LMFDB - Embedded newform 84.2.n.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(11,84)]

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

lf = mfeigenbasis(mf)

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")

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

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			11.5
Character	$\chi$	$=$	84.11
Dual form			84.2.n.a.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430790 - 1.34700i) q^{2} +(0.420559 + 1.68022i) q^{3} +(-1.62884 + 1.16055i) q^{4} +(2.36229 - 1.36387i) q^{5} +(2.08209 - 1.29031i) q^{6} +(1.89768 - 1.84359i) q^{7} +(2.26495 + 1.69410i) q^{8} +(-2.64626 + 1.41326i) q^{9} +O(q^{10})$	\(q+(-0.430790 - 1.34700i) q^{2} +(0.420559 + 1.68022i) q^{3} +(-1.62884 + 1.16055i) q^{4} +(2.36229 - 1.36387i) q^{5} +(2.08209 - 1.29031i) q^{6} +(1.89768 - 1.84359i) q^{7} +(2.26495 + 1.69410i) q^{8} +(-2.64626 + 1.41326i) q^{9} +(-2.85479 - 2.59447i) q^{10} +(-1.02012 + 1.76690i) q^{11} +(-2.63500 - 2.24873i) q^{12} -4.44055 q^{13} +(-3.30082 - 1.76198i) q^{14} +(3.28508 + 3.39557i) q^{15} +(1.30624 - 3.78070i) q^{16} +(-0.571980 - 0.330233i) q^{17} +(3.04365 + 2.95571i) 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} +(-1.89391 + 4.51809i) q^{24} +(1.22028 - 2.11358i) q^{25} +(1.91294 + 5.98144i) q^{26} +(-3.48749 - 3.85193i) q^{27} +(-0.951438 + 5.20526i) q^{28} -2.06727i q^{29} +(3.15867 - 5.88779i) q^{30} +(-2.68812 - 1.55199i) q^{31} +(-5.65534 - 0.130827i) q^{32} +(-3.39781 - 0.970941i) q^{33} +(-0.198422 + 0.912721i) q^{34} +(1.96845 - 6.94327i) q^{35} +(2.67018 - 5.37310i) q^{36} +(4.76004 + 8.24463i) q^{37} +(3.07611 + 2.79562i) q^{38} +(-1.86751 - 7.46109i) q^{39} +(7.66101 + 0.912859i) q^{40} -7.85889i q^{41} +(1.57232 - 6.28711i) q^{42} +0.530567i q^{43} +(-0.388965 - 4.06191i) q^{44} +(-4.32373 + 6.94768i) q^{45} +(-0.991489 + 1.09097i) q^{46} +(0.521208 + 0.902759i) q^{47} +(6.90176 + 0.604764i) q^{48} +(0.202367 - 6.99707i) q^{49} +(-3.37268 - 0.733208i) q^{50} +(0.314312 - 1.09993i) q^{51} +(7.23295 - 5.15349i) q^{52} +(9.16829 + 5.29332i) q^{53} +(-3.68620 + 6.35704i) q^{54} +5.56526i q^{55} +(7.42138 - 0.960783i) q^{56} +(-3.53976 - 3.65883i) q^{57} +(-2.78462 + 0.890559i) q^{58} +(-1.74375 + 3.02026i) q^{59} +(-9.29160 - 1.71835i) 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} +(0.155878 + 4.99513i) q^{66} +(4.12631 + 2.38233i) q^{67} +(1.31492 - 0.125915i) q^{68} +(1.29763 - 1.25541i) q^{69} +(-10.2006 + 0.339574i) q^{70} -5.52774 q^{71} +(-8.38787 - 1.28206i) q^{72} +(1.51791 - 2.62910i) q^{73} +(9.05497 - 9.96349i) q^{74} +(4.06447 + 1.16144i) q^{75} +(2.44055 - 5.34786i) q^{76} +(1.32158 + 5.23370i) q^{77} +(-9.24562 + 5.72971i) q^{78} +(9.45104 - 5.45656i) q^{79} +(-2.07066 - 10.7127i) q^{80} +(5.00539 - 7.47971i) q^{81} +(-10.5860 + 3.38553i) q^{82} +9.15881 q^{83} +(-9.14611 + 0.590497i) q^{84} -1.80158 q^{85} +(0.714675 - 0.228563i) q^{86} +(3.47347 - 0.869409i) q^{87} +(-5.30385 + 2.27377i) q^{88} +(-0.468730 + 0.270622i) q^{89} +(11.2212 + 2.83110i) q^{90} +(-8.42674 + 8.18655i) q^{91} +(1.89666 + 0.865562i) q^{92} +(1.47716 - 5.16932i) q^{93} +(0.991489 - 1.09097i) q^{94} +(-4.00870 + 6.94327i) q^{95} +(-2.15859 - 9.55722i) q^{96} -6.91692 q^{97} +(-9.51227 + 2.74168i) q^{98} +(0.202415 - 6.11739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.430790	−	1.34700i	−0.304614	−	0.952476i
$2$	−0.430790	−	1.34700i	−0.304614	−	0.952476i
$3$	0.420559	+	1.68022i	0.242810	+	0.970074i
$3$	0.420559	+	1.68022i	0.242810	+	0.970074i
$4$	−1.62884	+	1.16055i	−0.814420	+	0.580275i
$5$	2.36229	−	1.36387i	1.05645	−	0.609941i	0.132001	−	0.991250i	$-0.457860\pi$
$5$	2.36229	−	1.36387i	1.05645	−	0.609941i	0.924448	+	0.381309i	$0.124527\pi$
$6$	2.08209	−	1.29031i	0.850009	−	0.526769i
$7$	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
$10$	−2.85479	−	2.59447i	−0.902763	−	0.820445i
$11$	−1.02012	+	1.76690i	−0.307579	+	0.532742i	−0.977832	−	0.209390i	$-0.932852\pi$
$11$	−1.02012	+	1.76690i	−0.307579	+	0.532742i	0.670253	+	0.742132i	$0.266185\pi$
$12$	−2.63500	−	2.24873i	−0.760659	−	0.649151i
$13$	−4.44055			−1.23159			−0.615794	−	0.787907i	$-0.711165\pi$
$13$	−4.44055			−1.23159			−0.615794	+	0.787907i	$0.711165\pi$
$14$	−3.30082	−	1.76198i	−0.882181	−	0.470910i
$15$	3.28508	+	3.39557i	0.848203	+	0.876733i
$16$	1.30624	−	3.78070i	0.326561	−	0.945176i
$17$	−0.571980	−	0.330233i	−0.138726	−	0.0800933i	0.429031	−	0.903290i	$-0.358855\pi$
$17$	−0.571980	−	0.330233i	−0.138726	−	0.0800933i	−0.567756	+	0.823197i	$0.692188\pi$
$18$	3.04365	+	2.95571i	0.717395	+	0.696667i
$19$	−2.54543	+	1.46961i	−0.583962	+	0.337151i	−0.762707	−	0.646745i	$-0.776130\pi$
$19$	−2.54543	+	1.46961i	−0.583962	+	0.337151i	0.178744	+	0.983896i	$0.442797\pi$
$20$	−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	$-0.201329\pi$
$23$	−0.521208	−	0.902759i	−0.108679	−	0.188238i	−0.915236	+	0.402919i	$0.867996\pi$
$24$	−1.89391	+	4.51809i	−0.386593	+	0.922250i
$25$	1.22028	−	2.11358i	0.244055	−	0.422716i
$26$	1.91294	+	5.98144i	0.375159	+	1.17306i
$27$	−3.48749	−	3.85193i	−0.671168	−	0.741305i
$28$	−0.951438	+	5.20526i	−0.179805	+	0.983702i
$29$		−	2.06727i		−	0.383883i	−0.981406	−	0.191941i	$-0.938522\pi$
$29$		−	2.06727i		−	0.383883i	0.981406	−	0.191941i	$-0.0614783\pi$
$30$	3.15867	−	5.88779i	0.576692	−	1.07496i
$31$	−2.68812	−	1.55199i	−0.482800	−	0.278745i	0.238782	−	0.971073i	$-0.423252\pi$
$31$	−2.68812	−	1.55199i	−0.482800	−	0.278745i	−0.721583	+	0.692328i	$0.756585\pi$
$32$	−5.65534	−	0.130827i	−0.999733	−	0.0231271i
$33$	−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
$36$	2.67018	−	5.37310i	0.445029	−	0.895516i
$37$	4.76004	+	8.24463i	0.782546	+	1.35541i	0.930454	+	0.366408i	$0.119412\pi$
$37$	4.76004	+	8.24463i	0.782546	+	1.35541i	−0.147909	+	0.989001i	$0.547254\pi$
$38$	3.07611	+	2.79562i	0.499011	+	0.453509i
$39$	−1.86751	−	7.46109i	−0.299041	−	1.19473i
$40$	7.66101	+	0.912859i	1.21131	+	0.144336i
$41$		−	7.85889i		−	1.22735i	−0.789558	−	0.613676i	$-0.789690\pi$
$41$		−	7.85889i		−	1.22735i	0.789558	−	0.613676i	$-0.210310\pi$
$42$	1.57232	−	6.28711i	0.242615	−	0.970123i
$43$			0.530567i			0.0809106i	0.999181	+	0.0404553i	$0.0128808\pi$
$43$			0.530567i			0.0809106i	−0.999181	+	0.0404553i	$0.987119\pi$
$44$	−0.388965	−	4.06191i	−0.0586387	−	0.612356i
$45$	−4.32373	+	6.94768i	−0.644544	+	1.03570i
$46$	−0.991489	+	1.09097i	−0.146187	+	0.160855i
$47$	0.521208	+	0.902759i	0.0760260	+	0.131681i	0.901532	−	0.432712i	$-0.142443\pi$
$47$	0.521208	+	0.902759i	0.0760260	+	0.131681i	−0.825506	+	0.564393i	$0.809110\pi$
$48$	6.90176	+	0.604764i	0.996183	+	0.0872901i
$49$	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
$52$	7.23295	−	5.15349i	1.00303	−	0.714660i
$53$	9.16829	+	5.29332i	1.25936	+	0.727093i	0.972950	−	0.231014i	$-0.0742043\pi$
$53$	9.16829	+	5.29332i	1.25936	+	0.727093i	0.286411	+	0.958107i	$0.407538\pi$
$54$	−3.68620	+	6.35704i	−0.501628	+	0.865084i
$55$			5.56526i			0.750419i
$56$	7.42138	−	0.960783i	0.991724	−	0.128390i
$57$	−3.53976	−	3.65883i	−0.468853	−	0.484623i
$58$	−2.78462	+	0.890559i	−0.365639	+	0.116936i
$59$	−1.74375	+	3.02026i	−0.227016	+	0.393204i	−0.956922	−	0.290343i	$-0.906230\pi$
$59$	−1.74375	+	3.02026i	−0.227016	+	0.393204i	0.729906	+	0.683547i	$0.239564\pi$
$60$	−9.29160	−	1.71835i	−1.19954	−	0.221838i
$61$	0.0992110	+	0.171839i	0.0127027	+	0.0220017i	0.872307	−	0.488959i	$-0.162623\pi$
$61$	0.0992110	+	0.171839i	0.0127027	+	0.0220017i	−0.859604	+	0.510960i	$0.829290\pi$
$62$	−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
$66$	0.155878	+	4.99513i	0.0191873	+	0.614858i
$67$	4.12631	+	2.38233i	0.504109	+	0.291048i	0.730409	−	0.683010i	$-0.239330\pi$
$67$	4.12631	+	2.38233i	0.504109	+	0.291048i	−0.226300	+	0.974058i	$0.572663\pi$
$68$	1.31492	−	0.125915i	0.159457	−	0.0152695i
$69$	1.29763	−	1.25541i	0.156217	−	0.151133i
$70$	−10.2006	+	0.339574i	−1.21921	+	0.0405868i
$71$	−5.52774			−0.656022			−0.328011	−	0.944674i	$-0.606378\pi$
$71$	−5.52774			−0.656022			−0.328011	+	0.944674i	$0.606378\pi$
$72$	−8.38787	−	1.28206i	−0.988520	−	0.151093i
$73$	1.51791	−	2.62910i	0.177658	−	0.307712i	−0.763420	−	0.645902i	$-0.776481\pi$
$73$	1.51791	−	2.62910i	0.177658	−	0.307712i	0.941078	+	0.338190i	$0.109815\pi$
$74$	9.05497	−	9.96349i	1.05262	−	1.15823i
$75$	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
$78$	−9.24562	+	5.72971i	−1.04686	+	0.648762i
$79$	9.45104	−	5.45656i	1.06332	−	0.613911i	0.136975	−	0.990575i	$-0.456262\pi$
$79$	9.45104	−	5.45656i	1.06332	−	0.613911i	0.926350	+	0.376664i	$0.122929\pi$
$80$	−2.07066	−	10.7127i	−0.231507	−	1.19771i
$81$	5.00539	−	7.47971i	0.556155	−	0.831079i
$82$	−10.5860	+	3.38553i	−1.16902	+	0.373869i
$83$	9.15881			1.00531			0.502655	−	0.864487i	$-0.332357\pi$
$83$	9.15881			1.00531			0.502655	+	0.864487i	$0.332357\pi$
$84$	−9.14611	+	0.590497i	−0.997922	+	0.0644285i
$85$	−1.80158			−0.195409
$86$	0.714675	−	0.228563i	0.0770654	−	0.0246465i
$87$	3.47347	−	0.869409i	0.372395	−	0.0932104i
$88$	−5.30385	+	2.27377i	−0.565392	+	0.242384i
$89$	−0.468730	+	0.270622i	−0.0496853	+	0.0286858i	−0.524637	−	0.851326i	$-0.675799\pi$
$89$	−0.468730	+	0.270622i	−0.0496853	+	0.0286858i	0.474952	+	0.880012i	$0.342466\pi$
$90$	11.2212	+	2.83110i	1.18282	+	0.298424i
$91$	−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
$94$	0.991489	−	1.09097i	0.102264	−	0.112525i
$95$	−4.00870	+	6.94327i	−0.411284	+	0.712365i
$96$	−2.15859	−	9.55722i	−0.220310	−	0.975430i
$97$	−6.91692			−0.702307			−0.351153	−	0.936318i	$-0.614210\pi$
$97$	−6.91692			−0.702307			−0.351153	+	0.936318i	$0.614210\pi$
$98$	−9.51227	+	2.74168i	−0.960884	+	0.276951i
$99$	0.202415	−	6.11739i	0.0203435	−	0.614821i
$100$	0.465282	+	4.85888i	0.0465282	+	0.485888i
$101$	−8.77393	−	5.06563i	−0.873039	−	0.504049i	−0.00468180	−	0.999989i	$-0.501490\pi$
$101$	−8.77393	−	5.06563i	−0.873039	−	0.504049i	−0.868357	+	0.495940i	$0.834824\pi$
$102$	−1.61702	+	0.0504606i	−0.160109	+	0.00499635i
$103$	6.34079	−	3.66086i	0.624777	−	0.360715i	−0.153950	−	0.988079i	$-0.549199\pi$
$103$	6.34079	−	3.66086i	0.624777	−	0.360715i	0.778726	+	0.627364i	$0.215866\pi$
$104$	−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	0.883713	+	0.468030i	$0.155036\pi$
$107$	8.76332	+	15.1785i	0.847182	+	1.46736i	−0.0365308	+	0.999333i	$0.511631\pi$
$108$	10.1509	+	2.22677i	0.976774	+	0.214271i
$109$	−0.319487	+	0.553367i	−0.0306013	+	0.0530030i	−0.880920	−	0.473264i	$-0.843076\pi$
$109$	−0.319487	+	0.553367i	−0.0306013	+	0.0530030i	0.850319	+	0.526267i	$0.176409\pi$
$110$	7.49642	−	2.39745i	0.714756	−	0.228588i
$111$	−11.8509	+	11.4653i	−1.12484	+	1.08823i
$112$	−4.49123	−	9.58274i	−0.424382	−	0.905483i
$113$			10.7917i			1.01520i	0.861593	+	0.507600i	$0.169467\pi$
$113$			10.7917i			1.01520i	−0.861593	+	0.507600i	$0.830533\pi$
$114$	−3.40356	+	6.34426i	−0.318773	+	0.594194i
$115$	−2.46249	−	1.42172i	−0.229628	−	0.132576i
$116$	2.39917	+	3.36726i	0.222758	+	0.312642i
$117$	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
$120$	1.68810	+	13.2561i	0.154102	+	1.21011i
$121$	3.41870	+	5.92136i	0.310791	+	0.538305i
$122$	0.188728	−	0.207664i	0.0170866	−	0.0188010i
$123$	13.2046	−	3.30513i	1.19062	−	0.298013i
$124$	6.17967	−	0.591761i	0.554951	−	0.0531417i
$125$			6.98150i			0.624445i
$126$	11.2250	−	0.00225489i	1.00000	−	0.000200881i
$127$		−	10.9563i		−	0.972210i	−0.873900	−	0.486105i	$-0.838417\pi$
$127$		−	10.9563i		−	0.972210i	0.873900	−	0.486105i	$-0.161583\pi$
$128$	9.36348	−	6.35022i	0.827623	−	0.561285i
$129$	−0.891467	+	0.223134i	−0.0784893	+	0.0196459i
$130$	12.6768	+	11.5209i	1.11183	+	1.01045i
$131$	−11.0778	−	19.1873i	−0.967869	−	1.67640i	−0.701700	−	0.712473i	$-0.747575\pi$
$131$	−11.0778	−	19.1873i	−0.967869	−	1.67640i	−0.266169	−	0.963926i	$-0.585758\pi$
$132$	6.66131	−	2.36182i	0.579793	−	0.205570i
$133$	−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
$136$	−0.736061	−	1.71696i	−0.0631167	−	0.147228i
$137$	−12.5610	−	7.25212i	−1.07316	−	0.619591i	−0.144119	−	0.989560i	$-0.546035\pi$
$137$	−12.5610	−	7.25212i	−1.07316	−	0.619591i	−0.929044	+	0.369970i	$0.879368\pi$
$138$	−2.25004	−	1.20710i	−0.191537	−	0.102755i
$139$		−	5.78265i		−	0.490478i	−0.969463	−	0.245239i	$-0.921134\pi$
$139$		−	5.78265i		−	0.490478i	0.969463	−	0.245239i	$-0.0788665\pi$
$140$	4.85172	+	13.5940i	0.410045	+	1.14890i
$141$	−1.29763	+	1.25541i	−0.109280	+	0.105724i
$142$	2.38129	+	7.44589i	0.199834	+	0.624845i
$143$	4.52991	−	7.84603i	0.378810	−	0.656118i
$144$	1.88646	+	11.8508i	0.157205	+	0.987566i
$145$	−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	0.0798408	−	0.996808i	$-0.474559\pi$
$149$	11.9993	−	6.92781i	0.983022	−	0.567548i	0.903181	+	0.429260i	$0.141225\pi$
$150$	−0.186462	−	5.97520i	−0.0152246	−	0.487873i
$151$	−10.1959	−	5.88660i	−0.829730	−	0.479045i	0.0240304	−	0.999711i	$-0.492350\pi$
$151$	−10.1959	−	5.88660i	−0.829730	−	0.479045i	−0.853760	+	0.520667i	$0.825683\pi$
$152$	−8.25495	−	0.983631i	−0.669565	−	0.0797830i
$153$	1.98031	+	0.0655255i	0.160099	+	0.00529742i
$154$	6.48050	−	4.03480i	0.522213	−	0.325133i
$155$	−8.46682			−0.680071
$156$	11.7009	+	9.98559i	0.936818	+	0.799487i
$157$	5.34134	−	9.25147i	0.426285	−	0.738348i	−0.570254	−	0.821468i	$-0.693155\pi$
$157$	5.34134	−	9.25147i	0.426285	−	0.738348i	0.996540	+	0.0831204i	$0.0264886\pi$
$158$	−11.4214	−	10.3800i	−0.908639	−	0.825785i
$159$	−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
$162$	−12.2315	−	3.52010i	−0.960995	−	0.276565i
$163$	−17.7351	+	10.2394i	−1.38912	+	0.802008i	−0.993216	−	0.116284i	$-0.962902\pi$
$163$	−17.7351	+	10.2394i	−1.38912	+	0.802008i	−0.395903	+	0.918292i	$0.629568\pi$
$164$	9.12065	+	12.8009i	0.712203	+	0.999581i
$165$	−9.35084	+	2.34052i	−0.727962	+	0.182209i
$166$	−3.94552	−	12.3370i	−0.306232	−	0.957534i
$167$	22.4614			1.73811			0.869057	−	0.494712i	$-0.164727\pi$
$167$	22.4614			1.73811			0.869057	+	0.494712i	$0.164727\pi$
$168$	4.73545	+	12.0655i	0.365348	+	0.930871i
$169$	6.71850			0.516808
$170$	0.776101	+	2.42673i	0.0595242	+	0.186122i
$171$	4.65894	−	7.48632i	0.356278	−	0.572493i
$172$	−0.615750	−	0.864208i	−0.0469505	−	0.0658953i
$173$	−16.8271	+	9.71515i	−1.27934	+	0.738630i	−0.976728	−	0.214483i	$-0.931193\pi$
$173$	−16.8271	+	9.71515i	−1.27934	+	0.738630i	−0.302616	+	0.953113i	$0.597860\pi$
$174$	−2.66743	−	4.30424i	−0.202217	−	0.326304i
$175$	−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
$178$	0.566453	+	0.514801i	0.0424574	+	0.0385860i
$179$	−2.51687	+	4.35934i	−0.188119	+	0.325833i	−0.944623	−	0.328157i	$-0.893573\pi$
$179$	−2.51687	+	4.35934i	−0.188119	+	0.325833i	0.756504	+	0.653989i	$0.226906\pi$
$180$	−1.02047	−	16.3346i	−0.0760611	−	1.21751i
$181$	5.71850			0.425053			0.212526	−	0.977155i	$-0.431831\pi$
$181$	5.71850			0.425053			0.212526	+	0.977155i	$0.431831\pi$
$182$	14.6575	+	7.82417i	1.08648	+	0.579966i
$183$	−0.247002	+	0.238964i	−0.0182589	+	0.0176647i
$184$	0.348853	−	2.92769i	0.0257178	−	0.215832i
$185$	22.4892	+	12.9841i	1.65344	+	0.954613i
$186$	−7.59945	+	0.237148i	−0.557218	+	0.0173886i
$187$	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	$-0.282219\pi$
$191$	−4.90753	−	8.50010i	−0.355097	−	0.615046i	−0.987135	+	0.159892i	$0.948885\pi$
$192$	−11.9437	+	7.02478i	−0.861964	+	0.506970i
$193$	−8.57953	+	14.8602i	−0.617568	+	1.06966i	0.372360	+	0.928088i	$0.378549\pi$
$193$	−8.57953	+	14.8602i	−0.617568	+	1.06966i	−0.989928	+	0.141571i	$0.954785\pi$
$194$	2.97974	+	9.31712i	0.213933	+	0.668930i
$195$	−14.5876	−	15.0782i	−1.04464	−	1.07977i
$196$	7.79084	+	11.6320i	0.556488	+	0.830855i
$197$		−	11.0302i		−	0.785867i	−0.919567	−	0.392934i	$-0.871460\pi$
$197$		−	11.0302i		−	0.785867i	0.919567	−	0.392934i	$-0.128540\pi$
$198$	−8.32735	+	2.36265i	−0.591799	+	0.167907i
$199$	19.3160	+	11.1521i	1.36927	+	0.790550i	0.990835	−	0.135077i	$-0.0431281\pi$
$199$	19.3160	+	11.1521i	1.36927	+	0.790550i	0.378438	+	0.925627i	$0.376461\pi$
$200$	6.34449	−	2.71989i	0.448623	−	0.192325i
$201$	−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
$204$	0.764565	+	2.15639i	0.0535303	+	0.150978i
$205$	−10.7185	−	18.5650i	−0.748612	−	1.29663i
$206$	−7.66274	−	6.96401i	−0.533888	−	0.485206i
$207$	2.65509	+	1.65233i	0.184541	+	0.114845i
$208$	−5.80044	+	16.7884i	−0.402188	+	1.16407i
$209$		−	5.99672i		−	0.414802i
$210$	−4.86051	−	16.9964i	−0.335407	−	1.17287i
$211$			17.9648i			1.23675i	0.785884	+	0.618374i	$0.212208\pi$
$211$			17.9648i			1.23675i	−0.785884	+	0.618374i	$0.787792\pi$
$212$	−21.0768	+	2.01830i	−1.44756	+	0.138618i
$213$	−2.32474	−	9.28780i	−0.159288	−	0.636390i
$214$	16.6704	−	18.3430i	1.13956	−	1.25390i
$215$	0.723623	+	1.25335i	0.0493507	+	0.0854779i
$216$	−1.37344	−	14.6326i	−0.0934510	−	0.995624i
$217$	−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
$220$	−6.45876	−	9.06491i	−0.435450	−	0.611156i
$221$	2.53991	+	1.46642i	0.170853	+	0.0986419i
$222$	20.5490	+	11.0241i	1.37916	+	0.739888i
$223$		−	1.95751i		−	0.131084i	−0.997850	−	0.0655422i	$-0.979122\pi$
$223$		−	1.95751i		−	0.131084i	0.997850	−	0.0655422i	$-0.0208777\pi$
$224$	−10.9732	+	10.1779i	−0.733178	+	0.680036i
$225$	−0.242130	+	7.31765i	−0.0161420	+	0.487843i
$226$	14.5365	−	4.64896i	0.966954	−	0.309245i
$227$	−9.08211	+	15.7307i	−0.602801	+	1.04408i	0.389594	+	0.920987i	$0.372615\pi$
$227$	−9.08211	+	15.7307i	−0.602801	+	1.04408i	−0.992395	+	0.123095i	$0.960718\pi$
$228$	10.0120	+	1.85157i	0.663058	+	0.122623i
$229$	4.92264	+	8.52627i	0.325297	+	0.563432i	0.981573	−	0.191090i	$-0.0612023\pi$
$229$	4.92264	+	8.52627i	0.325297	+	0.563432i	−0.656275	+	0.754522i	$0.727869\pi$
$230$	−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	0.486956	−	0.873426i	$-0.338107\pi$
$233$	22.6957	−	13.1034i	1.48684	−	0.858430i	0.999888	+	0.0149969i	$0.00477386\pi$
$234$	−13.5155	−	13.1250i	−0.883535	−	0.858006i
$235$	2.46249	+	1.42172i	0.160635	+	0.0927427i
$236$	−0.664878	−	6.94322i	−0.0432798	−	0.451965i
$237$	13.1429	+	13.5850i	0.853724	+	0.882440i
$238$	1.30614	+	2.09786i	0.0846645	+	0.135984i
$239$	16.9336			1.09535			0.547673	−	0.836692i	$-0.315514\pi$
$239$	16.9336			1.09535			0.547673	+	0.836692i	$0.315514\pi$
$240$	17.1288	−	7.98446i	1.10566	−	0.515395i
$241$	−2.91870	+	5.05533i	−0.188010	+	0.325643i	−0.944587	−	0.328262i	$-0.893537\pi$
$241$	−2.91870	+	5.05533i	−0.188010	+	0.325643i	0.756577	+	0.653905i	$0.226870\pi$
$242$	6.50335	−	7.15586i	0.418051	−	0.459996i
$243$	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
$246$	−10.1404	−	16.3629i	−0.646531	−	1.04326i
$247$	11.3031	−	6.52586i	0.719201	−	0.415231i
$248$	−3.45924	−	8.06912i	−0.219662	−	0.512390i
$249$	3.85182	+	15.3888i	0.244099	+	0.975225i
$250$	9.40411	−	3.00756i	0.594768	−	0.190215i
$251$	−10.1468			−0.640462			−0.320231	−	0.947340i	$-0.603760\pi$
$251$	−10.1468			−0.640462			−0.320231	+	0.947340i	$0.603760\pi$
$252$	−4.83864	−	15.1191i	−0.304806	−	0.952415i
$253$	2.12679			0.133710
$254$	−14.7581	+	4.71984i	−0.926007	+	0.296149i
$255$	−0.757669	−	3.02704i	−0.0474471	−	0.189561i
$256$	−12.5875	−	9.87704i	−0.786716	−	0.617315i
$257$	10.3764	−	5.99080i	0.647261	−	0.373696i	−0.140145	−	0.990131i	$-0.544757\pi$
$257$	10.3764	−	5.99080i	0.647261	−	0.373696i	0.787406	+	0.616435i	$0.211424\pi$
$258$	0.684598	+	1.10469i	0.0426212	+	0.0687748i
$259$	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
$262$	−21.0731	+	23.1875i	−1.30190	+	1.43253i
$263$	−7.22199	+	12.5088i	−0.445327	+	0.771329i	−0.998075	−	0.0620197i	$-0.980246\pi$
$263$	−7.22199	+	12.5088i	−0.445327	+	0.771329i	0.552748	+	0.833348i	$0.313579\pi$
$264$	−6.05100	−	7.95537i	−0.372414	−	0.489619i
$265$	28.8775			1.77393
$266$	10.9914	−	0.365900i	0.673928	−	0.0224348i
$267$	−0.651832	−	0.673757i	−0.0398915	−	0.0412332i
$268$	−9.48592	+	0.908364i	−0.579445	+	0.0554871i
$269$	−5.69092	−	3.28566i	−0.346982	−	0.200330i	0.316373	−	0.948635i	$-0.397535\pi$
$269$	−5.69092	−	3.28566i	−0.346982	−	0.200330i	−0.663355	+	0.748305i	$0.730868\pi$
$270$	−0.0376942	+	20.0447i	−0.00229400	+	1.21988i
$271$	−0.0141559	+	0.00817291i	−0.000859910	+	0.000496469i	−0.500430	−	0.865777i	$-0.666825\pi$
$271$	−0.0141559	+	0.00817291i	−0.000859910	+	0.000496469i	0.499570	+	0.866274i	$0.333491\pi$
$272$	−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
$276$	−0.656674	+	3.55083i	−0.0395271	+	0.213735i
$277$	9.15688	−	15.8602i	0.550184	−	0.952946i	−0.448077	−	0.893995i	$-0.647891\pi$
$277$	9.15688	−	15.8602i	0.550184	−	0.952946i	0.998261	−	0.0589513i	$-0.0187757\pi$
$278$	−7.78926	+	2.49111i	−0.467169	+	0.149407i
$279$	9.30682	+	0.307948i	0.557185	+	0.0184364i
$280$	16.2211	−	12.3914i	0.969394	−	0.740530i
$281$		−	1.61190i		−	0.0961580i	−0.998844	−	0.0480790i	$-0.984690\pi$
$281$		−	1.61190i		−	0.0961580i	0.998844	−	0.0480790i	$-0.0153099\pi$
$282$	2.25004	+	1.20710i	0.133988	+	0.0718818i
$283$	−17.8180	−	10.2872i	−1.05917	−	0.611513i	−0.133969	−	0.990986i	$-0.542772\pi$
$283$	−17.8180	−	10.2872i	−1.05917	−	0.611513i	−0.925203	+	0.379472i	$0.876106\pi$
$284$	9.00380	−	6.41522i	0.534278	−	0.380673i
$285$	−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
$288$	15.1504	−	7.64627i	0.892746	−	0.450561i
$289$	−8.28189	−	14.3447i	−0.487170	−	0.843803i
$290$	−5.36348	+	5.90162i	−0.314954	+	0.346555i
$291$	−2.90897	−	11.6219i	−0.170527	−	0.681290i
$292$	0.578767	+	6.04399i	0.0338698	+	0.353698i
$293$			11.6573i			0.681026i	0.940240	+	0.340513i	$0.110601\pi$
$293$			11.6573i			0.681026i	−0.940240	+	0.340513i	$0.889399\pi$
$294$	−8.60708	−	14.8296i	−0.501975	−	0.864882i
$295$			9.51296i			0.553866i
$296$	−3.18597	+	26.7377i	−0.185181	+	1.55410i
$297$	10.3637	−	2.23262i	0.601361	−	0.129550i
$298$	−14.5010	−	13.1787i	−0.840018	−	0.763421i
$299$	2.31445	+	4.00875i	0.133848	+	0.231832i
$300$	−7.96829	+	2.82522i	−0.460049	+	0.163114i
$301$	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
$304$	2.23119	+	11.5432i	0.127968	+	0.662048i
$305$	0.468730	+	0.270622i	0.0268394	+	0.0154957i
$306$	−0.764836	−	2.69572i	−0.0437228	−	0.154104i
$307$		−	3.66039i		−	0.208909i	−0.994530	−	0.104455i	$-0.966690\pi$
$307$		−	3.66039i		−	0.208909i	0.994530	−	0.104455i	$-0.0333097\pi$
$308$	−8.22662	−	6.99111i	−0.468755	−	0.398355i
$309$	8.81771	+	9.11430i	0.501622	+	0.518494i
$310$	3.64742	+	11.4048i	0.207159	+	0.647751i
$311$	−5.87374	+	10.1736i	−0.333069	+	0.576892i	−0.983112	−	0.183005i	$-0.941418\pi$
$311$	−5.87374	+	10.1736i	−0.333069	+	0.576892i	0.650043	+	0.759897i	$0.274751\pi$
$312$	8.41002	−	20.0628i	0.476123	−	1.13583i
$313$	7.41692	+	12.8465i	0.419229	+	0.726126i	0.995862	−	0.0908771i	$-0.0289670\pi$
$313$	7.41692	+	12.8465i	0.419229	+	0.726126i	−0.576633	+	0.817003i	$0.695634\pi$
$314$	−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	−0.688138	−	0.725579i	$-0.741572\pi$
$317$	−7.19012	+	4.15122i	−0.403837	+	0.233156i	0.284301	+	0.958735i	$0.408238\pi$
$318$	25.9192	−	0.808835i	1.45348	−	0.0453572i
$319$	3.65267	+	2.10887i	0.204510	+	0.118074i
$320$	15.8054	+	15.0461i	0.883547	+	0.841104i
$321$	−21.8177	+	21.1077i	−1.21775	+	1.17812i
$322$	0.129770	+	3.89821i	0.00723177	+	0.217239i
$323$	1.94125			0.108014
$324$	0.527601	+	17.9923i	0.0293112	+	0.999570i
$325$	−5.41870	+	9.38546i	−0.300575	+	0.520612i
$326$	21.4326	+	19.4782i	1.18704	+	1.07880i
$327$	−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
$330$	7.18093	+	11.5873i	0.395297	+	0.637863i
$331$	−13.2232	+	7.63441i	−0.726812	+	0.419625i	−0.817255	−	0.576276i	$-0.804505\pi$
$331$	−13.2232	+	7.63441i	−0.726812	+	0.419625i	0.0904426	+	0.995902i	$0.471172\pi$
$332$	−14.9182	+	10.6293i	−0.818745	+	0.583357i
$333$	−24.2481	−	15.0903i	−1.32879	−	0.826941i
$334$	−9.67613	−	30.2556i	−0.529454	−	1.65551i
$335$	12.9967			0.710087
$336$	14.2123	−	11.5764i	0.775342	−	0.631542i
$337$	−16.9606			−0.923904			−0.461952	−	0.886905i	$-0.652851\pi$
$337$	−16.9606			−0.923904			−0.461952	+	0.886905i	$0.652851\pi$
$338$	−2.89426	−	9.04985i	−0.157427	−	0.492247i
$339$	−18.1324	+	4.53856i	−0.984819	+	0.246500i
$340$	2.93448	−	2.09082i	0.159145	−	0.113391i
$341$	5.48442	−	3.16643i	0.296998	−	0.171472i
$342$	−12.0911	−	3.05059i	−0.653813	−	0.164957i
$343$	−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
$346$	20.3353	+	18.4810i	1.09323	+	0.993547i
$347$	11.0283	−	19.1015i	0.592029	−	1.02542i	−0.401930	−	0.915670i	$-0.631661\pi$
$347$	11.0283	−	19.1015i	0.592029	−	1.02542i	0.993959	−	0.109753i	$-0.0350061\pi$
$348$	−4.64873	+	5.44726i	−0.249198	+	0.292004i
$349$	−17.6748			−0.946110			−0.473055	−	0.881033i	$-0.656849\pi$
$349$	−17.6748			−0.946110			−0.473055	+	0.881033i	$0.656849\pi$
$350$	−7.75200	+	4.82644i	−0.414362	+	0.257984i
$351$	15.4864	+	17.1047i	0.826602	+	0.912982i
$352$	6.00030	−	9.85899i	0.319817	−	0.525486i
$353$	−0.365480	−	0.211010i	−0.0194526	−	0.0112309i	0.490242	−	0.871586i	$-0.336908\pi$
$353$	−0.365480	−	0.211010i	−0.0194526	−	0.0112309i	−0.509695	+	0.860355i	$0.670242\pi$
$354$	0.266450	+	8.53842i	0.0141616	+	0.453812i
$355$	−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	$-0.291143\pi$
$359$	−7.22199	−	12.5088i	−0.381162	−	0.660192i	−0.991229	+	0.132158i	$0.957809\pi$
$360$	−21.5631	+	8.41134i	−1.13648	+	0.443317i
$361$	−5.18051	+	8.97291i	−0.272659	+	0.472259i
$362$	−2.46347	−	7.70284i	−0.129477	−	0.404852i
$363$	−8.51141	+	8.23443i	−0.446733	+	0.432196i
$364$	4.22491	−	23.1142i	0.221445	−	1.21152i
$365$		−	8.28091i		−	0.433443i
$366$	0.428292	+	0.229769i	0.0223872	+	0.0120102i
$367$	−18.8797	−	10.9002i	−0.985512	−	0.568985i	−0.0815820	−	0.996667i	$-0.525997\pi$
$367$	−18.8797	−	10.9002i	−0.985512	−	0.568985i	−0.903930	+	0.427681i	$0.859331\pi$
$368$	−4.09389	+	0.791312i	−0.213409	+	0.0412500i
$369$	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
$372$	3.59320	+	10.1343i	0.186299	+	0.525440i
$373$	−9.76004	−	16.9049i	−0.505356	−	0.875302i	−0.999981	−	0.00619524i	$-0.998028\pi$
$373$	−9.76004	−	16.9049i	−0.505356	−	0.875302i	0.494625	−	0.869106i	$-0.335305\pi$
$374$	−1.41028	−	1.28168i	−0.0729236	−	0.0662741i
$375$	−11.7304	+	2.93613i	−0.605757	+	0.151621i
$376$	−0.348853	+	2.92769i	−0.0179907	+	0.150984i
$377$			9.17983i			0.472785i
$378$	4.72455	+	18.8594i	0.243005	+	0.970025i
$379$		−	34.1136i		−	1.75230i	−0.482038	−	0.876150i	$-0.660103\pi$
$379$		−	34.1136i		−	1.75230i	0.482038	−	0.876150i	$-0.339897\pi$
$380$	−1.52849	−	15.9618i	−0.0784098	−	0.818822i
$381$	18.4089	−	4.60775i	0.943116	−	0.236062i
$382$	−9.33555	+	10.2722i	−0.477649	+	0.525573i
$383$	−4.10770	−	7.11474i	−0.209893	−	0.363546i	0.741787	−	0.670635i	$-0.233978\pi$
$383$	−4.10770	−	7.11474i	−0.209893	−	0.363546i	−0.951681	+	0.307089i	$0.900645\pi$
$384$	14.6076	+	13.0620i	0.745443	+	0.666570i
$385$	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
$388$	11.2666	−	8.02744i	0.571973	−	0.407531i
$389$	−4.15260	−	2.39750i	−0.210545	−	0.121558i	0.391020	−	0.920382i	$-0.372122\pi$
$389$	−4.15260	−	2.39750i	−0.210545	−	0.121558i	−0.601565	+	0.798824i	$0.705456\pi$
$390$	−14.0263	+	26.1450i	−0.710247	+	1.32391i
$391$			0.688481i			0.0348180i
$392$	12.3121	−	15.5052i	0.621855	−	0.783132i
$393$	27.5799	−	26.6824i	1.39122	−	1.34595i
$394$	−14.8577	+	4.75168i	−0.748520	+	0.239386i
$395$	14.8841	−	25.7799i	0.748898	−	1.29713i
$396$	6.76984	+	10.1992i	0.340197	+	0.512527i
$397$	−5.20059	−	9.00769i	−0.261010	−	0.452083i	0.705500	−	0.708709i	$-0.250722\pi$
$397$	−5.20059	−	9.00769i	−0.261010	−	0.452083i	−0.966511	+	0.256627i	$0.917389\pi$
$398$	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	−0.728892	−	0.684629i	$-0.759964\pi$
$401$	−10.0211	+	5.78571i	−0.500432	+	0.288924i	0.228460	+	0.973553i	$0.426631\pi$
$402$	11.6653	−	0.364027i	0.581812	−	0.0181560i
$403$	11.9367	+	6.89167i	0.594611	+	0.343299i
$404$	20.1703	−	1.93149i	1.00351	−	0.0960951i
$405$	1.62284	−	24.4959i	0.0806396	−	1.21721i
$406$	−3.64250	+	6.82369i	−0.180774	+	0.338654i
$407$	−19.4233			−0.962777
$408$	2.57530	−	1.95882i	0.127496	−	0.0969762i
$409$	−10.2185	+	17.6990i	−0.505272	+	0.875157i	0.494709	+	0.869059i	$0.335275\pi$
$409$	−10.2185	+	17.6990i	−0.505272	+	0.875157i	−0.999981	+	0.00609862i	$0.998059\pi$
$410$	−20.3897	+	22.4355i	−1.00698	+	1.10801i
$411$	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
$414$	1.08192	−	4.28822i	0.0531733	−	0.210755i
$415$	21.6358	−	12.4914i	1.06206	−	0.613180i
$416$	25.1128	+	0.580942i	1.23126	+	0.0284830i
$417$	9.71611	−	2.43194i	0.475800	−	0.119093i
$418$	−8.07760	+	2.58332i	−0.395089	+	0.126355i
$419$	−21.9130			−1.07052			−0.535259	−	0.844688i	$-0.679786\pi$
$419$	−21.9130			−1.07052			−0.535259	+	0.844688i	$0.679786\pi$
$420$	−20.8004	+	13.8690i	−1.01496	+	0.676739i
$421$	14.1153			0.687940			0.343970	−	0.938981i	$-0.388228\pi$
$421$	14.1153			0.687940			0.343970	+	0.938981i	$0.388228\pi$
$422$	24.1987	−	7.73905i	1.17797	−	0.376731i
$423$	−2.65509	−	1.65233i	−0.129095	−	0.0803392i
$424$	11.7983	+	27.5211i	0.572978	+	1.33654i
$425$	−1.39595	+	0.805951i	−0.0677134	+	0.0390944i
$426$	−11.5092	+	7.13252i	−0.557624	+	0.345572i
$427$	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
$430$	1.37654	−	1.51465i	0.0663827	−	0.0730431i
$431$	−14.5604	+	25.2193i	−0.701348	+	1.21477i	0.266646	+	0.963795i	$0.414085\pi$
$431$	−14.5604	+	25.2193i	−0.701348	+	1.21477i	−0.967994	+	0.250975i	$0.919249\pi$
$432$	−19.1185	+	8.15362i	−0.919841	+	0.392291i
$433$	26.1153			1.25502			0.627512	−	0.778607i	$-0.284073\pi$
$433$	26.1153			1.25502			0.627512	+	0.778607i	$0.284073\pi$
$434$	6.13842	+	9.85924i	0.294654	+	0.473259i
$435$	7.01957	−	6.79115i	0.336563	−	0.325611i
$436$	−0.121818	−	1.27213i	−0.00583402	−	0.0609239i
$437$	2.65340	+	1.53194i	0.126929	+	0.0732827i
$438$	−0.231941	−	7.43259i	−0.0110826	−	0.355143i
$439$	−15.9204	+	9.19162i	−0.759837	+	0.438692i	−0.829237	−	0.558897i	$-0.811225\pi$
$439$	−15.9204	+	9.19162i	−0.759837	+	0.438692i	0.0694002	+	0.997589i	$0.477891\pi$
$440$	−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	$-0.103731\pi$
$443$	4.13441	+	7.16101i	0.196432	+	0.340230i	−0.750937	+	0.660374i	$0.770398\pi$
$444$	5.99721	−	32.4286i	0.284615	−	1.53899i
$445$	−0.738185	+	1.27857i	−0.0349933	+	0.0606102i
$446$	−2.63677	+	0.843274i	−0.124855	+	0.0399302i
$447$	16.6866	+	17.2479i	0.789251	+	0.815798i
$448$	18.4368	+	10.3964i	0.871055	+	0.491186i
$449$			24.1061i			1.13764i	0.822463	+	0.568818i	$0.192599\pi$
$449$			24.1061i			1.13764i	−0.822463	+	0.568818i	$0.807401\pi$
$450$	9.96121	−	2.82622i	0.469576	−	0.133229i
$451$	13.8859	+	8.01704i	0.653862	+	0.377508i
$452$	−12.5243	−	17.5780i	−0.589096	−	0.826800i
$453$	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
$456$	−1.81898	−	14.2838i	−0.0851815	−	0.668900i
$457$	9.34529	+	16.1865i	0.437154	+	0.757173i	0.997469	−	0.0711068i	$-0.0226531\pi$
$457$	9.34529	+	16.1865i	0.437154	+	0.757173i	−0.560315	+	0.828280i	$0.689320\pi$
$458$	9.36429	−	10.3038i	0.437565	−	0.481467i
$459$	0.722741	+	3.35492i	0.0337347	+	0.156594i
$460$	5.66098	−	0.542091i	0.263945	−	0.0252751i
$461$		−	16.3664i		−	0.762260i	−0.924521	−	0.381130i	$-0.875535\pi$
$461$		−	16.3664i		−	0.762260i	0.924521	−	0.381130i	$-0.124465\pi$
$462$	9.50477	+	9.19178i	0.442202	+	0.427640i
$463$			11.3643i			0.528142i	0.964503	+	0.264071i	$0.0850653\pi$
$463$			11.3643i			0.528142i	−0.964503	+	0.264071i	$0.914935\pi$
$464$	−7.81574	−	2.70036i	−0.362837	−	0.125361i
$465$	−3.56079	−	14.2261i	−0.165128	−	0.659719i
$466$	−27.4273	−	24.9264i	−1.27055	−	1.15469i
$467$	18.1468	+	31.4313i	0.839736	+	1.45446i	0.890116	+	0.455735i	$0.150623\pi$
$467$	18.1468	+	31.4313i	0.839736	+	1.45446i	−0.0503800	+	0.998730i	$0.516043\pi$
$468$	−11.8571	+	23.8595i	−0.548093	+	1.10291i
$469$	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
$472$	−9.06613	+	3.88666i	−0.417302	+	0.178898i
$473$	−0.937461	−	0.541243i	−0.0431045	−	0.0248864i
$474$	12.6372	−	23.5558i	0.580446	−	1.08196i
$475$			7.17330i			0.329134i
$476$	2.26315	−	2.66311i	0.103731	−	0.122064i
$477$	−31.7425	−	1.05031i	−1.45339	−	0.0480904i
$478$	−7.29484	−	22.8097i	−0.333658	−	1.04329i
$479$	5.59953	−	9.69867i	0.255849	−	0.443144i	−0.709277	−	0.704930i	$-0.750978\pi$
$479$	5.59953	−	9.69867i	0.255849	−	0.443144i	0.965126	+	0.261787i	$0.0843117\pi$
$480$	−18.1340	−	19.6329i	−0.827700	−	0.896115i
$481$	−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
$486$	0.770482	−	22.0319i	0.0349498	−	0.999389i
$487$	8.60678	+	4.96913i	0.390010	+	0.225173i	0.682165	−	0.731199i	$-0.261039\pi$
$487$	8.60678	+	4.96913i	0.390010	+	0.225173i	−0.292154	+	0.956371i	$0.594372\pi$
$488$	−0.0664035	+	0.557280i	−0.00300595	+	0.0252269i
$489$	−24.6630	−	25.4926i	−1.11530	−	1.15281i
$490$	−18.7314	+	19.4501i	−0.846200	+	0.878667i
$491$	2.64307			0.119280			0.0596400	−	0.998220i	$-0.481005\pi$
$491$	2.64307			0.119280			0.0596400	+	0.998220i	$0.481005\pi$
$492$	−17.6725	+	20.7082i	−0.796738	+	0.933597i
$493$	−0.682681	+	1.18244i	−0.0307464	+	0.0532544i
$494$	−13.6596	−	12.4141i	−0.614576	−	0.558536i
$495$	−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
$498$	19.0695	−	11.8178i	0.854523	−	0.529566i
$499$	−17.1844	+	9.92144i	−0.769281	+	0.444145i	−0.832618	−	0.553848i	$-0.813159\pi$
$499$	−17.1844	+	9.92144i	−0.769281	+	0.444145i	0.0633371	+	0.997992i	$0.479826\pi$
$500$	−8.10239	−	11.3718i	−0.362350	−	0.508560i
$501$	9.44633	+	37.7400i	0.422031	+	1.68610i
$502$	4.37115	+	13.6678i	0.195094	+	0.610024i
$503$	3.07284			0.137011			0.0685056	−	0.997651i	$-0.478177\pi$
$503$	3.07284			0.137011			0.0685056	+	0.997651i	$0.478177\pi$
$504$	−18.2811	+	13.0308i	−0.814304	+	0.580439i
$505$	−27.6354			−1.22976
$506$	−0.916198	−	2.86479i	−0.0407300	−	0.127355i
$507$	2.82552	+	11.2885i	0.125486	+	0.501342i
$508$	12.7153	+	17.8460i	0.564150	+	0.791788i
$509$	−14.6238	+	8.44307i	−0.648190	+	0.374233i	−0.787762	−	0.615979i	$-0.788761\pi$
$509$	−14.6238	+	8.44307i	−0.648190	+	0.374233i	0.139572	+	0.990212i	$0.455427\pi$
$510$	−3.75104	+	2.32460i	−0.166099	+	0.102935i
$511$	−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
$514$	−12.5397	−	11.3962i	−0.553101	−	0.502667i
$515$	9.98586	−	17.2960i	0.440029	−	0.762153i
$516$	1.19310	−	1.39804i	0.0525233	−	0.0615454i
$517$	−2.12679			−0.0935360
$518$	−1.18515	−	35.6011i	−0.0520723	−	1.56422i
$519$	−23.4004	−	24.1875i	−1.02716	−	1.06171i
$520$	−34.0191	−	4.05360i	−1.49184	−	0.177762i
$521$	−27.3170	−	15.7715i	−1.19678	−	0.690961i	−0.236944	−	0.971523i	$-0.576146\pi$
$521$	−27.3170	−	15.7715i	−1.19678	−	0.690961i	−0.959836	+	0.280562i	$0.909479\pi$
$522$	6.11025	−	6.29205i	0.267438	−	0.275396i
$523$	29.0382	−	16.7652i	1.26975	−	0.733092i	0.294812	−	0.955555i	$-0.404743\pi$
$523$	29.0382	−	16.7652i	1.26975	−	0.733092i	0.974941	+	0.222463i	$0.0714098\pi$
$524$	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
$528$	−8.10920	+	11.5778i	−0.352908	+	0.503860i
$529$	10.9567	−	18.9775i	0.476378	−	0.825110i
$530$	−12.4401	−	38.8982i	−0.540366	−	1.68963i
$531$	0.345998	−	10.4568i	0.0150150	−	0.453785i
$532$	−5.22787	−	14.6479i	−0.226657	−	0.635067i
$533$			34.8978i			1.51159i
$534$	−0.626751	+	1.16827i	−0.0271222	+	0.0505559i
$535$	41.4030	+	23.9040i	1.79001	+	1.03346i
$536$	5.31000	+	12.3863i	0.229357	+	0.535005i
$537$	−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
$540$	27.0165	−	8.58426i	1.16260	−	0.369408i
$541$	11.8396	+	20.5067i	0.509023	+	0.881653i	0.999945	+	0.0104499i	$0.00332638\pi$
$541$	11.8396	+	20.5067i	0.509023	+	0.881653i	−0.490923	+	0.871203i	$0.663340\pi$
$542$	0.0171072	+	0.0155472i	0.000734815	+	0.000667811i
$543$	2.40496	+	9.60832i	0.103207	+	0.412333i
$544$	3.19154	+	1.94241i	0.136836	+	0.0832802i
$545$			1.74295i			0.0746599i
$546$	−6.98199	+	27.9183i	−0.298801	+	1.19479i
$547$			10.9063i			0.466318i	0.972439	+	0.233159i	$0.0749063\pi$
$547$			10.9063i			0.466318i	−0.972439	+	0.233159i	$0.925094\pi$
$548$	28.8764	−	2.76518i	1.23354	−	0.118123i
$549$	−0.505391	−	0.314519i	−0.0215696	−	0.0134233i
$550$	4.73606	−	5.21125i	0.201946	−	0.222208i
$551$	3.03808	+	5.26210i	0.129426	+	0.224173i
$552$	5.06587	−	0.645116i	0.215618	−	0.0274580i
$553$	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
$556$	6.71106	+	9.41902i	0.284612	+	0.399455i
$557$	9.47804	+	5.47215i	0.401597	+	0.231862i	0.687173	−	0.726494i	$-0.258851\pi$
$557$	9.47804	+	5.47215i	0.401597	+	0.231862i	−0.285576	+	0.958356i	$0.592185\pi$
$558$	−3.59447	−	12.6690i	−0.152166	−	0.536321i
$559$		−	2.35601i		−	0.0996485i
$560$	−23.6792	−	16.5117i	−1.00063	−	0.697749i
$561$	1.62284	+	1.67743i	0.0685164	+	0.0708210i
$562$	−2.17124	+	0.694390i	−0.0915881	+	0.0292911i
$563$	−14.1475	+	24.5041i	−0.596245	+	1.03273i	0.397125	+	0.917765i	$0.370008\pi$
$563$	−14.1475	+	24.5041i	−0.596245	+	1.03273i	−0.993370	+	0.114962i	$0.963325\pi$
$564$	0.656674	−	3.55083i	0.0276510	−	0.149517i
$565$	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	−0.482629	−	0.875825i	$-0.660318\pi$
$569$	0.823967	−	0.475718i	0.0345425	−	0.0199431i	0.517172	+	0.855882i	$0.326985\pi$
$570$	0.612542	+	19.6290i	0.0256566	+	0.822168i
$571$	−14.1886	−	8.19177i	−0.593773	−	0.342815i	0.172815	−	0.984954i	$-0.444714\pi$
$571$	−14.1886	−	8.19177i	−0.593773	−	0.342815i	−0.766588	+	0.642139i	$0.778047\pi$
$572$	1.72722	+	18.0371i	0.0722187	+	0.754170i
$573$	12.2181	−	11.8205i	0.510419	−	0.493809i
$574$	−13.8472	+	25.9408i	−0.577972	+	1.08275i
$575$	−2.54407			−0.106095
$576$	−16.8262	−	17.1137i	−0.701091	−	0.713072i
$577$	4.98426	−	8.63299i	0.207497	−	0.359396i	−0.743428	−	0.668816i	$-0.766801\pi$
$577$	4.98426	−	8.63299i	0.207497	−	0.359396i	0.950926	+	0.309420i	$0.100135\pi$
$578$	−15.7546	+	17.3353i	−0.655303	+	0.721052i
$579$	−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
$582$	−14.4016	+	8.92500i	−0.596967	+	0.369953i
$583$	−18.7056	+	10.7997i	−0.774706	+	0.447276i
$584$	7.89195	−	3.38329i	0.326571	−	0.140002i
$585$	19.1998	−	30.8515i	0.793812	−	1.27555i
$586$	15.7024	−	5.02184i	0.648661	−	0.207450i
$587$	−29.5354			−1.21905			−0.609527	−	0.792765i	$-0.708641\pi$
$587$	−29.5354			−1.21905			−0.609527	+	0.792765i	$0.708641\pi$
$588$	−16.2677	+	17.9822i	−0.670870	+	0.741575i
$589$	9.12323			0.375916
$590$	12.8140	−	4.09809i	0.527544	−	0.168716i
$591$	18.5331	−	4.63884i	0.762349	−	0.190816i
$592$	37.3883	−	7.22681i	1.53665	−	0.297020i
$593$	18.2436	−	10.5329i	0.749174	−	0.432536i	−0.0762215	−	0.997091i	$-0.524286\pi$
$593$	18.2436	−	10.5329i	0.749174	−	0.432536i	0.825395	+	0.564555i	$0.190952\pi$
$594$	−7.47191	−	12.9981i	−0.306576	−	0.533319i
$595$	−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
$598$	4.40276	−	4.84450i	0.180042	−	0.198107i
$599$	19.8683	−	34.4129i	0.811796	−	1.40607i	−0.0998091	−	0.995007i	$-0.531823\pi$
$599$	19.8683	−	34.4129i	0.811796	−	1.40607i	0.911606	−	0.411066i	$-0.134843\pi$
$600$	7.23824	+	9.51625i	0.295500	+	0.388499i
$601$	−36.5567			−1.49118			−0.745589	−	0.666406i	$-0.767832\pi$
$601$	−36.5567			−1.49118			−0.745589	+	0.666406i	$0.767832\pi$
$602$	0.934849	−	1.75131i	0.0381016	−	0.0713779i
$603$	−14.2861	−	0.472706i	−0.581777	−	0.0192501i
$604$	23.4392	−	2.24452i	0.953727	−	0.0913281i
$605$	16.1519	+	9.32531i	0.656669	+	0.379128i
$606$	−24.8043	+	0.774044i	−1.00761	+	0.0314434i
$607$	−11.4085	+	6.58667i	−0.463055	+	0.267345i	−0.713328	−	0.700830i	$-0.752813\pi$
$607$	−11.4085	+	6.58667i	−0.463055	+	0.267345i	0.250273	+	0.968175i	$0.419480\pi$
$608$	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
$612$	−3.30166	+	2.19153i	−0.133462	+	0.0885871i
$613$	9.50394	−	16.4613i	0.383861	−	0.664866i	−0.607750	−	0.794129i	$-0.707928\pi$
$613$	9.50394	−	16.4613i	0.383861	−	0.664866i	0.991610	+	0.129262i	$0.0412609\pi$
$614$	−4.93055	+	1.57686i	−0.198981	+	0.0636367i
$615$	26.6855	−	25.8171i	1.07606	−	1.04104i
$616$	−5.87311	+	14.0930i	−0.236634	+	0.567823i
$617$		−	41.6979i		−	1.67869i	−0.543596	−	0.839347i	$-0.682938\pi$
$617$		−	41.6979i		−	1.67869i	0.543596	−	0.839347i	$-0.317062\pi$
$618$	8.47842	−	15.8038i	0.341052	−	0.635724i
$619$	11.6140	+	6.70535i	0.466806	+	0.269511i	0.714902	−	0.699225i	$-0.246471\pi$
$619$	11.6140	+	6.70535i	0.466806	+	0.269511i	−0.248096	+	0.968736i	$0.579805\pi$
$620$	13.7911	−	9.82617i	0.553864	−	0.394629i
$621$	−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
$624$	−30.6476	−	2.68549i	−1.22689	−	0.107505i
$625$	15.6232	+	27.0602i	0.624929	+	1.08241i
$626$	14.1091	−	15.5248i	0.563914	−	0.620494i
$627$	10.0758	−	2.52197i	0.402388	−	0.100718i
$628$	2.03661	+	21.2681i	0.0812697	+	0.848689i
$629$		−	6.28769i		−	0.250707i
$630$	26.5136	−	15.3147i	1.05633	−	0.610153i
$631$			10.7225i			0.426856i	0.976959	+	0.213428i	$0.0684629\pi$
$631$			10.7225i			0.426856i	−0.976959	+	0.213428i	$0.931537\pi$
$632$	30.6501	+	3.65216i	1.21920	+	0.145275i
$633$	−30.1848	+	7.55525i	−1.19974	+	0.300294i
$634$	8.68914	+	7.89682i	0.345090	+	0.313623i
$635$	−14.9429	−	25.8818i	−0.592990	−	1.02709i
$636$	−12.2552	−	34.5649i	−0.485952	−	1.37059i
$637$	−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
$640$	13.4584	−	27.7716i	0.531990	−	1.09777i
$641$	20.7630	+	11.9875i	0.820089	+	0.473479i	0.850447	−	0.526060i	$-0.176331\pi$
$641$	20.7630	+	11.9875i	0.820089	+	0.473479i	−0.0303581	+	0.999539i	$0.509665\pi$
$642$	37.8311	+	20.2956i	1.49307	+	0.801002i
$643$		−	24.5118i		−	0.966649i	−0.875441	−	0.483325i	$-0.839429\pi$
$643$		−	24.5118i		−	0.966649i	0.875441	−	0.483325i	$-0.160571\pi$
$644$	5.19500	−	1.85411i	0.204712	−	0.0730621i
$645$	−1.80158	+	1.74295i	−0.0709371	+	0.0686287i
$646$	−0.836271	−	2.61487i	−0.0329026	−	0.102881i
$647$	21.2165	−	36.7481i	0.834108	−	1.44472i	−0.0606458	−	0.998159i	$-0.519316\pi$
$647$	21.2165	−	36.7481i	0.834108	−	1.44472i	0.894754	−	0.446559i	$-0.147351\pi$
$648$	24.0084	−	8.46156i	0.943138	−	0.332402i
$649$	−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	−0.816413	−	0.577469i	$-0.804041\pi$
$653$	−18.5142	+	10.6892i	−0.724517	+	0.418300i	0.0918961	+	0.995769i	$0.470707\pi$
$654$	0.0488186	+	1.56440i	0.00190896	+	0.0611728i
$655$	−52.3378	−	30.2173i	−2.04501	−	1.18069i
$656$	−29.7122	−	10.2656i	−1.16006	−	0.400805i
$657$	−0.301187	+	9.10247i	−0.0117504	+	0.355121i
$658$	−0.129770	−	3.89821i	−0.00505894	−	0.151968i
$659$	−0.835578			−0.0325495			−0.0162748	−	0.999868i	$-0.505181\pi$
$659$	−0.835578			−0.0325495			−0.0162748	+	0.999868i	$0.505181\pi$
$660$	12.5147	−	14.6645i	0.487135	−	0.570813i
$661$	−9.00217	+	15.5922i	−0.350144	+	0.606467i	−0.986274	−	0.165115i	$-0.947201\pi$
$661$	−9.00217	+	15.5922i	−0.350144	+	0.606467i	0.636131	+	0.771581i	$0.280534\pi$
$662$	15.9800	+	14.5229i	0.621080	+	0.564447i
$663$	−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
$666$	−9.88081	+	39.1630i	−0.382874	+	1.51754i
$667$	−1.86625	+	1.07748i	−0.0722614	+	0.0417202i
$668$	−36.5860	+	26.0676i	−1.41555	+	1.00858i
$669$	3.28904	−	0.823247i	0.127162	−	0.0318286i
$670$	−5.59886	−	17.5066i	−0.216303	−	0.676341i
$671$	−0.404830			−0.0156283
$672$	−21.7159	−	14.1570i	−0.837708	−	0.546118i
$673$	3.35747			0.129421			0.0647105	−	0.997904i	$-0.479388\pi$
$673$	3.35747			0.129421			0.0647105	+	0.997904i	$0.479388\pi$
$674$	7.30646	+	22.8460i	0.281434	+	0.879996i
$675$	−12.3971	+	2.67067i	−0.477164	+	0.102794i
$676$	−10.9434	+	7.79716i	−0.420899	+	0.299891i
$677$	31.9197	−	18.4288i	1.22677	−	0.708278i	0.260420	−	0.965495i	$-0.416139\pi$
$677$	31.9197	−	18.4288i	1.22677	−	0.708278i	0.966354	+	0.257217i	$0.0828056\pi$
$678$	13.9247	+	22.4693i	0.534776	+	0.862929i
$679$	−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
$682$	−6.62783	−	6.02347i	−0.253793	−	0.230651i
$683$	2.19316	−	3.79867i	0.0839191	−	0.145352i	−0.821011	−	0.570912i	$-0.806590\pi$
$683$	2.19316	−	3.79867i	0.0839191	−	0.145352i	0.904930	+	0.425560i	$0.139923\pi$
$684$	1.09958	+	17.6010i	0.0420436	+	0.672990i
$685$	−39.5638			−1.51165
$686$	−12.9967	+	22.7395i	−0.496216	+	0.868199i
$687$	−12.2557	+	11.8569i	−0.467585	+	0.452369i
$688$	2.00592	+	0.693049i	0.0764748	+	0.0264222i
$689$	−40.7123	−	23.5052i	−1.55101	−	0.895478i
$690$	−6.96159	+	0.217243i	−0.265023	+	0.00827031i
$691$	34.8657	−	20.1297i	1.32635	−	0.765771i	0.341620	−	0.939838i	$-0.389024\pi$
$691$	34.8657	−	20.1297i	1.32635	−	0.765771i	0.984734	+	0.174067i	$0.0556910\pi$
$692$	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
$696$	9.34011	+	3.91523i	0.354036	+	0.148406i
$697$	−2.59527	+	4.49513i	−0.0983027	+	0.170265i
$698$	7.61412	+	23.8080i	0.288199	+	0.901147i
$699$	31.5614	+	32.6229i	1.19376	+	1.23391i
$700$	9.84072	+	8.36280i	0.371944	+	0.316084i
$701$		−	25.7395i		−	0.972168i	−0.873912	−	0.486084i	$-0.838425\pi$
$701$		−	25.7395i		−	0.972168i	0.873912	−	0.486084i	$-0.161575\pi$
$702$	16.3687	−	28.2288i	0.617798	−	1.06543i
$703$	−24.2327	−	13.9908i	−0.913954	−	0.527672i
$704$	−15.8650	−	3.83528i	−0.597934	−	0.144548i
$705$	−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
$708$	11.3865	−	4.03717i	0.427931	−	0.151726i
$709$	−7.50394	−	12.9972i	−0.281817	−	0.488121i	0.690016	−	0.723794i	$-0.257604\pi$
$709$	−7.50394	−	12.9972i	−0.281817	−	0.488121i	−0.971832	+	0.235674i	$0.924270\pi$
$710$	15.7805	+	14.3416i	0.592232	+	0.538230i
$711$	−17.2984	+	27.7962i	−0.648739	+	1.04244i
$712$	−1.52011	−	0.181131i	−0.0569687	−	0.00678818i
$713$			3.23563i			0.121175i
$714$	−2.97555	+	3.07687i	−0.111357	+	0.115149i
$715$		−	24.7128i		−	0.924207i
$716$	−0.959663	−	10.0216i	−0.0358643	−	0.374526i
$717$	7.12159	+	28.4522i	0.265961	+	1.06257i
$718$	−13.7383	+	15.1167i	−0.512709	+	0.564151i
$719$	19.2753	+	33.3858i	0.718847	+	1.24508i	0.961457	+	0.274956i	$0.0886632\pi$
$719$	19.2753	+	33.3858i	0.718847	+	1.24508i	−0.242610	+	0.970124i	$0.578003\pi$
$720$	20.6193	+	25.4221i	0.768436	+	0.947427i
$721$	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
$724$	−9.31452	+	6.63661i	−0.346172	+	0.246648i
$725$	−4.36934	−	2.52264i	−0.162273	−	0.0936885i
$726$	14.7584	+	7.91759i	0.547737	+	0.293849i
$727$			50.3452i			1.86720i	0.358318	+	0.933600i	$0.383350\pi$
$727$			50.3452i			1.86720i	−0.358318	+	0.933600i	$0.616650\pi$
$728$	−32.9550	+	4.26640i	−1.22139	+	0.158123i
$729$	−2.67479	+	26.8672i	−0.0990664	+	0.995081i
$730$	−11.1544	+	3.56733i	−0.412844	+	0.132033i
$731$	0.175211	−	0.303474i	0.00648040	−	0.0112244i
$732$	0.124997	−	0.675893i	0.00462001	−	0.0249817i
$733$	6.27578	+	10.8700i	0.231801	+	0.401491i	0.958338	−	0.285636i	$-0.0922048\pi$
$733$	6.27578	+	10.8700i	0.231801	+	0.401491i	−0.726537	+	0.687127i	$0.758871\pi$
$734$	−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
$738$	23.2286	−	23.9197i	0.855056	−	0.880497i
$739$	5.42182	+	3.13029i	0.199445	+	0.115150i	0.596397	−	0.802690i	$-0.296599\pi$
$739$	5.42182	+	3.13029i	0.199445	+	0.115150i	−0.396952	+	0.917840i	$0.629932\pi$
$740$	−51.7000	+	4.95075i	−1.90053	+	0.181993i
$741$	15.7185	+	16.2472i	0.577433	+	0.596856i
$742$	−20.9362	−	33.6267i	−0.768591	−	1.23447i
$743$	34.2633			1.25700			0.628498	−	0.777811i	$-0.283670\pi$
$743$	34.2633			1.25700			0.628498	+	0.777811i	$0.283670\pi$
$744$	12.1031	−	9.20582i	0.443720	−	0.337502i
$745$	18.8972	−	32.7310i	0.692341	−	1.19917i
$746$	−18.5664	+	20.4293i	−0.679765	+	0.747968i
$747$	−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
$750$	9.00834	+	14.5361i	0.328938	+	0.530783i
$751$	25.1285	−	14.5079i	0.916952	−	0.529402i	0.0342903	−	0.999412i	$-0.489083\pi$
$751$	25.1285	−	14.5079i	0.916952	−	0.529402i	0.882661	+	0.470010i	$0.155750\pi$
$752$	4.09389	−	0.791312i	0.149289	−	0.0288562i
$753$	−4.26733	−	17.0489i	−0.155510	−	0.621295i
$754$	12.3653	−	3.95457i	0.450316	−	0.144017i
$755$	−32.1142			−1.16876
$756$	23.3685	−	14.4884i	0.849903	−	0.526939i
$757$	−10.5717			−0.384234			−0.192117	−	0.981372i	$-0.561535\pi$
$757$	−10.5717			−0.384234			−0.192117	+	0.981372i	$0.561535\pi$
$758$	−45.9512	+	14.6958i	−1.66902	+	0.533776i
$759$	0.894439	+	3.57346i	0.0324661	+	0.129709i
$760$	−20.8421	+	8.93505i	−0.756024	+	0.324108i
$761$	−33.6645	+	19.4362i	−1.22034	+	0.704563i	−0.964990	−	0.262287i	$-0.915523\pi$
$761$	−33.6645	+	19.4362i	−1.22034	+	0.704563i	−0.255348	+	0.966849i	$0.582190\pi$
$762$	−14.1370	−	22.8119i	−0.512130	−	0.826387i
$763$	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
$766$	−7.81403	+	8.59804i	−0.282332	+	0.310660i
$767$	7.74320	−	13.4116i	0.279591	−	0.484265i
$768$	11.3018	−	25.3035i	0.407819	−	0.913063i
$769$	25.5953			0.922989			0.461494	−	0.887143i	$-0.347313\pi$
$769$	25.5953			0.922989			0.461494	+	0.887143i	$0.347313\pi$
$770$	9.80588	−	18.3699i	0.353379	−	0.662006i
$771$	14.4297	+	14.9151i	0.519674	+	0.537154i
$772$	−3.27131	−	34.1618i	−0.117737	−	1.22951i
$773$	24.6534	+	14.2336i	0.886720	+	0.511948i	0.872868	−	0.487956i	$-0.162257\pi$
$773$	24.6534	+	14.2336i	0.886720	+	0.511948i	0.0138518	+	0.999904i	$0.495591\pi$
$774$	−1.56820	+	1.61486i	−0.0563678	+	0.0580449i
$775$	−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
$780$	41.2598	+	7.63041i	1.47734	+	0.273213i
$781$	5.63897	−	9.76699i	0.201778	−	0.349490i
$782$	0.927386	−	0.296590i	0.0331633	−	0.0106061i
$783$	−7.96299	+	7.20959i	−0.284574	+	0.257650i
$784$	−26.1895	−	9.90497i	−0.935340	−	0.353749i
$785$		−	29.1395i		−	1.04004i
$786$	−47.8225	−	25.6557i	−1.70577	−	0.915110i
$787$	−27.6598	−	15.9694i	−0.985964	−	0.569247i	−0.0818987	−	0.996641i	$-0.526098\pi$
$787$	−27.6598	−	15.9694i	−0.985964	−	0.569247i	−0.904065	+	0.427394i	$0.859432\pi$
$788$	12.8011	+	17.9664i	0.456019	+	0.640026i
$789$	−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
$792$	10.8219	−	13.5127i	0.384541	−	0.480153i
$793$	−0.440552	−	0.763058i	−0.0156444	−	0.0270970i
$794$	−9.89303	+	10.8856i	−0.351091	+	0.386317i
$795$	12.1447	+	48.5206i	0.430728	+	1.72085i
$796$	−44.4052	+	4.25221i	−1.57390	+	0.150715i
$797$		−	37.7330i		−	1.33657i	−0.743905	−	0.668285i	$-0.767029\pi$
$797$		−	37.7330i		−	1.33657i	0.743905	−	0.668285i	$-0.232971\pi$
$798$	5.23734	+	18.3141i	0.185400	+	0.648313i
$799$		−	0.688481i		−	0.0243567i
$800$	−7.17759	+	11.7934i	−0.253766	+	0.416959i
$801$	0.857924	−	1.37857i	0.0303133	−	0.0487095i
$802$	12.1104	+	11.0061i	0.427632	+	0.388639i
$803$	3.09691	+	5.36400i	0.109288	+	0.189292i
$804$	−5.51563	−	15.5564i	−0.194521	−	0.548631i
$805$	−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
$808$	−11.2909	−	26.3374i	−0.397211	−	0.926545i
$809$	−22.6957	−	13.1034i	−0.797938	−	0.460690i	0.0448118	−	0.998995i	$-0.485731\pi$
$809$	−22.6957	−	13.1034i	−0.797938	−	0.460690i	−0.842750	+	0.538306i	$0.819065\pi$
$810$	−33.6952	+	8.36662i	−1.18393	+	0.293973i
$811$		−	32.1734i		−	1.12976i	−0.825172	−	0.564881i	$-0.808922\pi$
$811$		−	32.1734i		−	1.12976i	0.825172	−	0.564881i	$-0.191078\pi$
$812$	10.7607	+	1.96688i	0.377626	+	0.0690240i
$813$	−0.0196857	−	0.0203478i	−0.000690406	−	0.000713628i
$814$	8.36736	+	26.1633i	0.293276	+	0.917022i
$815$	−27.9303	+	48.3767i	−0.978355	+	1.69456i
$816$	−3.74796	−	2.62510i	−0.131205	−	0.0918969i
$817$	−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	−0.121994	−	0.992531i	$-0.538929\pi$
$821$	19.3857	−	11.1923i	0.676565	−	0.390615i	0.798560	+	0.601916i	$0.205596\pi$
$822$	−35.5107	+	1.10815i	−1.23858	+	0.0386511i
$823$	28.4876	+	16.4473i	0.993014	+	0.573317i	0.906174	−	0.422905i	$-0.138990\pi$
$823$	28.4876	+	16.4473i	0.993014	+	0.573317i	0.0868401	+	0.996222i	$0.472323\pi$
$824$	20.5635	+	2.45027i	0.716362	+	0.0853592i
$825$	−6.19842	+	5.99672i	−0.215801	+	0.208779i
$826$	11.0774	−	6.89688i	0.385433	−	0.239973i
$827$	−16.7455			−0.582297			−0.291148	−	0.956678i	$-0.594037\pi$
$827$	−16.7455			−0.582297			−0.291148	+	0.956678i	$0.594037\pi$
$828$	−6.24233	+	0.389976i	−0.216936	+	0.0135526i
$829$	0.474201	−	0.821341i	0.0164697	−	0.0285263i	−0.857673	−	0.514195i	$-0.828091\pi$
$829$	0.474201	−	0.821341i	0.0164697	−	0.0285263i	0.874143	+	0.485669i	$0.161424\pi$
$830$	−26.1465	−	23.7623i	−0.907557	−	0.824802i
$831$	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
$834$	−7.46144	−	12.0400i	−0.258369	−	0.416911i
$835$	53.0603	−	30.6344i	1.83623	−	1.06015i
$836$	6.95950	+	9.76770i	0.240699	+	0.337823i
$837$	3.39665	+	15.7670i	0.117405	+	0.544987i
$838$	9.43988	+	29.5169i	0.326095	+	1.01964i
$839$	−35.5384			−1.22692			−0.613461	−	0.789725i	$-0.710223\pi$
$839$	−35.5384			−1.22692			−0.613461	+	0.789725i	$0.710223\pi$
$840$	27.6422	+	22.0436i	0.953747	+	0.760576i
$841$	24.7264			0.852634
$842$	−6.08074	−	19.0134i	−0.209556	−	0.655246i
$843$	2.70834	−	0.677899i	0.0932804	−	0.0233481i
$844$	−20.8491	−	29.2618i	−0.717654	−	1.00723i
$845$	15.8710	−	9.16315i	0.545980	−	0.315222i
$846$	−1.08192	+	4.28822i	−0.0371970	+	0.147432i
$847$	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
$850$	1.68698	+	1.53315i	0.0578629	+	0.0525867i
$851$	4.96194	−	8.59434i	0.170093	−	0.294610i
$852$	14.5656	+	12.4304i	0.499009	+	0.425858i
$853$	−35.8618			−1.22788			−0.613942	−	0.789351i	$-0.710417\pi$
$853$	−35.8618			−1.22788			−0.613942	+	0.789351i	$0.710417\pi$
$854$	−0.0247014	−	0.742016i	−0.000845264	−	0.0253913i
$855$	0.795415	−	24.0390i	0.0272026	−	0.822118i
$856$	−5.86543	+	49.2246i	−0.200476	+	1.68246i
$857$	32.9586	+	19.0286i	1.12584	+	0.650006i	0.942886	−	0.333115i	$-0.108100\pi$
$857$	32.9586	+	19.0286i	1.12584	+	0.650006i	0.182957	+	0.983121i	$0.441433\pi$
$858$	−0.692184	−	22.1811i	−0.0236308	−	0.757251i
$859$	−18.6659	+	10.7768i	−0.636873	+	0.367699i	−0.783409	−	0.621507i	$-0.786521\pi$
$859$	−18.6659	+	10.7768i	−0.636873	+	0.367699i	0.146536	+	0.989205i	$0.453188\pi$
$860$	−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	−0.998077	−	0.0619877i	$-0.980256\pi$
$863$	−16.2372	−	28.1237i	−0.552721	−	0.957341i	0.445356	−	0.895354i	$-0.353077\pi$
$864$	19.2190	+	22.2403i	0.653845	+	0.756629i
$865$	−26.5004	+	45.9000i	−0.901040	+	1.56065i
$866$	−11.2502	−	35.1775i	−0.382298	−	1.19538i
$867$	20.6191	−	19.9482i	0.700262	−	0.677475i
$868$	10.6361	−	12.5157i	0.361012	−	0.424812i
$869$			22.2654i			0.755303i
$870$	−12.1717	−	6.52984i	−0.412658	−	0.221382i
$871$	−18.3231	−	10.5788i	−0.620855	−	0.358451i
$872$	−1.66108	+	0.712109i	−0.0562514	+	0.0241151i
$873$	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
$876$	−9.91181	+	3.51431i	−0.334889	+	0.118737i
$877$	14.0957	+	24.4144i	0.475977	+	0.824416i	0.999621	−	0.0275212i	$-0.00876138\pi$
$877$	14.0957	+	24.4144i	0.475977	+	0.824416i	−0.523645	+	0.851937i	$0.675428\pi$
$878$	19.2395	+	17.4851i	0.649301	+	0.590095i
$879$	−19.5868	+	4.90258i	−0.660646	+	0.165360i
$880$	21.0406	+	7.26958i	0.709278	+	0.245057i
$881$		−	5.81314i		−	0.195850i	−0.995194	−	0.0979249i	$-0.968780\pi$
$881$		−	5.81314i		−	0.195850i	0.995194	−	0.0979249i	$-0.0312205\pi$
$882$	21.2972	−	20.6985i	0.717115	−	0.696955i
$883$			47.2938i			1.59156i	0.605583	+	0.795782i	$0.292940\pi$
$883$			47.2938i			1.59156i	−0.605583	+	0.795782i	$0.707060\pi$
$884$	−5.83896	+	0.559134i	−0.196385	+	0.0188057i
$885$	−15.9838	+	4.00076i	−0.537291	+	0.134484i
$886$	7.86485	−	8.65396i	0.264225	−	0.290736i
$887$	−15.1948	−	26.3182i	−0.510192	−	0.883678i	−0.999930	−	0.0118084i	$-0.996241\pi$
$887$	−15.1948	−	26.3182i	−0.510192	−	0.883678i	0.489739	−	0.871869i	$-0.337092\pi$
$888$	−46.2650	+	5.89165i	−1.55255	+	0.197711i
$889$	−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
$892$	2.27179	+	3.18847i	0.0760651	+	0.106758i
$893$	−2.65340	−	1.53194i	−0.0887927	−	0.0512645i
$894$	16.0446	−	29.9072i	0.536611	−	1.00025i
$895$			13.7307i			0.458967i
$896$	6.06169	−	29.3131i	0.202507	−	0.979281i
$897$	−5.76221	+	5.57470i	−0.192394	+	0.186134i
$898$	32.4710	−	10.3847i	1.08357	−	0.346540i
$899$	−3.20838	+	5.55707i	−0.107005	+	0.185339i
$900$	−8.09812	−	12.2003i	−0.269937	−	0.406676i
$901$	−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
$906$	−28.8243	+	0.899491i	−0.957623	+	0.0298836i
$907$	36.9772	+	21.3488i	1.22781	+	0.708874i	0.966571	−	0.256401i	$-0.0825366\pi$
$907$	36.9772	+	21.3488i	1.22781	+	0.708874i	0.261236	+	0.965275i	$0.415870\pi$
$908$	−3.46294	−	36.1630i	−0.114922	−	1.20011i
$909$	30.3772	+	1.00513i	1.00755	+	0.0333381i
$910$	45.2963	−	1.50789i	1.50156	−	0.0499862i
$911$	42.4679			1.40702			0.703511	−	0.710684i	$-0.251614\pi$
$911$	42.4679			1.40702			0.703511	+	0.710684i	$0.251614\pi$
$912$	−18.4567	+	8.60348i	−0.611163	+	0.284890i
$913$	−9.34312	+	16.1828i	−0.309212	+	0.535571i
$914$	17.7774	−	19.5611i	0.588026	−	0.647024i
$915$	−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
$918$	4.20774	−	2.41880i	0.138876	−	0.0798323i
$919$	−18.3769	+	10.6099i	−0.606199	+	0.349989i	−0.771476	−	0.636258i	$-0.780481\pi$
$919$	−18.3769	+	10.6099i	−0.606199	+	0.349989i	0.165278	+	0.986247i	$0.447148\pi$
$920$	−3.16889	−	7.39184i	−0.104475	−	0.243702i
$921$	6.15024	−	1.53941i	0.202657	−	0.0507252i
$922$	−22.0456	+	7.05049i	−0.726035	+	0.232195i
$923$	24.5462			0.807948
$924$	8.28681	−	16.7627i	0.272616	−	0.551452i
$925$	23.2342			0.763937
$926$	15.3077	−	4.89560i	0.503042	−	0.160879i
$927$	−11.6056	+	18.6488i	−0.381179	+	0.612506i
$928$	−0.270454	+	11.6911i	−0.00887809	+	0.383780i
$929$	23.4266	−	13.5254i	0.768603	−	0.443753i	−0.0637729	−	0.997964i	$-0.520313\pi$
$929$	23.4266	−	13.5254i	0.768603	−	0.443753i	0.832376	+	0.554211i	$0.186980\pi$
$930$	−17.6287	+	10.9249i	−0.578066	+	0.358240i
$931$	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
$934$	34.5206	−	37.9841i	1.12955	−	1.24288i
$935$	1.83783	−	3.18322i	0.0601035	−	0.104102i
$936$	37.2468	+	5.69307i	1.21745	+	0.186084i
$937$	47.2071			1.54219			0.771094	−	0.636721i	$-0.219710\pi$
$937$	47.2071			1.54219			0.771094	+	0.636721i	$0.219710\pi$
$938$	−9.42260	−	15.1341i	−0.307659	−	0.494147i
$939$	−18.4656	+	17.8647i	−0.602603	+	0.582994i
$940$	−5.66098	+	0.542091i	−0.184641	+	0.0176811i
$941$	13.9134	+	8.03288i	0.453563	+	0.261864i	0.709334	−	0.704873i	$-0.248996\pi$
$941$	13.9134	+	8.03288i	0.453563	+	0.261864i	−0.255771	+	0.966737i	$0.582329\pi$
$942$	−0.816173	−	26.1544i	−0.0265924	−	0.852156i
$943$	−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	$-0.303151\pi$
$947$	−12.7943	−	22.1604i	−0.415759	−	0.720116i	−0.995508	+	0.0946792i	$0.969817\pi$
$948$	−37.1738	−	6.87476i	−1.20735	−	0.223282i
$949$	−6.74035	+	11.6746i	−0.218801	+	0.378975i
$950$	9.66247	−	3.09018i	0.313492	−	0.100259i
$951$	−9.99882	−	10.3351i	−0.324234	−	0.335140i
$952$	−4.56217	−	1.90124i	−0.147861	−	0.0616194i
$953$			25.0168i			0.810375i	0.914234	+	0.405187i	$0.132794\pi$
$953$			25.0168i			0.810375i	−0.914234	+	0.405187i	$0.867206\pi$
$954$	12.2596	+	43.2098i	0.396918	+	1.39897i
$955$	−23.1860	−	13.3865i	−0.750283	−	0.433176i
$956$	−27.5822	+	19.6523i	−0.892072	+	0.635602i
$957$	−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
$960$	−18.6337	+	32.8842i	−0.601399	+	1.06133i
$961$	−10.6827	−	18.5029i	−0.344603	−	0.596869i
$962$	−40.2091	+	44.2434i	−1.29639	+	1.42646i
$963$	−44.6412	−	27.7815i	−1.43854	−	0.895245i
$964$	−1.11288	−	11.6216i	−0.0358434	−	0.374307i
$965$			46.8054i			1.50672i
$966$	−6.49526	+	1.85747i	−0.208982	+	0.0597630i
$967$		−	25.4408i		−	0.818122i	−0.912507	−	0.409061i	$-0.865856\pi$
$967$		−	25.4408i		−	0.818122i	0.912507	−	0.409061i	$-0.134144\pi$
$968$	−2.28819	+	19.2032i	−0.0735452	+	0.617215i
$969$	0.816410	+	3.26172i	0.0262269	+	0.104782i
$970$	19.7463	+	17.9458i	0.634017	+	0.576204i
$971$	3.28999	+	5.69843i	0.105581	+	0.182871i	0.913975	−	0.405770i	$-0.132997\pi$
$971$	3.28999	+	5.69843i	0.105581	+	0.182871i	−0.808395	+	0.588641i	$0.799663\pi$
$972$	−30.0090	+	8.45329i	−0.962540	+	0.271139i
$973$	−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
$976$	0.779264	−	0.150625i	0.0249436	−	0.00482138i
$977$	4.46235	+	2.57634i	0.142763	+	0.0824244i	0.569680	−	0.821866i	$-0.307067\pi$
$977$	4.46235	+	2.57634i	0.142763	+	0.0824244i	−0.426917	+	0.904291i	$0.640400\pi$
$978$	−23.7140	+	44.2031i	−0.758291	+	1.41346i
$979$		−	1.10427i		−	0.0352926i
$980$	34.2687	+	16.8524i	1.09467	+	0.538331i
$981$	0.0633932	−	1.91587i	0.00202399	−	0.0611691i
$982$	−1.13861	−	3.56022i	−0.0363344	−	0.113611i
$983$	16.1512	−	27.9747i	0.515143	−	0.892253i	−0.484703	−	0.874679i	$-0.661072\pi$
$983$	16.1512	−	27.9747i	0.515143	−	0.892253i	0.999846	−	0.0175745i	$-0.00559441\pi$
$984$	35.5072	+	14.8841i	1.13193	+	0.474486i
$985$	−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
$990$	−16.4493	+	16.9387i	−0.522792	+	0.538347i
$991$	2.23686	+	1.29145i	0.0710563	+	0.0410244i	0.535107	−	0.844784i	$-0.320271\pi$
$991$	2.23686	+	1.29145i	0.0710563	+	0.0410244i	−0.464051	+	0.885809i	$0.653605\pi$
$992$	14.9992	+	9.12869i	0.476225	+	0.289836i
$993$	−18.3886	−	19.0071i	−0.583545	−	0.603173i
$994$	18.2461	+	9.73978i	0.578730	+	0.308927i
$995$	60.8399			1.92875
$996$	−24.1335	−	20.5957i	−0.764699	−	0.652599i
$997$	21.4033	−	37.0717i	0.677851	−	1.17407i	−0.297776	−	0.954636i	$-0.596245\pi$
$997$	21.4033	−	37.0717i	0.677851	−	1.17407i	0.975627	−	0.219436i	$-0.0704218\pi$
$998$	20.7671	+	18.8735i	0.657371	+	0.597429i
$999$	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.11.5	yes	24
3.2	odd	2	inner	84.2.n.a.11.8	yes	24
4.3	odd	2	inner	84.2.n.a.11.9	yes	24
7.2	even	3	inner	84.2.n.a.23.4	yes	24
7.3	odd	6		588.2.e.d.491.12		12
7.4	even	3		588.2.e.e.491.12		12
7.5	odd	6		588.2.n.e.275.4		24
7.6	odd	2		588.2.n.e.263.5		24
12.11	even	2	inner	84.2.n.a.11.4	✓	24
21.2	odd	6	inner	84.2.n.a.23.9	yes	24
21.5	even	6		588.2.n.e.275.9		24
21.11	odd	6		588.2.e.e.491.1		12
21.17	even	6		588.2.e.d.491.1		12
21.20	even	2		588.2.n.e.263.8		24
28.3	even	6		588.2.e.d.491.2		12
28.11	odd	6		588.2.e.e.491.2		12
28.19	even	6		588.2.n.e.275.8		24
28.23	odd	6	inner	84.2.n.a.23.8	yes	24
28.27	even	2		588.2.n.e.263.9		24
84.11	even	6		588.2.e.e.491.11		12
84.23	even	6	inner	84.2.n.a.23.5	yes	24
84.47	odd	6		588.2.n.e.275.5		24
84.59	odd	6		588.2.e.d.491.11		12
84.83	odd	2		588.2.n.e.263.4		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.430790 - 1.34700i) q^{2} +(0.420559 + 1.68022i) q^{3} +(-1.62884 + 1.16055i) q^{4} +(2.36229 - 1.36387i) q^{5} +(2.08209 - 1.29031i) q^{6} +(1.89768 - 1.84359i) q^{7} +(2.26495 + 1.69410i) q^{8} +(-2.64626 + 1.41326i) q^{9} +O(q^{10})\)	\(q+(-0.430790 - 1.34700i) q^{2} +(0.420559 + 1.68022i) q^{3} +(-1.62884 + 1.16055i) q^{4} +(2.36229 - 1.36387i) q^{5} +(2.08209 - 1.29031i) q^{6} +(1.89768 - 1.84359i) q^{7} +(2.26495 + 1.69410i) q^{8} +(-2.64626 + 1.41326i) q^{9} +(-2.85479 - 2.59447i) q^{10} +(-1.02012 + 1.76690i) q^{11} +(-2.63500 - 2.24873i) q^{12} -4.44055 q^{13} +(-3.30082 - 1.76198i) q^{14} +(3.28508 + 3.39557i) q^{15} +(1.30624 - 3.78070i) q^{16} +(-0.571980 - 0.330233i) q^{17} +(3.04365 + 2.95571i) 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} +(-1.89391 + 4.51809i) q^{24} +(1.22028 - 2.11358i) q^{25} +(1.91294 + 5.98144i) q^{26} +(-3.48749 - 3.85193i) q^{27} +(-0.951438 + 5.20526i) q^{28} -2.06727i q^{29} +(3.15867 - 5.88779i) q^{30} +(-2.68812 - 1.55199i) q^{31} +(-5.65534 - 0.130827i) q^{32} +(-3.39781 - 0.970941i) q^{33} +(-0.198422 + 0.912721i) q^{34} +(1.96845 - 6.94327i) q^{35} +(2.67018 - 5.37310i) q^{36} +(4.76004 + 8.24463i) q^{37} +(3.07611 + 2.79562i) q^{38} +(-1.86751 - 7.46109i) q^{39} +(7.66101 + 0.912859i) q^{40} -7.85889i q^{41} +(1.57232 - 6.28711i) q^{42} +0.530567i q^{43} +(-0.388965 - 4.06191i) q^{44} +(-4.32373 + 6.94768i) q^{45} +(-0.991489 + 1.09097i) q^{46} +(0.521208 + 0.902759i) q^{47} +(6.90176 + 0.604764i) q^{48} +(0.202367 - 6.99707i) q^{49} +(-3.37268 - 0.733208i) q^{50} +(0.314312 - 1.09993i) q^{51} +(7.23295 - 5.15349i) q^{52} +(9.16829 + 5.29332i) q^{53} +(-3.68620 + 6.35704i) q^{54} +5.56526i q^{55} +(7.42138 - 0.960783i) q^{56} +(-3.53976 - 3.65883i) q^{57} +(-2.78462 + 0.890559i) q^{58} +(-1.74375 + 3.02026i) q^{59} +(-9.29160 - 1.71835i) 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} +(0.155878 + 4.99513i) q^{66} +(4.12631 + 2.38233i) q^{67} +(1.31492 - 0.125915i) q^{68} +(1.29763 - 1.25541i) q^{69} +(-10.2006 + 0.339574i) q^{70} -5.52774 q^{71} +(-8.38787 - 1.28206i) q^{72} +(1.51791 - 2.62910i) q^{73} +(9.05497 - 9.96349i) q^{74} +(4.06447 + 1.16144i) q^{75} +(2.44055 - 5.34786i) q^{76} +(1.32158 + 5.23370i) q^{77} +(-9.24562 + 5.72971i) q^{78} +(9.45104 - 5.45656i) q^{79} +(-2.07066 - 10.7127i) q^{80} +(5.00539 - 7.47971i) q^{81} +(-10.5860 + 3.38553i) q^{82} +9.15881 q^{83} +(-9.14611 + 0.590497i) q^{84} -1.80158 q^{85} +(0.714675 - 0.228563i) q^{86} +(3.47347 - 0.869409i) q^{87} +(-5.30385 + 2.27377i) q^{88} +(-0.468730 + 0.270622i) q^{89} +(11.2212 + 2.83110i) q^{90} +(-8.42674 + 8.18655i) q^{91} +(1.89666 + 0.865562i) q^{92} +(1.47716 - 5.16932i) q^{93} +(0.991489 - 1.09097i) q^{94} +(-4.00870 + 6.94327i) q^{95} +(-2.15859 - 9.55722i) q^{96} -6.91692 q^{97} +(-9.51227 + 2.74168i) q^{98} +(0.202415 - 6.11739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 - 2 * q^9	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37} + 34 q^{40} + 38 q^{42} - 18 q^{45} + 24 q^{46} + 8 q^{48} + 16 q^{52} + 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} + 4 q^{61} - 68 q^{64} + 30 q^{66} + 36 q^{69} - 90 q^{70} + 20 q^{72} - 24 q^{76} - 104 q^{78} + 26 q^{81} - 68 q^{82} - 76 q^{84} - 40 q^{85} - 34 q^{88} - 40 q^{90} - 6 q^{93} - 24 q^{94} - 62 q^{96} + 72 q^{97}+O(q^{100}) \) 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

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