LMFDB - Embedded newform 195.2.i.e.16.2

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:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$1.08504 - 1.87935i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.e.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.269594 + 0.466951i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} -1.00000 q^{5} +(-0.269594 + 0.466951i) q^{6} +(2.40049 - 4.15777i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.269594 + 0.466951i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} -1.00000 q^{5} +(-0.269594 + 0.466951i) q^{6} +(2.40049 - 4.15777i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.269594 - 0.466951i) q^{10} +(1.70928 + 2.96055i) q^{11} +1.70928 q^{12} +(-2.25513 + 2.81325i) q^{13} +2.58864 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.17009 - 2.02665i) q^{16} +(-1.43968 + 2.49360i) q^{17} -0.539189 q^{18} +(-2.48554 + 4.30507i) q^{19} +(-0.854638 + 1.48028i) q^{20} +4.80098 q^{21} +(-0.921622 + 1.59630i) q^{22} +(-4.24846 - 7.35856i) q^{23} +(1.00000 + 1.73205i) q^{24} +1.00000 q^{25} +(-1.92162 - 0.294598i) q^{26} -1.00000 q^{27} +(-4.10310 - 7.10678i) q^{28} +(1.75513 + 3.03997i) q^{29} +(0.269594 - 0.466951i) q^{30} +3.04945 q^{31} +(2.63090 - 4.55685i) q^{32} +(-1.70928 + 2.96055i) q^{33} -1.55252 q^{34} +(-2.40049 + 4.15777i) q^{35} +(0.854638 + 1.48028i) q^{36} +(-1.34017 - 2.32125i) q^{37} -2.68035 q^{38} +(-3.56391 - 0.546373i) q^{39} -2.00000 q^{40} +(1.87577 + 3.24893i) q^{41} +(1.29432 + 2.24183i) q^{42} +(-0.794319 + 1.37580i) q^{43} +5.84324 q^{44} +(0.500000 - 0.866025i) q^{45} +(2.29072 - 3.96765i) q^{46} -0.539189 q^{47} +(1.17009 - 2.02665i) q^{48} +(-8.02472 - 13.8992i) q^{49} +(0.269594 + 0.466951i) q^{50} -2.87936 q^{51} +(2.23707 + 5.74253i) q^{52} -13.7587 q^{53} +(-0.269594 - 0.466951i) q^{54} +(-1.70928 - 2.96055i) q^{55} +(4.80098 - 8.31555i) q^{56} -4.97107 q^{57} +(-0.946346 + 1.63912i) q^{58} +(-4.20261 + 7.27913i) q^{59} -1.70928 q^{60} +(1.52472 - 2.64090i) q^{61} +(0.822114 + 1.42394i) q^{62} +(2.40049 + 4.15777i) q^{63} -1.84324 q^{64} +(2.25513 - 2.81325i) q^{65} -1.84324 q^{66} +(6.42522 + 11.1288i) q^{67} +(2.46081 + 4.26225i) q^{68} +(4.24846 - 7.35856i) q^{69} -2.58864 q^{70} +(-1.04585 + 1.81147i) q^{71} +(-1.00000 + 1.73205i) q^{72} -5.53919 q^{73} +(0.722606 - 1.25159i) q^{74} +(0.500000 + 0.866025i) q^{75} +(4.24846 + 7.35856i) q^{76} +16.4124 q^{77} +(-0.705681 - 1.81147i) q^{78} +2.21235 q^{79} +(1.17009 + 2.02665i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.01139 + 1.75178i) q^{82} +4.34017 q^{83} +(4.10310 - 7.10678i) q^{84} +(1.43968 - 2.49360i) q^{85} -0.856576 q^{86} +(-1.75513 + 3.03997i) q^{87} +(3.41855 + 5.92110i) q^{88} +(3.50667 + 6.07372i) q^{89} +0.539189 q^{90} +(6.28345 + 16.1295i) q^{91} -14.5236 q^{92} +(1.52472 + 2.64090i) q^{93} +(-0.145362 - 0.251775i) q^{94} +(2.48554 - 4.30507i) q^{95} +5.26180 q^{96} +(7.13449 - 12.3573i) q^{97} +(4.32684 - 7.49431i) q^{98} -3.41855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 2 q^{4} - 6 q^{5} + 5 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 2 * q^4 - 6 * q^5 + 5 * q^7 + 12 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 2 q^{4} - 6 q^{5} + 5 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{11} - 4 q^{12} + 3 q^{13} - 24 q^{14} - 3 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{20} + 10 q^{21} - 12 q^{22} - 8 q^{23} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 6 q^{29} - 18 q^{31} + 8 q^{32} + 4 q^{33} - 8 q^{34} - 5 q^{35} - 2 q^{36} + 14 q^{37} + 28 q^{38} - 12 q^{40} + 20 q^{41} - 12 q^{42} + 15 q^{43} + 48 q^{44} + 3 q^{45} + 28 q^{46} - 4 q^{48} - 30 q^{49} + 8 q^{51} + 16 q^{52} - 32 q^{53} + 4 q^{55} + 10 q^{56} + 6 q^{58} - 10 q^{59} + 4 q^{60} - 9 q^{61} + 2 q^{62} + 5 q^{63} - 24 q^{64} - 3 q^{65} - 24 q^{66} + 11 q^{67} + 18 q^{68} + 8 q^{69} + 24 q^{70} - 4 q^{71} - 6 q^{72} - 30 q^{73} - 8 q^{74} + 3 q^{75} + 8 q^{76} - 24 q^{78} + 34 q^{79} - 4 q^{80} - 3 q^{81} + 14 q^{82} + 4 q^{83} - 4 q^{85} - 20 q^{86} + 6 q^{87} - 8 q^{88} + 22 q^{89} - 31 q^{91} - 56 q^{92} - 9 q^{93} - 8 q^{94} + 16 q^{96} + q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 2 * q^4 - 6 * q^5 + 5 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^11 - 4 * q^12 + 3 * q^13 - 24 * q^14 - 3 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^20 + 10 * q^21 - 12 * q^22 - 8 * q^23 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 6 * q^29 - 18 * q^31 + 8 * q^32 + 4 * q^33 - 8 * q^34 - 5 * q^35 - 2 * q^36 + 14 * q^37 + 28 * q^38 - 12 * q^40 + 20 * q^41 - 12 * q^42 + 15 * q^43 + 48 * q^44 + 3 * q^45 + 28 * q^46 - 4 * q^48 - 30 * q^49 + 8 * q^51 + 16 * q^52 - 32 * q^53 + 4 * q^55 + 10 * q^56 + 6 * q^58 - 10 * q^59 + 4 * q^60 - 9 * q^61 + 2 * q^62 + 5 * q^63 - 24 * q^64 - 3 * q^65 - 24 * q^66 + 11 * q^67 + 18 * q^68 + 8 * q^69 + 24 * q^70 - 4 * q^71 - 6 * q^72 - 30 * q^73 - 8 * q^74 + 3 * q^75 + 8 * q^76 - 24 * q^78 + 34 * q^79 - 4 * q^80 - 3 * q^81 + 14 * q^82 + 4 * q^83 - 4 * q^85 - 20 * q^86 + 6 * q^87 - 8 * q^88 + 22 * q^89 - 31 * q^91 - 56 * q^92 - 9 * q^93 - 8 * q^94 + 16 * q^96 + q^97 + 2 * q^98 + 8 * q^99

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 $

$2$	0.269594	+	0.466951i	0.190632	+	0.330184i	0.945460	−	0.325739i	$-0.105613\pi$
$2$	0.269594	+	0.466951i	0.190632	+	0.330184i	−0.754828	+	0.655923i	$0.772280\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.854638	−	1.48028i	0.427319	−	0.740138i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.269594	+	0.466951i	−0.110061	+	0.190632i
$7$	2.40049	−	4.15777i	0.907301	−	1.57149i	0.0895019	−	0.995987i	$-0.471472\pi$
$7$	2.40049	−	4.15777i	0.907301	−	1.57149i	0.817799	−	0.575504i	$-0.195194\pi$
$8$	2.00000			0.707107
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.269594	−	0.466951i	−0.0852532	−	0.147663i
$11$	1.70928	+	2.96055i	0.515366	+	0.892640i	0.999841	+	0.0178349i	$0.00567731\pi$
$11$	1.70928	+	2.96055i	0.515366	+	0.892640i	−0.484475	+	0.874805i	$0.660989\pi$
$12$	1.70928			0.493425
$13$	−2.25513	+	2.81325i	−0.625460	+	0.780256i
$13$	−2.25513	+	2.81325i	−0.625460	+	0.780256i
$14$	2.58864			0.691842
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−1.17009	−	2.02665i	−0.292522	−	0.506662i
$17$	−1.43968	+	2.49360i	−0.349174	+	0.604787i	−0.986103	−	0.166135i	$-0.946871\pi$
$17$	−1.43968	+	2.49360i	−0.349174	+	0.604787i	0.636929	+	0.770922i	$0.280204\pi$
$18$	−0.539189			−0.127088
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	0.426322	+	0.904571i	$0.359809\pi$
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	−0.996543	+	0.0830801i	$0.973524\pi$
$20$	−0.854638	+	1.48028i	−0.191103	+	0.331000i
$21$	4.80098			1.04766
$22$	−0.921622	+	1.59630i	−0.196491	+	0.340332i
$23$	−4.24846	−	7.35856i	−0.885866	−	1.53436i	−0.844718	−	0.535212i	$-0.820232\pi$
$23$	−4.24846	−	7.35856i	−0.885866	−	1.53436i	−0.0411482	−	0.999153i	$-0.513102\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$	1.00000			0.200000
$26$	−1.92162	−	0.294598i	−0.376861	−	0.0577755i
$27$	−1.00000			−0.192450
$28$	−4.10310	−	7.10678i	−0.775413	−	1.34306i
$29$	1.75513	+	3.03997i	0.325919	+	0.564509i	0.981698	−	0.190444i	$-0.0609929\pi$
$29$	1.75513	+	3.03997i	0.325919	+	0.564509i	−0.655779	+	0.754953i	$0.727660\pi$
$30$	0.269594	−	0.466951i	0.0492210	−	0.0852532i
$31$	3.04945			0.547697			0.273849	−	0.961773i	$-0.411703\pi$
$31$	3.04945			0.547697			0.273849	+	0.961773i	$0.411703\pi$
$32$	2.63090	−	4.55685i	0.465081	−	0.805545i
$33$	−1.70928	+	2.96055i	−0.297547	+	0.515366i
$34$	−1.55252			−0.266255
$35$	−2.40049	+	4.15777i	−0.405757	+	0.702792i
$36$	0.854638	+	1.48028i	0.142440	+	0.246713i
$37$	−1.34017	−	2.32125i	−0.220323	−	0.381611i	0.734583	−	0.678519i	$-0.237378\pi$
$37$	−1.34017	−	2.32125i	−0.220323	−	0.381611i	−0.954906	+	0.296908i	$0.904044\pi$
$38$	−2.68035			−0.434810
$39$	−3.56391	−	0.546373i	−0.570683	−	0.0874898i
$40$	−2.00000			−0.316228
$41$	1.87577	+	3.24893i	0.292946	+	0.507397i	0.974505	−	0.224366i	$-0.0720311\pi$
$41$	1.87577	+	3.24893i	0.292946	+	0.507397i	−0.681559	+	0.731763i	$0.738698\pi$
$42$	1.29432	+	2.24183i	0.199718	+	0.345921i
$43$	−0.794319	+	1.37580i	−0.121132	+	0.209808i	−0.920215	−	0.391414i	$-0.871986\pi$
$43$	−0.794319	+	1.37580i	−0.121132	+	0.209808i	0.799082	+	0.601222i	$0.205319\pi$
$44$	5.84324			0.880902
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	2.29072	−	3.96765i	0.337749	−	0.584998i
$47$	−0.539189			−0.0786488			−0.0393244	−	0.999226i	$-0.512521\pi$
$47$	−0.539189			−0.0786488			−0.0393244	+	0.999226i	$0.512521\pi$
$48$	1.17009	−	2.02665i	0.168887	−	0.292522i
$49$	−8.02472	−	13.8992i	−1.14639	−	1.98560i
$50$	0.269594	+	0.466951i	0.0381264	+	0.0660369i
$51$	−2.87936			−0.403191
$52$	2.23707	+	5.74253i	0.310226	+	0.796345i
$53$	−13.7587			−1.88991			−0.944953	−	0.327206i	$-0.893893\pi$
$53$	−13.7587			−1.88991			−0.944953	+	0.327206i	$0.893893\pi$
$54$	−0.269594	−	0.466951i	−0.0366872	−	0.0635440i
$55$	−1.70928	−	2.96055i	−0.230479	−	0.399201i
$56$	4.80098	−	8.31555i	0.641558	−	1.11121i
$57$	−4.97107			−0.658434
$58$	−0.946346	+	1.63912i	−0.124261	+	0.215227i
$59$	−4.20261	+	7.27913i	−0.547133	+	0.947663i	0.451336	+	0.892354i	$0.350948\pi$
$59$	−4.20261	+	7.27913i	−0.547133	+	0.947663i	−0.998469	+	0.0553085i	$0.982386\pi$
$60$	−1.70928			−0.220667
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	−0.751752	−	0.659446i	$-0.770791\pi$
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	0.946973	+	0.321313i	$0.104124\pi$
$62$	0.822114	+	1.42394i	0.104409	+	0.180841i
$63$	2.40049	+	4.15777i	0.302434	+	0.523830i
$64$	−1.84324			−0.230406
$65$	2.25513	−	2.81325i	0.279714	−	0.348941i
$66$	−1.84324			−0.226888
$67$	6.42522	+	11.1288i	0.784965	+	1.35960i	0.929020	+	0.370030i	$0.120653\pi$
$67$	6.42522	+	11.1288i	0.784965	+	1.35960i	−0.144055	+	0.989570i	$0.546014\pi$
$68$	2.46081	+	4.26225i	0.298417	+	0.516874i
$69$	4.24846	−	7.35856i	0.511455	−	0.885866i
$70$	−2.58864			−0.309401
$71$	−1.04585	+	1.81147i	−0.124120	+	0.214982i	−0.921389	−	0.388642i	$-0.872944\pi$
$71$	−1.04585	+	1.81147i	−0.124120	+	0.214982i	0.797269	+	0.603625i	$0.206277\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−5.53919			−0.648313			−0.324157	−	0.946003i	$-0.605080\pi$
$73$	−5.53919			−0.648313			−0.324157	+	0.946003i	$0.605080\pi$
$74$	0.722606	−	1.25159i	0.0840013	−	0.145494i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	4.24846	+	7.35856i	0.487332	+	0.844084i
$77$	16.4124			1.87037
$78$	−0.705681	−	1.81147i	−0.0799027	−	0.205109i
$79$	2.21235			0.248908			0.124454	−	0.992225i	$-0.460282\pi$
$79$	2.21235			0.248908			0.124454	+	0.992225i	$0.460282\pi$
$80$	1.17009	+	2.02665i	0.130820	+	0.226586i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.01139	+	1.75178i	−0.111690	+	0.193452i
$83$	4.34017			0.476396			0.238198	−	0.971217i	$-0.423443\pi$
$83$	4.34017			0.476396			0.238198	+	0.971217i	$0.423443\pi$
$84$	4.10310	−	7.10678i	0.447685	−	0.775413i
$85$	1.43968	−	2.49360i	0.156155	−	0.270469i
$86$	−0.856576			−0.0923669
$87$	−1.75513	+	3.03997i	−0.188170	+	0.325919i
$88$	3.41855	+	5.92110i	0.364419	+	0.631192i
$89$	3.50667	+	6.07372i	0.371706	+	0.643813i	0.989828	−	0.142269i	$-0.0454397\pi$
$89$	3.50667	+	6.07372i	0.371706	+	0.643813i	−0.618122	+	0.786082i	$0.712106\pi$
$90$	0.539189			0.0568355
$91$	6.28345	+	16.1295i	0.658684	+	1.69083i
$92$	−14.5236			−1.51419
$93$	1.52472	+	2.64090i	0.158107	+	0.273849i
$94$	−0.145362	−	0.251775i	−0.0149930	−	0.0259686i
$95$	2.48554	−	4.30507i	0.255011	−	0.441691i
$96$	5.26180			0.537030
$97$	7.13449	−	12.3573i	0.724398	−	1.25469i	−0.234824	−	0.972038i	$-0.575451\pi$
$97$	7.13449	−	12.3573i	0.724398	−	1.25469i	0.959221	−	0.282656i	$-0.0912154\pi$
$98$	4.32684	−	7.49431i	0.437077	−	0.757040i
$99$	−3.41855			−0.343577
$100$	0.854638	−	1.48028i	0.0854638	−	0.148028i
$101$	−6.24846	−	10.8227i	−0.621745	−	1.07689i	−0.989161	−	0.146838i	$-0.953091\pi$
$101$	−6.24846	−	10.8227i	−0.621745	−	1.07689i	0.367415	−	0.930057i	$-0.380243\pi$
$102$	−0.776260	−	1.34452i	−0.0768612	−	0.133127i
$103$	6.85043			0.674993			0.337497	−	0.941327i	$-0.390420\pi$
$103$	6.85043			0.674993			0.337497	+	0.941327i	$0.390420\pi$
$104$	−4.51026	+	5.62651i	−0.442267	+	0.551724i
$105$	−4.80098			−0.468528
$106$	−3.70928	−	6.42465i	−0.360277	−	0.624018i
$107$	−7.77985	−	13.4751i	−0.752107	−	1.30269i	−0.946800	−	0.321823i	$-0.895704\pi$
$107$	−7.77985	−	13.4751i	−0.752107	−	1.30269i	0.194693	−	0.980864i	$-0.437629\pi$
$108$	−0.854638	+	1.48028i	−0.0822375	+	0.142440i
$109$	15.8371			1.51692			0.758460	−	0.651720i	$-0.225952\pi$
$109$	15.8371			1.51692			0.758460	+	0.651720i	$0.225952\pi$
$110$	0.921622	−	1.59630i	0.0878732	−	0.152201i
$111$	1.34017	−	2.32125i	0.127204	−	0.220323i
$112$	−11.2351			−1.06162
$113$	1.53919	−	2.66595i	0.144795	−	0.250792i	−0.784502	−	0.620127i	$-0.787081\pi$
$113$	1.53919	−	2.66595i	0.144795	−	0.250792i	0.929296	+	0.369335i	$0.120414\pi$
$114$	−1.34017	−	2.32125i	−0.125519	−	0.217405i
$115$	4.24846	+	7.35856i	0.396171	+	0.686189i
$116$	6.00000			0.557086
$117$	−1.30878	−	3.35963i	−0.120997	−	0.310598i
$118$	−4.53200			−0.417205
$119$	6.91189	+	11.9717i	0.633611	+	1.09745i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−0.343245	+	0.594517i	−0.0312040	+	0.0540470i
$122$	1.64423			0.148861
$123$	−1.87577	+	3.24893i	−0.169132	+	0.292946i
$124$	2.60617	−	4.51402i	0.234041	−	0.405371i
$125$	−1.00000			−0.0894427
$126$	−1.29432	+	2.24183i	−0.115307	+	0.199718i
$127$	3.72733	+	6.45593i	0.330747	+	0.572871i	0.982659	−	0.185424i	$-0.0593659\pi$
$127$	3.72733	+	6.45593i	0.330747	+	0.572871i	−0.651911	+	0.758295i	$0.726033\pi$
$128$	−5.75872	−	9.97440i	−0.509004	−	0.881621i
$129$	−1.58864			−0.139872
$130$	1.92162	+	0.294598i	0.168537	+	0.0258380i
$131$	11.6937			1.02168			0.510841	−	0.859675i	$-0.329334\pi$
$131$	11.6937			1.02168			0.510841	+	0.859675i	$0.329334\pi$
$132$	2.92162	+	5.06040i	0.254295	+	0.440451i
$133$	11.9330	+	20.6686i	1.03472	+	1.79219i
$134$	−3.46441	+	6.00053i	−0.299279	+	0.518366i
$135$	1.00000			0.0860663
$136$	−2.87936	+	4.98720i	−0.246903	+	0.427649i
$137$	4.63870	−	8.03446i	0.396311	−	0.686430i	−0.596957	−	0.802273i	$-0.703624\pi$
$137$	4.63870	−	8.03446i	0.396311	−	0.686430i	0.993268	+	0.115843i	$0.0369570\pi$
$138$	4.58145			0.389999
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	0.450691	+	0.892680i	$0.351178\pi$
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	−0.998429	+	0.0560304i	$0.982156\pi$
$140$	4.10310	+	7.10678i	0.346775	+	0.600633i
$141$	−0.269594	−	0.466951i	−0.0227039	−	0.0393244i
$142$	−1.12783			−0.0946451
$143$	−12.1834	−	1.86781i	−1.01883	−	0.156194i
$144$	2.34017			0.195014
$145$	−1.75513	−	3.03997i	−0.145756	−	0.252456i
$146$	−1.49333	−	2.58653i	−0.123589	−	0.214063i
$147$	8.02472	−	13.8992i	0.661868	−	1.14639i
$148$	−4.58145			−0.376593
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$	−0.269594	+	0.466951i	−0.0220123	+	0.0381264i
$151$	−8.60424			−0.700203			−0.350101	−	0.936712i	$-0.613853\pi$
$151$	−8.60424			−0.700203			−0.350101	+	0.936712i	$0.613853\pi$
$152$	−4.97107	+	8.61015i	−0.403207	+	0.698375i
$153$	−1.43968	−	2.49360i	−0.116391	−	0.201596i
$154$	4.42469	+	7.66379i	0.356552	+	0.617566i
$155$	−3.04945			−0.244938
$156$	−3.85464	+	4.80862i	−0.308618	+	0.384998i
$157$	0.908291			0.0724895			0.0362448	−	0.999343i	$-0.488460\pi$
$157$	0.908291			0.0724895			0.0362448	+	0.999343i	$0.488460\pi$
$158$	0.596436	+	1.03306i	0.0474499	+	0.0821857i
$159$	−6.87936	−	11.9154i	−0.545569	−	0.944953i
$160$	−2.63090	+	4.55685i	−0.207991	+	0.360250i
$161$	−40.7936			−3.21499
$162$	0.269594	−	0.466951i	0.0211813	−	0.0366872i
$163$	7.32211	−	12.6823i	0.573512	−	0.993352i	−0.422689	−	0.906275i	$-0.638914\pi$
$163$	7.32211	−	12.6823i	0.573512	−	0.993352i	0.996202	−	0.0870777i	$-0.0277528\pi$
$164$	6.41241			0.500725
$165$	1.70928	−	2.96055i	0.133067	−	0.230479i
$166$	1.17009	+	2.02665i	0.0908163	+	0.157298i
$167$	2.44748	+	4.23916i	0.189392	+	0.328036i	0.945048	−	0.326933i	$-0.106015\pi$
$167$	2.44748	+	4.23916i	0.189392	+	0.328036i	−0.755656	+	0.654969i	$0.772682\pi$
$168$	9.60197			0.740808
$169$	−2.82878	−	12.6885i	−0.217598	−	0.976038i
$170$	1.55252			0.119073
$171$	−2.48554	−	4.30507i	−0.190074	−	0.329217i
$172$	1.35771	+	2.35162i	0.103524	+	0.179309i
$173$	8.77985	−	15.2072i	0.667520	−	1.15618i	−0.311076	−	0.950385i	$-0.600689\pi$
$173$	8.77985	−	15.2072i	0.667520	−	1.15618i	0.978595	−	0.205793i	$-0.0659774\pi$
$174$	−1.89269			−0.143485
$175$	2.40049	−	4.15777i	0.181460	−	0.314298i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	−8.40522			−0.631775
$178$	−1.89076	+	3.27488i	−0.141718	+	0.245463i
$179$	−0.692350	−	1.19919i	−0.0517487	−	0.0896314i	0.838991	−	0.544146i	$-0.183146\pi$
$179$	−0.692350	−	1.19919i	−0.0517487	−	0.0896314i	−0.890739	+	0.454514i	$0.849813\pi$
$180$	−0.854638	−	1.48028i	−0.0637009	−	0.110333i
$181$	−7.46800			−0.555092			−0.277546	−	0.960712i	$-0.589521\pi$
$181$	−7.46800			−0.555092			−0.277546	+	0.960712i	$0.589521\pi$
$182$	−5.83771	+	7.28249i	−0.432720	+	0.539814i
$183$	3.04945			0.225422
$184$	−8.49693	−	14.7171i	−0.626402	−	1.08496i
$185$	1.34017	+	2.32125i	0.0985315	+	0.170662i
$186$	−0.822114	+	1.42394i	−0.0602803	+	0.104409i
$187$	−9.84324			−0.719809
$188$	−0.460811	+	0.798148i	−0.0336081	+	0.0582109i
$189$	−2.40049	+	4.15777i	−0.174610	+	0.302434i
$190$	2.68035			0.194453
$191$	1.20261	−	2.08298i	0.0870178	−	0.150719i	−0.819231	−	0.573463i	$-0.805600\pi$
$191$	1.20261	−	2.08298i	0.0870178	−	0.150719i	0.906249	+	0.422744i	$0.138933\pi$
$192$	−0.921622	−	1.59630i	−0.0665124	−	0.115203i
$193$	7.91075	+	13.7018i	0.569428	+	0.986279i	0.996623	+	0.0821189i	$0.0261687\pi$
$193$	7.91075	+	13.7018i	0.569428	+	0.986279i	−0.427194	+	0.904160i	$0.640498\pi$
$194$	7.69368			0.552374
$195$	3.56391	+	0.546373i	0.255217	+	0.0391266i
$196$	−27.4329			−1.95949
$197$	−9.23287	−	15.9918i	−0.657814	−	1.13937i	−0.981180	−	0.193094i	$-0.938148\pi$
$197$	−9.23287	−	15.9918i	−0.657814	−	1.13937i	0.323366	−	0.946274i	$-0.395186\pi$
$198$	−0.921622	−	1.59630i	−0.0654968	−	0.113444i
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	−0.992158	−	0.124991i	$-0.960110\pi$
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	0.604324	+	0.796739i	$0.293443\pi$
$200$	2.00000			0.141421
$201$	−6.42522	+	11.1288i	−0.453200	+	0.784965i
$202$	3.36910	−	5.83546i	0.237049	−	0.410581i
$203$	16.8527			1.18283
$204$	−2.46081	+	4.26225i	−0.172291	+	0.298417i
$205$	−1.87577	−	3.24893i	−0.131009	−	0.226915i
$206$	1.84684	+	3.19882i	0.128675	+	0.222872i
$207$	8.49693			0.590577
$208$	8.34017	+	1.27861i	0.578287	+	0.0886555i
$209$	−16.9939			−1.17549
$210$	−1.29432	−	2.24183i	−0.0893165	−	0.154701i
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	0.999905	−	0.0137992i	$-0.00439257\pi$
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	−0.511903	+	0.859043i	$0.671059\pi$
$212$	−11.7587	+	20.3667i	−0.807592	+	1.39879i
$213$	−2.09171			−0.143322
$214$	4.19481	−	7.26563i	0.286751	−	0.496668i
$215$	0.794319	−	1.37580i	0.0541721	−	0.0938288i
$216$	−2.00000			−0.136083
$217$	7.32018	−	12.6789i	0.496926	−	0.860701i
$218$	4.26959	+	7.39515i	0.289173	+	0.500863i
$219$	−2.76959	−	4.79708i	−0.187152	−	0.324157i
$220$	−5.84324			−0.393951
$221$	−3.76846	−	9.67358i	−0.253494	−	0.650715i
$222$	1.44521			0.0969963
$223$	2.82991	+	4.90155i	0.189505	+	0.328232i	0.945085	−	0.326824i	$-0.105978\pi$
$223$	2.82991	+	4.90155i	0.189505	+	0.328232i	−0.755580	+	0.655056i	$0.772645\pi$
$224$	−12.6309	−	21.8774i	−0.843937	−	1.46174i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	1.65983			0.110410
$227$	−10.4397	+	18.0821i	−0.692906	+	1.20015i	0.277976	+	0.960588i	$0.410337\pi$
$227$	−10.4397	+	18.0821i	−0.692906	+	1.20015i	−0.970882	+	0.239560i	$0.922997\pi$
$228$	−4.24846	+	7.35856i	−0.281361	+	0.487332i
$229$	−11.5525			−0.763412			−0.381706	−	0.924284i	$-0.624663\pi$
$229$	−11.5525			−0.763412			−0.381706	+	0.924284i	$0.624663\pi$
$230$	−2.29072	+	3.96765i	−0.151046	+	0.261619i
$231$	8.20620	+	14.2136i	0.539929	+	0.935184i
$232$	3.51026	+	6.07995i	0.230460	+	0.399168i
$233$	−3.73206			−0.244495			−0.122248	−	0.992500i	$-0.539010\pi$
$233$	−3.73206			−0.244495			−0.122248	+	0.992500i	$0.539010\pi$
$234$	1.21594	−	1.51687i	0.0794885	−	0.0991612i
$235$	0.539189			0.0351728
$236$	7.18342	+	12.4420i	0.467601	+	0.809908i
$237$	1.10617	+	1.91595i	0.0718537	+	0.124454i
$238$	−3.72681	+	6.45503i	−0.241573	+	0.418417i
$239$	27.0928			1.75248			0.876242	−	0.481871i	$-0.160043\pi$
$239$	27.0928			1.75248			0.876242	+	0.481871i	$0.160043\pi$
$240$	−1.17009	+	2.02665i	−0.0755288	+	0.130820i
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	−0.182784	−	0.983153i	$-0.558511\pi$
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	0.942828	−	0.333281i	$-0.108156\pi$
$242$	−0.370147			−0.0237940
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.60617	−	4.51402i	−0.166843	−	0.288981i
$245$	8.02472	+	13.8992i	0.512681	+	0.887989i
$246$	−2.02279			−0.128968
$247$	−6.50605	−	16.7009i	−0.413970	−	1.06266i
$248$	6.09890			0.387280
$249$	2.17009	+	3.75870i	0.137524	+	0.238198i
$250$	−0.269594	−	0.466951i	−0.0170506	−	0.0295326i
$251$	13.4319	−	23.2647i	0.847813	−	1.46845i	−0.0353430	−	0.999375i	$-0.511252\pi$
$251$	13.4319	−	23.2647i	0.847813	−	1.46845i	0.883156	−	0.469080i	$-0.155414\pi$
$252$	8.20620			0.516942
$253$	14.5236	−	25.1556i	0.913090	−	1.58152i
$254$	−2.00974	+	3.48097i	−0.126102	+	0.218415i
$255$	2.87936			0.180313
$256$	1.26180	−	2.18549i	0.0788622	−	0.136593i
$257$	1.75933	+	3.04726i	0.109744	+	0.190083i	0.915667	−	0.401939i	$-0.131663\pi$
$257$	1.75933	+	3.04726i	0.109744	+	0.190083i	−0.805922	+	0.592021i	$0.798330\pi$
$258$	−0.428288	−	0.741816i	−0.0266640	−	0.0461835i
$259$	−12.8683			−0.799597
$260$	−2.23707	−	5.74253i	−0.138737	−	0.356136i
$261$	−3.51026			−0.217280
$262$	3.15255	+	5.46038i	0.194765	+	0.337343i
$263$	4.42635	+	7.66666i	0.272940	+	0.472747i	0.969613	−	0.244642i	$-0.0786705\pi$
$263$	4.42635	+	7.66666i	0.272940	+	0.472747i	−0.696673	+	0.717389i	$0.745337\pi$
$264$	−3.41855	+	5.92110i	−0.210397	+	0.364419i
$265$	13.7587			0.845192
$266$	−6.43415	+	11.1443i	−0.394503	+	0.683299i
$267$	−3.50667	+	6.07372i	−0.214604	+	0.371706i
$268$	21.9649			1.34172
$269$	−13.6212	+	23.5925i	−0.830497	+	1.43846i	0.0671480	+	0.997743i	$0.478610\pi$
$269$	−13.6212	+	23.5925i	−0.830497	+	1.43846i	−0.897645	+	0.440720i	$0.854723\pi$
$270$	0.269594	+	0.466951i	0.0164070	+	0.0284177i
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	0.574964	−	0.818179i	$-0.305016\pi$
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	−0.996046	+	0.0888438i	$0.971683\pi$
$272$	6.73820			0.408564
$273$	−10.8268	+	13.5064i	−0.655270	+	0.817443i
$274$	5.00227			0.302198
$275$	1.70928	+	2.96055i	0.103073	+	0.178528i
$276$	−7.26180	−	12.5778i	−0.437109	−	0.757094i
$277$	−1.29072	+	2.23560i	−0.0775521	+	0.134324i	−0.902193	−	0.431332i	$-0.858044\pi$
$277$	−1.29072	+	2.23560i	−0.0775521	+	0.134324i	0.824641	+	0.565656i	$0.191377\pi$
$278$	−6.96388			−0.417666
$279$	−1.52472	+	2.64090i	−0.0912828	+	0.158107i
$280$	−4.80098	+	8.31555i	−0.286914	+	0.496949i
$281$	−5.35350			−0.319363			−0.159682	−	0.987169i	$-0.551047\pi$
$281$	−5.35350			−0.319363			−0.159682	+	0.987169i	$0.551047\pi$
$282$	0.145362	−	0.251775i	0.00865620	−	0.0149930i
$283$	−7.94687	−	13.7644i	−0.472392	−	0.818207i	0.527109	−	0.849798i	$-0.323276\pi$
$283$	−7.94687	−	13.7644i	−0.472392	−	0.818207i	−0.999501	+	0.0315904i	$0.989943\pi$
$284$	1.78765	+	3.09631i	0.106078	+	0.183732i
$285$	4.97107			0.294461
$286$	−2.41241	−	6.19261i	−0.142649	−	0.366177i
$287$	18.0111			1.06316
$288$	2.63090	+	4.55685i	0.155027	+	0.268515i
$289$	4.35464	+	7.54245i	0.256155	+	0.443674i
$290$	0.946346	−	1.63912i	0.0555714	−	0.0962524i
$291$	14.2690			0.836463
$292$	−4.73400	+	8.19953i	−0.277036	+	0.479841i
$293$	1.24067	−	2.14889i	0.0724804	−	0.125540i	−0.827507	−	0.561455i	$-0.810242\pi$
$293$	1.24067	−	2.14889i	0.0724804	−	0.125540i	0.899988	+	0.435915i	$0.143575\pi$
$294$	8.65368			0.504693
$295$	4.20261	−	7.27913i	0.244685	−	0.423808i
$296$	−2.68035	−	4.64250i	−0.155792	−	0.269840i
$297$	−1.70928	−	2.96055i	−0.0991822	−	0.171789i
$298$	1.07838			0.0624687
$299$	30.2823	+	4.64250i	1.75127	+	0.268482i
$300$	1.70928			0.0986851
$301$	3.81351	+	6.60519i	0.219807	+	0.380717i
$302$	−2.31965	−	4.01776i	−0.133481	−	0.231196i
$303$	6.24846	−	10.8227i	0.358965	−	0.621745i
$304$	11.6332			0.667208
$305$	−1.52472	+	2.64090i	−0.0873055	+	0.151217i
$306$	0.776260	−	1.34452i	0.0443758	−	0.0768612i
$307$	−22.2423			−1.26944			−0.634718	−	0.772744i	$-0.718884\pi$
$307$	−22.2423			−1.26944			−0.634718	+	0.772744i	$0.718884\pi$
$308$	14.0267	−	24.2949i	0.799243	−	1.38433i
$309$	3.42522	+	5.93265i	0.194854	+	0.337497i
$310$	−0.822114	−	1.42394i	−0.0466930	−	0.0808746i
$311$	−0.405220			−0.0229779			−0.0114890	−	0.999934i	$-0.503657\pi$
$311$	−0.405220			−0.0229779			−0.0114890	+	0.999934i	$0.503657\pi$
$312$	−7.12783	−	1.09275i	−0.403534	−	0.0618646i
$313$	−0.353504			−0.0199812			−0.00999061	−	0.999950i	$-0.503180\pi$
$313$	−0.353504			−0.0199812			−0.00999061	+	0.999950i	$0.503180\pi$
$314$	0.244870	+	0.424128i	0.0138188	+	0.0239349i
$315$	−2.40049	−	4.15777i	−0.135252	−	0.234264i
$316$	1.89076	−	3.27488i	0.106363	−	0.184227i
$317$	25.3028			1.42115			0.710574	−	0.703622i	$-0.248435\pi$
$317$	25.3028			1.42115			0.710574	+	0.703622i	$0.248435\pi$
$318$	3.70928	−	6.42465i	0.208006	−	0.360277i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	1.84324			0.103041
$321$	7.77985	−	13.4751i	0.434229	−	0.752107i
$322$	−10.9977	−	19.0486i	−0.612880	−	1.06154i
$323$	−7.15676	−	12.3959i	−0.398213	−	0.689724i
$324$	−1.70928			−0.0949597
$325$	−2.25513	+	2.81325i	−0.125092	+	0.156051i
$326$	7.89601			0.437319
$327$	7.91855	+	13.7153i	0.437897	+	0.758460i
$328$	3.75154	+	6.49785i	0.207144	+	0.358784i
$329$	−1.29432	+	2.24183i	−0.0713581	+	0.123596i
$330$	1.84324			0.101467
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	−0.922308	−	0.386456i	$-0.873699\pi$
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	0.795834	+	0.605514i	$0.207033\pi$
$332$	3.70928	−	6.42465i	0.203573	−	0.352599i
$333$	2.68035			0.146882
$334$	−1.31965	+	2.28571i	−0.0722083	+	0.125068i
$335$	−6.42522	−	11.1288i	−0.351047	−	0.608031i
$336$	−5.61757	−	9.72991i	−0.306463	−	0.530810i
$337$	−31.0338			−1.69052			−0.845261	−	0.534354i	$-0.820555\pi$
$337$	−31.0338			−1.69052			−0.845261	+	0.534354i	$0.820555\pi$
$338$	5.16229	−	4.74165i	0.280791	−	0.257912i
$339$	3.07838			0.167195
$340$	−2.46081	−	4.26225i	−0.133456	−	0.231153i
$341$	5.21235	+	9.02805i	0.282264	+	0.488896i
$342$	1.34017	−	2.32125i	0.0724683	−	0.125519i
$343$	−43.4463			−2.34588
$344$	−1.58864	+	2.75160i	−0.0856536	+	0.148356i
$345$	−4.24846	+	7.35856i	−0.228730	+	0.396171i
$346$	9.46800			0.509003
$347$	8.97826	−	15.5508i	0.481978	−	0.834811i	−0.517808	−	0.855497i	$-0.673252\pi$
$347$	8.97826	−	15.5508i	0.481978	−	0.834811i	0.999786	+	0.0206863i	$0.00658511\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	0.864668	−	0.502343i	$-0.167529\pi$
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	−0.867376	+	0.497653i	$0.834195\pi$
$350$	2.58864			0.138368
$351$	2.25513	−	2.81325i	0.120370	−	0.150160i
$352$	17.9877			0.958748
$353$	14.6803	+	25.4271i	0.781356	+	1.35335i	0.931152	+	0.364631i	$0.118805\pi$
$353$	14.6803	+	25.4271i	0.781356	+	1.35335i	−0.149796	+	0.988717i	$0.547862\pi$
$354$	−2.26600	−	3.92483i	−0.120437	−	0.208602i
$355$	1.04585	−	1.81147i	0.0555082	−	0.0961430i
$356$	11.9877			0.635348
$357$	−6.91189	+	11.9717i	−0.365816	+	0.633611i
$358$	0.373308	−	0.646588i	0.0197299	−	0.0341732i
$359$	−11.5369			−0.608895			−0.304448	−	0.952529i	$-0.598472\pi$
$359$	−11.5369			−0.608895			−0.304448	+	0.952529i	$0.598472\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	−2.85577	−	4.94634i	−0.150304	−	0.260334i
$362$	−2.01333	−	3.48719i	−0.105818	−	0.183283i
$363$	−0.686489			−0.0360313
$364$	29.2462	+	4.48365i	1.53292	+	0.235007i
$365$	5.53919			0.289934
$366$	0.822114	+	1.42394i	0.0429726	+	0.0744307i
$367$	17.8148	+	30.8562i	0.929927	+	1.61068i	0.783439	+	0.621468i	$0.213464\pi$
$367$	17.8148	+	30.8562i	0.929927	+	1.61068i	0.146488	+	0.989213i	$0.453203\pi$
$368$	−9.94214	+	17.2203i	−0.518270	+	0.897670i
$369$	−3.75154			−0.195297
$370$	−0.722606	+	1.25159i	−0.0375665	+	0.0650671i
$371$	−33.0277	+	57.2057i	−1.71471	+	2.96997i
$372$	5.21235			0.270248
$373$	4.80571	−	8.32374i	0.248830	−	0.430987i	−0.714371	−	0.699767i	$-0.753287\pi$
$373$	4.80571	−	8.32374i	0.248830	−	0.430987i	0.963202	+	0.268780i	$0.0866205\pi$
$374$	−2.65368	−	4.59632i	−0.137219	−	0.237670i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−1.07838			−0.0556131
$377$	−12.5103	−	1.91791i	−0.644311	−	0.0987775i
$378$	−2.58864			−0.133145
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	0.761638	−	0.648003i	$-0.224396\pi$
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	−0.942006	+	0.335596i	$0.891062\pi$
$380$	−4.24846	−	7.35856i	−0.217942	−	0.377486i
$381$	−3.72733	+	6.45593i	−0.190957	+	0.330747i
$382$	1.29687			0.0663535
$383$	−10.1067	+	17.5053i	−0.516428	+	0.894480i	0.483390	+	0.875405i	$0.339405\pi$
$383$	−10.1067	+	17.5053i	−0.516428	+	0.894480i	−0.999818	+	0.0190745i	$0.993928\pi$
$384$	5.75872	−	9.97440i	0.293874	−	0.509004i
$385$	−16.4124			−0.836454
$386$	−4.26539	+	7.38787i	−0.217103	+	0.376033i
$387$	−0.794319	−	1.37580i	−0.0403775	−	0.0699359i
$388$	−12.1948	−	21.1220i	−0.619098	−	1.07231i
$389$	−15.7587			−0.798999			−0.399500	−	0.916733i	$-0.630816\pi$
$389$	−15.7587			−0.798999			−0.399500	+	0.916733i	$0.630816\pi$
$390$	0.705681	+	1.81147i	0.0357336	+	0.0917275i
$391$	24.4657			1.23729
$392$	−16.0494	−	27.7985i	−0.810620	−	1.40403i
$393$	5.84684	+	10.1270i	0.294934	+	0.510841i
$394$	4.97826	−	8.62260i	0.250801	−	0.434400i
$395$	−2.21235			−0.111315
$396$	−2.92162	+	5.06040i	−0.146817	+	0.254295i
$397$	−5.67368	+	9.82710i	−0.284754	+	0.493208i	−0.972549	−	0.232696i	$-0.925245\pi$
$397$	−5.67368	+	9.82710i	−0.284754	+	0.493208i	0.687796	+	0.725904i	$0.258579\pi$
$398$	−5.89988			−0.295734
$399$	−11.9330	+	20.6686i	−0.597398	+	1.03472i
$400$	−1.17009	−	2.02665i	−0.0585043	−	0.101332i
$401$	−13.3268	−	23.0828i	−0.665511	−	1.15270i	−0.979147	−	0.203155i	$-0.934880\pi$
$401$	−13.3268	−	23.0828i	−0.665511	−	1.15270i	0.313636	−	0.949543i	$-0.398453\pi$
$402$	−6.92881			−0.345578
$403$	−6.87690	+	8.57887i	−0.342563	+	0.427344i
$404$	−21.3607			−1.06273
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	4.54339	+	7.86939i	0.225485	+	0.390551i
$407$	4.58145	−	7.93530i	0.227094	−	0.393338i
$408$	−5.75872			−0.285099
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	−0.177120	−	0.984189i	$-0.556678\pi$
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	0.940893	−	0.338704i	$-0.109988\pi$
$410$	1.01139	−	1.75178i	0.0499491	−	0.0865145i
$411$	9.27739			0.457620
$412$	5.85464	−	10.1405i	0.288437	−	0.499588i
$413$	20.1767	+	34.9470i	0.992829	+	1.71963i
$414$	2.29072	+	3.96765i	0.112583	+	0.194999i
$415$	−4.34017			−0.213051
$416$	6.88655	+	17.6777i	0.337641	+	0.866719i
$417$	−12.9155			−0.632474
$418$	−4.58145	−	7.93530i	−0.224086	−	0.388128i
$419$	−17.1581	−	29.7187i	−0.838227	−	1.45185i	−0.891376	−	0.453265i	$-0.850259\pi$
$419$	−17.1581	−	29.7187i	−0.838227	−	1.45185i	0.0531484	−	0.998587i	$-0.483074\pi$
$420$	−4.10310	+	7.10678i	−0.200211	+	0.346775i
$421$	−13.5320			−0.659509			−0.329755	−	0.944067i	$-0.606966\pi$
$421$	−13.5320			−0.659509			−0.329755	+	0.944067i	$0.606966\pi$
$422$	−3.82211	+	6.62010i	−0.186058	+	0.322261i
$423$	0.269594	−	0.466951i	0.0131081	−	0.0227039i
$424$	−27.5174			−1.33637
$425$	−1.43968	+	2.49360i	−0.0698348	+	0.120957i
$426$	−0.563913	−	0.976726i	−0.0273217	−	0.0473225i
$427$	−7.32018	−	12.6789i	−0.354248	−	0.613576i
$428$	−26.5958			−1.28556
$429$	−4.47414	−	11.4851i	−0.216014	−	0.554504i
$430$	0.856576			0.0413077
$431$	−7.63090	−	13.2171i	−0.367567	−	0.636645i	0.621617	−	0.783321i	$-0.286476\pi$
$431$	−7.63090	−	13.2171i	−0.367567	−	0.636645i	−0.989185	+	0.146676i	$0.953143\pi$
$432$	1.17009	+	2.02665i	0.0562958	+	0.0975072i
$433$	−1.93968	+	3.35963i	−0.0932151	+	0.161453i	−0.908862	−	0.417096i	$-0.863048\pi$
$433$	−1.93968	+	3.35963i	−0.0932151	+	0.161453i	0.815647	+	0.578550i	$0.196381\pi$
$434$	7.89392			0.378920
$435$	1.75513	−	3.03997i	0.0841520	−	0.145756i
$436$	13.5350	−	23.4433i	0.648208	−	1.12273i
$437$	42.2388			2.02056
$438$	1.49333	−	2.58653i	0.0713543	−	0.123589i
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	0.999846	−	0.0175761i	$-0.00559495\pi$
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	−0.515144	+	0.857104i	$0.672262\pi$
$440$	−3.41855	−	5.92110i	−0.162973	−	0.282278i
$441$	16.0494			0.764259
$442$	3.50113	−	4.36763i	0.166532	−	0.207747i
$443$	−35.0772			−1.66657			−0.833283	−	0.552847i	$-0.813542\pi$
$443$	−35.0772			−1.66657			−0.833283	+	0.552847i	$0.813542\pi$
$444$	−2.29072	−	3.96765i	−0.108713	−	0.188296i
$445$	−3.50667	−	6.07372i	−0.166232	−	0.287922i
$446$	−1.52586	+	2.64286i	−0.0722515	+	0.125143i
$447$	2.00000			0.0945968
$448$	−4.42469	+	7.66379i	−0.209047	+	0.362080i
$449$	−3.98667	+	6.90511i	−0.188143	+	0.325872i	−0.944631	−	0.328135i	$-0.893580\pi$
$449$	−3.98667	+	6.90511i	−0.188143	+	0.325872i	0.756488	+	0.654007i	$0.226913\pi$
$450$	−0.539189			−0.0254176
$451$	−6.41241	+	11.1066i	−0.301948	+	0.522990i
$452$	−2.63090	−	4.55685i	−0.123747	−	0.214336i
$453$	−4.30212	−	7.45149i	−0.202131	−	0.350101i
$454$	−11.2579			−0.528360
$455$	−6.28345	−	16.1295i	−0.294573	−	0.756163i
$456$	−9.94214			−0.465583
$457$	−1.30458	−	2.25960i	−0.0610256	−	0.105699i	0.833899	−	0.551918i	$-0.186104\pi$
$457$	−1.30458	−	2.25960i	−0.0610256	−	0.105699i	−0.894924	+	0.446218i	$0.852770\pi$
$458$	−3.11450	−	5.39446i	−0.145531	−	0.252067i
$459$	1.43968	−	2.49360i	0.0671986	−	0.116391i
$460$	14.5236			0.677166
$461$	15.0397	−	26.0495i	0.700469	−	1.21325i	−0.267833	−	0.963465i	$-0.586307\pi$
$461$	15.0397	−	26.0495i	0.700469	−	1.21325i	0.968302	−	0.249783i	$-0.0803592\pi$
$462$	−4.42469	+	7.66379i	−0.205855	+	0.356552i
$463$	−6.36788			−0.295940			−0.147970	−	0.988992i	$-0.547274\pi$
$463$	−6.36788			−0.295940			−0.147970	+	0.988992i	$0.547274\pi$
$464$	4.10731	−	7.11406i	0.190677	−	0.330262i
$465$	−1.52472	−	2.64090i	−0.0707074	−	0.122469i
$466$	−1.00614	−	1.74269i	−0.0466087	−	0.0807286i
$467$	−2.06892			−0.0957383			−0.0478692	−	0.998854i	$-0.515243\pi$
$467$	−2.06892			−0.0957383			−0.0478692	+	0.998854i	$0.515243\pi$
$468$	−6.09171	−	0.933903i	−0.281589	−	0.0431697i
$469$	61.6947			2.84880
$470$	0.145362	+	0.251775i	0.00670506	+	0.0116135i
$471$	0.454146	+	0.786603i	0.0209259	+	0.0362448i
$472$	−8.40522	+	14.5583i	−0.386882	+	0.670099i
$473$	−5.43084			−0.249710
$474$	−0.596436	+	1.03306i	−0.0273952	+	0.0474499i
$475$	−2.48554	+	4.30507i	−0.114044	+	0.197530i
$476$	23.6286			1.08302
$477$	6.87936	−	11.9154i	0.314984	−	0.545569i
$478$	7.30406	+	12.6510i	0.334080	+	0.578643i
$479$	−5.75513	−	9.96818i	−0.262959	−	0.455458i	0.704068	−	0.710132i	$-0.251365\pi$
$479$	−5.75513	−	9.96818i	−0.262959	−	0.455458i	−0.967027	+	0.254675i	$0.918032\pi$
$480$	−5.26180			−0.240167
$481$	9.55252	+	1.46447i	0.435557	+	0.0667741i
$482$	12.7238			0.579555
$483$	−20.3968	−	35.3283i	−0.928087	−	1.60749i
$484$	0.586699	+	1.01619i	0.0266682	+	0.0461906i
$485$	−7.13449	+	12.3573i	−0.323961	+	0.561116i
$486$	0.539189			0.0244581
$487$	−10.0742	+	17.4490i	−0.456504	+	0.790689i	−0.998773	−	0.0495162i	$-0.984232\pi$
$487$	−10.0742	+	17.4490i	−0.456504	+	0.790689i	0.542269	+	0.840205i	$0.317565\pi$
$488$	3.04945	−	5.28180i	0.138042	−	0.239096i
$489$	14.6442			0.662235
$490$	−4.32684	+	7.49431i	−0.195467	+	0.338558i
$491$	10.9408	+	18.9500i	0.493752	+	0.855204i	0.999974	−	0.00719955i	$-0.00229171\pi$
$491$	10.9408	+	18.9500i	0.493752	+	0.855204i	−0.506222	+	0.862403i	$0.668958\pi$
$492$	3.20620	+	5.55331i	0.144547	+	0.250362i
$493$	−10.1073			−0.455210
$494$	6.04453	−	7.54049i	0.271956	−	0.339263i
$495$	3.41855			0.153652
$496$	−3.56812	−	6.18016i	−0.160213	−	0.277497i
$497$	5.02113	+	8.69685i	0.225228	+	0.390107i
$498$	−1.17009	+	2.02665i	−0.0524328	+	0.0908163i
$499$	−23.8225			−1.06644			−0.533222	−	0.845975i	$-0.679019\pi$
$499$	−23.8225			−1.06644			−0.533222	+	0.845975i	$0.679019\pi$
$500$	−0.854638	+	1.48028i	−0.0382206	+	0.0662000i
$501$	−2.44748	+	4.23916i	−0.109345	+	0.189392i
$502$	14.4846			0.646481
$503$	−2.15449	+	3.73168i	−0.0960639	+	0.166388i	−0.910052	−	0.414494i	$-0.863959\pi$
$503$	−2.15449	+	3.73168i	−0.0960639	+	0.166388i	0.813988	+	0.580881i	$0.197292\pi$
$504$	4.80098	+	8.31555i	0.213853	+	0.370404i
$505$	6.24846	+	10.8227i	0.278053	+	0.481602i
$506$	15.6619			0.696257
$507$	9.57417	−	8.79404i	0.425204	−	0.390557i
$508$	12.7421			0.565338
$509$	−0.496928	−	0.860705i	−0.0220260	−	0.0381501i	0.854802	−	0.518954i	$-0.173678\pi$
$509$	−0.496928	−	0.860705i	−0.0220260	−	0.0381501i	−0.876828	+	0.480804i	$0.840345\pi$
$510$	0.776260	+	1.34452i	0.0343734	+	0.0595364i
$511$	−13.2968	+	23.0307i	−0.588215	+	1.01882i
$512$	−21.6742			−0.957873
$513$	2.48554	−	4.30507i	0.109739	−	0.190074i
$514$	−0.948614	+	1.64305i	−0.0418416	+	0.0724717i
$515$	−6.85043			−0.301866
$516$	−1.35771	+	2.35162i	−0.0597698	+	0.103524i
$517$	−0.921622	−	1.59630i	−0.0405329	−	0.0702050i
$518$	−3.46922	−	6.00887i	−0.152429	−	0.264015i
$519$	17.5597			0.770786
$520$	4.51026	−	5.62651i	0.197788	−	0.246739i
$521$	9.75154			0.427223			0.213611	−	0.976919i	$-0.431477\pi$
$521$	9.75154			0.427223			0.213611	+	0.976919i	$0.431477\pi$
$522$	−0.946346	−	1.63912i	−0.0414205	−	0.0717423i
$523$	5.51026	+	9.54405i	0.240947	+	0.417332i	0.960984	−	0.276603i	$-0.0892087\pi$
$523$	5.51026	+	9.54405i	0.240947	+	0.417332i	−0.720037	+	0.693935i	$0.755875\pi$
$524$	9.99386	−	17.3099i	0.436584	−	0.756185i
$525$	4.80098			0.209532
$526$	−2.38664	+	4.13378i	−0.104062	+	0.180241i
$527$	−4.39023	+	7.60411i	−0.191242	+	0.331240i
$528$	8.00000			0.348155
$529$	−24.5989	+	42.6065i	−1.06952	+	1.85246i
$530$	3.70928	+	6.42465i	0.161121	+	0.279069i
$531$	−4.20261	−	7.27913i	−0.182378	−	0.315888i
$532$	40.7936			1.76863
$533$	−13.3701	−	2.04974i	−0.579125	−	0.0887841i
$534$	−3.78151			−0.163642
$535$	7.77985	+	13.4751i	0.336352	+	0.582579i
$536$	12.8504	+	22.2576i	0.555054	+	0.961382i
$537$	0.692350	−	1.19919i	0.0298771	−	0.0517487i
$538$	−14.6888			−0.633277
$539$	27.4329	−	47.5152i	1.18162	−	2.04663i
$540$	0.854638	−	1.48028i	0.0367778	−	0.0637009i
$541$	−6.28846			−0.270362			−0.135181	−	0.990821i	$-0.543162\pi$
$541$	−6.28846			−0.270362			−0.135181	+	0.990821i	$0.543162\pi$
$542$	3.73759	−	6.47370i	0.160543	−	0.278069i
$543$	−3.73400	−	6.46748i	−0.160241	−	0.277546i
$544$	7.57531	+	13.1208i	0.324789	+	0.562550i
$545$	−15.8371			−0.678387
$546$	−9.22568	−	1.41436i	−0.394823	−	0.0605291i
$547$	27.6875			1.18383			0.591917	−	0.805999i	$-0.298371\pi$
$547$	27.6875			1.18383			0.591917	+	0.805999i	$0.298371\pi$
$548$	−7.92881	−	13.7331i	−0.338702	−	0.586649i
$549$	1.52472	+	2.64090i	0.0650736	+	0.112711i
$550$	−0.921622	+	1.59630i	−0.0392981	+	0.0680663i
$551$	−17.4497			−0.743384
$552$	8.49693	−	14.7171i	0.361653	−	0.626402i
$553$	5.31072	−	9.19844i	0.225835	−	0.391157i
$554$	−1.39189			−0.0591357
$555$	−1.34017	+	2.32125i	−0.0568872	+	0.0985315i
$556$	11.0381	+	19.1185i	0.468118	+	0.810804i
$557$	10.7321	+	18.5885i	0.454732	+	0.787619i	0.998673	−	0.0515046i	$-0.0164017\pi$
$557$	10.7321	+	18.5885i	0.454732	+	0.787619i	−0.543941	+	0.839124i	$0.683068\pi$
$558$	−1.64423			−0.0696057
$559$	−2.07918	−	5.33723i	−0.0879400	−	0.225741i
$560$	11.2351			0.474771
$561$	−4.92162	−	8.52450i	−0.207791	−	0.359905i
$562$	−1.44327	−	2.49983i	−0.0608809	−	0.105449i
$563$	7.83710	−	13.5743i	0.330294	−	0.572087i	−0.652275	−	0.757982i	$-0.726185\pi$
$563$	7.83710	−	13.5743i	0.330294	−	0.572087i	0.982570	+	0.185896i	$0.0595186\pi$
$564$	−0.921622			−0.0388073
$565$	−1.53919	+	2.66595i	−0.0647542	+	0.112157i
$566$	4.28486	−	7.42160i	0.180106	−	0.311953i
$567$	−4.80098			−0.201622
$568$	−2.09171	+	3.62295i	−0.0877661	+	0.152015i
$569$	−8.21594	−	14.2304i	−0.344430	−	0.596571i	0.640820	−	0.767691i	$-0.278595\pi$
$569$	−8.21594	−	14.2304i	−0.344430	−	0.596571i	−0.985250	+	0.171121i	$0.945261\pi$
$570$	1.34017	+	2.32125i	0.0561337	+	0.0972264i
$571$	14.6765			0.614191			0.307096	−	0.951679i	$-0.400643\pi$
$571$	14.6765			0.614191			0.307096	+	0.951679i	$0.400643\pi$
$572$	−13.1773	+	16.4385i	−0.550970	+	0.687329i
$573$	2.40522			0.100479
$574$	4.85568	+	8.41029i	0.202672	+	0.351039i
$575$	−4.24846	−	7.35856i	−0.177173	−	0.306873i
$576$	0.921622	−	1.59630i	0.0384009	−	0.0665124i
$577$	−17.8622			−0.743611			−0.371806	−	0.928311i	$-0.621261\pi$
$577$	−17.8622			−0.743611			−0.371806	+	0.928311i	$0.621261\pi$
$578$	−2.34797	+	4.06681i	−0.0976628	+	0.169157i
$579$	−7.91075	+	13.7018i	−0.328760	+	0.569428i
$580$	−6.00000			−0.249136
$581$	10.4186	−	18.0455i	0.432234	−	0.748652i
$582$	3.84684	+	6.66292i	0.159457	+	0.276187i
$583$	−23.5174	−	40.7334i	−0.973993	−	1.68701i
$584$	−11.0784			−0.458427
$585$	1.30878	+	3.35963i	0.0541115	+	0.138903i
$586$	1.33791			0.0552684
$587$	2.21174	+	3.83084i	0.0912881	+	0.158116i	0.908053	−	0.418854i	$-0.137568\pi$
$587$	2.21174	+	3.83084i	0.0912881	+	0.158116i	−0.816765	+	0.576970i	$0.804235\pi$
$588$	−13.7165	−	23.7576i	−0.565657	−	0.979747i
$589$	−7.57951	+	13.1281i	−0.312308	+	0.540934i
$590$	4.53200			0.186580
$591$	9.23287	−	15.9918i	0.379789	−	0.657814i
$592$	−3.13624	+	5.43212i	−0.128899	+	0.223259i
$593$	12.5380			0.514873			0.257436	−	0.966295i	$-0.417122\pi$
$593$	12.5380			0.514873			0.257436	+	0.966295i	$0.417122\pi$
$594$	0.921622	−	1.59630i	0.0378146	−	0.0654968i
$595$	−6.91189	−	11.9717i	−0.283360	−	0.490793i
$596$	−1.70928	−	2.96055i	−0.0700146	−	0.121269i
$597$	−10.9421			−0.447832
$598$	5.99612	+	15.3920i	0.245200	+	0.629424i
$599$	23.5825			0.963555			0.481777	−	0.876294i	$-0.339991\pi$
$599$	23.5825			0.963555			0.481777	+	0.876294i	$0.339991\pi$
$600$	1.00000	+	1.73205i	0.0408248	+	0.0707107i
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	0.830585	−	0.556892i	$-0.188006\pi$
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	−0.897575	+	0.440861i	$0.854673\pi$
$602$	−2.05620	+	3.56145i	−0.0838046	+	0.145154i
$603$	−12.8504			−0.523310
$604$	−7.35350	+	12.7366i	−0.299210	+	0.518247i
$605$	0.343245	−	0.594517i	0.0139549	−	0.0241706i
$606$	6.73820			0.273721
$607$	3.00421	−	5.20344i	0.121937	−	0.211201i	−0.798595	−	0.601869i	$-0.794423\pi$
$607$	3.00421	−	5.20344i	0.121937	−	0.211201i	0.920531	+	0.390668i	$0.127756\pi$
$608$	13.0784	+	22.6524i	0.530398	+	0.918677i
$609$	8.42635	+	14.5949i	0.341453	+	0.591414i
$610$	−1.64423			−0.0665729
$611$	1.21594	−	1.51687i	0.0491917	−	0.0613662i
$612$	−4.92162			−0.198945
$613$	2.76539	+	4.78979i	0.111693	+	0.193458i	0.916453	−	0.400142i	$-0.131039\pi$
$613$	2.76539	+	4.78979i	0.111693	+	0.193458i	−0.804760	+	0.593600i	$0.797706\pi$
$614$	−5.99641	−	10.3861i	−0.241995	−	0.419148i
$615$	1.87577	−	3.24893i	0.0756383	−	0.131009i
$616$	32.8248			1.32255
$617$	−5.94214	+	10.2921i	−0.239222	+	0.414344i	−0.960491	−	0.278311i	$-0.910226\pi$
$617$	−5.94214	+	10.2921i	−0.239222	+	0.414344i	0.721270	+	0.692654i	$0.243559\pi$
$618$	−1.84684	+	3.19882i	−0.0742907	+	0.128675i
$619$	32.2183			1.29496			0.647482	−	0.762081i	$-0.275822\pi$
$619$	32.2183			1.29496			0.647482	+	0.762081i	$0.275822\pi$
$620$	−2.60617	+	4.51402i	−0.104666	+	0.181288i
$621$	4.24846	+	7.35856i	0.170485	+	0.295289i
$622$	−0.109245	−	0.189218i	−0.00438032	−	0.00758695i
$623$	33.6709			1.34900
$624$	3.06278	+	7.86211i	0.122609	+	0.314736i
$625$	1.00000			0.0400000
$626$	−0.0953027	−	0.165069i	−0.00380906	−	0.00659749i
$627$	−8.49693	−	14.7171i	−0.339335	−	0.587745i
$628$	0.776260	−	1.34452i	0.0309761	−	0.0536523i
$629$	7.71769			0.307724
$630$	1.29432	−	2.24183i	0.0515669	−	0.0893165i
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	−0.599842	−	0.800118i	$-0.704770\pi$
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	0.992844	+	0.119420i	$0.0381034\pi$
$632$	4.42469			0.176005
$633$	−7.08864	+	12.2779i	−0.281748	+	0.488002i
$634$	6.82150	+	11.8152i	0.270916	+	0.469241i
$635$	−3.72733	−	6.45593i	−0.147915	−	0.256196i
$636$	−23.5174			−0.932527
$637$	57.1988	+	8.76899i	2.26630	+	0.347440i
$638$	−6.47027			−0.256160
$639$	−1.04585	−	1.81147i	−0.0413734	−	0.0716608i
$640$	5.75872	+	9.97440i	0.227634	+	0.394273i
$641$	−18.0566	+	31.2750i	−0.713194	+	1.23529i	0.250458	+	0.968128i	$0.419419\pi$
$641$	−18.0566	+	31.2750i	−0.713194	+	1.23529i	−0.963652	+	0.267161i	$0.913914\pi$
$642$	8.38962			0.331112
$643$	−19.5911	+	33.9328i	−0.772597	+	1.33818i	0.163537	+	0.986537i	$0.447710\pi$
$643$	−19.5911	+	33.9328i	−0.772597	+	1.33818i	−0.936135	+	0.351641i	$0.885624\pi$
$644$	−34.8638	+	60.3858i	−1.37382	+	2.37953i
$645$	1.58864			0.0625525
$646$	3.85884	−	6.68371i	0.151824	−	0.262967i
$647$	21.0856	+	36.5213i	0.828959	+	1.43580i	0.898856	+	0.438245i	$0.144400\pi$
$647$	21.0856	+	36.5213i	0.828959	+	1.43580i	−0.0698964	+	0.997554i	$0.522267\pi$
$648$	−1.00000	−	1.73205i	−0.0392837	−	0.0680414i
$649$	−28.7337			−1.12790
$650$	−1.92162	−	0.294598i	−0.0753722	−	0.0115551i
$651$	14.6404			0.573801
$652$	−12.5155	−	21.6775i	−0.490145	−	0.848956i
$653$	16.9233	+	29.3120i	0.662259	+	1.14707i	0.980021	+	0.198896i	$0.0637355\pi$
$653$	16.9233	+	29.3120i	0.662259	+	1.14707i	−0.317762	+	0.948171i	$0.602931\pi$
$654$	−4.26959	+	7.39515i	−0.166954	+	0.289173i
$655$	−11.6937			−0.456910
$656$	4.38962	−	7.60305i	0.171386	−	0.296849i
$657$	2.76959	−	4.79708i	0.108052	−	0.187152i
$658$	−1.39576			−0.0544126
$659$	15.7659	−	27.3074i	0.614153	−	1.06374i	−0.376380	−	0.926465i	$-0.622831\pi$
$659$	15.7659	−	27.3074i	0.614153	−	1.06374i	0.990533	−	0.137278i	$-0.0438355\pi$
$660$	−2.92162	−	5.06040i	−0.113724	−	0.196976i
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	0.921353	−	0.388728i	$-0.127085\pi$
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	−0.797324	+	0.603551i	$0.793752\pi$
$662$	−2.48133			−0.0964396
$663$	6.49333	−	8.10037i	0.252180	−	0.314592i
$664$	8.68035			0.336863
$665$	−11.9330	−	20.6686i	−0.462742	−	0.801494i
$666$	0.722606	+	1.25159i	0.0280004	+	0.0484982i
$667$	14.9132	−	25.8304i	0.577442	−	1.00016i
$668$	8.36683			0.323723
$669$	−2.82991	+	4.90155i	−0.109411	+	0.189505i
$670$	3.46441	−	6.00053i	0.133842	−	0.231821i
$671$	10.4247			0.402441
$672$	12.6309	−	21.8774i	0.487247	−	0.843937i
$673$	−4.86130	−	8.42002i	−0.187389	−	0.324568i	0.756990	−	0.653427i	$-0.226669\pi$
$673$	−4.86130	−	8.42002i	−0.187389	−	0.324568i	−0.944379	+	0.328859i	$0.893336\pi$
$674$	−8.36655	−	14.4913i	−0.322268	−	0.558184i
$675$	−1.00000			−0.0384900
$676$	−21.2001	−	6.65669i	−0.815387	−	0.256027i
$677$	−10.0845			−0.387580			−0.193790	−	0.981043i	$-0.562078\pi$
$677$	−10.0845			−0.387580			−0.193790	+	0.981043i	$0.562078\pi$
$678$	0.829914	+	1.43745i	0.0318726	+	0.0552050i
$679$	−34.2526	−	59.3272i	−1.31449	−	2.27677i
$680$	2.87936	−	4.98720i	0.110418	−	0.191250i
$681$	−20.8794			−0.800099
$682$	−2.81044	+	4.86782i	−0.107617	+	0.186399i
$683$	3.36849	−	5.83440i	0.128892	−	0.223247i	−0.794356	−	0.607453i	$-0.792191\pi$
$683$	3.36849	−	5.83440i	0.128892	−	0.223247i	0.923247	+	0.384206i	$0.125525\pi$
$684$	−8.49693			−0.324888
$685$	−4.63870	+	8.03446i	−0.177235	+	0.306981i
$686$	−11.7129	−	20.2873i	−0.447199	−	0.774572i
$687$	−5.77626	−	10.0048i	−0.220378	−	0.381706i
$688$	3.71769			0.141735
$689$	31.0277	−	38.7068i	1.18206	−	1.47461i
$690$	−4.58145			−0.174413
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	0.984678	−	0.174383i	$-0.0557931\pi$
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	−0.643359	+	0.765565i	$0.722460\pi$
$692$	−15.0072	−	25.9932i	−0.570488	−	0.988114i
$693$	−8.20620	+	14.2136i	−0.311728	+	0.539929i
$694$	9.68195			0.367522
$695$	6.45774	−	11.1851i	0.244956	−	0.424276i
$696$	−3.51026	+	6.07995i	−0.133056	+	0.230460i
$697$	−10.8020			−0.409156
$698$	0.0272733	−	0.0472387i	0.00103231	−	0.00178801i
$699$	−1.86603	−	3.23206i	−0.0705798	−	0.122248i
$700$	−4.10310	−	7.10678i	−0.155083	−	0.268611i
$701$	41.2762			1.55898			0.779490	−	0.626415i	$-0.215478\pi$
$701$	41.2762			1.55898			0.779490	+	0.626415i	$0.215478\pi$
$702$	1.92162	+	0.294598i	0.0725270	+	0.0111189i
$703$	13.3242			0.502531
$704$	−3.15061	−	5.45702i	−0.118743	−	0.205669i
$705$	0.269594	+	0.466951i	0.0101535	+	0.0175864i
$706$	−7.91548	+	13.7100i	−0.297903	+	0.515983i
$707$	−59.9976			−2.25644
$708$	−7.18342	+	12.4420i	−0.269969	+	0.467601i
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	−0.879459	−	0.475975i	$-0.842095\pi$
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	0.851936	+	0.523647i	$0.175429\pi$
$710$	1.12783			0.0423266
$711$	−1.10617	+	1.91595i	−0.0414847	+	0.0718537i
$712$	7.01333	+	12.1474i	0.262836	+	0.455245i
$713$	−12.9555	−	22.4395i	−0.485186	−	0.840367i
$714$	−7.45362			−0.278945
$715$	12.1834	+	1.86781i	0.455634	+	0.0698519i
$716$	−2.36683			−0.0884528
$717$	13.5464	+	23.4630i	0.505899	+	0.876242i
$718$	−3.11029	−	5.38718i	−0.116075	−	0.201048i
$719$	4.80685	−	8.32570i	0.179265	−	0.310496i	−0.762364	−	0.647149i	$-0.775961\pi$
$719$	4.80685	−	8.32570i	0.179265	−	0.310496i	0.941629	+	0.336652i	$0.109295\pi$
$720$	−2.34017			−0.0872131
$721$	16.4444	−	28.4826i	0.612422	−	1.06075i
$722$	1.53980	−	2.66701i	0.0573054	−	0.0992559i
$723$	23.5981			0.877623
$724$	−6.38243	+	11.0547i	−0.237201	+	0.410845i
$725$	1.75513	+	3.03997i	0.0651839	+	0.112902i
$726$	−0.185074	−	0.320557i	−0.00686873	−	0.0118970i
$727$	−42.6547			−1.58198			−0.790988	−	0.611831i	$-0.790433\pi$
$727$	−42.6547			−1.58198			−0.790988	+	0.611831i	$0.790433\pi$
$728$	12.5669	+	32.2590i	0.465760	+	1.19560i
$729$	1.00000			0.0370370
$730$	1.49333	+	2.58653i	0.0552708	+	0.0957318i
$731$	−2.28713	−	3.96143i	−0.0845926	−	0.146519i
$732$	2.60617	−	4.51402i	0.0963269	−	0.166843i
$733$	−6.48360			−0.239477			−0.119739	−	0.992805i	$-0.538206\pi$
$733$	−6.48360			−0.239477			−0.119739	+	0.992805i	$0.538206\pi$
$734$	−9.60556	+	16.6373i	−0.354548	+	0.614095i
$735$	−8.02472	+	13.8992i	−0.295996	+	0.512681i
$736$	−44.7091			−1.64800
$737$	−21.9649	+	38.0444i	−0.809089	+	1.40138i
$738$	−1.01139	−	1.75178i	−0.0372299	−	0.0644841i
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	0.932355	+	0.361543i	$0.117750\pi$
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	−0.153072	+	0.988215i	$0.548917\pi$
$740$	4.58145			0.168417
$741$	11.2104	−	13.9849i	0.411825	−	0.513747i
$742$	−35.6163			−1.30752
$743$	8.71481	+	15.0945i	0.319715	+	0.553763i	0.980429	−	0.196875i	$-0.0630794\pi$
$743$	8.71481	+	15.0945i	0.319715	+	0.553763i	−0.660713	+	0.750638i	$0.729746\pi$
$744$	3.04945	+	5.28180i	0.111798	+	0.193640i
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$	5.18237			0.189740
$747$	−2.17009	+	3.75870i	−0.0793993	+	0.137524i
$748$	−8.41241	+	14.5707i	−0.307588	+	0.532758i
$749$	−74.7019			−2.72955
$750$	0.269594	−	0.466951i	0.00984420	−	0.0170506i
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	0.717905	−	0.696141i	$-0.245101\pi$
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	−0.961828	+	0.273654i	$0.911768\pi$
$752$	0.630898	+	1.09275i	0.0230065	+	0.0398484i
$753$	26.8638			0.978970
$754$	−2.47712	−	6.35874i	−0.0902116	−	0.231572i
$755$	8.60424			0.313140
$756$	4.10310	+	7.10678i	0.149228	+	0.258471i
$757$	−13.8462	−	23.9824i	−0.503250	−	0.871654i	−0.999993	−	0.00375649i	$-0.998804\pi$
$757$	−13.8462	−	23.9824i	−0.503250	−	0.871654i	0.496743	−	0.867898i	$-0.334529\pi$
$758$	1.89330	−	3.27930i	0.0687679	−	0.119110i
$759$	29.0472			1.05435
$760$	4.97107	−	8.61015i	0.180320	−	0.312323i
$761$	0.261795	−	0.453443i	0.00949007	−	0.0164373i	−0.861241	−	0.508196i	$-0.830313\pi$
$761$	0.261795	−	0.453443i	0.00949007	−	0.0164373i	0.870731	+	0.491759i	$0.163646\pi$
$762$	−4.01947			−0.145610
$763$	38.0168	−	65.8471i	1.37630	−	2.38382i
$764$	−2.05559	−	3.56039i	−0.0743687	−	0.128810i
$765$	1.43968	+	2.49360i	0.0520518	+	0.0901563i
$766$	−10.8988			−0.393791
$767$	−11.0006	−	28.2384i	−0.397209	−	1.01963i
$768$	2.52359			0.0910622
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	0.964983	−	0.262312i	$-0.0844850\pi$
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	−0.709660	+	0.704544i	$0.751152\pi$
$770$	−4.42469	−	7.66379i	−0.159455	−	0.276184i
$771$	−1.75933	+	3.04726i	−0.0633609	+	0.109744i
$772$	27.0433			0.973310
$773$	−13.7093	+	23.7452i	−0.493088	+	0.854054i	−0.999968	−	0.00796257i	$-0.997465\pi$
$773$	−13.7093	+	23.7452i	−0.493088	+	0.854054i	0.506880	+	0.862017i	$0.330799\pi$
$774$	0.428288	−	0.741816i	0.0153945	−	0.0266640i
$775$	3.04945			0.109539
$776$	14.2690	−	24.7146i	0.512227	−	0.887203i
$777$	−6.43415	−	11.1443i	−0.230824	−	0.399799i
$778$	−4.24846	−	7.35856i	−0.152315	−	0.263817i
$779$	−18.6491			−0.668175
$780$	3.85464	−	4.80862i	0.138018	−	0.172176i
$781$	−7.15061			−0.255869
$782$	6.59583	+	11.4243i	0.235866	+	0.408532i
$783$	−1.75513	−	3.03997i	−0.0627232	−	0.108640i
$784$	−18.7792	+	32.5266i	−0.670687	+	1.16166i
$785$	−0.908291			−0.0324183
$786$	−3.15255	+	5.46038i	−0.112448	+	0.194765i
$787$	−10.6851	+	18.5071i	−0.380882	+	0.659707i	−0.991189	−	0.132459i	$-0.957713\pi$
$787$	−10.6851	+	18.5071i	−0.380882	+	0.659707i	0.610307	+	0.792165i	$0.291046\pi$
$788$	−31.5630			−1.12439
$789$	−4.42635	+	7.66666i	−0.157582	+	0.272940i
$790$	−0.596436	−	1.03306i	−0.0212203	−	0.0367546i
$791$	−7.38962	−	12.7992i	−0.262745	−	0.455087i
$792$	−6.83710			−0.242946
$793$	3.99107	+	10.2450i	0.141727	+	0.363811i
$794$	−6.11837			−0.217133
$795$	6.87936	+	11.9154i	0.243986	+	0.422596i
$796$	9.35157	+	16.1974i	0.331457	+	0.574101i
$797$	−1.94275	+	3.36495i	−0.0688158	+	0.119193i	−0.898380	−	0.439218i	$-0.855255\pi$
$797$	−1.94275	+	3.36495i	−0.0688158	+	0.119193i	0.829564	+	0.558411i	$0.188589\pi$
$798$	−12.8683			−0.455533
$799$	0.776260	−	1.34452i	0.0274621	−	0.0475658i
$800$	2.63090	−	4.55685i	0.0930163	−	0.161109i
$801$	−7.01333			−0.247804
$802$	7.18568	−	12.4460i	0.253735	−	0.439483i
$803$	−9.46800	−	16.3991i	−0.334118	−	0.578710i
$804$	10.9825	+	19.0222i	0.387322	+	0.670861i
$805$	40.7936			1.43779
$806$	−5.85989	−	0.898363i	−0.206406	−	0.0316435i
$807$	−27.2423			−0.958975
$808$	−12.4969	−	21.6453i	−0.439640	−	0.761480i
$809$	25.4524	+	44.0849i	0.894859	+	1.54994i	0.833979	+	0.551796i	$0.186057\pi$
$809$	25.4524	+	44.0849i	0.894859	+	1.54994i	0.0608794	+	0.998145i	$0.480609\pi$
$810$	−0.269594	+	0.466951i	−0.00947258	+	0.0164070i
$811$	−42.5174			−1.49299			−0.746495	−	0.665391i	$-0.768265\pi$
$811$	−42.5174			−1.49299			−0.746495	+	0.665391i	$0.768265\pi$
$812$	14.4030	−	24.9466i	0.505445	−	0.875456i
$813$	6.93188	−	12.0064i	0.243112	−	0.421082i
$814$	4.94053			0.173166
$815$	−7.32211	+	12.6823i	−0.256482	+	0.444241i
$816$	3.36910	+	5.83546i	0.117942	+	0.204282i
$817$	−3.94861	−	6.83920i	−0.138145	−	0.239273i
$818$	16.6570			0.582398
$819$	−17.1103	−	2.62313i	−0.597882	−	0.0916596i
$820$	−6.41241			−0.223931
$821$	1.99773	+	3.46017i	0.0697213	+	0.120761i	0.898779	−	0.438403i	$-0.144456\pi$
$821$	1.99773	+	3.46017i	0.0697213	+	0.120761i	−0.829057	+	0.559164i	$0.811122\pi$
$822$	2.50113	+	4.33209i	0.0872371	+	0.151099i
$823$	0.787653	−	1.36426i	0.0274559	−	0.0475549i	−0.851971	−	0.523589i	$-0.824593\pi$
$823$	0.787653	−	1.36426i	0.0274559	−	0.0475549i	0.879427	+	0.476034i	$0.157926\pi$
$824$	13.7009			0.477292
$825$	−1.70928	+	2.96055i	−0.0595093	+	0.103073i
$826$	−10.8790	+	18.8430i	−0.378530	+	0.655633i
$827$	9.17850			0.319168			0.159584	−	0.987184i	$-0.448985\pi$
$827$	9.17850			0.319168			0.159584	+	0.987184i	$0.448985\pi$
$828$	7.26180	−	12.5778i	0.252365	−	0.437109i
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	−0.872778	−	0.488118i	$-0.837683\pi$
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	0.0136660	−	0.999907i	$-0.495650\pi$
$830$	−1.17009	−	2.02665i	−0.0406143	−	0.0703460i
$831$	−2.58145			−0.0895495
$832$	4.15676	−	5.18551i	0.144110	−	0.179775i
$833$	46.2122			1.60116
$834$	−3.48194	−	6.03090i	−0.120570	−	0.208833i
$835$	−2.44748	−	4.23916i	−0.0846985	−	0.146702i
$836$	−14.5236	+	25.1556i	−0.502309	+	0.870024i
$837$	−3.04945			−0.105404
$838$	9.25145	−	16.0240i	0.319586	−	0.553539i
$839$	−4.64650	+	8.04797i	−0.160415	+	0.277847i	−0.935018	−	0.354601i	$-0.884617\pi$
$839$	−4.64650	+	8.04797i	−0.160415	+	0.277847i	0.774603	+	0.632448i	$0.217950\pi$
$840$	−9.60197			−0.331299
$841$	8.33904	−	14.4436i	0.287553	−	0.498057i
$842$	−3.64815	−	6.31878i	−0.125724	−	0.217760i
$843$	−2.67675	−	4.63627i	−0.0921922	−	0.159682i
$844$	24.2329			0.834130
$845$	2.82878	+	12.6885i	0.0973130	+	0.436498i
$846$	0.290725			0.00999532
$847$	1.64791	+	2.85427i	0.0566229	+	0.0980738i
$848$	16.0989	+	27.8841i	0.552838	+	0.957544i
$849$	7.94687	−	13.7644i	0.272736	−	0.472392i
$850$	−1.55252			−0.0532510
$851$	−11.3874	+	19.7235i	−0.390353	+	0.676112i
$852$	−1.78765	+	3.09631i	−0.0612440	+	0.106078i
$853$	−11.0423			−0.378080			−0.189040	−	0.981969i	$-0.560538\pi$
$853$	−11.0423			−0.378080			−0.189040	+	0.981969i	$0.560538\pi$
$854$	3.94696	−	6.83633i	0.135062	−	0.233934i
$855$	2.48554	+	4.30507i	0.0850035	+	0.147230i
$856$	−15.5597	−	26.9502i	−0.531820	−	0.921139i
$857$	−8.58476			−0.293250			−0.146625	−	0.989192i	$-0.546841\pi$
$857$	−8.58476			−0.293250			−0.146625	+	0.989192i	$0.546841\pi$
$858$	4.15676	−	5.18551i	0.141909	−	0.177030i
$859$	−46.6202			−1.59066			−0.795331	−	0.606176i	$-0.792703\pi$
$859$	−46.6202			−1.59066			−0.795331	+	0.606176i	$0.792703\pi$
$860$	−1.35771	−	2.35162i	−0.0462975	−	0.0801896i
$861$	9.00553	+	15.5980i	0.306908	+	0.531580i
$862$	4.11450	−	7.12651i	0.140140	−	0.242730i
$863$	10.6947			0.364053			0.182026	−	0.983294i	$-0.441734\pi$
$863$	10.6947			0.364053			0.182026	+	0.983294i	$0.441734\pi$
$864$	−2.63090	+	4.55685i	−0.0895050	+	0.155027i
$865$	−8.77985	+	15.2072i	−0.298524	+	0.517059i
$866$	−2.09171			−0.0710792
$867$	−4.35464	+	7.54245i	−0.147891	+	0.256155i
$868$	−12.5122	−	21.6718i	−0.424692	−	0.735588i
$869$	3.78151	+	6.54977i	0.128279	+	0.222186i
$870$	1.89269			0.0641683
$871$	−45.7978	−	7.02113i	−1.55180	−	0.237902i
$872$	31.6742			1.07262
$873$	7.13449	+	12.3573i	0.241466	+	0.418231i
$874$	11.3874	+	19.7235i	0.385183	+	0.667157i
$875$	−2.40049	+	4.15777i	−0.0811514	+	0.140558i
$876$	−9.46800			−0.319894
$877$	5.29791	−	9.17625i	0.178898	−	0.309860i	−0.762605	−	0.646864i	$-0.776080\pi$
$877$	5.29791	−	9.17625i	0.178898	−	0.309860i	0.941503	+	0.337004i	$0.109414\pi$
$878$	−5.47580	+	9.48436i	−0.184799	+	0.320082i
$879$	2.48133			0.0836932
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	8.11450	+	14.0547i	0.273384	+	0.473515i	0.969726	−	0.244195i	$-0.0785236\pi$
$881$	8.11450	+	14.0547i	0.273384	+	0.473515i	−0.696342	+	0.717710i	$0.745190\pi$
$882$	4.32684	+	7.49431i	0.145692	+	0.252347i
$883$	12.6137			0.424484			0.212242	−	0.977217i	$-0.431923\pi$
$883$	12.6137			0.424484			0.212242	+	0.977217i	$0.431923\pi$
$884$	−17.5402	−	2.68904i	−0.589942	−	0.0904423i
$885$	8.40522			0.282538
$886$	−9.45661	−	16.3793i	−0.317701	−	0.550274i
$887$	6.69533	+	11.5967i	0.224807	+	0.389378i	0.956262	−	0.292513i	$-0.0944914\pi$
$887$	6.69533	+	11.5967i	0.224807	+	0.389378i	−0.731454	+	0.681890i	$0.761158\pi$
$888$	2.68035	−	4.64250i	0.0899465	−	0.155792i
$889$	35.7897			1.20035
$890$	1.89076	−	3.27488i	0.0633783	−	0.109774i
$891$	1.70928	−	2.96055i	0.0572629	−	0.0991822i
$892$	9.67420			0.323916
$893$	1.34017	−	2.32125i	0.0448472	−	0.0776776i
$894$	0.539189	+	0.933903i	0.0180332	+	0.0312344i
$895$	0.692350	+	1.19919i	0.0231427	+	0.0400844i
$896$	−55.2951			−1.84728
$897$	11.1206	+	28.5465i	0.371307	+	0.953140i
$898$	−4.29914			−0.143464
$899$	5.35218	+	9.27024i	0.178505	+	0.309180i
$900$	0.854638	+	1.48028i	0.0284879	+	0.0493425i
$901$	19.8082	−	34.3088i	0.659906	−	1.14299i
$902$	−6.91500			−0.230244
$903$	−3.81351	+	6.60519i	−0.126906	+	0.219807i
$904$	3.07838	−	5.33191i	0.102385	−	0.177337i
$905$	7.46800			0.248245
$906$	2.31965	−	4.01776i	0.0770653	−	0.133481i
$907$	23.1526	+	40.1014i	0.768768	+	1.33154i	0.938231	+	0.346008i	$0.112463\pi$
$907$	23.1526	+	40.1014i	0.768768	+	1.33154i	−0.169464	+	0.985536i	$0.554204\pi$
$908$	17.8443	+	30.9072i	0.592184	+	1.02569i
$909$	12.4969			0.414497
$910$	5.83771	−	7.28249i	0.193518	−	0.241412i
$911$	−40.6947			−1.34828			−0.674138	−	0.738605i	$-0.735485\pi$
$911$	−40.6947			−1.34828			−0.674138	+	0.738605i	$0.735485\pi$
$912$	5.81658	+	10.0746i	0.192606	+	0.333604i
$913$	7.41855	+	12.8493i	0.245518	+	0.425250i
$914$	0.703414	−	1.21835i	0.0232669	−	0.0402994i
$915$	−3.04945			−0.100812
$916$	−9.87322	+	17.1009i	−0.326220	+	0.565030i
$917$	28.0706	−	48.6197i	0.926972	−	1.60556i
$918$	1.55252			0.0512408
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	−0.219145	−	0.975692i	$-0.570327\pi$
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	0.954547	−	0.298061i	$-0.0963398\pi$
$920$	8.49693	+	14.7171i	0.280135	+	0.485209i
$921$	−11.1212	−	19.2624i	−0.366455	−	0.634718i
$922$	16.2185			0.534128
$923$	−2.73759	−	7.02736i	−0.0901090	−	0.231308i
$924$	28.0533			0.922887
$925$	−1.34017	−	2.32125i	−0.0440646	−	0.0763222i
$926$	−1.71674	−	2.97349i	−0.0564157	−	0.0977149i
$927$	−3.42522	+	5.93265i	−0.112499	+	0.194854i
$928$	18.4703			0.606316
$929$	−14.4885	+	25.0948i	−0.475353	+	0.823335i	−0.999601	−	0.0282300i	$-0.991013\pi$
$929$	−14.4885	+	25.0948i	−0.475353	+	0.823335i	0.524249	+	0.851565i	$0.324346\pi$
$930$	0.822114	−	1.42394i	0.0269582	−	0.0466930i
$931$	79.7829			2.61478
$932$	−3.18956	+	5.52448i	−0.104478	+	0.180960i
$933$	−0.202610	−	0.350931i	−0.00663315	−	0.0114890i
$934$	−0.557770	−	0.966086i	−0.0182508	−	0.0316113i
$935$	9.84324			0.321909
$936$	−2.61757	−	6.71925i	−0.0855578	−	0.219626i
$937$	−53.1871			−1.73755			−0.868774	−	0.495209i	$-0.835091\pi$
$937$	−53.1871			−1.73755			−0.868774	+	0.495209i	$0.835091\pi$
$938$	16.6326	+	28.8084i	0.543072	+	0.940629i
$939$	−0.176752	−	0.306143i	−0.00576808	−	0.00999061i
$940$	0.460811	−	0.798148i	0.0150300	−	0.0260327i
$941$	26.3617			0.859368			0.429684	−	0.902979i	$-0.358625\pi$
$941$	26.3617			0.859368			0.429684	+	0.902979i	$0.358625\pi$
$942$	−0.244870	+	0.424128i	−0.00797830	+	0.0138188i
$943$	15.9383	−	27.6059i	0.519021	−	0.898971i
$944$	19.6697			0.640193
$945$	2.40049	−	4.15777i	0.0780880	−	0.135252i
$946$	−1.46412	−	2.53594i	−0.0476028	−	0.0824504i
$947$	25.3890	+	43.9751i	0.825032	+	1.42900i	0.901895	+	0.431956i	$0.142176\pi$
$947$	25.3890	+	43.9751i	0.825032	+	1.42900i	−0.0768629	+	0.997042i	$0.524490\pi$
$948$	3.78151			0.122818
$949$	12.4916	−	15.5831i	0.405494	−	0.505850i
$950$	−2.68035			−0.0869619
$951$	12.6514	+	21.9129i	0.410250	+	0.710574i
$952$	13.8238	+	23.9435i	0.448031	+	0.776012i
$953$	10.4163	−	18.0415i	0.337417	−	0.584423i	−0.646529	−	0.762889i	$-0.723780\pi$
$953$	10.4163	−	18.0415i	0.337417	−	0.584423i	0.983946	+	0.178466i	$0.0571136\pi$
$954$	7.41855			0.240184
$955$	−1.20261	+	2.08298i	−0.0389155	+	0.0674037i
$956$	23.1545	−	40.1047i	0.748870	−	1.29708i
$957$	−12.0000			−0.387905
$958$	3.10310	−	5.37473i	0.100257	−	0.173650i
$959$	−22.2703	−	38.5733i	−0.719146	−	1.24560i
$960$	0.921622	+	1.59630i	0.0297452	+	0.0515203i
$961$	−21.7009			−0.700028
$962$	1.89147	+	4.85537i	0.0609834	+	0.156544i
$963$	15.5597			0.501405
$964$	−20.1678	−	34.9317i	−0.649562	−	1.12507i
$965$	−7.91075	−	13.7018i	−0.254656	−	0.441077i
$966$	10.9977	−	19.0486i	0.353846	−	0.612880i
$967$	−5.92777			−0.190624			−0.0953120	−	0.995447i	$-0.530385\pi$
$967$	−5.92777			−0.190624			−0.0953120	+	0.995447i	$0.530385\pi$
$968$	−0.686489	+	1.18903i	−0.0220646	+	0.0382170i
$969$	7.15676	−	12.3959i	0.229908	−	0.398213i
$970$	−7.69368			−0.247029
$971$	−5.24846	+	9.09061i	−0.168431	+	0.291731i	−0.937868	−	0.346991i	$-0.887203\pi$
$971$	−5.24846	+	9.09061i	−0.168431	+	0.291731i	0.769437	+	0.638722i	$0.220537\pi$
$972$	−0.854638	−	1.48028i	−0.0274125	−	0.0474799i
$973$	31.0035	+	53.6996i	0.993927	+	1.72153i
$974$	−10.8638			−0.348097
$975$	−3.56391	−	0.546373i	−0.114137	−	0.0174980i
$976$	−7.13624			−0.228425
$977$	−26.6609	−	46.1780i	−0.852957	−	1.47736i	−0.878528	−	0.477692i	$-0.841474\pi$
$977$	−26.6609	−	46.1780i	−0.852957	−	1.47736i	0.0255707	−	0.999673i	$-0.491860\pi$
$978$	3.94800	+	6.83814i	0.126243	+	0.218660i
$979$	−11.9877	+	20.7633i	−0.383129	+	0.663599i
$980$	27.4329			0.876313
$981$	−7.91855	+	13.7153i	−0.252820	+	0.437897i
$982$	−5.89917	+	10.2177i	−0.188250	+	0.326058i
$983$	21.7275			0.693000			0.346500	−	0.938050i	$-0.387370\pi$
$983$	21.7275			0.693000			0.346500	+	0.938050i	$0.387370\pi$
$984$	−3.75154	+	6.49785i	−0.119595	+	0.207144i
$985$	9.23287	+	15.9918i	0.294184	+	0.509541i
$986$	−2.72487	−	4.71962i	−0.0867777	−	0.150303i
$987$	−2.58864			−0.0823972
$988$	−30.2823	−	4.64250i	−0.963409	−	0.147697i
$989$	13.4985			0.429228
$990$	0.921622	+	1.59630i	0.0292911	+	0.0507336i
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	0.927148	−	0.374695i	$-0.122252\pi$
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	−0.788069	+	0.615587i	$0.788919\pi$
$992$	8.02279	−	13.8959i	0.254724	−	0.441194i
$993$	−4.60197			−0.146039
$994$	−2.70734	+	4.68925i	−0.0858715	+	0.148734i
$995$	5.47107	−	9.47617i	0.173445	−	0.300415i
$996$	7.41855			0.235066
$997$	−1.72960	+	2.99576i	−0.0547770	+	0.0948766i	−0.892114	−	0.451811i	$-0.850778\pi$
$997$	−1.72960	+	2.99576i	−0.0547770	+	0.0948766i	0.837337	+	0.546688i	$0.184111\pi$
$998$	−6.42243	−	11.1240i	−0.203298	−	0.352123i
$999$	1.34017	+	2.32125i	0.0424012	+	0.0734410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.i.e.16.2	✓	6
3.2	odd	2		585.2.j.g.406.2		6
5.2	odd	4		975.2.bb.j.874.3		12
5.3	odd	4		975.2.bb.j.874.4		12
5.4	even	2		975.2.i.m.601.2		6
13.3	even	3		2535.2.a.y.1.2		3
13.9	even	3	inner	195.2.i.e.61.2	yes	6
13.10	even	6		2535.2.a.z.1.2		3
39.23	odd	6		7605.2.a.bt.1.2		3
39.29	odd	6		7605.2.a.bu.1.2		3
39.35	odd	6		585.2.j.g.451.2		6
65.9	even	6		975.2.i.m.451.2		6
65.22	odd	12		975.2.bb.j.724.4		12
65.48	odd	12		975.2.bb.j.724.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.2	✓	6	1.1	even	1	trivial
195.2.i.e.61.2	yes	6	13.9	even	3	inner
585.2.j.g.406.2		6	3.2	odd	2
585.2.j.g.451.2		6	39.35	odd	6
975.2.i.m.451.2		6	65.9	even	6
975.2.i.m.601.2		6	5.4	even	2
975.2.bb.j.724.3		12	65.48	odd	12
975.2.bb.j.724.4		12	65.22	odd	12
975.2.bb.j.874.3		12	5.2	odd	4
975.2.bb.j.874.4		12	5.3	odd	4
2535.2.a.y.1.2		3	13.3	even	3
2535.2.a.z.1.2		3	13.10	even	6
7605.2.a.bt.1.2		3	39.23	odd	6
7605.2.a.bu.1.2		3	39.29	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)

\(f(q)\)	\(=\)	\(q+(0.269594 + 0.466951i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} -1.00000 q^{5} +(-0.269594 + 0.466951i) q^{6} +(2.40049 - 4.15777i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.269594 + 0.466951i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} -1.00000 q^{5} +(-0.269594 + 0.466951i) q^{6} +(2.40049 - 4.15777i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.269594 - 0.466951i) q^{10} +(1.70928 + 2.96055i) q^{11} +1.70928 q^{12} +(-2.25513 + 2.81325i) q^{13} +2.58864 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.17009 - 2.02665i) q^{16} +(-1.43968 + 2.49360i) q^{17} -0.539189 q^{18} +(-2.48554 + 4.30507i) q^{19} +(-0.854638 + 1.48028i) q^{20} +4.80098 q^{21} +(-0.921622 + 1.59630i) q^{22} +(-4.24846 - 7.35856i) q^{23} +(1.00000 + 1.73205i) q^{24} +1.00000 q^{25} +(-1.92162 - 0.294598i) q^{26} -1.00000 q^{27} +(-4.10310 - 7.10678i) q^{28} +(1.75513 + 3.03997i) q^{29} +(0.269594 - 0.466951i) q^{30} +3.04945 q^{31} +(2.63090 - 4.55685i) q^{32} +(-1.70928 + 2.96055i) q^{33} -1.55252 q^{34} +(-2.40049 + 4.15777i) q^{35} +(0.854638 + 1.48028i) q^{36} +(-1.34017 - 2.32125i) q^{37} -2.68035 q^{38} +(-3.56391 - 0.546373i) q^{39} -2.00000 q^{40} +(1.87577 + 3.24893i) q^{41} +(1.29432 + 2.24183i) q^{42} +(-0.794319 + 1.37580i) q^{43} +5.84324 q^{44} +(0.500000 - 0.866025i) q^{45} +(2.29072 - 3.96765i) q^{46} -0.539189 q^{47} +(1.17009 - 2.02665i) q^{48} +(-8.02472 - 13.8992i) q^{49} +(0.269594 + 0.466951i) q^{50} -2.87936 q^{51} +(2.23707 + 5.74253i) q^{52} -13.7587 q^{53} +(-0.269594 - 0.466951i) q^{54} +(-1.70928 - 2.96055i) q^{55} +(4.80098 - 8.31555i) q^{56} -4.97107 q^{57} +(-0.946346 + 1.63912i) q^{58} +(-4.20261 + 7.27913i) q^{59} -1.70928 q^{60} +(1.52472 - 2.64090i) q^{61} +(0.822114 + 1.42394i) q^{62} +(2.40049 + 4.15777i) q^{63} -1.84324 q^{64} +(2.25513 - 2.81325i) q^{65} -1.84324 q^{66} +(6.42522 + 11.1288i) q^{67} +(2.46081 + 4.26225i) q^{68} +(4.24846 - 7.35856i) q^{69} -2.58864 q^{70} +(-1.04585 + 1.81147i) q^{71} +(-1.00000 + 1.73205i) q^{72} -5.53919 q^{73} +(0.722606 - 1.25159i) q^{74} +(0.500000 + 0.866025i) q^{75} +(4.24846 + 7.35856i) q^{76} +16.4124 q^{77} +(-0.705681 - 1.81147i) q^{78} +2.21235 q^{79} +(1.17009 + 2.02665i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.01139 + 1.75178i) q^{82} +4.34017 q^{83} +(4.10310 - 7.10678i) q^{84} +(1.43968 - 2.49360i) q^{85} -0.856576 q^{86} +(-1.75513 + 3.03997i) q^{87} +(3.41855 + 5.92110i) q^{88} +(3.50667 + 6.07372i) q^{89} +0.539189 q^{90} +(6.28345 + 16.1295i) q^{91} -14.5236 q^{92} +(1.52472 + 2.64090i) q^{93} +(-0.145362 - 0.251775i) q^{94} +(2.48554 - 4.30507i) q^{95} +5.26180 q^{96} +(7.13449 - 12.3573i) q^{97} +(4.32684 - 7.49431i) q^{98} -3.41855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 2 q^{4} - 6 q^{5} + 5 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 2 * q^4 - 6 * q^5 + 5 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 2 q^{4} - 6 q^{5} + 5 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{11} - 4 q^{12} + 3 q^{13} - 24 q^{14} - 3 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{20} + 10 q^{21} - 12 q^{22} - 8 q^{23} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 6 q^{29} - 18 q^{31} + 8 q^{32} + 4 q^{33} - 8 q^{34} - 5 q^{35} - 2 q^{36} + 14 q^{37} + 28 q^{38} - 12 q^{40} + 20 q^{41} - 12 q^{42} + 15 q^{43} + 48 q^{44} + 3 q^{45} + 28 q^{46} - 4 q^{48} - 30 q^{49} + 8 q^{51} + 16 q^{52} - 32 q^{53} + 4 q^{55} + 10 q^{56} + 6 q^{58} - 10 q^{59} + 4 q^{60} - 9 q^{61} + 2 q^{62} + 5 q^{63} - 24 q^{64} - 3 q^{65} - 24 q^{66} + 11 q^{67} + 18 q^{68} + 8 q^{69} + 24 q^{70} - 4 q^{71} - 6 q^{72} - 30 q^{73} - 8 q^{74} + 3 q^{75} + 8 q^{76} - 24 q^{78} + 34 q^{79} - 4 q^{80} - 3 q^{81} + 14 q^{82} + 4 q^{83} - 4 q^{85} - 20 q^{86} + 6 q^{87} - 8 q^{88} + 22 q^{89} - 31 q^{91} - 56 q^{92} - 9 q^{93} - 8 q^{94} + 16 q^{96} + q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 2 * q^4 - 6 * q^5 + 5 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^11 - 4 * q^12 + 3 * q^13 - 24 * q^14 - 3 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^20 + 10 * q^21 - 12 * q^22 - 8 * q^23 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 6 * q^29 - 18 * q^31 + 8 * q^32 + 4 * q^33 - 8 * q^34 - 5 * q^35 - 2 * q^36 + 14 * q^37 + 28 * q^38 - 12 * q^40 + 20 * q^41 - 12 * q^42 + 15 * q^43 + 48 * q^44 + 3 * q^45 + 28 * q^46 - 4 * q^48 - 30 * q^49 + 8 * q^51 + 16 * q^52 - 32 * q^53 + 4 * q^55 + 10 * q^56 + 6 * q^58 - 10 * q^59 + 4 * q^60 - 9 * q^61 + 2 * q^62 + 5 * q^63 - 24 * q^64 - 3 * q^65 - 24 * q^66 + 11 * q^67 + 18 * q^68 + 8 * q^69 + 24 * q^70 - 4 * q^71 - 6 * q^72 - 30 * q^73 - 8 * q^74 + 3 * q^75 + 8 * q^76 - 24 * q^78 + 34 * q^79 - 4 * q^80 - 3 * q^81 + 14 * q^82 + 4 * q^83 - 4 * q^85 - 20 * q^86 + 6 * q^87 - 8 * q^88 + 22 * q^89 - 31 * q^91 - 56 * q^92 - 9 * q^93 - 8 * q^94 + 16 * q^96 + q^97 + 2 * q^98 + 8 * q^99

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