LMFDB - Embedded newform 84.2.n.a.11.9

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			11.9
Character	$\chi$	$=$	84.11
Dual form			84.2.n.a.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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

Twists

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

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

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