LMFDB - Embedded newform 525.2.z.b.64.9

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			64.9
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227844 - 0.313601i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.571602 - 1.75921i) q^{4} +(1.55920 - 1.60277i) q^{5} +(-0.119785 - 0.368660i) q^{6} -1.00000i q^{7} +(-1.41925 + 0.461141i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.227844 - 0.313601i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.571602 - 1.75921i) q^{4} +(1.55920 - 1.60277i) q^{5} +(-0.119785 - 0.368660i) q^{6} -1.00000i q^{7} +(-1.41925 + 0.461141i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.857887 - 0.123785i) q^{10} +(0.0542779 - 0.0394352i) q^{11} +(1.08725 - 1.49647i) q^{12} +(1.27629 - 1.75667i) q^{13} +(-0.313601 + 0.227844i) q^{14} +(1.97818 - 1.04251i) q^{15} +(-2.52496 - 1.83449i) q^{16} +(-0.943150 + 0.306448i) q^{17} -0.387632i q^{18} +(1.47670 + 4.54482i) q^{19} +(-1.92837 - 3.65911i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-0.0247338 - 0.00803650i) q^{22} +(-1.60621 - 2.21076i) q^{23} -1.49228 q^{24} +(-0.137760 - 4.99810i) q^{25} -0.841689 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.75921 - 0.571602i) q^{28} +(-3.08754 + 9.50246i) q^{29} +(-0.777647 - 0.382828i) q^{30} +(-0.658308 - 2.02606i) q^{31} +4.19438i q^{32} +(0.0638075 - 0.0207323i) q^{33} +(0.310994 + 0.225950i) q^{34} +(-1.60277 - 1.55920i) q^{35} +(1.49647 - 1.08725i) q^{36} +(1.81890 - 2.50351i) q^{37} +(1.08880 - 1.49861i) q^{38} +(1.75667 - 1.27629i) q^{39} +(-1.47379 + 2.99374i) q^{40} +(4.27471 + 3.10576i) q^{41} +(-0.368660 + 0.119785i) q^{42} -5.53396i q^{43} +(-0.0383494 - 0.118027i) q^{44} +(2.20351 - 0.380193i) q^{45} +(-0.327330 + 1.00742i) q^{46} +(-4.34843 - 1.41289i) q^{47} +(-1.83449 - 2.52496i) q^{48} -1.00000 q^{49} +(-1.53602 + 1.18199i) q^{50} -0.991687 q^{51} +(-2.36081 - 3.24938i) q^{52} +(10.8196 + 3.51549i) q^{53} +(0.119785 - 0.368660i) q^{54} +(0.0214247 - 0.148483i) q^{55} +(0.461141 + 1.41925i) q^{56} +4.77870i q^{57} +(3.68346 - 1.19683i) q^{58} +(2.66030 + 1.93282i) q^{59} +(-0.703258 - 4.07592i) q^{60} +(11.1703 - 8.11573i) q^{61} +(-0.485383 + 0.668073i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-3.73457 + 2.71332i) q^{64} +(-0.825536 - 4.78461i) q^{65} +(-0.0210398 - 0.0152863i) q^{66} +(8.02865 - 2.60867i) q^{67} +1.83436i q^{68} +(-0.844436 - 2.59891i) q^{69} +(-0.123785 + 0.857887i) q^{70} +(-1.09984 + 3.38495i) q^{71} +(-1.41925 - 0.461141i) q^{72} +(-0.960950 - 1.32263i) q^{73} -1.19953 q^{74} +(1.41348 - 4.79605i) q^{75} +8.83937 q^{76} +(-0.0394352 - 0.0542779i) q^{77} +(-0.800494 - 0.260096i) q^{78} +(-4.04882 + 12.4610i) q^{79} +(-6.87721 + 1.18659i) q^{80} +(0.309017 + 0.951057i) q^{81} -2.04818i q^{82} +(-13.5653 + 4.40763i) q^{83} +(-1.49647 - 1.08725i) q^{84} +(-0.979398 + 1.98947i) q^{85} +(-1.73545 + 1.26088i) q^{86} +(-5.87284 + 8.08328i) q^{87} +(-0.0588484 + 0.0809979i) q^{88} +(-0.557747 + 0.405227i) q^{89} +(-0.621286 - 0.604398i) q^{90} +(-1.75667 - 1.27629i) q^{91} +(-4.80730 + 1.56199i) q^{92} -2.13033i q^{93} +(0.547681 + 1.68559i) q^{94} +(9.58679 + 4.71949i) q^{95} +(-1.29613 + 3.98909i) q^{96} +(-10.0144 - 3.25388i) q^{97} +(0.227844 + 0.313601i) q^{98} +0.0670911 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 $

$2$	−0.227844	−	0.313601i	−0.161110	−	0.221749i	0.720828	−	0.693114i	$-0.243762\pi$
$2$	−0.227844	−	0.313601i	−0.161110	−	0.221749i	−0.881939	+	0.471364i	$0.843762\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.571602	−	1.75921i	0.285801	−	0.879604i
$5$	1.55920	−	1.60277i	0.697298	−	0.716782i
$5$	1.55920	−	1.60277i	0.697298	−	0.716782i
$6$	−0.119785	−	0.368660i	−0.0489020	−	0.150505i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.41925	+	0.461141i	−0.501779	+	0.163038i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.857887	−	0.123785i	−0.271288	−	0.0391443i
$11$	0.0542779	−	0.0394352i	0.0163654	−	0.0118902i	−0.579572	−	0.814921i	$-0.696780\pi$
$11$	0.0542779	−	0.0394352i	0.0163654	−	0.0118902i	0.595938	+	0.803031i	$0.296780\pi$
$12$	1.08725	−	1.49647i	0.313862	−	0.431994i
$13$	1.27629	−	1.75667i	0.353980	−	0.487212i	−0.594479	−	0.804111i	$-0.702642\pi$
$13$	1.27629	−	1.75667i	0.353980	−	0.487212i	0.948459	+	0.316899i	$0.102642\pi$
$14$	−0.313601	+	0.227844i	−0.0838133	+	0.0608940i
$15$	1.97818	−	1.04251i	0.510763	−	0.269174i
$16$	−2.52496	−	1.83449i	−0.631241	−	0.458623i
$17$	−0.943150	+	0.306448i	−0.228748	+	0.0743246i	−0.421148	−	0.906992i	$-0.638373\pi$
$17$	−0.943150	+	0.306448i	−0.228748	+	0.0743246i	0.192401	+	0.981316i	$0.438373\pi$
$18$		−	0.387632i		−	0.0913657i
$19$	1.47670	+	4.54482i	0.338778	+	1.04265i	0.964831	+	0.262872i	$0.0846696\pi$
$19$	1.47670	+	4.54482i	0.338778	+	1.04265i	−0.626052	+	0.779781i	$0.715330\pi$
$20$	−1.92837	−	3.65911i	−0.431196	−	0.818203i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	−0.0247338	−	0.00803650i	−0.00527327	−	0.00171339i
$23$	−1.60621	−	2.21076i	−0.334918	−	0.460976i	0.608030	−	0.793914i	$-0.291960\pi$
$23$	−1.60621	−	2.21076i	−0.334918	−	0.460976i	−0.942949	+	0.332938i	$0.891960\pi$
$24$	−1.49228			−0.304611
$25$	−0.137760	−	4.99810i	−0.0275521	−	0.999620i
$26$	−0.841689			−0.165069
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−1.75921	−	0.571602i	−0.332459	−	0.108023i
$29$	−3.08754	+	9.50246i	−0.573341	+	1.76456i	0.0684179	+	0.997657i	$0.478205\pi$
$29$	−3.08754	+	9.50246i	−0.573341	+	1.76456i	−0.641759	+	0.766906i	$0.721795\pi$
$30$	−0.777647	−	0.382828i	−0.141978	−	0.0698946i
$31$	−0.658308	−	2.02606i	−0.118236	−	0.363892i	0.874373	−	0.485255i	$-0.161273\pi$
$31$	−0.658308	−	2.02606i	−0.118236	−	0.363892i	−0.992608	+	0.121364i	$0.961273\pi$
$32$			4.19438i			0.741468i
$33$	0.0638075	−	0.0207323i	0.0111075	−	0.00360903i
$34$	0.310994	+	0.225950i	0.0533350	+	0.0387501i
$35$	−1.60277	−	1.55920i	−0.270918	−	0.263554i
$36$	1.49647	−	1.08725i	0.249412	−	0.181208i
$37$	1.81890	−	2.50351i	0.299026	−	0.411574i	−0.632894	−	0.774239i	$-0.718133\pi$
$37$	1.81890	−	2.50351i	0.299026	−	0.411574i	0.931920	+	0.362665i	$0.118133\pi$
$38$	1.08880	−	1.49861i	0.176627	−	0.243106i
$39$	1.75667	−	1.27629i	0.281292	−	0.204371i
$40$	−1.47379	+	2.99374i	−0.233027	+	0.473352i
$41$	4.27471	+	3.10576i	0.667598	+	0.485038i	0.869220	−	0.494425i	$-0.164621\pi$
$41$	4.27471	+	3.10576i	0.667598	+	0.485038i	−0.201623	+	0.979463i	$0.564621\pi$
$42$	−0.368660	+	0.119785i	−0.0568855	+	0.0184832i
$43$		−	5.53396i		−	0.843921i	−0.906614	−	0.421960i	$-0.861342\pi$
$43$		−	5.53396i		−	0.843921i	0.906614	−	0.421960i	$-0.138658\pi$
$44$	−0.0383494	−	0.118027i	−0.00578139	−	0.0177933i
$45$	2.20351	−	0.380193i	0.328480	−	0.0566758i
$46$	−0.327330	+	1.00742i	−0.0482622	+	0.148536i
$47$	−4.34843	−	1.41289i	−0.634284	−	0.206091i	−0.0258120	−	0.999667i	$-0.508217\pi$
$47$	−4.34843	−	1.41289i	−0.634284	−	0.206091i	−0.608472	+	0.793576i	$0.708217\pi$
$48$	−1.83449	−	2.52496i	−0.264786	−	0.364447i
$49$	−1.00000			−0.142857
$50$	−1.53602	+	1.18199i	−0.217226	+	0.167159i
$51$	−0.991687			−0.138864
$52$	−2.36081	−	3.24938i	−0.327386	−	0.450608i
$53$	10.8196	+	3.51549i	1.48618	+	0.482889i	0.935953	−	0.352126i	$-0.114541\pi$
$53$	10.8196	+	3.51549i	1.48618	+	0.482889i	0.550227	+	0.835015i	$0.314541\pi$
$54$	0.119785	−	0.368660i	0.0163007	−	0.0501683i
$55$	0.0214247	−	0.148483i	0.00288890	−	0.0200214i
$56$	0.461141	+	1.41925i	0.0616225	+	0.189655i
$57$			4.77870i			0.632955i
$58$	3.68346	−	1.19683i	0.483662	−	0.157151i
$59$	2.66030	+	1.93282i	0.346341	+	0.251631i	0.747332	−	0.664450i	$-0.231334\pi$
$59$	2.66030	+	1.93282i	0.346341	+	0.251631i	−0.400991	+	0.916082i	$0.631334\pi$
$60$	−0.703258	−	4.07592i	−0.0907902	−	0.526199i
$61$	11.1703	−	8.11573i	1.43022	−	1.03911i	0.440239	−	0.897881i	$-0.354894\pi$
$61$	11.1703	−	8.11573i	1.43022	−	1.03911i	0.989977	−	0.141232i	$-0.0451062\pi$
$62$	−0.485383	+	0.668073i	−0.0616438	+	0.0848454i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−3.73457	+	2.71332i	−0.466821	+	0.339165i
$65$	−0.825536	−	4.78461i	−0.102395	−	0.593458i
$66$	−0.0210398	−	0.0152863i	−0.00258983	−	0.00188162i
$67$	8.02865	−	2.60867i	0.980855	−	0.318699i	0.225665	−	0.974205i	$-0.427544\pi$
$67$	8.02865	−	2.60867i	0.980855	−	0.318699i	0.755190	+	0.655506i	$0.227544\pi$
$68$			1.83436i			0.222449i
$69$	−0.844436	−	2.59891i	−0.101658	−	0.312872i
$70$	−0.123785	+	0.857887i	−0.0147952	+	0.102537i
$71$	−1.09984	+	3.38495i	−0.130527	+	0.401720i	−0.994867	−	0.101187i	$-0.967736\pi$
$71$	−1.09984	+	3.38495i	−0.130527	+	0.401720i	0.864341	+	0.502907i	$0.167736\pi$
$72$	−1.41925	−	0.461141i	−0.167260	−	0.0543460i
$73$	−0.960950	−	1.32263i	−0.112471	−	0.154803i	0.749071	−	0.662490i	$-0.230500\pi$
$73$	−0.960950	−	1.32263i	−0.112471	−	0.154803i	−0.861541	+	0.507688i	$0.830500\pi$
$74$	−1.19953			−0.139442
$75$	1.41348	−	4.79605i	0.163215	−	0.553800i
$76$	8.83937			1.01394
$77$	−0.0394352	−	0.0542779i	−0.00449406	−	0.00618554i
$78$	−0.800494	−	0.260096i	−0.0906381	−	0.0294501i
$79$	−4.04882	+	12.4610i	−0.455527	+	1.40197i	0.414988	+	0.909827i	$0.363786\pi$
$79$	−4.04882	+	12.4610i	−0.455527	+	1.40197i	−0.870515	+	0.492142i	$0.836214\pi$
$80$	−6.87721	+	1.18659i	−0.768896	+	0.132665i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	2.04818i		−	0.226184i
$83$	−13.5653	+	4.40763i	−1.48898	+	0.483800i	−0.936783	−	0.349911i	$-0.886212\pi$
$83$	−13.5653	+	4.40763i	−1.48898	+	0.483800i	−0.552200	+	0.833711i	$0.686212\pi$
$84$	−1.49647	−	1.08725i	−0.163279	−	0.118629i
$85$	−0.979398	+	1.98947i	−0.106231	+	0.215788i
$86$	−1.73545	+	1.26088i	−0.187139	+	0.135964i
$87$	−5.87284	+	8.08328i	−0.629635	+	0.866618i
$88$	−0.0588484	+	0.0809979i	−0.00627327	+	0.00863441i
$89$	−0.557747	+	0.405227i	−0.0591211	+	0.0429540i	−0.616953	−	0.787000i	$-0.711633\pi$
$89$	−0.557747	+	0.405227i	−0.0591211	+	0.0429540i	0.557832	+	0.829954i	$0.311633\pi$
$90$	−0.621286	−	0.604398i	−0.0654893	−	0.0637091i
$91$	−1.75667	−	1.27629i	−0.184149	−	0.133792i
$92$	−4.80730	+	1.56199i	−0.501196	+	0.162848i
$93$		−	2.13033i		−	0.220905i
$94$	0.547681	+	1.68559i	0.0564890	+	0.173855i
$95$	9.58679	+	4.71949i	0.983584	+	0.484209i
$96$	−1.29613	+	3.98909i	−0.132286	+	0.407135i
$97$	−10.0144	−	3.25388i	−1.01681	−	0.330381i	−0.247246	−	0.968953i	$-0.579526\pi$
$97$	−10.0144	−	3.25388i	−1.01681	−	0.330381i	−0.769563	+	0.638571i	$0.779526\pi$
$98$	0.227844	+	0.313601i	0.0230158	+	0.0316785i
$99$	0.0670911			0.00674291
$100$	−8.87145	−	2.61457i	−0.887145	−	0.261457i
$101$	2.02717			0.201711			0.100856	−	0.994901i	$-0.467842\pi$
$101$	2.02717			0.201711			0.100856	+	0.994901i	$0.467842\pi$
$102$	0.225950	+	0.310994i	0.0223724	+	0.0307930i
$103$	7.46447	+	2.42535i	0.735497	+	0.238977i	0.652729	−	0.757592i	$-0.273624\pi$
$103$	7.46447	+	2.42535i	0.735497	+	0.238977i	0.0827676	+	0.996569i	$0.473624\pi$
$104$	−1.00130	+	3.08169i	−0.0981858	+	0.302185i
$105$	−1.04251	−	1.97818i	−0.101738	−	0.193050i
$106$	−1.36271	−	4.19400i	−0.132359	−	0.407358i
$107$			19.1777i			1.85398i	0.375085	+	0.926990i	$0.377613\pi$
$107$			19.1777i			1.85398i	−0.375085	+	0.926990i	$0.622387\pi$
$108$	1.75921	−	0.571602i	0.169280	−	0.0550024i
$109$	8.27896	+	6.01502i	0.792981	+	0.576134i	0.908847	−	0.417131i	$-0.136964\pi$
$109$	8.27896	+	6.01502i	0.792981	+	0.576134i	−0.115866	+	0.993265i	$0.536964\pi$
$110$	−0.0514458	+	0.0271121i	−0.00490516	+	0.00258504i
$111$	2.50351	−	1.81890i	0.237622	−	0.172643i
$112$	−1.83449	+	2.52496i	−0.173343	+	0.238587i
$113$	1.06805	−	1.47004i	0.100474	−	0.138290i	−0.755820	−	0.654779i	$-0.772761\pi$
$113$	1.06805	−	1.47004i	0.100474	−	0.138290i	0.856294	+	0.516490i	$0.172761\pi$
$114$	1.49861	−	1.08880i	0.140357	−	0.101976i
$115$	−6.04776	−	0.872637i	−0.563957	−	0.0813738i
$116$	14.9520	+	10.8632i	1.38826	+	1.00863i
$117$	2.06509	−	0.670988i	0.190917	−	0.0620328i
$118$		−	1.27465i		−	0.117341i
$119$	0.306448	+	0.943150i	0.0280921	+	0.0864584i
$120$	−2.32677	+	2.39179i	−0.212404	+	0.218340i
$121$	−3.39780	+	10.4573i	−0.308891	+	0.950667i
$122$	−5.09020	−	1.65391i	−0.460845	−	0.149738i
$123$	3.10576	+	4.27471i	0.280037	+	0.385438i
$124$	−3.94056			−0.353873
$125$	−8.22562	−	7.57227i	−0.735722	−	0.677284i
$126$	−0.387632			−0.0345330
$127$	−8.47678	−	11.6673i	−0.752192	−	1.03530i	−0.997824	−	0.0659407i	$-0.978995\pi$
$127$	−8.47678	−	11.6673i	−0.752192	−	1.03530i	0.245631	−	0.969363i	$-0.421005\pi$
$128$	9.67998	+	3.14521i	0.855597	+	0.278000i
$129$	1.71009	−	5.26311i	0.150565	−	0.463391i
$130$	−1.31237	+	1.34904i	−0.115102	+	0.118318i
$131$	−0.272814	−	0.839634i	−0.0238358	−	0.0733592i	0.938431	−	0.345467i	$-0.112279\pi$
$131$	−0.272814	−	0.839634i	−0.0238358	−	0.0733592i	−0.962267	+	0.272108i	$0.912279\pi$
$132$		−	0.124101i		−	0.0108016i
$133$	4.54482	−	1.47670i	0.394086	−	0.128046i
$134$	−2.64736	−	1.92342i	−0.228697	−	0.166158i
$135$	2.21315	+	0.319337i	0.190477	+	0.0274842i
$136$	1.19725	−	0.869850i	0.102663	−	0.0745890i
$137$	−7.42788	+	10.2236i	−0.634606	+	0.873461i	−0.998314	−	0.0580526i	$-0.981511\pi$
$137$	−7.42788	+	10.2236i	−0.634606	+	0.873461i	0.363707	+	0.931513i	$0.381511\pi$
$138$	−0.622619	+	0.856962i	−0.0530009	+	0.0729494i
$139$	−12.0712	+	8.77022i	−1.02386	+	0.743880i	−0.967071	−	0.254506i	$-0.918087\pi$
$139$	−12.0712	+	8.77022i	−1.02386	+	0.743880i	−0.0567923	+	0.998386i	$0.518087\pi$
$140$	−3.65911	+	1.92837i	−0.309252	+	0.162977i
$141$	−3.69900	−	2.68748i	−0.311512	−	0.226326i
$142$	1.31212	−	0.426332i	0.110110	−	0.0357770i
$143$		−	0.145679i		−	0.0121823i
$144$	−0.964450	−	2.96827i	−0.0803709	−	0.247356i
$145$	10.4162	+	19.7649i	0.865017	+	1.64139i
$146$	−0.195832	+	0.602709i	−0.0162072	+	0.0498806i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	−3.36450	−	4.63084i	−0.276560	−	0.380653i
$149$	14.5624			1.19300			0.596500	−	0.802613i	$-0.296558\pi$
$149$	14.5624			1.19300			0.596500	+	0.802613i	$0.296558\pi$
$150$	−1.82610	+	0.649484i	−0.149100	+	0.0530301i
$151$	19.1234			1.55624			0.778118	−	0.628118i	$-0.216174\pi$
$151$	19.1234			1.55624			0.778118	+	0.628118i	$0.216174\pi$
$152$	−4.19160	−	5.76924i	−0.339984	−	0.467947i
$153$	−0.943150	−	0.306448i	−0.0762492	−	0.0247749i
$154$	−0.00803650	+	0.0247338i	−0.000647600	+	0.00199311i
$155$	−4.27376	−	2.10393i	−0.343276	−	0.168992i
$156$	−1.24115	−	3.81988i	−0.0993718	−	0.305835i
$157$			3.91899i			0.312769i	0.987696	+	0.156385i	$0.0499840\pi$
$157$			3.91899i			0.312769i	−0.987696	+	0.156385i	$0.950016\pi$
$158$	4.83027	−	1.56945i	0.384276	−	0.124859i
$159$	9.20366	+	6.68685i	0.729898	+	0.530302i
$160$	6.72263	+	6.53989i	0.531471	+	0.517024i
$161$	−2.21076	+	1.60621i	−0.174232	+	0.126587i
$162$	0.227844	−	0.313601i	0.0179011	−	0.0246388i
$163$	0.986330	−	1.35757i	0.0772554	−	0.106333i	−0.768640	−	0.639681i	$-0.779066\pi$
$163$	0.986330	−	1.35757i	0.0772554	−	0.106333i	0.845896	+	0.533348i	$0.179066\pi$
$164$	7.90711	−	5.74485i	0.617441	−	0.448597i
$165$	0.0662597	−	0.134595i	0.00515831	−	0.0104782i
$166$	4.47301	+	3.24983i	0.347173	+	0.252236i
$167$	−14.1772	+	4.60646i	−1.09707	+	0.356458i	−0.800973	−	0.598701i	$-0.795684\pi$
$167$	−14.1772	+	4.60646i	−1.09707	+	0.356458i	−0.296093	+	0.955159i	$0.595684\pi$
$168$			1.49228i			0.115132i
$169$	2.56026	+	7.87968i	0.196943	+	0.606130i
$170$	0.847050	−	0.146150i	0.0649658	−	0.0112092i
$171$	−1.47670	+	4.54482i	−0.112926	+	0.347551i
$172$	−9.73539	−	3.16322i	−0.742316	−	0.241193i
$173$	−8.40742	−	11.5718i	−0.639205	−	0.879790i	0.359368	−	0.933196i	$-0.382992\pi$
$173$	−8.40742	−	11.5718i	−0.639205	−	0.879790i	−0.998573	+	0.0534063i	$0.982992\pi$
$174$	3.87302			0.293613
$175$	−4.99810	+	0.137760i	−0.377821	+	0.0104137i
$176$	−0.209393			−0.0157836
$177$	1.93282	+	2.66030i	0.145279	+	0.199960i
$178$	0.254159	+	0.0825813i	0.0190500	+	0.00618973i
$179$	3.62859	−	11.1677i	0.271214	−	0.834710i	−0.718983	−	0.695028i	$-0.755392\pi$
$179$	3.62859	−	11.1677i	0.271214	−	0.834710i	0.990196	−	0.139682i	$-0.0446081\pi$
$180$	0.590691	−	4.09375i	0.0440275	−	0.305130i
$181$	3.44679	+	10.6081i	0.256198	+	0.788495i	0.993591	+	0.113032i	$0.0360562\pi$
$181$	3.44679	+	10.6081i	0.256198	+	0.788495i	−0.737394	+	0.675463i	$0.763944\pi$
$182$			0.841689i			0.0623901i
$183$	13.1315	−	4.26669i	0.970710	−	0.315403i
$184$	3.29908	+	2.39692i	0.243211	+	0.176703i
$185$	−1.17651	−	6.81877i	−0.0864986	−	0.501326i
$186$	−0.668073	+	0.485383i	−0.0489855	+	0.0355900i
$187$	−0.0391074	+	0.0538267i	−0.00285981	+	0.00393620i
$188$	−4.97114	+	6.84219i	−0.362558	+	0.499018i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−0.704261	−	4.08173i	−0.0510924	−	0.296120i
$191$	−2.95053	−	2.14368i	−0.213493	−	0.155112i	0.475900	−	0.879500i	$-0.342122\pi$
$191$	−2.95053	−	2.14368i	−0.213493	−	0.155112i	−0.689393	+	0.724388i	$0.742122\pi$
$192$	−4.39025	+	1.42648i	−0.316839	+	0.102947i
$193$		−	17.2160i		−	1.23924i	−0.784903	−	0.619618i	$-0.787287\pi$
$193$		−	17.2160i		−	1.23924i	0.784903	−	0.619618i	$-0.212713\pi$
$194$	1.26131	+	3.88190i	0.0905566	+	0.278704i
$195$	0.693396	−	4.80554i	0.0496551	−	0.344132i
$196$	−0.571602	+	1.75921i	−0.0408287	+	0.125658i
$197$	−0.127262	−	0.0413499i	−0.00906704	−	0.00294606i	0.304480	−	0.952519i	$-0.401517\pi$
$197$	−0.127262	−	0.0413499i	−0.00906704	−	0.00294606i	−0.313547	+	0.949573i	$0.601517\pi$
$198$	−0.0152863	−	0.0210398i	−0.00108635	−	0.00149524i
$199$	−11.6892			−0.828626			−0.414313	−	0.910134i	$-0.635978\pi$
$199$	−11.6892			−0.828626			−0.414313	+	0.910134i	$0.635978\pi$
$200$	2.50034	+	7.03001i	0.176801	+	0.497096i
$201$	8.44182			0.595440
$202$	−0.461880	−	0.635724i	−0.0324978	−	0.0447294i
$203$	9.50246	+	3.08754i	0.666942	+	0.216703i
$204$	−0.566850	+	1.74458i	−0.0396874	+	0.122145i
$205$	11.6430	−	2.00887i	0.813181	−	0.140306i
$206$	−0.940145	−	2.89347i	−0.0655030	−	0.201598i
$207$		−	2.73265i		−	0.189932i
$208$	−6.44519	+	2.09417i	−0.446894	+	0.145205i
$209$	0.259378	+	0.188449i	0.0179415	+	0.0130353i
$210$	−0.382828	+	0.777647i	−0.0264177	+	0.0536627i
$211$	−6.20614	+	4.50902i	−0.427248	+	0.310414i	−0.780548	−	0.625096i	$-0.785060\pi$
$211$	−6.20614	+	4.50902i	−0.427248	+	0.310414i	0.353299	+	0.935510i	$0.385060\pi$
$212$	12.3689	−	17.0244i	0.849503	−	1.16924i
$213$	−2.09202	+	2.87941i	−0.143343	+	0.197294i
$214$	6.01415	−	4.36954i	0.411119	−	0.298695i
$215$	−8.86968	−	8.62857i	−0.604907	−	0.588464i
$216$	−1.20728	−	0.877142i	−0.0821451	−	0.0596819i
$217$	−2.02606	+	0.658308i	−0.137538	+	0.0446889i
$218$		−	3.96678i		−	0.268664i
$219$	−0.505201	−	1.55485i	−0.0341383	−	0.105067i
$220$	−0.248966	−	0.122563i	−0.0167853	−	0.00826322i
$221$	−0.665410	+	2.04792i	−0.0447603	+	0.137758i
$222$	−1.14082	−	0.370675i	−0.0765668	−	0.0248781i
$223$	−5.99142	−	8.24648i	−0.401215	−	0.552225i	0.559833	−	0.828605i	$-0.310865\pi$
$223$	−5.99142	−	8.24648i	−0.401215	−	0.552225i	−0.961048	+	0.276380i	$0.910865\pi$
$224$	4.19438			0.280248
$225$	2.82636	−	4.12452i	0.188424	−	0.274968i
$226$	−0.704355			−0.0468530
$227$	−0.634226	−	0.872937i	−0.0420951	−	0.0579389i	0.787451	−	0.616378i	$-0.211401\pi$
$227$	−0.634226	−	0.872937i	−0.0420951	−	0.0579389i	−0.829546	+	0.558439i	$0.811401\pi$
$228$	8.40674	+	2.73151i	0.556750	+	0.180899i
$229$	−4.33923	+	13.3548i	−0.286744	+	0.882508i	0.699126	+	0.714998i	$0.253573\pi$
$229$	−4.33923	+	13.3548i	−0.286744	+	0.882508i	−0.985870	+	0.167510i	$0.946427\pi$
$230$	1.10429	+	2.09541i	0.0728146	+	0.138167i
$231$	−0.0207323	−	0.0638075i	−0.00136409	−	0.00419822i
$232$		−	14.9101i		−	0.978897i
$233$	7.41653	−	2.40978i	0.485873	−	0.157870i	−0.0558290	−	0.998440i	$-0.517780\pi$
$233$	7.41653	−	2.40978i	0.485873	−	0.157870i	0.541702	+	0.840571i	$0.317780\pi$
$234$	−0.680941	−	0.494732i	−0.0445145	−	0.0323417i
$235$	−9.04464	+	4.76656i	−0.590007	+	0.310936i
$236$	4.92086	−	3.57521i	0.320321	−	0.232727i
$237$	−7.70131	+	10.5999i	−0.500254	+	0.688540i
$238$	0.225950	−	0.310994i	0.0146462	−	0.0201587i
$239$	4.22240	−	3.06776i	0.273125	−	0.198437i	−0.442788	−	0.896626i	$-0.646011\pi$
$239$	4.22240	−	3.06776i	0.273125	−	0.198437i	0.715913	+	0.698189i	$0.246011\pi$
$240$	−6.90729	−	0.996660i	−0.445864	−	0.0643341i
$241$	4.53940	+	3.29806i	0.292408	+	0.212447i	0.724311	−	0.689473i	$-0.242158\pi$
$241$	4.53940	+	3.29806i	0.292408	+	0.212447i	−0.431903	+	0.901920i	$0.642158\pi$
$242$	4.05360	−	1.31709i	0.260575	−	0.0846660i
$243$			1.00000i			0.0641500i
$244$	−7.89227	−	24.2899i	−0.505251	−	1.55500i
$245$	−1.55920	+	1.60277i	−0.0996139	+	0.102397i
$246$	0.632923	−	1.94794i	0.0403537	−	0.124196i
$247$	9.86844	+	3.20645i	0.627914	+	0.204022i
$248$	1.86860	+	2.57191i	0.118656	+	0.163316i
$249$	−14.2634			−0.903905
$250$	−0.500509	+	4.30486i	−0.0316549	+	0.272263i
$251$	−11.7693			−0.742872			−0.371436	−	0.928459i	$-0.621134\pi$
$251$	−11.7693			−0.742872			−0.371436	+	0.928459i	$0.621134\pi$
$252$	−1.08725	−	1.49647i	−0.0684904	−	0.0942689i
$253$	−0.174364	−	0.0566542i	−0.0109621	−	0.00356182i
$254$	−1.72748	+	5.31665i	−0.108392	+	0.333596i
$255$	−1.54624	+	1.58945i	−0.0968295	+	0.0995351i
$256$	1.63377	+	5.02823i	0.102111	+	0.314264i
$257$		−	19.4067i		−	1.21056i	−0.796014	−	0.605278i	$-0.793062\pi$
$257$		−	19.4067i		−	1.21056i	0.796014	−	0.605278i	$-0.206938\pi$
$258$	−2.04015	+	0.662884i	−0.127014	+	0.0412694i
$259$	−2.50351	−	1.81890i	−0.155560	−	0.113021i
$260$	−8.88901	−	1.28260i	−0.551273	−	0.0795437i
$261$	−8.08328	+	5.87284i	−0.500342	+	0.363520i
$262$	−0.201151	+	0.276860i	−0.0124271	+	0.0171045i
$263$	−2.23328	+	3.07385i	−0.137710	+	0.189542i	−0.872302	−	0.488968i	$-0.837374\pi$
$263$	−2.23328	+	3.07385i	−0.137710	+	0.189542i	0.734592	+	0.678509i	$0.237374\pi$
$264$	−0.0809979	+	0.0588484i	−0.00498508	+	0.00362187i
$265$	22.5044	−	11.8599i	1.38244	−	0.728549i
$266$	−1.49861	−	1.08880i	−0.0918854	−	0.0667586i
$267$	−0.655671	+	0.213041i	−0.0401264	+	0.0130379i
$268$		−	15.6152i		−	0.953849i
$269$	−8.76082	−	26.9630i	−0.534157	−	1.64396i	−0.745465	−	0.666545i	$-0.767772\pi$
$269$	−8.76082	−	26.9630i	−0.534157	−	1.64396i	0.211308	−	0.977420i	$-0.432228\pi$
$270$	−0.404109	−	0.766804i	−0.0245933	−	0.0466662i
$271$	8.02222	−	24.6899i	0.487315	−	1.49980i	−0.341284	−	0.939960i	$-0.610862\pi$
$271$	8.02222	−	24.6899i	0.487315	−	1.49980i	0.828599	−	0.559842i	$-0.189138\pi$
$272$	2.94360	+	0.956433i	0.178482	+	0.0579922i
$273$	−1.27629	−	1.75667i	−0.0772448	−	0.106318i
$274$	4.89853			0.295931
$275$	−0.204578	−	0.265854i	−0.0123365	−	0.0160316i
$276$	−5.05470			−0.304257
$277$	10.2897	+	14.1625i	0.618246	+	0.850943i	0.997224	−	0.0744629i	$-0.0237242\pi$
$277$	10.2897	+	14.1625i	0.618246	+	0.850943i	−0.378978	+	0.925406i	$0.623724\pi$
$278$	5.50070	+	1.78728i	0.329910	+	0.107194i
$279$	0.658308	−	2.02606i	0.0394119	−	0.121297i
$280$	2.99374	+	1.47379i	0.178910	+	0.0880758i
$281$	−7.59803	−	23.3843i	−0.453261	−	1.39499i	−0.873165	−	0.487424i	$-0.837936\pi$
$281$	−7.59803	−	23.3843i	−0.453261	−	1.39499i	0.419905	−	0.907568i	$-0.362064\pi$
$282$			1.77233i			0.105541i
$283$	−22.7767	+	7.40059i	−1.35393	+	0.439920i	−0.894013	−	0.448040i	$-0.852122\pi$
$283$	−22.7767	+	7.40059i	−1.35393	+	0.439920i	−0.459920	+	0.887960i	$0.652122\pi$
$284$	5.32617	+	3.86969i	0.316050	+	0.229624i
$285$	7.65918	+	7.45098i	0.453690	+	0.441358i
$286$	−0.0456851	+	0.0331922i	−0.00270142	+	0.00196269i
$287$	3.10576	−	4.27471i	0.183327	−	0.252328i
$288$	−2.46539	+	3.39332i	−0.145275	+	0.199953i
$289$	−12.9577	+	9.41430i	−0.762216	+	0.553782i
$290$	3.82502	−	7.76985i	0.224613	−	0.456261i
$291$	−8.51876	−	6.18924i	−0.499379	−	0.362820i
$292$	−2.87607	+	0.934491i	−0.168309	+	0.0546870i
$293$		−	19.2110i		−	1.12232i	−0.827708	−	0.561159i	$-0.810356\pi$
$293$		−	19.2110i		−	1.12232i	0.827708	−	0.561159i	$-0.189644\pi$
$294$	0.119785	+	0.368660i	0.00698599	+	0.0215007i
$295$	7.24581	−	1.25019i	0.421868	−	0.0727889i
$296$	−1.42700	+	4.39186i	−0.0829428	+	0.255272i
$297$	0.0638075	+	0.0207323i	0.00370248	+	0.00120301i
$298$	−3.31796	−	4.56679i	−0.192204	−	0.264547i
$299$	−5.93357			−0.343147
$300$	−7.62930	−	5.22804i	−0.440478	−	0.301841i
$301$	−5.53396			−0.318972
$302$	−4.35715	−	5.99710i	−0.250726	−	0.345094i
$303$	1.92796	+	0.626431i	0.110758	+	0.0359875i
$304$	4.60882	−	14.1845i	0.264334	−	0.813537i
$305$	4.40918	−	30.5576i	0.252469	−	1.74972i
$306$	0.118789	+	0.365595i	0.00679072	+	0.0208997i
$307$			22.7002i			1.29557i	0.761824	+	0.647784i	$0.224304\pi$
$307$			22.7002i			1.29557i	−0.761824	+	0.647784i	$0.775696\pi$
$308$	−0.118027	+	0.0383494i	−0.00672523	+	0.00218516i
$309$	6.34966	+	4.61330i	0.361220	+	0.262441i
$310$	0.313957	+	1.81962i	0.0178316	+	0.103348i
$311$	−4.10729	+	2.98412i	−0.232903	+	0.169214i	−0.698116	−	0.715985i	$-0.745978\pi$
$311$	−4.10729	+	2.98412i	−0.232903	+	0.169214i	0.465213	+	0.885199i	$0.345978\pi$
$312$	−1.90459	+	2.62145i	−0.107826	+	0.148410i
$313$	7.51694	−	10.3462i	0.424882	−	0.584800i	−0.541887	−	0.840451i	$-0.682290\pi$
$313$	7.51694	−	10.3462i	0.424882	−	0.584800i	0.966769	+	0.255651i	$0.0822899\pi$
$314$	1.22900	−	0.892920i	0.0693564	−	0.0503904i
$315$	−0.380193	−	2.20351i	−0.0214214	−	0.124154i
$316$	19.6071	+	14.2454i	1.10299	+	0.801368i
$317$	11.7369	−	3.81354i	0.659207	−	0.214189i	0.0397379	−	0.999210i	$-0.487348\pi$
$317$	11.7369	−	3.81354i	0.659207	−	0.214189i	0.619470	+	0.785021i	$0.287348\pi$
$318$		−	4.40984i		−	0.247291i
$319$	0.207146	+	0.637531i	0.0115980	+	0.0356949i
$320$	−1.47412	+	10.2163i	−0.0824057	+	0.571108i
$321$	−5.92624	+	18.2391i	−0.330771	+	1.01801i
$322$	1.00742	+	0.327330i	0.0561413	+	0.0182414i
$323$	−2.78550	−	3.83391i	−0.154989	−	0.213325i
$324$	1.84974			0.102763
$325$	−8.95583	−	6.13705i	−0.496780	−	0.340422i
$326$	−0.650464			−0.0360259
$327$	6.01502	+	8.27896i	0.332631	+	0.457828i
$328$	−7.49905	−	2.43659i	−0.414066	−	0.134538i
$329$	−1.41289	+	4.34843i	−0.0778952	+	0.239737i
$330$	−0.0573059	+	0.00988755i	−0.00315459	+	0.000544291i
$331$	−6.15460	−	18.9419i	−0.338288	−	1.04114i	−0.965080	−	0.261956i	$-0.915632\pi$
$331$	−6.15460	−	18.9419i	−0.338288	−	1.04114i	0.626792	−	0.779186i	$-0.284368\pi$
$332$			26.3836i			1.44799i
$333$	2.94305	−	0.956254i	0.161278	−	0.0524024i
$334$	4.67479	+	3.39643i	0.255793	+	0.185844i
$335$	8.33721	−	16.9355i	0.455510	−	0.925287i
$336$	−2.52496	+	1.83449i	−0.137748	+	0.100080i
$337$	13.8290	−	19.0340i	0.753316	−	1.03685i	−0.244425	−	0.969668i	$-0.578599\pi$
$337$	13.8290	−	19.0340i	0.753316	−	1.03685i	0.997741	−	0.0671821i	$-0.0214009\pi$
$338$	1.88773	−	2.59824i	0.102679	−	0.141326i
$339$	1.47004	−	1.06805i	0.0798418	−	0.0580084i
$340$	2.94007	+	2.86015i	0.159448	+	0.155113i
$341$	−0.115630	−	0.0840099i	−0.00626170	−	0.00454939i
$342$	1.76172	−	0.572416i	0.0952627	−	0.0309527i
$343$			1.00000i			0.0539949i
$344$	2.55193	+	7.85404i	0.137591	+	0.423462i
$345$	−5.48210	−	2.69879i	−0.295147	−	0.145298i
$346$	−1.71335	+	5.27315i	−0.0921103	+	0.283486i
$347$	11.7550	+	3.81943i	0.631041	+	0.205038i	0.607036	−	0.794674i	$-0.292358\pi$
$347$	11.7550	+	3.81943i	0.631041	+	0.205038i	0.0240050	+	0.999712i	$0.492358\pi$
$348$	10.8632	+	14.9520i	0.582331	+	0.801510i
$349$	−19.5074			−1.04421			−0.522104	−	0.852882i	$-0.674853\pi$
$349$	−19.5074			−1.04421			−0.522104	+	0.852882i	$0.674853\pi$
$350$	1.18199	+	1.53602i	0.0631801	+	0.0821038i
$351$	2.17136			0.115899
$352$	0.165406	+	0.227662i	0.00881617	+	0.0121344i
$353$	9.34251	+	3.03557i	0.497252	+	0.161567i	0.546897	−	0.837200i	$-0.315809\pi$
$353$	9.34251	+	3.03557i	0.497252	+	0.161567i	−0.0496450	+	0.998767i	$0.515809\pi$
$354$	0.393889	−	1.21227i	0.0209350	−	0.0644312i
$355$	3.71044	+	7.04063i	0.196930	+	0.373678i
$356$	0.394070	+	1.21282i	0.0208857	+	0.0642795i
$357$			0.991687i			0.0524856i
$358$	−4.32894	+	1.40656i	−0.228792	+	0.0743389i
$359$	7.94229	+	5.77041i	0.419178	+	0.304551i	0.777307	−	0.629121i	$-0.216585\pi$
$359$	7.94229	+	5.77041i	0.419178	+	0.304551i	−0.358129	+	0.933672i	$0.616585\pi$
$360$	−2.95200	+	1.55571i	−0.155584	+	0.0819934i
$361$	−3.10340	+	2.25475i	−0.163337	+	0.118671i
$362$	2.54138	−	3.49791i	0.133572	−	0.183846i
$363$	−6.46299	+	8.89555i	−0.339219	+	0.466895i
$364$	−3.24938	+	2.36081i	−0.170314	+	0.123740i
$365$	−3.61820	−	0.522073i	−0.189385	−	0.0273266i
$366$	−4.32998	−	3.14592i	−0.226332	−	0.164440i
$367$	26.1910	−	8.50998i	1.36716	−	0.444217i	0.468733	−	0.883340i	$-0.344711\pi$
$367$	26.1910	−	8.50998i	1.36716	−	0.444217i	0.898427	+	0.439122i	$0.144711\pi$
$368$			8.52868i			0.444588i
$369$	1.63279	+	5.02522i	0.0849999	+	0.261603i
$370$	−1.87031	+	1.92257i	−0.0972328	+	0.0999497i
$371$	3.51549	−	10.8196i	0.182515	−	0.561723i
$372$	−3.74769	−	1.21770i	−0.194309	−	0.0631348i
$373$	−1.96386	−	2.70302i	−0.101685	−	0.139957i	0.755142	−	0.655561i	$-0.227568\pi$
$373$	−1.96386	−	2.70302i	−0.101685	−	0.139957i	−0.856827	+	0.515604i	$0.827568\pi$
$374$	0.0257905			0.00133359
$375$	−5.48307	−	9.74351i	−0.283144	−	0.503153i
$376$	6.82303			0.351871
$377$	12.7521	+	17.5517i	0.656765	+	0.903959i
$378$	−0.368660	−	0.119785i	−0.0189618	−	0.00616107i
$379$	−7.74770	+	23.8450i	−0.397973	+	1.22483i	0.528649	+	0.848840i	$0.322699\pi$
$379$	−7.74770	+	23.8450i	−0.397973	+	1.22483i	−0.926622	+	0.375994i	$0.877301\pi$
$380$	13.7824	−	14.1675i	0.707021	−	0.726777i
$381$	−4.45651	−	13.7157i	−0.228314	−	0.702677i
$382$			1.41371i			0.0723319i
$383$	−12.9508	+	4.20797i	−0.661755	+	0.215017i	−0.620590	−	0.784135i	$-0.713107\pi$
$383$	−12.9508	+	4.20797i	−0.661755	+	0.215017i	−0.0411652	+	0.999152i	$0.513107\pi$
$384$	8.23428	+	5.98255i	0.420204	+	0.305296i
$385$	−0.148483	−	0.0214247i	−0.00756738	−	0.00109190i
$386$	−5.39896	+	3.92258i	−0.274800	+	0.199654i
$387$	3.25278	−	4.47707i	0.165348	−	0.227582i
$388$	−11.4485	+	15.7575i	−0.581210	+	0.799966i
$389$	20.8549	−	15.1520i	1.05739	−	0.768237i	0.0837842	−	0.996484i	$-0.473299\pi$
$389$	20.8549	−	15.1520i	1.05739	−	0.768237i	0.973603	+	0.228247i	$0.0732994\pi$
$390$	−1.66501	+	0.877466i	−0.0843110	+	0.0444322i
$391$	2.19238	+	1.59286i	0.110874	+	0.0805544i
$392$	1.41925	−	0.461141i	0.0716827	−	0.0232911i
$393$		−	0.882844i		−	0.0445336i
$394$	0.0160286	+	0.0493308i	0.000807507	+	0.00248525i
$395$	13.6592	+	25.9185i	0.687268	+	1.30410i
$396$	0.0383494	−	0.118027i	0.00192713	−	0.00593110i
$397$	4.25268	+	1.38178i	0.213436	+	0.0693495i	0.413783	−	0.910375i	$-0.364207\pi$
$397$	4.25268	+	1.38178i	0.213436	+	0.0693495i	−0.200348	+	0.979725i	$0.564207\pi$
$398$	2.66332	+	3.66575i	0.133500	+	0.183747i
$399$	4.77870			0.239234
$400$	−8.82114	+	12.8727i	−0.441057	+	0.643637i
$401$	−21.4889			−1.07310			−0.536552	−	0.843867i	$-0.680273\pi$
$401$	−21.4889			−1.07310			−0.536552	+	0.843867i	$0.680273\pi$
$402$	−1.92342	−	2.64736i	−0.0959315	−	0.132038i
$403$	−4.39932	−	1.42942i	−0.219146	−	0.0712047i
$404$	1.15874	−	3.56622i	0.0576493	−	0.177426i
$405$	2.00615	+	0.987608i	0.0996863	+	0.0490746i
$406$	−1.19683	−	3.68346i	−0.0593976	−	0.182807i
$407$		−	0.207614i		−	0.0102910i
$408$	1.40745	−	0.457307i	0.0696790	−	0.0226401i
$409$	−2.35720	−	1.71261i	−0.116556	−	0.0846829i	0.527980	−	0.849257i	$-0.322950\pi$
$409$	−2.35720	−	1.71261i	−0.116556	−	0.0846829i	−0.644536	+	0.764574i	$0.722950\pi$
$410$	−3.28277	−	3.19354i	−0.162124	−	0.157717i
$411$	−10.2236	+	7.42788i	−0.504293	+	0.366390i
$412$	8.53341	−	11.7452i	0.420411	−	0.578646i
$413$	1.93282	−	2.66030i	0.0951077	−	0.130905i
$414$	−0.856962	+	0.622619i	−0.0421174	+	0.0306001i
$415$	−14.0866	+	28.6145i	−0.691486	+	1.40463i
$416$	7.36812	+	5.35326i	0.361252	+	0.262465i
$417$	−14.1905	+	4.61078i	−0.694913	+	0.225791i
$418$		−	0.124278i		−	0.00607864i
$419$	−8.57701	−	26.3973i	−0.419014	−	1.28959i	−0.908611	−	0.417644i	$-0.862856\pi$
$419$	−8.57701	−	26.3973i	−0.419014	−	1.28959i	0.489596	−	0.871949i	$-0.337144\pi$
$420$	−4.07592	+	0.703258i	−0.198885	+	0.0343155i
$421$	−8.76543	+	26.9772i	−0.427201	+	1.31479i	0.473670	+	0.880702i	$0.342929\pi$
$421$	−8.76543	+	26.9772i	−0.427201	+	1.31479i	−0.900871	+	0.434087i	$0.857071\pi$
$422$	2.82807	+	0.918894i	0.137668	+	0.0447311i
$423$	−2.68748	−	3.69900i	−0.130670	−	0.179851i
$424$	−16.9767			−0.824463
$425$	1.66159	+	4.67174i	0.0805988	+	0.226613i
$426$	1.37964			0.0668438
$427$	−8.11573	−	11.1703i	−0.392748	−	0.540571i
$428$	33.7376	+	10.9620i	1.63077	+	0.529869i
$429$	0.0450173	−	0.138549i	0.00217346	−	0.00668921i
$430$	−0.685023	+	4.74751i	−0.0330347	+	0.228945i
$431$	7.82965	+	24.0972i	0.377141	+	1.16072i	0.942023	+	0.335549i	$0.108922\pi$
$431$	7.82965	+	24.0972i	0.377141	+	1.16072i	−0.564882	+	0.825172i	$0.691078\pi$
$432$		−	3.12103i		−	0.150160i
$433$	−22.6266	+	7.35182i	−1.08736	+	0.353306i	−0.797227	−	0.603680i	$-0.793701\pi$
$433$	−22.6266	+	7.35182i	−1.08736	+	0.353306i	−0.290136	+	0.956985i	$0.593701\pi$
$434$	0.668073	+	0.485383i	0.0320685	+	0.0232991i
$435$	3.79869	+	22.0163i	0.182133	+	1.05560i
$436$	15.3139	−	11.1262i	0.733405	−	0.532850i
$437$	7.67561	−	10.5646i	0.367174	−	0.505372i
$438$	−0.372495	+	0.512695i	−0.0177985	+	0.0244975i
$439$	0.912633	−	0.663067i	0.0435576	−	0.0316464i	−0.565793	−	0.824547i	$-0.691430\pi$
$439$	0.912633	−	0.663067i	0.0435576	−	0.0316464i	0.609351	+	0.792901i	$0.291430\pi$
$440$	0.0380645	+	0.220613i	0.00181465	+	0.0105173i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	0.793839	−	0.257934i	0.0377591	−	0.0122687i
$443$			4.53356i			0.215396i	0.994184	+	0.107698i	$0.0343479\pi$
$443$			4.53356i			0.215396i	−0.994184	+	0.107698i	$0.965652\pi$
$444$	−1.76882	−	5.44388i	−0.0839446	−	0.258355i
$445$	−0.220155	+	1.52577i	−0.0104364	+	0.0723286i
$446$	−1.22099	+	3.75783i	−0.0578157	+	0.177938i
$447$	13.8497	+	4.50003i	0.655067	+	0.212844i
$448$	2.71332	+	3.73457i	0.128192	+	0.176442i
$449$	−7.28490			−0.343795			−0.171898	−	0.985115i	$-0.554990\pi$
$449$	−7.28490			−0.343795			−0.171898	+	0.985115i	$0.554990\pi$
$450$	−1.93742	+	0.0534003i	−0.0913310	+	0.00251732i
$451$	0.354498			0.0166927
$452$	−1.97561	−	2.71920i	−0.0929250	−	0.127900i
$453$	18.1874	+	5.90944i	0.854518	+	0.277650i
$454$	−0.129249	+	0.397788i	−0.00606596	+	0.0186691i
$455$	−4.78461	+	0.825536i	−0.224306	+	0.0387017i
$456$	−2.20365	−	6.78215i	−0.103196	−	0.317603i
$457$		−	23.4010i		−	1.09465i	−0.836919	−	0.547327i	$-0.815645\pi$
$457$		−	23.4010i		−	1.09465i	0.836919	−	0.547327i	$-0.184355\pi$
$458$	5.17673	−	1.68202i	0.241893	−	0.0785958i
$459$	−0.802292	−	0.582899i	−0.0374478	−	0.0272074i
$460$	−4.99206	+	10.1405i	−0.232756	+	0.472802i
$461$	11.3756	−	8.26483i	0.529813	−	0.384932i	−0.290475	−	0.956883i	$-0.593813\pi$
$461$	11.3756	−	8.26483i	0.529813	−	0.384932i	0.820288	+	0.571951i	$0.193813\pi$
$462$	−0.0152863	+	0.0210398i	−0.000711185	+	0.000978862i
$463$	−23.1942	+	31.9241i	−1.07793	+	1.48364i	−0.216145	+	0.976361i	$0.569348\pi$
$463$	−23.1942	+	31.9241i	−1.07793	+	1.48364i	−0.861782	+	0.507278i	$0.830652\pi$
$464$	25.2281	−	18.3293i	1.17119	−	0.850917i
$465$	−3.41443	−	3.32162i	−0.158341	−	0.154036i
$466$	−2.44552	−	1.77678i	−0.113287	−	0.0823075i
$467$	−5.16341	+	1.67769i	−0.238934	+	0.0776344i	−0.426036	−	0.904706i	$-0.640090\pi$
$467$	−5.16341	+	1.67769i	−0.238934	+	0.0776344i	0.187102	+	0.982340i	$0.440090\pi$
$468$		−	4.01646i		−	0.185661i
$469$	−2.60867	−	8.02865i	−0.120457	−	0.370729i
$470$	3.55557	+	1.75037i	0.164006	+	0.0807386i
$471$	−1.21103	+	3.72718i	−0.0558015	+	0.171739i
$472$	−4.66691	−	1.51637i	−0.214812	−	0.0697967i
$473$	−0.218233	−	0.300372i	−0.0100343	−	0.0138111i
$474$	5.07885			0.233279
$475$	22.5120	−	8.00680i	1.03292	−	0.367377i
$476$	1.83436			0.0840780
$477$	6.68685	+	9.20366i	0.306170	+	0.421407i
$478$	−1.92410	−	0.625179i	−0.0880064	−	0.0285950i
$479$	−9.76025	+	30.0389i	−0.445957	+	1.37251i	0.435474	+	0.900201i	$0.356581\pi$
$479$	−9.76025	+	30.0389i	−0.445957	+	1.37251i	−0.881431	+	0.472313i	$0.843419\pi$
$480$	4.37266	+	8.29721i	0.199584	+	0.378714i
$481$	−2.07637	−	6.39042i	−0.0946745	−	0.291378i
$482$		−	2.17500i		−	0.0990687i
$483$	−2.59891	+	0.844436i	−0.118254	+	0.0384232i
$484$	16.4545	+	11.9549i	0.747930	+	0.543403i
$485$	−20.8297	+	10.9774i	−0.945830	+	0.498456i
$486$	0.313601	−	0.227844i	0.0142252	−	0.0103352i
$487$	−16.2915	+	22.4234i	−0.738240	+	1.01610i	0.260478	+	0.965480i	$0.416120\pi$
$487$	−16.2915	+	22.4234i	−0.738240	+	1.01610i	−0.998718	+	0.0506201i	$0.983880\pi$
$488$	−12.1110	+	16.6693i	−0.548237	+	0.754584i
$489$	1.35757	−	0.986330i	0.0613913	−	0.0446034i
$490$	0.857887	+	0.123785i	0.0387554	+	0.00559205i
$491$	−31.7789	−	23.0887i	−1.43416	−	1.04198i	−0.989223	−	0.146417i	$-0.953226\pi$
$491$	−31.7789	−	23.0887i	−1.43416	−	1.04198i	−0.444937	−	0.895562i	$-0.646774\pi$
$492$	9.29536	−	3.02025i	0.419067	−	0.136163i
$493$		−	9.90842i		−	0.446253i
$494$	−1.24292	−	3.82532i	−0.0559217	−	0.172109i
$495$	0.104609	−	0.107532i	0.00470182	−	0.00483320i
$496$	−2.05460	+	6.32340i	−0.0922541	+	0.283929i
$497$	3.38495	+	1.09984i	0.151836	+	0.0493345i
$498$	3.24983	+	4.47301i	0.145628	+	0.200440i
$499$	−23.7848			−1.06475			−0.532376	−	0.846508i	$-0.678701\pi$
$499$	−23.7848			−1.06475			−0.532376	+	0.846508i	$0.678701\pi$
$500$	−18.0230	+	10.1423i	−0.806012	+	0.453576i
$501$	−14.9068			−0.665987
$502$	2.68157	+	3.69086i	0.119684	+	0.164731i
$503$	−13.0418	−	4.23754i	−0.581505	−	0.188942i	0.00346963	−	0.999994i	$-0.498896\pi$
$503$	−13.0418	−	4.23754i	−0.581505	−	0.188942i	−0.584975	+	0.811052i	$0.698896\pi$
$504$	−0.461141	+	1.41925i	−0.0205408	+	0.0632182i
$505$	3.16078	−	3.24910i	0.140653	−	0.144583i
$506$	0.0219610	+	0.0675889i	0.000976284	+	0.00300469i
$507$			8.28519i			0.367958i
$508$	−25.3705	+	8.24338i	−1.12564	+	0.365741i
$509$	−10.1070	−	7.34316i	−0.447985	−	0.325480i	0.340815	−	0.940130i	$-0.389297\pi$
$509$	−10.1070	−	7.34316i	−0.447985	−	0.325480i	−0.788800	+	0.614651i	$0.789297\pi$
$510$	0.850755	+	0.122756i	0.0376721	+	0.00543574i
$511$	−1.32263	+	0.960950i	−0.0585099	+	0.0425099i
$512$	13.1697	−	18.1266i	0.582025	−	0.801088i
$513$	−2.80885	+	3.86605i	−0.124014	+	0.170690i
$514$	−6.08595	+	4.42170i	−0.268440	+	0.195033i
$515$	15.5259	−	8.18223i	0.684155	−	0.360552i
$516$	−8.28142	−	6.01680i	−0.364569	−	0.264875i
$517$	−0.291741	+	0.0947924i	−0.0128308	+	0.00416897i
$518$			1.19953i			0.0527042i
$519$	−4.42004	−	13.6035i	−0.194018	−	0.597127i
$520$	3.37802	+	6.40985i	0.148136	+	0.281091i
$521$	8.76515	−	26.9764i	0.384008	−	1.18186i	−0.553189	−	0.833056i	$-0.686589\pi$
$521$	8.76515	−	26.9764i	0.384008	−	1.18186i	0.937197	−	0.348800i	$-0.113411\pi$
$522$	3.68346	+	1.19683i	0.161221	+	0.0523837i
$523$	−4.57367	−	6.29512i	−0.199993	−	0.275266i	0.697227	−	0.716850i	$-0.254417\pi$
$523$	−4.57367	−	6.29512i	−0.199993	−	0.275266i	−0.897220	+	0.441584i	$0.854417\pi$
$524$	−1.63303			−0.0713393
$525$	−4.79605	−	1.41348i	−0.209317	−	0.0616893i
$526$	1.47280			0.0642172
$527$	1.24177	+	1.70915i	0.0540922	+	0.0744515i
$528$	−0.199145	−	0.0647061i	−0.00866667	−	0.00281597i
$529$	4.79984	−	14.7724i	0.208689	−	0.642278i
$530$	−8.84678	−	4.35519i	−0.384280	−	0.189177i
$531$	1.01614	+	3.12736i	0.0440968	+	0.135716i
$532$		−	8.83937i		−	0.383235i
$533$	10.9116	−	3.54539i	0.472633	−	0.153568i
$534$	0.216201	+	0.157079i	0.00935592	+	0.00679747i
$535$	30.7375	+	29.9020i	1.32890	+	1.29278i
$536$	−10.1917	+	7.40467i	−0.440213	+	0.319833i
$537$	6.90199	−	9.49978i	0.297843	−	0.409946i
$538$	−6.45952	+	8.89077i	−0.278490	+	0.383308i
$539$	−0.0542779	+	0.0394352i	−0.00233791	+	0.00169859i
$540$	1.82682	−	3.71086i	0.0786138	−	0.159690i
$541$	−21.5822	−	15.6804i	−0.927892	−	0.674153i	0.0175839	−	0.999845i	$-0.494403\pi$
$541$	−21.5822	−	15.6804i	−0.927892	−	0.674153i	−0.945476	+	0.325693i	$0.894403\pi$
$542$	−9.57058	+	3.10967i	−0.411091	+	0.133572i
$543$			11.1540i			0.478665i
$544$	−1.28536	−	3.95593i	−0.0551093	−	0.169609i
$545$	22.5493	−	3.89065i	0.965906	−	0.166657i
$546$	−0.260096	+	0.800494i	−0.0111311	+	0.0342580i
$547$	37.9739	+	12.3385i	1.62365	+	0.527555i	0.972799	−	0.231651i	$-0.0744128\pi$
$547$	37.9739	+	12.3385i	1.62365	+	0.527555i	0.650850	+	0.759207i	$0.274413\pi$
$548$	13.7397	+	18.9110i	0.586929	+	0.807838i
$549$	13.8073			0.589281
$550$	−0.0367599	+	0.124729i	−0.00156745	+	0.00531847i
$551$	−47.7463			−2.03406
$552$	2.39692	+	3.29908i	0.102020	+	0.140418i
$553$	12.4610	+	4.04882i	0.529894	+	0.172173i
$554$	2.09693	−	6.45370i	0.0890902	−	0.274191i
$555$	0.988190	−	6.84859i	0.0419463	−	0.290707i
$556$	8.52875	+	26.2488i	0.361699	+	1.11320i
$557$		−	1.51738i		−	0.0642936i	−0.999483	−	0.0321468i	$-0.989766\pi$
$557$		−	1.51738i		−	0.0642936i	0.999483	−	0.0321468i	$-0.0102344\pi$
$558$	−0.785367	+	0.255181i	−0.0332472	+	0.0108027i
$559$	−9.72133	−	7.06296i	−0.411168	−	0.298731i
$560$	1.18659	+	6.87721i	0.0501426	+	0.290615i
$561$	−0.0538267	+	0.0391074i	−0.00227256	+	0.00165111i
$562$	−5.60218	+	7.71074i	−0.236314	+	0.325258i
$563$	−4.78534	+	6.58646i	−0.201678	+	0.277586i	−0.897862	−	0.440278i	$-0.854880\pi$
$563$	−4.78534	+	6.58646i	−0.201678	+	0.277586i	0.696184	+	0.717864i	$0.254880\pi$
$564$	−6.84219	+	4.97114i	−0.288108	+	0.209323i
$565$	−0.690838	−	4.00394i	−0.0290638	−	0.168447i
$566$	7.51037	+	5.45660i	0.315685	+	0.229358i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$		−	5.31126i		−	0.222855i
$569$	11.8953	+	36.6100i	0.498677	+	1.53477i	0.811146	+	0.584843i	$0.198844\pi$
$569$	11.8953	+	36.6100i	0.498677	+	1.53477i	−0.312469	+	0.949928i	$0.601156\pi$
$570$	0.591533	−	4.09959i	0.0247766	−	0.171713i
$571$	12.4432	−	38.2961i	0.520730	−	1.60264i	−0.251877	−	0.967759i	$-0.581048\pi$
$571$	12.4432	−	38.2961i	0.520730	−	1.60264i	0.772607	−	0.634884i	$-0.218952\pi$
$572$	−0.256280	−	0.0832704i	−0.0107156	−	0.00348171i
$573$	−2.14368	−	2.95053i	−0.0895537	−	0.123260i
$574$	−2.04818			−0.0854895
$575$	−10.8283	+	8.33257i	−0.451573	+	0.347492i
$576$	−4.61618			−0.192341
$577$	−19.9594	−	27.4718i	−0.830922	−	1.14367i	−0.987751	−	0.156041i	$-0.950127\pi$
$577$	−19.9594	−	27.4718i	−0.830922	−	1.14367i	0.156828	−	0.987626i	$-0.449873\pi$
$578$	5.90466	+	1.91854i	0.245602	+	0.0798008i
$579$	5.32005	−	16.3734i	0.221094	−	0.680456i
$580$	40.7245	−	7.02659i	1.69099	−	0.291763i
$581$	4.40763	+	13.5653i	0.182859	+	0.562783i
$582$			4.08168i			0.169191i
$583$	0.725896	−	0.235858i	0.0300635	−	0.00976824i
$584$	1.97374	+	1.43401i	0.0816741	+	0.0593397i
$585$	2.14445	−	4.35607i	0.0886622	−	0.180101i
$586$	−6.02458	+	4.37711i	−0.248873	+	0.180817i
$587$	−11.2140	+	15.4348i	−0.462852	+	0.637062i	−0.975097	−	0.221778i	$-0.928814\pi$
$587$	−11.2140	+	15.4348i	−0.462852	+	0.637062i	0.512245	+	0.858839i	$0.328814\pi$
$588$	−1.08725	+	1.49647i	−0.0448375	+	0.0617135i
$589$	8.23596	−	5.98378i	0.339357	−	0.246557i
$590$	−2.04298	−	1.98744i	−0.0841081	−	0.0818218i
$591$	−0.108256	−	0.0786522i	−0.00445304	−	0.00323532i
$592$	−9.18533	+	2.98449i	−0.377515	+	0.122662i
$593$		−	6.03148i		−	0.247683i	−0.992302	−	0.123842i	$-0.960479\pi$
$593$		−	6.03148i		−	0.247683i	0.992302	−	0.123842i	$-0.0395215\pi$
$594$	−0.00803650	−	0.0247338i	−0.000329742	−	0.00101484i
$595$	1.98947	+	0.979398i	0.0815604	+	0.0401514i
$596$	8.32390	−	25.6183i	0.340960	−	1.04937i
$597$	−11.1171	−	3.61216i	−0.454993	−	0.147836i
$598$	1.35193	+	1.86077i	0.0552846	+	0.0760927i
$599$	−32.1579			−1.31394			−0.656968	−	0.753918i	$-0.728162\pi$
$599$	−32.1579			−1.31394			−0.656968	+	0.753918i	$0.728162\pi$
$600$	0.205577	+	7.45858i	0.00839266	+	0.304495i
$601$	46.4095			1.89308			0.946541	−	0.322582i	$-0.104551\pi$
$601$	46.4095			1.89308			0.946541	+	0.322582i	$0.104551\pi$
$602$	1.26088	+	1.73545i	0.0513897	+	0.0707318i
$603$	8.02865	+	2.60867i	0.326952	+	0.106233i
$604$	10.9309	−	33.6420i	0.444774	−	1.36887i
$605$	11.4629	+	21.7510i	0.466032	+	0.884305i
$606$	−0.242825	−	0.747338i	−0.00986409	−	0.0303585i
$607$		−	9.67223i		−	0.392584i	−0.980546	−	0.196292i	$-0.937110\pi$
$607$		−	9.67223i		−	0.392584i	0.980546	−	0.196292i	$-0.0628900\pi$
$608$	−19.0627	+	6.19384i	−0.773093	+	0.251193i
$609$	8.08328	+	5.87284i	0.327551	+	0.237980i
$610$	−10.5875	+	5.57965i	−0.428675	+	0.225914i
$611$	−8.03185	+	5.83548i	−0.324934	+	0.236078i
$612$	−1.07821	+	1.48403i	−0.0435842	+	0.0599884i
$613$	−15.9309	+	21.9270i	−0.643442	+	0.885622i	−0.998793	−	0.0491105i	$-0.984361\pi$
$613$	−15.9309	+	21.9270i	−0.643442	+	0.885622i	0.355351	+	0.934733i	$0.384361\pi$
$614$	7.11880	−	5.17211i	0.287291	−	0.208729i
$615$	11.6939	+	1.68732i	0.471544	+	0.0680395i
$616$	0.0809979	+	0.0588484i	0.00326350	+	0.00237107i
$617$	−33.4411	+	10.8657i	−1.34629	+	0.437436i	−0.891443	−	0.453134i	$-0.850306\pi$
$617$	−33.4411	+	10.8657i	−1.34629	+	0.437436i	−0.454847	+	0.890570i	$0.650306\pi$
$618$		−	3.04237i		−	0.122382i
$619$	−9.67199	−	29.7673i	−0.388750	−	1.19645i	−0.933723	−	0.357996i	$-0.883460\pi$
$619$	−9.67199	−	29.7673i	−0.388750	−	1.19645i	0.544973	−	0.838453i	$-0.316540\pi$
$620$	−6.14414	+	6.31582i	−0.246754	+	0.253649i
$621$	0.844436	−	2.59891i	0.0338860	−	0.104291i
$622$	1.87165	+	0.608134i	0.0750461	+	0.0243840i
$623$	0.405227	+	0.557747i	0.0162351	+	0.0223457i
$624$	−6.77688			−0.271292
$625$	−24.9620	+	1.37708i	−0.998482	+	0.0550832i
$626$	−4.95726			−0.198132
$627$	0.188449	+	0.259378i	0.00752593	+	0.0103586i
$628$	6.89432	+	2.24010i	0.275113	+	0.0893898i
$629$	−0.948305	+	2.91858i	−0.0378114	+	0.116371i
$630$	−0.604398	+	0.621286i	−0.0240798	+	0.0247526i
$631$	7.88735	+	24.2748i	0.313990	+	0.966363i	0.976168	+	0.217016i	$0.0696325\pi$
$631$	7.88735	+	24.2748i	0.313990	+	0.966363i	−0.662177	+	0.749347i	$0.730368\pi$
$632$		−	19.5523i		−	0.777747i
$633$	−7.29575	+	2.37053i	−0.289980	+	0.0942202i
$634$	−3.87010	−	2.81180i	−0.153701	−	0.111671i
$635$	−31.9170	−	4.60534i	−1.26659	−	0.182757i
$636$	17.0244	−	12.3689i	0.675061	−	0.490461i
$637$	−1.27629	+	1.75667i	−0.0505686	+	0.0696017i
$638$	0.152733	−	0.210219i	0.00604676	−	0.00832266i
$639$	−2.87941	+	2.09202i	−0.113908	+	0.0827589i
$640$	20.1341	−	10.6108i	0.795871	−	0.419427i
$641$	1.25899	+	0.914707i	0.0497270	+	0.0361288i	0.612371	−	0.790570i	$-0.290216\pi$
$641$	1.25899	+	0.914707i	0.0497270	+	0.0361288i	−0.562644	+	0.826699i	$0.690216\pi$
$642$	7.07006	−	2.29720i	0.279033	−	0.0906633i
$643$		−	11.7264i		−	0.462446i	−0.972901	−	0.231223i	$-0.925727\pi$
$643$		−	11.7264i		−	0.462446i	0.972901	−	0.231223i	$-0.0742726\pi$
$644$	1.56199	+	4.80730i	0.0615509	+	0.189434i
$645$	−5.76919	−	10.9471i	−0.227162	−	0.431043i
$646$	−0.567658	+	1.74707i	−0.0223342	+	0.0687376i
$647$	46.7542	+	15.1914i	1.83810	+	0.597234i	0.998543	+	0.0539578i	$0.0171836\pi$
$647$	46.7542	+	15.1914i	1.83810	+	0.597234i	0.839554	+	0.543276i	$0.182816\pi$
$648$	−0.877142	−	1.20728i	−0.0344574	−	0.0474265i
$649$	0.220616			0.00865994
$650$	0.115951	+	4.20685i	0.00454799	+	0.165006i
$651$	−2.13033			−0.0834942
$652$	−1.82446	−	2.51115i	−0.0714512	−	0.0983442i
$653$	11.0619	+	3.59422i	0.432884	+	0.140653i	0.517350	−	0.855774i	$-0.326918\pi$
$653$	11.0619	+	3.59422i	0.432884	+	0.140653i	−0.0844659	+	0.996426i	$0.526918\pi$
$654$	1.22580	−	3.77263i	0.0479326	−	0.147521i
$655$	−1.77111	−	0.871903i	−0.0692032	−	0.0340681i
$656$	−5.09599	−	15.6839i	−0.198965	−	0.612352i
$657$		−	1.63487i		−	0.0637822i
$658$	1.68559	−	0.547681i	0.0657112	−	0.0213508i
$659$	−9.61404	−	6.98501i	−0.374510	−	0.272097i	0.384569	−	0.923096i	$-0.374350\pi$
$659$	−9.61404	−	6.98501i	−0.374510	−	0.272097i	−0.759079	+	0.650999i	$0.774350\pi$
$660$	−0.198906	−	0.193499i	−0.00774241	−	0.00753195i
$661$	−4.53609	+	3.29566i	−0.176433	+	0.128186i	−0.672497	−	0.740100i	$-0.734778\pi$
$661$	−4.53609	+	3.29566i	−0.176433	+	0.128186i	0.496064	+	0.868286i	$0.334778\pi$
$662$	−4.53791	+	6.24590i	−0.176371	+	0.242754i
$663$	−1.26568	+	1.74206i	−0.0491551	+	0.0676562i
$664$	17.2199	−	12.5110i	0.668263	−	0.485521i
$665$	4.71949	−	9.58679i	0.183014	−	0.371760i
$666$	−0.970439	−	0.705065i	−0.0376037	−	0.0273207i
$667$	25.9669	−	8.43716i	1.00544	−	0.326688i
$668$			27.5737i			1.06686i
$669$	−3.14988	−	9.69432i	−0.121781	−	0.374804i
$670$	−7.21059	+	1.24411i	−0.278569	+	0.0480642i
$671$	0.286257	−	0.881009i	0.0110508	−	0.0340110i
$672$	3.98909	+	1.29613i	0.153882	+	0.0499994i
$673$	15.9864	+	22.0033i	0.616229	+	0.848167i	0.997072	−	0.0764732i	$-0.0243660\pi$
$673$	15.9864	+	22.0033i	0.616229	+	0.848167i	−0.380842	+	0.924640i	$0.624366\pi$
$674$	−9.11996			−0.351288
$675$	3.96258	−	3.04926i	0.152520	−	0.117366i
$676$	15.3255			0.589441
$677$	−17.1473	−	23.6013i	−0.659026	−	0.907071i	0.340423	−	0.940272i	$-0.389430\pi$
$677$	−17.1473	−	23.6013i	−0.659026	−	0.907071i	−0.999449	+	0.0332014i	$0.989430\pi$
$678$	−0.669882	−	0.217658i	−0.0257267	−	0.00835910i
$679$	−3.25388	+	10.0144i	−0.124872	+	0.384318i
$680$	0.472580	−	3.27519i	0.0181226	−	0.125598i
$681$	−0.333432	−	1.02620i	−0.0127772	−	0.0393240i
$682$			0.0554028i			0.00212148i
$683$	−29.9637	+	9.73579i	−1.14653	+	0.372530i	−0.819834	−	0.572601i	$-0.805935\pi$
$683$	−29.9637	+	9.73579i	−1.14653	+	0.372530i	−0.326694	+	0.945130i	$0.605935\pi$
$684$	7.15120	+	5.19565i	0.273433	+	0.198661i
$685$	4.80452	+	27.8459i	0.183571	+	1.06394i
$686$	0.313601	−	0.227844i	0.0119733	−	0.00869914i
$687$	−8.25370	+	11.3602i	−0.314898	+	0.433420i
$688$	−10.1520	+	13.9730i	−0.387042	+	0.532717i
$689$	19.9845	−	14.5196i	0.761348	−	0.553151i
$690$	0.402724	+	2.33410i	0.0153314	+	0.0888575i
$691$	−17.8742	−	12.9864i	−0.679968	−	0.494025i	0.193379	−	0.981124i	$-0.438055\pi$
$691$	−17.8742	−	12.9864i	−0.679968	−	0.494025i	−0.873347	+	0.487099i	$0.838055\pi$
$692$	−25.1630	+	8.17594i	−0.956552	+	0.310803i
$693$		−	0.0670911i		−	0.00254858i
$694$	−1.48053	−	4.55661i	−0.0562003	−	0.172967i
$695$	−4.76476	+	33.0219i	−0.180738	+	1.25259i
$696$	4.60748	−	14.1804i	0.174646	−	0.537505i
$697$	−4.98345	−	1.61922i	−0.188762	−	0.0613323i
$698$	4.44465	+	6.11754i	0.168233	+	0.231552i
$699$	7.79820			0.294955
$700$	−2.61457	+	8.87145i	−0.0988216	+	0.335309i
$701$	−0.918434			−0.0346888			−0.0173444	−	0.999850i	$-0.505521\pi$
$701$	−0.918434			−0.0346888			−0.0173444	+	0.999850i	$0.505521\pi$
$702$	−0.494732	−	0.680941i	−0.0186725	−	0.0257004i
$703$	14.0640	+	4.56965i	0.530432	+	0.172348i
$704$	−0.0957040	+	0.294547i	−0.00360698	+	0.0111011i
$705$	−10.0749	+	1.73832i	−0.379443	+	0.0654689i
$706$	−1.17668	−	3.62146i	−0.0442850	−	0.136295i
$707$		−	2.02717i		−	0.0762398i
$708$	5.78482	−	1.87960i	0.217407	−	0.0706397i
$709$	22.5141	+	16.3574i	0.845534	+	0.614316i	0.923911	−	0.382607i	$-0.124974\pi$
$709$	22.5141	+	16.3574i	0.845534	+	0.614316i	−0.0783771	+	0.996924i	$0.524974\pi$
$710$	1.36254	−	2.76776i	0.0511354	−	0.103872i
$711$	−10.5999	+	7.70131i	−0.397529	+	0.288822i
$712$	0.604714	−	0.832317i	0.0226626	−	0.0311924i
$713$	−3.42176	+	4.70965i	−0.128146	+	0.176378i
$714$	0.310994	−	0.225950i	0.0116387	−	0.00845598i
$715$	−0.233490	−	0.227144i	−0.00873205	−	0.00849469i
$716$	−17.5721	−	12.7669i	−0.656702	−	0.477122i
$717$	4.96373	−	1.61282i	0.185374	−	0.0602317i
$718$		−	3.80547i		−	0.142019i
$719$	−8.78604	−	27.0406i	−0.327664	−	1.00845i	−0.970224	−	0.242210i	$-0.922128\pi$
$719$	−8.78604	−	27.0406i	−0.327664	−	1.00845i	0.642560	−	0.766235i	$-0.277872\pi$
$720$	−6.26124	−	3.08235i	−0.233343	−	0.114872i
$721$	2.42535	−	7.46447i	0.0903249	−	0.277992i
$722$	1.41418	+	0.459496i	0.0526304	+	0.0171007i
$723$	3.29806	+	4.53940i	0.122656	+	0.168822i
$724$	20.6321			0.766785
$725$	47.9196	+	14.1228i	1.77969	+	0.524506i
$726$	4.26221			0.158185
$727$	9.60701	+	13.2229i	0.356304	+	0.490411i	0.949114	−	0.314931i	$-0.101982\pi$
$727$	9.60701	+	13.2229i	0.356304	+	0.490411i	−0.592810	+	0.805342i	$0.701982\pi$
$728$	3.08169	+	1.00130i	0.114215	+	0.0371108i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	0.660663	+	1.25362i	0.0244523	+	0.0463986i
$731$	1.69587	+	5.21935i	0.0627241	+	0.193045i
$732$		−	25.5399i		−	0.943983i
$733$	18.4200	−	5.98503i	0.680360	−	0.221062i	0.0516069	−	0.998667i	$-0.483566\pi$
$733$	18.4200	−	5.98503i	0.680360	−	0.221062i	0.628753	+	0.777605i	$0.283566\pi$
$734$	−8.63622	−	6.27458i	−0.318769	−	0.231599i
$735$	−1.97818	+	1.04251i	−0.0729661	+	0.0384534i
$736$	9.27276	−	6.73706i	0.341799	−	0.248331i
$737$	0.332905	−	0.458204i	0.0122627	−	0.0168782i
$738$	1.20389	−	1.65701i	0.0443158	−	0.0609955i
$739$	−4.94105	+	3.58988i	−0.181759	+	0.132056i	−0.674945	−	0.737868i	$-0.735833\pi$
$739$	−4.94105	+	3.58988i	−0.181759	+	0.132056i	0.493185	+	0.869924i	$0.335833\pi$
$740$	−12.6681	−	1.82790i	−0.465690	−	0.0671948i
$741$	8.39460	+	6.09903i	0.308383	+	0.224054i
$742$	−4.19400	+	1.36271i	−0.153967	+	0.0500268i
$743$		−	4.52562i		−	0.166029i	−0.996548	−	0.0830144i	$-0.973545\pi$
$743$		−	4.52562i		−	0.166029i	0.996548	−	0.0830144i	$-0.0264548\pi$
$744$	0.982382	+	3.02346i	0.0360159	+	0.110845i
$745$	22.7058	−	23.3402i	0.831876	−	0.855120i
$746$	−0.400215	+	1.23174i	−0.0146529	+	0.0450970i
$747$	−13.5653	−	4.40763i	−0.496328	−	0.161267i
$748$	0.0723385	+	0.0995654i	0.00264496	+	0.00364047i
$749$	19.1777			0.700739
$750$	−1.80629	+	3.93950i	−0.0659563	+	0.143850i
$751$	−1.81881			−0.0663693			−0.0331846	−	0.999449i	$-0.510565\pi$
$751$	−1.81881			−0.0663693			−0.0331846	+	0.999449i	$0.510565\pi$
$752$	8.38769	+	11.5447i	0.305868	+	0.420991i
$753$	−11.1933	−	3.63691i	−0.407905	−	0.132537i
$754$	2.59875	−	7.99812i	0.0946407	−	0.291274i
$755$	29.8172	−	30.6504i	1.08516	−	1.11548i
$756$	−0.571602	−	1.75921i	−0.0207889	−	0.0639818i
$757$		−	38.8141i		−	1.41072i	−0.708848	−	0.705362i	$-0.750785\pi$
$757$		−	38.8141i		−	1.41072i	0.708848	−	0.705362i	$-0.249215\pi$
$758$	9.24307	−	3.00326i	0.335724	−	0.109083i
$759$	−0.148323	−	0.107763i	−0.00538377	−	0.00391154i
$760$	−15.7823	−	2.27725i	−0.572486	−	0.0826045i
$761$	−13.8101	+	10.0336i	−0.500616	+	0.363719i	−0.809252	−	0.587461i	$-0.800128\pi$
$761$	−13.8101	+	10.0336i	−0.500616	+	0.363719i	0.308636	+	0.951180i	$0.400128\pi$
$762$	−3.28587	+	4.52261i	−0.119035	+	0.163837i
$763$	6.01502	−	8.27896i	0.217758	−	0.299719i
$764$	−5.45772	+	3.96526i	−0.197453	+	0.143458i
$765$	−1.96173	+	1.03384i	−0.0709265	+	0.0373786i
$766$	4.27039	+	3.10262i	0.154296	+	0.112102i
$767$	6.79064	−	2.20641i	0.245196	−	0.0796689i
$768$			5.28699i			0.190778i
$769$	−9.85834	−	30.3409i	−0.355501	−	1.09412i	−0.955719	−	0.294282i	$-0.904919\pi$
$769$	−9.85834	−	30.3409i	−0.355501	−	1.09412i	0.600218	−	0.799837i	$-0.295081\pi$
$770$	0.0271121	+	0.0514458i	0.000977053	+	0.00185398i
$771$	5.99700	−	18.4569i	0.215977	−	0.664708i
$772$	−30.2866	−	9.84071i	−1.09004	−	0.354175i
$773$	−28.3024	−	38.9549i	−1.01797	−	1.40111i	−0.913620	−	0.406570i	$-0.866725\pi$
$773$	−28.3024	−	38.9549i	−1.01797	−	1.40111i	−0.104347	−	0.994541i	$-0.533275\pi$
$774$	−2.14514			−0.0771054
$775$	−10.0358	+	3.56940i	−0.360496	+	0.128217i
$776$	15.7134			0.564078
$777$	−1.81890	−	2.50351i	−0.0652528	−	0.0898128i
$778$	−9.50336	−	3.08783i	−0.340712	−	0.110704i
$779$	−7.80264	+	24.0140i	−0.279559	+	0.860393i
$780$	−8.05761	−	3.96668i	−0.288509	−	0.142030i
$781$	0.0737894	+	0.227100i	0.00264039	+	0.00812629i
$782$		−	1.05046i		−	0.0375643i
$783$	−9.50246	+	3.08754i	−0.339590	+	0.110340i
$784$	2.52496	+	1.83449i	0.0901773	+	0.0655176i
$785$	6.28125	+	6.11051i	0.224187	+	0.218093i
$786$	−0.276860	+	0.201151i	−0.00987529	+	0.00717482i
$787$	15.9241	−	21.9177i	0.567634	−	0.781281i	−0.424638	−	0.905363i	$-0.639599\pi$
$787$	15.9241	−	21.9177i	0.567634	−	0.781281i	0.992272	+	0.124082i	$0.0395986\pi$
$788$	−0.145486	+	0.200245i	−0.00518274	+	0.00713342i
$789$	−3.07385	+	2.23328i	−0.109432	+	0.0795069i
$790$	5.01591	−	10.1889i	0.178458	−	0.362506i
$791$	−1.47004	−	1.06805i	−0.0522687	−	0.0379754i
$792$	−0.0952188	+	0.0309385i	−0.00338345	+	0.00109935i
$793$		−	29.9806i		−	1.06464i
$794$	−0.535621	−	1.64847i	−0.0190085	−	0.0585021i
$795$	25.0679	−	4.32520i	0.889066	−	0.153399i
$796$	−6.68157	+	20.5638i	−0.236822	+	0.728863i
$797$	32.6331	+	10.6031i	1.15592	+	0.375582i	0.823371	−	0.567503i	$-0.192090\pi$
$797$	32.6331	+	10.6031i	1.15592	+	0.375582i	0.332551	+	0.943085i	$0.392090\pi$
$798$	−1.08880	−	1.49861i	−0.0385431	−	0.0530501i
$799$	4.53420			0.160408
$800$	20.9639	−	0.577819i	0.741186	−	0.0204290i
$801$	−0.689414			−0.0243592
$802$	4.89612	+	6.73893i	0.172888	+	0.237960i
$803$	−0.104317	−	0.0338945i	−0.00368125	−	0.00119611i
$804$	4.82536	−	14.8509i	0.170177	−	0.523752i
$805$	−0.872637	+	6.04776i	−0.0307564	+	0.213156i
$806$	0.554090	+	1.70532i	0.0195170	+	0.0600672i
$807$		−	28.3506i		−	0.997988i
$808$	−2.87706	+	0.934813i	−0.101215	+	0.0328866i
$809$	−39.2091	−	28.4871i	−1.37852	−	1.00155i	−0.997017	−	0.0771850i	$-0.975407\pi$
$809$	−39.2091	−	28.4871i	−1.37852	−	1.00155i	−0.381502	−	0.924368i	$-0.624593\pi$
$810$	−0.147375	−	0.854151i	−0.00517822	−	0.0300118i
$811$	−26.8524	+	19.5094i	−0.942915	+	0.685068i	−0.949121	−	0.314913i	$-0.898025\pi$
$811$	−26.8524	+	19.5094i	−0.942915	+	0.685068i	0.00620554	+	0.999981i	$0.498025\pi$
$812$	10.8632	−	14.9520i	0.381225	−	0.524711i
$813$	15.2592	−	21.0024i	0.535162	−	0.736588i
$814$	−0.0651078	+	0.0473036i	−0.00228203	+	0.00165799i
$815$	−0.637981	−	3.69759i	−0.0223475	−	0.129521i
$816$	2.50397	+	1.81924i	0.0876566	+	0.0636862i
$817$	25.1508	−	8.17200i	0.879916	−	0.285902i
$818$			1.12943i			0.0394895i
$819$	−0.670988	−	2.06509i	−0.0234462	−	0.0721600i
$820$	3.12111	−	21.6307i	0.108994	−	0.755377i
$821$	−4.97375	+	15.3076i	−0.173585	+	0.534240i	−0.999566	−	0.0294582i	$-0.990622\pi$
$821$	−4.97375	+	15.3076i	−0.173585	+	0.534240i	0.825981	+	0.563698i	$0.190622\pi$
$822$	4.65878	+	1.51373i	0.162494	+	0.0527973i
$823$	−30.0477	−	41.3572i	−1.04740	−	1.44162i	−0.891043	−	0.453919i	$-0.850026\pi$
$823$	−30.0477	−	41.3572i	−1.04740	−	1.44162i	−0.156355	−	0.987701i	$-0.549974\pi$
$824$	−11.7123			−0.408019
$825$	−0.112412	−	0.316060i	−0.00391369	−	0.0110038i
$826$	−1.27465			−0.0443508
$827$	9.52882	+	13.1153i	0.331349	+	0.456063i	0.941890	−	0.335922i	$-0.109048\pi$
$827$	9.52882	+	13.1153i	0.331349	+	0.456063i	−0.610540	+	0.791985i	$0.709048\pi$
$828$	−4.80730	−	1.56199i	−0.167065	−	0.0542828i
$829$	−7.62943	+	23.4810i	−0.264981	+	0.815528i	0.726717	+	0.686937i	$0.241045\pi$
$829$	−7.62943	+	23.4810i	−0.264981	+	0.815528i	−0.991698	+	0.128591i	$0.958955\pi$
$830$	12.1831	−	2.10206i	0.422881	−	0.0729637i
$831$	5.40960	+	16.6490i	0.187657	+	0.577549i
$832$			10.0234i			0.347499i
$833$	0.943150	−	0.306448i	0.0326782	−	0.0106178i
$834$	4.67917	+	3.39962i	0.162027	+	0.117719i
$835$	−14.7221	+	29.9053i	−0.509478	+	1.03491i
$836$	0.479782	−	0.348582i	0.0165936	−	0.0120560i
$837$	1.25218	−	1.72347i	0.0432815	−	0.0595719i
$838$	−6.32400	+	8.70424i	−0.218459	+	0.300683i
$839$	41.5787	−	30.2087i	1.43546	−	1.04292i	0.446487	−	0.894790i	$-0.352675\pi$
$839$	41.5787	−	30.2087i	1.43546	−	1.04292i	0.988968	−	0.148129i	$-0.0473251\pi$
$840$	2.39179	+	2.32677i	0.0825246	+	0.0802813i
$841$	−57.3024	−	41.6326i	−1.97595	−	1.43561i
$842$	10.4572	−	3.39776i	0.360380	−	0.117095i
$843$		−	24.5877i		−	0.846847i
$844$	4.38487	+	13.4953i	0.150934	+	0.464526i
$845$	16.6213	+	8.18252i	0.571791	+	0.281487i
$846$	−0.547681	+	1.68559i	−0.0188297	+	0.0579518i
$847$	10.4573	+	3.39780i	0.359318	+	0.116750i
$848$	−20.8698	−	28.7249i	−0.716673	−	0.986416i
$849$	−23.9488			−0.821922
$850$	1.08648	−	1.58551i	0.0372659	−	0.0543824i
$851$	−8.45620			−0.289875
$852$	3.86969	+	5.32617i	0.132573	+	0.182472i
$853$	35.7576	+	11.6184i	1.22432	+	0.397805i	0.848653	−	0.528951i	$-0.177414\pi$
$853$	35.7576	+	11.6184i	1.22432	+	0.397805i	0.375665	+	0.926756i	$0.377414\pi$
$854$	−1.65391	+	5.09020i	−0.0565955	+	0.174183i
$855$	4.98183	+	9.45312i	0.170375	+	0.323290i
$856$	−8.84363	−	27.2179i	−0.302269	−	0.930288i
$857$			23.5129i			0.803184i	0.915819	+	0.401592i	$0.131543\pi$
$857$			23.5129i			0.803184i	−0.915819	+	0.401592i	$0.868457\pi$
$858$	−0.0537060	+	0.0174502i	−0.00183349	+	0.000595738i
$859$	14.2736	+	10.3704i	0.487008	+	0.353832i	0.804033	−	0.594585i	$-0.202684\pi$
$859$	14.2736	+	10.3704i	0.487008	+	0.353832i	−0.317024	+	0.948417i	$0.602684\pi$
$860$	−20.2494	+	10.6715i	−0.690498	+	0.363895i
$861$	4.27471	−	3.10576i	0.145682	−	0.105844i
$862$	5.77296	−	7.94579i	0.196628	−	0.270635i
$863$	−28.5165	+	39.2496i	−0.970713	+	1.33607i	−0.0290266	+	0.999579i	$0.509241\pi$
$863$	−28.5165	+	39.2496i	−0.970713	+	1.33607i	−0.941686	+	0.336493i	$0.890759\pi$
$864$	−3.39332	+	2.46539i	−0.115443	+	0.0838743i
$865$	−31.6559	−	4.56766i	−1.07633	−	0.155305i
$866$	7.46087	+	5.42064i	0.253531	+	0.184201i
$867$	−15.2327	+	4.94939i	−0.517328	+	0.168090i
$868$			3.94056i			0.133751i
$869$	0.271640	+	0.836021i	0.00921474	+	0.0283601i
$870$	6.03883	−	6.20757i	0.204735	−	0.210456i
$871$	5.66436	−	17.4331i	0.191929	−	0.590698i
$872$	−14.5236	−	4.71902i	−0.491833	−	0.159806i
$873$	−6.18924	−	8.51876i	−0.209474	−	0.288316i
$874$	−5.06190			−0.171221
$875$	−7.57227	+	8.22562i	−0.255989	+	0.278077i
$876$	−3.02408			−0.102174
$877$	−1.62611	−	2.23814i	−0.0549097	−	0.0755767i	0.780679	−	0.624932i	$-0.214873\pi$
$877$	−1.62611	−	2.23814i	−0.0549097	−	0.0755767i	−0.835589	+	0.549355i	$0.814873\pi$
$878$	−0.415877	−	0.135126i	−0.0140352	−	0.00456030i
$879$	5.93652	−	18.2707i	0.200234	−	0.616257i
$880$	−0.326487	+	0.335610i	−0.0110059	+	0.0113134i
$881$	15.9002	+	48.9357i	0.535690	+	1.64868i	0.742153	+	0.670230i	$0.233805\pi$
$881$	15.9002	+	48.9357i	0.535690	+	1.64868i	−0.206463	+	0.978454i	$0.566195\pi$
$882$			0.387632i			0.0130522i
$883$	44.6173	−	14.4970i	1.50149	−	0.487864i	0.561039	−	0.827790i	$-0.310402\pi$
$883$	44.6173	−	14.4970i	1.50149	−	0.487864i	0.940452	+	0.339926i	$0.110402\pi$
$884$	3.22237	+	2.34119i	0.108380	+	0.0787427i
$885$	7.27751	+	1.05008i	0.244631	+	0.0352980i
$886$	1.42173	−	1.03295i	0.0477639	−	0.0347025i
$887$	−18.6576	+	25.6800i	−0.626462	+	0.862251i	−0.997803	−	0.0662452i	$-0.978898\pi$
$887$	−18.6576	+	25.6800i	−0.626462	+	0.862251i	0.371341	+	0.928497i	$0.378898\pi$
$888$	−2.71432	+	3.73594i	−0.0910866	+	0.125370i
$889$	−11.6673	+	8.47678i	−0.391308	+	0.284302i
$890$	0.528645	−	0.278598i	0.0177202	−	0.00933863i
$891$	0.0542779	+	0.0394352i	0.00181838	+	0.00132113i
$892$	−17.9320	+	5.82646i	−0.600407	+	0.195084i
$893$		−	21.8492i		−	0.731157i
$894$	−1.74436	−	5.36858i	−0.0583400	−	0.179552i
$895$	−12.2415	−	23.2285i	−0.409188	−	0.776443i
$896$	3.14521	−	9.67998i	0.105074	−	0.323385i
$897$	−5.64316	−	1.83357i	−0.188420	−	0.0612213i
$898$	1.65982	+	2.28455i	0.0553890	+	0.0762364i
$899$	21.2851			0.709899
$900$	−5.64034	−	7.32974i	−0.188011	−	0.244325i
$901$	−11.2818			−0.375850
$902$	−0.0807704	−	0.111171i	−0.00268936	−	0.00370159i
$903$	−5.26311	−	1.71009i	−0.175145	−	0.0569081i
$904$	−0.837926	+	2.57887i	−0.0278690	+	0.0857720i
$905$	22.3766	+	11.0158i	0.743825	+	0.366178i
$906$	−2.29069	−	7.05002i	−0.0761030	−	0.234221i
$907$		−	14.7019i		−	0.488170i	−0.969754	−	0.244085i	$-0.921512\pi$
$907$		−	14.7019i		−	0.488170i	0.969754	−	0.244085i	$-0.0784876\pi$
$908$	−1.89820	+	0.616764i	−0.0629941	+	0.0204680i
$909$	1.64002	+	1.19154i	0.0543960	+	0.0395210i
$910$	1.34904	+	1.31237i	0.0447201	+	0.0435045i
$911$	−10.7365	+	7.80051i	−0.355716	+	0.258443i	−0.751263	−	0.660003i	$-0.770555\pi$
$911$	−10.7365	+	7.80051i	−0.355716	+	0.258443i	0.395547	+	0.918446i	$0.370555\pi$
$912$	8.76650	−	12.0661i	0.290288	−	0.399547i
$913$	−0.562479	+	0.774186i	−0.0186153	+	0.0256218i
$914$	−7.33859	+	5.33179i	−0.242739	+	0.176360i
$915$	13.6362	−	27.6995i	0.450799	−	0.915717i
$916$	21.0135	+	15.2672i	0.694306	+	0.504443i
$917$	−0.839634	+	0.272814i	−0.0277272	+	0.00900910i
$918$			0.384410i			0.0126874i
$919$	4.88289	+	15.0280i	0.161072	+	0.495728i	0.998725	−	0.0504740i	$-0.0160732\pi$
$919$	4.88289	+	15.0280i	0.161072	+	0.495728i	−0.837654	+	0.546202i	$0.816073\pi$
$920$	8.98567	−	1.55038i	0.296249	−	0.0511146i
$921$	−7.01475	+	21.5892i	−0.231144	+	0.711388i
$922$	−5.18372	−	1.68429i	−0.170717	−	0.0554692i
$923$	4.54252	+	6.25225i	0.149519	+	0.205795i
$924$	−0.124101			−0.00408263
$925$	−12.7633	−	8.74618i	−0.419656	−	0.287573i
$926$	15.2961			0.502661
$927$	4.61330	+	6.34966i	0.151521	+	0.208550i
$928$	−39.8569	−	12.9503i	−1.30837	−	0.425114i
$929$	−9.74579	+	29.9945i	−0.319749	+	0.984086i	0.654006	+	0.756489i	$0.273087\pi$
$929$	−9.74579	+	29.9945i	−0.319749	+	0.984086i	−0.973755	+	0.227597i	$0.926913\pi$
$930$	−0.263703	+	1.82758i	−0.00864717	+	0.0599287i
$931$	−1.47670	−	4.54482i	−0.0483969	−	0.148950i
$932$		−	14.4247i		−	0.472495i
$933$	−4.82841	+	1.56885i	−0.158075	+	0.0513617i
$934$	1.70258	+	1.23700i	0.0557101	+	0.0404758i
$935$	0.0252955	+	0.146607i	0.000827252	+	0.00479456i
$936$	−2.62145	+	1.90459i	−0.0856846	+	0.0622535i
$937$	−19.2340	+	26.4734i	−0.628348	+	0.864847i	−0.997927	−	0.0643524i	$-0.979502\pi$
$937$	−19.2340	+	26.4734i	−0.628348	+	0.864847i	0.369579	+	0.929199i	$0.379502\pi$
$938$	−1.92342	+	2.64736i	−0.0628019	+	0.0864394i
$939$	10.3462	−	7.51694i	0.337635	−	0.245306i
$940$	3.21544	+	18.6360i	0.104876	+	0.607838i
$941$	27.1056	+	19.6934i	0.883619	+	0.641986i	0.934206	−	0.356733i	$-0.116109\pi$
$941$	27.1056	+	19.6934i	0.883619	+	0.641986i	−0.0505878	+	0.998720i	$0.516109\pi$
$942$	1.44477	−	0.469436i	0.0470733	−	0.0152950i
$943$		−	14.4389i		−	0.470194i
$944$	−3.17141	−	9.76059i	−0.103221	−	0.317680i
$945$	0.319337	−	2.21315i	0.0103880	−	0.0719937i
$946$	−0.0444737	+	0.136876i	−0.00144596	+	0.00445022i
$947$	−50.3908	−	16.3730i	−1.63748	−	0.532049i	−0.661507	−	0.749939i	$-0.730083\pi$
$947$	−50.3908	−	16.3730i	−1.63748	−	0.532049i	−0.975973	+	0.217890i	$0.930083\pi$
$948$	14.2454	+	19.6071i	0.462670	+	0.636810i
$949$	−3.54988			−0.115234
$950$	−7.64018	−	5.23549i	−0.247880	−	0.169862i
$951$	12.3409			0.400180
$952$	−0.869850	−	1.19725i	−0.0281920	−	0.0388030i
$953$	34.8767	+	11.3321i	1.12977	+	0.367084i	0.813487	−	0.581582i	$-0.197566\pi$
$953$	34.8767	+	11.3321i	1.12977	+	0.367084i	0.316280	+	0.948666i	$0.397566\pi$
$954$	1.36271	−	4.19400i	0.0441195	−	0.135786i
$955$	−8.03632	+	1.38658i	−0.260049	+	0.0448688i
$956$	−2.98329	−	9.18163i	−0.0964865	−	0.296955i
$957$			0.670340i			0.0216690i
$958$	11.6441	−	3.78338i	0.376202	−	0.122236i
$959$	10.2236	+	7.42788i	0.330137	+	0.239859i
$960$	−4.55898	+	9.26074i	−0.147140	+	0.298889i
$961$	21.4080	−	15.5538i	0.690579	−	0.501735i
$962$	−1.53095	+	2.10717i	−0.0493598	+	0.0679380i
$963$	−11.2724	+	15.5151i	−0.363247	+	0.499967i
$964$	8.39671	−	6.10057i	0.270440	−	0.196486i
$965$	−27.5934	−	26.8433i	−0.888262	−	0.864117i
$966$	0.856962	+	0.622619i	0.0275723	+	0.0200324i
$967$	39.8372	−	12.9439i	1.28108	−	0.416248i	0.412119	−	0.911130i	$-0.364789\pi$
$967$	39.8372	−	12.9439i	1.28108	−	0.416248i	0.868960	+	0.494882i	$0.164789\pi$
$968$		−	16.4084i		−	0.527386i
$969$	−1.46442	−	4.50704i	−0.0470441	−	0.144787i
$970$	8.18845	+	4.03109i	0.262915	+	0.129431i
$971$	3.04607	−	9.37483i	0.0977530	−	0.300853i	−0.890208	−	0.455554i	$-0.849441\pi$
$971$	3.04607	−	9.37483i	0.0977530	−	0.300853i	0.987961	+	0.154701i	$0.0494414\pi$
$972$	1.75921	+	0.571602i	0.0564266	+	0.0183341i
$973$	8.77022	+	12.0712i	0.281160	+	0.386984i
$974$	10.7439			0.344257
$975$	−6.62105	−	8.60418i	−0.212043	−	0.275554i
$976$	−43.0929			−1.37937
$977$	−11.4061	−	15.6991i	−0.364912	−	0.502258i	0.586597	−	0.809879i	$-0.300467\pi$
$977$	−11.4061	−	15.6991i	−0.364912	−	0.502258i	−0.951509	+	0.307621i	$0.900467\pi$
$978$	−0.618628	−	0.201004i	−0.0197815	−	0.00642741i
$979$	−0.0142931	+	0.0439897i	−0.000456811	+	0.00140592i
$980$	1.92837	+	3.65911i	0.0615994	+	0.116886i
$981$	3.16228	+	9.73250i	0.100964	+	0.310735i
$982$			15.2265i			0.485897i
$983$	−17.3671	+	5.64292i	−0.553926	+	0.179981i	−0.572586	−	0.819845i	$-0.694060\pi$
$983$	−17.3671	+	5.64292i	−0.553926	+	0.179981i	0.0186606	+	0.999826i	$0.494060\pi$
$984$	−6.37908	−	4.63467i	−0.203358	−	0.147748i
$985$	−0.264702	+	0.139499i	−0.00843411	+	0.00444481i
$986$	−3.10729	+	2.25758i	−0.0989562	+	0.0718959i
$987$	−2.68748	+	3.69900i	−0.0855433	+	0.117740i
$988$	11.2816	−	15.5278i	0.358916	−	0.494006i
$989$	−12.2343	+	8.88871i	−0.389027	+	0.282645i
$990$	−0.0575566	−	0.00830489i	−0.00182927	−	0.000263947i
$991$	14.0581	+	10.2138i	0.446571	+	0.324453i	0.788241	−	0.615367i	$-0.210992\pi$
$991$	14.0581	+	10.2138i	0.446571	+	0.324453i	−0.341669	+	0.939820i	$0.610992\pi$
$992$	8.49807	−	2.76119i	0.269814	−	0.0876679i
$993$		−	19.9167i		−	0.632038i
$994$	−0.426332	−	1.31212i	−0.0135224	−	0.0416178i
$995$	−18.2259	+	18.7351i	−0.577799	+	0.593944i
$996$	−8.15297	+	25.0923i	−0.258337	+	0.795079i
$997$	−12.0140	−	3.90359i	−0.380487	−	0.123628i	0.112528	−	0.993649i	$-0.464105\pi$
$997$	−12.0140	−	3.90359i	−0.380487	−	0.123628i	−0.493015	+	0.870021i	$0.664105\pi$
$998$	5.41922	+	7.45892i	0.171543	+	0.236108i
$999$	3.09450			0.0979057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.9	✓	72
25.9	even	10	inner	525.2.z.b.484.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.9	✓	72	1.1	even	1	trivial
525.2.z.b.484.9	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)

\(f(q)\)	\(=\)	\(q+(-0.227844 - 0.313601i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.571602 - 1.75921i) q^{4} +(1.55920 - 1.60277i) q^{5} +(-0.119785 - 0.368660i) q^{6} -1.00000i q^{7} +(-1.41925 + 0.461141i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.227844 - 0.313601i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.571602 - 1.75921i) q^{4} +(1.55920 - 1.60277i) q^{5} +(-0.119785 - 0.368660i) q^{6} -1.00000i q^{7} +(-1.41925 + 0.461141i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.857887 - 0.123785i) q^{10} +(0.0542779 - 0.0394352i) q^{11} +(1.08725 - 1.49647i) q^{12} +(1.27629 - 1.75667i) q^{13} +(-0.313601 + 0.227844i) q^{14} +(1.97818 - 1.04251i) q^{15} +(-2.52496 - 1.83449i) q^{16} +(-0.943150 + 0.306448i) q^{17} -0.387632i q^{18} +(1.47670 + 4.54482i) q^{19} +(-1.92837 - 3.65911i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-0.0247338 - 0.00803650i) q^{22} +(-1.60621 - 2.21076i) q^{23} -1.49228 q^{24} +(-0.137760 - 4.99810i) q^{25} -0.841689 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.75921 - 0.571602i) q^{28} +(-3.08754 + 9.50246i) q^{29} +(-0.777647 - 0.382828i) q^{30} +(-0.658308 - 2.02606i) q^{31} +4.19438i q^{32} +(0.0638075 - 0.0207323i) q^{33} +(0.310994 + 0.225950i) q^{34} +(-1.60277 - 1.55920i) q^{35} +(1.49647 - 1.08725i) q^{36} +(1.81890 - 2.50351i) q^{37} +(1.08880 - 1.49861i) q^{38} +(1.75667 - 1.27629i) q^{39} +(-1.47379 + 2.99374i) q^{40} +(4.27471 + 3.10576i) q^{41} +(-0.368660 + 0.119785i) q^{42} -5.53396i q^{43} +(-0.0383494 - 0.118027i) q^{44} +(2.20351 - 0.380193i) q^{45} +(-0.327330 + 1.00742i) q^{46} +(-4.34843 - 1.41289i) q^{47} +(-1.83449 - 2.52496i) q^{48} -1.00000 q^{49} +(-1.53602 + 1.18199i) q^{50} -0.991687 q^{51} +(-2.36081 - 3.24938i) q^{52} +(10.8196 + 3.51549i) q^{53} +(0.119785 - 0.368660i) q^{54} +(0.0214247 - 0.148483i) q^{55} +(0.461141 + 1.41925i) q^{56} +4.77870i q^{57} +(3.68346 - 1.19683i) q^{58} +(2.66030 + 1.93282i) q^{59} +(-0.703258 - 4.07592i) q^{60} +(11.1703 - 8.11573i) q^{61} +(-0.485383 + 0.668073i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-3.73457 + 2.71332i) q^{64} +(-0.825536 - 4.78461i) q^{65} +(-0.0210398 - 0.0152863i) q^{66} +(8.02865 - 2.60867i) q^{67} +1.83436i q^{68} +(-0.844436 - 2.59891i) q^{69} +(-0.123785 + 0.857887i) q^{70} +(-1.09984 + 3.38495i) q^{71} +(-1.41925 - 0.461141i) q^{72} +(-0.960950 - 1.32263i) q^{73} -1.19953 q^{74} +(1.41348 - 4.79605i) q^{75} +8.83937 q^{76} +(-0.0394352 - 0.0542779i) q^{77} +(-0.800494 - 0.260096i) q^{78} +(-4.04882 + 12.4610i) q^{79} +(-6.87721 + 1.18659i) q^{80} +(0.309017 + 0.951057i) q^{81} -2.04818i q^{82} +(-13.5653 + 4.40763i) q^{83} +(-1.49647 - 1.08725i) q^{84} +(-0.979398 + 1.98947i) q^{85} +(-1.73545 + 1.26088i) q^{86} +(-5.87284 + 8.08328i) q^{87} +(-0.0588484 + 0.0809979i) q^{88} +(-0.557747 + 0.405227i) q^{89} +(-0.621286 - 0.604398i) q^{90} +(-1.75667 - 1.27629i) q^{91} +(-4.80730 + 1.56199i) q^{92} -2.13033i q^{93} +(0.547681 + 1.68559i) q^{94} +(9.58679 + 4.71949i) q^{95} +(-1.29613 + 3.98909i) q^{96} +(-10.0144 - 3.25388i) q^{97} +(0.227844 + 0.313601i) q^{98} +0.0670911 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

Introduction

L-functions

Modular forms

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