LMFDB - Embedded newform 429.2.bv.a.20.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(20,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 36, 55]))

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

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

chi := DirichletCharacter("429.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bv (of order $60$, degree $16$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$52$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			20.19
Character	$\chi$	$=$	429.20
Dual form			429.2.bv.a.236.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03370 - 0.0541738i) q^{2} +(-1.71154 - 0.265772i) q^{3} +(-0.923448 - 0.0970583i) q^{4} +(2.13376 + 1.08720i) q^{5} +(1.75482 + 0.367448i) q^{6} +(-2.13395 - 2.63521i) q^{7} +(2.99405 + 0.474211i) q^{8} +(2.85873 + 0.909757i) q^{9} +O(q^{10})$	\(q+(-1.03370 - 0.0541738i) q^{2} +(-1.71154 - 0.265772i) q^{3} +(-0.923448 - 0.0970583i) q^{4} +(2.13376 + 1.08720i) q^{5} +(1.75482 + 0.367448i) q^{6} +(-2.13395 - 2.63521i) q^{7} +(2.99405 + 0.474211i) q^{8} +(2.85873 + 0.909757i) q^{9} +(-2.14676 - 1.23943i) q^{10} +(-2.71923 + 1.89890i) q^{11} +(1.55472 + 0.411545i) q^{12} +(2.81890 + 2.24807i) q^{13} +(2.06310 + 2.83962i) q^{14} +(-3.36306 - 2.42788i) q^{15} +(-1.25277 - 0.266284i) q^{16} +(-1.27897 + 1.42044i) q^{17} +(-2.90578 - 1.09528i) q^{18} +(-2.45682 - 6.40024i) q^{19} +(-1.86489 - 1.21108i) q^{20} +(2.95198 + 5.07742i) q^{21} +(2.91373 - 1.81558i) q^{22} +(1.87297 - 3.24408i) q^{23} +(-4.99840 - 1.60736i) q^{24} +(0.431983 + 0.594574i) q^{25} +(-2.79210 - 2.47653i) q^{26} +(-4.65104 - 2.31685i) q^{27} +(1.71483 + 2.64060i) q^{28} +(-4.02756 - 9.04604i) q^{29} +(3.34486 + 2.69189i) q^{30} +(-0.498069 + 0.253779i) q^{31} +(-4.57561 - 1.22603i) q^{32} +(5.15873 - 2.52735i) q^{33} +(1.39902 - 1.39902i) q^{34} +(-1.68833 - 7.94295i) q^{35} +(-2.55159 - 1.11758i) q^{36} +(0.868139 - 2.26158i) q^{37} +(2.19289 + 6.74901i) q^{38} +(-4.22719 - 4.59683i) q^{39} +(5.87302 + 4.26700i) q^{40} +(-4.53928 - 3.67584i) q^{41} +(-2.77639 - 5.40843i) q^{42} +(-9.47899 + 5.47270i) q^{43} +(2.69537 - 1.48961i) q^{44} +(5.11075 + 5.04922i) q^{45} +(-2.11183 + 3.25193i) q^{46} +(-3.77754 - 0.598303i) q^{47} +(2.07339 + 0.788705i) q^{48} +(-0.935210 + 4.39982i) q^{49} +(-0.414330 - 0.638012i) q^{50} +(2.56652 - 2.09122i) q^{51} +(-2.38492 - 2.34957i) q^{52} +(-4.73627 - 1.53891i) q^{53} +(4.68226 + 2.64689i) q^{54} +(-7.86666 + 1.09544i) q^{55} +(-5.13952 - 8.90191i) q^{56} +(2.50394 + 11.6072i) q^{57} +(3.67322 + 9.56906i) q^{58} +(-0.0146499 + 0.0118633i) q^{59} +(2.86997 + 2.56844i) q^{60} +(5.88048 - 6.53094i) q^{61} +(0.528601 - 0.235348i) q^{62} +(-3.70300 - 9.47475i) q^{63} +(7.09951 + 2.30677i) q^{64} +(3.57075 + 7.86155i) q^{65} +(-5.46949 + 2.33304i) q^{66} +(14.0051 - 3.75266i) q^{67} +(1.31893 - 1.18757i) q^{68} +(-4.06784 + 5.05458i) q^{69} +(1.31492 + 8.30207i) q^{70} +(0.0784042 + 1.49604i) q^{71} +(8.12777 + 4.07950i) q^{72} +(0.246729 - 0.0390780i) q^{73} +(-1.01991 + 2.29076i) q^{74} +(-0.581335 - 1.13245i) q^{75} +(1.64755 + 6.14874i) q^{76} +(10.8067 + 3.11358i) q^{77} +(4.12060 + 4.98074i) q^{78} +(3.20883 - 9.87577i) q^{79} +(-2.38360 - 1.93020i) q^{80} +(7.34469 + 5.20150i) q^{81} +(4.49311 + 4.04562i) q^{82} +(8.00617 + 4.07935i) q^{83} +(-2.23320 - 4.97524i) q^{84} +(-4.27331 + 1.64037i) q^{85} +(10.0949 - 5.14360i) q^{86} +(4.48914 + 16.5531i) q^{87} +(-9.04198 + 4.39591i) q^{88} +(-9.00795 + 2.41367i) q^{89} +(-5.00943 - 5.49624i) q^{90} +(-0.0912730 - 12.2257i) q^{91} +(-2.04445 + 2.81395i) q^{92} +(0.919912 - 0.301980i) q^{93} +(3.87242 + 0.823108i) q^{94} +(1.71610 - 16.3276i) q^{95} +(7.50549 + 3.31446i) q^{96} +(-6.41704 - 4.16727i) q^{97} +(1.20508 - 4.49742i) q^{98} +(-9.50107 + 2.95461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−1.03370	−	0.0541738i	−0.730935	−	0.0383067i	−0.316762	−	0.948505i	$-0.602596\pi$
$2$	−1.03370	−	0.0541738i	−0.730935	−	0.0383067i	−0.414173	+	0.910198i	$0.635929\pi$
$3$	−1.71154	−	0.265772i	−0.988157	−	0.153443i
$3$	−1.71154	−	0.265772i	−0.988157	−	0.153443i
$4$	−0.923448	−	0.0970583i	−0.461724	−	0.0485292i
$5$	2.13376	+	1.08720i	0.954245	+	0.486212i	0.860537	−	0.509387i	$-0.170128\pi$
$5$	2.13376	+	1.08720i	0.954245	+	0.486212i	0.0937081	+	0.995600i	$0.470128\pi$
$6$	1.75482	+	0.367448i	0.716400	+	0.150010i
$7$	−2.13395	−	2.63521i	−0.806559	−	0.996017i	−0.999889	−	0.0148835i	$-0.995262\pi$
$7$	−2.13395	−	2.63521i	−0.806559	−	0.996017i	0.193330	−	0.981134i	$-0.438071\pi$
$8$	2.99405	+	0.474211i	1.05856	+	0.167659i
$9$	2.85873	+	0.909757i	0.952910	+	0.303252i
$10$	−2.14676	−	1.23943i	−0.678866	−	0.391943i
$11$	−2.71923	+	1.89890i	−0.819877	+	0.572539i
$11$	−2.71923	+	1.89890i	−0.819877	+	0.572539i
$12$	1.55472	+	0.411545i	0.448810	+	0.118803i
$13$	2.81890	+	2.24807i	0.781822	+	0.623501i
$13$	2.81890	+	2.24807i	0.781822	+	0.623501i
$14$	2.06310	+	2.83962i	0.551388	+	0.758920i
$15$	−3.36306	−	2.42788i	−0.868339	−	0.626877i
$16$	−1.25277	−	0.266284i	−0.313192	−	0.0665709i
$17$	−1.27897	+	1.42044i	−0.310195	+	0.344507i	−0.878004	−	0.478654i	$-0.841125\pi$
$17$	−1.27897	+	1.42044i	−0.310195	+	0.344507i	0.567808	+	0.823161i	$0.307791\pi$
$18$	−2.90578	−	1.09528i	−0.684898	−	0.258160i
$19$	−2.45682	−	6.40024i	−0.563634	−	1.46832i	−0.858518	−	0.512783i	$-0.828615\pi$
$19$	−2.45682	−	6.40024i	−0.563634	−	1.46832i	0.294885	−	0.955533i	$-0.404719\pi$
$20$	−1.86489	−	1.21108i	−0.417003	−	0.270805i
$21$	2.95198	+	5.07742i	0.644175	+	1.10798i
$22$	2.91373	−	1.81558i	0.621209	−	0.387082i
$23$	1.87297	−	3.24408i	0.390541	−	0.676437i	−0.601980	−	0.798511i	$-0.705621\pi$
$23$	1.87297	−	3.24408i	0.390541	−	0.676437i	0.992521	+	0.122074i	$0.0389546\pi$
$24$	−4.99840	−	1.60736i	−1.02030	−	0.328102i
$25$	0.431983	+	0.594574i	0.0863966	+	0.118915i
$26$	−2.79210	−	2.47653i	−0.547577	−	0.485687i
$27$	−4.65104	−	2.31685i	−0.895093	−	0.445879i
$28$	1.71483	+	2.64060i	0.324072	+	0.499027i
$29$	−4.02756	−	9.04604i	−0.747899	−	1.67981i	−0.733292	−	0.679914i	$-0.762017\pi$
$29$	−4.02756	−	9.04604i	−0.747899	−	1.67981i	−0.0146069	−	0.999893i	$-0.504650\pi$
$30$	3.34486	+	2.69189i	0.610685	+	0.491469i
$31$	−0.498069	+	0.253779i	−0.0894559	+	0.0455800i	−0.498146	−	0.867093i	$-0.665986\pi$
$31$	−0.498069	+	0.253779i	−0.0894559	+	0.0455800i	0.408690	+	0.912673i	$0.365986\pi$
$32$	−4.57561	−	1.22603i	−0.808861	−	0.216734i
$33$	5.15873	−	2.52735i	0.898020	−	0.439954i
$34$	1.39902	−	1.39902i	0.239929	−	0.239929i
$35$	−1.68833	−	7.94295i	−0.285379	−	1.34260i
$36$	−2.55159	−	1.11758i	−0.425265	−	0.186263i
$37$	0.868139	−	2.26158i	0.142721	−	0.371801i	−0.843524	−	0.537092i	$-0.819523\pi$
$37$	0.868139	−	2.26158i	0.142721	−	0.371801i	0.986245	+	0.165291i	$0.0528562\pi$
$38$	2.19289	+	6.74901i	0.355733	+	1.09483i
$39$	−4.22719	−	4.59683i	−0.676892	−	0.736083i
$40$	5.87302	+	4.26700i	0.928606	+	0.674671i
$41$	−4.53928	−	3.67584i	−0.708917	−	0.574070i	0.205591	−	0.978638i	$-0.434088\pi$
$41$	−4.53928	−	3.67584i	−0.708917	−	0.574070i	−0.914508	+	0.404568i	$0.867422\pi$
$42$	−2.77639	−	5.40843i	−0.428407	−	0.834539i
$43$	−9.47899	+	5.47270i	−1.44553	+	0.834578i	−0.998211	−	0.0597952i	$-0.980955\pi$
$43$	−9.47899	+	5.47270i	−1.44553	+	0.834578i	−0.447321	+	0.894373i	$0.647622\pi$
$44$	2.69537	−	1.48961i	0.406342	−	0.224567i
$45$	5.11075	+	5.04922i	0.761865	+	0.752694i
$46$	−2.11183	+	3.25193i	−0.311372	+	0.479471i
$47$	−3.77754	−	0.598303i	−0.551010	−	0.0872714i	−0.125280	−	0.992121i	$-0.539983\pi$
$47$	−3.77754	−	0.598303i	−0.551010	−	0.0872714i	−0.425730	+	0.904850i	$0.639983\pi$
$48$	2.07339	+	0.788705i	0.299268	+	0.113840i
$49$	−0.935210	+	4.39982i	−0.133601	+	0.628546i
$50$	−0.414330	−	0.638012i	−0.0585951	−	0.0902285i
$51$	2.56652	−	2.09122i	0.359384	−	0.292830i
$52$	−2.38492	−	2.34957i	−0.330728	−	0.325827i
$53$	−4.73627	−	1.53891i	−0.650577	−	0.211385i	−0.0349085	−	0.999391i	$-0.511114\pi$
$53$	−4.73627	−	1.53891i	−0.650577	−	0.211385i	−0.615669	+	0.788005i	$0.711114\pi$
$54$	4.68226	+	2.64689i	0.637175	+	0.360196i
$55$	−7.86666	+	1.09544i	−1.06074	+	0.147709i
$56$	−5.13952	−	8.90191i	−0.686798	−	1.18957i
$57$	2.50394	+	11.6072i	0.331656	+	1.53741i
$58$	3.67322	+	9.56906i	0.482317	+	1.25648i
$59$	−0.0146499	+	0.0118633i	−0.00190726	+	0.00154447i	−0.630274	−	0.776373i	$-0.717057\pi$
$59$	−0.0146499	+	0.0118633i	−0.00190726	+	0.00154447i	0.628366	+	0.777918i	$0.283724\pi$
$60$	2.86997	+	2.56844i	0.370511	+	0.331584i
$61$	5.88048	−	6.53094i	0.752919	−	0.836201i	−0.237915	−	0.971286i	$-0.576464\pi$
$61$	5.88048	−	6.53094i	0.752919	−	0.836201i	0.990834	+	0.135085i	$0.0431307\pi$
$62$	0.528601	−	0.235348i	0.0671324	−	0.0298893i
$63$	−3.70300	−	9.47475i	−0.466534	−	1.19371i
$64$	7.09951	+	2.30677i	0.887439	+	0.288347i
$65$	3.57075	+	7.86155i	0.442897	+	0.975105i
$66$	−5.46949	+	2.33304i	−0.673247	+	0.287178i
$67$	14.0051	−	3.75266i	1.71100	−	0.458460i	0.735328	−	0.677711i	$-0.237028\pi$
$67$	14.0051	−	3.75266i	1.71100	−	0.458460i	0.975668	+	0.219251i	$0.0703615\pi$
$68$	1.31893	−	1.18757i	0.159943	−	0.144014i
$69$	−4.06784	+	5.05458i	−0.489711	+	0.608500i
$70$	1.31492	+	8.30207i	0.157163	+	0.992287i
$71$	0.0784042	+	1.49604i	0.00930486	+	0.177547i	0.999328	+	0.0366449i	$0.0116671\pi$
$71$	0.0784042	+	1.49604i	0.00930486	+	0.177547i	−0.990023	+	0.140902i	$0.955000\pi$
$72$	8.12777	+	4.07950i	0.957867	+	0.480774i
$73$	0.246729	−	0.0390780i	0.0288775	−	0.00457374i	−0.141979	−	0.989870i	$-0.545347\pi$
$73$	0.246729	−	0.0390780i	0.0288775	−	0.00457374i	0.170856	+	0.985296i	$0.445347\pi$
$74$	−1.01991	+	2.29076i	−0.118562	+	0.266295i
$75$	−0.581335	−	1.13245i	−0.0671268	−	0.130764i
$76$	1.64755	+	6.14874i	0.188987	+	0.705309i
$77$	10.8067	+	3.11358i	1.23154	+	0.354825i
$78$	4.12060	+	4.98074i	0.466567	+	0.563958i
$79$	3.20883	−	9.87577i	0.361022	−	1.11111i	−0.591413	−	0.806369i	$-0.701430\pi$
$79$	3.20883	−	9.87577i	0.361022	−	1.11111i	0.952435	−	0.304742i	$-0.0985703\pi$
$80$	−2.38360	−	1.93020i	−0.266494	−	0.215803i
$81$	7.34469	+	5.20150i	0.816076	+	0.577944i
$82$	4.49311	+	4.04562i	0.496181	+	0.446763i
$83$	8.00617	+	4.07935i	0.878791	+	0.447766i	0.834343	−	0.551245i	$-0.185847\pi$
$83$	8.00617	+	4.07935i	0.878791	+	0.447766i	0.0444478	+	0.999012i	$0.485847\pi$
$84$	−2.23320	−	4.97524i	−0.243662	−	0.542844i
$85$	−4.27331	+	1.64037i	−0.463506	+	0.177923i
$86$	10.0949	−	5.14360i	1.08856	−	0.554648i
$87$	4.48914	+	16.5531i	0.481286	+	1.77467i
$88$	−9.04198	+	4.39591i	−0.963878	+	0.468606i
$89$	−9.00795	+	2.41367i	−0.954841	+	0.255849i	−0.702415	−	0.711767i	$-0.747895\pi$
$89$	−9.00795	+	2.41367i	−0.954841	+	0.255849i	−0.252426	+	0.967616i	$0.581228\pi$
$90$	−5.00943	−	5.49624i	−0.528041	−	0.579354i
$91$	−0.0912730	−	12.2257i	−0.00956801	−	1.28160i
$92$	−2.04445	+	2.81395i	−0.213149	+	0.293375i
$93$	0.919912	−	0.301980i	0.0953904	−	0.0313139i
$94$	3.87242	+	0.823108i	0.399409	+	0.0848971i
$95$	1.71610	−	16.3276i	0.176068	−	1.67518i
$96$	7.50549	+	3.31446i	0.766026	+	0.338281i
$97$	−6.41704	−	4.16727i	−0.651552	−	0.423123i	0.176094	−	0.984373i	$-0.443654\pi$
$97$	−6.41704	−	4.16727i	−0.651552	−	0.423123i	−0.827646	+	0.561251i	$0.810320\pi$
$98$	1.20508	−	4.49742i	0.121731	−	0.454308i
$99$	−9.50107	+	2.95461i	−0.954893	+	0.296949i
$100$	−0.341206	−	0.590986i	−0.0341206	−	0.0590986i
$101$	−1.43997	−	1.59925i	−0.143283	−	0.159131i	0.667232	−	0.744850i	$-0.267479\pi$
$101$	−1.43997	−	1.59925i	−0.143283	−	0.159131i	−0.810514	+	0.585719i	$0.800812\pi$
$102$	−2.76629	+	2.02265i	−0.273903	+	0.200272i
$103$	−5.63047	+	7.74967i	−0.554786	+	0.763598i	−0.990652	−	0.136414i	$-0.956442\pi$
$103$	−5.63047	+	7.74967i	−0.554786	+	0.763598i	0.435866	+	0.900012i	$0.356442\pi$
$104$	7.37388	+	8.06758i	0.723068	+	0.791091i
$105$	0.778626	+	14.0434i	0.0759861	+	1.37049i
$106$	4.81250	+	1.84735i	0.467432	+	0.179430i
$107$	2.48019	−	0.260679i	0.239769	−	0.0252008i	0.0161184	−	0.999870i	$-0.494869\pi$
$107$	2.48019	−	0.260679i	0.239769	−	0.0252008i	0.223651	+	0.974669i	$0.428202\pi$
$108$	4.07013	+	2.59092i	0.391648	+	0.249311i
$109$	−8.72629	−	8.72629i	−0.835827	−	0.835827i	0.152480	−	0.988307i	$-0.451274\pi$
$109$	−8.72629	−	8.72629i	−0.835827	−	0.835827i	−0.988307	+	0.152480i	$0.951274\pi$
$110$	8.19109	−	0.706183i	0.780990	−	0.0673319i
$111$	−2.08692	+	3.64005i	−0.198081	+	0.345499i
$112$	1.97163	+	3.86954i	0.186302	+	0.365638i
$113$	−4.96351	+	11.1482i	−0.466927	+	1.04874i	0.514603	+	0.857429i	$0.327939\pi$
$113$	−4.96351	+	11.1482i	−0.466927	+	1.04874i	−0.981530	+	0.191307i	$0.938727\pi$
$114$	−1.95951	−	12.1340i	−0.183525	−	1.13645i
$115$	7.52344	−	4.88578i	0.701564	−	0.455601i
$116$	2.84125	+	8.74446i	0.263803	+	0.811902i
$117$	6.01329	+	8.99113i	0.555929	+	0.831230i
$118$	0.0157863	−	0.0114694i	0.00145325	−	0.00105585i
$119$	6.47242	+	0.339205i	0.593325	+	0.0310949i
$120$	−8.91785	−	8.86401i	−0.814085	−	0.809170i
$121$	3.78837	−	10.3271i	0.344397	−	0.938824i
$122$	−6.43245	+	6.43245i	−0.582366	+	0.582366i
$123$	6.79223	+	7.49775i	0.612434	+	0.676050i
$124$	0.484572	−	0.186010i	0.0435159	−	0.0167042i
$125$	−1.59780	−	10.0881i	−0.142912	−	0.902308i
$126$	3.31450	+	9.99463i	0.295279	+	0.890392i
$127$	−1.80094	+	8.47274i	−0.159807	+	0.751834i	0.823124	+	0.567862i	$0.192229\pi$
$127$	−1.80094	+	8.47274i	−0.159807	+	0.751834i	−0.982931	+	0.183973i	$0.941104\pi$
$128$	1.63099	+	0.626079i	0.144161	+	0.0553380i
$129$	17.6781	−	6.84749i	1.55647	−	0.602888i
$130$	−3.26518	−	8.31990i	−0.286375	−	0.729704i
$131$		−	10.2502i		−	0.895561i	−0.894144	−	0.447780i	$-0.852215\pi$
$131$		−	10.2502i		−	0.895561i	0.894144	−	0.447780i	$-0.147785\pi$
$132$	−5.00912	+	1.83317i	−0.435988	+	0.159557i
$133$	−11.6233	+	20.1321i	−1.00786	+	1.74567i
$134$	−14.6803	+	3.12040i	−1.26819	+	0.269562i
$135$	−7.40530	−	10.0002i	−0.637347	−	0.860683i
$136$	−4.50288	+	3.64636i	−0.386119	+	0.312673i
$137$	−6.91834	+	0.362575i	−0.591074	+	0.0309768i	−0.345528	−	0.938408i	$-0.612300\pi$
$137$	−6.91834	+	0.362575i	−0.591074	+	0.0309768i	−0.245545	+	0.969385i	$0.578967\pi$
$138$	4.47874	−	5.00454i	0.381256	−	0.426015i
$139$	−1.00748	+	9.58557i	−0.0854537	+	0.813037i	0.864916	+	0.501916i	$0.167371\pi$
$139$	−1.00748	+	9.58557i	−0.0854537	+	0.813037i	−0.950370	+	0.311122i	$0.899295\pi$
$140$	0.788152	+	7.49877i	0.0666110	+	0.633762i
$141$	6.30639	+	2.02798i	0.531094	+	0.170787i
$142$		−	1.55070i		−	0.130132i
$143$	−11.9341	−	0.760190i	−0.997977	−	0.0635703i
$144$	−3.33907	−	1.90095i	−0.278256	−	0.158412i
$145$	1.24106	−	23.6808i	0.103064	−	1.96659i
$146$	−0.257160	+	0.0270286i	−0.0212827	+	0.00223691i
$147$	2.77000	−	7.28191i	0.228465	−	0.600602i
$148$	−1.02119	+	2.00419i	−0.0839410	+	0.164743i
$149$	−1.05224	−	20.0779i	−0.0862028	−	1.64485i	−0.609564	−	0.792737i	$-0.708655\pi$
$149$	−1.05224	−	20.0779i	−0.0862028	−	1.64485i	0.523361	−	0.852111i	$-0.324678\pi$
$150$	0.539576	+	1.20210i	0.0440562	+	0.0981510i
$151$	−0.263419	+	1.66316i	−0.0214367	+	0.135346i	−0.996086	−	0.0883938i	$-0.971827\pi$
$151$	−0.263419	+	1.66316i	−0.0214367	+	0.135346i	0.974649	+	0.223740i	$0.0718266\pi$
$152$	−4.32079	−	20.3277i	−0.350462	−	1.64879i
$153$	−4.94848	+	2.89710i	−0.400061	+	0.234217i
$154$	−11.0022	−	3.80394i	−0.886582	−	0.306530i
$155$	−1.33867			−0.107524
$156$	3.45743	+	4.65522i	0.276816	+	0.372716i
$157$	−0.555574	+	0.403648i	−0.0443396	+	0.0322146i	−0.609734	−	0.792606i	$-0.708724\pi$
$157$	−0.555574	+	0.403648i	−0.0443396	+	0.0322146i	0.565395	+	0.824820i	$0.308724\pi$
$158$	−3.85197	+	10.0347i	−0.306446	+	0.798320i
$159$	7.69732	+	3.89267i	0.610437	+	0.308709i
$160$	−8.43029	−	7.59067i	−0.666473	−	0.600095i
$161$	−12.5457	+	1.98704i	−0.988737	+	0.156601i
$162$	−7.31040	−	5.77467i	−0.574359	−	0.453701i
$163$	−5.58181	+	8.59524i	−0.437201	+	0.673231i	−0.986753	−	0.162228i	$-0.948132\pi$
$163$	−5.58181	+	8.59524i	−0.437201	+	0.673231i	0.549552	+	0.835460i	$0.314799\pi$
$164$	3.83502	+	3.83502i	0.299465	+	0.299465i
$165$	13.7552	+	0.215851i	1.07084	+	0.0168040i
$166$	−8.05496	−	4.65053i	−0.625186	−	0.360951i
$167$	0.187878	−	3.58492i	0.0145384	−	0.277409i	−0.981681	−	0.190533i	$-0.938978\pi$
$167$	0.187878	−	3.58492i	0.0145384	−	0.277409i	0.996219	−	0.0868760i	$-0.0276884\pi$
$168$	6.43062	+	16.6019i	0.496133	+	1.28087i
$169$	2.89241	+	12.6741i	0.222493	+	0.974934i
$170$	4.50618	−	1.46415i	0.345608	−	0.112295i
$171$	−1.20073	−	20.5317i	−0.0918223	−	1.57010i
$172$	9.28452	−	4.13374i	0.707938	−	0.315194i
$173$	13.2058	+	5.87959i	1.00402	+	0.447017i	0.841830	−	0.539743i	$-0.181478\pi$
$173$	13.2058	+	5.87959i	1.00402	+	0.447017i	0.162187	+	0.986760i	$0.448145\pi$
$174$	−3.74367	−	17.3541i	−0.283807	−	1.31561i
$175$	0.644997	−	2.40716i	0.0487572	−	0.181964i
$176$	3.91220	−	1.65479i	0.294893	−	0.124735i
$177$	0.0282269	−	0.0164110i	0.00212166	−	0.00123352i
$178$	9.44226	−	2.00701i	0.707727	−	0.150432i
$179$	1.55119	+	14.7586i	0.115941	+	1.10311i	0.885534	+	0.464574i	$0.153792\pi$
$179$	1.55119	+	14.7586i	0.115941	+	1.10311i	−0.769593	+	0.638535i	$0.779541\pi$
$180$	−4.22944	−	5.15874i	−0.315244	−	0.384509i
$181$	22.7790	−	7.40133i	1.69315	−	0.550137i	0.705758	−	0.708453i	$-0.250606\pi$
$181$	22.7790	−	7.40133i	1.69315	−	0.550137i	0.987389	+	0.158316i	$0.0506064\pi$
$182$	−0.567962	+	12.6426i	−0.0421002	+	0.937131i
$183$	−11.8004	+	9.61509i	−0.872312	+	0.710768i
$184$	7.14615	−	8.82475i	0.526821	−	0.650570i
$185$	4.31119	−	3.88182i	0.316965	−	0.285397i
$186$	−0.967270	+	0.262321i	−0.0709237	+	0.0192343i
$187$	0.780535	−	6.29112i	0.0570784	−	0.460052i
$188$	3.43029	+	0.919143i	0.250179	+	0.0670354i
$189$	3.81971	+	17.2005i	0.277843	+	1.25116i
$190$	−2.65846	+	16.7849i	−0.192865	+	1.21770i
$191$	23.2311	+	2.44169i	1.68094	+	0.176674i	0.896353	−	0.443341i	$-0.146207\pi$
$191$	23.2311	+	2.44169i	1.68094	+	0.176674i	0.784590	+	0.620015i	$0.212873\pi$
$192$	−11.5380	−	5.83498i	−0.832685	−	0.421103i
$193$	−5.68080	+	3.68915i	−0.408913	+	0.265551i	−0.732663	−	0.680592i	$-0.761723\pi$
$193$	−5.68080	+	3.68915i	−0.408913	+	0.265551i	0.323750	+	0.946143i	$0.395056\pi$
$194$	6.40752	+	4.65534i	0.460033	+	0.334234i
$195$	−4.02210	−	14.4043i	−0.288028	−	1.03152i
$196$	1.29066	−	3.97223i	0.0921898	−	0.283731i
$197$	−5.96812	−	22.2733i	−0.425211	−	1.58691i	−0.763462	−	0.645853i	$-0.776502\pi$
$197$	−5.96812	−	22.2733i	−0.425211	−	1.58691i	0.338251	−	0.941056i	$-0.390165\pi$
$198$	9.98129	−	2.53946i	0.709340	−	0.180472i
$199$	−5.61913	+	3.24420i	−0.398329	+	0.229976i	−0.685763	−	0.727825i	$-0.740531\pi$
$199$	−5.61913	+	3.24420i	−0.398329	+	0.229976i	0.287434	+	0.957801i	$0.407198\pi$
$200$	1.01143	+	1.98504i	0.0715187	+	0.140363i
$201$	−24.9676	+	2.70066i	−1.76108	+	0.190490i
$202$	1.40186	+	1.73115i	0.0986344	+	0.121803i
$203$	−15.2436	+	29.9173i	−1.06989	+	2.09978i
$204$	−2.57301	+	1.68203i	−0.180147	+	0.117766i
$205$	−5.68934	−	12.7785i	−0.397361	−	0.892487i
$206$	6.24003	−	7.70579i	0.434763	−	0.536888i
$207$	8.30564	−	7.57000i	0.577282	−	0.526151i
$208$	−2.93280	−	3.56693i	−0.203353	−	0.247322i
$209$	18.8341	+	12.7384i	1.30278	+	0.881136i
$210$	−0.0440809	−	14.5588i	−0.00304187	−	1.00465i
$211$	0.910094	+	1.01076i	0.0626535	+	0.0695837i	0.773657	−	0.633605i	$-0.218426\pi$
$211$	0.910094	+	1.01076i	0.0626535	+	0.0695837i	−0.711003	+	0.703189i	$0.751759\pi$
$212$	4.22434	+	1.88080i	0.290129	+	0.129174i
$213$	0.263413	−	2.58137i	0.0180488	−	0.176873i
$214$	−2.57789	+	0.135102i	−0.176221	+	0.00923535i
$215$	−26.1758	+	1.37182i	−1.78517	+	0.0935570i
$216$	−12.8268	−	9.14236i	−0.872752	−	0.622058i
$217$	1.73162	+	0.770966i	0.117550	+	0.0523366i
$218$	8.54760	+	9.49308i	0.578917	+	0.642952i
$219$	−0.432672	+	0.00131004i	−0.0292373	+	8.85242e-5i
$220$	7.37077	−	0.248054i	0.496937	−	0.0167238i
$221$	−6.79852	+	1.12887i	−0.457318	+	0.0759360i
$222$	2.35444	−	3.64966i	0.158019	−	0.244949i
$223$	11.0879	−	13.6925i	0.742503	−	0.916915i	−0.256262	−	0.966607i	$-0.582491\pi$
$223$	11.0879	−	13.6925i	0.742503	−	0.916915i	0.998765	+	0.0496926i	$0.0158242\pi$
$224$	6.53328	+	14.6740i	0.436523	+	0.980448i
$225$	0.694006	+	2.09273i	0.0462671	+	0.139515i
$226$	5.73470	−	11.2550i	0.381467	−	0.748671i
$227$	−3.05588	−	3.77370i	−0.202826	−	0.250469i	0.665576	−	0.746330i	$-0.268186\pi$
$227$	−3.05588	−	3.77370i	−0.202826	−	0.250469i	−0.868402	+	0.495861i	$0.834853\pi$
$228$	−1.18569	−	10.9617i	−0.0785240	−	0.725955i
$229$	6.17380	+	12.1168i	0.407976	+	0.800698i	0.999986	−	0.00523227i	$-0.00166549\pi$
$229$	6.17380	+	12.1168i	0.407976	+	0.800698i	−0.592010	+	0.805930i	$0.701665\pi$
$230$	−8.04164	+	4.64284i	−0.530250	+	0.306140i
$231$	−17.6686	−	8.20113i	−1.16251	−	0.539594i
$232$	−7.76898	−	28.9942i	−0.510059	−	1.90356i
$233$	4.13317	−	12.7206i	0.270773	−	0.833353i	−0.719534	−	0.694457i	$-0.755645\pi$
$233$	4.13317	−	12.7206i	0.270773	−	0.833353i	0.990307	−	0.138896i	$-0.0443554\pi$
$234$	−5.72884	−	9.61987i	−0.374506	−	0.628870i
$235$	−7.40987	−	5.38358i	−0.483366	−	0.351186i
$236$	0.0146799	−	0.00953324i	0.000955580	−	0.000620561i
$237$	−8.11674	+	16.0499i	−0.527239	+	1.04256i
$238$	−6.67214	−	0.701271i	−0.432491	−	0.0454566i
$239$	0.445062	−	2.81001i	0.0287887	−	0.181765i	−0.969104	−	0.246653i	$-0.920669\pi$
$239$	0.445062	−	2.81001i	0.0287887	−	0.181765i	0.997893	+	0.0648886i	$0.0206692\pi$
$240$	3.56662	+	3.93710i	0.230225	+	0.254139i
$241$	−22.0899	−	5.91898i	−1.42294	−	0.381275i	−0.536413	−	0.843956i	$-0.680221\pi$
$241$	−22.0899	−	5.91898i	−1.42294	−	0.381275i	−0.886525	+	0.462681i	$0.846888\pi$
$242$	−4.47549	+	10.4698i	−0.287695	+	0.673026i
$243$	−11.1883	−	10.8546i	−0.717730	−	0.696321i
$244$	−6.06420	+	5.46023i	−0.388221	+	0.349556i
$245$	−6.77901	+	8.37138i	−0.433095	+	0.534828i
$246$	−6.61493	−	8.11837i	−0.421752	−	0.517608i
$247$	7.46262	−	23.5647i	0.474835	−	1.49939i
$248$	−1.61159	+	0.523637i	−0.102336	+	0.0332510i
$249$	−12.6187	−	9.10977i	−0.799677	−	0.577308i
$250$	1.10513	+	10.5146i	0.0698946	+	0.665003i
$251$	−4.60613	+	0.979063i	−0.290736	+	0.0617979i	−0.350971	−	0.936386i	$-0.614148\pi$
$251$	−4.60613	+	0.979063i	−0.290736	+	0.0617979i	0.0602347	+	0.998184i	$0.480815\pi$
$252$	2.49992	+	9.10884i	0.157480	+	0.573803i
$253$	1.06715	+	12.3780i	0.0670910	+	0.778195i
$254$	2.32062	−	8.66069i	0.145609	−	0.543420i
$255$	7.74990	−	1.67183i	0.485318	−	0.104694i
$256$	−15.2910	−	6.80801i	−0.955689	−	0.425500i
$257$	−14.1553	+	6.30236i	−0.882986	+	0.393131i	−0.797578	−	0.603216i	$-0.793886\pi$
$257$	−14.1553	+	6.30236i	−0.882986	+	0.393131i	−0.0854074	+	0.996346i	$0.527219\pi$
$258$	−18.6448	+	6.12054i	−1.16077	+	0.381048i
$259$	−7.81231	+	2.53837i	−0.485433	+	0.157727i
$260$	−2.53437	−	7.60630i	−0.157175	−	0.471723i
$261$	−3.28401	−	29.5243i	−0.203275	−	1.82751i
$262$	−0.555290	+	10.5956i	−0.0343059	+	0.654596i
$263$	1.65814	+	0.957328i	0.102245	+	0.0590313i	0.550251	−	0.834999i	$-0.314532\pi$
$263$	1.65814	+	0.957328i	0.102245	+	0.0590313i	−0.448005	+	0.894031i	$0.647865\pi$
$264$	16.6440	−	5.12067i	1.02437	−	0.315156i
$265$	−8.43295	−	8.43295i	−0.518032	−	0.518032i
$266$	13.1056	−	20.1808i	0.803554	−	1.23736i
$267$	16.0589	−	1.73704i	0.982792	−	0.106305i
$268$	−13.2972	+	2.10607i	−0.812257	+	0.128649i
$269$	1.22035	+	1.09881i	0.0744062	+	0.0669956i	0.705495	−	0.708715i	$-0.250725\pi$
$269$	1.22035	+	1.09881i	0.0744062	+	0.0669956i	−0.631089	+	0.775711i	$0.717392\pi$
$270$	7.11309	+	10.7384i	0.432889	+	0.653518i
$271$	−2.08309	+	5.42662i	−0.126538	+	0.329644i	−0.982185	−	0.187917i	$-0.939826\pi$
$271$	−2.08309	+	5.42662i	−0.126538	+	0.329644i	0.855647	+	0.517561i	$0.173160\pi$
$272$	1.98049	−	1.43891i	0.120085	−	0.0872466i
$273$	−3.09302	+	20.9490i	−0.187198	+	1.26789i
$274$	7.17111			0.433223
$275$	−2.30369	−	0.796488i	−0.138918	−	0.0480300i
$276$	4.24703	−	4.27283i	0.255641	−	0.257194i
$277$	1.92979	+	9.07895i	0.115950	+	0.545501i	0.997326	+	0.0730853i	$0.0232845\pi$
$277$	1.92979	+	9.07895i	0.115950	+	0.545501i	−0.881376	+	0.472416i	$0.843382\pi$
$278$	1.56072	−	9.85400i	0.0936058	−	0.591004i
$279$	−1.65472	+	0.272364i	−0.0990657	+	0.0163060i
$280$	−1.28830	−	24.5822i	−0.0769907	−	1.46907i
$281$	9.11662	−	17.8924i	0.543852	−	1.06737i	−0.441568	−	0.897228i	$-0.645578\pi$
$281$	9.11662	−	17.8924i	0.543852	−	1.06737i	0.985420	−	0.170141i	$-0.0544224\pi$
$282$	−6.40903	−	2.43796i	−0.381652	−	0.145178i
$283$	14.1618	−	1.48846i	0.841831	−	0.0884801i	0.326211	−	0.945297i	$-0.394228\pi$
$283$	14.1618	−	1.48846i	0.841831	−	0.0884801i	0.515621	+	0.856817i	$0.327561\pi$
$284$	0.0728010	−	1.38913i	0.00431994	−	0.0824294i
$285$	−7.27659	+	27.4893i	−0.431028	+	1.62832i
$286$	12.2950	+	1.43232i	0.727021	+	0.0846949i
$287$			19.8061i			1.16911i
$288$	−11.9650	−	7.66758i	−0.705047	−	0.451817i
$289$	1.39510	+	13.2735i	0.0820647	+	0.780793i
$290$	−2.56576	+	24.4116i	−0.150667	+	1.43350i
$291$	9.87547	+	8.83792i	0.578910	+	0.518088i
$292$	−0.231634	+	0.0121394i	−0.0135554	+	0.000710407i
$293$	−5.61294	+	4.54527i	−0.327911	+	0.265537i	−0.779111	−	0.626885i	$-0.784329\pi$
$293$	−5.61294	+	4.54527i	−0.327911	+	0.265537i	0.451200	+	0.892423i	$0.350996\pi$
$294$	−3.25783	+	7.37723i	−0.190000	+	0.430249i
$295$	−0.0441573	+	0.00938591i	−0.00257093	+	0.000546469i
$296$	3.67172	−	6.35960i	0.213414	−	0.369644i
$297$	17.0467	−	2.53181i	0.989150	−	0.146910i
$298$			20.8115i			1.20558i
$299$	12.5726	−	4.93418i	0.727093	−	0.285351i
$300$	0.426920	+	1.10218i	0.0246482	+	0.0636343i
$301$	34.6494	+	13.3007i	1.99716	+	0.766638i
$302$	0.362395	−	1.70493i	0.0208535	−	0.0981079i
$303$	2.03953	+	3.11988i	0.117168	+	0.179233i
$304$	1.37354	+	8.67222i	0.0787782	+	0.497386i
$305$	19.6480	−	7.54216i	1.12504	−	0.431863i
$306$	5.27218	−	2.72665i	0.301390	−	0.155872i
$307$	7.04209	−	7.04209i	0.401913	−	0.401913i	−0.476993	−	0.878907i	$-0.658273\pi$
$307$	7.04209	−	7.04209i	0.401913	−	0.401913i	0.878907	+	0.476993i	$0.158273\pi$
$308$	−9.67723	−	3.92411i	−0.551411	−	0.223597i
$309$	11.6964	−	11.7674i	0.665385	−	0.669427i
$310$	1.38378	+	0.0725207i	0.0785933	+	0.00411890i
$311$	−16.1380	+	11.7249i	−0.915101	+	0.664860i	−0.942300	−	0.334770i	$-0.891341\pi$
$311$	−16.1380	+	11.7249i	−0.915101	+	0.664860i	0.0271986	+	0.999630i	$0.491341\pi$
$312$	−10.4765	−	15.7677i	−0.593118	−	0.892673i
$313$	10.0580	+	30.9554i	0.568513	+	1.74970i	0.657277	+	0.753649i	$0.271708\pi$
$313$	10.0580	+	30.9554i	0.568513	+	1.74970i	−0.0887642	+	0.996053i	$0.528292\pi$
$314$	0.596162	−	0.387152i	0.0336434	−	0.0218483i
$315$	2.39968	−	24.2427i	0.135207	−	1.36592i
$316$	−3.92171	+	8.80832i	−0.220614	+	0.495506i
$317$	5.84518	+	11.4718i	0.328298	+	0.644321i	0.994875	−	0.101116i	$-0.0322412\pi$
$317$	5.84518	+	11.4718i	0.328298	+	0.644321i	−0.666577	+	0.745436i	$0.732241\pi$
$318$	−7.74582	−	4.44083i	−0.434364	−	0.249030i
$319$	28.1293	+	16.9503i	1.57494	+	0.949035i
$320$	12.6407	+	12.6407i	0.706637	+	0.706637i
$321$	−4.31423	−	0.213003i	−0.240797	−	0.0118887i
$322$	13.0761	−	1.37435i	0.728701	−	0.0765896i
$323$	12.2333	+	4.69594i	0.680681	+	0.261289i
$324$	−6.27759	−	5.51618i	−0.348755	−	0.306454i
$325$	−0.118923	+	2.64717i	−0.00659666	+	0.146839i
$326$	6.23554	−	8.58249i	0.345355	−	0.475340i
$327$	12.6162	+	17.2546i	0.697676	+	0.954180i
$328$	−11.8477	−	13.1582i	−0.654181	−	0.726542i
$329$	6.48443	+	11.2314i	0.357498	+	0.619205i
$330$	−14.2070	−	0.968298i	−0.782072	−	0.0533030i
$331$	4.68511	−	17.4851i	0.257517	−	0.961066i	−0.709156	−	0.705051i	$-0.750924\pi$
$331$	4.68511	−	17.4851i	0.257517	−	0.961066i	0.966673	−	0.256014i	$-0.0824094\pi$
$332$	−6.99734	−	4.54413i	−0.384029	−	0.249391i
$333$	4.53926	−	5.67545i	0.248750	−	0.311013i
$334$	−0.388417	+	3.69554i	−0.0212533	+	0.202211i
$335$	33.9634	+	7.21915i	1.85562	+	0.394424i
$336$	−2.34611	−	7.14688i	−0.127991	−	0.389894i
$337$	−11.9896	+	16.5022i	−0.653112	+	0.898932i	−0.999229	−	0.0392594i	$-0.987500\pi$
$337$	−11.9896	+	16.5022i	−0.653112	+	0.898932i	0.346117	+	0.938191i	$0.387500\pi$
$338$	−2.30327	−	13.2579i	−0.125281	−	0.721136i
$339$	11.4581	−	17.7614i	0.622319	−	0.964669i
$340$	4.10539	−	1.10004i	0.222646	−	0.0596579i
$341$	0.872462	−	1.63586i	0.0472465	−	0.0885870i
$342$	0.128916	+	21.2886i	0.00697096	+	1.15115i
$343$	−7.55896	+	3.85148i	−0.408145	+	0.207960i
$344$	−30.9758	+	11.8905i	−1.67010	+	0.641092i
$345$	−14.1752	+	6.36268i	−0.763165	+	0.342555i
$346$	−13.3323	−	6.79313i	−0.716747	−	0.365201i
$347$	7.17778	+	6.46290i	0.385323	+	0.346947i	0.838915	−	0.544263i	$-0.183191\pi$
$347$	7.17778	+	6.46290i	0.385323	+	0.346947i	−0.453591	+	0.891210i	$0.649857\pi$
$348$	−2.53888	−	15.7216i	−0.136098	−	0.842766i
$349$	−22.6579	−	18.3480i	−1.21285	−	0.982146i	−0.999987	−	0.00506314i	$-0.998388\pi$
$349$	−22.6579	−	18.3480i	−1.21285	−	0.982146i	−0.212862	−	0.977082i	$-0.568278\pi$
$350$	−0.797137	+	2.45334i	−0.0426088	+	0.131136i
$351$	−7.90239	−	16.9868i	−0.421798	−	0.906690i
$352$	14.7702	−	5.35476i	0.787255	−	0.285410i
$353$	2.01519	+	7.52078i	0.107258	+	0.400290i	0.998591	−	0.0530568i	$-0.0168964\pi$
$353$	2.01519	+	7.52078i	0.107258	+	0.400290i	−0.891334	+	0.453347i	$0.850230\pi$
$354$	−0.0300671	+	0.0154348i	−0.00159805	+	0.000820350i
$355$	−1.45921	+	3.27743i	−0.0774466	+	0.173948i
$356$	8.55265	−	1.35461i	0.453289	−	0.0717940i
$357$	−10.9876	−	2.30075i	−0.581528	−	0.121768i
$358$	−0.803932	−	15.3399i	−0.0424891	−	0.810741i
$359$	−0.962759	−	6.07862i	−0.0508125	−	0.320817i	−0.999982	−	0.00605108i	$-0.998074\pi$
$359$	−0.962759	−	6.07862i	−0.0508125	−	0.320817i	0.949169	−	0.314766i	$-0.101926\pi$
$360$	12.9074	+	17.5412i	0.680282	+	0.924503i
$361$	−20.8073	+	18.7350i	−1.09512	+	0.986053i
$362$	−23.9475	+	6.41672i	−1.25865	+	0.337255i
$363$	−9.22859	+	16.6683i	−0.484375	+	0.874860i
$364$	−1.10232	+	11.2986i	−0.0577771	+	0.592209i
$365$	0.568946	+	0.184862i	0.0297800	+	0.00967610i
$366$	12.7189	−	9.29982i	0.664830	−	0.486110i
$367$	4.11670	−	1.83287i	0.214890	−	0.0956752i	−0.296469	−	0.955043i	$-0.595809\pi$
$367$	4.11670	−	1.83287i	0.214890	−	0.0956752i	0.511359	+	0.859367i	$0.329142\pi$
$368$	−3.21024	+	3.56533i	−0.167345	+	0.185856i
$369$	−9.63247	−	14.6379i	−0.501446	−	0.762017i
$370$	−4.66676	+	3.77907i	−0.242613	+	0.196465i
$371$	6.05164	+	15.7650i	0.314185	+	0.818481i
$372$	−0.878801	+	0.189578i	−0.0455637	+	0.00982914i
$373$	11.8579	+	20.5386i	0.613981	+	1.06345i	0.990562	+	0.137063i	$0.0437662\pi$
$373$	11.8579	+	20.5386i	0.613981	+	1.06345i	−0.376581	+	0.926384i	$0.622900\pi$
$374$	−1.14765	+	6.46083i	−0.0593436	+	0.334082i
$375$	0.0535641	+	17.6908i	0.00276604	+	0.913551i
$376$	−11.0264	−	3.58270i	−0.568644	−	0.184764i
$377$	8.98280	−	34.5541i	0.462638	−	1.77963i
$378$	−3.01660	−	17.9871i	−0.155157	−	0.925156i
$379$	−4.63281	−	7.13390i	−0.237971	−	0.366444i	0.699426	−	0.714705i	$-0.253439\pi$
$379$	−4.63281	−	7.13390i	−0.237971	−	0.366444i	−0.937398	+	0.348261i	$0.886772\pi$
$380$	−3.16946	+	14.9112i	−0.162590	+	0.764926i
$381$	5.33419	−	14.0228i	0.273279	−	0.718409i
$382$	−23.8817	−	3.78248i	−1.22189	−	0.193529i
$383$	1.25608	−	1.93420i	0.0641829	−	0.0988329i	−0.805122	−	0.593109i	$-0.797900\pi$
$383$	1.25608	−	1.93420i	0.0641829	−	0.0988329i	0.869305	+	0.494276i	$0.164567\pi$
$384$	−2.62511	−	1.50503i	−0.133962	−	0.0768032i
$385$	19.6738	+	18.3927i	1.00267	+	0.937379i
$386$	6.07208	−	3.50572i	0.309061	−	0.178436i
$387$	−32.0767	+	7.02139i	−1.63055	+	0.356917i
$388$	5.52133	+	4.47109i	0.280303	+	0.226985i
$389$	−22.6513	−	16.4572i	−1.14847	−	0.834411i	−0.160192	−	0.987086i	$-0.551211\pi$
$389$	−22.6513	−	16.4572i	−1.14847	−	0.834411i	−0.988276	+	0.152675i	$0.951211\pi$
$390$	3.37729	+	15.1076i	0.171016	+	0.765004i
$391$	2.21254	+	6.80951i	0.111893	+	0.344372i
$392$	−4.88651	+	12.7298i	−0.246806	+	0.642952i
$393$	−2.72420	+	17.5435i	−0.137418	+	0.884955i
$394$	4.96260	+	23.3472i	0.250012	+	1.17621i
$395$	17.5838	−	17.5838i	0.884739	−	0.884739i
$396$	9.06051	−	1.80627i	0.455308	−	0.0907684i
$397$	11.5358	+	3.09102i	0.578968	+	0.155134i	0.536406	−	0.843960i	$-0.319782\pi$
$397$	11.5358	+	3.09102i	0.578968	+	0.155134i	0.0425615	+	0.999094i	$0.486448\pi$
$398$	5.98423	−	3.04912i	0.299962	−	0.152838i
$399$	25.2442	−	31.3677i	1.26379	−	1.57035i
$400$	−0.382849	−	0.859892i	−0.0191424	−	0.0429946i
$401$	17.0437	+	26.2450i	0.851122	+	1.31061i	0.948955	+	0.315410i	$0.102142\pi$
$401$	17.0437	+	26.2450i	0.851122	+	1.31061i	−0.0978334	+	0.995203i	$0.531191\pi$
$402$	25.9553	−	1.43907i	1.29453	−	0.0717745i
$403$	−1.97452	−	0.404314i	−0.0983578	−	0.0201403i
$404$	1.17452	+	1.61659i	0.0584345	+	0.0804282i
$405$	10.0167	+	19.0839i	0.497733	+	0.948287i
$406$	17.3780	−	30.0996i	0.862458	−	1.49382i
$407$	1.93384	+	7.79825i	0.0958570	+	0.386545i
$408$	8.67596	−	5.04415i	0.429524	−	0.249723i
$409$	32.5789	+	21.1570i	1.61092	+	1.04615i	0.957207	+	0.289404i	$0.0934572\pi$
$409$	32.5789	+	21.1570i	1.61092	+	1.04615i	0.653715	+	0.756741i	$0.273209\pi$
$410$	5.18880	+	13.5173i	0.256257	+	0.667571i
$411$	11.9374	+	1.21814i	0.588827	+	0.0600862i
$412$	5.95161	−	6.60994i	0.293215	−	0.325648i
$413$	0.0625246	+	0.0132900i	0.00307664	+	0.000653959i
$414$	−8.99561	+	7.37514i	−0.442110	+	0.362468i
$415$	12.6481	+	17.4087i	0.620873	+	0.854558i
$416$	−10.1420	−	13.7423i	−0.497252	−	0.673773i
$417$	4.27192	−	16.1383i	0.209197	−	0.790297i
$418$	−18.7786	−	14.1880i	−0.918493	−	0.693958i
$419$	−1.49589	−	0.863652i	−0.0730790	−	0.0421922i	0.463015	−	0.886350i	$-0.346768\pi$
$419$	−1.49589	−	0.863652i	−0.0730790	−	0.0421922i	−0.536094	+	0.844158i	$0.680101\pi$
$420$	0.644006	−	13.0439i	0.0314243	−	0.636477i
$421$	−34.8721	−	5.52320i	−1.69956	−	0.269184i	−0.770053	−	0.637980i	$-0.779770\pi$
$421$	−34.8721	−	5.52320i	−1.69956	−	0.269184i	−0.929511	+	0.368796i	$0.879770\pi$
$422$	−0.886005	−	1.09413i	−0.0431301	−	0.0532612i
$423$	−10.2546	−	5.14702i	−0.498598	−	0.250257i
$424$	−13.4509	−	6.85356i	−0.653232	−	0.332839i
$425$	−1.39705	−	0.146836i	−0.0677668	−	0.00712257i
$426$	−0.412132	+	2.65408i	−0.0199679	+	0.128591i
$427$	−29.7591	−	1.55961i	−1.44014	−	0.0754748i
$428$	−2.31563			−0.111930
$429$	20.2236	+	4.47283i	0.976404	+	0.215950i
$430$	27.1322			1.30843
$431$	−12.7187	−	0.666560i	−0.612639	−	0.0321071i	−0.256506	−	0.966543i	$-0.582572\pi$
$431$	−12.7187	−	0.666560i	−0.612639	−	0.0321071i	−0.356133	+	0.934435i	$0.615905\pi$
$432$	5.20973	+	4.14097i	0.250653	+	0.199233i
$433$	28.6351	+	3.00967i	1.37612	+	0.144636i	0.763532	−	0.645770i	$-0.223463\pi$
$433$	28.6351	+	3.00967i	1.37612	+	0.144636i	0.612584	+	0.790405i	$0.290130\pi$
$434$	−1.74820	−	0.890754i	−0.0839165	−	0.0427576i
$435$	−8.41781	+	40.2008i	−0.403603	+	1.92748i
$436$	7.21131	+	8.90523i	0.345359	+	0.426483i
$437$	−25.3644	−	4.01733i	−1.21335	−	0.192175i
$438$	0.447323	+	0.0220853i	0.0213739	+	0.00105528i
$439$	14.3469	+	8.28320i	0.684742	+	0.395336i	0.801639	−	0.597808i	$-0.203962\pi$
$439$	14.3469	+	8.28320i	0.684742	+	0.395336i	−0.116898	+	0.993144i	$0.537295\pi$
$440$	−24.0726	−	0.450664i	−1.14762	−	0.0214846i
$441$	−6.67628	+	11.7271i	−0.317918	+	0.558433i
$442$	7.08877	−	0.798609i	0.337178	−	0.0379859i
$443$	−6.48401	−	8.92447i	−0.308065	−	0.424014i	0.626712	−	0.779251i	$-0.284400\pi$
$443$	−6.48401	−	8.92447i	−0.308065	−	0.424014i	−0.934776	+	0.355237i	$0.884400\pi$
$444$	2.28046	−	3.15885i	0.108226	−	0.149912i
$445$	−21.8449	−	4.64329i	−1.03555	−	0.220113i
$446$	−12.2033	+	13.5532i	−0.577845	+	0.641762i
$447$	−3.53519	+	34.6438i	−0.167209	+	1.63860i
$448$	−9.07120	−	23.6313i	−0.428574	−	1.11647i
$449$	−1.30543	−	0.847756i	−0.0616071	−	0.0400081i	0.513468	−	0.858109i	$-0.328361\pi$
$449$	−1.30543	−	0.847756i	−0.0616071	−	0.0400081i	−0.575075	+	0.818101i	$0.695027\pi$
$450$	−0.604022	−	2.20084i	−0.0284739	−	0.103749i
$451$	19.3234	+	1.37580i	0.909902	+	0.0647838i
$452$	5.66557	−	9.81305i	0.266486	−	0.461567i
$453$	0.892872	−	2.77655i	0.0419508	−	0.130454i
$454$	2.95442	+	4.06642i	0.138658	+	0.190846i
$455$	13.0970	−	26.1859i	0.613999	−	1.22761i
$456$	1.99267	+	35.9400i	0.0933153	+	1.68304i
$457$	11.8962	+	18.3185i	0.556481	+	0.856906i	0.999210	−	0.0397501i	$-0.0126562\pi$
$457$	11.8962	+	18.3185i	0.556481	+	0.856906i	−0.442729	+	0.896656i	$0.645990\pi$
$458$	−5.72543	−	12.8595i	−0.267532	−	0.600886i
$459$	9.23948	−	3.64333i	0.431262	−	0.170056i
$460$	−7.42171	+	3.78155i	−0.346039	+	0.176316i
$461$	32.8930	+	8.81365i	1.53198	+	0.410493i	0.923664	−	0.383202i	$-0.125179\pi$
$461$	32.8930	+	8.81365i	1.53198	+	0.410493i	0.608316	+	0.793695i	$0.291846\pi$
$462$	17.8197	+	9.43466i	0.829047	+	0.438940i
$463$	−17.2350	+	17.2350i	−0.800980	+	0.800980i	−0.983249	−	0.182269i	$-0.941656\pi$
$463$	−17.2350	+	17.2350i	−0.800980	+	0.800980i	0.182269	+	0.983249i	$0.441656\pi$
$464$	2.63677	+	12.4050i	0.122409	+	0.575890i
$465$	2.29118	+	0.355780i	0.106251	+	0.0164989i
$466$	−4.96157	+	12.9253i	−0.229840	+	0.598754i
$467$	−3.49768	−	10.7648i	−0.161853	−	0.498134i	0.836937	−	0.547299i	$-0.184344\pi$
$467$	−3.49768	−	10.7648i	−0.161853	−	0.498134i	−0.998791	+	0.0491652i	$0.984344\pi$
$468$	−4.68030	−	8.88648i	−0.216347	−	0.410778i
$469$	−39.7753	−	28.8985i	−1.83665	−	1.33441i
$470$	7.36791	+	5.96642i	0.339856	+	0.275210i
$471$	1.05816	−	0.543204i	0.0487576	−	0.0250295i
$472$	−0.0494884	+	0.0285721i	−0.00227789	+	0.00131514i
$473$	15.3834	−	32.8811i	0.707330	−	1.51188i
$474$	9.25974	−	16.1511i	0.425314	−	0.741843i
$475$	2.74411	−	4.22556i	0.125908	−	0.193882i
$476$	−5.94402	−	0.941440i	−0.272444	−	0.0431508i
$477$	−12.1397	−	8.70818i	−0.555838	−	0.398720i
$478$	−0.612288	+	2.88059i	−0.0280054	+	0.131755i
$479$	0.264941	+	0.407974i	0.0121055	+	0.0186408i	0.844672	−	0.535285i	$-0.179796\pi$
$479$	0.264941	+	0.407974i	0.0121055	+	0.0186408i	−0.832566	+	0.553926i	$0.813129\pi$
$480$	12.4114	+	15.2323i	0.566500	+	0.695254i
$481$	7.53137	−	4.42353i	0.343401	−	0.201696i
$482$	22.5137	+	7.31513i	1.02547	+	0.333195i
$483$	22.0005	−	0.0666128i	1.00106	−	0.00303099i
$484$	−4.50069	+	9.16881i	−0.204577	+	0.416764i
$485$	−9.16173	−	15.8686i	−0.416013	−	0.720555i
$486$	10.9773	+	11.8265i	0.497940	+	0.536459i
$487$	−7.06994	−	18.4178i	−0.320369	−	0.834591i	−0.995312	−	0.0967202i	$-0.969165\pi$
$487$	−7.06994	−	18.4178i	−0.320369	−	0.834591i	0.674942	−	0.737871i	$-0.264169\pi$
$488$	20.7035	−	16.7654i	0.937204	−	0.758933i
$489$	11.8379	−	13.2276i	0.535327	−	0.598173i
$490$	7.46096	−	8.28623i	0.337052	−	0.374334i
$491$	−37.6264	+	16.7523i	−1.69805	+	0.756023i	−0.698887	+	0.715232i	$0.746321\pi$
$491$	−37.6264	+	16.7523i	−1.69805	+	0.756023i	−0.999168	+	0.0407906i	$0.987012\pi$
$492$	−5.54455	−	7.58303i	−0.249968	−	0.341869i
$493$	18.0005	+	5.84870i	0.810700	+	0.263412i
$494$	−8.99068	+	23.9545i	−0.404510	+	1.07777i
$495$	−23.4852	−	4.02519i	−1.05558	−	0.180919i
$496$	0.691541	−	0.185298i	0.0310511	−	0.00832013i
$497$	3.77508	−	3.39909i	0.169335	−	0.152470i
$498$	12.5504	+	10.1003i	0.562397	+	0.452607i
$499$	−3.61487	−	22.8234i	−0.161824	−	1.02172i	−0.926224	−	0.376974i	$-0.876965\pi$
$499$	−3.61487	−	22.8234i	−0.161824	−	1.02172i	0.764400	−	0.644742i	$-0.223035\pi$
$500$	0.496350	+	9.47093i	0.0221975	+	0.423553i
$501$	−1.27433	+	6.08580i	−0.0569328	+	0.271893i
$502$	4.81438	−	0.762523i	0.214876	−	0.0340331i
$503$	2.70948	−	6.08559i	0.120810	−	0.271343i	−0.843010	−	0.537898i	$-0.819219\pi$
$503$	2.70948	−	6.08559i	0.120810	−	0.271343i	0.963820	+	0.266555i	$0.0858853\pi$
$504$	−6.59394	−	30.1239i	−0.293717	−	1.34182i
$505$	−1.33384	−	4.97796i	−0.0593551	−	0.221516i
$506$	−0.432547	−	12.8529i	−0.0192291	−	0.571380i
$507$	−1.58204	−	22.4610i	−0.0702608	−	0.997529i
$508$	2.48542	−	7.64934i	0.110273	−	0.339385i
$509$	−12.0009	−	9.71811i	−0.531929	−	0.430747i	0.325355	−	0.945592i	$-0.394516\pi$
$509$	−12.0009	−	9.71811i	−0.531929	−	0.430747i	−0.857284	+	0.514845i	$0.827850\pi$
$510$	−8.10163	+	1.30833i	−0.358746	+	0.0579338i
$511$	−0.629488	−	0.566793i	−0.0278469	−	0.0250735i
$512$	12.3243	+	6.27952i	0.544661	+	0.277518i
$513$	−3.40163	+	35.4599i	−0.150186	+	1.56559i
$514$	14.9738	−	5.74789i	0.660464	−	0.253528i
$515$	−20.4395	+	10.4145i	−0.900673	+	0.458916i
$516$	−16.9894	+	4.60749i	−0.747919	+	0.202833i
$517$	11.4081	−	5.54623i	0.501727	−	0.243923i
$518$	8.21308	−	2.20069i	0.360862	−	0.0966927i
$519$	−21.0396	−	13.5729i	−0.923535	−	0.595783i
$520$	6.96297	+	25.2312i	0.305346	+	1.10646i
$521$	−0.229477	+	0.315847i	−0.0100536	+	0.0138375i	−0.814014	−	0.580845i	$-0.802722\pi$
$521$	−0.229477	+	0.315847i	−0.0100536	+	0.0138375i	0.803961	+	0.594683i	$0.202722\pi$
$522$	1.79523	+	30.6971i	0.0785749	+	1.34358i
$523$	−21.1998	−	4.50616i	−0.927004	−	0.197041i	−0.280414	−	0.959879i	$-0.590472\pi$
$523$	−21.1998	−	4.50616i	−0.927004	−	0.197041i	−0.646589	+	0.762838i	$0.723805\pi$
$524$	−0.994863	+	9.46549i	−0.0434608	+	0.413502i
$525$	−1.74369	+	3.94853i	−0.0761010	+	0.172328i
$526$	−1.66215	−	1.07941i	−0.0724733	−	0.0470647i
$527$	0.276537	−	1.03205i	0.0120462	−	0.0449569i
$528$	−7.13568	+	1.79249i	−0.310541	+	0.0780080i
$529$	4.48397	+	7.76647i	0.194955	+	0.337673i
$530$	8.26027	+	9.17396i	0.358803	+	0.398492i
$531$	−0.0526730	+	0.0205861i	−0.00228581	+	0.000893360i
$532$	12.6875	−	17.4628i	0.550071	−	0.757108i
$533$	−4.53226	−	20.5664i	−0.196314	−	0.890831i
$534$	−16.6942	+	0.925599i	−0.722429	+	0.0400546i
$535$	5.57554	+	2.14025i	0.241052	+	0.0925311i
$536$	43.7116	−	4.59427i	1.88805	−	0.198442i
$537$	1.26749	−	25.6722i	0.0546962	−	1.10784i
$538$	−1.20195	−	1.20195i	−0.0518197	−	0.0518197i
$539$	−5.81176	−	13.7400i	−0.250330	−	0.591822i
$540$	5.86781	+	9.95344i	0.252510	+	0.428328i
$541$	−6.01646	−	11.8080i	−0.258668	−	0.507664i	0.724752	−	0.689010i	$-0.241955\pi$
$541$	−6.01646	−	11.8080i	−0.258668	−	0.507664i	−0.983419	+	0.181346i	$0.941955\pi$
$542$	2.44726	−	5.49664i	0.105119	−	0.236101i
$543$	−40.9541	+	6.61367i	−1.75751	+	0.283820i
$544$	7.59355	−	4.93131i	0.325571	−	0.211428i
$545$	−9.13253	−	28.1070i	−0.391195	−	1.20397i
$546$	4.33213	−	21.4873i	0.185398	−	0.919573i
$547$	−20.9241	+	15.2022i	−0.894649	+	0.650000i	−0.937086	−	0.349099i	$-0.886488\pi$
$547$	−20.9241	+	15.2022i	−0.894649	+	0.650000i	0.0424373	+	0.999099i	$0.486488\pi$
$548$	6.42392	+	0.336663i	0.274416	+	0.0143815i
$549$	22.7523	−	13.3204i	0.971044	−	0.568500i
$550$	2.33817	+	0.948128i	0.0997001	+	0.0404283i
$551$	−48.0018	+	48.0018i	−2.04495	+	2.04495i
$552$	−14.5763	+	13.2047i	−0.620407	+	0.562028i
$553$	−32.8723	+	12.6185i	−1.39787	+	0.536592i
$554$	−1.50298	−	9.48943i	−0.0638554	−	0.403167i
$555$	−8.41045	+	5.49809i	−0.357004	+	0.233381i
$556$	1.86072	−	8.75399i	0.0789120	−	0.371252i
$557$	24.5893	+	9.43893i	1.04188	+	0.399940i	0.818328	−	0.574751i	$-0.194901\pi$
$557$	24.5893	+	9.43893i	1.04188	+	0.399940i	0.223553	+	0.974692i	$0.428235\pi$
$558$	1.72524	−	0.191899i	0.0730351	−	0.00812375i
$559$	−39.0233	−	5.88239i	−1.65051	−	0.248799i
$560$			10.4002i			0.439490i
$561$	−3.00792	+	10.5601i	−0.126994	+	0.445846i
$562$	−10.3931	+	18.0014i	−0.438407	+	0.759344i
$563$	−17.9323	+	3.81162i	−0.755756	+	0.160641i	−0.569648	−	0.821889i	$-0.692921\pi$
$563$	−17.9323	+	3.81162i	−0.755756	+	0.160641i	−0.186107	+	0.982529i	$0.559587\pi$
$564$	−5.62679	−	2.48482i	−0.236931	−	0.104630i
$565$	−22.7113	+	18.3913i	−0.955472	+	0.773726i
$566$	−14.7197	+	0.771424i	−0.618713	+	0.0324254i
$567$	−1.96616	−	30.4546i	−0.0825710	−	1.27897i
$568$	−0.474693	+	4.51640i	−0.0199177	+	0.189504i
$569$	0.157028	+	1.49402i	0.00658294	+	0.0626325i	0.997320	−	0.0731604i	$-0.0233085\pi$
$569$	0.157028	+	1.49402i	0.00658294	+	0.0626325i	−0.990737	+	0.135793i	$0.956642\pi$
$570$	9.01100	−	28.0214i	0.377429	−	1.17369i
$571$		−	28.0980i		−	1.17586i	−0.808910	−	0.587932i	$-0.799942\pi$
$571$		−	28.0980i		−	1.17586i	0.808910	−	0.587932i	$-0.200058\pi$
$572$	10.9467	+	1.86030i	0.457705	+	0.0777829i
$573$	−39.1120	−	10.3532i	−1.63393	−	0.432511i
$574$	1.07297	−	20.4735i	0.0447849	−	0.854546i
$575$	2.73793	−	0.287769i	0.114180	−	0.0120008i
$576$	18.1970	+	13.0533i	0.758208	+	0.543886i
$577$	−0.963218	+	1.89042i	−0.0400993	+	0.0786993i	−0.910187	−	0.414198i	$-0.864062\pi$
$577$	−0.963218	+	1.89042i	−0.0400993	+	0.0786993i	0.870088	+	0.492897i	$0.164062\pi$
$578$	−0.723036	−	13.7963i	−0.0300743	−	0.573852i
$579$	10.7034	−	4.80433i	0.444817	−	0.199661i
$580$	−3.44448	+	21.7476i	−0.143024	+	0.903018i
$581$	−6.33484	−	29.8031i	−0.262814	−	1.23644i
$582$	−9.72946	−	9.67072i	−0.403299	−	0.400864i
$583$	15.8012	−	4.80906i	0.654420	−	0.199171i
$584$	0.757251			0.0313353
$585$	3.05571	+	25.7226i	0.126338	+	1.06350i
$586$	6.04831	−	4.39436i	0.249854	−	0.181529i
$587$	5.15826	−	13.4377i	0.212904	−	0.554634i	−0.784989	−	0.619509i	$-0.787332\pi$
$587$	5.15826	−	13.4377i	0.212904	−	0.554634i	0.997893	+	0.0648750i	$0.0206649\pi$
$588$	−3.26472	+	6.45561i	−0.134635	+	0.266225i
$589$	2.84791	+	2.56427i	0.117346	+	0.105659i
$590$	0.0461537	−	0.00731003i	0.00190012	−	0.000300949i
$591$	4.29505	+	39.7078i	0.176675	+	1.63336i
$592$	−1.68980	+	2.60206i	−0.0694502	+	0.106944i
$593$	−11.8165	−	11.8165i	−0.485247	−	0.485247i	0.421556	−	0.906803i	$-0.361484\pi$
$593$	−11.8165	−	11.8165i	−0.485247	−	0.485247i	−0.906803	+	0.421556i	$0.861484\pi$
$594$	−17.7583	+	1.69364i	−0.728631	+	0.0694909i
$595$	13.4418	+	7.76062i	0.551059	+	0.318154i
$596$	−0.977041	+	18.6431i	−0.0400212	+	0.763649i
$597$	10.4796	−	4.05918i	0.428900	−	0.166131i
$598$	−13.2636	+	4.41934i	−0.542388	+	0.180720i
$599$	32.7785	−	10.6504i	1.33929	−	0.435163i	0.450215	−	0.892920i	$-0.351347\pi$
$599$	32.7785	−	10.6504i	1.33929	−	0.435163i	0.889077	+	0.457757i	$0.151347\pi$
$600$	−1.20353	−	3.66628i	−0.0491339	−	0.149675i
$601$	30.5189	−	13.5879i	1.24489	−	0.554262i	0.324733	−	0.945806i	$-0.394725\pi$
$601$	30.5189	−	13.5879i	1.24489	−	0.554262i	0.920160	+	0.391543i	$0.128059\pi$
$602$	−35.0965	−	15.6260i	−1.43043	−	0.636867i
$603$	43.4508	+	2.01340i	1.76946	+	0.0819920i
$604$	0.404677	−	1.51027i	0.0164661	−	0.0614522i
$605$	19.3111	−	17.9167i	0.785107	−	0.728418i
$606$	−1.93924	−	3.33550i	−0.0787764	−	0.135496i
$607$	33.3889	−	7.09703i	1.35521	−	0.288060i	0.527664	−	0.849453i	$-0.323068\pi$
$607$	33.3889	−	7.09703i	1.35521	−	0.288060i	0.827549	+	0.561393i	$0.189735\pi$
$608$	3.39456	+	32.2971i	0.137668	+	1.30982i
$609$	34.0412	−	47.1533i	1.37942	−	1.91075i
$610$	−20.7187	+	6.73190i	−0.838874	+	0.272567i
$611$	−9.30347	−	10.1787i	−0.376378	−	0.411786i
$612$	4.85085	−	2.19503i	0.196084	−	0.0887288i
$613$	−18.8385	+	23.2636i	−0.760879	+	0.939607i	−0.999504	−	0.0315050i	$-0.989970\pi$
$613$	−18.8385	+	23.2636i	−0.760879	+	0.939607i	0.238625	+	0.971112i	$0.423303\pi$
$614$	−7.66089	+	6.89790i	−0.309168	+	0.278376i
$615$	6.34138	+	23.3829i	0.255709	+	0.942890i
$616$	30.8793	+	14.4469i	1.24416	+	0.582081i
$617$	6.49483	+	1.74028i	0.261472	+	0.0700612i	0.387173	−	0.922007i	$-0.373451\pi$
$617$	6.49483	+	1.74028i	0.261472	+	0.0700612i	−0.125701	+	0.992068i	$0.540118\pi$
$618$	−12.7280	+	11.5303i	−0.511997	+	0.463818i
$619$	5.40517	−	34.1269i	0.217252	−	1.37168i	−0.602116	−	0.798409i	$-0.705676\pi$
$619$	5.40517	−	34.1269i	0.217252	−	1.37168i	0.819368	−	0.573268i	$-0.194324\pi$
$620$	1.23619	+	0.129929i	0.0496466	+	0.00521807i
$621$	−16.2273	+	10.7489i	−0.651179	+	0.431340i
$622$	17.3170	−	11.2458i	0.694348	−	0.450915i
$623$	25.5831	+	18.5872i	1.02497	+	0.744681i
$624$	4.07162	+	6.88439i	0.162995	+	0.275596i
$625$	8.69405	−	26.7575i	0.347762	−	1.07030i
$626$	−8.71997	−	32.5434i	−0.348520	−	1.30070i
$627$	−28.8497	−	26.8079i	−1.15215	−	1.07060i
$628$	0.552221	−	0.318825i	0.0220360	−	0.0127225i
$629$	2.10211	+	4.12562i	0.0838166	+	0.164499i
$630$	−3.79386	+	24.9296i	−0.151151	+	0.993221i
$631$	−6.30852	−	7.79037i	−0.251138	−	0.310130i	0.635950	−	0.771731i	$-0.280609\pi$
$631$	−6.30852	−	7.79037i	−0.251138	−	0.310130i	−0.887088	+	0.461601i	$0.847275\pi$
$632$	14.2906	−	28.0469i	0.568450	−	1.11565i
$633$	−1.28903	−	1.97184i	−0.0512343	−	0.0783734i
$634$	−5.42067	−	12.1750i	−0.215282	−	0.483532i
$635$	−13.0544	+	16.1208i	−0.518046	+	0.639734i
$636$	−6.73026	−	4.34176i	−0.266872	−	0.172162i
$637$	−12.5273	+	10.3002i	−0.496351	+	0.408110i
$638$	−28.1590	−	19.0454i	−1.11482	−	0.754013i
$639$	−1.13690	+	4.34811i	−0.0449749	+	0.172008i
$640$	2.79946	+	3.10912i	0.110658	+	0.122899i
$641$	−1.83058	−	0.815027i	−0.0723036	−	0.0321916i	0.370266	−	0.928926i	$-0.379266\pi$
$641$	−1.83058	−	0.815027i	−0.0723036	−	0.0321916i	−0.442570	+	0.896734i	$0.645933\pi$
$642$	4.44807	+	0.453898i	0.175551	+	0.0179139i
$643$	13.7508	−	0.720650i	0.542280	−	0.0284197i	0.220770	−	0.975326i	$-0.429143\pi$
$643$	13.7508	−	0.720650i	0.542280	−	0.0284197i	0.321510	+	0.946906i	$0.395810\pi$
$644$	11.7781	−	0.617266i	0.464123	−	0.0243237i
$645$	45.1655	+	4.60887i	1.77839	+	0.181474i
$646$	−12.3912	−	5.51691i	−0.487524	−	0.217060i
$647$	10.5550	+	11.7225i	0.414958	+	0.460858i	0.913997	−	0.405722i	$-0.132980\pi$
$647$	10.5550	+	11.7225i	0.414958	+	0.460858i	−0.499038	+	0.866580i	$0.666313\pi$
$648$	19.5238	+	19.0565i	0.766966	+	0.748610i
$649$	0.0173093	−	0.0600777i	0.000679450	−	0.00235826i
$650$	0.266338	−	2.72993i	0.0104466	−	0.107077i
$651$	−2.75883	−	1.77975i	−0.108127	−	0.0697540i
$652$	5.98876	−	7.39550i	0.234538	−	0.289630i
$653$	−4.06293	−	9.12549i	−0.158995	−	0.357108i	0.816429	−	0.577446i	$-0.195951\pi$
$653$	−4.06293	−	9.12549i	−0.158995	−	0.357108i	−0.975424	+	0.220338i	$0.929284\pi$
$654$	−12.1066	−	18.5195i	−0.473404	−	0.724169i
$655$	11.1440	−	21.8714i	0.435433	−	0.854585i
$656$	4.70785	+	5.81370i	0.183810	+	0.226987i
$657$	0.740883	+	0.112750i	0.0289046	+	0.00439879i
$658$	−6.09450	−	11.9611i	−0.237588	−	0.466293i
$659$	−2.88083	+	1.66325i	−0.112221	+	0.0647908i	−0.555060	−	0.831810i	$-0.687305\pi$
$659$	−2.88083	+	1.66325i	−0.112221	+	0.0647908i	0.442839	+	0.896601i	$0.353971\pi$
$660$	−12.6813	−	1.53439i	−0.493618	−	0.0597259i
$661$	−0.171306	−	0.639324i	−0.00666305	−	0.0248668i	0.962514	−	0.271231i	$-0.0874307\pi$
$661$	−0.171306	−	0.639324i	−0.00666305	−	0.0248668i	−0.969177	+	0.246364i	$0.920764\pi$
$662$	−5.79022	+	17.8205i	−0.225043	+	0.692612i
$663$	11.9360	−	0.125252i	0.463554	−	0.00486440i
$664$	22.0364	+	16.0104i	0.855179	+	0.621324i
$665$	−46.6889	+	30.3201i	−1.81052	+	1.17576i
$666$	−4.99968	+	5.62079i	−0.193734	+	0.217801i
$667$	−36.8895	−	3.87725i	−1.42837	−	0.150128i
$668$	−0.521441	+	3.29225i	−0.0201752	+	0.127381i
$669$	−22.6165	+	20.4883i	−0.874404	+	0.792124i
$670$	−34.7168	−	9.30234i	−1.34123	−	0.359381i
$671$	−3.58877	+	28.9255i	−0.138543	+	1.11666i
$672$	−7.28204	−	26.8515i	−0.280911	−	1.03582i
$673$	16.3167	−	14.6917i	0.628964	−	0.566322i	−0.291782	−	0.956485i	$-0.594248\pi$
$673$	16.3167	−	14.6917i	0.628964	−	0.566322i	0.920746	+	0.390163i	$0.127581\pi$
$674$	13.2876	−	16.4088i	0.511817	−	0.632042i
$675$	−0.631632	−	3.76623i	−0.0243115	−	0.144962i
$676$	−1.44086	−	11.9846i	−0.0554175	−	0.460948i
$677$	0.548741	−	0.178297i	0.0210898	−	0.00685250i	−0.298453	−	0.954424i	$-0.596471\pi$
$677$	0.548741	−	0.178297i	0.0210898	−	0.00685250i	0.319543	+	0.947572i	$0.396471\pi$
$678$	−12.8064	+	17.7392i	−0.491828	+	0.681271i
$679$	2.71201	+	25.8030i	0.104077	+	0.990230i
$680$	−13.5724	+	2.88490i	−0.520478	+	0.110631i
$681$	4.22732	+	7.27101i	0.161991	+	0.278626i
$682$	−0.990483	+	1.64372i	−0.0379275	+	0.0629415i
$683$	2.24050	−	8.36168i	0.0857305	−	0.319951i	−0.909721	−	0.415220i	$-0.863705\pi$
$683$	2.24050	−	8.36168i	0.0857305	−	0.319951i	0.995452	+	0.0952694i	$0.0303713\pi$
$684$	−0.883955	+	19.0765i	−0.0337989	+	0.729407i
$685$	−15.1562	−	6.74800i	−0.579091	−	0.257828i
$686$	8.02232	−	3.57177i	0.306294	−	0.136371i
$687$	−7.34641	−	22.3791i	−0.280283	−	0.853817i
$688$	13.3322	−	4.33191i	0.508287	−	0.165152i
$689$	−9.89152	−	14.9855i	−0.376837	−	0.570901i
$690$	14.9975	−	5.80917i	0.570945	−	0.221151i
$691$	1.20935	−	23.0759i	0.0460060	−	0.877847i	−0.873996	−	0.485933i	$-0.838480\pi$
$691$	1.20935	−	23.0759i	0.0460060	−	0.877847i	0.920002	−	0.391914i	$-0.128187\pi$
$692$	−11.6242	−	6.71123i	−0.441886	−	0.255123i
$693$	28.0609	+	18.7324i	1.06594	+	0.711583i
$694$	−7.06953	−	7.06953i	−0.268356	−	0.268356i
$695$	−12.5712	+	19.3579i	−0.476853	+	0.734289i
$696$	5.59107	+	51.6895i	0.211929	+	1.95929i
$697$	11.0269	−	1.74649i	0.417673	−	0.0661530i
$698$	22.4274	+	20.1937i	0.848890	+	0.764344i
$699$	−10.4548	+	20.6733i	−0.395439	+	0.781936i
$700$	−0.829256	+	2.16029i	−0.0313429	+	0.0816512i
$701$	−33.5927	+	24.4065i	−1.26878	+	0.921820i	−0.999153	−	0.0411453i	$-0.986899\pi$
$701$	−33.5927	+	24.4065i	−1.26878	+	0.921820i	−0.269624	+	0.962966i	$0.586899\pi$
$702$	7.24844	+	17.9873i	0.273575	+	0.678888i
$703$	−16.6075			−0.626364
$704$	−23.6855	+	7.20862i	−0.892681	+	0.271685i
$705$	11.2515	+	11.1835i	0.423755	+	0.421197i
$706$	−1.67566	−	7.88338i	−0.0630644	−	0.296695i
$707$	−1.14153	+	7.20736i	−0.0429318	+	0.271061i
$708$	−0.0276589	+	0.0124150i	−0.00103948	+	0.000466585i
$709$	−1.13908	−	21.7350i	−0.0427792	−	0.816276i	−0.932809	−	0.360372i	$-0.882650\pi$
$709$	−1.13908	−	21.7350i	−0.0427792	−	0.816276i	0.890029	−	0.455903i	$-0.150684\pi$
$710$	1.68593	−	3.30882i	0.0632717	−	0.124178i
$711$	18.1577	−	25.3129i	0.680968	−	0.949308i
$712$	−28.1149	+	2.95499i	−1.05365	+	0.110743i
$713$	−0.109590	+	2.09109i	−0.00410416	+	0.0783121i
$714$	11.2333	+	2.97352i	0.420394	+	0.111281i
$715$	−24.6379	−	14.5968i	−0.921407	−	0.545891i
$716$		−	13.7793i		−	0.514958i
$717$	−1.50856	+	4.69116i	−0.0563383	+	0.175195i
$718$	0.665900	+	6.33561i	0.0248512	+	0.236443i
$719$	−0.605735	+	5.76318i	−0.0225901	+	0.214930i	0.977404	+	0.211382i	$0.0677963\pi$
$719$	−0.605735	+	5.76318i	−0.0225901	+	0.214930i	−0.999994	+	0.00354881i	$0.998870\pi$
$720$	−5.05805	−	7.68641i	−0.188502	−	0.286455i
$721$	32.4372	−	1.69996i	1.20802	−	0.0633099i
$722$	22.5234	−	18.2391i	0.838236	−	0.678790i
$723$	36.2347	+	16.0014i	1.34758	+	0.595100i
$724$	−21.7535	+	4.62386i	−0.808464	+	0.171844i
$725$	3.63870	−	6.30242i	0.135138	−	0.234066i
$726$	10.4426	−	16.7301i	0.387559	−	0.620911i
$727$		−	14.7256i		−	0.546144i	−0.961994	−	0.273072i	$-0.911960\pi$
$727$		−	14.7256i		−	0.546144i	0.961994	−	0.273072i	$-0.0880397\pi$
$728$	5.52428	−	36.6476i	0.204743	−	1.35825i
$729$	16.2644	+	21.5516i	0.602385	+	0.798206i
$730$	−0.578103	−	0.221913i	−0.0213966	−	0.00821337i
$731$	4.34970	−	20.4637i	0.160879	−	0.756878i
$732$	11.8303	−	7.73371i	0.437260	−	0.285846i
$733$	−0.521269	−	3.29116i	−0.0192535	−	0.121562i	0.976190	−	0.216919i	$-0.0696007\pi$
$733$	−0.521269	−	3.29116i	−0.0192535	−	0.121562i	−0.995443	+	0.0953570i	$0.969601\pi$
$734$	−4.35472	+	1.67162i	−0.160735	+	0.0617006i
$735$	13.8274	−	12.5263i	0.510032	−	0.462039i
$736$	−12.5473	+	12.5473i	−0.462500	+	0.462500i
$737$	−30.9571	+	36.7986i	−1.14032	+	1.35549i
$738$	9.16407	+	15.6530i	0.337334	+	0.576194i
$739$	−17.9046	−	0.938339i	−0.658631	−	0.0345174i	−0.279907	−	0.960027i	$-0.590304\pi$
$739$	−17.9046	−	0.938339i	−0.658631	−	0.0345174i	−0.378724	+	0.925510i	$0.623637\pi$
$740$	−4.35793	+	3.16622i	−0.160201	+	0.116393i
$741$	−19.0354	+	38.3486i	−0.699283	+	1.40877i
$742$	−5.40151	−	16.6241i	−0.198296	−	0.610291i
$743$	36.6232	−	23.7834i	1.34358	−	0.872528i	0.345743	−	0.938329i	$-0.387627\pi$
$743$	36.6232	−	23.7834i	1.34358	−	0.872528i	0.997833	+	0.0658012i	$0.0209603\pi$
$744$	2.89747	−	0.467911i	0.106226	−	0.0171544i
$745$	19.5836	−	43.9854i	0.717487	−	1.61150i
$746$	−11.1449	−	21.8730i	−0.408043	−	0.800829i
$747$	19.1763	+	18.9454i	0.701623	+	0.693176i
$748$	−1.33139	+	5.73376i	−0.0486804	+	0.209647i
$749$	−5.97956	−	5.97956i	−0.218488	−	0.218488i
$750$	0.903011	−	18.2899i	0.0329733	−	0.667852i
$751$	6.54523	−	0.687932i	0.238839	−	0.0251030i	0.0156473	−	0.999878i	$-0.495019\pi$
$751$	6.54523	−	0.687932i	0.238839	−	0.0251030i	0.223192	+	0.974775i	$0.428352\pi$
$752$	4.57305	+	1.75543i	0.166762	+	0.0640139i
$753$	8.14378	−	0.451526i	0.296776	−	0.0164545i
$754$	−11.1574	+	35.2319i	−0.406330	+	1.28307i
$755$	−2.37026	+	3.26239i	−0.0862628	+	0.118731i
$756$	−1.85785	−	16.2545i	−0.0675692	−	0.591172i
$757$	−6.66347	−	7.40053i	−0.242188	−	0.268977i	0.609780	−	0.792570i	$-0.291258\pi$
$757$	−6.66347	−	7.40053i	−0.242188	−	0.268977i	−0.851968	+	0.523594i	$0.824591\pi$
$758$	4.40245	+	7.62527i	0.159904	+	0.276962i
$759$	1.46324	−	21.4690i	0.0531123	−	0.779274i
$760$	12.8808	−	48.0720i	0.467237	−	1.74375i
$761$	−17.8066	−	11.5638i	−0.645490	−	0.419186i	0.179950	−	0.983676i	$-0.442406\pi$
$761$	−17.8066	−	11.5638i	−0.645490	−	0.419186i	−0.825440	+	0.564490i	$0.809073\pi$
$762$	−6.27360	+	14.2063i	−0.227269	+	0.514642i
$763$	−4.37414	+	41.6171i	−0.158354	+	1.50664i
$764$	−21.2157	−	4.50954i	−0.767558	−	0.163149i
$765$	−13.7086	+	0.801705i	−0.495635	+	0.0289857i
$766$	−1.40319	+	1.93133i	−0.0506994	+	0.0697818i
$767$	−0.0679662		0.000507414i	−0.00245412		1.83217e-5i
$768$	24.3618	+	15.7161i	0.879082	+	0.567105i
$769$	−41.2273	+	11.0468i	−1.48669	+	0.398359i	−0.908620	−	0.417625i	$-0.862863\pi$
$769$	−41.2273	+	11.0468i	−1.48669	+	0.398359i	−0.578075	+	0.815984i	$0.696196\pi$
$770$	−19.3403	−	20.0783i	−0.696978	−	0.723572i
$771$	25.9024	−	7.02465i	0.932852	−	0.252987i
$772$	5.60398	−	2.85537i	0.201692	−	0.102767i
$773$	41.2598	−	15.8382i	1.48401	−	0.569659i	0.524521	−	0.851397i	$-0.324244\pi$
$773$	41.2598	−	15.8382i	1.48401	−	0.569659i	0.959491	+	0.281738i	$0.0909109\pi$
$774$	33.5380	−	5.52028i	1.20550	−	0.198422i
$775$	−0.366048	−	0.186511i	−0.0131488	−	0.00669966i
$776$	−17.2368	−	15.5201i	−0.618764	−	0.557138i
$777$	14.0457	−	2.26824i	0.503887	−	0.0813725i
$778$	22.5231	+	18.2388i	0.807492	+	0.653894i
$779$	−12.3740	+	38.0834i	−0.443346	+	1.36448i
$780$	2.31614	+	13.6920i	0.0829310	+	0.490254i
$781$	−3.05403	−	3.91919i	−0.109282	−	0.140240i
$782$	−1.91820	−	7.15883i	−0.0685948	−	0.255999i
$783$	−2.22601	+	51.4048i	−0.0795511	+	1.83706i
$784$	2.34320	−	5.26291i	0.0836857	−	0.187961i
$785$	−1.62431	+	0.257265i	−0.0579740	+	0.00918218i
$786$	3.76640	−	17.9871i	0.134343	−	0.641580i
$787$	0.776526	+	14.8170i	0.0276802	+	0.528169i	0.976919	+	0.213612i	$0.0685227\pi$
$787$	0.776526	+	14.8170i	0.0276802	+	0.528169i	−0.949239	+	0.314557i	$0.898144\pi$
$788$	3.34944	+	21.1475i	0.119319	+	0.753349i
$789$	−2.58354	−	2.07919i	−0.0919765	−	0.0740211i
$790$	−19.1290	+	17.2238i	−0.680578	+	0.612795i
$791$	39.9698	−	10.7099i	1.42116	−	0.380800i
$792$	−29.8478	+	4.34073i	−1.06060	+	0.154241i
$793$	31.2585	−	5.19036i	1.11002	−	0.184315i
$794$	−11.7571	−	3.82012i	−0.417245	−	0.135571i
$795$	12.1921	+	16.6746i	0.432409	+	0.591386i
$796$	5.50385	−	2.45047i	0.195079	−	0.0868546i
$797$	23.6838	−	26.3035i	0.838924	−	0.931719i	−0.159536	−	0.987192i	$-0.551000\pi$
$797$	23.6838	−	26.3035i	0.838924	−	0.931719i	0.998460	+	0.0554728i	$0.0176666\pi$
$798$	−27.7942	+	31.0571i	−0.983903	+	1.09941i
$799$	5.68120	−	4.60054i	0.200986	−	0.162756i
$800$	−1.24762	−	3.25016i	−0.0441100	−	0.114911i
$801$	−27.9472	−	1.29500i	−0.987465	−	0.0457566i
$802$	−16.1962	−	28.0527i	−0.571909	−	0.990576i
$803$	−0.596707	+	0.574775i	−0.0210573	+	0.0202834i
$804$	23.3184	−	0.0706032i	0.822378	−	0.00248998i
$805$	−28.9297	−	9.39984i	−1.01964	−	0.331301i
$806$	2.01915	+	0.524906i	0.0711216	+	0.0184890i
$807$	−1.79665	−	2.20499i	−0.0632450	−	0.0776193i
$808$	−3.55297	−	5.47109i	−0.124993	−	0.192472i
$809$	−0.783689	+	3.68697i	−0.0275530	+	0.129627i	−0.989774	−	0.142641i	$-0.954440\pi$
$809$	−0.783689	+	3.68697i	−0.0275530	+	0.129627i	0.962221	+	0.272268i	$0.0877738\pi$
$810$	−9.32038	−	20.2696i	−0.327485	−	0.712202i
$811$	41.5394	+	6.57919i	1.45865	+	0.231027i	0.834814	−	0.550532i	$-0.185575\pi$
$811$	41.5394	+	6.57919i	1.45865	+	0.231027i	0.623831	+	0.781559i	$0.285575\pi$
$812$	16.9804	−	26.1476i	0.595896	−	0.917600i
$813$	5.00752	−	8.73425i	0.175621	−	0.306324i
$814$	−1.57655	−	8.16579i	−0.0552580	−	0.286211i
$815$	−21.2550	+	12.2716i	−0.744531	+	0.429855i
$816$	−3.77210	+	1.93639i	−0.132050	+	0.0677872i
$817$	58.3147	+	47.2223i	2.04017	+	1.65210i
$818$	−32.5306	−	23.6348i	−1.13740	−	0.826373i
$819$	10.8615	−	35.0330i	0.379530	−	1.22415i
$820$	4.01356	+	12.3525i	0.140159	+	0.431366i
$821$	−13.2902	+	34.6221i	−0.463830	+	1.20832i	0.479817	+	0.877368i	$0.340703\pi$
$821$	−13.2902	+	34.6221i	−0.463830	+	1.20832i	−0.943648	+	0.330951i	$0.892630\pi$
$822$	−12.2736	−	1.90588i	−0.428092	−	0.0664751i
$823$	4.52872	+	21.3060i	0.157861	+	0.742679i	0.983850	+	0.178993i	$0.0572839\pi$
$823$	4.52872	+	21.3060i	0.157861	+	0.742679i	−0.825989	+	0.563686i	$0.809383\pi$
$824$	−20.5329	+	20.5329i	−0.715297	+	0.715297i
$825$	3.73118	+	1.97548i	0.129903	+	0.0687773i
$826$	−0.0639116	−	0.0171251i	−0.00222377	−	0.000595857i
$827$	34.6731	−	17.6668i	1.20570	−	0.614336i	0.268552	−	0.963265i	$-0.413455\pi$
$827$	34.6731	−	17.6668i	1.20570	−	0.614336i	0.937149	+	0.348929i	$0.113455\pi$
$828$	−8.40455	+	6.18437i	−0.292078	+	0.214922i
$829$	−3.12764	−	7.02479i	−0.108627	−	0.243981i	0.851050	−	0.525085i	$-0.175966\pi$
$829$	−3.12764	−	7.02479i	−0.108627	−	0.243981i	−0.959678	+	0.281103i	$0.909300\pi$
$830$	−12.1313	−	18.6805i	−0.421082	−	0.648409i
$831$	−0.889985	−	16.0519i	−0.0308732	−	0.556833i
$832$	14.8271	+	22.4627i	0.514036	+	0.778755i
$833$	−5.05356	−	6.95563i	−0.175096	−	0.240998i
$834$	−5.29015	+	16.4507i	−0.183183	+	0.569641i
$835$	4.29842	−	7.44509i	0.148753	−	0.257648i
$836$	−16.1559	−	13.5913i	−0.558764	−	0.470065i
$837$	2.90451	−	0.0263833i	0.100395	−	0.000911941i
$838$	1.49951	+	0.973793i	0.0517997	+	0.0336391i
$839$	−17.3881	−	45.2974i	−0.600302	−	1.56384i	−0.810223	−	0.586122i	$-0.800654\pi$
$839$	−17.3881	−	45.2974i	−0.600302	−	1.56384i	0.209920	−	0.977718i	$-0.432679\pi$
$840$	−4.32828	+	42.4158i	−0.149340	+	1.46349i
$841$	−46.2048	+	51.3157i	−1.59327	+	1.76951i
$842$	35.7480	+	7.59848i	1.23196	+	0.261861i
$843$	−20.3587	+	28.2005i	−0.701192	+	0.971278i
$844$	−0.742322	−	1.02172i	−0.0255518	−	0.0351690i
$845$	−7.60769	+	30.1882i	−0.261712	+	1.03851i
$846$	10.3214	+	5.87600i	0.354856	+	0.202021i
$847$	−35.2982	+	12.0543i	−1.21286	+	0.414191i
$848$	5.52366	+	3.18908i	0.189683	+	0.109514i
$849$	−24.6341	−	1.21624i	−0.845439	−	0.0417411i
$850$	1.43617	+	0.227467i	0.0492602	+	0.00780205i
$851$	−5.71074	−	7.05218i	−0.195762	−	0.241745i
$852$	−0.493792	+	2.35819i	−0.0169170	+	0.0807904i
$853$	−23.6866	−	12.0689i	−0.811013	−	0.413232i	−0.00125767	−	0.999999i	$-0.500400\pi$
$853$	−23.6866	−	12.0689i	−0.811013	−	0.413232i	−0.809756	+	0.586767i	$0.800400\pi$
$854$	30.6774	+	3.22433i	1.04976	+	0.110334i
$855$	19.7600	−	45.1151i	0.675779	−	1.54290i
$856$	7.54944	+	0.395650i	0.258035	+	0.0135230i
$857$	25.1700			0.859791			0.429895	−	0.902879i	$-0.358550\pi$
$857$	25.1700			0.859791			0.429895	+	0.902879i	$0.358550\pi$
$858$	−20.6628	−	5.71914i	−0.705415	−	0.195248i
$859$	24.2942			0.828907			0.414453	−	0.910071i	$-0.363973\pi$
$859$	24.2942			0.828907			0.414453	+	0.910071i	$0.363973\pi$
$860$	24.3051	+	1.27378i	0.828798	+	0.0434355i
$861$	5.26388	−	33.8988i	0.179393	−	1.15527i
$862$	13.1112	+	1.37804i	0.446569	+	0.0469363i
$863$	−47.0834	−	23.9902i	−1.60274	−	0.816635i	−0.999823	−	0.0188286i	$-0.994006\pi$
$863$	−47.0834	−	23.9902i	−1.60274	−	0.816635i	−0.602914	−	0.797806i	$-0.705994\pi$
$864$	18.4408	+	16.3033i	0.627369	+	0.554651i
$865$	21.7856	+	26.9030i	0.740734	+	0.914730i
$866$	−29.4370	−	4.66237i	−1.00031	−	0.158434i
$867$	1.13995	−	23.0889i	0.0387146	−	0.784139i
$868$	−1.52423	−	0.880015i	−0.0517358	−	0.0298697i
$869$	10.0275	+	32.9477i	0.340161	+	1.11767i
$870$	10.8793	−	41.0995i	0.368843	−	1.39340i
$871$	47.9152	+	20.9060i	1.62355	+	0.708374i
$872$	−21.9889	−	30.2651i	−0.744637	−	1.02490i
$873$	−14.5534	−	17.7511i	−0.492557	−	0.600782i
$874$	26.0015	+	5.52679i	0.879514	+	0.186947i
$875$	−23.1747	+	25.7381i	−0.783448	+	0.870107i
$876$	0.399677	+	0.0407847i	0.0135039	+	0.00137799i
$877$	−8.26032	−	21.5189i	−0.278931	−	0.726641i	−0.999449	−	0.0332040i	$-0.989429\pi$
$877$	−8.26032	−	21.5189i	−0.278931	−	0.726641i	0.720517	−	0.693437i	$-0.243904\pi$
$878$	−14.3817	−	9.33955i	−0.485357	−	0.315195i
$879$	10.8148	−	6.28764i	0.364773	−	0.212077i
$880$	10.1468	+	0.722437i	0.342048	+	0.0243533i
$881$	23.1195	−	40.0442i	0.778917	−	1.34912i	−0.153649	−	0.988125i	$-0.549103\pi$
$881$	23.1195	−	40.0442i	0.778917	−	1.34912i	0.932566	−	0.360998i	$-0.117564\pi$
$882$	7.53655	−	11.7606i	0.253769	−	0.395999i
$883$	−18.0458	−	24.8379i	−0.607289	−	0.835861i	0.389062	−	0.921211i	$-0.372799\pi$
$883$	−18.0458	−	24.8379i	−0.607289	−	0.835861i	−0.996351	+	0.0853503i	$0.972799\pi$
$884$	6.38765	−	0.382600i	0.214840	−	0.0128682i
$885$	0.0780714	−	0.00432862i	0.00262434	−	0.000145505i
$886$	6.21903	+	9.57647i	0.208932	+	0.321728i
$887$	6.42433	+	14.4293i	0.215708	+	0.484487i	0.988696	−	0.149933i	$-0.0479057\pi$
$887$	6.42433	+	14.4293i	0.215708	+	0.484487i	−0.772989	+	0.634420i	$0.781239\pi$
$888$	−7.97449	+	9.90887i	−0.267606	+	0.332520i
$889$	26.1706	−	13.3346i	0.877734	−	0.447228i
$890$	22.3295	+	5.98318i	0.748487	+	0.200557i
$891$	−29.8490	−	0.197236i	−0.999978	−	0.00660767i
$892$	−11.5681	+	11.5681i	−0.387329	+	0.387329i
$893$	5.45145	+	25.6471i	0.182426	+	0.858246i
$894$	5.53111	−	35.6197i	0.184988	−	1.19130i
$895$	−12.7357	+	33.1777i	−0.425708	+	1.10901i
$896$	−1.83061	−	5.63403i	−0.0611563	−	0.188220i
$897$	−22.8299	+	5.10359i	−0.762267	+	0.170404i
$898$	1.30349	+	0.947044i	0.0434982	+	0.0316033i
$899$	4.30170	+	3.48344i	0.143470	+	0.116179i
$900$	−0.437762	−	1.99988i	−0.0145921	−	0.0666628i
$901$	8.24346	−	4.75937i	0.274630	−	0.158557i
$902$	−19.9000	−	2.46898i	−0.662597	−	0.0822080i
$903$	−55.7689	−	31.9735i	−1.85587	−	1.06401i
$904$	−20.1476	+	31.0246i	−0.670099	+	1.03186i
$905$	56.6515	+	8.97272i	1.88316	+	0.298263i
$906$	−1.07338	+	2.82175i	−0.0356605	+	0.0937462i
$907$	−0.899930	+	4.23384i	−0.0298817	+	0.140582i	−0.990560	−	0.137083i	$-0.956227\pi$
$907$	−0.899930	+	4.23384i	−0.0298817	+	0.140582i	0.960678	+	0.277665i	$0.0895606\pi$
$908$	2.45568	+	3.78142i	0.0814946	+	0.125491i
$909$	−2.66156	−	5.88185i	−0.0882785	−	0.195089i
$910$	−14.9570	+	26.3587i	−0.495819	+	0.873784i
$911$	32.0757	+	10.4220i	1.06272	+	0.345297i	0.787647	−	0.616127i	$-0.211299\pi$
$911$	32.0757	+	10.4220i	1.06272	+	0.345297i	0.275069	+	0.961424i	$0.411299\pi$
$912$	−0.0460462	−	15.2079i	−0.00152474	−	0.503583i
$913$	−29.5168	+	4.11024i	−0.976865	+	0.136029i
$914$	−11.3047	−	19.5803i	−0.373926	−	0.647659i
$915$	−35.6328	+	7.68682i	−1.17798	+	0.254118i
$916$	−4.52515	−	11.7884i	−0.149515	−	0.389500i
$917$	−27.0114	+	21.8734i	−0.891994	+	0.722322i
$918$	−9.74820	+	3.26557i	−0.321739	+	0.107780i
$919$	−31.5026	+	34.9872i	−1.03917	+	1.15412i	−0.0513290	+	0.998682i	$0.516346\pi$
$919$	−31.5026	+	34.9872i	−1.03917	+	1.15412i	−0.987846	+	0.155439i	$0.950321\pi$
$920$	24.8424	−	11.0606i	0.819031	−	0.364656i
$921$	−13.9244	+	10.1812i	−0.458825	+	0.335483i
$922$	−33.5239	−	10.8926i	−1.10405	−	0.358728i
$923$	−3.14218	+	4.39345i	−0.103426	+	0.144612i
$924$	15.5200	+	9.28820i	0.510572	+	0.305559i
$925$	1.71970	−	0.460791i	0.0565433	−	0.0151507i
$926$	18.7495	−	16.8821i	0.616147	−	0.554781i
$927$	−23.1463	+	17.0319i	−0.760224	+	0.559400i
$928$	7.33780	+	46.3290i	0.240875	+	1.52083i
$929$	−2.16085	−	41.2315i	−0.0708952	−	1.35276i	−0.770138	−	0.637877i	$-0.779813\pi$
$929$	−2.16085	−	41.2315i	−0.0708952	−	1.35276i	0.699243	−	0.714884i	$-0.253520\pi$
$930$	−2.34912	−	0.491891i	−0.0770305	−	0.0161297i
$931$	30.4575	−	4.82400i	0.998206	−	0.158100i
$932$	−5.05140	+	11.3456i	−0.165464	+	0.371639i
$933$	30.7369	−	15.7787i	1.00628	−	0.516570i
$934$	3.03238	+	11.3170i	0.0992224	+	0.370303i
$935$	8.50520	−	12.5751i	0.278150	−	0.411251i
$936$	13.7404	+	29.7715i	0.449119	+	0.973111i
$937$	5.18253	−	15.9502i	0.169306	−	0.521070i	−0.830022	−	0.557731i	$-0.811672\pi$
$937$	5.18253	−	15.9502i	0.169306	−	0.521070i	0.999328	+	0.0366607i	$0.0116721\pi$
$938$	39.5501	+	32.0270i	1.29136	+	1.04572i
$939$	−8.98762	−	55.6545i	−0.293300	−	1.81622i
$940$	6.32011	+	5.69065i	0.206139	+	0.185609i
$941$	32.9365	+	16.7820i	1.07370	+	0.547077i	0.899181	−	0.437578i	$-0.144163\pi$
$941$	32.9365	+	16.7820i	1.07370	+	0.547077i	0.174517	+	0.984654i	$0.444163\pi$
$942$	−1.12325	+	0.504183i	−0.0365974	+	0.0164272i
$943$	−20.4266	+	7.84105i	−0.665183	+	0.255340i
$944$	0.0215120	−	0.0109609i	0.000700155	−	0.000356747i
$945$	−10.5502	+	40.8546i	−0.343197	+	1.32900i
$946$	−17.6831	+	33.1558i	−0.574927	+	1.07799i
$947$	−1.44035	+	0.385941i	−0.0468051	+	0.0125414i	−0.282146	−	0.959372i	$-0.591046\pi$
$947$	−1.44035	+	0.385941i	−0.0468051	+	0.0125414i	0.235341	+	0.971913i	$0.424379\pi$
$948$	9.05317	−	14.0335i	0.294033	−	0.455787i
$949$	0.783355	+	0.444506i	0.0254288	+	0.0144293i
$950$	−3.06549	+	4.21929i	−0.0994577	+	0.136892i
$951$	−6.95537	−	21.1879i	−0.225543	−	0.687065i
$952$	19.2179	+	4.08489i	0.622856	+	0.132392i
$953$	1.71964	−	16.3612i	0.0557045	−	0.529993i	−0.930715	−	0.365746i	$-0.880814\pi$
$953$	1.71964	−	16.3612i	0.0557045	−	0.529993i	0.986419	−	0.164247i	$-0.0525194\pi$
$954$	12.0770	+	9.65928i	0.391008	+	0.312731i
$955$	46.9149	+	30.4669i	1.51813	+	0.985886i
$956$	−0.683727	+	2.55170i	−0.0221133	+	0.0825280i
$957$	−43.6396	−	36.4871i	−1.41067	−	1.17946i
$958$	−0.251768	−	0.436074i	−0.00813425	−	0.0140889i
$959$	15.7189	+	17.4576i	0.507589	+	0.563735i
$960$	−18.2755	−	24.9946i	−0.589840	−	0.806698i
$961$	−18.0377	+	24.8267i	−0.581860	+	0.800862i
$962$	−8.02480	+	4.16459i	−0.258730	+	0.134272i
$963$	7.32736	+	1.51116i	0.236121	+	0.0486965i
$964$	19.8244	+	7.60988i	0.638502	+	0.245098i
$965$	−16.1323	+	1.69557i	−0.519317	+	0.0545824i
$966$	−22.7455	−	1.12299i	−0.731823	−	0.0361317i
$967$	−13.8007	−	13.8007i	−0.443802	−	0.443802i	0.449486	−	0.893288i	$-0.351607\pi$
$967$	−13.8007	−	13.8007i	−0.443802	−	0.443802i	−0.893288	+	0.449486i	$0.851607\pi$
$968$	16.2398	−	29.1233i	0.521967	−	0.936058i
$969$	−19.6898	−	11.2886i	−0.632527	−	0.362641i
$970$	8.61080	+	16.8996i	0.276476	+	0.542615i
$971$	16.5952	−	37.2734i	0.532564	−	1.19616i	−0.424273	−	0.905535i	$-0.639470\pi$
$971$	16.5952	−	37.2734i	0.532564	−	1.19616i	0.956837	−	0.290625i	$-0.0938632\pi$
$972$	9.27829	+	11.1096i	0.297601	+	0.356339i
$973$	27.4099	−	17.8002i	0.878723	−	0.570649i
$974$	6.31041	+	19.4215i	0.202199	+	0.622303i
$975$	0.907084	−	4.49913i	0.0290499	−	0.144087i
$976$	−9.10596	+	6.61586i	−0.291475	+	0.211769i
$977$	−14.9126	−	0.781535i	−0.477096	−	0.0250035i	−0.187727	−	0.982221i	$-0.560112\pi$
$977$	−14.9126	−	0.781535i	−0.477096	−	0.0250035i	−0.289369	+	0.957218i	$0.593445\pi$
$978$	−12.9534	+	13.0320i	−0.414203	+	0.416719i
$979$	19.9113	−	23.6685i	0.636369	−	0.756449i
$980$	7.07258	−	7.07258i	0.225925	−	0.225925i
$981$	−17.0073	−	32.8849i	−0.543002	−	1.04993i
$982$	39.8018	−	15.2785i	1.27013	−	0.487556i
$983$	0.839543	+	5.30067i	0.0267773	+	0.169065i	0.997453	−	0.0713280i	$-0.0227237\pi$
$983$	0.839543	+	5.30067i	0.0267773	+	0.169065i	−0.970676	+	0.240393i	$0.922724\pi$
$984$	16.7808	+	25.6696i	0.534951	+	0.818317i
$985$	11.4811	−	54.0144i	0.365819	−	1.72104i
$986$	−18.2902	−	7.02094i	−0.582478	−	0.223592i
$987$	−8.11338	−	20.9463i	−0.258252	−	0.666728i
$988$	−9.17849	+	21.0365i	−0.292007	+	0.669260i
$989$			41.0008i			1.30375i
$990$	24.0586	+	5.43311i	0.764632	+	0.172676i
$991$	−13.5564	+	23.4803i	−0.430633	+	0.745877i	−0.996928	−	0.0783249i	$-0.975043\pi$
$991$	−13.5564	+	23.4803i	−0.430633	+	0.745877i	0.566295	+	0.824202i	$0.308376\pi$
$992$	2.59011	−	0.550545i	0.0822361	−	0.0174798i
$993$	−12.6658	+	28.6812i	−0.401936	+	0.910170i
$994$	−4.08643	+	3.30912i	−0.129614	+	0.104959i
$995$	−15.5170	+	0.813210i	−0.491921	+	0.0257805i
$996$	10.7685	+	9.63715i	0.341214	+	0.305365i
$997$	3.92957	−	37.3873i	0.124451	−	1.18407i	−0.736880	−	0.676024i	$-0.763702\pi$
$997$	3.92957	−	37.3873i	0.124451	−	1.18407i	0.861331	−	0.508045i	$-0.169632\pi$
$998$	2.50025	+	23.7883i	0.0791441	+	0.753006i
$999$	−9.27749	+	8.50735i	−0.293527	+	0.269161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bv.a.20.19	✓	832
3.2	odd	2	inner	429.2.bv.a.20.34	yes	832
11.5	even	5	inner	429.2.bv.a.137.34	yes	832
13.2	odd	12	inner	429.2.bv.a.119.19	yes	832
33.5	odd	10	inner	429.2.bv.a.137.19	yes	832
39.2	even	12	inner	429.2.bv.a.119.34	yes	832
143.93	odd	60	inner	429.2.bv.a.236.34	yes	832
429.236	even	60	inner	429.2.bv.a.236.19	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bv.a.20.19	✓	832	1.1	even	1	trivial
429.2.bv.a.20.34	yes	832	3.2	odd	2	inner
429.2.bv.a.119.19	yes	832	13.2	odd	12	inner
429.2.bv.a.119.34	yes	832	39.2	even	12	inner
429.2.bv.a.137.19	yes	832	33.5	odd	10	inner
429.2.bv.a.137.34	yes	832	11.5	even	5	inner
429.2.bv.a.236.19	yes	832	429.236	even	60	inner
429.2.bv.a.236.34	yes	832	143.93	odd	60	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03370 - 0.0541738i) q^{2} +(-1.71154 - 0.265772i) q^{3} +(-0.923448 - 0.0970583i) q^{4} +(2.13376 + 1.08720i) q^{5} +(1.75482 + 0.367448i) q^{6} +(-2.13395 - 2.63521i) q^{7} +(2.99405 + 0.474211i) q^{8} +(2.85873 + 0.909757i) q^{9} +O(q^{10})\)	\(q+(-1.03370 - 0.0541738i) q^{2} +(-1.71154 - 0.265772i) q^{3} +(-0.923448 - 0.0970583i) q^{4} +(2.13376 + 1.08720i) q^{5} +(1.75482 + 0.367448i) q^{6} +(-2.13395 - 2.63521i) q^{7} +(2.99405 + 0.474211i) q^{8} +(2.85873 + 0.909757i) q^{9} +(-2.14676 - 1.23943i) q^{10} +(-2.71923 + 1.89890i) q^{11} +(1.55472 + 0.411545i) q^{12} +(2.81890 + 2.24807i) q^{13} +(2.06310 + 2.83962i) q^{14} +(-3.36306 - 2.42788i) q^{15} +(-1.25277 - 0.266284i) q^{16} +(-1.27897 + 1.42044i) q^{17} +(-2.90578 - 1.09528i) q^{18} +(-2.45682 - 6.40024i) q^{19} +(-1.86489 - 1.21108i) q^{20} +(2.95198 + 5.07742i) q^{21} +(2.91373 - 1.81558i) q^{22} +(1.87297 - 3.24408i) q^{23} +(-4.99840 - 1.60736i) q^{24} +(0.431983 + 0.594574i) q^{25} +(-2.79210 - 2.47653i) q^{26} +(-4.65104 - 2.31685i) q^{27} +(1.71483 + 2.64060i) q^{28} +(-4.02756 - 9.04604i) q^{29} +(3.34486 + 2.69189i) q^{30} +(-0.498069 + 0.253779i) q^{31} +(-4.57561 - 1.22603i) q^{32} +(5.15873 - 2.52735i) q^{33} +(1.39902 - 1.39902i) q^{34} +(-1.68833 - 7.94295i) q^{35} +(-2.55159 - 1.11758i) q^{36} +(0.868139 - 2.26158i) q^{37} +(2.19289 + 6.74901i) q^{38} +(-4.22719 - 4.59683i) q^{39} +(5.87302 + 4.26700i) q^{40} +(-4.53928 - 3.67584i) q^{41} +(-2.77639 - 5.40843i) q^{42} +(-9.47899 + 5.47270i) q^{43} +(2.69537 - 1.48961i) q^{44} +(5.11075 + 5.04922i) q^{45} +(-2.11183 + 3.25193i) q^{46} +(-3.77754 - 0.598303i) q^{47} +(2.07339 + 0.788705i) q^{48} +(-0.935210 + 4.39982i) q^{49} +(-0.414330 - 0.638012i) q^{50} +(2.56652 - 2.09122i) q^{51} +(-2.38492 - 2.34957i) q^{52} +(-4.73627 - 1.53891i) q^{53} +(4.68226 + 2.64689i) q^{54} +(-7.86666 + 1.09544i) q^{55} +(-5.13952 - 8.90191i) q^{56} +(2.50394 + 11.6072i) q^{57} +(3.67322 + 9.56906i) q^{58} +(-0.0146499 + 0.0118633i) q^{59} +(2.86997 + 2.56844i) q^{60} +(5.88048 - 6.53094i) q^{61} +(0.528601 - 0.235348i) q^{62} +(-3.70300 - 9.47475i) q^{63} +(7.09951 + 2.30677i) q^{64} +(3.57075 + 7.86155i) q^{65} +(-5.46949 + 2.33304i) q^{66} +(14.0051 - 3.75266i) q^{67} +(1.31893 - 1.18757i) q^{68} +(-4.06784 + 5.05458i) q^{69} +(1.31492 + 8.30207i) q^{70} +(0.0784042 + 1.49604i) q^{71} +(8.12777 + 4.07950i) q^{72} +(0.246729 - 0.0390780i) q^{73} +(-1.01991 + 2.29076i) q^{74} +(-0.581335 - 1.13245i) q^{75} +(1.64755 + 6.14874i) q^{76} +(10.8067 + 3.11358i) q^{77} +(4.12060 + 4.98074i) q^{78} +(3.20883 - 9.87577i) q^{79} +(-2.38360 - 1.93020i) q^{80} +(7.34469 + 5.20150i) q^{81} +(4.49311 + 4.04562i) q^{82} +(8.00617 + 4.07935i) q^{83} +(-2.23320 - 4.97524i) q^{84} +(-4.27331 + 1.64037i) q^{85} +(10.0949 - 5.14360i) q^{86} +(4.48914 + 16.5531i) q^{87} +(-9.04198 + 4.39591i) q^{88} +(-9.00795 + 2.41367i) q^{89} +(-5.00943 - 5.49624i) q^{90} +(-0.0912730 - 12.2257i) q^{91} +(-2.04445 + 2.81395i) q^{92} +(0.919912 - 0.301980i) q^{93} +(3.87242 + 0.823108i) q^{94} +(1.71610 - 16.3276i) q^{95} +(7.50549 + 3.31446i) q^{96} +(-6.41704 - 4.16727i) q^{97} +(1.20508 - 4.49742i) q^{98} +(-9.50107 + 2.95461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

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