LMFDB - Embedded newform 133.2.w.a.100.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(4,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 2]))

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

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

chi := DirichletCharacter("133.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$133 = 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	133.w (of order $9$ , degree $6$ , 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.7
Character	$\chi$	$=$	133.100
Dual form			133.2.w.a.4.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.102976 - 0.584006i) q^{2} +(1.17895 - 0.429103i) q^{3} +(1.54893 + 0.563763i) q^{4} +(0.270927 - 0.0986092i) q^{5} +(-0.129195 - 0.732703i) q^{6} +(-2.06872 + 1.64936i) q^{7} +(1.08176 - 1.87366i) q^{8} +(-1.09234 + 0.916579i) q^{9} +(-0.0296895 - 0.168377i) q^{10} -1.76959 q^{11} +2.06802 q^{12} +(-0.484870 - 2.74983i) q^{13} +(0.750211 + 1.37799i) q^{14} +(0.277096 - 0.232511i) q^{15} +(1.54256 + 1.29436i) q^{16} +(-4.70176 - 3.94525i) q^{17} +(0.422804 + 0.732317i) q^{18} +(4.30521 - 0.682012i) q^{19} +0.475238 q^{20} +(-1.73117 + 2.83221i) q^{21} +(-0.182225 + 1.03345i) q^{22} +(-0.255609 - 1.44963i) q^{23} +(0.471347 - 2.67314i) q^{24} +(-3.76654 + 3.16051i) q^{25} -1.65585 q^{26} +(-2.77643 + 4.80891i) q^{27} +(-4.13414 + 1.38848i) q^{28} +(3.80099 + 1.38345i) q^{29} +(-0.107254 - 0.185769i) q^{30} +(-0.560630 + 0.971040i) q^{31} +(4.22946 - 3.54894i) q^{32} +(-2.08626 + 0.759336i) q^{33} +(-2.78822 + 2.33959i) q^{34} +(-0.397829 + 0.650852i) q^{35} +(-2.20868 + 0.803894i) q^{36} +(-5.38550 + 9.32797i) q^{37} +(0.0450346 - 2.58450i) q^{38} +(-1.75160 - 3.03386i) q^{39} +(0.108317 - 0.614296i) q^{40} +(0.604547 - 3.42856i) q^{41} +(1.47576 + 1.30267i) q^{42} +(4.66018 + 3.91036i) q^{43} +(-2.74096 - 0.997628i) q^{44} +(-0.205560 + 0.356040i) q^{45} -0.872914 q^{46} +(6.62086 - 5.55556i) q^{47} +(2.37401 + 0.864070i) q^{48} +(1.55920 - 6.82414i) q^{49} +(1.45789 + 2.52514i) q^{50} +(-7.23607 - 2.63371i) q^{51} +(0.799227 - 4.53264i) q^{52} +(0.953558 + 0.347067i) q^{53} +(2.52253 + 2.11665i) q^{54} +(-0.479429 + 0.174498i) q^{55} +(0.852495 + 5.66029i) q^{56} +(4.78298 - 2.65144i) q^{57} +(1.19935 - 2.07734i) q^{58} +(-0.102872 - 0.0863195i) q^{59} +(0.560282 - 0.203926i) q^{60} +(0.238792 + 1.35426i) q^{61} +(0.509362 + 0.427406i) q^{62} +(0.747964 - 3.69781i) q^{63} +(0.376594 + 0.652280i) q^{64} +(-0.402523 - 0.697191i) q^{65} +(0.228622 + 1.29658i) q^{66} +(-1.72197 - 9.76577i) q^{67} +(-5.05850 - 8.76157i) q^{68} +(-0.923390 - 1.59936i) q^{69} +(0.339135 + 0.299357i) q^{70} +(9.42745 + 7.91057i) q^{71} +(0.535714 + 3.03819i) q^{72} +(8.43429 - 3.06983i) q^{73} +(4.89301 + 4.10573i) q^{74} +(-3.08439 + 5.34232i) q^{75} +(7.05295 + 1.37073i) q^{76} +(3.66078 - 2.91870i) q^{77} +(-1.95217 + 0.710531i) q^{78} +(4.22712 + 3.54697i) q^{79} +(0.545555 + 0.198566i) q^{80} +(-0.466914 + 2.64800i) q^{81} +(-1.94004 - 0.706118i) q^{82} +(-5.49743 - 9.52183i) q^{83} +(-4.27815 + 3.41092i) q^{84} +(-1.66287 - 0.605235i) q^{85} +(2.76356 - 2.31890i) q^{86} +5.07482 q^{87} +(-1.91427 + 3.31561i) q^{88} +(-12.1792 - 4.43285i) q^{89} +(0.186762 + 0.156712i) q^{90} +(5.53854 + 4.88891i) q^{91} +(0.421328 - 2.38947i) q^{92} +(-0.244279 + 1.38538i) q^{93} +(-2.56269 - 4.43871i) q^{94} +(1.09914 - 0.609309i) q^{95} +(3.46347 - 5.99890i) q^{96} +(-0.566238 + 0.206094i) q^{97} +(-3.82478 - 1.61330i) q^{98} +(1.93299 - 1.62197i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9} + 15 q^{10} - 54 q^{12} - 12 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{16} - 18 q^{18} + 6 q^{19} + 18 q^{21} - 12 q^{22}+ \cdots - 156 q^{99}+O(q^{100})$ 66 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 - 9 * q^7 - 6 * q^8 - 3 * q^9 + 15 * q^10 - 54 * q^12 - 12 * q^13 - 3 * q^14 - 9 * q^15 + 9 * q^16 - 18 * q^18 + 6 * q^19 + 18 * q^21 - 12 * q^22 - 3 * q^23 - 36 * q^24 - 3 * q^25 - 18 * q^26 + 30 * q^27 + 45 * q^28 + 6 * q^29 + 3 * q^30 + 39 * q^31 + 6 * q^32 - 39 * q^33 - 24 * q^34 - 27 * q^35 + 51 * q^36 + 6 * q^37 - 72 * q^38 - 24 * q^39 + 57 * q^40 - 30 * q^41 + 87 * q^42 + 12 * q^43 - 48 * q^44 - 3 * q^45 - 12 * q^46 - 21 * q^47 - 21 * q^48 - 21 * q^49 + 27 * q^50 - 3 * q^51 - 9 * q^52 - 9 * q^53 + 93 * q^54 - 27 * q^55 + 12 * q^56 + 6 * q^57 - 42 * q^58 + 6 * q^59 + 48 * q^60 + 18 * q^61 - 27 * q^62 - 87 * q^63 + 24 * q^64 + 21 * q^65 + 15 * q^66 - 18 * q^67 - 15 * q^68 + 42 * q^69 + 15 * q^70 + 30 * q^71 + 48 * q^72 - 78 * q^73 + 21 * q^74 + 57 * q^75 + 42 * q^76 + 18 * q^77 - 51 * q^78 - 81 * q^79 - 3 * q^80 + 48 * q^81 + 117 * q^82 - 18 * q^83 - 51 * q^84 - 24 * q^85 - 66 * q^86 + 18 * q^87 - 45 * q^88 - 3 * q^89 - 48 * q^90 + 78 * q^91 + 12 * q^92 + 33 * q^93 + 72 * q^94 + 93 * q^95 + 69 * q^96 + 3 * q^97 + 6 * q^98 - 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$ .

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	0.102976	−	0.584006i	0.0728151	−	0.412955i	−0.926512	−	0.376266i	$-0.877208\pi$
$2$	0.102976	−	0.584006i	0.0728151	−	0.412955i	0.999327	−	0.0366888i	$-0.0116810\pi$
$3$	1.17895	−	0.429103i	0.680668	−	0.247743i	0.0215336	−	0.999768i	$-0.493145\pi$
$3$	1.17895	−	0.429103i	0.680668	−	0.247743i	0.659134	+	0.752025i	$0.270923\pi$
$4$	1.54893	+	0.563763i	0.774463	+	0.281881i
$5$	0.270927	−	0.0986092i	0.121162	−	0.0440994i	−0.280728	−	0.959787i	$-0.590576\pi$
$5$	0.270927	−	0.0986092i	0.121162	−	0.0440994i	0.401890	+	0.915688i	$0.368354\pi$
$6$	−0.129195	−	0.732703i	−0.0527437	−	0.299125i
$7$	−2.06872	+	1.64936i	−0.781902	+	0.623401i
$7$	−2.06872	+	1.64936i	−0.781902	+	0.623401i
$8$	1.08176	−	1.87366i	0.382460	−	0.662439i
$9$	−1.09234	+	0.916579i	−0.364112	+	0.305526i
$10$	−0.0296895	−	0.168377i	−0.00938863	−	0.0532456i
$11$	−1.76959			−0.533551			−0.266775	−	0.963759i	$-0.585958\pi$
$11$	−1.76959			−0.533551			−0.266775	+	0.963759i	$0.585958\pi$
$12$	2.06802			0.596986
$13$	−0.484870	−	2.74983i	−0.134479	−	0.762667i	−0.975221	−	0.221232i	$-0.928992\pi$
$13$	−0.484870	−	2.74983i	−0.134479	−	0.762667i	0.840742	−	0.541435i	$-0.182119\pi$
$14$	0.750211	+	1.37799i	0.200502	+	0.368283i
$15$	0.277096	−	0.232511i	0.0715458	−	0.0600341i
$16$	1.54256	+	1.29436i	0.385639	+	0.323590i
$17$	−4.70176	−	3.94525i	−1.14034	−	0.956863i	−0.140895	−	0.990025i	$-0.544998\pi$
$17$	−4.70176	−	3.94525i	−1.14034	−	0.956863i	−0.999450	+	0.0331619i	$0.989442\pi$
$18$	0.422804	+	0.732317i	0.0996558	+	0.172609i
$19$	4.30521	−	0.682012i	0.987684	−	0.156464i
$19$	4.30521	−	0.682012i	0.987684	−	0.156464i
$20$	0.475238			0.106266
$21$	−1.73117	+	2.83221i	−0.377773	+	0.618040i
$22$	−0.182225	+	1.03345i	−0.0388506	+	0.220332i
$23$	−0.255609	−	1.44963i	−0.0532981	−	0.302268i	0.946493	−	0.322725i	$-0.104599\pi$
$23$	−0.255609	−	1.44963i	−0.0532981	−	0.302268i	−0.999791	+	0.0204569i	$0.993488\pi$
$24$	0.471347	−	2.67314i	0.0962133	−	0.545653i
$25$	−3.76654	+	3.16051i	−0.753309	+	0.632101i
$26$	−1.65585			−0.324739
$27$	−2.77643	+	4.80891i	−0.534323	+	0.925475i
$28$	−4.13414	+	1.38848i	−0.781279	+	0.262397i
$29$	3.80099	+	1.38345i	0.705826	+	0.256900i	0.669896	−	0.742455i	$-0.266339\pi$
$29$	3.80099	+	1.38345i	0.705826	+	0.256900i	0.0359295	+	0.999354i	$0.488561\pi$
$30$	−0.107254	−	0.185769i	−0.0195818	−	0.0339166i
$31$	−0.560630	+	0.971040i	−0.100692	+	0.174404i	−0.911970	−	0.410257i	$-0.865439\pi$
$31$	−0.560630	+	0.971040i	−0.100692	+	0.174404i	0.811278	+	0.584661i	$0.198772\pi$
$32$	4.22946	−	3.54894i	0.747670	−	0.627370i
$33$	−2.08626	+	0.759336i	−0.363171	+	0.132183i
$34$	−2.78822	+	2.33959i	−0.478175	+	0.401237i
$35$	−0.397829	+	0.650852i	−0.0672453	+	0.110014i
$36$	−2.20868	+	0.803894i	−0.368114	+	0.133982i
$37$	−5.38550	+	9.32797i	−0.885371	+	1.53351i	−0.0400839	+	0.999196i	$0.512763\pi$
$37$	−5.38550	+	9.32797i	−0.885371	+	1.53351i	−0.845287	+	0.534312i	$0.820571\pi$
$38$	0.0450346	−	2.58450i	0.00730557	−	0.419262i
$39$	−1.75160	−	3.03386i	−0.280481	−	0.485807i
$40$	0.108317	−	0.614296i	0.0171264	−	0.0971288i
$41$	0.604547	−	3.42856i	0.0944144	−	0.535450i	−0.900511	−	0.434833i	$-0.856807\pi$
$41$	0.604547	−	3.42856i	0.0944144	−	0.535450i	0.994925	−	0.100617i	$-0.0320817\pi$
$42$	1.47576	+	1.30267i	0.227715	+	0.201006i
$43$	4.66018	+	3.91036i	0.710671	+	0.596324i	0.924787	−	0.380485i	$-0.124243\pi$
$43$	4.66018	+	3.91036i	0.710671	+	0.596324i	−0.214117	+	0.976808i	$0.568687\pi$
$44$	−2.74096	−	0.997628i	−0.413215	−	0.150398i
$45$	−0.205560	+	0.356040i	−0.0306431	+	0.0530753i
$46$	−0.872914			−0.128704
$47$	6.62086	−	5.55556i	0.965751	−	0.810362i	−0.0161277	−	0.999870i	$-0.505134\pi$
$47$	6.62086	−	5.55556i	0.965751	−	0.810362i	0.981879	+	0.189508i	$0.0606894\pi$
$48$	2.37401	+	0.864070i	0.342659	+	0.124718i
$49$	1.55920	−	6.82414i	0.222742	−	0.974877i
$50$	1.45789	+	2.52514i	0.206177	+	0.357109i
$51$	−7.23607	−	2.63371i	−1.01325	−	0.368794i
$52$	0.799227	−	4.53264i	0.110833	−	0.628564i
$53$	0.953558	+	0.347067i	0.130981	+	0.0476733i	0.406679	−	0.913571i	$-0.366687\pi$
$53$	0.953558	+	0.347067i	0.130981	+	0.0476733i	−0.275698	+	0.961244i	$0.588909\pi$
$54$	2.52253	+	2.11665i	0.343273	+	0.288040i
$55$	−0.479429	+	0.174498i	−0.0646461	+	0.0235293i
$56$	0.852495	+	5.66029i	0.113919	+	0.756389i
$57$	4.78298	−	2.65144i	0.633522	−	0.351192i
$58$	1.19935	−	2.07734i	0.157483	−	0.272768i
$59$	−0.102872	−	0.0863195i	−0.0133927	−	0.0112378i	0.636067	−	0.771634i	$-0.280560\pi$
$59$	−0.102872	−	0.0863195i	−0.0133927	−	0.0112378i	−0.649459	+	0.760396i	$0.725005\pi$
$60$	0.560282	−	0.203926i	0.0723321	−	0.0263267i
$61$	0.238792	+	1.35426i	0.0305742	+	0.173395i	0.996271	−	0.0862764i	$-0.0274968\pi$
$61$	0.238792	+	1.35426i	0.0305742	+	0.173395i	−0.965697	+	0.259672i	$0.916386\pi$
$62$	0.509362	+	0.427406i	0.0646891	+	0.0542806i
$63$	0.747964	−	3.69781i	0.0942346	−	0.465880i
$64$	0.376594	+	0.652280i	0.0470742	+	0.0815350i
$65$	−0.402523	−	0.697191i	−0.0499269	−	0.0864759i
$66$	0.228622	+	1.29658i	0.0281415	+	0.159598i
$67$	−1.72197	−	9.76577i	−0.210372	−	1.19308i	−0.888759	−	0.458374i	$-0.848432\pi$
$67$	−1.72197	−	9.76577i	−0.210372	−	1.19308i	0.678387	−	0.734704i	$-0.262679\pi$
$68$	−5.05850	−	8.76157i	−0.613433	−	1.06250i
$69$	−0.923390	−	1.59936i	−0.111163	−	0.192540i
$70$	0.339135	+	0.299357i	0.0405343	+	0.0357800i
$71$	9.42745	+	7.91057i	1.11883	+	0.938812i	0.998545	−	0.0539276i	$-0.0171740\pi$
$71$	9.42745	+	7.91057i	1.11883	+	0.938812i	0.120287	+	0.992739i	$0.461618\pi$
$72$	0.535714	+	3.03819i	0.0631345	+	0.358054i
$73$	8.43429	−	3.06983i	0.987159	−	0.359297i	0.202540	−	0.979274i	$-0.435080\pi$
$73$	8.43429	−	3.06983i	0.987159	−	0.359297i	0.784620	+	0.619977i	$0.212858\pi$
$74$	4.89301	+	4.10573i	0.568801	+	0.477281i
$75$	−3.08439	+	5.34232i	−0.356155	+	0.616878i
$76$	7.05295	+	1.37073i	0.809029	+	0.157234i
$77$	3.66078	−	2.91870i	0.417185	−	0.332616i
$78$	−1.95217	+	0.710531i	−0.221040	+	0.0804518i
$79$	4.22712	+	3.54697i	0.475588	+	0.399066i	0.848828	−	0.528669i	$-0.177309\pi$
$79$	4.22712	+	3.54697i	0.475588	+	0.399066i	−0.373240	+	0.927735i	$0.621753\pi$
$80$	0.545555	+	0.198566i	0.0609950	+	0.0222003i
$81$	−0.466914	+	2.64800i	−0.0518794	+	0.294222i
$82$	−1.94004	−	0.706118i	−0.214242	−	0.0779777i
$83$	−5.49743	−	9.52183i	−0.603421	−	1.04516i	−0.992299	−	0.123867i	$-0.960470\pi$
$83$	−5.49743	−	9.52183i	−0.603421	−	1.04516i	0.388877	−	0.921290i	$-0.372863\pi$
$84$	−4.27815	+	3.41092i	−0.466785	+	0.372162i
$85$	−1.66287	−	0.605235i	−0.180364	−	0.0656470i
$86$	2.76356	−	2.31890i	0.298002	−	0.250054i
$87$	5.07482			0.544078
$88$	−1.91427	+	3.31561i	−0.204062	+	0.353445i
$89$	−12.1792	−	4.43285i	−1.29099	−	0.469882i	−0.396937	−	0.917846i	$-0.629927\pi$
$89$	−12.1792	−	4.43285i	−1.29099	−	0.469882i	−0.894052	+	0.447964i	$0.852149\pi$
$90$	0.186762	+	0.156712i	0.0196864	+	0.0165189i
$91$	5.53854	+	4.88891i	0.580597	+	0.512497i
$92$	0.421328	−	2.38947i	0.0439265	−	0.249119i
$93$	−0.244279	+	1.38538i	−0.0253306	+	0.143657i
$94$	−2.56269	−	4.43871i	−0.264322	−	0.457818i
$95$	1.09914	−	0.609309i	0.112770	−	0.0625138i
$96$	3.46347	−	5.99890i	0.353489	−	0.612261i
$97$	−0.566238	+	0.206094i	−0.0574928	+	0.0209257i	−0.370606	−	0.928790i	$-0.620850\pi$
$97$	−0.566238	+	0.206094i	−0.0574928	+	0.0209257i	0.313114	+	0.949716i	$0.398628\pi$
$98$	−3.82478	−	1.61330i	−0.386361	−	0.162968i
$99$	1.93299	−	1.62197i	0.194272	−	0.163014i
$100$	−7.61587	+	2.77195i	−0.761587	+	0.277195i
$101$	−5.82599	+	4.88859i	−0.579708	+	0.486432i	−0.884851	−	0.465874i	$-0.845740\pi$
$101$	−5.82599	+	4.88859i	−0.579708	+	0.486432i	0.305143	+	0.952306i	$0.401296\pi$
$102$	−2.28325	+	3.95470i	−0.226075	+	0.391574i
$103$	3.40274	+	5.89372i	0.335282	+	0.580725i	0.983539	−	0.180696i	$-0.0578351\pi$
$103$	3.40274	+	5.89372i	0.335282	+	0.580725i	−0.648257	+	0.761422i	$0.724502\pi$
$104$	−5.67677	−	2.06618i	−0.556653	−	0.202605i
$105$	−0.189738	+	0.938032i	−0.0185165	+	0.0915425i
$106$	0.300883	−	0.521144i	0.0292243	−	0.0506180i
$107$	15.1397			1.46361			0.731806	−	0.681513i	$-0.238678\pi$
$107$	15.1397			1.46361			0.731806	+	0.681513i	$0.238678\pi$
$108$	−7.01156	+	5.88340i	−0.674688	+	0.566130i
$109$	1.26530	−	7.17589i	0.121194	−	0.687326i	−0.862302	−	0.506395i	$-0.830978\pi$
$109$	1.26530	−	7.17589i	0.121194	−	0.687326i	0.983496	−	0.180931i	$-0.0579111\pi$
$110$	0.0525381	+	0.297958i	0.00500931	+	0.0284092i
$111$	−2.34659	+	13.3082i	−0.222728	+	1.26315i
$112$	−5.32598	−	0.133426i	−0.503258	−	0.0126076i
$113$	−15.7003			−1.47696			−0.738480	−	0.674275i	$-0.764456\pi$
$113$	−15.7003			−1.47696			−0.738480	+	0.674275i	$0.764456\pi$
$114$	−1.05593	−	3.06633i	−0.0988964	−	0.287188i
$115$	−0.212198	−	0.367538i	−0.0197876	−	0.0342731i
$116$	5.10751	+	4.28571i	0.474221	+	0.397918i
$117$	3.05008	+	2.55932i	0.281980	+	0.236610i
$118$	−0.0610045	+	0.0511888i	−0.00561591	+	0.00471231i
$119$	16.2338	+	0.406688i	1.48815	+	0.0372810i
$120$	−0.135896	−	0.770705i	−0.0124056	−	0.0703554i
$121$	−7.86856			−0.715323
$122$	0.815486			0.0738306
$123$	−0.758473	−	4.30151i	−0.0683892	−	0.387854i
$124$	−1.41581	+	1.18801i	−0.127144	+	0.106686i
$125$	−1.42959	+	2.47612i	−0.127866	+	0.221471i
$126$	−2.08252	−	0.817601i	−0.185526	−	0.0728377i
$127$	−1.10780	−	6.28264i	−0.0983012	−	0.557494i	−0.993686	−	0.112200i	$-0.964210\pi$
$127$	−1.10780	−	6.28264i	−0.0983012	−	0.557494i	0.895384	−	0.445294i	$-0.146901\pi$
$128$	10.7961	−	3.92947i	0.954252	−	0.347319i
$129$	7.17207	+	2.61042i	0.631466	+	0.229835i
$130$	−0.448614	+	0.163282i	−0.0393461	+	0.0143208i
$131$	−2.76482	+	15.6801i	−0.241564	+	1.36998i	0.586776	+	0.809749i	$0.300397\pi$
$131$	−2.76482	+	15.6801i	−0.241564	+	1.36998i	−0.828340	+	0.560226i	$0.810714\pi$
$132$	−3.65954			−0.318522
$133$	−7.78139	+	8.51176i	−0.674732	+	0.738063i
$134$	−5.88059			−0.508006
$135$	−0.278005	+	1.57664i	−0.0239268	+	0.135696i
$136$	−12.4782	+	4.54170i	−1.07000	+	0.389448i
$137$	−19.0684	−	6.94032i	−1.62912	−	0.592951i	−0.644032	−	0.764999i	$-0.722740\pi$
$137$	−19.0684	−	6.94032i	−1.62912	−	0.592951i	−0.985089	+	0.172047i	$0.944962\pi$
$138$	−1.02912	+	0.374570i	−0.0876048	+	0.0318855i
$139$	−0.895706	−	5.07980i	−0.0759728	−	0.430863i	−0.998942	−	0.0459891i	$-0.985356\pi$
$139$	−0.895706	−	5.07980i	−0.0759728	−	0.430863i	0.922969	−	0.384874i	$-0.125755\pi$
$140$	−0.983133	+	0.783840i	−0.0830899	+	0.0662466i
$141$	5.42176	−	9.39077i	0.456595	−	0.790845i
$142$	5.59062	−	4.69109i	0.469155	−	0.393668i
$143$	0.858020	+	4.86607i	0.0717513	+	0.406922i
$144$	−2.87137			−0.239281
$145$	1.16621			0.0968484
$146$	−0.924271	−	5.24180i	−0.0764932	−	0.433815i
$147$	−1.09005	−	8.71439i	−0.0899055	−	0.718751i
$148$	−13.6005	+	11.4122i	−1.11795	+	0.938075i
$149$	4.35510	+	3.65436i	0.356784	+	0.299377i	0.803507	−	0.595295i	$-0.202965\pi$
$149$	4.35510	+	3.65436i	0.356784	+	0.299377i	−0.446723	+	0.894672i	$0.647409\pi$
$150$	2.80233	+	2.35143i	0.228809	+	0.191994i
$151$	3.65283	+	6.32688i	0.297263	+	0.514874i	0.975509	−	0.219961i	$-0.0705929\pi$
$151$	3.65283	+	6.32688i	0.297263	+	0.514874i	−0.678246	+	0.734835i	$0.737260\pi$
$152$	3.37934	−	8.80429i	0.274101	−	0.714122i
$153$	8.75203			0.707560
$154$	−1.32756	−	2.43847i	−0.106978	−	0.196498i
$155$	−0.0561362	+	0.318364i	−0.00450897	+	0.0255716i
$156$	−1.00272	−	5.68672i	−0.0802820	−	0.455302i
$157$	1.32436	−	7.51084i	0.105696	−	0.599430i	−0.885244	−	0.465126i	$-0.846009\pi$
$157$	1.32436	−	7.51084i	0.105696	−	0.599430i	0.990940	−	0.134304i	$-0.0428799\pi$
$158$	2.50675	−	2.10341i	0.199426	−	0.167338i
$159$	1.27313			0.100965
$160$	0.795916	−	1.37857i	0.0629227	−	0.108985i
$161$	2.91975	+	2.57728i	0.230108	+	0.203118i
$162$	1.49837	+	0.545362i	0.117723	+	0.0428477i
$163$	−5.30471	−	9.18803i	−0.415497	−	0.719662i	0.579983	−	0.814628i	$-0.303059\pi$
$163$	−5.30471	−	9.18803i	−0.415497	−	0.719662i	−0.995481	+	0.0949662i	$0.969726\pi$
$164$	2.86929	−	4.96976i	0.224054	−	0.388073i
$165$	−0.490345	+	0.411449i	−0.0381733	+	0.0320312i
$166$	−6.12691	+	2.23001i	−0.475541	+	0.173083i
$167$	5.13892	−	4.31206i	0.397661	−	0.333677i	−0.421928	−	0.906630i	$-0.638646\pi$
$167$	5.13892	−	4.31206i	0.397661	−	0.333677i	0.819589	+	0.572952i	$0.194202\pi$
$168$	3.43390	+	6.30740i	0.264931	+	0.486627i
$169$	4.88951	−	1.77964i	0.376116	−	0.136895i
$170$	−0.524697	+	0.908802i	−0.0402424	+	0.0697019i
$171$	−4.07762	+	4.69106i	−0.311824	+	0.358734i
$172$	5.01376	+	8.68409i	0.382296	+	0.662155i
$173$	−3.31845	+	18.8199i	−0.252297	+	1.43085i	0.550618	+	0.834757i	$0.314392\pi$
$173$	−3.31845	+	18.8199i	−0.252297	+	1.43085i	−0.802916	+	0.596092i	$0.796719\pi$
$174$	0.522585	−	2.96373i	0.0396171	−	0.224680i
$175$	2.57910	−	12.7506i	0.194961	−	0.963855i
$176$	−2.72969	−	2.29048i	−0.205758	−	0.172652i
$177$	−0.158321	−	0.0576240i	−0.0119001	−	0.00433128i
$178$	−3.84298	+	6.65623i	−0.288043	+	0.498906i
$179$	10.6807			0.798312			0.399156	−	0.916883i	$-0.369303\pi$
$179$	10.6807			0.798312			0.399156	+	0.916883i	$0.369303\pi$
$180$	−0.519119	+	0.435593i	−0.0386929	+	0.0324672i
$181$	5.32528	+	1.93824i	0.395825	+	0.144068i	0.532261	−	0.846580i	$-0.321343\pi$
$181$	5.32528	+	1.93824i	0.395825	+	0.144068i	−0.136436	+	0.990649i	$0.543565\pi$
$182$	3.42549	−	2.73110i	0.253914	−	0.202443i
$183$	0.862642	+	1.49414i	0.0637683	+	0.110450i
$184$	−2.99262	−	1.08922i	−0.220619	−	0.0802987i
$185$	−0.539253	+	3.05826i	−0.0396467	+	0.224847i
$186$	0.783914	+	0.285321i	0.0574794	+	0.0209208i
$187$	8.32018	+	6.98146i	0.608432	+	0.510535i
$188$	13.3872	−	4.87256i	0.976365	−	0.355368i
$189$	−2.18800	−	14.5276i	−0.159154	−	1.05673i
$190$	−0.242655	−	0.704652i	−0.0176040	−	0.0511208i
$191$	−0.796101	+	1.37889i	−0.0576039	+	0.0997728i	−0.893389	−	0.449283i	$-0.851679\pi$
$191$	−0.796101	+	1.37889i	−0.0576039	+	0.0997728i	0.835785	+	0.549056i	$0.185013\pi$
$192$	0.723881	+	0.607409i	0.0522416	+	0.0438359i
$193$	11.1564	−	4.06061i	0.803058	−	0.292289i	0.0923051	−	0.995731i	$-0.470577\pi$
$193$	11.1564	−	4.06061i	0.803058	−	0.292289i	0.710753	+	0.703441i	$0.248354\pi$
$194$	0.0620512	+	0.351910i	0.00445501	+	0.0252656i
$195$	−0.773722	−	0.649230i	−0.0554074	−	0.0464923i
$196$	6.26228	−	9.69107i	0.447305	−	0.692219i
$197$	−11.1040	−	19.2327i	−0.791127	−	1.37027i	−0.925269	−	0.379310i	$-0.876161\pi$
$197$	−11.1040	−	19.2327i	−0.791127	−	1.37027i	0.134142	−	0.990962i	$-0.457172\pi$
$198$	−0.748188	−	1.29590i	−0.0531714	−	0.0920956i
$199$	3.79589	+	21.5275i	0.269083	+	1.52605i	0.757150	+	0.653241i	$0.226591\pi$
$199$	3.79589	+	21.5275i	0.269083	+	1.52605i	−0.488067	+	0.872806i	$0.662298\pi$
$200$	1.84723	+	10.4761i	0.130619	+	0.740775i
$201$	−6.22064	−	10.7745i	−0.438770	−	0.759972i
$202$	2.25503	+	3.90582i	0.158663	+	0.274813i
$203$	−10.1450	+	3.40725i	−0.712038	+	0.239142i
$204$	−9.72334	−	8.15885i	−0.680770	−	0.571234i
$205$	−0.174299	−	0.988501i	−0.0121736	−	0.0690399i
$206$	3.79237	−	1.38031i	0.264227	−	0.0961707i
$207$	1.60791	+	1.34920i	0.111757	+	0.0937756i
$208$	2.81133	−	4.86937i	0.194931	−	0.337630i
$209$	−7.61845	+	1.20688i	−0.526979	+	0.0834817i
$210$	0.528278	+	0.207403i	0.0364547	+	0.0143122i
$211$	−2.98980	+	1.08820i	−0.205827	+	0.0749147i	−0.442876	−	0.896583i	$-0.646042\pi$
$211$	−2.98980	+	1.08820i	−0.205827	+	0.0749147i	0.237050	+	0.971498i	$0.423820\pi$
$212$	1.28133	+	1.07516i	0.0880019	+	0.0738424i
$213$	14.5090	+	5.28083i	0.994137	+	0.361836i
$214$	1.55903	−	8.84169i	0.106573	−	0.604406i
$215$	1.64816	+	0.599883i	0.112404	+	0.0409117i
$216$	6.00685	+	10.4042i	0.408714	+	0.707914i
$217$	−0.441812	−	2.93349i	−0.0299922	−	0.199138i
$218$	−4.06047	−	1.47789i	−0.275010	−	0.100095i
$219$	8.62635	−	7.23837i	0.582915	−	0.489123i
$220$	−0.840975			−0.0566985
$221$	−8.56903	+	14.8420i	−0.576415	+	0.998381i
$222$	7.53041	+	2.74084i	0.505408	+	0.183953i
$223$	14.5053	+	12.1714i	0.971344	+	0.815055i	0.982761	−	0.184880i	$-0.0591897\pi$
$223$	14.5053	+	12.1714i	0.971344	+	0.815055i	−0.0114166	+	0.999935i	$0.503634\pi$
$224$	−2.89607	+	14.3177i	−0.193502	+	0.956641i
$225$	1.21748	−	6.90467i	0.0811653	−	0.460312i
$226$	−1.61676	+	9.16908i	−0.107545	+	0.609918i
$227$	0.480603	+	0.832428i	0.0318987	+	0.0552502i	0.881534	−	0.472120i	$-0.156511\pi$
$227$	0.480603	+	0.832428i	0.0318987	+	0.0552502i	−0.849635	+	0.527371i	$0.823178\pi$
$228$	8.90327	−	1.41042i	0.589633	−	0.0934070i
$229$	11.5339	−	19.9773i	0.762182	−	1.32014i	−0.179542	−	0.983750i	$-0.557462\pi$
$229$	11.5339	−	19.9773i	0.762182	−	1.32014i	0.941724	−	0.336387i	$-0.109205\pi$
$230$	−0.236496	+	0.0860774i	−0.0155941	+	0.00567577i
$231$	3.06346	−	5.01185i	0.201561	−	0.329756i
$232$	6.70386	−	5.62521i	0.440130	−	0.369313i
$233$	10.3564	−	3.76941i	0.678468	−	0.246942i	0.0202786	−	0.999794i	$-0.493545\pi$
$233$	10.3564	−	3.76941i	0.678468	−	0.246942i	0.658190	+	0.752852i	$0.271322\pi$
$234$	1.80875	−	1.51772i	0.118241	−	0.0992164i
$235$	1.24594	−	2.15803i	0.0812760	−	0.140774i
$236$	−0.110677	−	0.191698i	−0.00720444	−	0.0124785i
$237$	6.50558	+	2.36784i	0.422583	+	0.153808i
$238$	1.90920	−	9.43875i	0.123755	−	0.611823i
$239$	−3.80873	+	6.59691i	−0.246366	+	0.426719i	−0.962515	−	0.271229i	$-0.912570\pi$
$239$	−3.80873	+	6.59691i	−0.246366	+	0.426719i	0.716149	+	0.697948i	$0.245903\pi$
$240$	0.728389			0.0470173
$241$	−7.07421	+	5.93597i	−0.455690	+	0.382369i	−0.841542	−	0.540191i	$-0.818352\pi$
$241$	−7.07421	+	5.93597i	−0.455690	+	0.382369i	0.385852	+	0.922561i	$0.373907\pi$
$242$	−0.810273	+	4.59529i	−0.0520863	+	0.295396i
$243$	−2.30693	−	13.0833i	−0.147990	−	0.839291i
$244$	−0.393609	+	2.23227i	−0.0251983	+	0.142906i
$245$	−0.250496	−	2.00259i	−0.0160036	−	0.127941i
$246$	−2.59022			−0.165146
$247$	−3.96289	−	11.5079i	−0.252153	−	0.732233i
$248$	1.21293	+	2.10086i	0.0770214	+	0.133405i
$249$	−10.5671	−	8.86681i	−0.669660	−	0.561911i
$250$	1.29886	+	1.08987i	0.0821469	+	0.0689294i
$251$	−22.1000	+	18.5441i	−1.39494	+	1.17049i	−0.431642	+	0.902045i	$0.642066\pi$
$251$	−22.1000	+	18.5441i	−1.39494	+	1.17049i	−0.963295	+	0.268446i	$0.913490\pi$
$252$	3.24323	−	5.30595i	0.204304	−	0.334244i
$253$	0.452322	+	2.56524i	0.0284372	+	0.161276i
$254$	−3.78318			−0.237378
$255$	−2.22015			−0.139031
$256$	−0.921512	−	5.22616i	−0.0575945	−	0.326635i
$257$	−23.6554	+	19.8492i	−1.47558	+	1.23816i	−0.564827	+	0.825209i	$0.691057\pi$
$257$	−23.6554	+	19.8492i	−1.47558	+	1.23816i	−0.910754	+	0.412950i	$0.864498\pi$
$258$	2.26305	−	3.91973i	0.140892	−	0.244031i
$259$	−4.24412	−	28.1796i	−0.263717	−	1.75099i
$260$	−0.230428	−	1.30682i	−0.0142906	−	0.0810458i
$261$	−5.41999	+	1.97272i	−0.335489	+	0.122108i
$262$	8.87256	+	3.22935i	0.548148	+	0.199510i
$263$	−12.8349	+	4.67151i	−0.791431	+	0.288057i	−0.705931	−	0.708281i	$-0.749471\pi$
$263$	−12.8349	+	4.67151i	−0.791431	+	0.288057i	−0.0855003	+	0.996338i	$0.527249\pi$
$264$	−0.834090	+	4.73036i	−0.0513347	+	0.291134i
$265$	0.292568			0.0179723
$266$	4.16962	+	5.42089i	0.255656	+	0.332376i
$267$	−16.2608			−0.995144
$268$	2.83838	−	16.0972i	0.173381	−	0.983295i
$269$	−13.7110	+	4.99041i	−0.835977	+	0.304271i	−0.724309	−	0.689475i	$-0.757841\pi$
$269$	−13.7110	+	4.99041i	−0.835977	+	0.304271i	−0.111667	+	0.993746i	$0.535619\pi$
$270$	0.892142	+	0.324713i	0.0542940	+	0.0197614i
$271$	−17.2334	+	6.27245i	−1.04686	+	0.381024i	−0.807475	−	0.589902i	$-0.799166\pi$
$271$	−17.2334	+	6.27245i	−1.04686	+	0.381024i	−0.239380	+	0.970926i	$0.576944\pi$
$272$	−2.14617	−	12.1715i	−0.130131	−	0.738007i
$273$	8.62751	+	3.38718i	0.522161	+	0.205001i
$274$	−6.01678	+	10.4214i	−0.363487	+	0.629578i
$275$	6.66523	−	5.59279i	0.401929	−	0.337258i
$276$	−0.528604	−	2.99786i	−0.0318182	−	0.180450i
$277$	−13.5287			−0.812859			−0.406430	−	0.913682i	$-0.633226\pi$
$277$	−13.5287			−0.812859			−0.406430	+	0.913682i	$0.633226\pi$
$278$	−3.05887			−0.183459
$279$	−0.277638	−	1.57456i	−0.0166218	−	0.0942667i
$280$	0.789121	+	1.44946i	0.0471590	+	0.0866219i
$281$	−11.7968	+	9.89871i	−0.703739	+	0.590507i	−0.922835	−	0.385196i	$-0.874134\pi$
$281$	−11.7968	+	9.89871i	−0.703739	+	0.590507i	0.219095	+	0.975703i	$0.429689\pi$
$282$	−4.92596	−	4.13337i	−0.293336	−	0.246138i
$283$	−16.7657	−	14.0681i	−0.996617	−	0.836261i	−0.0101044	−	0.999949i	$-0.503216\pi$
$283$	−16.7657	−	14.0681i	−0.996617	−	0.836261i	−0.986512	+	0.163688i	$0.947661\pi$
$284$	10.1427	+	17.5677i	0.601860	+	1.04245i
$285$	1.03438	−	1.18999i	0.0612715	−	0.0704891i
$286$	2.93017			0.173265
$287$	4.40430	+	8.08983i	0.259978	+	0.477528i
$288$	−1.36711	+	7.75327i	−0.0805578	+	0.456866i
$289$	3.58957	+	20.3575i	0.211151	+	1.19750i
$290$	0.120092	−	0.681074i	0.00705203	−	0.0399940i
$291$	−0.579132	+	0.485949i	−0.0339493	+	0.0284869i
$292$	14.7948			0.865797
$293$	−2.75336	+	4.76895i	−0.160853	+	0.278605i	−0.935175	−	0.354187i	$-0.884758\pi$
$293$	−2.75336	+	4.76895i	−0.160853	+	0.278605i	0.774322	+	0.632792i	$0.218091\pi$
$294$	−5.20151	−	0.260780i	−0.303358	−	0.0152090i
$295$	−0.0363826	−	0.0132422i	−0.00211827	−	0.000770989i
$296$	11.6516	+	20.1812i	0.677238	+	1.17301i
$297$	4.91313	−	8.50979i	0.285089	−	0.493788i
$298$	2.58264	−	2.16709i	0.149609	−	0.125536i
$299$	−3.86230	+	1.40576i	−0.223363	+	0.0812974i
$300$	−7.78929	+	6.53599i	−0.449715	+	0.377356i
$301$	−16.0902	−	0.403091i	−0.927424	−	0.0232338i
$302$	4.07109	−	1.48176i	0.234265	−	0.0852655i
$303$	−4.77085	+	8.26336i	−0.274078	+	0.474717i
$304$	7.52380	+	4.52045i	0.431520	+	0.259265i
$305$	0.198238	+	0.343358i	0.0113511	+	0.0196606i
$306$	0.901250	−	5.11124i	0.0515211	−	0.292190i
$307$	0.427244	−	2.42302i	0.0243841	−	0.138289i	−0.970185	−	0.242364i	$-0.922077\pi$
$307$	0.427244	−	2.42302i	0.0243841	−	0.138289i	0.994569	+	0.104075i	$0.0331882\pi$
$308$	7.31573	−	2.45703i	0.416852	−	0.140002i
$309$	6.54068	+	5.48828i	0.372086	+	0.312217i
$310$	0.180146	+	0.0655678i	0.0102316	+	0.00372400i
$311$	4.82376	−	8.35500i	0.273531	−	0.473769i	−0.696233	−	0.717816i	$-0.745142\pi$
$311$	4.82376	−	8.35500i	0.273531	−	0.473769i	0.969763	+	0.244047i	$0.0784752\pi$
$312$	−7.57924			−0.429090
$313$	−1.38048	+	1.15836i	−0.0780295	+	0.0654745i	−0.680968	−	0.732313i	$-0.738441\pi$
$313$	−1.38048	+	1.15836i	−0.0780295	+	0.0654745i	0.602939	+	0.797788i	$0.293996\pi$
$314$	−4.25000	−	1.54687i	−0.239841	−	0.0872951i
$315$	−0.161994	−	1.07559i	−0.00912735	−	0.0606026i
$316$	4.54784	+	7.87709i	0.255836	+	0.443121i
$317$	23.1333	+	8.41983i	1.29929	+	0.472905i	0.896767	−	0.442503i	$-0.145910\pi$
$317$	23.1333	+	8.41983i	1.29929	+	0.472905i	0.402528	+	0.915408i	$0.368132\pi$
$318$	0.131102	−	0.743514i	0.00735181	−	0.0416942i
$319$	−6.72618	−	2.44813i	−0.376594	−	0.137069i
$320$	0.166350	+	0.139584i	0.00929926	+	0.00780300i
$321$	17.8490	−	6.49650i	0.996234	−	0.362599i
$322$	1.80581	−	1.43975i	0.100634	−	0.0802343i
$323$	−22.9328	−	13.7785i	−1.27601	−	0.766654i
$324$	−2.21606	+	3.83833i	−0.123114	+	0.213241i
$325$	10.5172	+	8.82494i	0.583387	+	0.489520i
$326$	−5.91213	+	2.15184i	−0.327442	+	0.119179i
$327$	−1.58747	−	9.00298i	−0.0877871	−	0.497866i
$328$	−5.76998	−	4.84159i	−0.318594	−	0.267332i
$329$	−4.53355	+	22.4131i	−0.249943	+	1.23567i
$330$	0.189795	+	0.328734i	0.0104479	+	0.0180962i
$331$	−8.08743	−	14.0078i	−0.444526	−	0.769941i	0.553493	−	0.832854i	$-0.313294\pi$
$331$	−8.08743	−	14.0078i	−0.444526	−	0.769941i	−0.998019	+	0.0629126i	$0.979961\pi$
$332$	−3.14706	−	17.8479i	−0.172717	−	0.979528i
$333$	−2.66704	−	15.1255i	−0.146153	−	0.828873i
$334$	−1.98909	−	3.44520i	−0.108838	−	0.188513i
$335$	−1.42952	−	2.47601i	−0.0781032	−	0.135279i
$336$	−6.33633	+	2.12809i	−0.345675	+	0.116097i
$337$	14.0876	+	11.8209i	0.767401	+	0.643926i	0.940042	−	0.341059i	$-0.110785\pi$
$337$	14.0876	+	11.8209i	0.767401	+	0.643926i	−0.172641	+	0.984985i	$0.555230\pi$
$338$	−0.535816	−	3.03877i	−0.0291446	−	0.165287i
$339$	−18.5099	+	6.73705i	−1.00532	+	0.365906i
$340$	−2.23445	−	1.87493i	−0.121180	−	0.101682i
$341$	0.992085	−	1.71834i	0.0537244	−	0.0930534i
$342$	2.31971	+	2.86442i	0.125435	+	0.154890i
$343$	8.02996	+	16.6889i	0.433577	+	0.901116i
$344$	12.3679	−	4.50154i	0.666831	−	0.242707i
$345$	−0.407883	−	0.342254i	−0.0219597	−	0.0184263i
$346$	10.6492	+	3.87600i	0.572505	+	0.208375i
$347$	−1.08574	+	6.15753i	−0.0582855	+	0.330553i	−0.999983	−	0.00590859i	$-0.998119\pi$
$347$	−1.08574	+	6.15753i	−0.0582855	+	0.330553i	0.941697	+	0.336462i	$0.109230\pi$
$348$	7.86052	+	2.86100i	0.421368	+	0.153365i
$349$	−5.05062	−	8.74794i	−0.270354	−	0.468266i	0.698599	−	0.715514i	$-0.253807\pi$
$349$	−5.05062	−	8.74794i	−0.270354	−	0.468266i	−0.968952	+	0.247247i	$0.920474\pi$
$350$	−7.18085	−	2.81922i	−0.383833	−	0.150693i
$351$	14.5699	+	5.30301i	0.777684	+	0.283054i
$352$	−7.48441	+	6.28016i	−0.398920	+	0.334734i
$353$	29.3409			1.56166			0.780830	−	0.624744i	$-0.214797\pi$
$353$	29.3409			1.56166			0.780830	+	0.624744i	$0.214797\pi$
$354$	−0.0499560	+	0.0865263i	−0.00265513	+	0.00459882i
$355$	3.33420	+	1.21355i	0.176961	+	0.0644086i
$356$	−16.3655	−	13.7323i	−0.867372	−	0.727812i
$357$	19.3133	−	6.48650i	1.02217	−	0.343302i
$358$	1.09986	−	6.23759i	0.0581292	−	0.329667i
$359$	3.35662	−	19.0363i	0.177156	−	1.00470i	−0.758471	−	0.651707i	$-0.774053\pi$
$359$	3.35662	−	19.0363i	0.177156	−	1.00470i	0.935626	−	0.352992i	$-0.114836\pi$
$360$	0.444733	+	0.770300i	0.0234395	+	0.0405984i
$361$	18.0697	−	5.87241i	0.951038	−	0.309074i
$362$	1.68032	−	2.91040i	0.0883158	−	0.152967i
$363$	−9.27665	+	3.37642i	−0.486898	+	0.177216i
$364$	5.82260	+	10.6950i	0.305187	+	0.560569i
$365$	1.98236	−	1.66340i	0.103762	−	0.0870663i
$366$	0.961418	−	0.349928i	0.0502541	−	0.0182910i
$367$	1.39061	−	1.16686i	0.0725892	−	0.0609095i	−0.605771	−	0.795639i	$-0.707135\pi$
$367$	1.39061	−	1.16686i	0.0725892	−	0.0609095i	0.678360	+	0.734729i	$0.262691\pi$
$368$	1.48205	−	2.56698i	0.0772571	−	0.133813i
$369$	2.48217	+	4.29925i	0.129217	+	0.223810i
$370$	1.73051	+	0.629854i	0.0899650	+	0.0327446i
$371$	−2.54508	+	0.854781i	−0.132134	+	0.0443780i
$372$	−1.15940	+	2.00813i	−0.0601118	+	0.104117i
$373$	3.71423			0.192316			0.0961579	−	0.995366i	$-0.469345\pi$
$373$	3.71423			0.192316			0.0961579	+	0.995366i	$0.469345\pi$
$374$	4.93400	−	4.14012i	0.255131	−	0.214080i
$375$	−0.622904	+	3.53266i	−0.0321666	+	0.182426i
$376$	−3.24707	−	18.4150i	−0.167455	−	0.949682i
$377$	1.96126	−	11.1229i	0.101010	−	0.572857i
$378$	−8.70953	−	0.218191i	−0.447970	−	0.0112225i
$379$	23.3684			1.20036			0.600178	−	0.799867i	$-0.295096\pi$
$379$	23.3684			1.20036			0.600178	+	0.799867i	$0.295096\pi$
$380$	2.04600	−	0.324118i	0.104958	−	0.0166269i
$381$	−4.00194	−	6.93157i	−0.205026	−	0.355115i
$382$	0.723300	+	0.606921i	0.0370072	+	0.0310528i
$383$	4.97168	+	4.17173i	0.254041	+	0.213165i	0.760910	−	0.648857i	$-0.224753\pi$
$383$	4.97168	+	4.17173i	0.254041	+	0.213165i	−0.506869	+	0.862023i	$0.669197\pi$
$384$	11.0420	−	9.26530i	0.563483	−	0.472818i
$385$	0.703993	−	1.15174i	0.0358788	−	0.0586981i
$386$	−1.22258	−	6.93358i	−0.0622275	−	0.352910i
$387$	−8.67463			−0.440956
$388$	−0.993249			−0.0504246
$389$	4.28863	+	24.3220i	0.217442	+	1.23317i	0.876618	+	0.481186i	$0.159794\pi$
$389$	4.28863	+	24.3220i	0.217442	+	1.23317i	−0.659176	+	0.751988i	$0.729095\pi$
$390$	−0.458830	+	0.385004i	−0.0232337	+	0.0194954i
$391$	−4.51733	+	7.82424i	−0.228451	+	0.395689i
$392$	−11.0995	−	10.3035i	−0.560607	−	0.520404i
$393$	3.46878	+	19.6724i	0.174977	+	0.992344i
$394$	−12.3755	+	4.50430i	−0.623467	+	0.226923i
$395$	1.49500	+	0.544137i	0.0752218	+	0.0273785i
$396$	3.90846	−	1.42256i	0.196407	−	0.0714864i
$397$	−1.39982	+	7.93875i	−0.0702548	+	0.398435i	0.929320	+	0.369275i	$0.120394\pi$
$397$	−1.39982	+	7.93875i	−0.0702548	+	0.398435i	−0.999575	+	0.0291592i	$0.990717\pi$
$398$	12.9631			0.649782
$399$	−5.52146	+	13.3740i	−0.276419	+	0.669536i
$400$	−9.90094			−0.495047
$401$	0.393700	−	2.23278i	0.0196604	−	0.111500i	−0.973398	−	0.229120i	$-0.926415\pi$
$401$	0.393700	−	2.23278i	0.0196604	−	0.111500i	0.993059	+	0.117620i	$0.0375264\pi$
$402$	−6.93293	+	2.52338i	−0.345783	+	0.125855i
$403$	2.94203	+	1.07081i	0.146553	+	0.0533410i
$404$	−11.7800	+	4.28758i	−0.586078	+	0.213315i
$405$	0.134618	+	0.763456i	0.00668922	+	0.0379365i
$406$	0.945166	+	6.27560i	0.0469078	+	0.311453i
$407$	9.53012	−	16.5067i	0.472391	−	0.818205i
$408$	−12.7624	+	10.7089i	−0.631831	+	0.530169i
$409$	−6.08689	−	34.5204i	−0.300977	−	1.70693i	−0.641861	−	0.766821i	$-0.721837\pi$
$409$	−6.08689	−	34.5204i	−0.300977	−	1.70693i	0.340884	−	0.940105i	$-0.389274\pi$
$410$	−0.595240			−0.0293968
$411$	−25.4588			−1.25579
$412$	1.94793	+	11.0473i	0.0959677	+	0.544260i
$413$	0.355185	+	0.00889807i	0.0174775	+	0.000437846i
$414$	0.953516	−	0.800095i	0.0468627	−	0.0393225i
$415$	−2.42834	−	2.03762i	−0.119203	−	0.100023i
$416$	−11.8097	−	9.90955i	−0.579020	−	0.485856i
$417$	−3.23575	−	5.60449i	−0.158455	−	0.274453i
$418$	−0.0796926	+	4.57351i	−0.00389789	+	0.223697i
$419$	−23.1509			−1.13099			−0.565497	−	0.824751i	$-0.691315\pi$
$419$	−23.1509			−1.13099			−0.565497	+	0.824751i	$0.691315\pi$
$420$	−0.822718	+	1.34597i	−0.0401445	+	0.0656768i
$421$	4.94972	−	28.0712i	0.241234	−	1.36811i	−0.587843	−	0.808975i	$-0.700023\pi$
$421$	4.94972	−	28.0712i	0.241234	−	1.36811i	0.829077	−	0.559134i	$-0.188866\pi$
$422$	0.327637	+	1.85812i	0.0159491	+	0.0904520i
$423$	−2.14009	+	12.1371i	−0.104055	+	0.590125i
$424$	1.68181	−	1.41120i	0.0816757	−	0.0685341i
$425$	30.1784			1.46387
$426$	4.57811	−	7.92952i	0.221810	−	0.384187i
$427$	−2.72766	−	2.40773i	−0.132001	−	0.116518i
$428$	23.4503	+	8.53521i	1.13351	+	0.412565i
$429$	3.09961	+	5.36869i	0.149651	+	0.259203i
$430$	0.520057	−	0.900765i	0.0250794	−	0.0434387i
$431$	28.0458	−	23.5332i	1.35092	−	1.13356i	0.372246	−	0.928134i	$-0.378588\pi$
$431$	28.0458	−	23.5332i	1.35092	−	1.13356i	0.978674	−	0.205421i	$-0.0658565\pi$
$432$	−10.5072	+	3.82433i	−0.505530	+	0.183998i
$433$	17.1374	−	14.3800i	0.823572	−	0.691059i	−0.130233	−	0.991483i	$-0.541573\pi$
$433$	17.1374	−	14.3800i	0.823572	−	0.691059i	0.953806	+	0.300424i	$0.0971282\pi$
$434$	−1.75867	−	0.0440583i	−0.0844191	−	0.00211486i
$435$	1.37490	−	0.500424i	0.0659216	−	0.0239935i
$436$	6.00536	−	10.4016i	0.287605	−	0.498146i
$437$	−2.08911	−	6.06663i	−0.0999358	−	0.290206i
$438$	−3.33894	−	5.78322i	−0.159541	−	0.276333i
$439$	5.08541	−	28.8408i	0.242713	−	1.37650i	−0.583031	−	0.812450i	$-0.698133\pi$
$439$	5.08541	−	28.8408i	0.242713	−	1.37650i	0.825744	−	0.564045i	$-0.190756\pi$
$440$	−0.191677	+	1.08705i	−0.00913782	+	0.0518232i
$441$	4.55170	+	8.88338i	0.216748	+	0.423018i
$442$	7.78542	+	6.53274i	0.370315	+	0.310731i
$443$	−10.2665	−	3.73671i	−0.487777	−	0.177536i	0.0864111	−	0.996260i	$-0.472460\pi$
$443$	−10.2665	−	3.73671i	−0.487777	−	0.177536i	−0.574189	+	0.818723i	$0.694682\pi$
$444$	−11.1373	+	19.2904i	−0.528554	+	0.915483i
$445$	−3.73678			−0.177140
$446$	8.60185	−	7.21781i	0.407309	−	0.341773i
$447$	6.70255	+	2.43953i	0.317020	+	0.115386i
$448$	−1.85491	−	0.728243i	−0.0876365	−	0.0344062i
$449$	19.9729	+	34.5940i	0.942578	+	1.63259i	0.760530	+	0.649303i	$0.224939\pi$
$449$	19.9729	+	34.5940i	0.942578	+	1.63259i	0.182048	+	0.983290i	$0.441727\pi$
$450$	−3.90700	−	1.42203i	−0.184178	−	0.0670353i
$451$	−1.06980	+	6.06713i	−0.0503749	+	0.285690i
$452$	−24.3186	−	8.85125i	−1.14385	−	0.416328i
$453$	7.02139	+	5.89165i	0.329894	+	0.276814i
$454$	0.535634	−	0.194955i	0.0251385	−	0.00914968i
$455$	1.98263	+	0.778384i	0.0929471	+	0.0364912i
$456$	0.206134	−	11.8299i	0.00965313	−	0.553986i
$457$	−17.9064	+	31.0148i	−0.837626	+	1.45081i	0.0542476	+	0.998528i	$0.482724\pi$
$457$	−17.9064	+	31.0148i	−0.837626	+	1.45081i	−0.891874	+	0.452284i	$0.850609\pi$
$458$	−10.4792	−	8.79306i	−0.489659	−	0.410873i
$459$	32.0264	−	11.6567i	1.49487	−	0.544086i
$460$	−0.121475	−	0.688918i	−0.00566379	−	0.0321210i
$461$	−5.00132	−	4.19661i	−0.232935	−	0.195455i	0.518848	−	0.854867i	$-0.326361\pi$
$461$	−5.00132	−	4.19661i	−0.232935	−	0.195455i	−0.751782	+	0.659411i	$0.770806\pi$
$462$	−2.61149	−	2.30518i	−0.121498	−	0.107247i
$463$	3.90848	+	6.76968i	0.181642	+	0.314614i	0.942440	−	0.334375i	$-0.108525\pi$
$463$	3.90848	+	6.76968i	0.181642	+	0.314614i	−0.760798	+	0.648989i	$0.775192\pi$
$464$	4.07256	+	7.05388i	0.189064	+	0.327468i
$465$	0.0704292	+	0.399424i	0.00326608	+	0.0185228i
$466$	−1.13490	−	6.43635i	−0.0525733	−	0.298158i
$467$	11.2329	+	19.4560i	0.519799	+	0.900318i	0.999735	+	0.0230144i	$0.00732636\pi$
$467$	11.2329	+	19.4560i	0.519799	+	0.900318i	−0.479937	+	0.877303i	$0.659340\pi$
$468$	3.28150	+	5.68372i	0.151687	+	0.262730i
$469$	19.6696	+	17.3625i	0.908257	+	0.801725i
$470$	−1.13200	−	0.949861i	−0.0522153	−	0.0438138i
$471$	−1.66156	−	9.42320i	−0.0765609	−	0.434198i
$472$	−0.273016	+	0.0993696i	−0.0125666	+	0.00457386i
$473$	−8.24660	−	6.91972i	−0.379179	−	0.318169i
$474$	2.05275	−	3.55547i	0.0942860	−	0.163308i
$475$	−14.0603	+	16.1755i	−0.645130	+	0.742182i
$476$	24.9156	+	9.78193i	1.14201	+	0.448354i
$477$	−1.35972	+	0.494898i	−0.0622573	+	0.0226598i
$478$	3.46043	+	2.90364i	0.158276	+	0.132810i
$479$	−7.10092	−	2.58452i	−0.324449	−	0.118090i	0.174660	−	0.984629i	$-0.444117\pi$
$479$	−7.10092	−	2.58452i	−0.324449	−	0.118090i	−0.499110	+	0.866539i	$0.666340\pi$
$480$	0.346799	−	1.96679i	0.0158291	−	0.0897714i
$481$	28.2616	+	10.2864i	1.28862	+	0.469019i
$482$	2.73817	+	4.74265i	0.124720	+	0.216022i
$483$	4.54816	+	1.78562i	0.206948	+	0.0812484i
$484$	−12.1878	−	4.43600i	−0.553992	−	0.201636i
$485$	−0.133086	+	0.111673i	−0.00604314	+	0.00507080i
$486$	−7.87826			−0.357365
$487$	−9.07390	+	15.7164i	−0.411177	+	0.712180i	−0.995019	−	0.0996875i	$-0.968216\pi$
$487$	−9.07390	+	15.7164i	−0.411177	+	0.712180i	0.583841	+	0.811868i	$0.301549\pi$
$488$	2.79574	+	1.01757i	0.126557	+	0.0460630i
$489$	−10.1966	−	8.55597i	−0.461107	−	0.386914i
$490$	−1.19532	−	0.0599280i	−0.0539992	−	0.00270727i
$491$	4.95204	−	28.0844i	0.223483	−	1.26743i	−0.642082	−	0.766636i	$-0.721929\pi$
$491$	4.95204	−	28.0844i	0.223483	−	1.26743i	0.865565	−	0.500797i	$-0.166960\pi$
$492$	1.25022	−	7.09032i	0.0563641	−	0.319656i
$493$	−12.4133	−	21.5005i	−0.559067	−	0.968332i
$494$	−7.12879	+	1.12931i	−0.320740	+	0.0508101i
$495$	0.363756	−	0.630044i	0.0163496	−	0.0283184i
$496$	−2.12168	+	0.772228i	−0.0952662	+	0.0346740i
$497$	−32.5501	−	0.815445i	−1.46007	−	0.0365777i
$498$	−6.26643	+	5.25816i	−0.280805	+	0.235624i
$499$	−34.5090	+	12.5603i	−1.54484	+	0.562274i	−0.967199	−	0.254019i	$-0.918247\pi$
$499$	−34.5090	+	12.5603i	−1.54484	+	0.562274i	−0.577637	+	0.816294i	$0.696025\pi$
$500$	−3.61027	+	3.02938i	−0.161456	+	0.135478i
$501$	4.20821	−	7.28884i	0.188009	−	0.325641i
$502$	8.55409	+	14.8161i	0.381788	+	0.661275i
$503$	−17.2716	−	6.28637i	−0.770105	−	0.280295i	−0.0730644	−	0.997327i	$-0.523278\pi$
$503$	−17.2716	−	6.28637i	−0.770105	−	0.280295i	−0.697040	+	0.717032i	$0.745500\pi$
$504$	−6.11932	−	5.40157i	−0.272576	−	0.240605i
$505$	−1.09636	+	1.89894i	−0.0487872	+	0.0845019i
$506$	1.54470			0.0686702
$507$	5.00085	−	4.19621i	0.222095	−	0.186360i
$508$	1.82602	−	10.3559i	0.0810166	−	0.459468i
$509$	−6.99265	−	39.6573i	−0.309944	−	1.75778i	−0.599270	−	0.800547i	$-0.704542\pi$
$509$	−6.99265	−	39.6573i	−0.309944	−	1.75778i	0.289326	−	0.957231i	$-0.406569\pi$
$510$	−0.228623	+	1.29658i	−0.0101236	+	0.0574137i
$511$	−12.3849	+	20.2618i	−0.547876	+	0.896331i
$512$	19.8310			0.876414
$513$	−8.67337	+	22.5969i	−0.382939	+	0.997679i
$514$	9.15613	+	15.8589i	0.403859	+	0.699505i
$515$	1.50307	+	1.26122i	0.0662331	+	0.0555762i
$516$	9.63735	+	8.08670i	0.424261	+	0.355997i
$517$	−11.7162	+	9.83105i	−0.515277	+	0.432369i
$518$	−16.8941	−	0.423231i	−0.742285	−	0.0185957i
$519$	4.16338	+	23.6117i	0.182752	+	1.03644i
$520$	−1.74173			−0.0763801
$521$	1.20008			0.0525764			0.0262882	−	0.999654i	$-0.491631\pi$
$521$	1.20008			0.0525764			0.0262882	+	0.999654i	$0.491631\pi$
$522$	0.593949	+	3.36845i	0.0259965	+	0.147433i
$523$	−31.4684	+	26.4051i	−1.37602	+	1.15462i	−0.405359	+	0.914158i	$0.632853\pi$
$523$	−31.4684	+	26.4051i	−1.37602	+	1.15462i	−0.970659	+	0.240459i	$0.922702\pi$
$524$	−13.1224	+	22.7286i	−0.573253	+	0.992903i
$525$	−2.43070	−	16.1390i	−0.106084	−	0.704365i
$526$	1.40651	+	7.97669i	0.0613266	+	0.347800i
$527$	6.46694	−	2.35377i	0.281704	−	0.102532i
$528$	−4.20102	−	1.52905i	−0.182826	−	0.0665433i
$529$	19.5768	−	7.12539i	0.851167	−	0.309799i
$530$	0.0301275	−	0.170862i	0.00130866	−	0.00742176i
$531$	0.191489			0.00830992
$532$	−16.8514	+	8.79722i	−0.730601	+	0.381408i
$533$	−9.72109			−0.421067
$534$	−1.67447	+	9.49641i	−0.0724615	+	0.410950i
$535$	4.10175	−	1.49292i	0.177334	−	0.0645444i
$536$	−20.1605	−	7.33782i	−0.870801	−	0.316946i
$537$	12.5920	−	4.58312i	0.543385	−	0.197776i
$538$	1.50252	+	8.52123i	0.0647783	+	0.367376i
$539$	−2.75913	+	12.0759i	−0.118844	+	0.520147i
$540$	−1.31946	+	2.28537i	−0.0567806	+	0.0983469i
$541$	−1.17392	+	0.985036i	−0.0504708	+	0.0423500i	−0.667674	−	0.744454i	$-0.732710\pi$
$541$	−1.17392	+	0.985036i	−0.0504708	+	0.0423500i	0.617203	+	0.786804i	$0.288266\pi$
$542$	1.88852	+	10.7103i	0.0811189	+	0.460048i
$543$	7.10995			0.305117
$544$	−33.8874			−1.45291
$545$	−0.364805	−	2.06891i	−0.0156265	−	0.0886224i
$546$	2.86656	−	4.68973i	0.122678	−	0.200702i
$547$	−4.98768	+	4.18516i	−0.213258	+	0.178944i	−0.743159	−	0.669115i	$-0.766673\pi$
$547$	−4.98768	+	4.18516i	−0.213258	+	0.178944i	0.529901	+	0.848059i	$0.322229\pi$
$548$	−25.6228	−	21.5001i	−1.09455	−	0.918438i
$549$	−1.50213	−	1.26043i	−0.0641092	−	0.0537940i
$550$	−2.57987	−	4.46846i	−0.110006	−	0.190536i
$551$	17.3076	+	3.36371i	0.737328	+	0.143299i
$552$	−3.99554			−0.170062
$553$	−14.5950	−	0.365633i	−0.620641	−	0.0155483i
$554$	−1.39313	+	7.90083i	−0.0591884	+	0.335674i
$555$	0.676554	+	3.83693i	0.0287181	+	0.162869i
$556$	1.47642	−	8.37320i	0.0626142	−	0.355103i
$557$	−23.1564	+	19.4305i	−0.981167	+	0.823297i	−0.984265	−	0.176698i	$-0.943458\pi$
$557$	−23.1564	+	19.4305i	−0.981167	+	0.823297i	0.00309821	+	0.999995i	$0.499014\pi$
$558$	−0.948146			−0.0401382
$559$	8.49325	−	14.7107i	0.359226	−	0.622198i
$560$	−1.45611	+	0.489043i	−0.0615318	+	0.0206658i
$561$	12.8049	+	4.66059i	0.540621	+	0.196770i
$562$	4.56612	+	7.90875i	0.192610	+	0.333610i
$563$	18.1070	−	31.3623i	0.763121	−	1.32176i	−0.178113	−	0.984010i	$-0.556999\pi$
$563$	18.1070	−	31.3623i	0.763121	−	1.32176i	0.941234	−	0.337754i	$-0.109667\pi$
$564$	13.6921	−	11.4890i	0.576540	−	0.483775i
$565$	−4.25363	+	1.54819i	−0.178952	+	0.0651330i
$566$	−9.94231	+	8.34259i	−0.417907	+	0.350665i
$567$	−3.40161	−	6.24808i	−0.142854	−	0.262395i
$568$	25.0200	−	9.10652i	1.04981	−	0.382101i
$569$	15.6787	−	27.1564i	0.657286	−	1.13845i	−0.324029	−	0.946047i	$-0.605037\pi$
$569$	15.6787	−	27.1564i	0.657286	−	1.13845i	0.981315	−	0.192406i	$-0.0616292\pi$
$570$	−0.588447	−	0.726626i	−0.0246473	−	0.0304350i
$571$	−13.6536	−	23.6488i	−0.571387	−	0.989672i	−0.996424	−	0.0844958i	$-0.973072\pi$
$571$	−13.6536	−	23.6488i	−0.571387	−	0.989672i	0.425036	−	0.905176i	$-0.360261\pi$
$572$	−1.41430	+	8.02091i	−0.0591350	+	0.335371i
$573$	−0.346879	+	1.96725i	−0.0144911	+	0.0821831i
$574$	5.17805	−	1.73908i	0.216128	−	0.0725878i
$575$	5.54432	+	4.65224i	0.231214	+	0.194012i
$576$	−1.00923	−	0.367331i	−0.0420514	−	0.0153055i
$577$	−0.617642	+	1.06979i	−0.0257128	+	0.0445358i	−0.878595	−	0.477567i	$-0.841519\pi$
$577$	−0.617642	+	1.06979i	−0.0257128	+	0.0445358i	0.852883	+	0.522103i	$0.174852\pi$
$578$	12.2585			0.509888
$579$	11.4105	−	9.57453i	0.474203	−	0.397904i
$580$	1.80637	+	0.657466i	0.0750055	+	0.0272998i
$581$	27.0776	+	10.6307i	1.12337	+	0.441037i
$582$	0.224161	+	0.388258i	0.00929177	+	0.0160938i
$583$	−1.68740	−	0.614165i	−0.0698852	−	0.0254361i
$584$	3.37205	−	19.1238i	0.139536	−	0.791350i
$585$	1.07872	+	0.392623i	0.0445997	+	0.0162329i
$586$	2.50157	+	2.09907i	0.103339	+	0.0867116i
$587$	0.854071	−	0.310856i	0.0352513	−	0.0128304i	−0.324334	−	0.945943i	$-0.605140\pi$
$587$	0.854071	−	0.310856i	0.0352513	−	0.0128304i	0.359586	+	0.933112i	$0.382918\pi$
$588$	3.22445	−	14.1125i	0.132974	−	0.581988i
$589$	−1.75137	+	4.56289i	−0.0721640	+	0.188011i
$590$	−0.0114800	+	0.0198840i	−0.000472626	+	0.000818612i
$591$	−21.3439	−	17.9096i	−0.877970	−	0.736704i
$592$	−20.3812	+	7.41814i	−0.837661	+	0.304884i
$593$	−5.21327	−	29.5659i	−0.214083	−	1.21413i	−0.882490	−	0.470331i	$-0.844135\pi$
$593$	−5.21327	−	29.5659i	−0.214083	−	1.21413i	0.668407	−	0.743796i	$-0.266976\pi$
$594$	−4.46384	−	3.74560i	−0.183153	−	0.153684i
$595$	4.43826	−	1.49062i	0.181951	−	0.0611093i
$596$	4.68553	+	8.11558i	0.191927	+	0.332427i
$597$	13.7127	+	23.7511i	0.561224	+	0.972068i
$598$	0.423250	+	2.40037i	0.0173080	+	0.0981584i
$599$	5.15528	+	29.2371i	0.210639	+	1.19459i	0.888316	+	0.459233i	$0.151876\pi$
$599$	5.15528	+	29.2371i	0.210639	+	1.19459i	−0.677677	+	0.735360i	$0.737013\pi$
$600$	6.67313	+	11.5582i	0.272430	+	0.471862i
$601$	1.45519	+	2.52046i	0.0593583	+	0.102812i	0.894178	−	0.447713i	$-0.147761\pi$
$601$	1.45519	+	2.52046i	0.0593583	+	0.102812i	−0.834819	+	0.550524i	$0.814428\pi$
$602$	−1.89231	+	9.35527i	−0.0771250	+	0.381292i
$603$	10.8321	+	9.08919i	0.441116	+	0.370140i
$604$	2.09110	+	11.8592i	0.0850855	+	0.482544i
$605$	−2.13180	+	0.775913i	−0.0866701	+	0.0315453i
$606$	4.33457	+	3.63714i	0.176080	+	0.147749i
$607$	14.6857	−	25.4363i	0.596072	−	1.03243i	−0.397322	−	0.917679i	$-0.630061\pi$
$607$	14.6857	−	25.4363i	0.596072	−	1.03243i	0.993395	−	0.114748i	$-0.0366062\pi$
$608$	15.7883	−	18.1635i	0.640301	−	0.736627i
$609$	−10.4984	+	8.37023i	−0.425416	+	0.339179i
$610$	0.220937	−	0.0804145i	0.00894547	−	0.00325589i
$611$	−18.4871	−	15.5125i	−0.747909	−	0.627570i
$612$	13.5563	+	4.93407i	0.547979	+	0.199448i
$613$	−2.14689	+	12.1756i	−0.0867122	+	0.491769i	0.910262	+	0.414033i	$0.135880\pi$
$613$	−2.14689	+	12.1756i	−0.0867122	+	0.491769i	−0.996974	+	0.0777360i	$0.975231\pi$
$614$	−1.37106	−	0.499026i	−0.0553316	−	0.0201391i
$615$	−0.629660	−	1.09060i	−0.0253903	−	0.0439773i
$616$	−1.50857	−	10.0164i	−0.0607818	−	0.403572i
$617$	−13.9918	−	5.09261i	−0.563290	−	0.205021i	0.0446517	−	0.999003i	$-0.485782\pi$
$617$	−13.9918	−	5.09261i	−0.563290	−	0.205021i	−0.607941	+	0.793982i	$0.708004\pi$
$618$	3.87872	−	3.25464i	0.156025	−	0.130921i
$619$	−2.87439			−0.115532			−0.0577658	−	0.998330i	$-0.518398\pi$
$619$	−2.87439			−0.115532			−0.0577658	+	0.998330i	$0.518398\pi$
$620$	−0.266433	+	0.461475i	−0.0107002	+	0.0185333i
$621$	7.68081	+	2.79559i	0.308220	+	0.112183i
$622$	−4.38264	−	3.67748i	−0.175728	−	0.147453i
$623$	32.5067	−	10.9176i	1.30235	−	0.437402i
$624$	1.22496	−	6.94710i	0.0490377	−	0.278107i
$625$	4.12589	−	23.3991i	0.165035	−	0.935963i
$626$	0.534334	+	0.925494i	0.0213563	+	0.0369902i
$627$	−8.46391	+	4.69196i	−0.338016	+	0.187379i
$628$	6.28567	−	10.8871i	0.250826	−	0.434443i
$629$	62.1225	−	22.6107i	2.47699	−	0.901549i
$630$	−0.644833	−	0.0161543i	−0.0256908	−	0.000643604i
$631$	−32.2324	+	27.0462i	−1.28315	+	1.07669i	−0.290348	+	0.956921i	$0.593771\pi$
$631$	−32.2324	+	27.0462i	−1.28315	+	1.07669i	−0.992802	+	0.119770i	$0.961784\pi$
$632$	11.2185	−	4.08322i	0.446250	−	0.162422i
$633$	−3.05788	+	2.56587i	−0.121540	+	0.101984i
$634$	7.29941	−	12.6429i	0.289896	−	0.502115i
$635$	−0.919659	−	1.59290i	−0.0364955	−	0.0632121i
$636$	1.97198	+	0.717741i	0.0781940	+	0.0284603i
$637$	−19.5213	−	0.978707i	−0.773461	−	0.0387778i
$638$	−2.12236	+	3.67603i	−0.0840250	+	0.145536i
$639$	−17.5486			−0.694212
$640$	2.53748	−	2.12920i	0.100303	−	0.0841638i
$641$	−0.755760	+	4.28613i	−0.0298507	+	0.169292i	−0.996089	−	0.0883596i	$-0.971838\pi$
$641$	−0.755760	+	4.28613i	−0.0298507	+	0.169292i	0.966238	+	0.257652i	$0.0829486\pi$
$642$	−1.95598	−	11.0929i	−0.0771964	−	0.437802i
$643$	3.14486	−	17.8354i	0.124021	−	0.703359i	−0.857863	−	0.513878i	$-0.828208\pi$
$643$	3.14486	−	17.8354i	0.124021	−	0.703359i	0.981884	−	0.189481i	$-0.0606805\pi$
$644$	3.06950	+	5.63806i	0.120955	+	0.222171i
$645$	2.20052			0.0866453
$646$	−10.4082	+	11.9740i	−0.409507	+	0.471112i
$647$	23.8502	+	41.3098i	0.937648	+	1.62405i	0.769842	+	0.638234i	$0.220335\pi$
$647$	23.8502	+	41.3098i	0.937648	+	1.62405i	0.167806	+	0.985820i	$0.446332\pi$
$648$	4.45637	+	3.73934i	0.175063	+	0.146895i
$649$	0.182040	+	0.152750i	0.00714571	+	0.00599596i
$650$	6.23684	−	5.23333i	0.244629	−	0.205268i
$651$	−1.77965	−	3.26886i	−0.0697498	−	0.128117i
$652$	−3.03673	−	17.2222i	−0.118928	−	0.674473i
$653$	29.7031			1.16237			0.581186	−	0.813771i	$-0.302589\pi$
$653$	29.7031			1.16237			0.581186	+	0.813771i	$0.302589\pi$
$654$	−5.42127			−0.211988
$655$	0.797137	+	4.52079i	0.0311467	+	0.176642i
$656$	5.37033	−	4.50624i	0.209676	−	0.175939i
$657$	−6.39934	+	11.0840i	−0.249662	+	0.432428i
$658$	12.6225	+	4.95564i	0.492078	+	0.193191i
$659$	−3.40316	−	19.3003i	−0.132568	−	0.751832i	−0.976522	−	0.215416i	$-0.930889\pi$
$659$	−3.40316	−	19.3003i	−0.132568	−	0.751832i	0.843954	−	0.536415i	$-0.180222\pi$
$660$	−0.991468	+	0.360865i	−0.0385929	+	0.0140466i
$661$	28.5948	+	10.4077i	1.11221	+	0.404811i	0.831803	−	0.555071i	$-0.187309\pi$
$661$	28.5948	+	10.4077i	1.11221	+	0.404811i	0.280405	+	0.959882i	$0.409531\pi$
$662$	−9.01349	+	3.28064i	−0.350319	+	0.127506i
$663$	−3.73372	+	21.1750i	−0.145006	+	0.822369i
$664$	−23.7876			−0.923137
$665$	−1.26885	+	3.07338i	−0.0492038	+	0.119181i
$666$	−9.10804			−0.352929
$667$	1.03392	−	5.86364i	0.0400335	−	0.227041i
$668$	10.3908	−	3.78194i	0.402031	−	0.146327i
$669$	22.3238	+	8.12519i	0.863087	+	0.314138i
$670$	−1.59321	+	0.579881i	−0.0615511	+	0.0224028i
$671$	−0.422564	−	2.39648i	−0.0163129	−	0.0925151i
$672$	2.72943	+	18.1226i	0.105290	+	0.699093i
$673$	7.77725	−	13.4706i	0.299791	−	0.519253i	−0.676297	−	0.736629i	$-0.736416\pi$
$673$	7.77725	−	13.4706i	0.299791	−	0.519253i	0.976088	+	0.217376i	$0.0697498\pi$
$674$	8.35418	−	7.00999i	0.321791	−	0.270015i
$675$	−4.74106	−	26.8879i	−0.182483	−	1.03492i
$676$	8.57678			0.329876
$677$	−42.3323			−1.62696			−0.813481	−	0.581591i	$-0.802430\pi$
$677$	−42.3323			−1.62696			−0.813481	+	0.581591i	$0.802430\pi$
$678$	2.02840	+	11.5036i	0.0779004	+	0.441795i
$679$	0.831464	−	1.36028i	0.0319087	−	0.0522029i
$680$	−2.93283	+	2.46094i	−0.112469	+	0.0943727i
$681$	0.923805	+	0.775164i	0.0354003	+	0.0297044i
$682$	−0.901361	−	0.756332i	−0.0345149	−	0.0289614i
$683$	6.27970	+	10.8768i	0.240286	+	0.416188i	0.960796	−	0.277257i	$-0.0894254\pi$
$683$	6.27970	+	10.8768i	0.240286	+	0.416188i	−0.720510	+	0.693445i	$0.756092\pi$
$684$	−8.96058	+	4.96728i	−0.342616	+	0.189929i
$685$	−5.85051			−0.223536
$686$	10.5733	−	2.97099i	0.403691	−	0.113433i
$687$	5.02559	−	28.5015i	0.191738	−	1.08740i
$688$	2.12719	+	12.0639i	0.0810983	+	0.459931i
$689$	0.492024	−	2.79041i	0.0187446	−	0.106306i
$690$	−0.241881	+	0.202962i	−0.00920824	+	0.00772663i
$691$	26.5693			1.01075			0.505373	−	0.862901i	$-0.331355\pi$
$691$	26.5693			1.01075			0.505373	+	0.862901i	$0.331355\pi$
$692$	−15.7500	+	27.2798i	−0.598725	+	1.03702i
$693$	−1.32359	+	6.54359i	−0.0502790	+	0.248570i
$694$	3.48423	+	1.26816i	0.132260	+	0.0481385i
$695$	−0.743586	−	1.28793i	−0.0282058	−	0.0488539i
$696$	5.48973	−	9.50850i	0.208088	−	0.360419i
$697$	−16.3689	+	13.7352i	−0.620017	+	0.520256i
$698$	−5.62895	+	2.04877i	−0.213059	+	0.0775470i
$699$	10.5922	−	8.88790i	0.400633	−	0.336171i
$700$	11.1831	−	18.2957i	0.422683	−	0.691514i
$701$	−2.59115	+	0.943100i	−0.0978662	+	0.0356204i	−0.390489	−	0.920608i	$-0.627694\pi$
$701$	−2.59115	+	0.943100i	−0.0978662	+	0.0356204i	0.292623	+	0.956228i	$0.405472\pi$
$702$	4.59735	−	7.96284i	0.173516	−	0.300538i
$703$	−16.8240	+	43.8319i	−0.634527	+	1.65315i
$704$	−0.666416	−	1.15427i	−0.0251165	−	0.0435031i
$705$	0.542883	−	3.07884i	0.0204462	−	0.115956i
$706$	3.02141	−	17.1353i	0.113712	−	0.644895i
$707$	3.98928	−	19.7223i	0.150032	−	0.741733i
$708$	−0.212741	−	0.178511i	−0.00799528	−	0.00670884i
$709$	32.2278	+	11.7300i	1.21034	+	0.440528i	0.866822	−	0.498618i	$-0.166159\pi$
$709$	32.2278	+	11.7300i	1.21034	+	0.440528i	0.343518	+	0.939146i	$0.388381\pi$
$710$	1.05206	−	1.82223i	0.0394833	−	0.0683870i
$711$	−7.86852			−0.295092
$712$	−21.4806	+	18.0244i	−0.805019	+	0.675491i
$713$	1.55095	+	0.564499i	0.0580835	+	0.0211407i
$714$	−1.79934	−	11.9471i	−0.0673388	−	0.447108i
$715$	0.712301	+	1.23374i	0.0266385	+	0.0461393i
$716$	16.5436	+	6.02137i	0.618263	+	0.225029i
$717$	−1.65955	+	9.41177i	−0.0619770	+	0.351489i
$718$	−10.7717	−	3.92058i	−0.401996	−	0.146315i
$719$	−12.1061	−	10.1582i	−0.451480	−	0.378837i	0.388505	−	0.921447i	$-0.372992\pi$
$719$	−12.1061	−	10.1582i	−0.451480	−	0.378837i	−0.839985	+	0.542610i	$0.817436\pi$
$720$	−0.777932	+	0.283144i	−0.0289918	+	0.0105522i
$721$	−16.7602	−	6.58009i	−0.624182	−	0.245055i
$722$	−1.56878	−	11.1576i	−0.0583839	−	0.415241i
$723$	−5.79301	+	10.0338i	−0.215444	+	0.373160i
$724$	7.15575	+	6.00439i	0.265941	+	0.223151i
$725$	−18.6890	+	6.80223i	−0.694091	+	0.252629i
$726$	1.01658	+	5.76531i	0.0377288	+	0.213971i
$727$	11.0859	+	9.30215i	0.411152	+	0.344998i	0.824785	−	0.565446i	$-0.191296\pi$
$727$	11.0859	+	9.30215i	0.411152	+	0.344998i	−0.413633	+	0.910444i	$0.635740\pi$
$728$	15.1515	−	5.08873i	0.561553	−	0.188601i
$729$	−12.3671	−	21.4204i	−0.458041	−	0.793350i
$730$	−0.767300	−	1.32900i	−0.0283990	−	0.0491886i
$731$	−6.48374	−	36.7711i	−0.239810	−	1.36003i
$732$	0.493828	+	2.80064i	0.0182524	+	0.103514i
$733$	−19.1658	−	33.1961i	−0.707903	−	1.22612i	−0.965634	−	0.259908i	$-0.916308\pi$
$733$	−19.1658	−	33.1961i	−0.707903	−	1.22612i	0.257730	−	0.966217i	$-0.417025\pi$
$734$	−0.538254	−	0.932283i	−0.0198673	−	0.0344112i
$735$	−1.15464	−	2.25347i	−0.0425896	−	0.0831205i
$736$	−6.22573	−	5.22401i	−0.229484	−	0.192560i
$737$	3.04718	+	17.2814i	0.112244	+	0.636568i
$738$	2.76639	−	1.00689i	0.101832	−	0.0370640i
$739$	35.0671	+	29.4247i	1.28996	+	1.08241i	0.991788	+	0.127896i	$0.0408222\pi$
$739$	35.0671	+	29.4247i	1.28996	+	1.08241i	0.298175	+	0.954511i	$0.403622\pi$
$740$	−2.55939	+	4.43300i	−0.0940852	+	0.162960i
$741$	−9.61015	−	11.8668i	−0.353038	−	0.435938i
$742$	0.237115	+	1.57437i	0.00870476	+	0.0577968i
$743$	−15.0151	+	5.46503i	−0.550849	+	0.200493i	−0.602424	−	0.798177i	$-0.705798\pi$
$743$	−15.0151	+	5.46503i	−0.550849	+	0.200493i	0.0515747	+	0.998669i	$0.483576\pi$
$744$	2.33148	+	1.95634i	0.0854761	+	0.0717230i
$745$	1.54027	+	0.560611i	0.0564310	+	0.0205392i
$746$	0.382477	−	2.16914i	0.0140035	−	0.0794177i
$747$	14.7326	+	5.36221i	0.539036	+	0.196193i
$748$	8.95145	+	15.5044i	0.327298	+	0.566896i
$749$	−31.3198	+	24.9709i	−1.14440	+	0.912417i
$750$	1.99895	+	0.727560i	0.0729915	+	0.0265667i
$751$	24.7316	−	20.7523i	0.902470	−	0.757262i	−0.0682018	−	0.997672i	$-0.521726\pi$
$751$	24.7316	−	20.7523i	0.902470	−	0.757262i	0.970672	+	0.240409i	$0.0772817\pi$
$752$	17.4039			0.634656
$753$	−18.0975	+	31.3457i	−0.659508	+	1.14230i
$754$	−6.29387	−	2.29078i	−0.229209	−	0.0834253i
$755$	1.61354	+	1.35392i	0.0587226	+	0.0492742i
$756$	4.80108	−	23.7357i	0.174614	−	0.863260i
$757$	−1.66155	+	9.42311i	−0.0603900	+	0.342489i	0.939610	+	0.342247i	$0.111188\pi$
$757$	−1.66155	+	9.42311i	−0.0603900	+	0.342489i	−1.00000		0.000241635i	$0.999923\pi$
$758$	2.40639	−	13.6473i	0.0874040	−	0.495693i
$759$	1.63402	+	2.83021i	0.0593112	+	0.102730i
$760$	0.0473703	−	2.71855i	0.00171830	−	0.0986122i
$761$	11.2152	−	19.4252i	0.406549	−	0.704164i	−0.587951	−	0.808896i	$-0.700065\pi$
$761$	11.2152	−	19.4252i	0.406549	−	0.704164i	0.994500	+	0.104732i	$0.0333986\pi$
$762$	−4.46018	+	1.62337i	−0.161575	+	0.0588086i
$763$	9.21810	+	16.9319i	0.333718	+	0.612974i
$764$	−2.01047	+	1.68698i	−0.0727362	+	0.0610329i
$765$	2.37116	−	0.863032i	0.0857295	−	0.0312030i
$766$	2.94828	−	2.47390i	0.106526	−	0.0893857i
$767$	−0.187485	+	0.324734i	−0.00676969	+	0.0117254i
$768$	−3.32898	−	5.76596i	−0.120124	−	0.208061i
$769$	9.78480	+	3.56137i	0.352849	+	0.128426i	0.512363	−	0.858769i	$-0.328770\pi$
$769$	9.78480	+	3.56137i	0.352849	+	0.128426i	−0.159514	+	0.987196i	$0.550993\pi$
$770$	−0.600129	−	0.529738i	−0.0216271	−	0.0190904i
$771$	−19.3712	+	33.5518i	−0.697635	+	1.20834i
$772$	19.5697			0.704330
$773$	−23.5239	+	19.7389i	−0.846096	+	0.709959i	−0.958926	−	0.283655i	$-0.908453\pi$
$773$	−23.5239	+	19.7389i	−0.846096	+	0.709959i	0.112830	+	0.993614i	$0.464008\pi$
$774$	−0.893280	+	5.06604i	−0.0321083	+	0.182095i
$775$	−0.957339	−	5.42934i	−0.0343886	−	0.195028i
$776$	−0.226383	+	1.28388i	−0.00812669	+	0.0460887i
$777$	−17.0956	−	31.4012i	−0.613300	−	1.12651i
$778$	14.6458			0.525079
$779$	0.264387	−	15.1730i	0.00947263	−	0.543628i
$780$	−0.832427	−	1.44181i	−0.0298057	−	0.0516249i
$781$	−16.6827	−	13.9984i	−0.596954	−	0.500904i
$782$	4.10423	+	3.44386i	0.146767	+	0.123152i
$783$	−17.2060	+	14.4376i	−0.614893	+	0.515957i
$784$	11.2380	−	8.50847i	0.401358	−	0.303874i
$785$	−0.381833	−	2.16548i	−0.0136282	−	0.0772893i
$786$	11.8460			0.422534
$787$	−28.6863			−1.02256			−0.511278	−	0.859415i	$-0.670828\pi$
$787$	−28.6863			−1.02256			−0.511278	+	0.859415i	$0.670828\pi$
$788$	−6.35659	−	36.0500i	−0.226444	−	1.28423i
$789$	−13.1271	+	11.0150i	−0.467338	+	0.392143i
$790$	0.471729	−	0.817058i	0.0167834	−	0.0290696i
$791$	32.4795	−	25.8955i	1.15484	−	0.920738i
$792$	−0.947994	−	5.37634i	−0.0336855	−	0.191040i
$793$	3.60821	−	1.31328i	0.128131	−	0.0466359i
$794$	4.49213	+	1.63500i	0.159420	+	0.0580241i
$795$	0.344924	−	0.125542i	0.0122332	−	0.00445252i
$796$	−6.25688	+	35.4846i	−0.221769	+	1.25772i
$797$	7.55314			0.267546			0.133773	−	0.991012i	$-0.457291\pi$
$797$	7.55314			0.267546			0.133773	+	0.991012i	$0.457291\pi$
$798$	7.24190	+	4.60177i	0.256361	+	0.162901i
$799$	−53.0477			−1.87669
$800$	−4.71401	+	26.7345i	−0.166665	+	0.945207i
$801$	17.3668	−	6.32100i	0.613626	−	0.223342i
$802$	−1.26342	−	0.459846i	−0.0446128	−	0.0162377i
$803$	−14.9252	+	5.43234i	−0.526700	+	0.191703i
$804$	−3.56107	−	20.1958i	−0.125589	−	0.712251i
$805$	1.04518	+	0.410340i	0.0368378	+	0.0144626i
$806$	0.928320	−	1.60790i	0.0326987	−	0.0566358i
$807$	−14.0232	+	11.7669i	−0.493642	+	0.414215i
$808$	2.85724	+	16.2042i	0.100517	+	0.570062i
$809$	−3.70169			−0.130145			−0.0650723	−	0.997881i	$-0.520728\pi$
$809$	−3.70169			−0.130145			−0.0650723	+	0.997881i	$0.520728\pi$
$810$	0.459726			0.0161531
$811$	4.87760	+	27.6622i	0.171276	+	0.971353i	0.942355	+	0.334614i	$0.108606\pi$
$811$	4.87760	+	27.6622i	0.171276	+	0.971353i	−0.771080	+	0.636739i	$0.780283\pi$
$812$	−17.6347	−	0.441784i	−0.618857	−	0.0155036i
$813$	−17.6258	+	14.7898i	−0.618165	+	0.518702i
$814$	−8.65862	−	7.26544i	−0.303484	−	0.254654i
$815$	−2.34321	−	1.96619i	−0.0820792	−	0.0688726i
$816$	−7.75307	−	13.4287i	−0.271412	−	0.470099i
$817$	22.7300	+	13.6566i	0.795221	+	0.477784i
$818$	−20.7870			−0.726799
$819$	−10.5310	−	0.263823i	−0.367984	−	0.00921871i
$820$	0.287303	−	1.62938i	0.0100331	−	0.0569004i
$821$	−1.92440	−	10.9138i	−0.0671619	−	0.380894i	−0.999798	−	0.0200769i	$-0.993609\pi$
$821$	−1.92440	−	10.9138i	−0.0671619	−	0.380894i	0.932636	−	0.360817i	$-0.117502\pi$
$822$	−2.62165	+	14.8681i	−0.0914404	+	0.518584i
$823$	28.8924	−	24.2436i	1.00712	−	0.845078i	0.0191689	−	0.999816i	$-0.493898\pi$
$823$	28.8924	−	24.2436i	1.00712	−	0.845078i	0.987955	+	0.154739i	$0.0494535\pi$
$824$	14.7238			0.512927
$825$	5.45810	−	9.45370i	0.190027	−	0.329136i
$826$	0.0417721	−	0.206514i	0.00145344	−	0.00718553i
$827$	−5.67829	−	2.06673i	−0.197454	−	0.0718672i	0.241400	−	0.970426i	$-0.422393\pi$
$827$	−5.67829	−	2.06673i	−0.197454	−	0.0718672i	−0.438854	+	0.898558i	$0.644615\pi$
$828$	1.72991	+	2.99628i	0.0601184	+	0.104128i
$829$	−2.11187	+	3.65787i	−0.0733484	+	0.127043i	−0.900367	−	0.435132i	$-0.856702\pi$
$829$	−2.11187	+	3.65787i	−0.0733484	+	0.127043i	0.827018	+	0.562175i	$0.190035\pi$
$830$	−1.44004	+	1.20834i	−0.0499847	+	0.0419421i
$831$	−15.9497	+	5.80520i	−0.553287	+	0.201380i
$832$	1.61106	−	1.35184i	0.0558536	−	0.0468667i
$833$	−34.2539	+	25.9341i	−1.18683	+	0.898562i
$834$	−3.60626	+	1.31257i	−0.124875	+	0.0454506i
$835$	0.967060	−	1.67500i	0.0334665	−	0.0579657i
$836$	−12.4808	−	2.42563i	−0.431658	−	0.0838923i
$837$	−3.11310	−	5.39204i	−0.107604	−	0.186376i
$838$	−2.38398	+	13.5202i	−0.0823534	+	0.467049i
$839$	−6.63381	+	37.6222i	−0.229024	+	1.29886i	0.625816	+	0.779971i	$0.284766\pi$
$839$	−6.63381	+	37.6222i	−0.229024	+	1.29886i	−0.854840	+	0.518891i	$0.826345\pi$
$840$	1.55230	+	1.37023i	0.0535596	+	0.0472774i
$841$	−9.68171	−	8.12392i	−0.333852	−	0.280135i
$842$	−15.8841	−	5.78133i	−0.547402	−	0.199238i
$843$	−9.66031	+	16.7321i	−0.332719	+	0.576286i
$844$	−5.24447			−0.180522
$845$	1.14921	−	0.964302i	0.0395340	−	0.0331730i
$846$	6.86775	+	2.49966i	0.236118	+	0.0859400i
$847$	16.2778	−	12.9781i	0.559313	−	0.445933i
$848$	1.02169	+	1.76962i	0.0350849	+	0.0607689i
$849$	−25.8026	−	9.39137i	−0.885542	−	0.322311i
$850$	3.10765	−	17.6244i	0.106592	−	0.604511i
$851$	14.8987	+	5.42267i	0.510720	+	0.185887i
$852$	19.4962	+	16.3592i	0.667927	+	0.560458i
$853$	−12.2656	+	4.46431i	−0.419966	+	0.152855i	−0.543355	−	0.839503i	$-0.682846\pi$
$853$	−12.2656	+	4.46431i	−0.419966	+	0.152855i	0.123388	+	0.992358i	$0.460624\pi$
$854$	−1.68701	+	1.34503i	−0.0577283	+	0.0460261i
$855$	−0.642156	+	1.67302i	−0.0219613	+	0.0572162i
$856$	16.3775	−	28.3667i	0.559772	−	0.969554i
$857$	22.3427	+	18.7478i	0.763212	+	0.640411i	0.938961	−	0.344024i	$-0.111790\pi$
$857$	22.3427	+	18.7478i	0.763212	+	0.640411i	−0.175749	+	0.984435i	$0.556235\pi$
$858$	3.45453	−	1.25735i	0.117936	−	0.0429251i
$859$	−1.54703	−	8.77366i	−0.0527841	−	0.299353i	0.946975	−	0.321308i	$-0.104122\pi$
$859$	−1.54703	−	8.77366i	−0.0527841	−	0.299353i	−0.999759	+	0.0219541i	$0.993011\pi$
$860$	2.21469	+	1.85835i	0.0755204	+	0.0633691i
$861$	8.66383	+	7.64762i	0.295263	+	0.260630i
$862$	−10.8555	−	18.8023i	−0.369740	−	0.640409i
$863$	−12.7581	−	22.0976i	−0.434289	−	0.752211i	0.562948	−	0.826492i	$-0.309667\pi$
$863$	−12.7581	−	22.0976i	−0.434289	−	0.752211i	−0.997237	+	0.0742812i	$0.976334\pi$
$864$	5.32375	+	30.1925i	0.181118	+	1.02717i
$865$	0.956757	+	5.42604i	0.0325307	+	0.184491i
$866$	−6.63327	−	11.4892i	−0.225408	−	0.390418i
$867$	12.9674	+	22.4602i	0.440396	+	0.762788i
$868$	0.969459	−	4.79284i	0.0329056	−	0.162680i
$869$	−7.48026	−	6.27668i	−0.253750	−	0.212922i
$870$	−0.150669	−	0.854485i	−0.00510815	−	0.0289697i
$871$	−26.0193	+	9.47026i	−0.881631	+	0.320887i
$872$	−12.0764	−	10.1333i	−0.408960	−	0.343158i
$873$	0.429621	−	0.744126i	0.0145405	−	0.0251849i
$874$	−3.75808	+	0.595338i	−0.127119	+	0.0201376i
$875$	−1.12661	−	7.48030i	−0.0380862	−	0.252880i
$876$	17.4423	−	6.34848i	0.589321	−	0.214495i
$877$	−26.8966	−	22.5690i	−0.908235	−	0.762099i	0.0635476	−	0.997979i	$-0.479759\pi$
$877$	−26.8966	−	22.5690i	−0.908235	−	0.762099i	−0.971782	+	0.235879i	$0.924203\pi$
$878$	−16.3195	−	5.93982i	−0.550757	−	0.200459i
$879$	−1.19970	+	6.80384i	−0.0404649	+	0.229488i
$880$	−0.965408	−	0.351380i	−0.0325439	−	0.0118450i
$881$	−20.1042	−	34.8214i	−0.677326	−	1.17316i	−0.975783	−	0.218740i	$-0.929805\pi$
$881$	−20.1042	−	34.8214i	−0.677326	−	1.17316i	0.298457	−	0.954423i	$-0.403528\pi$
$882$	5.65667	−	1.74345i	0.190470	−	0.0587049i
$883$	−6.13733	−	2.23381i	−0.206538	−	0.0751735i	0.236680	−	0.971588i	$-0.423941\pi$
$883$	−6.13733	−	2.23381i	−0.206538	−	0.0751735i	−0.443217	+	0.896414i	$0.646163\pi$
$884$	−21.6402	+	18.1583i	−0.727837	+	0.610728i
$885$	−0.0485755			−0.00163285
$886$	−3.23947	+	5.61093i	−0.108832	+	0.188503i
$887$	51.0763	+	18.5903i	1.71497	+	0.624200i	0.997385	−	0.0722674i	$-0.0230235\pi$
$887$	51.0763	+	18.5903i	1.71497	+	0.624200i	0.717589	+	0.696467i	$0.245246\pi$
$888$	22.3965	+	18.7929i	0.751579	+	0.630649i
$889$	12.6541	+	11.1698i	0.424404	+	0.374625i
$890$	−0.384799	+	2.18230i	−0.0128985	+	0.0731510i
$891$	0.826246	−	4.68587i	0.0276803	−	0.156983i
$892$	15.6058	+	27.0301i	0.522521	+	0.905034i
$893$	24.7152	−	28.4334i	0.827064	−	0.951487i
$894$	2.11490	−	3.66312i	0.0707330	−	0.122513i
$895$	2.89368	−	1.05321i	0.0967252	−	0.0352051i
$896$	−15.8530	+	25.9357i	−0.529612	+	0.866451i
$897$	−3.95025	+	3.31465i	−0.131895	+	0.110673i
$898$	22.2599	−	8.10192i	0.742821	−	0.270365i
$899$	−3.47433	+	2.91531i	−0.115875	+	0.0972310i
$900$	5.77838	−	10.0085i	0.192613	−	0.333615i
$901$	−3.11414	−	5.39385i	−0.103747	−	0.179695i
$902$	3.43308	+	1.24954i	0.114309	+	0.0416051i
$903$	−19.1425	+	6.42913i	−0.637024	+	0.213948i
$904$	−16.9839	+	29.4171i	−0.564878	+	0.978397i
$905$	1.63389			0.0543123
$906$	4.16380	−	3.49384i	0.138333	−	0.116075i
$907$	−7.74755	+	43.9385i	−0.257253	+	1.45895i	0.532969	+	0.846135i	$0.321076\pi$
$907$	−7.74755	+	43.9385i	−0.257253	+	1.45895i	−0.790222	+	0.612820i	$0.790035\pi$
$908$	0.275126	+	1.56032i	0.00913037	+	0.0517809i
$909$	1.88317	−	10.6800i	0.0624607	−	0.354232i
$910$	0.658745	−	1.07771i	0.0218372	−	0.0357259i
$911$	−8.93982			−0.296189			−0.148095	−	0.988973i	$-0.547314\pi$
$911$	−8.93982			−0.296189			−0.148095	+	0.988973i	$0.547314\pi$
$912$	10.8099	+	2.10090i	0.357953	+	0.0695677i
$913$	9.72819	+	16.8497i	0.321956	+	0.557644i
$914$	16.2689	+	13.6512i	0.538128	+	0.451543i
$915$	0.381049	+	0.319738i	0.0125971	+	0.0105702i
$916$	29.1276	−	24.4410i	0.962404	−	0.807553i
$917$	−20.1425	−	36.9979i	−0.665165	−	1.22178i
$918$	−3.50961	−	19.9040i	−0.115834	−	0.656930i
$919$	−28.3708			−0.935865			−0.467933	−	0.883764i	$-0.655001\pi$
$919$	−28.3708			−0.935865			−0.467933	+	0.883764i	$0.655001\pi$
$920$	−0.918188			−0.0302718
$921$	−0.536026	−	3.03995i	−0.0176627	−	0.100170i
$922$	−2.96586	+	2.48865i	−0.0976754	+	0.0819594i
$923$	17.1817	−	29.7595i	0.565541	−	0.979546i
$924$	7.57057	−	6.03592i	0.249053	−	0.198567i
$925$	−9.19635	−	52.1551i	−0.302374	−	1.71485i
$926$	4.35602	−	1.58546i	0.143148	−	0.0521015i
$927$	−9.11899	−	3.31904i	−0.299507	−	0.109012i
$928$	20.9859	−	7.63824i	0.688896	−	0.250738i
$929$	−4.41078	+	25.0148i	−0.144713	+	0.820708i	0.822884	+	0.568209i	$0.192364\pi$
$929$	−4.41078	+	25.0148i	−0.144713	+	0.820708i	−0.967597	+	0.252499i	$0.918748\pi$
$930$	0.240519			0.00788692
$931$	2.05852	−	30.4428i	0.0674653	−	0.997722i
$932$	18.1663			0.595057
$933$	2.10182	−	11.9200i	0.0688106	−	0.390245i
$934$	12.5192	−	4.55661i	0.409640	−	0.149097i
$935$	2.94260	+	1.07102i	0.0962332	+	0.0350260i
$936$	8.09476	−	2.94625i	0.264586	−	0.0963013i
$937$	3.24378	+	18.3964i	0.105970	+	0.600984i	0.990829	+	0.135125i	$0.0431435\pi$
$937$	3.24378	+	18.3964i	0.105970	+	0.600984i	−0.884859	+	0.465859i	$0.845745\pi$
$938$	12.1653	−	9.69924i	0.397211	−	0.316691i
$939$	−1.13046	+	1.95802i	−0.0368913	+	0.0638977i
$940$	3.14648	−	2.64021i	0.102627	−	0.0861142i
$941$	4.05981	+	23.0243i	0.132346	+	0.750571i	0.976671	+	0.214740i	$0.0688905\pi$
$941$	4.05981	+	23.0243i	0.132346	+	0.750571i	−0.844325	+	0.535831i	$0.819998\pi$
$942$	−5.67431			−0.184879
$943$	−5.12466			−0.166882
$944$	−0.0469568	−	0.266305i	−0.00152831	−	0.00866750i
$945$	−2.02535	−	3.72016i	−0.0658845	−	0.121017i
$946$	−4.89036	+	4.10350i	−0.158999	+	0.133416i
$947$	21.7390	+	18.2412i	0.706422	+	0.592759i	0.923593	−	0.383375i	$-0.125238\pi$
$947$	21.7390	+	18.2412i	0.706422	+	0.592759i	−0.217170	+	0.976134i	$0.569683\pi$
$948$	8.74177	+	7.33521i	0.283919	+	0.238237i
$949$	−12.5311	−	21.7044i	−0.406776	−	0.704556i
$950$	7.99871	+	9.87698i	0.259513	+	0.320451i
$951$	30.8860			1.00155
$952$	18.3230	−	29.9767i	0.593853	−	0.971549i
$953$	−0.890102	+	5.04802i	−0.0288332	+	0.163521i	−0.995825	−	0.0912880i	$-0.970902\pi$
$953$	−0.890102	+	5.04802i	−0.0288332	+	0.163521i	0.966991	+	0.254809i	$0.0820127\pi$
$954$	0.149005	+	0.845048i	0.00482421	+	0.0273594i
$955$	−0.0797140	+	0.452080i	−0.00257948	+	0.0146290i
$956$	−9.61853	+	8.07090i	−0.311085	+	0.261032i
$957$	−8.98034			−0.290293
$958$	−2.24060	+	3.88084i	−0.0723906	+	0.125384i
$959$	50.8942	−	17.0931i	1.64346	−	0.551966i
$960$	0.256015	+	0.0931818i	0.00826285	+	0.00300743i
$961$	14.8714	+	25.7580i	0.479722	+	0.830903i
$962$	8.91759	−	15.4457i	0.287515	−	0.497990i
$963$	−16.5377	+	13.8768i	−0.532919	+	0.447172i
$964$	−14.3039	+	5.20620i	−0.460698	+	0.167680i
$965$	2.62216	−	2.20026i	0.0844104	−	0.0708288i
$966$	1.51116	−	2.47228i	0.0486209	−	0.0795443i
$967$	37.1610	−	13.5255i	1.19502	−	0.434951i	0.333536	−	0.942738i	$-0.391758\pi$
$967$	37.1610	−	13.5255i	1.19502	−	0.434951i	0.861483	+	0.507786i	$0.169536\pi$
$968$	−8.51189	+	14.7430i	−0.273582	+	0.473859i
$969$	−32.9490	−	6.40361i	−1.05848	−	0.205714i
$970$	0.0515129	+	0.0892229i	0.00165398	+	0.00286477i
$971$	−4.77843	+	27.0998i	−0.153347	+	0.869675i	0.806934	+	0.590641i	$0.201125\pi$
$971$	−4.77843	+	27.0998i	−0.153347	+	0.869675i	−0.960281	+	0.279033i	$0.909986\pi$
$972$	3.80259	−	21.5655i	0.121968	−	0.691715i
$973$	10.2314	+	9.03133i	0.328004	+	0.289531i
$974$	8.24411	+	6.91763i	0.264158	+	0.221655i
$975$	16.1860	+	5.89123i	0.518368	+	0.188670i
$976$	−1.38455	+	2.39810i	−0.0443182	+	0.0767614i
$977$	34.1076			1.09120			0.545600	−	0.838046i	$-0.316302\pi$
$977$	34.1076			1.09120			0.545600	+	0.838046i	$0.316302\pi$
$978$	−6.04675	+	5.07383i	−0.193354	+	0.162243i
$979$	21.5521	+	7.84432i	0.688808	+	0.250706i
$980$	0.740988	−	3.24309i	0.0236700	−	0.103597i
$981$	5.19514	+	8.99824i	0.165868	+	0.287292i
$982$	−15.8915	−	5.78405i	−0.507120	−	0.184576i
$983$	1.58651	−	8.99752i	0.0506017	−	0.286976i	−0.948998	−	0.315283i	$-0.897900\pi$
$983$	1.58651	−	8.99752i	0.0506017	−	0.286976i	0.999599	+	0.0283069i	$0.00901158\pi$
$984$	−8.88007	−	3.23208i	−0.283086	−	0.103035i
$985$	−4.90489	−	4.11569i	−0.156283	−	0.131137i
$986$	−13.8347	+	5.03541i	−0.440586	+	0.160360i
$987$	4.27269	+	28.3693i	0.136001	+	0.903005i
$988$	0.349526	−	20.0591i	0.0111199	−	0.638164i
$989$	4.47738	−	7.75505i	0.142372	−	0.246596i
$990$	−0.330492	−	0.277316i	−0.0105037	−	0.00881367i
$991$	36.8194	−	13.4012i	1.16961	−	0.425702i	0.317087	−	0.948396i	$-0.397295\pi$
$991$	36.8194	−	13.4012i	1.16961	−	0.425702i	0.852520	+	0.522694i	$0.175073\pi$
$992$	1.07500	+	6.09662i	0.0341312	+	0.193568i
$993$	−15.5455	−	13.0442i	−0.493322	−	0.413946i
$994$	−3.82811	+	18.9255i	−0.121420	+	0.600281i
$995$	3.15122	+	5.45808i	0.0999005	+	0.173033i
$996$	−11.3688	−	19.6913i	−0.360234	−	0.623944i
$997$	5.47017	+	31.0229i	0.173242	+	0.982505i	0.940153	+	0.340752i	$0.110682\pi$
$997$	5.47017	+	31.0229i	0.173242	+	0.982505i	−0.766911	+	0.641753i	$0.778207\pi$
$998$	3.78167	+	21.4469i	0.119707	+	0.678890i
$999$	−29.9049	−	51.7968i	−0.946149	−	1.63878i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.w.a.100.7	yes	66
7.2	even	3		931.2.w.f.442.5		66
7.3	odd	6		931.2.v.h.214.7		66
7.4	even	3		133.2.u.a.81.7	yes	66
7.5	odd	6		931.2.w.e.442.5		66
7.6	odd	2		931.2.x.h.765.7		66
19.4	even	9		133.2.u.a.23.7	✓	66
133.4	even	9	inner	133.2.w.a.4.7	yes	66
133.23	even	9		931.2.w.f.99.5		66
133.61	odd	18		931.2.w.e.99.5		66
133.80	odd	18		931.2.x.h.802.7		66
133.118	odd	18		931.2.v.h.422.7		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.u.a.23.7	✓	66	19.4	even	9
133.2.u.a.81.7	yes	66	7.4	even	3
133.2.w.a.4.7	yes	66	133.4	even	9	inner
133.2.w.a.100.7	yes	66	1.1	even	1	trivial
931.2.v.h.214.7		66	7.3	odd	6
931.2.v.h.422.7		66	133.118	odd	18
931.2.w.e.99.5		66	133.61	odd	18
931.2.w.e.442.5		66	7.5	odd	6
931.2.w.f.99.5		66	133.23	even	9
931.2.w.f.442.5		66	7.2	even	3
931.2.x.h.765.7		66	7.6	odd	2
931.2.x.h.802.7		66	133.80	odd	18

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	133.2.w.a.100.7

Level	$133$
Weight	$2$
Character	133.100
Analytic conductor	$1.062$
Analytic rank	$0$
Dimension	$66$
Inner twists	$2$