LMFDB - Embedded newform 961.2.d.r.531.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.4
Character	$\chi$	$=$	961.531
Dual form			961.2.d.r.628.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.557046 - 1.71441i) q^{2} +(0.0590122 - 0.181621i) q^{3} +(-1.01088 + 0.734444i) q^{4} -2.46636 q^{5} -0.344245 q^{6} +(0.851208 - 0.618439i) q^{7} +(-1.09449 - 0.795192i) q^{8} +(2.39755 + 1.74192i) q^{9} +(1.37388 + 4.22837i) q^{10} +(4.34407 - 3.15615i) q^{11} +(0.0737363 + 0.226937i) q^{12} +(-0.381155 + 1.17308i) q^{13} +(-1.53442 - 1.11482i) q^{14} +(-0.145545 + 0.447943i) q^{15} +(-1.52585 + 4.69607i) q^{16} +(-4.59028 - 3.33504i) q^{17} +(1.65082 - 5.08072i) q^{18} +(-1.44089 - 4.43461i) q^{19} +(2.49319 - 1.81141i) q^{20} +(-0.0620897 - 0.191092i) q^{21} +(-7.83080 - 5.68941i) q^{22} +(-4.84106 - 3.51724i) q^{23} +(-0.209012 + 0.151856i) q^{24} +1.08295 q^{25} +2.22346 q^{26} +(0.921341 - 0.669393i) q^{27} +(-0.406257 + 1.25033i) q^{28} +(-1.11492 - 3.43137i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(-0.316870 - 0.975226i) q^{33} +(-3.16063 + 9.72741i) q^{34} +(-2.09939 + 1.52530i) q^{35} -3.70296 q^{36} -5.35407 q^{37} +(-6.80010 + 4.94056i) q^{38} +(0.190562 + 0.138451i) q^{39} +(2.69941 + 1.96123i) q^{40} +(3.26410 + 10.0459i) q^{41} +(-0.293024 + 0.212895i) q^{42} +(0.934399 + 2.87578i) q^{43} +(-2.07330 + 6.38096i) q^{44} +(-5.91323 - 4.29621i) q^{45} +(-3.33330 + 10.2588i) q^{46} +(1.74104 - 5.35837i) q^{47} +(0.762861 + 0.554251i) q^{48} +(-1.82103 + 5.60456i) q^{49} +(-0.603255 - 1.85663i) q^{50} +(-0.876594 + 0.636883i) q^{51} +(-0.476258 - 1.46577i) q^{52} +(0.735142 + 0.534112i) q^{53} +(-1.66085 - 1.20668i) q^{54} +(-10.7141 + 7.78423i) q^{55} -1.42341 q^{56} -0.890447 q^{57} +(-5.26172 + 3.82286i) q^{58} +(0.947187 - 2.91514i) q^{59} +(-0.181861 - 0.559710i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(-0.399349 - 1.22907i) q^{64} +(0.940068 - 2.89323i) q^{65} +(-1.49543 + 1.08649i) q^{66} +7.96488 q^{67} +7.08960 q^{68} +(-0.924485 + 0.671678i) q^{69} +(3.78444 + 2.74956i) q^{70} +(-4.90960 - 3.56703i) q^{71} +(-1.23893 - 3.81302i) q^{72} +(-3.06534 + 2.22710i) q^{73} +(2.98246 + 9.17908i) q^{74} +(0.0639074 - 0.196687i) q^{75} +(4.71353 + 3.42458i) q^{76} +(1.74582 - 5.37309i) q^{77} +(0.131211 - 0.403826i) q^{78} +(-6.88485 - 5.00213i) q^{79} +(3.76329 - 11.5822i) q^{80} +(2.68014 + 8.24862i) q^{81} +(15.4045 - 11.1920i) q^{82} +(-4.08933 - 12.5857i) q^{83} +(0.203112 + 0.147569i) q^{84} +(11.3213 + 8.22541i) q^{85} +(4.40978 - 3.20389i) q^{86} -0.689002 q^{87} -7.26429 q^{88} +(0.713499 - 0.518388i) q^{89} +(-4.07153 + 12.5309i) q^{90} +(0.401033 + 1.23425i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(3.55376 + 10.9374i) q^{95} +(0.365595 - 1.12519i) q^{96} +(-6.99151 + 5.07963i) q^{97} +10.6229 q^{98} +15.9129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) $ 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.557046	−	1.71441i	−0.393891	−	1.21227i	−0.929822	−	0.368011i	$-0.880039\pi$
$2$	−0.557046	−	1.71441i	−0.393891	−	1.21227i	0.535930	−	0.844262i	$-0.319961\pi$
$3$	0.0590122	−	0.181621i	0.0340707	−	0.104859i	−0.932575	−	0.360976i	$-0.882443\pi$
$3$	0.0590122	−	0.181621i	0.0340707	−	0.104859i	0.966646	+	0.256118i	$0.0824435\pi$
$4$	−1.01088	+	0.734444i	−0.505438	+	0.367222i
$5$	−2.46636			−1.10299			−0.551496	−	0.834178i	$-0.685943\pi$
$5$	−2.46636			−1.10299			−0.551496	+	0.834178i	$0.685943\pi$
$6$	−0.344245			−0.140538
$7$	0.851208	−	0.618439i	0.321726	−	0.233748i	−0.415185	−	0.909737i	$-0.636283\pi$
$7$	0.851208	−	0.618439i	0.321726	−	0.233748i	0.736912	+	0.675989i	$0.236283\pi$
$8$	−1.09449	−	0.795192i	−0.386960	−	0.281143i
$9$	2.39755	+	1.74192i	0.799182	+	0.580640i
$10$	1.37388	+	4.22837i	0.434459	+	1.33713i
$11$	4.34407	−	3.15615i	1.30979	−	0.951616i	0.309788	−	0.950806i	$-0.399742\pi$
$11$	4.34407	−	3.15615i	1.30979	−	0.951616i	1.00000		0.000810714i	$-0.000258058\pi$
$12$	0.0737363	+	0.226937i	0.0212858	+	0.0655111i
$13$	−0.381155	+	1.17308i	−0.105714	+	0.325353i	−0.989897	−	0.141787i	$-0.954715\pi$
$13$	−0.381155	+	1.17308i	−0.105714	+	0.325353i	0.884184	+	0.467139i	$0.154715\pi$
$14$	−1.53442	−	1.11482i	−0.410091	−	0.297949i
$15$	−0.145545	+	0.447943i	−0.0375797	+	0.115658i
$16$	−1.52585	+	4.69607i	−0.381462	+	1.17402i
$17$	−4.59028	−	3.33504i	−1.11331	−	0.808865i	−0.130126	−	0.991497i	$-0.541538\pi$
$17$	−4.59028	−	3.33504i	−1.11331	−	0.808865i	−0.983181	+	0.182633i	$0.941538\pi$
$18$	1.65082	−	5.08072i	0.389103	−	1.19754i
$19$	−1.44089	−	4.43461i	−0.330563	−	1.01737i	−0.968867	−	0.247584i	$-0.920364\pi$
$19$	−1.44089	−	4.43461i	−0.330563	−	1.01737i	0.638304	−	0.769785i	$-0.279636\pi$
$20$	2.49319	−	1.81141i	0.557494	−	0.405043i
$21$	−0.0620897	−	0.191092i	−0.0135491	−	0.0416998i
$22$	−7.83080	−	5.68941i	−1.66953	−	1.21299i
$23$	−4.84106	−	3.51724i	−1.00943	−	0.733395i	−0.0453419	−	0.998972i	$-0.514438\pi$
$23$	−4.84106	−	3.51724i	−1.00943	−	0.733395i	−0.964090	+	0.265576i	$0.914438\pi$
$24$	−0.209012	+	0.151856i	−0.0426643	+	0.0309974i
$25$	1.08295			0.216591
$26$	2.22346			0.436056
$27$	0.921341	−	0.669393i	0.177312	−	0.128825i
$28$	−0.406257	+	1.25033i	−0.0767753	+	0.236290i
$29$	−1.11492	−	3.43137i	−0.207035	−	0.637189i	−0.999624	−	0.0274321i	$-0.991267\pi$
$29$	−1.11492	−	3.43137i	−0.207035	−	0.637189i	0.792588	−	0.609757i	$-0.208733\pi$
$30$	0.849035			0.155012
$31$		0			0
$31$		0			0
$32$	6.19525			1.09518
$33$	−0.316870	−	0.975226i	−0.0551600	−	0.169765i
$34$	−3.16063	+	9.72741i	−0.542043	+	1.66824i
$35$	−2.09939	+	1.52530i	−0.354862	+	0.257822i
$36$	−3.70296			−0.617161
$37$	−5.35407			−0.880203			−0.440102	−	0.897948i	$-0.645058\pi$
$37$	−5.35407			−0.880203			−0.440102	+	0.897948i	$0.645058\pi$
$38$	−6.80010	+	4.94056i	−1.10312	+	0.801465i
$39$	0.190562	+	0.138451i	0.0305144	+	0.0221700i
$40$	2.69941	+	1.96123i	0.426814	+	0.310098i
$41$	3.26410	+	10.0459i	0.509767	+	1.56890i	0.792607	+	0.609733i	$0.208723\pi$
$41$	3.26410	+	10.0459i	0.509767	+	1.56890i	−0.282840	+	0.959167i	$0.591277\pi$
$42$	−0.293024	+	0.212895i	−0.0452146	+	0.0328504i
$43$	0.934399	+	2.87578i	0.142494	+	0.438553i	0.996680	−	0.0814150i	$-0.0259439\pi$
$43$	0.934399	+	2.87578i	0.142494	+	0.438553i	−0.854186	+	0.519968i	$0.825944\pi$
$44$	−2.07330	+	6.38096i	−0.312562	+	0.961966i
$45$	−5.91323	−	4.29621i	−0.881492	−	0.640441i
$46$	−3.33330	+	10.2588i	−0.491468	+	1.51258i
$47$	1.74104	−	5.35837i	0.253957	−	0.781599i	−0.740076	−	0.672523i	$-0.765211\pi$
$47$	1.74104	−	5.35837i	0.253957	−	0.781599i	0.994033	−	0.109076i	$-0.0347893\pi$
$48$	0.762861	+	0.554251i	0.110109	+	0.0799992i
$49$	−1.82103	+	5.60456i	−0.260147	+	0.800651i
$50$	−0.603255	−	1.85663i	−0.0853132	−	0.262567i
$51$	−0.876594	+	0.636883i	−0.122748	+	0.0891815i
$52$	−0.476258	−	1.46577i	−0.0660451	−	0.203266i
$53$	0.735142	+	0.534112i	0.100980	+	0.0733659i	0.637129	−	0.770757i	$-0.280122\pi$
$53$	0.735142	+	0.534112i	0.100980	+	0.0733659i	−0.536150	+	0.844123i	$0.680122\pi$
$54$	−1.66085	−	1.20668i	−0.226012	−	0.164208i
$55$	−10.7141	+	7.78423i	−1.44468	+	1.04962i
$56$	−1.42341			−0.190212
$57$	−0.890447			−0.117943
$58$	−5.26172	+	3.82286i	−0.690898	+	0.501967i
$59$	0.947187	−	2.91514i	0.123313	−	0.379519i	−0.870277	−	0.492563i	$-0.836060\pi$
$59$	0.947187	−	2.91514i	0.123313	−	0.379519i	0.993590	+	0.113044i	$0.0360601\pi$
$60$	−0.181861	−	0.559710i	−0.0234781	−	0.0722582i
$61$	−9.12376			−1.16818			−0.584089	−	0.811690i	$-0.698548\pi$
$61$	−9.12376			−1.16818			−0.584089	+	0.811690i	$0.698548\pi$
$62$		0			0
$63$	3.11808			0.392841
$64$	−0.399349	−	1.22907i	−0.0499186	−	0.153634i
$65$	0.940068	−	2.89323i	0.116601	−	0.358861i
$66$	−1.49543	+	1.08649i	−0.184074	+	0.133738i
$67$	7.96488			0.973065			0.486532	−	0.873663i	$-0.338262\pi$
$67$	7.96488			0.973065			0.486532	+	0.873663i	$0.338262\pi$
$68$	7.08960			0.859741
$69$	−0.924485	+	0.671678i	−0.111295	+	0.0808605i
$70$	3.78444	+	2.74956i	0.452327	+	0.328635i
$71$	−4.90960	−	3.56703i	−0.582662	−	0.423329i	0.257021	−	0.966406i	$-0.417259\pi$
$71$	−4.90960	−	3.56703i	−0.582662	−	0.423329i	−0.839683	+	0.543077i	$0.817259\pi$
$72$	−1.23893	−	3.81302i	−0.146009	−	0.449369i
$73$	−3.06534	+	2.22710i	−0.358770	+	0.260662i	−0.752539	−	0.658548i	$-0.771171\pi$
$73$	−3.06534	+	2.22710i	−0.358770	+	0.260662i	0.393769	+	0.919210i	$0.371171\pi$
$74$	2.98246	+	9.17908i	0.346704	+	1.06705i
$75$	0.0639074	−	0.196687i	0.00737939	−	0.0227114i
$76$	4.71353	+	3.42458i	0.540679	+	0.392826i
$77$	1.74582	−	5.37309i	0.198955	−	0.612320i
$78$	0.131211	−	0.403826i	0.0148567	−	0.0457243i
$79$	−6.88485	−	5.00213i	−0.774606	−	0.562784i	0.128749	−	0.991677i	$-0.458904\pi$
$79$	−6.88485	−	5.00213i	−0.774606	−	0.562784i	−0.903355	+	0.428893i	$0.858904\pi$
$80$	3.76329	−	11.5822i	0.420749	−	1.29493i
$81$	2.68014	+	8.24862i	0.297793	+	0.916513i
$82$	15.4045	−	11.1920i	1.70114	−	1.23595i
$83$	−4.08933	−	12.5857i	−0.448863	−	1.38146i	−0.878192	−	0.478309i	$-0.841250\pi$
$83$	−4.08933	−	12.5857i	−0.448863	−	1.38146i	0.429329	−	0.903148i	$-0.358750\pi$
$84$	0.203112	+	0.147569i	0.0221613	+	0.0161011i
$85$	11.3213	+	8.22541i	1.22797	+	0.892171i
$86$	4.40978	−	3.20389i	0.475518	−	0.345484i
$87$	−0.689002			−0.0738687
$88$	−7.26429			−0.774376
$89$	0.713499	−	0.518388i	0.0756308	−	0.0549490i	−0.549327	−	0.835607i	$-0.685116\pi$
$89$	0.713499	−	0.518388i	0.0756308	−	0.0549490i	0.624958	+	0.780658i	$0.285116\pi$
$90$	−4.07153	+	12.5309i	−0.429177	+	1.32087i
$91$	0.401033	+	1.23425i	0.0420397	+	0.129385i
$92$	7.47693			0.779524
$93$		0			0
$94$	−10.1563			−1.04754
$95$	3.55376	+	10.9374i	0.364608	+	1.12215i
$96$	0.365595	−	1.12519i	0.0373134	−	0.114839i
$97$	−6.99151	+	5.07963i	−0.709881	+	0.515759i	−0.883135	−	0.469119i	$-0.844572\pi$
$97$	−6.99151	+	5.07963i	−0.709881	+	0.515759i	0.173254	+	0.984877i	$0.444572\pi$
$98$	10.6229			1.07308
$99$	15.9129			1.59931
$100$	−1.09473	+	0.795369i	−0.109473	+	0.0795369i
$101$	−8.04270	−	5.84336i	−0.800278	−	0.581436i	0.110718	−	0.993852i	$-0.464685\pi$
$101$	−8.04270	−	5.84336i	−0.800278	−	0.581436i	−0.910996	+	0.412416i	$0.864685\pi$
$102$	1.58018	+	1.14807i	0.156462	+	0.113676i
$103$	−2.78364	−	8.56717i	−0.274281	−	0.844149i	−0.989409	−	0.145156i	$-0.953632\pi$
$103$	−2.78364	−	8.56717i	−0.274281	−	0.844149i	0.715128	−	0.698993i	$-0.246368\pi$
$104$	1.34999	−	0.980826i	0.132377	−	0.0961779i
$105$	0.153136	+	0.471304i	0.0149445	+	0.0459945i
$106$	0.506180	−	1.55786i	0.0491646	−	0.151313i
$107$	−0.238541	−	0.173310i	−0.0230607	−	0.0167545i	0.576195	−	0.817312i	$-0.304537\pi$
$107$	−0.238541	−	0.173310i	−0.0230607	−	0.0167545i	−0.599256	+	0.800558i	$0.704537\pi$
$108$	−0.439729	+	1.35335i	−0.0423129	+	0.130226i
$109$	0.675483	−	2.07892i	0.0646996	−	0.199125i	−0.913481	−	0.406881i	$-0.866616\pi$
$109$	0.675483	−	2.07892i	0.0646996	−	0.199125i	0.978181	+	0.207757i	$0.0666162\pi$
$110$	19.3136	+	14.0322i	1.84148	+	1.33791i
$111$	−0.315955	+	0.972410i	−0.0299891	+	0.0922970i
$112$	1.60542	+	4.94098i	0.151698	+	0.466879i
$113$	−8.58185	+	6.23508i	−0.807313	+	0.586547i	−0.913050	−	0.407847i	$-0.866280\pi$
$113$	−8.58185	+	6.23508i	−0.807313	+	0.586547i	0.105738	+	0.994394i	$0.466280\pi$
$114$	0.496020	+	1.52659i	0.0464565	+	0.142979i
$115$	11.9398	+	8.67479i	1.11339	+	0.808929i
$116$	3.64719	+	2.64984i	0.338633	+	0.246032i
$117$	−2.95724	+	2.14856i	−0.273397	+	0.198635i
$118$	−5.52539			−0.508653
$119$	−5.96980			−0.547251
$120$	0.515499	−	0.374532i	0.0470584	−	0.0341899i
$121$	5.51048	−	16.9595i	0.500953	−	1.54177i
$122$	5.08236	+	15.6419i	0.460135	+	1.41615i
$123$	2.01716			0.181881
$124$		0			0
$125$	9.66086			0.864094
$126$	−1.73692	−	5.34568i	−0.154737	−	0.476231i
$127$	6.28326	−	19.3379i	0.557549	−	1.71596i	−0.131565	−	0.991308i	$-0.542000\pi$
$127$	6.28326	−	19.3379i	0.557549	−	1.71596i	0.689114	−	0.724653i	$-0.258000\pi$
$128$	8.13945	−	5.91366i	0.719433	−	0.522698i
$129$	0.577443			0.0508410
$130$	−5.48386			−0.480966
$131$	−4.40055	+	3.19718i	−0.384477	+	0.279339i	−0.763189	−	0.646176i	$-0.776367\pi$
$131$	−4.40055	+	3.19718i	−0.384477	+	0.279339i	0.378711	+	0.925515i	$0.376367\pi$
$132$	1.03656	+	0.753108i	0.0902214	+	0.0655497i
$133$	−3.96903	−	2.88367i	−0.344159	−	0.250046i
$134$	−4.43681	−	13.6551i	−0.383282	−	1.17962i
$135$	−2.27236	+	1.65097i	−0.195574	+	0.142093i
$136$	2.37202	+	7.30031i	0.203399	+	0.625997i
$137$	1.35654	−	4.17500i	0.115897	−	0.356694i	−0.876236	−	0.481882i	$-0.839953\pi$
$137$	1.35654	−	4.17500i	0.115897	−	0.356694i	0.992133	+	0.125188i	$0.0399533\pi$
$138$	1.66651	+	1.21079i	0.141863	+	0.103070i
$139$	−2.07819	+	6.39602i	−0.176270	+	0.542504i	−0.999689	−	0.0249300i	$-0.992064\pi$
$139$	−2.07819	+	6.39602i	−0.176270	+	0.542504i	0.823419	+	0.567434i	$0.192064\pi$
$140$	1.00198	−	3.08377i	0.0846825	−	0.260626i
$141$	−0.870449	−	0.632418i	−0.0733050	−	0.0532592i
$142$	−3.38049	+	10.4041i	−0.283684	+	0.873091i
$143$	2.04664	+	6.29891i	0.171149	+	0.526742i
$144$	−11.8385	+	8.60116i	−0.986540	+	0.716763i
$145$	2.74980	+	8.46301i	0.228358	+	0.702814i
$146$	5.52570	+	4.01465i	0.457310	+	0.332255i
$147$	0.910441	+	0.661474i	0.0750919	+	0.0545574i
$148$	5.41230	−	3.93226i	0.444888	−	0.323230i
$149$	2.21695			0.181619			0.0908097	−	0.995868i	$-0.471055\pi$
$149$	2.21695			0.181619			0.0908097	+	0.995868i	$0.471055\pi$
$150$	−0.372802			−0.0304391
$151$	3.83884	−	2.78908i	0.312400	−	0.226972i	−0.420525	−	0.907281i	$-0.638154\pi$
$151$	3.83884	−	2.78908i	0.312400	−	0.226972i	0.732926	+	0.680309i	$0.238154\pi$
$152$	−1.94933	+	5.99941i	−0.158111	+	0.486616i
$153$	−5.19605	−	15.9918i	−0.420076	−	1.29286i
$154$	−10.1842			−0.820666
$155$		0			0
$156$	−0.294319			−0.0235644
$157$	1.25102	+	3.85024i	0.0998423	+	0.307283i	0.988485	−	0.151317i	$-0.0483513\pi$
$157$	1.25102	+	3.85024i	0.0998423	+	0.307283i	−0.888643	+	0.458599i	$0.848351\pi$
$158$	−4.74054	+	14.5899i	−0.377137	+	1.16071i
$159$	0.140388	−	0.101998i	0.0111335	−	0.00808897i
$160$	−15.2797			−1.20797
$161$	−6.29595			−0.496190
$162$	12.6486	−	9.18973i	0.993766	−	0.722013i
$163$	0.877212	+	0.637332i	0.0687085	+	0.0499197i	0.621609	−	0.783327i	$-0.286479\pi$
$163$	0.877212	+	0.637332i	0.0687085	+	0.0499197i	−0.552901	+	0.833247i	$0.686479\pi$
$164$	−10.6777	−	7.75782i	−0.833790	−	0.605784i
$165$	0.781517	+	2.40526i	0.0608410	+	0.187249i
$166$	−19.2991	+	14.0216i	−1.49790	+	1.08829i
$167$	−3.44554	−	10.6043i	−0.266624	−	0.820585i	−0.991315	−	0.131511i	$-0.958017\pi$
$167$	−3.44554	−	10.6043i	−0.266624	−	0.820585i	0.724690	−	0.689075i	$-0.241983\pi$
$168$	−0.0839988	+	0.258522i	−0.00648065	+	0.0199454i
$169$	9.28639	+	6.74696i	0.714338	+	0.518997i
$170$	7.79526	−	23.9913i	0.597869	−	1.84005i
$171$	4.27013	−	13.1421i	0.326545	−	1.00500i
$172$	−3.05666	−	2.22080i	−0.233068	−	0.169334i
$173$	−2.36032	+	7.26433i	−0.179452	+	0.552297i	−0.999809	−	0.0195553i	$-0.993775\pi$
$173$	−2.36032	+	7.26433i	−0.179452	+	0.552297i	0.820357	+	0.571852i	$0.193775\pi$
$174$	0.383806	+	1.18123i	0.0290963	+	0.0895491i
$175$	0.921819	−	0.669740i	0.0696829	−	0.0506276i
$176$	8.19314	+	25.2159i	0.617581	+	1.90072i
$177$	−0.473555	−	0.344058i	−0.0355946	−	0.0258610i
$178$	−1.28618	−	0.934466i	−0.0964035	−	0.0700412i
$179$	10.7855	−	7.83611i	0.806144	−	0.585698i	−0.106566	−	0.994306i	$-0.533986\pi$
$179$	10.7855	−	7.83611i	0.806144	−	0.585698i	0.912710	+	0.408608i	$0.133986\pi$
$180$	9.13286			0.680723
$181$	20.9779			1.55928			0.779638	−	0.626231i	$-0.215403\pi$
$181$	20.9779			1.55928			0.779638	+	0.626231i	$0.215403\pi$
$182$	1.89262	−	1.37507i	0.140291	−	0.101927i
$183$	−0.538413	+	1.65706i	−0.0398006	+	0.122494i
$184$	2.50161	+	7.69915i	0.184421	+	0.567589i
$185$	13.2051			0.970857
$186$		0			0
$187$	−30.4664			−2.22793
$188$	2.17545	+	6.69534i	0.158661	+	0.488308i
$189$	0.370274	−	1.13959i	0.0269335	−	0.0828927i
$190$	16.7715	−	12.1852i	1.21673	−	0.884009i
$191$	7.56661			0.547501			0.273750	−	0.961801i	$-0.411736\pi$
$191$	7.56661			0.547501			0.273750	+	0.961801i	$0.411736\pi$
$192$	−0.246791			−0.0178106
$193$	10.3776	−	7.53979i	0.746999	−	0.542726i	−0.147896	−	0.989003i	$-0.547250\pi$
$193$	10.3776	−	7.53979i	0.746999	−	0.542726i	0.894895	+	0.446277i	$0.147250\pi$
$194$	12.6032	+	9.15675i	0.904856	+	0.657416i
$195$	−0.469996	−	0.341472i	−0.0336571	−	0.0244533i
$196$	−2.27540	−	7.00295i	−0.162528	−	0.500211i
$197$	14.3369	−	10.4164i	1.02146	−	0.742138i	0.0548822	−	0.998493i	$-0.482522\pi$
$197$	14.3369	−	10.4164i	1.02146	−	0.742138i	0.966583	+	0.256355i	$0.0825217\pi$
$198$	−8.86422	−	27.2813i	−0.629953	−	1.93879i
$199$	0.0724616	−	0.223014i	0.00513667	−	0.0158090i	−0.948455	−	0.316911i	$-0.897354\pi$
$199$	0.0724616	−	0.223014i	0.00513667	−	0.0158090i	0.953592	+	0.301102i	$0.0973544\pi$
$200$	−1.18528	−	0.861156i	−0.0838119	−	0.0608929i
$201$	0.470025	−	1.44659i	0.0331530	−	0.102034i
$202$	−5.53778	+	17.0435i	−0.389637	+	1.19918i
$203$	−3.07112	−	2.23130i	−0.215550	−	0.156607i
$204$	0.418373	−	1.28762i	0.0292919	−	0.0901514i
$205$	−8.05046	−	24.7768i	−0.562268	−	1.73048i
$206$	−13.1371	+	9.54463i	−0.915302	+	0.665006i
$207$	−5.47993	−	16.8655i	−0.380882	−	1.17223i
$208$	−4.92727	−	3.57987i	−0.341644	−	0.248219i
$209$	−20.2556	−	14.7166i	−1.40111	−	1.01797i
$210$	0.722705	−	0.525076i	0.0498714	−	0.0362337i
$211$	16.3756			1.12734			0.563670	−	0.826000i	$-0.309389\pi$
$211$	16.3756			1.12734			0.563670	+	0.826000i	$0.309389\pi$
$212$	−1.13541			−0.0779805
$213$	−0.937573	+	0.681187i	−0.0642414	+	0.0466741i
$214$	−0.164247	+	0.505500i	−0.0112277	+	0.0345553i
$215$	−2.30457	−	7.09273i	−0.157170	−	0.483720i
$216$	−1.54069			−0.104831
$217$		0			0
$218$	−3.94041			−0.266878
$219$	0.223595	+	0.688154i	0.0151091	+	0.0465012i
$220$	5.11351	−	15.7378i	0.344753	−	1.06104i
$221$	5.66186	−	4.11358i	0.380858	−	0.276710i
$222$	1.84311			0.123702
$223$	−9.79748			−0.656088			−0.328044	−	0.944663i	$-0.606389\pi$
$223$	−9.79748			−0.656088			−0.328044	+	0.944663i	$0.606389\pi$
$224$	5.27345	−	3.83138i	0.352347	−	0.255995i
$225$	2.59643	+	1.88642i	0.173095	+	0.125761i
$226$	15.4700	+	11.2396i	1.02905	+	0.747647i
$227$	−0.445809	−	1.37206i	−0.0295894	−	0.0910668i	0.935171	−	0.354196i	$-0.115245\pi$
$227$	−0.445809	−	1.37206i	−0.0295894	−	0.0910668i	−0.964761	+	0.263129i	$0.915245\pi$
$228$	0.900131	−	0.653983i	0.0596126	−	0.0433111i
$229$	−8.60857	−	26.4945i	−0.568871	−	1.75080i	−0.656161	−	0.754621i	$-0.727821\pi$
$229$	−8.60857	−	26.4945i	−0.568871	−	1.75080i	0.0872909	−	0.996183i	$-0.472179\pi$
$230$	8.22114	−	25.3021i	0.542086	−	1.66837i
$231$	−0.872839	−	0.634155i	−0.0574286	−	0.0417243i
$232$	−1.50833	+	4.64217i	−0.0990268	+	0.304773i
$233$	−4.72131	+	14.5307i	−0.309303	+	0.951938i	0.668733	+	0.743503i	$0.266837\pi$
$233$	−4.72131	+	14.5307i	−0.309303	+	0.951938i	−0.978036	+	0.208435i	$0.933163\pi$
$234$	5.33084	+	3.87308i	0.348488	+	0.253191i
$235$	−4.29404	+	13.2157i	−0.280112	+	0.862097i
$236$	1.18352	+	3.64250i	0.0770407	+	0.237107i
$237$	−1.31478	+	0.955244i	−0.0854042	+	0.0620498i
$238$	3.32546	+	10.2347i	0.215557	+	0.663417i
$239$	−3.68752	−	2.67914i	−0.238526	−	0.173299i	0.462100	−	0.886828i	$-0.347096\pi$
$239$	−3.68752	−	2.67914i	−0.238526	−	0.173299i	−0.700626	+	0.713528i	$0.747096\pi$
$240$	−1.88149	−	1.36698i	−0.121450	−	0.0882385i
$241$	6.48872	−	4.71433i	0.417975	−	0.303677i	−0.358848	−	0.933396i	$-0.616830\pi$
$241$	6.48872	−	4.71433i	0.417975	−	0.303677i	0.776823	+	0.629720i	$0.216830\pi$
$242$	−32.1452			−2.06637
$243$	5.07280			0.325420
$244$	9.22299	−	6.70089i	0.590441	−	0.428981i
$245$	4.49132	−	13.8229i	0.286940	−	0.883111i
$246$	−1.12365	−	3.45824i	−0.0716414	−	0.220489i
$247$	5.75133			0.365949
$248$		0			0
$249$	−2.52714			−0.160151
$250$	−5.38155	−	16.5627i	−0.340359	−	1.04752i
$251$	−3.64758	+	11.2261i	−0.230233	+	0.708584i	0.767485	+	0.641067i	$0.221508\pi$
$251$	−3.64758	+	11.2261i	−0.230233	+	0.708584i	−0.997718	+	0.0675175i	$0.978492\pi$
$252$	−3.15199	+	2.29006i	−0.198557	+	0.144260i
$253$	−32.1309			−2.02005
$254$	−36.6532			−2.29983
$255$	2.16200	−	1.57079i	0.135390	−	0.0983664i
$256$	−16.7635	−	12.1794i	−1.04772	−	0.761213i
$257$	−0.0859265	−	0.0624293i	−0.00535995	−	0.00389423i	0.585102	−	0.810960i	$-0.301054\pi$
$257$	−0.0859265	−	0.0624293i	−0.00535995	−	0.00389423i	−0.590462	+	0.807065i	$0.701054\pi$
$258$	−0.321663	−	0.989975i	−0.0200258	−	0.0616332i
$259$	−4.55742	+	3.31116i	−0.283185	+	0.205746i
$260$	1.17463	+	3.61513i	0.0728472	+	0.224201i
$261$	3.30410	−	10.1690i	0.204519	−	0.629443i
$262$	7.93260	+	5.76337i	0.490078	+	0.356062i
$263$	7.34257	−	22.5981i	0.452763	−	1.39346i	−0.420980	−	0.907070i	$-0.638314\pi$
$263$	7.34257	−	22.5981i	0.452763	−	1.39346i	0.873742	−	0.486390i	$-0.161686\pi$
$264$	−0.428681	+	1.31935i	−0.0263835	+	0.0812001i
$265$	−1.81313	−	1.31732i	−0.111380	−	0.0809220i
$266$	−2.73286	+	8.41089i	−0.167563	+	0.515705i
$267$	−0.0520448	−	0.160177i	−0.00318509	−	0.00980270i
$268$	−8.05150	+	5.84976i	−0.491824	+	0.357331i
$269$	0.796394	+	2.45105i	0.0485570	+	0.149443i	0.972395	−	0.233340i	$-0.0749656\pi$
$269$	0.796394	+	2.45105i	0.0485570	+	0.149443i	−0.923838	+	0.382783i	$0.874966\pi$
$270$	4.09625	+	2.97610i	0.249290	+	0.181120i
$271$	23.5264	+	17.0929i	1.42912	+	1.03832i	0.990179	+	0.139806i	$0.0446479\pi$
$271$	23.5264	+	17.0929i	1.42912	+	1.03832i	0.438946	+	0.898514i	$0.355352\pi$
$272$	22.6656	−	16.4676i	1.37431	−	0.998492i
$273$	0.247832			0.0149995
$274$	−7.91333			−0.478062
$275$	4.70443	−	3.41797i	0.283688	−	0.206111i
$276$	0.441230	−	1.35797i	0.0265589	−	0.0817399i
$277$	3.71797	+	11.4427i	0.223391	+	0.687527i	0.998451	+	0.0556392i	$0.0177196\pi$
$277$	3.71797	+	11.4427i	0.223391	+	0.687527i	−0.775060	+	0.631888i	$0.782280\pi$
$278$	12.1231			0.727094
$279$		0			0
$280$	3.51066			0.209802
$281$	−9.62207	−	29.6137i	−0.574005	−	1.76660i	−0.639544	−	0.768755i	$-0.720877\pi$
$281$	−9.62207	−	29.6137i	−0.574005	−	1.76660i	0.0655393	−	0.997850i	$-0.479123\pi$
$282$	−0.599345	+	1.84460i	−0.0356905	+	0.109844i
$283$	−4.64215	+	3.37272i	−0.275947	+	0.200487i	−0.717148	−	0.696921i	$-0.754553\pi$
$283$	−4.64215	+	3.37272i	−0.275947	+	0.200487i	0.441201	+	0.897409i	$0.354553\pi$
$284$	7.58278			0.449955
$285$	2.19617			0.130090
$286$	9.65886	−	7.01757i	0.571141	−	0.414958i
$287$	8.99118	+	6.53247i	0.530732	+	0.385600i
$288$	14.8534	+	10.7916i	0.875246	+	0.635903i
$289$	4.69494	+	14.4496i	0.276173	+	0.849974i
$290$	12.9773	−	9.42858i	0.762054	−	0.553665i
$291$	0.509982	+	1.56956i	0.0298957	+	0.0920095i
$292$	1.46299	−	4.50264i	0.0856153	−	0.263497i
$293$	−1.03475	−	0.751793i	−0.0604510	−	0.0439202i	0.557149	−	0.830412i	$-0.311895\pi$
$293$	−1.03475	−	0.751793i	−0.0604510	−	0.0439202i	−0.617600	+	0.786492i	$0.711895\pi$
$294$	0.626881	−	1.92934i	0.0365605	−	0.112522i
$295$	−2.33611	+	7.18981i	−0.136014	+	0.418607i
$296$	5.85996	+	4.25751i	0.340603	+	0.247463i
$297$	1.88966	−	5.81579i	0.109649	−	0.337466i
$298$	−1.23494	−	3.80076i	−0.0715383	−	0.220172i
$299$	5.97119	−	4.33832i	0.345323	−	0.250892i
$300$	0.0798530	+	0.245762i	0.00461032	+	0.0141891i
$301$	2.57386	+	1.87002i	0.148355	+	0.107786i
$302$	−6.92005	−	5.02771i	−0.398204	−	0.289312i
$303$	−1.53589	+	1.11589i	−0.0882347	+	0.0641063i
$304$	23.0238			1.32051
$305$	22.5025			1.28849
$306$	−24.5221	+	17.8164i	−1.40184	+	1.01849i
$307$	−4.84946	+	14.9251i	−0.276773	+	0.851820i	0.711972	+	0.702208i	$0.247802\pi$
$307$	−4.84946	+	14.9251i	−0.276773	+	0.851820i	−0.988745	+	0.149612i	$0.952198\pi$
$308$	2.18142	+	6.71373i	0.124298	+	0.382550i
$309$	−1.72025			−0.0978613
$310$		0			0
$311$	27.4565			1.55692			0.778459	−	0.627695i	$-0.216002\pi$
$311$	27.4565			1.55692			0.778459	+	0.627695i	$0.216002\pi$
$312$	−0.0984724	−	0.303067i	−0.00557490	−	0.0171578i
$313$	3.95795	−	12.1813i	0.223716	−	0.688528i	−0.774703	−	0.632325i	$-0.782101\pi$
$313$	3.95795	−	12.1813i	0.223716	−	0.688528i	0.998419	−	0.0562028i	$-0.0178993\pi$
$314$	5.90403	−	4.28953i	0.333184	−	0.242072i
$315$	−7.69033			−0.433301
$316$	10.6335			0.598182
$317$	7.70415	−	5.59739i	0.432708	−	0.314381i	−0.350023	−	0.936741i	$-0.613826\pi$
$317$	7.70415	−	5.59739i	0.432708	−	0.314381i	0.782731	+	0.622360i	$0.213826\pi$
$318$	−0.253069	−	0.183866i	−0.0141914	−	0.0103107i
$319$	−15.6732	−	11.3873i	−0.877532	−	0.637564i
$320$	0.984940	+	3.03133i	0.0550598	+	0.169457i
$321$	−0.0455536	+	0.0330966i	−0.00254255	+	0.00184727i
$322$	3.50714	+	10.7939i	0.195445	+	0.601518i
$323$	−8.17547	+	25.1615i	−0.454895	+	1.40002i
$324$	−8.76744	−	6.36992i	−0.487080	−	0.353884i
$325$	−0.412774	+	1.27039i	−0.0228966	+	0.0704684i
$326$	0.604002	−	1.85893i	0.0334526	−	0.102956i
$327$	−0.337714	−	0.245364i	−0.0186756	−	0.0135686i
$328$	4.41587	−	13.5907i	0.243826	−	0.750419i
$329$	−1.83184	−	5.63782i	−0.100992	−	0.310823i
$330$	3.68827	−	2.67968i	0.203033	−	0.147512i
$331$	6.66956	+	20.5268i	0.366592	+	1.12826i	0.948978	+	0.315342i	$0.102119\pi$
$331$	6.66956	+	20.5268i	0.366592	+	1.12826i	−0.582386	+	0.812913i	$0.697881\pi$
$332$	13.3773	+	9.71916i	0.734174	+	0.533408i
$333$	−12.8366	−	9.32636i	−0.703443	−	0.511081i
$334$	−16.2608	+	11.8142i	−0.889752	+	0.646443i
$335$	−19.6443			−1.07328
$336$	0.992124			0.0541248
$337$	3.67939	−	2.67324i	0.200429	−	0.145620i	−0.483044	−	0.875596i	$-0.660469\pi$
$337$	3.67939	−	2.67324i	0.200429	−	0.145620i	0.683473	+	0.729976i	$0.260469\pi$
$338$	6.39412	−	19.6791i	0.347794	−	1.07040i
$339$	0.625986	+	1.92659i	0.0339989	+	0.104638i
$340$	−17.4855			−0.948287
$341$		0			0
$342$	−24.9096			−1.34696
$343$	4.19193	+	12.9014i	0.226343	+	0.696611i
$344$	1.26411	−	3.89054i	0.0681564	−	0.209764i
$345$	2.28012	−	1.65660i	0.122757	−	0.0891885i
$346$	13.7689			0.740219
$347$	29.3895			1.57771			0.788855	−	0.614579i	$-0.210674\pi$
$347$	29.3895			1.57771			0.788855	+	0.614579i	$0.210674\pi$
$348$	0.696495	−	0.506033i	0.0373360	−	0.0271262i
$349$	5.46187	+	3.96828i	0.292367	+	0.212417i	0.724294	−	0.689492i	$-0.242166\pi$
$349$	5.46187	+	3.96828i	0.292367	+	0.212417i	−0.431926	+	0.901909i	$0.642166\pi$
$350$	−1.66171	−	1.20730i	−0.0888220	−	0.0645329i
$351$	0.434075	+	1.33595i	0.0231692	+	0.0713075i
$352$	26.9126	−	19.5532i	1.43445	−	1.04219i
$353$	2.40436	+	7.39987i	0.127971	+	0.393855i	0.994431	−	0.105392i	$-0.0336098\pi$
$353$	2.40436	+	7.39987i	0.127971	+	0.393855i	−0.866459	+	0.499248i	$0.833610\pi$
$354$	−0.326065	+	1.00352i	−0.0173302	+	0.0533367i
$355$	12.1089	+	8.79760i	0.642671	+	0.466928i
$356$	−0.340532	+	1.04805i	−0.0180482	+	0.0555466i
$357$	−0.352291	+	1.08424i	−0.0186452	+	0.0573840i
$358$	−19.4423	−	14.1257i	−1.02756	−	0.746565i
$359$	0.799540	−	2.46073i	0.0421981	−	0.129872i	−0.927738	−	0.373232i	$-0.878250\pi$
$359$	0.799540	−	2.46073i	0.0421981	−	0.129872i	0.969936	+	0.243360i	$0.0782495\pi$
$360$	3.05564	+	9.40430i	0.161047	+	0.495650i
$361$	−2.21824	+	1.61165i	−0.116750	+	0.0848235i
$362$	−11.6857	−	35.9648i	−0.614185	−	1.89027i
$363$	−2.75501	−	2.00164i	−0.144601	−	0.105059i
$364$	−1.31188	−	0.953140i	−0.0687614	−	0.0499581i
$365$	7.56024	−	5.49283i	0.395721	−	0.287508i
$366$	3.14081			0.164173
$367$	−35.2278			−1.83887			−0.919437	−	0.393236i	$-0.871355\pi$
$367$	−35.2278			−1.83887			−0.919437	+	0.393236i	$0.871355\pi$
$368$	23.9039	−	17.3672i	1.24608	−	0.905329i
$369$	−9.67326	+	29.7712i	−0.503570	+	1.54983i
$370$	−7.35584	−	22.6390i	−0.382412	−	1.17694i
$371$	0.956075			0.0496369
$372$		0			0
$373$	6.68493			0.346133			0.173066	−	0.984910i	$-0.444632\pi$
$373$	6.68493			0.346133			0.173066	+	0.984910i	$0.444632\pi$
$374$	16.9712	+	52.2320i	0.877560	+	2.70085i
$375$	0.570108	−	1.75461i	0.0294403	−	0.0906078i
$376$	−6.16648	+	4.48021i	−0.318012	+	0.231049i
$377$	4.45021			0.229198
$378$	−2.15998			−0.111097
$379$	−14.2216	+	10.3326i	−0.730514	+	0.530750i	−0.889726	−	0.456495i	$-0.849105\pi$
$379$	−14.2216	+	10.3326i	−0.730514	+	0.530750i	0.159212	+	0.987244i	$0.449105\pi$
$380$	−11.6253	−	8.44626i	−0.596365	−	0.433284i
$381$	−3.14137	−	2.28234i	−0.160937	−	0.116928i
$382$	−4.21495	−	12.9723i	−0.215656	−	0.663720i
$383$	−26.3559	+	19.1487i	−1.34673	+	0.978453i	−0.347558	+	0.937659i	$0.612989\pi$
$383$	−26.3559	+	19.1487i	−1.34673	+	0.978453i	−0.999168	+	0.0407947i	$0.987011\pi$
$384$	−0.593716	−	1.82727i	−0.0302980	−	0.0932475i
$385$	−4.30583	+	13.2520i	−0.219446	+	0.675384i
$386$	−18.7071	−	13.5915i	−0.952169	−	0.691791i
$387$	−2.76912	+	8.52248i	−0.140762	+	0.433222i
$388$	3.33684	−	10.2698i	0.169403	−	0.521368i
$389$	−6.78604	−	4.93034i	−0.344066	−	0.249978i	0.402310	−	0.915504i	$-0.368208\pi$
$389$	−6.78604	−	4.93034i	−0.344066	−	0.249978i	−0.746375	+	0.665525i	$0.768208\pi$
$390$	−0.323614	+	0.995982i	−0.0163868	+	0.0504335i
$391$	10.4917	+	32.2902i	0.530590	+	1.63299i
$392$	6.44979	−	4.68605i	0.325764	−	0.236681i
$393$	0.320989	+	0.987903i	0.0161918	+	0.0498331i
$394$	−25.8443	−	18.7770i	−1.30202	−	0.945972i
$395$	16.9805	+	12.3371i	0.854384	+	0.620746i
$396$	−16.0860	+	11.6871i	−0.808350	+	0.587300i
$397$	26.2501			1.31745			0.658727	−	0.752382i	$-0.271095\pi$
$397$	26.2501			1.31745			0.658727	+	0.752382i	$0.271095\pi$
$398$	−0.422702			−0.0211881
$399$	−0.757955	+	0.550687i	−0.0379452	+	0.0275688i
$400$	−1.65242	+	5.08563i	−0.0826211	+	0.254281i
$401$	0.830713	+	2.55667i	0.0414838	+	0.127674i	0.969654	−	0.244483i	$-0.0786182\pi$
$401$	0.830713	+	2.55667i	0.0414838	+	0.127674i	−0.928170	+	0.372157i	$0.878618\pi$
$402$	−2.74187			−0.136752
$403$		0			0
$404$	12.4218			0.618007
$405$	−6.61020	−	20.3441i	−0.328463	−	1.01091i
$406$	−2.11461	+	6.50810i	−0.104946	+	0.322992i
$407$	−23.2585	+	16.8983i	−1.15288	+	0.837616i
$408$	1.46587			0.0725712
$409$	3.09551			0.153063			0.0765316	−	0.997067i	$-0.475615\pi$
$409$	3.09551			0.153063			0.0765316	+	0.997067i	$0.475615\pi$
$410$	−37.9931	+	27.6036i	−1.87635	+	1.36324i
$411$	−0.678214	−	0.492752i	−0.0334538	−	0.0243056i
$412$	9.10603	+	6.61592i	0.448622	+	0.325943i
$413$	−0.996584	−	3.06717i	−0.0490387	−	0.150926i
$414$	−25.8618	+	18.7897i	−1.27104	+	0.923465i
$415$	10.0858	+	31.0409i	0.495092	+	1.52374i
$416$	−2.36135	+	7.26750i	−0.115775	+	0.356319i
$417$	1.03901	+	0.754887i	0.0508806	+	0.0369670i
$418$	−13.9470	+	42.9243i	−0.682168	+	2.09950i
$419$	10.0985	−	31.0801i	0.493346	−	1.51836i	−0.326173	−	0.945310i	$-0.605759\pi$
$419$	10.0985	−	31.0801i	0.493346	−	1.51836i	0.819519	−	0.573052i	$-0.194241\pi$
$420$	−0.500947	−	0.363960i	−0.0244437	−	0.0177594i
$421$	4.21324	−	12.9670i	0.205341	−	0.631974i	−0.794358	−	0.607449i	$-0.792193\pi$
$421$	4.21324	−	12.9670i	0.205341	−	0.631974i	0.999699	−	0.0245248i	$-0.00780726\pi$
$422$	−9.12195	−	28.0745i	−0.444049	−	1.36664i
$423$	13.5081	−	9.81420i	0.656786	−	0.477183i
$424$	−0.379883	−	1.16916i	−0.0184487	−	0.0567794i
$425$	−4.97106	−	3.61169i	−0.241132	−	0.175193i
$426$	1.69011	+	1.22793i	0.0818859	+	0.0594936i
$427$	−7.76622	+	5.64249i	−0.375834	+	0.273059i
$428$	0.368422			0.0178084
$429$	1.26479			0.0610647
$430$	−10.8761	+	7.90196i	−0.524493	+	0.381066i
$431$	8.59890	−	26.4647i	0.414194	−	1.27476i	−0.498775	−	0.866731i	$-0.666217\pi$
$431$	8.59890	−	26.4647i	0.414194	−	1.27476i	0.912969	−	0.408028i	$-0.133783\pi$
$432$	1.73770	+	5.34808i	0.0836049	+	0.257309i
$433$	2.12857			0.102292			0.0511462	−	0.998691i	$-0.483713\pi$
$433$	2.12857			0.102292			0.0511462	+	0.998691i	$0.483713\pi$
$434$		0			0
$435$	1.69933			0.0814766
$436$	0.844024	+	2.59764i	0.0404214	+	0.124404i
$437$	−8.62212	+	26.5362i	−0.412452	+	1.26940i
$438$	1.05523	−	0.766668i	0.0504207	−	0.0366328i
$439$	9.39981			0.448629			0.224314	−	0.974517i	$-0.427986\pi$
$439$	9.39981			0.448629			0.224314	+	0.974517i	$0.427986\pi$
$440$	17.9164			0.854130
$441$	−14.1287	+	10.2651i	−0.672795	+	0.488814i
$442$	−10.2063	−	7.41531i	−0.485464	−	0.352710i
$443$	−25.4097	−	18.4612i	−1.20725	−	0.877120i	−0.212274	−	0.977210i	$-0.568087\pi$
$443$	−25.4097	−	18.4612i	−1.20725	−	0.877120i	−0.994978	+	0.100090i	$0.968087\pi$
$444$	−0.394789	−	1.21504i	−0.0187359	−	0.0576631i
$445$	−1.75975	+	1.27853i	−0.0834201	+	0.0606083i
$446$	5.45765	+	16.7969i	0.258427	+	0.795357i
$447$	0.130827	−	0.402644i	0.00618790	−	0.0190444i
$448$	−1.10003	−	0.799221i	−0.0519717	−	0.0377596i
$449$	−7.45194	+	22.9347i	−0.351679	+	1.08236i	0.606231	+	0.795288i	$0.292680\pi$
$449$	−7.45194	+	22.9347i	−0.351679	+	1.08236i	−0.957910	+	0.287068i	$0.907320\pi$
$450$	1.78777	−	5.50218i	0.0842761	−	0.259375i
$451$	45.8858	+	33.3380i	2.16068	+	1.56982i
$452$	4.09587	−	12.6058i	0.192653	−	0.592926i
$453$	−0.280017	−	0.861803i	−0.0131563	−	0.0404910i
$454$	−2.10394	+	1.52860i	−0.0987428	+	0.0717409i
$455$	−0.989094	−	3.04412i	−0.0463694	−	0.142710i
$456$	0.974583	+	0.708076i	0.0456390	+	0.0331587i
$457$	−2.99832	−	2.17841i	−0.140255	−	0.101902i	0.515445	−	0.856923i	$-0.327627\pi$
$457$	−2.99832	−	2.17841i	−0.140255	−	0.101902i	−0.655701	+	0.755021i	$0.727627\pi$
$458$	−40.6271	+	29.5173i	−1.89838	+	1.37925i
$459$	−6.46167			−0.301605
$460$	−18.4408			−0.859808
$461$	−13.8119	+	10.0349i	−0.643285	+	0.467374i	−0.860977	−	0.508644i	$-0.830147\pi$
$461$	−13.8119	+	10.0349i	−0.643285	+	0.467374i	0.217692	+	0.976017i	$0.430147\pi$
$462$	−0.600991	+	1.84966i	−0.0279606	+	0.0860540i
$463$	1.51803	+	4.67202i	0.0705489	+	0.217127i	0.980114	−	0.198434i	$-0.0635854\pi$
$463$	1.51803	+	4.67202i	0.0705489	+	0.217127i	−0.909565	+	0.415561i	$0.863585\pi$
$464$	17.8152			0.827048
$465$		0			0
$466$	27.5416			1.27584
$467$	−0.794318	−	2.44466i	−0.0367567	−	0.113125i	0.930995	−	0.365033i	$-0.118942\pi$
$467$	−0.794318	−	2.44466i	−0.0367567	−	0.113125i	−0.967751	+	0.251907i	$0.918942\pi$
$468$	1.41141	−	4.34386i	0.0652422	−	0.200795i
$469$	6.77977	−	4.92579i	0.313060	−	0.227452i
$470$	25.0491			1.15543
$471$	0.773110			0.0356230
$472$	−3.35478	+	2.43739i	−0.154416	+	0.112190i
$473$	13.1355	+	9.54351i	0.603972	+	0.438811i
$474$	2.37008	+	1.72196i	0.108861	+	0.0790923i
$475$	−1.56042	−	4.80247i	−0.0715969	−	0.220353i
$476$	6.03473	−	4.38448i	0.276601	−	0.200963i
$477$	0.832158	+	2.56112i	0.0381019	+	0.117266i
$478$	−2.53903	+	7.81434i	−0.116133	+	0.357419i
$479$	−1.66109	−	1.20686i	−0.0758973	−	0.0551426i	0.549190	−	0.835698i	$-0.314936\pi$
$479$	−1.66109	−	1.20686i	−0.0758973	−	0.0551426i	−0.625087	+	0.780555i	$0.714936\pi$
$480$	−0.901691	+	2.77512i	−0.0411564	+	0.126666i
$481$	2.04073	−	6.28073i	0.0930494	−	0.286377i
$482$	−11.6968	−	8.49824i	−0.532775	−	0.387084i
$483$	−0.371538	+	1.14348i	−0.0169055	+	0.0520299i
$484$	6.88541	+	21.1911i	0.312973	+	0.963232i
$485$	17.2436	−	12.5282i	0.782993	−	0.568877i
$486$	−2.82579	−	8.69687i	−0.128180	−	0.394498i
$487$	14.3288	+	10.4105i	0.649299	+	0.471744i	0.863032	−	0.505149i	$-0.168562\pi$
$487$	14.3288	+	10.4105i	0.649299	+	0.471744i	−0.213733	+	0.976892i	$0.568562\pi$
$488$	9.98585	+	7.25514i	0.452038	+	0.328425i
$489$	0.167519	−	0.121710i	0.00757546	−	0.00550390i
$490$	−26.2000			−1.18359
$491$	22.4719			1.01414			0.507072	−	0.861904i	$-0.330728\pi$
$491$	22.4719			1.01414			0.507072	+	0.861904i	$0.330728\pi$
$492$	−2.03910	+	1.48149i	−0.0919296	+	0.0667907i
$493$	−6.32594	+	19.4693i	−0.284906	+	0.876851i
$494$	−3.20376	−	9.86016i	−0.144144	−	0.443629i
$495$	−39.2470			−1.76402
$496$		0			0
$497$	−6.38508			−0.286410
$498$	1.40773	+	4.33256i	0.0630821	+	0.194147i
$499$	−6.18043	+	19.0214i	−0.276674	+	0.851516i	0.712097	+	0.702081i	$0.247745\pi$
$499$	−6.18043	+	19.0214i	−0.276674	+	0.851516i	−0.988772	+	0.149435i	$0.952255\pi$
$500$	−9.76593	+	7.09536i	−0.436746	+	0.317314i
$501$	−2.12929			−0.0951296
$502$	21.2780			0.949684
$503$	−10.1376	+	7.36538i	−0.452012	+	0.328406i	−0.790390	−	0.612604i	$-0.790122\pi$
$503$	−10.1376	+	7.36538i	−0.452012	+	0.328406i	0.338377	+	0.941010i	$0.390122\pi$
$504$	−3.41270	−	2.47947i	−0.152014	−	0.110445i
$505$	19.8362	+	14.4119i	0.882700	+	0.641319i
$506$	17.8984	+	55.0856i	0.795681	+	2.44885i
$507$	1.77340	−	1.28845i	0.0787594	−	0.0572220i
$508$	7.85100	+	24.1629i	0.348332	+	1.07206i
$509$	−8.16009	+	25.1142i	−0.361690	+	1.11317i	0.590338	+	0.807156i	$0.298994\pi$
$509$	−8.16009	+	25.1142i	−0.361690	+	1.11317i	−0.952028	+	0.306011i	$0.901006\pi$
$510$	−3.89731	−	2.83156i	−0.172576	−	0.125384i
$511$	−1.23192	+	3.79144i	−0.0544967	+	0.167724i
$512$	−5.32449	+	16.3871i	−0.235311	+	0.724214i
$513$	−4.29605	−	3.12126i	−0.189675	−	0.137807i
$514$	−0.0591645	+	0.182090i	−0.00260963	+	0.00803163i
$515$	6.86548	+	21.1298i	0.302529	+	0.931089i
$516$	−0.583723	+	0.424100i	−0.0256970	+	0.0186699i
$517$	−9.34864	−	28.7722i	−0.411153	−	1.26540i
$518$	8.21540	+	5.96883i	0.360964	+	0.262256i
$519$	1.18007	+	0.857368i	0.0517991	+	0.0376343i
$520$	−3.32957	+	2.41907i	−0.146011	+	0.106083i
$521$	−24.2494			−1.06239			−0.531193	−	0.847251i	$-0.678256\pi$
$521$	−24.2494			−1.06239			−0.531193	+	0.847251i	$0.678256\pi$
$522$	−19.2743			−0.843615
$523$	−29.0062	+	21.0742i	−1.26835	+	0.921512i	−0.999136	−	0.0415670i	$-0.986765\pi$
$523$	−29.0062	+	21.0742i	−1.26835	+	0.921512i	−0.269217	+	0.963079i	$0.586765\pi$
$524$	2.10025	−	6.46391i	0.0917499	−	0.282377i
$525$	−0.0672403	−	0.206944i	−0.00293461	−	0.00903179i
$526$	−42.8327			−1.86759
$527$		0			0
$528$	5.06323			0.220349
$529$	3.95754	+	12.1801i	0.172067	+	0.529568i
$530$	−1.24842	+	3.84226i	−0.0542281	+	0.166897i
$531$	7.34887	−	5.33927i	0.318914	−	0.231705i
$532$	6.13009			0.265773
$533$	−13.0287			−0.564335
$534$	−0.245619	+	0.178453i	−0.0106290	+	0.00772240i
$535$	0.588330	+	0.427447i	0.0254357	+	0.0184801i
$536$	−8.71746	−	6.33361i	−0.376537	−	0.273570i
$537$	−0.786725	−	2.42129i	−0.0339497	−	0.104486i
$538$	3.75848	−	2.73069i	0.162040	−	0.117729i
$539$	9.77815	+	30.0941i	0.421175	+	1.29624i
$540$	1.08453	−	3.33785i	0.0466708	−	0.143638i
$541$	−12.1654	−	8.83866i	−0.523030	−	0.380003i	0.294714	−	0.955585i	$-0.404776\pi$
$541$	−12.1654	−	8.83866i	−0.523030	−	0.380003i	−0.817744	+	0.575582i	$0.804776\pi$
$542$	16.1990	−	49.8554i	0.695807	−	2.14147i
$543$	1.23795	−	3.81002i	0.0531256	−	0.163504i
$544$	−28.4380	−	20.6614i	−1.21927	−	0.885850i
$545$	−1.66599	+	5.12738i	−0.0713631	+	0.219633i
$546$	−0.138054	−	0.424886i	−0.00590816	−	0.0181834i
$547$	32.7642	−	23.8046i	1.40090	−	1.01781i	0.406330	−	0.913727i	$-0.366808\pi$
$547$	32.7642	−	23.8046i	1.40090	−	1.01781i	0.994568	−	0.104085i	$-0.0331915\pi$
$548$	1.69501	+	5.21671i	0.0724073	+	0.222847i
$549$	−21.8747	−	15.8929i	−0.933587	−	0.678291i
$550$	−8.48039	−	6.16137i	−0.361605	−	0.262722i
$551$	−13.6103	+	9.88846i	−0.579818	+	0.421262i
$552$	1.54595			0.0658001
$553$	−8.95395			−0.380761
$554$	17.5465	−	12.7483i	0.745478	−	0.541622i
$555$	0.779260	−	2.39832i	0.0330778	−	0.101803i
$556$	−2.59673	−	7.99190i	−0.110126	−	0.338932i
$557$	32.3465			1.37057			0.685284	−	0.728276i	$-0.259678\pi$
$557$	32.3465			1.37057			0.685284	+	0.728276i	$0.259678\pi$
$558$		0			0
$559$	−3.72966			−0.157748
$560$	−3.95955	−	12.1863i	−0.167322	−	0.514963i
$561$	−1.79789	+	5.53333i	−0.0759069	+	0.233618i
$562$	−45.4101	+	32.9924i	−1.91551	+	1.39170i
$563$	28.6186			1.20613			0.603064	−	0.797693i	$-0.293946\pi$
$563$	28.6186			1.20613			0.603064	+	0.797693i	$0.293946\pi$
$564$	1.34439			0.0566091
$565$	21.1660	−	15.3780i	0.890459	−	0.646956i
$566$	8.36813	+	6.07980i	0.351739	+	0.255553i
$567$	7.38262	+	5.36379i	0.310041	+	0.225258i
$568$	2.53702	+	7.80815i	0.106451	+	0.327623i
$569$	30.2167	−	21.9537i	1.26675	−	0.920347i	0.267680	−	0.963508i	$-0.413743\pi$
$569$	30.2167	−	21.9537i	1.26675	−	0.920347i	0.999068	+	0.0431612i	$0.0137429\pi$
$570$	−1.22337	−	3.76513i	−0.0512412	−	0.157704i
$571$	3.08420	−	9.49220i	0.129070	−	0.397236i	−0.865551	−	0.500821i	$-0.833031\pi$
$571$	3.08420	−	9.49220i	0.129070	−	0.397236i	0.994621	+	0.103585i	$0.0330314\pi$
$572$	−6.69510	−	4.86427i	−0.279936	−	0.203386i
$573$	0.446522	−	1.37425i	0.0186537	−	0.0574103i
$574$	6.19085	−	19.0535i	0.258401	−	0.795277i
$575$	−5.24265	−	3.80901i	−0.218634	−	0.158847i
$576$	1.18348	−	3.64239i	0.0493118	−	0.151766i
$577$	−11.8762	−	36.5513i	−0.494415	−	1.52165i	−0.817867	−	0.575407i	$-0.804844\pi$
$577$	−11.8762	−	36.5513i	−0.494415	−	1.52165i	0.323452	−	0.946244i	$-0.395156\pi$
$578$	22.1572	−	16.0981i	0.921618	−	0.669594i
$579$	−0.756976	−	2.32973i	−0.0314589	−	0.0968204i
$580$	−8.99531	−	6.53547i	−0.373510	−	0.271371i
$581$	−11.2643	−	8.18402i	−0.467324	−	0.339530i
$582$	2.40680	−	1.74864i	0.0997649	−	0.0724835i
$583$	4.87925			0.202078
$584$	5.12594			0.212113
$585$	7.29364	−	5.29914i	0.301555	−	0.219092i
$586$	−0.712477	+	2.19278i	−0.0294322	+	0.0905829i
$587$	9.36540	+	28.8237i	0.386551	+	1.18968i	0.935349	+	0.353728i	$0.115086\pi$
$587$	9.36540	+	28.8237i	0.386551	+	1.18968i	−0.548797	+	0.835956i	$0.684914\pi$
$588$	−1.40616			−0.0579890
$589$		0			0
$590$	13.6276			0.561040
$591$	−1.04578	−	3.21858i	−0.0430176	−	0.132395i
$592$	8.16949	−	25.1431i	0.335764	−	1.03337i
$593$	−1.75119	+	1.27231i	−0.0719126	+	0.0522476i	−0.623161	−	0.782094i	$-0.714152\pi$
$593$	−1.75119	+	1.27231i	−0.0719126	+	0.0522476i	0.551248	+	0.834341i	$0.314152\pi$
$594$	−11.0233			−0.452291
$595$	14.7237			0.603613
$596$	−2.24106	+	1.62822i	−0.0917973	+	0.0666946i
$597$	−0.0362278	−	0.0263211i	−0.00148271	−	0.00107725i
$598$	−10.7639	−	7.82043i	−0.440169	−	0.319801i
$599$	−8.18117	−	25.1791i	−0.334274	−	1.02879i	−0.967079	−	0.254477i	$-0.918097\pi$
$599$	−8.18117	−	25.1791i	−0.334274	−	1.02879i	0.632805	−	0.774311i	$-0.281903\pi$
$600$	−0.226350	+	0.164453i	−0.00924069	+	0.00671375i
$601$	−12.6919	−	39.0616i	−0.517713	−	1.59336i	−0.778291	−	0.627904i	$-0.783913\pi$
$601$	−12.6919	−	39.0616i	−0.517713	−	1.59336i	0.260578	−	0.965453i	$-0.416087\pi$
$602$	1.77223	−	5.45435i	0.0722306	−	0.222303i
$603$	19.0962	+	13.8742i	0.777656	+	0.565000i
$604$	−1.83217	+	5.63883i	−0.0745498	+	0.229441i
$605$	−13.5909	+	41.8283i	−0.552547	+	1.70056i
$606$	2.76866	+	2.01155i	0.112469	+	0.0817136i
$607$	12.1198	−	37.3008i	0.491926	−	1.51399i	−0.329767	−	0.944062i	$-0.606970\pi$
$607$	12.1198	−	37.3008i	0.491926	−	1.51399i	0.821693	−	0.569930i	$-0.193030\pi$
$608$	−8.92668	−	27.4735i	−0.362025	−	1.11420i
$609$	−0.586484	+	0.426105i	−0.0237655	+	0.0172667i
$610$	−12.5349	−	38.5786i	−0.507525	−	1.56200i
$611$	5.62217	+	4.08475i	0.227449	+	0.165251i
$612$	16.9977	+	12.3495i	0.687090	+	0.499200i
$613$	17.5833	−	12.7750i	0.710183	−	0.515978i	−0.173050	−	0.984913i	$-0.555362\pi$
$613$	17.5833	−	12.7750i	0.710183	−	0.515978i	0.883233	+	0.468935i	$0.155362\pi$
$614$	28.2891			1.14166
$615$	−4.97505			−0.200613
$616$	−6.18342	+	4.49252i	−0.249137	+	0.181009i
$617$	−4.18600	+	12.8832i	−0.168522	+	0.518657i	−0.999279	−	0.0379787i	$-0.987908\pi$
$617$	−4.18600	+	12.8832i	−0.168522	+	0.518657i	0.830757	+	0.556636i	$0.187908\pi$
$618$	0.958257	+	2.94921i	0.0385467	+	0.118635i
$619$	42.3785			1.70334			0.851668	−	0.524082i	$-0.175592\pi$
$619$	42.3785			1.70334			0.851668	+	0.524082i	$0.175592\pi$
$620$		0			0
$621$	−6.81469			−0.273464
$622$	−15.2946	−	47.0719i	−0.613256	−	1.88741i
$623$	0.286745	−	0.882511i	0.0114882	−	0.0353571i
$624$	−0.940947	+	0.683638i	−0.0376680	+	0.0273674i
$625$	−29.2420			−1.16968
$626$	−23.0885			−0.922804
$627$	−3.86817	+	2.81039i	−0.154480	+	0.112236i
$628$	−4.09242	−	2.97331i	−0.163305	−	0.118648i
$629$	24.5767	+	17.8560i	0.979936	+	0.711966i
$630$	4.28387	+	13.1844i	0.170673	+	0.525279i
$631$	−18.5138	+	13.4510i	−0.737022	+	0.535478i	−0.891777	−	0.452475i	$-0.850541\pi$
$631$	−18.5138	+	13.4510i	−0.737022	+	0.535478i	0.154755	+	0.987953i	$0.450541\pi$
$632$	3.55773	+	10.9496i	0.141519	+	0.435550i
$633$	0.966357	−	2.97414i	0.0384092	−	0.118212i
$634$	−13.8878	−	10.0901i	−0.551556	−	0.400729i
$635$	−15.4968	+	47.6943i	−0.614972	+	1.89269i
$636$	−0.0670032	+	0.206215i	−0.00265685	+	0.00817694i
$637$	−5.88047	−	4.27241i	−0.232993	−	0.169279i
$638$	−10.7918	+	33.2136i	−0.427250	+	1.31494i
$639$	−5.55751	−	17.1043i	−0.219852	−	0.676634i
$640$	−20.0749	+	14.5852i	−0.793528	+	0.576532i
$641$	7.24739	+	22.3052i	0.286255	+	0.881001i	0.986020	+	0.166628i	$0.0532880\pi$
$641$	7.24739	+	22.3052i	0.286255	+	0.881001i	−0.699765	+	0.714373i	$0.746712\pi$
$642$	0.0821167	+	0.0596613i	0.00324089	+	0.00235464i
$643$	−11.7586	−	8.54309i	−0.463712	−	0.336907i	0.331273	−	0.943535i	$-0.392522\pi$
$643$	−11.7586	−	8.54309i	−0.463712	−	0.336907i	−0.794986	+	0.606628i	$0.792522\pi$
$644$	6.36442	−	4.62402i	0.250793	−	0.182212i
$645$	−1.42418			−0.0560772
$646$	47.6913			1.87639
$647$	3.99958	−	2.90587i	0.157240	−	0.114241i	−0.506383	−	0.862309i	$-0.669018\pi$
$647$	3.99958	−	2.90587i	0.157240	−	0.114241i	0.663623	+	0.748067i	$0.269018\pi$
$648$	3.62586	−	11.1592i	0.142437	−	0.438376i
$649$	−5.08599	−	15.6531i	−0.199643	−	0.614437i
$650$	2.40790			0.0944456
$651$		0			0
$652$	−1.35484			−0.0530595
$653$	4.89446	+	15.0636i	0.191535	+	0.589484i	1.00000		0.000939296i	$0.000298987\pi$
$653$	4.89446	+	15.0636i	0.191535	+	0.589484i	−0.808465	+	0.588545i	$0.799701\pi$
$654$	−0.232532	+	0.715660i	−0.00909272	+	0.0279845i
$655$	10.8533	−	7.88542i	0.424075	−	0.308109i
$656$	−52.1566			−2.03637
$657$	−11.2287			−0.438074
$658$	−8.64512	+	6.28105i	−0.337022	+	0.244861i
$659$	−19.2714	−	14.0015i	−0.750708	−	0.545421i	0.145339	−	0.989382i	$-0.453573\pi$
$659$	−19.2714	−	14.0015i	−0.750708	−	0.545421i	−0.896046	+	0.443961i	$0.853573\pi$
$660$	−2.55655	−	1.85744i	−0.0995134	−	0.0723007i
$661$	12.7346	+	39.1930i	0.495318	+	1.52443i	0.816461	+	0.577400i	$0.195933\pi$
$661$	12.7346	+	39.1930i	0.495318	+	1.52443i	−0.321144	+	0.947030i	$0.604067\pi$
$662$	31.4762	−	22.8688i	1.22336	−	0.888820i
$663$	−0.412993	−	1.27106i	−0.0160393	−	0.0493640i
$664$	−5.53230	+	17.0267i	−0.214695	+	0.660763i
$665$	9.78907	+	7.11218i	0.379604	+	0.275798i
$666$	−8.83862	+	27.2025i	−0.342490	+	1.05408i
$667$	−6.67155	+	20.5329i	−0.258323	+	0.795038i
$668$	11.2713	+	8.18906i	0.436099	+	0.316844i
$669$	−0.578170	+	1.77943i	−0.0223534	+	0.0687965i
$670$	10.9428	+	33.6784i	0.422756	+	1.30111i
$671$	−39.6343	+	28.7960i	−1.53007	+	1.11166i
$672$	−0.384661	−	1.18387i	−0.0148386	−	0.0456686i
$673$	−32.5287	−	23.6334i	−1.25389	−	0.911003i	−0.255447	−	0.966823i	$-0.582222\pi$
$673$	−32.5287	−	23.6334i	−1.25389	−	0.911003i	−0.998441	+	0.0558207i	$0.982222\pi$
$674$	−6.63262	−	4.81888i	−0.255479	−	0.185616i
$675$	0.997769	−	0.724922i	0.0384042	−	0.0279023i
$676$	−14.3427			−0.551640
$677$	−31.6579			−1.21671			−0.608356	−	0.793664i	$-0.708171\pi$
$677$	−31.6579			−1.21671			−0.608356	+	0.793664i	$0.708171\pi$
$678$	2.95426	−	2.14640i	0.113458	−	0.0824319i
$679$	−2.80979	+	8.64765i	−0.107830	+	0.331866i
$680$	−5.85026	−	18.0052i	−0.224347	−	0.690469i
$681$	−0.275503			−0.0105573
$682$		0			0
$683$	10.8397			0.414771			0.207386	−	0.978259i	$-0.433505\pi$
$683$	10.8397			0.414771			0.207386	+	0.978259i	$0.433505\pi$
$684$	5.33557	+	16.4212i	0.204011	+	0.627880i
$685$	−3.34572	+	10.2971i	−0.127833	+	0.393431i
$686$	19.7833	−	14.3734i	0.755328	−	0.548778i
$687$	−5.31995			−0.202969
$688$	−14.9306			−0.569225
$689$	−0.906758	+	0.658798i	−0.0345447	+	0.0250982i
$690$	−4.11023	−	2.98626i	−0.156474	−	0.113685i
$691$	21.4195	+	15.5622i	0.814836	+	0.592013i	0.915229	−	0.402935i	$-0.132010\pi$
$691$	21.4195	+	15.5622i	0.814836	+	0.592013i	−0.100392	+	0.994948i	$0.532010\pi$
$692$	−2.94925	−	9.07686i	−0.112114	−	0.345051i
$693$	13.5452	−	9.84115i	0.514539	−	0.373834i
$694$	−16.3713	−	50.3857i	−0.621446	−	1.91262i
$695$	5.12558	−	15.7749i	0.194425	−	0.598377i
$696$	0.754104	+	0.547889i	0.0285842	+	0.0207677i
$697$	18.5202	−	56.9992i	0.701502	−	2.15900i
$698$	3.76076	−	11.5744i	0.142347	−	0.438098i
$699$	2.36046	+	1.71498i	0.0892809	+	0.0648664i
$700$	−0.439957	+	1.35405i	−0.0166288	+	0.0511782i
$701$	3.31472	+	10.2017i	0.125195	+	0.385311i	0.993937	−	0.109955i	$-0.0350706\pi$
$701$	3.31472	+	10.2017i	0.125195	+	0.385311i	−0.868741	+	0.495266i	$0.835071\pi$
$702$	2.04856	−	1.48837i	0.0773180	−	0.0561748i
$703$	7.71463	+	23.7432i	0.290963	+	0.895491i
$704$	−5.61393	−	4.07876i	−0.211583	−	0.153724i
$705$	2.14684	+	1.55977i	0.0808548	+	0.0587445i
$706$	11.3471	−	8.24414i	0.427053	−	0.310272i
$707$	−10.4598			−0.393380
$708$	0.731396			0.0274876
$709$	27.1529	−	19.7278i	1.01975	−	0.740892i	0.0535184	−	0.998567i	$-0.482956\pi$
$709$	27.1529	−	19.7278i	1.01975	−	0.740892i	0.966232	+	0.257675i	$0.0829564\pi$
$710$	8.33752	−	25.6602i	0.312902	−	0.963012i
$711$	−7.79343	−	23.9857i	−0.292276	−	0.899534i
$712$	−1.19313			−0.0447146
$713$		0			0
$714$	2.05508			0.0769093
$715$	−5.04776	−	15.5354i	−0.188776	−	0.580992i
$716$	−5.14759	+	15.8427i	−0.192374	+	0.592068i
$717$	−0.704196	+	0.511628i	−0.0262987	+	0.0191071i
$718$	−4.66409			−0.174062
$719$	−9.25379			−0.345108			−0.172554	−	0.985000i	$-0.555202\pi$
$719$	−9.25379			−0.345108			−0.172554	+	0.985000i	$0.555202\pi$
$720$	29.1980	−	21.2136i	1.08815	−	0.790584i
$721$	−7.66773	−	5.57093i	−0.285561	−	0.207472i
$722$	3.99869	+	2.90522i	0.148816	+	0.108121i
$723$	−0.473307	−	1.45669i	−0.0176025	−	0.0541748i
$724$	−21.2060	+	15.4071i	−0.788117	+	0.572600i
$725$	−1.20741	−	3.71601i	−0.0448419	−	0.138009i
$726$	−1.89696	+	5.83824i	−0.0704027	+	0.216677i
$727$	−36.8950	−	26.8058i	−1.36836	−	0.994172i	−0.997863	−	0.0653386i	$-0.979187\pi$
$727$	−36.8950	−	26.8058i	−1.36836	−	0.994172i	−0.370497	−	0.928833i	$-0.620813\pi$
$728$	0.542542	−	1.66977i	0.0201080	−	0.0618859i
$729$	−7.74106	+	23.8245i	−0.286706	+	0.882390i
$730$	−13.6284	−	9.90160i	−0.504409	−	0.366475i
$731$	5.30169	−	16.3169i	0.196090	−	0.603503i
$732$	−0.672753	−	2.07052i	−0.0248657	−	0.0765286i
$733$	−30.7184	+	22.3182i	−1.13461	+	0.824341i	−0.986359	−	0.164609i	$-0.947364\pi$
$733$	−30.7184	+	22.3182i	−1.13461	+	0.824341i	−0.148249	+	0.988950i	$0.547364\pi$
$734$	19.6235	+	60.3949i	0.724317	+	2.22922i
$735$	−2.24548	−	1.63144i	−0.0828257	−	0.0601764i
$736$	−29.9916	−	21.7902i	−1.10551	−	0.803197i
$737$	34.6000	−	25.1384i	1.27451	−	0.925984i
$738$	56.4286			2.07717
$739$	26.3219			0.968268			0.484134	−	0.874994i	$-0.339135\pi$
$739$	26.3219			0.968268			0.484134	+	0.874994i	$0.339135\pi$
$740$	−13.3487	+	9.69839i	−0.490708	+	0.356520i
$741$	0.339399	−	1.04456i	0.0124681	−	0.0383729i
$742$	−0.532578	−	1.63911i	−0.0195515	−	0.0601735i
$743$	−53.3973			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$743$	−53.3973			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$744$		0			0
$745$	−5.46780			−0.200325
$746$	−3.72382	−	11.4607i	−0.136339	−	0.419607i
$747$	12.1189	−	37.2980i	0.443406	−	1.36466i
$748$	30.7978	−	22.3759i	1.12608	−	0.818143i
$749$	−0.310230			−0.0113356
$750$	−3.32571			−0.121438
$751$	−7.19021	+	5.22399i	−0.262375	+	0.190626i	−0.711193	−	0.702997i	$-0.751845\pi$
$751$	−7.19021	+	5.22399i	−0.262375	+	0.190626i	0.448819	+	0.893623i	$0.351845\pi$
$752$	22.5068	+	16.3521i	0.820737	+	0.596300i
$753$	1.82364	+	1.32495i	0.0664571	+	0.0482839i
$754$	−2.47898	−	7.62950i	−0.0902790	−	0.277850i
$755$	−9.46798	+	6.87889i	−0.344575	+	0.250348i
$756$	0.462661	+	1.42392i	0.0168268	+	0.0517876i
$757$	12.0944	−	37.2227i	0.439578	−	1.35288i	−0.448743	−	0.893661i	$-0.648128\pi$
$757$	12.0944	−	37.2227i	0.439578	−	1.35288i	0.888321	−	0.459222i	$-0.151872\pi$
$758$	25.6364	+	18.6259i	0.931157	+	0.676525i
$759$	−1.89611	+	5.83564i	−0.0688246	+	0.211820i
$760$	4.80775	−	14.7967i	0.174395	−	0.536734i
$761$	−13.5540	−	9.84754i	−0.491331	−	0.356973i	0.314365	−	0.949302i	$-0.398208\pi$
$761$	−13.5540	−	9.84754i	−0.491331	−	0.356973i	−0.805696	+	0.592329i	$0.798208\pi$
$762$	−2.16298	+	6.65698i	−0.0783566	+	0.241157i
$763$	−0.710711	−	2.18734i	−0.0257294	−	0.0791871i
$764$	−7.64890	+	5.55725i	−0.276727	+	0.201054i
$765$	12.8154	+	39.4416i	0.463340	+	1.42602i
$766$	47.5103	+	34.5182i	1.71662	+	1.24719i
$767$	3.05866	+	2.22225i	0.110442	+	0.0802406i
$768$	−3.20129	+	2.32587i	−0.115516	+	0.0839276i
$769$	17.2215			0.621023			0.310511	−	0.950570i	$-0.399500\pi$
$769$	17.2215			0.621023			0.310511	+	0.950570i	$0.399500\pi$
$770$	25.1179			0.905187
$771$	−0.0164092	+	0.0119220i	−0.000590962	+	0.000429359i
$772$	−4.95294	+	15.2436i	−0.178260	+	0.548629i
$773$	9.11444	+	28.0514i	0.327824	+	1.00894i	0.970150	+	0.242506i	$0.0779694\pi$
$773$	9.11444	+	28.0514i	0.327824	+	1.00894i	−0.642326	+	0.766431i	$0.722031\pi$
$774$	16.1536			0.580628
$775$		0			0
$776$	11.6914			0.419697
$777$	0.332432	+	1.02312i	0.0119259	+	0.0367043i
$778$	−4.67251	+	14.3805i	−0.167517	+	0.515566i
$779$	39.8462	−	28.9500i	1.42764	−	1.03724i
$780$	0.725899			0.0259914
$781$	−32.5858			−1.16601
$782$	49.5144	−	35.9743i	1.77063	−	1.28644i
$783$	−3.32416	−	2.41514i	−0.118796	−	0.0863101i
$784$	−23.5408	−	17.1034i	−0.840743	−	0.610835i
$785$	−3.08547	−	9.49611i	−0.110125	−	0.338931i
$786$	1.51487	−	1.10062i	0.0540335	−	0.0392577i
$787$	−4.66771	−	14.3657i	−0.166386	−	0.512083i	0.832750	−	0.553649i	$-0.186765\pi$
$787$	−4.66771	−	14.3657i	−0.166386	−	0.512083i	−0.999136	+	0.0415663i	$0.986765\pi$
$788$	−6.84260	+	21.0594i	−0.243758	+	0.750209i
$789$	−3.67099	−	2.66713i	−0.130691	−	0.0949523i
$790$	11.6919	−	35.9840i	0.415979	−	1.28025i
$791$	−3.44892	+	10.6147i	−0.122630	+	0.377415i
$792$	−17.4165	−	12.6538i	−0.618867	−	0.449633i
$793$	3.47757	−	10.7029i	0.123492	−	0.380070i
$794$	−14.6225	−	45.0034i	−0.518933	−	1.59711i
$795$	−0.346248	+	0.251564i	−0.0122802	+	0.00892206i
$796$	0.0905415	+	0.278658i	0.00320916	+	0.00987678i
$797$	−33.3791	−	24.2513i	−1.18235	−	0.859026i	−0.189914	−	0.981801i	$-0.560821\pi$
$797$	−33.3791	−	24.2513i	−1.18235	−	0.859026i	−0.992435	+	0.122774i	$0.960821\pi$
$798$	1.36632	+	0.992690i	0.0483672	+	0.0351408i
$799$	−25.8622	+	18.7900i	−0.914940	+	0.664743i
$800$	6.70917			0.237205
$801$	2.61364			0.0923484
$802$	3.92045	−	2.84837i	0.138436	−	0.100579i
$803$	−6.28698	+	19.3493i	−0.221863	+	0.682824i
$804$	0.587301	+	1.80753i	0.0207125	+	0.0637465i
$805$	15.5281			0.547294
$806$		0			0
$807$	0.492158			0.0173248
$808$	4.15604	+	12.7910i	0.146209	+	0.449985i
$809$	−6.01014	+	18.4973i	−0.211305	+	0.650331i	0.788090	+	0.615560i	$0.211070\pi$
$809$	−6.01014	+	18.4973i	−0.211305	+	0.650331i	−0.999395	+	0.0347707i	$0.988930\pi$
$810$	−31.1960	+	22.6652i	−1.09612	+	0.796375i
$811$	16.0338			0.563022			0.281511	−	0.959558i	$-0.409164\pi$
$811$	16.0338			0.563022			0.281511	+	0.959558i	$0.409164\pi$
$812$	4.74328			0.166457
$813$	4.49277	−	3.26419i	0.157568	−	0.114480i
$814$	41.9266	+	30.4615i	1.46953	+	1.06767i
$815$	−2.16352	−	1.57189i	−0.0757849	−	0.0550610i
$816$	−1.65330	−	5.08834i	−0.0578771	−	0.178127i
$817$	11.4066	−	8.28738i	0.399066	−	0.289939i
$818$	−1.72434	−	5.30699i	−0.0602903	−	0.185554i
$819$	−1.18847	+	3.65775i	−0.0415286	+	0.127812i
$820$	26.3352	+	19.1336i	0.919663	+	0.668175i
$821$	6.34275	−	19.5210i	0.221364	−	0.681287i	−0.777277	−	0.629159i	$-0.783400\pi$
$821$	6.34275	−	19.5210i	0.221364	−	0.681287i	0.998640	−	0.0521282i	$-0.0166004\pi$
$822$	−0.466983	+	1.43722i	−0.0162879	+	0.0501290i
$823$	21.5621	+	15.6658i	0.751609	+	0.546076i	0.896325	−	0.443397i	$-0.146227\pi$
$823$	21.5621	+	15.6658i	0.751609	+	0.546076i	−0.144716	+	0.989473i	$0.546227\pi$
$824$	−3.76588	+	11.5902i	−0.131191	+	0.403764i
$825$	−0.343155	−	1.05612i	−0.0119471	−	0.0367695i
$826$	−4.70325	+	3.41711i	−0.163647	+	0.118897i
$827$	−7.91384	−	24.3563i	−0.275191	−	0.846951i	−0.989169	−	0.146783i	$-0.953108\pi$
$827$	−7.91384	−	24.3563i	−0.275191	−	0.846951i	0.713978	−	0.700168i	$-0.246892\pi$
$828$	17.9263	+	13.0242i	0.622982	+	0.452623i
$829$	−28.5293	−	20.7277i	−0.990863	−	0.719904i	−0.0307533	−	0.999527i	$-0.509791\pi$
$829$	−28.5293	−	20.7277i	−0.990863	−	0.719904i	−0.960110	+	0.279623i	$0.909791\pi$
$830$	47.5986	−	34.5824i	1.65217	−	1.20037i
$831$	2.29764			0.0797043
$832$	1.59401			0.0552622
$833$	27.0504	−	19.6533i	0.937242	−	0.680946i
$834$	0.715409	−	2.20180i	0.0247726	−	0.0762422i
$835$	8.49797	+	26.1541i	0.294084	+	0.905099i
$836$	31.2844			1.08199
$837$		0			0
$838$	−58.9095			−2.03499
$839$	6.60260	+	20.3207i	0.227947	+	0.701549i	0.997979	+	0.0635436i	$0.0202402\pi$
$839$	6.60260	+	20.3207i	0.227947	+	0.701549i	−0.770032	+	0.638005i	$0.779760\pi$
$840$	0.207172	−	0.637609i	0.00714810	−	0.0219996i
$841$	12.9302	−	9.39437i	0.445870	−	0.323944i
$842$	−24.5778			−0.847007
$843$	−5.94628			−0.204801
$844$	−16.5537	+	12.0269i	−0.569800	+	0.413984i
$845$	−22.9036	−	16.6405i	−0.787909	−	0.572449i
$846$	−24.3502	−	17.6915i	−0.837178	−	0.608245i
$847$	−5.79786	−	17.8440i	−0.199217	−	0.613126i
$848$	−3.62994	+	2.63731i	−0.124653	+	0.0905656i
$849$	0.338613	+	1.04214i	0.0116212	+	0.0357662i
$850$	−3.42281	+	10.5343i	−0.117401	+	0.361325i
$851$	25.9194	+	18.8315i	0.888505	+	0.645537i
$852$	0.447476	−	1.37719i	0.0153303	−	0.0471817i
$853$	5.52630	−	17.0082i	0.189217	−	0.582349i	−0.810779	−	0.585353i	$-0.800956\pi$
$853$	5.52630	−	17.0082i	0.189217	−	0.582349i	0.999995	+	0.00300347i	$0.000956035\pi$
$854$	13.9997	+	10.1714i	0.479060	+	0.348057i
$855$	−10.5317	+	32.4132i	−0.360176	+	1.10851i
$856$	0.123266	+	0.379372i	0.00421313	+	0.0129667i
$857$	16.5940	−	12.0562i	0.566839	−	0.411833i	−0.267117	−	0.963664i	$-0.586071\pi$
$857$	16.5940	−	12.0562i	0.566839	−	0.411833i	0.833956	+	0.551832i	$0.186071\pi$
$858$	−0.704547	−	2.16837i	−0.0240528	−	0.0740270i
$859$	22.5717	+	16.3993i	0.770138	+	0.559538i	0.902003	−	0.431730i	$-0.142097\pi$
$859$	22.5717	+	16.3993i	0.770138	+	0.559538i	−0.131865	+	0.991268i	$0.542097\pi$
$860$	7.53885	+	5.47729i	0.257073	+	0.186774i
$861$	1.71702	−	1.24749i	0.0585159	−	0.0425143i
$862$	−50.1614			−1.70850
$863$	−36.1617			−1.23096			−0.615480	−	0.788153i	$-0.711038\pi$
$863$	−36.1617			−1.23096			−0.615480	+	0.788153i	$0.711038\pi$
$864$	5.70794	−	4.14706i	0.194188	−	0.141086i
$865$	5.82142	−	17.9165i	0.197934	−	0.609179i
$866$	−1.18571	−	3.64924i	−0.0402921	−	0.124006i
$867$	2.90140			0.0985366
$868$		0			0
$869$	−45.6958			−1.55012
$870$	−0.946605	−	2.91335i	−0.0320929	−	0.0987719i
$871$	−3.03586	+	9.34340i	−0.102866	+	0.316589i
$872$	−2.39245	+	1.73822i	−0.0810187	+	0.0588635i
$873$	−25.6108			−0.866794
$874$	50.2969			1.70132
$875$	8.22340	−	5.97465i	0.278002	−	0.201980i
$876$	−0.731438	−	0.531420i	−0.0247130	−	0.0179550i
$877$	14.8839	+	10.8138i	0.502592	+	0.365155i	0.810006	−	0.586421i	$-0.199464\pi$
$877$	14.8839	+	10.8138i	0.502592	+	0.365155i	−0.307414	+	0.951576i	$0.599464\pi$
$878$	−5.23613	−	16.1152i	−0.176711	−	0.543860i
$879$	−0.197604	+	0.143568i	−0.00666503	+	0.00484243i
$880$	−20.2073	−	62.1916i	−0.681187	−	2.09648i
$881$	10.2877	−	31.6623i	0.346602	−	1.06673i	−0.614118	−	0.789214i	$-0.710488\pi$
$881$	10.2877	−	31.6623i	0.346602	−	1.06673i	0.960721	−	0.277518i	$-0.0895117\pi$
$882$	25.4690	+	18.5043i	0.857584	+	0.623071i
$883$	1.62460	−	5.00001i	0.0546722	−	0.168264i	−0.919992	−	0.391937i	$-0.871805\pi$
$883$	1.62460	−	5.00001i	0.0546722	−	0.168264i	0.974664	+	0.223674i	$0.0718050\pi$
$884$	−2.70224	+	8.31664i	−0.0908862	+	0.279719i
$885$	1.16796	+	0.848572i	0.0392605	+	0.0285244i
$886$	−17.4958	+	53.8465i	−0.587783	+	1.80901i
$887$	11.1951	+	34.4548i	0.375893	+	1.15688i	0.942874	+	0.333150i	$0.108111\pi$
$887$	11.1951	+	34.4548i	0.375893	+	1.15688i	−0.566981	+	0.823731i	$0.691889\pi$
$888$	1.11906	−	0.813046i	0.0375532	−	0.0272840i
$889$	−6.61094	−	20.3464i	−0.221724	−	0.682396i
$890$	3.17220	+	2.30473i	0.106332	+	0.0772549i
$891$	37.6766	+	27.3737i	1.26222	+	0.917053i
$892$	9.90403	−	7.19570i	0.331611	−	0.240930i
$893$	−26.2709			−0.879123
$894$	−0.763174			−0.0255244
$895$	−26.6009	+	19.3267i	−0.889170	+	0.646020i
$896$	3.27113	−	10.0675i	0.109281	−	0.336332i
$897$	−0.435557	−	1.34051i	−0.0145428	−	0.0447582i
$898$	43.4706			1.45063
$899$		0			0
$900$	−4.01014			−0.133671
$901$	−1.59323	−	4.90345i	−0.0530781	−	0.163358i
$902$	31.5945	−	97.2380i	1.05198	−	3.23767i
$903$	0.491524	−	0.357113i	0.0163569	−	0.0118840i
$904$	14.3508			0.477301
$905$	−51.7392			−1.71987
$906$	−1.32150	+	0.960128i	−0.0439040	+	0.0318981i
$907$	14.1026	+	10.2462i	0.468270	+	0.340218i	0.796767	−	0.604287i	$-0.206542\pi$
$907$	14.1026	+	10.2462i	0.468270	+	0.340218i	−0.328496	+	0.944505i	$0.606542\pi$
$908$	1.45836	+	1.05956i	0.0483973	+	0.0351627i
$909$	−9.10408	−	28.0195i	−0.301963	−	0.929347i
$910$	−4.66790	+	3.39143i	−0.154739	+	0.112425i
$911$	5.68116	+	17.4848i	0.188225	+	0.579297i	0.999989	−	0.00468848i	$-0.00149240\pi$
$911$	5.68116	+	17.4848i	0.188225	+	0.579297i	−0.811764	+	0.583986i	$0.801492\pi$
$912$	1.35869	−	4.18160i	0.0449906	−	0.138467i
$913$	−57.4867	−	41.7665i	−1.90253	−	1.38227i
$914$	−2.06448	+	6.35383i	−0.0682870	+	0.210166i
$915$	1.32792	−	4.08692i	0.0438998	−	0.135110i
$916$	28.1609	+	20.4601i	0.930462	+	0.676020i
$917$	−1.76852	+	5.44294i	−0.0584016	+	0.179742i
$918$	3.59945	+	11.0780i	0.118799	+	0.365627i
$919$	−31.4203	+	22.8282i	−1.03646	+	0.753033i	−0.969592	−	0.244729i	$-0.921301\pi$
$919$	−31.4203	+	22.8282i	−1.03646	+	0.753033i	−0.0668692	+	0.997762i	$0.521301\pi$
$920$	−6.16987	−	18.9889i	−0.203415	−	0.626046i
$921$	2.42453	+	1.76152i	0.0798910	+	0.0580442i
$922$	24.8979	+	18.0894i	0.819969	+	0.595742i
$923$	6.05572	−	4.39974i	0.199326	−	0.144819i
$924$	1.34808			0.0443487
$925$	−5.79821			−0.190644
$926$	7.16415	−	5.20506i	0.235429	−	0.171049i
$927$	8.24942	−	25.3891i	0.270946	−	0.833887i
$928$	−6.90721	−	21.2582i	−0.226740	−	0.697835i
$929$	−45.3781			−1.48881			−0.744404	−	0.667729i	$-0.767266\pi$
$929$	−45.3781			−1.48881			−0.744404	+	0.667729i	$0.767266\pi$
$930$		0			0
$931$	27.4779			0.900552
$932$	−5.89933	−	18.1563i	−0.193239	−	0.594728i
$933$	1.62027	−	4.98668i	0.0530453	−	0.163257i
$934$	−3.74868	+	2.72358i	−0.122661	+	0.0891182i
$935$	75.1413			2.45738
$936$	4.94519			0.161638
$937$	21.0743	−	15.3114i	0.688468	−	0.500201i	−0.187688	−	0.982229i	$-0.560099\pi$
$937$	21.0743	−	15.3114i	0.688468	−	0.500201i	0.876156	+	0.482028i	$0.160099\pi$
$938$	−12.2215	−	8.87942i	−0.399045	−	0.289923i
$939$	−1.97881	−	1.43769i	−0.0645760	−	0.0469172i
$940$	−5.36545	−	16.5132i	−0.175002	−	0.538600i
$941$	−33.0951	+	24.0450i	−1.07887	+	0.783843i	−0.977485	−	0.211004i	$-0.932327\pi$
$941$	−33.0951	+	24.0450i	−1.07887	+	0.783843i	−0.101383	+	0.994847i	$0.532327\pi$
$942$	−0.430658	−	1.32543i	−0.0140316	−	0.0431848i
$943$	19.5320	−	60.1133i	0.636049	−	1.95756i
$944$	12.2445	+	8.89612i	0.398523	+	0.289544i
$945$	−0.913230	+	2.81063i	−0.0297074	+	0.0914299i
$946$	9.04442	−	27.8359i	0.294060	−	0.905022i
$947$	31.5954	+	22.9554i	1.02671	+	0.745951i	0.967648	−	0.252303i	$-0.0811881\pi$
$947$	31.5954	+	22.9554i	1.02671	+	0.745951i	0.0590649	+	0.998254i	$0.481188\pi$
$948$	0.627507	−	1.93127i	0.0203805	−	0.0627246i
$949$	−1.44418	−	4.44474i	−0.0468802	−	0.144282i
$950$	−7.36419	+	5.35040i	−0.238926	+	0.173590i
$951$	−0.561964	−	1.72955i	−0.0182229	−	0.0560844i
$952$	6.53388	+	4.74714i	0.211764	+	0.153856i
$953$	6.40158	+	4.65102i	0.207368	+	0.150661i	0.686622	−	0.727015i	$-0.259093\pi$
$953$	6.40158	+	4.65102i	0.207368	+	0.150661i	−0.479254	+	0.877676i	$0.659093\pi$
$954$	3.92726	−	2.85332i	0.127150	−	0.0923797i
$955$	−18.6620			−0.603889
$956$	5.69530			0.184199
$957$	−2.99307	+	2.17460i	−0.0967524	+	0.0702947i
$958$	−1.14374	+	3.52008i	−0.0369526	+	0.113728i
$959$	−1.42728	−	4.39273i	−0.0460894	−	0.141849i
$960$	0.608676			0.0196449
$961$		0			0
$962$	−11.9045			−0.383818
$963$	−0.270021	−	0.831040i	−0.00870131	−	0.0267799i
$964$	−3.09687	+	9.53120i	−0.0997436	+	0.306979i
$965$	−25.5950	+	18.5959i	−0.823933	+	0.598623i
$966$	2.16735			0.0697334
$967$	11.4381			0.367825			0.183912	−	0.982943i	$-0.441124\pi$
$967$	11.4381			0.367825			0.183912	+	0.982943i	$0.441124\pi$
$968$	−19.5172	+	14.1801i	−0.627308	+	0.455766i
$969$	4.08740	+	2.96967i	0.131306	+	0.0953996i
$970$	−31.0840	−	22.5839i	−0.998049	−	0.725125i
$971$	−9.86886	−	30.3732i	−0.316707	−	0.974724i	−0.975046	−	0.222002i	$-0.928741\pi$
$971$	−9.86886	−	30.3732i	−0.316707	−	0.974724i	0.658339	−	0.752721i	$-0.271259\pi$
$972$	−5.12797	+	3.72569i	−0.164480	+	0.119502i
$973$	2.18657	+	6.72958i	0.0700983	+	0.215741i
$974$	9.86605	−	30.3646i	0.316128	−	0.972943i
$975$	0.206370	+	0.149937i	0.00660913	+	0.00480181i
$976$	13.9215	−	42.8459i	0.445615	−	1.37146i
$977$	−3.63699	+	11.1935i	−0.116358	+	0.358112i	−0.992228	−	0.124435i	$-0.960288\pi$
$977$	−3.63699	+	11.1935i	−0.116358	+	0.358112i	0.875870	+	0.482547i	$0.160288\pi$
$978$	−0.301976	−	0.219398i	−0.00965613	−	0.00701559i
$979$	1.46338	−	4.50383i	0.0467699	−	0.143943i
$980$	5.61196	+	17.2718i	0.179267	+	0.551729i
$981$	5.24082	−	3.80768i	0.167327	−	0.121570i
$982$	−12.5179	−	38.5262i	−0.399463	−	1.22942i
$983$	43.1727	+	31.3668i	1.37699	+	1.00045i	0.997154	+	0.0753933i	$0.0240212\pi$
$983$	43.1727	+	31.3668i	1.37699	+	1.00045i	0.379841	+	0.925052i	$0.375979\pi$
$984$	−2.20776	−	1.60403i	−0.0703807	−	0.0511346i
$985$	−35.3601	+	25.6906i	−1.12667	+	0.818572i
$986$	36.9022			1.17520
$987$	−1.13205			−0.0360334
$988$	−5.81388	+	4.22403i	−0.184964	+	0.134384i
$989$	5.59133	−	17.2084i	0.177794	−	0.547194i
$990$	21.8624	+	67.2855i	0.694833	+	2.13847i
$991$	−11.6584			−0.370343			−0.185171	−	0.982706i	$-0.559284\pi$
$991$	−11.6584			−0.370343			−0.185171	+	0.982706i	$0.559284\pi$
$992$		0			0
$993$	4.12168			0.130798
$994$	3.55679	+	10.9467i	0.112814	+	0.347207i
$995$	−0.178717	+	0.550033i	−0.00566570	+	0.0174372i
$996$	2.55462	−	1.85604i	0.0809464	−	0.0588110i
$997$	26.1488			0.828141			0.414071	−	0.910245i	$-0.364107\pi$
$997$	26.1488			0.828141			0.414071	+	0.910245i	$0.364107\pi$
$998$	36.0533			1.14125
$999$	−4.93292	+	3.58398i	−0.156071	+	0.113392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.r.531.4		48
31.2	even	5	inner	961.2.d.r.388.9		48
31.3	odd	30		961.2.c.k.439.4		24
31.4	even	5	inner	961.2.d.r.374.9		48
31.5	even	3		961.2.g.v.844.3		96
31.6	odd	6		961.2.g.v.547.3		96
31.7	even	15		961.2.g.v.816.9		96
31.8	even	5	inner	961.2.d.r.628.4		48
31.9	even	15		961.2.g.v.448.4		96
31.10	even	15		961.2.g.v.338.9		96
31.11	odd	30		961.2.g.v.732.9		96
31.12	odd	30		961.2.g.v.235.9		96
31.13	odd	30		961.2.c.k.521.4		24
31.14	even	15		961.2.g.v.846.3		96
31.15	odd	10		961.2.a.k.1.3	✓	12
31.16	even	5		961.2.a.k.1.4	yes	12
31.17	odd	30		961.2.g.v.846.4		96
31.18	even	15		961.2.c.k.521.3		24
31.19	even	15		961.2.g.v.235.10		96
31.20	even	15		961.2.g.v.732.10		96
31.21	odd	30		961.2.g.v.338.10		96
31.22	odd	30		961.2.g.v.448.3		96
31.23	odd	10	inner	961.2.d.r.628.3		48
31.24	odd	30		961.2.g.v.816.10		96
31.25	even	3		961.2.g.v.547.4		96
31.26	odd	6		961.2.g.v.844.4		96
31.27	odd	10	inner	961.2.d.r.374.10		48
31.28	even	15		961.2.c.k.439.3		24
31.29	odd	10	inner	961.2.d.r.388.10		48
31.30	odd	2	inner	961.2.d.r.531.3		48
93.47	odd	10		8649.2.a.bp.1.10		12
93.77	even	10		8649.2.a.bp.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.3	✓	12	31.15	odd	10
961.2.a.k.1.4	yes	12	31.16	even	5
961.2.c.k.439.3		24	31.28	even	15
961.2.c.k.439.4		24	31.3	odd	30
961.2.c.k.521.3		24	31.18	even	15
961.2.c.k.521.4		24	31.13	odd	30
961.2.d.r.374.9		48	31.4	even	5	inner
961.2.d.r.374.10		48	31.27	odd	10	inner
961.2.d.r.388.9		48	31.2	even	5	inner
961.2.d.r.388.10		48	31.29	odd	10	inner
961.2.d.r.531.3		48	31.30	odd	2	inner
961.2.d.r.531.4		48	1.1	even	1	trivial
961.2.d.r.628.3		48	31.23	odd	10	inner
961.2.d.r.628.4		48	31.8	even	5	inner
961.2.g.v.235.9		96	31.12	odd	30
961.2.g.v.235.10		96	31.19	even	15
961.2.g.v.338.9		96	31.10	even	15
961.2.g.v.338.10		96	31.21	odd	30
961.2.g.v.448.3		96	31.22	odd	30
961.2.g.v.448.4		96	31.9	even	15
961.2.g.v.547.3		96	31.6	odd	6
961.2.g.v.547.4		96	31.25	even	3
961.2.g.v.732.9		96	31.11	odd	30
961.2.g.v.732.10		96	31.20	even	15
961.2.g.v.816.9		96	31.7	even	15
961.2.g.v.816.10		96	31.24	odd	30
961.2.g.v.844.3		96	31.5	even	3
961.2.g.v.844.4		96	31.26	odd	6
961.2.g.v.846.3		96	31.14	even	15
961.2.g.v.846.4		96	31.17	odd	30
8649.2.a.bp.1.9		12	93.77	even	10
8649.2.a.bp.1.10		12	93.47	odd	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.557046 - 1.71441i) q^{2} +(0.0590122 - 0.181621i) q^{3} +(-1.01088 + 0.734444i) q^{4} -2.46636 q^{5} -0.344245 q^{6} +(0.851208 - 0.618439i) q^{7} +(-1.09449 - 0.795192i) q^{8} +(2.39755 + 1.74192i) q^{9} +(1.37388 + 4.22837i) q^{10} +(4.34407 - 3.15615i) q^{11} +(0.0737363 + 0.226937i) q^{12} +(-0.381155 + 1.17308i) q^{13} +(-1.53442 - 1.11482i) q^{14} +(-0.145545 + 0.447943i) q^{15} +(-1.52585 + 4.69607i) q^{16} +(-4.59028 - 3.33504i) q^{17} +(1.65082 - 5.08072i) q^{18} +(-1.44089 - 4.43461i) q^{19} +(2.49319 - 1.81141i) q^{20} +(-0.0620897 - 0.191092i) q^{21} +(-7.83080 - 5.68941i) q^{22} +(-4.84106 - 3.51724i) q^{23} +(-0.209012 + 0.151856i) q^{24} +1.08295 q^{25} +2.22346 q^{26} +(0.921341 - 0.669393i) q^{27} +(-0.406257 + 1.25033i) q^{28} +(-1.11492 - 3.43137i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(-0.316870 - 0.975226i) q^{33} +(-3.16063 + 9.72741i) q^{34} +(-2.09939 + 1.52530i) q^{35} -3.70296 q^{36} -5.35407 q^{37} +(-6.80010 + 4.94056i) q^{38} +(0.190562 + 0.138451i) q^{39} +(2.69941 + 1.96123i) q^{40} +(3.26410 + 10.0459i) q^{41} +(-0.293024 + 0.212895i) q^{42} +(0.934399 + 2.87578i) q^{43} +(-2.07330 + 6.38096i) q^{44} +(-5.91323 - 4.29621i) q^{45} +(-3.33330 + 10.2588i) q^{46} +(1.74104 - 5.35837i) q^{47} +(0.762861 + 0.554251i) q^{48} +(-1.82103 + 5.60456i) q^{49} +(-0.603255 - 1.85663i) q^{50} +(-0.876594 + 0.636883i) q^{51} +(-0.476258 - 1.46577i) q^{52} +(0.735142 + 0.534112i) q^{53} +(-1.66085 - 1.20668i) q^{54} +(-10.7141 + 7.78423i) q^{55} -1.42341 q^{56} -0.890447 q^{57} +(-5.26172 + 3.82286i) q^{58} +(0.947187 - 2.91514i) q^{59} +(-0.181861 - 0.559710i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(-0.399349 - 1.22907i) q^{64} +(0.940068 - 2.89323i) q^{65} +(-1.49543 + 1.08649i) q^{66} +7.96488 q^{67} +7.08960 q^{68} +(-0.924485 + 0.671678i) q^{69} +(3.78444 + 2.74956i) q^{70} +(-4.90960 - 3.56703i) q^{71} +(-1.23893 - 3.81302i) q^{72} +(-3.06534 + 2.22710i) q^{73} +(2.98246 + 9.17908i) q^{74} +(0.0639074 - 0.196687i) q^{75} +(4.71353 + 3.42458i) q^{76} +(1.74582 - 5.37309i) q^{77} +(0.131211 - 0.403826i) q^{78} +(-6.88485 - 5.00213i) q^{79} +(3.76329 - 11.5822i) q^{80} +(2.68014 + 8.24862i) q^{81} +(15.4045 - 11.1920i) q^{82} +(-4.08933 - 12.5857i) q^{83} +(0.203112 + 0.147569i) q^{84} +(11.3213 + 8.22541i) q^{85} +(4.40978 - 3.20389i) q^{86} -0.689002 q^{87} -7.26429 q^{88} +(0.713499 - 0.518388i) q^{89} +(-4.07153 + 12.5309i) q^{90} +(0.401033 + 1.23425i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(3.55376 + 10.9374i) q^{95} +(0.365595 - 1.12519i) q^{96} +(-6.99151 + 5.07963i) q^{97} +10.6229 q^{98} +15.9129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) \) 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

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