LMFDB - Embedded newform 425.2.k.b.86.3

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			86.3
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.3

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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	−0.340268	+	0.940328i	$0.610518\pi$
$2$	−1.89465	+	1.37655i	−1.33972	+	0.973365i	−0.999454	+	0.0330368i	$0.989482\pi$
$3$	−0.866934	+	2.66815i	−0.500525	+	1.54046i	0.307641	+	0.951502i	$0.400460\pi$
$3$	−0.866934	+	2.66815i	−0.500525	+	1.54046i	−0.808166	+	0.588954i	$0.799540\pi$
$4$	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	−0.660376	−	0.750935i	$-0.729603\pi$
$11$	−0.498365	+	0.362083i	−0.150263	+	0.109172i	0.510114	+	0.860107i	$0.329603\pi$
$12$	7.90885	+	5.74612i	2.28309	+	1.65876i
$13$	1.02753	+	0.746547i	0.284987	+	0.207055i	0.721089	−	0.692842i	$-0.243642\pi$
$13$	1.02753	+	0.746547i	0.284987	+	0.207055i	−0.436103	+	0.899897i	$0.643642\pi$
$14$	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	−0.862692	−	0.505729i	$-0.831224\pi$
$19$	−2.01390	−	6.19814i	−0.462020	−	1.42195i	0.400673	−	0.916221i	$-0.368776\pi$
$20$	−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	−0.734664	−	0.678431i	$-0.762660\pi$
$23$	−1.51770	+	1.10267i	−0.316462	+	0.229923i	0.418202	+	0.908354i	$0.362660\pi$
$24$	−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	0.556753	+	0.830678i	$0.312047\pi$
$29$	−2.05676	+	6.33004i	−0.381930	+	1.17546i	−0.938683	+	0.344781i	$0.887953\pi$
$30$	8.48632	+	11.9924i	1.54938	+	2.18950i
$31$	0.848576	+	2.61165i	0.152409	+	0.469066i	0.997889	−	0.0649406i	$-0.0206858\pi$
$31$	0.848576	+	2.61165i	0.152409	+	0.469066i	−0.845480	+	0.534006i	$0.820686\pi$
$32$	−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	0.0766100	−	0.997061i	$-0.475590\pi$
$37$	−5.15805	−	3.74754i	−0.847978	−	0.616092i	−0.924588	+	0.380969i	$0.875590\pi$
$38$	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	0.707452	−	0.706762i	$-0.249845\pi$
$41$	1.62573	+	1.18116i	0.253896	+	0.184466i	−0.453556	+	0.891228i	$0.649845\pi$
$42$	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	−0.412561	−	0.910930i	$-0.635365\pi$
$47$	3.13056	−	9.63488i	0.456639	−	1.40539i	0.869200	−	0.494461i	$-0.164635\pi$
$48$	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	0.271525	+	0.962431i	$0.412472\pi$
$53$	−3.74086	+	11.5132i	−0.513846	+	1.58146i	−0.785372	+	0.619025i	$0.787528\pi$
$54$	−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	0.902021	−	0.431693i	$-0.142084\pi$
$59$	5.91599	+	4.29822i	0.770196	+	0.559580i	−0.131825	+	0.991273i	$0.542084\pi$
$60$	−20.7037	−	7.01392i	−2.67284	−	0.905494i
$61$	1.15130	−	0.836472i	0.147409	−	0.107099i	−0.511636	−	0.859202i	$-0.670960\pi$
$61$	1.15130	−	0.836472i	0.147409	−	0.107099i	0.659046	+	0.752103i	$0.270960\pi$
$62$	−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	−0.999965	−	0.00836725i	$-0.997337\pi$
$67$	−1.60347	−	4.93496i	−0.195894	−	0.602901i	0.804071	−	0.594534i	$-0.202663\pi$
$68$	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	−0.724310	−	0.689474i	$-0.757842\pi$
$71$	2.24921	−	6.92235i	0.266932	−	0.821532i	0.991242	−	0.132058i	$-0.0421584\pi$
$72$	5.23292	−	16.1053i	0.616705	−	1.89802i
$73$	−10.7537	+	7.81304i	−1.25863	+	0.914447i	−0.998690	−	0.0511783i	$-0.983702\pi$
$73$	−10.7537	+	7.81304i	−1.25863	+	0.914447i	−0.259939	+	0.965625i	$0.583702\pi$
$74$	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	−0.319884	−	0.947457i	$-0.603644\pi$
$79$	4.40684	−	13.5629i	0.495809	−	1.52594i	0.815693	−	0.578485i	$-0.196356\pi$
$80$	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	−0.853642	−	0.520860i	$-0.825612\pi$
$83$	−4.27448	−	13.1555i	−0.469185	−	1.44400i	0.384458	−	0.923143i	$-0.374388\pi$
$84$	−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	−0.475211	−	0.879872i	$-0.657628\pi$
$89$	2.02593	−	1.47192i	0.214748	−	0.156024i	0.689959	+	0.723848i	$0.257628\pi$
$90$	−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	−0.0632756	−	0.997996i	$-0.520155\pi$
$97$	5.65839	−	17.4147i	0.574523	−	1.76820i	0.637798	−	0.770203i	$-0.279845\pi$
$98$	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	−0.808222	−	0.588878i	$-0.799570\pi$
$103$	1.94633	−	5.99017i	0.191777	−	0.590229i	0.999999	−	0.00135131i	$-0.000430136\pi$
$104$	−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	0.789467	−	0.613793i	$-0.210357\pi$
$109$	4.69474	+	3.41093i	0.449674	+	0.326708i	−0.339793	+	0.940500i	$0.610357\pi$
$110$	−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	0.201207	−	0.979549i	$-0.435514\pi$
$113$	−7.10330	−	5.16085i	−0.668223	−	0.485492i	−0.869430	+	0.494057i	$0.835514\pi$
$114$	−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	−0.966939	−	0.255006i	$-0.917922\pi$
$127$	−11.5310	+	8.37779i	−1.02321	+	0.743409i	−0.0562754	+	0.998415i	$0.517922\pi$
$128$	−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	−0.795552	−	0.605886i	$-0.792819\pi$
$131$	−5.81510	−	17.8970i	−0.508068	−	1.56367i	0.287484	−	0.957785i	$-0.407181\pi$
$132$	−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	−0.305251	−	0.952272i	$-0.598741\pi$
$137$	−15.2775	−	11.0997i	−1.30524	−	0.948315i	−0.999992	+	0.00395679i	$0.998741\pi$
$138$	9.97153	+	7.24474i	0.848833	+	0.616713i
$139$	−7.39931	+	5.37591i	−0.627601	+	0.455979i	−0.855568	−	0.517690i	$-0.826792\pi$
$139$	−7.39931	+	5.37591i	−0.627601	+	0.455979i	0.227967	+	0.973669i	$0.426792\pi$
$140$	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	0.840027	−	0.542544i	$-0.182539\pi$
$163$	7.45115	+	5.41358i	0.583619	+	0.424024i	−0.256408	+	0.966569i	$0.582539\pi$
$164$	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	0.891146	−	0.453716i	$-0.149902\pi$
$167$	−1.24697	−	3.83779i	−0.0964937	−	0.296977i	−0.987640	+	0.156739i	$0.949902\pi$
$168$	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	−0.174340	−	0.984686i	$-0.555779\pi$
$173$	9.31594	−	6.76843i	0.708278	−	0.514594i	0.882618	+	0.470092i	$0.155779\pi$
$174$	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	−0.466519	−	0.884511i	$-0.654492\pi$
$179$	5.76378	−	17.7391i	0.430805	−	1.32588i	0.897325	−	0.441371i	$-0.145508\pi$
$180$	22.6883	−	30.4219i	1.69109	−	2.26751i
$181$	2.66390	+	8.19865i	0.198006	+	0.609401i	0.999928	+	0.0119722i	$0.00381097\pi$
$181$	2.66390	+	8.19865i	0.198006	+	0.609401i	−0.801922	+	0.597429i	$0.796189\pi$
$182$	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	0.348686	−	0.937239i	$-0.386628\pi$
$191$	−6.01087	−	4.36715i	−0.434931	−	0.315996i	−0.783618	+	0.621243i	$0.786628\pi$
$192$	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	−0.980659	−	0.195724i	$-0.937294\pi$
$197$	−1.01401	+	3.12081i	−0.0722455	+	0.222349i	0.908414	+	0.418073i	$0.137294\pi$
$198$	−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	−0.938972	−	0.343993i	$-0.888220\pi$
$211$	−13.1019	+	9.51911i	−0.901974	+	0.655322i	0.0369983	+	0.999315i	$0.488220\pi$
$212$	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	−0.810770	−	0.585365i	$-0.800951\pi$
$223$	−7.53523	+	5.47467i	−0.504597	+	0.366611i	0.306173	+	0.951976i	$0.400951\pi$
$224$	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	−0.951724	−	0.306956i	$-0.900690\pi$
$227$	−14.3718	+	10.4417i	−0.953890	+	0.693042i	−0.00216620	+	0.999998i	$0.500690\pi$
$228$	19.6876	−	60.5922i	1.30384	−	4.01282i
$229$	−4.83924	+	14.8936i	−0.319786	+	0.984199i	0.653954	+	0.756535i	$0.273109\pi$
$229$	−4.83924	+	14.8936i	−0.319786	+	0.984199i	−0.973740	+	0.227665i	$0.926891\pi$
$230$	−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	0.928564	−	0.371171i	$-0.121044\pi$
$233$	−0.623226	−	1.91809i	−0.0408289	−	0.125658i	−0.969393	+	0.245513i	$0.921044\pi$
$234$	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	−0.934702	−	0.355433i	$-0.884334\pi$
$239$	−13.6896	+	9.94605i	−0.885504	+	0.643356i	0.0491978	+	0.998789i	$0.484334\pi$
$240$	−4.39990	+	5.89966i	−0.284012	+	0.380821i
$241$	−22.0749	−	16.0383i	−1.42197	−	1.03312i	−0.991443	−	0.130541i	$-0.958329\pi$
$241$	−22.0749	−	16.0383i	−1.42197	−	1.03312i	−0.430524	−	0.902579i	$-0.641671\pi$
$242$	−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	0.655137	−	0.755510i	$-0.272611\pi$
$263$	2.25505	+	1.63839i	0.139053	+	0.101028i	−0.516084	+	0.856538i	$0.672611\pi$
$264$	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	0.988062	−	0.154058i	$-0.0492342\pi$
$269$	1.60978	+	4.95440i	0.0981501	+	0.302075i	−0.889912	+	0.456133i	$0.849234\pi$
$270$	0.343009	−	27.4794i	0.0208748	−	1.67234i
$271$	−1.69634	+	5.22078i	−0.103045	+	0.317140i	−0.989267	−	0.146121i	$-0.953321\pi$
$271$	−1.69634	+	5.22078i	−0.103045	+	0.317140i	0.886222	+	0.463262i	$0.153321\pi$
$272$	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	−0.859463	−	0.511199i	$-0.829202\pi$
$277$	−10.6330	+	7.72529i	−0.638872	+	0.464168i	0.220590	+	0.975367i	$0.429202\pi$
$278$	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	0.978737	+	0.205120i	$0.0657586\pi$
$281$	5.15445	+	15.8638i	0.307489	+	0.946353i	−0.671248	+	0.741233i	$0.734241\pi$
$282$	−66.5604			−3.96361
$283$	0.498940	+	1.53558i	0.0296589	+	0.0912807i	0.964790	−	0.263021i	$-0.0847187\pi$
$283$	0.498940	+	1.53558i	0.0296589	+	0.0912807i	−0.935131	+	0.354301i	$0.884719\pi$
$284$	−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	−0.802946	−	0.596052i	$-0.796735\pi$
$311$	−8.53880	+	6.20380i	−0.484191	+	0.351785i	0.318755	+	0.947837i	$0.396735\pi$
$312$	−10.0226	−	7.28182i	−0.567416	−	0.412252i
$313$	−18.1133	−	13.1601i	−1.02383	−	0.743853i	−0.0567622	−	0.998388i	$-0.518078\pi$
$313$	−18.1133	−	13.1601i	−1.02383	−	0.743853i	−0.967064	+	0.254535i	$0.918078\pi$
$314$	−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	0.958738	−	0.284291i	$-0.0917582\pi$
$317$	0.284883	+	0.876780i	0.0160006	+	0.0492449i	−0.942737	+	0.333536i	$0.891758\pi$
$318$	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	0.917687	+	0.397305i	$0.130055\pi$
$331$	7.43733	+	22.8897i	0.408793	+	1.25813i	−0.508894	+	0.860829i	$0.669945\pi$
$332$	−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	0.847687	−	0.530497i	$-0.177995\pi$
$337$	11.1082	+	8.07059i	0.605103	+	0.439633i	−0.242584	+	0.970131i	$0.577995\pi$
$338$	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	−0.889139	−	0.457636i	$-0.848696\pi$
$347$	1.84754	−	5.68615i	0.0991813	−	0.305249i	0.988321	+	0.152388i	$0.0486962\pi$
$348$	−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	−0.712628	−	0.701542i	$-0.752495\pi$
$353$	5.19038	−	15.9743i	0.276256	−	0.850228i	0.988884	−	0.148687i	$-0.0475046\pi$
$354$	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	−0.0904299	−	0.995903i	$-0.528824\pi$
$359$	−20.1890	−	14.6682i	−1.06553	−	0.774156i	−0.975104	+	0.221747i	$0.928824\pi$
$360$	−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	0.994039	+	0.109026i	$0.0347733\pi$
$367$	4.86457	+	14.9716i	0.253929	+	0.781512i	−0.740110	+	0.672486i	$0.765227\pi$
$368$	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	−0.710118	−	0.704083i	$-0.751358\pi$
$373$	−5.02015	+	3.64735i	−0.259933	+	0.188853i	0.450184	+	0.892936i	$0.351358\pi$
$374$	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	−0.160854	−	0.986978i	$-0.551425\pi$
$379$	10.6959	−	32.9186i	0.549411	−	1.69091i	0.710265	−	0.703935i	$-0.248575\pi$
$380$	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	−0.997365	−	0.0725486i	$-0.976887\pi$
$383$	−4.56230	−	14.0413i	−0.233123	−	0.717478i	0.764242	−	0.644929i	$-0.223113\pi$
$384$	−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	−0.153872	−	0.988091i	$-0.549174\pi$
$389$	14.5617	−	10.5797i	0.738309	−	0.536413i	0.892181	+	0.451678i	$0.149174\pi$
$390$	−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	−0.882233	−	0.470813i	$-0.843961\pi$
$397$	2.15678	−	6.63788i	0.108246	−	0.333146i	0.990478	+	0.137668i	$0.0439606\pi$
$398$	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	0.641756	−	0.766909i	$-0.278206\pi$
$409$	2.23867	+	1.62649i	0.110695	+	0.0804247i	−0.531061	+	0.847334i	$0.678206\pi$
$410$	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	0.842676	−	0.538421i	$-0.180979\pi$
$419$	−3.18381	−	9.79876i	−0.155539	−	0.478701i	−0.998215	+	0.0597206i	$0.980979\pi$
$420$	42.3043	+	14.3317i	2.06424	+	0.699315i
$421$	−3.91651	+	12.0538i	−0.190879	+	0.587465i	−1.00000		0.000176949i	$-0.999944\pi$
$421$	−3.91651	+	12.0538i	−0.190879	+	0.587465i	0.809121	+	0.587642i	$0.199944\pi$
$422$	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	0.821627	−	0.570026i	$-0.193067\pi$
$431$	−3.69820	−	11.3819i	−0.178136	−	0.548246i	−0.999763	+	0.0217798i	$0.993067\pi$
$432$	−6.15680			−0.296219
$433$	−12.6762	−	39.0134i	−0.609181	−	1.87487i	−0.464991	−	0.885315i	$-0.653942\pi$
$433$	−12.6762	−	39.0134i	−0.609181	−	1.87487i	−0.144190	−	0.989550i	$-0.546058\pi$
$434$	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	−0.764564	−	0.644547i	$-0.777046\pi$
$439$	−8.12587	+	5.90379i	−0.387827	+	0.281773i	0.376738	+	0.926320i	$0.377046\pi$
$440$	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	−0.936561	−	0.350506i	$-0.886010\pi$
$461$	−19.1654	+	13.9245i	−0.892623	+	0.648529i	0.0439375	+	0.999034i	$0.486010\pi$
$462$	−6.69052	−	4.86095i	−0.311271	−	0.226152i
$463$	−29.5464	−	21.4667i	−1.37314	−	0.997641i	−0.997485	−	0.0708802i	$-0.977419\pi$
$463$	−29.5464	−	21.4667i	−1.37314	−	0.997641i	−0.375651	−	0.926761i	$-0.622581\pi$
$464$	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	0.927437	−	0.373980i	$-0.122007\pi$
$467$	−0.922647	−	2.83962i	−0.0426950	−	0.131402i	−0.970132	+	0.242578i	$0.922007\pi$
$468$	−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	−0.755166	−	0.655533i	$-0.772444\pi$
$479$	5.27649	−	16.2394i	0.241089	−	0.741995i	0.996255	−	0.0864619i	$-0.0275561\pi$
$480$	−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	0.979196	−	0.202915i	$-0.0650416\pi$
$487$	24.0277	+	17.4572i	1.08880	+	0.791060i	0.109604	+	0.993975i	$0.465042\pi$
$488$	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	0.360302	−	0.932836i	$-0.382674\pi$
$491$	−9.20772	−	6.68980i	−0.415539	−	0.301906i	−0.775840	+	0.630929i	$0.782674\pi$
$492$	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	−0.983309	−	0.181943i	$-0.941761\pi$
$503$	−1.81332	+	5.58081i	−0.0808517	+	0.248836i	0.902457	+	0.430779i	$0.141761\pi$
$504$	−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	0.00178339	−	0.999998i	$-0.499432\pi$
$509$	−21.4041	−	15.5510i	−0.948721	−	0.689286i	−0.950504	+	0.310713i	$0.899432\pi$
$510$	−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	−0.610457	−	0.792049i	$-0.709014\pi$
$521$	7.96534	−	24.5148i	0.348968	−	1.07401i	0.959425	−	0.281963i	$-0.0909856\pi$
$522$	−23.4605	+	72.2040i	−1.02684	+	3.16028i
$523$	18.8355	−	13.6848i	0.823618	−	0.598393i	−0.0941287	−	0.995560i	$-0.530007\pi$
$523$	18.8355	−	13.6848i	0.823618	−	0.598393i	0.917746	+	0.397167i	$0.130007\pi$
$524$	−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	0.931682	−	0.363274i	$-0.118341\pi$
$541$	20.3309	+	14.7713i	0.874093	+	0.635066i	−0.0575889	+	0.998340i	$0.518341\pi$
$542$	−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	−0.854780	−	0.518991i	$-0.826308\pi$
$547$	3.31659	−	10.2074i	0.141807	−	0.436437i	0.996587	+	0.0825541i	$0.0263077\pi$
$548$	−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	0.539875	−	0.841745i	$-0.318472\pi$
$563$	−2.22666	−	1.61776i	−0.0938423	−	0.0681804i	−0.633717	+	0.773565i	$0.718472\pi$
$564$	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	0.991993	+	0.126290i	$0.0403068\pi$
$569$	6.28987	+	19.3582i	0.263685	+	0.811539i	−0.728308	+	0.685249i	$0.759693\pi$
$570$	57.2399	−	76.7508i	2.39752	−	3.21474i
$571$	−6.18462	+	19.0343i	−0.258818	+	0.796560i	0.734235	+	0.678895i	$0.237541\pi$
$571$	−6.18462	+	19.0343i	−0.258818	+	0.796560i	−0.993053	+	0.117665i	$0.962459\pi$
$572$	−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	−0.0875606	−	0.996159i	$-0.527907\pi$
$577$	20.0042	−	14.5339i	0.832785	−	0.605054i	0.920346	+	0.391105i	$0.127907\pi$
$578$	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	−0.153628	−	0.988129i	$-0.549096\pi$
$587$	−27.6410	−	20.0824i	−1.14087	−	0.828889i	−0.987240	+	0.159240i	$0.949096\pi$
$588$	−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	0.470436	−	0.882434i	$-0.344097\pi$
$613$	−5.53203	−	4.01926i	−0.223437	−	0.162336i	−0.693872	+	0.720098i	$0.744097\pi$
$614$	−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	0.998708	−	0.0508186i	$-0.0161830\pi$
$617$	3.99582	+	12.2979i	0.160866	+	0.495094i	−0.837842	+	0.545913i	$0.816183\pi$
$618$	−41.3818			−1.66462
$619$	8.55615	+	26.3331i	0.343901	+	1.05842i	0.962170	+	0.272451i	$0.0878343\pi$
$619$	8.55615	+	26.3331i	0.343901	+	1.05842i	−0.618269	+	0.785967i	$0.712166\pi$
$620$	−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	0.958831	+	0.283976i	$0.0916537\pi$
$631$	8.79284	+	27.0616i	0.350038	+	1.07730i	−0.608794	+	0.793329i	$0.708346\pi$
$632$	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	0.874758	−	0.484560i	$-0.161020\pi$
$641$	17.3233	+	12.5861i	0.684230	+	0.497122i	−0.190528	+	0.981682i	$0.561020\pi$
$642$	−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	0.498625	+	0.866818i	$0.333838\pi$
$647$	−10.5375	+	32.4312i	−0.414274	+	1.27500i	−0.912899	+	0.408186i	$0.866162\pi$
$648$	−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	−0.978810	−	0.204768i	$-0.934356\pi$
$653$	−1.70129	+	5.23602i	−0.0665764	+	0.204901i	0.912234	+	0.409669i	$0.134356\pi$
$654$	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	0.828400	−	0.560137i	$-0.189252\pi$
$659$	14.1619	+	10.2892i	0.551667	+	0.400810i	−0.276733	+	0.960947i	$0.589252\pi$
$660$	12.8576	−	4.00097i	0.500482	−	0.155738i
$661$	26.1104	−	18.9703i	1.01558	−	0.737860i	0.0502060	−	0.998739i	$-0.484012\pi$
$661$	26.1104	−	18.9703i	1.01558	−	0.737860i	0.965372	+	0.260879i	$0.0840122\pi$
$662$	−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	−0.0449273	−	0.998990i	$-0.514306\pi$
$673$	23.1219	−	16.7991i	0.891286	−	0.647557i	0.936213	+	0.351433i	$0.114306\pi$
$674$	−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	−0.495365	−	0.868685i	$-0.664966\pi$
$677$	4.62434	−	3.35978i	0.177728	−	0.129127i	0.673093	+	0.739558i	$0.264966\pi$
$678$	−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	−0.964037	−	0.265768i	$-0.914375\pi$
$683$	−8.89425	−	27.3737i	−0.340329	−	1.04742i	0.623708	−	0.781657i	$-0.285625\pi$
$684$	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	−0.998596	−	0.0529804i	$-0.983128\pi$
$691$	−35.6862	−	25.9275i	−1.35757	−	0.986329i	−0.358970	−	0.933349i	$-0.616872\pi$
$692$	−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	0.273224	−	0.961951i	$-0.411910\pi$
$709$	−14.8370	−	10.7797i	−0.557215	−	0.404840i	−0.830439	+	0.557110i	$0.811910\pi$
$710$	−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	0.927609	−	0.373552i	$-0.121860\pi$
$719$	−1.13722	−	3.49999i	−0.0424110	−	0.130528i	−0.970020	+	0.243025i	$0.921860\pi$
$720$	−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	−0.473419	−	0.880837i	$-0.656980\pi$
$727$	5.87824	−	4.27079i	0.218012	−	0.158395i	0.691431	+	0.722442i	$0.256980\pi$
$728$	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	0.995480	+	0.0949690i	$0.0302752\pi$
$733$	6.65860	+	20.4931i	0.245941	+	0.756929i	−0.749539	+	0.661960i	$0.769725\pi$
$734$	−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	−0.441945	−	0.897042i	$-0.645711\pi$
$739$	7.46555	−	5.42404i	0.274625	−	0.199526i	0.716569	+	0.697516i	$0.245711\pi$
$740$	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	−0.875591	−	0.483054i	$-0.839528\pi$
$761$	−18.9449	+	13.7643i	−0.686752	+	0.498954i	0.188839	+	0.982008i	$0.439528\pi$
$762$	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	0.991364	+	0.131139i	$0.0418635\pi$
$769$	7.38793	+	22.7377i	0.266415	+	0.819942i	−0.724949	+	0.688803i	$0.758136\pi$
$770$	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	0.404006	−	0.914756i	$-0.367618\pi$
$773$	38.8917	−	28.2564i	1.39884	−	1.01631i	0.994830	−	0.101557i	$-0.0323825\pi$
$774$	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	−0.952610	−	0.304195i	$-0.901613\pi$
$787$	−43.0983	−	31.3128i	−1.53629	−	1.11618i	−0.583679	−	0.811984i	$-0.698387\pi$
$788$	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	0.654808	+	0.755796i	$0.272750\pi$
$797$	−9.01107	+	27.7332i	−0.319188	+	0.982361i	−0.973996	+	0.226565i	$0.927250\pi$
$798$	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	0.527386	−	0.849626i	$-0.323172\pi$
$809$	−3.34731	−	2.43196i	−0.117685	−	0.0855033i	−0.645071	+	0.764123i	$0.723172\pi$
$810$	0.550160	+	0.186381i	0.0193306	+	0.00654876i
$811$	−13.9174	+	10.1116i	−0.488705	+	0.355065i	−0.804686	−	0.593700i	$-0.797666\pi$
$811$	−13.9174	+	10.1116i	−0.488705	+	0.355065i	0.315981	+	0.948766i	$0.397666\pi$
$812$	−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	−0.969185	−	0.246334i	$-0.920774\pi$
$821$	−1.15490	+	3.55441i	−0.0403062	+	0.124050i	0.928879	+	0.370384i	$0.120774\pi$
$822$	−38.3400	+	117.999i	−1.33726	+	4.11567i
$823$	11.2042	−	8.14035i	0.390555	−	0.283755i	−0.375128	−	0.926973i	$-0.622401\pi$
$823$	11.2042	−	8.14035i	0.390555	−	0.283755i	0.765683	+	0.643218i	$0.222401\pi$
$824$	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	−0.984888	−	0.173191i	$-0.944592\pi$
$827$	−32.3385	+	23.4953i	−1.12452	+	0.817012i	−0.139633	+	0.990203i	$0.544592\pi$
$828$	9.83886	−	30.2809i	0.341924	−	1.05233i
$829$	−6.49095	+	19.9771i	−0.225440	+	0.693833i	0.772807	+	0.634642i	$0.218852\pi$
$829$	−6.49095	+	19.9771i	−0.225440	+	0.693833i	−0.998247	+	0.0591916i	$0.981148\pi$
$830$	−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	0.0273922	−	0.999625i	$-0.491280\pi$
$839$	28.5761	−	20.7618i	0.986556	−	0.716775i	0.959164	+	0.282850i	$0.0912797\pi$
$840$	−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	0.801030	+	0.598624i	$0.204286\pi$
$853$	−5.80850	+	17.8767i	−0.198879	+	0.612087i	−0.999909	+	0.0134632i	$0.995714\pi$
$854$	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	0.719171	−	0.694833i	$-0.244522\pi$
$859$	8.22351	+	5.97473i	0.280582	+	0.203855i	−0.438589	+	0.898688i	$0.644522\pi$
$860$	−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	−0.987386	−	0.158332i	$-0.949388\pi$
$863$	−42.3934	−	30.8006i	−1.44309	−	1.04846i	−0.455702	−	0.890132i	$-0.650612\pi$
$864$	−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	−0.857896	−	0.513824i	$-0.828228\pi$
$877$	−18.7850	+	13.6481i	−0.634324	+	0.460864i	0.223571	+	0.974688i	$0.428228\pi$
$878$	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	−0.999715	−	0.0238693i	$-0.992401\pi$
$881$	−6.08351	−	18.7231i	−0.204959	−	0.630798i	0.794756	−	0.606928i	$-0.207599\pi$
$882$	−32.2216			−1.08496
$883$	8.07827	+	24.8624i	0.271855	+	0.836685i	0.990034	+	0.140826i	$0.0449759\pi$
$883$	8.07827	+	24.8624i	0.271855	+	0.836685i	−0.718179	+	0.695859i	$0.755024\pi$
$884$	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	0.869579	−	0.493795i	$-0.164391\pi$
$887$	19.9146	+	14.4688i	0.668667	+	0.485815i	−0.200912	+	0.979609i	$0.564391\pi$
$888$	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	−0.326814	−	0.945089i	$-0.605975\pi$
$911$	14.2169	−	10.3292i	0.471028	−	0.342222i	0.797842	+	0.602867i	$0.205975\pi$
$912$	−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	0.905825	−	0.423653i	$-0.139252\pi$
$919$	−2.30454	−	7.09264i	−0.0760198	−	0.233965i	−0.981844	+	0.189688i	$0.939252\pi$
$920$	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	−0.731504	−	0.681837i	$-0.761181\pi$
$929$	7.95724	−	24.4899i	0.261069	−	0.803487i	0.992573	−	0.121650i	$-0.0388185\pi$
$930$	−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	0.981290	−	0.192536i	$-0.0616711\pi$
$937$	33.7147	+	24.4952i	1.10141	+	0.800223i	0.120123	+	0.992759i	$0.461671\pi$
$938$	−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	0.324695	−	0.945819i	$-0.394738\pi$
$941$	−14.5555	−	10.5752i	−0.474495	−	0.344741i	−0.799191	+	0.601078i	$0.794738\pi$
$942$	−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	−0.910798	−	0.412852i	$-0.864533\pi$
$947$	2.11478	−	6.50863i	0.0687212	−	0.211502i	0.979519	+	0.201350i	$0.0645328\pi$
$948$	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	0.679478	+	0.733696i	$0.262206\pi$
$953$	−9.30712	+	28.6444i	−0.301487	+	0.927882i	−0.980965	+	0.194186i	$0.937794\pi$
$954$	−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	0.945962	−	0.324278i	$-0.105121\pi$
$967$	−0.309195	−	0.951606i	−0.00994305	−	0.0306016i	−0.955905	+	0.293676i	$0.905121\pi$
$968$	−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	−0.247321	−	0.968934i	$-0.579550\pi$
$971$	16.2750	−	50.0894i	0.522291	−	1.60745i	0.769612	−	0.638512i	$-0.220450\pi$
$972$	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	−0.930653	−	0.365902i	$-0.880761\pi$
$977$	−27.2013	+	19.7629i	−0.870248	+	0.632272i	0.0604058	+	0.998174i	$0.480761\pi$
$978$	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	0.907136	−	0.420838i	$-0.138264\pi$
$983$	−2.32370	−	7.15162i	−0.0741146	−	0.228101i	−0.981251	+	0.192736i	$0.938264\pi$
$984$	−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	0.999244	+	0.0388766i	$0.0123779\pi$
$991$	42.3408	+	30.7624i	1.34500	+	0.977201i	0.345757	+	0.938324i	$0.387622\pi$
$992$	−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	−0.992882	−	0.119099i	$-0.961999\pi$
$997$	−3.77700	+	11.6244i	−0.119619	+	0.368149i	0.873264	+	0.487248i	$0.161999\pi$
$998$	−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.86.3	✓	76
25.16	even	5	inner	425.2.k.b.341.3	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.3	✓	76	1.1	even	1	trivial
425.2.k.b.341.3	yes	76	25.16	even	5	inner

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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