LMFDB - Embedded newform 84.2.n.a.23.8

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			23.8
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.430790 - 1.34700i) q^{2} +(1.66539 + 0.475894i) q^{3} +(-1.62884 - 1.16055i) q^{4} +(-2.36229 - 1.36387i) q^{5} +(1.35846 - 2.03828i) q^{6} +(1.89768 + 1.84359i) q^{7} +(-2.26495 + 1.69410i) q^{8} +(2.54705 + 1.58510i) q^{9} +O(q^{10})$	\(q+(0.430790 - 1.34700i) q^{2} +(1.66539 + 0.475894i) q^{3} +(-1.62884 - 1.16055i) 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} +(2.54705 + 1.58510i) q^{9} +(-2.85479 + 2.59447i) q^{10} +(1.02012 + 1.76690i) q^{11} +(-2.16036 - 2.70793i) 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} +(3.23238 - 2.74804i) q^{18} +(-2.54543 - 1.46961i) q^{19} +(2.26495 + 4.96308i) q^{20} +(2.28302 + 3.97339i) q^{21} +(2.81949 - 0.612946i) q^{22} +(0.521208 - 0.902759i) q^{23} +(-4.57825 + 1.74346i) 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} +(-5.98903 + 2.96224i) q^{30} +(-2.68812 + 1.55199i) q^{31} +(5.65534 - 0.130827i) q^{32} +(0.858043 + 3.42806i) 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} +(-3.07611 + 2.79562i) q^{38} +(-7.39525 - 2.11323i) q^{39} +(7.66101 - 0.912859i) q^{40} -7.85889i q^{41} +(6.33567 - 1.36355i) q^{42} -0.530567i q^{43} +(0.388965 - 4.06191i) q^{44} +(-3.85500 - 7.21830i) q^{45} +(-0.991489 - 1.09097i) 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} +(1.10973 - 0.277765i) q^{51} +(7.23295 + 5.15349i) q^{52} +(-9.16829 + 5.29332i) q^{53} +(6.69095 - 3.03829i) 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} +(1.41013 + 9.34335i) q^{60} +(0.0992110 - 0.171839i) q^{61} +(0.932518 + 4.28949i) q^{62} +(1.91121 + 7.70372i) q^{63} +(2.26004 - 7.67413i) q^{64} +(10.4899 + 6.05633i) q^{65} +(4.98724 + 0.320983i) 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} +(-8.45427 + 0.724784i) q^{72} +(1.51791 + 2.62910i) q^{73} +(-9.05497 - 9.96349i) q^{74} +(1.02640 + 4.10066i) 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} +(2.07066 - 10.7127i) q^{80} +(3.97492 + 8.07465i) q^{81} +(-10.5860 - 3.38553i) q^{82} -9.15881 q^{83} +(0.892639 - 9.12158i) q^{84} -1.80158 q^{85} +(-0.714675 - 0.228563i) q^{86} +(0.983802 - 3.44281i) q^{87} +(-5.30385 - 2.27377i) 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} +(-5.21535 + 1.30540i) q^{93} +(0.991489 + 1.09097i) q^{94} +(4.00870 + 6.94327i) q^{95} +(9.48061 + 2.47347i) 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 $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.430790	−	1.34700i	0.304614	−	0.952476i
$2$	0.430790	−	1.34700i	0.304614	−	0.952476i
$3$	1.66539	+	0.475894i	0.961514	+	0.274758i
$3$	1.66539	+	0.475894i	0.961514	+	0.274758i
$4$	−1.62884	−	1.16055i	−0.814420	−	0.580275i
$5$	−2.36229	−	1.36387i	−1.05645	−	0.609941i	−0.132001	−	0.991250i	$-0.542140\pi$
$5$	−2.36229	−	1.36387i	−1.05645	−	0.609941i	−0.924448	+	0.381309i	$0.875473\pi$
$6$	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
$9$	2.54705	+	1.58510i	0.849017	+	0.528366i
$10$	−2.85479	+	2.59447i	−0.902763	+	0.820445i
$11$	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	$0.733815\pi$
$12$	−2.16036	−	2.70793i	−0.623641	−	0.781711i
$13$	−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	$-0.641145\pi$
$17$	0.571980	−	0.330233i	0.138726	−	0.0800933i	0.567756	+	0.823197i	$0.307812\pi$
$18$	3.23238	−	2.74804i	0.761879	−	0.647720i
$19$	−2.54543	−	1.46961i	−0.583962	−	0.337151i	0.178744	−	0.983896i	$-0.442797\pi$
$19$	−2.54543	−	1.46961i	−0.583962	−	0.337151i	−0.762707	+	0.646745i	$0.776130\pi$
$20$	2.26495	+	4.96308i	0.506459	+	1.10978i
$21$	2.28302	+	3.97339i	0.498196	+	0.867064i
$22$	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	$0.132004\pi$
$24$	−4.57825	+	1.74346i	−0.934531	+	0.355883i
$25$	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	$-0.0614783\pi$
$30$	−5.98903	+	2.96224i	−1.09344	+	0.540828i
$31$	−2.68812	+	1.55199i	−0.482800	+	0.278745i	−0.721583	−	0.692328i	$-0.756585\pi$
$31$	−2.68812	+	1.55199i	−0.482800	+	0.278745i	0.238782	+	0.971073i	$0.423252\pi$
$32$	5.65534	−	0.130827i	0.999733	−	0.0231271i
$33$	0.858043	+	3.42806i	0.149366	+	0.596748i
$34$	−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	$-0.119412\pi$
$38$	−3.07611	+	2.79562i	−0.499011	+	0.453509i
$39$	−7.39525	−	2.11323i	−1.18419	−	0.338388i
$40$	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	$-0.210310\pi$
$42$	6.33567	−	1.36355i	0.977615	−	0.210400i
$43$		−	0.530567i		−	0.0809106i	−0.999181	−	0.0404553i	$-0.987119\pi$
$43$		−	0.530567i		−	0.0809106i	0.999181	−	0.0404553i	$-0.0128808\pi$
$44$	0.388965	−	4.06191i	0.0586387	−	0.612356i
$45$	−3.85500	−	7.21830i	−0.574670	−	1.07604i
$46$	−0.991489	−	1.09097i	−0.146187	−	0.160855i
$47$	−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
$51$	1.10973	−	0.277765i	0.155393	−	0.0388948i
$52$	7.23295	+	5.15349i	1.00303	+	0.714660i
$53$	−9.16829	+	5.29332i	−1.25936	+	0.727093i	−0.972950	−	0.231014i	$-0.925796\pi$
$53$	−9.16829	+	5.29332i	−1.25936	+	0.727093i	−0.286411	+	0.958107i	$0.592462\pi$
$54$	6.69095	−	3.03829i	0.910523	−	0.413459i
$55$		−	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	$-0.0937696\pi$
$59$	1.74375	+	3.02026i	0.227016	+	0.393204i	−0.729906	+	0.683547i	$0.760436\pi$
$60$	1.41013	+	9.34335i	0.182047	+	1.20622i
$61$	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
$63$	1.91121	+	7.70372i	0.240790	+	0.970577i
$64$	2.26004	−	7.67413i	0.282505	−	0.959266i
$65$	10.4899	+	6.05633i	1.30111	+	0.751195i
$66$	4.98724	+	0.320983i	0.613887	+	0.0395103i
$67$	4.12631	−	2.38233i	0.504109	−	0.291048i	−0.226300	−	0.974058i	$-0.572663\pi$
$67$	4.12631	−	2.38233i	0.504109	−	0.291048i	0.730409	+	0.683010i	$0.239330\pi$
$68$	−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	$-0.393622\pi$
$71$	5.52774			0.656022			0.328011	+	0.944674i	$0.393622\pi$
$72$	−8.45427	+	0.724784i	−0.996345	+	0.0854167i
$73$	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	$0.776481\pi$
$74$	−9.05497	−	9.96349i	−1.05262	−	1.15823i
$75$	1.02640	+	4.10066i	0.118518	+	0.473503i
$76$	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	0.926350	−	0.376664i	$-0.122929\pi$
$79$	9.45104	+	5.45656i	1.06332	+	0.613911i	0.136975	+	0.990575i	$0.456262\pi$
$80$	2.07066	−	10.7127i	0.231507	−	1.19771i
$81$	3.97492	+	8.07465i	0.441658	+	0.897183i
$82$	−10.5860	−	3.38553i	−1.16902	−	0.373869i
$83$	−9.15881			−1.00531			−0.502655	−	0.864487i	$-0.667643\pi$
$83$	−9.15881			−1.00531			−0.502655	+	0.864487i	$0.667643\pi$
$84$	0.892639	−	9.12158i	0.0973948	−	0.995246i
$85$	−1.80158			−0.195409
$86$	−0.714675	−	0.228563i	−0.0770654	−	0.0246465i
$87$	0.983802	−	3.44281i	0.105475	−	0.369108i
$88$	−5.30385	−	2.27377i	−0.565392	−	0.242384i
$89$	0.468730	+	0.270622i	0.0496853	+	0.0286858i	0.524637	−	0.851326i	$-0.324201\pi$
$89$	0.468730	+	0.270622i	0.0496853	+	0.0286858i	−0.474952	+	0.880012i	$0.657534\pi$
$90$	−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
$93$	−5.21535	+	1.30540i	−0.540806	+	0.135364i
$94$	0.991489	+	1.09097i	0.102264	+	0.112525i
$95$	4.00870	+	6.94327i	0.411284	+	0.712365i
$96$	9.48061	+	2.47347i	0.967611	+	0.252447i
$97$	−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	$-0.498510\pi$
$101$	8.77393	−	5.06563i	0.873039	−	0.504049i	0.868357	+	0.495940i	$0.165176\pi$
$102$	0.103908	−	1.61446i	0.0102885	−	0.159856i
$103$	6.34079	+	3.66086i	0.624777	+	0.360715i	0.778726	−	0.627364i	$-0.215866\pi$
$103$	6.34079	+	3.66086i	0.624777	+	0.360715i	−0.153950	+	0.988079i	$0.549199\pi$
$104$	10.0576	−	7.52275i	0.986234	−	0.737666i
$105$	0.0260175	−	12.5000i	0.00253905	−	1.21988i
$106$	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	$0.844964\pi$
$108$	−1.21020	−	10.3216i	−0.116452	−	0.993196i
$109$	−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	$0.843076\pi$
$110$	−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	$0.830533\pi$
$114$	−6.45335	+	3.19189i	−0.604411	+	0.298948i
$115$	−2.46249	+	1.42172i	−0.229628	+	0.132576i
$116$	−2.39917	+	3.36726i	−0.222758	+	0.312642i
$117$	−11.3103	−	7.03871i	−1.04564	−	0.650729i
$118$	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
$122$	−0.188728	−	0.207664i	−0.0170866	−	0.0188010i
$123$	3.74000	−	13.0881i	0.337225	−	1.18012i
$124$	6.17967	+	0.591761i	0.554951	+	0.0531417i
$125$			6.98150i			0.624445i
$126$	11.2003	+	0.744271i	0.997799	+	0.0663049i
$127$			10.9563i			0.972210i	0.873900	+	0.486105i	$0.161583\pi$
$127$			10.9563i			0.972210i	−0.873900	+	0.486105i	$0.838417\pi$
$128$	−9.36348	−	6.35022i	−0.827623	−	0.561285i
$129$	0.252494	−	0.883600i	0.0222308	−	0.0777967i
$130$	12.6768	−	11.5209i	1.11183	−	1.01045i
$131$	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
$135$	−2.98494	−	13.8559i	−0.256902	−	1.19252i
$136$	−0.736061	+	1.71696i	−0.0631167	+	0.147228i
$137$	12.5610	−	7.25212i	1.07316	−	0.619591i	0.144119	−	0.989560i	$-0.453965\pi$
$137$	12.5610	−	7.25212i	1.07316	−	0.619591i	0.929044	+	0.369970i	$0.120632\pi$
$138$	−1.13203	−	2.28873i	−0.0963649	−	0.194830i
$139$			5.78265i			0.490478i	0.969463	+	0.245239i	$0.0788665\pi$
$139$			5.78265i			0.490478i	−0.969463	+	0.245239i	$0.921134\pi$
$140$	−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
$144$	−2.66572	+	11.7002i	−0.222144	+	0.975014i
$145$	−2.81949	+	4.88349i	−0.234146	+	0.405552i
$146$	4.19530	−	0.912043i	0.347206	−	0.0754812i
$147$	−2.99285	+	11.7492i	−0.246846	+	0.969055i
$148$	−17.3217	+	7.90492i	−1.42383	+	0.649780i
$149$	−11.9993	−	6.92781i	−0.983022	−	0.567548i	−0.0798408	−	0.996808i	$-0.525441\pi$
$149$	−11.9993	−	6.92781i	−0.983022	−	0.567548i	−0.903181	+	0.429260i	$0.858775\pi$
$150$	5.96576	+	0.383962i	0.487103	+	0.0313503i
$151$	−10.1959	+	5.88660i	−0.829730	+	0.479045i	−0.853760	−	0.520667i	$-0.825683\pi$
$151$	−10.1959	+	5.88660i	−0.829730	+	0.479045i	0.0240304	+	0.999711i	$0.492350\pi$
$152$	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
$156$	9.59317	+	12.0247i	0.768068	+	0.962745i
$157$	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	$0.693155\pi$
$158$	11.4214	−	10.3800i	0.908639	−	0.825785i
$159$	−17.7878	+	4.45230i	−1.41067	+	0.353090i
$160$	−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	−0.395903	−	0.918292i	$-0.629568\pi$
$163$	−17.7351	−	10.2394i	−1.38912	−	0.802008i	−0.993216	+	0.116284i	$0.962902\pi$
$164$	−9.12065	+	12.8009i	−0.712203	+	0.999581i
$165$	2.64847	−	9.26832i	0.206183	−	0.721538i
$166$	−3.94552	+	12.3370i	−0.306232	+	0.957534i
$167$	−22.4614			−1.73811			−0.869057	−	0.494712i	$-0.835273\pi$
$167$	−22.4614			−1.73811			−0.869057	+	0.494712i	$0.835273\pi$
$168$	−11.9023	−	5.13187i	−0.918280	−	0.395932i
$169$	6.71850			0.516808
$170$	−0.776101	+	2.42673i	−0.0595242	+	0.186122i
$171$	−4.15387	−	7.77792i	−0.317655	−	0.594793i
$172$	−0.615750	+	0.864208i	−0.0469505	+	0.0658953i
$173$	16.8271	+	9.71515i	1.27934	+	0.738630i	0.976728	−	0.214483i	$-0.0688066\pi$
$173$	16.8271	+	9.71515i	1.27934	+	0.738630i	0.302616	+	0.953113i	$0.402140\pi$
$174$	−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
$177$	1.46670	+	5.85975i	0.110244	+	0.440445i
$178$	0.566453	−	0.514801i	0.0424574	−	0.0385860i
$179$	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	$0.773094\pi$
$180$	−2.09802	+	16.2314i	−0.156378	+	1.20982i
$181$	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
$186$	−0.488335	+	7.58745i	−0.0358064	+	0.556339i
$187$	1.16698	+	0.673757i	0.0853381	+	0.0492700i
$188$	1.89666	−	0.865562i	0.138328	−	0.0631276i
$189$	−0.483240	+	13.7392i	−0.0351505	+	0.999382i
$190$	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	$0.0511146\pi$
$192$	7.41592	−	11.7049i	0.535198	−	0.844727i
$193$	−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	$-0.378549\pi$
$194$	−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	$-0.128540\pi$
$198$	8.15295	+	2.90796i	0.579405	+	0.206660i
$199$	19.3160	−	11.1521i	1.36927	−	0.790550i	0.378438	−	0.925627i	$-0.376461\pi$
$199$	19.3160	−	11.1521i	1.36927	−	0.790550i	0.990835	+	0.135077i	$0.0431281\pi$
$200$	−6.34449	−	2.71989i	−0.448623	−	0.192325i
$201$	8.00566	−	2.00382i	0.564675	−	0.141338i
$202$	−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
$206$	7.66274	−	6.96401i	0.533888	−	0.485206i
$207$	2.75851	−	1.47321i	0.191729	−	0.102395i
$208$	−5.80044	−	16.7884i	−0.402188	−	1.16407i
$209$		−	5.99672i		−	0.414802i
$210$	−16.8264	−	5.41993i	−1.16113	−	0.374011i
$211$		−	17.9648i		−	1.23675i	−0.785884	−	0.618374i	$-0.787792\pi$
$211$		−	17.9648i		−	1.23675i	0.785884	−	0.618374i	$-0.212208\pi$
$212$	21.0768	+	2.01830i	1.44756	+	0.138618i
$213$	9.20584	+	2.63062i	0.630774	+	0.180247i
$214$	16.6704	+	18.3430i	1.13956	+	1.25390i
$215$	−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
$219$	1.27674	+	5.10083i	0.0862741	+	0.344682i
$220$	−6.45876	+	9.06491i	−0.435450	+	0.611156i
$221$	−2.53991	+	1.46642i	−0.170853	+	0.0986419i
$222$	−10.3385	−	20.9023i	−0.693875	−	1.40287i
$223$			1.95751i			0.131084i	0.997850	+	0.0655422i	$0.0208777\pi$
$223$			1.95751i			0.131084i	−0.997850	+	0.0655422i	$0.979122\pi$
$224$	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	0.992395	+	0.123095i	$0.0392820\pi$
$227$	9.08211	+	15.7307i	0.602801	+	1.04408i	−0.389594	+	0.920987i	$0.627385\pi$
$228$	1.51946	+	10.0677i	0.100628	+	0.666751i
$229$	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
$231$	−4.69163	+	8.08723i	−0.308687	+	0.532101i
$232$	3.50217	+	4.68228i	0.229929	+	0.307406i
$233$	−22.6957	−	13.1034i	−1.48684	−	0.858430i	−0.486956	−	0.873426i	$-0.661893\pi$
$233$	−22.6957	−	13.1034i	−1.48684	−	0.858430i	−0.999888	+	0.0149969i	$0.995226\pi$
$234$	−14.3535	+	12.2028i	−0.938320	+	0.797724i
$235$	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	$-0.684486\pi$
$239$	−16.9336			−1.09535			−0.547673	+	0.836692i	$0.684486\pi$
$240$	8.54655	−	16.8554i	0.551677	−	1.08801i
$241$	−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	$0.893537\pi$
$242$	−6.50335	−	7.15586i	−0.418051	−	0.459996i
$243$	2.77712	+	15.3391i	0.178152	+	0.984003i
$244$	−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
$248$	3.45924	−	8.06912i	0.219662	−	0.512390i
$249$	−15.2530	−	4.35863i	−0.966620	−	0.276217i
$250$	9.40411	+	3.00756i	0.594768	+	0.190215i
$251$	10.1468			0.640462			0.320231	−	0.947340i	$-0.396240\pi$
$251$	10.1468			0.640462			0.320231	+	0.947340i	$0.396240\pi$
$252$	5.82750	−	14.7662i	0.367098	−	0.930182i
$253$	2.12679			0.133710
$254$	14.7581	+	4.71984i	0.926007	+	0.296149i
$255$	−3.00033	−	0.857360i	−0.187888	−	0.0536900i
$256$	−12.5875	+	9.87704i	−0.786716	+	0.617315i
$257$	−10.3764	−	5.99080i	−0.647261	−	0.373696i	0.140145	−	0.990131i	$-0.455243\pi$
$257$	−10.3764	−	5.99080i	−0.647261	−	0.373696i	−0.787406	+	0.616435i	$0.788576\pi$
$258$	−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
$261$	3.27683	−	5.26544i	0.202831	−	0.325923i
$262$	−21.0731	−	23.1875i	−1.30190	−	1.43253i
$263$	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	$0.686421\pi$
$264$	−7.75091	−	6.31078i	−0.477035	−	0.388402i
$265$	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	$-0.602465\pi$
$269$	5.69092	−	3.28566i	0.346982	−	0.200330i	0.663355	+	0.748305i	$0.269132\pi$
$270$	−19.9498	−	1.94824i	−1.21411	−	0.118566i
$271$	−0.0141559	−	0.00817291i	−0.000859910	−	0.000496469i	0.499570	−	0.866274i	$-0.333491\pi$
$271$	−0.0141559	−	0.00817291i	−0.000859910	−	0.000496469i	−0.500430	+	0.865777i	$0.666825\pi$
$272$	1.99566	+	1.73112i	0.121005	+	0.104965i
$273$	−10.1379	−	17.6440i	−0.613572	−	1.06787i
$274$	−4.35747	−	20.0439i	−0.263245	−	1.21090i
$275$	−2.48966	+	4.31222i	−0.150132	+	0.260037i
$276$	−3.57060	+	0.538888i	−0.214925	+	0.0324372i
$277$	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	$0.647891\pi$
$278$	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	$-0.0153099\pi$
$282$	1.13203	+	2.28873i	0.0674115	+	0.136292i
$283$	−17.8180	+	10.2872i	−1.05917	+	0.611513i	−0.925203	−	0.379472i	$-0.876106\pi$
$283$	−17.8180	+	10.2872i	−1.05917	+	0.611513i	−0.133969	+	0.990986i	$0.542772\pi$
$284$	−9.00380	−	6.41522i	−0.534278	−	0.380673i
$285$	3.37179	+	13.4710i	0.199728	+	0.797952i
$286$	−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
$290$	5.36348	+	5.90162i	0.314954	+	0.346555i
$291$	−11.5194	−	3.29172i	−0.675278	−	0.192964i
$292$	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	$0.889399\pi$
$294$	14.5369	+	9.09280i	0.847808	+	0.530303i
$295$		−	9.51296i		−	0.553866i
$296$	3.18597	+	26.7377i	0.185181	+	1.55410i
$297$	−3.24833	+	10.0915i	−0.188487	+	0.585569i
$298$	−14.5010	+	13.1787i	−0.840018	+	0.763421i
$299$	−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
$303$	17.0227	−	4.26079i	0.977930	−	0.244776i
$304$	2.23119	−	11.5432i	0.127968	−	0.662048i
$305$	−0.468730	+	0.270622i	−0.0268394	+	0.0154957i
$306$	0.941362	−	2.63926i	0.0538141	−	0.150877i
$307$			3.66039i			0.208909i	0.994530	+	0.104455i	$0.0333097\pi$
$307$			3.66039i			0.208909i	−0.994530	+	0.104455i	$0.966690\pi$
$308$	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	$-0.0585824\pi$
$311$	5.87374	+	10.1736i	0.333069	+	0.576892i	−0.650043	+	0.759897i	$0.725249\pi$
$312$	20.3299	−	7.74193i	1.15096	−	0.438301i
$313$	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
$315$	5.99202	−	20.8051i	0.337612	−	1.17223i
$316$	−9.06162	−	19.8563i	−0.509756	−	1.11700i
$317$	7.19012	+	4.15122i	0.403837	+	0.233156i	0.688138	−	0.725579i	$-0.258428\pi$
$317$	7.19012	+	4.15122i	0.403837	+	0.233156i	−0.284301	+	0.958735i	$0.591762\pi$
$318$	−1.66555	+	25.8783i	−0.0933994	+	1.45118i
$319$	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
$324$	2.89653	−	17.7654i	0.160918	−	0.986968i
$325$	−5.41870	−	9.38546i	−0.300575	−	0.520612i
$326$	−21.4326	+	19.4782i	−1.18704	+	1.07880i
$327$	−0.268726	−	1.07361i	−0.0148606	−	0.0593710i
$328$	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	0.0904426	−	0.995902i	$-0.471172\pi$
$331$	−13.2232	−	7.63441i	−0.726812	−	0.419625i	−0.817255	+	0.576276i	$0.804505\pi$
$332$	14.9182	+	10.6293i	0.818745	+	0.583357i
$333$	25.1926	−	13.4543i	1.38055	−	0.737294i
$334$	−9.67613	+	30.2556i	−0.529454	+	1.65551i
$335$	−12.9967			−0.710087
$336$	−12.0400	+	13.8216i	−0.656837	+	0.754033i
$337$	−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
$339$	−5.13572	+	17.9724i	−0.278934	+	0.976129i
$340$	2.93448	+	2.09082i	0.159145	+	0.113391i
$341$	−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
$345$	−4.77760	+	1.19583i	−0.257217	+	0.0643815i
$346$	20.3353	−	18.4810i	1.09323	−	0.993547i
$347$	−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	$-0.368339\pi$
$348$	−5.59802	+	4.46604i	−0.300085	+	0.239405i
$349$	−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	$-0.663092\pi$
$353$	0.365480	−	0.211010i	0.0194526	−	0.0112309i	0.509695	+	0.860355i	$0.329758\pi$
$354$	8.52494	+	0.548673i	0.453095	+	0.0291616i
$355$	−13.0581	−	7.53911i	−0.693053	−	0.400134i
$356$	−0.449417	−	0.984785i	−0.0238190	−	0.0521935i
$357$	2.61799	+	1.51877i	0.138559	+	0.0803818i
$358$	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	$0.0421907\pi$
$360$	20.9599	+	9.81836i	1.10469	+	0.517473i
$361$	−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
$366$	−0.215480	−	0.435656i	−0.0112633	−	0.0227721i
$367$	−18.8797	+	10.9002i	−0.985512	+	0.568985i	−0.903930	−	0.427681i	$-0.859331\pi$
$367$	−18.8797	+	10.9002i	−0.985512	+	0.568985i	−0.0815820	+	0.996667i	$0.525997\pi$
$368$	4.09389	+	0.791312i	0.213409	+	0.0412500i
$369$	12.4571	−	20.0170i	0.648492	−	1.04204i
$370$	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	$0.998028\pi$
$374$	1.41028	−	1.28168i	0.0729236	−	0.0662741i
$375$	−3.32246	+	11.6269i	−0.171571	+	0.600412i
$376$	−0.348853	−	2.92769i	−0.0179907	−	0.150984i
$377$			9.17983i			0.472785i
$378$	18.2986	+	6.56964i	0.941180	+	0.337906i
$379$			34.1136i			1.75230i	0.482038	+	0.876150i	$0.339897\pi$
$379$			34.1136i			1.75230i	−0.482038	+	0.876150i	$0.660103\pi$
$380$	1.52849	−	15.9618i	0.0784098	−	0.818822i
$381$	−5.21402	+	18.2464i	−0.267122	+	0.934793i
$382$	−9.33555	−	10.2722i	−0.477649	−	0.525573i
$383$	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
$387$	0.841000	−	1.35138i	0.0427505	−	0.0686945i
$388$	11.2666	+	8.02744i	0.571973	+	0.407531i
$389$	4.15260	−	2.39750i	0.210545	−	0.121558i	−0.391020	−	0.920382i	$-0.627878\pi$
$389$	4.15260	−	2.39750i	0.210545	−	0.121558i	0.601565	+	0.798824i	$0.294544\pi$
$390$	26.5946	−	13.1540i	1.34667	−	0.666077i
$391$		−	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
$396$	7.42924	−	9.72934i	0.373334	−	0.488918i
$397$	−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
$399$	0.0280346	−	13.4691i	0.00140348	−	0.674300i
$400$	−6.39684	+	7.37435i	−0.319842	+	0.368718i
$401$	10.0211	+	5.78571i	0.500432	+	0.288924i	0.728892	−	0.684629i	$-0.240036\pi$
$401$	10.0211	+	5.78571i	0.500432	+	0.288924i	−0.228460	+	0.973553i	$0.573369\pi$
$402$	0.749603	−	11.6469i	0.0373868	−	0.580893i
$403$	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
$408$	−2.04292	+	2.50911i	−0.101140	+	0.124220i
$409$	−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	$-0.335275\pi$
$410$	20.3897	+	22.4355i	1.00698	+	1.10801i
$411$	24.3703	−	6.09989i	1.20210	−	0.300885i
$412$	−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
$416$	−25.1128	+	0.580942i	−1.23126	+	0.0284830i
$417$	−2.75193	+	9.63037i	−0.134763	+	0.471601i
$418$	−8.07760	−	2.58332i	−0.395089	−	0.126355i
$419$	21.9130			1.07052			0.535259	−	0.844688i	$-0.320214\pi$
$419$	21.9130			1.07052			0.535259	+	0.844688i	$0.320214\pi$
$420$	−14.5493	+	20.3304i	−0.709933	+	0.992021i
$421$	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
$423$	−2.75851	+	1.47321i	−0.134123	+	0.0716297i
$424$	11.7983	−	27.5211i	0.572978	−	1.33654i
$425$	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
$429$	−3.81019	−	15.2225i	−0.183958	−	0.734947i
$430$	1.37654	+	1.51465i	0.0663827	+	0.0730431i
$431$	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	$0.585915\pi$
$432$	−10.0075	+	18.2167i	−0.481487	+	0.876453i
$433$	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
$438$	7.42085	+	0.477612i	0.354582	+	0.0228212i
$439$	−15.9204	−	9.19162i	−0.759837	−	0.438692i	0.0694002	−	0.997589i	$-0.477891\pi$
$439$	−15.9204	−	9.19162i	−0.759837	−	0.438692i	−0.829237	+	0.558897i	$0.811225\pi$
$440$	9.42811	+	12.6051i	0.449467	+	0.600922i
$441$	−10.5756	+	18.1427i	−0.503601	+	0.863937i
$442$	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	$0.229602\pi$
$444$	−32.6092	+	4.92150i	−1.54757	+	0.233564i
$445$	−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	$0.807401\pi$
$450$	9.75260	+	3.47852i	0.459742	+	0.163979i
$451$	13.8859	−	8.01704i	0.653862	−	0.377508i
$452$	12.5243	−	17.5780i	0.589096	−	0.826800i
$453$	−19.7815	+	4.95132i	−0.929417	+	0.232633i
$454$	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	$0.0226531\pi$
$458$	−9.36429	−	10.3038i	−0.437565	−	0.481467i
$459$	3.26681	+	1.05155i	0.152482	+	0.0490819i
$460$	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	$-0.124465\pi$
$462$	8.87242	+	9.80354i	0.412782	+	0.456102i
$463$		−	11.3643i		−	0.528142i	−0.964503	−	0.264071i	$-0.914935\pi$
$463$		−	11.3643i		−	0.528142i	0.964503	−	0.264071i	$-0.0850653\pi$
$464$	7.81574	−	2.70036i	0.362837	−	0.125361i
$465$	14.1006	+	4.02931i	0.653898	+	0.186855i
$466$	−27.4273	+	24.9264i	−1.27055	+	1.15469i
$467$	−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
$471$	4.49270	+	17.9492i	0.207012	+	0.827057i
$472$	−9.06613	−	3.88666i	−0.417302	−	0.178898i
$473$	0.937461	−	0.541243i	0.0431045	−	0.0248864i
$474$	23.9609	−	11.8513i	1.10056	−	0.544348i
$475$		−	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	$-0.249022\pi$
$479$	−5.59953	−	9.69867i	−0.255849	−	0.443144i	−0.965126	+	0.261787i	$0.915688\pi$
$480$	−19.0225	−	18.7734i	−0.868253	−	0.856882i
$481$	−21.1372	+	36.6107i	−0.963773	+	1.66930i
$482$	−8.06690	+	1.75371i	−0.367437	+	0.0798794i
$483$	4.77694	+	0.00994270i	0.217358	+	0.000452408i
$484$	−12.4406	+	5.67738i	−0.565480	+	0.258063i
$485$	16.3398	+	9.43377i	0.741951	+	0.428366i
$486$	21.8582	+	2.86713i	0.991507	+	0.130056i
$487$	8.60678	−	4.96913i	0.390010	−	0.225173i	−0.292154	−	0.956371i	$-0.594372\pi$
$487$	8.60678	−	4.96913i	0.390010	−	0.225173i	0.682165	+	0.731199i	$0.261039\pi$
$488$	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	$-0.518995\pi$
$491$	−2.64307			−0.119280			−0.0596400	+	0.998220i	$0.518995\pi$
$492$	−21.2813	+	16.9780i	−0.959435	+	0.765428i
$493$	−0.682681	−	1.18244i	−0.0307464	−	0.0532544i
$494$	13.6596	−	12.4141i	0.614576	−	0.558536i
$495$	8.82148	−	14.1750i	0.396496	−	0.637118i
$496$	−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	0.0633371	−	0.997992i	$-0.479826\pi$
$499$	−17.1844	−	9.92144i	−0.769281	−	0.444145i	−0.832618	+	0.553848i	$0.813159\pi$
$500$	8.10239	−	11.3718i	0.362350	−	0.508560i
$501$	−37.4070	−	10.6892i	−1.67122	−	0.477560i
$502$	4.37115	−	13.6678i	0.195094	−	0.610024i
$503$	−3.07284			−0.137011			−0.0685056	−	0.997651i	$-0.521823\pi$
$503$	−3.07284			−0.137011			−0.0685056	+	0.997651i	$0.521823\pi$
$504$	−17.3797	−	14.2108i	−0.774153	−	0.632999i
$505$	−27.6354			−1.22976
$506$	0.916198	−	2.86479i	0.0407300	−	0.127355i
$507$	11.1889	+	3.19729i	0.496918	+	0.141997i
$508$	12.7153	−	17.8460i	0.564150	−	0.791788i
$509$	14.6238	+	8.44307i	0.648190	+	0.374233i	0.787762	−	0.615979i	$-0.211239\pi$
$509$	14.6238	+	8.44307i	0.648190	+	0.374233i	−0.139572	+	0.990212i	$0.544573\pi$
$510$	−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
$513$	−3.21635	−	14.9301i	−0.142005	−	0.659179i
$514$	−12.5397	+	11.3962i	−0.553101	+	0.502667i
$515$	−9.98586	−	17.2960i	−0.440029	−	0.762153i
$516$	−1.43674	+	1.14621i	−0.0632487	+	0.0504592i
$517$	−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	$-0.423854\pi$
$521$	27.3170	−	15.7715i	1.19678	−	0.690961i	0.959836	+	0.280562i	$0.0905208\pi$
$522$	−5.68095	−	6.68220i	−0.248648	−	0.292472i
$523$	29.0382	+	16.7652i	1.26975	+	0.733092i	0.974941	−	0.222463i	$-0.0714098\pi$
$523$	29.0382	+	16.7652i	1.26975	+	0.733092i	0.294812	+	0.955555i	$0.404743\pi$
$524$	−40.3117	+	18.3967i	−1.76103	+	0.803662i
$525$	−5.61215	+	9.67398i	−0.244934	+	0.422207i
$526$	19.9606	−	4.33936i	0.870325	−	0.189205i
$527$	−1.02503	+	1.77541i	−0.0446512	+	0.0773381i
$528$	−11.8397	+	7.72188i	−0.515255	+	0.336052i
$529$	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
$534$	1.18836	−	0.587773i	0.0514252	−	0.0254354i
$535$	41.4030	−	23.9040i	1.79001	−	1.03346i
$536$	−5.31000	+	12.3863i	−0.229357	+	0.535005i
$537$	2.11698	+	8.45777i	0.0913545	+	0.364980i
$538$	−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	$-0.00332638\pi$
$542$	−0.0171072	+	0.0155472i	−0.000734815	+	0.000667811i
$543$	9.52353	+	2.72140i	0.408694	+	0.116786i
$544$	3.19154	−	1.94241i	0.136836	−	0.0832802i
$545$			1.74295i			0.0746599i
$546$	−28.1339	+	6.05490i	−1.20402	+	0.259126i
$547$		−	10.9063i		−	0.466318i	−0.972439	−	0.233159i	$-0.925094\pi$
$547$		−	10.9063i		−	0.466318i	0.972439	−	0.233159i	$-0.0749063\pi$
$548$	−28.8764	−	2.76518i	−1.23354	−	0.118123i
$549$	0.525076	−	0.280422i	0.0224097	−	0.0119681i
$550$	4.73606	+	5.21125i	0.201946	+	0.222208i
$551$	−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
$555$	−43.6323	+	10.9212i	−1.85209	+	0.463578i
$556$	6.71106	−	9.41902i	0.284612	−	0.399455i
$557$	−9.47804	+	5.47215i	−0.401597	+	0.231862i	−0.687173	−	0.726494i	$-0.741149\pi$
$557$	−9.47804	+	5.47215i	−0.401597	+	0.231862i	0.285576	+	0.958356i	$0.407815\pi$
$558$	−4.42409	+	12.4037i	−0.187287	+	0.525089i
$559$			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	0.993370	+	0.114962i	$0.0366746\pi$
$563$	14.1475	+	24.5041i	0.596245	+	1.03273i	−0.397125	+	0.917765i	$0.629992\pi$
$564$	3.57060	−	0.538888i	0.150349	−	0.0226913i
$565$	14.7185	−	25.4932i	0.619212	−	1.07251i
$566$	6.18114	+	28.4326i	0.259813	+	1.19511i
$567$	−7.34320	+	22.6512i	−0.308385	+	0.951261i
$568$	−12.5201	+	9.36455i	−0.525331	+	0.392928i
$569$	−0.823967	−	0.475718i	−0.0345425	−	0.0199431i	0.482629	−	0.875825i	$-0.339682\pi$
$569$	−0.823967	−	0.475718i	−0.0345425	−	0.0199431i	−0.517172	+	0.855882i	$0.673015\pi$
$570$	19.5980	+	1.26134i	0.820870	+	0.0528319i
$571$	−14.1886	+	8.19177i	−0.593773	+	0.342815i	−0.766588	−	0.642139i	$-0.778047\pi$
$571$	−14.1886	+	8.19177i	−0.593773	+	0.342815i	0.172815	+	0.984954i	$0.444714\pi$
$572$	−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
$576$	17.9207	−	15.9640i	0.746695	−	0.665167i
$577$	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	$0.766801\pi$
$578$	15.7546	+	17.3353i	0.655303	+	0.721052i
$579$	−7.21639	−	28.8309i	−0.299903	−	1.19817i
$580$	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
$584$	−7.89195	−	3.38329i	−0.326571	−	0.140002i
$585$	17.1183	+	32.0533i	0.707756	+	1.32524i
$586$	15.7024	+	5.02184i	0.648661	+	0.207450i
$587$	29.5354			1.21905			0.609527	−	0.792765i	$-0.291359\pi$
$587$	29.5354			1.21905			0.609527	+	0.792765i	$0.291359\pi$
$588$	18.5104	−	15.6642i	0.763355	−	0.645979i
$589$	9.12323			0.375916
$590$	−12.8140	−	4.09809i	−0.527544	−	0.168716i
$591$	5.24919	−	18.3695i	0.215923	−	0.755622i
$592$	37.3883	+	7.22681i	1.53665	+	0.297020i
$593$	−18.2436	−	10.5329i	−0.749174	−	0.432536i	0.0762215	−	0.997091i	$-0.475714\pi$
$593$	−18.2436	−	10.5329i	−0.749174	−	0.432536i	−0.825395	+	0.564555i	$0.809048\pi$
$594$	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
$597$	37.4758	−	9.38021i	1.53378	−	0.383906i
$598$	4.40276	+	4.84450i	0.180042	+	0.198107i
$599$	−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	$-0.468177\pi$
$600$	−9.27167	−	7.54898i	−0.378514	−	0.308186i
$601$	−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
$606$	1.59391	−	24.7652i	0.0647481	−	1.00602i
$607$	−11.4085	−	6.58667i	−0.463055	−	0.267345i	0.250273	−	0.968175i	$-0.419480\pi$
$607$	−11.4085	−	6.58667i	−0.463055	−	0.267345i	−0.713328	+	0.700830i	$0.752813\pi$
$608$	−14.5876	−	7.97812i	−0.591604	−	0.323555i
$609$	8.21407	−	4.71963i	0.332851	−	0.191249i
$610$	0.162604	+	0.747963i	0.00658365	+	0.0302841i
$611$	2.31445	−	4.00875i	0.0936327	−	0.162177i
$612$	−3.14957	−	2.40499i	−0.127314	−	0.0972158i
$613$	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	$0.707928\pi$
$614$	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	$-0.317062\pi$
$618$	16.0756	−	7.95115i	0.646655	−	0.319842i
$619$	11.6140	−	6.70535i	0.466806	−	0.269511i	−0.248096	−	0.968736i	$-0.579805\pi$
$619$	11.6140	−	6.70535i	0.466806	−	0.269511i	0.714902	+	0.699225i	$0.246471\pi$
$620$	−13.7911	−	9.82617i	−0.553864	−	0.394629i
$621$	5.29508	−	1.14071i	0.212484	−	0.0457750i
$622$	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
$626$	−14.1091	−	15.5248i	−0.563914	−	0.620494i
$627$	2.85380	−	9.98688i	0.113970	−	0.398837i
$628$	2.03661	−	21.2681i	0.0812697	−	0.848689i
$629$		−	6.28769i		−	0.250707i
$630$	−25.4432	−	17.0339i	−1.01368	−	0.678646i
$631$		−	10.7225i		−	0.426856i	−0.976959	−	0.213428i	$-0.931537\pi$
$631$		−	10.7225i		−	0.426856i	0.976959	−	0.213428i	$-0.0684629\pi$
$632$	−30.6501	+	3.65216i	−1.21920	+	0.145275i
$633$	8.54934	−	29.9184i	0.339806	−	1.18915i
$634$	8.68914	−	7.89682i	0.345090	−	0.313623i
$635$	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
$639$	14.0794	+	8.76201i	0.556973	+	0.346620i
$640$	13.4584	+	27.7716i	0.531990	+	1.09777i
$641$	−20.7630	+	11.9875i	−0.820089	+	0.473479i	−0.850447	−	0.526060i	$-0.823669\pi$
$641$	−20.7630	+	11.9875i	−0.820089	+	0.473479i	0.0303581	+	0.999539i	$0.490335\pi$
$642$	19.0334	+	38.4815i	0.751187	+	1.51875i
$643$			24.5118i			0.966649i	0.875441	+	0.483325i	$0.160571\pi$
$643$			24.5118i			0.966649i	−0.875441	+	0.483325i	$0.839429\pi$
$644$	−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	−0.894754	−	0.446559i	$-0.852649\pi$
$647$	−21.2165	−	36.7481i	−0.834108	−	1.44472i	0.0606458	−	0.998159i	$-0.480684\pi$
$648$	−22.6823	−	11.5548i	−0.891045	−	0.453915i
$649$	−3.55767	+	6.16207i	−0.139651	+	0.241882i
$650$	−14.9766	+	3.25585i	−0.587430	+	0.127705i
$651$	−12.3037	−	7.13772i	−0.482219	−	0.279749i
$652$	17.0043	+	37.2608i	0.665941	+	1.45924i
$653$	18.5142	+	10.6892i	0.724517	+	0.418300i	0.816413	−	0.577469i	$-0.195959\pi$
$653$	18.5142	+	10.6892i	0.724517	+	0.418300i	−0.0918961	+	0.995769i	$0.529293\pi$
$654$	−1.56193	−	0.100527i	−0.0610762	−	0.00393092i
$655$	−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	$-0.494819\pi$
$659$	0.835578			0.0325495			0.0162748	+	0.999868i	$0.494819\pi$
$660$	−15.0703	+	12.0229i	−0.586611	+	0.467992i
$661$	−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	$0.947201\pi$
$662$	−15.9800	+	14.5229i	−0.621080	+	0.564447i
$663$	−4.92780	+	1.23343i	−0.191380	+	0.0479024i
$664$	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
$668$	36.5860	+	26.0676i	1.41555	+	1.00858i
$669$	−0.931567	+	3.26002i	−0.0360164	+	0.126039i
$670$	−5.59886	+	17.5066i	−0.216303	+	0.676341i
$671$	0.404830			0.0156283
$672$	13.4311	+	22.1722i	0.518116	+	0.855310i
$673$	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
$675$	−3.88567	+	12.0715i	−0.149559	+	0.464633i
$676$	−10.9434	−	7.79716i	−0.420899	−	0.299891i
$677$	−31.9197	−	18.4288i	−1.22677	−	0.708278i	−0.260420	−	0.965495i	$-0.583861\pi$
$677$	−31.9197	−	18.4288i	−1.22677	−	0.708278i	−0.966354	+	0.257217i	$0.917194\pi$
$678$	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
$681$	7.63912	+	30.5198i	0.292732	+	1.16952i
$682$	−6.62783	+	6.02347i	−0.253793	+	0.230651i
$683$	−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	$0.860077\pi$
$684$	−2.26068	+	17.4898i	−0.0864392	+	0.668738i
$685$	−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
$690$	−0.447346	+	6.95059i	−0.0170302	+	0.264605i
$691$	34.8657	+	20.1297i	1.32635	+	0.765771i	0.984734	−	0.174067i	$-0.0556910\pi$
$691$	34.8657	+	20.1297i	1.32635	+	0.765771i	0.341620	+	0.939838i	$0.389024\pi$
$692$	−16.1338	−	35.3532i	−0.613315	−	1.34393i
$693$	−11.6621	+	11.2357i	−0.443005	+	0.426808i
$694$	−30.4807	+	6.62639i	−1.15703	+	0.251534i
$695$	7.88678	−	13.6603i	0.299163	−	0.518165i
$696$	3.60421	+	9.46448i	0.136617	+	0.358750i
$697$	−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	$-0.161575\pi$
$702$	−29.7115	+	13.4917i	−1.12139	+	0.509211i
$703$	−24.2327	+	13.9908i	−0.913954	+	0.527672i
$704$	15.8650	−	3.83528i	0.597934	−	0.144548i
$705$	4.77760	−	1.19583i	0.179935	−	0.0450377i
$706$	−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	$0.257604\pi$
$710$	−15.7805	+	14.3416i	−0.592232	+	0.538230i
$711$	15.4231	+	28.8789i	0.578410	+	1.08305i
$712$	−1.52011	+	0.181131i	−0.0569687	+	0.00678818i
$713$			3.23563i			0.121175i
$714$	3.17359	−	2.87217i	0.118769	−	0.107488i
$715$			24.7128i			0.924207i
$716$	0.959663	−	10.0216i	0.0358643	−	0.374526i
$717$	−28.2011	−	8.05862i	−1.05319	−	0.300955i
$718$	−13.7383	−	15.1167i	−0.512709	−	0.564151i
$719$	−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
$723$	−2.45497	−	9.80809i	−0.0913012	−	0.364767i
$724$	−9.31452	−	6.63661i	−0.346172	−	0.246648i
$725$	4.36934	−	2.52264i	0.162273	−	0.0936885i
$726$	−7.42519	−	15.0122i	−0.275575	−	0.557155i
$727$		−	50.3452i		−	1.86720i	−0.358318	−	0.933600i	$-0.616650\pi$
$727$		−	50.3452i		−	1.86720i	0.358318	−	0.933600i	$-0.383350\pi$
$728$	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
$732$	−0.679657	+	0.102576i	−0.0251208	+	0.00379133i
$733$	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
$735$	23.0943	−	23.6731i	0.851846	−	0.873195i
$736$	2.82951	−	5.17360i	0.104297	−	0.190701i
$737$	8.41869	+	4.86053i	0.310107	+	0.179040i
$738$	−21.5966	−	25.4029i	−0.794981	−	0.935094i
$739$	5.42182	−	3.13029i	0.199445	−	0.115150i	−0.396952	−	0.917840i	$-0.629932\pi$
$739$	5.42182	−	3.13029i	0.199445	−	0.115150i	0.596397	+	0.802690i	$0.296599\pi$
$740$	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	$-0.716330\pi$
$743$	−34.2633			−1.25700			−0.628498	+	0.777811i	$0.716330\pi$
$744$	9.60104	−	11.7920i	0.351991	−	0.432316i
$745$	18.8972	+	32.7310i	0.692341	+	1.19917i
$746$	18.5664	+	20.4293i	0.679765	+	0.747968i
$747$	−23.3280	−	14.5176i	−0.853525	−	0.531172i
$748$	−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	0.882661	−	0.470010i	$-0.155750\pi$
$751$	25.1285	+	14.5079i	0.916952	+	0.529402i	0.0342903	+	0.999412i	$0.489083\pi$
$752$	−4.09389	−	0.791312i	−0.149289	−	0.0288562i
$753$	16.8984	+	4.82881i	0.615813	+	0.175972i
$754$	12.3653	+	3.95457i	0.450316	+	0.144017i
$755$	32.1142			1.16876
$756$	16.7322	−	21.8182i	0.608544	−	0.793520i
$757$	−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
$759$	3.54193	+	1.01213i	0.128564	+	0.0367378i
$760$	−20.8421	−	8.93505i	−0.756024	−	0.324108i
$761$	33.6645	+	19.4362i	1.22034	+	0.704563i	0.964990	−	0.262287i	$-0.0844766\pi$
$761$	33.6645	+	19.4362i	1.22034	+	0.704563i	0.255348	+	0.966849i	$0.417810\pi$
$762$	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
$765$	−4.58871	−	2.85568i	−0.165905	−	0.103247i
$766$	−7.81403	−	8.59804i	−0.282332	−	0.310660i
$767$	−7.74320	−	13.4116i	−0.279591	−	0.484265i
$768$	−25.6635	+	10.4588i	−0.926050	+	0.377400i
$769$	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	$-0.837743\pi$
$773$	−24.6534	+	14.2336i	−0.886720	+	0.511948i	−0.0138518	+	0.999904i	$0.504409\pi$
$774$	−1.45802	−	1.71499i	−0.0524074	−	0.0616441i
$775$	−6.56049	−	3.78770i	−0.235660	−	0.136058i
$776$	15.6665	−	11.7180i	0.562395	−	0.420651i
$777$	43.6264	+	0.0908036i	1.56509	+	0.00325756i
$778$	−1.44055	−	6.62639i	−0.0516463	−	0.237568i
$779$	−11.5495	+	20.0043i	−0.413803	+	0.716728i
$780$	−6.26176	−	41.4896i	−0.224207	−	1.48557i
$781$	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
$786$	−24.0602	−	48.6448i	−0.858199	−	1.73510i
$787$	−27.6598	+	15.9694i	−0.985964	+	0.569247i	−0.904065	−	0.427394i	$-0.859432\pi$
$787$	−27.6598	+	15.9694i	−0.985964	+	0.569247i	−0.0818987	+	0.996641i	$0.526098\pi$
$788$	−12.8011	+	17.9664i	−0.456019	+	0.640026i
$789$	6.07454	+	24.2690i	0.216259	+	0.864000i
$790$	−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
$794$	9.89303	+	10.8856i	0.351091	+	0.386317i
$795$	48.0924	+	13.7427i	1.70566	+	0.487402i
$796$	−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	$-0.232971\pi$
$798$	−18.1309	−	5.84013i	−0.641827	−	0.206738i
$799$			0.688481i			0.0243567i
$800$	7.17759	+	11.7934i	0.253766	+	0.416959i
$801$	0.764918	+	1.43227i	0.0270270	+	0.0506068i
$802$	12.1104	−	11.0061i	0.427632	−	0.388639i
$803$	−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
$807$	11.0412	−	2.76362i	0.388670	−	0.0972841i
$808$	−11.2909	+	26.3374i	−0.397211	+	0.926545i
$809$	22.6957	−	13.1034i	0.797938	−	0.460690i	−0.0448118	−	0.998995i	$-0.514269\pi$
$809$	22.6957	−	13.1034i	0.797938	−	0.460690i	0.842750	+	0.538306i	$0.180935\pi$
$810$	−32.2970	−	12.7386i	−1.13480	−	0.447588i
$811$			32.1734i			1.12976i	0.825172	+	0.564881i	$0.191078\pi$
$811$			32.1734i			1.12976i	−0.825172	+	0.564881i	$0.808922\pi$
$812$	−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
$816$	2.49972	+	3.83272i	0.0875077	+	0.134172i
$817$	−0.779724	+	1.35052i	−0.0272791	+	0.0472488i
$818$	−28.2426	+	6.13983i	−0.987479	+	0.214674i
$819$	−8.48684	−	34.2088i	−0.296554	−	1.19535i
$820$	39.0043	−	17.8000i	1.36209	−	0.621604i
$821$	−19.3857	−	11.1923i	−0.676565	−	0.390615i	0.121994	−	0.992531i	$-0.461071\pi$
$821$	−19.3857	−	11.1923i	−0.676565	−	0.390615i	−0.798560	+	0.601916i	$0.794404\pi$
$822$	2.28189	−	35.4547i	0.0795901	−	1.23662i
$823$	28.4876	−	16.4473i	0.993014	−	0.573317i	0.0868401	−	0.996222i	$-0.472323\pi$
$823$	28.4876	−	16.4473i	0.993014	−	0.573317i	0.906174	+	0.422905i	$0.138990\pi$
$824$	−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	$-0.405963\pi$
$827$	16.7455			0.582297			0.291148	+	0.956678i	$0.405963\pi$
$828$	−6.20290	−	0.801769i	−0.215566	−	0.0278634i
$829$	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	$0.828091\pi$
$830$	26.1465	−	23.7623i	0.907557	−	0.824802i
$831$	7.70201	+	30.7711i	0.267180	+	1.06744i
$832$	−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
$836$	−6.95950	+	9.76770i	−0.240699	+	0.337823i
$837$	−15.3529	−	4.94191i	−0.530675	−	0.170818i
$838$	9.43988	−	29.5169i	0.326095	−	1.01964i
$839$	35.5384			1.22692			0.613461	−	0.789725i	$-0.289777\pi$
$839$	35.5384			1.22692			0.613461	+	0.789725i	$0.289777\pi$
$840$	21.1174	+	28.3561i	0.728620	+	0.978378i
$841$	24.7264			0.852634
$842$	6.08074	−	19.0134i	0.209556	−	0.655246i
$843$	0.767094	−	2.68445i	0.0264201	−	0.0924572i
$844$	−20.8491	+	29.2618i	−0.717654	+	1.00723i
$845$	−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
$849$	−34.5696	+	8.65278i	−1.18643	+	0.296963i
$850$	1.68698	−	1.53315i	0.0578629	−	0.0525867i
$851$	−4.96194	−	8.59434i	−0.170093	−	0.294610i
$852$	−11.9419	−	14.9687i	−0.409122	−	0.512819i
$853$	−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	$-0.891900\pi$
$857$	−32.9586	+	19.0286i	−1.12584	+	0.650006i	−0.182957	+	0.983121i	$0.558567\pi$
$858$	−22.1461	−	1.42534i	−0.756056	−	0.0486604i
$859$	−18.6659	−	10.7768i	−0.636873	−	0.367699i	0.146536	−	0.989205i	$-0.453188\pi$
$859$	−18.6659	−	10.7768i	−0.636873	−	0.367699i	−0.783409	+	0.621507i	$0.786521\pi$
$860$	2.63325	−	1.20171i	0.0897929	−	0.0409779i
$861$	31.2264	−	17.9420i	1.06419	−	0.611463i
$862$	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	$-0.0197439\pi$
$864$	20.2269	+	21.3277i	0.688133	+	0.725585i
$865$	−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
$870$	6.12374	+	12.3809i	0.207614	+	0.419753i
$871$	−18.3231	+	10.5788i	−0.620855	+	0.358451i
$872$	1.66108	+	0.712109i	0.0562514	+	0.0241151i
$873$	−17.6177	−	10.9640i	−0.596270	−	0.371075i
$874$	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	$0.00876138\pi$
$878$	−19.2395	+	17.4851i	−0.649301	+	0.590095i
$879$	−5.54764	+	19.4139i	−0.187117	+	0.654816i
$880$	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	$-0.0312205\pi$
$882$	19.8824	+	22.0611i	0.669475	+	0.742835i
$883$		−	47.2938i		−	1.59156i	−0.605583	−	0.795782i	$-0.707060\pi$
$883$		−	47.2938i		−	1.59156i	0.605583	−	0.795782i	$-0.292940\pi$
$884$	5.83896	+	0.559134i	0.196385	+	0.0188057i
$885$	4.52716	−	15.8428i	0.152179	−	0.532550i
$886$	7.86485	+	8.65396i	0.264225	+	0.290736i
$887$	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
$891$	−10.2122	+	15.2604i	−0.342123	+	0.511244i
$892$	2.27179	−	3.18847i	0.0760651	−	0.106758i
$893$	2.65340	−	1.53194i	0.0887927	−	0.0512645i
$894$	−30.4214	+	15.0467i	−1.01744	+	0.503239i
$895$		−	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
$900$	8.88690	−	11.6383i	0.296230	−	0.387943i
$901$	−3.49606	+	6.05535i	−0.116470	+	0.201733i
$902$	−4.81707	−	22.1580i	−0.160391	−	0.737782i
$903$	2.10815	−	1.21130i	0.0701547	−	0.0403094i
$904$	−18.2823	−	24.4428i	−0.608060	−	0.812954i
$905$	−13.5088	−	7.79928i	−0.449046	−	0.259257i
$906$	−1.85223	+	28.7788i	−0.0615362	+	0.956111i
$907$	36.9772	−	21.3488i	1.22781	−	0.708874i	0.261236	−	0.965275i	$-0.415870\pi$
$907$	36.9772	−	21.3488i	1.22781	−	0.708874i	0.966571	+	0.256401i	$0.0825366\pi$
$908$	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	$-0.748386\pi$
$911$	−42.4679			−1.40702			−0.703511	+	0.710684i	$0.748386\pi$
$912$	9.20915	−	18.1621i	0.304945	−	0.601408i
$913$	−9.34312	−	16.1828i	−0.309212	−	0.535571i
$914$	−17.7774	−	19.5611i	−0.588026	−	0.647024i
$915$	−0.909406	+	0.227625i	−0.0300640	+	0.00752504i
$916$	−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	0.165278	−	0.986247i	$-0.447148\pi$
$919$	−18.3769	−	10.6099i	−0.606199	−	0.349989i	−0.771476	+	0.636258i	$0.780481\pi$
$920$	3.16889	−	7.39184i	0.104475	−	0.243702i
$921$	−1.74196	+	6.09597i	−0.0573994	+	0.200869i
$922$	−22.0456	−	7.05049i	−0.726035	−	0.232195i
$923$	−24.5462			−0.807948
$924$	17.0276	−	7.72793i	0.560166	−	0.254230i
$925$	23.2342			0.763937
$926$	−15.3077	−	4.89560i	−0.503042	−	0.160879i
$927$	10.3475	+	19.3752i	0.339856	+	0.636364i
$928$	−0.270454	−	11.6911i	−0.00887809	−	0.383780i
$929$	−23.4266	−	13.5254i	−0.768603	−	0.443753i	0.0637729	−	0.997964i	$-0.479687\pi$
$929$	−23.4266	−	13.5254i	−0.768603	−	0.443753i	−0.832376	+	0.554211i	$0.813020\pi$
$930$	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
$933$	4.94050	+	19.7383i	0.161745	+	0.646203i
$934$	34.5206	+	37.9841i	1.12955	+	1.24288i
$935$	−1.83783	−	3.18322i	−0.0601035	−	0.104102i
$936$	37.5416	−	3.21844i	1.22709	−	0.105198i
$937$	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	$-0.751004\pi$
$941$	−13.9134	+	8.03288i	−0.453563	+	0.261864i	0.255771	+	0.966737i	$0.417671\pi$
$942$	26.1131	+	1.68066i	0.850810	+	0.0547589i
$943$	−7.09469	−	4.09612i	−0.231035	−	0.133388i
$944$	−9.14094	+	10.5378i	−0.297512	+	0.342976i
$945$	19.8801	−	31.7970i	0.646698	−	1.03436i
$946$	−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	$0.0301825\pi$
$948$	−5.64165	−	37.3808i	−0.183232	−	1.21407i
$949$	−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	$0.867206\pi$
$954$	−15.0891	+	42.3048i	−0.488528	+	1.36967i
$955$	−23.1860	+	13.3865i	−0.750283	+	0.433176i
$956$	27.5822	+	19.6523i	0.892072	+	0.635602i
$957$	7.08672	−	1.77381i	0.229081	−	0.0573391i
$958$	−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
$962$	40.2091	+	44.2434i	1.29639	+	1.42646i
$963$	−46.3800	+	24.7697i	−1.49458	+	0.798192i
$964$	−1.11288	+	11.6216i	−0.0358434	+	0.374307i
$965$			46.8054i			1.50672i
$966$	2.07125	−	6.43028i	0.0666414	−	0.206891i
$967$			25.4408i			0.818122i	0.912507	+	0.409061i	$0.134144\pi$
$967$			25.4408i			0.818122i	−0.912507	+	0.409061i	$0.865856\pi$
$968$	2.28819	+	19.2032i	0.0735452	+	0.617215i
$969$	−3.23294	−	0.923830i	−0.103857	−	0.0296777i
$970$	19.7463	−	17.9458i	0.634017	−	0.576204i
$971$	−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
$975$	−4.55776	−	18.2092i	−0.145965	−	0.583160i
$976$	0.779264	+	0.150625i	0.0249436	+	0.00482138i
$977$	−4.46235	+	2.57634i	−0.142763	+	0.0824244i	−0.569680	−	0.821866i	$-0.692933\pi$
$977$	−4.46235	+	2.57634i	−0.142763	+	0.0824244i	0.426917	+	0.904291i	$0.359600\pi$
$978$	−44.9631	+	22.2392i	−1.43776	+	0.711132i
$979$			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	−0.999846	−	0.0175745i	$-0.994406\pi$
$983$	−16.1512	−	27.9747i	−0.515143	−	0.892253i	0.484703	−	0.874679i	$-0.338928\pi$
$984$	13.7017	+	35.9800i	0.436794	+	1.14700i
$985$	−15.0437	+	26.0565i	−0.479332	+	0.830228i
$986$	−1.88684	+	0.410192i	−0.0600893	+	0.0130632i
$987$	−4.77694	−	0.00994270i	−0.152052	−	0.000316479i
$988$	−10.8374	−	23.7474i	−0.344783	−	0.755507i
$989$	−0.478974	−	0.276536i	−0.0152305	−	0.00879332i
$990$	−15.2936	−	17.9890i	−0.486061	−	0.571728i
$991$	2.23686	−	1.29145i	0.0710563	−	0.0410244i	−0.464051	−	0.885809i	$-0.653605\pi$
$991$	2.23686	−	1.29145i	0.0710563	−	0.0410244i	0.535107	+	0.844784i	$0.320271\pi$
$992$	−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
$996$	19.7863	+	24.8014i	0.626953	+	0.785862i
$997$	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	$0.596245\pi$
$998$	−20.7671	+	18.8735i	−0.657371	+	0.597429i
$999$	48.3584	−	10.4177i	1.52999	−	0.329602i

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(0.430790 - 1.34700i) q^{2} +(1.66539 + 0.475894i) q^{3} +(-1.62884 - 1.16055i) q^{4} +(-2.36229 - 1.36387i) q^{5} +(1.35846 - 2.03828i) q^{6} +(1.89768 + 1.84359i) q^{7} +(-2.26495 + 1.69410i) q^{8} +(2.54705 + 1.58510i) q^{9} +O(q^{10})\)	\(q+(0.430790 - 1.34700i) q^{2} +(1.66539 + 0.475894i) q^{3} +(-1.62884 - 1.16055i) 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} +(2.54705 + 1.58510i) q^{9} +(-2.85479 + 2.59447i) q^{10} +(1.02012 + 1.76690i) q^{11} +(-2.16036 - 2.70793i) 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} +(3.23238 - 2.74804i) q^{18} +(-2.54543 - 1.46961i) q^{19} +(2.26495 + 4.96308i) q^{20} +(2.28302 + 3.97339i) q^{21} +(2.81949 - 0.612946i) q^{22} +(0.521208 - 0.902759i) q^{23} +(-4.57825 + 1.74346i) 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} +(-5.98903 + 2.96224i) q^{30} +(-2.68812 + 1.55199i) q^{31} +(5.65534 - 0.130827i) q^{32} +(0.858043 + 3.42806i) 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} +(-3.07611 + 2.79562i) q^{38} +(-7.39525 - 2.11323i) q^{39} +(7.66101 - 0.912859i) q^{40} -7.85889i q^{41} +(6.33567 - 1.36355i) q^{42} -0.530567i q^{43} +(0.388965 - 4.06191i) q^{44} +(-3.85500 - 7.21830i) q^{45} +(-0.991489 - 1.09097i) 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} +(1.10973 - 0.277765i) q^{51} +(7.23295 + 5.15349i) q^{52} +(-9.16829 + 5.29332i) q^{53} +(6.69095 - 3.03829i) 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} +(1.41013 + 9.34335i) q^{60} +(0.0992110 - 0.171839i) q^{61} +(0.932518 + 4.28949i) q^{62} +(1.91121 + 7.70372i) q^{63} +(2.26004 - 7.67413i) q^{64} +(10.4899 + 6.05633i) q^{65} +(4.98724 + 0.320983i) 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} +(-8.45427 + 0.724784i) q^{72} +(1.51791 + 2.62910i) q^{73} +(-9.05497 - 9.96349i) q^{74} +(1.02640 + 4.10066i) 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} +(2.07066 - 10.7127i) q^{80} +(3.97492 + 8.07465i) q^{81} +(-10.5860 - 3.38553i) q^{82} -9.15881 q^{83} +(0.892639 - 9.12158i) q^{84} -1.80158 q^{85} +(-0.714675 - 0.228563i) q^{86} +(0.983802 - 3.44281i) q^{87} +(-5.30385 - 2.27377i) 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} +(-5.21535 + 1.30540i) q^{93} +(0.991489 + 1.09097i) q^{94} +(4.00870 + 6.94327i) q^{95} +(9.48061 + 2.47347i) 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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