LMFDB - Embedded newform 195.2.i.d.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(16,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("195.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.i (of order $3$, degree $2$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$0.500000 - 2.23871i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.d.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13090 + 1.95878i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.55787 + 2.69832i) q^{4} +1.00000 q^{5} +(-1.13090 + 1.95878i) q^{6} +(0.630901 - 1.09275i) q^{7} -2.52360 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.13090 + 1.95878i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.55787 + 2.69832i) q^{4} +1.00000 q^{5} +(-1.13090 + 1.95878i) q^{6} +(0.630901 - 1.09275i) q^{7} -2.52360 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.13090 + 1.95878i) q^{10} +(-2.26180 - 3.91756i) q^{11} -3.11575 q^{12} +(-3.45058 - 1.04571i) q^{13} +2.85395 q^{14} +(0.500000 + 0.866025i) q^{15} +(0.261802 + 0.453455i) q^{16} +(2.24665 - 3.89131i) q^{17} -2.26180 q^{18} +(-2.55787 + 4.43037i) q^{19} +(-1.55787 + 2.69832i) q^{20} +1.26180 q^{21} +(5.11575 - 8.86074i) q^{22} +(-1.11575 - 1.93253i) q^{23} +(-1.26180 - 2.18551i) q^{24} +1.00000 q^{25} +(-1.85395 - 7.94151i) q^{26} -1.00000 q^{27} +(1.96573 + 3.40474i) q^{28} +(0.688776 + 1.19299i) q^{29} +(-1.13090 + 1.95878i) q^{30} +8.87085 q^{31} +(-3.11575 + 5.39664i) q^{32} +(2.26180 - 3.91756i) q^{33} +10.1630 q^{34} +(0.630901 - 1.09275i) q^{35} +(-1.55787 - 2.69832i) q^{36} +(0.115749 + 0.200484i) q^{37} -11.5708 q^{38} +(-0.819677 - 3.51114i) q^{39} -2.52360 q^{40} +(-0.573026 - 0.992511i) q^{41} +(1.42697 + 2.47159i) q^{42} +(-3.18878 + 5.52312i) q^{43} +14.0944 q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.52360 - 4.37101i) q^{46} -10.7854 q^{47} +(-0.261802 + 0.453455i) q^{48} +(2.70393 + 4.68334i) q^{49} +(1.13090 + 1.95878i) q^{50} +4.49330 q^{51} +(8.19723 - 7.68167i) q^{52} +4.52360 q^{53} +(-1.13090 - 1.95878i) q^{54} +(-2.26180 - 3.91756i) q^{55} +(-1.59214 + 2.75768i) q^{56} -5.11575 q^{57} +(-1.55787 + 2.69832i) q^{58} +(0.426974 - 0.739540i) q^{59} -3.11575 q^{60} +(-2.31968 + 4.01780i) q^{61} +(10.0321 + 17.3760i) q^{62} +(0.630901 + 1.09275i) q^{63} -13.0472 q^{64} +(-3.45058 - 1.04571i) q^{65} +10.2315 q^{66} +(-6.56633 - 11.3732i) q^{67} +(7.00000 + 12.1244i) q^{68} +(1.11575 - 1.93253i) q^{69} +2.85395 q^{70} +(4.80453 - 8.32168i) q^{71} +(1.26180 - 2.18551i) q^{72} +13.7854 q^{73} +(-0.261802 + 0.453455i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-7.96970 - 13.8039i) q^{76} -5.70789 q^{77} +(5.95058 - 5.57632i) q^{78} -8.87085 q^{79} +(0.261802 + 0.453455i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.29607 - 2.24486i) q^{82} -8.23150 q^{83} +(-1.96573 + 3.40474i) q^{84} +(2.24665 - 3.89131i) q^{85} -14.4248 q^{86} +(-0.688776 + 1.19299i) q^{87} +(5.70789 + 9.88636i) q^{88} +(-3.31122 - 5.73521i) q^{89} -2.26180 q^{90} +(-3.31968 + 3.11089i) q^{91} +6.95279 q^{92} +(4.43543 + 7.68238i) q^{93} +(-12.1972 - 21.1262i) q^{94} +(-2.55787 + 4.43037i) q^{95} -6.23150 q^{96} +(-5.33483 + 9.24019i) q^{97} +(-6.11575 + 10.5928i) q^{98} +4.52360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.13090	+	1.95878i	0.799668	+	1.38507i	0.919832	+	0.392311i	$0.128324\pi$
$2$	1.13090	+	1.95878i	0.799668	+	1.38507i	−0.120165	+	0.992754i	$0.538342\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.55787	+	2.69832i	−0.778937	+	1.34916i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.13090	+	1.95878i	−0.461688	+	0.799668i
$7$	0.630901	−	1.09275i	0.238458	−	0.413022i	−0.721814	−	0.692087i	$-0.756691\pi$
$7$	0.630901	−	1.09275i	0.238458	−	0.413022i	0.960272	+	0.279066i	$0.0900247\pi$
$8$	−2.52360			−0.892229
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.13090	+	1.95878i	0.357622	+	0.619420i
$11$	−2.26180	−	3.91756i	−0.681959	−	1.18119i	−0.974382	−	0.224899i	$-0.927795\pi$
$11$	−2.26180	−	3.91756i	−0.681959	−	1.18119i	0.292423	−	0.956289i	$-0.405538\pi$
$12$	−3.11575			−0.899439
$13$	−3.45058	−	1.04571i	−0.957018	−	0.290028i
$13$	−3.45058	−	1.04571i	−0.957018	−	0.290028i
$14$	2.85395			0.762749
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	0.261802	+	0.453455i	0.0654506	+	0.113364i
$17$	2.24665	−	3.89131i	0.544893	−	0.943782i	−0.453721	−	0.891144i	$-0.649904\pi$
$17$	2.24665	−	3.89131i	0.544893	−	0.943782i	0.998614	−	0.0526381i	$-0.0167630\pi$
$18$	−2.26180			−0.533112
$19$	−2.55787	+	4.43037i	−0.586817	+	1.01640i	0.407830	+	0.913058i	$0.366286\pi$
$19$	−2.55787	+	4.43037i	−0.586817	+	1.01640i	−0.994646	+	0.103338i	$0.967048\pi$
$20$	−1.55787	+	2.69832i	−0.348351	+	0.603362i
$21$	1.26180			0.275348
$22$	5.11575	−	8.86074i	1.09068	−	1.88912i
$23$	−1.11575	−	1.93253i	−0.232650	−	0.402961i	0.725937	−	0.687761i	$-0.241406\pi$
$23$	−1.11575	−	1.93253i	−0.232650	−	0.402961i	−0.958587	+	0.284800i	$0.908073\pi$
$24$	−1.26180	−	2.18551i	−0.257564	−	0.446114i
$25$	1.00000			0.200000
$26$	−1.85395	−	7.94151i	−0.363589	−	1.55746i
$27$	−1.00000			−0.192450
$28$	1.96573	+	3.40474i	0.371488	+	0.643436i
$29$	0.688776	+	1.19299i	0.127902	+	0.221534i	0.922864	−	0.385127i	$-0.125842\pi$
$29$	0.688776	+	1.19299i	0.127902	+	0.221534i	−0.794961	+	0.606660i	$0.792509\pi$
$30$	−1.13090	+	1.95878i	−0.206473	+	0.357622i
$31$	8.87085			1.59325			0.796626	−	0.604472i	$-0.206616\pi$
$31$	8.87085			1.59325			0.796626	+	0.604472i	$0.206616\pi$
$32$	−3.11575	+	5.39664i	−0.550792	+	0.954000i
$33$	2.26180	−	3.91756i	0.393729	−	0.681959i
$34$	10.1630			1.74293
$35$	0.630901	−	1.09275i	0.106642	−	0.184709i
$36$	−1.55787	−	2.69832i	−0.259646	−	0.449720i
$37$	0.115749	+	0.200484i	0.0190291	+	0.0329593i	0.875383	−	0.483430i	$-0.160609\pi$
$37$	0.115749	+	0.200484i	0.0190291	+	0.0329593i	−0.856354	+	0.516389i	$0.827276\pi$
$38$	−11.5708			−1.87703
$39$	−0.819677	−	3.51114i	−0.131253	−	0.562233i
$40$	−2.52360			−0.399017
$41$	−0.573026	−	0.992511i	−0.0894917	−	0.155004i	0.817805	−	0.575496i	$-0.195191\pi$
$41$	−0.573026	−	0.992511i	−0.0894917	−	0.155004i	−0.907296	+	0.420492i	$0.861858\pi$
$42$	1.42697	+	2.47159i	0.220187	+	0.381375i
$43$	−3.18878	+	5.52312i	−0.486284	+	0.842268i	−0.999876	−	0.0157664i	$-0.994981\pi$
$43$	−3.18878	+	5.52312i	−0.486284	+	0.842268i	0.513592	+	0.858035i	$0.328315\pi$
$44$	14.0944			2.12481
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	2.52360	−	4.37101i	0.372085	−	0.644470i
$47$	−10.7854			−1.57321			−0.786607	−	0.617454i	$-0.788164\pi$
$47$	−10.7854			−1.57321			−0.786607	+	0.617454i	$0.788164\pi$
$48$	−0.261802	+	0.453455i	−0.0377879	+	0.0654506i
$49$	2.70393	+	4.68334i	0.386275	+	0.669049i
$50$	1.13090	+	1.95878i	0.159934	+	0.277013i
$51$	4.49330			0.629188
$52$	8.19723	−	7.68167i	1.13675	−	1.06526i
$53$	4.52360			0.621365			0.310682	−	0.950514i	$-0.399442\pi$
$53$	4.52360			0.621365			0.310682	+	0.950514i	$0.399442\pi$
$54$	−1.13090	−	1.95878i	−0.153896	−	0.266556i
$55$	−2.26180	−	3.91756i	−0.304981	−	0.528243i
$56$	−1.59214	+	2.75768i	−0.212759	+	0.368510i
$57$	−5.11575			−0.677598
$58$	−1.55787	+	2.69832i	−0.204559	+	0.354307i
$59$	0.426974	−	0.739540i	0.0555872	−	0.0962799i	−0.836893	−	0.547367i	$-0.815630\pi$
$59$	0.426974	−	0.739540i	0.0555872	−	0.0962799i	0.892480	+	0.451087i	$0.148964\pi$
$60$	−3.11575			−0.402242
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	−0.975449	−	0.220225i	$-0.929321\pi$
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	0.678445	+	0.734651i	$0.262654\pi$
$62$	10.0321	+	17.3760i	1.27407	+	2.20676i
$63$	0.630901	+	1.09275i	0.0794861	+	0.137674i
$64$	−13.0472			−1.63090
$65$	−3.45058	−	1.04571i	−0.427992	−	0.129704i
$66$	10.2315			1.25941
$67$	−6.56633	−	11.3732i	−0.802205	−	1.38946i	−0.918162	−	0.396205i	$-0.870327\pi$
$67$	−6.56633	−	11.3732i	−0.802205	−	1.38946i	0.115958	−	0.993254i	$-0.463006\pi$
$68$	7.00000	+	12.1244i	0.848875	+	1.47029i
$69$	1.11575	−	1.93253i	0.134320	−	0.232650i
$70$	2.85395			0.341112
$71$	4.80453	−	8.32168i	0.570192	−	0.987602i	−0.426354	−	0.904557i	$-0.640202\pi$
$71$	4.80453	−	8.32168i	0.570192	−	0.987602i	0.996546	−	0.0830453i	$-0.0264646\pi$
$72$	1.26180	−	2.18551i	0.148705	−	0.257564i
$73$	13.7854			1.61346			0.806730	−	0.590920i	$-0.201235\pi$
$73$	13.7854			1.61346			0.806730	+	0.590920i	$0.201235\pi$
$74$	−0.261802	+	0.453455i	−0.0304339	+	0.0527130i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−7.96970	−	13.8039i	−0.914187	−	1.58342i
$77$	−5.70789			−0.650475
$78$	5.95058	−	5.57632i	0.673770	−	0.631394i
$79$	−8.87085			−0.998049			−0.499024	−	0.866588i	$-0.666308\pi$
$79$	−8.87085			−0.998049			−0.499024	+	0.866588i	$0.666308\pi$
$80$	0.261802	+	0.453455i	0.0292704	+	0.0506978i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.29607	−	2.24486i	0.143127	−	0.247904i
$83$	−8.23150			−0.903524			−0.451762	−	0.892138i	$-0.649204\pi$
$83$	−8.23150			−0.903524			−0.451762	+	0.892138i	$0.649204\pi$
$84$	−1.96573	+	3.40474i	−0.214479	+	0.371488i
$85$	2.24665	−	3.89131i	0.243683	−	0.422072i
$86$	−14.4248			−1.55546
$87$	−0.688776	+	1.19299i	−0.0738445	+	0.127902i
$88$	5.70789	+	9.88636i	0.608464	+	1.05389i
$89$	−3.31122	−	5.73521i	−0.350989	−	0.607931i	0.635434	−	0.772155i	$-0.280821\pi$
$89$	−3.31122	−	5.73521i	−0.350989	−	0.607931i	−0.986423	+	0.164224i	$0.947488\pi$
$90$	−2.26180			−0.238415
$91$	−3.31968	+	3.11089i	−0.347997	+	0.326110i
$92$	6.95279			0.724879
$93$	4.43543	+	7.68238i	0.459932	+	0.796626i
$94$	−12.1972	−	21.1262i	−1.25805	−	2.17900i
$95$	−2.55787	+	4.43037i	−0.262432	+	0.454546i
$96$	−6.23150			−0.636000
$97$	−5.33483	+	9.24019i	−0.541670	+	0.938200i	0.457139	+	0.889395i	$0.348874\pi$
$97$	−5.33483	+	9.24019i	−0.541670	+	0.938200i	−0.998808	+	0.0488041i	$0.984459\pi$
$98$	−6.11575	+	10.5928i	−0.617784	+	1.07003i
$99$	4.52360			0.454639
$100$	−1.55787	+	2.69832i	−0.155787	+	0.269832i
$101$	8.52360	+	14.7633i	0.848130	+	1.46900i	0.882875	+	0.469609i	$0.155605\pi$
$101$	8.52360	+	14.7633i	0.848130	+	1.46900i	−0.0347444	+	0.999396i	$0.511062\pi$
$102$	5.08148	+	8.80138i	0.503141	+	0.871466i
$103$	−13.9484			−1.37437			−0.687187	−	0.726481i	$-0.741155\pi$
$103$	−13.9484			−1.37437			−0.687187	+	0.726481i	$0.741155\pi$
$104$	8.70789	+	2.63896i	0.853879	+	0.258771i
$105$	1.26180			0.123139
$106$	5.11575	+	8.86074i	0.496886	+	0.860631i
$107$	−6.24665	−	10.8195i	−0.603886	−	1.04596i	−0.992226	−	0.124446i	$-0.960285\pi$
$107$	−6.24665	−	10.8195i	−0.603886	−	1.04596i	0.388340	−	0.921516i	$-0.373049\pi$
$108$	1.55787	−	2.69832i	0.149907	−	0.259646i
$109$	−2.27871			−0.218261			−0.109130	−	0.994027i	$-0.534807\pi$
$109$	−2.27871			−0.218261			−0.109130	+	0.994027i	$0.534807\pi$
$110$	5.11575	−	8.86074i	0.487768	−	0.844838i
$111$	−0.115749	+	0.200484i	−0.0109864	+	0.0190291i
$112$	0.660685			0.0624289
$113$	0.738198	−	1.27860i	0.0694438	−	0.120280i	−0.829213	−	0.558933i	$-0.811211\pi$
$113$	0.738198	−	1.27860i	0.0694438	−	0.120280i	0.898657	+	0.438653i	$0.144544\pi$
$114$	−5.78541	−	10.0206i	−0.541853	−	0.938517i
$115$	−1.11575	−	1.93253i	−0.104044	−	0.180210i
$116$	−4.29211			−0.398512
$117$	2.63090	−	2.46543i	0.243227	−	0.227929i
$118$	1.93146			0.177805
$119$	−2.83483	−	4.91007i	−0.259868	−	0.450105i
$120$	−1.26180	−	2.18551i	−0.115186	−	0.199508i
$121$	−4.73150	+	8.19520i	−0.430136	+	0.745018i
$122$	−10.4933			−0.950019
$123$	0.573026	−	0.992511i	0.0516681	−	0.0894917i
$124$	−13.8197	+	23.9364i	−1.24104	+	2.14955i
$125$	1.00000			0.0894427
$126$	−1.42697	+	2.47159i	−0.127125	+	0.220187i
$127$	8.89270	+	15.4026i	0.789100	+	1.36676i	0.926519	+	0.376248i	$0.122786\pi$
$127$	8.89270	+	15.4026i	0.789100	+	1.36676i	−0.137419	+	0.990513i	$0.543881\pi$
$128$	−8.52360	−	14.7633i	−0.753387	−	1.30491i
$129$	−6.37755			−0.561512
$130$	−1.85395	−	7.94151i	−0.162602	−	0.696517i
$131$	11.6697			1.01958			0.509791	−	0.860298i	$-0.329723\pi$
$131$	11.6697			1.01958			0.509791	+	0.860298i	$0.329723\pi$
$132$	7.04721	+	12.2061i	0.613381	+	1.06241i
$133$	3.22753	+	5.59025i	0.279863	+	0.484736i
$134$	14.8517	−	25.7240i	1.28299	−	2.22221i
$135$	−1.00000			−0.0860663
$136$	−5.66966	+	9.82013i	−0.486169	+	0.842070i
$137$	10.0321	−	17.3760i	0.857096	−	1.48453i	−0.0175898	−	0.999845i	$-0.505599\pi$
$137$	10.0321	−	17.3760i	0.857096	−	1.48453i	0.874686	−	0.484689i	$-0.161067\pi$
$138$	5.04721			0.429647
$139$	−8.16966	+	14.1503i	−0.692941	+	1.20021i	0.277928	+	0.960602i	$0.410352\pi$
$139$	−8.16966	+	14.1503i	−0.692941	+	1.20021i	−0.970870	+	0.239608i	$0.922981\pi$
$140$	1.96573	+	3.40474i	0.166134	+	0.287753i
$141$	−5.39270	−	9.34044i	−0.454148	−	0.786607i
$142$	21.7338			1.82386
$143$	3.70789	+	15.8830i	0.310070	+	1.32821i
$144$	−0.523604			−0.0436337
$145$	0.688776	+	1.19299i	0.0571997	+	0.0990728i
$146$	15.5899	+	27.0026i	1.29023	+	2.23475i
$147$	−2.70393	+	4.68334i	−0.223016	+	0.386275i
$148$	−0.721292			−0.0592899
$149$	1.62245	−	2.81016i	0.132916	−	0.230218i	−0.791883	−	0.610672i	$-0.790899\pi$
$149$	1.62245	−	2.81016i	0.132916	−	0.230218i	0.924799	+	0.380455i	$0.124233\pi$
$150$	−1.13090	+	1.95878i	−0.0923377	+	0.159934i
$151$	5.69996			0.463856			0.231928	−	0.972733i	$-0.425497\pi$
$151$	5.69996			0.463856			0.231928	+	0.972733i	$0.425497\pi$
$152$	6.45506	−	11.1805i	0.523575	−	0.906858i
$153$	2.24665	+	3.89131i	0.181631	+	0.314594i
$154$	−6.45506	−	11.1805i	−0.520164	−	0.900950i
$155$	8.87085			0.712524
$156$	10.7511	+	3.25817i	0.860780	+	0.260863i
$157$	−3.85395			−0.307578			−0.153789	−	0.988104i	$-0.549148\pi$
$157$	−3.85395			−0.307578			−0.153789	+	0.988104i	$0.549148\pi$
$158$	−10.0321	−	17.3760i	−0.798108	−	1.38236i
$159$	2.26180	+	3.91756i	0.179373	+	0.310682i
$160$	−3.11575	+	5.39664i	−0.246322	+	0.426642i
$161$	−2.81571			−0.221909
$162$	1.13090	−	1.95878i	0.0888520	−	0.153896i
$163$	4.86240	−	8.42192i	0.380853	−	0.659656i	−0.610332	−	0.792146i	$-0.708964\pi$
$163$	4.86240	−	8.42192i	0.380853	−	0.659656i	0.991184	+	0.132490i	$0.0422972\pi$
$164$	3.57081			0.278834
$165$	2.26180	−	3.91756i	0.176081	−	0.304981i
$166$	−9.30901	−	16.1237i	−0.722519	−	1.25144i
$167$	9.63935	+	16.6959i	0.745916	+	1.29196i	0.949766	+	0.312962i	$0.101321\pi$
$167$	9.63935	+	16.6959i	0.745916	+	1.29196i	−0.203850	+	0.979002i	$0.565346\pi$
$168$	−3.18429			−0.245673
$169$	10.8130	+	7.21661i	0.831768	+	0.555124i
$170$	10.1630			0.779463
$171$	−2.55787	−	4.43037i	−0.195606	−	0.338799i
$172$	−9.93543	−	17.2087i	−0.757569	−	1.31215i
$173$	1.50845	−	2.61272i	0.114686	−	0.198641i	−0.802968	−	0.596022i	$-0.796747\pi$
$173$	1.50845	−	2.61272i	0.114686	−	0.198641i	0.917654	+	0.397380i	$0.130081\pi$
$174$	−3.11575			−0.236204
$175$	0.630901	−	1.09275i	0.0476916	−	0.0826043i
$176$	1.18429	−	2.05125i	0.0892692	−	0.154619i
$177$	0.853947			0.0641866
$178$	7.48933	−	12.9719i	0.561349	−	0.972286i
$179$	2.65847	+	4.60461i	0.198704	+	0.344165i	0.948108	−	0.317947i	$-0.102994\pi$
$179$	2.65847	+	4.60461i	0.198704	+	0.344165i	−0.749405	+	0.662112i	$0.769660\pi$
$180$	−1.55787	−	2.69832i	−0.116117	−	0.201121i
$181$	25.8709			1.92297			0.961483	−	0.274866i	$-0.0886333\pi$
$181$	25.8709			1.92297			0.961483	+	0.274866i	$0.0886333\pi$
$182$	−9.84777	−	2.98440i	−0.729965	−	0.221219i
$183$	−4.63935			−0.342951
$184$	2.81571	+	4.87695i	0.207577	+	0.359534i
$185$	0.115749	+	0.200484i	0.00851006	+	0.0147399i
$186$	−10.0321	+	17.3760i	−0.735586	+	1.27407i
$187$	−20.3259			−1.48638
$188$	16.8023	−	29.1025i	1.22543	−	2.12251i
$189$	−0.630901	+	1.09275i	−0.0458913	+	0.0794861i
$190$	−11.5708			−0.839435
$191$	−5.32813	+	9.22859i	−0.385530	+	0.667757i	−0.991843	−	0.127469i	$-0.959315\pi$
$191$	−5.32813	+	9.22859i	−0.385530	+	0.667757i	0.606313	+	0.795226i	$0.292648\pi$
$192$	−6.52360	−	11.2992i	−0.470801	−	0.815451i
$193$	−3.99155	−	6.91356i	−0.287318	−	0.497649i	0.685851	−	0.727742i	$-0.259430\pi$
$193$	−3.99155	−	6.91356i	−0.287318	−	0.497649i	−0.973169	+	0.230093i	$0.926097\pi$
$194$	−24.1327			−1.73262
$195$	−0.819677	−	3.51114i	−0.0586983	−	0.251438i
$196$	−16.8495			−1.20354
$197$	−8.66966	−	15.0163i	−0.617688	−	1.06987i	−0.989907	−	0.141721i	$-0.954736\pi$
$197$	−8.66966	−	15.0163i	−0.617688	−	1.06987i	0.372219	−	0.928145i	$-0.378597\pi$
$198$	5.11575	+	8.86074i	0.363560	+	0.629705i
$199$	0.615749	−	1.06651i	0.0436493	−	0.0756028i	−0.843375	−	0.537325i	$-0.819435\pi$
$199$	0.615749	−	1.06651i	0.0436493	−	0.0756028i	0.887025	+	0.461722i	$0.152768\pi$
$200$	−2.52360			−0.178446
$201$	6.56633	−	11.3732i	0.463153	−	0.802205i
$202$	−19.2787	+	33.3917i	−1.35645	+	2.34943i
$203$	1.73820			0.121998
$204$	−7.00000	+	12.1244i	−0.490098	+	0.848875i
$205$	−0.573026	−	0.992511i	−0.0400219	−	0.0693200i
$206$	−15.7742	−	27.3218i	−1.09904	−	1.90360i
$207$	2.23150			0.155100
$208$	−0.429187	−	1.83845i	−0.0297587	−	0.127474i
$209$	23.1416			1.60074
$210$	1.42697	+	2.47159i	0.0984705	+	0.170556i
$211$	−5.16966	−	8.95411i	−0.355894	−	0.616426i	0.631377	−	0.775476i	$-0.282490\pi$
$211$	−5.16966	−	8.95411i	−0.355894	−	0.616426i	−0.987271	+	0.159050i	$0.949157\pi$
$212$	−7.04721	+	12.2061i	−0.484004	+	0.838320i
$213$	9.60905			0.658401
$214$	14.1287	−	24.4716i	0.965817	−	1.67284i
$215$	−3.18878	+	5.52312i	−0.217473	+	0.376674i
$216$	2.52360			0.171710
$217$	5.59663	−	9.69365i	0.379924	−	0.658048i
$218$	−2.57699	−	4.46348i	−0.174536	−	0.302305i
$219$	6.89270	+	11.9385i	0.465766	+	0.806730i
$220$	14.0944			0.950245
$221$	−11.8214	+	11.0779i	−0.795195	+	0.745182i
$222$	−0.523604			−0.0351420
$223$	−10.7854	−	18.6809i	−0.722244	−	1.25096i	−0.960098	−	0.279663i	$-0.909777\pi$
$223$	−10.7854	−	18.6809i	−0.722244	−	1.25096i	0.237854	−	0.971301i	$-0.423556\pi$
$224$	3.93146	+	6.80949i	0.262682	+	0.454978i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	3.33931			0.222128
$227$	−2.72305	+	4.71645i	−0.180735	+	0.313042i	−0.942131	−	0.335245i	$-0.891181\pi$
$227$	−2.72305	+	4.71645i	−0.180735	+	0.313042i	0.761396	+	0.648287i	$0.224514\pi$
$228$	7.96970	−	13.8039i	0.527806	−	0.914187i
$229$	21.9315			1.44927			0.724636	−	0.689132i	$-0.242008\pi$
$229$	21.9315			1.44927			0.724636	+	0.689132i	$0.242008\pi$
$230$	2.52360	−	4.37101i	0.166402	−	0.288216i
$231$	−2.85395	−	4.94318i	−0.187776	−	0.325237i
$232$	−1.73820	−	3.01065i	−0.114118	−	0.197659i
$233$	25.3125			1.65828			0.829139	−	0.559042i	$-0.188831\pi$
$233$	25.3125			1.65828			0.829139	+	0.559042i	$0.188831\pi$
$234$	7.80453	+	2.36519i	0.510198	+	0.154617i
$235$	−10.7854			−0.703562
$236$	1.33034	+	2.30422i	0.0865979	+	0.149992i
$237$	−4.43543	−	7.68238i	−0.288112	−	0.499024i
$238$	6.41182	−	11.1056i	0.415617	−	0.719869i
$239$	22.5236			1.45693			0.728465	−	0.685083i	$-0.240234\pi$
$239$	22.5236			1.45693			0.728465	+	0.685083i	$0.240234\pi$
$240$	−0.261802	+	0.453455i	−0.0168993	+	0.0292704i
$241$	−5.55787	+	9.62652i	−0.358014	+	0.620099i	−0.987629	−	0.156809i	$-0.949879\pi$
$241$	−5.55787	+	9.62652i	−0.358014	+	0.620099i	0.629615	+	0.776907i	$0.283213\pi$
$242$	−21.4034			−1.37586
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−7.22753	−	12.5185i	−0.462695	−	0.801412i
$245$	2.70393	+	4.68334i	0.172748	+	0.299208i
$246$	2.59214			0.165269
$247$	13.4590	−	12.6125i	0.856378	−	0.802516i
$248$	−22.3865			−1.42155
$249$	−4.11575	−	7.12869i	−0.260825	−	0.451762i
$250$	1.13090	+	1.95878i	0.0715245	+	0.123884i
$251$	−5.52360	+	9.56716i	−0.348647	+	0.603874i	−0.986009	−	0.166690i	$-0.946692\pi$
$251$	−5.52360	+	9.56716i	−0.348647	+	0.603874i	0.637363	+	0.770564i	$0.280025\pi$
$252$	−3.93146			−0.247659
$253$	−5.04721	+	8.74202i	−0.317315	+	0.549606i
$254$	−20.1135	+	34.8377i	−1.26204	+	2.18591i
$255$	4.49330			0.281381
$256$	6.23150	−	10.7933i	0.389469	−	0.674580i
$257$	1.01515	+	1.75829i	0.0633234	+	0.109679i	0.895949	−	0.444157i	$-0.146497\pi$
$257$	1.01515	+	1.75829i	0.0633234	+	0.109679i	−0.832626	+	0.553836i	$0.813163\pi$
$258$	−7.21238	−	12.4922i	−0.449023	−	0.777731i
$259$	0.292106			0.0181506
$260$	8.19723	−	7.68167i	0.508371	−	0.476397i
$261$	−1.37755			−0.0852683
$262$	13.1972	+	22.8583i	0.815328	+	1.41219i
$263$	−1.62420	−	2.81320i	−0.100153	−	0.173469i	0.811595	−	0.584221i	$-0.198600\pi$
$263$	−1.62420	−	2.81320i	−0.100153	−	0.173469i	−0.911747	+	0.410751i	$0.865266\pi$
$264$	−5.70789	+	9.88636i	−0.351297	+	0.608464i
$265$	4.52360			0.277883
$266$	−7.30004	+	12.6440i	−0.447594	+	0.775256i
$267$	3.31122	−	5.73521i	0.202644	−	0.350989i
$268$	40.9181			2.49947
$269$	−13.4742	+	23.3380i	−0.821535	+	1.42294i	0.0830032	+	0.996549i	$0.473549\pi$
$269$	−13.4742	+	23.3380i	−0.821535	+	1.42294i	−0.904539	+	0.426392i	$0.859784\pi$
$270$	−1.13090	−	1.95878i	−0.0688245	−	0.119207i
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	0.992382	+	0.123201i	$0.0393161\pi$
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	−0.389495	+	0.921028i	$0.627351\pi$
$272$	2.35271			0.142654
$273$	−4.35395	−	1.31948i	−0.263513	−	0.0798586i
$274$	45.3811			2.74157
$275$	−2.26180	−	3.91756i	−0.136392	−	0.236238i
$276$	3.47640	+	6.02129i	0.209254	+	0.362439i
$277$	−8.04721	+	13.9382i	−0.483510	+	0.837464i	−0.999821	−	0.0189376i	$-0.993972\pi$
$277$	−8.04721	+	13.9382i	−0.483510	+	0.837464i	0.516311	+	0.856401i	$0.327305\pi$
$278$	−36.9563			−2.21649
$279$	−4.43543	+	7.68238i	−0.265542	+	0.459932i
$280$	−1.59214	+	2.75768i	−0.0951489	+	0.164803i
$281$	−5.37755			−0.320798			−0.160399	−	0.987052i	$-0.551278\pi$
$281$	−5.37755			−0.320798			−0.160399	+	0.987052i	$0.551278\pi$
$282$	12.1972	−	21.1262i	0.726334	−	1.25805i
$283$	−13.4332	−	23.2670i	−0.798522	−	1.38308i	−0.920579	−	0.390557i	$-0.872282\pi$
$283$	−13.4332	−	23.2670i	−0.798522	−	1.38308i	0.122057	−	0.992523i	$-0.461051\pi$
$284$	14.9697	+	25.9283i	0.888288	+	1.53856i
$285$	−5.11575			−0.303031
$286$	−26.9181	+	25.2251i	−1.59170	+	1.49159i
$287$	−1.44609			−0.0853601
$288$	−3.11575	−	5.39664i	−0.183597	−	0.318000i
$289$	−1.59488	−	2.76241i	−0.0938163	−	0.162495i
$290$	−1.55787	+	2.69832i	−0.0914816	+	0.158451i
$291$	−10.6697			−0.625466
$292$	−21.4759	+	37.1974i	−1.25678	+	2.17681i
$293$	−10.7096	+	18.5497i	−0.625664	+	1.08368i	0.362748	+	0.931887i	$0.381839\pi$
$293$	−10.7096	+	18.5497i	−0.625664	+	1.08368i	−0.988412	+	0.151795i	$0.951495\pi$
$294$	−12.2315			−0.713355
$295$	0.426974	−	0.739540i	0.0248594	−	0.0430577i
$296$	−0.292106	−	0.505942i	−0.0169783	−	0.0294073i
$297$	2.26180	+	3.91756i	0.131243	+	0.227320i
$298$	7.33931			0.425155
$299$	1.82911	+	7.83511i	0.105780	+	0.453116i
$300$	−3.11575			−0.179888
$301$	4.02360	+	6.96909i	0.231917	+	0.401692i
$302$	6.44609	+	11.1650i	0.370931	+	0.642471i
$303$	−8.52360	+	14.7633i	−0.489668	+	0.848130i
$304$	−2.67863			−0.153630
$305$	−2.31968	+	4.01780i	−0.132824	+	0.230058i
$306$	−5.08148	+	8.80138i	−0.290489	+	0.503141i
$307$	−7.85395			−0.448248			−0.224124	−	0.974561i	$-0.571952\pi$
$307$	−7.85395			−0.448248			−0.224124	+	0.974561i	$0.571952\pi$
$308$	8.89218	−	15.4017i	0.506679	−	0.877594i
$309$	−6.97418	−	12.0796i	−0.396747	−	0.687187i
$310$	10.0321	+	17.3760i	0.569783	+	0.986892i
$311$	−27.8744			−1.58061			−0.790305	−	0.612714i	$-0.790078\pi$
$311$	−27.8744			−1.58061			−0.790305	+	0.612714i	$0.790078\pi$
$312$	2.06854	+	8.86074i	0.117108	+	0.501641i
$313$	7.88776			0.445842			0.222921	−	0.974836i	$-0.428441\pi$
$313$	7.88776			0.445842			0.222921	+	0.974836i	$0.428441\pi$
$314$	−4.35843	−	7.54903i	−0.245961	−	0.426016i
$315$	0.630901	+	1.09275i	0.0355473	+	0.0615696i
$316$	13.8197	−	23.9364i	0.777418	−	1.34653i
$317$	13.2181			0.742403			0.371201	−	0.928552i	$-0.378946\pi$
$317$	13.2181			0.742403			0.371201	+	0.928552i	$0.378946\pi$
$318$	−5.11575	+	8.86074i	−0.286877	+	0.496886i
$319$	3.11575	−	5.39664i	0.174448	−	0.302154i
$320$	−13.0472			−0.729361
$321$	6.24665	−	10.8195i	0.348654	−	0.603886i
$322$	−3.18429	−	5.51535i	−0.177454	−	0.307359i
$323$	11.4933	+	19.9070i	0.639504	+	1.10765i
$324$	3.11575			0.173097
$325$	−3.45058	−	1.04571i	−0.191404	−	0.0580056i
$326$	21.9956			1.21822
$327$	−1.13935	−	1.97342i	−0.0630064	−	0.109130i
$328$	1.44609	+	2.50470i	0.0798471	+	0.138299i
$329$	−6.80453	+	11.7858i	−0.375146	+	0.649771i
$330$	10.2315			0.563225
$331$	11.9248	−	20.6543i	0.655444	−	1.13526i	−0.326338	−	0.945253i	$-0.605815\pi$
$331$	11.9248	−	20.6543i	0.655444	−	1.13526i	0.981782	−	0.190009i	$-0.0608519\pi$
$332$	12.8236	−	22.2112i	0.703789	−	1.21900i
$333$	−0.231499			−0.0126861
$334$	−21.8023	+	37.7627i	−1.19297	+	2.06628i
$335$	−6.56633	−	11.3732i	−0.358757	−	0.621385i
$336$	0.330343	+	0.572170i	0.0180217	+	0.0312144i
$337$	5.68306			0.309576			0.154788	−	0.987948i	$-0.450531\pi$
$337$	5.68306			0.309576			0.154788	+	0.987948i	$0.450531\pi$
$338$	−1.90734	+	29.3415i	−0.103745	+	1.59597i
$339$	1.47640			0.0801868
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	−20.0641	−	34.7521i	−1.08653	−	1.88193i
$342$	5.78541	−	10.0206i	0.312839	−	0.541853i
$343$	15.6563			0.845359
$344$	8.04721	−	13.9382i	0.433876	−	0.751496i
$345$	1.11575	−	1.93253i	0.0600699	−	0.104044i
$346$	6.82364			0.366841
$347$	10.7248	−	18.5759i	0.575737	−	0.997206i	−0.420224	−	0.907421i	$-0.638048\pi$
$347$	10.7248	−	18.5759i	0.575737	−	0.997206i	0.995961	−	0.0897859i	$-0.0286183\pi$
$348$	−2.14605	−	3.71707i	−0.115041	−	0.199256i
$349$	−3.43543	−	5.95033i	−0.183894	−	0.318514i	0.759309	−	0.650730i	$-0.225537\pi$
$349$	−3.43543	−	5.95033i	−0.183894	−	0.318514i	−0.943203	+	0.332216i	$0.892204\pi$
$350$	2.85395			0.152550
$351$	3.45058	+	1.04571i	0.184178	+	0.0558159i
$352$	28.1888			1.50247
$353$	−17.2484	−	29.8751i	−0.918040	−	1.59009i	−0.802389	−	0.596802i	$-0.796438\pi$
$353$	−17.2484	−	29.8751i	−0.918040	−	1.59009i	−0.115651	−	0.993290i	$-0.536896\pi$
$354$	0.965730	+	1.67269i	0.0513280	+	0.0889026i
$355$	4.80453	−	8.32168i	0.254998	−	0.441669i
$356$	20.6339			1.09359
$357$	2.83483	−	4.91007i	0.150035	−	0.259868i
$358$	−6.01294	+	10.4147i	−0.317794	+	0.550435i
$359$	−8.15945			−0.430639			−0.215320	−	0.976544i	$-0.569079\pi$
$359$	−8.15945			−0.430639			−0.215320	+	0.976544i	$0.569079\pi$
$360$	1.26180	−	2.18551i	0.0665028	−	0.115186i
$361$	−3.58545	−	6.21017i	−0.188708	−	0.326851i
$362$	29.2574	+	50.6753i	1.53773	+	2.66343i
$363$	−9.46300			−0.496679
$364$	−3.22253	−	13.8039i	−0.168906	−	0.723522i
$365$	13.7854			0.721561
$366$	−5.24665	−	9.08747i	−0.274247	−	0.475009i
$367$	3.42027	+	5.92409i	0.178537	+	0.309235i	0.941380	−	0.337349i	$-0.109530\pi$
$367$	3.42027	+	5.92409i	0.178537	+	0.309235i	−0.762843	+	0.646584i	$0.776197\pi$
$368$	0.584211	−	1.01188i	0.0304541	−	0.0527481i
$369$	1.14605			0.0596611
$370$	−0.261802	+	0.453455i	−0.0136105	+	0.0235740i
$371$	2.85395	−	4.94318i	0.148170	−	0.256637i
$372$	−27.6394			−1.43303
$373$	−6.90961	+	11.9678i	−0.357766	+	0.619669i	−0.987587	−	0.157071i	$-0.949795\pi$
$373$	−6.90961	+	11.9678i	−0.357766	+	0.619669i	0.629821	+	0.776740i	$0.283128\pi$
$374$	−22.9866	−	39.8140i	−1.18861	−	2.05873i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	27.2181			1.40367
$377$	−1.12915	−	4.83678i	−0.0581540	−	0.249107i
$378$	−2.85395			−0.146791
$379$	−5.75784	−	9.97286i	−0.295760	−	0.512272i	0.679401	−	0.733767i	$-0.262240\pi$
$379$	−5.75784	−	9.97286i	−0.295760	−	0.512272i	−0.975161	+	0.221495i	$0.928906\pi$
$380$	−7.96970	−	13.8039i	−0.408837	−	0.708126i
$381$	−8.89270	+	15.4026i	−0.455587	+	0.789100i
$382$	−24.1024			−1.23318
$383$	−11.4399	+	19.8145i	−0.584552	+	1.01247i	0.410379	+	0.911915i	$0.365396\pi$
$383$	−11.4399	+	19.8145i	−0.584552	+	1.01247i	−0.994931	+	0.100559i	$0.967937\pi$
$384$	8.52360	−	14.7633i	0.434968	−	0.753387i
$385$	−5.70789			−0.290901
$386$	9.02809	−	15.6371i	0.459518	−	0.795908i
$387$	−3.18878	−	5.52312i	−0.162095	−	0.280756i
$388$	−16.6220	−	28.7901i	−0.843854	−	1.46160i
$389$	−4.35271			−0.220691			−0.110346	−	0.993893i	$-0.535196\pi$
$389$	−4.35271			−0.220691			−0.110346	+	0.993893i	$0.535196\pi$
$390$	5.95058	−	5.57632i	0.301319	−	0.282368i
$391$	−10.0268			−0.507077
$392$	−6.82364	−	11.8189i	−0.344646	−	0.596944i
$393$	5.83483	+	10.1062i	0.294328	+	0.509791i
$394$	19.6091	−	33.9639i	0.987890	−	1.71108i
$395$	−8.87085			−0.446341
$396$	−7.04721	+	12.2061i	−0.354136	+	0.613381i
$397$	−3.81122	+	6.60123i	−0.191280	+	0.331306i	−0.945675	−	0.325115i	$-0.894597\pi$
$397$	−3.81122	+	6.60123i	−0.191280	+	0.331306i	0.754395	+	0.656421i	$0.227930\pi$
$398$	2.78541			0.139620
$399$	−3.22753	+	5.59025i	−0.161579	+	0.279863i
$400$	0.261802	+	0.453455i	0.0130901	+	0.0226727i
$401$	−10.4248	−	18.0562i	−0.520588	−	0.901684i	−0.999713	−	0.0239381i	$-0.992380\pi$
$401$	−10.4248	−	18.0562i	−0.520588	−	0.901684i	0.479126	−	0.877746i	$-0.340954\pi$
$402$	29.7035			1.48147
$403$	−30.6096	−	9.27635i	−1.52477	−	0.462088i
$404$	−53.1148			−2.64256
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	1.96573	+	3.40474i	0.0975575	+	0.168975i
$407$	0.523604	−	0.906910i	0.0259541	−	0.0449538i
$408$	−11.3393			−0.561380
$409$	8.48264	−	14.6924i	0.419439	−	0.726490i	−0.576444	−	0.817137i	$-0.695560\pi$
$409$	8.48264	−	14.6924i	0.419439	−	0.726490i	0.995883	+	0.0906466i	$0.0288934\pi$
$410$	1.29607	−	2.24486i	0.0640085	−	0.110866i
$411$	20.0641			0.989690
$412$	21.7298	−	37.6371i	1.07055	−	1.85425i
$413$	−0.538756	−	0.933153i	−0.0265105	−	0.0459175i
$414$	2.52360	+	4.37101i	0.124028	+	0.214823i
$415$	−8.23150			−0.404068
$416$	16.3945	−	15.3633i	0.803804	−	0.753250i
$417$	−16.3393			−0.800140
$418$	26.1709	+	45.3293i	1.28006	+	2.21713i
$419$	−1.04942	−	1.81765i	−0.0512676	−	0.0887981i	0.839253	−	0.543742i	$-0.182993\pi$
$419$	−1.04942	−	1.81765i	−0.0512676	−	0.0887981i	−0.890520	+	0.454943i	$0.849659\pi$
$420$	−1.96573	+	3.40474i	−0.0959178	+	0.166134i
$421$	−39.6598			−1.93290			−0.966449	−	0.256857i	$-0.917313\pi$
$421$	−39.6598			−1.93290			−0.966449	+	0.256857i	$0.917313\pi$
$422$	11.6927	−	20.2524i	0.569194	−	0.985873i
$423$	5.39270	−	9.34044i	0.262202	−	0.454148i
$424$	−11.4158			−0.554400
$425$	2.24665	−	3.89131i	0.108979	−	0.188756i
$426$	10.8669	+	18.8220i	0.526502	+	0.911929i
$427$	2.92697	+	5.06967i	0.141646	+	0.245338i
$428$	38.9260			1.88156
$429$	−11.9012	+	11.1526i	−0.574593	+	0.538455i
$430$	−14.4248			−0.695624
$431$	11.0641	+	19.1636i	0.532940	+	0.923079i	0.999260	+	0.0384626i	$0.0122461\pi$
$431$	11.0641	+	19.1636i	0.532940	+	0.923079i	−0.466320	+	0.884616i	$0.654421\pi$
$432$	−0.261802	−	0.453455i	−0.0125960	−	0.0218169i
$433$	15.6781	−	27.1553i	0.753442	−	1.30500i	−0.192703	−	0.981257i	$-0.561725\pi$
$433$	15.6781	−	27.1553i	0.753442	−	1.30500i	0.946145	−	0.323743i	$-0.104941\pi$
$434$	25.3169			1.21525
$435$	−0.688776	+	1.19299i	−0.0330243	+	0.0571997i
$436$	3.54994	−	6.14868i	0.170011	−	0.294468i
$437$	11.4158			0.546091
$438$	−15.5899	+	27.0026i	−0.744916	+	1.29023i
$439$	−2.15672	−	3.73555i	−0.102935	−	0.178288i	0.809958	−	0.586488i	$-0.199490\pi$
$439$	−2.15672	−	3.73555i	−0.102935	−	0.178288i	−0.912892	+	0.408200i	$0.866157\pi$
$440$	5.70789	+	9.88636i	0.272113	+	0.471314i
$441$	−5.40786			−0.257517
$442$	−35.0681	−	10.6275i	−1.66802	−	0.505499i
$443$	0.493301			0.0234374			0.0117187	−	0.999931i	$-0.496270\pi$
$443$	0.493301			0.0234374			0.0117187	+	0.999931i	$0.496270\pi$
$444$	−0.360646	−	0.624657i	−0.0171155	−	0.0296449i
$445$	−3.31122	−	5.73521i	−0.156967	−	0.271875i
$446$	24.3945	−	42.2524i	1.15511	−	2.00071i
$447$	3.24490			0.153478
$448$	−8.23150	+	14.2574i	−0.388902	+	0.673598i
$449$	11.6563	−	20.1892i	0.550093	−	0.952789i	−0.448174	−	0.893946i	$-0.647926\pi$
$449$	11.6563	−	20.1892i	0.550093	−	0.952789i	0.998267	−	0.0588427i	$-0.0187410\pi$
$450$	−2.26180			−0.106622
$451$	−2.59214	+	4.48973i	−0.122059	+	0.211413i
$452$	2.30004	+	3.98378i	0.108185	+	0.187381i
$453$	2.84998	+	4.93631i	0.133904	+	0.231928i
$454$	−12.3180			−0.578112
$455$	−3.31968	+	3.11089i	−0.155629	+	0.145841i
$456$	12.9101			0.604572
$457$	−3.33483	−	5.77609i	−0.155997	−	0.270194i	0.777425	−	0.628976i	$-0.216526\pi$
$457$	−3.33483	−	5.77609i	−0.155997	−	0.270194i	−0.933422	+	0.358782i	$0.883192\pi$
$458$	24.8023	+	42.9589i	1.15894	+	2.00734i
$459$	−2.24665	+	3.89131i	−0.104865	+	0.181631i
$460$	6.95279			0.324176
$461$	−14.5596	+	25.2180i	−0.678110	+	1.17452i	0.297440	+	0.954740i	$0.403867\pi$
$461$	−14.5596	+	25.2180i	−0.678110	+	1.17452i	−0.975550	+	0.219780i	$0.929466\pi$
$462$	6.45506	−	11.1805i	0.300317	−	0.520164i
$463$	−1.79334			−0.0833436			−0.0416718	−	0.999131i	$-0.513268\pi$
$463$	−1.79334			−0.0833436			−0.0416718	+	0.999131i	$0.513268\pi$
$464$	−0.360646	+	0.624657i	−0.0167426	+	0.0289990i
$465$	4.43543	+	7.68238i	0.205688	+	0.356262i
$466$	28.6260	+	49.5816i	1.32607	+	2.29682i
$467$	16.8192			0.778301			0.389150	−	0.921174i	$-0.372769\pi$
$467$	16.8192			0.778301			0.389150	+	0.921174i	$0.372769\pi$
$468$	2.55391	+	10.9398i	0.118054	+	0.505694i
$469$	−16.5708			−0.765169
$470$	−12.1972	−	21.1262i	−0.562616	−	0.974480i
$471$	−1.92697	−	3.33762i	−0.0887903	−	0.153789i
$472$	−1.07751	+	1.86631i	−0.0495965	+	0.0859037i
$473$	28.8495			1.32650
$474$	10.0321	−	17.3760i	0.460788	−	0.798108i
$475$	−2.55787	+	4.43037i	−0.117363	+	0.203279i
$476$	17.6652			0.809685
$477$	−2.26180	+	3.91756i	−0.103561	+	0.179373i
$478$	25.4720	+	44.1187i	1.16506	+	2.01794i
$479$	−17.5765	−	30.4434i	−0.803092	−	1.39100i	−0.917571	−	0.397571i	$-0.869853\pi$
$479$	−17.5765	−	30.4434i	−0.803092	−	1.39100i	0.114479	−	0.993426i	$-0.463480\pi$
$480$	−6.23150			−0.284428
$481$	−0.189754	−	0.812826i	−0.00865205	−	0.0370617i
$482$	−25.1416			−1.14517
$483$	−1.40786	−	2.43848i	−0.0640596	−	0.110955i
$484$	−14.7422	−	25.5342i	−0.670098	−	1.16064i
$485$	−5.33483	+	9.24019i	−0.242242	+	0.419576i
$486$	2.26180			0.102597
$487$	4.31298	−	7.47030i	0.195440	−	0.338511i	−0.751605	−	0.659614i	$-0.770720\pi$
$487$	4.31298	−	7.47030i	0.195440	−	0.338511i	0.947045	+	0.321102i	$0.104053\pi$
$488$	5.85395	−	10.1393i	0.264996	−	0.458986i
$489$	9.72480			0.439771
$490$	−6.11575	+	10.5928i	−0.276281	+	0.478533i
$491$	11.6068	+	20.1036i	0.523809	+	0.907264i	0.999616	+	0.0277143i	$0.00882287\pi$
$491$	11.6068	+	20.1036i	0.523809	+	0.907264i	−0.475807	+	0.879550i	$0.657844\pi$
$492$	1.78541	+	3.09242i	0.0804924	+	0.139417i
$493$	6.18975			0.278773
$494$	39.9260	+	12.0997i	1.79636	+	0.544392i
$495$	4.52360			0.203321
$496$	2.32241	+	4.02253i	0.104279	+	0.180617i
$497$	−6.06236	−	10.5003i	−0.271934	−	0.471004i
$498$	9.30901	−	16.1237i	0.417147	−	0.722519i
$499$	29.0393			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$499$	29.0393			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$500$	−1.55787	+	2.69832i	−0.0696703	+	0.120672i
$501$	−9.63935	+	16.6959i	−0.430655	+	0.745916i
$502$	−24.9866			−1.11521
$503$	8.69996	−	15.0688i	0.387912	−	0.671883i	−0.604256	−	0.796790i	$-0.706530\pi$
$503$	8.69996	−	15.0688i	0.387912	−	0.671883i	0.992169	+	0.124906i	$0.0398631\pi$
$504$	−1.59214	−	2.75768i	−0.0709198	−	0.122837i
$505$	8.52360	+	14.7633i	0.379295	+	0.656959i
$506$	−22.8316			−1.01499
$507$	−0.843281	+	12.9726i	−0.0374514	+	0.576134i
$508$	−55.4149			−2.45864
$509$	11.4382	+	19.8115i	0.506987	+	0.878128i	0.999967	+	0.00808731i	$0.00257430\pi$
$509$	11.4382	+	19.8115i	0.506987	+	0.878128i	−0.492980	+	0.870041i	$0.664092\pi$
$510$	5.08148	+	8.80138i	0.225012	+	0.389732i
$511$	8.69723	−	15.0640i	0.384743	−	0.666394i
$512$	−5.90558			−0.260992
$513$	2.55787	−	4.43037i	0.112933	−	0.195606i
$514$	−2.29607	+	3.97691i	−0.101275	+	0.175414i
$515$	−13.9484			−0.614638
$516$	9.93543	−	17.2087i	0.437383	−	0.757569i
$517$	24.3945	+	42.2524i	1.07287	+	1.85826i
$518$	0.330343	+	0.572170i	0.0145144	+	0.0251397i
$519$	3.01691			0.132427
$520$	8.70789	+	2.63896i	0.381866	+	0.115726i
$521$	−26.3642			−1.15503			−0.577517	−	0.816378i	$-0.695978\pi$
$521$	−26.3642			−1.15503			−0.577517	+	0.816378i	$0.695978\pi$
$522$	−1.55787	−	2.69832i	−0.0681863	−	0.118102i
$523$	13.1461	+	22.7696i	0.574837	+	0.995646i	0.996059	+	0.0886892i	$0.0282678\pi$
$523$	13.1461	+	22.7696i	0.574837	+	0.995646i	−0.421223	+	0.906957i	$0.638399\pi$
$524$	−18.1799	+	31.4884i	−0.794191	+	1.37558i
$525$	1.26180			0.0550696
$526$	3.67362	−	6.36290i	0.160178	−	0.277436i
$527$	19.9297	−	34.5193i	0.868152	−	1.50368i
$528$	2.36858			0.103079
$529$	9.01021	−	15.6061i	0.391748	−	0.678528i
$530$	5.11575	+	8.86074i	0.222214	+	0.384886i
$531$	0.426974	+	0.739540i	0.0185291	+	0.0320933i
$532$	−20.1124			−0.871981
$533$	0.939393	+	4.02396i	0.0406896	+	0.174297i
$534$	14.9787			0.648190
$535$	−6.24665	−	10.8195i	−0.270066	−	0.467768i
$536$	16.5708	+	28.7015i	0.715750	+	1.23972i
$537$	−2.65847	+	4.60461i	−0.114722	+	0.198704i
$538$	−60.9519			−2.62782
$539$	12.2315	−	21.1856i	0.526848	−	0.912527i
$540$	1.55787	−	2.69832i	0.0670403	−	0.116117i
$541$	−0.107816			−0.00463537			−0.00231768	−	0.999997i	$-0.500738\pi$
$541$	−0.107816			−0.00463537			−0.00231768	+	0.999997i	$0.500738\pi$
$542$	−22.4478	+	38.8808i	−0.964218	+	1.67007i
$543$	12.9354	+	22.4048i	0.555112	+	0.961483i
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	−2.27871			−0.0976091
$546$	−2.33931	−	10.0206i	−0.100113	−	0.428843i
$547$	12.1193			0.518182			0.259091	−	0.965853i	$-0.416577\pi$
$547$	12.1193			0.518182			0.259091	+	0.965853i	$0.416577\pi$
$548$	31.2574	+	54.1394i	1.33525	+	2.31272i
$549$	−2.31968	−	4.01780i	−0.0990014	−	0.171475i
$550$	5.11575	−	8.86074i	0.218136	−	0.377823i
$551$	−7.04721			−0.300221
$552$	−2.81571	+	4.87695i	−0.119845	+	0.207577i
$553$	−5.59663	+	9.69365i	−0.237993	+	0.412216i
$554$	−36.4024			−1.54659
$555$	−0.115749	+	0.200484i	−0.00491329	+	0.00851006i
$556$	−25.4546	−	44.0887i	−1.07952	−	1.86978i
$557$	−19.0035	−	32.9150i	−0.805204	−	1.39466i	−0.916153	−	0.400829i	$-0.868722\pi$
$557$	−19.0035	−	32.9150i	−0.805204	−	1.39466i	0.110948	−	0.993826i	$-0.464611\pi$
$558$	−20.0641			−0.849382
$559$	16.7787	−	15.7234i	0.709664	−	0.665030i
$560$	0.660685			0.0279191
$561$	−10.1630	−	17.6028i	−0.429080	−	0.743189i
$562$	−6.08148	−	10.5334i	−0.256532	−	0.444326i
$563$	−7.75510	+	13.4322i	−0.326839	+	0.566101i	−0.981883	−	0.189490i	$-0.939317\pi$
$563$	−7.75510	+	13.4322i	−0.326839	+	0.566101i	0.655044	+	0.755591i	$0.272650\pi$
$564$	33.6046			1.41501
$565$	0.738198	−	1.27860i	0.0310562	−	0.0537909i
$566$	30.3833	−	52.6254i	1.27710	−	2.21201i
$567$	−1.26180			−0.0529907
$568$	−12.1247	+	21.0006i	−0.508742	+	0.881167i
$569$	−9.62024	−	16.6627i	−0.403301	−	0.698538i	0.590821	−	0.806803i	$-0.298804\pi$
$569$	−9.62024	−	16.6627i	−0.403301	−	0.698538i	−0.994122	+	0.108265i	$0.965471\pi$
$570$	−5.78541	−	10.0206i	−0.242324	−	0.419718i
$571$	27.7338			1.16062			0.580311	−	0.814395i	$-0.302931\pi$
$571$	27.7338			1.16062			0.580311	+	0.814395i	$0.302931\pi$
$572$	−48.6339	−	14.7387i	−2.03349	−	0.616255i
$573$	−10.6563			−0.445172
$574$	−1.63539	−	2.83257i	−0.0682597	−	0.118229i
$575$	−1.11575	−	1.93253i	−0.0465300	−	0.0805923i
$576$	6.52360	−	11.2992i	0.271817	−	0.470801i
$577$	26.9866			1.12347			0.561733	−	0.827318i	$-0.310135\pi$
$577$	26.9866			1.12347			0.561733	+	0.827318i	$0.310135\pi$
$578$	3.60730	−	6.24802i	0.150044	−	0.259883i
$579$	3.99155	−	6.91356i	0.165883	−	0.287318i
$580$	−4.29211			−0.178220
$581$	−5.19326	+	8.99499i	−0.215453	+	0.373175i
$582$	−12.0663	−	20.8995i	−0.500165	−	0.866312i
$583$	−10.2315	−	17.7215i	−0.423745	−	0.733949i
$584$	−34.7889			−1.43958
$585$	2.63090	−	2.46543i	0.108774	−	0.101933i
$586$	−48.4462			−2.00129
$587$	15.4265	+	26.7195i	0.636720	+	1.10283i	0.986148	+	0.165869i	$0.0530428\pi$
$587$	15.4265	+	26.7195i	0.636720	+	1.10283i	−0.349427	+	0.936963i	$0.613624\pi$
$588$	−8.42476	−	14.5921i	−0.347431	−	0.601769i
$589$	−22.6905	+	39.3012i	−0.934947	+	1.61938i
$590$	1.93146			0.0795169
$591$	8.66966	−	15.0163i	0.356622	−	0.617688i
$592$	−0.0606069	+	0.104974i	−0.00249093	+	0.00431441i
$593$	4.29211			0.176256			0.0881278	−	0.996109i	$-0.471912\pi$
$593$	4.29211			0.176256			0.0881278	+	0.996109i	$0.471912\pi$
$594$	−5.11575	+	8.86074i	−0.209902	+	0.363560i
$595$	−2.83483	−	4.91007i	−0.116217	−	0.201293i
$596$	5.05514	+	8.75576i	0.207067	+	0.358650i
$597$	1.23150			0.0504019
$598$	−13.2787	+	12.4436i	−0.543007	+	0.508855i
$599$	−24.0224			−0.981527			−0.490764	−	0.871293i	$-0.663282\pi$
$599$	−24.0224			−0.981527			−0.490764	+	0.871293i	$0.663282\pi$
$600$	−1.26180	−	2.18551i	−0.0515129	−	0.0892229i
$601$	−1.26577	−	2.19238i	−0.0516318	−	0.0894289i	0.839054	−	0.544048i	$-0.183109\pi$
$601$	−1.26577	−	2.19238i	−0.0516318	−	0.0894289i	−0.890686	+	0.454619i	$0.849776\pi$
$602$	−9.10060	+	15.7627i	−0.370913	+	0.642440i
$603$	13.1327			0.534803
$604$	−8.87982	+	15.3803i	−0.361315	+	0.625816i
$605$	−4.73150	+	8.19520i	−0.192363	+	0.333182i
$606$	−38.5574			−1.56629
$607$	−5.72083	+	9.90877i	−0.232201	+	0.402185i	−0.958456	−	0.285242i	$-0.907926\pi$
$607$	−5.72083	+	9.90877i	−0.232201	+	0.402185i	0.726254	+	0.687426i	$0.241260\pi$
$608$	−15.9394	−	27.6078i	−0.646428	−	1.11965i
$609$	0.869099	+	1.50532i	0.0352177	+	0.0609988i
$610$	−10.4933			−0.424861
$611$	37.2159	+	11.2784i	1.50559	+	0.456276i
$612$	−14.0000			−0.565916
$613$	3.59663	+	6.22955i	0.145267	+	0.251609i	0.929472	−	0.368892i	$-0.120263\pi$
$613$	3.59663	+	6.22955i	0.145267	+	0.251609i	−0.784206	+	0.620501i	$0.786929\pi$
$614$	−8.88204	−	15.3841i	−0.358450	−	0.620853i
$615$	0.573026	−	0.992511i	0.0231067	−	0.0400219i
$616$	14.4045			0.580373
$617$	−12.7854	+	22.1450i	−0.514721	+	0.891523i	0.485133	+	0.874440i	$0.338771\pi$
$617$	−12.7854	+	22.1450i	−0.514721	+	0.891523i	−0.999854	+	0.0170827i	$0.994562\pi$
$618$	15.7742	−	27.3218i	0.634532	−	1.09904i
$619$	5.98660			0.240622			0.120311	−	0.992736i	$-0.461611\pi$
$619$	5.98660			0.240622			0.120311	+	0.992736i	$0.461611\pi$
$620$	−13.8197	+	23.9364i	−0.555012	+	0.961308i
$621$	1.11575	+	1.93253i	0.0447735	+	0.0775499i
$622$	−31.5231	−	54.5997i	−1.26396	−	2.18925i
$623$	−8.35622			−0.334785
$624$	1.37755	−	1.29091i	0.0551462	−	0.0516778i
$625$	1.00000			0.0400000
$626$	8.92027	+	15.4504i	0.356526	+	0.617521i
$627$	11.5708	+	20.0412i	0.462094	+	0.800370i
$628$	6.00397	−	10.3992i	0.239584	−	0.414972i
$629$	1.04019			0.0414752
$630$	−1.42697	+	2.47159i	−0.0568520	+	0.0984705i
$631$	21.5129	−	37.2615i	0.856417	−	1.48336i	−0.0189080	−	0.999821i	$-0.506019\pi$
$631$	21.5129	−	37.2615i	0.856417	−	1.48336i	0.875325	−	0.483536i	$-0.160648\pi$
$632$	22.3865			0.890488
$633$	5.16966	−	8.95411i	0.205475	−	0.355894i
$634$	14.9484	+	25.8913i	0.593675	+	1.02828i
$635$	8.89270	+	15.4026i	0.352896	+	0.611234i
$636$	−14.0944			−0.558880
$637$	−4.43269	−	18.9878i	−0.175630	−	0.752322i
$638$	14.0944			0.558003
$639$	4.80453	+	8.32168i	0.190064	+	0.329201i
$640$	−8.52360	−	14.7633i	−0.336925	−	0.583571i
$641$	3.34725	−	5.79760i	0.132208	−	0.228992i	−0.792319	−	0.610107i	$-0.791127\pi$
$641$	3.34725	−	5.79760i	0.132208	−	0.228992i	0.924528	+	0.381115i	$0.124460\pi$
$642$	28.2574			1.11523
$643$	−4.09039	+	7.08477i	−0.161309	+	0.279396i	−0.935338	−	0.353754i	$-0.884905\pi$
$643$	−4.09039	+	7.08477i	−0.161309	+	0.279396i	0.774029	+	0.633150i	$0.218238\pi$
$644$	4.38652	−	7.59768i	0.172853	−	0.299391i
$645$	−6.37755			−0.251116
$646$	−25.9956	+	45.0257i	−1.02278	+	1.77151i
$647$	5.63935	+	9.76765i	0.221706	+	0.384006i	0.955326	−	0.295554i	$-0.0955042\pi$
$647$	5.63935	+	9.76765i	0.221706	+	0.384006i	−0.733620	+	0.679560i	$0.762171\pi$
$648$	1.26180	+	2.18551i	0.0495683	+	0.0858548i
$649$	−3.86292			−0.151633
$650$	−1.85395	−	7.94151i	−0.0727178	−	0.311492i
$651$	11.1933			0.438699
$652$	15.1500	+	26.2406i	0.593321	+	1.02766i
$653$	−13.6242	−	23.5978i	−0.533156	−	0.923454i	−0.999250	−	0.0387184i	$-0.987672\pi$
$653$	−13.6242	−	23.5978i	−0.533156	−	0.923454i	0.466094	−	0.884735i	$-0.345661\pi$
$654$	2.57699	−	4.46348i	0.100768	−	0.174536i
$655$	11.6697			0.455971
$656$	0.300039	−	0.519683i	0.0117146	−	0.0202902i
$657$	−6.89270	+	11.9385i	−0.268910	+	0.465766i
$658$	−30.7810			−1.19997
$659$	−3.37755	+	5.85009i	−0.131571	+	0.227887i	−0.924282	−	0.381710i	$-0.875335\pi$
$659$	−3.37755	+	5.85009i	−0.131571	+	0.227887i	0.792711	+	0.609597i	$0.208669\pi$
$660$	7.04721	+	12.2061i	0.274312	+	0.475123i
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	0.999837	+	0.0180657i	$0.00575081\pi$
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	−0.484273	+	0.874917i	$0.660916\pi$
$662$	53.9429			2.09655
$663$	−15.5045	−	4.69869i	−0.602144	−	0.182482i
$664$	20.7730			0.806151
$665$	3.22753	+	5.59025i	0.125158	+	0.216781i
$666$	−0.261802	−	0.453455i	−0.0101446	−	0.0175710i
$667$	1.53700	−	2.66217i	0.0595130	−	0.103079i
$668$	−60.0676			−2.32409
$669$	10.7854	−	18.6809i	0.416988	−	0.722244i
$670$	14.8517	−	25.7240i	0.573773	−	0.993803i
$671$	20.9866			0.810179
$672$	−3.93146	+	6.80949i	−0.151659	+	0.262682i
$673$	0.338795	+	0.586811i	0.0130596	+	0.0226199i	0.872481	−	0.488647i	$-0.162510\pi$
$673$	0.338795	+	0.586811i	0.0130596	+	0.0226199i	−0.859422	+	0.511267i	$0.829176\pi$
$674$	6.42697	+	11.1318i	0.247558	+	0.428783i
$675$	−1.00000			−0.0384900
$676$	−36.3180	+	17.9343i	−1.39685	+	0.689780i
$677$	−10.4630			−0.402126			−0.201063	−	0.979578i	$-0.564440\pi$
$677$	−10.4630			−0.402126			−0.201063	+	0.979578i	$0.564440\pi$
$678$	1.66966	+	2.89193i	0.0641228	+	0.111064i
$679$	6.73150	+	11.6593i	0.258331	+	0.447443i
$680$	−5.66966	+	9.82013i	−0.217421	+	0.376585i
$681$	−5.44609			−0.208695
$682$	45.3811	−	78.6023i	1.73773	−	3.00984i
$683$	9.37580	−	16.2394i	0.358755	−	0.621382i	−0.628998	−	0.777407i	$-0.716535\pi$
$683$	9.37580	−	16.2394i	0.358755	−	0.621382i	0.987753	+	0.156025i	$0.0498680\pi$
$684$	15.9394			0.609458
$685$	10.0321	−	17.3760i	0.383305	−	0.663904i
$686$	17.7057	+	30.6671i	0.676006	+	1.17088i
$687$	10.9657	+	18.9932i	0.418369	+	0.724636i
$688$	−3.33931			−0.127310
$689$	−15.6091	−	4.73038i	−0.594657	−	0.180213i
$690$	5.04721			0.192144
$691$	−21.7827	−	37.7287i	−0.828652	−	1.43527i	−0.899096	−	0.437752i	$-0.855775\pi$
$691$	−21.7827	−	37.7287i	−0.828652	−	1.43527i	0.0704440	−	0.997516i	$-0.477558\pi$
$692$	4.69996	+	8.14057i	0.178666	+	0.309458i
$693$	2.85395	−	4.94318i	0.108412	−	0.187776i
$694$	48.5148			1.84159
$695$	−8.16966	+	14.1503i	−0.309893	+	0.536750i
$696$	1.73820	−	3.01065i	0.0658862	−	0.114118i
$697$	−5.14956			−0.195054
$698$	7.77026	−	13.4585i	0.294108	−	0.509411i
$699$	12.6563	+	21.9213i	0.478704	+	0.829139i
$700$	1.96573	+	3.40474i	0.0742976	+	0.128687i
$701$	−19.0810			−0.720680			−0.360340	−	0.932821i	$-0.617339\pi$
$701$	−19.0810			−0.720680			−0.360340	+	0.932821i	$0.617339\pi$
$702$	1.85395	+	7.94151i	0.0699727	+	0.299733i
$703$	−1.18429			−0.0446663
$704$	29.5102	+	51.1132i	1.11221	+	1.92640i
$705$	−5.39270	−	9.34044i	−0.203101	−	0.351781i
$706$	39.0125	−	67.5716i	1.46825	−	2.54309i
$707$	21.5102			0.808975
$708$	−1.33034	+	2.30422i	−0.0499973	+	0.0865979i
$709$	−22.3023	+	38.6287i	−0.837581	+	1.45073i	0.0543307	+	0.998523i	$0.482697\pi$
$709$	−22.3023	+	38.6287i	−0.837581	+	1.45073i	−0.891912	+	0.452210i	$0.850636\pi$
$710$	21.7338			0.815654
$711$	4.43543	−	7.68238i	0.166341	−	0.288112i
$712$	8.35622	+	14.4734i	0.313163	+	0.542414i
$713$	−9.89765	−	17.1432i	−0.370670	−	0.642019i
$714$	12.8236			0.479913
$715$	3.70789	+	15.8830i	0.138667	+	0.593991i
$716$	−16.5663			−0.619110
$717$	11.2618	+	19.5060i	0.420580	+	0.728465i
$718$	−9.22753	−	15.9826i	−0.344368	−	0.596464i
$719$	6.49109	−	11.2429i	0.242077	−	0.419289i	−0.719229	−	0.694773i	$-0.755505\pi$
$719$	6.49109	−	11.2429i	0.242077	−	0.419289i	0.961306	+	0.275484i	$0.0888381\pi$
$720$	−0.523604			−0.0195136
$721$	−8.80004	+	15.2421i	−0.327731	+	0.567646i
$722$	8.10957	−	14.0462i	0.301807	−	0.522745i
$723$	−11.1157			−0.413399
$724$	−40.3035	+	69.8078i	−1.49787	+	2.59439i
$725$	0.688776	+	1.19299i	0.0255805	+	0.0443067i
$726$	−10.7017	−	18.5359i	−0.397178	−	0.687932i
$727$	17.3980			0.645255			0.322627	−	0.946526i	$-0.395434\pi$
$727$	17.3980			0.645255			0.322627	+	0.946526i	$0.395434\pi$
$728$	8.37755	−	7.85065i	0.310493	−	0.290965i
$729$	1.00000			0.0370370
$730$	15.5899	+	27.0026i	0.577009	+	0.999409i
$731$	14.3281	+	24.8170i	0.529945	+	0.917892i
$732$	7.22753	−	12.5185i	0.267137	−	0.462695i
$733$	45.8272			1.69266			0.846332	−	0.532655i	$-0.178806\pi$
$733$	45.8272			1.69266			0.846332	+	0.532655i	$0.178806\pi$
$734$	−7.73598	+	13.3991i	−0.285540	+	0.494570i
$735$	−2.70393	+	4.68334i	−0.0997359	+	0.172748i
$736$	13.9056			0.512567
$737$	−29.7035	+	51.4479i	−1.09414	+	1.89511i
$738$	1.29607	+	2.24486i	0.0477091	+	0.0826346i
$739$	−8.78541	−	15.2168i	−0.323176	−	0.559758i	0.657965	−	0.753048i	$-0.271417\pi$
$739$	−8.78541	−	15.2168i	−0.323176	−	0.559758i	−0.981142	+	0.193290i	$0.938084\pi$
$740$	−0.721292			−0.0265152
$741$	17.6523	+	5.34959i	0.648473	+	0.196522i
$742$	12.9101			0.473946
$743$	15.1781	+	26.2893i	0.556831	+	0.964459i	0.997759	+	0.0669167i	$0.0213162\pi$
$743$	15.1781	+	26.2893i	0.556831	+	0.964459i	−0.440928	+	0.897543i	$0.645350\pi$
$744$	−11.1933	−	19.3873i	−0.410365	−	0.710773i
$745$	1.62245	−	2.81016i	0.0594419	−	0.102956i
$746$	−31.2563			−1.14438
$747$	4.11575	−	7.12869i	0.150587	−	0.260825i
$748$	31.6652	−	54.8458i	1.15780	−	2.00536i
$749$	−15.7641			−0.576007
$750$	−1.13090	+	1.95878i	−0.0412947	+	0.0715245i
$751$	−1.90162	−	3.29369i	−0.0693909	−	0.120189i	0.829242	−	0.558889i	$-0.188772\pi$
$751$	−1.90162	−	3.29369i	−0.0693909	−	0.120189i	−0.898633	+	0.438700i	$0.855439\pi$
$752$	−2.82364	−	4.89069i	−0.102968	−	0.178345i
$753$	−11.0472			−0.402583
$754$	8.19723	−	7.68167i	0.298525	−	0.279750i
$755$	5.69996			0.207443
$756$	−1.96573	−	3.40474i	−0.0714929	−	0.123829i
$757$	1.70393	+	2.95129i	0.0619303	+	0.107266i	0.895328	−	0.445407i	$-0.146941\pi$
$757$	1.70393	+	2.95129i	0.0619303	+	0.107266i	−0.833398	+	0.552673i	$0.813608\pi$
$758$	13.0231	−	22.5566i	0.473020	−	0.819294i
$759$	−10.0944			−0.366404
$760$	6.45506	−	11.1805i	0.234150	−	0.405559i
$761$	−3.62245	+	6.27426i	−0.131314	+	0.227442i	−0.924183	−	0.381949i	$-0.875253\pi$
$761$	−3.62245	+	6.27426i	−0.131314	+	0.227442i	0.792870	+	0.609391i	$0.208586\pi$
$762$	−40.2271			−1.45727
$763$	−1.43764	+	2.49006i	−0.0520460	+	0.0901464i
$764$	−16.6011	−	28.7540i	−0.600607	−	1.04028i
$765$	2.24665	+	3.89131i	0.0812278	+	0.140691i
$766$	−51.7496			−1.86979
$767$	−2.24665	+	2.10535i	−0.0811218	+	0.0760198i
$768$	12.4630			0.449720
$769$	−15.5882	−	26.9995i	−0.562124	−	0.973627i	−0.997311	−	0.0732873i	$-0.976651\pi$
$769$	−15.5882	−	26.9995i	−0.562124	−	0.973627i	0.435187	−	0.900340i	$-0.356682\pi$
$770$	−6.45506	−	11.1805i	−0.232624	−	0.402917i
$771$	−1.01515	+	1.75829i	−0.0365598	+	0.0633234i
$772$	24.8733			0.895210
$773$	−9.73026	+	16.8533i	−0.349973	+	0.606172i	−0.986244	−	0.165294i	$-0.947143\pi$
$773$	−9.73026	+	16.8533i	−0.349973	+	0.606172i	0.636271	+	0.771466i	$0.280476\pi$
$774$	7.21238	−	12.4922i	0.259244	−	0.449023i
$775$	8.87085			0.318650
$776$	13.4630	−	23.3186i	0.483293	−	0.837089i
$777$	0.146053	+	0.252971i	0.00523962	+	0.00907528i
$778$	−4.92249	−	8.52600i	−0.176480	−	0.305672i
$779$	5.86292			0.210061
$780$	10.7511	+	3.25817i	0.384952	+	0.116661i
$781$	−43.4675			−1.55539
$782$	−11.3393	−	19.6403i	−0.405493	−	0.702335i
$783$	−0.688776	−	1.19299i	−0.0246148	−	0.0426342i
$784$	−1.41579	+	2.45222i	−0.0505639	+	0.0875792i
$785$	−3.85395			−0.137553
$786$	−13.1972	+	22.8583i	−0.470730	+	0.815328i
$787$	−7.20171	+	12.4737i	−0.256713	+	0.444641i	−0.965359	−	0.260923i	$-0.915973\pi$
$787$	−7.20171	+	12.4737i	−0.256713	+	0.444641i	0.708646	+	0.705564i	$0.249306\pi$
$788$	54.0250			1.92456
$789$	1.62420	−	2.81320i	0.0578231	−	0.100153i
$790$	−10.0321	−	17.3760i	−0.356925	−	0.618212i
$791$	−0.931460	−	1.61334i	−0.0331189	−	0.0573636i
$792$	−11.4158			−0.405642
$793$	12.2057	−	11.4380i	0.433436	−	0.406176i
$794$	−17.2405			−0.611841
$795$	2.26180	+	3.91756i	0.0802179	+	0.138941i
$796$	1.91852	+	3.32298i	0.0680002	+	0.117780i
$797$	11.8006	−	20.4392i	0.417997	−	0.723992i	−0.577741	−	0.816220i	$-0.696066\pi$
$797$	11.8006	−	20.4392i	0.417997	−	0.723992i	0.995738	+	0.0922279i	$0.0293988\pi$
$798$	−14.6001			−0.516837
$799$	−24.2310	+	41.9694i	−0.857233	+	1.48477i
$800$	−3.11575	+	5.39664i	−0.110158	+	0.190800i
$801$	6.62245			0.233993
$802$	23.5787	−	40.8396i	0.832595	−	1.44210i
$803$	−31.1799	−	54.0051i	−1.10031	−	1.90580i
$804$	20.4590	+	35.4361i	0.721534	+	1.24973i
$805$	−2.81571			−0.0992407
$806$	−16.4461	−	70.4480i	−0.579289	−	2.48142i
$807$	−26.9484			−0.948627
$808$	−21.5102	−	37.2568i	−0.756726	−	1.31069i
$809$	−13.3776	−	23.1706i	−0.470330	−	0.814635i	0.529095	−	0.848563i	$-0.322532\pi$
$809$	−13.3776	−	23.1706i	−0.470330	−	0.814635i	−0.999424	+	0.0339280i	$0.989198\pi$
$810$	1.13090	−	1.95878i	0.0397358	−	0.0688245i
$811$	−3.58421			−0.125859			−0.0629293	−	0.998018i	$-0.520044\pi$
$811$	−3.58421			−0.125859			−0.0629293	+	0.998018i	$0.520044\pi$
$812$	−2.70789	+	4.69021i	−0.0950285	+	0.164594i
$813$	−9.92476	+	17.1902i	−0.348077	+	0.602886i
$814$	2.36858			0.0830187
$815$	4.86240	−	8.42192i	0.170322	−	0.295007i
$816$	1.17636	+	2.03751i	0.0411807	+	0.0713271i
$817$	−16.3130	−	28.2549i	−0.570719	−	0.988514i
$818$	38.3721			1.34165
$819$	−1.03427	−	4.43037i	−0.0361403	−	0.154810i
$820$	3.57081			0.124698
$821$	−7.91806	−	13.7145i	−0.276342	−	0.478639i	0.694131	−	0.719849i	$-0.255789\pi$
$821$	−7.91806	−	13.7145i	−0.276342	−	0.478639i	−0.970473	+	0.241210i	$0.922456\pi$
$822$	22.6905	+	39.3012i	0.791423	+	1.37079i
$823$	−3.70789	+	6.42226i	−0.129249	+	0.223866i	−0.923386	−	0.383873i	$-0.874590\pi$
$823$	−3.70789	+	6.42226i	−0.129249	+	0.223866i	0.794137	+	0.607739i	$0.207923\pi$
$824$	35.2002			1.22626
$825$	2.26180	−	3.91756i	0.0787458	−	0.136392i
$826$	1.21856	−	2.11061i	0.0423991	−	0.0734374i
$827$	−16.6036			−0.577363			−0.288682	−	0.957425i	$-0.593217\pi$
$827$	−16.6036			−0.577363			−0.288682	+	0.957425i	$0.593217\pi$
$828$	−3.47640	+	6.02129i	−0.120813	+	0.209254i
$829$	14.6421	+	25.3608i	0.508541	+	0.880818i	0.999951	+	0.00989015i	$0.00314819\pi$
$829$	14.6421	+	25.3608i	0.508541	+	0.880818i	−0.491410	+	0.870928i	$0.663518\pi$
$830$	−9.30901	−	16.1237i	−0.323120	−	0.559661i
$831$	−16.0944			−0.558309
$832$	45.0204	+	13.6436i	1.56080	+	0.473007i
$833$	24.2991			0.841915
$834$	−18.4781	−	32.0051i	−0.639846	−	1.10825i
$835$	9.63935	+	16.6959i	0.333584	+	0.577784i
$836$	−36.0518	+	62.4435i	−1.24688	+	2.15965i
$837$	−8.87085			−0.306622
$838$	2.37358	−	4.11117i	0.0819941	−	0.142018i
$839$	15.0810	−	26.1211i	0.520655	−	0.901800i	−0.479057	−	0.877784i	$-0.659021\pi$
$839$	15.0810	−	26.1211i	0.520655	−	0.901800i	0.999712	−	0.0240164i	$-0.00764541\pi$
$840$	−3.18429			−0.109868
$841$	13.5512	−	23.4713i	0.467282	−	0.809356i
$842$	−44.8513	−	77.6847i	−1.54568	−	2.67719i
$843$	−2.68878	−	4.65710i	−0.0926064	−	0.160399i
$844$	32.2147			1.10888
$845$	10.8130	+	7.21661i	0.371978	+	0.248259i
$846$	24.3945			0.838699
$847$	5.97022	+	10.3407i	0.205139	+	0.355311i
$848$	1.18429	+	2.05125i	0.0406687	+	0.0704402i
$849$	13.4332	−	23.2670i	0.461027	−	0.798522i
$850$	10.1630			0.348587
$851$	0.258295	−	0.447379i	0.00885423	−	0.0153360i
$852$	−14.9697	+	25.9283i	−0.512853	+	0.888288i
$853$	−2.50670			−0.0858277			−0.0429139	−	0.999079i	$-0.513664\pi$
$853$	−2.50670			−0.0858277			−0.0429139	+	0.999079i	$0.513664\pi$
$854$	−6.62024	+	11.4666i	−0.226540	+	0.392378i
$855$	−2.55787	−	4.43037i	−0.0874775	−	0.151515i
$856$	15.7641	+	27.3042i	0.538805	+	0.933238i
$857$	−24.4327			−0.834605			−0.417302	−	0.908768i	$-0.637024\pi$
$857$	−24.4327			−0.834605			−0.417302	+	0.908768i	$0.637024\pi$
$858$	−35.3046	−	10.6992i	−1.20528	−	0.365264i
$859$	−7.10235			−0.242329			−0.121165	−	0.992632i	$-0.538663\pi$
$859$	−7.10235			−0.242329			−0.121165	+	0.992632i	$0.538663\pi$
$860$	−9.93543	−	17.2087i	−0.338795	−	0.586811i
$861$	−0.723046	−	1.25235i	−0.0246413	−	0.0426801i
$862$	−25.0248	+	43.3443i	−0.852349	+	1.47631i
$863$	−3.24490			−0.110458			−0.0552288	−	0.998474i	$-0.517589\pi$
$863$	−3.24490			−0.110458			−0.0552288	+	0.998474i	$0.517589\pi$
$864$	3.11575	−	5.39664i	0.106000	−	0.183597i
$865$	1.50845	−	2.61272i	0.0512889	−	0.0888350i
$866$	70.9216			2.41001
$867$	1.59488	−	2.76241i	0.0541649	−	0.0938163i
$868$	17.4377	+	30.2030i	0.591874	+	1.02516i
$869$	20.0641	+	34.7521i	0.680628	+	1.17888i
$870$	−3.11575			−0.105634
$871$	10.7645	+	46.1106i	0.364742	+	1.56240i
$872$	5.75056			0.194738
$873$	−5.33483	−	9.24019i	−0.180557	−	0.312733i
$874$	12.9101	+	22.3610i	0.436692	+	0.756372i
$875$	0.630901	−	1.09275i	0.0213284	−	0.0369418i
$876$	−42.9519			−1.45121
$877$	−9.49330	+	16.4429i	−0.320566	+	0.555237i	−0.980605	−	0.195995i	$-0.937206\pi$
$877$	−9.49330	+	16.4429i	−0.320566	+	0.555237i	0.660039	+	0.751231i	$0.270540\pi$
$878$	4.87807	−	8.44907i	0.164627	−	0.285142i
$879$	−21.4193			−0.722455
$880$	1.18429	−	2.05125i	0.0399224	−	0.0691476i
$881$	9.73820	+	16.8671i	0.328088	+	0.568265i	0.982132	−	0.188191i	$-0.0602623\pi$
$881$	9.73820	+	16.8671i	0.328088	+	0.568265i	−0.654044	+	0.756456i	$0.726929\pi$
$882$	−6.11575	−	10.5928i	−0.205928	−	0.356678i
$883$	−50.5664			−1.70169			−0.850847	−	0.525413i	$-0.823911\pi$
$883$	−50.5664			−1.70169			−0.850847	+	0.525413i	$0.823911\pi$
$884$	−11.4755	−	49.1560i	−0.385962	−	1.65330i
$885$	0.853947			0.0287051
$886$	0.557875	+	0.966267i	0.0187422	+	0.0324624i
$887$	6.26356	+	10.8488i	0.210310	+	0.364267i	0.951811	−	0.306684i	$-0.0992195\pi$
$887$	6.26356	+	10.8488i	0.210310	+	0.364267i	−0.741502	+	0.670951i	$0.765886\pi$
$888$	0.292106	−	0.505942i	0.00980243	−	0.0169783i
$889$	22.4417			0.752669
$890$	7.48933	−	12.9719i	0.251043	−	0.434819i
$891$	−2.26180	+	3.91756i	−0.0757732	+	0.131243i
$892$	67.2092			2.25033
$893$	27.5877	−	47.7833i	0.923188	−	1.59901i
$894$	3.66966	+	6.35603i	0.122732	+	0.212578i
$895$	2.65847	+	4.60461i	0.0888629	+	0.153915i
$896$	−21.5102			−0.718606
$897$	−5.87085	+	5.50161i	−0.196022	+	0.183693i
$898$	52.7283			1.75957
$899$	6.11003	+	10.5829i	0.203781	+	0.352959i
$900$	−1.55787	−	2.69832i	−0.0519292	−	0.0899439i
$901$	10.1630	−	17.6028i	0.338577	−	0.586433i
$902$	−11.7258			−0.390428
$903$	−4.02360	+	6.96909i	−0.133897	+	0.231917i
$904$	−1.86292	+	3.22667i	−0.0619598	+	0.107317i
$905$	25.8709			0.859976
$906$	−6.44609	+	11.1650i	−0.214157	+	0.370931i
$907$	−14.0209	−	24.2849i	−0.465555	−	0.806366i	0.533671	−	0.845692i	$-0.320812\pi$
$907$	−14.0209	−	24.2849i	−0.465555	−	0.806366i	−0.999226	+	0.0393265i	$0.987479\pi$
$908$	−8.48433	−	14.6953i	−0.281562	−	0.487680i
$909$	−17.0472			−0.565420
$910$	−9.84777	−	2.98440i	−0.326450	−	0.0989320i
$911$	16.1977			0.536653			0.268327	−	0.963328i	$-0.413529\pi$
$911$	16.1977			0.536653			0.268327	+	0.963328i	$0.413529\pi$
$912$	−1.33931	−	2.31976i	−0.0443491	−	0.0768150i
$913$	18.6180	+	32.2474i	0.616167	+	1.06723i
$914$	7.54272	−	13.0644i	0.249491	−	0.432131i
$915$	−4.63935			−0.153372
$916$	−34.1665	+	59.1781i	−1.12889	+	1.95530i
$917$	7.36240	−	12.7521i	0.243128	−	0.421110i
$918$	−10.1630			−0.335428
$919$	21.6389	−	37.4797i	0.713801	−	1.23634i	−0.249619	−	0.968344i	$-0.580305\pi$
$919$	21.6389	−	37.4797i	0.713801	−	1.23634i	0.963420	−	0.267996i	$-0.0863614\pi$
$920$	2.81571	+	4.87695i	0.0928312	+	0.160788i
$921$	−3.92697	−	6.80172i	−0.129398	−	0.224124i
$922$	−65.8620			−2.16905
$923$	−25.2805	+	23.6905i	−0.832117	+	0.779781i
$924$	17.7844			0.585063
$925$	0.115749	+	0.200484i	0.00380582	+	0.00659187i
$926$	−2.02809	−	3.51276i	−0.0666472	−	0.115436i
$927$	6.97418	−	12.0796i	0.229062	−	0.396747i
$928$	−8.58421			−0.281791
$929$	−6.88425	+	11.9239i	−0.225865	+	0.391210i	−0.956579	−	0.291475i	$-0.905854\pi$
$929$	−6.88425	+	11.9239i	−0.225865	+	0.391210i	0.730714	+	0.682684i	$0.239187\pi$
$930$	−10.0321	+	17.3760i	−0.328964	+	0.569783i
$931$	−27.6652			−0.906691
$932$	−39.4337	+	68.3012i	−1.29169	+	2.23728i
$933$	−13.9372	−	24.1399i	−0.456283	−	0.790305i
$934$	19.0209	+	32.9451i	0.622382	+	1.07800i
$935$	−20.3259			−0.664729
$936$	−6.63935	+	6.22178i	−0.217014	+	0.203365i
$937$	−38.1888			−1.24757			−0.623787	−	0.781594i	$-0.714407\pi$
$937$	−38.1888			−1.24757			−0.623787	+	0.781594i	$0.714407\pi$
$938$	−18.7400	−	32.4585i	−0.611881	−	1.05981i
$939$	3.94388	+	6.83100i	0.128704	+	0.222921i
$940$	16.8023	−	29.1025i	0.548031	−	0.949218i
$941$	−13.9618			−0.455140			−0.227570	−	0.973762i	$-0.573078\pi$
$941$	−13.9618			−0.455140			−0.227570	+	0.973762i	$0.573078\pi$
$942$	4.35843	−	7.54903i	0.142005	−	0.245961i
$943$	−1.27871	+	2.21479i	−0.0416405	+	0.0721234i
$944$	0.447131			0.0145529
$945$	−0.630901	+	1.09275i	−0.0205232	+	0.0355473i
$946$	32.6260	+	56.5098i	1.06076	+	1.83729i
$947$	−3.68481	−	6.38228i	−0.119740	−	0.207396i	0.799924	−	0.600101i	$-0.204873\pi$
$947$	−3.68481	−	6.38228i	−0.119740	−	0.207396i	−0.919665	+	0.392705i	$0.871539\pi$
$948$	27.6394			0.897684
$949$	−47.5676	−	14.4155i	−1.54411	−	0.467948i
$950$	−11.5708			−0.375407
$951$	6.60905	+	11.4472i	0.214313	+	0.371201i
$952$	7.15399	+	12.3911i	0.231862	+	0.401597i
$953$	−11.6091	+	20.1075i	−0.376054	+	0.651345i	−0.990484	−	0.137627i	$-0.956053\pi$
$953$	−11.6091	+	20.1075i	−0.376054	+	0.651345i	0.614430	+	0.788971i	$0.289386\pi$
$954$	−10.2315			−0.331257
$955$	−5.32813	+	9.22859i	−0.172414	+	0.298630i
$956$	−35.0890	+	60.7759i	−1.13486	+	1.96563i
$957$	6.23150			0.201436
$958$	39.7546	−	68.8571i	1.28441	−	2.22467i
$959$	−12.6585	−	21.9251i	−0.408763	−	0.707999i
$960$	−6.52360	−	11.2992i	−0.210548	−	0.364681i
$961$	47.6920			1.53845
$962$	1.37755	−	1.29091i	0.0444140	−	0.0416207i
$963$	12.4933			0.402591
$964$	−17.3169	−	29.9938i	−0.557741	−	0.966036i
$965$	−3.99155	−	6.91356i	−0.128492	−	0.222555i
$966$	3.18429	−	5.51535i	0.102453	−	0.177454i
$967$	−7.54402			−0.242599			−0.121300	−	0.992616i	$-0.538706\pi$
$967$	−7.54402			−0.242599			−0.121300	+	0.992616i	$0.538706\pi$
$968$	11.9404	−	20.6814i	0.383780	−	0.664726i
$969$	−11.4933	+	19.9070i	−0.369218	+	0.639504i
$970$	−24.1327			−0.774853
$971$	15.2921	−	26.4867i	0.490747	−	0.849999i	−0.509196	−	0.860650i	$-0.670057\pi$
$971$	15.2921	−	26.4867i	0.490747	−	0.849999i	0.999943	+	0.0106517i	$0.00339059\pi$
$972$	1.55787	+	2.69832i	0.0499689	+	0.0865486i
$973$	10.3085	+	17.8548i	0.330475	+	0.572400i
$974$	19.5102			0.625147
$975$	−0.819677	−	3.51114i	−0.0262507	−	0.112447i
$976$	−2.42919			−0.0777564
$977$	17.8405	+	30.9007i	0.570770	+	0.988602i	0.996487	+	0.0837460i	$0.0266884\pi$
$977$	17.8405	+	30.9007i	0.570770	+	0.988602i	−0.425717	+	0.904856i	$0.639978\pi$
$978$	10.9978	+	19.0487i	0.351670	+	0.609111i
$979$	−14.9787	+	25.9438i	−0.478720	+	0.829168i
$980$	−16.8495			−0.538238
$981$	1.13935	−	1.97342i	0.0363768	−	0.0630064i
$982$	−26.2524	+	45.4704i	−0.837747	+	1.45102i
$983$	12.9866			0.414208			0.207104	−	0.978319i	$-0.433596\pi$
$983$	12.9866			0.414208			0.207104	+	0.978319i	$0.433596\pi$
$984$	−1.44609	+	2.50470i	−0.0460997	+	0.0798471i
$985$	−8.66966	−	15.0163i	−0.276238	−	0.478459i
$986$	7.00000	+	12.1244i	0.222925	+	0.386118i
$987$	−13.6091			−0.433181
$988$	13.0652	+	55.9655i	0.415658	+	1.78050i
$989$	14.2315			0.452535
$990$	5.11575	+	8.86074i	0.162589	+	0.281613i
$991$	11.3736	+	19.6996i	0.361294	+	0.625779i	0.988174	−	0.153336i	$-0.0490018\pi$
$991$	11.3736	+	19.6996i	0.361294	+	0.625779i	−0.626880	+	0.779116i	$0.715668\pi$
$992$	−27.6394	+	47.8728i	−0.877550	+	1.51996i
$993$	23.8495			0.756842
$994$	13.7119	−	23.7496i	0.434914	−	0.753293i
$995$	0.615749	−	1.06651i	0.0195206	−	0.0338106i
$996$	25.6473			0.812665
$997$	6.92301	−	11.9910i	0.219254	−	0.379759i	−0.735326	−	0.677713i	$-0.762971\pi$
$997$	6.92301	−	11.9910i	0.219254	−	0.379759i	0.954580	+	0.297955i	$0.0963044\pi$
$998$	32.8405	+	56.8815i	1.03955	+	1.80055i
$999$	−0.115749	−	0.200484i	−0.00366215	−	0.00634303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.i.d.16.3	✓	6
3.2	odd	2		585.2.j.f.406.1		6
5.2	odd	4		975.2.bb.k.874.2		12
5.3	odd	4		975.2.bb.k.874.5		12
5.4	even	2		975.2.i.l.601.1		6
13.3	even	3		2535.2.a.bb.1.1		3
13.9	even	3	inner	195.2.i.d.61.3	yes	6
13.10	even	6		2535.2.a.ba.1.3		3
39.23	odd	6		7605.2.a.bw.1.1		3
39.29	odd	6		7605.2.a.bv.1.3		3
39.35	odd	6		585.2.j.f.451.1		6
65.9	even	6		975.2.i.l.451.1		6
65.22	odd	12		975.2.bb.k.724.5		12
65.48	odd	12		975.2.bb.k.724.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	1.1	even	1	trivial
195.2.i.d.61.3	yes	6	13.9	even	3	inner
585.2.j.f.406.1		6	3.2	odd	2
585.2.j.f.451.1		6	39.35	odd	6
975.2.i.l.451.1		6	65.9	even	6
975.2.i.l.601.1		6	5.4	even	2
975.2.bb.k.724.2		12	65.48	odd	12
975.2.bb.k.724.5		12	65.22	odd	12
975.2.bb.k.874.2		12	5.2	odd	4
975.2.bb.k.874.5		12	5.3	odd	4
2535.2.a.ba.1.3		3	13.10	even	6
2535.2.a.bb.1.1		3	13.3	even	3
7605.2.a.bv.1.3		3	39.29	odd	6
7605.2.a.bw.1.1		3	39.23	odd	6

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13090 + 1.95878i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.55787 + 2.69832i) q^{4} +1.00000 q^{5} +(-1.13090 + 1.95878i) q^{6} +(0.630901 - 1.09275i) q^{7} -2.52360 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.13090 + 1.95878i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.55787 + 2.69832i) q^{4} +1.00000 q^{5} +(-1.13090 + 1.95878i) q^{6} +(0.630901 - 1.09275i) q^{7} -2.52360 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.13090 + 1.95878i) q^{10} +(-2.26180 - 3.91756i) q^{11} -3.11575 q^{12} +(-3.45058 - 1.04571i) q^{13} +2.85395 q^{14} +(0.500000 + 0.866025i) q^{15} +(0.261802 + 0.453455i) q^{16} +(2.24665 - 3.89131i) q^{17} -2.26180 q^{18} +(-2.55787 + 4.43037i) q^{19} +(-1.55787 + 2.69832i) q^{20} +1.26180 q^{21} +(5.11575 - 8.86074i) q^{22} +(-1.11575 - 1.93253i) q^{23} +(-1.26180 - 2.18551i) q^{24} +1.00000 q^{25} +(-1.85395 - 7.94151i) q^{26} -1.00000 q^{27} +(1.96573 + 3.40474i) q^{28} +(0.688776 + 1.19299i) q^{29} +(-1.13090 + 1.95878i) q^{30} +8.87085 q^{31} +(-3.11575 + 5.39664i) q^{32} +(2.26180 - 3.91756i) q^{33} +10.1630 q^{34} +(0.630901 - 1.09275i) q^{35} +(-1.55787 - 2.69832i) q^{36} +(0.115749 + 0.200484i) q^{37} -11.5708 q^{38} +(-0.819677 - 3.51114i) q^{39} -2.52360 q^{40} +(-0.573026 - 0.992511i) q^{41} +(1.42697 + 2.47159i) q^{42} +(-3.18878 + 5.52312i) q^{43} +14.0944 q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.52360 - 4.37101i) q^{46} -10.7854 q^{47} +(-0.261802 + 0.453455i) q^{48} +(2.70393 + 4.68334i) q^{49} +(1.13090 + 1.95878i) q^{50} +4.49330 q^{51} +(8.19723 - 7.68167i) q^{52} +4.52360 q^{53} +(-1.13090 - 1.95878i) q^{54} +(-2.26180 - 3.91756i) q^{55} +(-1.59214 + 2.75768i) q^{56} -5.11575 q^{57} +(-1.55787 + 2.69832i) q^{58} +(0.426974 - 0.739540i) q^{59} -3.11575 q^{60} +(-2.31968 + 4.01780i) q^{61} +(10.0321 + 17.3760i) q^{62} +(0.630901 + 1.09275i) q^{63} -13.0472 q^{64} +(-3.45058 - 1.04571i) q^{65} +10.2315 q^{66} +(-6.56633 - 11.3732i) q^{67} +(7.00000 + 12.1244i) q^{68} +(1.11575 - 1.93253i) q^{69} +2.85395 q^{70} +(4.80453 - 8.32168i) q^{71} +(1.26180 - 2.18551i) q^{72} +13.7854 q^{73} +(-0.261802 + 0.453455i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-7.96970 - 13.8039i) q^{76} -5.70789 q^{77} +(5.95058 - 5.57632i) q^{78} -8.87085 q^{79} +(0.261802 + 0.453455i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.29607 - 2.24486i) q^{82} -8.23150 q^{83} +(-1.96573 + 3.40474i) q^{84} +(2.24665 - 3.89131i) q^{85} -14.4248 q^{86} +(-0.688776 + 1.19299i) q^{87} +(5.70789 + 9.88636i) q^{88} +(-3.31122 - 5.73521i) q^{89} -2.26180 q^{90} +(-3.31968 + 3.11089i) q^{91} +6.95279 q^{92} +(4.43543 + 7.68238i) q^{93} +(-12.1972 - 21.1262i) q^{94} +(-2.55787 + 4.43037i) q^{95} -6.23150 q^{96} +(-5.33483 + 9.24019i) q^{97} +(-6.11575 + 10.5928i) q^{98} +4.52360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

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