LMFDB - Embedded newform 425.2.k.b.341.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			341.3
Character	$\chi$	$=$	425.341
Dual form			425.2.k.b.86.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89465 - 1.37655i) q^{2} +(-0.866934 - 2.66815i) q^{3} +(1.07680 + 3.31404i) q^{4} +(-2.13509 - 0.664386i) q^{5} +(-2.03029 + 6.24859i) q^{6} -2.04332 q^{7} +(1.07439 - 3.30663i) q^{8} +(-3.94040 + 2.86287i) q^{9} +(3.13069 + 4.19783i) q^{10} +(-0.498365 - 0.362083i) q^{11} +(7.90885 - 5.74612i) q^{12} +(1.02753 - 0.746547i) q^{13} +(3.87139 + 2.81273i) q^{14} +(0.0782984 + 6.27271i) q^{15} +(-0.949136 + 0.689588i) q^{16} +(0.309017 - 0.951057i) q^{17} +11.4066 q^{18} +(-2.01390 + 6.19814i) q^{19} +(-0.0972525 - 7.79118i) q^{20} +(1.77143 + 5.45189i) q^{21} +(0.445804 + 1.37204i) q^{22} +(-1.51770 - 1.10267i) q^{23} -9.75401 q^{24} +(4.11718 + 2.83704i) q^{25} -2.97448 q^{26} +(4.24563 + 3.08463i) q^{27} +(-2.20024 - 6.77166i) q^{28} +(-2.05676 - 6.33004i) q^{29} +(8.48632 - 11.9924i) q^{30} +(0.848576 - 2.61165i) q^{31} -4.20606 q^{32} +(-0.534042 + 1.64361i) q^{33} +(-1.89465 + 1.37655i) q^{34} +(4.36267 + 1.35755i) q^{35} +(-13.7307 - 9.97592i) q^{36} +(-5.15805 + 3.74754i) q^{37} +(12.3477 - 8.97110i) q^{38} +(-2.88270 - 2.09441i) q^{39} +(-4.49079 + 6.34613i) q^{40} +(1.62573 - 1.18116i) q^{41} +(4.14854 - 12.7679i) q^{42} +9.73154 q^{43} +(0.663321 - 2.04149i) q^{44} +(10.3151 - 3.49452i) q^{45} +(1.35763 + 4.17837i) q^{46} +(3.13056 + 9.63488i) q^{47} +(2.66276 + 1.93461i) q^{48} -2.82484 q^{49} +(-3.89532 - 11.0427i) q^{50} -2.80546 q^{51} +(3.58054 + 2.60141i) q^{52} +(-3.74086 - 11.5132i) q^{53} +(-3.79786 - 11.6886i) q^{54} +(0.823488 + 1.10418i) q^{55} +(-2.19532 + 6.75651i) q^{56} +18.2835 q^{57} +(-4.81676 + 14.8245i) q^{58} +(5.91599 - 4.29822i) q^{59} +(-20.7037 + 7.01392i) q^{60} +(1.15130 + 0.836472i) q^{61} +(-5.20281 + 3.78006i) q^{62} +(8.05150 - 5.84975i) q^{63} +(9.86730 + 7.16901i) q^{64} +(-2.68987 + 0.911263i) q^{65} +(3.27434 - 2.37894i) q^{66} +(-1.60347 + 4.93496i) q^{67} +3.48459 q^{68} +(-1.62635 + 5.00540i) q^{69} +(-6.39701 - 8.57751i) q^{70} +(2.24921 + 6.92235i) q^{71} +(5.23292 + 16.1053i) q^{72} +(-10.7537 - 7.81304i) q^{73} +14.9314 q^{74} +(4.00032 - 13.4448i) q^{75} -22.7095 q^{76} +(1.01832 + 0.739852i) q^{77} +(2.57868 + 7.93635i) q^{78} +(4.40684 + 13.5629i) q^{79} +(2.48464 - 0.841736i) q^{80} +(0.0342773 - 0.105495i) q^{81} -4.70612 q^{82} +(-4.27448 + 13.1555i) q^{83} +(-16.1603 + 11.7412i) q^{84} +(-1.29165 + 1.82528i) q^{85} +(-18.4379 - 13.3959i) q^{86} +(-15.1064 + 10.9755i) q^{87} +(-1.73271 + 1.25889i) q^{88} +(2.02593 + 1.47192i) q^{89} +(-24.3540 - 7.57835i) q^{90} +(-2.09958 + 1.52544i) q^{91} +(2.02005 - 6.21708i) q^{92} -7.70393 q^{93} +(7.33153 - 22.5641i) q^{94} +(8.41780 - 11.8956i) q^{95} +(3.64638 + 11.2224i) q^{96} +(5.65839 + 17.4147i) q^{97} +(5.35209 + 3.88852i) q^{98} +3.00035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−1.89465	−	1.37655i	−1.33972	−	0.973365i	−0.999454	−	0.0330368i	$-0.989482\pi$
$2$	−1.89465	−	1.37655i	−1.33972	−	0.973365i	−0.340268	−	0.940328i	$-0.610518\pi$
$3$	−0.866934	−	2.66815i	−0.500525	−	1.54046i	−0.808166	−	0.588954i	$-0.799540\pi$
$3$	−0.866934	−	2.66815i	−0.500525	−	1.54046i	0.307641	−	0.951502i	$-0.400460\pi$
$4$	1.07680	+	3.31404i	0.538399	+	1.65702i
$5$	−2.13509	−	0.664386i	−0.954839	−	0.297122i
$5$	−2.13509	−	0.664386i	−0.954839	−	0.297122i
$6$	−2.03029	+	6.24859i	−0.828863	+	2.55098i
$7$	−2.04332			−0.772303			−0.386151	−	0.922435i	$-0.626196\pi$
$7$	−2.04332			−0.772303			−0.386151	+	0.922435i	$0.626196\pi$
$8$	1.07439	−	3.30663i	0.379854	−	1.16907i
$9$	−3.94040	+	2.86287i	−1.31347	+	0.954288i
$10$	3.13069	+	4.19783i	0.990011	+	1.32747i
$11$	−0.498365	−	0.362083i	−0.150263	−	0.109172i	0.510114	−	0.860107i	$-0.329603\pi$
$11$	−0.498365	−	0.362083i	−0.150263	−	0.109172i	−0.660376	+	0.750935i	$0.729603\pi$
$12$	7.90885	−	5.74612i	2.28309	−	1.65876i
$13$	1.02753	−	0.746547i	0.284987	−	0.207055i	−0.436103	−	0.899897i	$-0.643642\pi$
$13$	1.02753	−	0.746547i	0.284987	−	0.207055i	0.721089	+	0.692842i	$0.243642\pi$
$14$	3.87139	+	2.81273i	1.03467	+	0.751733i
$15$	0.0782984	+	6.27271i	0.0202166	+	1.61961i
$16$	−0.949136	+	0.689588i	−0.237284	+	0.172397i
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i
$18$	11.4066			2.68855
$19$	−2.01390	+	6.19814i	−0.462020	+	1.42195i	0.400673	+	0.916221i	$0.368776\pi$
$19$	−2.01390	+	6.19814i	−0.462020	+	1.42195i	−0.862692	+	0.505729i	$0.831224\pi$
$20$	−0.0972525	−	7.79118i	−0.0217463	−	1.74216i
$21$	1.77143	+	5.45189i	0.386557	+	1.18970i
$22$	0.445804	+	1.37204i	0.0950458	+	0.292521i
$23$	−1.51770	−	1.10267i	−0.316462	−	0.229923i	0.418202	−	0.908354i	$-0.362660\pi$
$23$	−1.51770	−	1.10267i	−0.316462	−	0.229923i	−0.734664	+	0.678431i	$0.762660\pi$
$24$	−9.75401			−1.99103
$25$	4.11718	+	2.83704i	0.823437	+	0.567408i
$26$	−2.97448			−0.583343
$27$	4.24563	+	3.08463i	0.817071	+	0.593637i
$28$	−2.20024	−	6.77166i	−0.415807	−	1.27972i
$29$	−2.05676	−	6.33004i	−0.381930	−	1.17546i	−0.938683	−	0.344781i	$-0.887953\pi$
$29$	−2.05676	−	6.33004i	−0.381930	−	1.17546i	0.556753	−	0.830678i	$-0.312047\pi$
$30$	8.48632	−	11.9924i	1.54938	−	2.18950i
$31$	0.848576	−	2.61165i	0.152409	−	0.469066i	−0.845480	−	0.534006i	$-0.820686\pi$
$31$	0.848576	−	2.61165i	0.152409	−	0.469066i	0.997889	+	0.0649406i	$0.0206858\pi$
$32$	−4.20606			−0.743533
$33$	−0.534042	+	1.64361i	−0.0929649	+	0.286116i
$34$	−1.89465	+	1.37655i	−0.324930	+	0.236076i
$35$	4.36267	+	1.35755i	0.737425	+	0.229469i
$36$	−13.7307	−	9.97592i	−2.28845	−	1.66265i
$37$	−5.15805	+	3.74754i	−0.847978	+	0.616092i	−0.924588	−	0.380969i	$-0.875590\pi$
$37$	−5.15805	+	3.74754i	−0.847978	+	0.616092i	0.0766100	+	0.997061i	$0.475590\pi$
$38$	12.3477	−	8.97110i	2.00306	−	1.45530i
$39$	−2.88270	−	2.09441i	−0.461602	−	0.335373i
$40$	−4.49079	+	6.34613i	−0.710056	+	1.00341i
$41$	1.62573	−	1.18116i	0.253896	−	0.184466i	−0.453556	−	0.891228i	$-0.649845\pi$
$41$	1.62573	−	1.18116i	0.253896	−	0.184466i	0.707452	+	0.706762i	$0.249845\pi$
$42$	4.14854	−	12.7679i	0.640133	−	1.97013i
$43$	9.73154			1.48405			0.742023	−	0.670374i	$-0.233866\pi$
$43$	9.73154			1.48405			0.742023	+	0.670374i	$0.233866\pi$
$44$	0.663321	−	2.04149i	0.0999994	−	0.307767i
$45$	10.3151	−	3.49452i	1.53769	−	0.520932i
$46$	1.35763	+	4.17837i	0.200172	+	0.616067i
$47$	3.13056	+	9.63488i	0.456639	+	1.40539i	0.869200	+	0.494461i	$0.164635\pi$
$47$	3.13056	+	9.63488i	0.456639	+	1.40539i	−0.412561	+	0.910930i	$0.635365\pi$
$48$	2.66276	+	1.93461i	0.384337	+	0.279237i
$49$	−2.82484			−0.403548
$50$	−3.89532	−	11.0427i	−0.550881	−	1.56167i
$51$	−2.80546			−0.392843
$52$	3.58054	+	2.60141i	0.496531	+	0.360751i
$53$	−3.74086	−	11.5132i	−0.513846	−	1.58146i	−0.785372	−	0.619025i	$-0.787528\pi$
$53$	−3.74086	−	11.5132i	−0.513846	−	1.58146i	0.271525	−	0.962431i	$-0.412472\pi$
$54$	−3.79786	−	11.6886i	−0.516823	−	1.59062i
$55$	0.823488	+	1.10418i	0.111039	+	0.148888i
$56$	−2.19532	+	6.75651i	−0.293362	+	0.902876i
$57$	18.2835			2.42171
$58$	−4.81676	+	14.8245i	−0.632471	+	1.94655i
$59$	5.91599	−	4.29822i	0.770196	−	0.559580i	−0.131825	−	0.991273i	$-0.542084\pi$
$59$	5.91599	−	4.29822i	0.770196	−	0.559580i	0.902021	+	0.431693i	$0.142084\pi$
$60$	−20.7037	+	7.01392i	−2.67284	+	0.905494i
$61$	1.15130	+	0.836472i	0.147409	+	0.107099i	0.659046	−	0.752103i	$-0.270960\pi$
$61$	1.15130	+	0.836472i	0.147409	+	0.107099i	−0.511636	+	0.859202i	$0.670960\pi$
$62$	−5.20281	+	3.78006i	−0.660758	+	0.480069i
$63$	8.05150	−	5.84975i	1.01439	−	0.737000i
$64$	9.86730	+	7.16901i	1.23341	+	0.896126i
$65$	−2.68987	+	0.911263i	−0.333637	+	0.113028i
$66$	3.27434	−	2.37894i	0.403043	−	0.292828i
$67$	−1.60347	+	4.93496i	−0.195894	+	0.602901i	0.804071	+	0.594534i	$0.202663\pi$
$67$	−1.60347	+	4.93496i	−0.195894	+	0.602901i	−0.999965	+	0.00836725i	$0.997337\pi$
$68$	3.48459			0.422569
$69$	−1.62635	+	5.00540i	−0.195790	+	0.602579i
$70$	−6.39701	−	8.57751i	−0.764589	−	1.02521i
$71$	2.24921	+	6.92235i	0.266932	+	0.821532i	0.991242	+	0.132058i	$0.0421584\pi$
$71$	2.24921	+	6.92235i	0.266932	+	0.821532i	−0.724310	+	0.689474i	$0.757842\pi$
$72$	5.23292	+	16.1053i	0.616705	+	1.89802i
$73$	−10.7537	−	7.81304i	−1.25863	−	0.914447i	−0.259939	−	0.965625i	$-0.583702\pi$
$73$	−10.7537	−	7.81304i	−1.25863	−	0.914447i	−0.998690	+	0.0511783i	$0.983702\pi$
$74$	14.9314			1.73574
$75$	4.00032	−	13.4448i	0.461918	−	1.55247i
$76$	−22.7095			−2.60495
$77$	1.01832	+	0.739852i	0.116048	+	0.0843140i
$78$	2.57868	+	7.93635i	0.291978	+	0.898615i
$79$	4.40684	+	13.5629i	0.495809	+	1.52594i	0.815693	+	0.578485i	$0.196356\pi$
$79$	4.40684	+	13.5629i	0.495809	+	1.52594i	−0.319884	+	0.947457i	$0.603644\pi$
$80$	2.48464	−	0.841736i	0.277791	−	0.0941090i
$81$	0.0342773	−	0.105495i	0.00380859	−	0.0117216i
$82$	−4.70612			−0.519704
$83$	−4.27448	+	13.1555i	−0.469185	+	1.44400i	0.384458	+	0.923143i	$0.374388\pi$
$83$	−4.27448	+	13.1555i	−0.469185	+	1.44400i	−0.853642	+	0.520860i	$0.825612\pi$
$84$	−16.1603	+	11.7412i	−1.76324	+	1.28107i
$85$	−1.29165	+	1.82528i	−0.140099	+	0.197979i
$86$	−18.4379	−	13.3959i	−1.98821	−	1.44452i
$87$	−15.1064	+	10.9755i	−1.61958	+	1.17669i
$88$	−1.73271	+	1.25889i	−0.184708	+	0.134198i
$89$	2.02593	+	1.47192i	0.214748	+	0.156024i	0.689959	−	0.723848i	$-0.257628\pi$
$89$	2.02593	+	1.47192i	0.214748	+	0.156024i	−0.475211	+	0.879872i	$0.657628\pi$
$90$	−24.3540	−	7.57835i	−2.56713	−	0.798828i
$91$	−2.09958	+	1.52544i	−0.220096	+	0.159909i
$92$	2.02005	−	6.21708i	0.210605	−	0.648175i
$93$	−7.70393			−0.798860
$94$	7.33153	−	22.5641i	0.756189	−	2.32731i
$95$	8.41780	−	11.8956i	0.863648	−	1.22046i
$96$	3.64638	+	11.2224i	0.372157	+	1.14538i
$97$	5.65839	+	17.4147i	0.574523	+	1.76820i	0.637798	+	0.770203i	$0.279845\pi$
$97$	5.65839	+	17.4147i	0.574523	+	1.76820i	−0.0632756	+	0.997996i	$0.520155\pi$
$98$	5.35209	+	3.88852i	0.540642	+	0.392800i
$99$	3.00035			0.301546
$100$	−4.96871	+	16.6994i	−0.496871	+	1.66994i
$101$	−1.87423			−0.186493			−0.0932464	−	0.995643i	$-0.529724\pi$
$101$	−1.87423			−0.186493			−0.0932464	+	0.995643i	$0.529724\pi$
$102$	5.31537	+	3.86184i	0.526300	+	0.382379i
$103$	1.94633	+	5.99017i	0.191777	+	0.590229i	0.999999	+	0.00135131i	$0.000430136\pi$
$103$	1.94633	+	5.99017i	0.191777	+	0.590229i	−0.808222	+	0.588878i	$0.799570\pi$
$104$	−1.36458	−	4.19976i	−0.133808	−	0.411820i
$105$	−0.159989	−	12.8172i	−0.0156133	−	1.25083i
$106$	−8.76079	+	26.9629i	−0.850923	+	2.61887i
$107$	1.38817			0.134199			0.0670996	−	0.997746i	$-0.478625\pi$
$107$	1.38817			0.134199			0.0670996	+	0.997746i	$0.478625\pi$
$108$	−5.65091	+	17.3917i	−0.543759	+	1.67352i
$109$	4.69474	−	3.41093i	0.449674	−	0.326708i	−0.339793	−	0.940500i	$-0.610357\pi$
$109$	4.69474	−	3.41093i	0.449674	−	0.326708i	0.789467	+	0.613793i	$0.210357\pi$
$110$	−0.0402634	−	3.22562i	−0.00383897	−	0.307551i
$111$	14.4707	+	10.5136i	1.37350	+	0.997904i
$112$	1.93939	−	1.40905i	0.183255	−	0.133143i
$113$	−7.10330	+	5.16085i	−0.668223	+	0.485492i	−0.869430	−	0.494057i	$-0.835514\pi$
$113$	−7.10330	+	5.16085i	−0.668223	+	0.485492i	0.201207	+	0.979549i	$0.435514\pi$
$114$	−34.6409	−	25.1681i	−3.24441	−	2.35720i
$115$	2.50782	+	3.36264i	0.233855	+	0.313568i
$116$	18.7633	−	13.6324i	1.74213	−	1.26573i
$117$	−1.91163	+	5.88338i	−0.176730	+	0.543919i
$118$	−17.1254			−1.57652
$119$	−0.631421	+	1.94331i	−0.0578823	+	0.178143i
$120$	20.8256	+	6.48042i	1.90111	+	0.591579i
$121$	−3.28192	−	10.1007i	−0.298357	−	0.918248i
$122$	−1.02988	−	3.16965i	−0.0932411	−	0.286967i
$123$	−4.56092	−	3.31370i	−0.411244	−	0.298786i
$124$	9.56886			0.859309
$125$	−6.90565	−	8.79273i	−0.617660	−	0.786445i
$126$	−23.3073			−2.07638
$127$	−11.5310	−	8.37779i	−1.02321	−	0.743409i	−0.0562754	−	0.998415i	$-0.517922\pi$
$127$	−11.5310	−	8.37779i	−1.02321	−	0.743409i	−0.966939	+	0.255006i	$0.917922\pi$
$128$	−6.22715	−	19.1652i	−0.550407	−	1.69398i
$129$	−8.43661	−	25.9652i	−0.742802	−	2.28611i
$130$	6.35076	+	1.97620i	0.556999	+	0.173324i
$131$	−5.81510	+	17.8970i	−0.508068	+	1.56367i	0.287484	+	0.957785i	$0.407181\pi$
$131$	−5.81510	+	17.8970i	−0.508068	+	1.56367i	−0.795552	+	0.605886i	$0.792819\pi$
$132$	−6.02206			−0.524153
$133$	4.11504	−	12.6648i	0.356819	−	1.09818i
$134$	9.83121	−	7.14279i	0.849287	−	0.617043i
$135$	−7.01539	−	9.40668i	−0.603789	−	0.809598i
$136$	−2.81279	−	2.04361i	−0.241195	−	0.175238i
$137$	−15.2775	+	11.0997i	−1.30524	+	0.948315i	−0.999992	−	0.00395679i	$-0.998741\pi$
$137$	−15.2775	+	11.0997i	−1.30524	+	0.948315i	−0.305251	+	0.952272i	$0.598741\pi$
$138$	9.97153	−	7.24474i	0.848833	−	0.616713i
$139$	−7.39931	−	5.37591i	−0.627601	−	0.455979i	0.227967	−	0.973669i	$-0.426792\pi$
$139$	−7.39931	−	5.37591i	−0.627601	−	0.455979i	−0.855568	+	0.517690i	$0.826792\pi$
$140$	0.198718	+	15.9199i	0.0167948	+	1.34548i
$141$	22.9933	−	16.7056i	1.93639	−	1.40687i
$142$	5.26747	−	16.2116i	0.442036	−	1.36045i
$143$	−0.782398			−0.0654274
$144$	1.76577	−	5.43450i	0.147148	−	0.452875i
$145$	0.185759	+	14.8817i	0.0154264	+	1.23585i
$146$	9.61957	+	29.6060i	0.796121	+	2.45021i
$147$	2.44895	+	7.53709i	0.201986	+	0.621648i
$148$	−17.9737	−	13.0586i	−1.47743	−	1.07341i
$149$	10.3225			0.845654			0.422827	−	0.906210i	$-0.361038\pi$
$149$	10.3225			0.845654			0.422827	+	0.906210i	$0.361038\pi$
$150$	−26.0866	+	19.9666i	−2.12996	+	1.63026i
$151$	18.5244			1.50749			0.753747	−	0.657164i	$-0.228244\pi$
$151$	18.5244			1.50749			0.753747	+	0.657164i	$0.228244\pi$
$152$	18.3312	+	13.3184i	1.48686	+	1.08027i
$153$	1.50510	+	4.63221i	0.121680	+	0.374492i
$154$	−0.910921	−	2.80353i	−0.0734041	−	0.225915i
$155$	−3.54692	+	5.01231i	−0.284896	+	0.402598i
$156$	3.83687	−	11.8087i	0.307195	−	0.945449i
$157$	9.51917			0.759713			0.379856	−	0.925045i	$-0.375973\pi$
$157$	9.51917			0.759713			0.379856	+	0.925045i	$0.375973\pi$
$158$	10.3205	−	31.7632i	0.821053	−	2.52694i
$159$	−27.4758	+	19.9623i	−2.17897	+	1.58312i
$160$	8.98030	+	2.79445i	0.709955	+	0.220920i
$161$	3.10115	+	2.25312i	0.244405	+	0.177570i
$162$	−0.210162	+	0.152691i	−0.0165119	+	0.0119966i
$163$	7.45115	−	5.41358i	0.583619	−	0.424024i	−0.256408	−	0.966569i	$-0.582539\pi$
$163$	7.45115	−	5.41358i	0.583619	−	0.424024i	0.840027	+	0.542544i	$0.182539\pi$
$164$	5.66500	+	4.11587i	0.442363	+	0.321395i
$165$	2.23222	−	3.15445i	0.173778	−	0.245573i
$166$	26.2078	−	19.0411i	2.03412	−	1.47787i
$167$	−1.24697	+	3.83779i	−0.0964937	+	0.296977i	−0.987640	−	0.156739i	$-0.949902\pi$
$167$	−1.24697	+	3.83779i	−0.0964937	+	0.296977i	0.891146	+	0.453716i	$0.149902\pi$
$168$	19.9306			1.53768
$169$	−3.51873	+	10.8295i	−0.270671	+	0.833041i
$170$	4.95981	−	1.68026i	0.380400	−	0.128870i
$171$	−9.80888	−	30.1886i	−0.750104	−	2.30858i
$172$	10.4789	+	32.2508i	0.799009	+	2.45910i
$173$	9.31594	+	6.76843i	0.708278	+	0.514594i	0.882618	−	0.470092i	$-0.155779\pi$
$173$	9.31594	+	6.76843i	0.708278	+	0.514594i	−0.174340	+	0.984686i	$0.555779\pi$
$174$	43.7297			3.31514
$175$	−8.41273	−	5.79699i	−0.635943	−	0.438211i
$176$	0.722704			0.0544759
$177$	−16.5971	−	12.0585i	−1.24751	−	0.906370i
$178$	−1.81226	−	5.57758i	−0.135835	−	0.418057i
$179$	5.76378	+	17.7391i	0.430805	+	1.32588i	0.897325	+	0.441371i	$0.145508\pi$
$179$	5.76378	+	17.7391i	0.430805	+	1.32588i	−0.466519	+	0.884511i	$0.654492\pi$
$180$	22.6883	+	30.4219i	1.69109	+	2.26751i
$181$	2.66390	−	8.19865i	0.198006	−	0.609401i	−0.801922	−	0.597429i	$-0.796189\pi$
$181$	2.66390	−	8.19865i	0.198006	−	0.609401i	0.999928	−	0.0119722i	$-0.00381097\pi$
$182$	6.07781			0.450517
$183$	1.23373	−	3.79702i	0.0911997	−	0.280684i
$184$	−5.27673	+	3.83377i	−0.389006	+	0.282629i
$185$	13.5027	−	4.57439i	0.992737	−	0.336316i
$186$	14.5963	+	10.6048i	1.07025	+	0.777583i
$187$	−0.498365	+	0.362083i	−0.0364440	+	0.0264781i
$188$	−28.5594	+	20.7496i	−2.08291	+	1.51332i
$189$	−8.67518	−	6.30289i	−0.631026	−	0.458468i
$190$	−32.3236	+	10.9505i	−2.34500	+	0.794430i
$191$	−6.01087	+	4.36715i	−0.434931	+	0.315996i	−0.783618	−	0.621243i	$-0.786628\pi$
$191$	−6.01087	+	4.36715i	−0.434931	+	0.315996i	0.348686	+	0.937239i	$0.386628\pi$
$192$	10.5737	−	32.5425i	0.763091	−	2.34855i
$193$	7.91531			0.569756			0.284878	−	0.958564i	$-0.408047\pi$
$193$	7.91531			0.569756			0.284878	+	0.958564i	$0.408047\pi$
$194$	13.2515	−	40.7839i	0.951403	−	2.92812i
$195$	4.76332	+	6.38696i	0.341109	+	0.457380i
$196$	−3.04178	−	9.36163i	−0.217270	−	0.668688i
$197$	−1.01401	−	3.12081i	−0.0722455	−	0.222349i	0.908414	−	0.418073i	$-0.137294\pi$
$197$	−1.01401	−	3.12081i	−0.0722455	−	0.222349i	−0.980659	+	0.195724i	$0.937294\pi$
$198$	−5.68462	−	4.13012i	−0.403988	−	0.293515i
$199$	−18.7781			−1.33114			−0.665572	−	0.746334i	$-0.731812\pi$
$199$	−18.7781			−1.33114			−0.665572	+	0.746334i	$0.731812\pi$
$200$	13.8045	−	10.5659i	0.976126	−	0.747123i
$201$	14.5573			1.02679
$202$	3.55102	+	2.57997i	0.249849	+	0.181526i
$203$	4.20261	+	12.9343i	0.294966	+	0.907811i
$204$	−3.02091	−	9.29741i	−0.211506	−	0.650949i
$205$	−4.25582	+	1.44177i	−0.297239	+	0.100698i
$206$	4.55814	−	14.0285i	0.317581	−	0.977413i
$207$	9.13714			0.635075
$208$	−0.460460	+	1.41715i	−0.0319271	+	0.0982616i
$209$	3.24790	−	2.35973i	0.224662	−	0.163226i
$210$	−17.3403	+	24.5043i	−1.19659	+	1.69096i
$211$	−13.1019	−	9.51911i	−0.901974	−	0.655322i	0.0369983	−	0.999315i	$-0.488220\pi$
$211$	−13.1019	−	9.51911i	−0.901974	−	0.655322i	−0.938972	+	0.343993i	$0.888220\pi$
$212$	34.1270	−	24.7947i	2.34385	−	1.70291i
$213$	16.5200	−	12.0024i	1.13193	−	0.822394i
$214$	−2.63010	−	1.91088i	−0.179790	−	0.130625i
$215$	−20.7777	−	6.46550i	−1.41703	−	0.440943i
$216$	14.7612	−	10.7246i	1.00437	−	0.729718i
$217$	−1.73391	+	5.33644i	−0.117706	+	0.362261i
$218$	−13.5902			−0.920445
$219$	−11.5236	+	35.4659i	−0.778691	+	2.39657i
$220$	−2.77259	+	3.91806i	−0.186928	+	0.264156i
$221$	−0.392483	−	1.20794i	−0.0264013	−	0.0812547i
$222$	−12.9445	−	39.8391i	−0.868779	−	2.67383i
$223$	−7.53523	−	5.47467i	−0.504597	−	0.366611i	0.306173	−	0.951976i	$-0.400951\pi$
$223$	−7.53523	−	5.47467i	−0.504597	−	0.366611i	−0.810770	+	0.585365i	$0.800951\pi$
$224$	8.59433			0.574233
$225$	−24.3454	+	0.607872i	−1.62303	+	0.0405248i
$226$	20.5624			1.36779
$227$	−14.3718	−	10.4417i	−0.953890	−	0.693042i	−0.00216620	−	0.999998i	$-0.500690\pi$
$227$	−14.3718	−	10.4417i	−0.953890	−	0.693042i	−0.951724	+	0.306956i	$0.900690\pi$
$228$	19.6876	+	60.5922i	1.30384	+	4.01282i
$229$	−4.83924	−	14.8936i	−0.319786	−	0.984199i	−0.973740	−	0.227665i	$-0.926891\pi$
$229$	−4.83924	−	14.8936i	−0.319786	−	0.984199i	0.653954	−	0.756535i	$-0.273109\pi$
$230$	−0.122617	−	9.82317i	−0.00808510	−	0.647720i
$231$	1.09122	−	3.35843i	0.0717970	−	0.220969i
$232$	−23.1409			−1.51927
$233$	−0.623226	+	1.91809i	−0.0408289	+	0.125658i	−0.969393	−	0.245513i	$-0.921044\pi$
$233$	−0.623226	+	1.91809i	−0.0408289	+	0.125658i	0.928564	+	0.371171i	$0.121044\pi$
$234$	11.7206	−	8.51553i	0.766201	−	0.556677i
$235$	−0.282741	−	22.6512i	−0.0184440	−	1.47760i
$236$	20.6148	+	14.9775i	1.34191	+	0.974954i
$237$	32.3673	−	23.5162i	2.10248	−	1.52754i
$238$	3.87139	−	2.81273i	0.250945	−	0.182322i
$239$	−13.6896	−	9.94605i	−0.885504	−	0.643356i	0.0491978	−	0.998789i	$-0.484334\pi$
$239$	−13.6896	−	9.94605i	−0.885504	−	0.643356i	−0.934702	+	0.355433i	$0.884334\pi$
$240$	−4.39990	−	5.89966i	−0.284012	−	0.380821i
$241$	−22.0749	+	16.0383i	−1.42197	+	1.03312i	−0.430524	+	0.902579i	$0.641671\pi$
$241$	−22.0749	+	16.0383i	−1.42197	+	1.03312i	−0.991443	+	0.130541i	$0.958329\pi$
$242$	−7.68600	+	23.6551i	−0.494075	+	1.52061i
$243$	15.4325			0.989992
$244$	−1.53238	+	4.71619i	−0.0981007	+	0.301923i
$245$	6.03127	+	1.87678i	0.385324	+	0.119903i
$246$	4.07990	+	12.5566i	0.260125	+	0.800581i
$247$	2.55785	+	7.87226i	0.162752	+	0.500900i
$248$	−7.72405	−	5.61185i	−0.490478	−	0.356353i
$249$	38.8065			2.45926
$250$	0.980217	+	26.1651i	0.0619944	+	1.65483i
$251$	−26.0086			−1.64165			−0.820824	−	0.571181i	$-0.806485\pi$
$251$	−26.0086			−1.64165			−0.820824	+	0.571181i	$0.806485\pi$
$252$	28.0562	+	20.3840i	1.76737	+	1.28407i
$253$	0.357108	+	1.09907i	0.0224512	+	0.0690977i
$254$	10.3149	+	31.7460i	0.647215	+	1.99192i
$255$	5.98989	+	1.86391i	0.375102	+	0.116722i
$256$	−7.04554	+	21.6839i	−0.440346	+	1.35525i
$257$	−24.3344			−1.51794			−0.758970	−	0.651126i	$-0.774297\pi$
$257$	−24.3344			−1.51794			−0.758970	+	0.651126i	$0.774297\pi$
$258$	−19.7579	+	60.8084i	−1.23007	+	3.78577i
$259$	10.5395	−	7.65743i	0.654896	−	0.475810i
$260$	−5.91641	−	7.93309i	−0.366920	−	0.491990i
$261$	26.2265	+	19.0547i	1.62338	+	1.17945i
$262$	35.6537	−	25.9039i	2.20269	−	1.60035i
$263$	2.25505	−	1.63839i	0.139053	−	0.101028i	−0.516084	−	0.856538i	$-0.672611\pi$
$263$	2.25505	−	1.63839i	0.139053	−	0.101028i	0.655137	+	0.755510i	$0.272611\pi$
$264$	4.86105	+	3.53176i	0.299177	+	0.217365i
$265$	0.337861	+	27.0670i	0.0207546	+	1.66271i
$266$	−25.2302	+	18.3308i	−1.54697	+	1.12394i
$267$	2.17097	−	6.68155i	0.132861	−	0.408904i
$268$	−18.0813			−1.10449
$269$	1.60978	−	4.95440i	0.0981501	−	0.302075i	−0.889912	−	0.456133i	$-0.849234\pi$
$269$	1.60978	−	4.95440i	0.0981501	−	0.302075i	0.988062	+	0.154058i	$0.0492342\pi$
$270$	0.343009	+	27.4794i	0.0208748	+	1.67234i
$271$	−1.69634	−	5.22078i	−0.103045	−	0.317140i	0.886222	−	0.463262i	$-0.153321\pi$
$271$	−1.69634	−	5.22078i	−0.103045	−	0.317140i	−0.989267	+	0.146121i	$0.953321\pi$
$272$	0.362538	+	1.11578i	0.0219821	+	0.0676539i
$273$	5.89029	+	4.27955i	0.356497	+	0.259010i
$274$	44.2249			2.67172
$275$	−1.02461	−	2.90464i	−0.0617865	−	0.175157i
$276$	−18.3394			−1.10390
$277$	−10.6330	−	7.72529i	−0.638872	−	0.464168i	0.220590	−	0.975367i	$-0.429202\pi$
$277$	−10.6330	−	7.72529i	−0.638872	−	0.464168i	−0.859463	+	0.511199i	$0.829202\pi$
$278$	6.61893	+	20.3710i	0.396977	+	1.22177i
$279$	4.13307	+	12.7203i	0.247440	+	0.761544i
$280$	9.17613	−	12.9672i	0.548379	−	0.774937i
$281$	5.15445	−	15.8638i	0.307489	−	0.946353i	−0.671248	−	0.741233i	$-0.734241\pi$
$281$	5.15445	−	15.8638i	0.307489	−	0.946353i	0.978737	−	0.205120i	$-0.0657586\pi$
$282$	−66.5604			−3.96361
$283$	0.498940	−	1.53558i	0.0296589	−	0.0912807i	−0.935131	−	0.354301i	$-0.884719\pi$
$283$	0.498940	−	1.53558i	0.0296589	−	0.0912807i	0.964790	+	0.263021i	$0.0847187\pi$
$284$	−20.5190	+	14.9079i	−1.21758	+	0.884624i
$285$	−39.0368	−	12.1473i	−2.31234	−	0.719543i
$286$	1.48237	+	1.07701i	0.0876546	+	0.0636848i
$287$	−3.32189	+	2.41349i	−0.196085	+	0.142464i
$288$	16.5735	−	12.0414i	0.976605	−	0.709545i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	20.1334	−	28.4513i	1.18227	−	1.67072i
$291$	41.5597	−	30.1949i	2.43627	−	1.77006i
$292$	14.3132	−	44.0514i	0.837614	−	2.57791i
$293$	−9.43665			−0.551295			−0.275647	−	0.961259i	$-0.588892\pi$
$293$	−9.43665			−0.551295			−0.275647	+	0.961259i	$0.588892\pi$
$294$	5.73524	−	17.6513i	0.334486	−	1.02944i
$295$	−15.4868	+	5.24656i	−0.901677	+	0.305467i
$296$	6.84998	+	21.0821i	0.398147	+	1.22537i
$297$	−0.998978	−	3.07454i	−0.0579666	−	0.178403i
$298$	−19.5576	−	14.2094i	−1.13294	−	0.823130i
$299$	−2.38269			−0.137794
$300$	48.8642	−	1.22007i	2.82117	−	0.0704410i
$301$	−19.8847			−1.14613
$302$	−35.0973	−	25.4997i	−2.01962	−	1.46734i
$303$	1.62483	+	5.00073i	0.0933443	+	0.287284i
$304$	−2.36270	−	7.27163i	−0.135510	−	0.417057i
$305$	−1.90239	−	2.55085i	−0.108931	−	0.146061i
$306$	3.52482	−	10.8483i	0.201500	−	0.620155i
$307$	8.80194			0.502353			0.251177	−	0.967941i	$-0.419183\pi$
$307$	8.80194			0.502353			0.251177	+	0.967941i	$0.419183\pi$
$308$	−1.35538	+	4.17143i	−0.0772299	+	0.237689i
$309$	14.2953	−	10.3862i	0.813234	−	0.590849i
$310$	13.6199	−	4.61409i	0.773557	−	0.262062i
$311$	−8.53880	−	6.20380i	−0.484191	−	0.351785i	0.318755	−	0.947837i	$-0.396735\pi$
$311$	−8.53880	−	6.20380i	−0.484191	−	0.351785i	−0.802946	+	0.596052i	$0.796735\pi$
$312$	−10.0226	+	7.28182i	−0.567416	+	0.412252i
$313$	−18.1133	+	13.1601i	−1.02383	+	0.743853i	−0.967064	−	0.254535i	$-0.918078\pi$
$313$	−18.1133	+	13.1601i	−1.02383	+	0.743853i	−0.0567622	+	0.998388i	$0.518078\pi$
$314$	−18.0355	−	13.1036i	−1.01780	−	0.739478i
$315$	−21.0771	+	7.14043i	−1.18756	+	0.402317i
$316$	−40.2027	+	29.2089i	−2.26158	+	1.64313i
$317$	0.284883	−	0.876780i	0.0160006	−	0.0492449i	−0.942737	−	0.333536i	$-0.891758\pi$
$317$	0.284883	−	0.876780i	0.0160006	−	0.0492449i	0.958738	+	0.284291i	$0.0917582\pi$
$318$	79.5362			4.46017
$319$	−1.26699	+	3.89939i	−0.0709377	+	0.218324i
$320$	−16.3045	−	21.8621i	−0.911451	−	1.22213i
$321$	−1.20345	−	3.70384i	−0.0671700	−	0.206728i
$322$	−2.77408	−	8.53775i	−0.154594	−	0.475790i
$323$	5.27245	+	3.83066i	0.293367	+	0.213144i
$324$	0.386524			0.0214735
$325$	6.34853	−	0.158514i	0.352153	−	0.00879279i
$326$	−21.5694			−1.19462
$327$	−13.1709	−	9.56921i	−0.728352	−	0.529179i
$328$	−2.15900	−	6.64471i	−0.119211	−	0.366893i
$329$	−6.39674	−	19.6872i	−0.352664	−	1.08539i
$330$	−8.57152	+	2.90383i	−0.471847	+	0.159850i
$331$	7.43733	−	22.8897i	0.408793	−	1.25813i	−0.508894	−	0.860829i	$-0.669945\pi$
$331$	7.43733	−	22.8897i	0.408793	−	1.25813i	0.917687	−	0.397305i	$-0.130055\pi$
$332$	−48.2006			−2.64535
$333$	9.59604	−	29.5336i	0.525860	−	1.61843i
$334$	7.64547	−	5.55476i	0.418342	−	0.303943i
$335$	6.70225	−	9.47124i	0.366183	−	0.517469i
$336$	−5.44088	−	3.95303i	−0.296824	−	0.215655i
$337$	11.1082	−	8.07059i	0.605103	−	0.439633i	−0.242584	−	0.970131i	$-0.577995\pi$
$337$	11.1082	−	8.07059i	0.605103	−	0.439633i	0.847687	+	0.530497i	$0.177995\pi$
$338$	21.5741	−	15.6745i	1.17348	−	0.852581i
$339$	19.9280	+	14.4786i	1.08234	+	0.786367i
$340$	−7.43990	−	2.31511i	−0.403485	−	0.125555i
$341$	−1.36853	+	0.994298i	−0.0741103	+	0.0538443i
$342$	−22.9716	+	70.6994i	−1.24216	+	3.82298i
$343$	20.0753			1.08396
$344$	10.4555	−	32.1786i	0.563721	−	1.73495i
$345$	6.79791	−	9.60642i	0.365987	−	0.517192i
$346$	−8.33342	−	25.6476i	−0.448008	−	1.37883i
$347$	1.84754	+	5.68615i	0.0991813	+	0.305249i	0.988321	−	0.152388i	$-0.0486962\pi$
$347$	1.84754	+	5.68615i	0.0991813	+	0.305249i	−0.889139	+	0.457636i	$0.848696\pi$
$348$	−52.6397	−	38.2450i	−2.82179	−	2.05015i
$349$	−10.1724			−0.544517			−0.272258	−	0.962224i	$-0.587771\pi$
$349$	−10.1724			−0.544517			−0.272258	+	0.962224i	$0.587771\pi$
$350$	7.95938	+	22.5638i	0.425447	+	1.20609i
$351$	6.66534			0.355770
$352$	2.09615	+	1.52294i	0.111725	+	0.0811731i
$353$	5.19038	+	15.9743i	0.276256	+	0.850228i	0.988884	+	0.148687i	$0.0475046\pi$
$353$	5.19038	+	15.9743i	0.276256	+	0.850228i	−0.712628	+	0.701542i	$0.752495\pi$
$354$	14.8466	+	45.6932i	0.789090	+	2.42857i
$355$	−0.203140	−	16.2742i	−0.0107816	−	0.863742i
$356$	−2.69651	+	8.29899i	−0.142914	+	0.439846i
$357$	5.73245			0.303394
$358$	13.4983	−	41.5436i	0.713408	−	2.19565i
$359$	−20.1890	+	14.6682i	−1.06553	+	0.774156i	−0.975104	−	0.221747i	$-0.928824\pi$
$359$	−20.1890	+	14.6682i	−1.06553	+	0.774156i	−0.0904299	+	0.995903i	$0.528824\pi$
$360$	−0.472618	−	37.8628i	−0.0249092	−	1.99554i
$361$	−18.9898	−	13.7969i	−0.999464	−	0.726153i
$362$	−16.3330	+	11.8666i	−0.858443	+	0.623696i
$363$	−24.1050	+	17.5133i	−1.26519	+	0.919211i
$364$	−7.31619	−	5.31552i	−0.383472	−	0.278609i
$365$	17.7693	+	23.8261i	0.930085	+	1.24712i
$366$	−7.56426	+	5.49575i	−0.395390	+	0.287268i
$367$	4.86457	−	14.9716i	0.253929	−	0.781512i	−0.740110	−	0.672486i	$-0.765227\pi$
$367$	4.86457	−	14.9716i	0.253929	−	0.781512i	0.994039	−	0.109026i	$-0.0347733\pi$
$368$	2.20089			0.114730
$369$	−3.02451	+	9.30849i	−0.157450	+	0.484581i
$370$	−31.8798	−	9.92019i	−1.65735	−	0.515726i
$371$	7.64377	+	23.5251i	0.396845	+	1.22136i
$372$	−8.29557	−	25.5312i	−0.430105	−	1.32373i
$373$	−5.02015	−	3.64735i	−0.259933	−	0.188853i	0.450184	−	0.892936i	$-0.351358\pi$
$373$	−5.02015	−	3.64735i	−0.259933	−	0.188853i	−0.710118	+	0.704083i	$0.751358\pi$
$374$	1.44265			0.0745978
$375$	−17.4736	+	26.0480i	−0.902331	+	1.34511i
$376$	35.2224			1.81646
$377$	−6.83906	−	4.96887i	−0.352229	−	0.255910i
$378$	7.76024	+	23.8836i	0.399144	+	1.22844i
$379$	10.6959	+	32.9186i	0.549411	+	1.69091i	0.710265	+	0.703935i	$0.248575\pi$
$379$	10.6959	+	32.9186i	0.549411	+	1.69091i	−0.160854	+	0.986978i	$0.551425\pi$
$380$	48.4866	+	15.0878i	2.48731	+	0.773990i
$381$	−12.3566	+	38.0296i	−0.633045	+	1.94831i
$382$	17.4001			0.890267
$383$	−4.56230	+	14.0413i	−0.233123	+	0.717478i	0.764242	+	0.644929i	$0.223113\pi$
$383$	−4.56230	+	14.0413i	−0.233123	+	0.717478i	−0.997365	+	0.0725486i	$0.976887\pi$
$384$	−45.7370	+	33.2299i	−2.33401	+	1.69576i
$385$	−1.68265	−	2.25620i	−0.0857559	−	0.114987i
$386$	−14.9968	−	10.8958i	−0.763315	−	0.554581i
$387$	−38.3461	+	27.8601i	−1.94924	+	1.41621i
$388$	−51.6203	+	37.5043i	−2.62062	+	1.90399i
$389$	14.5617	+	10.5797i	0.738309	+	0.536413i	0.892181	−	0.451678i	$-0.149174\pi$
$389$	14.5617	+	10.5797i	0.738309	+	0.536413i	−0.153872	+	0.988091i	$0.549174\pi$
$390$	−0.232897	−	18.6580i	−0.0117932	−	0.944786i
$391$	−1.51770	+	1.10267i	−0.0767534	+	0.0557646i
$392$	−3.03497	+	9.34069i	−0.153289	+	0.471776i
$393$	52.7933			2.66307
$394$	−2.37474	+	7.30870i	−0.119638	+	0.368207i
$395$	−0.398010	−	31.8857i	−0.0200261	−	1.60435i
$396$	3.23077	+	9.94329i	0.162352	+	0.499669i
$397$	2.15678	+	6.63788i	0.108246	+	0.333146i	0.990478	−	0.137668i	$-0.0439606\pi$
$397$	2.15678	+	6.63788i	0.108246	+	0.333146i	−0.882233	+	0.470813i	$0.843961\pi$
$398$	35.5780	+	25.8489i	1.78336	+	1.29569i
$399$	−37.3590			−1.87029
$400$	−5.86416	+	0.146420i	−0.293208	+	0.00732101i
$401$	16.0214			0.800072			0.400036	−	0.916500i	$-0.368998\pi$
$401$	16.0214			0.800072			0.400036	+	0.916500i	$0.368998\pi$
$402$	−27.5811	−	20.0388i	−1.37562	−	0.999445i
$403$	−1.07778	−	3.31706i	−0.0536879	−	0.165234i
$404$	−2.01817	−	6.21128i	−0.100408	−	0.309023i
$405$	−0.143274	+	0.202467i	−0.00711935	+	0.0100607i
$406$	9.84219	−	30.2911i	0.488459	−	1.50332i
$407$	3.92751			0.194679
$408$	−3.01415	+	9.27661i	−0.149223	+	0.459261i
$409$	2.23867	−	1.62649i	0.110695	−	0.0804247i	−0.531061	−	0.847334i	$-0.678206\pi$
$409$	2.23867	−	1.62649i	0.110695	−	0.0804247i	0.641756	+	0.766909i	$0.278206\pi$
$410$	10.0480	+	3.12668i	0.496234	+	0.154416i
$411$	42.8603	+	31.1399i	2.11415	+	1.53602i
$412$	−17.7559	+	12.9004i	−0.874770	+	0.635558i
$413$	−12.0883	+	8.78264i	−0.594825	+	0.432165i
$414$	−17.3117	−	12.5777i	−0.850825	−	0.618160i
$415$	17.8667	−	25.2482i	0.877041	−	1.23938i
$416$	−4.32187	+	3.14002i	−0.211897	+	0.153952i
$417$	−7.92902	+	24.4030i	−0.388286	+	1.19502i
$418$	−9.40192			−0.459863
$419$	−3.18381	+	9.79876i	−0.155539	+	0.478701i	−0.998215	−	0.0597206i	$-0.980979\pi$
$419$	−3.18381	+	9.79876i	−0.155539	+	0.478701i	0.842676	+	0.538421i	$0.180979\pi$
$420$	42.3043	−	14.3317i	2.06424	−	0.699315i
$421$	−3.91651	−	12.0538i	−0.190879	−	0.587465i	0.809121	−	0.587642i	$-0.199944\pi$
$421$	−3.91651	−	12.0538i	−0.190879	−	0.587465i	−1.00000		0.000176949i	$0.999944\pi$
$422$	11.7201	+	36.0708i	0.570527	+	1.75590i
$423$	−39.9190	−	29.0029i	−1.94093	−	1.41017i
$424$	−42.0889			−2.04402
$425$	3.97047	−	3.03898i	0.192596	−	0.147412i
$426$	−47.8215			−2.31696
$427$	−2.35249	−	1.70918i	−0.113845	−	0.0827131i
$428$	1.49478	+	4.60045i	0.0722527	+	0.222371i
$429$	0.678288	+	2.08756i	0.0327481	+	0.100788i
$430$	30.4664	+	40.8513i	1.46922	+	1.97003i
$431$	−3.69820	+	11.3819i	−0.178136	+	0.548246i	−0.999763	−	0.0217798i	$-0.993067\pi$
$431$	−3.69820	+	11.3819i	−0.178136	+	0.548246i	0.821627	+	0.570026i	$0.193067\pi$
$432$	−6.15680			−0.296219
$433$	−12.6762	+	39.0134i	−0.609181	+	1.87487i	−0.144190	+	0.989550i	$0.546058\pi$
$433$	−12.6762	+	39.0134i	−0.609181	+	1.87487i	−0.464991	+	0.885315i	$0.653942\pi$
$434$	10.6310	−	7.72389i	0.510305	−	0.370758i
$435$	39.5455	−	13.3971i	1.89606	−	0.642340i
$436$	16.3592	+	11.8857i	0.783466	+	0.569221i
$437$	9.89101	−	7.18624i	0.473151	−	0.343765i
$438$	70.6537	−	51.3329i	3.37596	−	2.45278i
$439$	−8.12587	−	5.90379i	−0.387827	−	0.281773i	0.376738	−	0.926320i	$-0.377046\pi$
$439$	−8.12587	−	5.90379i	−0.387827	−	0.281773i	−0.764564	+	0.644547i	$0.777046\pi$
$440$	4.53588	−	1.53665i	0.216239	−	0.0732568i
$441$	11.1310	−	8.08713i	0.530046	−	0.385101i
$442$	−0.919164	+	2.82890i	−0.0437202	+	0.134557i
$443$	32.7636			1.55664			0.778322	−	0.627865i	$-0.216071\pi$
$443$	32.7636			1.55664			0.778322	+	0.627865i	$0.216071\pi$
$444$	−19.2604	+	59.2775i	−0.914059	+	2.81318i
$445$	−3.34761	−	4.48869i	−0.158692	−	0.212784i
$446$	6.74052	+	20.7452i	0.319173	+	0.982314i
$447$	−8.94895	−	27.5420i	−0.423271	−	1.30269i
$448$	−20.1621	−	14.6486i	−0.952568	−	0.692081i
$449$	−2.69908			−0.127377			−0.0636887	−	0.997970i	$-0.520286\pi$
$449$	−2.69908			−0.127377			−0.0636887	+	0.997970i	$0.520286\pi$
$450$	46.9629	+	32.3609i	2.21385	+	1.52551i
$451$	−1.23788			−0.0582897
$452$	−24.7521	−	17.9835i	−1.16424	−	0.845871i
$453$	−16.0594	−	49.4259i	−0.754539	−	2.32223i
$454$	12.8561	+	39.5669i	0.603365	+	1.85697i
$455$	5.49627	−	1.86200i	0.257669	−	0.0872921i
$456$	19.6436	−	60.4567i	0.919894	−	2.83114i
$457$	15.2180			0.711869			0.355935	−	0.934511i	$-0.384163\pi$
$457$	15.2180			0.711869			0.355935	+	0.934511i	$0.384163\pi$
$458$	−11.3331	+	34.8797i	−0.529561	+	1.62982i
$459$	4.24563	−	3.08463i	0.198169	−	0.143978i
$460$	−8.44352	+	11.9319i	−0.393681	+	0.556328i
$461$	−19.1654	−	13.9245i	−0.892623	−	0.648529i	0.0439375	−	0.999034i	$-0.486010\pi$
$461$	−19.1654	−	13.9245i	−0.892623	−	0.648529i	−0.936561	+	0.350506i	$0.886010\pi$
$462$	−6.69052	+	4.86095i	−0.311271	+	0.226152i
$463$	−29.5464	+	21.4667i	−1.37314	+	0.997641i	−0.375651	+	0.926761i	$0.622581\pi$
$463$	−29.5464	+	21.4667i	−1.37314	+	0.997641i	−0.997485	+	0.0708802i	$0.977419\pi$
$464$	6.31726	+	4.58976i	0.293271	+	0.213074i
$465$	16.4485	+	5.11838i	0.762783	+	0.237359i
$466$	3.82114	−	2.77622i	0.177011	−	0.128606i
$467$	−0.922647	+	2.83962i	−0.0426950	+	0.131402i	−0.970132	−	0.242578i	$-0.922007\pi$
$467$	−0.922647	+	2.83962i	−0.0426950	+	0.131402i	0.927437	+	0.373980i	$0.122007\pi$
$468$	−21.5562			−0.996436
$469$	3.27640	−	10.0837i	0.151290	−	0.465622i
$470$	−30.6447	+	43.3054i	−1.41354	+	1.99753i
$471$	−8.25250	−	25.3986i	−0.380255	−	1.17030i
$472$	−7.85654	−	24.1799i	−0.361627	−	1.11297i
$473$	−4.84986	−	3.52363i	−0.222997	−	0.162017i
$474$	−93.6960			−4.30360
$475$	−25.8760	+	19.8054i	−1.18727	+	0.908732i
$476$	−7.12014			−0.326351
$477$	47.7011	+	34.6569i	2.18408	+	1.58683i
$478$	12.2458	+	37.6886i	0.560109	+	1.72384i
$479$	5.27649	+	16.2394i	0.241089	+	0.741995i	0.996255	+	0.0864619i	$0.0275561\pi$
$479$	5.27649	+	16.2394i	0.241089	+	0.741995i	−0.755166	+	0.655533i	$0.772444\pi$
$480$	−0.329328	−	26.3834i	−0.0150317	−	1.20423i
$481$	−2.50235	+	7.70145i	−0.114097	+	0.351156i
$482$	63.9017			2.91064
$483$	3.32316	−	10.2276i	0.151209	−	0.465373i
$484$	29.9403	−	21.7529i	1.36092	−	0.988767i
$485$	−0.511046	−	40.9413i	−0.0232054	−	1.85905i
$486$	−29.2392	−	21.2435i	−1.32631	−	0.963624i
$487$	24.0277	−	17.4572i	1.08880	−	0.791060i	0.109604	−	0.993975i	$-0.465042\pi$
$487$	24.0277	−	17.4572i	1.08880	−	0.791060i	0.979196	+	0.202915i	$0.0650416\pi$
$488$	4.00285	−	2.90824i	0.181201	−	0.131650i
$489$	−20.9039	−	15.1876i	−0.945307	−	0.686806i
$490$	−8.84369	−	11.8582i	−0.399517	−	0.535698i
$491$	−9.20772	+	6.68980i	−0.415539	+	0.301906i	−0.775840	−	0.630929i	$-0.782674\pi$
$491$	−9.20772	+	6.68980i	−0.415539	+	0.301906i	0.360302	+	0.932836i	$0.382674\pi$
$492$	6.07056	−	18.6833i	0.273682	−	0.842307i
$493$	−6.65580			−0.299762
$494$	5.99029	−	18.4362i	0.269516	−	0.829485i
$495$	−6.40600	−	1.99339i	−0.287928	−	0.0895962i
$496$	0.995546	+	3.06398i	0.0447013	+	0.137577i
$497$	−4.59586	−	14.1446i	−0.206152	−	0.634472i
$498$	−73.5249	−	53.4189i	−3.29473	−	2.39376i
$499$	14.9329			0.668487			0.334244	−	0.942487i	$-0.391519\pi$
$499$	14.9329			0.668487			0.334244	+	0.942487i	$0.391519\pi$
$500$	21.7035	−	32.3536i	0.970609	−	1.44690i
$501$	11.3208			0.505778
$502$	49.2773	+	35.8020i	2.19935	+	1.59792i
$503$	−1.81332	−	5.58081i	−0.0808517	−	0.248836i	0.902457	−	0.430779i	$-0.141761\pi$
$503$	−1.81332	−	5.58081i	−0.0808517	−	0.248836i	−0.983309	+	0.181943i	$0.941761\pi$
$504$	−10.6925	−	32.9082i	−0.476283	−	1.46585i
$505$	4.00164	+	1.24521i	0.178071	+	0.0554112i
$506$	0.836320	−	2.57393i	0.0371789	−	0.114425i
$507$	31.9453			1.41874
$508$	15.3478	−	47.2356i	0.680947	−	2.09574i
$509$	−21.4041	+	15.5510i	−0.948721	+	0.689286i	−0.950504	−	0.310713i	$-0.899432\pi$
$509$	−21.4041	+	15.5510i	−0.948721	+	0.689286i	0.00178339	+	0.999998i	$0.499432\pi$
$510$	−8.78302	−	11.7768i	−0.388919	−	0.521487i
$511$	21.9733	+	15.9645i	0.972042	+	0.706230i
$512$	10.5920	−	7.69556i	0.468106	−	0.340099i
$513$	−27.6692	+	20.1029i	−1.22163	+	0.887563i
$514$	46.1053	+	33.4975i	2.03362	+	1.47751i
$515$	−0.175785	−	14.0826i	−0.00774602	−	0.620555i
$516$	76.9653	−	55.9186i	3.38821	−	2.46168i
$517$	1.92846	−	5.93520i	0.0848138	−	0.261030i
$518$	−30.5096			−1.34051
$519$	9.98286	−	30.7241i	0.438199	−	1.34864i
$520$	0.123244	+	9.87345i	0.00540462	+	0.432979i
$521$	7.96534	+	24.5148i	0.348968	+	1.07401i	0.959425	+	0.281963i	$0.0909856\pi$
$521$	7.96534	+	24.5148i	0.348968	+	1.07401i	−0.610457	+	0.792049i	$0.709014\pi$
$522$	−23.4605	−	72.2040i	−1.02684	−	3.16028i
$523$	18.8355	+	13.6848i	0.823618	+	0.598393i	0.917746	−	0.397167i	$-0.130007\pi$
$523$	18.8355	+	13.6848i	0.823618	+	0.598393i	−0.0941287	+	0.995560i	$0.530007\pi$
$524$	−65.5732			−2.86458
$525$	−8.17395	+	27.4720i	−0.356740	+	1.19898i
$526$	−6.52787			−0.284629
$527$	−2.22160	−	1.61409i	−0.0967744	−	0.0703107i
$528$	−0.626537	−	1.92828i	−0.0272665	−	0.0839177i
$529$	−6.01987	−	18.5272i	−0.261733	−	0.805532i
$530$	36.6188	−	51.7476i	1.59062	−	2.24777i
$531$	−11.0061	+	33.8734i	−0.477625	+	1.46998i
$532$	46.4027			2.01181
$533$	0.788699	−	2.42737i	0.0341624	−	0.105141i
$534$	−13.3107	+	9.67078i	−0.576010	+	0.418496i
$535$	−2.96386	−	0.922279i	−0.128139	−	0.0398736i
$536$	14.5953	+	10.6041i	0.630422	+	0.458029i
$537$	42.3337	−	30.7573i	1.82684	−	1.32727i
$538$	−9.86993	+	7.17093i	−0.425523	+	0.309161i
$539$	1.40780	+	1.02283i	0.0606382	+	0.0440562i
$540$	23.6200	−	33.3784i	1.01644	−	1.43638i
$541$	20.3309	−	14.7713i	0.874093	−	0.635066i	−0.0575889	−	0.998340i	$-0.518341\pi$
$541$	20.3309	−	14.7713i	0.874093	−	0.635066i	0.931682	+	0.363274i	$0.118341\pi$
$542$	−3.97268	+	12.2267i	−0.170641	+	0.525180i
$543$	−24.1847			−1.03786
$544$	−1.29974	+	4.00020i	−0.0557261	+	0.171507i
$545$	−12.2898	+	4.16350i	−0.526439	+	0.178345i
$546$	−5.26906	−	16.2165i	−0.225495	−	0.694003i
$547$	3.31659	+	10.2074i	0.141807	+	0.436437i	0.996587	−	0.0825541i	$-0.0263077\pi$
$547$	3.31659	+	10.2074i	0.141807	+	0.436437i	−0.854780	+	0.518991i	$0.826308\pi$
$548$	−53.2358	−	38.6781i	−2.27412	−	1.65225i
$549$	−6.93130			−0.295821
$550$	−2.05709	+	6.91372i	−0.0877146	+	0.294802i
$551$	43.3766			1.84790
$552$	14.8037	+	10.7555i	0.630085	+	0.457784i
$553$	−9.00460	−	27.7133i	−0.382914	−	1.17849i
$554$	9.51154	+	29.2735i	0.404106	+	1.24371i
$555$	−23.9111	−	32.0615i	−1.01497	−	1.36093i
$556$	9.84844	−	30.3104i	0.417667	−	1.28545i
$557$	30.9620			1.31190			0.655951	−	0.754804i	$-0.272268\pi$
$557$	30.9620			1.31190			0.655951	+	0.754804i	$0.272268\pi$
$558$	9.67932	−	29.7899i	0.409758	−	1.26111i
$559$	9.99949	−	7.26505i	0.422933	−	0.307279i
$560$	−5.07692	+	1.71994i	−0.214539	+	0.0726806i
$561$	1.39814	+	1.01581i	0.0590296	+	0.0428875i
$562$	−31.6031	+	22.9610i	−1.33310	+	0.968552i
$563$	−2.22666	+	1.61776i	−0.0938423	+	0.0681804i	−0.633717	−	0.773565i	$-0.718472\pi$
$563$	−2.22666	+	1.61776i	−0.0938423	+	0.0681804i	0.539875	+	0.841745i	$0.318472\pi$
$564$	80.1223	+	58.2122i	3.37376	+	2.45118i
$565$	18.5950	−	6.29953i	0.782296	−	0.265023i
$566$	−3.05911	+	2.22258i	−0.128584	+	0.0934219i
$567$	−0.0700395	+	0.215559i	−0.00294138	+	0.00905265i
$568$	25.3062			1.06182
$569$	6.28987	−	19.3582i	0.263685	−	0.811539i	−0.728308	−	0.685249i	$-0.759693\pi$
$569$	6.28987	−	19.3582i	0.263685	−	0.811539i	0.991993	−	0.126290i	$-0.0403068\pi$
$570$	57.2399	+	76.7508i	2.39752	+	3.21474i
$571$	−6.18462	−	19.0343i	−0.258818	−	0.796560i	−0.993053	−	0.117665i	$-0.962459\pi$
$571$	−6.18462	−	19.0343i	−0.258818	−	0.796560i	0.734235	−	0.678895i	$-0.237541\pi$
$572$	−0.842485	−	2.59290i	−0.0352261	−	0.108415i
$573$	16.8633	+	12.2519i	0.704472	+	0.511829i
$574$	9.61611			0.401369
$575$	−3.12032	−	8.84569i	−0.130126	−	0.368891i
$576$	−59.4050			−2.47521
$577$	20.0042	+	14.5339i	0.832785	+	0.605054i	0.920346	−	0.391105i	$-0.127907\pi$
$577$	20.0042	+	14.5339i	0.832785	+	0.605054i	−0.0875606	+	0.996159i	$0.527907\pi$
$578$	0.723693	+	2.22730i	0.0301017	+	0.0926434i
$579$	−6.86205	−	21.1192i	−0.285177	−	0.877685i
$580$	−49.1185	+	16.6402i	−2.03953	+	0.690945i
$581$	8.73413	−	26.8809i	0.362353	−	1.11521i
$582$	−120.306			−4.98684
$583$	−2.30441	+	7.09226i	−0.0954391	+	0.293731i
$584$	−37.3885	+	27.1643i	−1.54715	+	1.12407i
$585$	7.99032	−	11.2915i	0.330359	−	0.466845i
$586$	17.8792	+	12.9900i	0.738582	+	0.536611i
$587$	−27.6410	+	20.0824i	−1.14087	+	0.828889i	−0.987240	−	0.159240i	$-0.949096\pi$
$587$	−27.6410	+	20.0824i	−1.14087	+	0.828889i	−0.153628	+	0.988129i	$0.549096\pi$
$588$	−22.3412	+	16.2318i	−0.921336	+	0.669390i
$589$	14.4784	+	10.5192i	0.596572	+	0.433435i
$590$	36.5643	+	11.3779i	1.50533	+	0.468421i
$591$	−7.44771	+	5.41108i	−0.306358	+	0.222582i
$592$	2.31143	−	7.11385i	0.0949992	−	0.292377i
$593$	−30.2787			−1.24340			−0.621699	−	0.783257i	$-0.713557\pi$
$593$	−30.2787			−1.24340			−0.621699	+	0.783257i	$0.713557\pi$
$594$	−2.33953	+	7.20032i	−0.0959920	+	0.295433i
$595$	2.63925	−	3.72964i	0.108199	−	0.152900i
$596$	11.1153	+	34.2093i	0.455299	+	1.40127i
$597$	16.2794	+	50.1028i	0.666271	+	2.05057i
$598$	4.51436	+	3.27988i	0.184606	+	0.134124i
$599$	5.21581			0.213112			0.106556	−	0.994307i	$-0.466018\pi$
$599$	5.21581			0.213112			0.106556	+	0.994307i	$0.466018\pi$
$600$	−40.1590	−	27.6725i	−1.63949	−	1.12973i
$601$	−21.1872			−0.864244			−0.432122	−	0.901815i	$-0.642235\pi$
$601$	−21.1872			−0.864244			−0.432122	+	0.901815i	$0.642235\pi$
$602$	37.6746	+	27.3722i	1.53550	+	1.11561i
$603$	−7.80983	−	24.0362i	−0.318041	−	0.978830i
$604$	19.9470	+	61.3907i	0.811634	+	2.49795i
$605$	0.296412	+	23.7464i	0.0120508	+	0.965427i
$606$	3.80523	−	11.7113i	0.154577	−	0.475739i
$607$	−40.6509			−1.64997			−0.824985	−	0.565154i	$-0.808817\pi$
$607$	−40.6509			−1.64997			−0.824985	+	0.565154i	$0.808817\pi$
$608$	8.47057	−	26.0697i	0.343527	−	1.05727i
$609$	30.8673	−	22.4264i	1.25081	−	0.908764i
$610$	0.0930152	+	7.45171i	0.00376607	+	0.301711i
$611$	10.4096	+	7.56305i	0.421129	+	0.305968i
$612$	−13.7307	+	9.97592i	−0.555029	+	0.403253i
$613$	−5.53203	+	4.01926i	−0.223437	+	0.162336i	−0.693872	−	0.720098i	$-0.744097\pi$
$613$	−5.53203	+	4.01926i	−0.223437	+	0.162336i	0.470436	+	0.882434i	$0.344097\pi$
$614$	−16.6766	−	12.1163i	−0.673014	−	0.488973i
$615$	7.53637	+	10.1052i	0.303896	+	0.407483i
$616$	3.54049	−	2.57232i	0.142650	−	0.103642i
$617$	3.99582	−	12.2979i	0.160866	−	0.495094i	−0.837842	−	0.545913i	$-0.816183\pi$
$617$	3.99582	−	12.2979i	0.160866	−	0.495094i	0.998708	+	0.0508186i	$0.0161830\pi$
$618$	−41.3818			−1.66462
$619$	8.55615	−	26.3331i	0.343901	−	1.05842i	−0.618269	−	0.785967i	$-0.712166\pi$
$619$	8.55615	−	26.3331i	0.343901	−	1.05842i	0.962170	−	0.272451i	$-0.0878343\pi$
$620$	−20.4303	−	6.35742i	−0.820502	−	0.255320i
$621$	−3.04225	−	9.36308i	−0.122081	−	0.375727i
$622$	7.63825	+	23.5081i	0.306266	+	0.942590i
$623$	−4.13963	−	3.00762i	−0.165851	−	0.120498i
$624$	4.18035			0.167348
$625$	8.90239	+	23.3612i	0.356096	+	0.934450i
$626$	52.4340			2.09568
$627$	−9.11184	−	6.62014i	−0.363892	−	0.264383i
$628$	10.2502	+	31.5470i	0.409029	+	1.25886i
$629$	1.97020	+	6.06365i	0.0785570	+	0.241773i
$630$	49.7630	+	15.4850i	1.98260	+	0.616938i
$631$	8.79284	−	27.0616i	0.350038	−	1.07730i	−0.608794	−	0.793329i	$-0.708346\pi$
$631$	8.79284	−	27.0616i	0.350038	−	1.07730i	0.958831	−	0.283976i	$-0.0916537\pi$
$632$	49.5821			1.97227
$633$	−14.0399	+	43.2103i	−0.558036	+	1.71746i
$634$	−1.74668	+	1.26904i	−0.0693697	+	0.0504000i
$635$	19.0537	+	25.5484i	0.756122	+	1.01386i
$636$	−95.7419	−	69.5606i	−3.79641	−	2.75826i
$637$	−2.90261	+	2.10887i	−0.115006	+	0.0835566i
$638$	7.76819	−	5.64392i	0.307545	−	0.223445i
$639$	−28.6805	−	20.8376i	−1.13458	−	0.824324i
$640$	0.562413	+	45.0565i	0.0222313	+	1.78102i
$641$	17.3233	−	12.5861i	0.684230	−	0.497122i	−0.190528	−	0.981682i	$-0.561020\pi$
$641$	17.3233	−	12.5861i	0.684230	−	0.497122i	0.874758	+	0.484560i	$0.161020\pi$
$642$	−2.81838	+	8.67409i	−0.111233	+	0.342339i
$643$	−1.60008			−0.0631011			−0.0315505	−	0.999502i	$-0.510045\pi$
$643$	−1.60008			−0.0631011			−0.0315505	+	0.999502i	$0.510045\pi$
$644$	−4.12762	+	12.7035i	−0.162651	+	0.500588i
$645$	0.761964	+	61.0431i	0.0300023	+	2.40357i
$646$	−4.71639	−	14.5155i	−0.185564	−	0.571107i
$647$	−10.5375	−	32.4312i	−0.414274	−	1.27500i	−0.912899	−	0.408186i	$-0.866162\pi$
$647$	−10.5375	−	32.4312i	−0.414274	−	1.27500i	0.498625	−	0.866818i	$-0.333838\pi$
$648$	−0.312005	−	0.226685i	−0.0122567	−	0.00890501i
$649$	−4.50463			−0.176822
$650$	−12.2465	−	8.43871i	−0.480346	−	0.330994i
$651$	15.7416			0.616962
$652$	25.9642	+	18.8641i	1.01684	+	0.738776i
$653$	−1.70129	−	5.23602i	−0.0665764	−	0.204901i	0.912234	−	0.409669i	$-0.134356\pi$
$653$	−1.70129	−	5.23602i	−0.0665764	−	0.204901i	−0.978810	+	0.204768i	$0.934356\pi$
$654$	11.7818	+	36.2607i	0.460705	+	1.41791i
$655$	24.3063	−	34.3482i	0.949725	−	1.34210i
$656$	−0.728524	+	2.24217i	−0.0284441	+	0.0875419i
$657$	64.7416			2.52581
$658$	−14.9807	+	46.1057i	−0.584007	+	1.79739i
$659$	14.1619	−	10.2892i	0.551667	−	0.400810i	−0.276733	−	0.960947i	$-0.589252\pi$
$659$	14.1619	−	10.2892i	0.551667	−	0.400810i	0.828400	+	0.560137i	$0.189252\pi$
$660$	12.8576	+	4.00097i	0.500482	+	0.155738i
$661$	26.1104	+	18.9703i	1.01558	+	0.737860i	0.965372	−	0.260879i	$-0.0840122\pi$
$661$	26.1104	+	18.9703i	1.01558	+	0.737860i	0.0502060	+	0.998739i	$0.484012\pi$
$662$	−45.6000	+	33.1303i	−1.77229	+	1.28765i
$663$	−2.88270	+	2.09441i	−0.111955	+	0.0813400i
$664$	38.9079	+	28.2682i	1.50992	+	1.09702i
$665$	−17.2003	+	24.3064i	−0.666998	+	0.942563i
$666$	−58.8355	+	42.7465i	−2.27983	+	1.65639i
$667$	−3.85843	+	11.8750i	−0.149399	+	0.459803i
$668$	−14.0613			−0.544049
$669$	−8.07468	+	24.8513i	−0.312185	+	0.960807i
$670$	−25.7360	+	8.71876i	−0.994270	+	0.336835i
$671$	−0.270897	−	0.833736i	−0.0104579	−	0.0321860i
$672$	−7.45072	−	22.9310i	−0.287418	−	0.884581i
$673$	23.1219	+	16.7991i	0.891286	+	0.647557i	0.936213	−	0.351433i	$-0.114306\pi$
$673$	23.1219	+	16.7991i	0.891286	+	0.647557i	−0.0449273	+	0.998990i	$0.514306\pi$
$674$	−32.1558			−1.23859
$675$	8.72880	+	24.7450i	0.335972	+	0.952435i
$676$	−39.6785			−1.52610
$677$	4.62434	+	3.35978i	0.177728	+	0.129127i	0.673093	−	0.739558i	$-0.264966\pi$
$677$	4.62434	+	3.35978i	0.177728	+	0.129127i	−0.495365	+	0.868685i	$0.664966\pi$
$678$	−17.8263	−	54.8637i	−0.684615	−	2.10703i
$679$	−11.5619	−	35.5839i	−0.443706	−	1.36559i
$680$	4.64780	+	6.23206i	0.178235	+	0.238989i
$681$	−15.4007	+	47.3984i	−0.590155	+	1.81631i
$682$	3.96159			0.151697
$683$	−8.89425	+	27.3737i	−0.340329	+	1.04742i	0.623708	+	0.781657i	$0.285625\pi$
$683$	−8.89425	+	27.3737i	−0.340329	+	1.04742i	−0.964037	+	0.265768i	$0.914375\pi$
$684$	89.4843	−	65.0141i	3.42152	−	2.48588i
$685$	39.9933	−	13.5488i	1.52806	−	0.517671i
$686$	−38.0357	−	27.6346i	−1.45221	−	1.05509i
$687$	−35.5432	+	25.8236i	−1.35606	+	0.985232i
$688$	−9.23656	+	6.71075i	−0.352140	+	0.255845i
$689$	−12.4390	−	9.03745i	−0.473887	−	0.344299i
$690$	−26.1034	+	8.84320i	−0.993739	+	0.336655i
$691$	−35.6862	+	25.9275i	−1.35757	+	0.986329i	−0.358970	+	0.933349i	$0.616872\pi$
$691$	−35.6862	+	25.9275i	−1.35757	+	0.986329i	−0.998596	+	0.0529804i	$0.983128\pi$
$692$	−12.3995	+	38.1617i	−0.471357	+	1.45069i
$693$	−6.13068			−0.232885
$694$	4.32680	−	13.3165i	0.164243	−	0.505488i
$695$	12.2265	+	16.3940i	0.463777	+	0.621861i
$696$	20.0616	+	61.7433i	0.760433	+	2.34037i
$697$	−0.620973	−	1.91116i	−0.0235210	−	0.0723903i
$698$	19.2732	+	14.0028i	0.729501	+	0.530013i
$699$	5.65805			0.214007
$700$	10.1527	−	34.1223i	0.383735	−	1.28970i
$701$	−34.8242			−1.31529			−0.657647	−	0.753326i	$-0.728448\pi$
$701$	−34.8242			−1.31529			−0.657647	+	0.753326i	$0.728448\pi$
$702$	−12.6285	−	9.17515i	−0.476633	−	0.346294i
$703$	−12.8400	−	39.5174i	−0.484270	−	1.49043i
$704$	−2.32173	−	7.14556i	−0.0875036	−	0.269309i
$705$	−60.1916	+	20.3915i	−2.26695	+	0.767988i
$706$	12.1555	−	37.4106i	0.457476	−	1.40797i
$707$	3.82966			0.144029
$708$	22.0906	−	67.9879i	0.830216	−	2.55514i
$709$	−14.8370	+	10.7797i	−0.557215	+	0.404840i	−0.830439	−	0.557110i	$-0.811910\pi$
$709$	−14.8370	+	10.7797i	−0.557215	+	0.404840i	0.273224	+	0.961951i	$0.411910\pi$
$710$	−22.0172	+	31.1135i	−0.826293	+	1.16767i
$711$	−56.1934	−	40.8269i	−2.10742	−	1.53113i
$712$	7.04375	−	5.11758i	0.263976	−	0.191790i
$713$	−4.16768	+	3.02800i	−0.156081	+	0.113399i
$714$	−10.8610	−	7.89099i	−0.406463	−	0.295313i
$715$	1.67049	+	0.519814i	0.0624727	+	0.0194400i
$716$	−52.5817	+	38.2029i	−1.96507	+	1.42771i
$717$	−14.6696	+	45.1484i	−0.547846	+	1.68610i
$718$	58.4425			2.18106
$719$	−1.13722	+	3.49999i	−0.0424110	+	0.130528i	−0.970020	−	0.243025i	$-0.921860\pi$
$719$	−1.13722	+	3.49999i	−0.0424110	+	0.130528i	0.927609	+	0.373552i	$0.121860\pi$
$720$	−7.38068	+	10.4300i	−0.275062	+	0.388702i
$721$	−3.97697	−	12.2398i	−0.148110	−	0.455836i
$722$	16.9870	+	52.2807i	0.632192	+	1.94569i
$723$	61.9301	+	44.9949i	2.30321	+	1.67338i
$724$	30.0392			1.11640
$725$	9.49056	−	31.8970i	0.352470	−	1.18463i
$726$	69.7786			2.58973
$727$	5.87824	+	4.27079i	0.218012	+	0.158395i	0.691431	−	0.722442i	$-0.256980\pi$
$727$	5.87824	+	4.27079i	0.218012	+	0.158395i	−0.473419	+	0.880837i	$0.656980\pi$
$728$	2.78828	+	8.58145i	0.103341	+	0.318050i
$729$	−13.4818	−	41.4926i	−0.499324	−	1.53676i
$730$	−0.868805	−	69.6025i	−0.0321559	−	2.57610i
$731$	3.00721	−	9.25525i	0.111226	−	0.342318i
$732$	13.9120			0.514201
$733$	6.65860	−	20.4931i	0.245941	−	0.756929i	−0.749539	−	0.661960i	$-0.769725\pi$
$733$	6.65860	−	20.4931i	0.245941	−	0.756929i	0.995480	−	0.0949690i	$-0.0302752\pi$
$734$	−29.8258	+	21.6697i	−1.10089	+	0.799844i
$735$	−0.221180	−	17.7194i	−0.00815835	−	0.653589i
$736$	6.38353	+	4.63791i	0.235300	+	0.170956i
$737$	2.58598	−	1.87882i	0.0952556	−	0.0692073i
$738$	18.5440	−	13.4730i	0.682613	−	0.495947i
$739$	7.46555	+	5.42404i	0.274625	+	0.199526i	0.716569	−	0.697516i	$-0.245711\pi$
$739$	7.46555	+	5.42404i	0.274625	+	0.199526i	−0.441945	+	0.897042i	$0.645711\pi$
$740$	29.6994	+	39.8228i	1.09177	+	1.46392i
$741$	18.7869	−	13.6495i	0.690154	−	0.501426i
$742$	17.9011	−	55.0940i	0.657170	−	2.02256i
$743$	−7.61834			−0.279490			−0.139745	−	0.990188i	$-0.544628\pi$
$743$	−7.61834			−0.279490			−0.139745	+	0.990188i	$0.544628\pi$
$744$	−8.27701	+	25.4740i	−0.303450	+	0.933923i
$745$	−22.0395	−	6.85814i	−0.807464	−	0.251263i
$746$	4.49069	+	13.8209i	0.164416	+	0.506020i
$747$	−20.8193	−	64.0751i	−0.761737	−	2.34438i
$748$	−1.73660	−	1.26171i	−0.0634963	−	0.0461328i
$749$	−2.83647			−0.103642
$750$	68.9627	−	25.2988i	2.51816	−	0.923782i
$751$	−24.9877			−0.911815			−0.455907	−	0.890027i	$-0.650685\pi$
$751$	−24.9877			−0.911815			−0.455907	+	0.890027i	$0.650685\pi$
$752$	−9.61542	−	6.98601i	−0.350638	−	0.254754i
$753$	22.5477	+	69.3948i	0.821685	+	2.52889i
$754$	6.11777	+	18.8286i	0.222796	+	0.685696i
$755$	−39.5512	−	12.3074i	−1.43942	−	0.447910i
$756$	11.5466	−	35.5369i	0.419947	−	1.29246i
$757$	15.3548			0.558078			0.279039	−	0.960280i	$-0.409984\pi$
$757$	15.3548			0.558078			0.279039	+	0.960280i	$0.409984\pi$
$758$	25.0489	−	77.0926i	0.909818	−	2.80013i
$759$	2.62289	−	1.90564i	0.0952047	−	0.0691703i
$760$	−30.2902	−	40.6150i	−1.09874	−	1.47326i
$761$	−18.9449	−	13.7643i	−0.686752	−	0.498954i	0.188839	−	0.982008i	$-0.439528\pi$
$761$	−18.9449	−	13.7643i	−0.686752	−	0.498954i	−0.875591	+	0.483054i	$0.839528\pi$
$762$	75.7608	−	55.0435i	2.74453	−	1.99401i
$763$	−9.59286	+	6.96962i	−0.347285	+	0.252317i
$764$	−20.9454	−	15.2177i	−0.757779	−	0.550559i
$765$	−0.135935	−	10.8901i	−0.00491474	−	0.393734i
$766$	27.9725	−	20.3232i	1.01069	−	0.734308i
$767$	2.87006	−	8.83313i	0.103632	−	0.318946i
$768$	63.9640			2.30810
$769$	7.38793	−	22.7377i	0.266415	−	0.819942i	−0.724949	−	0.688803i	$-0.758136\pi$
$769$	7.38793	−	22.7377i	0.266415	−	0.819942i	0.991364	−	0.131139i	$-0.0418635\pi$
$770$	0.0822711	+	6.59097i	0.00296485	+	0.237522i
$771$	21.0964	+	64.9279i	0.759767	+	2.33832i
$772$	8.52319	+	26.2317i	0.306756	+	0.944099i
$773$	38.8917	+	28.2564i	1.39884	+	1.01631i	0.994830	+	0.101557i	$0.0323825\pi$
$773$	38.8917	+	28.2564i	1.39884	+	1.01631i	0.404006	+	0.914756i	$0.367618\pi$
$774$	111.003			3.98993
$775$	10.9031	−	8.34519i	0.391651	−	0.299768i
$776$	63.6634			2.28538
$777$	−29.5683	−	21.4826i	−1.06076	−	0.770684i
$778$	−13.0260	−	40.0898i	−0.467003	−	1.43729i
$779$	4.04695	+	12.4552i	0.144997	+	0.446255i
$780$	−16.0375	+	22.6633i	−0.574236	+	0.811478i
$781$	1.38554	−	4.26425i	0.0495785	−	0.152587i
$782$	4.39340			0.157108
$783$	10.7936	−	33.2193i	0.385732	−	1.18716i
$784$	2.68115	−	1.94797i	0.0957555	−	0.0695704i
$785$	−20.3243	−	6.32440i	−0.725404	−	0.225728i
$786$	−100.025	−	72.6724i	−3.56777	−	2.59214i
$787$	−43.0983	+	31.3128i	−1.53629	+	1.11618i	−0.583679	+	0.811984i	$0.698387\pi$
$787$	−43.0983	+	31.3128i	−1.53629	+	1.11618i	−0.952610	+	0.304195i	$0.901613\pi$
$788$	9.25062	−	6.72097i	0.329540	−	0.239425i
$789$	−6.32646	−	4.59644i	−0.225228	−	0.163638i
$790$	−43.1381	+	60.9603i	−1.53478	+	2.16887i
$791$	14.5143	−	10.5453i	0.516070	−	0.374947i
$792$	3.22354	−	9.92104i	0.114544	−	0.352529i
$793$	1.80747			0.0641851
$794$	5.05100	−	15.5454i	0.179253	−	0.551685i
$795$	71.9259	−	24.3668i	2.55095	−	0.864200i
$796$	−20.2202	−	62.2314i	−0.716687	−	2.20573i
$797$	−9.01107	−	27.7332i	−0.319188	−	0.982361i	−0.973996	−	0.226565i	$-0.927250\pi$
$797$	−9.01107	−	27.7332i	−0.319188	−	0.982361i	0.654808	−	0.755796i	$-0.272750\pi$
$798$	70.7824	+	51.4264i	2.50567	+	1.82048i
$799$	10.1307			0.358399
$800$	−17.3171	−	11.9328i	−0.612252	−	0.421887i
$801$	−12.1969			−0.430956
$802$	−30.3550	−	22.0542i	−1.07187	−	0.778762i
$803$	2.53031	+	7.78748i	0.0892926	+	0.274814i
$804$	15.6753	+	48.2436i	0.552825	+	1.70142i
$805$	−5.12428	−	6.87096i	−0.180607	−	0.242169i
$806$	−2.52407	+	7.76829i	−0.0889065	+	0.273626i
$807$	−14.6146			−0.514460
$808$	−2.01365	+	6.19739i	−0.0708401	+	0.218023i
$809$	−3.34731	+	2.43196i	−0.117685	+	0.0855033i	−0.645071	−	0.764123i	$-0.723172\pi$
$809$	−3.34731	+	2.43196i	−0.117685	+	0.0855033i	0.527386	+	0.849626i	$0.323172\pi$
$810$	0.550160	−	0.186381i	0.0193306	−	0.00654876i
$811$	−13.9174	−	10.1116i	−0.488705	−	0.355065i	0.315981	−	0.948766i	$-0.397666\pi$
$811$	−13.9174	−	10.1116i	−0.488705	−	0.355065i	−0.804686	+	0.593700i	$0.797666\pi$
$812$	−38.3395	+	27.8553i	−1.34545	+	0.977529i
$813$	−12.4592	+	9.05215i	−0.436964	+	0.317473i
$814$	−7.44127	−	5.40640i	−0.260816	−	0.189494i
$815$	−19.5056	+	6.60801i	−0.683250	+	0.231469i
$816$	2.66276	−	1.93461i	0.0932153	−	0.0677249i
$817$	−19.5983	+	60.3174i	−0.685659	+	2.11024i
$818$	−6.48044			−0.226583
$819$	3.90607	−	12.0216i	0.136489	−	0.420070i
$820$	−9.36075	−	12.5515i	−0.326891	−	0.438317i
$821$	−1.15490	−	3.55441i	−0.0403062	−	0.124050i	0.928879	−	0.370384i	$-0.120774\pi$
$821$	−1.15490	−	3.55441i	−0.0403062	−	0.124050i	−0.969185	+	0.246334i	$0.920774\pi$
$822$	−38.3400	−	117.999i	−1.33726	−	4.11567i
$823$	11.2042	+	8.14035i	0.390555	+	0.283755i	0.765683	−	0.643218i	$-0.222401\pi$
$823$	11.2042	+	8.14035i	0.390555	+	0.283755i	−0.375128	+	0.926973i	$0.622401\pi$
$824$	21.8984			0.762867
$825$	−6.86175	+	5.25196i	−0.238895	+	0.182850i
$826$	34.9928			1.21755
$827$	−32.3385	−	23.4953i	−1.12452	−	0.817012i	−0.139633	−	0.990203i	$-0.544592\pi$
$827$	−32.3385	−	23.4953i	−1.12452	−	0.817012i	−0.984888	+	0.173191i	$0.944592\pi$
$828$	9.83886	+	30.2809i	0.341924	+	1.05233i
$829$	−6.49095	−	19.9771i	−0.225440	−	0.693833i	−0.998247	−	0.0591916i	$-0.981148\pi$
$829$	−6.49095	−	19.9771i	−0.225440	−	0.693833i	0.772807	−	0.634642i	$-0.218852\pi$
$830$	−68.6065	+	23.2422i	−2.38137	+	0.806750i
$831$	−11.3942	+	35.0676i	−0.395259	+	1.21648i
$832$	15.4910			0.537053
$833$	−0.872923	+	2.68658i	−0.0302450	+	0.0930845i
$834$	48.6146	−	35.3206i	1.68339	−	1.22305i
$835$	5.21217	−	7.36554i	0.180374	−	0.254895i
$836$	11.3176	+	8.22271i	0.391427	+	0.284388i
$837$	11.6587	−	8.47054i	0.402984	−	0.292785i
$838$	19.5207	−	14.1826i	0.674330	−	0.489929i
$839$	28.5761	+	20.7618i	0.986556	+	0.716775i	0.959164	−	0.282850i	$-0.0912797\pi$
$839$	28.5761	+	20.7618i	0.986556	+	0.716775i	0.0273922	+	0.999625i	$0.491280\pi$
$840$	−42.5535	−	13.2416i	−1.46823	−	0.456878i
$841$	−12.3777	+	8.99293i	−0.426817	+	0.310101i
$842$	−9.17215	+	28.2290i	−0.316093	+	0.972835i
$843$	−46.7955			−1.61172
$844$	17.4386	−	53.6705i	0.600262	−	1.84742i
$845$	14.7078	−	20.7842i	0.505963	−	0.714998i
$846$	35.7089	+	109.901i	1.22770	+	3.77846i
$847$	6.70603	+	20.6390i	0.230422	+	0.709165i
$848$	11.4899	+	8.34792i	0.394566	+	0.286669i
$849$	−4.52970			−0.155459
$850$	−11.7060	+	0.292282i	−0.401511	+	0.0100252i
$851$	11.9607			0.410007
$852$	57.5653	+	41.8236i	1.97215	+	1.43285i
$853$	−5.80850	−	17.8767i	−0.198879	−	0.612087i	−0.999909	−	0.0134632i	$-0.995714\pi$
$853$	−5.80850	−	17.8767i	−0.198879	−	0.612087i	0.801030	−	0.598624i	$-0.204286\pi$
$854$	2.10438	+	6.47661i	0.0720104	+	0.221625i
$855$	0.885903	+	70.9722i	0.0302972	+	2.42720i
$856$	1.49143	−	4.59016i	0.0509761	−	0.156888i
$857$	9.73099			0.332404			0.166202	−	0.986092i	$-0.446850\pi$
$857$	9.73099			0.332404			0.166202	+	0.986092i	$0.446850\pi$
$858$	1.58850	−	4.88889i	0.0542304	−	0.166904i
$859$	8.22351	−	5.97473i	0.280582	−	0.203855i	−0.438589	−	0.898688i	$-0.644522\pi$
$859$	8.22351	−	5.97473i	0.280582	−	0.203855i	0.719171	+	0.694833i	$0.244522\pi$
$860$	−0.946417	−	75.8202i	−0.0322725	−	2.58545i
$861$	9.31942	+	6.77096i	0.317605	+	0.230754i
$862$	22.6745	−	16.4740i	0.772296	−	0.561106i
$863$	−42.3934	+	30.8006i	−1.44309	+	1.04846i	−0.455702	+	0.890132i	$0.650612\pi$
$863$	−42.3934	+	30.8006i	−1.44309	+	1.04846i	−0.987386	+	0.158332i	$0.949388\pi$
$864$	−17.8574	−	12.9741i	−0.607519	−	0.441389i
$865$	−15.3935	−	20.6405i	−0.523394	−	0.701800i
$866$	77.7209	−	56.4675i	2.64106	−	1.91884i
$867$	−0.866934	+	2.66815i	−0.0294426	+	0.0906151i
$868$	−19.5523			−0.663647
$869$	2.71467	−	8.35490i	0.0920889	−	0.283420i
$870$	−93.3666	−	29.0534i	−3.16542	−	0.985002i
$871$	2.03656	+	6.26790i	0.0690063	+	0.212380i
$872$	−6.23470	−	19.1884i	−0.211133	−	0.649802i
$873$	−72.1524	−	52.4218i	−2.44199	−	1.77421i
$874$	−28.6322			−0.968500
$875$	14.1105	+	17.9664i	0.477021	+	0.607374i
$876$	−129.944			−4.39041
$877$	−18.7850	−	13.6481i	−0.634324	−	0.460864i	0.223571	−	0.974688i	$-0.428228\pi$
$877$	−18.7850	−	13.6481i	−0.634324	−	0.460864i	−0.857896	+	0.513824i	$0.828228\pi$
$878$	7.26887	+	22.3713i	0.245312	+	0.754994i
$879$	8.18096	+	25.1784i	0.275937	+	0.849246i
$880$	−1.54303	−	0.480154i	−0.0520157	−	0.0161860i
$881$	−6.08351	+	18.7231i	−0.204959	+	0.630798i	0.794756	+	0.606928i	$0.207599\pi$
$881$	−6.08351	+	18.7231i	−0.204959	+	0.630798i	−0.999715	+	0.0238693i	$0.992401\pi$
$882$	−32.2216			−1.08496
$883$	8.07827	−	24.8624i	0.271855	−	0.836685i	−0.718179	−	0.695859i	$-0.755024\pi$
$883$	8.07827	−	24.8624i	0.271855	−	0.836685i	0.990034	−	0.140826i	$-0.0449759\pi$
$884$	3.58054	−	2.60141i	0.120426	−	0.0874949i
$885$	27.4247	+	36.7727i	0.921870	+	1.23610i
$886$	−62.0756	−	45.1006i	−2.08547	−	1.51518i
$887$	19.9146	−	14.4688i	0.668667	−	0.485815i	−0.200912	−	0.979609i	$-0.564391\pi$
$887$	19.9146	−	14.4688i	0.668667	−	0.485815i	0.869579	+	0.493795i	$0.164391\pi$
$888$	50.3116	−	36.5535i	1.68835	−	1.22666i
$889$	23.5616	+	17.1185i	0.790232	+	0.574137i
$890$	0.163677	+	13.1126i	0.00548647	+	0.439537i
$891$	−0.0552804	+	0.0401636i	−0.00185196	+	0.00134553i
$892$	10.0294	−	30.8672i	0.335808	−	1.03351i
$893$	−66.0229			−2.20937
$894$	−20.9577	+	64.5013i	−0.700931	+	2.15725i
$895$	−0.520564	−	41.7039i	−0.0174005	−	1.39401i
$896$	12.7241	+	39.1606i	0.425081	+	1.30826i
$897$	2.06563	+	6.35736i	0.0689694	+	0.212266i
$898$	5.11382	+	3.71541i	0.170650	+	0.123985i
$899$	−18.2772			−0.609577
$900$	−28.2296	−	80.0272i	−0.940986	−	2.66757i
$901$	−12.1057			−0.403298
$902$	2.34536	+	1.70401i	0.0780920	+	0.0567372i
$903$	17.2387	+	53.0553i	0.573668	+	1.76557i
$904$	9.43331	+	29.0328i	0.313747	+	0.965615i
$905$	−11.1347	+	15.7350i	−0.370131	+	0.523048i
$906$	−37.6099	+	115.752i	−1.24951	+	3.84559i
$907$	−2.07603			−0.0689336			−0.0344668	−	0.999406i	$-0.510973\pi$
$907$	−2.07603			−0.0689336			−0.0344668	+	0.999406i	$0.510973\pi$
$908$	19.1288	−	58.8724i	0.634812	−	1.95375i
$909$	7.38521	−	5.36567i	0.244952	−	0.177968i
$910$	−12.9767	−	4.03801i	−0.430172	−	0.133859i
$911$	14.2169	+	10.3292i	0.471028	+	0.342222i	0.797842	−	0.602867i	$-0.205975\pi$
$911$	14.2169	+	10.3292i	0.471028	+	0.342222i	−0.326814	+	0.945089i	$0.605975\pi$
$912$	−17.3535	+	12.6081i	−0.574632	+	0.417495i
$913$	6.89363	−	5.00851i	0.228146	−	0.165758i
$914$	−28.8329	−	20.9483i	−0.953707	−	0.692909i
$915$	−5.15680	+	7.28729i	−0.170478	+	0.240910i
$916$	44.1473	−	32.0749i	1.45867	−	1.05978i
$917$	11.8821	−	36.5694i	0.392382	−	1.20763i
$918$	−12.2901			−0.405634
$919$	−2.30454	+	7.09264i	−0.0760198	+	0.233965i	−0.981844	−	0.189688i	$-0.939252\pi$
$919$	−2.30454	+	7.09264i	−0.0760198	+	0.233965i	0.905825	+	0.423653i	$0.139252\pi$
$920$	13.8134	−	4.67964i	0.455414	−	0.154283i
$921$	−7.63070	−	23.4849i	−0.251440	−	0.773853i
$922$	17.1441	+	52.7642i	0.564612	+	1.73770i
$923$	7.47900	+	5.43381i	0.246174	+	0.178856i
$924$	12.3050			0.404805
$925$	−31.8686	+	0.795715i	−1.04783	+	0.0261630i
$926$	85.5300			2.81069
$927$	−24.8183	−	18.0316i	−0.815141	−	0.592235i
$928$	8.65083	+	26.6245i	0.283978	+	0.873993i
$929$	7.95724	+	24.4899i	0.261069	+	0.803487i	0.992573	+	0.121650i	$0.0388185\pi$
$929$	7.95724	+	24.4899i	0.261069	+	0.803487i	−0.731504	+	0.681837i	$0.761181\pi$
$930$	−24.1186	−	32.3397i	−0.790880	−	1.06046i
$931$	5.68893	−	17.5087i	0.186447	−	0.573825i
$932$	−7.02773			−0.230201
$933$	−9.15010	+	28.1611i	−0.299561	+	0.921953i
$934$	5.65696	−	4.11002i	0.185101	−	0.134484i
$935$	1.30461	−	0.441972i	0.0426654	−	0.0144540i
$936$	17.4003	+	12.6421i	0.568748	+	0.413219i
$937$	33.7147	−	24.4952i	1.10141	−	0.800223i	0.120123	−	0.992759i	$-0.461671\pi$
$937$	33.7147	−	24.4952i	1.10141	−	0.800223i	0.981290	+	0.192536i	$0.0616711\pi$
$938$	−20.0883	+	14.5950i	−0.655907	+	0.476544i
$939$	50.8162	+	36.9201i	1.65832	+	1.20484i
$940$	74.7626	−	25.3278i	2.43849	−	0.826101i
$941$	−14.5555	+	10.5752i	−0.474495	+	0.344741i	−0.799191	−	0.601078i	$-0.794738\pi$
$941$	−14.5555	+	10.5752i	−0.474495	+	0.344741i	0.324695	+	0.945819i	$0.394738\pi$
$942$	−19.3267	+	59.4814i	−0.629698	+	1.93801i
$943$	−3.76981			−0.122762
$944$	−2.65108	+	8.15919i	−0.0862853	+	0.265559i
$945$	14.3347	+	19.2209i	0.466308	+	0.625255i
$946$	4.33836	+	13.3521i	0.141052	+	0.434114i
$947$	2.11478	+	6.50863i	0.0687212	+	0.211502i	0.979519	−	0.201350i	$-0.0645328\pi$
$947$	2.11478	+	6.50863i	0.0687212	+	0.211502i	−0.910798	+	0.412852i	$0.864533\pi$
$948$	112.787	+	81.9445i	3.66315	+	2.66143i
$949$	−16.8826			−0.548033
$950$	76.2890	−	1.90483i	2.47514	−	0.0618010i
$951$	−2.58636			−0.0838684
$952$	5.74743	+	4.17575i	0.186275	+	0.135337i
$953$	−9.30712	−	28.6444i	−0.301487	−	0.927882i	−0.980965	−	0.194186i	$-0.937794\pi$
$953$	−9.30712	−	28.6444i	−0.301487	−	0.927882i	0.679478	−	0.733696i	$-0.262206\pi$
$954$	−42.6703	−	131.326i	−1.38150	−	4.25182i
$955$	15.7352	−	5.33071i	0.509179	−	0.172498i
$956$	18.2207	−	56.0777i	0.589301	−	1.81368i
$957$	11.5025			0.371824
$958$	12.3571	−	38.0313i	0.399240	−	1.22873i
$959$	31.2168	−	22.6803i	1.00804	−	0.732387i
$960$	−44.1965	+	62.4560i	−1.42644	+	2.01576i
$961$	18.9789	+	13.7890i	0.612223	+	0.444806i
$962$	15.3425	−	11.1470i	0.494662	−	0.359393i
$963$	−5.46993	+	3.97414i	−0.176266	+	0.128065i
$964$	−76.9219	−	55.8870i	−2.47749	−	1.80000i
$965$	−16.8999	−	5.25882i	−0.544026	−	0.169287i
$966$	−20.3750	+	14.8033i	−0.655556	+	0.476290i
$967$	−0.309195	+	0.951606i	−0.00994305	+	0.0306016i	−0.955905	−	0.293676i	$-0.905121\pi$
$967$	−0.309195	+	0.951606i	−0.00994305	+	0.0306016i	0.945962	+	0.324278i	$0.105121\pi$
$968$	−36.9254			−1.18683
$969$	5.64990	−	17.3886i	0.181501	−	0.558603i
$970$	−55.3894	+	78.2731i	−1.77845	+	2.51320i
$971$	16.2750	+	50.0894i	0.522291	+	1.60745i	0.769612	+	0.638512i	$0.220450\pi$
$971$	16.2750	+	50.0894i	0.522291	+	1.60745i	−0.247321	+	0.968934i	$0.579550\pi$
$972$	16.6176	+	51.1438i	0.533011	+	1.64044i
$973$	15.1192	+	10.9847i	0.484698	+	0.352154i
$974$	−69.5548			−2.22868
$975$	−5.92670	−	16.8014i	−0.189806	−	0.538076i
$976$	−1.66957			−0.0534415
$977$	−27.2013	−	19.7629i	−0.870248	−	0.632272i	0.0604058	−	0.998174i	$-0.480761\pi$
$977$	−27.2013	−	19.7629i	−0.870248	−	0.632272i	−0.930653	+	0.365902i	$0.880761\pi$
$978$	18.6992	+	57.5504i	0.597936	+	1.84026i
$979$	−0.476693	−	1.46711i	−0.0152352	−	0.0468891i
$980$	0.274722	+	22.0088i	0.00877569	+	0.703045i
$981$	−8.73410	+	26.8808i	−0.278858	+	0.858238i
$982$	26.6543			0.850572
$983$	−2.32370	+	7.15162i	−0.0741146	+	0.228101i	−0.981251	−	0.192736i	$-0.938264\pi$
$983$	−2.32370	+	7.15162i	−0.0741146	+	0.228101i	0.907136	+	0.420838i	$0.138264\pi$
$984$	−15.8574	+	11.5211i	−0.505515	+	0.367278i
$985$	0.0915820	+	7.33690i	0.00291805	+	0.233773i
$986$	12.6104	+	9.16202i	0.401598	+	0.291778i
$987$	−46.9827	+	34.1349i	−1.49548	+	1.08653i
$988$	−23.3347	+	16.9537i	−0.742377	+	0.539368i
$989$	−14.7696	−	10.7307i	−0.469645	−	0.341217i
$990$	9.39316	+	12.5949i	0.298534	+	0.400294i
$991$	42.3408	−	30.7624i	1.34500	−	0.977201i	0.345757	−	0.938324i	$-0.387622\pi$
$991$	42.3408	−	30.7624i	1.34500	−	0.977201i	0.999244	−	0.0388766i	$-0.0123779\pi$
$992$	−3.56916	+	10.9847i	−0.113321	+	0.348766i
$993$	−67.5209			−2.14271
$994$	−10.7631	+	33.1255i	−0.341386	+	1.05068i
$995$	40.0929	+	12.4759i	1.27103	+	0.395513i
$996$	41.7868	+	128.606i	1.32406	+	4.07505i
$997$	−3.77700	−	11.6244i	−0.119619	−	0.368149i	0.873264	−	0.487248i	$-0.161999\pi$
$997$	−3.77700	−	11.6244i	−0.119619	−	0.368149i	−0.992882	+	0.119099i	$0.961999\pi$
$998$	−28.2926	−	20.5558i	−0.895587	−	0.650682i
$999$	−33.4589			−1.05859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.341.3	yes	76
25.11	even	5	inner	425.2.k.b.86.3	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.3	✓	76	25.11	even	5	inner
425.2.k.b.341.3	yes	76	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89465 - 1.37655i) q^{2} +(-0.866934 - 2.66815i) q^{3} +(1.07680 + 3.31404i) q^{4} +(-2.13509 - 0.664386i) q^{5} +(-2.03029 + 6.24859i) q^{6} -2.04332 q^{7} +(1.07439 - 3.30663i) q^{8} +(-3.94040 + 2.86287i) q^{9} +(3.13069 + 4.19783i) q^{10} +(-0.498365 - 0.362083i) q^{11} +(7.90885 - 5.74612i) q^{12} +(1.02753 - 0.746547i) q^{13} +(3.87139 + 2.81273i) q^{14} +(0.0782984 + 6.27271i) q^{15} +(-0.949136 + 0.689588i) q^{16} +(0.309017 - 0.951057i) q^{17} +11.4066 q^{18} +(-2.01390 + 6.19814i) q^{19} +(-0.0972525 - 7.79118i) q^{20} +(1.77143 + 5.45189i) q^{21} +(0.445804 + 1.37204i) q^{22} +(-1.51770 - 1.10267i) q^{23} -9.75401 q^{24} +(4.11718 + 2.83704i) q^{25} -2.97448 q^{26} +(4.24563 + 3.08463i) q^{27} +(-2.20024 - 6.77166i) q^{28} +(-2.05676 - 6.33004i) q^{29} +(8.48632 - 11.9924i) q^{30} +(0.848576 - 2.61165i) q^{31} -4.20606 q^{32} +(-0.534042 + 1.64361i) q^{33} +(-1.89465 + 1.37655i) q^{34} +(4.36267 + 1.35755i) q^{35} +(-13.7307 - 9.97592i) q^{36} +(-5.15805 + 3.74754i) q^{37} +(12.3477 - 8.97110i) q^{38} +(-2.88270 - 2.09441i) q^{39} +(-4.49079 + 6.34613i) q^{40} +(1.62573 - 1.18116i) q^{41} +(4.14854 - 12.7679i) q^{42} +9.73154 q^{43} +(0.663321 - 2.04149i) q^{44} +(10.3151 - 3.49452i) q^{45} +(1.35763 + 4.17837i) q^{46} +(3.13056 + 9.63488i) q^{47} +(2.66276 + 1.93461i) q^{48} -2.82484 q^{49} +(-3.89532 - 11.0427i) q^{50} -2.80546 q^{51} +(3.58054 + 2.60141i) q^{52} +(-3.74086 - 11.5132i) q^{53} +(-3.79786 - 11.6886i) q^{54} +(0.823488 + 1.10418i) q^{55} +(-2.19532 + 6.75651i) q^{56} +18.2835 q^{57} +(-4.81676 + 14.8245i) q^{58} +(5.91599 - 4.29822i) q^{59} +(-20.7037 + 7.01392i) q^{60} +(1.15130 + 0.836472i) q^{61} +(-5.20281 + 3.78006i) q^{62} +(8.05150 - 5.84975i) q^{63} +(9.86730 + 7.16901i) q^{64} +(-2.68987 + 0.911263i) q^{65} +(3.27434 - 2.37894i) q^{66} +(-1.60347 + 4.93496i) q^{67} +3.48459 q^{68} +(-1.62635 + 5.00540i) q^{69} +(-6.39701 - 8.57751i) q^{70} +(2.24921 + 6.92235i) q^{71} +(5.23292 + 16.1053i) q^{72} +(-10.7537 - 7.81304i) q^{73} +14.9314 q^{74} +(4.00032 - 13.4448i) q^{75} -22.7095 q^{76} +(1.01832 + 0.739852i) q^{77} +(2.57868 + 7.93635i) q^{78} +(4.40684 + 13.5629i) q^{79} +(2.48464 - 0.841736i) q^{80} +(0.0342773 - 0.105495i) q^{81} -4.70612 q^{82} +(-4.27448 + 13.1555i) q^{83} +(-16.1603 + 11.7412i) q^{84} +(-1.29165 + 1.82528i) q^{85} +(-18.4379 - 13.3959i) q^{86} +(-15.1064 + 10.9755i) q^{87} +(-1.73271 + 1.25889i) q^{88} +(2.02593 + 1.47192i) q^{89} +(-24.3540 - 7.57835i) q^{90} +(-2.09958 + 1.52544i) q^{91} +(2.02005 - 6.21708i) q^{92} -7.70393 q^{93} +(7.33153 - 22.5641i) q^{94} +(8.41780 - 11.8956i) q^{95} +(3.64638 + 11.2224i) q^{96} +(5.65839 + 17.4147i) q^{97} +(5.35209 + 3.88852i) q^{98} +3.00035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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