LMFDB - Embedded newform 525.2.z.b.64.14

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			64.14
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.972332 + 1.33830i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.227584 + 0.700432i) q^{4} +(-0.366564 - 2.20582i) q^{5} +(0.511185 + 1.57327i) q^{6} -1.00000i q^{7} +(1.98786 - 0.645894i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.972332 + 1.33830i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.227584 + 0.700432i) q^{4} +(-0.366564 - 2.20582i) q^{5} +(0.511185 + 1.57327i) q^{6} -1.00000i q^{7} +(1.98786 - 0.645894i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.59562 - 2.63536i) q^{10} +(0.908054 - 0.659740i) q^{11} +(-0.432891 + 0.595823i) q^{12} +(0.325348 - 0.447803i) q^{13} +(1.33830 - 0.972332i) q^{14} +(0.333012 - 2.21113i) q^{15} +(3.98890 + 2.89811i) q^{16} +(-0.791933 + 0.257315i) q^{17} +1.65423i q^{18} +(-0.246002 - 0.757116i) q^{19} +(1.62845 + 0.245256i) q^{20} +(0.309017 - 0.951057i) q^{21} +(1.76586 + 0.573763i) q^{22} +(2.27749 + 3.13469i) q^{23} +2.09016 q^{24} +(-4.73126 + 1.61715i) q^{25} +0.915642 q^{26} +(0.587785 + 0.809017i) q^{27} +(0.700432 + 0.227584i) q^{28} +(0.371243 - 1.14257i) q^{29} +(3.28296 - 1.70428i) q^{30} +(1.32940 + 4.09148i) q^{31} +3.97596i q^{32} +(1.06748 - 0.346846i) q^{33} +(-1.11439 - 0.809649i) q^{34} +(-2.20582 + 0.366564i) q^{35} +(-0.595823 + 0.432891i) q^{36} +(-2.49508 + 3.43418i) q^{37} +(0.774053 - 1.06539i) q^{38} +(0.447803 - 0.325348i) q^{39} +(-2.15340 - 4.14809i) q^{40} +(-3.37556 - 2.45249i) q^{41} +(1.57327 - 0.511185i) q^{42} +4.09905i q^{43} +(0.255444 + 0.786176i) q^{44} +(0.999991 - 2.00000i) q^{45} +(-1.98069 + 6.09592i) q^{46} +(-6.37228 - 2.07048i) q^{47} +(2.89811 + 3.98890i) q^{48} -1.00000 q^{49} +(-6.76458 - 4.75945i) q^{50} -0.832687 q^{51} +(0.239612 + 0.329797i) q^{52} +(5.83886 + 1.89716i) q^{53} +(-0.511185 + 1.57327i) q^{54} +(-1.78813 - 1.76116i) q^{55} +(-0.645894 - 1.98786i) q^{56} -0.796079i q^{57} +(1.89007 - 0.614121i) q^{58} +(-9.27869 - 6.74136i) q^{59} +(1.47296 + 0.736471i) q^{60} +(-11.4835 + 8.34327i) q^{61} +(-4.18301 + 5.75742i) q^{62} +(0.587785 - 0.809017i) q^{63} +(2.65678 - 1.93026i) q^{64} +(-1.10703 - 0.553510i) q^{65} +(1.50213 + 1.09136i) q^{66} +(-3.30571 + 1.07409i) q^{67} -0.613256i q^{68} +(1.19735 + 3.68505i) q^{69} +(-2.63536 - 2.59562i) q^{70} +(2.09985 - 6.46268i) q^{71} +(1.98786 + 0.645894i) q^{72} +(2.08808 + 2.87399i) q^{73} -7.02201 q^{74} +(-4.99942 + 0.0759566i) q^{75} +0.586295 q^{76} +(-0.659740 - 0.908054i) q^{77} +(0.870827 + 0.282949i) q^{78} +(-4.37900 + 13.4772i) q^{79} +(4.93051 - 9.86114i) q^{80} +(0.309017 + 0.951057i) q^{81} -6.90215i q^{82} +(11.4504 - 3.72047i) q^{83} +(0.595823 + 0.432891i) q^{84} +(0.857883 + 1.65254i) q^{85} +(-5.48577 + 3.98564i) q^{86} +(0.706146 - 0.971927i) q^{87} +(1.37896 - 1.89797i) q^{88} +(3.36361 - 2.44381i) q^{89} +(3.64893 - 0.606381i) q^{90} +(-0.447803 - 0.325348i) q^{91} +(-2.71396 + 0.881818i) q^{92} +4.30204i q^{93} +(-3.42505 - 10.5412i) q^{94} +(-1.57988 + 0.820167i) q^{95} +(-1.22864 + 3.78136i) q^{96} +(0.150018 + 0.0487437i) q^{97} +(-0.972332 - 1.33830i) q^{98} +1.12242 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 $

$2$	0.972332	+	1.33830i	0.687543	+	0.946321i	0.999993	−	0.00361266i	$-0.00114995\pi$
$2$	0.972332	+	1.33830i	0.687543	+	0.946321i	−0.312451	+	0.949934i	$0.601150\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.227584	+	0.700432i	−0.113792	+	0.350216i
$5$	−0.366564	−	2.20582i	−0.163932	−	0.986472i
$5$	−0.366564	−	2.20582i	−0.163932	−	0.986472i
$6$	0.511185	+	1.57327i	0.208691	+	0.642283i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.98786	−	0.645894i	0.702814	−	0.228358i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	2.59562	−	2.63536i	0.820809	−	0.833374i
$11$	0.908054	−	0.659740i	0.273789	−	0.198919i	−0.442415	−	0.896810i	$-0.645878\pi$
$11$	0.908054	−	0.659740i	0.273789	−	0.198919i	0.716204	+	0.697891i	$0.245878\pi$
$12$	−0.432891	+	0.595823i	−0.124965	+	0.171999i
$13$	0.325348	−	0.447803i	0.0902353	−	0.124198i	−0.761512	−	0.648150i	$-0.775543\pi$
$13$	0.325348	−	0.447803i	0.0902353	−	0.124198i	0.851748	+	0.523952i	$0.175543\pi$
$14$	1.33830	−	0.972332i	0.357676	−	0.259867i
$15$	0.333012	−	2.21113i	0.0859834	−	0.570912i
$16$	3.98890	+	2.89811i	0.997226	+	0.724527i
$17$	−0.791933	+	0.257315i	−0.192072	+	0.0624080i	−0.403473	−	0.914991i	$-0.632197\pi$
$17$	−0.791933	+	0.257315i	−0.192072	+	0.0624080i	0.211402	+	0.977399i	$0.432197\pi$
$18$			1.65423i			0.389906i
$19$	−0.246002	−	0.757116i	−0.0564367	−	0.173694i	0.918865	−	0.394573i	$-0.129108\pi$
$19$	−0.246002	−	0.757116i	−0.0564367	−	0.173694i	−0.975301	+	0.220879i	$0.929108\pi$
$20$	1.62845	+	0.245256i	0.364132	+	0.0548409i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	1.76586	+	0.573763i	0.376483	+	0.122327i
$23$	2.27749	+	3.13469i	0.474889	+	0.653628i	0.977513	−	0.210877i	$-0.0676319\pi$
$23$	2.27749	+	3.13469i	0.474889	+	0.653628i	−0.502624	+	0.864505i	$0.667632\pi$
$24$	2.09016			0.426651
$25$	−4.73126	+	1.61715i	−0.946252	+	0.323429i
$26$	0.915642			0.179572
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	0.700432	+	0.227584i	0.132369	+	0.0430094i
$29$	0.371243	−	1.14257i	0.0689381	−	0.212170i	−0.910652	−	0.413173i	$-0.864420\pi$
$29$	0.371243	−	1.14257i	0.0689381	−	0.212170i	0.979590	+	0.201004i	$0.0644203\pi$
$30$	3.28296	−	1.70428i	0.599383	−	0.311158i
$31$	1.32940	+	4.09148i	0.238768	+	0.734852i	0.996599	+	0.0824015i	$0.0262590\pi$
$31$	1.32940	+	4.09148i	0.238768	+	0.734852i	−0.757831	+	0.652451i	$0.773741\pi$
$32$			3.97596i			0.702857i
$33$	1.06748	−	0.346846i	0.185825	−	0.0603781i
$34$	−1.11439	−	0.809649i	−0.191116	−	0.138854i
$35$	−2.20582	+	0.366564i	−0.372851	+	0.0619606i
$36$	−0.595823	+	0.432891i	−0.0993038	+	0.0721485i
$37$	−2.49508	+	3.43418i	−0.410188	+	0.564576i	−0.963264	−	0.268555i	$-0.913454\pi$
$37$	−2.49508	+	3.43418i	−0.410188	+	0.564576i	0.553076	+	0.833131i	$0.313454\pi$
$38$	0.774053	−	1.06539i	0.125568	−	0.172830i
$39$	0.447803	−	0.325348i	0.0717059	−	0.0520974i
$40$	−2.15340	−	4.14809i	−0.340483	−	0.655870i
$41$	−3.37556	−	2.45249i	−0.527174	−	0.383014i	0.292125	−	0.956380i	$-0.405638\pi$
$41$	−3.37556	−	2.45249i	−0.527174	−	0.383014i	−0.819300	+	0.573366i	$0.805638\pi$
$42$	1.57327	−	0.511185i	0.242760	−	0.0788776i
$43$			4.09905i			0.625100i	0.949901	+	0.312550i	$0.101183\pi$
$43$			4.09905i			0.625100i	−0.949901	+	0.312550i	$0.898817\pi$
$44$	0.255444	+	0.786176i	0.0385097	+	0.118521i
$45$	0.999991	−	2.00000i	0.149070	−	0.298143i
$46$	−1.98069	+	6.09592i	−0.292036	+	0.898795i
$47$	−6.37228	−	2.07048i	−0.929493	−	0.302011i	−0.195138	−	0.980776i	$-0.562515\pi$
$47$	−6.37228	−	2.07048i	−0.929493	−	0.302011i	−0.734355	+	0.678765i	$0.762515\pi$
$48$	2.89811	+	3.98890i	0.418306	+	0.575749i
$49$	−1.00000			−0.142857
$50$	−6.76458	−	4.75945i	−0.956657	−	0.673087i
$51$	−0.832687			−0.116600
$52$	0.239612	+	0.329797i	0.0332282	+	0.0457346i
$53$	5.83886	+	1.89716i	0.802030	+	0.260595i	0.681218	−	0.732080i	$-0.261450\pi$
$53$	5.83886	+	1.89716i	0.802030	+	0.260595i	0.120811	+	0.992676i	$0.461450\pi$
$54$	−0.511185	+	1.57327i	−0.0695635	+	0.214094i
$55$	−1.78813	−	1.76116i	−0.241111	−	0.237475i
$56$	−0.645894	−	1.98786i	−0.0863112	−	0.265639i
$57$		−	0.796079i		−	0.105443i
$58$	1.89007	−	0.614121i	0.248179	−	0.0806381i
$59$	−9.27869	−	6.74136i	−1.20798	−	0.877651i	−0.212937	−	0.977066i	$-0.568303\pi$
$59$	−9.27869	−	6.74136i	−1.20798	−	0.877651i	−0.995046	+	0.0994151i	$0.968303\pi$
$60$	1.47296	+	0.736471i	0.190158	+	0.0950780i
$61$	−11.4835	+	8.34327i	−1.47032	+	1.06825i	−0.489793	+	0.871839i	$0.662928\pi$
$61$	−11.4835	+	8.34327i	−1.47032	+	1.06825i	−0.980522	+	0.196408i	$0.937072\pi$
$62$	−4.18301	+	5.75742i	−0.531243	+	0.731193i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	2.65678	−	1.93026i	0.332097	−	0.241283i
$65$	−1.10703	−	0.553510i	−0.137311	−	0.0686545i
$66$	1.50213	+	1.09136i	0.184899	+	0.134337i
$67$	−3.30571	+	1.07409i	−0.403856	+	0.131221i	−0.503900	−	0.863762i	$-0.668102\pi$
$67$	−3.30571	+	1.07409i	−0.403856	+	0.131221i	0.100043	+	0.994983i	$0.468102\pi$
$68$		−	0.613256i		−	0.0743682i
$69$	1.19735	+	3.68505i	0.144143	+	0.443628i
$70$	−2.63536	−	2.59562i	−0.314986	−	0.310236i
$71$	2.09985	−	6.46268i	0.249206	−	0.766978i	−0.745710	−	0.666271i	$-0.767889\pi$
$71$	2.09985	−	6.46268i	0.249206	−	0.766978i	0.994916	−	0.100707i	$-0.0321106\pi$
$72$	1.98786	+	0.645894i	0.234271	+	0.0761193i
$73$	2.08808	+	2.87399i	0.244391	+	0.336376i	0.913537	−	0.406755i	$-0.133340\pi$
$73$	2.08808	+	2.87399i	0.244391	+	0.336376i	−0.669146	+	0.743131i	$0.733340\pi$
$74$	−7.02201			−0.816292
$75$	−4.99942	+	0.0759566i	−0.577284	+	0.00877072i
$76$	0.586295			0.0672526
$77$	−0.659740	−	0.908054i	−0.0751843	−	0.103482i
$78$	0.870827	+	0.282949i	0.0986018	+	0.0320377i
$79$	−4.37900	+	13.4772i	−0.492675	+	1.51630i	0.327873	+	0.944722i	$0.393668\pi$
$79$	−4.37900	+	13.4772i	−0.492675	+	1.51630i	−0.820548	+	0.571577i	$0.806332\pi$
$80$	4.93051	−	9.86114i	0.551248	−	1.10251i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	6.90215i		−	0.762215i
$83$	11.4504	−	3.72047i	1.25685	−	0.408375i	0.396478	−	0.918044i	$-0.370232\pi$
$83$	11.4504	−	3.72047i	1.25685	−	0.408375i	0.860370	+	0.509670i	$0.170232\pi$
$84$	0.595823	+	0.432891i	0.0650096	+	0.0472323i
$85$	0.857883	+	1.65254i	0.0930505	+	0.179243i
$86$	−5.48577	+	3.98564i	−0.591545	+	0.429783i
$87$	0.706146	−	0.971927i	0.0757068	−	0.104201i
$88$	1.37896	−	1.89797i	0.146998	−	0.202325i
$89$	3.36361	−	2.44381i	0.356542	−	0.259043i	−0.395066	−	0.918653i	$-0.629278\pi$
$89$	3.36361	−	2.44381i	0.356542	−	0.259043i	0.751609	+	0.659609i	$0.229278\pi$
$90$	3.64893	−	0.606381i	0.384631	−	0.0639182i
$91$	−0.447803	−	0.325348i	−0.0469425	−	0.0341058i
$92$	−2.71396	+	0.881818i	−0.282950	+	0.0919359i
$93$			4.30204i			0.446101i
$94$	−3.42505	−	10.5412i	−0.353267	−	1.08724i
$95$	−1.57988	+	0.820167i	−0.162093	+	0.0841474i
$96$	−1.22864	+	3.78136i	−0.125398	+	0.385934i
$97$	0.150018	+	0.0487437i	0.0152320	+	0.00494917i	0.316623	−	0.948551i	$-0.397451\pi$
$97$	0.150018	+	0.0487437i	0.0152320	+	0.00494917i	−0.301391	+	0.953501i	$0.597451\pi$
$98$	−0.972332	−	1.33830i	−0.0982204	−	0.135189i
$99$	1.12242			0.112807
$100$	−0.0559404	−	3.68196i	−0.00559404	−	0.368196i
$101$	−1.19010			−0.118419			−0.0592096	−	0.998246i	$-0.518858\pi$
$101$	−1.19010			−0.118419			−0.0592096	+	0.998246i	$0.518858\pi$
$102$	−0.809649	−	1.11439i	−0.0801672	−	0.110341i
$103$	6.82906	+	2.21890i	0.672887	+	0.218634i	0.625479	−	0.780241i	$-0.284904\pi$
$103$	6.82906	+	2.21890i	0.672887	+	0.218634i	0.0474085	+	0.998876i	$0.484904\pi$
$104$	0.357512	−	1.10031i	0.0350570	−	0.107894i
$105$	−2.21113	−	0.333012i	−0.215784	−	0.0324987i
$106$	3.13834	+	9.65882i	0.304823	+	0.938148i
$107$		−	5.98329i		−	0.578426i	−0.957265	−	0.289213i	$-0.906606\pi$
$107$		−	5.98329i		−	0.578426i	0.957265	−	0.289213i	$-0.0933937\pi$
$108$	−0.700432	+	0.227584i	−0.0673991	+	0.0218993i
$109$	−3.13786	−	2.27979i	−0.300552	−	0.218364i	0.427280	−	0.904120i	$-0.359472\pi$
$109$	−3.13786	−	2.27979i	−0.300552	−	0.218364i	−0.727832	+	0.685755i	$0.759472\pi$
$110$	0.618315	−	4.10549i	0.0589541	−	0.391443i
$111$	−3.43418	+	2.49508i	−0.325958	+	0.236822i
$112$	2.89811	−	3.98890i	0.273845	−	0.376916i
$113$	4.30469	−	5.92490i	0.404951	−	0.557368i	−0.557027	−	0.830495i	$-0.688058\pi$
$113$	4.30469	−	5.92490i	0.404951	−	0.557368i	0.961978	+	0.273127i	$0.0880579\pi$
$114$	1.06539	−	0.774053i	0.0997832	−	0.0724967i
$115$	6.07971	−	6.17278i	0.566936	−	0.575615i
$116$	0.715802	+	0.520061i	0.0664606	+	0.0482864i
$117$	0.526424	−	0.171046i	0.0486680	−	0.0158132i
$118$		−	18.9725i		−	1.74656i
$119$	0.257315	+	0.791933i	0.0235880	+	0.0725964i
$120$	−0.766176	−	4.61050i	−0.0699420	−	0.420880i
$121$	−3.00988	+	9.26346i	−0.273626	+	0.842133i
$122$	−22.3316	−	7.25598i	−2.02181	−	0.656926i
$123$	−2.45249	−	3.37556i	−0.221134	−	0.304364i
$124$	−3.16836			−0.284527
$125$	5.30144	+	9.84351i	0.474175	+	0.880431i
$126$	1.65423			0.147371
$127$	7.99712	+	11.0071i	0.709630	+	0.976721i	0.999805	+	0.0197480i	$0.00628638\pi$
$127$	7.99712	+	11.0071i	0.709630	+	0.976721i	−0.290175	+	0.956974i	$0.593714\pi$
$128$	12.7293	+	4.13599i	1.12512	+	0.365573i
$129$	−1.26668	+	3.89843i	−0.111525	+	0.343238i
$130$	−0.335641	−	2.01974i	−0.0294377	−	0.177143i
$131$	−4.39934	−	13.5398i	−0.384372	−	1.18298i	−0.936935	−	0.349504i	$-0.886350\pi$
$131$	−4.39934	−	13.5398i	−0.384372	−	1.18298i	0.552563	−	0.833471i	$-0.313650\pi$
$132$			0.826635i			0.0719493i
$133$	−0.757116	+	0.246002i	−0.0656503	+	0.0213311i
$134$	−4.65170	−	3.37966i	−0.401845	−	0.291958i
$135$	1.56908	−	1.59310i	0.135045	−	0.137113i
$136$	−1.40805	+	1.02301i	−0.120739	+	0.0877223i
$137$	−6.85250	+	9.43166i	−0.585448	+	0.805801i	−0.994280	−	0.106809i	$-0.965937\pi$
$137$	−6.85250	+	9.43166i	−0.585448	+	0.805801i	0.408831	+	0.912610i	$0.365937\pi$
$138$	−3.76749	+	5.18550i	−0.320710	+	0.441419i
$139$	7.79762	−	5.66530i	0.661385	−	0.480525i	−0.205745	−	0.978606i	$-0.565962\pi$
$139$	7.79762	−	5.66530i	0.661385	−	0.480525i	0.867130	+	0.498081i	$0.165962\pi$
$140$	0.245256	−	1.62845i	0.0207279	−	0.137629i
$141$	−5.42059	−	3.93829i	−0.456496	−	0.331664i
$142$	10.6908	−	3.47364i	0.897148	−	0.291501i
$143$		−	0.621275i		−	0.0519536i
$144$	1.52363	+	4.68924i	0.126969	+	0.390770i
$145$	−2.65638	−	0.400070i	−0.220601	−	0.0332240i
$146$	−1.81596	+	5.58895i	−0.150290	+	0.462545i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	−1.83757	−	2.52920i	−0.151047	−	0.207899i
$149$	−22.9618			−1.88110			−0.940551	−	0.339653i	$-0.889691\pi$
$149$	−22.9618			−1.88110			−0.940551	+	0.339653i	$0.889691\pi$
$150$	−4.96275	−	6.61687i	−0.405207	−	0.540266i
$151$	6.40478			0.521213			0.260607	−	0.965445i	$-0.416077\pi$
$151$	6.40478			0.521213			0.260607	+	0.965445i	$0.416077\pi$
$152$	−0.978034	−	1.34615i	−0.0793290	−	0.109187i
$153$	−0.791933	−	0.257315i	−0.0640240	−	0.0208027i
$154$	0.573763	−	1.76586i	0.0462351	−	0.142297i
$155$	8.53775	−	4.43221i	0.685769	−	0.356004i
$156$	0.125971	+	0.387700i	0.0100858	+	0.0310408i
$157$		−	22.7826i		−	1.81825i	−0.416526	−	0.909124i	$-0.636752\pi$
$157$		−	22.7826i		−	1.81825i	0.416526	−	0.909124i	$-0.363248\pi$
$158$	−22.2943	+	7.24387i	−1.77364	+	0.576291i
$159$	4.96683	+	3.60862i	0.393896	+	0.286182i
$160$	8.77025	−	1.45744i	0.693349	−	0.115221i
$161$	3.13469	−	2.27749i	0.247048	−	0.179491i
$162$	−0.972332	+	1.33830i	−0.0763936	+	0.105147i
$163$	1.64131	−	2.25906i	0.128557	−	0.176944i	−0.739886	−	0.672732i	$-0.765121\pi$
$163$	1.64131	−	2.25906i	0.128557	−	0.176944i	0.868443	+	0.495788i	$0.165121\pi$
$164$	2.48603	−	1.80620i	0.194126	−	0.141041i
$165$	−1.15638	−	2.22753i	−0.0900239	−	0.173413i
$166$	16.1127	+	11.7066i	1.25059	+	0.908607i
$167$	−4.36866	+	1.41946i	−0.338057	+	0.109841i	−0.473126	−	0.880995i	$-0.656874\pi$
$167$	−4.36866	+	1.41946i	−0.338057	+	0.109841i	0.135069	+	0.990836i	$0.456874\pi$
$168$		−	2.09016i		−	0.161259i
$169$	3.92254	+	12.0724i	0.301734	+	0.928642i
$170$	−1.37744	+	2.75492i	−0.105645	+	0.211293i
$171$	0.246002	−	0.757116i	0.0188122	−	0.0578981i
$172$	−2.87111	−	0.932880i	−0.218920	−	0.0711314i
$173$	11.2192	+	15.4420i	0.852984	+	1.17403i	0.983197	+	0.182545i	$0.0584336\pi$
$173$	11.2192	+	15.4420i	0.852984	+	1.17403i	−0.130214	+	0.991486i	$0.541566\pi$
$174$	1.98734			0.150660
$175$	1.61715	+	4.73126i	0.122245	+	0.357650i
$176$	5.53414			0.417151
$177$	−6.74136	−	9.27869i	−0.506712	−	0.697429i
$178$	6.54110	+	2.12533i	0.490276	+	0.159300i
$179$	−4.73318	+	14.5672i	−0.353775	+	1.08881i	0.602942	+	0.797785i	$0.293995\pi$
$179$	−4.73318	+	14.5672i	−0.353775	+	1.08881i	−0.956717	+	0.291021i	$0.906005\pi$
$180$	1.17329	+	1.15559i	0.0874515	+	0.0861329i
$181$	−2.61951	−	8.06201i	−0.194706	−	0.599245i	−0.999980	−	0.00634118i	$-0.997982\pi$
$181$	−2.61951	−	8.06201i	−0.194706	−	0.599245i	0.805273	−	0.592904i	$-0.202018\pi$
$182$		−	0.915642i		−	0.0678719i
$183$	−13.4997	+	4.38632i	−0.997926	+	0.324246i
$184$	6.55200	+	4.76030i	0.483020	+	0.350934i
$185$	8.48978	+	4.24484i	0.624181	+	0.312087i
$186$	−5.75742	+	4.18301i	−0.422155	+	0.306713i
$187$	−0.549357	+	0.756125i	−0.0401730	+	0.0552933i
$188$	2.90046	−	3.99214i	0.211538	−	0.291157i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−2.63380	−	1.31689i	−0.191076	−	0.0955370i
$191$	−11.4950	−	8.35162i	−0.831751	−	0.604302i	0.0883033	−	0.996094i	$-0.471856\pi$
$191$	−11.4950	−	8.35162i	−0.831751	−	0.604302i	−0.920054	+	0.391791i	$0.871856\pi$
$192$	3.12323	−	1.01480i	0.225400	−	0.0732368i
$193$		−	12.1722i		−	0.876173i	−0.898933	−	0.438087i	$-0.855656\pi$
$193$		−	12.1722i		−	0.876173i	0.898933	−	0.438087i	$-0.144344\pi$
$194$	0.0806332	+	0.248164i	0.00578913	+	0.0178171i
$195$	−0.881807	−	0.868512i	−0.0631475	−	0.0621954i
$196$	0.227584	−	0.700432i	0.0162560	−	0.0500309i
$197$	3.57456	+	1.16144i	0.254677	+	0.0827495i	0.433573	−	0.901118i	$-0.357253\pi$
$197$	3.57456	+	1.16144i	0.254677	+	0.0827495i	−0.178896	+	0.983868i	$0.557253\pi$
$198$	1.09136	+	1.50213i	0.0775597	+	0.106752i
$199$	−22.4143			−1.58891			−0.794455	−	0.607324i	$-0.792243\pi$
$199$	−22.4143			−1.58891			−0.794455	+	0.607324i	$0.792243\pi$
$200$	−8.36057	+	6.27055i	−0.591181	+	0.443395i
$201$	−3.47582			−0.245166
$202$	−1.15717	−	1.59271i	−0.0814183	−	0.112063i
$203$	−1.14257	−	0.371243i	−0.0801926	−	0.0260562i
$204$	0.189506	−	0.583241i	0.0132681	−	0.0408350i
$205$	−4.17239	+	8.34487i	−0.291412	+	0.582831i
$206$	3.67056	+	11.2968i	0.255740	+	0.787088i
$207$			3.87469i			0.269310i
$208$	2.59556	−	0.843350i	0.179970	−	0.0584758i
$209$	−0.722883	−	0.525205i	−0.0500028	−	0.0363292i
$210$	−1.70428	−	3.28296i	−0.117607	−	0.226546i
$211$	11.0397	−	8.02079i	0.760002	−	0.552174i	−0.138909	−	0.990305i	$-0.544360\pi$
$211$	11.0397	−	8.02079i	0.760002	−	0.552174i	0.898911	+	0.438131i	$0.144360\pi$
$212$	−2.65767	+	3.65796i	−0.182529	+	0.251230i
$213$	3.99415	−	5.49748i	0.273675	−	0.376681i
$214$	8.00744	−	5.81774i	0.547377	−	0.397693i
$215$	9.04177	−	1.50256i	0.616643	−	0.102474i
$216$	1.69097	+	1.22856i	0.115056	+	0.0835931i
$217$	4.09148	−	1.32940i	0.277748	−	0.0902458i
$218$		−	6.41611i		−	0.434554i
$219$	1.09777	+	3.37858i	0.0741803	+	0.228303i
$220$	1.64052	−	0.851647i	0.110604	−	0.0574180i
$221$	−0.142428	+	0.438347i	−0.00958072	+	0.0294864i
$222$	−6.67833	−	2.16992i	−0.448220	−	0.145636i
$223$	−14.5785	−	20.0656i	−0.976247	−	1.34369i	−0.938827	−	0.344389i	$-0.888086\pi$
$223$	−14.5785	−	20.0656i	−0.976247	−	1.34369i	−0.0374199	−	0.999300i	$-0.511914\pi$
$224$	3.97596			0.265655
$225$	−4.77821	−	1.47267i	−0.318547	−	0.0981778i
$226$	12.1149			0.805870
$227$	−9.19298	−	12.6531i	−0.610160	−	0.839813i	0.386431	−	0.922318i	$-0.373708\pi$
$227$	−9.19298	−	12.6531i	−0.610160	−	0.839813i	−0.996591	+	0.0825055i	$0.973708\pi$
$228$	0.557599	+	0.181175i	0.0369279	+	0.0119986i
$229$	−8.84830	+	27.2323i	−0.584712	+	1.79956i	0.0157102	+	0.999877i	$0.494999\pi$
$229$	−8.84830	+	27.2323i	−0.584712	+	1.79956i	−0.600422	+	0.799683i	$0.705001\pi$
$230$	14.1725	+	2.13449i	0.934510	+	0.140744i
$231$	−0.346846	−	1.06748i	−0.0228208	−	0.0702351i
$232$		−	2.51105i		−	0.164858i
$233$	12.9964	−	4.22280i	0.851425	−	0.276645i	0.149382	−	0.988780i	$-0.452272\pi$
$233$	12.9964	−	4.22280i	0.851425	−	0.276645i	0.702043	+	0.712135i	$0.252272\pi$
$234$	0.740770	+	0.538201i	0.0484256	+	0.0351833i
$235$	−2.23125	+	14.8151i	−0.145551	+	0.966428i
$236$	6.83355	−	4.96486i	0.444826	−	0.323185i
$237$	−8.32934	+	11.4644i	−0.541049	+	0.744690i
$238$	−0.809649	+	1.11439i	−0.0524817	+	0.0722349i
$239$	8.73149	−	6.34380i	0.564793	−	0.410346i	−0.268417	−	0.963303i	$-0.586500\pi$
$239$	8.73149	−	6.34380i	0.564793	−	0.410346i	0.833210	+	0.552957i	$0.186500\pi$
$240$	7.73645	−	7.85489i	0.499386	−	0.507031i
$241$	13.1117	+	9.52618i	0.844596	+	0.613635i	0.923651	−	0.383235i	$-0.125190\pi$
$241$	13.1117	+	9.52618i	0.844596	+	0.613635i	−0.0790544	+	0.996870i	$0.525190\pi$
$242$	−15.3239	+	4.97904i	−0.985058	+	0.320065i
$243$			1.00000i			0.0641500i
$244$	−3.23043	−	9.94223i	−0.206807	−	0.636486i
$245$	0.366564	+	2.20582i	0.0234189	+	0.140925i
$246$	2.13288	−	6.56433i	0.135988	−	0.418527i
$247$	−0.419076	−	0.136166i	−0.0266651	−	0.00866403i
$248$	5.28533	+	7.27463i	0.335619	+	0.461940i
$249$	12.0397			0.762984
$250$	−8.01882	+	16.6661i	−0.507155	+	1.05406i
$251$	18.2948			1.15476			0.577378	−	0.816477i	$-0.304076\pi$
$251$	18.2948			1.15476			0.577378	+	0.816477i	$0.304076\pi$
$252$	0.432891	+	0.595823i	0.0272696	+	0.0375333i
$253$	4.13616	+	1.34392i	0.260038	+	0.0844915i
$254$	−6.95494	+	21.4051i	−0.436392	+	1.34308i
$255$	0.305233	+	1.83676i	0.0191144	+	0.115022i
$256$	4.81228	+	14.8107i	0.300768	+	0.925668i
$257$		−	4.64574i		−	0.289793i	−0.989447	−	0.144897i	$-0.953715\pi$
$257$		−	4.64574i		−	0.289793i	0.989447	−	0.144897i	$-0.0462849\pi$
$258$	−6.44890	+	2.09538i	−0.401491	+	0.130452i
$259$	3.43418	+	2.49508i	0.213390	+	0.155037i
$260$	0.639639	−	0.649431i	0.0396688	−	0.0402760i
$261$	0.971927	−	0.706146i	0.0601608	−	0.0437094i
$262$	13.8427	−	19.0528i	0.855203	−	1.17709i
$263$	−6.81652	+	9.38213i	−0.420325	+	0.578527i	−0.965699	−	0.259666i	$-0.916388\pi$
$263$	−6.81652	+	9.38213i	−0.420325	+	0.578527i	0.545374	+	0.838193i	$0.316388\pi$
$264$	1.89797	−	1.37896i	0.116812	−	0.0848691i
$265$	2.04448	−	13.5749i	0.125591	−	0.833899i
$266$	−1.06539	−	0.774053i	−0.0653234	−	0.0474603i
$267$	3.95417	−	1.28479i	0.241991	−	0.0786276i
$268$		−	2.55987i		−	0.156369i
$269$	8.65641	+	26.6417i	0.527790	+	1.62437i	0.758731	+	0.651404i	$0.225820\pi$
$269$	8.65641	+	26.6417i	0.527790	+	1.62437i	−0.230941	+	0.972968i	$0.574180\pi$
$270$	3.65772	+	0.550879i	0.222602	+	0.0335254i
$271$	−3.11024	+	9.57232i	−0.188933	+	0.581477i	−0.999994	−	0.00348510i	$-0.998891\pi$
$271$	−3.11024	+	9.57232i	−0.188933	+	0.581477i	0.811061	+	0.584962i	$0.198891\pi$
$272$	−3.90467	−	1.26870i	−0.236755	−	0.0769265i
$273$	−0.325348	−	0.447803i	−0.0196910	−	0.0271023i
$274$	−19.2853			−1.16507
$275$	−3.22935	+	4.58986i	−0.194737	+	0.276779i
$276$	−2.85362			−0.171768
$277$	9.42457	+	12.9718i	0.566267	+	0.779400i	0.992106	−	0.125399i	$-0.0400210\pi$
$277$	9.42457	+	12.9718i	0.566267	+	0.779400i	−0.425839	+	0.904799i	$0.640021\pi$
$278$	15.1637	+	4.92700i	0.909461	+	0.295502i
$279$	−1.32940	+	4.09148i	−0.0795893	+	0.244951i
$280$	−4.14809	+	2.15340i	−0.247896	+	0.128690i
$281$	−3.22816	−	9.93527i	−0.192576	−	0.592689i	−0.999996	−	0.00271166i	$-0.999137\pi$
$281$	−3.22816	−	9.93527i	−0.192576	−	0.592689i	0.807420	−	0.589977i	$-0.200863\pi$
$282$		−	11.0837i		−	0.660024i
$283$	8.62224	−	2.80154i	0.512539	−	0.166534i	−0.0413177	−	0.999146i	$-0.513156\pi$
$283$	8.62224	−	2.80154i	0.512539	−	0.166534i	0.553857	+	0.832612i	$0.313156\pi$
$284$	4.04877	+	2.94160i	0.240250	+	0.174552i
$285$	−1.75601	+	0.291814i	−0.104017	+	0.0172856i
$286$	0.831452	−	0.604085i	0.0491648	−	0.0357203i
$287$	−2.45249	+	3.37556i	−0.144766	+	0.199253i
$288$	−2.33701	+	3.21662i	−0.137710	+	0.189541i
$289$	−13.1923	+	9.58480i	−0.776020	+	0.563812i
$290$	−2.04747	−	3.94404i	−0.120232	−	0.231602i
$291$	0.127613	+	0.0927160i	0.00748078	+	0.00543511i
$292$	−2.48825	+	0.808482i	−0.145614	+	0.0473128i
$293$		−	9.63530i		−	0.562900i	−0.959576	−	0.281450i	$-0.909185\pi$
$293$		−	9.63530i		−	0.562900i	0.959576	−	0.281450i	$-0.0908154\pi$
$294$	−0.511185	−	1.57327i	−0.0298129	−	0.0917548i
$295$	−11.4690	+	22.9382i	−0.667750	+	1.33552i
$296$	−2.74174	+	8.43822i	−0.159361	+	0.490462i
$297$	1.06748	+	0.346846i	0.0619415	+	0.0201260i
$298$	−22.3265	−	30.7298i	−1.29334	−	1.78013i
$299$	2.14470			0.124031
$300$	1.08459	−	3.51904i	0.0626187	−	0.203172i
$301$	4.09905			0.236266
$302$	6.22757	+	8.57151i	0.358356	+	0.493235i
$303$	−1.13185	−	0.367761i	−0.0650232	−	0.0211273i
$304$	1.21293	−	3.73300i	0.0695661	−	0.214102i
$305$	22.6132	+	22.2722i	1.29483	+	1.27530i
$306$	−0.425658	−	1.31004i	−0.0243332	−	0.0748900i
$307$		−	15.1354i		−	0.863820i	−0.901917	−	0.431910i	$-0.857840\pi$
$307$		−	15.1354i		−	0.863820i	0.901917	−	0.431910i	$-0.142160\pi$
$308$	0.786176	−	0.255444i	0.0447965	−	0.0145553i
$309$	5.80914	+	4.22059i	0.330471	+	0.240101i
$310$	14.2332	+	7.11650i	0.808389	+	0.404190i
$311$	3.91390	−	2.84362i	0.221937	−	0.161247i	−0.471261	−	0.881994i	$-0.656201\pi$
$311$	3.91390	−	2.84362i	0.221937	−	0.161247i	0.693198	+	0.720747i	$0.256201\pi$
$312$	0.680029	−	0.935979i	0.0384990	−	0.0529894i
$313$	−12.0974	+	16.6506i	−0.683784	+	0.941148i	−0.999972	−	0.00754866i	$-0.997597\pi$
$313$	−12.0974	+	16.6506i	−0.683784	+	0.941148i	0.316187	+	0.948697i	$0.397597\pi$
$314$	30.4899	−	22.1522i	1.72065	−	1.25012i
$315$	−2.00000	−	0.999991i	−0.112687	−	0.0563431i
$316$	−8.44325	−	6.13438i	−0.474970	−	0.345086i
$317$	12.8729	−	4.18265i	0.723012	−	0.234921i	0.0756836	−	0.997132i	$-0.475886\pi$
$317$	12.8729	−	4.18265i	0.723012	−	0.234921i	0.647329	+	0.762211i	$0.275886\pi$
$318$			10.1559i			0.569514i
$319$	−0.416689	−	1.28244i	−0.0233301	−	0.0718027i
$320$	−5.23168	−	5.15280i	−0.292460	−	0.288050i
$321$	1.84894	−	5.69045i	0.103198	−	0.317610i
$322$	6.09592	+	1.98069i	0.339712	+	0.110379i
$323$	0.389634	+	0.536285i	0.0216798	+	0.0298397i
$324$	−0.736478			−0.0409154
$325$	−0.815144	+	2.64481i	−0.0452161	+	0.146708i
$326$	4.61920			0.255834
$327$	−2.27979	−	3.13786i	−0.126073	−	0.173524i
$328$	−8.29418	−	2.69494i	−0.457970	−	0.148803i
$329$	−2.07048	+	6.37228i	−0.114149	+	0.351315i
$330$	1.85672	−	3.71348i	0.102209	−	0.204420i
$331$	−7.32953	−	22.5580i	−0.402867	−	1.23990i	−0.922663	−	0.385607i	$-0.873992\pi$
$331$	−7.32953	−	22.5580i	−0.402867	−	1.23990i	0.519796	−	0.854291i	$-0.326008\pi$
$332$			8.86696i			0.486638i
$333$	−4.03712	+	1.31174i	−0.221233	+	0.0718829i
$334$	−6.14745	−	4.46638i	−0.336374	−	0.244390i
$335$	3.58100	+	6.89806i	0.195651	+	0.376881i
$336$	3.98890	−	2.89811i	0.217613	−	0.158105i
$337$	1.03751	−	1.42801i	0.0565169	−	0.0777888i	−0.779823	−	0.626000i	$-0.784691\pi$
$337$	1.03751	−	1.42801i	0.0565169	−	0.0777888i	0.836340	+	0.548211i	$0.184691\pi$
$338$	−12.3424	+	16.9879i	−0.671339	+	0.924019i
$339$	5.92490	−	4.30469i	0.321796	−	0.233799i
$340$	−1.35273	+	0.224797i	−0.0733621	+	0.0121913i
$341$	3.90648	+	2.83823i	0.211548	+	0.153699i
$342$	1.25244	−	0.406944i	0.0677245	−	0.0220050i
$343$			1.00000i			0.0539949i
$344$	2.64755	+	8.14833i	0.142747	+	0.439329i
$345$	7.68965	−	3.99193i	0.413997	−	0.214918i
$346$	−9.75716	+	30.0294i	−0.524548	+	1.61439i
$347$	6.38085	+	2.07326i	0.342542	+	0.111299i	0.475236	−	0.879858i	$-0.342363\pi$
$347$	6.38085	+	2.07326i	0.342542	+	0.111299i	−0.132694	+	0.991157i	$0.542363\pi$
$348$	0.520061	+	0.715802i	0.0278782	+	0.0383710i
$349$	−6.88840			−0.368727			−0.184364	−	0.982858i	$-0.559022\pi$
$349$	−6.88840			−0.368727			−0.184364	+	0.982858i	$0.559022\pi$
$350$	−4.75945	+	6.76458i	−0.254403	+	0.361582i
$351$	0.553515			0.0295445
$352$	2.62310	+	3.61039i	0.139812	+	0.192434i
$353$	33.3103	+	10.8232i	1.77293	+	0.576059i	0.998403	−	0.0564878i	$-0.0179902\pi$
$353$	33.3103	+	10.8232i	1.77293	+	0.576059i	0.774523	+	0.632546i	$0.217990\pi$
$354$	5.86283	−	18.0439i	0.311606	−	0.959025i
$355$	−15.0252	−	2.26290i	−0.797455	−	0.120102i
$356$	0.946217	+	2.91216i	0.0501494	+	0.154344i
$357$			0.832687i			0.0440705i
$358$	−24.0976	+	7.82977i	−1.27360	+	0.413816i
$359$	−29.6092	−	21.5123i	−1.56271	−	1.13538i	−0.933742	−	0.357947i	$-0.883477\pi$
$359$	−29.6092	−	21.5123i	−1.56271	−	1.13538i	−0.628970	−	0.777430i	$-0.716523\pi$
$360$	0.696048	−	4.62161i	0.0366849	−	0.243580i
$361$	14.8586	−	10.7954i	0.782032	−	0.568180i
$362$	8.24236	−	11.3446i	0.433209	−	0.596261i
$363$	−5.72514	+	7.87997i	−0.300492	+	0.413591i
$364$	0.329797	−	0.239612i	0.0172861	−	0.0125591i
$365$	5.57409	−	5.65942i	0.291761	−	0.296228i
$366$	−18.9964	−	13.8017i	−0.992958	−	0.721426i
$367$	15.8583	−	5.15266i	0.827794	−	0.268967i	0.135678	−	0.990753i	$-0.456679\pi$
$367$	15.8583	−	5.15266i	0.827794	−	0.268967i	0.692116	+	0.721786i	$0.256679\pi$
$368$			19.1044i			0.995885i
$369$	−1.28935	−	3.96821i	−0.0671209	−	0.206577i
$370$	2.57402	+	15.4893i	0.133817	+	0.805249i
$371$	1.89716	−	5.83886i	0.0984957	−	0.303139i
$372$	−3.01329	−	0.979076i	−0.156232	−	0.0507627i
$373$	−0.498841	−	0.686596i	−0.0258290	−	0.0355506i	0.795907	−	0.605419i	$-0.206994\pi$
$373$	−0.498841	−	0.686596i	−0.0258290	−	0.0355506i	−0.821736	+	0.569868i	$0.806994\pi$
$374$	−1.54608			−0.0799459
$375$	2.00015	+	11.0000i	0.103288	+	0.568036i
$376$	−14.0045			−0.722227
$377$	−0.390863	−	0.537976i	−0.0201305	−	0.0277072i
$378$	1.57327	+	0.511185i	0.0809201	+	0.0262925i
$379$	2.30072	−	7.08088i	0.118180	−	0.363720i	−0.874417	−	0.485175i	$-0.838756\pi$
$379$	2.30072	−	7.08088i	0.118180	−	0.363720i	0.992597	+	0.121455i	$0.0387559\pi$
$380$	−0.214914	−	1.29326i	−0.0110249	−	0.0663428i
$381$	4.20433	+	12.9396i	0.215395	+	0.662916i
$382$		−	23.5043i		−	1.20259i
$383$	5.17852	−	1.68260i	0.264610	−	0.0859771i	−0.173707	−	0.984797i	$-0.555575\pi$
$383$	5.17852	−	1.68260i	0.264610	−	0.0859771i	0.438317	+	0.898820i	$0.355575\pi$
$384$	10.8282	+	7.86712i	0.552572	+	0.401467i
$385$	−1.76116	+	1.78813i	−0.0897572	+	0.0911313i
$386$	16.2900	−	11.8354i	0.829141	−	0.602407i
$387$	−2.40936	+	3.31620i	−0.122475	+	0.168572i
$388$	−0.0682832	+	0.0939838i	−0.00346656	+	0.00477131i
$389$	15.7263	−	11.4258i	0.797356	−	0.579313i	−0.112781	−	0.993620i	$-0.535976\pi$
$389$	15.7263	−	11.4258i	0.797356	−	0.579313i	0.910137	+	0.414307i	$0.135976\pi$
$390$	0.304920	−	2.02460i	0.0154402	−	0.102520i
$391$	−2.61022	−	1.89643i	−0.132004	−	0.0959068i
$392$	−1.98786	+	0.645894i	−0.100402	+	0.0326226i
$393$		−	14.2366i		−	0.718139i
$394$	1.92130	+	5.91314i	0.0967935	+	0.297900i
$395$	31.3333	+	4.71903i	1.57655	+	0.237440i
$396$	−0.255444	+	0.786176i	−0.0128366	+	0.0395068i
$397$	12.3559	+	4.01467i	0.620125	+	0.201491i	0.602196	−	0.798349i	$-0.294293\pi$
$397$	12.3559	+	4.01467i	0.620125	+	0.201491i	0.0179291	+	0.999839i	$0.494293\pi$
$398$	−21.7942	−	29.9971i	−1.09244	−	1.50362i
$399$	−0.796079			−0.0398538
$400$	−23.5592	−	7.26107i	−1.17796	−	0.363054i
$401$	5.41081			0.270203			0.135101	−	0.990832i	$-0.456864\pi$
$401$	5.41081			0.270203			0.135101	+	0.990832i	$0.456864\pi$
$402$	−3.37966	−	4.65170i	−0.168562	−	0.232006i
$403$	2.26470	+	0.735845i	0.112813	+	0.0366551i
$404$	0.270848	−	0.833583i	0.0134752	−	0.0414723i
$405$	1.98458	−	1.03026i	0.0986147	−	0.0511939i
$406$	−0.614121	−	1.89007i	−0.0304783	−	0.0938027i
$407$			4.76452i			0.236169i
$408$	−1.65526	+	0.537828i	−0.0819478	+	0.0266264i
$409$	−20.7639	−	15.0859i	−1.02671	−	0.745948i	−0.0590616	−	0.998254i	$-0.518811\pi$
$409$	−20.7639	−	15.0859i	−1.02671	−	0.745948i	−0.967647	+	0.252307i	$0.918811\pi$
$410$	−15.2249	+	2.53008i	−0.751903	+	0.124952i
$411$	−9.43166	+	6.85250i	−0.465229	+	0.338009i
$412$	−3.10837	+	4.27831i	−0.153138	+	0.210777i
$413$	−6.74136	+	9.27869i	−0.331721	+	0.456575i
$414$	−5.18550	+	3.76749i	−0.254853	+	0.185162i
$415$	−12.4040	−	23.8938i	−0.608888	−	1.17290i
$416$	1.78045	+	1.29357i	0.0872937	+	0.0634226i
$417$	9.16665	−	2.97842i	0.448893	−	0.145854i
$418$		−	1.47811i		−	0.0722966i
$419$	−4.36075	−	13.4210i	−0.213037	−	0.655659i	−0.999287	−	0.0377513i	$-0.987981\pi$
$419$	−4.36075	−	13.4210i	−0.213037	−	0.655659i	0.786251	−	0.617908i	$-0.212019\pi$
$420$	0.736471	−	1.47296i	0.0359361	−	0.0718730i
$421$	8.97245	−	27.6144i	0.437291	−	1.34584i	−0.453431	−	0.891292i	$-0.649800\pi$
$421$	8.97245	−	27.6144i	0.437291	−	1.34584i	0.890721	−	0.454550i	$-0.150200\pi$
$422$	21.4684	+	6.97552i	1.04507	+	0.339563i
$423$	−3.93829	−	5.42059i	−0.191486	−	0.263558i
$424$	12.8322			0.623186
$425$	3.33073	−	2.49809i	0.161564	−	0.121175i
$426$	11.2409			0.544624
$427$	8.34327	+	11.4835i	0.403759	+	0.555727i
$428$	4.19089	+	1.36170i	0.202574	+	0.0658203i
$429$	0.191984	−	0.590867i	0.00926910	−	0.0285273i
$430$	10.8025	+	10.6396i	0.520942	+	0.513087i
$431$	−3.68640	−	11.3456i	−0.177567	−	0.546496i	0.822174	−	0.569236i	$-0.192761\pi$
$431$	−3.68640	−	11.3456i	−0.177567	−	0.546496i	−0.999741	+	0.0227399i	$0.992761\pi$
$432$			4.93056i			0.237221i
$433$	−4.70086	+	1.52740i	−0.225909	+	0.0734022i	−0.419784	−	0.907624i	$-0.637894\pi$
$433$	−4.70086	+	1.52740i	−0.225909	+	0.0734022i	0.193875	+	0.981026i	$0.437894\pi$
$434$	5.75742	+	4.18301i	0.276365	+	0.200791i
$435$	−2.40274	−	1.20136i	−0.115203	−	0.0576006i
$436$	2.31096	−	1.67901i	0.110675	−	0.0804102i
$437$	1.81306	−	2.49546i	0.0867304	−	0.119374i
$438$	−3.45416	+	4.75425i	−0.165046	+	0.227167i
$439$	−0.470028	+	0.341495i	−0.0224332	+	0.0162987i	−0.598945	−	0.800790i	$-0.704413\pi$
$439$	−0.470028	+	0.341495i	−0.0224332	+	0.0162987i	0.576512	+	0.817089i	$0.304413\pi$
$440$	−4.69206	−	2.34600i	−0.223685	−	0.111841i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−0.725127	+	0.235608i	−0.0344908	+	0.0112067i
$443$		−	30.0726i		−	1.42879i	−0.699742	−	0.714396i	$-0.746702\pi$
$443$		−	30.0726i		−	1.42879i	0.699742	−	0.714396i	$-0.253298\pi$
$444$	−0.966068	−	2.97325i	−0.0458475	−	0.141104i
$445$	−6.62358	−	6.52371i	−0.313988	−	0.309253i
$446$	12.6786	−	39.0208i	0.600350	−	1.84769i
$447$	−21.8379	−	7.09558i	−1.03290	−	0.335609i
$448$	−1.93026	−	2.65678i	−0.0911963	−	0.125521i
$449$	26.3584			1.24393			0.621965	−	0.783045i	$-0.286335\pi$
$449$	26.3584			1.24393			0.621965	+	0.783045i	$0.286335\pi$
$450$	−2.67513	−	7.82660i	−0.126107	−	0.368949i
$451$	−4.68320			−0.220523
$452$	3.17031	+	4.36356i	0.149119	+	0.205245i
$453$	6.09130	+	1.97918i	0.286194	+	0.0929902i
$454$	7.99496	−	24.6059i	0.375222	−	1.15481i
$455$	−0.553510	+	1.10703i	−0.0259490	+	0.0518985i
$456$	−0.514183	−	1.58249i	−0.0240788	−	0.0741070i
$457$		−	10.9224i		−	0.510929i	−0.966818	−	0.255465i	$-0.917772\pi$
$457$		−	10.9224i		−	0.510929i	0.966818	−	0.255465i	$-0.0822284\pi$
$458$	−45.0485	+	14.6371i	−2.10498	+	0.683948i
$459$	−0.673658	−	0.489441i	−0.0314437	−	0.0228452i
$460$	2.93997	+	5.66325i	0.137077	+	0.264051i
$461$	−20.6073	+	14.9721i	−0.959777	+	0.697318i	−0.953099	−	0.302659i	$-0.902126\pi$
$461$	−20.6073	+	14.9721i	−0.959777	+	0.697318i	−0.00667770	+	0.999978i	$0.502126\pi$
$462$	1.09136	−	1.50213i	0.0507747	−	0.0698854i
$463$	3.02872	−	4.16867i	0.140756	−	0.193735i	−0.732819	−	0.680424i	$-0.761796\pi$
$463$	3.02872	−	4.16867i	0.140756	−	0.193735i	0.873575	+	0.486689i	$0.161796\pi$
$464$	4.79214	−	3.48169i	0.222469	−	0.161634i
$465$	9.48952	−	1.57697i	0.440066	−	0.0731303i
$466$	18.2882	+	13.2872i	0.847186	+	0.615517i
$467$	19.2758	−	6.26309i	0.891979	−	0.289821i	0.173056	−	0.984912i	$-0.444636\pi$
$467$	19.2758	−	6.26309i	0.891979	−	0.289821i	0.718922	+	0.695090i	$0.244636\pi$
$468$			0.407652i			0.0188437i
$469$	1.07409	+	3.30571i	0.0495968	+	0.152643i
$470$	−21.9965	+	11.4191i	−1.01462	+	0.526722i
$471$	7.04020	−	21.6675i	0.324395	−	0.998387i
$472$	−22.7989	−	7.40782i	−1.04941	−	0.340972i
$473$	2.70431	+	3.72216i	0.124344	+	0.171145i
$474$	−23.4416			−1.07671
$475$	2.38827	+	3.18429i	0.109581	+	0.146105i
$476$	−0.613256			−0.0281085
$477$	3.60862	+	4.96683i	0.165227	+	0.227416i
$478$	16.9798	+	5.51708i	0.776639	+	0.252345i
$479$	−0.830865	+	2.55714i	−0.0379632	+	0.116839i	−0.968242	−	0.250014i	$-0.919565\pi$
$479$	−0.830865	+	2.55714i	−0.0379632	+	0.116839i	0.930279	+	0.366853i	$0.119565\pi$
$480$	8.79137	+	1.32404i	0.401269	+	0.0604341i
$481$	0.726069	+	2.23461i	0.0331059	+	0.101889i
$482$			26.8100i			1.22116i
$483$	3.68505	−	1.19735i	0.167676	−	0.0544811i
$484$	−5.80342	−	4.21643i	−0.263792	−	0.191656i
$485$	0.0525286	−	0.348779i	0.00238520	−	0.0158372i
$486$	−1.33830	+	0.972332i	−0.0607065	+	0.0441059i
$487$	−10.5857	+	14.5700i	−0.479686	+	0.660231i	−0.978444	−	0.206510i	$-0.933789\pi$
$487$	−10.5857	+	14.5700i	−0.479686	+	0.660231i	0.498759	+	0.866741i	$0.333789\pi$
$488$	−17.4387	+	24.0024i	−0.789415	+	1.08654i
$489$	2.25906	−	1.64131i	0.102158	−	0.0742224i
$490$	−2.59562	+	2.63536i	−0.117258	+	0.119053i
$491$	−24.3961	−	17.7248i	−1.10098	−	0.799908i	−0.119759	−	0.992803i	$-0.538212\pi$
$491$	−24.3961	−	17.7248i	−1.10098	−	0.799908i	−0.981219	+	0.192895i	$0.938212\pi$
$492$	2.92250	−	0.949578i	0.131756	−	0.0428103i
$493$			1.00036i			0.0450541i
$494$	−0.225250	−	0.693247i	−0.0101345	−	0.0311907i
$495$	−0.411437	−	2.47585i	−0.0184927	−	0.111281i
$496$	−6.55470	+	20.1733i	−0.294315	+	0.905807i
$497$	−6.46268	−	2.09985i	−0.289891	−	0.0941912i
$498$	11.7066	+	16.1127i	0.524584	+	0.722028i
$499$	−31.3271			−1.40239			−0.701196	−	0.712969i	$-0.747350\pi$
$499$	−31.3271			−1.40239			−0.701196	+	0.712969i	$0.747350\pi$
$500$	−8.10123	+	1.47307i	−0.362298	+	0.0658776i
$501$	−4.59348			−0.205221
$502$	17.7886	+	24.4839i	0.793944	+	1.09277i
$503$	−26.2019	−	8.51353i	−1.16829	−	0.379599i	−0.340284	−	0.940323i	$-0.610523\pi$
$503$	−26.2019	−	8.51353i	−1.16829	−	0.379599i	−0.828003	+	0.560723i	$0.810523\pi$
$504$	0.645894	−	1.98786i	0.0287704	−	0.0885462i
$505$	0.436247	+	2.62514i	0.0194127	+	0.116817i
$506$	2.22315	+	6.84216i	0.0988312	+	0.304171i
$507$			12.6936i			0.563743i
$508$	−9.52974	+	3.09640i	−0.422814	+	0.137380i
$509$	1.86426	+	1.35446i	0.0826318	+	0.0600355i	0.628334	−	0.777944i	$-0.283737\pi$
$509$	1.86426	+	1.35446i	0.0826318	+	0.0600355i	−0.545702	+	0.837979i	$0.683737\pi$
$510$	−2.16134	+	2.19443i	−0.0957059	+	0.0971710i
$511$	2.87399	−	2.08808i	0.127138	−	0.0923712i
$512$	0.592234	−	0.815140i	0.0261733	−	0.0360245i
$513$	0.467924	−	0.644042i	0.0206593	−	0.0284351i
$514$	6.21739	−	4.51720i	0.274237	−	0.199245i
$515$	2.39119	−	15.8770i	0.105369	−	0.699625i
$516$	−2.44231	−	1.77444i	−0.107517	−	0.0781155i
$517$	−7.15235	+	2.32394i	−0.314560	+	0.102207i
$518$			7.02201i			0.308530i
$519$	5.89831	+	18.1531i	0.258907	+	0.796834i
$520$	−2.55813	−	0.385273i	−0.112182	−	0.0168953i
$521$	−10.9741	+	33.7747i	−0.480783	+	1.47970i	0.357214	+	0.934023i	$0.383727\pi$
$521$	−10.9741	+	33.7747i	−0.480783	+	1.47970i	−0.837997	+	0.545675i	$0.816273\pi$
$522$	1.89007	+	0.614121i	0.0827262	+	0.0268794i
$523$	−15.1447	−	20.8449i	−0.662231	−	0.911483i	0.337321	−	0.941390i	$-0.390479\pi$
$523$	−15.1447	−	20.8449i	−0.662231	−	0.911483i	−0.999553	+	0.0299063i	$0.990479\pi$
$524$	10.4849			0.458035
$525$	0.0759566	+	4.99942i	0.00331502	+	0.218193i
$526$	−19.1840			−0.836463
$527$	−2.10560	−	2.89811i	−0.0917212	−	0.126243i
$528$	5.26328	+	1.71014i	0.229055	+	0.0744244i
$529$	2.46805	−	7.59587i	0.107306	−	0.330255i
$530$	20.1552	−	10.4632i	0.875486	−	0.454492i
$531$	−3.54415	−	10.9078i	−0.153803	−	0.473356i
$532$		−	0.586295i		−	0.0254191i
$533$	−2.19647	+	0.713675i	−0.0951395	+	0.0309127i
$534$	5.56419	+	4.04262i	0.240786	+	0.174941i
$535$	−13.1980	+	2.19326i	−0.570601	+	0.0948228i
$536$	−5.87752	+	4.27027i	−0.253870	+	0.184448i
$537$	−9.00305	+	12.3916i	−0.388510	+	0.534738i
$538$	−27.2377	+	37.4894i	−1.17430	+	1.61628i
$539$	−0.908054	+	0.659740i	−0.0391126	+	0.0284170i
$540$	0.758762	+	1.46160i	0.0326519	+	0.0628973i
$541$	−22.5367	−	16.3739i	−0.968929	−	0.703968i	−0.0137220	−	0.999906i	$-0.504368\pi$
$541$	−22.5367	−	16.3739i	−0.968929	−	0.703968i	−0.955207	+	0.295937i	$0.904368\pi$
$542$	−15.8348	+	5.14505i	−0.680164	+	0.220999i
$543$		−	8.47690i		−	0.363779i
$544$	−1.02307	−	3.14869i	−0.0438639	−	0.134999i
$545$	−3.87857	+	7.75723i	−0.166140	+	0.332283i
$546$	0.282949	−	0.870827i	0.0121091	−	0.0372680i
$547$	33.8242	+	10.9902i	1.44622	+	0.469905i	0.923831	−	0.382801i	$-0.125041\pi$
$547$	33.8242	+	10.9902i	1.44622	+	0.469905i	0.522390	+	0.852707i	$0.325041\pi$
$548$	−5.04671	−	6.94620i	−0.215585	−	0.296727i
$549$	−14.1944			−0.605803
$550$	−9.28260	+	0.141031i	−0.395812	+	0.00601360i
$551$	−0.956384			−0.0407433
$552$	4.76030	+	6.55200i	0.202612	+	0.278871i
$553$	13.4772	+	4.37900i	0.573107	+	0.186214i
$554$	−8.19636	+	25.2258i	−0.348230	+	1.07174i
$555$	6.76254	+	6.66057i	0.287054	+	0.282726i
$556$	2.19354	+	6.75103i	0.0930270	+	0.286308i
$557$			29.3268i			1.24262i	0.783567	+	0.621308i	$0.213398\pi$
$557$			29.3268i			1.24262i	−0.783567	+	0.621308i	$0.786602\pi$
$558$	−6.76826	+	2.19914i	−0.286523	+	0.0930970i
$559$	1.83557	+	1.33362i	0.0776363	+	0.0564061i
$560$	−9.86114	−	4.93051i	−0.416709	−	0.208352i
$561$	−0.756125	+	0.549357i	−0.0319236	+	0.0231939i
$562$	10.1575	−	13.9806i	0.428469	−	0.589738i
$563$	−4.03569	+	5.55466i	−0.170084	+	0.234101i	−0.885547	−	0.464550i	$-0.846216\pi$
$563$	−4.03569	+	5.55466i	−0.170084	+	0.234101i	0.715463	+	0.698651i	$0.246216\pi$
$564$	3.99214	−	2.90046i	0.168099	−	0.122131i
$565$	−14.6472	−	7.32351i	−0.616212	−	0.308103i
$566$	12.1330	+	8.81512i	0.509987	+	0.370527i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$		−	14.2032i		−	0.595951i
$569$	−10.0734	−	31.0027i	−0.422299	−	1.29970i	−0.905557	−	0.424224i	$-0.860547\pi$
$569$	−10.0734	−	31.0027i	−0.422299	−	1.29970i	0.483259	−	0.875478i	$-0.339453\pi$
$570$	−2.09796	−	2.06632i	−0.0878737	−	0.0865487i
$571$	6.34133	−	19.5166i	0.265377	−	0.816745i	−0.726230	−	0.687452i	$-0.758729\pi$
$571$	6.34133	−	19.5166i	0.265377	−	0.816745i	0.991606	−	0.129293i	$-0.0412708\pi$
$572$	0.435161	+	0.141392i	0.0181950	+	0.00591191i
$573$	−8.35162	−	11.4950i	−0.348894	−	0.480212i
$574$	−6.90215			−0.288090
$575$	−15.8446	−	11.1480i	−0.660767	−	0.464904i
$576$	3.28396			0.136832
$577$	11.4735	+	15.7919i	0.477647	+	0.657425i	0.978051	−	0.208367i	$-0.0668149\pi$
$577$	11.4735	+	15.7919i	0.477647	+	0.657425i	−0.500403	+	0.865792i	$0.666815\pi$
$578$	−25.6547	−	8.33571i	−1.06709	−	0.346720i
$579$	3.76141	−	11.5764i	0.156319	−	0.481100i
$580$	0.884772	−	1.76957i	0.0367382	−	0.0734772i
$581$	−3.72047	−	11.4504i	−0.154351	−	0.475044i
$582$			0.260935i			0.0108161i
$583$	6.55364	−	2.12941i	0.271424	−	0.0881909i
$584$	6.00710	+	4.36441i	0.248575	+	0.180601i
$585$	−0.570264	−	1.09850i	−0.0235775	−	0.0454173i
$586$	12.8949	−	9.36871i	0.532684	−	0.387018i
$587$	−17.6178	+	24.2488i	−0.727163	+	1.00085i	0.272092	+	0.962271i	$0.412284\pi$
$587$	−17.6178	+	24.2488i	−0.727163	+	1.00085i	−0.999255	+	0.0385833i	$0.987716\pi$
$588$	0.432891	−	0.595823i	0.0178521	−	0.0245713i
$589$	2.77069	−	2.01303i	0.114164	−	0.0829453i
$590$	−41.8499	+	6.95464i	−1.72293	+	0.286318i
$591$	3.04070	+	2.20920i	0.125078	+	0.0908743i
$592$	−19.9053	+	6.46761i	−0.818101	+	0.265817i
$593$		−	0.539226i		−	0.0221434i	−0.999939	−	0.0110717i	$-0.996476\pi$
$593$		−	0.539226i		−	0.0221434i	0.999939	−	0.0110717i	$-0.00352430\pi$
$594$	0.573763	+	1.76586i	0.0235418	+	0.0724541i
$595$	1.65254	−	0.857883i	0.0677474	−	0.0351698i
$596$	5.22574	−	16.0832i	0.214054	−	0.658792i
$597$	−21.3173	−	6.92641i	−0.872458	−	0.283479i
$598$	2.08536	+	2.87025i	0.0852768	+	0.117373i
$599$	38.2276			1.56194			0.780970	−	0.624569i	$-0.214725\pi$
$599$	38.2276			1.56194			0.780970	+	0.624569i	$0.214725\pi$
$600$	−9.88908	+	3.38009i	−0.403720	+	0.137992i
$601$	−20.0421			−0.817533			−0.408767	−	0.912639i	$-0.634041\pi$
$601$	−20.0421			−0.817533			−0.408767	+	0.912639i	$0.634041\pi$
$602$	3.98564	+	5.48577i	0.162443	+	0.223583i
$603$	−3.30571	−	1.07409i	−0.134619	−	0.0437403i
$604$	−1.45763	+	4.48611i	−0.0593099	+	0.182537i
$605$	21.5368	+	3.24360i	0.875596	+	0.131871i
$606$	−0.608361	−	1.87234i	−0.0247130	−	0.0760587i
$607$			4.59618i			0.186553i	0.995640	+	0.0932766i	$0.0297341\pi$
$607$			4.59618i			0.186553i	−0.995640	+	0.0932766i	$0.970266\pi$
$608$	3.01027	−	0.978094i	0.122082	−	0.0396670i
$609$	−0.971927	−	0.706146i	−0.0393845	−	0.0286145i
$610$	−7.81941	+	51.9192i	−0.316599	+	2.10215i
$611$	−3.00038	+	2.17990i	−0.121382	+	0.0881894i
$612$	0.360463	−	0.496134i	0.0145708	−	0.0200550i
$613$	21.6072	−	29.7397i	0.872706	−	1.20118i	−0.105683	−	0.994400i	$-0.533703\pi$
$613$	21.6072	−	29.7397i	0.872706	−	1.20118i	0.978388	−	0.206776i	$-0.0662973\pi$
$614$	20.2556	−	14.7166i	0.817451	−	0.593913i
$615$	−6.54688	+	6.64710i	−0.263996	+	0.268037i
$616$	−1.89797	−	1.37896i	−0.0764716	−	0.0555599i
$617$	28.4803	−	9.25383i	1.14658	−	0.372545i	0.326723	−	0.945120i	$-0.394055\pi$
$617$	28.4803	−	9.25383i	1.14658	−	0.372545i	0.819852	+	0.572575i	$0.194055\pi$
$618$			11.8782i			0.477811i
$619$	−11.8720	−	36.5384i	−0.477177	−	1.46860i	−0.842999	−	0.537916i	$-0.819212\pi$
$619$	−11.8720	−	36.5384i	−0.477177	−	1.46860i	0.365821	−	0.930685i	$-0.380788\pi$
$620$	1.16140	+	6.98882i	0.0466431	+	0.280678i
$621$	−1.19735	+	3.68505i	−0.0480478	+	0.147876i
$622$	7.61122	+	2.47304i	0.305182	+	0.0991597i
$623$	−2.44381	−	3.36361i	−0.0979091	−	0.134760i
$624$	2.72914			0.109253
$625$	19.7697	−	15.3023i	0.790787	−	0.612091i
$626$	−34.0462			−1.36076
$627$	−0.525205	−	0.722883i	−0.0209747	−	0.0288692i
$628$	15.9576	+	5.18495i	0.636779	+	0.206902i
$629$	1.09227	−	3.36166i	0.0435517	−	0.134038i
$630$	−0.606381	−	3.64893i	−0.0241588	−	0.145377i
$631$	−14.0349	−	43.1948i	−0.558719	−	1.71956i	−0.685915	−	0.727682i	$-0.740598\pi$
$631$	−14.0349	−	43.1948i	−0.558719	−	1.71956i	0.127197	−	0.991878i	$-0.459402\pi$
$632$			29.6190i			1.17818i
$633$	12.9779	−	4.21678i	0.515825	−	0.167602i
$634$	18.1143	+	13.1608i	0.719412	+	0.522684i
$635$	21.3482	−	21.6750i	0.847177	−	0.860146i
$636$	−3.65796	+	2.65767i	−0.145048	+	0.105383i
$637$	−0.325348	+	0.447803i	−0.0128908	+	0.0177426i
$638$	1.31113	−	1.80461i	0.0519080	−	0.0714452i
$639$	5.49748	−	3.99415i	0.217477	−	0.158006i
$640$	4.45715	−	29.5945i	0.176184	−	1.16983i
$641$	−23.9225	−	17.3807i	−0.944881	−	0.686496i	0.00470934	−	0.999989i	$-0.498501\pi$
$641$	−23.9225	−	17.3807i	−0.944881	−	0.686496i	−0.949591	+	0.313492i	$0.898501\pi$
$642$	9.41331	−	3.05857i	0.371514	−	0.120712i
$643$		−	17.1601i		−	0.676729i	−0.941015	−	0.338364i	$-0.890126\pi$
$643$		−	17.1601i		−	0.676729i	0.941015	−	0.338364i	$-0.109874\pi$
$644$	0.881818	+	2.71396i	0.0347485	+	0.106945i
$645$	9.06355	+	1.36504i	0.356877	+	0.0537482i
$646$	−0.338857	+	1.04290i	−0.0133322	+	0.0410322i
$647$	−12.8953	−	4.18994i	−0.506967	−	0.164723i	0.0443556	−	0.999016i	$-0.485877\pi$
$647$	−12.8953	−	4.18994i	−0.506967	−	0.164723i	−0.551322	+	0.834292i	$0.685877\pi$
$648$	1.22856	+	1.69097i	0.0482625	+	0.0664277i
$649$	−12.8731			−0.505313
$650$	−4.33214	+	1.48073i	−0.169921	+	0.0580789i
$651$	4.30204			0.168610
$652$	1.20879	+	1.66375i	0.0473397	+	0.0651575i
$653$	30.6075	+	9.94498i	1.19776	+	0.389177i	0.838938	−	0.544227i	$-0.183177\pi$
$653$	30.6075	+	9.94498i	1.19776	+	0.389177i	0.358827	+	0.933404i	$0.383177\pi$
$654$	1.98269	−	6.10208i	0.0775292	−	0.238610i
$655$	−28.2536	+	14.6673i	−1.10396	+	0.573100i
$656$	−6.35721	−	19.5655i	−0.248207	−	0.763904i
$657$			3.55245i			0.138594i
$658$	−10.5412	+	3.42505i	−0.410940	+	0.133522i
$659$	3.77999	+	2.74632i	0.147247	+	0.106981i	0.658970	−	0.752169i	$-0.270992\pi$
$659$	3.77999	+	2.74632i	0.147247	+	0.106981i	−0.511723	+	0.859151i	$0.670992\pi$
$660$	1.82341	−	0.303014i	0.0709759	−	0.0117948i
$661$	−2.00749	+	1.45853i	−0.0780823	+	0.0567301i	−0.626142	−	0.779709i	$-0.715367\pi$
$661$	−2.00749	+	1.45853i	−0.0780823	+	0.0567301i	0.548059	+	0.836439i	$0.315367\pi$
$662$	23.0626	−	31.7429i	0.896353	−	1.23372i
$663$	−0.270913	+	0.372880i	−0.0105214	+	0.0144815i
$664$	20.3588	−	14.7915i	0.790074	−	0.574022i
$665$	0.820167	+	1.57988i	0.0318047	+	0.0612653i
$666$	−5.68093	−	4.12744i	−0.220131	−	0.159935i
$667$	4.42710	−	1.43845i	0.171418	−	0.0556971i
$668$		−	3.38299i		−	0.130892i
$669$	−7.66436	−	23.5885i	−0.296321	−	0.911983i
$670$	−5.74976	+	11.4997i	−0.222133	+	0.444270i
$671$	−4.92327	+	15.1523i	−0.190061	+	0.584947i
$672$	3.78136	+	1.22864i	0.145869	+	0.0473958i
$673$	24.5659	+	33.8120i	0.946944	+	1.30336i	0.952871	+	0.303375i	$0.0981134\pi$
$673$	24.5659	+	33.8120i	0.946944	+	1.30336i	−0.00592679	+	0.999982i	$0.501887\pi$
$674$	2.91992			0.112471
$675$	−4.08926	−	2.87714i	−0.157396	−	0.110741i
$676$	−9.34857			−0.359560
$677$	−7.81327	−	10.7540i	−0.300288	−	0.413311i	0.632034	−	0.774941i	$-0.282220\pi$
$677$	−7.81327	−	10.7540i	−0.300288	−	0.413311i	−0.932322	+	0.361630i	$0.882220\pi$
$678$	11.5219	+	3.74371i	0.442498	+	0.143776i
$679$	0.0487437	−	0.150018i	0.00187061	−	0.00575715i
$680$	2.77271	+	2.73091i	0.106329	+	0.104725i
$681$	−4.83304	−	14.8746i	−0.185202	−	0.569994i
$682$			7.98775i			0.305867i
$683$	−9.48852	+	3.08301i	−0.363068	+	0.117968i	−0.484870	−	0.874586i	$-0.661133\pi$
$683$	−9.48852	+	3.08301i	−0.363068	+	0.117968i	0.121801	+	0.992554i	$0.461133\pi$
$684$	0.474322	+	0.344615i	0.0181362	+	0.0131767i
$685$	23.3164	+	11.6581i	0.890873	+	0.445432i
$686$	−1.33830	+	0.972332i	−0.0510965	+	0.0371238i
$687$	−16.8305	+	23.1652i	−0.642123	+	0.883806i
$688$	−11.8795	+	16.3507i	−0.452902	+	0.623366i
$689$	2.74922	−	1.99742i	0.104737	−	0.0760958i
$690$	12.8193	+	6.40957i	0.488022	+	0.244008i
$691$	35.4424	+	25.7504i	1.34829	+	0.979592i	0.999095	+	0.0425430i	$0.0135459\pi$
$691$	35.4424	+	25.7504i	1.34829	+	0.979592i	0.349198	+	0.937049i	$0.386454\pi$
$692$	−13.3694	+	4.34397i	−0.508227	+	0.165133i
$693$		−	1.12242i		−	0.0426371i
$694$	3.42965	+	10.5554i	0.130188	+	0.400677i
$695$	−15.3549	−	15.1234i	−0.582446	−	0.573664i
$696$	0.775956	−	2.38815i	0.0294125	−	0.0905225i
$697$	3.30428	+	1.07363i	0.125159	+	0.0406665i
$698$	−6.69781	−	9.21874i	−0.253516	−	0.348935i
$699$	13.6653			0.516868
$700$	−3.68196	+	0.0559404i	−0.139165	+	0.00211435i
$701$	−0.439993			−0.0166183			−0.00830915	−	0.999965i	$-0.502645\pi$
$701$	−0.439993			−0.0166183			−0.00830915	+	0.999965i	$0.502645\pi$
$702$	0.538201	+	0.740770i	0.0203131	+	0.0279586i
$703$	3.21387	+	1.04425i	0.121213	+	0.0393846i
$704$	1.13903	−	3.50556i	0.0429287	−	0.132121i
$705$	−6.70015	+	13.4005i	−0.252342	+	0.504690i
$706$	17.9040	+	55.1028i	0.673826	+	2.07382i
$707$			1.19010i			0.0447583i
$708$	8.03332	−	2.61018i	0.301911	−	0.0980967i
$709$	20.4068	+	14.8264i	0.766395	+	0.556818i	0.900865	−	0.434099i	$-0.142933\pi$
$709$	20.4068	+	14.8264i	0.766395	+	0.556818i	−0.134470	+	0.990918i	$0.542933\pi$
$710$	−11.5811	−	22.3085i	−0.434629	−	0.837225i
$711$	−11.4644	+	8.32934i	−0.429947	+	0.312375i
$712$	5.10794	−	7.03048i	0.191428	−	0.263478i
$713$	−9.79784	+	13.4856i	−0.366932	+	0.505038i
$714$	−1.11439	+	0.809649i	−0.0417048	+	0.0303003i
$715$	−1.37042	+	0.227737i	−0.0512507	+	0.00851687i
$716$	−9.12616	−	6.63055i	−0.341061	−	0.247795i
$717$	10.2645	−	3.33513i	0.383334	−	0.124553i
$718$		−	60.5431i		−	2.25945i
$719$	−2.33420	−	7.18394i	−0.0870511	−	0.267916i	0.898050	−	0.439894i	$-0.144984\pi$
$719$	−2.33420	−	7.18394i	−0.0870511	−	0.267916i	−0.985101	+	0.171979i	$0.944984\pi$
$720$	9.78510	−	5.07974i	0.364669	−	0.189311i
$721$	2.21890	−	6.82906i	0.0826360	−	0.254327i
$722$	28.8950	+	9.38856i	1.07536	+	0.349406i
$723$	9.52618	+	13.1117i	0.354282	+	0.487628i
$724$	6.24305			0.232021
$725$	0.0912519	+	6.00615i	0.00338901	+	0.223063i
$726$	−16.1125			−0.597991
$727$	20.8825	+	28.7423i	0.774488	+	1.06599i	0.995869	+	0.0908039i	$0.0289436\pi$
$727$	20.8825	+	28.7423i	0.774488	+	1.06599i	−0.221381	+	0.975187i	$0.571056\pi$
$728$	−1.10031	−	0.357512i	−0.0407802	−	0.0132503i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	12.9939	+	1.95697i	0.480925	+	0.0724307i
$731$	−1.05475	−	3.24618i	−0.0390112	−	0.120064i
$732$		−	10.4539i		−	0.386386i
$733$	29.1572	−	9.47376i	1.07695	−	0.349921i	0.283757	−	0.958896i	$-0.408419\pi$
$733$	29.1572	−	9.47376i	1.07695	−	0.349921i	0.793189	+	0.608975i	$0.208419\pi$
$734$	22.3153	+	16.2130i	0.823673	+	0.598433i
$735$	−0.333012	+	2.21113i	−0.0122833	+	0.0815588i
$736$	−12.4634	+	9.05520i	−0.459407	+	0.333779i
$737$	−2.29314	+	3.15624i	−0.0844689	+	0.116261i
$738$	4.05698	−	5.58396i	0.149340	−	0.205548i
$739$	25.0419	−	18.1940i	0.921181	−	0.669277i	−0.0226369	−	0.999744i	$-0.507206\pi$
$739$	25.0419	−	18.1940i	0.921181	−	0.669277i	0.943818	+	0.330467i	$0.107206\pi$
$740$	−4.90536	+	4.98046i	−0.180325	+	0.183085i
$741$	−0.356487	−	0.259003i	−0.0130959	−	0.00951471i
$742$	9.65882	−	3.13834i	0.354587	−	0.115212i
$743$		−	33.8308i		−	1.24113i	−0.784155	−	0.620565i	$-0.786903\pi$
$743$		−	33.8308i		−	1.24113i	0.784155	−	0.620565i	$-0.213097\pi$
$744$	2.77866	+	8.55184i	0.101871	+	0.313526i
$745$	8.41696	+	50.6495i	0.308373	+	1.85565i
$746$	0.433832	−	1.33520i	0.0158837	−	0.0488851i
$747$	11.4504	+	3.72047i	0.418949	+	0.136125i
$748$	−0.404589	−	0.556869i	−0.0147932	−	0.0203612i
$749$	−5.98329			−0.218625
$750$	−12.7765	+	13.3724i	−0.466530	+	0.488292i
$751$	19.8726			0.725161			0.362580	−	0.931952i	$-0.381896\pi$
$751$	19.8726			0.725161			0.362580	+	0.931952i	$0.381896\pi$
$752$	−19.4179	−	26.7265i	−0.708100	−	0.974615i
$753$	17.3994	+	5.65339i	0.634068	+	0.206021i
$754$	0.339926	−	1.04618i	0.0123794	−	0.0380998i
$755$	−2.34776	−	14.1278i	−0.0854437	−	0.514162i
$756$	0.227584	+	0.700432i	0.00827716	+	0.0254745i
$757$		−	15.3007i		−	0.556113i	−0.960565	−	0.278056i	$-0.910310\pi$
$757$		−	15.3007i		−	0.556113i	0.960565	−	0.278056i	$-0.0896902\pi$
$758$	11.7134	−	3.80592i	0.425450	−	0.138237i
$759$	3.51843	+	2.55629i	0.127711	+	0.0927874i
$760$	−2.61084	+	2.65081i	−0.0947053	+	0.0961551i
$761$	−11.2809	+	8.19603i	−0.408931	+	0.297106i	−0.773169	−	0.634200i	$-0.781330\pi$
$761$	−11.2809	+	8.19603i	−0.408931	+	0.297106i	0.364238	+	0.931306i	$0.381330\pi$
$762$	−13.2291	+	18.2083i	−0.479239	+	0.659616i
$763$	−2.27979	+	3.13786i	−0.0825339	+	0.113598i
$764$	8.46583	−	6.15079i	0.306283	−	0.222528i
$765$	−0.277295	+	1.84118i	−0.0100256	+	0.0665681i
$766$	7.28708	+	5.29437i	0.263293	+	0.191293i
$767$	−6.03761	+	1.96174i	−0.218005	+	0.0708343i
$768$			15.5729i			0.561938i
$769$	1.05701	+	3.25314i	0.0381168	+	0.117311i	0.968304	−	0.249773i	$-0.0803560\pi$
$769$	1.05701	+	3.25314i	0.0381168	+	0.117311i	−0.930188	+	0.367084i	$0.880356\pi$
$770$	−4.10549	−	0.618315i	−0.147951	−	0.0222825i
$771$	1.43561	−	4.41836i	0.0517023	−	0.159123i
$772$	8.52579	+	2.77020i	0.306850	+	0.0997016i
$773$	15.2120	+	20.9376i	0.547139	+	0.753072i	0.989621	−	0.143705i	$-0.0459018\pi$
$773$	15.2120	+	20.9376i	0.547139	+	0.753072i	−0.442481	+	0.896778i	$0.645902\pi$
$774$	−6.78078			−0.243730
$775$	−12.9063	−	17.2080i	−0.463607	−	0.618131i
$776$	0.329697			0.0118354
$777$	2.49508	+	3.43418i	0.0895105	+	0.123201i
$778$	30.5824	+	9.93682i	1.09643	+	0.356252i
$779$	−1.02642	+	3.15901i	−0.0367755	+	0.113183i
$780$	0.809019	−	0.419986i	0.0289675	−	0.0150379i
$781$	−2.35691	−	7.25381i	−0.0843367	−	0.259562i
$782$		−	5.33722i		−	0.190859i
$783$	1.14257	−	0.371243i	0.0408321	−	0.0132671i
$784$	−3.98890	−	2.89811i	−0.142461	−	0.103504i
$785$	−50.2542	+	8.35127i	−1.79365	+	0.298070i
$786$	19.0528	−	13.8427i	0.679591	−	0.493752i
$787$	−14.2669	+	19.6367i	−0.508560	+	0.699972i	−0.983676	−	0.179951i	$-0.942406\pi$
$787$	−14.2669	+	19.6367i	−0.508560	+	0.699972i	0.475116	+	0.879923i	$0.342406\pi$
$788$	−1.62703	+	2.23941i	−0.0579604	+	0.0797756i
$789$	−9.38213	+	6.81652i	−0.334013	+	0.242674i
$790$	24.1509	+	46.5219i	0.859252	+	1.65517i
$791$	−5.92490	−	4.30469i	−0.210665	−	0.153057i
$792$	2.23120	−	0.724962i	0.0792824	−	0.0257604i
$793$			7.85683i			0.279004i
$794$	6.64120	+	20.4395i	0.235687	+	0.725371i
$795$	6.13929	−	12.2787i	0.217738	−	0.435481i
$796$	5.10114	−	15.6997i	0.180805	−	0.556461i
$797$	4.41570	+	1.43475i	0.156412	+	0.0508214i	0.386176	−	0.922425i	$-0.373796\pi$
$797$	4.41570	+	1.43475i	0.156412	+	0.0508214i	−0.229764	+	0.973246i	$0.573796\pi$
$798$	−0.774053	−	1.06539i	−0.0274012	−	0.0377145i
$799$	5.57918			0.197377
$800$	−6.42971	−	18.8113i	−0.227325	−	0.665080i
$801$	4.15766			0.146904
$802$	5.26110	+	7.24129i	0.185776	+	0.255699i
$803$	3.79218	+	1.23215i	0.133823	+	0.0434817i
$804$	0.791042	−	2.43458i	0.0278979	−	0.0858610i
$805$	−6.17278	−	6.07971i	−0.217562	−	0.214282i
$806$	1.21726	+	3.74633i	0.0428761	+	0.131959i
$807$			28.0127i			0.986094i
$808$	−2.36575	+	0.768678i	−0.0832267	+	0.0270420i
$809$	−19.1699	−	13.9277i	−0.673978	−	0.489673i	0.197377	−	0.980328i	$-0.436758\pi$
$809$	−19.1699	−	13.9277i	−0.673978	−	0.489673i	−0.871354	+	0.490654i	$0.836758\pi$
$810$	3.30847	+	1.65421i	0.116248	+	0.0581232i
$811$	5.49052	−	3.98910i	0.192798	−	0.140076i	−0.487198	−	0.873291i	$-0.661981\pi$
$811$	5.49052	−	3.98910i	0.192798	−	0.140076i	0.679997	+	0.733215i	$0.261981\pi$
$812$	0.520061	−	0.715802i	0.0182506	−	0.0251197i
$813$	−5.91602	+	8.14270i	−0.207484	+	0.285577i
$814$	−6.37636	+	4.63270i	−0.223491	+	0.162376i
$815$	−5.58472	−	2.79233i	−0.195624	−	0.0978110i
$816$	−3.32151	−	2.41322i	−0.116276	−	0.0844795i
$817$	3.10346	−	1.00838i	0.108576	−	0.0352786i
$818$		−	42.4568i		−	1.48447i
$819$	−0.171046	−	0.526424i	−0.00597682	−	0.0183948i
$820$	−4.89544	−	4.82163i	−0.170956	−	0.168379i
$821$	−14.5620	+	44.8173i	−0.508218	+	1.56414i	0.287074	+	0.957909i	$0.407318\pi$
$821$	−14.5620	+	44.8173i	−0.508218	+	1.56414i	−0.795292	+	0.606227i	$0.792682\pi$
$822$	−18.3414	−	5.95948i	−0.639730	−	0.207861i
$823$	11.5349	+	15.8764i	0.402081	+	0.553417i	0.961265	−	0.275627i	$-0.0888854\pi$
$823$	11.5349	+	15.8764i	0.402081	+	0.553417i	−0.559184	+	0.829044i	$0.688885\pi$
$824$	15.0084			0.522841
$825$	−4.48963	+	3.36729i	−0.156309	+	0.117234i
$826$	−18.9725			−0.660138
$827$	−11.7683	−	16.1977i	−0.409225	−	0.563250i	0.553804	−	0.832647i	$-0.313176\pi$
$827$	−11.7683	−	16.1977i	−0.409225	−	0.563250i	−0.963029	+	0.269397i	$0.913176\pi$
$828$	−2.71396	−	0.881818i	−0.0943166	−	0.0306453i
$829$	4.93498	−	15.1883i	0.171399	−	0.527512i	−0.828052	−	0.560652i	$-0.810551\pi$
$829$	4.93498	−	15.1883i	0.171399	−	0.527512i	0.999451	+	0.0331400i	$0.0105507\pi$
$830$	19.9162	−	39.8329i	0.691303	−	1.38262i
$831$	4.95479	+	15.2493i	0.171880	+	0.528991i
$832$		−	1.81772i		−	0.0630181i
$833$	0.791933	−	0.257315i	0.0274388	−	0.00891542i
$834$	12.8991	+	9.37171i	0.446658	+	0.324516i
$835$	4.73247	+	9.11613i	0.163774	+	0.315477i
$836$	0.532387	−	0.386802i	0.0184130	−	0.0133778i
$837$	−2.52868	+	3.48042i	−0.0874038	+	0.120301i
$838$	13.7212	−	18.8857i	0.473992	−	0.652394i
$839$	31.1684	−	22.6452i	1.07605	−	0.781798i	0.0990626	−	0.995081i	$-0.468416\pi$
$839$	31.1684	−	22.6452i	1.07605	−	0.781798i	0.976990	+	0.213283i	$0.0684156\pi$
$840$	−4.61050	+	0.766176i	−0.159078	+	0.0264356i
$841$	22.2939	+	16.1974i	0.768753	+	0.558532i
$842$	45.6805	−	14.8425i	1.57425	−	0.511506i
$843$		−	10.4466i		−	0.359799i
$844$	3.10556	+	9.55794i	0.106898	+	0.328998i
$845$	25.1915	−	13.0777i	0.866615	−	0.449887i
$846$	3.42505	−	10.5412i	0.117756	−	0.362415i
$847$	9.26346	+	3.00988i	0.318296	+	0.103421i
$848$	17.7925	+	24.4893i	0.610996	+	0.840964i
$849$	9.06596			0.311143
$850$	6.58177	+	2.02854i	0.225753	+	0.0695782i
$851$	−16.4476			−0.563817
$852$	2.94160	+	4.04877i	0.100778	+	0.138709i
$853$	−15.6696	−	5.09137i	−0.536517	−	0.174325i	0.0282109	−	0.999602i	$-0.491019\pi$
$853$	−15.6696	−	5.09137i	−0.536517	−	0.174325i	−0.564728	+	0.825277i	$0.691019\pi$
$854$	−7.25598	+	22.3316i	−0.248295	+	0.764172i
$855$	−1.76024	−	0.265104i	−0.0601988	−	0.00906637i
$856$	−3.86457	−	11.8939i	−0.132088	−	0.406526i
$857$			1.76856i			0.0604130i	0.999544	+	0.0302065i	$0.00961648\pi$
$857$			1.76856i			0.0604130i	−0.999544	+	0.0302065i	$0.990384\pi$
$858$	0.977431	−	0.317586i	0.0333689	−	0.0108422i
$859$	26.4676	+	19.2298i	0.903062	+	0.656113i	0.939251	−	0.343232i	$-0.111522\pi$
$859$	26.4676	+	19.2298i	0.903062	+	0.656113i	−0.0361885	+	0.999345i	$0.511522\pi$
$860$	−1.00532	+	6.67510i	−0.0342811	+	0.227619i
$861$	−3.37556	+	2.45249i	−0.115039	+	0.0835806i
$862$	11.5994	−	15.9652i	0.395076	−	0.543775i
$863$	−10.9840	+	15.1181i	−0.373898	+	0.514627i	−0.953955	−	0.299949i	$-0.903030\pi$
$863$	−10.9840	+	15.1181i	−0.373898	+	0.514627i	0.580057	+	0.814576i	$0.303030\pi$
$864$	−3.21662	+	2.33701i	−0.109432	+	0.0795067i
$865$	29.9496	−	30.4081i	1.01832	−	1.03391i
$866$	−6.61492	−	4.80602i	−0.224784	−	0.163315i
$867$	−15.5085	+	5.03903i	−0.526697	+	0.171134i
$868$			3.16836i			0.107541i
$869$	4.91506	+	15.1270i	0.166732	+	0.513148i
$870$	−0.728486	−	4.38371i	−0.0246980	−	0.148622i
$871$	−0.594525	+	1.82976i	−0.0201447	+	0.0619990i
$872$	−7.71012	−	2.50517i	−0.261098	−	0.0848357i
$873$	0.0927160	+	0.127613i	0.00313796	+	0.00431903i
$874$	5.10257			0.172597
$875$	9.84351	−	5.30144i	0.332771	−	0.179221i
$876$	−2.61630			−0.0883966
$877$	−4.89532	−	6.73783i	−0.165303	−	0.227520i	0.718327	−	0.695705i	$-0.244908\pi$
$877$	−4.89532	−	6.73783i	−0.165303	−	0.227520i	−0.883630	+	0.468185i	$0.844908\pi$
$878$	−0.914047	−	0.296992i	−0.0308476	−	0.0100230i
$879$	2.97747	−	9.16371i	0.100428	−	0.309084i
$880$	−2.02861	−	12.2073i	−0.0683846	−	0.411508i
$881$	16.6122	+	51.1272i	0.559680	+	1.72252i	0.683252	+	0.730182i	$0.260565\pi$
$881$	16.6122	+	51.1272i	0.559680	+	1.72252i	−0.123573	+	0.992336i	$0.539435\pi$
$882$		−	1.65423i		−	0.0557008i
$883$	−22.4708	+	7.30122i	−0.756204	+	0.245706i	−0.661649	−	0.749814i	$-0.730143\pi$
$883$	−22.4708	+	7.30122i	−0.756204	+	0.245706i	−0.0945552	+	0.995520i	$0.530143\pi$
$884$	−0.274618	−	0.199522i	−0.00923640	−	0.00671064i
$885$	−17.9960	+	18.2715i	−0.604928	+	0.614188i
$886$	40.2461	−	29.2405i	1.35210	−	0.982355i
$887$	33.1935	−	45.6869i	1.11453	−	1.53402i	0.299955	−	0.953953i	$-0.403028\pi$
$887$	33.1935	−	45.6869i	1.11453	−	1.53402i	0.814572	−	0.580062i	$-0.196972\pi$
$888$	−5.21511	+	7.17798i	−0.175008	+	0.240877i
$889$	11.0071	−	7.99712i	0.369166	−	0.268215i
$890$	2.29036	−	15.2075i	0.0767732	−	0.509758i
$891$	0.908054	+	0.659740i	0.0304209	+	0.0221021i
$892$	17.3724	−	5.64463i	0.581670	−	0.188996i
$893$			5.33390i			0.178492i
$894$	−11.7377	−	36.1250i	−0.392568	−	1.20820i
$895$	33.8677	+	5.10072i	1.13207	+	0.170498i
$896$	4.13599	−	12.7293i	0.138174	−	0.425255i
$897$	2.03973	+	0.662749i	0.0681047	+	0.0221285i
$898$	25.6291	+	35.2755i	0.855255	+	1.17716i
$899$	5.16833			0.172374
$900$	2.11895	−	3.01165i	0.0706316	−	0.100388i
$901$	−5.11216			−0.170311
$902$	−4.55362	−	6.26752i	−0.151619	−	0.208686i
$903$	3.89843	+	1.26668i	0.129732	+	0.0421524i
$904$	4.73026	−	14.5582i	0.157326	−	0.484200i
$905$	−16.8231	+	8.73340i	−0.559219	+	0.290308i
$906$	3.27403	+	10.0764i	0.108772	+	0.334767i
$907$			52.0594i			1.72860i	0.502974	+	0.864302i	$0.332239\pi$
$907$			52.0594i			1.72860i	−0.502974	+	0.864302i	$0.667761\pi$
$908$	10.9548	−	3.55942i	0.363547	−	0.118124i
$909$	−0.962810	−	0.699523i	−0.0319344	−	0.0232017i
$910$	−2.01974	+	0.335641i	−0.0669537	+	0.0111264i
$911$	−39.7540	+	28.8830i	−1.31711	+	0.956935i	−0.317145	+	0.948377i	$0.602724\pi$
$911$	−39.7540	+	28.8830i	−1.31711	+	0.956935i	−0.999963	+	0.00855792i	$0.997276\pi$
$912$	2.30712	−	3.17548i	0.0763965	−	0.105151i
$913$	7.94306	−	10.9327i	0.262877	−	0.361819i
$914$	14.6175	−	10.6202i	0.483503	−	0.351285i
$915$	14.6239	+	28.1700i	0.483452	+	0.931272i
$916$	−17.0606	−	12.3953i	−0.563699	−	0.409551i
$917$	−13.5398	+	4.39934i	−0.447123	+	0.145279i
$918$		−	1.37746i		−	0.0454628i
$919$	−12.8427	−	39.5257i	−0.423641	−	1.30383i	−0.904290	−	0.426920i	$-0.859599\pi$
$919$	−12.8427	−	39.5257i	−0.423641	−	1.30383i	0.480648	−	0.876913i	$-0.340401\pi$
$920$	8.09864	−	16.1975i	0.267004	−	0.534015i
$921$	4.67708	−	14.3946i	0.154115	−	0.474317i
$922$	−40.0742	−	13.0209i	−1.31977	−	0.428821i
$923$	−2.21082	−	3.04294i	−0.0727702	−	0.100160i
$924$	0.826635			0.0271943
$925$	6.25130	−	20.2829i	0.205541	−	0.666898i
$926$	8.52385			0.280111
$927$	4.22059	+	5.80914i	0.138622	+	0.190797i
$928$	4.54281	+	1.47605i	0.149125	+	0.0484536i
$929$	−14.8452	+	45.6887i	−0.487054	+	1.49900i	0.341930	+	0.939726i	$0.388920\pi$
$929$	−14.8452	+	45.6887i	−0.487054	+	1.49900i	−0.828984	+	0.559273i	$0.811080\pi$
$930$	11.3374	+	11.1665i	0.371769	+	0.366163i
$931$	0.246002	+	0.757116i	0.00806239	+	0.0248135i
$932$			10.0642i			0.329663i
$933$	4.60107	−	1.49498i	0.150632	−	0.0489433i
$934$	27.1244	+	19.7070i	0.887538	+	0.644834i
$935$	1.86925	+	0.934613i	0.0611310	+	0.0305651i
$936$	0.935979	−	0.680029i	0.0305934	−	0.0222274i
$937$	−13.6944	+	18.8487i	−0.447377	+	0.615762i	−0.971832	−	0.235677i	$-0.924269\pi$
$937$	−13.6944	+	18.8487i	−0.447377	+	0.615762i	0.524454	+	0.851439i	$0.324269\pi$
$938$	−3.37966	+	4.65170i	−0.110350	+	0.151883i
$939$	−16.6506	+	12.0974i	−0.543372	+	0.394783i
$940$	−9.86914	−	4.93451i	−0.321896	−	0.160946i
$941$	5.52316	+	4.01281i	0.180050	+	0.130814i	0.674160	−	0.738586i	$-0.264506\pi$
$941$	5.52316	+	4.01281i	0.180050	+	0.130814i	−0.494110	+	0.869400i	$0.664506\pi$
$942$	35.8431	−	11.6461i	1.16783	−	0.379451i
$943$		−	16.1669i		−	0.526465i
$944$	−17.4746	−	53.7813i	−0.568750	−	1.75043i
$945$	−1.59310	−	1.56908i	−0.0518237	−	0.0510423i
$946$	−2.35188	+	7.23836i	−0.0764663	+	0.235339i
$947$	47.1980	+	15.3356i	1.53373	+	0.498339i	0.949638	−	0.313348i	$-0.101451\pi$
$947$	47.1980	+	15.3356i	1.53373	+	0.498339i	0.584092	+	0.811688i	$0.301451\pi$
$948$	−6.13438	−	8.44325i	−0.199235	−	0.274224i
$949$	1.96634			0.0638300
$950$	−1.93935	+	6.29241i	−0.0629209	+	0.204153i
$951$	13.5353			0.438913
$952$	1.02301	+	1.40805i	0.0331559	+	0.0456352i
$953$	−48.6840	−	15.8184i	−1.57703	−	0.512408i	−0.615741	−	0.787948i	$-0.711143\pi$
$953$	−48.6840	−	15.8184i	−1.57703	−	0.512408i	−0.961290	+	0.275540i	$0.911143\pi$
$954$	−3.13834	+	9.65882i	−0.101608	+	0.312716i
$955$	−14.2085	+	28.4173i	−0.459776	+	0.919563i
$956$	2.45625	+	7.55956i	0.0794408	+	0.244494i
$957$		−	1.34843i		−	0.0435887i
$958$	−4.23010	+	1.37444i	−0.136668	+	0.0444062i
$959$	9.43166	+	6.85250i	0.304564	+	0.221279i
$960$	−3.38332	−	6.51728i	−0.109196	−	0.210344i
$961$	10.1066	−	7.34288i	0.326019	−	0.236867i
$962$	−2.28460	+	3.14448i	−0.0736584	+	0.101382i
$963$	3.51689	−	4.84058i	0.113330	−	0.155986i
$964$	−9.65645	+	7.01582i	−0.311013	+	0.225964i
$965$	−26.8496	+	4.46188i	−0.864320	+	0.143633i
$966$	5.18550	+	3.76749i	0.166841	+	0.121217i
$967$	−35.0466	+	11.3873i	−1.12702	+	0.366192i	−0.812444	−	0.583040i	$-0.801863\pi$
$967$	−35.0466	+	11.3873i	−1.12702	+	0.366192i	−0.314578	+	0.949231i	$0.601863\pi$
$968$			20.3585i			0.654347i
$969$	0.204843	+	0.630441i	0.00658050	+	0.0202527i
$970$	0.517846	−	0.268830i	0.0166270	−	0.00863161i
$971$	12.7532	−	39.2502i	0.409268	−	1.25960i	−0.508010	−	0.861351i	$-0.669619\pi$
$971$	12.7532	−	39.2502i	0.409268	−	1.25960i	0.917278	−	0.398247i	$-0.130381\pi$
$972$	−0.700432	−	0.227584i	−0.0224664	−	0.00729976i
$973$	−5.66530	−	7.79762i	−0.181621	−	0.249980i
$974$	−29.7919			−0.954595
$975$	−1.59254	+	2.26347i	−0.0510021	+	0.0724891i
$976$	−69.9864			−2.24021
$977$	−33.6146	−	46.2665i	−1.07543	−	1.48020i	−0.864460	−	0.502702i	$-0.832339\pi$
$977$	−33.6146	−	46.2665i	−1.07543	−	1.48020i	−0.210965	−	0.977494i	$-0.567661\pi$
$978$	4.39312	+	1.42741i	0.140476	+	0.0456436i
$979$	1.44207	−	4.43822i	0.0460886	−	0.141846i
$980$	−1.62845	−	0.245256i	−0.0520189	−	0.00783442i
$981$	−1.19856	−	3.68878i	−0.0382669	−	0.117774i
$982$		−	49.8836i		−	1.59185i
$983$	−38.5654	+	12.5306i	−1.23004	+	0.399665i	−0.850730	−	0.525603i	$-0.823840\pi$
$983$	−38.5654	+	12.5306i	−1.23004	+	0.399665i	−0.379314	+	0.925268i	$0.623840\pi$
$984$	−7.05545	−	5.12609i	−0.224920	−	0.163414i
$985$	1.25163	−	8.31057i	0.0398803	−	0.264797i
$986$	−1.33879	+	0.972686i	−0.0426357	+	0.0309766i
$987$	−3.93829	+	5.42059i	−0.125357	+	0.172539i
$988$	0.190750	−	0.262545i	0.00606856	−	0.00835266i
$989$	−12.8493	+	9.33554i	−0.408583	+	0.296853i
$990$	2.91337	−	2.95797i	0.0925930	−	0.0940105i
$991$	14.6176	+	10.6203i	0.464343	+	0.337365i	0.795232	−	0.606305i	$-0.207349\pi$
$991$	14.6176	+	10.6203i	0.464343	+	0.337365i	−0.330890	+	0.943669i	$0.607349\pi$
$992$	−16.2676	+	5.28566i	−0.516496	+	0.167820i
$993$		−	23.7188i		−	0.752695i
$994$	−3.47364	−	10.6908i	−0.110177	−	0.339090i
$995$	8.21628	+	49.4419i	0.260474	+	1.56741i
$996$	−2.74004	+	8.43298i	−0.0868216	+	0.267209i
$997$	−7.75873	−	2.52097i	−0.245722	−	0.0798398i	0.183567	−	0.983007i	$-0.441236\pi$
$997$	−7.75873	−	2.52097i	−0.245722	−	0.0798398i	−0.429288	+	0.903167i	$0.641236\pi$
$998$	−30.4603	−	41.9250i	−0.964204	−	1.32711i
$999$	−4.24488			−0.134302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.14	✓	72
25.9	even	10	inner	525.2.z.b.484.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.14	✓	72	1.1	even	1	trivial
525.2.z.b.484.14	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)

\(f(q)\)	\(=\)	\(q+(0.972332 + 1.33830i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.227584 + 0.700432i) q^{4} +(-0.366564 - 2.20582i) q^{5} +(0.511185 + 1.57327i) q^{6} -1.00000i q^{7} +(1.98786 - 0.645894i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.972332 + 1.33830i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.227584 + 0.700432i) q^{4} +(-0.366564 - 2.20582i) q^{5} +(0.511185 + 1.57327i) q^{6} -1.00000i q^{7} +(1.98786 - 0.645894i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.59562 - 2.63536i) q^{10} +(0.908054 - 0.659740i) q^{11} +(-0.432891 + 0.595823i) q^{12} +(0.325348 - 0.447803i) q^{13} +(1.33830 - 0.972332i) q^{14} +(0.333012 - 2.21113i) q^{15} +(3.98890 + 2.89811i) q^{16} +(-0.791933 + 0.257315i) q^{17} +1.65423i q^{18} +(-0.246002 - 0.757116i) q^{19} +(1.62845 + 0.245256i) q^{20} +(0.309017 - 0.951057i) q^{21} +(1.76586 + 0.573763i) q^{22} +(2.27749 + 3.13469i) q^{23} +2.09016 q^{24} +(-4.73126 + 1.61715i) q^{25} +0.915642 q^{26} +(0.587785 + 0.809017i) q^{27} +(0.700432 + 0.227584i) q^{28} +(0.371243 - 1.14257i) q^{29} +(3.28296 - 1.70428i) q^{30} +(1.32940 + 4.09148i) q^{31} +3.97596i q^{32} +(1.06748 - 0.346846i) q^{33} +(-1.11439 - 0.809649i) q^{34} +(-2.20582 + 0.366564i) q^{35} +(-0.595823 + 0.432891i) q^{36} +(-2.49508 + 3.43418i) q^{37} +(0.774053 - 1.06539i) q^{38} +(0.447803 - 0.325348i) q^{39} +(-2.15340 - 4.14809i) q^{40} +(-3.37556 - 2.45249i) q^{41} +(1.57327 - 0.511185i) q^{42} +4.09905i q^{43} +(0.255444 + 0.786176i) q^{44} +(0.999991 - 2.00000i) q^{45} +(-1.98069 + 6.09592i) q^{46} +(-6.37228 - 2.07048i) q^{47} +(2.89811 + 3.98890i) q^{48} -1.00000 q^{49} +(-6.76458 - 4.75945i) q^{50} -0.832687 q^{51} +(0.239612 + 0.329797i) q^{52} +(5.83886 + 1.89716i) q^{53} +(-0.511185 + 1.57327i) q^{54} +(-1.78813 - 1.76116i) q^{55} +(-0.645894 - 1.98786i) q^{56} -0.796079i q^{57} +(1.89007 - 0.614121i) q^{58} +(-9.27869 - 6.74136i) q^{59} +(1.47296 + 0.736471i) q^{60} +(-11.4835 + 8.34327i) q^{61} +(-4.18301 + 5.75742i) q^{62} +(0.587785 - 0.809017i) q^{63} +(2.65678 - 1.93026i) q^{64} +(-1.10703 - 0.553510i) q^{65} +(1.50213 + 1.09136i) q^{66} +(-3.30571 + 1.07409i) q^{67} -0.613256i q^{68} +(1.19735 + 3.68505i) q^{69} +(-2.63536 - 2.59562i) q^{70} +(2.09985 - 6.46268i) q^{71} +(1.98786 + 0.645894i) q^{72} +(2.08808 + 2.87399i) q^{73} -7.02201 q^{74} +(-4.99942 + 0.0759566i) q^{75} +0.586295 q^{76} +(-0.659740 - 0.908054i) q^{77} +(0.870827 + 0.282949i) q^{78} +(-4.37900 + 13.4772i) q^{79} +(4.93051 - 9.86114i) q^{80} +(0.309017 + 0.951057i) q^{81} -6.90215i q^{82} +(11.4504 - 3.72047i) q^{83} +(0.595823 + 0.432891i) q^{84} +(0.857883 + 1.65254i) q^{85} +(-5.48577 + 3.98564i) q^{86} +(0.706146 - 0.971927i) q^{87} +(1.37896 - 1.89797i) q^{88} +(3.36361 - 2.44381i) q^{89} +(3.64893 - 0.606381i) q^{90} +(-0.447803 - 0.325348i) q^{91} +(-2.71396 + 0.881818i) q^{92} +4.30204i q^{93} +(-3.42505 - 10.5412i) q^{94} +(-1.57988 + 0.820167i) q^{95} +(-1.22864 + 3.78136i) q^{96} +(0.150018 + 0.0487437i) q^{97} +(-0.972332 - 1.33830i) q^{98} +1.12242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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