LMFDB - Embedded newform 525.2.z.b.64.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.17
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60595 + 2.21041i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.68877 + 5.19751i) q^{4} +(-2.23410 + 0.0937129i) q^{5} +(0.844300 + 2.59849i) q^{6} -1.00000i q^{7} +(-9.00374 + 2.92549i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.60595 + 2.21041i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.68877 + 5.19751i) q^{4} +(-2.23410 + 0.0937129i) q^{5} +(0.844300 + 2.59849i) q^{6} -1.00000i q^{7} +(-9.00374 + 2.92549i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-3.79501 - 4.78778i) q^{10} +(-3.47250 + 2.52292i) q^{11} +(-3.21224 + 4.42127i) q^{12} +(0.825990 - 1.13688i) q^{13} +(2.21041 - 1.60595i) q^{14} +(-2.15372 - 0.601250i) q^{15} +(-12.0836 - 8.77924i) q^{16} +(6.10011 - 1.98205i) q^{17} +2.73221i q^{18} +(1.48846 + 4.58100i) q^{19} +(3.28582 - 11.7700i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-11.1534 - 3.62394i) q^{22} +(4.64169 + 6.38874i) q^{23} -9.46709 q^{24} +(4.98244 - 0.418729i) q^{25} +3.83947 q^{26} +(0.587785 + 0.809017i) q^{27} +(5.19751 + 1.68877i) q^{28} +(-1.44955 + 4.46127i) q^{29} +(-2.12977 - 5.72617i) q^{30} +(0.870374 + 2.67873i) q^{31} -21.8745i q^{32} +(-4.08217 + 1.32638i) q^{33} +(14.1776 + 10.3007i) q^{34} +(0.0937129 + 2.23410i) q^{35} +(-4.42127 + 3.21224i) q^{36} +(4.41222 - 6.07290i) q^{37} +(-7.73548 + 10.6470i) q^{38} +(1.13688 - 0.825990i) q^{39} +(19.8411 - 7.37962i) q^{40} +(-5.35535 - 3.89089i) q^{41} +(2.59849 - 0.844300i) q^{42} -6.32527i q^{43} +(-7.24864 - 22.3090i) q^{44} +(-1.86251 - 1.23736i) q^{45} +(-6.66737 + 20.5201i) q^{46} +(3.52407 + 1.14504i) q^{47} +(-8.77924 - 12.0836i) q^{48} -1.00000 q^{49} +(8.92713 + 10.3408i) q^{50} +6.41404 q^{51} +(4.51403 + 6.21303i) q^{52} +(-4.41792 - 1.43547i) q^{53} +(-0.844300 + 2.59849i) q^{54} +(7.52149 - 5.96188i) q^{55} +(2.92549 + 9.00374i) q^{56} +4.81675i q^{57} +(-12.1891 + 3.96049i) q^{58} +(-1.38123 - 1.00352i) q^{59} +(6.76215 - 10.1786i) q^{60} +(8.01186 - 5.82096i) q^{61} +(-4.52331 + 6.22581i) q^{62} +(0.587785 - 0.809017i) q^{63} +(24.1844 - 17.5710i) q^{64} +(-1.73881 + 2.61731i) q^{65} +(-9.48761 - 6.89315i) q^{66} +(-6.86068 + 2.22917i) q^{67} +35.0526i q^{68} +(2.44028 + 7.51042i) q^{69} +(-4.78778 + 3.79501i) q^{70} +(0.0563661 - 0.173477i) q^{71} +(-9.00374 - 2.92549i) q^{72} +(2.72271 + 3.74748i) q^{73} +20.5094 q^{74} +(4.86797 + 1.14142i) q^{75} -26.3235 q^{76} +(2.52292 + 3.47250i) q^{77} +(3.65155 + 1.18646i) q^{78} +(4.14012 - 12.7420i) q^{79} +(27.8187 + 18.4813i) q^{80} +(0.309017 + 0.951057i) q^{81} -18.0861i q^{82} +(-5.86479 + 1.90559i) q^{83} +(4.42127 + 3.21224i) q^{84} +(-13.4425 + 4.99975i) q^{85} +(13.9814 - 10.1581i) q^{86} +(-2.75722 + 3.79498i) q^{87} +(23.8847 - 32.8745i) q^{88} +(4.63594 - 3.36821i) q^{89} +(-0.256044 - 6.10405i) q^{90} +(-1.13688 - 0.825990i) q^{91} +(-41.0444 + 13.3361i) q^{92} +2.81659i q^{93} +(3.12849 + 9.62851i) q^{94} +(-3.75467 - 10.0949i) q^{95} +(6.75960 - 20.8039i) q^{96} +(6.85358 + 2.22686i) q^{97} +(-1.60595 - 2.21041i) q^{98} -4.29225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	1.60595	+	2.21041i	1.13558	+	1.56299i	0.777006	+	0.629493i	$0.216737\pi$
$2$	1.60595	+	2.21041i	1.13558	+	1.56299i	0.358575	+	0.933501i	$0.383263\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−1.68877	+	5.19751i	−0.844387	+	2.59876i
$5$	−2.23410	+	0.0937129i	−0.999121	+	0.0419097i
$5$	−2.23410	+	0.0937129i	−0.999121	+	0.0419097i
$6$	0.844300	+	2.59849i	0.344684	+	1.06083i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−9.00374	+	2.92549i	−3.18330	+	1.03432i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−3.79501	−	4.78778i	−1.20009	−	1.51403i
$11$	−3.47250	+	2.52292i	−1.04700	+	0.760689i	−0.971639	−	0.236468i	$-0.924010\pi$
$11$	−3.47250	+	2.52292i	−1.04700	+	0.760689i	−0.0753587	+	0.997156i	$0.524010\pi$
$12$	−3.21224	+	4.42127i	−0.927294	+	1.27631i
$13$	0.825990	−	1.13688i	0.229088	−	0.315313i	−0.678962	−	0.734173i	$-0.737570\pi$
$13$	0.825990	−	1.13688i	0.229088	−	0.315313i	0.908051	+	0.418860i	$0.137570\pi$
$14$	2.21041	−	1.60595i	0.590756	−	0.429209i
$15$	−2.15372	−	0.601250i	−0.556087	−	0.155242i
$16$	−12.0836	−	8.77924i	−3.02090	−	2.19481i
$17$	6.10011	−	1.98205i	1.47949	−	0.480717i	0.545532	−	0.838090i	$-0.316328\pi$
$17$	6.10011	−	1.98205i	1.47949	−	0.480717i	0.933962	+	0.357373i	$0.116328\pi$
$18$			2.73221i			0.643989i
$19$	1.48846	+	4.58100i	0.341476	+	1.05095i	0.963444	+	0.267911i	$0.0863334\pi$
$19$	1.48846	+	4.58100i	0.341476	+	1.05095i	−0.621968	+	0.783043i	$0.713667\pi$
$20$	3.28582	−	11.7700i	0.734732	−	2.63186i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	−11.1534	−	3.62394i	−2.37790	−	0.772628i
$23$	4.64169	+	6.38874i	0.967860	+	1.33215i	0.943120	+	0.332451i	$0.107876\pi$
$23$	4.64169	+	6.38874i	0.967860	+	1.33215i	0.0247395	+	0.999694i	$0.492124\pi$
$24$	−9.46709			−1.93246
$25$	4.98244	−	0.418729i	0.996487	−	0.0837457i
$26$	3.83947			0.752981
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	5.19751	+	1.68877i	0.982238	+	0.319148i
$29$	−1.44955	+	4.46127i	−0.269176	+	0.828437i	0.721526	+	0.692387i	$0.243441\pi$
$29$	−1.44955	+	4.46127i	−0.269176	+	0.828437i	−0.990702	+	0.136050i	$0.956559\pi$
$30$	−2.12977	−	5.72617i	−0.388840	−	1.04545i
$31$	0.870374	+	2.67873i	0.156324	+	0.481115i	0.998293	−	0.0584111i	$-0.0186034\pi$
$31$	0.870374	+	2.67873i	0.156324	+	0.481115i	−0.841969	+	0.539526i	$0.818603\pi$
$32$		−	21.8745i		−	3.86691i
$33$	−4.08217	+	1.32638i	−0.710614	+	0.230893i
$34$	14.1776	+	10.3007i	2.43144	+	1.76655i
$35$	0.0937129	+	2.23410i	0.0158404	+	0.377632i
$36$	−4.42127	+	3.21224i	−0.736878	+	0.535373i
$37$	4.41222	−	6.07290i	0.725365	−	0.998379i	−0.273964	−	0.961740i	$-0.588335\pi$
$37$	4.41222	−	6.07290i	0.725365	−	0.998379i	0.999329	−	0.0366387i	$-0.0116651\pi$
$38$	−7.73548	+	10.6470i	−1.25486	+	1.72717i
$39$	1.13688	−	0.825990i	0.182046	−	0.132264i
$40$	19.8411	−	7.37962i	3.13716	−	1.16682i
$41$	−5.35535	−	3.89089i	−0.836366	−	0.607655i	0.0849875	−	0.996382i	$-0.472915\pi$
$41$	−5.35535	−	3.89089i	−0.836366	−	0.607655i	−0.921353	+	0.388727i	$0.872915\pi$
$42$	2.59849	−	0.844300i	0.400956	−	0.130278i
$43$		−	6.32527i		−	0.964595i	−0.876007	−	0.482298i	$-0.839802\pi$
$43$		−	6.32527i		−	0.964595i	0.876007	−	0.482298i	$-0.160198\pi$
$44$	−7.24864	−	22.3090i	−1.09277	−	3.36321i
$45$	−1.86251	−	1.23736i	−0.277647	−	0.184454i
$46$	−6.66737	+	20.5201i	−0.983051	+	3.02552i
$47$	3.52407	+	1.14504i	0.514039	+	0.167021i	0.554538	−	0.832158i	$-0.312895\pi$
$47$	3.52407	+	1.14504i	0.514039	+	0.167021i	−0.0404996	+	0.999180i	$0.512895\pi$
$48$	−8.77924	−	12.0836i	−1.26717	−	1.74412i
$49$	−1.00000			−0.142857
$50$	8.92713	+	10.3408i	1.26249	+	1.46240i
$51$	6.41404			0.898145
$52$	4.51403	+	6.21303i	0.625983	+	0.861592i
$53$	−4.41792	−	1.43547i	−0.606848	−	0.197177i	−0.0105559	−	0.999944i	$-0.503360\pi$
$53$	−4.41792	−	1.43547i	−0.606848	−	0.197177i	−0.596292	+	0.802767i	$0.703360\pi$
$54$	−0.844300	+	2.59849i	−0.114895	+	0.353610i
$55$	7.52149	−	5.96188i	1.01420	−	0.803900i
$56$	2.92549	+	9.00374i	0.390935	+	1.20318i
$57$			4.81675i			0.637994i
$58$	−12.1891	+	3.96049i	−1.60051	+	0.520038i
$59$	−1.38123	−	1.00352i	−0.179821	−	0.130648i	0.494233	−	0.869329i	$-0.335449\pi$
$59$	−1.38123	−	1.00352i	−0.179821	−	0.130648i	−0.674055	+	0.738681i	$0.735449\pi$
$60$	6.76215	−	10.1786i	0.872990	−	1.31405i
$61$	8.01186	−	5.82096i	1.02581	−	0.745297i	0.0583469	−	0.998296i	$-0.481417\pi$
$61$	8.01186	−	5.82096i	1.02581	−	0.745297i	0.967466	+	0.252999i	$0.0814170\pi$
$62$	−4.52331	+	6.22581i	−0.574461	+	0.790678i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	24.1844	−	17.5710i	3.02306	−	2.19638i
$65$	−1.73881	+	2.61731i	−0.215673	+	0.324637i
$66$	−9.48761	−	6.89315i	−1.16784	−	0.848488i
$67$	−6.86068	+	2.22917i	−0.838165	+	0.272336i	−0.696481	−	0.717576i	$-0.745252\pi$
$67$	−6.86068	+	2.22917i	−0.838165	+	0.272336i	−0.141684	+	0.989912i	$0.545252\pi$
$68$			35.0526i			4.25076i
$69$	2.44028	+	7.51042i	0.293776	+	0.904148i
$70$	−4.78778	+	3.79501i	−0.572249	+	0.453591i
$71$	0.0563661	−	0.173477i	0.00668942	−	0.0205879i	−0.947656	−	0.319293i	$-0.896555\pi$
$71$	0.0563661	−	0.173477i	0.00668942	−	0.0205879i	0.954346	+	0.298705i	$0.0965546\pi$
$72$	−9.00374	−	2.92549i	−1.06110	−	0.344773i
$73$	2.72271	+	3.74748i	0.318669	+	0.438610i	0.938060	−	0.346473i	$-0.112621\pi$
$73$	2.72271	+	3.74748i	0.318669	+	0.438610i	−0.619391	+	0.785082i	$0.712621\pi$
$74$	20.5094			2.38417
$75$	4.86797	+	1.14142i	0.562105	+	0.131800i
$76$	−26.3235			−3.01951
$77$	2.52292	+	3.47250i	0.287513	+	0.395728i
$78$	3.65155	+	1.18646i	0.413457	+	0.134340i
$79$	4.14012	−	12.7420i	0.465800	−	1.43359i	−0.392173	−	0.919891i	$-0.628277\pi$
$79$	4.14012	−	12.7420i	0.465800	−	1.43359i	0.857973	−	0.513694i	$-0.171723\pi$
$80$	27.8187	+	18.4813i	3.11023	+	2.06628i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	18.0861i		−	1.99728i
$83$	−5.86479	+	1.90559i	−0.643745	+	0.209165i	−0.612654	−	0.790351i	$-0.709898\pi$
$83$	−5.86479	+	1.90559i	−0.643745	+	0.209165i	−0.0310907	+	0.999517i	$0.509898\pi$
$84$	4.42127	+	3.21224i	0.482400	+	0.350484i
$85$	−13.4425	+	4.99975i	−1.45805	+	0.542300i
$86$	13.9814	−	10.1581i	1.50766	−	1.09538i
$87$	−2.75722	+	3.79498i	−0.295605	+	0.406865i
$88$	23.8847	−	32.8745i	2.54612	−	3.50443i
$89$	4.63594	−	3.36821i	0.491409	−	0.357030i	−0.314317	−	0.949318i	$-0.601775\pi$
$89$	4.63594	−	3.36821i	0.491409	−	0.357030i	0.805726	+	0.592289i	$0.201775\pi$
$90$	−0.256044	−	6.10405i	−0.0269894	−	0.643423i
$91$	−1.13688	−	0.825990i	−0.119177	−	0.0865873i
$92$	−41.0444	+	13.3361i	−4.27917	+	1.39039i
$93$			2.81659i			0.292067i
$94$	3.12849	+	9.62851i	0.322680	+	0.993105i
$95$	−3.75467	−	10.0949i	−0.385221	−	1.03572i
$96$	6.75960	−	20.8039i	0.689899	−	2.12329i
$97$	6.85358	+	2.22686i	0.695875	+	0.226104i	0.635533	−	0.772074i	$-0.280781\pi$
$97$	6.85358	+	2.22686i	0.695875	+	0.226104i	0.0603429	+	0.998178i	$0.480781\pi$
$98$	−1.60595	−	2.21041i	−0.162226	−	0.223285i
$99$	−4.29225			−0.431387
$100$	−6.23786	+	26.6034i	−0.623786	+	2.66034i
$101$	15.7456			1.56674			0.783372	−	0.621553i	$-0.213498\pi$
$101$	15.7456			1.56674			0.783372	+	0.621553i	$0.213498\pi$
$102$	10.3007	+	14.1776i	1.01992	+	1.40379i
$103$	2.31166	+	0.751105i	0.227775	+	0.0740086i	0.420681	−	0.907209i	$-0.361791\pi$
$103$	2.31166	+	0.751105i	0.227775	+	0.0740086i	−0.192906	+	0.981217i	$0.561791\pi$
$104$	−4.11107	+	12.6526i	−0.403124	+	1.24069i
$105$	−0.601250	+	2.15372i	−0.0586760	+	0.210181i
$106$	−3.92201	−	12.0707i	−0.380939	−	1.17241i
$107$			0.898387i			0.0868504i	0.999057	+	0.0434252i	$0.0138270\pi$
$107$			0.898387i			0.0868504i	−0.999057	+	0.0434252i	$0.986173\pi$
$108$	−5.19751	+	1.68877i	−0.500131	+	0.162502i
$109$	−12.5293	−	9.10304i	−1.20009	−	0.871914i	−0.205793	−	0.978596i	$-0.565977\pi$
$109$	−12.5293	−	9.10304i	−1.20009	−	0.871914i	−0.994293	+	0.106682i	$0.965977\pi$
$110$	25.2574	+	7.05105i	2.40819	+	0.672292i
$111$	6.07290	−	4.41222i	0.576414	−	0.418789i
$112$	−8.77924	+	12.0836i	−0.829560	+	1.14179i
$113$	−7.82338	+	10.7680i	−0.735962	+	1.01296i	0.262879	+	0.964829i	$0.415328\pi$
$113$	−7.82338	+	10.7680i	−0.735962	+	1.01296i	−0.998841	+	0.0481358i	$0.984672\pi$
$114$	−10.6470	+	7.73548i	−0.997181	+	0.724494i
$115$	−10.9687	−	13.8381i	−1.02284	−	1.29041i
$116$	−20.7395	−	15.0682i	−1.92562	−	1.39904i
$117$	1.33648	−	0.434249i	0.123558	−	0.0401463i
$118$		−	4.66470i		−	0.429421i
$119$	−1.98205	−	6.10011i	−0.181694	−	0.559196i
$120$	21.1505	−	0.887189i	1.93076	−	0.0809889i
$121$	2.29395	−	7.06005i	0.208541	−	0.641822i
$122$	25.7334	+	8.36128i	2.32979	+	0.756994i
$123$	−3.89089	−	5.35535i	−0.350830	−	0.482876i
$124$	−15.3926			−1.38230
$125$	−11.0920	+	1.40240i	−0.992102	+	0.125435i
$126$	2.73221			0.243405
$127$	−1.60566	−	2.21000i	−0.142479	−	0.196106i	0.731813	−	0.681505i	$-0.238674\pi$
$127$	−1.60566	−	2.21000i	−0.142479	−	0.196106i	−0.874293	+	0.485399i	$0.838674\pi$
$128$	36.0704	+	11.7200i	3.18820	+	1.03591i
$129$	1.95462	−	6.01569i	0.172094	−	0.529652i
$130$	−8.57777	+	0.359808i	−0.752320	+	0.0315572i
$131$	−1.86960	−	5.75403i	−0.163348	−	0.502732i	0.835563	−	0.549394i	$-0.185142\pi$
$131$	−1.86960	−	5.75403i	−0.163348	−	0.502732i	−0.998911	+	0.0466624i	$0.985142\pi$
$132$		−	23.4571i		−	2.04168i
$133$	4.58100	−	1.48846i	0.397223	−	0.129066i
$134$	−15.9453	−	11.5849i	−1.37746	−	1.00079i
$135$	−1.38899	−	1.75234i	−0.119545	−	0.150818i
$136$	−49.1254	+	35.6917i	−4.21246	+	3.06053i
$137$	−2.63211	+	3.62279i	−0.224876	+	0.309516i	−0.906515	−	0.422173i	$-0.861268\pi$
$137$	−2.63211	+	3.62279i	−0.224876	+	0.309516i	0.681639	+	0.731689i	$0.261268\pi$
$138$	−12.6821	+	17.4554i	−1.07957	+	1.48590i
$139$	−9.34562	+	6.78999i	−0.792685	+	0.575919i	−0.908759	−	0.417321i	$-0.862969\pi$
$139$	−9.34562	+	6.78999i	−0.792685	+	0.575919i	0.116074	+	0.993241i	$0.462969\pi$
$140$	−11.7700	−	3.28582i	−0.994750	−	0.277703i
$141$	2.99775	+	2.17800i	0.252456	+	0.183420i
$142$	0.473976	−	0.154004i	0.0397752	−	0.0129237i
$143$			6.03172i			0.504397i
$144$	−4.61552	−	14.2051i	−0.384627	−	1.18376i
$145$	2.82038	−	10.1028i	0.234220	−	0.838990i
$146$	−3.91092	+	12.0366i	−0.323670	+	0.996154i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	24.1127	+	33.1883i	1.98206	+	2.72806i
$149$	−4.38636			−0.359345			−0.179672	−	0.983727i	$-0.557504\pi$
$149$	−4.38636			−0.359345			−0.179672	+	0.983727i	$0.557504\pi$
$150$	5.29473	+	12.5933i	0.432313	+	1.02824i
$151$	22.4651			1.82818			0.914092	−	0.405506i	$-0.132905\pi$
$151$	22.4651			1.82818			0.914092	+	0.405506i	$0.132905\pi$
$152$	−26.8034	−	36.8917i	−2.17404	−	2.99231i
$153$	6.10011	+	1.98205i	0.493165	+	0.160239i
$154$	−3.62394	+	11.1534i	−0.292026	+	0.898763i
$155$	−2.19554	−	5.90301i	−0.176350	−	0.474141i
$156$	2.37317	+	7.30385i	0.190005	+	0.584776i
$157$		−	14.1890i		−	1.13240i	−0.824266	−	0.566202i	$-0.808412\pi$
$157$		−	14.1890i		−	1.13240i	0.824266	−	0.566202i	$-0.191588\pi$
$158$	34.8138	−	11.3117i	2.76964	−	0.899910i
$159$	−3.75811	−	2.73043i	−0.298037	−	0.216537i
$160$	2.04993	+	48.8700i	0.162061	+	3.86351i
$161$	6.38874	−	4.64169i	0.503503	−	0.365817i
$162$	−1.60595	+	2.21041i	−0.126176	+	0.173666i
$163$	1.11250	−	1.53122i	0.0871376	−	0.119935i	−0.763223	−	0.646136i	$-0.776384\pi$
$163$	1.11250	−	1.53122i	0.0871376	−	0.119935i	0.850360	+	0.526201i	$0.176384\pi$
$164$	29.2670	−	21.2637i	2.28536	−	1.66041i
$165$	8.99569	−	3.34581i	0.700313	−	0.260471i
$166$	−13.6307	−	9.90330i	−1.05795	−	0.768645i
$167$	11.1336	−	3.61754i	0.861547	−	0.279934i	0.155273	−	0.987872i	$-0.450374\pi$
$167$	11.1336	−	3.61754i	0.861547	−	0.279934i	0.706274	+	0.707938i	$0.250374\pi$
$168$			9.46709i			0.730402i
$169$	3.40699	+	10.4856i	0.262076	+	0.806587i
$170$	−32.6396	−	21.6841i	−2.50334	−	1.66309i
$171$	−1.48846	+	4.58100i	−0.113825	+	0.350318i
$172$	32.8757	+	10.6820i	2.50675	+	0.814492i
$173$	1.94484	+	2.67684i	0.147863	+	0.203516i	0.876524	−	0.481359i	$-0.159857\pi$
$173$	1.94484	+	2.67684i	0.147863	+	0.203516i	−0.728660	+	0.684875i	$0.759857\pi$
$174$	−12.8164			−0.971611
$175$	−0.418729	−	4.98244i	−0.0316529	−	0.376637i
$176$	64.1096			4.83244
$177$	−1.00352	−	1.38123i	−0.0754295	−	0.103820i
$178$	14.8902	+	4.83813i	1.11607	+	0.362633i
$179$	−4.72504	+	14.5422i	−0.353166	+	1.08693i	0.603899	+	0.797061i	$0.293613\pi$
$179$	−4.72504	+	14.5422i	−0.353166	+	1.08693i	−0.957065	+	0.289873i	$0.906387\pi$
$180$	9.57655	−	7.59081i	0.713794	−	0.565785i
$181$	−5.40412	−	16.6322i	−0.401685	−	1.23626i	−0.923631	−	0.383282i	$-0.874794\pi$
$181$	−5.40412	−	16.6322i	−0.401685	−	1.23626i	0.521946	−	0.852979i	$-0.325206\pi$
$182$		−	3.83947i		−	0.284600i
$183$	9.41850	−	3.06026i	0.696236	−	0.226221i
$184$	−60.4828	−	43.9433i	−4.45885	−	3.23955i
$185$	−9.28825	+	13.9810i	−0.682885	+	1.02790i
$186$	−6.22581	+	4.52331i	−0.456498	+	0.331665i
$187$	−16.1821	+	22.2727i	−1.18335	+	1.62874i
$188$	−11.9027	+	16.3827i	−0.868096	+	1.19483i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	16.2841	−	24.5114i	1.18137	−	1.77824i
$191$	10.9931	+	7.98693i	0.795431	+	0.577914i	0.909570	−	0.415550i	$-0.136411\pi$
$191$	10.9931	+	7.98693i	0.795431	+	0.577914i	−0.114139	+	0.993465i	$0.536411\pi$
$192$	28.4305	−	9.23764i	2.05180	−	0.666669i
$193$			22.4945i			1.61919i	0.586991	+	0.809594i	$0.300312\pi$
$193$			22.4945i			1.61919i	−0.586991	+	0.809594i	$0.699688\pi$
$194$	6.08426	+	18.7254i	0.436825	+	1.34441i
$195$	−2.46250	+	1.95189i	−0.176343	+	0.139778i
$196$	1.68877	−	5.19751i	0.120627	−	0.371251i
$197$	−3.63189	−	1.18007i	−0.258761	−	0.0840767i	0.176763	−	0.984253i	$-0.443437\pi$
$197$	−3.63189	−	1.18007i	−0.258761	−	0.0840767i	−0.435525	+	0.900177i	$0.643437\pi$
$198$	−6.89315	−	9.48761i	−0.489875	−	0.674255i
$199$	3.23356			0.229221			0.114610	−	0.993411i	$-0.463438\pi$
$199$	3.23356			0.229221			0.114610	+	0.993411i	$0.463438\pi$
$200$	−43.6356	+	18.3462i	−3.08550	+	1.29727i
$201$	−7.21374			−0.508818
$202$	25.2867	+	34.8041i	1.77917	+	2.44881i
$203$	4.46127	+	1.44955i	0.313120	+	0.101739i
$204$	−10.8319	+	33.3370i	−0.758382	+	2.33406i
$205$	12.3290	+	8.19079i	0.861097	+	0.572069i
$206$	2.05218	+	6.31596i	0.142982	+	0.440054i
$207$			7.89692i			0.548874i
$208$	−19.9619	+	6.48600i	−1.38411	+	0.449723i
$209$	−16.7262	−	12.1523i	−1.15697	−	0.840590i
$210$	−5.72617	+	2.12977i	−0.395143	+	0.146968i
$211$	−0.537697	+	0.390659i	−0.0370166	+	0.0268941i	−0.606140	−	0.795358i	$-0.707283\pi$
$211$	−0.537697	+	0.390659i	−0.0370166	+	0.0268941i	0.569123	+	0.822252i	$0.307283\pi$
$212$	14.9218	−	20.5380i	1.02483	−	1.41056i
$213$	0.107215	−	0.147568i	0.00734623	−	0.0101112i
$214$	−1.98580	+	1.44277i	−0.135747	+	0.0986257i
$215$	0.592760	+	14.1313i	0.0404259	+	0.963748i
$216$	−7.65904	−	5.56462i	−0.521132	−	0.378624i
$217$	2.67873	−	0.870374i	0.181844	−	0.0590848i
$218$		−	42.3139i		−	2.86586i
$219$	1.43141	+	4.40543i	0.0967258	+	0.297691i
$220$	18.2848	+	49.1613i	1.23276	+	3.31446i
$221$	2.78529	−	8.57223i	0.187359	−	0.576631i
$222$	19.5056	+	6.33776i	1.30913	+	0.425362i
$223$	−9.27101	−	12.7605i	−0.620833	−	0.854503i	0.376580	−	0.926384i	$-0.377100\pi$
$223$	−9.27101	−	12.7605i	−0.620833	−	0.854503i	−0.997413	+	0.0718809i	$0.977100\pi$
$224$	−21.8745			−1.46155
$225$	4.27700	+	2.58984i	0.285133	+	0.172656i
$226$	−36.3656			−2.41900
$227$	−3.51179	−	4.83356i	−0.233085	−	0.320815i	0.676413	−	0.736523i	$-0.263534\pi$
$227$	−3.51179	−	4.83356i	−0.233085	−	0.320815i	−0.909498	+	0.415708i	$0.863534\pi$
$228$	−25.0351	−	8.13441i	−1.65799	−	0.538714i
$229$	−0.698244	+	2.14897i	−0.0461413	+	0.142008i	−0.971473	−	0.237150i	$-0.923787\pi$
$229$	−0.698244	+	2.14897i	−0.0461413	+	0.142008i	0.925332	+	0.379159i	$0.123787\pi$
$230$	12.9726	−	46.4688i	0.855388	−	3.06406i
$231$	1.32638	+	4.08217i	0.0872692	+	0.268587i
$232$		−	44.4088i		−	2.91558i
$233$	13.3825	−	4.34825i	0.876719	−	0.284863i	0.164125	−	0.986440i	$-0.447520\pi$
$233$	13.3825	−	4.34825i	0.876719	−	0.284863i	0.712594	+	0.701576i	$0.247520\pi$
$234$	3.10619	+	2.25678i	0.203058	+	0.147530i
$235$	−7.98044	−	2.22789i	−0.520587	−	0.145331i
$236$	7.54842	−	5.48425i	0.491361	−	0.356994i
$237$	7.87498	−	10.8390i	0.511535	−	0.704068i
$238$	10.3007	−	14.1776i	0.667692	−	0.918999i
$239$	−4.37850	+	3.18117i	−0.283222	+	0.205773i	−0.720321	−	0.693640i	$-0.756006\pi$
$239$	−4.37850	+	3.18117i	−0.283222	+	0.205773i	0.437100	+	0.899413i	$0.356006\pi$
$240$	20.7461	+	26.1733i	1.33916	+	1.68948i
$241$	−0.785563	−	0.570745i	−0.0506026	−	0.0367649i	0.562196	−	0.827004i	$-0.309956\pi$
$241$	−0.785563	−	0.570745i	−0.0506026	−	0.0367649i	−0.612799	+	0.790239i	$0.709956\pi$
$242$	19.2896	−	6.26756i	1.23998	−	0.402894i
$243$			1.00000i			0.0641500i
$244$	16.7243	+	51.4720i	1.07066	+	3.29516i
$245$	2.23410	−	0.0937129i	0.142732	−	0.00598710i
$246$	5.58891	−	17.2009i	0.356336	−	1.09669i
$247$	6.43749	+	2.09167i	0.409608	+	0.133090i
$248$	−15.6732	−	21.5724i	−0.995252	−	1.36985i
$249$	−6.16661			−0.390793
$250$	−20.9132	−	22.2657i	−1.32267	−	1.40821i
$251$	25.1361			1.58658			0.793289	−	0.608845i	$-0.208367\pi$
$251$	25.1361			1.58658			0.793289	+	0.608845i	$0.208367\pi$
$252$	3.21224	+	4.42127i	0.202352	+	0.278514i
$253$	−32.2366	−	10.4743i	−2.02670	−	0.658513i
$254$	2.30638	−	7.09831i	0.144715	−	0.445388i
$255$	−14.3296	+	0.601078i	−0.897356	+	0.0376410i
$256$	13.5462	+	41.6910i	0.846640	+	2.60569i
$257$		−	4.83510i		−	0.301605i	−0.988564	−	0.150803i	$-0.951814\pi$
$257$		−	4.83510i		−	0.301605i	0.988564	−	0.150803i	$-0.0481858\pi$
$258$	16.4362	−	5.34043i	1.02327	−	0.332481i
$259$	−6.07290	−	4.41222i	−0.377352	−	0.274162i
$260$	−10.6670	−	13.4575i	−0.661542	−	0.834600i
$261$	−3.79498	+	2.75722i	−0.234904	+	0.170667i
$262$	9.71626	−	13.3733i	0.600273	−	0.826204i
$263$	−1.95333	+	2.68853i	−0.120447	+	0.165782i	−0.864983	−	0.501801i	$-0.832671\pi$
$263$	−1.95333	+	2.68853i	−0.120447	+	0.165782i	0.744536	+	0.667583i	$0.232671\pi$
$264$	32.8745	−	23.8847i	2.02328	−	1.47000i
$265$	10.0046	+	2.79297i	0.614579	+	0.171571i
$266$	10.6470	+	7.73548i	0.652808	+	0.474293i
$267$	5.44988	−	1.77077i	0.333527	−	0.108370i
$268$		−	39.4230i		−	2.40815i
$269$	−9.61612	−	29.5954i	−0.586305	−	1.80446i	−0.593964	−	0.804492i	$-0.702438\pi$
$269$	−9.61612	−	29.5954i	−0.586305	−	1.80446i	0.00765874	−	0.999971i	$-0.497562\pi$
$270$	1.64274	−	5.88442i	0.0999741	−	0.358114i
$271$	7.50961	−	23.1122i	0.456176	−	1.40397i	−0.413572	−	0.910471i	$-0.635719\pi$
$271$	7.50961	−	23.1122i	0.456176	−	1.40397i	0.869749	−	0.493495i	$-0.164281\pi$
$272$	−91.1121	−	29.6041i	−5.52448	−	1.79501i
$273$	−0.825990	−	1.13688i	−0.0499912	−	0.0688070i
$274$	−12.2349			−0.739137
$275$	−16.2451	+	14.0243i	−0.979616	+	0.845698i
$276$	−43.1566			−2.59772
$277$	−10.4281	−	14.3530i	−0.626564	−	0.862391i	0.371246	−	0.928534i	$-0.378931\pi$
$277$	−10.4281	−	14.3530i	−0.626564	−	0.862391i	−0.997810	+	0.0661433i	$0.978931\pi$
$278$	−30.0173	−	9.75321i	−1.80032	−	0.584958i
$279$	−0.870374	+	2.67873i	−0.0521079	+	0.160372i
$280$	−7.37962	−	19.8411i	−0.441017	−	1.18573i
$281$	−7.81460	−	24.0509i	−0.466180	−	1.43475i	−0.857493	−	0.514496i	$-0.827979\pi$
$281$	−7.81460	−	24.0509i	−0.466180	−	1.43475i	0.391313	−	0.920258i	$-0.372021\pi$
$282$			10.1240i			0.602877i
$283$	−1.23414	+	0.400995i	−0.0733618	+	0.0238367i	−0.345468	−	0.938431i	$-0.612280\pi$
$283$	−1.23414	+	0.400995i	−0.0733618	+	0.0238367i	0.272106	+	0.962267i	$0.412280\pi$
$284$	0.806460	+	0.585927i	0.0478546	+	0.0347684i
$285$	−0.451392	−	10.7611i	−0.0267381	−	0.637434i
$286$	−13.3325	+	9.68666i	−0.788370	+	0.572784i
$287$	−3.89089	+	5.35535i	−0.229672	+	0.316116i
$288$	12.8575	−	17.6969i	0.757637	−	1.04280i
$289$	19.5295	−	14.1890i	1.14880	−	0.834650i
$290$	26.8607	−	9.99043i	1.57731	−	0.586658i
$291$	5.83000	+	4.23574i	0.341761	+	0.248304i
$292$	−24.0756	+	7.82265i	−1.40892	+	0.457786i
$293$			2.89661i			0.169222i	0.996414	+	0.0846109i	$0.0269647\pi$
$293$			2.89661i			0.169222i	−0.996414	+	0.0846109i	$0.973035\pi$
$294$	−0.844300	−	2.59849i	−0.0492406	−	0.151547i
$295$	3.17986	+	2.11254i	0.185139	+	0.122997i
$296$	−21.9603	+	67.5867i	−1.27641	+	3.92840i
$297$	−4.08217	−	1.32638i	−0.236871	−	0.0769642i
$298$	−7.04430	−	9.69565i	−0.408065	−	0.561654i
$299$	11.0972			0.641769
$300$	−14.1535	+	23.3738i	−0.817151	+	1.34948i
$301$	−6.32527			−0.364583
$302$	36.0779	+	49.6570i	2.07605	+	2.85744i
$303$	14.9749	+	4.86565i	0.860288	+	0.279524i
$304$	22.2318	−	68.4225i	1.27508	−	3.92430i
$305$	−17.3538	+	13.7554i	−0.993677	+	0.787634i
$306$	5.41537	+	16.6668i	0.309576	+	0.952778i
$307$		−	8.90192i		−	0.508060i	−0.967196	−	0.254030i	$-0.918244\pi$
$307$		−	8.90192i		−	0.508060i	0.967196	−	0.254030i	$-0.0817561\pi$
$308$	−22.3090	+	7.24864i	−1.27117	+	0.413029i
$309$	1.96642	+	1.42869i	0.111866	+	0.0812751i
$310$	9.52211	−	14.3330i	0.540820	−	0.814059i
$311$	−23.1647	+	16.8302i	−1.31355	+	0.954352i	−0.313564	+	0.949567i	$0.601523\pi$
$311$	−23.1647	+	16.8302i	−1.31355	+	0.954352i	−0.999989	+	0.00478452i	$0.998477\pi$
$312$	−7.81973	+	10.7629i	−0.442705	+	0.609331i
$313$	0.254293	−	0.350004i	0.0143735	−	0.0197834i	−0.801770	−	0.597633i	$-0.796108\pi$
$313$	0.254293	−	0.350004i	0.0143735	−	0.0197834i	0.816143	+	0.577850i	$0.196108\pi$
$314$	31.3634	−	22.7869i	1.76994	−	1.28594i
$315$	−1.23736	+	1.86251i	−0.0697172	+	0.104941i
$316$	59.2349	+	43.0367i	3.33223	+	2.42100i
$317$	1.75782	−	0.571151i	0.0987291	−	0.0320790i	−0.259236	−	0.965814i	$-0.583471\pi$
$317$	1.75782	−	0.571151i	0.0987291	−	0.0320790i	0.357965	+	0.933735i	$0.383471\pi$
$318$		−	12.6919i		−	0.711726i
$319$	−6.22184	−	19.1489i	−0.348356	−	1.07213i
$320$	−52.3839	+	41.5219i	−2.92835	+	2.32114i
$321$	−0.277617	+	0.854417i	−0.0154951	+	0.0476889i
$322$	20.5201	+	6.66737i	1.14354	+	0.371558i
$323$	18.1595	+	24.9944i	1.01042	+	1.39073i
$324$	−5.46499			−0.303611
$325$	3.63940	−	6.01029i	0.201878	−	0.333391i
$326$	5.17124			0.286409
$327$	−9.10304	−	12.5293i	−0.503399	−	0.692870i
$328$	59.6010	+	19.3655i	3.29091	+	1.06928i
$329$	1.14504	−	3.52407i	0.0631281	−	0.194288i
$330$	21.8423	+	14.5109i	1.20238	+	0.798799i
$331$	2.44695	+	7.53095i	0.134497	+	0.413938i	0.995511	−	0.0946417i	$-0.0301706\pi$
$331$	2.44695	+	7.53095i	0.134497	+	0.413938i	−0.861015	+	0.508580i	$0.830171\pi$
$332$		−	33.7005i		−	1.84955i
$333$	7.13912	−	2.31964i	0.391221	−	0.127116i
$334$	25.8764	+	18.8003i	1.41589	+	1.02871i
$335$	15.1186	−	5.62313i	0.826015	−	0.307224i
$336$	−12.0836	+	8.77924i	−0.659214	+	0.478947i
$337$	−5.62454	+	7.74151i	−0.306388	+	0.421707i	−0.934251	−	0.356617i	$-0.883930\pi$
$337$	−5.62454	+	7.74151i	−0.306388	+	0.421707i	0.627862	+	0.778324i	$0.283930\pi$
$338$	−17.7060	+	24.3703i	−0.963082	+	1.32557i
$339$	−10.7680	+	7.82338i	−0.584835	+	0.424908i
$340$	−3.28489	−	78.3112i	−0.178148	−	4.24702i
$341$	−9.78060	−	7.10602i	−0.529649	−	0.384813i
$342$	−12.5163	+	4.06678i	−0.676803	+	0.219906i
$343$			1.00000i			0.0539949i
$344$	18.5045	+	56.9511i	0.997698	+	3.07060i
$345$	−6.15567	−	16.5504i	−0.331410	−	0.891042i
$346$	−2.79358	+	8.59777i	−0.150184	+	0.462219i
$347$	6.10151	+	1.98250i	0.327546	+	0.106426i	0.468174	−	0.883636i	$-0.344912\pi$
$347$	6.10151	+	1.98250i	0.327546	+	0.106426i	−0.140628	+	0.990063i	$0.544912\pi$
$348$	−15.0682	−	20.7395i	−0.807738	−	1.11176i
$349$	−20.8215			−1.11455			−0.557276	−	0.830327i	$-0.688153\pi$
$349$	−20.8215			−1.11455			−0.557276	+	0.830327i	$0.688153\pi$
$350$	10.3408	−	8.92713i	0.552736	−	0.477175i
$351$	1.40526			0.0750072
$352$	55.1877	+	75.9593i	2.94151	+	4.04865i
$353$	−33.7291	−	10.9592i	−1.79522	−	0.583302i	−0.795475	−	0.605986i	$-0.792779\pi$
$353$	−33.7291	−	10.9592i	−1.79522	−	0.583302i	−0.999743	+	0.0226848i	$0.992779\pi$
$354$	1.44147	−	4.43640i	0.0766134	−	0.235792i
$355$	−0.109671	+	0.392848i	−0.00582071	+	0.0208502i
$356$	9.67726	+	29.7835i	0.512894	+	1.57852i
$357$		−	6.41404i		−	0.339467i
$358$	−39.7323	+	12.9098i	−2.09992	+	0.682305i
$359$	19.7866	+	14.3758i	1.04429	+	0.758725i	0.971119	−	0.238594i	$-0.0766866\pi$
$359$	19.7866	+	14.3758i	1.04429	+	0.758725i	0.0731756	+	0.997319i	$0.476687\pi$
$360$	20.3894	+	5.69209i	1.07462	+	0.299999i
$361$	−3.39874	+	2.46933i	−0.178881	+	0.129965i
$362$	28.0851	−	38.6559i	1.47612	−	2.03171i
$363$	4.36335	−	6.00563i	0.229016	−	0.315214i
$364$	6.21303	−	4.51403i	0.325651	−	0.236599i
$365$	−6.43399	−	8.11711i	−0.336771	−	0.424869i
$366$	21.8901	+	15.9041i	1.14421	+	0.831320i
$367$	16.6165	−	5.39902i	0.867373	−	0.281827i	0.158668	−	0.987332i	$-0.449280\pi$
$367$	16.6165	−	5.39902i	0.867373	−	0.281827i	0.708705	+	0.705505i	$0.249280\pi$
$368$		−	117.950i		−	6.14854i
$369$	−2.04556	−	6.29559i	−0.106488	−	0.327736i
$370$	−45.8201	+	1.92200i	−2.38208	+	0.0999198i
$371$	−1.43547	+	4.41792i	−0.0745259	+	0.229367i
$372$	−14.6393	−	4.75658i	−0.759010	−	0.246617i
$373$	12.3105	+	16.9440i	0.637416	+	0.877328i	0.998474	−	0.0552153i	$-0.0175845\pi$
$373$	12.3105	+	16.9440i	0.637416	+	0.877328i	−0.361058	+	0.932543i	$0.617585\pi$
$374$	−75.2195			−3.88951
$375$	−10.9825	−	2.09386i	−0.567135	−	0.108127i
$376$	−35.0796			−1.80909
$377$	3.87460	+	5.33293i	0.199552	+	0.274660i
$378$	2.59849	+	0.844300i	0.133652	+	0.0434261i
$379$	1.40039	−	4.30995i	0.0719331	−	0.221387i	−0.908626	−	0.417610i	$-0.862868\pi$
$379$	1.40039	−	4.30995i	0.0719331	−	0.221387i	0.980559	+	0.196223i	$0.0628677\pi$
$380$	58.8094	−	2.46685i	3.01686	−	0.126547i
$381$	−0.844144	−	2.59801i	−0.0432468	−	0.133100i
$382$			37.1258i			1.89952i
$383$	0.982980	−	0.319390i	0.0502279	−	0.0163200i	−0.283795	−	0.958885i	$-0.591594\pi$
$383$	0.982980	−	0.319390i	0.0502279	−	0.0163200i	0.334023	+	0.942565i	$0.391594\pi$
$384$	30.6833	+	22.2927i	1.56580	+	1.13762i
$385$	−5.96188	−	7.52149i	−0.303846	−	0.383331i
$386$	−49.7219	+	36.1251i	−2.53078	+	1.83872i
$387$	3.71790	−	5.11725i	0.188992	−	0.260125i
$388$	−23.1483	+	31.8609i	−1.17518	+	1.61749i
$389$	0.452424	−	0.328706i	0.0229388	−	0.0166660i	−0.576257	−	0.817269i	$-0.695487\pi$
$389$	0.452424	−	0.328706i	0.0229388	−	0.0166660i	0.599196	+	0.800603i	$0.295487\pi$
$390$	−8.26913	−	2.30848i	−0.418723	−	0.116894i
$391$	40.9776	+	29.7720i	2.07233	+	1.50563i
$392$	9.00374	−	2.92549i	0.454758	−	0.147760i
$393$		−	6.05015i		−	0.305189i
$394$	−3.22421	−	9.92310i	−0.162433	−	0.499919i
$395$	−8.05537	+	28.8549i	−0.405310	+	1.45185i
$396$	7.24864	−	22.3090i	0.364258	−	1.12107i
$397$	29.7436	+	9.66429i	1.49279	+	0.485037i	0.937906	−	0.346891i	$-0.112762\pi$
$397$	29.7436	+	9.66429i	1.49279	+	0.485037i	0.554884	+	0.831927i	$0.312762\pi$
$398$	5.19294	+	7.14748i	0.260299	+	0.358271i
$399$	4.81675			0.241139
$400$	−63.8818	−	38.6823i	−3.19409	−	1.93411i
$401$	−30.5209			−1.52414			−0.762070	−	0.647494i	$-0.775817\pi$
$401$	−30.5209			−1.52414			−0.762070	+	0.647494i	$0.775817\pi$
$402$	−11.5849	−	15.9453i	−0.577805	−	0.795280i
$403$	3.76432	+	1.22310i	0.187514	+	0.0609270i
$404$	−26.5907	+	81.8379i	−1.32294	+	4.07159i
$405$	−0.779502	−	2.09580i	−0.0387338	−	0.104141i
$406$	3.96049	+	12.1891i	0.196556	+	0.604937i
$407$			32.2198i			1.59708i
$408$	−57.7503	+	18.7642i	−2.85907	+	0.928967i
$409$	−23.1453	−	16.8160i	−1.14446	−	0.831499i	−0.156726	−	0.987642i	$-0.550094\pi$
$409$	−23.1453	−	16.8160i	−1.14446	−	0.831499i	−0.987734	+	0.156143i	$0.950094\pi$
$410$	1.69490	+	40.4062i	0.0837052	+	1.99552i
$411$	−3.62279	+	2.63211i	−0.178699	+	0.129832i
$412$	−7.80776	+	10.7465i	−0.384661	+	0.529440i
$413$	−1.00352	+	1.38123i	−0.0493802	+	0.0679660i
$414$	−17.4554	+	12.6821i	−0.857887	+	0.623291i
$415$	12.9240	−	4.80689i	0.634413	−	0.235961i
$416$	−24.8687	−	18.0682i	−1.21929	−	0.885864i
$417$	−10.9864	+	3.56971i	−0.538008	+	0.174809i
$418$		−	56.4876i		−	2.76290i
$419$	1.83074	+	5.63443i	0.0894373	+	0.275260i	0.985764	−	0.168134i	$-0.0537742\pi$
$419$	1.83074	+	5.63443i	0.0894373	+	0.275260i	−0.896327	+	0.443394i	$0.853774\pi$
$420$	−10.1786	−	6.76215i	−0.496665	−	0.329959i
$421$	−3.04312	+	9.36577i	−0.148313	+	0.456460i	−0.997422	−	0.0717573i	$-0.977139\pi$
$421$	−3.04312	+	9.36577i	−0.148313	+	0.456460i	0.849109	+	0.528217i	$0.177139\pi$
$422$	−1.72703	−	0.561147i	−0.0840707	−	0.0273162i
$423$	2.17800	+	2.99775i	0.105898	+	0.145756i
$424$	43.9773			2.13573
$425$	29.5635	−	12.4297i	1.43404	−	0.602929i
$426$	0.498368			0.0241460
$427$	−5.82096	−	8.01186i	−0.281696	−	0.387721i
$428$	−4.66938	−	1.51717i	−0.225703	−	0.0733353i
$429$	−1.86390	+	5.73650i	−0.0899901	+	0.276961i
$430$	−30.2840	+	24.0045i	−1.46042	+	1.15760i
$431$	−3.68440	−	11.3394i	−0.177471	−	0.546201i	0.822266	−	0.569103i	$-0.192709\pi$
$431$	−3.68440	−	11.3394i	−0.177471	−	0.546201i	−0.999738	+	0.0229021i	$0.992709\pi$
$432$		−	14.9361i		−	0.718615i
$433$	18.4862	−	6.00653i	0.888391	−	0.288656i	0.170954	−	0.985279i	$-0.445315\pi$
$433$	18.4862	−	6.00653i	0.888391	−	0.288656i	0.717437	+	0.696623i	$0.245315\pi$
$434$	6.22581	+	4.52331i	0.298848	+	0.217126i
$435$	5.80427	−	8.73677i	0.278293	−	0.418896i
$436$	68.4723	−	49.7480i	3.27923	−	2.38250i
$437$	−22.3579	+	30.7730i	−1.06952	+	1.47207i
$438$	−7.43901	+	10.2389i	−0.355450	+	0.489235i
$439$	−31.5435	+	22.9177i	−1.50549	+	1.09380i	−0.537359	+	0.843354i	$0.680578\pi$
$439$	−31.5435	+	22.9177i	−1.50549	+	1.09380i	−0.968130	+	0.250448i	$0.919422\pi$
$440$	−50.2801	+	75.6833i	−2.39701	+	3.60806i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	23.4212	−	7.61000i	1.11403	−	0.361971i
$443$			26.1305i			1.24150i	0.784010	+	0.620748i	$0.213171\pi$
$443$			26.1305i			1.24150i	−0.784010	+	0.620748i	$0.786829\pi$
$444$	12.6768	+	39.0152i	0.601615	+	1.85158i
$445$	−10.0415	+	7.95938i	−0.476014	+	0.377311i
$446$	13.3170	−	40.9854i	0.630577	−	1.94072i
$447$	−4.17168	−	1.35546i	−0.197314	−	0.0641111i
$448$	−17.5710	−	24.1844i	−0.830153	−	1.14261i
$449$	−16.2358			−0.766217			−0.383108	−	0.923703i	$-0.625146\pi$
$449$	−16.2358			−0.766217			−0.383108	+	0.923703i	$0.625146\pi$
$450$	1.14406	+	13.6131i	0.0539313	+	0.641727i
$451$	28.4129			1.33791
$452$	−42.7547	−	58.8468i	−2.01101	−	2.76792i
$453$	21.3656	+	6.94210i	1.00384	+	0.326168i
$454$	5.04436	−	15.5250i	0.236744	−	0.728622i
$455$	2.61731	+	1.73881i	0.122701	+	0.0815166i
$456$	−14.0914	−	43.3688i	−0.659889	−	2.03093i
$457$			24.1888i			1.13151i	0.824575	+	0.565753i	$0.191414\pi$
$457$			24.1888i			1.13151i	−0.824575	+	0.565753i	$0.808586\pi$
$458$	−5.87146	+	1.90775i	−0.274355	+	0.0891434i
$459$	5.18906	+	3.77008i	0.242205	+	0.175972i
$460$	90.4476	−	33.6407i	4.21714	−	1.56850i
$461$	25.1881	−	18.3003i	1.17313	−	0.852328i	0.181748	−	0.983345i	$-0.441824\pi$
$461$	25.1881	−	18.3003i	1.17313	−	0.852328i	0.991380	+	0.131017i	$0.0418244\pi$
$462$	−6.89315	+	9.48761i	−0.320698	+	0.441404i
$463$	−2.77939	+	3.82551i	−0.129169	+	0.177786i	−0.868703	−	0.495333i	$-0.835046\pi$
$463$	−2.77939	+	3.82551i	−0.129169	+	0.177786i	0.739534	+	0.673119i	$0.235046\pi$
$464$	56.6824	−	41.1822i	2.63141	−	1.91183i
$465$	−0.263951	−	6.29255i	−0.0122404	−	0.291810i
$466$	31.1032	+	22.5978i	1.44083	+	1.04682i
$467$	27.3604	−	8.88995i	1.26609	−	0.411378i	0.402429	−	0.915451i	$-0.368166\pi$
$467$	27.3604	−	8.88995i	1.26609	−	0.411378i	0.863661	+	0.504073i	$0.168166\pi$
$468$			7.67973i			0.354995i
$469$	2.22917	+	6.86068i	0.102933	+	0.316797i
$470$	−7.89170	−	21.2179i	−0.364017	−	0.978710i
$471$	4.38464	−	13.4945i	0.202034	−	0.621795i
$472$	15.3721	+	4.99469i	0.707557	+	0.229899i
$473$	15.9581	+	21.9645i	0.733756	+	1.00993i
$474$	36.6054			1.68134
$475$	9.33434	+	22.2013i	0.428289	+	1.01866i
$476$	35.0526			1.60664
$477$	−2.73043	−	3.75811i	−0.125018	−	0.172072i
$478$	−14.0633	−	4.56946i	−0.643242	−	0.209002i
$479$	1.20973	−	3.72316i	0.0552739	−	0.170115i	−0.919608	−	0.392836i	$-0.871494\pi$
$479$	1.20973	−	3.72316i	0.0552739	−	0.170115i	0.974882	+	0.222721i	$0.0714939\pi$
$480$	−13.1521	+	47.1116i	−0.600306	+	2.15034i
$481$	−3.25970	−	10.0323i	−0.148629	−	0.457434i
$482$		−	2.65300i		−	0.120841i
$483$	7.51042	−	2.44028i	0.341736	−	0.111037i
$484$	32.8207	+	23.8457i	1.49185	+	1.08389i
$485$	−15.5203	−	4.33277i	−0.704740	−	0.196741i
$486$	−2.21041	+	1.60595i	−0.100266	+	0.0728476i
$487$	−7.55378	+	10.3969i	−0.342294	+	0.471128i	−0.945110	−	0.326753i	$-0.894045\pi$
$487$	−7.55378	+	10.3969i	−0.342294	+	0.471128i	0.602816	+	0.797881i	$0.294045\pi$
$488$	−55.1075	+	75.8490i	−2.49460	+	3.43352i
$489$	1.53122	−	1.11250i	0.0692442	−	0.0503089i
$490$	3.79501	+	4.78778i	0.171441	+	0.216290i
$491$	−20.6728	−	15.0197i	−0.932951	−	0.677829i	0.0137626	−	0.999905i	$-0.495619\pi$
$491$	−20.6728	−	15.0197i	−0.932951	−	0.677829i	−0.946714	+	0.322077i	$0.895619\pi$
$492$	34.4054	−	11.1790i	1.55111	−	0.503987i
$493$			30.0873i			1.35507i
$494$	5.71488	+	17.5886i	0.257125	+	0.791349i
$495$	9.58932	−	0.402239i	0.431008	−	0.0180793i
$496$	13.0000	−	40.0100i	0.583718	−	1.79650i
$497$	−0.173477	−	0.0563661i	−0.00778151	−	0.00252836i
$498$	−9.90330	−	13.6307i	−0.443777	−	0.610807i
$499$	−14.2341			−0.637206			−0.318603	−	0.947888i	$-0.603214\pi$
$499$	−14.2341			−0.637206			−0.318603	+	0.947888i	$0.603214\pi$
$500$	11.4429	−	60.0194i	0.511744	−	2.68415i
$501$	11.7066			0.523012
$502$	40.3675	+	55.5611i	1.80169	+	2.47981i
$503$	−0.148102	−	0.0481212i	−0.00660354	−	0.00214562i	0.305713	−	0.952124i	$-0.401105\pi$
$503$	−0.148102	−	0.0481212i	−0.00660354	−	0.00214562i	−0.312317	+	0.949978i	$0.601105\pi$
$504$	−2.92549	+	9.00374i	−0.130312	+	0.401059i
$505$	−35.1773	+	1.47556i	−1.56537	+	0.0656617i
$506$	−28.6180	−	88.0772i	−1.27223	−	3.91551i
$507$			11.0252i			0.489648i
$508$	14.1981	−	4.61324i	0.629939	−	0.204679i
$509$	−11.5290	−	8.37631i	−0.511014	−	0.371274i	0.302194	−	0.953246i	$-0.402281\pi$
$509$	−11.5290	−	8.37631i	−0.511014	−	0.371274i	−0.813208	+	0.581973i	$0.802281\pi$
$510$	−24.3413	−	30.7090i	−1.07785	−	1.35982i
$511$	3.74748	−	2.72271i	0.165779	−	0.120445i
$512$	−25.8140	+	35.5300i	−1.14083	+	1.57022i
$513$	−2.83121	+	3.89683i	−0.125001	+	0.172049i
$514$	10.6875	−	7.76495i	0.471407	−	0.342497i
$515$	−5.23488	−	1.46141i	−0.230676	−	0.0643976i
$516$	27.9657	+	20.3183i	1.23112	+	0.894463i
$517$	−15.1262	+	4.91479i	−0.665249	+	0.216152i
$518$		−	20.5094i		−	0.901132i
$519$	1.02246	+	3.14681i	0.0448811	+	0.138130i
$520$	7.99885	−	28.6524i	0.350773	−	1.25649i
$521$	3.09980	−	9.54020i	0.135805	−	0.417964i	−0.859910	−	0.510446i	$-0.829480\pi$
$521$	3.09980	−	9.54020i	0.135805	−	0.417964i	0.995714	+	0.0924824i	$0.0294802\pi$
$522$	−12.1891	−	3.96049i	−0.533504	−	0.173346i
$523$	3.29820	+	4.53958i	0.144220	+	0.198502i	0.875016	−	0.484094i	$-0.160851\pi$
$523$	3.29820	+	4.53958i	0.144220	+	0.198502i	−0.730796	+	0.682596i	$0.760851\pi$
$524$	33.0640			1.44441
$525$	1.14142	−	4.86797i	0.0498158	−	0.212456i
$526$	−9.07970			−0.395894
$527$	10.6188	+	14.6155i	0.462560	+	0.636659i
$528$	60.9718	+	19.8110i	2.65346	+	0.862161i
$529$	−12.1633	+	37.4349i	−0.528840	+	1.62760i
$530$	9.89336	+	26.5997i	0.429740	+	1.15542i
$531$	−0.527584	−	1.62374i	−0.0228952	−	0.0704642i
$532$			26.3235i			1.14127i
$533$	−8.84694	+	2.87454i	−0.383203	+	0.124510i
$534$	12.6664	+	9.20267i	0.548128	+	0.398238i
$535$	−0.0841905	−	2.00709i	−0.00363987	−	0.0867740i
$536$	55.2503	−	40.1417i	2.38645	−	1.73386i
$537$	−8.98756	+	12.3703i	−0.387842	+	0.533819i
$538$	49.9748	−	68.7844i	2.15457	−	2.96551i
$539$	3.47250	−	2.52292i	0.149571	−	0.108670i
$540$	11.4535	−	4.25997i	0.492881	−	0.183320i
$541$	25.3196	+	18.3958i	1.08857	+	0.790896i	0.979158	−	0.203100i	$-0.0651017\pi$
$541$	25.3196	+	18.3958i	1.08857	+	0.790896i	0.109417	+	0.993996i	$0.465102\pi$
$542$	63.1475	−	20.5179i	2.71242	−	0.881317i
$543$		−	17.4881i		−	0.750487i
$544$	−43.3563	−	133.437i	−1.85889	−	5.72107i
$545$	28.8447	+	19.1630i	1.23557	+	0.820852i
$546$	1.18646	−	3.65155i	0.0507758	−	0.156272i
$547$	−36.7596	−	11.9439i	−1.57172	−	0.510684i	−0.611817	−	0.790999i	$-0.709561\pi$
$547$	−36.7596	−	11.9439i	−1.57172	−	0.510684i	−0.959908	+	0.280315i	$0.909561\pi$
$548$	−14.3845	−	19.7985i	−0.614474	−	0.845751i
$549$	9.90320			0.422658
$550$	−57.0883	−	13.3858i	−2.43425	−	0.570774i
$551$	−22.5947			−0.962566
$552$	−43.9433	−	60.4828i	−1.87035	−	2.57432i
$553$	−12.7420	−	4.14012i	−0.541844	−	0.176056i
$554$	14.9790	−	46.1007i	0.636398	−	1.95863i
$555$	−13.1540	+	10.4265i	−0.558356	+	0.442579i
$556$	−19.5084	−	60.0408i	−0.827341	−	2.54630i
$557$		−	34.4301i		−	1.45885i	−0.684060	−	0.729426i	$-0.739787\pi$
$557$		−	34.4301i		−	1.45885i	0.684060	−	0.729426i	$-0.260213\pi$
$558$	−7.31888	+	2.37805i	−0.309833	+	0.100671i
$559$	−7.19106	−	5.22461i	−0.304150	−	0.220978i
$560$	18.4813	−	27.8187i	0.780979	−	1.17556i
$561$	−22.2727	+	16.1821i	−0.940356	+	0.683208i
$562$	40.6123	−	55.8980i	1.71313	−	2.35792i
$563$	−0.00191935	+	0.00264176i	−8.08911e−5	+	0.000111337i	−0.809057	−	0.587730i	$-0.800022\pi$
$563$	−0.00191935	+	0.00264176i	−8.08911e−5	+	0.000111337i	0.808977	+	0.587841i	$0.200022\pi$
$564$	−16.3827	+	11.9027i	−0.689836	+	0.501195i
$565$	16.4691	−	24.7899i	0.692862	−	1.04292i
$566$	−2.86833	−	2.08396i	−0.120565	−	0.0875955i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			1.72684i			0.0724566i
$569$	−7.53194	−	23.1809i	−0.315756	−	0.971796i	−0.975442	−	0.220255i	$-0.929311\pi$
$569$	−7.53194	−	23.1809i	−0.315756	−	0.971796i	0.659687	−	0.751541i	$-0.270689\pi$
$570$	23.0615	−	18.2796i	0.965941	−	0.765649i
$571$	4.34937	−	13.3860i	0.182015	−	0.560186i	−0.817869	−	0.575405i	$-0.804845\pi$
$571$	4.34937	−	13.3860i	0.182015	−	0.560186i	0.999884	+	0.0152189i	$0.00484450\pi$
$572$	−31.3499	−	10.1862i	−1.31081	−	0.425907i
$573$	7.98693	+	10.9931i	0.333659	+	0.459242i
$574$	−18.0861			−0.754899
$575$	25.8021	+	29.8879i	1.07602	+	1.24641i
$576$	29.8936			1.24557
$577$	20.8729	+	28.7291i	0.868952	+	1.19601i	0.979360	+	0.202124i	$0.0647843\pi$
$577$	20.8729	+	28.7291i	0.868952	+	1.19601i	−0.110408	+	0.993886i	$0.535216\pi$
$578$	62.7271	+	20.3813i	2.60911	+	0.847750i
$579$	−6.95117	+	21.3935i	−0.288881	+	0.889084i
$580$	47.7464	+	31.7203i	1.98256	+	1.31711i
$581$	1.90559	+	5.86479i	0.0790571	+	0.243313i
$582$			19.6891i			0.816139i
$583$	18.9628	−	6.16139i	0.785359	−	0.255179i
$584$	−35.4778	−	25.7761i	−1.46808	−	1.06662i
$585$	−2.94514	+	1.09540i	−0.121767	+	0.0452893i
$586$	−6.40269	+	4.65183i	−0.264493	+	0.192165i
$587$	−13.5144	+	18.6010i	−0.557800	+	0.767746i	−0.991045	−	0.133531i	$-0.957369\pi$
$587$	−13.5144	+	18.6010i	−0.557800	+	0.767746i	0.433245	+	0.901276i	$0.357369\pi$
$588$	3.21224	−	4.42127i	0.132471	−	0.182330i
$589$	−10.9758	+	7.97437i	−0.452249	+	0.328578i
$590$	0.437143	+	10.4214i	0.0179969	+	0.429043i
$591$	−3.08947	−	2.24463i	−0.127084	−	0.0923318i
$592$	−106.631	+	34.6465i	−4.38250	+	1.42396i
$593$		−	25.9063i		−	1.06384i	−0.846794	−	0.531921i	$-0.821470\pi$
$593$		−	25.9063i		−	1.06384i	0.846794	−	0.531921i	$-0.178530\pi$
$594$	−3.62394	−	11.1534i	−0.148692	−	0.457628i
$595$	4.99975	+	13.4425i	0.204970	+	0.551090i
$596$	7.40758	−	22.7982i	0.303426	−	0.933850i
$597$	3.07529	+	0.999224i	0.125863	+	0.0408955i
$598$	17.8216	+	24.5294i	0.728781	+	1.00308i
$599$	47.8981			1.95706			0.978531	−	0.206099i	$-0.0660769\pi$
$599$	47.8981			1.95706			0.978531	+	0.206099i	$0.0660769\pi$
$600$	−47.1692	+	3.96414i	−1.92567	+	0.161835i
$601$	0.411229			0.0167744			0.00838719	−	0.999965i	$-0.497330\pi$
$601$	0.411229			0.0167744			0.00838719	+	0.999965i	$0.497330\pi$
$602$	−10.1581	−	13.9814i	−0.414013	−	0.569840i
$603$	−6.86068	−	2.22917i	−0.279388	−	0.0907788i
$604$	−37.9385	+	116.763i	−1.54370	+	4.75101i
$605$	−4.46330	+	15.9878i	−0.181459	+	0.649998i
$606$	13.2940	+	40.9147i	0.540032	+	1.66205i
$607$		−	5.04036i		−	0.204582i	−0.994755	−	0.102291i	$-0.967383\pi$
$607$		−	5.04036i		−	0.204582i	0.994755	−	0.102291i	$-0.0326173\pi$
$608$	100.207	−	32.5593i	4.06394	−	1.32045i
$609$	3.79498	+	2.75722i	0.153780	+	0.111728i
$610$	−58.2746	−	16.2684i	−2.35947	−	0.658689i
$611$	4.21262	−	3.06065i	0.170424	−	0.123821i
$612$	−20.6034	+	28.3582i	−0.832844	+	1.14631i
$613$	−28.0173	+	38.5625i	−1.13161	+	1.55753i	−0.346633	+	0.938001i	$0.612675\pi$
$613$	−28.0173	+	38.5625i	−1.13161	+	1.55753i	−0.784976	+	0.619526i	$0.787325\pi$
$614$	19.6769	−	14.2961i	0.794094	−	0.576943i
$615$	9.19452	+	11.5998i	0.370759	+	0.467748i
$616$	−32.8745	−	23.8847i	−1.32455	−	0.962342i
$617$	22.5120	−	7.31459i	0.906298	−	0.294474i	0.181464	−	0.983398i	$-0.441916\pi$
$617$	22.5120	−	7.31459i	0.906298	−	0.294474i	0.724834	+	0.688923i	$0.241916\pi$
$618$			6.64099i			0.267140i
$619$	1.57174	+	4.83731i	0.0631735	+	0.194428i	0.977662	−	0.210184i	$-0.0674064\pi$
$619$	1.57174	+	4.83731i	0.0631735	+	0.194428i	−0.914488	+	0.404612i	$0.867406\pi$
$620$	34.3887	−	1.44249i	1.38108	−	0.0579317i
$621$	−2.44028	+	7.51042i	−0.0979252	+	0.301383i
$622$	−74.4031	−	24.1750i	−2.98329	−	0.969330i
$623$	−3.36821	−	4.63594i	−0.134944	−	0.185735i
$624$	−20.9891			−0.840238
$625$	24.6493	−	4.17258i	0.985973	−	0.166903i
$626$	1.18203			0.0472436
$627$	−12.1523	−	16.7262i	−0.485315	−	0.667979i
$628$	73.7475	+	23.9620i	2.94285	+	0.956188i
$629$	14.8783	−	45.7906i	0.593235	−	1.82579i
$630$	−6.10405	+	0.256044i	−0.243191	+	0.0102010i
$631$	12.6138	+	38.8213i	0.502148	+	1.54545i	0.805513	+	0.592578i	$0.201890\pi$
$631$	12.6138	+	38.8213i	0.502148	+	1.54545i	−0.303365	+	0.952874i	$0.598110\pi$
$632$			126.837i			5.04532i
$633$	−0.632100	+	0.205382i	−0.0251237	+	0.00816320i
$634$	4.08546	+	2.96826i	0.162254	+	0.117885i
$635$	3.79431	+	4.78689i	0.150573	+	0.189962i
$636$	20.5380	−	14.9218i	0.814386	−	0.591686i
$637$	−0.825990	+	1.13688i	−0.0327269	+	0.0450448i
$638$	32.3348	−	44.5050i	1.28015	−	1.76197i
$639$	0.147568	−	0.107215i	0.00583771	−	0.00424135i
$640$	−81.6834	−	22.8034i	−3.22882	−	0.901384i
$641$	−31.6043	−	22.9619i	−1.24829	−	0.906939i	−0.250173	−	0.968201i	$-0.580487\pi$
$641$	−31.6043	−	22.9619i	−1.24829	−	0.906939i	−0.998122	+	0.0612624i	$0.980487\pi$
$642$	−2.33445	+	0.758509i	−0.0921334	+	0.0299359i
$643$			31.8832i			1.25735i	0.777668	+	0.628675i	$0.216402\pi$
$643$			31.8832i			1.25735i	−0.777668	+	0.628675i	$0.783598\pi$
$644$	13.3361	+	41.0444i	0.525517	+	1.61737i
$645$	−3.80307	+	13.6229i	−0.149746	+	0.536399i
$646$	−26.0845	+	80.2798i	−1.02628	+	3.15857i
$647$	−15.3338	−	4.98226i	−0.602834	−	0.195873i	−0.00833025	−	0.999965i	$-0.502652\pi$
$647$	−15.3338	−	4.98226i	−0.602834	−	0.195873i	−0.594504	+	0.804093i	$0.702652\pi$
$648$	−5.56462	−	7.65904i	−0.218599	−	0.300875i
$649$	7.32814			0.287655
$650$	19.1299	−	1.60769i	0.750336	−	0.0630590i
$651$	2.81659			0.110391
$652$	6.07979	+	8.36811i	0.238103	+	0.327721i
$653$	−8.08473	−	2.62689i	−0.316380	−	0.102798i	0.146522	−	0.989207i	$-0.453192\pi$
$653$	−8.08473	−	2.62689i	−0.316380	−	0.102798i	−0.462902	+	0.886409i	$0.653192\pi$
$654$	13.0757	−	40.2429i	0.511300	−	1.57362i
$655$	4.71610	+	12.6799i	0.184273	+	0.495444i
$656$	30.5528	+	94.0319i	1.19289	+	3.67133i
$657$			4.63214i			0.180717i
$658$	9.62851	−	3.12849i	0.375359	−	0.121961i
$659$	10.2954	+	7.48008i	0.401054	+	0.291382i	0.769970	−	0.638080i	$-0.220271\pi$
$659$	10.2954	+	7.48008i	0.401054	+	0.291382i	−0.368916	+	0.929463i	$0.620271\pi$
$660$	2.19823	+	52.4055i	0.0855660	+	2.03988i
$661$	1.10387	−	0.802006i	0.0429354	−	0.0311944i	−0.566111	−	0.824329i	$-0.691552\pi$
$661$	1.10387	−	0.802006i	0.0429354	−	0.0311944i	0.609046	+	0.793135i	$0.291552\pi$
$662$	−12.7168	+	17.5031i	−0.494251	+	0.680278i
$663$	5.29793	−	7.29198i	0.205755	−	0.283197i
$664$	47.2303	−	34.3148i	1.83289	−	1.33167i
$665$	−10.0949	+	3.75467i	−0.391465	+	0.145600i
$666$	16.5925	+	12.0551i	0.642945	+	0.467127i
$667$	−35.2303	+	11.4470i	−1.36412	+	0.443230i
$668$			63.9765i			2.47532i
$669$	−4.87406	−	15.0008i	−0.188442	−	0.579965i
$670$	36.7091	+	24.3877i	1.41820	+	0.942178i
$671$	−13.1354	+	40.4265i	−0.507086	+	1.56065i
$672$	−20.8039	−	6.75960i	−0.802529	−	0.260757i
$673$	−7.53932	−	10.3770i	−0.290619	−	0.400003i	0.638596	−	0.769542i	$-0.279516\pi$
$673$	−7.53932	−	10.3770i	−0.290619	−	0.400003i	−0.929215	+	0.369539i	$0.879516\pi$
$674$	−26.1447			−1.00705
$675$	3.26736	+	3.78475i	0.125761	+	0.145675i
$676$	−60.2529			−2.31742
$677$	−10.1536	−	13.9753i	−0.390236	−	0.537114i	0.568024	−	0.823012i	$-0.307708\pi$
$677$	−10.1536	−	13.9753i	−0.390236	−	0.537114i	−0.958260	+	0.285898i	$0.907708\pi$
$678$	−34.5857	−	11.2376i	−1.32826	−	0.431577i
$679$	2.22686	−	6.85358i	0.0854591	−	0.263016i
$680$	106.406	−	84.3425i	4.08050	−	3.23439i
$681$	−1.84626	−	5.68219i	−0.0707487	−	0.217742i
$682$		−	33.0311i		−	1.26482i
$683$	−43.1605	+	14.0237i	−1.65149	+	0.536602i	−0.979062	−	0.203561i	$-0.934748\pi$
$683$	−43.1605	+	14.0237i	−1.65149	+	0.536602i	−0.672428	+	0.740163i	$0.734748\pi$
$684$	−21.2962	−	15.4726i	−0.814279	−	0.591608i
$685$	5.54091	−	8.34035i	0.211707	−	0.318668i
$686$	−2.21041	+	1.60595i	−0.0843937	+	0.0613156i
$687$	−1.32814	+	1.82803i	−0.0506717	+	0.0697436i
$688$	−55.5311	+	76.4320i	−2.11710	+	2.91394i
$689$	−5.28112	+	3.83695i	−0.201194	+	0.146176i
$690$	26.6973	−	40.1857i	1.01635	−	1.52984i
$691$	−9.14270	−	6.64256i	−0.347805	−	0.252695i	0.400143	−	0.916453i	$-0.368961\pi$
$691$	−9.14270	−	6.64256i	−0.347805	−	0.252695i	−0.747947	+	0.663758i	$0.768961\pi$
$692$	−17.1973	+	5.58774i	−0.653743	+	0.212414i
$693$			4.29225i			0.163049i
$694$	5.41662	+	16.6706i	0.205612	+	0.632809i
$695$	20.2428	−	16.0453i	0.767852	−	0.608635i
$696$	13.7231	−	42.2353i	0.520172	−	1.60092i
$697$	−40.3802	−	13.1203i	−1.52951	−	0.496967i
$698$	−33.4385	−	46.0241i	−1.26566	−	1.74204i
$699$	14.0712			0.532223
$700$	26.6034	+	6.23786i	1.00551	+	0.235769i
$701$	13.1664			0.497288			0.248644	−	0.968595i	$-0.420015\pi$
$701$	13.1664			0.497288			0.248644	+	0.968595i	$0.420015\pi$
$702$	2.25678	+	3.10619i	0.0851767	+	0.117236i
$703$	34.3874	+	11.1731i	1.29694	+	0.421403i
$704$	−39.6502	+	122.031i	−1.49437	+	4.59921i
$705$	−6.90140	−	4.58494i	−0.259922	−	0.172679i
$706$	−29.9430	−	92.1550i	−1.12692	−	3.46830i
$707$		−	15.7456i		−	0.592173i
$708$	8.87371	−	2.88324i	0.333494	−	0.108359i
$709$	21.4595	+	15.5913i	0.805930	+	0.585543i	0.912648	−	0.408747i	$-0.134034\pi$
$709$	21.4595	+	15.5913i	0.805930	+	0.585543i	−0.106718	+	0.994289i	$0.534034\pi$
$710$	−1.04448	+	0.388479i	−0.0391986	+	0.0145794i
$711$	10.8390	−	7.87498i	0.406494	−	0.295335i
$712$	−31.8872	+	43.8889i	−1.19502	+	1.64481i
$713$	−13.0737	+	17.9945i	−0.489615	+	0.673898i
$714$	14.1776	−	10.3007i	0.530584	−	0.385492i
$715$	−0.565250	−	13.4755i	−0.0211391	−	0.503954i
$716$	−67.6037	−	49.1169i	−2.52647	−	1.83559i
$717$	−5.14724	+	1.67244i	−0.192227	+	0.0624583i
$718$			66.8232i			2.49382i
$719$	−1.98132	−	6.09787i	−0.0738907	−	0.227412i	0.907290	−	0.420507i	$-0.138148\pi$
$719$	−1.98132	−	6.09787i	−0.0738907	−	0.227412i	−0.981180	+	0.193094i	$0.938148\pi$
$720$	11.6428	+	31.3032i	0.433900	+	1.16660i
$721$	0.751105	−	2.31166i	0.0279726	−	0.0860908i
$722$	−10.9165	−	3.54697i	−0.406269	−	0.132005i
$723$	−0.570745	−	0.785563i	−0.0212262	−	0.0292154i
$724$	95.5724			3.55192
$725$	−5.35425	+	22.8350i	−0.198852	+	0.848069i
$726$	20.2822			0.752745
$727$	−0.775130	−	1.06688i	−0.0287480	−	0.0395682i	0.794401	−	0.607394i	$-0.207785\pi$
$727$	−0.775130	−	1.06688i	−0.0287480	−	0.0395682i	−0.823149	+	0.567825i	$0.807785\pi$
$728$	12.6526	+	4.11107i	0.468936	+	0.152367i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	7.60942	−	27.2575i	0.281637	−	1.00884i
$731$	−12.5370	−	38.5849i	−0.463697	−	1.42711i
$732$			54.1209i			2.00037i
$733$	27.1706	−	8.82827i	1.00357	−	0.326079i	0.239278	−	0.970951i	$-0.423089\pi$
$733$	27.1706	−	8.82827i	1.00357	−	0.326079i	0.764291	+	0.644872i	$0.223089\pi$
$734$	38.6193	+	28.0586i	1.42547	+	1.03566i
$735$	2.15372	+	0.601250i	0.0794411	+	0.0221774i
$736$	139.751	−	101.535i	5.15128	−	3.74263i
$737$	18.1997	−	25.0497i	0.670394	−	0.922718i
$738$	10.6307	−	14.6320i	0.391323	−	0.538610i
$739$	43.6212	−	31.6927i	1.60463	−	1.16583i	0.726821	−	0.686827i	$-0.240997\pi$
$739$	43.6212	−	31.6927i	1.60463	−	1.16583i	0.877811	−	0.479007i	$-0.159003\pi$
$740$	−56.9805	−	71.8865i	−2.09465	−	2.64260i
$741$	5.47606	+	3.97859i	0.201168	+	0.146157i
$742$	−12.0707	+	3.92201i	−0.443130	+	0.143982i
$743$		−	42.1708i		−	1.54710i	−0.633737	−	0.773549i	$-0.718480\pi$
$743$		−	42.1708i		−	1.54710i	0.633737	−	0.773549i	$-0.281520\pi$
$744$	−8.23991	−	25.3598i	−0.302090	−	0.929737i
$745$	9.79959	−	0.411059i	0.359029	−	0.0150600i
$746$	−17.6830	+	54.4226i	−0.647420	+	1.99255i
$747$	−5.86479	−	1.90559i	−0.214582	−	0.0697218i
$748$	−88.4350	−	121.720i	−3.23350	−	4.45053i
$749$	0.898387			0.0328263
$750$	−13.0091	−	27.6385i	−0.475027	−	1.00921i
$751$	12.1513			0.443408			0.221704	−	0.975114i	$-0.428838\pi$
$751$	12.1513			0.443408			0.221704	+	0.975114i	$0.428838\pi$
$752$	−32.5308	−	44.7749i	−1.18628	−	1.63277i
$753$	23.9059	+	7.76749i	0.871179	+	0.283063i
$754$	−5.56552	+	17.1289i	−0.202684	+	0.623798i
$755$	−50.1894	+	2.10527i	−1.82658	+	0.0766186i
$756$	1.68877	+	5.19751i	0.0614202	+	0.189032i
$757$			4.36711i			0.158725i	0.996846	+	0.0793626i	$0.0252885\pi$
$757$			4.36711i			0.158725i	−0.996846	+	0.0793626i	$0.974712\pi$
$758$	11.7757	−	3.82616i	0.427713	−	0.138972i
$759$	−27.4221	−	19.9233i	−0.995358	−	0.723170i
$760$	63.3387	+	79.9080i	2.29754	+	2.89857i
$761$	−40.7093	+	29.5771i	−1.47571	+	1.07217i	−0.496805	+	0.867862i	$0.665494\pi$
$761$	−40.7093	+	29.5771i	−1.47571	+	1.07217i	−0.978907	+	0.204306i	$0.934506\pi$
$762$	4.38700	−	6.03819i	0.158924	−	0.218740i
$763$	−9.10304	+	12.5293i	−0.329552	+	0.453590i
$764$	−60.0770	+	43.6485i	−2.17351	+	1.57915i
$765$	−13.8140	−	3.85644i	−0.499447	−	0.139430i
$766$	2.28460	+	1.65986i	0.0825460	+	0.0599732i
$767$	−2.28177	+	0.741392i	−0.0823899	+	0.0267701i
$768$			43.8366i			1.58182i
$769$	5.42958	+	16.7105i	0.195796	+	0.602597i	0.999966	+	0.00819857i	$0.00260972\pi$
$769$	5.42958	+	16.7105i	0.195796	+	0.602597i	−0.804171	+	0.594398i	$0.797390\pi$
$770$	7.05105	−	25.2574i	0.254102	−	0.910212i
$771$	1.49413	−	4.59845i	0.0538097	−	0.165609i
$772$	−116.915	−	37.9881i	−4.20787	−	1.36722i
$773$	3.36923	+	4.63735i	0.121183	+	0.166794i	0.865298	−	0.501257i	$-0.167129\pi$
$773$	3.36923	+	4.63735i	0.121183	+	0.166794i	−0.744116	+	0.668051i	$0.767129\pi$
$774$	17.2820			0.621188
$775$	5.45824	+	12.9822i	0.196066	+	0.466333i
$776$	−68.2225			−2.44905
$777$	−4.41222	−	6.07290i	−0.158288	−	0.217864i
$778$	1.45315	+	0.472156i	0.0520978	+	0.0169276i
$779$	9.85296	−	30.3243i	0.353019	−	1.08648i
$780$	−5.98636	−	16.0952i	−0.214346	−	0.576299i
$781$	0.241937	+	0.744606i	0.00865719	+	0.0266441i
$782$			138.390i			4.94881i
$783$	−4.46127	+	1.44955i	−0.159433	+	0.0518029i
$784$	12.0836	+	8.77924i	0.431557	+	0.313544i
$785$	1.32969	+	31.6997i	0.0474587	+	1.13141i
$786$	13.3733	−	9.71626i	0.477009	−	0.346567i
$787$	−0.457864	+	0.630196i	−0.0163211	+	0.0224640i	−0.817100	−	0.576497i	$-0.804419\pi$
$787$	−0.457864	+	0.630196i	−0.0163211	+	0.0224640i	0.800778	+	0.598961i	$0.204419\pi$
$788$	12.2669	−	16.8839i	0.436990	−	0.601465i
$789$	−2.68853	+	1.95333i	−0.0957141	+	0.0695404i
$790$	−76.7176	+	28.5340i	−2.72949	+	1.01519i
$791$	10.7680	+	7.82338i	0.382865	+	0.278167i
$792$	38.6463	−	12.5569i	1.37324	−	0.446191i
$793$		−	13.9166i		−	0.494192i
$794$	26.4049	+	81.2660i	0.937075	+	2.88402i
$795$	8.65188	+	5.74787i	0.306851	+	0.203856i
$796$	−5.46075	+	16.8065i	−0.193551	+	0.595689i
$797$	34.6193	+	11.2485i	1.22628	+	0.398442i	0.849364	−	0.527807i	$-0.176986\pi$
$797$	34.6193	+	11.2485i	1.22628	+	0.398442i	0.376913	+	0.926249i	$0.376986\pi$
$798$	7.73548	+	10.6470i	0.273833	+	0.376899i
$799$	23.7667			0.840807
$800$	−9.15950	−	108.988i	−0.323837	−	3.85332i
$801$	5.73034			0.202472
$802$	−49.0152	−	67.4636i	−1.73079	−	2.38222i
$803$	−18.9092	−	6.14397i	−0.667291	−	0.216816i
$804$	12.1824	−	37.4935i	0.429640	−	1.32230i
$805$	−13.8381	+	10.9687i	−0.487730	+	0.386597i
$806$	3.34177	+	10.2849i	0.117709	+	0.362271i
$807$		−	31.1184i		−	1.09542i
$808$	−141.769	+	46.0636i	−4.98742	+	1.62051i
$809$	−12.0319	−	8.74170i	−0.423020	−	0.307342i	0.355832	−	0.934550i	$-0.384198\pi$
$809$	−12.0319	−	8.74170i	−0.423020	−	0.307342i	−0.778852	+	0.627208i	$0.784198\pi$
$810$	3.38073	−	5.08878i	0.118787	−	0.178801i
$811$	−28.4154	+	20.6450i	−0.997800	+	0.724944i	−0.961615	−	0.274401i	$-0.911520\pi$
$811$	−28.4154	+	20.6450i	−0.997800	+	0.724944i	−0.0361847	+	0.999345i	$0.511520\pi$
$812$	−15.0682	+	20.7395i	−0.528789	+	0.727815i
$813$	14.2841	−	19.6604i	0.500966	−	0.689521i
$814$	−71.2189	+	51.7436i	−2.49622	+	1.81361i
$815$	−2.34194	+	3.52516i	−0.0820346	+	0.123481i
$816$	−77.5046	−	56.3104i	−2.71320	−	1.97126i
$817$	28.9761	−	9.41490i	1.01374	−	0.329386i
$818$		−	78.1663i		−	2.73302i
$819$	−0.434249	−	1.33648i	−0.0151739	−	0.0467004i
$820$	−63.3927	+	50.2480i	−2.21377	+	1.75473i
$821$	−7.68675	+	23.6574i	−0.268269	+	0.825648i	0.722653	+	0.691211i	$0.242923\pi$
$821$	−7.68675	+	23.6574i	−0.268269	+	0.825648i	−0.990922	+	0.134437i	$0.957077\pi$
$822$	−11.6361	−	3.78079i	−0.405855	−	0.131870i
$823$	1.27305	+	1.75221i	0.0443758	+	0.0610781i	0.830628	−	0.556827i	$-0.187981\pi$
$823$	1.27305	+	1.75221i	0.0443758	+	0.0610781i	−0.786252	+	0.617905i	$0.787981\pi$
$824$	−23.0110			−0.801625
$825$	−19.7837	+	8.31791i	−0.688782	+	0.289592i
$826$	−4.66470			−0.162306
$827$	0.857034	+	1.17961i	0.0298020	+	0.0410189i	0.823658	−	0.567087i	$-0.191930\pi$
$827$	0.857034	+	1.17961i	0.0298020	+	0.0410189i	−0.793856	+	0.608106i	$0.791930\pi$
$828$	−41.0444	−	13.3361i	−1.42639	−	0.463462i
$829$	8.50405	−	26.1728i	0.295358	−	0.909018i	−0.687743	−	0.725954i	$-0.741398\pi$
$829$	8.50405	−	26.1728i	0.295358	−	0.909018i	0.983101	−	0.183064i	$-0.0586015\pi$
$830$	31.3805	+	20.8476i	1.08923	+	0.723631i
$831$	−5.48238	−	16.8730i	−0.190182	−	0.585319i
$832$		−	42.0083i		−	1.45637i
$833$	−6.10011	+	1.98205i	−0.211356	+	0.0686738i
$834$	−25.5342	−	18.5517i	−0.884178	−	0.642393i
$835$	−24.5347	+	9.12532i	−0.849058	+	0.315795i
$836$	91.4083	−	66.4120i	3.16142	−	2.29691i
$837$	−1.65555	+	2.27867i	−0.0572242	+	0.0787623i
$838$	−9.51430	+	13.0953i	−0.328666	+	0.452370i
$839$	14.7736	−	10.7337i	0.510043	−	0.370568i	−0.302797	−	0.953055i	$-0.597920\pi$
$839$	14.7736	−	10.7337i	0.510043	−	0.370568i	0.812840	+	0.582487i	$0.197920\pi$
$840$	−0.887189	−	21.1505i	−0.0306109	−	0.729760i
$841$	5.65977	+	4.11206i	0.195164	+	0.141795i
$842$	−25.5893	+	8.31446i	−0.881865	+	0.286535i
$843$		−	25.2886i		−	0.870985i
$844$	−1.12241	−	3.45442i	−0.0386349	−	0.118906i
$845$	−8.59420	−	23.1067i	−0.295650	−	0.794895i
$846$	−3.12849	+	9.62851i	−0.107560	+	0.331035i
$847$	−7.06005	−	2.29395i	−0.242586	−	0.0788210i
$848$	40.7820	+	56.1316i	1.40046	+	1.92757i
$849$	−1.29765			−0.0445352
$850$	74.9523	+	45.3858i	2.57084	+	1.55672i
$851$	59.2784			2.03204
$852$	0.585927	+	0.806460i	0.0200735	+	0.0276288i
$853$	−5.19418	−	1.68769i	−0.177845	−	0.0577854i	0.218741	−	0.975783i	$-0.429805\pi$
$853$	−5.19418	−	1.68769i	−0.177845	−	0.0577854i	−0.396586	+	0.917998i	$0.629805\pi$
$854$	8.36128	−	25.7334i	0.286117	−	0.880578i
$855$	2.89607	−	10.3739i	0.0990435	−	0.354781i
$856$	−2.62822	−	8.08884i	−0.0898309	−	0.276471i
$857$		−	25.1145i		−	0.857894i	−0.903330	−	0.428947i	$-0.858885\pi$
$857$		−	25.1145i		−	0.857894i	0.903330	−	0.428947i	$-0.141115\pi$
$858$	−15.6733	+	5.09258i	−0.535079	+	0.173858i
$859$	21.9886	+	15.9757i	0.750242	+	0.545083i	0.895902	−	0.444252i	$-0.146531\pi$
$859$	21.9886	+	15.9757i	0.750242	+	0.545083i	−0.145660	+	0.989335i	$0.546531\pi$
$860$	−74.4487	−	20.7837i	−2.53868	−	0.708719i
$861$	−5.35535	+	3.89089i	−0.182510	+	0.132601i
$862$	19.1478	−	26.3546i	0.652175	−	0.897642i
$863$	−3.95253	+	5.44019i	−0.134546	+	0.185186i	−0.870974	−	0.491330i	$-0.836511\pi$
$863$	−3.95253	+	5.44019i	−0.134546	+	0.185186i	0.736428	+	0.676516i	$0.236511\pi$
$864$	17.6969	−	12.8575i	0.602060	−	0.437422i
$865$	−4.59582	−	5.79808i	−0.156263	−	0.197141i
$866$	42.9649	+	31.2158i	1.46001	+	1.06076i
$867$	22.9584	−	7.45962i	0.779707	−	0.253342i
$868$			15.3926i			0.522460i
$869$	17.7704	+	54.6917i	0.602820	+	1.85529i
$870$	28.6332	−	1.20106i	0.970757	−	0.0407199i
$871$	−3.13256	+	9.64103i	−0.106143	+	0.326674i
$872$	139.441	+	45.3072i	4.72207	+	1.53429i
$873$	4.23574	+	5.83000i	0.143358	+	0.197316i
$874$	−103.927			−3.51537
$875$	1.40240	+	11.0920i	0.0474098	+	0.374979i
$876$	−25.3146			−0.855302
$877$	−15.6467	−	21.5359i	−0.528352	−	0.727214i	0.458526	−	0.888681i	$-0.348378\pi$
$877$	−15.6467	−	21.5359i	−0.528352	−	0.727214i	−0.986878	+	0.161467i	$0.948378\pi$
$878$	−101.315	−	32.9192i	−3.41921	−	1.11097i
$879$	−0.895102	+	2.75484i	−0.0301910	+	0.0929185i
$880$	−143.227	+	6.00790i	−4.82820	+	0.202526i
$881$	−10.6362	−	32.7350i	−0.358344	−	1.10287i	−0.954045	−	0.299664i	$-0.903125\pi$
$881$	−10.6362	−	32.7350i	−0.358344	−	1.10287i	0.595701	−	0.803207i	$-0.296875\pi$
$882$		−	2.73221i		−	0.0919984i
$883$	39.3961	−	12.8006i	1.32579	−	0.430774i	0.441307	−	0.897356i	$-0.354515\pi$
$883$	39.3961	−	12.8006i	1.32579	−	0.430774i	0.884478	+	0.466582i	$0.154515\pi$
$884$	39.8506	+	28.9531i	1.34032	+	0.973800i
$885$	2.37142	+	2.99177i	0.0797143	+	0.100567i
$886$	−57.7590	+	41.9644i	−1.94045	+	1.40982i
$887$	−15.9148	+	21.9049i	−0.534368	+	0.735495i	−0.987788	−	0.155802i	$-0.950204\pi$
$887$	−15.9148	+	21.9049i	−0.534368	+	0.735495i	0.453420	+	0.891297i	$0.350204\pi$
$888$	−41.7709	+	57.4927i	−1.40174	+	1.92933i
$889$	−2.21000	+	1.60566i	−0.0741210	+	0.0538520i
$890$	−33.7197	−	9.41347i	−1.13029	−	0.315540i
$891$	−3.47250	−	2.52292i	−0.116333	−	0.0845210i
$892$	81.9793	−	26.6367i	2.74487	−	0.891862i
$893$			17.8481i			0.597265i
$894$	−3.70341	−	11.3979i	−0.123860	−	0.381203i
$895$	9.19344	−	32.9315i	0.307303	−	1.10078i
$896$	11.7200	−	36.0704i	0.391537	−	1.20503i
$897$	10.5541	+	3.42923i	0.352390	+	0.114499i
$898$	−26.0740	−	35.8878i	−0.870102	−	1.19759i
$899$	−13.2122			−0.440652
$900$	−20.6836	+	17.8561i	−0.689455	+	0.595203i
$901$	−29.7950			−0.992615
$902$	45.6298	+	62.8040i	1.51931	+	2.09114i
$903$	−6.01569	−	1.95462i	−0.200190	−	0.0650456i
$904$	38.9381	−	119.839i	1.29506	−	3.98579i
$905$	13.6320	+	36.6516i	0.453144	+	1.21834i
$906$	18.9673	+	58.3753i	0.630146	+	1.93939i
$907$			27.5543i			0.914927i	0.889228	+	0.457463i	$0.151242\pi$
$907$			27.5543i			0.914927i	−0.889228	+	0.457463i	$0.848758\pi$
$908$	31.0531	−	10.0898i	1.03053	−	0.334841i
$909$	12.7384	+	9.25502i	0.422507	+	0.306970i
$910$	0.359808	+	8.57777i	0.0119275	+	0.284350i
$911$	31.3776	−	22.7972i	1.03959	−	0.755305i	0.0693827	−	0.997590i	$-0.477897\pi$
$911$	31.3776	−	22.7972i	1.03959	−	0.755305i	0.970205	+	0.242285i	$0.0778970\pi$
$912$	42.2874	−	58.2036i	1.40028	−	1.92731i
$913$	15.5579	−	21.4135i	0.514890	−	0.708685i
$914$	−53.4671	+	38.8462i	−1.76854	+	1.28492i
$915$	−20.7551	+	7.71957i	−0.686143	+	0.255201i
$916$	−9.99015	−	7.25827i	−0.330084	−	0.239820i
$917$	−5.75403	+	1.86960i	−0.190015	+	0.0617396i
$918$			17.5245i			0.578395i
$919$	−2.44715	−	7.53156i	−0.0807241	−	0.248443i	0.902547	−	0.430591i	$-0.141695\pi$
$919$	−2.44715	−	7.53156i	−0.0807241	−	0.248443i	−0.983271	+	0.182148i	$0.941695\pi$
$920$	139.243	+	92.5060i	4.59070	+	3.04983i
$921$	2.75085	−	8.46623i	0.0906434	−	0.278972i
$922$	80.9020	+	26.2867i	2.66437	+	0.865705i
$923$	−0.150664	−	0.207372i	−0.00495918	−	0.00682572i
$924$	−23.4571			−0.771681
$925$	19.4407	−	32.1054i	0.639206	−	1.05562i
$926$	−12.9195			−0.424561
$927$	1.42869	+	1.96642i	0.0469242	+	0.0645856i
$928$	97.5882	+	31.7083i	3.20349	+	1.04088i
$929$	6.41729	−	19.7504i	0.210544	−	0.647989i	−0.788896	−	0.614527i	$-0.789347\pi$
$929$	6.41729	−	19.7504i	0.210544	−	0.647989i	0.999440	−	0.0334617i	$-0.0106532\pi$
$930$	13.4852	−	10.6890i	0.442197	−	0.350506i
$931$	−1.48846	−	4.58100i	−0.0487822	−	0.150136i
$932$			76.8992i			2.51892i
$933$	−27.2318	+	8.84815i	−0.891529	+	0.289675i
$934$	63.5900	+	46.2009i	2.08073	+	1.51174i
$935$	34.0652	−	51.2761i	1.11405	−	1.67691i
$936$	−10.7629	+	7.81973i	−0.351797	+	0.255596i
$937$	−5.09289	+	7.00977i	−0.166378	+	0.228999i	−0.884062	−	0.467369i	$-0.845202\pi$
$937$	−5.09289	+	7.00977i	−0.166378	+	0.228999i	0.717685	+	0.696368i	$0.245202\pi$
$938$	−11.5849	+	15.9453i	−0.378262	+	0.520633i
$939$	0.350004	−	0.254293i	0.0114219	−	0.00829853i
$940$	25.0566	−	37.7161i	0.817258	−	1.23016i
$941$	−20.2763	−	14.7316i	−0.660988	−	0.480236i	0.206008	−	0.978550i	$-0.433953\pi$
$941$	−20.2763	−	14.7316i	−0.660988	−	0.480236i	−0.866997	+	0.498314i	$0.833953\pi$
$942$	36.8699	−	11.9798i	1.20129	−	0.390322i
$943$		−	52.2743i		−	1.70229i
$944$	7.88007	+	24.2524i	0.256474	+	0.789347i
$945$	−1.75234	+	1.38899i	−0.0570038	+	0.0451838i
$946$	−22.9224	+	70.5480i	−0.745273	+	2.29371i
$947$	−8.76267	−	2.84716i	−0.284748	−	0.0925204i	0.163161	−	0.986600i	$-0.447831\pi$
$947$	−8.76267	−	2.84716i	−0.284748	−	0.0925204i	−0.447909	+	0.894079i	$0.647831\pi$
$948$	43.0367	+	59.2349i	1.39777	+	1.92386i
$949$	6.50936			0.211303
$950$	−34.0833	+	56.2870i	−1.10581	+	1.82619i
$951$	1.84828			0.0599347
$952$	35.6917	+	49.1254i	1.15677	+	1.59216i
$953$	33.2814	+	10.8138i	1.07809	+	0.350292i	0.793633	−	0.608397i	$-0.208187\pi$
$953$	33.2814	+	10.8138i	1.07809	+	0.350292i	0.284456	+	0.958689i	$0.408187\pi$
$954$	3.92201	−	12.0707i	0.126980	−	0.390804i
$955$	−25.3081	−	16.8134i	−0.818952	−	0.544070i
$956$	−9.13986	−	28.1296i	−0.295604	−	0.909776i
$957$		−	20.1343i		−	0.650850i
$958$	10.1725	−	3.30523i	0.328657	−	0.106787i
$959$	3.62279	+	2.63211i	0.116986	+	0.0849953i
$960$	−62.6510	+	23.3021i	−2.02205	+	0.752073i
$961$	18.6615	−	13.5583i	0.601982	−	0.437366i
$962$	16.9406	−	23.3167i	0.546186	−	0.751760i
$963$	−0.528059	+	0.726810i	−0.0170165	+	0.0234211i
$964$	4.29309	−	3.11911i	0.138271	−	0.100460i
$965$	−2.10802	−	50.2550i	−0.0678596	−	1.61776i
$966$	17.4554	+	12.6821i	0.561619	+	0.408040i
$967$	−32.2006	+	10.4626i	−1.03550	+	0.336455i	−0.776963	−	0.629546i	$-0.783241\pi$
$967$	−32.2006	+	10.4626i	−1.03550	+	0.336455i	−0.258539	+	0.966001i	$0.583241\pi$
$968$			70.2778i			2.25881i
$969$	9.54702	+	29.3827i	0.306694	+	0.943908i
$970$	−15.3477	−	41.2644i	−0.492785	−	1.32492i
$971$	−11.6758	+	35.9345i	−0.374695	+	1.15319i	0.568990	+	0.822345i	$0.307334\pi$
$971$	−11.6758	+	35.9345i	−0.374695	+	1.15319i	−0.943684	+	0.330847i	$0.892666\pi$
$972$	−5.19751	−	1.68877i	−0.166710	−	0.0541675i
$973$	6.78999	+	9.34562i	0.217677	+	0.299607i
$974$	−35.1124			−1.12507
$975$	5.31856	−	4.59149i	0.170330	−	0.147045i
$976$	−147.916			−4.73466
$977$	−31.1440	−	42.8660i	−0.996385	−	1.37141i	−0.927517	−	0.373780i	$-0.878061\pi$
$977$	−31.1440	−	42.8660i	−0.996385	−	1.37141i	−0.0688673	−	0.997626i	$-0.521939\pi$
$978$	4.91815	+	1.59800i	0.157265	+	0.0510985i
$979$	−7.60059	+	23.3922i	−0.242916	+	0.747619i
$980$	−3.28582	+	11.7700i	−0.104962	+	0.375980i
$981$	−4.78575	−	14.7290i	−0.152797	−	0.470262i
$982$		−	69.8163i		−	2.22793i
$983$	42.0917	−	13.6764i	1.34252	−	0.436210i	0.452348	−	0.891842i	$-0.350587\pi$
$983$	42.0917	−	13.6764i	1.34252	−	0.436210i	0.890168	+	0.455632i	$0.150587\pi$
$984$	50.6996	+	36.8354i	1.61625	+	1.17427i
$985$	8.22461	+	2.29605i	0.262058	+	0.0731582i
$986$	−66.5052	+	48.3189i	−2.11796	+	1.53879i
$987$	2.17800	−	2.99775i	0.0693264	−	0.0954196i
$988$	−21.7429	+	29.9266i	−0.691735	+	0.952092i
$989$	40.4105	−	29.3600i	1.28498	−	0.933593i
$990$	16.2891	+	20.5503i	0.517702	+	0.653132i
$991$	−4.81445	−	3.49790i	−0.152936	−	0.111115i	0.508686	−	0.860952i	$-0.330132\pi$
$991$	−4.81445	−	3.49790i	−0.152936	−	0.111115i	−0.661622	+	0.749838i	$0.730132\pi$
$992$	58.5961	−	19.0390i	1.86043	−	0.604490i
$993$			7.91851i			0.251286i
$994$	−0.154004	−	0.473976i	−0.00488472	−	0.0150336i
$995$	−7.22410	+	0.303026i	−0.229019	+	0.00960657i
$996$	10.4140	−	32.0510i	0.329981	−	1.01558i
$997$	−21.7090	−	7.05369i	−0.687532	−	0.223393i	−0.0556420	−	0.998451i	$-0.517721\pi$
$997$	−21.7090	−	7.05369i	−0.687532	−	0.223393i	−0.631890	+	0.775058i	$0.717721\pi$
$998$	−22.8593	−	31.4632i	−0.723599	−	0.995949i
$999$	7.50652			0.237496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.17	✓	72
25.9	even	10	inner	525.2.z.b.484.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.17	✓	72	1.1	even	1	trivial
525.2.z.b.484.17	yes	72	25.9	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60595 + 2.21041i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.68877 + 5.19751i) q^{4} +(-2.23410 + 0.0937129i) q^{5} +(0.844300 + 2.59849i) q^{6} -1.00000i q^{7} +(-9.00374 + 2.92549i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.60595 + 2.21041i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.68877 + 5.19751i) q^{4} +(-2.23410 + 0.0937129i) q^{5} +(0.844300 + 2.59849i) q^{6} -1.00000i q^{7} +(-9.00374 + 2.92549i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-3.79501 - 4.78778i) q^{10} +(-3.47250 + 2.52292i) q^{11} +(-3.21224 + 4.42127i) q^{12} +(0.825990 - 1.13688i) q^{13} +(2.21041 - 1.60595i) q^{14} +(-2.15372 - 0.601250i) q^{15} +(-12.0836 - 8.77924i) q^{16} +(6.10011 - 1.98205i) q^{17} +2.73221i q^{18} +(1.48846 + 4.58100i) q^{19} +(3.28582 - 11.7700i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-11.1534 - 3.62394i) q^{22} +(4.64169 + 6.38874i) q^{23} -9.46709 q^{24} +(4.98244 - 0.418729i) q^{25} +3.83947 q^{26} +(0.587785 + 0.809017i) q^{27} +(5.19751 + 1.68877i) q^{28} +(-1.44955 + 4.46127i) q^{29} +(-2.12977 - 5.72617i) q^{30} +(0.870374 + 2.67873i) q^{31} -21.8745i q^{32} +(-4.08217 + 1.32638i) q^{33} +(14.1776 + 10.3007i) q^{34} +(0.0937129 + 2.23410i) q^{35} +(-4.42127 + 3.21224i) q^{36} +(4.41222 - 6.07290i) q^{37} +(-7.73548 + 10.6470i) q^{38} +(1.13688 - 0.825990i) q^{39} +(19.8411 - 7.37962i) q^{40} +(-5.35535 - 3.89089i) q^{41} +(2.59849 - 0.844300i) q^{42} -6.32527i q^{43} +(-7.24864 - 22.3090i) q^{44} +(-1.86251 - 1.23736i) q^{45} +(-6.66737 + 20.5201i) q^{46} +(3.52407 + 1.14504i) q^{47} +(-8.77924 - 12.0836i) q^{48} -1.00000 q^{49} +(8.92713 + 10.3408i) q^{50} +6.41404 q^{51} +(4.51403 + 6.21303i) q^{52} +(-4.41792 - 1.43547i) q^{53} +(-0.844300 + 2.59849i) q^{54} +(7.52149 - 5.96188i) q^{55} +(2.92549 + 9.00374i) q^{56} +4.81675i q^{57} +(-12.1891 + 3.96049i) q^{58} +(-1.38123 - 1.00352i) q^{59} +(6.76215 - 10.1786i) q^{60} +(8.01186 - 5.82096i) q^{61} +(-4.52331 + 6.22581i) q^{62} +(0.587785 - 0.809017i) q^{63} +(24.1844 - 17.5710i) q^{64} +(-1.73881 + 2.61731i) q^{65} +(-9.48761 - 6.89315i) q^{66} +(-6.86068 + 2.22917i) q^{67} +35.0526i q^{68} +(2.44028 + 7.51042i) q^{69} +(-4.78778 + 3.79501i) q^{70} +(0.0563661 - 0.173477i) q^{71} +(-9.00374 - 2.92549i) q^{72} +(2.72271 + 3.74748i) q^{73} +20.5094 q^{74} +(4.86797 + 1.14142i) q^{75} -26.3235 q^{76} +(2.52292 + 3.47250i) q^{77} +(3.65155 + 1.18646i) q^{78} +(4.14012 - 12.7420i) q^{79} +(27.8187 + 18.4813i) q^{80} +(0.309017 + 0.951057i) q^{81} -18.0861i q^{82} +(-5.86479 + 1.90559i) q^{83} +(4.42127 + 3.21224i) q^{84} +(-13.4425 + 4.99975i) q^{85} +(13.9814 - 10.1581i) q^{86} +(-2.75722 + 3.79498i) q^{87} +(23.8847 - 32.8745i) q^{88} +(4.63594 - 3.36821i) q^{89} +(-0.256044 - 6.10405i) q^{90} +(-1.13688 - 0.825990i) q^{91} +(-41.0444 + 13.3361i) q^{92} +2.81659i q^{93} +(3.12849 + 9.62851i) q^{94} +(-3.75467 - 10.0949i) q^{95} +(6.75960 - 20.8039i) q^{96} +(6.85358 + 2.22686i) q^{97} +(-1.60595 - 2.21041i) q^{98} -4.29225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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