29763 + 1.25541i) q^{69} +(-9.13896 - 4.54392i) q^{70} +5.52774 q^{71} +(3.59945 + 7.68401i) q^{72} +(1.51791 + 2.62910i) q^{73} +(-4.10115 - 12.8236i) q^{74} +(-4.06447 + 1.16144i) q^{75} +(2.44055 - 5.34786i) q^{76} +(1.32158 - 5.23370i) q^{77} +(-6.03233 - 9.05108i) q^{78} +(-9.45104 - 5.45656i) q^{79} +(-10.3128 - 3.56309i) q^{80} +(5.00539 + 7.47971i) q^{81} +(8.22494 + 7.47495i) q^{82} -9.15881 q^{83} +(-5.54708 - 7.29589i) q^{84} -1.80158 q^{85} +(0.555279 + 0.504646i) q^{86} +(-3.47347 - 0.869409i) q^{87} +(0.682784 - 5.73015i) q^{88} +(-0.468730 - 0.270622i) q^{89} +(-11.3838 - 2.08313i) q^{90} +(8.42674 + 8.18655i) q^{91} +(-1.89666 - 0.865562i) q^{92} +(1.47716 + 5.16932i) q^{93} +(0.449062 + 1.40414i) q^{94} +(4.00870 + 6.94327i) q^{95} +(-6.88239 - 6.97372i) q^{96} -6.91692 q^{97} +(7.51546 + 6.44344i) q^{98} +(-0.202415 - 6.11739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.951145	−	1.04658i	0.672561	−	0.740042i
$2$	0.951145	−	1.04658i	0.672561	−	0.740042i
$3$	−0.420559	+	1.68022i	−0.242810	+	0.970074i
$3$	−0.420559	+	1.68022i	−0.242810	+	0.970074i
$4$	−0.190646	−	1.99089i	−0.0953231	−	0.995446i
$5$	2.36229	+	1.36387i	1.05645	+	0.609941i	0.924448	−	0.381309i	$-0.124527\pi$
$5$	2.36229	+	1.36387i	1.05645	+	0.609941i	0.132001	+	0.991250i	$0.457860\pi$
$6$	1.35846	+	2.03828i	0.554591	+	0.832123i
$7$	−1.89768	−	1.84359i	−0.717255	−	0.696811i
$7$	−1.89768	−	1.84359i	−0.717255	−	0.696811i
$8$	−2.26495	−	1.69410i	−0.800782	−	0.598955i
$9$	−2.64626	−	1.41326i	−0.882087	−	0.471087i
$10$	3.67427	−	1.17508i	1.16191	−	0.371593i
$11$	1.02012	+	1.76690i	0.307579	+	0.532742i	0.977832	−	0.209390i	$-0.0671479\pi$
$11$	1.02012	+	1.76690i	0.307579	+	0.532742i	−0.670253	+	0.742132i	$0.733815\pi$
$12$	3.42531	+	0.516960i	0.988802	+	0.149234i
$13$	−4.44055			−1.23159			−0.615794	−	0.787907i	$-0.711165\pi$
$13$	−4.44055			−1.23159			−0.615794	+	0.787907i	$0.711165\pi$
$14$	−3.73442	+	0.232547i	−0.998067	+	0.0621508i
$15$	−3.28508	+	3.39557i	−0.848203	+	0.876733i
$16$	−3.92731	+	0.759113i	−0.981827	+	0.189778i
$17$	−0.571980	+	0.330233i	−0.138726	+	0.0800933i	−0.567756	−	0.823197i	$-0.692188\pi$
$17$	−0.571980	+	0.330233i	−0.138726	+	0.0800933i	0.429031	+	0.903290i	$0.358855\pi$
$18$	−3.99606	+	1.42530i	−0.941881	+	0.335946i
$19$	2.54543	+	1.46961i	0.583962	+	0.337151i	0.762707	−	0.646745i	$-0.223870\pi$
$19$	2.54543	+	1.46961i	0.583962	+	0.337151i	−0.178744	+	0.983896i	$0.557203\pi$
$20$	2.26495	−	4.96308i	0.506459	−	1.10978i
$21$	3.89571	−	2.41318i	0.850114	−	0.526598i
$22$	2.81949	+	0.612946i	0.601117	+	0.130680i
$23$	0.521208	−	0.902759i	0.108679	−	0.188238i	−0.806556	−	0.591158i	$-0.798671\pi$
$23$	0.521208	−	0.902759i	0.108679	−	0.188238i	0.915236	+	0.402919i	$0.132004\pi$
$24$	3.79901	−	3.09315i	0.775469	−	0.631386i
$25$	1.22028	+	2.11358i	0.244055	+	0.422716i
$26$	−4.22361	+	4.64738i	−0.828318	+	0.911426i
$27$	3.48749	−	3.85193i	0.671168	−	0.741305i
$28$	−3.30860	+	4.12955i	−0.625267	+	0.780411i
$29$			2.06727i			0.383883i	0.981406	+	0.191941i	$0.0614783\pi$
$29$			2.06727i			0.383883i	−0.981406	+	0.191941i	$0.938522\pi$
$30$	0.429143	+	6.66777i	0.0783505	+	1.21736i
$31$	2.68812	−	1.55199i	0.482800	−	0.278745i	−0.238782	−	0.971073i	$-0.576748\pi$
$31$	2.68812	−	1.55199i	0.482800	−	0.278745i	0.721583	+	0.692328i	$0.243415\pi$
$32$	−2.94097	+	4.83226i	−0.519895	+	0.854230i
$33$	−3.39781	+	0.970941i	−0.591482	+	0.169019i
$34$	−0.198422	+	0.912721i	−0.0340291	+	0.156530i
$35$	−1.96845	−	6.94327i	−0.332730	−	1.17363i
$36$	−2.30915	+	5.53785i	−0.384858	+	0.922976i
$37$	4.76004	−	8.24463i	0.782546	−	1.35541i	−0.147909	−	0.989001i	$-0.547254\pi$
$37$	4.76004	−	8.24463i	0.782546	−	1.35541i	0.930454	−	0.366408i	$-0.119412\pi$
$38$	3.95913	−	1.26618i	0.642256	−	0.205402i
$39$	1.86751	−	7.46109i	0.299041	−	1.19473i
$40$	−3.03995	−	7.09106i	−0.480658	−	1.12120i
$41$			7.85889i			1.22735i	0.789558	+	0.613676i	$0.210310\pi$
$41$			7.85889i			1.22735i	−0.789558	+	0.613676i	$0.789690\pi$
$42$	1.17982	−	6.37244i	0.182049	−	0.983289i
$43$			0.530567i			0.0809106i	0.999181	+	0.0404553i	$0.0128808\pi$
$43$			0.530567i			0.0809106i	−0.999181	+	0.0404553i	$0.987119\pi$
$44$	3.32324	−	2.36781i	0.500997	−	0.356961i
$45$	−4.32373	−	6.94768i	−0.644544	−	1.03570i
$46$	−0.449062	−	1.40414i	−0.0662106	−	0.207029i
$47$	−0.521208	+	0.902759i	−0.0760260	+	0.131681i	−0.901532	−	0.432712i	$-0.857557\pi$
$47$	−0.521208	+	0.902759i	−0.0760260	+	0.131681i	0.825506	+	0.564393i	$0.190890\pi$
$48$	0.376190	−	6.91798i	0.0542983	−	0.998525i
$49$	0.202367	+	6.99707i	0.0289096	+	0.999582i
$50$	3.37268	+	0.733208i	0.476969	+	0.103691i
$51$	−0.314312	−	1.09993i	−0.0440125	−	0.154022i
$52$	0.846575	+	8.84066i	0.117399	+	1.22598i
$53$	9.16829	−	5.29332i	1.25936	−	0.727093i	0.286411	−	0.958107i	$-0.407538\pi$
$53$	9.16829	−	5.29332i	1.25936	−	0.727093i	0.972950	+	0.231014i	$0.0742043\pi$
$54$	−0.714234	−	7.31368i	−0.0971949	−	0.995265i
$55$			5.56526i			0.750419i
$56$	1.17493	+	7.39050i	0.157007	+	0.987598i
$57$	−3.53976	+	3.65883i	−0.468853	+	0.484623i
$58$	2.16356	+	1.96627i	0.284089	+	0.258185i
$59$	1.74375	+	3.02026i	0.227016	+	0.393204i	0.956922	−	0.290343i	$-0.0937696\pi$
$59$	1.74375	+	3.02026i	0.227016	+	0.393204i	−0.729906	+	0.683547i	$0.760436\pi$
$60$	7.38651	+	5.89288i	0.953594	+	0.760768i
$61$	0.0992110	−	0.171839i	0.0127027	−	0.0220017i	−0.859604	−	0.510960i	$-0.829290\pi$
$61$	0.0992110	−	0.171839i	0.0127027	−	0.0220017i	0.872307	+	0.488959i	$0.162623\pi$
$62$	0.932518	−	4.28949i	0.118430	−	0.544765i
$63$	2.41628	+	7.56053i	0.304423	+	0.952537i
$64$	2.26004	+	7.67413i	0.282505	+	0.959266i
$65$	−10.4899	−	6.05633i	−1.30111	−	0.751195i
$66$	−2.21564	+	4.47957i	−0.272727	+	0.551397i
$67$	−4.12631	+	2.38233i	−0.504109	+	0.291048i	−0.730409	−	0.683010i	$-0.760670\pi$
$67$	−4.12631	+	2.38233i	−0.504109	+	0.291048i	0.226300	+	0.974058i	$0.427337\pi$
$68$	0.766504	+	1.07579i	0.0929523	+	0.130459i
$69$	1.29763	+	1.25541i	0.156217	+	0.151133i
$70$	−9.13896	−	4.54392i	−1.09231	−	0.543102i
$71$	5.52774			0.656022			0.328011	−	0.944674i	$-0.393622\pi$
$71$	5.52774			0.656022			0.328011	+	0.944674i	$0.393622\pi$
$72$	3.59945	+	7.68401i	0.424200	+	0.905569i
$73$	1.51791	+	2.62910i	0.177658	+	0.307712i	0.941078	−	0.338190i	$-0.109815\pi$
$73$	1.51791	+	2.62910i	0.177658	+	0.307712i	−0.763420	+	0.645902i	$0.776481\pi$
$74$	−4.10115	−	12.8236i	−0.476749	−	1.49071i
$75$	−4.06447	+	1.16144i	−0.469325	+	0.134112i
$76$	2.44055	−	5.34786i	0.279950	−	0.613442i
$77$	1.32158	−	5.23370i	0.150608	−	0.596436i
$78$	−6.03233	−	9.05108i	−0.683027	−	1.02483i
$79$	−9.45104	−	5.45656i	−1.06332	−	0.613911i	−0.136975	−	0.990575i	$-0.543738\pi$
$79$	−9.45104	−	5.45656i	−1.06332	−	0.613911i	−0.926350	+	0.376664i	$0.877071\pi$
$80$	−10.3128	−	3.56309i	−1.15300	−	0.398365i
$81$	5.00539	+	7.47971i	0.556155	+	0.831079i
$82$	8.22494	+	7.47495i	0.908292	+	0.825470i
$83$	−9.15881			−1.00531			−0.502655	−	0.864487i	$-0.667643\pi$
$83$	−9.15881			−1.00531			−0.502655	+	0.864487i	$0.667643\pi$
$84$	−5.54708	−	7.29589i	−0.605236	−	0.796046i
$85$	−1.80158			−0.195409
$86$	0.555279	+	0.504646i	0.0598772	+	0.0544174i
$87$	−3.47347	−	0.869409i	−0.372395	−	0.0932104i
$88$	0.682784	−	5.73015i	0.0727851	−	0.610836i
$89$	−0.468730	−	0.270622i	−0.0496853	−	0.0286858i	0.474952	−	0.880012i	$-0.342466\pi$
$89$	−0.468730	−	0.270622i	−0.0496853	−	0.0286858i	−0.524637	+	0.851326i	$0.675799\pi$
$90$	−11.3838	−	2.08313i	−1.19996	−	0.219582i
$91$	8.42674	+	8.18655i	0.883362	+	0.858183i
$92$	−1.89666	−	0.865562i	−0.197741	−	0.0902411i
$93$	1.47716	+	5.16932i	0.153175	+	0.536034i
$94$	0.449062	+	1.40414i	0.0463172	+	0.144826i
$95$	4.00870	+	6.94327i	0.411284	+	0.712365i
$96$	−6.88239	−	6.97372i	−0.702431	−	0.711752i
$97$	−6.91692			−0.702307			−0.351153	−	0.936318i	$-0.614210\pi$
$97$	−6.91692			−0.702307			−0.351153	+	0.936318i	$0.614210\pi$
$98$	7.51546	+	6.44344i	0.759176	+	0.650886i
$99$	−0.202415	−	6.11739i	−0.0203435	−	0.614821i
$100$	3.97527	−	2.83238i	0.397527	−	0.283238i
$101$	−8.77393	+	5.06563i	−0.873039	+	0.504049i	−0.868357	−	0.495940i	$-0.834824\pi$
$101$	−8.77393	+	5.06563i	−0.873039	+	0.504049i	−0.00468180	+	0.999989i	$0.501490\pi$
$102$	−1.45012	−	0.717245i	−0.143583	−	0.0710178i
$103$	−6.34079	−	3.66086i	−0.624777	−	0.360715i	0.153950	−	0.988079i	$-0.450801\pi$
$103$	−6.34079	−	3.66086i	−0.624777	−	0.360715i	−0.778726	+	0.627364i	$0.784134\pi$
$104$	10.0576	+	7.52275i	0.986234	+	0.737666i
$105$	12.4941	−	0.387377i	1.21930	−	0.0378041i
$106$	3.18051	−	14.6300i	0.308919	−	1.42099i
$107$	−8.76332	+	15.1785i	−0.847182	+	1.46736i	0.0365308	+	0.999333i	$0.488369\pi$
$107$	−8.76332	+	15.1785i	−0.847182	+	1.46736i	−0.883713	+	0.468030i	$0.844964\pi$
$108$	−8.33367	−	6.20887i	−0.801907	−	0.597448i
$109$	−0.319487	−	0.553367i	−0.0306013	−	0.0530030i	0.850319	−	0.526267i	$-0.176409\pi$
$109$	−0.319487	−	0.553367i	−0.0306013	−	0.0530030i	−0.880920	+	0.473264i	$0.843076\pi$
$110$	5.82447	+	5.29337i	0.555341	+	0.504703i
$111$	11.8509	+	11.4653i	1.12484	+	1.08823i
$112$	8.85226	+	5.79979i	0.836460	+	0.548028i
$113$		−	10.7917i		−	1.01520i	−0.861593	−	0.507600i	$-0.830533\pi$
$113$		−	10.7917i		−	1.01520i	0.861593	−	0.507600i	$-0.169467\pi$
$114$	0.462414	+	7.18471i	0.0433090	+	0.672909i
$115$	2.46249	−	1.42172i	0.229628	−	0.132576i
$116$	4.11572	−	0.394118i	0.382135	−	0.0365929i
$117$	11.7509	+	6.27566i	1.08637	+	0.580185i
$118$	4.81949	+	1.04774i	0.443670	+	0.0964521i
$119$	1.69425	+	0.427820i	0.155311	+	0.0392182i
$120$	13.1930	−	2.12556i	1.20435	−	0.194037i
$121$	3.41870	−	5.92136i	0.310791	−	0.538305i
$122$	−0.0854782	−	0.267275i	−0.00773883	−	0.0241980i
$123$	−13.2046	−	3.30513i	−1.19062	−	0.298013i
$124$	−3.60232	−	5.05587i	−0.323498	−	0.454031i
$125$		−	6.98150i		−	0.624445i
$126$	10.2109	+	4.66233i	0.909660	+	0.415354i
$127$		−	10.9563i		−	0.972210i	−0.873900	−	0.486105i	$-0.838417\pi$
$127$		−	10.9563i		−	0.972210i	0.873900	−	0.486105i	$-0.161583\pi$
$128$	10.1812	+	4.93390i	0.899898	+	0.436100i
$129$	−0.891467	−	0.223134i	−0.0784893	−	0.0196459i
$130$	−16.3158	+	5.21801i	−1.43099	+	0.457650i
$131$	11.0778	−	19.1873i	0.967869	−	1.67640i	0.266169	−	0.963926i	$-0.414242\pi$
$131$	11.0778	−	19.1873i	0.967869	−	1.67640i	0.701700	−	0.712473i	$-0.252425\pi$
$132$	2.58082	+	6.57956i	0.224631	+	0.572677i
$133$	−2.12106	−	7.48157i	−0.183920	−	0.648734i
$134$	−1.43143	+	6.58444i	−0.123657	+	0.568809i
$135$	13.4920	−	4.34290i	1.16121	−	0.373778i
$136$	1.85496	+	0.221030i	0.159061	+	0.0189532i
$137$	−12.5610	+	7.25212i	−1.07316	+	0.619591i	−0.929044	−	0.369970i	$-0.879368\pi$
$137$	−12.5610	+	7.25212i	−1.07316	+	0.619591i	−0.144119	+	0.989560i	$0.546035\pi$
$138$	2.54812	−	0.163999i	0.216910	−	0.0139605i
$139$		−	5.78265i		−	0.490478i	−0.969463	−	0.245239i	$-0.921134\pi$
$139$		−	5.78265i		−	0.490478i	0.969463	−	0.245239i	$-0.0788665\pi$
$140$	−13.4480	+	5.24269i	−1.13657	+	0.443088i
$141$	−1.29763	−	1.25541i	−0.109280	−	0.105724i
$142$	5.25768	−	5.78520i	0.441215	−	0.485483i
$143$	−4.52991	−	7.84603i	−0.378810	−	0.656118i
$144$	11.4655	+	3.54150i	0.955459	+	0.295125i
$145$	−2.81949	+	4.88349i	−0.234146	+	0.405552i
$146$	4.19530	+	0.912043i	0.347206	+	0.0754812i
$147$	−11.8417	−	2.60266i	−0.976688	−	0.214664i
$148$	−17.3217	−	7.90492i	−1.42383	−	0.649780i
$149$	11.9993	+	6.92781i	0.983022	+	0.567548i	0.903181	−	0.429260i	$-0.141225\pi$
$149$	11.9993	+	6.92781i	0.983022	+	0.567548i	0.0798408	+	0.996808i	$0.474559\pi$
$150$	−2.65036	+	5.35848i	−0.216401	+	0.437518i
$151$	10.1959	−	5.88660i	0.829730	−	0.479045i	−0.0240304	−	0.999711i	$-0.507650\pi$
$151$	10.1959	−	5.88660i	0.829730	−	0.479045i	0.853760	+	0.520667i	$0.174317\pi$
$152$	−3.27563	−	7.64081i	−0.265688	−	0.619752i
$153$	1.98031	−	0.0655255i	0.160099	−	0.00529742i
$154$	−4.22046	−	6.36115i	−0.340094	−	0.512596i
$155$	8.46682			0.680071
$156$	−15.2103	−	2.29559i	−1.21780	−	0.183794i
$157$	5.34134	+	9.25147i	0.426285	+	0.738348i	0.996540	−	0.0831204i	$-0.0264886\pi$
$157$	5.34134	+	9.25147i	0.426285	+	0.738348i	−0.570254	+	0.821468i	$0.693155\pi$
$158$	−14.7000	+	4.70126i	−1.16947	+	0.374012i
$159$	5.03812	+	17.6309i	0.399549	+	1.39822i
$160$	−13.5380	+	7.40409i	−1.07027	+	0.585345i
$161$	−2.65340	+	0.752253i	−0.209117	+	0.0592859i
$162$	12.5889	+	1.87576i	0.989081	+	0.147374i
$163$	17.7351	+	10.2394i	1.38912	+	0.802008i	0.993216	−	0.116284i	$-0.0370982\pi$
$163$	17.7351	+	10.2394i	1.38912	+	0.802008i	0.395903	+	0.918292i	$0.370432\pi$
$164$	15.6462	−	1.49827i	1.22176	−	0.116995i
$165$	−9.35084	−	2.34052i	−0.727962	−	0.182209i
$166$	−8.71136	+	9.58540i	−0.676133	+	0.743972i
$167$	−22.4614			−1.73811			−0.869057	−	0.494712i	$-0.835273\pi$
$167$	−22.4614			−1.73811			−0.869057	+	0.494712i	$0.835273\pi$
$168$	−12.9118	−	1.13400i	−0.996165	−	0.0874903i
$169$	6.71850			0.516808
$170$	−1.71356	+	1.88549i	−0.131424	+	0.144610i
$171$	−4.65894	−	7.48632i	−0.356278	−	0.572493i
$172$	1.05630	−	0.101151i	0.0805422	−	0.00771266i
$173$	−16.8271	−	9.71515i	−1.27934	−	0.738630i	−0.302616	−	0.953113i	$-0.597860\pi$
$173$	−16.8271	−	9.71515i	−1.27934	−	0.738630i	−0.976728	+	0.214483i	$0.931193\pi$
$174$	−4.21367	+	2.80831i	−0.319438	+	0.212898i
$175$	1.58088	−	6.26058i	0.119503	−	0.473255i
$176$	−5.34762	−	6.16479i	−0.403092	−	0.464689i
$177$	−5.80804	+	1.65968i	−0.436559	+	0.124749i
$178$	−0.729057	+	0.233162i	−0.0546451	+	0.0174762i
$179$	2.51687	+	4.35934i	0.188119	+	0.325833i	0.944623	−	0.328157i	$-0.106427\pi$
$179$	2.51687	+	4.35934i	0.188119	+	0.325833i	−0.756504	+	0.653989i	$0.773094\pi$
$180$	−13.0078	+	9.93264i	−0.969543	+	0.740335i
$181$	5.71850			0.425053			0.212526	−	0.977155i	$-0.431831\pi$
$181$	5.71850			0.425053			0.212526	+	0.977155i	$0.431831\pi$
$182$	16.5829	−	1.03264i	1.22921	−	0.0765441i
$183$	0.247002	+	0.238964i	0.0182589	+	0.0176647i
$184$	−2.70988	+	1.16173i	−0.199775	+	0.0856438i
$185$	22.4892	−	12.9841i	1.65344	−	0.954613i
$186$	6.81509	+	3.37081i	0.499707	+	0.247160i
$187$	−1.16698	−	0.673757i	−0.0853381	−	0.0492700i
$188$	1.89666	+	0.865562i	0.138328	+	0.0631276i
$189$	−13.7195	+	0.880233i	−0.997948	+	0.0640275i
$190$	11.0795	+	2.40865i	0.803793	+	0.174742i
$191$	4.90753	−	8.50010i	0.355097	−	0.615046i	−0.632038	−	0.774938i	$-0.717781\pi$
$191$	4.90753	−	8.50010i	0.355097	−	0.615046i	0.987135	+	0.159892i	$0.0511146\pi$
$192$	−13.8447	+	0.569934i	−0.999154	+	0.0411315i
$193$	−8.57953	−	14.8602i	−0.617568	−	1.06966i	−0.989928	−	0.141571i	$-0.954785\pi$
$193$	−8.57953	−	14.8602i	−0.617568	−	1.06966i	0.372360	−	0.928088i	$-0.378549\pi$
$194$	−6.57900	+	7.23909i	−0.472344	+	0.519736i
$195$	14.5876	−	15.0782i	1.04464	−	1.07977i
$196$	13.8918	−	1.73686i	0.992275	−	0.124061i
$197$			11.0302i			0.785867i	0.919567	+	0.392934i	$0.128540\pi$
$197$			11.0302i			0.785867i	−0.919567	+	0.392934i	$0.871460\pi$
$198$	−6.59485	−	5.60668i	−0.468675	−	0.398450i
$199$	−19.3160	+	11.1521i	−1.36927	+	0.790550i	−0.990835	−	0.135077i	$-0.956872\pi$
$199$	−19.3160	+	11.1521i	−1.36927	+	0.790550i	−0.378438	+	0.925627i	$0.623539\pi$
$200$	0.816750	−	6.85443i	0.0577529	−	0.484682i
$201$	−2.26747	−	7.93501i	−0.159935	−	0.559692i
$202$	−3.04371	+	14.0007i	−0.214155	+	0.985089i
$203$	3.81120	−	3.92302i	0.267494	−	0.275342i
$204$	−2.12993	+	0.835460i	−0.149125	+	0.0584939i
$205$	−10.7185	+	18.5650i	−0.748612	+	1.29663i
$206$	−9.86238	+	3.15412i	−0.687145	+	0.219758i
$207$	−2.65509	+	1.65233i	−0.184541	+	0.114845i
$208$	17.4394	−	3.37088i	1.20921	−	0.233728i
$209$			5.99672i			0.414802i
$210$	11.4782	−	13.4444i	0.792074	−	0.927755i
$211$			17.9648i			1.23675i	0.785884	+	0.618374i	$0.212208\pi$
$211$			17.9648i			1.23675i	−0.785884	+	0.618374i	$0.787792\pi$
$212$	−12.2863	−	17.2439i	−0.843828	−	1.18432i
$213$	−2.32474	+	9.28780i	−0.159288	+	0.636390i
$214$	7.55029	+	23.6085i	0.516127	+	1.61384i
$215$	−0.723623	+	1.25335i	−0.0493507	+	0.0854779i
$216$	−14.4246	+	2.81629i	−0.981468	+	0.191624i
$217$	−7.96241	−	2.01061i	−0.540523	−	0.136489i
$218$	−0.883020	−	0.191965i	−0.0598057	−	0.0130015i
$219$	−5.05582	+	1.44473i	−0.341641	+	0.0976257i
$220$	11.0798	−	1.06100i	0.747002	−	0.0715323i
$221$	2.53991	−	1.46642i	0.170853	−	0.0986419i
$222$	23.2712	−	1.49775i	1.56186	−	0.100523i
$223$		−	1.95751i		−	0.131084i	−0.997850	−	0.0655422i	$-0.979122\pi$
$223$		−	1.95751i		−	0.131084i	0.997850	−	0.0655422i	$-0.0208777\pi$
$224$	14.4897	−	3.74813i	0.968134	−	0.250433i
$225$	−0.242130	−	7.31765i	−0.0161420	−	0.487843i
$226$	−11.2944	−	10.2645i	−0.751290	−	0.682784i
$227$	9.08211	+	15.7307i	0.602801	+	1.04408i	0.992395	+	0.123095i	$0.0392820\pi$
$227$	9.08211	+	15.7307i	0.602801	+	1.04408i	−0.389594	+	0.920987i	$0.627385\pi$
$228$	7.95917	+	6.34975i	0.527109	+	0.420522i
$229$	4.92264	−	8.52627i	0.325297	−	0.563432i	−0.656275	−	0.754522i	$-0.727869\pi$
$229$	4.92264	−	8.52627i	0.325297	−	0.563432i	0.981573	+	0.191090i	$0.0612023\pi$
$230$	0.854247	−	3.92945i	0.0563274	−	0.259100i
$231$	8.23796	+	4.42162i	0.542018	+	0.290921i
$232$	3.50217	−	4.68228i	0.229929	−	0.307406i
$233$	22.6957	+	13.1034i	1.48684	+	0.858430i	0.999888	−	0.0149969i	$-0.00477386\pi$
$233$	22.6957	+	13.1034i	1.48684	+	0.858430i	0.486956	+	0.873426i	$0.338107\pi$
$234$	17.7447	−	6.32912i	1.16001	−	0.413747i
$235$	−2.46249	+	1.42172i	−0.160635	+	0.0927427i
$236$	5.68057	−	4.04741i	0.369774	−	0.263464i
$237$	13.1429	−	13.5850i	0.853724	−	0.882440i
$238$	2.05922	−	1.36624i	0.133480	−	0.0885603i
$239$	−16.9336			−1.09535			−0.547673	−	0.836692i	$-0.684486\pi$
$239$	−16.9336			−1.09535			−0.547673	+	0.836692i	$0.684486\pi$
$240$	10.3239	−	15.8292i	0.666404	−	1.02177i
$241$	−2.91870	−	5.05533i	−0.188010	−	0.325643i	0.756577	−	0.653905i	$-0.226870\pi$
$241$	−2.91870	−	5.05533i	−0.188010	−	0.325643i	−0.944587	+	0.328262i	$0.893537\pi$
$242$	−2.94548	−	9.21000i	−0.189343	−	0.592041i
$243$	−14.6726	+	5.26449i	−0.941248	+	0.337717i
$244$	−0.361026	−	0.164758i	−0.0231123	−	0.0105476i
$245$	−9.06504	+	16.8051i	−0.579144	+	1.07364i
$246$	−16.0186	+	10.6760i	−1.02131	+	0.680679i
$247$	−11.3031	−	6.52586i	−0.719201	−	0.415231i
$248$	−8.71769	−	1.03877i	−0.553574	−	0.0659619i
$249$	3.85182	−	15.3888i	0.244099	−	0.975225i
$250$	−7.30668	−	6.64042i	−0.462115	−	0.419977i
$251$	10.1468			0.640462			0.320231	−	0.947340i	$-0.396240\pi$
$251$	10.1468			0.640462			0.320231	+	0.947340i	$0.396240\pi$
$252$	14.5915	−	6.25195i	0.919181	−	0.393836i
$253$	2.12679			0.133710
$254$	−11.4666	−	10.4210i	−0.719476	−	0.653871i
$255$	0.757669	−	3.02704i	0.0474471	−	0.189561i
$256$	14.8475	−	5.96254i	0.927969	−	0.372659i
$257$	10.3764	+	5.99080i	0.647261	+	0.373696i	0.787406	−	0.616435i	$-0.211424\pi$
$257$	10.3764	+	5.99080i	0.647261	+	0.373696i	−0.140145	+	0.990131i	$0.544757\pi$
$258$	−1.08144	+	0.720756i	−0.0673276	+	0.0448723i
$259$	−24.2327	+	6.87010i	−1.50575	+	0.426888i
$260$	−10.0576	+	22.0388i	−0.623749	+	1.36679i
$261$	2.92159	−	5.47054i	0.180842	−	0.338618i
$262$	−9.54438	−	29.8436i	−0.589654	−	1.84374i
$263$	7.22199	+	12.5088i	0.445327	+	0.771329i	0.998075	−	0.0620197i	$-0.0197542\pi$
$263$	7.22199	+	12.5088i	0.445327	+	0.771329i	−0.552748	+	0.833348i	$0.686421\pi$
$264$	9.34075	+	3.55709i	0.574883	+	0.218924i
$265$	28.8775			1.77393
$266$	−9.84748	−	4.89620i	−0.603788	−	0.300205i
$267$	0.651832	−	0.673757i	0.0398915	−	0.0412332i
$268$	5.52962	+	7.76086i	0.337776	+	0.474070i
$269$	−5.69092	+	3.28566i	−0.346982	+	0.200330i	−0.663355	−	0.748305i	$-0.730868\pi$
$269$	−5.69092	+	3.28566i	−0.346982	+	0.200330i	0.316373	+	0.948635i	$0.397535\pi$
$270$	8.28767	−	18.2511i	0.504371	−	1.11073i
$271$	0.0141559	+	0.00817291i	0.000859910	+	0.000496469i	0.500430	−	0.865777i	$-0.333175\pi$
$271$	0.0141559	+	0.00817291i	0.000859910	+	0.000496469i	−0.499570	+	0.866274i	$0.666509\pi$
$272$	1.99566	−	1.73112i	0.121005	−	0.104965i
$273$	−17.2991	+	10.7158i	−1.04699	+	0.648551i
$274$	−4.35747	+	20.0439i	−0.263245	+	1.21090i
$275$	−2.48966	+	4.31222i	−0.150132	+	0.260037i
$276$	2.25199	−	2.82279i	0.135554	−	0.169912i
$277$	9.15688	+	15.8602i	0.550184	+	0.952946i	0.998261	+	0.0589513i	$0.0187757\pi$
$277$	9.15688	+	15.8602i	0.550184	+	0.952946i	−0.448077	+	0.893995i	$0.647891\pi$
$278$	−6.05199	−	5.50014i	−0.362974	−	0.329877i
$279$	−9.30682	+	0.307948i	−0.557185	+	0.0184364i
$280$	−7.30415	+	19.0610i	−0.436507	+	1.13911i
$281$			1.61190i			0.0961580i	0.998844	+	0.0480790i	$0.0153099\pi$
$281$			1.61190i			0.0961580i	−0.998844	+	0.0480790i	$0.984690\pi$
$282$	−2.54812	+	0.163999i	−0.151738	+	0.00976600i
$283$	17.8180	−	10.2872i	1.05917	−	0.611513i	0.133969	−	0.990986i	$-0.457228\pi$
$283$	17.8180	−	10.2872i	1.05917	−	0.611513i	0.925203	+	0.379472i	$0.123894\pi$
$284$	−1.05384	−	11.0051i	−0.0625341	−	0.653035i
$285$	−13.3521	+	3.81543i	−0.790910	+	0.226007i
$286$	−12.5201	−	2.72182i	−0.740328	−	0.160944i
$287$	14.4886	−	14.9137i	0.855233	−	0.880325i
$288$	14.6118	−	8.63105i	0.861009	−	0.508590i
$289$	−8.28189	+	14.3447i	−0.487170	+	0.843803i
$290$	2.42921	+	7.59572i	0.142648	+	0.446036i
$291$	2.90897	−	11.6219i	0.170527	−	0.681290i
$292$	4.94486	−	3.52322i	0.289376	−	0.206181i
$293$		−	11.6573i		−	0.681026i	−0.940240	−	0.340513i	$-0.889399\pi$
$293$		−	11.6573i		−	0.681026i	0.940240	−	0.340513i	$-0.110601\pi$
$294$	−13.9871	+	9.91775i	−0.815743	+	0.578415i
$295$			9.51296i			0.553866i
$296$	−24.7485	+	10.6097i	−1.43848	+	0.616677i
$297$	10.3637	+	2.23262i	0.601361	+	0.129550i
$298$	18.6636	−	5.96885i	1.08115	−	0.345766i
$299$	−2.31445	+	4.00875i	−0.133848	+	0.231832i
$300$	3.08719	+	7.87050i	0.178239	+	0.454404i
$301$	0.978146	−	1.00684i	0.0563794	−	0.0580336i
$302$	3.53699	−	16.2698i	0.203531	−	0.936221i
$303$	−4.82141	−	16.8725i	−0.276983	−	0.969300i
$304$	−11.1123	−	3.83933i	−0.637334	−	0.220201i
$305$	0.468730	−	0.270622i	0.0268394	−	0.0154957i
$306$	1.81499	−	2.13488i	0.103756	−	0.122043i
$307$		−	3.66039i		−	0.208909i	−0.994530	−	0.104455i	$-0.966690\pi$
$307$		−	3.66039i		−	0.208909i	0.994530	−	0.104455i	$-0.0333097\pi$
$308$	−10.6717	−	1.63334i	−0.608076	−	0.0930680i
$309$	8.81771	−	9.11430i	0.501622	−	0.518494i
$310$	8.05317	−	8.86118i	0.457389	−	0.503281i
$311$	5.87374	+	10.1736i	0.333069	+	0.576892i	0.983112	−	0.183005i	$-0.0585824\pi$
$311$	5.87374	+	10.1736i	0.333069	+	0.576892i	−0.650043	+	0.759897i	$0.725249\pi$
$312$	−16.8697	+	13.7353i	−0.955058	+	0.777607i
$313$	7.41692	−	12.8465i	0.419229	−	0.726126i	−0.576633	−	0.817003i	$-0.695634\pi$
$313$	7.41692	−	12.8465i	0.419229	−	0.726126i	0.995862	+	0.0908771i	$0.0289670\pi$
$314$	14.7628	+	3.20937i	0.833111	+	0.181115i
$315$	−4.60361	+	21.1557i	−0.259384	+	1.19199i
$316$	−9.06162	+	19.8563i	−0.509756	+	1.11700i
$317$	−7.19012	−	4.15122i	−0.403837	−	0.233156i	0.284301	−	0.958735i	$-0.408238\pi$
$317$	−7.19012	−	4.15122i	−0.403837	−	0.233156i	−0.688138	+	0.725579i	$0.741572\pi$
$318$	23.2440	+	11.4967i	1.30346	+	0.644705i
$319$	−3.65267	+	2.10887i	−0.204510	+	0.118074i
$320$	−5.12764	+	21.2109i	−0.286644	+	1.18573i
$321$	−21.8177	−	21.1077i	−1.21775	−	1.17812i
$322$	−1.73648	+	3.49249i	−0.0967702	+	0.194629i
$323$	−1.94125			−0.108014
$324$	13.9370	−	11.3912i	0.774280	−	0.632843i
$325$	−5.41870	−	9.38546i	−0.300575	−	0.520612i
$326$	27.5849	−	8.82202i	1.52779	−	0.488606i
$327$	1.06414	−	0.304084i	0.0588471	−	0.0168159i
$328$	13.3138	−	17.8000i	0.735130	−	0.982843i
$329$	2.65340	−	0.752253i	0.146287	−	0.0414731i
$330$	−11.3435	+	7.56020i	−0.624441	+	0.416175i
$331$	13.2232	+	7.63441i	0.726812	+	0.419625i	0.817255	−	0.576276i	$-0.195495\pi$
$331$	13.2232	+	7.63441i	0.726812	+	0.419625i	−0.0904426	+	0.995902i	$0.528828\pi$
$332$	1.74609	+	18.2342i	0.0958294	+	1.00073i
$333$	−24.2481	+	15.0903i	−1.32879	+	0.826941i
$334$	−21.3640	+	23.5076i	−1.16899	+	1.28628i
$335$	−12.9967			−0.710087
$336$	−13.4678	+	12.4346i	−0.734729	+	0.678361i
$337$	−16.9606			−0.923904			−0.461952	−	0.886905i	$-0.652851\pi$
$337$	−16.9606			−0.923904			−0.461952	+	0.886905i	$0.652851\pi$
$338$	6.39027	−	7.03143i	0.347585	−	0.382459i
$339$	18.1324	+	4.53856i	0.984819	+	0.246500i
$340$	0.343464	+	3.58675i	0.0186270	+	0.194519i
$341$	5.48442	+	3.16643i	0.296998	+	0.171472i
$342$	−12.2663	−	2.24464i	−0.663288	−	0.121376i
$343$	12.5157	−	13.6513i	0.675784	−	0.737100i
$344$	0.898834	−	1.20171i	0.0484619	−	0.0647918i
$345$	1.35318	+	4.73544i	0.0728525	+	0.254947i
$346$	−26.1727	+	8.37038i	−1.40705	+	0.449994i
$347$	−11.0283	−	19.1015i	−0.592029	−	1.02542i	−0.993959	−	0.109753i	$-0.964994\pi$
$347$	−11.0283	−	19.1015i	−0.592029	−	1.02542i	0.401930	−	0.915670i	$-0.368339\pi$
$348$	−1.06870	+	7.08105i	−0.0572882	+	0.379584i
$349$	−17.6748			−0.946110			−0.473055	−	0.881033i	$-0.656849\pi$
$349$	−17.6748			−0.946110			−0.473055	+	0.881033i	$0.656849\pi$
$350$	−5.04853	−	7.60923i	−0.269855	−	0.406731i
$351$	−15.4864	+	17.1047i	−0.826602	+	0.912982i
$352$	−11.5383	−	0.266918i	−0.614993	−	0.0142268i
$353$	−0.365480	+	0.211010i	−0.0194526	+	0.0112309i	−0.509695	−	0.860355i	$-0.670242\pi$
$353$	−0.365480	+	0.211010i	−0.0194526	+	0.0112309i	0.490242	+	0.871586i	$0.336908\pi$
$354$	−3.78731	+	7.65715i	−0.201293	+	0.406973i
$355$	13.0581	+	7.53911i	0.693053	+	0.400134i
$356$	−0.449417	+	0.984785i	−0.0238190	+	0.0521935i
$357$	−1.43136	+	2.66678i	−0.0757557	+	0.141141i
$358$	6.95629	+	1.51227i	0.367651	+	0.0799260i
$359$	7.22199	−	12.5088i	0.381162	−	0.660192i	−0.610067	−	0.792350i	$-0.708857\pi$
$359$	7.22199	−	12.5088i	0.381162	−	0.660192i	0.991229	+	0.132158i	$0.0421907\pi$
$360$	−1.97702	+	23.0610i	−0.104198	+	1.21542i
$361$	−5.18051	−	8.97291i	−0.272659	−	0.472259i
$362$	5.43912	−	5.98485i	0.285874	−	0.314557i
$363$	8.51141	+	8.23443i	0.446733	+	0.432196i
$364$	14.6920	−	18.3375i	0.770071	−	0.961145i
$365$			8.28091i			0.433443i
$366$	0.485029	−	0.0312169i	0.0253529	−	0.00163173i
$367$	18.8797	−	10.9002i	0.985512	−	0.568985i	0.0815820	−	0.996667i	$-0.474003\pi$
$367$	18.8797	−	10.9002i	0.985512	−	0.568985i	0.903930	+	0.427681i	$0.140669\pi$
$368$	−1.36165	+	3.94107i	−0.0709809	+	0.205442i
$369$	11.1067	−	20.7967i	0.578190	−	1.08263i
$370$	7.80158	−	35.8865i	0.405585	−	1.86565i
$371$	−27.1572	−	6.85754i	−1.40993	−	0.356026i
$372$	10.0100	−	3.92638i	0.518992	−	0.203573i
$373$	−9.76004	+	16.9049i	−0.505356	+	0.875302i	0.494625	+	0.869106i	$0.335305\pi$
$373$	−9.76004	+	16.9049i	−0.505356	+	0.875302i	−0.999981	+	0.00619524i	$0.998028\pi$
$374$	−1.81511	+	0.580495i	−0.0938569	+	0.0300167i
$375$	11.7304	+	2.93613i	0.605757	+	0.151621i
$376$	2.70988	−	1.16173i	0.139751	−	0.0599116i
$377$		−	9.17983i		−	0.472785i
$378$	−12.1280	+	15.1958i	−0.623798	+	0.781586i
$379$		−	34.1136i		−	1.75230i	−0.482038	−	0.876150i	$-0.660103\pi$
$379$		−	34.1136i		−	1.75230i	0.482038	−	0.876150i	$-0.339897\pi$
$380$	13.0591	−	9.30460i	0.669916	−	0.477316i
$381$	18.4089	+	4.60775i	0.943116	+	0.236062i
$382$	−4.22823	−	13.2209i	−0.216335	−	0.676442i
$383$	4.10770	−	7.11474i	0.209893	−	0.363546i	−0.741787	−	0.670635i	$-0.766022\pi$
$383$	4.10770	−	7.11474i	0.209893	−	0.363546i	0.951681	+	0.307089i	$0.0993549\pi$
$384$	−12.5718	+	15.0316i	−0.641553	+	0.767079i
$385$	10.2600	−	10.5611i	0.522900	−	0.538242i
$386$	−23.7127	−	5.15505i	−1.20694	−	0.262385i
$387$	0.749829	−	1.40402i	0.0381159	−	0.0713702i
$388$	1.31869	+	13.7708i	0.0669461	+	0.699109i
$389$	−4.15260	+	2.39750i	−0.210545	+	0.121558i	−0.601565	−	0.798824i	$-0.705456\pi$
$389$	−4.15260	+	2.39750i	−0.210545	+	0.121558i	0.391020	+	0.920382i	$0.372122\pi$
$390$	−1.90563	−	29.6086i	−0.0964955	−	1.49929i
$391$			0.688481i			0.0348180i
$392$	11.3954	−	16.1909i	0.575555	−	0.817763i
$393$	27.5799	+	26.6824i	1.39122	+	1.34595i
$394$	11.5439	+	10.4913i	0.581574	+	0.528544i
$395$	−14.8841	−	25.7799i	−0.748898	−	1.29713i
$396$	−12.1405	+	1.56924i	−0.610082	+	0.0788575i
$397$	−5.20059	+	9.00769i	−0.261010	+	0.452083i	−0.966511	−	0.256627i	$-0.917389\pi$
$397$	−5.20059	+	9.00769i	−0.261010	+	0.452083i	0.705500	+	0.708709i	$0.250722\pi$
$398$	−6.70078	+	30.8229i	−0.335880	+	1.54501i
$399$	13.4627	−	0.417410i	0.673978	−	0.0208966i
$400$	−6.39684	−	7.37435i	−0.319842	−	0.368718i
$401$	−10.0211	−	5.78571i	−0.500432	−	0.288924i	0.228460	−	0.973553i	$-0.426631\pi$
$401$	−10.0211	−	5.78571i	−0.500432	−	0.288924i	−0.728892	+	0.684629i	$0.759964\pi$
$402$	−10.4613	−	5.17426i	−0.521762	−	0.258069i
$403$	−11.9367	+	6.89167i	−0.594611	+	0.343299i
$404$	11.7578	+	16.5022i	0.584975	+	0.821016i
$405$	1.62284	+	24.4959i	0.0806396	+	1.21721i
$406$	−0.480737	−	7.72007i	−0.0238586	−	0.383141i
$407$	19.4233			0.962777
$408$	−1.15150	+	3.02378i	−0.0570076	+	0.149699i
$409$	−10.2185	−	17.6990i	−0.505272	−	0.875157i	−0.999981	−	0.00609862i	$-0.998059\pi$
$409$	−10.2185	−	17.6990i	−0.505272	−	0.875157i	0.494709	−	0.869059i	$-0.335275\pi$
$410$	9.23484	+	28.8757i	0.456076	+	1.42607i
$411$	−6.90249	−	24.1552i	−0.340475	−	1.19149i
$412$	−6.07953	+	13.3218i	−0.299517	+	0.656316i
$413$	2.25904	−	8.94623i	0.111160	−	0.440215i
$414$	−0.796079	+	4.35036i	−0.0391251	+	0.213809i
$415$	−21.6358	−	12.4914i	−1.06206	−	0.613180i
$416$	13.0595	−	21.4579i	0.640296	−	1.05206i
$417$	9.71611	+	2.43194i	0.475800	+	0.119093i
$418$	6.27603	+	5.70375i	0.306970	+	0.278979i
$419$	21.9130			1.07052			0.535259	−	0.844688i	$-0.320214\pi$
$419$	21.9130			1.07052			0.535259	+	0.844688i	$0.320214\pi$
$420$	−3.15317	−	24.8005i	−0.153859	−	1.21014i
$421$	14.1153			0.687940			0.343970	−	0.938981i	$-0.388228\pi$
$421$	14.1153			0.687940			0.343970	+	0.938981i	$0.388228\pi$
$422$	18.8015	+	17.0871i	0.915245	+	0.831788i
$423$	2.65509	−	1.65233i	0.129095	−	0.0803392i
$424$	−29.7332	−	3.54290i	−1.44397	−	0.172058i
$425$	−1.39595	−	0.805951i	−0.0677134	−	0.0390944i
$426$	7.50924	+	11.2671i	0.363824	+	0.545891i
$427$	−0.505070	+	0.143190i	−0.0244421	+	0.00692945i
$428$	31.8895	+	14.5531i	1.54144	+	0.703451i
$429$	15.0881	−	4.31151i	0.728462	−	0.208162i
$430$	0.623459	+	1.94945i	0.0300659	+	0.0940107i
$431$	14.5604	+	25.2193i	0.701348	+	1.21477i	0.967994	+	0.250975i	$0.0807512\pi$
$431$	14.5604	+	25.2193i	0.701348	+	1.21477i	−0.266646	+	0.963795i	$0.585915\pi$
$432$	−10.7724	+	17.7751i	−0.518288	+	0.855206i
$433$	26.1153			1.25502			0.627512	−	0.778607i	$-0.284073\pi$
$433$	26.1153			1.25502			0.627512	+	0.778607i	$0.284073\pi$
$434$	−9.67766	+	6.42089i	−0.464543	+	0.308212i
$435$	−7.01957	−	6.79115i	−0.336563	−	0.325611i
$436$	−1.04079	+	0.741562i	−0.0498446	+	0.0355144i
$437$	2.65340	−	1.53194i	0.126929	−	0.0732827i
$438$	−3.29680	+	6.66545i	−0.157527	+	0.318488i
$439$	15.9204	+	9.19162i	0.759837	+	0.438692i	0.829237	−	0.558897i	$-0.188775\pi$
$439$	15.9204	+	9.19162i	0.759837	+	0.438692i	−0.0694002	+	0.997589i	$0.522109\pi$
$440$	9.42811	−	12.6051i	0.449467	−	0.600922i
$441$	9.35317	−	18.8021i	0.445389	−	0.895337i
$442$	0.881103	−	4.05298i	0.0419098	−	0.192781i
$443$	−4.13441	+	7.16101i	−0.196432	+	0.340230i	−0.947369	−	0.320144i	$-0.896269\pi$
$443$	−4.13441	+	7.16101i	−0.196432	+	0.340230i	0.750937	+	0.660374i	$0.229602\pi$
$444$	20.5668	−	25.7797i	0.976055	−	1.22345i
$445$	−0.738185	−	1.27857i	−0.0349933	−	0.0606102i
$446$	−2.04868	−	1.86187i	−0.0970079	−	0.0881623i
$447$	−16.6866	+	17.2479i	−0.789251	+	0.815798i
$448$	9.85910	−	18.7296i	0.465799	−	0.884891i
$449$		−	24.1061i		−	1.13764i	−0.822463	−	0.568818i	$-0.807401\pi$
$449$		−	24.1061i		−	1.13764i	0.822463	−	0.568818i	$-0.192599\pi$
$450$	−7.88878	−	6.70674i	−0.371881	−	0.316159i
$451$	−13.8859	+	8.01704i	−0.653862	+	0.377508i
$452$	−21.4852	+	2.05740i	−1.01058	+	0.0967721i
$453$	5.60280	+	19.6070i	0.263242	+	0.921216i
$454$	25.1018	+	5.45703i	1.17808	+	0.256111i
$455$	8.74102	+	30.8320i	0.409786	+	1.44542i
$456$	14.2158	−	2.29035i	0.665717	−	0.107256i
$457$	9.34529	−	16.1865i	0.437154	−	0.757173i	−0.560315	−	0.828280i	$-0.689320\pi$
$457$	9.34529	−	16.1865i	0.437154	−	0.757173i	0.997469	+	0.0711068i	$0.0226531\pi$
$458$	−4.24125	−	13.2616i	−0.198180	−	0.619676i
$459$	−0.722741	+	3.35492i	−0.0337347	+	0.156594i
$460$	−3.29996	−	4.63151i	−0.153861	−	0.215945i
$461$			16.3664i			0.762260i	0.924521	+	0.381130i	$0.124465\pi$
$461$			16.3664i			0.762260i	−0.924521	+	0.381130i	$0.875535\pi$
$462$	12.4631	−	4.41605i	0.579834	−	0.205453i
$463$			11.3643i			0.528142i	0.964503	+	0.264071i	$0.0850653\pi$
$463$			11.3643i			0.528142i	−0.964503	+	0.264071i	$0.914935\pi$
$464$	−1.56929	−	8.11881i	−0.0728525	−	0.376906i
$465$	−3.56079	+	14.2261i	−0.165128	+	0.659719i
$466$	35.3006	−	11.2896i	1.63527	−	0.522980i
$467$	−18.1468	+	31.4313i	−0.839736	+	1.45446i	0.0503800	+	0.998730i	$0.483957\pi$
$467$	−18.1468	+	31.4313i	−0.839736	+	1.45446i	−0.890116	+	0.455735i	$0.849377\pi$
$468$	10.2539	−	24.5911i	0.473987	−	1.13673i
$469$	12.2224	+	3.08633i	0.564380	+	0.142513i
$470$	−0.854247	+	3.92945i	−0.0394035	+	0.181252i
$471$	−17.7908	+	5.08382i	−0.819758	+	0.234250i
$472$	1.16712	−	9.79483i	0.0537209	−	0.450844i
$473$	−0.937461	+	0.541243i	−0.0431045	+	0.0248864i
$474$	−1.71691	−	26.6764i	−0.0788605	−	1.22529i
$475$			7.17330i			0.329134i
$476$	0.528742	−	3.45463i	0.0242348	−	0.158343i
$477$	−31.7425	+	1.05031i	−1.45339	+	0.0480904i
$478$	−16.1063	+	17.7224i	−0.736687	+	0.810602i
$479$	−5.59953	−	9.69867i	−0.255849	−	0.443144i	0.709277	−	0.704930i	$-0.249022\pi$
$479$	−5.59953	−	9.69867i	−0.255849	−	0.443144i	−0.965126	+	0.261787i	$0.915688\pi$
$480$	−6.74697	−	25.8606i	−0.307955	−	1.18037i
$481$	−21.1372	+	36.6107i	−0.963773	+	1.66930i
$482$	−8.06690	−	1.75371i	−0.367437	−	0.0798794i
$483$	−0.148038	−	4.77466i	−0.00673596	−	0.217254i
$484$	−12.4406	−	5.67738i	−0.565480	−	0.258063i
$485$	−16.3398	−	9.43377i	−0.741951	−	0.428366i
$486$	−8.44608	+	20.3633i	−0.383122	+	0.923698i
$487$	−8.60678	+	4.96913i	−0.390010	+	0.225173i	−0.682165	−	0.731199i	$-0.738961\pi$
$487$	−8.60678	+	4.96913i	−0.390010	+	0.225173i	0.292154	+	0.956371i	$0.405628\pi$
$488$	−0.515820	+	0.221133i	−0.0233501	+	0.0100102i
$489$	−24.6630	+	25.4926i	−1.11530	+	1.15281i
$490$	8.96568	+	25.4714i	0.405028	+	1.15068i
$491$	−2.64307			−0.119280			−0.0596400	−	0.998220i	$-0.518995\pi$
$491$	−2.64307			−0.119280			−0.0596400	+	0.998220i	$0.518995\pi$
$492$	−4.06274	+	26.9192i	−0.183162	+	1.21361i
$493$	−0.682681	−	1.18244i	−0.0307464	−	0.0532544i
$494$	−17.5807	+	5.62255i	−0.790995	+	0.252970i
$495$	7.86515	−	14.7271i	0.353512	−	0.661935i
$496$	−9.37894	+	8.13571i	−0.421127	+	0.365304i
$497$	−10.4899	−	10.1909i	−0.470535	−	0.457123i
$498$	−12.4419	−	18.6682i	−0.557536	−	0.836542i
$499$	17.1844	+	9.92144i	0.769281	+	0.444145i	0.832618	−	0.553848i	$-0.186841\pi$
$499$	17.1844	+	9.92144i	0.769281	+	0.444145i	−0.0633371	+	0.997992i	$0.520174\pi$
$500$	−13.8994	+	1.33100i	−0.621601	+	0.0595240i
$501$	9.44633	−	37.7400i	0.422031	−	1.68610i
$502$	9.65110	−	10.6194i	0.430750	−	0.473968i
$503$	−3.07284			−0.137011			−0.0685056	−	0.997651i	$-0.521823\pi$
$503$	−3.07284			−0.137011			−0.0685056	+	0.997651i	$0.521823\pi$
$504$	7.33553	−	21.2177i	0.326751	−	0.945111i
$505$	−27.6354			−1.22976
$506$	2.02288	−	2.22585i	0.0899281	−	0.0989509i
$507$	−2.82552	+	11.2885i	−0.125486	+	0.501342i
$508$	−21.8127	+	2.08877i	−0.967783	+	0.0926741i
$509$	−14.6238	−	8.44307i	−0.648190	−	0.374233i	0.139572	−	0.990212i	$-0.455427\pi$
$509$	−14.6238	−	8.44307i	−0.648190	−	0.374233i	−0.787762	+	0.615979i	$0.788761\pi$
$510$	−2.44738	−	3.67212i	−0.108372	−	0.162604i
$511$	1.96647	−	7.78758i	0.0869913	−	0.344502i
$512$	7.88187	−	21.2103i	0.348333	−	0.937371i
$513$	14.5380	−	4.67960i	0.641869	−	0.206609i
$514$	16.1393	−	5.16155i	0.711873	−	0.227666i
$515$	−9.98586	−	17.2960i	−0.440029	−	0.762153i
$516$	−0.274282	+	1.81736i	−0.0120746	+	0.0800046i
$517$	−2.12679			−0.0935360
$518$	−15.8587	+	31.8959i	−0.696793	+	1.40142i
$519$	23.4004	−	24.1875i	1.02716	−	1.06171i
$520$	13.4990	+	31.4882i	0.591972	+	1.38085i
$521$	−27.3170	+	15.7715i	−1.19678	+	0.690961i	−0.959836	−	0.280562i	$-0.909479\pi$
$521$	−27.3170	+	15.7715i	−1.19678	+	0.690961i	−0.236944	+	0.971523i	$0.576146\pi$
$522$	−2.94648	−	8.26095i	−0.128964	−	0.361572i
$523$	−29.0382	−	16.7652i	−1.26975	−	0.733092i	−0.294812	−	0.955555i	$-0.595257\pi$
$523$	−29.0382	−	16.7652i	−1.26975	−	0.733092i	−0.974941	+	0.222463i	$0.928590\pi$
$524$	−40.3117	−	18.3967i	−1.76103	−	0.803662i
$525$	9.85428	+	5.28916i	0.430076	+	0.230838i
$526$	19.9606	+	4.33936i	0.870325	+	0.189205i
$527$	−1.02503	+	1.77541i	−0.0446512	+	0.0773381i
$528$	12.6072	−	6.39250i	0.548657	−	0.278198i
$529$	10.9567	+	18.9775i	0.476378	+	0.825110i
$530$	27.4667	−	30.2226i	1.19308	−	1.31278i
$531$	−0.345998	−	10.4568i	−0.0150150	−	0.453785i
$532$	−14.4906	+	5.64915i	−0.628249	+	0.244922i
$533$		−	34.8978i		−	1.51159i
$534$	−0.0851515	−	1.32303i	−0.00368487	−	0.0572532i
$535$	−41.4030	+	23.9040i	−1.79001	+	1.03346i
$536$	13.3818	+	1.59453i	0.578006	+	0.0688732i
$537$	−8.38313	+	2.39552i	−0.361759	+	0.103375i
$538$	−1.97420	+	9.08112i	−0.0851139	+	0.391515i
$539$	−12.1567	+	7.49544i	−0.523627	+	0.322851i
$540$	−11.2185	−	26.0332i	−0.482765	−	1.12029i
$541$	11.8396	−	20.5067i	0.509023	−	0.881653i	−0.490923	−	0.871203i	$-0.663340\pi$
$541$	11.8396	−	20.5067i	0.509023	−	0.881653i	0.999945	−	0.0104499i	$-0.00332638\pi$
$542$	0.0220179	−	0.00704161i	0.000945749	−	0.000302463i
$543$	−2.40496	+	9.60832i	−0.103207	+	0.412333i
$544$	0.0864065	−	3.73516i	0.00370465	−	0.160144i
$545$		−	1.74295i		−	0.0746599i
$546$	−5.23903	+	28.2972i	−0.224210	+	1.21101i
$547$			10.9063i			0.466318i	0.972439	+	0.233159i	$0.0749063\pi$
$547$			10.9063i			0.466318i	−0.972439	+	0.233159i	$0.925094\pi$
$548$	16.8329	+	23.6251i	0.719067	+	1.00921i
$549$	−0.505391	+	0.314519i	−0.0215696	+	0.0134233i
$550$	2.14504	+	6.70717i	0.0914649	+	0.285995i
$551$	−3.03808	+	5.26210i	−0.129426	+	0.224173i
$552$	−0.812293	−	5.04176i	−0.0345735	−	0.214592i
$553$	7.87538	+	27.7786i	0.334895	+	1.18127i
$554$	25.3084	+	5.50196i	1.07525	+	0.233756i
$555$	12.3581	+	43.2473i	0.524574	+	1.83575i
$556$	−11.5126	+	1.10244i	−0.488245	+	0.0467539i
$557$	9.47804	−	5.47215i	0.401597	−	0.231862i	−0.285576	−	0.958356i	$-0.592185\pi$
$557$	9.47804	−	5.47215i	0.401597	−	0.231862i	0.687173	+	0.726494i	$0.258851\pi$
$558$	−8.52984	+	10.0332i	−0.361097	+	0.424739i
$559$		−	2.35601i		−	0.0996485i
$560$	13.0015	+	25.7741i	0.549412	+	1.08915i
$561$	1.62284	−	1.67743i	0.0685164	−	0.0708210i
$562$	1.68698	+	1.53315i	0.0711609	+	0.0646721i
$563$	14.1475	+	24.5041i	0.596245	+	1.03273i	0.993370	+	0.114962i	$0.0366746\pi$
$563$	14.1475	+	24.5041i	0.596245	+	1.03273i	−0.397125	+	0.917765i	$0.629992\pi$
$564$	−2.25199	+	2.82279i	−0.0948259	+	0.118861i
$565$	14.7185	−	25.4932i	0.619212	−	1.07251i
$566$	6.18114	−	28.4326i	0.259813	−	1.19511i
$567$	4.29088	−	23.4220i	0.180200	−	0.983630i
$568$	−12.5201	−	9.36455i	−0.525331	−	0.392928i
$569$	0.823967	+	0.475718i	0.0345425	+	0.0199431i	0.517172	−	0.855882i	$-0.326985\pi$
$569$	0.823967	+	0.475718i	0.0345425	+	0.0199431i	−0.482629	+	0.875825i	$0.660318\pi$
$570$	−8.70664	+	17.6030i	−0.364681	+	0.737310i
$571$	14.1886	−	8.19177i	0.593773	−	0.342815i	−0.172815	−	0.984954i	$-0.555286\pi$
$571$	14.1886	−	8.19177i	0.593773	−	0.342815i	0.766588	+	0.642139i	$0.221953\pi$
$572$	−14.7570	+	10.5144i	−0.617021	+	0.439628i
$573$	12.2181	+	11.8205i	0.510419	+	0.493809i
$574$	−1.82756	−	29.3484i	−0.0762809	−	1.22498i
$575$	2.54407			0.106095
$576$	4.86489	−	23.5018i	0.202704	−	0.979240i
$577$	4.98426	+	8.63299i	0.207497	+	0.359396i	0.950926	−	0.309420i	$-0.100135\pi$
$577$	4.98426	+	8.63299i	0.207497	+	0.359396i	−0.743428	+	0.668816i	$0.766801\pi$
$578$	7.13551	+	22.3115i	0.296798	+	0.928036i
$579$	28.5765	−	8.16589i	1.18760	−	0.339363i
$580$	10.2600	+	4.68228i	0.426025	+	0.194421i
$581$	17.3805	+	16.8851i	0.721064	+	0.700511i
$582$	−9.39639	−	14.0986i	−0.389493	−	0.584406i
$583$	18.7056	+	10.7997i	0.774706	+	0.447276i
$584$	1.01596	−	8.52627i	0.0420407	−	0.352820i
$585$	19.1998	+	30.8515i	0.793812	+	1.27555i
$586$	−12.2002	−	11.0878i	−0.503988	−	0.458032i
$587$	29.5354			1.21905			0.609527	−	0.792765i	$-0.291359\pi$
$587$	29.5354			1.21905			0.609527	+	0.792765i	$0.291359\pi$
$588$	−2.92404	+	24.0718i	−0.120585	+	0.992703i
$589$	9.12323			0.375916
$590$	9.95605	+	9.04821i	0.409884	+	0.372509i
$591$	−18.5331	−	4.63884i	−0.762349	−	0.190816i
$592$	−12.4355	+	35.9926i	−0.511097	+	1.47929i
$593$	18.2436	+	10.5329i	0.749174	+	0.432536i	0.825395	−	0.564555i	$-0.190952\pi$
$593$	18.2436	+	10.5329i	0.749174	+	0.432536i	−0.0762215	+	0.997091i	$0.524286\pi$
$594$	12.1940	−	8.72283i	0.500324	−	0.357902i
$595$	3.41882	+	3.32137i	0.140158	+	0.136163i
$596$	11.5049	−	25.2101i	0.471259	−	1.03265i
$597$	−10.6144	−	37.1451i	−0.434419	−	1.52025i
$598$	1.99408	+	6.23515i	0.0815442	+	0.254974i
$599$	−19.8683	−	34.4129i	−0.811796	−	1.40607i	−0.911606	−	0.411066i	$-0.865157\pi$
$599$	−19.8683	−	34.4129i	−0.811796	−	1.40607i	0.0998091	−	0.995007i	$-0.468177\pi$
$600$	11.1734	+	4.25501i	0.456154	+	0.173710i
$601$	−36.5567			−1.49118			−0.745589	−	0.666406i	$-0.767832\pi$
$601$	−36.5567			−1.49118			−0.745589	+	0.666406i	$0.767832\pi$
$602$	−0.123382	−	1.98136i	−0.00502866	−	0.0807542i
$603$	14.2861	−	0.472706i	0.581777	−	0.0192501i
$604$	−13.6634	−	19.1767i	−0.555956	−	0.780287i
$605$	16.1519	−	9.32531i	0.656669	−	0.379128i
$606$	−22.2442	−	11.0022i	−0.903610	−	0.446935i
$607$	11.4085	+	6.58667i	0.463055	+	0.267345i	0.713328	−	0.700830i	$-0.247187\pi$
$607$	11.4085	+	6.58667i	0.463055	+	0.267345i	−0.250273	+	0.968175i	$0.580520\pi$
$608$	−14.5876	+	7.97812i	−0.591604	+	0.323555i
$609$	4.98869	+	8.05350i	0.202152	+	0.326344i
$610$	0.162604	−	0.747963i	0.00658365	−	0.0302841i
$611$	2.31445	−	4.00875i	0.0936327	−	0.162177i
$612$	−0.507994	−	3.93010i	−0.0205344	−	0.158865i
$613$	9.50394	+	16.4613i	0.383861	+	0.664866i	0.991610	−	0.129262i	$-0.0412609\pi$
$613$	9.50394	+	16.4613i	0.383861	+	0.664866i	−0.607750	+	0.794129i	$0.707928\pi$
$614$	−3.83087	−	3.48156i	−0.154602	−	0.140504i
$615$	−26.6855	−	25.8171i	−1.07606	−	1.04104i
$616$	−11.8597	+	9.61521i	−0.477843	+	0.387408i
$617$			41.6979i			1.67869i	0.543596	+	0.839347i	$0.317062\pi$
$617$			41.6979i			1.67869i	−0.543596	+	0.839347i	$0.682938\pi$
$618$	−1.15189	−	17.8974i	−0.0463360	−	0.719940i
$619$	−11.6140	+	6.70535i	−0.466806	+	0.269511i	−0.714902	−	0.699225i	$-0.753529\pi$
$619$	−11.6140	+	6.70535i	−0.466806	+	0.269511i	0.248096	+	0.968736i	$0.420195\pi$
$620$	−1.61417	−	16.8565i	−0.0648265	−	0.676974i
$621$	−1.65966	−	5.15603i	−0.0665998	−	0.206904i
$622$	16.2342	+	3.52926i	0.650934	+	0.141511i
$623$	0.390585	+	1.37770i	0.0156484	+	0.0551963i
$624$	−1.67049	+	30.7197i	−0.0668731	+	1.22977i
$625$	15.6232	−	27.0602i	0.624929	−	1.08241i
$626$	−6.39027	−	19.9812i	−0.255406	−	0.798611i
$627$	−10.0758	−	2.52197i	−0.402388	−	0.100718i
$628$	17.4004	−	12.3978i	0.694351	−	0.494726i
$629$			6.28769i			0.250707i
$630$	17.7623	+	24.9401i	0.707668	+	0.993638i
$631$			10.7225i			0.426856i	0.976959	+	0.213428i	$0.0684629\pi$
$631$			10.7225i			0.426856i	−0.976959	+	0.213428i	$0.931537\pi$
$632$	12.1622	+	28.3699i	0.483786	+	1.12849i
$633$	−30.1848	−	7.55525i	−1.19974	−	0.300294i
$634$	−11.1834	+	3.57660i	−0.444150	+	0.142045i
$635$	14.9429	−	25.8818i	0.592990	−	1.02709i
$636$	34.1407	−	13.3916i	1.35377	−	0.531012i
$637$	−0.898621	−	31.0709i	−0.0356047	−	1.23107i
$638$	−1.26713	+	5.82864i	−0.0501660	+	0.230758i
$639$	−14.6278	−	7.81213i	−0.578668	−	0.309043i
$640$	17.3217	+	25.5411i	0.684701	+	1.00960i
$641$	20.7630	−	11.9875i	0.820089	−	0.473479i	−0.0303581	−	0.999539i	$-0.509665\pi$
$641$	20.7630	−	11.9875i	0.820089	−	0.473479i	0.850447	+	0.526060i	$0.176331\pi$
$642$	−42.8427	+	2.75739i	−1.69087	+	0.108826i
$643$		−	24.5118i		−	0.966649i	−0.875441	−	0.483325i	$-0.839429\pi$
$643$		−	24.5118i		−	0.966649i	0.875441	−	0.483325i	$-0.160571\pi$
$644$	2.00352	+	5.13922i	0.0789496	+	0.202514i
$645$	−1.80158	−	1.74295i	−0.0709371	−	0.0686287i
$646$	−1.84641	+	2.03167i	−0.0726461	+	0.0799349i
$647$	−21.2165	−	36.7481i	−0.834108	−	1.44472i	−0.894754	−	0.446559i	$-0.852649\pi$
$647$	−21.2165	−	36.7481i	−0.834108	−	1.44472i	0.0606458	−	0.998159i	$-0.480684\pi$
$648$	1.33441	−	25.4208i	0.0524205	−	0.998625i
$649$	−3.55767	+	6.16207i	−0.139651	+	0.241882i
$650$	−14.9766	−	3.25585i	−0.587430	−	0.127705i
$651$	6.72692	−	12.5330i	0.263649	−	0.491207i
$652$	17.0043	−	37.2608i	0.665941	−	1.45924i
$653$	−18.5142	−	10.6892i	−0.724517	−	0.418300i	0.0918961	−	0.995769i	$-0.470707\pi$
$653$	−18.5142	−	10.6892i	−0.724517	−	0.418300i	−0.816413	+	0.577469i	$0.804041\pi$
$654$	0.693905	−	1.40293i	0.0271338	−	0.0548590i
$655$	52.3378	−	30.2173i	2.04501	−	1.18069i
$656$	−5.96579	−	30.8643i	−0.232925	−	1.20505i
$657$	−0.301187	−	9.10247i	−0.0117504	−	0.355121i
$658$	1.73648	−	3.49249i	0.0676950	−	0.136151i
$659$	0.835578			0.0325495			0.0162748	−	0.999868i	$-0.494819\pi$
$659$	0.835578			0.0325495			0.0162748	+	0.999868i	$0.494819\pi$
$660$	−2.87702	+	19.0627i	−0.111988	+	0.742016i
$661$	−9.00217	−	15.5922i	−0.350144	−	0.606467i	0.636131	−	0.771581i	$-0.280534\pi$
$661$	−9.00217	−	15.5922i	−0.350144	−	0.606467i	−0.986274	+	0.165115i	$0.947201\pi$
$662$	20.5672	−	6.57765i	0.799366	−	0.255648i
$663$	1.39572	+	4.88431i	0.0542052	+	0.189691i
$664$	20.7443	+	15.5160i	0.805035	+	0.602136i
$665$	5.19331	−	20.5665i	0.201388	−	0.797534i
$666$	−7.27035	+	39.7305i	−0.281720	+	1.53953i
$667$	1.86625	+	1.07748i	0.0722614	+	0.0417202i
$668$	4.28218	+	44.7182i	0.165682	+	1.73020i
$669$	3.28904	+	0.823247i	0.127162	+	0.0318286i
$670$	−12.3618	+	13.6021i	−0.477577	+	0.525494i
$671$	0.404830			0.0156283
$672$	0.203904	+	25.9222i	0.00786575	+	0.999969i
$673$	3.35747			0.129421			0.0647105	−	0.997904i	$-0.479388\pi$
$673$	3.35747			0.129421			0.0647105	+	0.997904i	$0.479388\pi$
$674$	−16.1320	+	17.7506i	−0.621382	+	0.683728i
$675$	12.3971	+	2.67067i	0.477164	+	0.102794i
$676$	−1.28086	−	13.3758i	−0.0492637	−	0.514454i
$677$	31.9197	+	18.4288i	1.22677	+	0.708278i	0.966354	−	0.257217i	$-0.0828056\pi$
$677$	31.9197	+	18.4288i	1.22677	+	0.708278i	0.260420	+	0.965495i	$0.416139\pi$
$678$	21.9965	−	14.6602i	0.844772	−	0.563021i
$679$	13.1261	+	12.7520i	0.503733	+	0.489375i
$680$	4.08049	+	3.05206i	0.156480	+	0.117041i
$681$	−30.2505	+	8.64425i	−1.15920	+	0.331248i
$682$	8.53040	−	2.72813i	0.326646	−	0.104466i
$683$	−2.19316	−	3.79867i	−0.0839191	−	0.145352i	0.821011	−	0.570912i	$-0.193410\pi$
$683$	−2.19316	−	3.79867i	−0.0839191	−	0.145352i	−0.904930	+	0.425560i	$0.860077\pi$
$684$	−14.0163	+	10.7027i	−0.535925	+	0.409228i
$685$	−39.5638			−1.51165
$686$	−2.38287	−	26.0830i	−0.0909785	−	0.995853i
$687$	12.2557	+	11.8569i	0.467585	+	0.452369i
$688$	−0.402760	−	2.08370i	−0.0153551	−	0.0794403i
$689$	−40.7123	+	23.5052i	−1.55101	+	0.895478i
$690$	6.24306	+	3.08788i	0.237669	+	0.117554i
$691$	−34.8657	−	20.1297i	−1.32635	−	0.765771i	−0.341620	−	0.939838i	$-0.610976\pi$
$691$	−34.8657	−	20.1297i	−1.32635	−	0.765771i	−0.984734	+	0.174067i	$0.944309\pi$
$692$	−16.1338	+	35.3532i	−0.613315	+	1.34393i
$693$	−10.8938	+	11.9820i	−0.413822	+	0.455159i
$694$	−30.4807	−	6.62639i	−1.15703	−	0.251534i
$695$	7.88678	−	13.6603i	0.299163	−	0.518165i
$696$	6.39437	+	7.85358i	0.242378	+	0.297689i
$697$	−2.59527	−	4.49513i	−0.0983027	−	0.170265i
$698$	−16.8113	+	18.4980i	−0.636317	+	0.700161i
$699$	−31.5614	+	32.6229i	−1.19376	+	1.23391i
$700$	−12.7655	−	1.95380i	−0.482492	−	0.0738469i
$701$			25.7395i			0.972168i	0.873912	+	0.486084i	$0.161575\pi$
$701$			25.7395i			0.972168i	−0.873912	+	0.486084i	$0.838425\pi$
$702$	3.17159	+	32.4768i	0.119704	+	1.22576i
$703$	24.2327	−	13.9908i	0.913954	−	0.527672i
$704$	−11.2539	+	11.8218i	−0.424149	+	0.445552i
$705$	−1.35318	−	4.73544i	−0.0509635	−	0.178347i
$706$	−0.126786	+	0.583205i	−0.00477167	+	0.0219492i
$707$	25.9890	+	6.56257i	0.977418	+	0.246811i
$708$	4.41152	+	11.2468i	0.165795	+	0.422679i
$709$	−7.50394	+	12.9972i	−0.281817	+	0.488121i	−0.971832	−	0.235674i	$-0.924270\pi$
$709$	−7.50394	+	12.9972i	−0.281817	+	0.488121i	0.690016	+	0.723794i	$0.257604\pi$
$710$	20.3104	−	6.49554i	0.762237	−	0.243773i
$711$	17.2984	+	27.7962i	0.648739	+	1.04244i
$712$	0.603192	+	1.40702i	0.0226056	+	0.0527304i
$713$		−	3.23563i		−	0.121175i
$714$	1.42956	+	4.03453i	0.0534999	+	0.150988i
$715$		−	24.7128i		−	0.924207i
$716$	8.19915	−	5.84191i	0.306417	−	0.218322i
$717$	7.12159	−	28.4522i	0.265961	−	1.06257i
$718$	−6.22231	−	19.4561i	−0.232215	−	0.726095i
$719$	−19.2753	+	33.3858i	−0.718847	+	1.24508i	0.242610	+	0.970124i	$0.421997\pi$
$719$	−19.2753	+	33.3858i	−0.718847	+	1.24508i	−0.961457	+	0.274956i	$0.911337\pi$
$720$	22.2547	+	24.0035i	0.829384	+	0.894557i
$721$	5.28367	+	18.6369i	0.196774	+	0.694076i
$722$	−14.3183	−	3.11274i	−0.532871	−	0.115844i
$723$	9.72154	−	2.77798i	0.361548	−	0.103314i
$724$	−1.09021	−	11.3849i	−0.0405174	−	0.423117i
$725$	−4.36934	+	2.52264i	−0.162273	+	0.0936885i
$726$	16.7136	−	1.07570i	0.620298	−	0.0399229i
$727$			50.3452i			1.86720i	0.358318	+	0.933600i	$0.383350\pi$
$727$			50.3452i			1.86720i	−0.358318	+	0.933600i	$0.616650\pi$
$728$	−5.21734	−	32.8179i	−0.193367	−	1.21631i
$729$	−2.67479	−	26.8672i	−0.0990664	−	0.995081i
$730$	8.66661	+	7.87635i	0.320766	+	0.291517i
$731$	−0.175211	−	0.303474i	−0.00648040	−	0.0112244i
$732$	0.428662	−	0.537312i	0.0158438	−	0.0198596i
$733$	6.27578	−	10.8700i	0.231801	−	0.401491i	−0.726537	−	0.687127i	$-0.758871\pi$
$733$	6.27578	−	10.8700i	0.231801	−	0.401491i	0.958338	+	0.285636i	$0.0922048\pi$
$734$	6.54943	−	30.1267i	0.241744	−	1.11200i
$735$	−24.4239	−	22.2988i	−0.900888	−	0.822503i
$736$	2.82951	+	5.17360i	0.104297	+	0.190701i
$737$	−8.41869	−	4.86053i	−0.310107	−	0.179040i
$738$	−11.2013	−	31.4046i	−0.412325	−	1.15602i
$739$	−5.42182	+	3.13029i	−0.199445	+	0.115150i	−0.596397	−	0.802690i	$-0.703401\pi$
$739$	−5.42182	+	3.13029i	−0.199445	+	0.115150i	0.396952	+	0.917840i	$0.370068\pi$
$740$	−30.1375	−	42.2982i	−1.10788	−	1.55491i
$741$	15.7185	−	16.2472i	0.577433	−	0.596856i
$742$	−33.0073	+	21.8995i	−1.21174	+	0.803957i
$743$	−34.2633			−1.25700			−0.628498	−	0.777811i	$-0.716330\pi$
$743$	−34.2633			−1.25700			−0.628498	+	0.777811i	$0.716330\pi$
$744$	5.41166	−	14.2107i	0.198401	−	0.520991i
$745$	18.8972	+	32.7310i	0.692341	+	1.19917i
$746$	8.40905	+	26.2936i	0.307877	+	0.962678i
$747$	24.2366	+	12.9438i	0.886771	+	0.473588i
$748$	−1.11890	+	2.45178i	−0.0409109	+	0.0896461i
$749$	44.6129	−	12.6480i	1.63012	−	0.462147i
$750$	14.2302	−	9.48412i	0.519615	−	0.346311i
$751$	−25.1285	−	14.5079i	−0.916952	−	0.529402i	−0.0342903	−	0.999412i	$-0.510917\pi$
$751$	−25.1285	−	14.5079i	−0.916952	−	0.529402i	−0.882661	+	0.470010i	$0.844250\pi$
$752$	1.36165	−	3.94107i	0.0496543	−	0.143716i
$753$	−4.26733	+	17.0489i	−0.155510	+	0.621295i
$754$	−9.60739	−	8.73135i	−0.349881	−	0.317977i
$755$	32.1142			1.16876
$756$	4.36802	+	27.1463i	0.158864	+	0.987301i
$757$	−10.5717			−0.384234			−0.192117	−	0.981372i	$-0.561535\pi$
$757$	−10.5717			−0.384234			−0.192117	+	0.981372i	$0.561535\pi$
$758$	−35.7026	−	32.4470i	−1.29678	−	1.17853i
$759$	−0.894439	+	3.57346i	−0.0324661	+	0.129709i
$760$	2.68309	−	22.5173i	0.0973258	−	0.816790i
$761$	−33.6645	−	19.4362i	−1.22034	−	0.704563i	−0.255348	−	0.966849i	$-0.582190\pi$
$761$	−33.6645	−	19.4362i	−1.22034	−	0.704563i	−0.964990	+	0.262287i	$0.915523\pi$
$762$	22.3319	−	14.8837i	0.808999	−	0.539179i
$763$	−0.413898	+	1.63912i	−0.0149841	+	0.0593400i
$764$	−17.8584	−	8.14986i	−0.646094	−	0.294852i
$765$	4.76744	+	2.54610i	0.172367	+	0.0920544i
$766$	−3.53911	−	11.0662i	−0.127873	−	0.399837i
$767$	−7.74320	−	13.4116i	−0.279591	−	0.484265i
$768$	3.77412	+	27.4546i	0.136187	+	0.990683i
$769$	25.5953			0.922989			0.461494	−	0.887143i	$-0.347313\pi$
$769$	25.5953			0.922989			0.461494	+	0.887143i	$0.347313\pi$
$770$	−1.29418	−	20.7830i	−0.0466391	−	0.748968i
$771$	−14.4297	+	14.9151i	−0.519674	+	0.537154i
$772$	−27.9494	+	19.9140i	−1.00592	+	0.716719i
$773$	24.6534	−	14.2336i	0.886720	−	0.511948i	0.0138518	−	0.999904i	$-0.495591\pi$
$773$	24.6534	−	14.2336i	0.886720	−	0.511948i	0.872868	+	0.487956i	$0.162257\pi$
$774$	−0.756216	−	2.12018i	−0.0271816	−	0.0762082i
$775$	6.56049	+	3.78770i	0.235660	+	0.136058i
$776$	15.6665	+	11.7180i	0.562395	+	0.420651i
$777$	−1.35199	−	43.6055i	−0.0485022	−	1.56434i
$778$	−1.44055	+	6.62639i	−0.0516463	+	0.237568i
$779$	−11.5495	+	20.0043i	−0.413803	+	0.716728i
$780$	−32.8002	−	26.1677i	−1.17443	−	0.936952i
$781$	5.63897	+	9.76699i	0.201778	+	0.349490i
$782$	0.720548	+	0.654845i	0.0257667	+	0.0234172i
$783$	7.96299	+	7.20959i	0.284574	+	0.257650i
$784$	−6.10632	−	27.3260i	−0.218083	−	0.975930i
$785$			29.1395i			1.04004i
$786$	54.1577	−	3.48564i	1.93174	−	0.124329i
$787$	27.6598	−	15.9694i	0.985964	−	0.569247i	0.0818987	−	0.996641i	$-0.473902\pi$
$787$	27.6598	−	15.9694i	0.985964	−	0.569247i	0.904065	+	0.427394i	$0.140568\pi$
$788$	21.9599	−	2.10286i	0.782289	−	0.0749113i
$789$	−24.0549	+	6.87380i	−0.856375	+	0.244714i
$790$	−41.1376	−	8.94315i	−1.46361	−	0.318183i
$791$	−19.8955	+	20.4792i	−0.707402	+	0.728158i
$792$	−9.90502	+	14.1985i	−0.351960	+	0.504523i
$793$	−0.440552	+	0.763058i	−0.0156444	+	0.0270970i
$794$	4.48072	+	14.0104i	0.159015	+	0.497212i
$795$	−12.1447	+	48.5206i	−0.430728	+	1.72085i
$796$	25.8851	+	36.3299i	0.917473	+	1.28768i
$797$			37.7330i			1.33657i	0.743905	+	0.668285i	$0.232971\pi$
$797$			37.7330i			1.33657i	−0.743905	+	0.668285i	$0.767029\pi$
$798$	12.3681	−	14.4868i	0.437827	−	0.512826i
$799$		−	0.688481i		−	0.0243567i
$800$	−13.8022	−	0.319289i	−0.487980	−	0.0112886i
$801$	0.857924	+	1.37857i	0.0303133	+	0.0487095i
$802$	−15.5867	+	4.98485i	−0.550387	+	0.176021i
$803$	−3.09691	+	5.36400i	−0.109288	+	0.189292i
$804$	−15.3655	+	6.02707i	−0.541898	+	0.212558i
$805$	−7.29408	−	1.84185i	−0.257083	−	0.0649167i
$806$	−4.14089	+	19.0477i	−0.145857	+	0.670926i
$807$	−3.12725	−	10.9438i	−0.110084	−	0.385240i
$808$	28.4542	+	3.39051i	1.00102	+	0.119278i
$809$	−22.6957	+	13.1034i	−0.797938	+	0.460690i	−0.842750	−	0.538306i	$-0.819065\pi$
$809$	−22.6957	+	13.1034i	−0.797938	+	0.460690i	0.0448118	+	0.998995i	$0.485731\pi$
$810$	27.1804	+	21.6008i	0.955023	+	0.758973i
$811$		−	32.1734i		−	1.12976i	−0.825172	−	0.564881i	$-0.808922\pi$
$811$		−	32.1734i		−	1.12976i	0.825172	−	0.564881i	$-0.191078\pi$
$812$	−8.53690	−	6.83978i	−0.299586	−	0.240029i
$813$	−0.0196857	+	0.0203478i	−0.000690406	+	0.000713628i
$814$	18.4744	−	20.3280i	0.647527	−	0.712495i
$815$	27.9303	+	48.3767i	0.978355	+	1.69456i
$816$	2.06937	+	4.08118i	0.0724426	+	0.142870i
$817$	−0.779724	+	1.35052i	−0.0272791	+	0.0472488i
$818$	−28.2426	−	6.13983i	−0.987479	−	0.214674i
$819$	−10.7296	−	33.5729i	−0.374923	−	1.17313i
$820$	39.0043	+	17.8000i	1.36209	+	0.621604i
$821$	19.3857	+	11.1923i	0.676565	+	0.390615i	0.798560	−	0.601916i	$-0.205596\pi$
$821$	19.3857	+	11.1923i	0.676565	+	0.390615i	−0.121994	+	0.992531i	$0.538929\pi$
$822$	−31.8456	−	15.7511i	−1.11074	−	0.549384i
$823$	−28.4876	+	16.4473i	−0.993014	+	0.573317i	−0.906174	−	0.422905i	$-0.861010\pi$
$823$	−28.4876	+	16.4473i	−0.993014	+	0.573317i	−0.0868401	+	0.996222i	$0.527677\pi$
$824$	8.15974	+	19.0336i	0.284258	+	0.663068i
$825$	−6.19842	−	5.99672i	−0.215801	−	0.208779i
$826$	−7.21424	−	10.8734i	−0.251015	−	0.378335i
$827$	16.7455			0.582297			0.291148	−	0.956678i	$-0.405963\pi$
$827$	16.7455			0.582297			0.291148	+	0.956678i	$0.405963\pi$
$828$	3.79580	+	4.97098i	0.131913	+	0.172754i
$829$	0.474201	+	0.821341i	0.0164697	+	0.0285263i	0.874143	−	0.485669i	$-0.161424\pi$
$829$	0.474201	+	0.821341i	0.0164697	+	0.0285263i	−0.857673	+	0.514195i	$0.828091\pi$
$830$	−33.6520	+	10.7623i	−1.16808	+	0.373567i
$831$	−30.4996	+	8.71541i	−1.05802	+	0.302334i
$832$	−10.0358	−	34.0774i	−0.347929	−	1.18142i
$833$	−2.42641	−	3.93536i	−0.0840703	−	0.136352i
$834$	11.7866	−	7.85553i	0.408138	−	0.272015i
$835$	−53.0603	−	30.6344i	−1.83623	−	1.06015i
$836$	11.9388	−	1.14325i	0.412913	−	0.0395402i
$837$	3.39665	−	15.7670i	0.117405	−	0.544987i
$838$	20.8424	−	22.9336i	0.719989	−	0.792228i
$839$	35.5384			1.22692			0.613461	−	0.789725i	$-0.289777\pi$
$839$	35.5384			1.22692			0.613461	+	0.789725i	$0.289777\pi$
$840$	−28.9547	−	20.2888i	−0.999033	−	0.700031i
$841$	24.7264			0.852634
$842$	13.4257	−	14.7728i	0.462682	−	0.509104i
$843$	−2.70834	−	0.677899i	−0.0932804	−	0.0233481i
$844$	35.7660	−	3.42492i	1.23112	−	0.117891i
$845$	15.8710	+	9.16315i	0.545980	+	0.315222i
$846$	0.796079	−	4.35036i	0.0273698	−	0.149568i
$847$	−17.4041	+	4.93416i	−0.598013	+	0.169540i
$848$	−31.9885	+	27.7482i	−1.09849	+	0.952879i
$849$	9.79128	+	34.2646i	0.336036	+	1.17596i
$850$	−2.17124	+	0.694390i	−0.0744729	+	0.0238174i
$851$	−4.96194	−	8.59434i	−0.170093	−	0.294610i
$852$	18.9342	+	2.85762i	0.648676	+	0.0979005i
$853$	−35.8618			−1.22788			−0.613942	−	0.789351i	$-0.710417\pi$
$853$	−35.8618			−1.22788			−0.613942	+	0.789351i	$0.710417\pi$
$854$	−0.330535	+	0.664789i	−0.0113107	+	0.0227486i
$855$	−0.795415	−	24.0390i	−0.0272026	−	0.822118i
$856$	45.5625	−	19.5327i	1.55729	−	0.667614i
$857$	32.9586	−	19.0286i	1.12584	−	0.650006i	0.182957	−	0.983121i	$-0.441433\pi$
$857$	32.9586	−	19.0286i	1.12584	−	0.650006i	0.942886	+	0.333115i	$0.108100\pi$
$858$	9.83867	−	19.8918i	0.335887	−	0.679094i
$859$	18.6659	+	10.7768i	0.636873	+	0.367699i	0.783409	−	0.621507i	$-0.213479\pi$
$859$	18.6659	+	10.7768i	0.636873	+	0.367699i	−0.146536	+	0.989205i	$0.546812\pi$
$860$	2.63325	+	1.20171i	0.0897929	+	0.0409779i
$861$	18.9649	+	30.6160i	0.646322	+	1.04339i
$862$	40.2429	+	8.74866i	1.37068	+	0.297980i
$863$	16.2372	−	28.1237i	0.552721	−	0.957341i	−0.445356	−	0.895354i	$-0.646923\pi$
$863$	16.2372	−	28.1237i	0.552721	−	0.957341i	0.998077	−	0.0619877i	$-0.0197439\pi$
$864$	8.35692	+	28.1809i	0.284308	+	0.958733i
$865$	−26.5004	−	45.9000i	−0.901040	−	1.56065i
$866$	24.8395	−	27.3317i	0.844080	−	0.928769i
$867$	−20.6191	−	19.9482i	−0.700262	−	0.677475i
$868$	−2.48491	+	16.2356i	−0.0843433	+	0.551073i
$869$		−	22.2654i		−	0.755303i
$870$	−13.7841	+	0.887156i	−0.467324	+	0.0300774i
$871$	18.3231	−	10.5788i	0.620855	−	0.358451i
$872$	−0.213838	+	1.79460i	−0.00724145	+	0.0607727i
$873$	18.3040	+	9.77541i	0.619496	+	0.330847i
$874$	0.920475	−	4.23409i	0.0311355	−	0.143220i
$875$	−12.8710	+	13.2486i	−0.435120	+	0.447886i
$876$	3.84017	+	9.79017i	0.129747	+	0.330779i
$877$	14.0957	−	24.4144i	0.475977	−	0.824416i	−0.523645	−	0.851937i	$-0.675428\pi$
$877$	14.0957	−	24.4144i	0.475977	−	0.824416i	0.999621	+	0.0275212i	$0.00876138\pi$
$878$	24.7623	−	7.91931i	0.835687	−	0.267264i
$879$	19.5868	+	4.90258i	0.660646	+	0.165360i
$880$	−4.22466	−	21.8565i	−0.142413	−	0.736782i
$881$			5.81314i			0.195850i	0.995194	+	0.0979249i	$0.0312205\pi$
$881$			5.81314i			0.195850i	−0.995194	+	0.0979249i	$0.968780\pi$
$882$	−10.7816	−	27.6723i	−0.363035	−	0.931775i
$883$			47.2938i			1.59156i	0.605583	+	0.795782i	$0.292940\pi$
$883$			47.2938i			1.59156i	−0.605583	+	0.795782i	$0.707060\pi$
$884$	−3.40370	−	4.77712i	−0.114479	−	0.160672i
$885$	−15.9838	−	4.00076i	−0.537291	−	0.134484i
$886$	3.56213	+	11.1381i	0.119672	+	0.374193i
$887$	15.1948	−	26.3182i	0.510192	−	0.883678i	−0.489739	−	0.871869i	$-0.662908\pi$
$887$	15.1948	−	26.3182i	0.510192	−	0.883678i	0.999930	−	0.0118084i	$-0.00375882\pi$
$888$	−7.41843	−	46.0449i	−0.248946	−	1.54517i
$889$	−20.1988	+	20.7914i	−0.677446	+	0.697323i
$890$	−2.04025	−	0.443542i	−0.0683892	−	0.0148676i
$891$	−8.10982	+	16.4743i	−0.271689	+	0.551909i
$892$	−3.89719	+	0.373192i	−0.130488	+	0.0124954i
$893$	−2.65340	+	1.53194i	−0.0887927	+	0.0512645i
$894$	2.17985	+	33.8691i	0.0729049	+	1.13275i
$895$			13.7307i			0.458967i
$896$	−10.2245	−	28.1329i	−0.341578	−	0.939854i
$897$	−5.76221	−	5.57470i	−0.192394	−	0.186134i
$898$	−25.2289	−	22.9284i	−0.841899	−	0.765130i
$899$	3.20838	+	5.55707i	0.107005	+	0.185339i
$900$	−14.5225	+	1.87714i	−0.484083	+	0.0625712i
$901$	−3.49606	+	6.05535i	−0.116470	+	0.201733i
$902$	−4.81707	+	22.1580i	−0.160391	+	0.737782i
$903$	1.28035	+	2.06694i	0.0426074	+	0.0687833i
$904$	−18.2823	+	24.4428i	−0.608060	+	0.812954i
$905$	13.5088	+	7.79928i	0.449046	+	0.259257i
$906$	25.8493	+	12.7853i	0.858785	+	0.424764i
$907$	−36.9772	+	21.3488i	−1.22781	+	0.708874i	−0.966571	−	0.256401i	$-0.917463\pi$
$907$	−36.9772	+	21.3488i	−1.22781	+	0.708874i	−0.261236	+	0.965275i	$0.584130\pi$
$908$	29.5866	−	21.0805i	0.981867	−	0.699581i
$909$	30.3772	−	1.00513i	1.00755	−	0.0333381i
$910$	40.5820	+	20.1775i	1.34528	+	0.668878i
$911$	−42.4679			−1.40702			−0.703511	−	0.710684i	$-0.748386\pi$
$911$	−42.4679			−1.40702			−0.703511	+	0.710684i	$0.748386\pi$
$912$	11.1243	−	17.0564i	0.368362	−	0.564794i
$913$	−9.34312	−	16.1828i	−0.309212	−	0.535571i
$914$	−8.05170	−	25.1763i	−0.266327	−	0.832757i
$915$	0.257574	+	0.901381i	0.00851515	+	0.0297987i
$916$	−17.9134	−	8.17495i	−0.591874	−	0.270108i
$917$	−56.3955	+	15.9884i	−1.86234	+	0.527984i
$918$	2.82375	+	3.94742i	0.0931975	+	0.130284i
$919$	18.3769	+	10.6099i	0.606199	+	0.349989i	0.771476	−	0.636258i	$-0.219519\pi$
$919$	18.3769	+	10.6099i	0.606199	+	0.349989i	−0.165278	+	0.986247i	$0.552852\pi$
$920$	−7.98597	−	0.951579i	−0.263290	−	0.0313726i
$921$	6.15024	+	1.53941i	0.202657	+	0.0507252i
$922$	17.1287	+	15.5668i	0.564104	+	0.512667i
$923$	−24.5462			−0.807948
$924$	7.23244	−	17.2439i	0.237930	−	0.567281i
$925$	23.2342			0.763937
$926$	11.8936	+	10.8091i	0.390847	+	0.355208i
$927$	11.6056	+	18.6488i	0.381179	+	0.612506i
$928$	−9.98958	−	6.07978i	−0.327924	−	0.199579i
$929$	23.4266	+	13.5254i	0.768603	+	0.443753i	0.832376	−	0.554211i	$-0.186980\pi$
$929$	23.4266	+	13.5254i	0.768603	+	0.443753i	−0.0637729	+	0.997964i	$0.520313\pi$
$930$	11.5019	+	17.2577i	0.377161	+	0.565903i
$931$	−9.76783	+	18.1080i	−0.320128	+	0.593465i
$932$	21.7605	−	47.6828i	0.712790	−	1.56190i
$933$	−19.5641	+	5.59055i	−0.640501	+	0.183026i
$934$	15.6349	+	48.8877i	0.511591	+	1.59966i
$935$	−1.83783	−	3.18322i	−0.0601035	−	0.104102i
$936$	−15.9836	−	34.1212i	−0.522439	−	1.11529i
$937$	47.2071			1.54219			0.771094	−	0.636721i	$-0.219710\pi$
$937$	47.2071			1.54219			0.771094	+	0.636721i	$0.219710\pi$
$938$	14.8554	−	9.85618i	0.485046	−	0.321816i
$939$	18.4656	+	17.8647i	0.602603	+	0.582994i
$940$	3.29996	+	4.63151i	0.107633	+	0.151063i
$941$	13.9134	−	8.03288i	0.453563	−	0.261864i	−0.255771	−	0.966737i	$-0.582329\pi$
$941$	13.9134	−	8.03288i	0.453563	−	0.261864i	0.709334	+	0.704873i	$0.248996\pi$
$942$	−11.6010	+	23.4549i	−0.377983	+	0.764203i
$943$	7.09469	+	4.09612i	0.231035	+	0.133388i
$944$	−9.14094	−	10.5378i	−0.297512	−	0.342976i
$945$	−33.6100	−	16.6323i	−1.09333	−	0.541047i
$946$	−0.325209	+	1.49593i	−0.0105734	+	0.0486367i
$947$	12.7943	−	22.1604i	0.415759	−	0.720116i	−0.579749	−	0.814795i	$-0.696849\pi$
$947$	12.7943	−	22.1604i	0.415759	−	0.720116i	0.995508	+	0.0946792i	$0.0301825\pi$
$948$	−29.5519	−	23.5762i	−0.959801	−	0.765720i
$949$	−6.74035	−	11.6746i	−0.218801	−	0.378975i
$950$	7.50741	+	6.82285i	0.243573	+	0.221362i
$951$	9.99882	−	10.3351i	0.324234	−	0.335140i
$952$	−3.11263	−	3.83922i	−0.100881	−	0.124430i
$953$		−	25.0168i		−	0.810375i	−0.914234	−	0.405187i	$-0.867206\pi$
$953$		−	25.0168i		−	0.810375i	0.914234	−	0.405187i	$-0.132794\pi$
$954$	−29.0925	+	34.2200i	−0.941905	+	1.10791i
$955$	23.1860	−	13.3865i	0.750283	−	0.433176i
$956$	3.22834	+	33.7131i	0.104412	+	1.09036i
$957$	−2.00720	−	7.02419i	−0.0648835	−	0.227060i
$958$	−15.4764	−	3.36450i	−0.500019	−	0.108702i
$959$	37.2068	+	9.39520i	1.20147	+	0.303387i
$960$	−33.4825	−	17.5360i	−1.08064	−	0.565971i
$961$	−10.6827	+	18.5029i	−0.344603	+	0.596869i
$962$	18.2114	+	56.9438i	0.587158	+	1.83594i
$963$	44.6412	−	27.7815i	1.43854	−	0.895245i
$964$	−9.50819	+	6.77459i	−0.306238	+	0.218195i
$965$		−	46.8054i		−	1.50672i
$966$	−5.13785	−	4.38646i	−0.165308	−	0.141132i
$967$		−	25.4408i		−	0.818122i	−0.912507	−	0.409061i	$-0.865856\pi$
$967$		−	25.4408i		−	0.818122i	0.912507	−	0.409061i	$-0.134144\pi$
$968$	−17.7746	+	7.61999i	−0.571297	+	0.244916i
$969$	0.816410	−	3.26172i	0.0262269	−	0.104782i
$970$	−25.4147	+	8.12794i	−0.816016	+	0.260973i
$971$	−3.28999	+	5.69843i	−0.105581	+	0.182871i	−0.913975	−	0.405770i	$-0.867003\pi$
$971$	−3.28999	+	5.69843i	−0.105581	+	0.182871i	0.808395	+	0.588641i	$0.200337\pi$
$972$	13.2783	+	28.2079i	0.425902	+	0.904769i
$973$	−10.6608	+	10.9736i	−0.341770	+	0.351798i
$974$	−2.98572	+	13.7340i	−0.0956687	+	0.440066i
$975$	18.0485	−	5.15745i	0.578014	−	0.165171i
$976$	−0.259187	+	0.750175i	−0.00829639	+	0.0240125i
$977$	4.46235	−	2.57634i	0.142763	−	0.0824244i	−0.426917	−	0.904291i	$-0.640400\pi$
$977$	4.46235	−	2.57634i	0.142763	−	0.0824244i	0.569680	+	0.821866i	$0.307067\pi$
$978$	3.22183	+	50.0588i	0.103023	+	1.60071i
$979$		−	1.10427i		−	0.0352926i
$980$	35.1854	+	14.8437i	1.12396	+	0.474164i
$981$	0.0633932	+	1.91587i	0.00202399	+	0.0611691i
$982$	−2.51394	+	2.76617i	−0.0802231	+	0.0882721i
$983$	−16.1512	−	27.9747i	−0.515143	−	0.892253i	−0.999846	−	0.0175745i	$-0.994406\pi$
$983$	−16.1512	−	27.9747i	−0.515143	−	0.892253i	0.484703	−	0.874679i	$-0.338928\pi$
$984$	24.3087	+	29.8560i	0.774933	+	0.951774i
$985$	−15.0437	+	26.0565i	−0.479332	+	0.830228i
$986$	−1.88684	−	0.410192i	−0.0600893	−	0.0130632i
$987$	0.148038	+	4.77466i	0.00471210	+	0.151979i
$988$	−10.8374	+	23.7474i	−0.344783	+	0.755507i
$989$	0.478974	+	0.276536i	0.0152305	+	0.00879332i
$990$	−7.93216	−	22.2391i	−0.252101	−	0.706805i
$991$	−2.23686	+	1.29145i	−0.0710563	+	0.0410244i	−0.535107	−	0.844784i	$-0.679729\pi$
$991$	−2.23686	+	1.29145i	−0.0710563	+	0.0410244i	0.464051	+	0.885809i	$0.346395\pi$
$992$	−0.406082	+	17.5540i	−0.0128931	+	0.557341i
$993$	−18.3886	+	19.0071i	−0.583545	+	0.603173i
$994$	−20.6429	+	1.28546i	−0.654754	+	0.0407723i
$995$	−60.8399			−1.92875
$996$	−31.3718	−	4.73474i	−0.994053	−	0.150026i
$997$	21.4033	+	37.0717i	0.677851	+	1.17407i	0.975627	+	0.219436i	$0.0704218\pi$
$997$	21.4033	+	37.0717i	0.677851	+	1.17407i	−0.297776	+	0.954636i	$0.596245\pi$
$998$	26.7284	−	8.54810i	0.846074	−	0.270586i
$999$	−15.1572	−	47.0884i	−0.479552	−	1.48981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.23.9	yes	24
3.2	odd	2	inner	84.2.n.a.23.4	yes	24
4.3	odd	2	inner	84.2.n.a.23.5	yes	24
7.2	even	3		588.2.e.e.491.1		12
7.3	odd	6		588.2.n.e.263.8		24
7.4	even	3	inner	84.2.n.a.11.8	yes	24
7.5	odd	6		588.2.e.d.491.1		12
7.6	odd	2		588.2.n.e.275.9		24
12.11	even	2	inner	84.2.n.a.23.8	yes	24
21.2	odd	6		588.2.e.e.491.12		12
21.5	even	6		588.2.e.d.491.12		12
21.11	odd	6	inner	84.2.n.a.11.5	yes	24
21.17	even	6		588.2.n.e.263.5		24
21.20	even	2		588.2.n.e.275.4		24
28.3	even	6		588.2.n.e.263.4		24
28.11	odd	6	inner	84.2.n.a.11.4	✓	24
28.19	even	6		588.2.e.d.491.11		12
28.23	odd	6		588.2.e.e.491.11		12
28.27	even	2		588.2.n.e.275.5		24
84.11	even	6	inner	84.2.n.a.11.9	yes	24
84.23	even	6		588.2.e.e.491.2		12
84.47	odd	6		588.2.e.d.491.2		12
84.59	odd	6		588.2.n.e.263.9		24
84.83	odd	2		588.2.n.e.275.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.4	✓	24	28.11	odd	6	inner
84.2.n.a.11.5	yes	24	21.11	odd	6	inner
84.2.n.a.11.8	yes	24	7.4	even	3	inner
84.2.n.a.11.9	yes	24	84.11	even	6	inner
84.2.n.a.23.4	yes	24	3.2	odd	2	inner
84.2.n.a.23.5	yes	24	4.3	odd	2	inner
84.2.n.a.23.8	yes	24	12.11	even	2	inner
84.2.n.a.23.9	yes	24	1.1	even	1	trivial
588.2.e.d.491.1		12	7.5	odd	6
588.2.e.d.491.2		12	84.47	odd	6
588.2.e.d.491.11		12	28.19	even	6
588.2.e.d.491.12		12	21.5	even	6
588.2.e.e.491.1		12	7.2	even	3
588.2.e.e.491.2		12	84.23	even	6
588.2.e.e.491.11		12	28.23	odd	6
588.2.e.e.491.12		12	21.2	odd	6
588.2.n.e.263.4		24	28.3	even	6
588.2.n.e.263.5		24	21.17	even	6
588.2.n.e.263.8		24	7.3	odd	6
588.2.n.e.263.9		24	84.59	odd	6
588.2.n.e.275.4		24	21.20	even	2
588.2.n.e.275.5		24	28.27	even	2
588.2.n.e.275.8		24	84.83	odd	2
588.2.n.e.275.9		24	7.6	odd	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951145 - 1.04658i) q^{2} +(-0.420559 + 1.68022i) q^{3} +(-0.190646 - 1.99089i) q^{4} +(2.36229 + 1.36387i) q^{5} +(1.35846 + 2.03828i) q^{6} +(-1.89768 - 1.84359i) q^{7} +(-2.26495 - 1.69410i) q^{8} +(-2.64626 - 1.41326i) q^{9} +(3.67427 - 1.17508i) q^{10} +(1.02012 + 1.76690i) q^{11} +(3.42531 + 0.516960i) q^{12} -4.44055 q^{13} +(-3.73442 + 0.232547i) q^{14} +(-3.28508 + 3.39557i) q^{15} +(-3.92731 + 0.759113i) q^{16} +(-0.571980 + 0.330233i) q^{17} +(-3.99606 + 1.42530i) q^{18} +(2.54543 + 1.46961i) q^{19} +(2.26495 - 4.96308i) q^{20} +(3.89571 - 2.41318i) q^{21} +(2.81949 + 0.612946i) q^{22} +(0.521208 - 0.902759i) q^{23} +(3.79901 - 3.09315i) q^{24} +(1.22028 + 2.11358i) q^{25} +(-4.22361 + 4.64738i) q^{26} +(3.48749 - 3.85193i) q^{27} +(-3.30860 + 4.12955i) q^{28} +2.06727i q^{29} +(0.429143 + 6.66777i) q^{30} +(2.68812 - 1.55199i) q^{31} +(-2.94097 + 4.83226i) q^{32} +(-3.39781 + 0.970941i) q^{33} +(-0.198422 + 0.912721i) q^{34} +(-1.96845 - 6.94327i) q^{35} +(-2.30915 + 5.53785i) q^{36} +(4.76004 - 8.24463i) q^{37} +(3.95913 - 1.26618i) q^{38} +(1.86751 - 7.46109i) q^{39} +(-3.03995 - 7.09106i) q^{40} +7.85889i q^{41} +(1.17982 - 6.37244i) q^{42} +0.530567i q^{43} +(3.32324 - 2.36781i) q^{44} +(-4.32373 - 6.94768i) q^{45} +(-0.449062 - 1.40414i) q^{46} +(-0.521208 + 0.902759i) q^{47} +(0.376190 - 6.91798i) q^{48} +(0.202367 + 6.99707i) q^{49} +(3.37268 + 0.733208i) q^{50} +(-0.314312 - 1.09993i) q^{51} +(0.846575 + 8.84066i) q^{52} +(9.16829 - 5.29332i) q^{53} +(-0.714234 - 7.31368i) q^{54} +5.56526i q^{55} +(1.17493 + 7.39050i) q^{56} +(-3.53976 + 3.65883i) q^{57} +(2.16356 + 1.96627i) q^{58} +(1.74375 + 3.02026i) q^{59} +(7.38651 + 5.89288i) q^{60} +(0.0992110 - 0.171839i) q^{61} +(0.932518 - 4.28949i) q^{62} +(2.41628 + 7.56053i) q^{63} +(2.26004 + 7.67413i) q^{64} +(-10.4899 - 6.05633i) q^{65} +(-2.21564 + 4.47957i) q^{66} +(-4.12631 + 2.38233i) q^{67} +(0.766504 + 1.07579i) q^{68} +(1.29763 + 1.25541i) q^{69} +(-9.13896 - 4.54392i) q^{70} +5.52774 q^{71} +(3.59945 + 7.68401i) q^{72} +(1.51791 + 2.62910i) q^{73} +(-4.10115 - 12.8236i) q^{74} +(-4.06447 + 1.16144i) q^{75} +(2.44055 - 5.34786i) q^{76} +(1.32158 - 5.23370i) q^{77} +(-6.03233 - 9.05108i) q^{78} +(-9.45104 - 5.45656i) q^{79} +(-10.3128 - 3.56309i) q^{80} +(5.00539 + 7.47971i) q^{81} +(8.22494 + 7.47495i) q^{82} -9.15881 q^{83} +(-5.54708 - 7.29589i) q^{84} -1.80158 q^{85} +(0.555279 + 0.504646i) q^{86} +(-3.47347 - 0.869409i) q^{87} +(0.682784 - 5.73015i) q^{88} +(-0.468730 - 0.270622i) q^{89} +(-11.3838 - 2.08313i) q^{90} +(8.42674 + 8.18655i) q^{91} +(-1.89666 - 0.865562i) q^{92} +(1.47716 + 5.16932i) q^{93} +(0.449062 + 1.40414i) q^{94} +(4.00870 + 6.94327i) q^{95} +(-6.88239 - 6.97372i) q^{96} -6.91692 q^{97} +(7.51546 + 6.44344i) q^{98} +(-0.202415 - 6.11739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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