LMFDB - Embedded newform 185.2.e.a.121.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(26,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 86 x^{10} - 18 x^{9} + 332 x^{8} - 110 x^{7} + 935 x^{6} - 290 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 86x^10 - 18x^9 + 332x^8 - 110x^7 + 935x^6 - 290x^5 + 985x^4 - 441x^3 + 792x^2 - 243x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.6
Root			$0.985880 + 1.70759i$ of defining polynomial
Character	$\chi$	$=$	185.121
Dual form			185.2.e.a.26.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.985880 - 1.70759i) q^{2} +(1.32465 + 2.29437i) q^{3} +(-0.943918 - 1.63491i) q^{4} +(-0.500000 - 0.866025i) q^{5} +5.22380 q^{6} +(-0.391800 - 0.678617i) q^{7} +0.221160 q^{8} +(-2.00941 + 3.48041i) q^{9} -1.97176 q^{10} -0.568551 q^{11} +(2.50073 - 4.33139i) q^{12} +(0.00305561 + 0.00529246i) q^{13} -1.54507 q^{14} +(1.32465 - 2.29437i) q^{15} +(2.10587 - 3.64748i) q^{16} +(-1.48282 + 2.56833i) q^{17} +(3.96208 + 6.86253i) q^{18} +(-0.517765 - 0.896796i) q^{19} +(-0.943918 + 1.63491i) q^{20} +(1.03800 - 1.79787i) q^{21} +(-0.560523 + 0.970854i) q^{22} -8.65194 q^{23} +(0.292960 + 0.507422i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.0120498 q^{26} -2.69919 q^{27} +(-0.739654 + 1.28112i) q^{28} -4.06655 q^{29} +(-2.61190 - 4.52394i) q^{30} -9.38666 q^{31} +(-3.93112 - 6.80889i) q^{32} +(-0.753133 - 1.30446i) q^{33} +(2.92377 + 5.06412i) q^{34} +(-0.391800 + 0.678617i) q^{35} +7.58689 q^{36} +(5.80482 - 1.81772i) q^{37} -2.04182 q^{38} +(-0.00809524 + 0.0140214i) q^{39} +(-0.110580 - 0.191530i) q^{40} +(2.06584 + 3.57814i) q^{41} +(-2.04668 - 3.54496i) q^{42} +7.06722 q^{43} +(0.536666 + 0.929532i) q^{44} +4.01883 q^{45} +(-8.52978 + 14.7740i) q^{46} +5.52310 q^{47} +11.1582 q^{48} +(3.19299 - 5.53041i) q^{49} +(0.985880 + 1.70759i) q^{50} -7.85691 q^{51} +(0.00576848 - 0.00999130i) q^{52} +(4.57125 - 7.91765i) q^{53} +(-2.66107 + 4.60911i) q^{54} +(0.284276 + 0.492380i) q^{55} +(-0.0866504 - 0.150083i) q^{56} +(1.37172 - 2.37589i) q^{57} +(-4.00913 + 6.94402i) q^{58} +(-4.62211 + 8.00573i) q^{59} -5.00146 q^{60} +(4.99164 + 8.64577i) q^{61} +(-9.25412 + 16.0286i) q^{62} +3.14915 q^{63} -7.07894 q^{64} +(0.00305561 - 0.00529246i) q^{65} -2.96999 q^{66} +(5.67853 + 9.83551i) q^{67} +5.59866 q^{68} +(-11.4608 - 19.8507i) q^{69} +(0.772535 + 1.33807i) q^{70} +(-1.96400 - 3.40174i) q^{71} +(-0.444402 + 0.769726i) q^{72} +16.5499 q^{73} +(2.61893 - 11.7043i) q^{74} -2.64931 q^{75} +(-0.977456 + 1.69300i) q^{76} +(0.222758 + 0.385829i) q^{77} +(0.0159619 + 0.0276468i) q^{78} +(-5.45167 - 9.44257i) q^{79} -4.21175 q^{80} +(2.45275 + 4.24830i) q^{81} +8.14668 q^{82} +(-0.430541 + 0.745719i) q^{83} -3.91914 q^{84} +2.96565 q^{85} +(6.96743 - 12.0679i) q^{86} +(-5.38677 - 9.33017i) q^{87} -0.125741 q^{88} +(0.143625 - 0.248765i) q^{89} +(3.96208 - 6.86253i) q^{90} +(0.00239437 - 0.00414717i) q^{91} +(8.16673 + 14.1452i) q^{92} +(-12.4341 - 21.5364i) q^{93} +(5.44512 - 9.43122i) q^{94} +(-0.517765 + 0.896796i) q^{95} +(10.4147 - 18.0388i) q^{96} -4.33052 q^{97} +(-6.29580 - 10.9046i) q^{98} +(1.14245 - 1.97879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.985880	−	1.70759i	0.697122	−	1.20745i	−0.272338	−	0.962202i	$-0.587797\pi$
$2$	0.985880	−	1.70759i	0.697122	−	1.20745i	0.969460	−	0.245250i	$-0.0788699\pi$
$3$	1.32465	+	2.29437i	0.764789	+	1.32465i	0.940358	+	0.340186i	$0.110490\pi$
$3$	1.32465	+	2.29437i	0.764789	+	1.32465i	−0.175569	+	0.984467i	$0.556177\pi$
$4$	−0.943918	−	1.63491i	−0.471959	−	0.817457i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	5.22380			2.13261
$7$	−0.391800	−	0.678617i	−0.148086	−	0.256493i	0.782434	−	0.622734i	$-0.213978\pi$
$7$	−0.391800	−	0.678617i	−0.148086	−	0.256493i	−0.930520	+	0.366241i	$0.880645\pi$
$8$	0.221160			0.0781918
$9$	−2.00941	+	3.48041i	−0.669805	+	1.16014i
$10$	−1.97176			−0.623525
$11$	−0.568551			−0.171425			−0.0857123	−	0.996320i	$-0.527317\pi$
$11$	−0.568551			−0.171425			−0.0857123	+	0.996320i	$0.527317\pi$
$12$	2.50073	−	4.33139i	0.721898	−	1.25036i
$13$	0.00305561	+	0.00529246i	0.000847472	+	0.00146787i	0.866449	−	0.499266i	$-0.166397\pi$
$13$	0.00305561	+	0.00529246i	0.000847472	+	0.00146787i	−0.865601	+	0.500734i	$0.833064\pi$
$14$	−1.54507			−0.412937
$15$	1.32465	−	2.29437i	0.342024	−	0.592403i
$16$	2.10587	−	3.64748i	0.526468	−	0.911870i
$17$	−1.48282	+	2.56833i	−0.359638	+	0.622911i	−0.987900	−	0.155091i	$-0.950433\pi$
$17$	−1.48282	+	2.56833i	−0.359638	+	0.622911i	0.628263	+	0.778001i	$0.283766\pi$
$18$	3.96208	+	6.86253i	0.933871	+	1.61751i
$19$	−0.517765	−	0.896796i	−0.118783	−	0.205739i	0.800502	−	0.599330i	$-0.204566\pi$
$19$	−0.517765	−	0.896796i	−0.118783	−	0.205739i	−0.919286	+	0.393591i	$0.871233\pi$
$20$	−0.943918	+	1.63491i	−0.211067	+	0.365578i
$21$	1.03800	−	1.79787i	0.226510	−	0.392326i
$22$	−0.560523	+	0.970854i	−0.119504	+	0.206987i
$23$	−8.65194			−1.80405			−0.902027	−	0.431679i	$-0.857921\pi$
$23$	−8.65194			−1.80405			−0.902027	+	0.431679i	$0.857921\pi$
$24$	0.292960	+	0.507422i	0.0598003	+	0.103577i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.0120498			0.00236317
$27$	−2.69919			−0.519459
$28$	−0.739654	+	1.28112i	−0.139781	+	0.242109i
$29$	−4.06655			−0.755140			−0.377570	−	0.925981i	$-0.623240\pi$
$29$	−4.06655			−0.755140			−0.377570	+	0.925981i	$0.623240\pi$
$30$	−2.61190	−	4.52394i	−0.476865	−	0.825955i
$31$	−9.38666			−1.68589			−0.842947	−	0.537997i	$-0.819181\pi$
$31$	−9.38666			−1.68589			−0.842947	+	0.537997i	$0.819181\pi$
$32$	−3.93112	−	6.80889i	−0.694930	−	1.20365i
$33$	−0.753133	−	1.30446i	−0.131104	−	0.227078i
$34$	2.92377	+	5.06412i	0.501423	+	0.868490i
$35$	−0.391800	+	0.678617i	−0.0662263	+	0.114707i
$36$	7.58689			1.26448
$37$	5.80482	−	1.81772i	0.954306	−	0.298831i
$37$	5.80482	−	1.81772i	0.954306	−	0.298831i
$38$	−2.04182			−0.331227
$39$	−0.00809524	+	0.0140214i	−0.00129628	+	0.00224521i
$40$	−0.110580	−	0.191530i	−0.0174842	−	0.0302836i
$41$	2.06584	+	3.57814i	0.322630	+	0.558811i	0.981030	−	0.193857i	$-0.0620997\pi$
$41$	2.06584	+	3.57814i	0.322630	+	0.558811i	−0.658400	+	0.752668i	$0.728766\pi$
$42$	−2.04668	−	3.54496i	−0.315810	−	0.546999i
$43$	7.06722			1.07774			0.538870	−	0.842389i	$-0.318851\pi$
$43$	7.06722			1.07774			0.538870	+	0.842389i	$0.318851\pi$
$44$	0.536666	+	0.929532i	0.0809054	+	0.140132i
$45$	4.01883			0.599091
$46$	−8.52978	+	14.7740i	−1.25765	+	2.17831i
$47$	5.52310			0.805628			0.402814	−	0.915282i	$-0.368032\pi$
$47$	5.52310			0.805628			0.402814	+	0.915282i	$0.368032\pi$
$48$	11.1582			1.61055
$49$	3.19299	−	5.53041i	0.456141	−	0.790059i
$50$	0.985880	+	1.70759i	0.139424	+	0.241490i
$51$	−7.85691			−1.10019
$52$	0.00576848	−	0.00999130i	0.000799945	−	0.00138554i
$53$	4.57125	−	7.91765i	0.627910	−	1.08757i	−0.360060	−	0.932929i	$-0.617244\pi$
$53$	4.57125	−	7.91765i	0.627910	−	1.08757i	0.987970	−	0.154643i	$-0.0494228\pi$
$54$	−2.66107	+	4.60911i	−0.362126	+	0.627221i
$55$	0.284276	+	0.492380i	0.0383317	+	0.0663925i
$56$	−0.0866504	−	0.150083i	−0.0115792	−	0.0200557i
$57$	1.37172	−	2.37589i	0.181689	−	0.314694i
$58$	−4.00913	+	6.94402i	−0.526425	+	0.911795i
$59$	−4.62211	+	8.00573i	−0.601747	+	1.04226i	0.390809	+	0.920472i	$0.372195\pi$
$59$	−4.62211	+	8.00573i	−0.601747	+	1.04226i	−0.992556	+	0.121785i	$0.961138\pi$
$60$	−5.00146			−0.645685
$61$	4.99164	+	8.64577i	0.639114	+	1.10698i	0.985628	+	0.168933i	$0.0540321\pi$
$61$	4.99164	+	8.64577i	0.639114	+	1.10698i	−0.346514	+	0.938045i	$0.612635\pi$
$62$	−9.25412	+	16.0286i	−1.17527	+	2.03563i
$63$	3.14915			0.396756
$64$	−7.07894			−0.884867
$65$	0.00305561	−	0.00529246i	0.000379001	−	0.000656449i
$66$	−2.96999			−0.365581
$67$	5.67853	+	9.83551i	0.693743	+	1.20160i	0.970602	+	0.240688i	$0.0773731\pi$
$67$	5.67853	+	9.83551i	0.693743	+	1.20160i	−0.276859	+	0.960911i	$0.589294\pi$
$68$	5.59866			0.678937
$69$	−11.4608	−	19.8507i	−1.37972	−	2.38975i
$70$	0.772535	+	1.33807i	0.0923356	+	0.159930i
$71$	−1.96400	−	3.40174i	−0.233084	−	0.403713i	0.725630	−	0.688085i	$-0.241548\pi$
$71$	−1.96400	−	3.40174i	−0.233084	−	0.403713i	−0.958714	+	0.284372i	$0.908215\pi$
$72$	−0.444402	+	0.769726i	−0.0523732	+	0.0907131i
$73$	16.5499			1.93701			0.968507	−	0.248987i	$-0.0800975\pi$
$73$	16.5499			1.93701			0.968507	+	0.248987i	$0.0800975\pi$
$74$	2.61893	−	11.7043i	0.304445	−	1.36060i
$75$	−2.64931			−0.305916
$76$	−0.977456	+	1.69300i	−0.112122	+	0.194201i
$77$	0.222758	+	0.385829i	0.0253857	+	0.0439692i
$78$	0.0159619	+	0.0276468i	0.00180732	+	0.00313038i
$79$	−5.45167	−	9.44257i	−0.613361	−	1.06237i	−0.990670	−	0.136284i	$-0.956484\pi$
$79$	−5.45167	−	9.44257i	−0.613361	−	1.06237i	0.377309	−	0.926087i	$-0.376849\pi$
$80$	−4.21175			−0.470888
$81$	2.45275	+	4.24830i	0.272528	+	0.472033i
$82$	8.14668			0.899650
$83$	−0.430541	+	0.745719i	−0.0472580	+	0.0818533i	−0.888687	−	0.458515i	$-0.848382\pi$
$83$	−0.430541	+	0.745719i	−0.0472580	+	0.0818533i	0.841429	+	0.540368i	$0.181715\pi$
$84$	−3.91914			−0.427613
$85$	2.96565			0.321670
$86$	6.96743	−	12.0679i	0.751317	−	1.30132i
$87$	−5.38677	−	9.33017i	−0.577523	−	1.00030i
$88$	−0.125741			−0.0134040
$89$	0.143625	−	0.248765i	0.0152242	−	0.0263691i	−0.858313	−	0.513127i	$-0.828487\pi$
$89$	0.143625	−	0.248765i	0.0152242	−	0.0263691i	0.873537	+	0.486758i	$0.161820\pi$
$90$	3.96208	−	6.86253i	0.417640	−	0.723374i
$91$	0.00239437	−	0.00414717i	0.000250998	−	0.000434742i
$92$	8.16673	+	14.1452i	0.851440	+	1.47474i
$93$	−12.4341	−	21.5364i	−1.28935	−	2.23323i
$94$	5.44512	−	9.43122i	0.561621	−	0.972756i
$95$	−0.517765	+	0.896796i	−0.0531216	+	0.0920093i
$96$	10.4147	−	18.0388i	1.06295	−	1.84108i
$97$	−4.33052			−0.439697			−0.219849	−	0.975534i	$-0.570556\pi$
$97$	−4.33052			−0.439697			−0.219849	+	0.975534i	$0.570556\pi$
$98$	−6.29580	−	10.9046i	−0.635972	−	1.10154i
$99$	1.14245	−	1.97879i	0.114821	−	0.198876i
$100$	1.88784			0.188784
$101$	−5.40523			−0.537840			−0.268920	−	0.963163i	$-0.586667\pi$
$101$	−5.40523			−0.537840			−0.268920	+	0.963163i	$0.586667\pi$
$102$	−7.74597	+	13.4164i	−0.766966	+	1.32842i
$103$	12.2753			1.20952			0.604759	−	0.796409i	$-0.293269\pi$
$103$	12.2753			1.20952			0.604759	+	0.796409i	$0.293269\pi$
$104$	0.000675777		0.00117048i	6.62654e−5		0.000114775i
$105$	−2.07600			−0.202596
$106$	−9.01342	−	15.6117i	−0.875460	−	1.51634i
$107$	−6.84634	−	11.8582i	−0.661860	−	1.14638i	−0.980126	−	0.198374i	$-0.936434\pi$
$107$	−6.84634	−	11.8582i	−0.661860	−	1.14638i	0.318266	−	0.948002i	$-0.396900\pi$
$108$	2.54781	+	4.41294i	0.245163	+	0.424635i
$109$	−3.66237	+	6.34340i	−0.350791	+	0.607588i	−0.986388	−	0.164433i	$-0.947421\pi$
$109$	−3.66237	+	6.34340i	−0.350791	+	0.607588i	0.635597	+	0.772021i	$0.280754\pi$
$110$	1.12105			0.106888
$111$	11.8599	+	10.9105i	1.12569	+	1.03558i
$112$	−3.30032			−0.311851
$113$	2.18762	−	3.78908i	0.205794	−	0.356446i	−0.744591	−	0.667521i	$-0.767356\pi$
$113$	2.18762	−	3.78908i	0.205794	−	0.356446i	0.950386	+	0.311075i	$0.100689\pi$
$114$	−2.70470	−	4.68468i	−0.253318	−	0.438760i
$115$	4.32597	+	7.49280i	0.403399	+	0.698707i
$116$	3.83849	+	6.64847i	0.356395	+	0.617295i
$117$	−0.0245599			−0.00227056
$118$	9.11369	+	15.7854i	0.838983	+	1.45316i
$119$	2.32388			0.213030
$120$	0.292960	−	0.507422i	0.0267435	−	0.0463211i
$121$	−10.6767			−0.970614
$122$	19.6846			1.78216
$123$	−5.47304	+	9.47959i	−0.493488	+	0.854746i
$124$	8.86024	+	15.3464i	0.795673	+	1.37815i
$125$	1.00000			0.0894427
$126$	3.10469	−	5.37747i	0.276587	−	0.479063i
$127$	−9.77590	+	16.9324i	−0.867471	+	1.50250i	−0.00289830	+	0.999996i	$0.500923\pi$
$127$	−9.77590	+	16.9324i	−0.867471	+	1.50250i	−0.864573	+	0.502508i	$0.832411\pi$
$128$	0.883248	−	1.52983i	0.0780689	−	0.135219i
$129$	9.36162	+	16.2148i	0.824244	+	1.42763i
$130$	−0.00602492	−	0.0104355i	−0.000528420	−	0.000915251i
$131$	−4.77698	+	8.27397i	−0.417366	+	0.722900i	−0.995674	−	0.0929193i	$-0.970380\pi$
$131$	−4.77698	+	8.27397i	−0.417366	+	0.722900i	0.578307	+	0.815819i	$0.303713\pi$
$132$	−1.42179	+	2.46262i	−0.123751	+	0.214343i
$133$	−0.405721	+	0.702729i	−0.0351804	+	0.0609343i
$134$	22.3934			1.93450
$135$	1.34959	+	2.33756i	0.116154	+	0.201185i
$136$	−0.327941	+	0.568011i	−0.0281207	+	0.0487065i
$137$	−5.12953			−0.438245			−0.219123	−	0.975697i	$-0.570319\pi$
$137$	−5.12953			−0.438245			−0.219123	+	0.975697i	$0.570319\pi$
$138$	−45.1960			−3.84734
$139$	5.17051	−	8.95559i	0.438557	−	0.759603i	−0.559021	−	0.829153i	$-0.688823\pi$
$139$	5.17051	−	8.95559i	0.438557	−	0.759603i	0.997578	+	0.0695499i	$0.0221563\pi$
$140$	1.47931			0.125024
$141$	7.31620	+	12.6720i	0.616135	+	1.06718i
$142$	−7.74506			−0.649951
$143$	−0.00173727	−	0.00300904i	−0.000145278	−	0.000251628i
$144$	8.46314	+	14.6586i	0.705262	+	1.22155i
$145$	2.03328	+	3.52174i	0.168854	+	0.292465i
$146$	16.3162	−	28.2604i	1.35034	−	2.33885i
$147$	16.9184			1.39541
$148$	−8.45108	−	7.77460i	−0.694675	−	0.639069i
$149$	−10.8779			−0.891149			−0.445575	−	0.895245i	$-0.647001\pi$
$149$	−10.8779			−0.891149			−0.445575	+	0.895245i	$0.647001\pi$
$150$	−2.61190	+	4.52394i	−0.213261	+	0.369378i
$151$	−0.00770952	−	0.0133533i	−0.000627392	−	0.00108667i	0.865712	−	0.500543i	$-0.166866\pi$
$151$	−0.00770952	−	0.0133533i	−0.000627392	−	0.00108667i	−0.866339	+	0.499457i	$0.833533\pi$
$152$	−0.114509	−	0.198335i	−0.00928790	−	0.0160871i
$153$	−5.95921	−	10.3217i	−0.481774	−	0.834457i
$154$	0.878451			0.0707876
$155$	4.69333	+	8.12909i	0.376977	+	0.652944i
$156$	0.0305650			0.00244716
$157$	7.06603	−	12.2387i	0.563930	−	0.976756i	−0.433218	−	0.901289i	$-0.642622\pi$
$157$	7.06603	−	12.2387i	0.563930	−	0.976756i	0.997148	−	0.0754667i	$-0.0240447\pi$
$158$	−21.4988			−1.71035
$159$	24.2213			1.92088
$160$	−3.93112	+	6.80889i	−0.310782	+	0.538290i
$161$	3.38983	+	5.87136i	0.267156	+	0.462728i
$162$	9.67249			0.759942
$163$	−10.6469	+	18.4409i	−0.833926	+	1.44440i	0.0609751	+	0.998139i	$0.480579\pi$
$163$	−10.6469	+	18.4409i	−0.833926	+	1.44440i	−0.894902	+	0.446264i	$0.852754\pi$
$164$	3.89997	−	6.75494i	0.304536	−	0.527472i
$165$	−0.753133	+	1.30446i	−0.0586313	+	0.101552i
$166$	0.848923	+	1.47038i	0.0658892	+	0.114123i
$167$	3.98568	+	6.90340i	0.308421	+	0.534201i	0.978017	−	0.208524i	$-0.0668660\pi$
$167$	3.98568	+	6.90340i	0.308421	+	0.534201i	−0.669596	+	0.742726i	$0.733533\pi$
$168$	0.229564	−	0.397616i	0.0177112	−	0.0306767i
$169$	6.49998	−	11.2583i	0.499999	−	0.866023i
$170$	2.92377	−	5.06412i	0.224243	−	0.388401i
$171$	4.16162			0.318247
$172$	−6.67088	−	11.5543i	−0.508650	−	0.881007i
$173$	7.45671	−	12.9154i	0.566923	−	0.981940i	−0.429945	−	0.902855i	$-0.641467\pi$
$173$	7.45671	−	12.9154i	0.566923	−	0.981940i	0.996868	−	0.0790846i	$-0.0251997\pi$
$174$	−21.2429			−1.61042
$175$	0.783600			0.0592346
$176$	−1.19730	+	2.07378i	−0.0902496	+	0.156317i
$177$	−24.4908			−1.84084
$178$	−0.283193	−	0.490505i	−0.0212262	−	0.0367649i
$179$	−7.73854			−0.578406			−0.289203	−	0.957268i	$-0.593390\pi$
$179$	−7.73854			−0.578406			−0.289203	+	0.957268i	$0.593390\pi$
$180$	−3.79344	−	6.57044i	−0.282747	−	0.489731i
$181$	−6.57794	−	11.3933i	−0.488935	−	0.846859i	0.510984	−	0.859590i	$-0.329281\pi$
$181$	−6.57794	−	11.3933i	−0.488935	−	0.846859i	−0.999919	+	0.0127305i	$0.995948\pi$
$182$	−0.00472113	−	0.00817723i	−0.000349953	−	0.000606137i
$183$	−13.2244	+	22.9053i	−0.977575	+	1.69321i
$184$	−1.91346			−0.141062
$185$	−4.47660	−	4.11826i	−0.329126	−	0.302781i
$186$	−49.0340			−3.59535
$187$	0.843061	−	1.46022i	0.0616507	−	0.106782i
$188$	−5.21336	−	9.02980i	−0.380223	−	0.658566i
$189$	1.05754	+	1.83171i	0.0769248	+	0.133238i
$190$	1.02091	+	1.76827i	0.0740645	+	0.128283i
$191$	23.2461			1.68203			0.841014	−	0.541013i	$-0.181959\pi$
$191$	23.2461			1.68203			0.841014	+	0.541013i	$0.181959\pi$
$192$	−9.37714	−	16.2417i	−0.676737	−	1.17214i
$193$	5.38208			0.387411			0.193705	−	0.981060i	$-0.437949\pi$
$193$	5.38208			0.387411			0.193705	+	0.981060i	$0.437949\pi$
$194$	−4.26937	+	7.39476i	−0.306523	+	0.530913i
$195$	0.0161905			0.00115942
$196$	−12.0557			−0.861119
$197$	0.368609	−	0.638450i	0.0262623	−	0.0454877i	−0.852596	−	0.522571i	$-0.824973\pi$
$197$	0.368609	−	0.638450i	0.0262623	−	0.0454877i	0.878858	+	0.477084i	$0.158306\pi$
$198$	−2.25265	−	3.90170i	−0.160089	−	0.277281i
$199$	3.52332			0.249762			0.124881	−	0.992172i	$-0.460145\pi$
$199$	3.52332			0.249762			0.124881	+	0.992172i	$0.460145\pi$
$200$	−0.110580	+	0.191530i	−0.00781918	+	0.0135432i
$201$	−15.0442	+	26.0573i	−1.06113	+	1.83794i
$202$	−5.32890	+	9.22993i	−0.374940	+	0.649416i
$203$	1.59328	+	2.75963i	0.111826	+	0.193688i
$204$	7.41628	+	12.8454i	0.519244	+	0.899356i
$205$	2.06584	−	3.57814i	0.144285	−	0.249908i
$206$	12.1019	−	20.9612i	0.843182	−	1.46043i
$207$	17.3853	−	30.1123i	1.20836	−	2.09295i
$208$	0.0257389			0.00178467
$209$	0.294376	+	0.509874i	0.0203624	+	0.0352687i
$210$	−2.04668	+	3.54496i	−0.141235	+	0.244625i
$211$	−14.6000			−1.00511			−0.502554	−	0.864546i	$-0.667606\pi$
$211$	−14.6000			−1.00511			−0.502554	+	0.864546i	$0.667606\pi$
$212$	−17.2596			−1.18539
$213$	5.20323	−	9.01226i	0.356520	−	0.617510i
$214$	−26.9987			−1.84559
$215$	−3.53361	−	6.12039i	−0.240990	−	0.417407i
$216$	−0.596952			−0.0406174
$217$	3.67769	+	6.36995i	0.249658	+	0.432420i
$218$	7.22130	+	12.5077i	0.489088	+	0.847126i
$219$	21.9228	+	37.9714i	1.48141	+	2.56587i
$220$	0.536666	−	0.929532i	0.0361820	−	0.0626690i
$221$	−0.0181237			−0.00121913
$222$	30.3232	−	9.49538i	2.03516	−	0.637288i
$223$	15.9258			1.06647			0.533236	−	0.845967i	$-0.320976\pi$
$223$	15.9258			1.06647			0.533236	+	0.845967i	$0.320976\pi$
$224$	−3.08042	+	5.33545i	−0.205819	+	0.356490i
$225$	−2.00941	−	3.48041i	−0.133961	−	0.232027i
$226$	−4.31347	−	7.47115i	−0.286928	−	0.496973i
$227$	−7.45104	−	12.9056i	−0.494543	−	0.856573i	0.505438	−	0.862863i	$-0.331331\pi$
$227$	−7.45104	−	12.9056i	−0.494543	−	0.856573i	−0.999980	+	0.00629015i	$0.997998\pi$
$228$	−5.17916			−0.342998
$229$	3.19623	+	5.53604i	0.211213	+	0.365832i	0.952094	−	0.305804i	$-0.0989253\pi$
$229$	3.19623	+	5.53604i	0.211213	+	0.365832i	−0.740881	+	0.671636i	$0.765592\pi$
$230$	17.0596			1.12487
$231$	−0.590155	+	1.02218i	−0.0388293	+	0.0672544i
$232$	−0.899359			−0.0590458
$233$	−11.8008			−0.773094			−0.386547	−	0.922270i	$-0.626332\pi$
$233$	−11.8008			−0.773094			−0.386547	+	0.922270i	$0.626332\pi$
$234$	−0.0242131	+	0.0419383i	−0.00158286	+	0.00274159i
$235$	−2.76155	−	4.78315i	−0.180144	−	0.312018i
$236$	17.4516			1.13600
$237$	14.4431	−	25.0163i	0.938183	−	1.62498i
$238$	2.29107	−	3.96825i	0.148508	−	0.257223i
$239$	1.91458	−	3.31616i	0.123844	−	0.214504i	−0.797436	−	0.603403i	$-0.793811\pi$
$239$	1.91458	−	3.31616i	0.123844	−	0.214504i	0.921281	+	0.388899i	$0.127144\pi$
$240$	−5.57910	−	9.66329i	−0.360130	−	0.623763i
$241$	9.66017	+	16.7319i	0.622266	+	1.07780i	0.989063	+	0.147495i	$0.0471212\pi$
$241$	9.66017	+	16.7319i	0.622266	+	1.07780i	−0.366797	+	0.930301i	$0.619545\pi$
$242$	−10.5260	+	18.2316i	−0.676636	+	1.17197i
$243$	−10.5469	+	18.2677i	−0.676583	+	1.17188i
$244$	9.42340	−	16.3218i	0.603271	−	1.04490i
$245$	−6.38597			−0.407985
$246$	10.7915	+	18.6915i	0.688043	+	1.19172i
$247$	0.00316417	−	0.00548051i	0.000201331	−	0.000348716i
$248$	−2.07595			−0.131823
$249$	−2.28127			−0.144570
$250$	0.985880	−	1.70759i	0.0623525	−	0.107998i
$251$	−0.889477			−0.0561433			−0.0280716	−	0.999606i	$-0.508937\pi$
$251$	−0.889477			−0.0561433			−0.0280716	+	0.999606i	$0.508937\pi$
$252$	−2.97254	−	5.14859i	−0.187253	−	0.324331i
$253$	4.91907			0.309259
$254$	19.2757	+	33.3865i	1.20947	+	2.09486i
$255$	3.92846	+	6.80429i	0.246009	+	0.426101i
$256$	−8.82049	−	15.2775i	−0.551281	−	0.954846i
$257$	−7.12546	+	12.3417i	−0.444474	+	0.769851i	−0.998015	−	0.0629705i	$-0.979943\pi$
$257$	−7.12546	+	12.3417i	−0.444474	+	0.769851i	0.553542	+	0.832821i	$0.313276\pi$
$258$	36.9177			2.29840
$259$	−3.50786	−	3.22707i	−0.217968	−	0.200520i
$260$	−0.0115370			−0.000715492
$261$	8.17139	−	14.1533i	0.505796	−	0.876065i
$262$	9.41905	+	16.3143i	0.581911	+	1.00790i
$263$	12.3919	+	21.4635i	0.764120	+	1.32349i	0.940711	+	0.339210i	$0.110160\pi$
$263$	12.3919	+	21.4635i	0.764120	+	1.32349i	−0.176591	+	0.984284i	$0.556507\pi$
$264$	−0.166563	−	0.288495i	−0.0102512	−	0.0177557i
$265$	−9.14251			−0.561620
$266$	0.799984	+	1.38561i	0.0490502	+	0.0849574i
$267$	0.761012			0.0465732
$268$	10.7201	−	18.5678i	0.654837	−	1.13421i
$269$	−9.55497			−0.582577			−0.291289	−	0.956635i	$-0.594084\pi$
$269$	−9.55497			−0.582577			−0.291289	+	0.956635i	$0.594084\pi$
$270$	5.32215			0.323895
$271$	−4.23718	+	7.33902i	−0.257391	+	0.445814i	−0.965542	−	0.260247i	$-0.916196\pi$
$271$	−4.23718	+	7.33902i	−0.257391	+	0.445814i	0.708151	+	0.706061i	$0.249529\pi$
$272$	6.24528	+	10.8171i	0.378676	+	0.655886i
$273$	0.0126868			0.000767843
$274$	−5.05710	+	8.75915i	−0.305510	+	0.529160i
$275$	0.284276	−	0.492380i	0.0171425	−	0.0296916i
$276$	−21.6362	+	37.4749i	−1.30234	+	2.25573i
$277$	−14.6366	−	25.3513i	−0.879426	−	1.52321i	−0.851972	−	0.523588i	$-0.824593\pi$
$277$	−14.6366	−	25.3513i	−0.879426	−	1.52321i	−0.0274542	−	0.999623i	$-0.508740\pi$
$278$	−10.1950	−	17.6583i	−0.611456	−	1.05907i
$279$	18.8617	−	32.6694i	1.12922	−	1.95587i
$280$	−0.0866504	+	0.150083i	−0.00517835	+	0.00896917i
$281$	7.29433	−	12.6342i	0.435143	−	0.753690i	−0.562164	−	0.827026i	$-0.690031\pi$
$281$	7.29433	−	12.6342i	0.435143	−	0.753690i	0.997307	+	0.0733354i	$0.0233644\pi$
$282$	28.8516			1.71809
$283$	−9.29663	−	16.1022i	−0.552627	−	0.957178i	−0.998084	−	0.0618747i	$-0.980292\pi$
$283$	−9.29663	−	16.1022i	−0.552627	−	0.957178i	0.445457	−	0.895303i	$-0.353041\pi$
$284$	−3.70771	+	6.42193i	−0.220012	+	0.381072i
$285$	−2.74344			−0.162507
$286$	−0.00685095			−0.000405105
$287$	1.61879	−	2.80383i	0.0955542	−	0.165505i
$288$	31.5970			1.86187
$289$	4.10246	+	7.10568i	0.241321	+	0.417981i
$290$	8.01827			0.470849
$291$	−5.73643	−	9.93579i	−0.336276	−	0.582446i
$292$	−15.6217	−	27.0576i	−0.914191	−	1.58343i
$293$	−2.90144	−	5.02544i	−0.169504	−	0.293589i	0.768742	−	0.639559i	$-0.220883\pi$
$293$	−2.90144	−	5.02544i	−0.169504	−	0.293589i	−0.938246	+	0.345970i	$0.887550\pi$
$294$	16.6795	−	28.8898i	0.972769	−	1.68488i
$295$	9.24422			0.538219
$296$	1.28379	−	0.402006i	0.0746190	−	0.0233661i
$297$	1.53462			0.0890480
$298$	−10.7243	+	18.5750i	−0.621240	+	1.07602i
$299$	−0.0264369	−	0.0457901i	−0.00152889	−	0.00264811i
$300$	2.50073	+	4.33139i	0.144380	+	0.250073i
$301$	−2.76894	−	4.79594i	−0.159599	−	0.276433i
$302$	−0.0304027			−0.00174948
$303$	−7.16005	−	12.4016i	−0.411334	−	0.712452i
$304$	−4.36139			−0.250143
$305$	4.99164	−	8.64577i	0.285820	−	0.495056i
$306$	−23.5003			−1.34342
$307$	−21.6882			−1.23781			−0.618907	−	0.785464i	$-0.712424\pi$
$307$	−21.6882			−1.23781			−0.618907	+	0.785464i	$0.712424\pi$
$308$	0.420531	−	0.728381i	0.0239620	−	0.0415034i
$309$	16.2605	+	28.1640i	0.925026	+	1.60219i
$310$	18.5082			1.05120
$311$	−3.51294	+	6.08460i	−0.199201	+	0.345026i	−0.948270	−	0.317466i	$-0.897168\pi$
$311$	−3.51294	+	6.08460i	−0.199201	+	0.345026i	0.749069	+	0.662492i	$0.230501\pi$
$312$	−0.00179034	+	0.00310096i	−0.000101358	+	0.000175557i
$313$	11.8855	−	20.5863i	0.671808	−	1.16361i	−0.305583	−	0.952165i	$-0.598851\pi$
$313$	11.8855	−	20.5863i	0.671808	−	1.16361i	0.977391	−	0.211440i	$-0.0678154\pi$
$314$	−13.9325	−	24.1318i	−0.786257	−	1.36184i
$315$	−1.57458	−	2.72725i	−0.0887173	−	0.153663i
$316$	−10.2919	+	17.8260i	−0.578962	+	1.00279i
$317$	−11.5553	+	20.0144i	−0.649012	+	1.12412i	0.334347	+	0.942450i	$0.391484\pi$
$317$	−11.5553	+	20.0144i	−0.649012	+	1.12412i	−0.983359	+	0.181672i	$0.941849\pi$
$318$	23.8793	−	41.3602i	1.33908	−	2.31936i
$319$	2.31204			0.129450
$320$	3.53947	+	6.13054i	0.197862	+	0.342708i
$321$	18.1381	−	31.4160i	1.01237	−	1.75347i
$322$	13.3679			0.744962
$323$	3.07102			0.170876
$324$	4.63040	−	8.02009i	0.257244	−	0.445560i
$325$	−0.00611121			−0.000338989
$326$	20.9930	+	36.3610i	1.16270	+	2.01385i
$327$	−19.4055			−1.07312
$328$	0.456881	+	0.791341i	0.0252270	+	0.0436945i
$329$	−2.16395	−	3.74807i	−0.119303	−	0.206638i
$330$	1.48500	+	2.57209i	0.0817464	+	0.141589i
$331$	5.23346	−	9.06462i	0.287657	−	0.498237i	−0.685593	−	0.727985i	$-0.740457\pi$
$331$	5.23346	−	9.06462i	0.287657	−	0.498237i	0.973250	+	0.229748i	$0.0737904\pi$
$332$	1.62558			0.0892154
$333$	−5.33789	+	23.8557i	−0.292515	+	1.30728i
$334$	15.7176			0.860029
$335$	5.67853	−	9.83551i	0.310251	−	0.537371i
$336$	−4.37179	−	7.57215i	−0.238500	−	0.413095i
$337$	5.26707	+	9.12282i	0.286915	+	0.496952i	0.973072	−	0.230502i	$-0.0740368\pi$
$337$	5.26707	+	9.12282i	0.286915	+	0.496952i	−0.686157	+	0.727454i	$0.740703\pi$
$338$	−12.8164	−	22.1987i	−0.697120	−	1.20745i
$339$	11.5914			0.629557
$340$	−2.79933	−	4.84858i	−0.151815	−	0.262951i
$341$	5.33680			0.289004
$342$	4.10286	−	7.10635i	0.221857	−	0.384268i
$343$	−10.4892			−0.566366
$344$	1.56299			0.0842705
$345$	−11.4608	+	19.8507i	−0.617030	+	1.06873i
$346$	−14.7028	−	25.4661i	−0.790430	−	1.36906i
$347$	−21.5633			−1.15758			−0.578789	−	0.815478i	$-0.696474\pi$
$347$	−21.5633			−1.15758			−0.578789	+	0.815478i	$0.696474\pi$
$348$	−10.1693	+	17.6138i	−0.545134	+	0.944200i
$349$	−5.28986	+	9.16231i	−0.283160	+	0.490447i	−0.972161	−	0.234313i	$-0.924716\pi$
$349$	−5.28986	+	9.16231i	−0.283160	+	0.490447i	0.689001	+	0.724760i	$0.258049\pi$
$350$	0.772535	−	1.33807i	0.0412937	−	0.0715229i
$351$	−0.00824765	−	0.0142853i	−0.000440227	−	0.000762495i
$352$	2.23504	+	3.87120i	0.119128	+	0.206336i
$353$	−5.49760	+	9.52213i	−0.292608	+	0.506812i	−0.974426	−	0.224710i	$-0.927856\pi$
$353$	−5.49760	+	9.52213i	−0.292608	+	0.506812i	0.681818	+	0.731522i	$0.261190\pi$
$354$	−24.1450	+	41.8203i	−1.28329	+	2.22272i
$355$	−1.96400	+	3.40174i	−0.104238	+	0.180546i
$356$	−0.542280			−0.0287408
$357$	3.07834	+	5.33184i	0.162923	+	0.282191i
$358$	−7.62927	+	13.2143i	−0.403220	+	0.698397i
$359$	−34.6984			−1.83131			−0.915657	−	0.401961i	$-0.868329\pi$
$359$	−34.6984			−1.83131			−0.915657	+	0.401961i	$0.868329\pi$
$360$	0.888803			0.0468441
$361$	8.96384	−	15.5258i	0.471781	−	0.817149i
$362$	−25.9402			−1.36339
$363$	−14.1430	−	24.4964i	−0.742315	−	1.28573i
$364$	−0.00904036			−0.000473844
$365$	−8.27493	−	14.3326i	−0.433129	−	0.750202i
$366$	26.0753	+	45.1638i	1.36298	+	2.36075i
$367$	5.77858	+	10.0088i	0.301639	+	0.522455i	0.976507	−	0.215484i	$-0.0691328\pi$
$367$	5.77858	+	10.0088i	0.301639	+	0.522455i	−0.674868	+	0.737938i	$0.735799\pi$
$368$	−18.2199	+	31.5578i	−0.949778	+	1.64506i
$369$	−16.6045			−0.864396
$370$	−11.4457	+	3.58410i	−0.595034	+	0.186328i
$371$	−7.16407			−0.371940
$372$	−23.4735	+	40.6573i	−1.21704	+	2.10798i
$373$	−5.12736	−	8.88085i	−0.265485	−	0.459833i	0.702206	−	0.711974i	$-0.252199\pi$
$373$	−5.12736	−	8.88085i	−0.265485	−	0.459833i	−0.967691	+	0.252141i	$0.918865\pi$
$374$	−1.66231	−	2.87921i	−0.0859562	−	0.148881i
$375$	1.32465	+	2.29437i	0.0684048	+	0.118481i
$376$	1.22149			0.0629935
$377$	−0.0124258	−	0.0215221i	−0.000639960	−	0.00110844i
$378$	4.17043			0.214504
$379$	−2.67929	+	4.64067i	−0.137626	+	0.238375i	−0.926598	−	0.376055i	$-0.877281\pi$
$379$	−2.67929	+	4.64067i	−0.137626	+	0.238375i	0.788972	+	0.614430i	$0.210614\pi$
$380$	1.95491			0.100285
$381$	−51.7987			−2.65373
$382$	22.9179	−	39.6949i	1.17258	−	2.03097i
$383$	11.6302	+	20.1441i	0.594276	+	1.02932i	0.993649	+	0.112528i	$0.0358948\pi$
$383$	11.6302	+	20.1441i	0.594276	+	1.02932i	−0.399372	+	0.916789i	$0.630772\pi$
$384$	4.67999			0.238825
$385$	0.222758	−	0.385829i	0.0113528	−	0.0196636i
$386$	5.30609	−	9.19041i	0.270073	−	0.467780i
$387$	−14.2010	+	24.5968i	−0.721876	+	1.25033i
$388$	4.08765	+	7.08002i	0.207519	+	0.359434i
$389$	−8.61377	−	14.9195i	−0.436735	−	0.756448i	0.560700	−	0.828019i	$-0.310532\pi$
$389$	−8.61377	−	14.9195i	−0.436735	−	0.756448i	−0.997435	+	0.0715711i	$0.977199\pi$
$390$	0.0159619	−	0.0276468i	0.000808260	−	0.00139995i
$391$	12.8293	−	22.2210i	0.648806	−	1.12377i
$392$	0.706160	−	1.22311i	0.0356665	−	0.0617762i
$393$	−25.3114			−1.27679
$394$	−0.726809	−	1.25887i	−0.0366161	−	0.0634210i
$395$	−5.45167	+	9.44257i	−0.274303	+	0.475107i
$396$	−4.31353			−0.216763
$397$	30.2268			1.51704			0.758520	−	0.651650i	$-0.225923\pi$
$397$	30.2268			1.51704			0.758520	+	0.651650i	$0.225923\pi$
$398$	3.47357	−	6.01640i	0.174114	−	0.301575i
$399$	−2.14976			−0.107622
$400$	2.10587	+	3.64748i	0.105294	+	0.182374i
$401$	12.0733			0.602909			0.301455	−	0.953480i	$-0.402528\pi$
$401$	12.0733			0.602909			0.301455	+	0.953480i	$0.402528\pi$
$402$	29.6635	+	51.3787i	1.47948	+	2.56254i
$403$	−0.0286819	−	0.0496786i	−0.00142875	−	0.00247467i
$404$	5.10209	+	8.83708i	0.253839	+	0.439661i
$405$	2.45275	−	4.24830i	0.121878	−	0.211100i
$406$	6.28311			0.311826
$407$	−3.30034	+	1.03346i	−0.163592	+	0.0512269i
$408$	−1.73763			−0.0860257
$409$	−0.454742	+	0.787637i	−0.0224856	+	0.0389461i	−0.877049	−	0.480401i	$-0.840491\pi$
$409$	−0.454742	+	0.787637i	−0.0224856	+	0.0389461i	0.854564	+	0.519347i	$0.173825\pi$
$410$	−4.07334	−	7.05523i	−0.201168	−	0.348433i
$411$	−6.79485	−	11.7690i	−0.335165	−	0.580523i
$412$	−11.5868	−	20.0690i	−0.570843	−	0.988729i
$413$	7.24377			0.356442
$414$	−34.2797	−	59.3742i	−1.68476	−	2.91808i
$415$	0.861082			0.0422688
$416$	0.0240239	−	0.0416106i	0.00117787	−	0.00204013i
$417$	27.3966			1.34162
$418$	1.16088			0.0567804
$419$	−2.72019	+	4.71151i	−0.132890	+	0.230172i	−0.924789	−	0.380479i	$-0.875759\pi$
$419$	−2.72019	+	4.71151i	−0.132890	+	0.230172i	0.791899	+	0.610652i	$0.209092\pi$
$420$	1.95957	+	3.39408i	0.0956172	+	0.165614i
$421$	32.1650			1.56762			0.783812	−	0.620998i	$-0.213273\pi$
$421$	32.1650			1.56762			0.783812	+	0.620998i	$0.213273\pi$
$422$	−14.3939	+	24.9310i	−0.700684	+	1.21362i
$423$	−11.0982	+	19.2226i	−0.539613	+	0.934637i
$424$	1.01098	−	1.75107i	0.0490974	−	0.0850393i
$425$	−1.48282	−	2.56833i	−0.0719275	−	0.124582i
$426$	−10.2595	−	17.7700i	−0.497076	−	0.860960i
$427$	3.91145	−	6.77483i	0.189288	−	0.327857i
$428$	−12.9248	+	22.3864i	−0.624742	+	1.08209i
$429$	0.00460255	−	0.00797186i	0.000222213	−	0.000384885i
$430$	−13.9349			−0.671999
$431$	−1.28753	−	2.23008i	−0.0620184	−	0.107419i	0.833349	−	0.552747i	$-0.186420\pi$
$431$	−1.28753	−	2.23008i	−0.0620184	−	0.107419i	−0.895367	+	0.445328i	$0.853087\pi$
$432$	−5.68414	+	9.84523i	−0.273478	+	0.473679i
$433$	32.5699			1.56521			0.782605	−	0.622519i	$-0.213891\pi$
$433$	32.5699			1.56521			0.782605	+	0.622519i	$0.213891\pi$
$434$	14.5031			0.696169
$435$	−5.38677	+	9.33017i	−0.258276	+	0.447347i
$436$	13.8279			0.662236
$437$	4.47968	+	7.75903i	0.214292	+	0.371165i
$438$	86.4531			4.13089
$439$	−19.0316	−	32.9636i	−0.908326	−	1.57327i	−0.816389	−	0.577503i	$-0.804027\pi$
$439$	−19.0316	−	32.9636i	−0.908326	−	1.57327i	−0.0919376	−	0.995765i	$-0.529306\pi$
$440$	0.0628703	+	0.108895i	0.00299723	+	0.00519135i
$441$	12.8321	+	22.2258i	0.611050	+	1.05837i
$442$	−0.0178678	+	0.0309479i	−0.000849884	+	0.00147204i
$443$	−9.79268			−0.465264			−0.232632	−	0.972565i	$-0.574734\pi$
$443$	−9.79268			−0.465264			−0.232632	+	0.972565i	$0.574734\pi$
$444$	6.64304	−	29.6885i	0.315265	−	1.40896i
$445$	−0.287249			−0.0136169
$446$	15.7009	−	27.1948i	0.743461	−	1.28771i
$447$	−14.4094	−	24.9578i	−0.681541	−	1.18046i
$448$	2.77353	+	4.80389i	0.131037	+	0.226963i
$449$	−6.14383	−	10.6414i	−0.289945	−	0.502200i	0.683851	−	0.729622i	$-0.260304\pi$
$449$	−6.14383	−	10.6414i	−0.289945	−	0.502200i	−0.973796	+	0.227422i	$0.926970\pi$
$450$	−7.92416			−0.373549
$451$	−1.17454	−	2.03435i	−0.0553067	−	0.0957940i
$452$	−8.25975			−0.388506
$453$	0.0204249	−	0.0353770i	0.000959645	−	0.00166215i
$454$	−29.3833			−1.37903
$455$	−0.00478874			−0.000224500
$456$	0.303369	−	0.525451i	0.0142066	−	0.0246065i
$457$	5.60472	+	9.70766i	0.262178	+	0.454105i	0.966820	−	0.255457i	$-0.0822260\pi$
$457$	5.60472	+	9.70766i	0.262178	+	0.454105i	−0.704643	+	0.709562i	$0.748893\pi$
$458$	12.6044			0.588965
$459$	4.00242	−	6.93239i	0.186817	−	0.323576i
$460$	8.16673	−	14.1452i	0.380776	−	0.659523i
$461$	−11.0096	+	19.0691i	−0.512767	+	0.888138i	0.487123	+	0.873333i	$0.338046\pi$
$461$	−11.0096	+	19.0691i	−0.512767	+	0.888138i	−0.999890	+	0.0148053i	$0.995287\pi$
$462$	1.16364	+	2.01549i	0.0541376	+	0.0937691i
$463$	−10.4737	−	18.1409i	−0.486752	−	0.843079i	0.513132	−	0.858310i	$-0.328485\pi$
$463$	−10.4737	−	18.1409i	−0.486752	−	0.843079i	−0.999884	+	0.0152306i	$0.995152\pi$
$464$	−8.56365	+	14.8327i	−0.397557	+	0.688590i
$465$	−12.4341	+	21.5364i	−0.576616	+	0.998729i
$466$	−11.6341	+	20.1509i	−0.538941	+	0.933473i
$467$	−1.71804			−0.0795016			−0.0397508	−	0.999210i	$-0.512656\pi$
$467$	−1.71804			−0.0795016			−0.0397508	+	0.999210i	$0.512656\pi$
$468$	0.0231825	+	0.0401533i	0.00107161	+	0.00185609i
$469$	4.44970	−	7.70710i	0.205468	−	0.355881i
$470$	−10.8902			−0.502329
$471$	37.4401			1.72515
$472$	−1.02222	+	1.77055i	−0.0470517	+	0.0814960i
$473$	−4.01808			−0.184751
$474$	−28.4784	−	49.3260i	−1.30806	−	2.26562i
$475$	1.03553			0.0475134
$476$	−2.19355	−	3.79935i	−0.100541	−	0.174143i
$477$	18.3711	+	31.8196i	0.841154	+	1.45692i
$478$	−3.77510	−	6.53867i	−0.172669	−	0.299072i
$479$	16.5168	−	28.6080i	0.754674	−	1.30713i	−0.190863	−	0.981617i	$-0.561128\pi$
$479$	16.5168	−	28.6080i	0.754674	−	1.30713i	0.945536	−	0.325517i	$-0.105538\pi$
$480$	−20.8295			−0.950731
$481$	0.0273574	+	0.0251676i	0.00124739	+	0.00114754i
$482$	38.0951			1.73518
$483$	−8.98070	+	15.5550i	−0.408636	+	0.707778i
$484$	10.0780	+	17.4556i	0.458090	+	0.793435i
$485$	2.16526	+	3.75034i	0.0983193	+	0.170294i
$486$	20.7959	+	36.0196i	0.943322	+	1.63388i
$487$	13.4557			0.609734			0.304867	−	0.952395i	$-0.401388\pi$
$487$	13.4557			0.609734			0.304867	+	0.952395i	$0.401388\pi$
$488$	1.10395	+	1.91210i	0.0499735	+	0.0865566i
$489$	−56.4136			−2.55111
$490$	−6.29580	+	10.9046i	−0.284415	+	0.492622i
$491$	13.8635			0.625650			0.312825	−	0.949811i	$-0.398725\pi$
$491$	13.8635			0.625650			0.312825	+	0.949811i	$0.398725\pi$
$492$	20.6644			0.931624
$493$	6.02998	−	10.4442i	0.271577	−	0.470385i
$494$	−0.00623899	−	0.0108062i	−0.000280705	−	0.000486196i
$495$	−2.28491			−0.102699
$496$	−19.7671	+	34.2377i	−0.887570	+	1.53732i
$497$	−1.53899	+	2.66561i	−0.0690330	+	0.119569i
$498$	−2.24906	+	3.89548i	−0.100783	+	0.174561i
$499$	−16.1046	−	27.8939i	−0.720940	−	1.24870i	−0.960624	−	0.277853i	$-0.910377\pi$
$499$	−16.1046	−	27.8939i	−0.720940	−	1.24870i	0.239684	−	0.970851i	$-0.422956\pi$
$500$	−0.943918	−	1.63491i	−0.0422133	−	0.0731156i
$501$	−10.5593	+	18.2892i	−0.471754	+	0.817102i
$502$	−0.876917	+	1.51887i	−0.0391387	+	0.0677903i
$503$	−19.0525	+	32.9999i	−0.849510	+	1.47139i	0.0321365	+	0.999483i	$0.489769\pi$
$503$	−19.0525	+	32.9999i	−0.849510	+	1.47139i	−0.881646	+	0.471911i	$0.843564\pi$
$504$	0.696466			0.0310231
$505$	2.70261	+	4.68106i	0.120265	+	0.208305i
$506$	4.84961	−	8.39978i	0.215592	−	0.373416i
$507$	34.4409			1.52957
$508$	36.9106			1.63764
$509$	−20.2427	+	35.0613i	−0.897240	+	1.55406i	−0.0662319	+	0.997804i	$0.521098\pi$
$509$	−20.2427	+	35.0613i	−0.897240	+	1.55406i	−0.831008	+	0.556261i	$0.812236\pi$
$510$	15.4919			0.685995
$511$	−6.48423	−	11.2310i	−0.286845	−	0.496831i
$512$	−31.2508			−1.38110
$513$	1.39754	+	2.42062i	0.0617031	+	0.106873i
$514$	14.0497	+	24.3348i	0.619705	+	1.07336i
$515$	−6.13763	−	10.6307i	−0.270456	−	0.468444i
$516$	17.6732	−	30.6109i	0.778019	−	1.34757i
$517$	−3.14017			−0.138104
$518$	−8.96885	+	2.80850i	−0.394069	+	0.123398i
$519$	39.5102			1.73431
$520$	0.000675777	−	0.00117048i	2.96348e−5	−	5.13290e-5i
$521$	−0.919502	−	1.59262i	−0.0402841	−	0.0697742i	0.845180	−	0.534481i	$-0.179493\pi$
$521$	−0.919502	−	1.59262i	−0.0402841	−	0.0697742i	−0.885464	+	0.464707i	$0.846160\pi$
$522$	−16.1120	−	27.9068i	−0.705204	−	1.22145i
$523$	−6.11530	−	10.5920i	−0.267403	−	0.463156i	0.700787	−	0.713370i	$-0.252832\pi$
$523$	−6.11530	−	10.5920i	−0.267403	−	0.463156i	−0.968190	+	0.250214i	$0.919499\pi$
$524$	18.0363			0.787919
$525$	1.03800	+	1.79787i	0.0453020	+	0.0784653i
$526$	48.8679			2.13074
$527$	13.9188	−	24.1080i	0.606311	−	1.05016i
$528$	−6.34401			−0.276088
$529$	51.8561			2.25461
$530$	−9.01342	+	15.6117i	−0.391518	+	0.678129i
$531$	−18.5755	−	32.1736i	−0.806106	−	1.39622i
$532$	1.53187			0.0664149
$533$	−0.0126248	+	0.0218668i	−0.000546840	+	0.000947155i
$534$	0.750266	−	1.29950i	0.0324672	−	0.0562348i
$535$	−6.84634	+	11.8582i	−0.295993	+	0.512675i
$536$	1.25586	+	2.17522i	0.0542451	+	0.0939552i
$537$	−10.2509	−	17.7551i	−0.442359	−	0.766187i
$538$	−9.42006	+	16.3160i	−0.406127	+	0.703433i
$539$	−1.81538	+	3.14432i	−0.0781938	+	0.135436i
$540$	2.54781	−	4.41294i	0.109640	−	0.189903i
$541$	−9.85561			−0.423726			−0.211863	−	0.977299i	$-0.567953\pi$
$541$	−9.85561			−0.423726			−0.211863	+	0.977299i	$0.567953\pi$
$542$	8.35471	+	14.4708i	0.358865	+	0.621573i
$543$	17.4270	−	30.1844i	0.747864	−	1.29534i
$544$	23.3166			0.999692
$545$	7.32473			0.313757
$546$	0.0125077	−	0.0216640i	0.000535281	−	0.000927133i
$547$	−22.7670			−0.973447			−0.486723	−	0.873556i	$-0.661808\pi$
$547$	−22.7670			−0.973447			−0.486723	+	0.873556i	$0.661808\pi$
$548$	4.84185	+	8.38634i	0.206834	+	0.358247i
$549$	−40.1211			−1.71233
$550$	−0.560523	−	0.970854i	−0.0239008	−	0.0413974i
$551$	2.10552	+	3.64687i	0.0896982	+	0.155362i
$552$	−2.53468	−	4.39019i	−0.107883	−	0.186859i
$553$	−4.27193	+	7.39919i	−0.181661	+	0.314646i
$554$	−57.7196			−2.45227
$555$	3.51887	−	15.7262i	0.149368	−	0.667541i
$556$	−19.5222			−0.827924
$557$	21.8322	−	37.8144i	0.925058	−	1.60225i	0.133591	−	0.991037i	$-0.457349\pi$
$557$	21.8322	−	37.8144i	0.925058	−	1.60225i	0.791467	−	0.611211i	$-0.209317\pi$
$558$	−37.1907	−	64.4162i	−1.57441	−	2.72695i
$559$	0.0215946	+	0.0374030i	0.000913356	+	0.00158198i
$560$	1.65016	+	2.85816i	0.0697321	+	0.120779i
$561$	4.46706			0.188599
$562$	−14.3827	−	24.9115i	−0.606696	−	1.05083i
$563$	24.4057			1.02858			0.514288	−	0.857617i	$-0.328056\pi$
$563$	24.4057			1.02858			0.514288	+	0.857617i	$0.328056\pi$
$564$	13.8118	−	23.9227i	0.581581	−	1.00733i
$565$	−4.37525			−0.184068
$566$	−36.6614			−1.54099
$567$	1.92198	−	3.32896i	0.0807155	−	0.139803i
$568$	−0.434358	−	0.752329i	−0.0182252	−	0.0315670i
$569$	41.3282			1.73257			0.866285	−	0.499550i	$-0.166501\pi$
$569$	41.3282			1.73257			0.866285	+	0.499550i	$0.166501\pi$
$570$	−2.70470	+	4.68468i	−0.113287	+	0.196220i
$571$	−9.18338	+	15.9061i	−0.384313	+	0.665649i	−0.991674	−	0.128777i	$-0.958895\pi$
$571$	−9.18338	+	15.9061i	−0.384313	+	0.665649i	0.607361	+	0.794426i	$0.292228\pi$
$572$	−0.00327968	+	0.00568057i	−0.000137130	+	0.000237516i
$573$	30.7930	+	53.3351i	1.28640	+	2.22810i
$574$	−3.19187	−	5.52848i	−0.133226	−	0.230754i
$575$	4.32597	−	7.49280i	0.180405	−	0.312471i
$576$	14.2245	−	24.6376i	0.592688	−	1.02657i
$577$	−9.87431	+	17.1028i	−0.411073	+	0.711999i	−0.995007	−	0.0998015i	$-0.968179\pi$
$577$	−9.87431	+	17.1028i	−0.411073	+	0.711999i	0.583934	+	0.811801i	$0.301513\pi$
$578$	16.1781			0.672922
$579$	7.12939	+	12.3485i	0.296288	+	0.513185i
$580$	3.83849	−	6.64847i	0.159385	−	0.276063i
$581$	0.674744			0.0279931
$582$	−22.6217			−0.937701
$583$	−2.59899	+	4.50159i	−0.107639	+	0.186437i
$584$	3.66016			0.151459
$585$	0.0122799	+	0.0212695i	0.000507713	+	0.000879385i
$586$	−11.4419			−0.472660
$587$	16.4636	+	28.5157i	0.679524	+	1.17697i	0.975125	+	0.221658i	$0.0711468\pi$
$587$	16.4636	+	28.5157i	0.679524	+	1.17697i	−0.295601	+	0.955311i	$0.595520\pi$
$588$	−15.9696	−	27.6601i	−0.658575	−	1.14068i
$589$	4.86009	+	8.41792i	0.200256	+	0.346854i
$590$	9.11369	−	15.7854i	0.375205	−	0.649873i
$591$	1.95312			0.0803405
$592$	5.59413	−	25.0008i	0.229917	−	1.02753i
$593$	16.7712			0.688712			0.344356	−	0.938839i	$-0.388097\pi$
$593$	16.7712			0.688712			0.344356	+	0.938839i	$0.388097\pi$
$594$	1.51296	−	2.62052i	0.0620773	−	0.107521i
$595$	−1.16194	−	2.01254i	−0.0476349	−	0.0825061i
$596$	10.2678	+	17.7844i	0.420586	+	0.728476i
$597$	4.66718	+	8.08379i	0.191015	+	0.330848i
$598$	−0.104255			−0.00426328
$599$	−5.75661	−	9.97074i	−0.235209	−	0.407393i	0.724125	−	0.689669i	$-0.242244\pi$
$599$	−5.75661	−	9.97074i	−0.235209	−	0.407393i	−0.959333	+	0.282276i	$0.908911\pi$
$600$	−0.585920			−0.0239201
$601$	−4.67853	+	8.10346i	−0.190841	+	0.330547i	−0.945529	−	0.325537i	$-0.894455\pi$
$601$	−4.67853	+	8.10346i	−0.190841	+	0.330547i	0.754688	+	0.656084i	$0.227788\pi$
$602$	−10.9194			−0.445040
$603$	−45.6421			−1.85869
$604$	−0.0145543	+	0.0252088i	−0.000592207	+	0.00102573i
$605$	5.33837	+	9.24634i	0.217036	+	0.375917i
$606$	−28.2358			−1.14700
$607$	−4.02620	+	6.97358i	−0.163418	+	0.283049i	−0.936092	−	0.351754i	$-0.885585\pi$
$607$	−4.02620	+	6.97358i	−0.163418	+	0.283049i	0.772674	+	0.634803i	$0.218919\pi$
$608$	−4.07079	+	7.05082i	−0.165092	+	0.285948i
$609$	−4.22108	+	7.31112i	−0.171047	+	0.296261i
$610$	−9.84231	−	17.0474i	−0.398504	−	0.690229i
$611$	0.0168764	+	0.0292308i	0.000682747	+	0.00118255i
$612$	−11.2500	+	19.4856i	−0.454755	+	0.787659i
$613$	−1.71014	+	2.96205i	−0.0690720	+	0.119636i	−0.898493	−	0.438988i	$-0.855337\pi$
$613$	−1.71014	+	2.96205i	−0.0690720	+	0.119636i	0.829421	+	0.558624i	$0.188670\pi$
$614$	−21.3820	+	37.0347i	−0.862907	+	1.49460i
$615$	10.9461			0.441389
$616$	0.0492652	+	0.0853298i	0.00198495	+	0.00343804i
$617$	8.94688	−	15.4965i	0.360188	−	0.623864i	−0.627804	−	0.778372i	$-0.716046\pi$
$617$	8.94688	−	15.4965i	0.360188	−	0.623864i	0.987992	+	0.154508i	$0.0493792\pi$
$618$	64.1235			2.57943
$619$	1.02595			0.0412363			0.0206182	−	0.999787i	$-0.493437\pi$
$619$	1.02595			0.0412363			0.0206182	+	0.999787i	$0.493437\pi$
$620$	8.86024	−	15.3464i	0.355836	−	0.616326i
$621$	23.3532			0.937132
$622$	6.92668	+	11.9974i	0.277735	+	0.481050i
$623$	−0.225089			−0.00901798
$624$	0.0340951	+	0.0590544i	0.00136490	+	0.00236407i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−23.4353	−	40.5912i	−0.936665	−	1.62235i
$627$	−0.779892	+	1.35081i	−0.0311459	+	0.0539463i
$628$	−26.6790			−1.06461
$629$	−3.93904	+	17.6040i	−0.157060	+	0.701918i
$630$	−6.20937			−0.247387
$631$	−22.8117	+	39.5110i	−0.908119	+	1.57291i	−0.0914449	+	0.995810i	$0.529149\pi$
$631$	−22.8117	+	39.5110i	−0.908119	+	1.57291i	−0.816674	+	0.577099i	$0.804185\pi$
$632$	−1.20569	−	2.08832i	−0.0479598	−	0.0830688i
$633$	−19.3400	−	33.4979i	−0.768696	−	1.33142i
$634$	22.7843	+	39.4636i	0.904882	+	1.56730i
$635$	19.5518			0.775890
$636$	−22.8629	−	39.5998i	−0.906574	−	1.57023i
$637$	0.0390260			0.00154627
$638$	2.27940	−	3.94803i	0.0902422	−	0.156304i
$639$	15.7859			0.624482
$640$	−1.76650			−0.0698269
$641$	−3.99054	+	6.91182i	−0.157617	+	0.273000i	−0.934009	−	0.357250i	$-0.883714\pi$
$641$	−3.99054	+	6.91182i	−0.157617	+	0.273000i	0.776392	+	0.630250i	$0.217048\pi$
$642$	−35.7639	−	61.9449i	−1.41149	−	2.44477i
$643$	−11.7007			−0.461432			−0.230716	−	0.973021i	$-0.574107\pi$
$643$	−11.7007			−0.461432			−0.230716	+	0.973021i	$0.574107\pi$
$644$	6.39944	−	11.0842i	0.252173	−	0.436777i
$645$	9.36162	−	16.2148i	0.368613	−	0.638457i
$646$	3.02766	−	5.24405i	0.119122	−	0.206325i
$647$	−1.00933	−	1.74821i	−0.0396807	−	0.0687291i	0.845503	−	0.533971i	$-0.179301\pi$
$647$	−1.00933	−	1.74821i	−0.0396807	−	0.0687291i	−0.885184	+	0.465242i	$0.845967\pi$
$648$	0.542451	+	0.939553i	0.0213095	+	0.0369091i
$649$	2.62790	−	4.55166i	0.103154	−	0.178668i
$650$	−0.00602492	+	0.0104355i	−0.000236317	+	0.000409313i
$651$	−9.74334	+	16.8760i	−0.381871	+	0.661421i
$652$	40.1991			1.57432
$653$	15.5042	+	26.8541i	0.606728	+	1.05088i	0.991776	+	0.127987i	$0.0408514\pi$
$653$	15.5042	+	26.8541i	0.606728	+	1.05088i	−0.385048	+	0.922896i	$0.625815\pi$
$654$	−19.1315	+	33.1366i	−0.748099	+	1.29575i
$655$	9.55395			0.373304
$656$	17.4016			0.679418
$657$	−33.2555	+	57.6002i	−1.29742	+	2.24720i
$658$	−8.53359			−0.332674
$659$	6.49329	+	11.2467i	0.252943	+	0.438110i	0.964335	−	0.264686i	$-0.0852683\pi$
$659$	6.49329	+	11.2467i	0.252943	+	0.438110i	−0.711392	+	0.702795i	$0.751935\pi$
$660$	2.84358			0.110686
$661$	1.63687	+	2.83514i	0.0636668	+	0.110274i	0.896102	−	0.443849i	$-0.146387\pi$
$661$	1.63687	+	2.83514i	0.0636668	+	0.110274i	−0.832435	+	0.554123i	$0.813054\pi$
$662$	−10.3191	−	17.8732i	−0.401064	−	0.694664i
$663$	−0.0240076	−	0.0415824i	−0.000932379	−	0.00161493i
$664$	−0.0952184	+	0.164923i	−0.00369519	+	0.00640026i
$665$	0.811441			0.0314663
$666$	35.4733	+	32.6338i	1.37456	+	1.26453i
$667$	35.1836			1.36231
$668$	7.52431	−	13.0325i	0.291124	−	0.504242i
$669$	21.0962	+	36.5397i	0.815626	+	1.41271i
$670$	−11.1967	−	19.3933i	−0.432566	−	0.749227i
$671$	−2.83800	−	4.91556i	−0.109560	−	0.189763i
$672$	−16.3220			−0.629633
$673$	−11.6797	−	20.2299i	−0.450220	−	0.779804i	0.548179	−	0.836361i	$-0.315321\pi$
$673$	−11.6797	−	20.2299i	−0.450220	−	0.779804i	−0.998399	+	0.0565566i	$0.981988\pi$
$674$	20.7708			0.800060
$675$	1.34959	−	2.33756i	0.0519459	−	0.0899729i
$676$	−24.5418			−0.943915
$677$	−15.6182			−0.600255			−0.300127	−	0.953899i	$-0.597029\pi$
$677$	−15.6182			−0.600255			−0.300127	+	0.953899i	$0.597029\pi$
$678$	11.4277	−	19.7934i	0.438878	−	0.760159i
$679$	1.69670	+	2.93876i	0.0651132	+	0.112779i
$680$	0.655883			0.0251519
$681$	19.7401	−	34.1908i	0.756442	−	1.31020i
$682$	5.26144	−	9.11308i	0.201471	−	0.348958i
$683$	10.1178	−	17.5245i	0.387145	−	0.670555i	−0.604919	−	0.796287i	$-0.706795\pi$
$683$	10.1178	−	17.5245i	0.387145	−	0.670555i	0.992064	+	0.125732i	$0.0401279\pi$
$684$	−3.92823	−	6.80389i	−0.150200	−	0.260153i
$685$	2.56476	+	4.44230i	0.0979946	+	0.169732i
$686$	−10.3411	+	17.9114i	−0.394826	+	0.683859i
$687$	−8.46780	+	14.6667i	−0.323067	+	0.559568i
$688$	14.8827	−	25.7775i	0.567396	−	0.982760i
$689$	0.0558718			0.00212855
$690$	22.5980	+	39.1409i	0.860291	+	1.49007i
$691$	3.30811	−	5.72981i	0.125846	−	0.217972i	−0.796217	−	0.605011i	$-0.793169\pi$
$691$	3.30811	−	5.72981i	0.125846	−	0.217972i	0.922063	+	0.387039i	$0.126502\pi$
$692$	−28.1541			−1.07026
$693$	−1.79045			−0.0680137
$694$	−21.2588	+	36.8213i	−0.806973	+	1.39772i
$695$	−10.3410			−0.392258
$696$	−1.19134	−	2.06346i	−0.0451576	−	0.0782152i
$697$	−12.2531			−0.464120
$698$	10.4303	+	18.0659i	0.394794	+	0.683803i
$699$	−15.6319	−	27.0753i	−0.591253	−	1.02408i
$700$	−0.739654	−	1.28112i	−0.0279563	−	0.0484217i
$701$	18.0334	−	31.2347i	0.681111	−	1.17972i	−0.293531	−	0.955950i	$-0.594830\pi$
$701$	18.0334	−	31.2347i	0.681111	−	1.17972i	0.974642	−	0.223769i	$-0.0718362\pi$
$702$	−0.0325248			−0.00122757
$703$	−4.63565	−	4.26459i	−0.174837	−	0.160842i
$704$	4.02474			0.151688
$705$	7.31620	−	12.6720i	0.275544	−	0.477256i
$706$	10.8400	+	18.7753i	0.407967	+	0.706619i
$707$	2.11777	+	3.66808i	0.0796468	+	0.137952i
$708$	23.1173	+	40.0403i	0.868800	+	1.50481i
$709$	−12.5403			−0.470960			−0.235480	−	0.971879i	$-0.575666\pi$
$709$	−12.5403			−0.470960			−0.235480	+	0.971879i	$0.575666\pi$
$710$	3.87253	+	6.70742i	0.145334	+	0.251725i
$711$	43.8186			1.64333
$712$	0.0317640	−	0.0550169i	0.00119041	−	0.00206185i
$713$	81.2129			3.04145
$714$	12.1395			0.454309
$715$	−0.00173727	+	0.00300904i	−6.49701e−5	+	0.000112532i
$716$	7.30455	+	12.6519i	0.272984	+	0.472822i
$717$	10.1446			0.378859
$718$	−34.2085	+	59.2508i	−1.27665	+	2.21122i
$719$	8.49541	−	14.7145i	0.316825	−	0.548758i	−0.662998	−	0.748621i	$-0.730716\pi$
$719$	8.49541	−	14.7145i	0.316825	−	0.548758i	0.979824	+	0.199863i	$0.0640497\pi$
$720$	8.46314	−	14.6586i	0.315403	−	0.546293i
$721$	−4.80945	−	8.33021i	−0.179113	−	0.310233i
$722$	−17.6745	−	30.6132i	−0.657778	−	1.13931i
$723$	−25.5928	+	44.3279i	−0.951805	+	1.64857i
$724$	−12.4181	+	21.5087i	−0.461514	+	0.799366i
$725$	2.03328	−	3.52174i	0.0755140	−	0.130794i
$726$	−55.7732			−2.06994
$727$	−11.4863	−	19.8949i	−0.426004	−	0.737860i	0.570510	−	0.821291i	$-0.306746\pi$
$727$	−11.4863	−	19.8949i	−0.426004	−	0.737860i	−0.996514	+	0.0834305i	$0.973412\pi$
$728$	0.000529539	0	0.000917188i	1.96260e−5	0	3.39933e-5i
$729$	−41.1673			−1.52472
$730$	−32.6323			−1.20778
$731$	−10.4794	+	18.1509i	−0.387596	+	0.671336i
$732$	49.9309			1.84550
$733$	−3.10435	−	5.37689i	−0.114662	−	0.198600i	0.802983	−	0.596002i	$-0.203245\pi$
$733$	−3.10435	−	5.37689i	−0.114662	−	0.198600i	−0.917644	+	0.397402i	$0.869912\pi$
$734$	22.7879			0.841118
$735$	−8.45920	−	14.6518i	−0.312022	−	0.540438i
$736$	34.0118	+	58.9102i	1.25369	+	2.17146i
$737$	−3.22854	−	5.59199i	−0.118925	−	0.205984i
$738$	−16.3700	+	28.3538i	−0.602590	+	1.04372i
$739$	−9.96051			−0.366403			−0.183202	−	0.983075i	$-0.558646\pi$
$739$	−9.96051			−0.366403			−0.183202	+	0.983075i	$0.558646\pi$
$740$	−2.50746	+	11.2062i	−0.0921762	+	0.411946i
$741$	0.0167657			0.000615904
$742$	−7.06291	+	12.2333i	−0.259288	+	0.449099i
$743$	−17.5892	−	30.4655i	−0.645287	−	1.11767i	−0.984235	−	0.176864i	$-0.943405\pi$
$743$	−17.5892	−	30.4655i	−0.645287	−	1.11767i	0.338949	−	0.940805i	$-0.389929\pi$
$744$	−2.74992	−	4.76300i	−0.100817	−	0.174620i
$745$	5.43893	+	9.42051i	0.199267	+	0.345141i
$746$	−20.2199			−0.740302
$747$	−1.73027	−	2.99692i	−0.0633073	−	0.109651i
$748$	−3.18312			−0.116387
$749$	−5.36479	+	9.29209i	−0.196025	+	0.339525i
$750$	5.22380			0.190746
$751$	−37.7381			−1.37708			−0.688542	−	0.725197i	$-0.741749\pi$
$751$	−37.7381			−1.37708			−0.688542	+	0.725197i	$0.741749\pi$
$752$	11.6310	−	20.1454i	0.424137	−	0.734628i
$753$	−1.17825	−	2.04079i	−0.0429378	−	0.0743704i
$754$	−0.0490013			−0.00178452
$755$	−0.00770952	+	0.0133533i	−0.000280578	+	0.000485976i
$756$	1.99646	−	3.45798i	0.0726107	−	0.125765i
$757$	−1.19262	+	2.06568i	−0.0433465	+	0.0750783i	−0.886885	−	0.461991i	$-0.847135\pi$
$757$	−1.19262	+	2.06568i	−0.0433465	+	0.0750783i	0.843538	+	0.537069i	$0.180469\pi$
$758$	5.28292	+	9.15028i	0.191884	+	0.332353i
$759$	6.51607	+	11.2862i	0.236518	+	0.409662i
$760$	−0.114509	+	0.198335i	−0.00415367	+	0.00719438i
$761$	−0.239975	+	0.415648i	−0.00869907	+	0.0150672i	−0.870342	−	0.492447i	$-0.836102\pi$
$761$	−0.239975	+	0.415648i	−0.00869907	+	0.0150672i	0.861643	+	0.507515i	$0.169436\pi$
$762$	−51.0673	+	88.4512i	−1.84997	+	3.20425i
$763$	5.73966			0.207790
$764$	−21.9424	−	38.0054i	−0.793849	−	1.37499i
$765$	−5.95921	+	10.3217i	−0.215456	+	0.373180i
$766$	45.8640			1.65713
$767$	−0.0564933			−0.00203986
$768$	23.3682	−	40.4749i	0.843227	−	1.46051i
$769$	−45.6865			−1.64750			−0.823748	−	0.566956i	$-0.808121\pi$
$769$	−45.6865			−1.64750			−0.823748	+	0.566956i	$0.808121\pi$
$770$	−0.439226	−	0.760761i	−0.0158286	−	0.0274159i
$771$	−37.7550			−1.35971
$772$	−5.08025	−	8.79924i	−0.182842	−	0.316692i
$773$	−7.54812	−	13.0737i	−0.271487	−	0.470229i	0.697756	−	0.716336i	$-0.254182\pi$
$773$	−7.54812	−	13.0737i	−0.271487	−	0.470229i	−0.969243	+	0.246107i	$0.920849\pi$
$774$	28.0009	+	48.4990i	1.00647	+	1.74326i
$775$	4.69333	−	8.12909i	0.168589	−	0.292005i
$776$	−0.957736			−0.0343807
$777$	2.75738	−	12.3231i	0.0989205	−	0.442088i
$778$	−33.9686			−1.21783
$779$	2.13924	−	3.70527i	0.0766462	−	0.132755i
$780$	−0.0152825	−	0.0264700i	−0.000547201	−	0.000947779i
$781$	1.11663	+	1.93406i	0.0399563	+	0.0692063i
$782$	−25.2963	−	43.8145i	−0.904595	−	1.56680i
$783$	10.9764			0.392264
$784$	−13.4480	−	23.2927i	−0.480287	−	0.831882i
$785$	−14.1321			−0.504395
$786$	−24.9540	+	43.2215i	−0.890078	+	1.54166i
$787$	20.9934			0.748334			0.374167	−	0.927361i	$-0.377929\pi$
$787$	20.9934			0.748334			0.374167	+	0.927361i	$0.377929\pi$
$788$	−1.39175			−0.0495790
$789$	−32.8301	+	56.8633i	−1.16878	+	2.02439i
$790$	10.7494	+	18.6185i	0.382446	+	0.662415i
$791$	−3.42844			−0.121901
$792$	0.252665	−	0.437629i	0.00897806	−	0.0155505i
$793$	−0.0305050	+	0.0528361i	−0.00108326	+	0.00187627i
$794$	29.8000	−	51.6151i	1.05756	−	1.83175i
$795$	−12.1107	−	20.9763i	−0.429521	−	0.743952i
$796$	−3.32573	−	5.76033i	−0.117877	−	0.204169i
$797$	10.4826	−	18.1564i	0.371314	−	0.643134i	−0.618454	−	0.785821i	$-0.712241\pi$
$797$	10.4826	−	18.1564i	0.371314	−	0.643134i	0.989768	+	0.142687i	$0.0455742\pi$
$798$	−2.11940	+	3.67091i	−0.0750260	+	0.129949i
$799$	−8.18979	+	14.1851i	−0.289734	+	0.501834i
$800$	7.86223			0.277972
$801$	0.577203	+	0.999745i	0.0203945	+	0.0353242i
$802$	11.9028	−	20.6162i	0.420302	−	0.727984i
$803$	−9.40944			−0.332052
$804$	56.8019			2.00325
$805$	3.38983	−	5.87136i	0.119476	−	0.206938i
$806$	−0.113108			−0.00398405
$807$	−12.6570	−	21.9226i	−0.445549	−	0.771713i
$808$	−1.19542			−0.0420547
$809$	4.09933	+	7.10024i	0.144125	+	0.249631i	0.929046	−	0.369964i	$-0.120630\pi$
$809$	4.09933	+	7.10024i	0.144125	+	0.249631i	−0.784921	+	0.619595i	$0.787297\pi$
$810$	−4.83624	−	8.37662i	−0.169928	−	0.294324i
$811$	−13.7999	−	23.9021i	−0.484579	−	0.839316i	0.515264	−	0.857032i	$-0.327694\pi$
$811$	−13.7999	−	23.9021i	−0.484579	−	0.839316i	−0.999843	+	0.0177158i	$0.994361\pi$
$812$	3.00784	−	5.20974i	0.105555	−	0.182826i
$813$	−22.4512			−0.787398
$814$	−1.48900	+	6.65450i	−0.0521893	+	0.233240i
$815$	21.2937			0.745886
$816$	−16.5457	+	28.6579i	−0.579214	+	1.00323i
$817$	−3.65916	−	6.33785i	−0.128018	−	0.221733i
$818$	0.896643	+	1.55303i	0.0313504	+	0.0543005i
$819$	0.00962256	+	0.0166668i	0.000336240	+	0.000582384i
$820$	−7.79993			−0.272386
$821$	5.10922	+	8.84943i	0.178313	+	0.308847i	0.941303	−	0.337563i	$-0.109603\pi$
$821$	5.10922	+	8.84943i	0.178313	+	0.308847i	−0.762990	+	0.646411i	$0.776269\pi$
$822$	−26.7956			−0.934604
$823$	−11.1505	+	19.3132i	−0.388681	+	0.673216i	−0.992272	−	0.124078i	$-0.960403\pi$
$823$	−11.1505	+	19.3132i	−0.388681	+	0.673216i	0.603591	+	0.797294i	$0.293736\pi$
$824$	2.71480			0.0945744
$825$	1.50627			0.0524415
$826$	7.14148	−	12.3694i	0.248484	−	0.430387i
$827$	21.3714	+	37.0164i	0.743157	+	1.28719i	0.951051	+	0.309034i	$0.100006\pi$
$827$	21.3714	+	37.0164i	0.743157	+	1.28719i	−0.207894	+	0.978151i	$0.566661\pi$
$828$	−65.6413			−2.28119
$829$	4.77897	−	8.27742i	0.165981	−	0.287487i	−0.771022	−	0.636808i	$-0.780254\pi$
$829$	4.77897	−	8.27742i	0.165981	−	0.287487i	0.937003	+	0.349321i	$0.113588\pi$
$830$	0.848923	−	1.47038i	0.0294666	−	0.0510376i
$831$	38.7768	−	67.1633i	1.34515	−	2.32987i
$832$	−0.0216304	−	0.0374650i	−0.000749901	−	0.00129887i
$833$	9.46927	+	16.4013i	0.328091	+	0.568270i
$834$	27.0097	−	46.7822i	0.935270	−	1.61993i
$835$	3.98568	−	6.90340i	0.137930	−	0.238902i
$836$	0.555734	−	0.962559i	0.0192204	−	0.0332908i
$837$	25.3363			0.875752
$838$	5.36356	+	9.28996i	0.185281	+	0.320916i
$839$	−16.4527	+	28.4968i	−0.568009	+	0.983820i	0.428754	+	0.903421i	$0.358953\pi$
$839$	−16.4527	+	28.4968i	−0.568009	+	0.983820i	−0.996763	+	0.0803989i	$0.974381\pi$
$840$	−0.459127			−0.0158414
$841$	−12.4631			−0.429763
$842$	31.7108	−	54.9247i	1.09283	−	1.89283i
$843$	38.6498			1.33117
$844$	13.7812	+	23.8698i	0.474370	+	0.821633i
$845$	−13.0000			−0.447212
$846$	21.8830	+	37.9024i	0.752353	+	1.30311i
$847$	4.18315	+	7.24543i	0.143735	+	0.248956i
$848$	−19.2530	−	33.3471i	−0.661150	−	1.14514i
$849$	24.6296	−	42.6597i	0.845286	−	1.46408i
$850$	−5.84755			−0.200569
$851$	−50.2230	+	15.7268i	−1.72162	+	0.539107i
$852$	−19.6457			−0.673051
$853$	−12.0712	+	20.9079i	−0.413310	+	0.715874i	−0.995249	−	0.0973579i	$-0.968961\pi$
$853$	−12.0712	+	20.9079i	−0.413310	+	0.715874i	0.581939	+	0.813232i	$0.302294\pi$
$854$	−7.71243	−	13.3583i	−0.263914	−	0.457113i
$855$	−2.08081	−	3.60407i	−0.0711622	−	0.123256i
$856$	−1.51414	−	2.62256i	−0.0517521	−	0.0896372i
$857$	−42.5290			−1.45276			−0.726382	−	0.687292i	$-0.758800\pi$
$857$	−42.5290			−1.45276			−0.726382	+	0.687292i	$0.758800\pi$
$858$	−0.00907513	−	0.0157186i	−0.000309820	−	0.000536624i
$859$	51.3470			1.75194			0.875968	−	0.482370i	$-0.160224\pi$
$859$	51.3470			1.75194			0.875968	+	0.482370i	$0.160224\pi$
$860$	−6.67088	+	11.5543i	−0.227475	+	0.393998i
$861$	8.57735			0.292315
$862$	−5.07742			−0.172938
$863$	24.7874	−	42.9330i	0.843772	−	1.46146i	−0.0429117	−	0.999079i	$-0.513663\pi$
$863$	24.7874	−	42.9330i	0.843772	−	1.46146i	0.886684	−	0.462377i	$-0.153003\pi$
$864$	10.6108	+	18.3785i	0.360987	+	0.625248i
$865$	−14.9134			−0.507072
$866$	32.1100	−	55.6162i	1.09114	−	1.88991i
$867$	−10.8687	+	18.8251i	−0.369120	+	0.639335i
$868$	6.94288	−	12.0254i	0.235657	−	0.408169i
$869$	3.09955	+	5.36858i	0.105145	+	0.182117i
$870$	10.6214	+	18.3968i	0.360100	+	0.623712i
$871$	−0.0347027	+	0.0601069i	−0.00117586	+	0.00203664i
$872$	−0.809968	+	1.40291i	−0.0274290	+	0.0475084i
$873$	8.70180	−	15.0720i	0.294511	−	0.510108i
$874$	17.6657			0.597551
$875$	−0.391800	−	0.678617i	−0.0132453	−	0.0229415i
$876$	41.3867	−	71.6839i	1.39833	−	2.42197i
$877$	27.7964			0.938618			0.469309	−	0.883034i	$-0.344503\pi$
$877$	27.7964			0.938618			0.469309	+	0.883034i	$0.344503\pi$
$878$	−75.0513			−2.53286
$879$	7.68680	−	13.3139i	0.259269	−	0.449068i
$880$	2.39459			0.0807217
$881$	−24.9175	−	43.1584i	−0.839492	−	1.45404i	−0.890320	−	0.455335i	$-0.849519\pi$
$881$	−24.9175	−	43.1584i	−0.839492	−	1.45404i	0.0508281	−	0.998707i	$-0.483814\pi$
$882$	50.6035			1.70391
$883$	−18.5385	−	32.1096i	−0.623870	−	1.08057i	−0.988758	−	0.149523i	$-0.952226\pi$
$883$	−18.5385	−	32.1096i	−0.623870	−	1.08057i	0.364889	−	0.931051i	$-0.381107\pi$
$884$	0.0171073	+	0.0296307i	0.000575380	+	0.000996588i
$885$	12.2454	+	21.2096i	0.411624	+	0.712954i
$886$	−9.65441	+	16.7219i	−0.324346	+	0.561784i
$887$	37.5487			1.26076			0.630380	−	0.776286i	$-0.282899\pi$
$887$	37.5487			1.26076			0.630380	+	0.776286i	$0.282899\pi$
$888$	2.62293	+	2.41297i	0.0880198	+	0.0809741i
$889$	15.3208			0.513843
$890$	−0.283193	+	0.490505i	−0.00949267	+	0.0164418i
$891$	−1.39452	−	2.41537i	−0.0467181	−	0.0809180i
$892$	−15.0327	−	26.0374i	−0.503331	−	0.871795i
$893$	−2.85967	−	4.95310i	−0.0956953	−	0.165749i
$894$	−56.8237			−1.90047
$895$	3.86927	+	6.70178i	0.129335	+	0.224016i
$896$	−1.38423			−0.0462438
$897$	0.0700395	−	0.121312i	0.00233855	−	0.00405049i
$898$	−24.2283			−0.808510
$899$	38.1714			1.27309
$900$	−3.79344	+	6.57044i	−0.126448	+	0.219015i
$901$	13.5567	+	23.4810i	0.451640	+	0.782264i
$902$	−4.63180			−0.154222
$903$	7.33576	−	12.7059i	0.244119	−	0.422826i
$904$	0.483815	−	0.837992i	0.0160914	−	0.0278712i
$905$	−6.57794	+	11.3933i	−0.218658	+	0.378727i
$906$	−0.0402730	−	0.0697548i	−0.00133798	−	0.00231745i
$907$	16.0352	+	27.7739i	0.532441	+	0.922216i	0.999283	+	0.0378744i	$0.0120587\pi$
$907$	16.0352	+	27.7739i	0.532441	+	0.922216i	−0.466841	+	0.884341i	$0.654608\pi$
$908$	−14.0663	+	24.3636i	−0.466808	+	0.808535i
$909$	10.8613	−	18.8124i	0.360248	−	0.623967i
$910$	−0.00472113	+	0.00817723i	−0.000156504	+	0.000271072i
$911$	26.0546			0.863229			0.431614	−	0.902058i	$-0.357944\pi$
$911$	26.0546			0.863229			0.431614	+	0.902058i	$0.357944\pi$
$912$	−5.77733	−	10.0066i	−0.191307	−	0.331353i
$913$	0.244785	−	0.423979i	0.00810119	−	0.0140317i
$914$	22.1023			0.731080
$915$	26.4488			0.874369
$916$	6.03396	−	10.4511i	0.199368	−	0.345315i
$917$	7.48647			0.247225
$918$	−7.89181	−	13.6690i	−0.260468	−	0.451145i
$919$	−5.23024			−0.172530			−0.0862648	−	0.996272i	$-0.527493\pi$
$919$	−5.23024			−0.172530			−0.0862648	+	0.996272i	$0.527493\pi$
$920$	0.956732	+	1.65711i	0.0315425	+	0.0546332i
$921$	−28.7294	−	49.7608i	−0.946666	−	1.63967i
$922$	21.7082	+	37.5998i	0.714923	+	1.23828i
$923$	0.0120024	−	0.0207888i	0.000395064	−	0.000684271i
$924$	2.22823			0.0733034
$925$	−1.32822	+	5.93598i	−0.0436716	+	0.195174i
$926$	−41.3031			−1.35730
$927$	−24.6661	+	42.7229i	−0.810141	+	1.40320i
$928$	15.9861	+	27.6887i	0.524769	+	0.908927i
$929$	1.59438	+	2.76154i	0.0523099	+	0.0906033i	0.890995	−	0.454014i	$-0.150008\pi$
$929$	1.59438	+	2.76154i	0.0523099	+	0.0906033i	−0.838685	+	0.544617i	$0.816675\pi$
$930$	24.5170	+	42.4647i	0.803944	+	1.39247i
$931$	−6.61287			−0.216728
$932$	11.1390	+	19.2932i	0.364868	+	0.631971i
$933$	−18.6137			−0.609386
$934$	−1.69378	+	2.93372i	−0.0554223	+	0.0959943i
$935$	−1.68612			−0.0551421
$936$	−0.00543166			−0.000177540
$937$	−27.2384	+	47.1783i	−0.889840	+	1.54125i	−0.0497763	+	0.998760i	$0.515851\pi$
$937$	−27.2384	+	47.1783i	−0.889840	+	1.54125i	−0.840064	+	0.542488i	$0.817482\pi$
$938$	−8.77373	−	15.1966i	−0.286473	−	0.496185i
$939$	62.9767			2.05517
$940$	−5.21336	+	9.02980i	−0.170041	+	0.294520i
$941$	22.1090	−	38.2939i	0.720733	−	1.24835i	−0.239974	−	0.970779i	$-0.577139\pi$
$941$	22.1090	−	38.2939i	0.720733	−	1.24835i	0.960707	−	0.277566i	$-0.0895277\pi$
$942$	36.9115	−	63.9326i	1.20264	−	2.08304i
$943$	−17.8735	−	30.9579i	−0.582042	−	1.00813i
$944$	19.4671	+	33.7181i	0.633602	+	1.09743i
$945$	1.05754	−	1.83171i	0.0344018	−	0.0595857i
$946$	−3.96134	+	6.86124i	−0.128794	+	0.223078i
$947$	−5.53233	+	9.58228i	−0.179777	+	0.311382i	−0.941804	−	0.336163i	$-0.890871\pi$
$947$	−5.53233	+	9.58228i	−0.179777	+	0.311382i	0.762027	+	0.647545i	$0.224204\pi$
$948$	−54.5326			−1.77114
$949$	0.0505698	+	0.0875895i	0.00164157	+	0.00284328i
$950$	1.02091	−	1.76827i	0.0331227	−	0.0573701i
$951$	−61.2272			−1.98543
$952$	0.513949			0.0166572
$953$	−21.8629	+	37.8677i	−0.708210	+	1.22666i	0.257311	+	0.966329i	$0.417164\pi$
$953$	−21.8629	+	37.8677i	−0.708210	+	1.22666i	−0.965521	+	0.260327i	$0.916170\pi$
$954$	72.4467			2.34555
$955$	−11.6230	−	20.1317i	−0.376113	−	0.651447i
$956$	−7.22884			−0.233798
$957$	3.06266	+	5.30468i	0.0990016	+	0.171476i
$958$	−32.5672	−	56.4081i	−1.05220	−	1.82246i
$959$	2.00975	+	3.48099i	0.0648982	+	0.112407i
$960$	−9.37714	+	16.2417i	−0.302646	+	0.524198i
$961$	57.1094			1.84224
$962$	0.0699471	−	0.0219032i	0.00225519	−	0.000706187i
$963$	55.0285			1.77327
$964$	18.2368	−	31.5871i	0.587368	−	1.01735i
$965$	−2.69104	−	4.66102i	−0.0866277	−	0.150044i
$966$	17.7078	+	30.6708i	0.569739	+	0.986816i
$967$	14.5173	+	25.1448i	0.466846	+	0.808601i	0.999283	−	0.0378687i	$-0.0120569\pi$
$967$	14.5173	+	25.1448i	0.466846	+	0.808601i	−0.532437	+	0.846470i	$0.678724\pi$
$968$	−2.36127			−0.0758941
$969$	4.06804	+	7.04605i	0.130684	+	0.226352i
$970$	8.53874			0.274162
$971$	−8.15440	+	14.1238i	−0.261687	+	0.453255i	−0.966690	−	0.255949i	$-0.917612\pi$
$971$	−8.15440	+	14.1238i	−0.261687	+	0.453255i	0.705003	+	0.709204i	$0.250946\pi$
$972$	39.8216			1.27728
$973$	−8.10323			−0.259778
$974$	13.2657	−	22.9768i	0.425059	−	0.736224i
$975$	−0.00809524	−	0.0140214i	−0.000259255	−	0.000449043i
$976$	42.0470			1.34589
$977$	9.80571	−	16.9840i	0.313712	−	0.543366i	−0.665450	−	0.746442i	$-0.731761\pi$
$977$	9.80571	−	16.9840i	0.313712	−	0.543366i	0.979163	+	0.203076i	$0.0650939\pi$
$978$	−55.6170	+	96.3315i	−1.77844	+	3.08034i
$979$	−0.0816580	+	0.141436i	−0.00260980	+	0.00452031i
$980$	6.02783	+	10.4405i	0.192552	+	0.333510i
$981$	−14.7184	−	25.4930i	−0.469923	−	0.813930i
$982$	13.6677	−	23.6732i	0.436154	−	0.755442i
$983$	26.7020	−	46.2491i	0.851660	−	1.47512i	−0.0280494	−	0.999607i	$-0.508930\pi$
$983$	26.7020	−	46.2491i	0.851660	−	1.47512i	0.879709	−	0.475512i	$-0.157737\pi$
$984$	−1.21042	+	2.09651i	−0.0385867	+	0.0668341i
$985$	−0.737219			−0.0234897
$986$	−11.8897	−	20.5935i	−0.378645	−	0.655832i
$987$	5.73297	−	9.92980i	0.182483	−	0.316069i
$988$	−0.0119469			−0.000380081
$989$	−61.1452			−1.94430
$990$	−2.25265	+	3.90170i	−0.0715938	+	0.124004i
$991$	47.7930			1.51820			0.759098	−	0.650976i	$-0.225640\pi$
$991$	47.7930			1.51820			0.759098	+	0.650976i	$0.225640\pi$
$992$	36.9001	+	63.9128i	1.17158	+	2.02923i
$993$	27.7301			0.879988
$994$	3.03451	+	5.25593i	0.0962490	+	0.166708i
$995$	−1.76166	−	3.05129i	−0.0558484	−	0.0967323i
$996$	2.15333	+	3.72968i	0.0682309	+	0.118179i
$997$	−28.3125	+	49.0387i	−0.896667	+	1.55307i	−0.0649381	+	0.997889i	$0.520685\pi$
$997$	−28.3125	+	49.0387i	−0.896667	+	1.55307i	−0.831728	+	0.555183i	$0.812648\pi$
$998$	−63.5087			−2.01033
$999$	−15.6683	+	4.90635i	−0.495723	+	0.155230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.a.121.6	yes	14
5.2	odd	4		925.2.o.b.824.11		28
5.3	odd	4		925.2.o.b.824.4		28
5.4	even	2		925.2.e.c.676.2		14
37.10	even	3		6845.2.a.l.1.2		7
37.26	even	3	inner	185.2.e.a.26.6	✓	14
37.27	even	6		6845.2.a.k.1.6		7
185.63	odd	12		925.2.o.b.174.11		28
185.137	odd	12		925.2.o.b.174.4		28
185.174	even	6		925.2.e.c.26.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.6	✓	14	37.26	even	3	inner
185.2.e.a.121.6	yes	14	1.1	even	1	trivial
925.2.e.c.26.2		14	185.174	even	6
925.2.e.c.676.2		14	5.4	even	2
925.2.o.b.174.4		28	185.137	odd	12
925.2.o.b.174.11		28	185.63	odd	12
925.2.o.b.824.4		28	5.3	odd	4
925.2.o.b.824.11		28	5.2	odd	4
6845.2.a.k.1.6		7	37.27	even	6
6845.2.a.l.1.2		7	37.10	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.985880 - 1.70759i) q^{2} +(1.32465 + 2.29437i) q^{3} +(-0.943918 - 1.63491i) q^{4} +(-0.500000 - 0.866025i) q^{5} +5.22380 q^{6} +(-0.391800 - 0.678617i) q^{7} +0.221160 q^{8} +(-2.00941 + 3.48041i) q^{9} -1.97176 q^{10} -0.568551 q^{11} +(2.50073 - 4.33139i) q^{12} +(0.00305561 + 0.00529246i) q^{13} -1.54507 q^{14} +(1.32465 - 2.29437i) q^{15} +(2.10587 - 3.64748i) q^{16} +(-1.48282 + 2.56833i) q^{17} +(3.96208 + 6.86253i) q^{18} +(-0.517765 - 0.896796i) q^{19} +(-0.943918 + 1.63491i) q^{20} +(1.03800 - 1.79787i) q^{21} +(-0.560523 + 0.970854i) q^{22} -8.65194 q^{23} +(0.292960 + 0.507422i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.0120498 q^{26} -2.69919 q^{27} +(-0.739654 + 1.28112i) q^{28} -4.06655 q^{29} +(-2.61190 - 4.52394i) q^{30} -9.38666 q^{31} +(-3.93112 - 6.80889i) q^{32} +(-0.753133 - 1.30446i) q^{33} +(2.92377 + 5.06412i) q^{34} +(-0.391800 + 0.678617i) q^{35} +7.58689 q^{36} +(5.80482 - 1.81772i) q^{37} -2.04182 q^{38} +(-0.00809524 + 0.0140214i) q^{39} +(-0.110580 - 0.191530i) q^{40} +(2.06584 + 3.57814i) q^{41} +(-2.04668 - 3.54496i) q^{42} +7.06722 q^{43} +(0.536666 + 0.929532i) q^{44} +4.01883 q^{45} +(-8.52978 + 14.7740i) q^{46} +5.52310 q^{47} +11.1582 q^{48} +(3.19299 - 5.53041i) q^{49} +(0.985880 + 1.70759i) q^{50} -7.85691 q^{51} +(0.00576848 - 0.00999130i) q^{52} +(4.57125 - 7.91765i) q^{53} +(-2.66107 + 4.60911i) q^{54} +(0.284276 + 0.492380i) q^{55} +(-0.0866504 - 0.150083i) q^{56} +(1.37172 - 2.37589i) q^{57} +(-4.00913 + 6.94402i) q^{58} +(-4.62211 + 8.00573i) q^{59} -5.00146 q^{60} +(4.99164 + 8.64577i) q^{61} +(-9.25412 + 16.0286i) q^{62} +3.14915 q^{63} -7.07894 q^{64} +(0.00305561 - 0.00529246i) q^{65} -2.96999 q^{66} +(5.67853 + 9.83551i) q^{67} +5.59866 q^{68} +(-11.4608 - 19.8507i) q^{69} +(0.772535 + 1.33807i) q^{70} +(-1.96400 - 3.40174i) q^{71} +(-0.444402 + 0.769726i) q^{72} +16.5499 q^{73} +(2.61893 - 11.7043i) q^{74} -2.64931 q^{75} +(-0.977456 + 1.69300i) q^{76} +(0.222758 + 0.385829i) q^{77} +(0.0159619 + 0.0276468i) q^{78} +(-5.45167 - 9.44257i) q^{79} -4.21175 q^{80} +(2.45275 + 4.24830i) q^{81} +8.14668 q^{82} +(-0.430541 + 0.745719i) q^{83} -3.91914 q^{84} +2.96565 q^{85} +(6.96743 - 12.0679i) q^{86} +(-5.38677 - 9.33017i) q^{87} -0.125741 q^{88} +(0.143625 - 0.248765i) q^{89} +(3.96208 - 6.86253i) q^{90} +(0.00239437 - 0.00414717i) q^{91} +(8.16673 + 14.1452i) q^{92} +(-12.4341 - 21.5364i) q^{93} +(5.44512 - 9.43122i) q^{94} +(-0.517765 + 0.896796i) q^{95} +(10.4147 - 18.0388i) q^{96} -4.33052 q^{97} +(-6.29580 - 10.9046i) q^{98} +(1.14245 - 1.97879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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