LMFDB - Embedded newform 961.2.c.f.439.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	961.439
Dual form			961.2.c.f.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.61803 q^{2} +(0.500000 - 0.866025i) q^{3} +0.618034 q^{4} +(0.190983 + 0.330792i) q^{5} +(0.809017 - 1.40126i) q^{6} +(-1.50000 + 2.59808i) q^{7} -2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.309017 + 0.535233i) q^{10} +(2.61803 + 4.53457i) q^{11} +(0.309017 - 0.535233i) q^{12} +(0.927051 + 1.60570i) q^{13} +(-2.42705 + 4.20378i) q^{14} +0.381966 q^{15} -4.85410 q^{16} +(2.11803 - 3.66854i) q^{17} +(1.61803 + 2.80252i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.118034 + 0.204441i) q^{20} +(1.50000 + 2.59808i) q^{21} +(4.23607 + 7.33708i) q^{22} +3.47214 q^{23} +(-1.11803 + 1.93649i) q^{24} +(2.42705 - 4.20378i) q^{25} +(1.50000 + 2.59808i) q^{26} +5.00000 q^{27} +(-0.927051 + 1.60570i) q^{28} -6.38197 q^{29} +0.618034 q^{30} -3.38197 q^{32} +5.23607 q^{33} +(3.42705 - 5.93583i) q^{34} -1.14590 q^{35} +(0.618034 + 1.07047i) q^{36} +(2.11803 - 3.66854i) q^{37} +(-4.04508 + 7.00629i) q^{38} +1.85410 q^{39} +(-0.427051 - 0.739674i) q^{40} +(1.23607 + 2.14093i) q^{41} +(2.42705 + 4.20378i) q^{42} +(1.19098 - 2.06284i) q^{43} +(1.61803 + 2.80252i) q^{44} +(-0.381966 + 0.661585i) q^{45} +5.61803 q^{46} -5.61803 q^{47} +(-2.42705 + 4.20378i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(3.92705 - 6.80185i) q^{50} +(-2.11803 - 3.66854i) q^{51} +(0.572949 + 0.992377i) q^{52} +(-0.354102 - 0.613323i) q^{53} +8.09017 q^{54} +(-1.00000 + 1.73205i) q^{55} +(3.35410 - 5.80948i) q^{56} +(2.50000 + 4.33013i) q^{57} -10.3262 q^{58} +(-0.263932 + 0.457144i) q^{59} +0.236068 q^{60} +10.9443 q^{61} -6.00000 q^{63} +4.23607 q^{64} +(-0.354102 + 0.613323i) q^{65} +8.47214 q^{66} +(-0.118034 - 0.204441i) q^{67} +(1.30902 - 2.26728i) q^{68} +(1.73607 - 3.00696i) q^{69} -1.85410 q^{70} +(5.54508 + 9.60437i) q^{71} +(-2.23607 - 3.87298i) q^{72} +(-5.78115 - 10.0133i) q^{73} +(3.42705 - 5.93583i) q^{74} +(-2.42705 - 4.20378i) q^{75} +(-1.54508 + 2.67617i) q^{76} -15.7082 q^{77} +3.00000 q^{78} +(-0.927051 - 1.60570i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +(-3.54508 - 6.14027i) q^{83} +(0.927051 + 1.60570i) q^{84} +1.61803 q^{85} +(1.92705 - 3.33775i) q^{86} +(-3.19098 + 5.52694i) q^{87} +(-5.85410 - 10.1396i) q^{88} -8.61803 q^{89} +(-0.618034 + 1.07047i) q^{90} -5.56231 q^{91} +2.14590 q^{92} -9.09017 q^{94} -1.90983 q^{95} +(-1.69098 + 2.92887i) q^{96} -18.7082 q^{97} +(-1.61803 - 2.80252i) q^{98} +(-5.23607 + 9.06914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{5} + q^{6} - 6 q^{7} + 4 q^{9} - q^{10} + 6 q^{11} - q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 6 q^{21}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^5 + q^6 - 6 * q^7 + 4 * q^9 - q^10 + 6 * q^11 - q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 + 6 * q^21 + 8 * q^22 - 4 * q^23 + 3 * q^25 + 6 * q^26 + 20 * q^27 + 3 * q^28 - 30 * q^29 - 2 * q^30 - 18 * q^32 + 12 * q^33 + 7 * q^34 - 18 * q^35 - 2 * q^36 + 4 * q^37 - 5 * q^38 - 6 * q^39 + 5 * q^40 - 4 * q^41 + 3 * q^42 + 7 * q^43 + 2 * q^44 - 6 * q^45 + 18 * q^46 - 18 * q^47 - 3 * q^48 - 4 * q^49 + 9 * q^50 - 4 * q^51 + 9 * q^52 + 12 * q^53 + 10 * q^54 - 4 * q^55 + 10 * q^57 - 10 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 - 24 * q^63 + 8 * q^64 + 12 * q^65 + 16 * q^66 + 4 * q^67 + 3 * q^68 - 2 * q^69 + 6 * q^70 + 11 * q^71 - 3 * q^73 + 7 * q^74 - 3 * q^75 + 5 * q^76 - 36 * q^77 + 12 * q^78 + 3 * q^80 - 2 * q^81 + 8 * q^82 - 3 * q^83 - 3 * q^84 + 2 * q^85 + q^86 - 15 * q^87 - 10 * q^88 - 30 * q^89 + 2 * q^90 + 18 * q^91 + 22 * q^92 - 14 * q^94 - 30 * q^95 - 9 * q^96 - 48 * q^97 - 2 * q^98 - 12 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.61803			1.14412			0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803			1.14412			0.572061	+	0.820211i	$0.306144\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	0.618034			0.309017
$5$	0.190983	+	0.330792i	0.0854102	+	0.147935i	0.905566	−	0.424206i	$-0.139447\pi$
$5$	0.190983	+	0.330792i	0.0854102	+	0.147935i	−0.820156	+	0.572140i	$0.806113\pi$
$6$	0.809017	−	1.40126i	0.330280	−	0.572061i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	−2.23607			−0.790569
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	0.309017	+	0.535233i	0.0977198	+	0.169256i
$11$	2.61803	+	4.53457i	0.789367	+	1.36722i	0.926355	+	0.376651i	$0.122924\pi$
$11$	2.61803	+	4.53457i	0.789367	+	1.36722i	−0.136988	+	0.990573i	$0.543742\pi$
$12$	0.309017	−	0.535233i	0.0892055	−	0.154508i
$13$	0.927051	+	1.60570i	0.257118	+	0.445341i	0.965469	−	0.260520i	$-0.0838939\pi$
$13$	0.927051	+	1.60570i	0.257118	+	0.445341i	−0.708351	+	0.705860i	$0.750561\pi$
$14$	−2.42705	+	4.20378i	−0.648657	+	1.12351i
$15$	0.381966			0.0986232
$16$	−4.85410			−1.21353
$17$	2.11803	−	3.66854i	0.513699	−	0.889752i	−0.486175	−	0.873861i	$-0.661608\pi$
$17$	2.11803	−	3.66854i	0.513699	−	0.889752i	0.999874	−	0.0158908i	$-0.00505841\pi$
$18$	1.61803	+	2.80252i	0.381374	+	0.660560i
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	0.118034	+	0.204441i	0.0263932	+	0.0457144i
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	4.23607	+	7.33708i	0.903133	+	1.56427i
$23$	3.47214			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$23$	3.47214			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$24$	−1.11803	+	1.93649i	−0.228218	+	0.395285i
$25$	2.42705	−	4.20378i	0.485410	−	0.840755i
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$	5.00000			0.962250
$28$	−0.927051	+	1.60570i	−0.175196	+	0.303449i
$29$	−6.38197			−1.18510			−0.592551	−	0.805533i	$-0.701879\pi$
$29$	−6.38197			−1.18510			−0.592551	+	0.805533i	$0.701879\pi$
$30$	0.618034			0.112837
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	5.23607			0.911482
$34$	3.42705	−	5.93583i	0.587734	−	1.01799i
$35$	−1.14590			−0.193692
$36$	0.618034	+	1.07047i	0.103006	+	0.178411i
$37$	2.11803	−	3.66854i	0.348203	−	0.603105i	−0.637728	−	0.770262i	$-0.720125\pi$
$37$	2.11803	−	3.66854i	0.348203	−	0.603105i	0.985930	+	0.167157i	$0.0534588\pi$
$38$	−4.04508	+	7.00629i	−0.656199	+	1.13657i
$39$	1.85410			0.296894
$40$	−0.427051	−	0.739674i	−0.0675227	−	0.116953i
$41$	1.23607	+	2.14093i	0.193041	+	0.334357i	0.946257	−	0.323417i	$-0.104832\pi$
$41$	1.23607	+	2.14093i	0.193041	+	0.334357i	−0.753215	+	0.657774i	$0.771498\pi$
$42$	2.42705	+	4.20378i	0.374502	+	0.648657i
$43$	1.19098	−	2.06284i	0.181623	−	0.314581i	−0.760810	−	0.648974i	$-0.775198\pi$
$43$	1.19098	−	2.06284i	0.181623	−	0.314581i	0.942433	+	0.334394i	$0.108532\pi$
$44$	1.61803	+	2.80252i	0.243928	+	0.422495i
$45$	−0.381966	+	0.661585i	−0.0569401	+	0.0986232i
$46$	5.61803			0.828334
$47$	−5.61803			−0.819474			−0.409737	−	0.912204i	$-0.634380\pi$
$47$	−5.61803			−0.819474			−0.409737	+	0.912204i	$0.634380\pi$
$48$	−2.42705	+	4.20378i	−0.350315	+	0.606763i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	3.92705	−	6.80185i	0.555369	−	0.961927i
$51$	−2.11803	−	3.66854i	−0.296584	−	0.513699i
$52$	0.572949	+	0.992377i	0.0794537	+	0.137618i
$53$	−0.354102	−	0.613323i	−0.0486396	−	0.0842463i	0.840681	−	0.541531i	$-0.182155\pi$
$53$	−0.354102	−	0.613323i	−0.0486396	−	0.0842463i	−0.889320	+	0.457285i	$0.848822\pi$
$54$	8.09017			1.10093
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	3.35410	−	5.80948i	0.448211	−	0.776324i
$57$	2.50000	+	4.33013i	0.331133	+	0.573539i
$58$	−10.3262			−1.35590
$59$	−0.263932	+	0.457144i	−0.0343610	+	0.0595150i	−0.882695	−	0.469947i	$-0.844273\pi$
$59$	−0.263932	+	0.457144i	−0.0343610	+	0.0595150i	0.848333	+	0.529462i	$0.177606\pi$
$60$	0.236068			0.0304762
$61$	10.9443			1.40127			0.700635	−	0.713520i	$-0.252900\pi$
$61$	10.9443			1.40127			0.700635	+	0.713520i	$0.252900\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	4.23607			0.529508
$65$	−0.354102	+	0.613323i	−0.0439209	+	0.0760733i
$66$	8.47214			1.04285
$67$	−0.118034	−	0.204441i	−0.0144201	−	0.0249764i	0.858725	−	0.512436i	$-0.171257\pi$
$67$	−0.118034	−	0.204441i	−0.0144201	−	0.0249764i	−0.873145	+	0.487460i	$0.837924\pi$
$68$	1.30902	−	2.26728i	0.158742	−	0.274949i
$69$	1.73607	−	3.00696i	0.208998	−	0.361995i
$70$	−1.85410			−0.221608
$71$	5.54508	+	9.60437i	0.658081	+	1.13983i	0.981112	+	0.193441i	$0.0619647\pi$
$71$	5.54508	+	9.60437i	0.658081	+	1.13983i	−0.323031	+	0.946388i	$0.604702\pi$
$72$	−2.23607	−	3.87298i	−0.263523	−	0.456435i
$73$	−5.78115	−	10.0133i	−0.676633	−	1.17196i	−0.975989	−	0.217821i	$-0.930105\pi$
$73$	−5.78115	−	10.0133i	−0.676633	−	1.17196i	0.299356	−	0.954141i	$-0.403228\pi$
$74$	3.42705	−	5.93583i	0.398387	−	0.690026i
$75$	−2.42705	−	4.20378i	−0.280252	−	0.485410i
$76$	−1.54508	+	2.67617i	−0.177233	+	0.306977i
$77$	−15.7082			−1.79012
$78$	3.00000			0.339683
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−0.927051	−	1.60570i	−0.103647	−	0.179523i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$	−3.54508	−	6.14027i	−0.389124	−	0.673982i	0.603208	−	0.797584i	$-0.293889\pi$
$83$	−3.54508	−	6.14027i	−0.389124	−	0.673982i	−0.992332	+	0.123602i	$0.960555\pi$
$84$	0.927051	+	1.60570i	0.101150	+	0.175196i
$85$	1.61803			0.175500
$86$	1.92705	−	3.33775i	0.207799	−	0.359919i
$87$	−3.19098	+	5.52694i	−0.342109	+	0.592551i
$88$	−5.85410	−	10.1396i	−0.624049	−	1.08089i
$89$	−8.61803			−0.913510			−0.456755	−	0.889593i	$-0.650988\pi$
$89$	−8.61803			−0.913510			−0.456755	+	0.889593i	$0.650988\pi$
$90$	−0.618034	+	1.07047i	−0.0651465	+	0.112837i
$91$	−5.56231			−0.583088
$92$	2.14590			0.223725
$93$		0			0
$94$	−9.09017			−0.937579
$95$	−1.90983			−0.195944
$96$	−1.69098	+	2.92887i	−0.172585	+	0.298926i
$97$	−18.7082			−1.89953			−0.949765	−	0.312963i	$-0.898678\pi$
$97$	−18.7082			−1.89953			−0.949765	+	0.312963i	$0.898678\pi$
$98$	−1.61803	−	2.80252i	−0.163446	−	0.283097i
$99$	−5.23607	+	9.06914i	−0.526245	+	0.911482i
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	9.23607			0.919023			0.459512	−	0.888172i	$-0.348024\pi$
$101$	9.23607			0.919023			0.459512	+	0.888172i	$0.348024\pi$
$102$	−3.42705	−	5.93583i	−0.339329	−	0.587734i
$103$	3.42705	+	5.93583i	0.337677	+	0.584874i	0.983995	−	0.178194i	$-0.0570254\pi$
$103$	3.42705	+	5.93583i	0.337677	+	0.584874i	−0.646318	+	0.763068i	$0.723692\pi$
$104$	−2.07295	−	3.59045i	−0.203269	−	0.352073i
$105$	−0.572949	+	0.992377i	−0.0559141	+	0.0968461i
$106$	−0.572949	−	0.992377i	−0.0556497	−	0.0963882i
$107$	5.04508	−	8.73834i	0.487727	−	0.844768i	−0.512174	−	0.858882i	$-0.671160\pi$
$107$	5.04508	−	8.73834i	0.487727	−	0.844768i	0.999900	+	0.0141144i	$0.00449290\pi$
$108$	3.09017			0.297352
$109$	18.4164			1.76397			0.881986	−	0.471276i	$-0.156206\pi$
$109$	18.4164			1.76397			0.881986	+	0.471276i	$0.156206\pi$
$110$	−1.61803	+	2.80252i	−0.154273	+	0.267210i
$111$	−2.11803	−	3.66854i	−0.201035	−	0.348203i
$112$	7.28115	−	12.6113i	0.688004	−	1.19166i
$113$	−2.42705	−	4.20378i	−0.228318	−	0.395458i	0.728992	−	0.684522i	$-0.239989\pi$
$113$	−2.42705	−	4.20378i	−0.228318	−	0.395458i	−0.957310	+	0.289064i	$0.906656\pi$
$114$	4.04508	+	7.00629i	0.378857	+	0.656199i
$115$	0.663119	+	1.14856i	0.0618362	+	0.107103i
$116$	−3.94427			−0.366216
$117$	−1.85410	+	3.21140i	−0.171412	+	0.296894i
$118$	−0.427051	+	0.739674i	−0.0393132	+	0.0680925i
$119$	6.35410	+	11.0056i	0.582480	+	1.00888i
$120$	−0.854102			−0.0779685
$121$	−8.20820	+	14.2170i	−0.746200	+	1.29246i
$122$	17.7082			1.60323
$123$	2.47214			0.222905
$124$		0			0
$125$	3.76393			0.336656
$126$	−9.70820			−0.864876
$127$	−2.88197	+	4.99171i	−0.255733	+	0.442943i	−0.965094	−	0.261902i	$-0.915650\pi$
$127$	−2.88197	+	4.99171i	−0.255733	+	0.442943i	0.709361	+	0.704845i	$0.248984\pi$
$128$	13.6180			1.20368
$129$	−1.19098	−	2.06284i	−0.104860	−	0.181623i
$130$	−0.572949	+	0.992377i	−0.0502510	+	0.0870372i
$131$	5.54508	−	9.60437i	0.484476	−	0.839138i	−0.515365	−	0.856971i	$-0.672344\pi$
$131$	5.54508	−	9.60437i	0.484476	−	0.839138i	0.999841	+	0.0178334i	$0.00567684\pi$
$132$	3.23607			0.281664
$133$	−7.50000	−	12.9904i	−0.650332	−	1.12641i
$134$	−0.190983	−	0.330792i	−0.0164984	−	0.0285761i
$135$	0.954915	+	1.65396i	0.0821860	+	0.142350i
$136$	−4.73607	+	8.20311i	−0.406114	+	0.703411i
$137$	−1.23607	−	2.14093i	−0.105604	−	0.182912i	0.808381	−	0.588660i	$-0.200344\pi$
$137$	−1.23607	−	2.14093i	−0.105604	−	0.182912i	−0.913985	+	0.405748i	$0.867011\pi$
$138$	2.80902	−	4.86536i	0.239119	−	0.414167i
$139$	−0.854102			−0.0724440			−0.0362220	−	0.999344i	$-0.511532\pi$
$139$	−0.854102			−0.0724440			−0.0362220	+	0.999344i	$0.511532\pi$
$140$	−0.708204			−0.0598542
$141$	−2.80902	+	4.86536i	−0.236562	+	0.409737i
$142$	8.97214	+	15.5402i	0.752925	+	1.30410i
$143$	−4.85410	+	8.40755i	−0.405920	+	0.703075i
$144$	−4.85410	−	8.40755i	−0.404508	−	0.700629i
$145$	−1.21885	−	2.11111i	−0.101220	−	0.175318i
$146$	−9.35410	−	16.2018i	−0.774151	−	1.34087i
$147$	−2.00000			−0.164957
$148$	1.30902	−	2.26728i	0.107601	−	0.186370i
$149$	−6.01722	+	10.4221i	−0.492950	+	0.853814i	−0.999967	−	0.00812166i	$-0.997415\pi$
$149$	−6.01722	+	10.4221i	−0.492950	+	0.853814i	0.507017	+	0.861936i	$0.330748\pi$
$150$	−3.92705	−	6.80185i	−0.320642	−	0.555369i
$151$	18.5066			1.50604			0.753022	−	0.657995i	$-0.228595\pi$
$151$	18.5066			1.50604			0.753022	+	0.657995i	$0.228595\pi$
$152$	5.59017	−	9.68246i	0.453423	−	0.785351i
$153$	8.47214			0.684932
$154$	−25.4164			−2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	−3.70820			−0.295947			−0.147973	−	0.988991i	$-0.547275\pi$
$157$	−3.70820			−0.295947			−0.147973	+	0.988991i	$0.547275\pi$
$158$		0			0
$159$	−0.708204			−0.0561642
$160$	−0.645898	−	1.11873i	−0.0510627	−	0.0884432i
$161$	−5.20820	+	9.02087i	−0.410464	+	0.710944i
$162$	−0.809017	+	1.40126i	−0.0635624	+	0.110093i
$163$	0.708204			0.0554708			0.0277354	−	0.999615i	$-0.491170\pi$
$163$	0.708204			0.0554708			0.0277354	+	0.999615i	$0.491170\pi$
$164$	0.763932	+	1.32317i	0.0596531	+	0.103322i
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	−5.73607	−	9.93516i	−0.445205	−	0.771118i
$167$	2.38197	−	4.12569i	0.184322	−	0.319255i	−0.759026	−	0.651061i	$-0.774324\pi$
$167$	2.38197	−	4.12569i	0.184322	−	0.319255i	0.943348	+	0.331805i	$0.107658\pi$
$168$	−3.35410	−	5.80948i	−0.258775	−	0.448211i
$169$	4.78115	−	8.28120i	0.367781	−	0.637015i
$170$	2.61803			0.200794
$171$	−10.0000			−0.764719
$172$	0.736068	−	1.27491i	0.0561247	−	0.0972108i
$173$	−6.04508	−	10.4704i	−0.459599	−	0.796049i	0.539340	−	0.842088i	$-0.318674\pi$
$173$	−6.04508	−	10.4704i	−0.459599	−	0.796049i	−0.998940	+	0.0460385i	$0.985340\pi$
$174$	−5.16312	+	8.94278i	−0.391415	+	0.677951i
$175$	7.28115	+	12.6113i	0.550403	+	0.953327i
$176$	−12.7082	−	22.0113i	−0.957917	−	1.65916i
$177$	0.263932	+	0.457144i	0.0198383	+	0.0343610i
$178$	−13.9443			−1.04517
$179$	2.39919	−	4.15551i	0.179324	−	0.310598i	−0.762325	−	0.647194i	$-0.775942\pi$
$179$	2.39919	−	4.15551i	0.179324	−	0.310598i	0.941649	+	0.336596i	$0.109276\pi$
$180$	−0.236068	+	0.408882i	−0.0175955	+	0.0304762i
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	−0.987184	−	0.159589i	$-0.948983\pi$
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	0.355383	−	0.934721i	$-0.384350\pi$
$182$	−9.00000			−0.667124
$183$	5.47214	−	9.47802i	0.404512	−	0.700635i
$184$	−7.76393			−0.572365
$185$	1.61803			0.118960
$186$		0			0
$187$	22.1803			1.62199
$188$	−3.47214			−0.253232
$189$	−7.50000	+	12.9904i	−0.545545	+	0.944911i
$190$	−3.09017			−0.224184
$191$	2.45492	+	4.25204i	0.177631	+	0.307667i	0.941069	−	0.338215i	$-0.109823\pi$
$191$	2.45492	+	4.25204i	0.177631	+	0.307667i	−0.763437	+	0.645882i	$0.776490\pi$
$192$	2.11803	−	3.66854i	0.152856	−	0.264754i
$193$	2.30902	−	3.99933i	0.166207	−	0.287878i	−0.770876	−	0.636985i	$-0.780181\pi$
$193$	2.30902	−	3.99933i	0.166207	−	0.287878i	0.937083	+	0.349106i	$0.113515\pi$
$194$	−30.2705			−2.17330
$195$	0.354102	+	0.613323i	0.0253578	+	0.0439209i
$196$	−0.618034	−	1.07047i	−0.0441453	−	0.0764619i
$197$	5.20820	+	9.02087i	0.371069	+	0.642711i	0.989730	−	0.142947i	$-0.0456579\pi$
$197$	5.20820	+	9.02087i	0.371069	+	0.642711i	−0.618661	+	0.785658i	$0.712325\pi$
$198$	−8.47214	+	14.6742i	−0.602088	+	1.04285i
$199$	6.64590	+	11.5110i	0.471115	+	0.815995i	0.999454	−	0.0330381i	$-0.0105183\pi$
$199$	6.64590	+	11.5110i	0.471115	+	0.815995i	−0.528339	+	0.849034i	$0.677185\pi$
$200$	−5.42705	+	9.39993i	−0.383750	+	0.664675i
$201$	−0.236068			−0.0166510
$202$	14.9443			1.05148
$203$	9.57295	−	16.5808i	0.671889	−	1.16375i
$204$	−1.30902	−	2.26728i	−0.0916495	−	0.158742i
$205$	−0.472136	+	0.817763i	−0.0329754	+	0.0571151i
$206$	5.54508	+	9.60437i	0.386344	+	0.669168i
$207$	3.47214	+	6.01392i	0.241330	+	0.417996i
$208$	−4.50000	−	7.79423i	−0.312019	−	0.540433i
$209$	−26.1803			−1.81093
$210$	−0.927051	+	1.60570i	−0.0639726	+	0.110804i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	−0.218847	−	0.379054i	−0.0150305	−	0.0260336i
$213$	11.0902			0.759886
$214$	8.16312	−	14.1389i	0.558019	−	0.966518i
$215$	0.909830			0.0620499
$216$	−11.1803			−0.760726
$217$		0			0
$218$	29.7984			2.01820
$219$	−11.5623			−0.781308
$220$	−0.618034	+	1.07047i	−0.0416678	+	0.0721708i
$221$	7.85410			0.528324
$222$	−3.42705	−	5.93583i	−0.230009	−	0.398387i
$223$	6.35410	−	11.0056i	0.425502	−	0.736991i	−0.570965	−	0.820974i	$-0.693431\pi$
$223$	6.35410	−	11.0056i	0.425502	−	0.736991i	0.996467	+	0.0839830i	$0.0267642\pi$
$224$	5.07295	−	8.78661i	0.338951	−	0.587080i
$225$	9.70820			0.647214
$226$	−3.92705	−	6.80185i	−0.261224	−	0.452452i
$227$	−10.8713	−	18.8297i	−0.721555	−	1.24977i	−0.960376	−	0.278706i	$-0.910094\pi$
$227$	−10.8713	−	18.8297i	−0.721555	−	1.24977i	0.238821	−	0.971064i	$-0.423239\pi$
$228$	1.54508	+	2.67617i	0.102326	+	0.177233i
$229$	1.38197	−	2.39364i	0.0913229	−	0.158176i	−0.816745	−	0.576999i	$-0.804224\pi$
$229$	1.38197	−	2.39364i	0.0913229	−	0.158176i	0.908068	+	0.418823i	$0.137557\pi$
$230$	1.07295	+	1.85840i	0.0707482	+	0.122539i
$231$	−7.85410	+	13.6037i	−0.516762	+	0.895058i
$232$	14.2705			0.936905
$233$	−5.79837			−0.379864			−0.189932	−	0.981797i	$-0.560827\pi$
$233$	−5.79837			−0.379864			−0.189932	+	0.981797i	$0.560827\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	−1.07295	−	1.85840i	−0.0699915	−	0.121229i
$236$	−0.163119	+	0.282530i	−0.0106181	+	0.0183912i
$237$		0			0
$238$	10.2812	+	17.8075i	0.666428	+	1.15429i
$239$	−6.70820	−	11.6190i	−0.433918	−	0.751567i	0.563289	−	0.826260i	$-0.309536\pi$
$239$	−6.70820	−	11.6190i	−0.433918	−	0.751567i	−0.997207	+	0.0746926i	$0.976202\pi$
$240$	−1.85410			−0.119682
$241$	8.73607	−	15.1313i	0.562740	−	0.974694i	−0.434516	−	0.900664i	$-0.643081\pi$
$241$	8.73607	−	15.1313i	0.562740	−	0.974694i	0.997256	−	0.0740297i	$-0.0235860\pi$
$242$	−13.2812	+	23.0036i	−0.853745	+	1.47873i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	6.76393			0.433016
$245$	0.381966	−	0.661585i	0.0244029	−	0.0422671i
$246$	4.00000			0.255031
$247$	−9.27051			−0.589868
$248$		0			0
$249$	−7.09017			−0.449321
$250$	6.09017			0.385176
$251$	8.47214	−	14.6742i	0.534756	−	0.926225i	−0.464419	−	0.885616i	$-0.653737\pi$
$251$	8.47214	−	14.6742i	0.534756	−	0.926225i	0.999175	−	0.0406096i	$-0.0129300\pi$
$252$	−3.70820			−0.233595
$253$	9.09017	+	15.7446i	0.571494	+	0.989857i
$254$	−4.66312	+	8.07676i	−0.292590	+	0.506781i
$255$	0.809017	−	1.40126i	0.0506626	−	0.0877502i
$256$	13.5623			0.847644
$257$	12.7082	+	22.0113i	0.792716	+	1.37302i	0.924279	+	0.381717i	$0.124667\pi$
$257$	12.7082	+	22.0113i	0.792716	+	1.37302i	−0.131563	+	0.991308i	$0.542000\pi$
$258$	−1.92705	−	3.33775i	−0.119973	−	0.207799i
$259$	6.35410	+	11.0056i	0.394825	+	0.683856i
$260$	−0.218847	+	0.379054i	−0.0135723	+	0.0235079i
$261$	−6.38197	−	11.0539i	−0.395034	−	0.684219i
$262$	8.97214	−	15.5402i	0.554300	−	0.960076i
$263$	13.7984			0.850844			0.425422	−	0.904995i	$-0.360126\pi$
$263$	13.7984			0.850844			0.425422	+	0.904995i	$0.360126\pi$
$264$	−11.7082			−0.720590
$265$	0.135255	−	0.234268i	0.00830864	−	0.0143910i
$266$	−12.1353	−	21.0189i	−0.744060	−	1.28875i
$267$	−4.30902	+	7.46344i	−0.263708	+	0.456755i
$268$	−0.0729490	−	0.126351i	−0.00445607	−	0.00771814i
$269$	1.80902	+	3.13331i	0.110298	+	0.191041i	0.915890	−	0.401429i	$-0.131486\pi$
$269$	1.80902	+	3.13331i	0.110298	+	0.191041i	−0.805593	+	0.592470i	$0.798153\pi$
$270$	1.54508	+	2.67617i	0.0940309	+	0.162866i
$271$	−10.5623			−0.641614			−0.320807	−	0.947145i	$-0.603954\pi$
$271$	−10.5623			−0.641614			−0.320807	+	0.947145i	$0.603954\pi$
$272$	−10.2812	+	17.8075i	−0.623386	+	1.07974i
$273$	−2.78115	+	4.81710i	−0.168323	+	0.291544i
$274$	−2.00000	−	3.46410i	−0.120824	−	0.209274i
$275$	25.4164			1.53267
$276$	1.07295	−	1.85840i	0.0645839	−	0.111863i
$277$	−2.32624			−0.139770			−0.0698850	−	0.997555i	$-0.522263\pi$
$277$	−2.32624			−0.139770			−0.0698850	+	0.997555i	$0.522263\pi$
$278$	−1.38197			−0.0828848
$279$		0			0
$280$	2.56231			0.153127
$281$	−10.0344			−0.598605			−0.299302	−	0.954158i	$-0.596754\pi$
$281$	−10.0344			−0.598605			−0.299302	+	0.954158i	$0.596754\pi$
$282$	−4.54508	+	7.87232i	−0.270656	+	0.468790i
$283$	−13.5623			−0.806195			−0.403098	−	0.915157i	$-0.632067\pi$
$283$	−13.5623			−0.806195			−0.403098	+	0.915157i	$0.632067\pi$
$284$	3.42705	+	5.93583i	0.203358	+	0.352226i
$285$	−0.954915	+	1.65396i	−0.0565643	+	0.0979722i
$286$	−7.85410	+	13.6037i	−0.464423	+	0.804404i
$287$	−7.41641			−0.437777
$288$	−3.38197	−	5.85774i	−0.199284	−	0.345170i
$289$	−0.472136	−	0.817763i	−0.0277727	−	0.0481037i
$290$	−1.97214	−	3.41584i	−0.115808	−	0.200585i
$291$	−9.35410	+	16.2018i	−0.548347	+	0.949765i
$292$	−3.57295	−	6.18853i	−0.209091	−	0.362156i
$293$	1.88197	−	3.25966i	0.109946	−	0.190431i	−0.805802	−	0.592185i	$-0.798266\pi$
$293$	1.88197	−	3.25966i	0.109946	−	0.190431i	0.915748	+	0.401753i	$0.131599\pi$
$294$	−3.23607			−0.188731
$295$	−0.201626			−0.0117391
$296$	−4.73607	+	8.20311i	−0.275278	+	0.476796i
$297$	13.0902	+	22.6728i	0.759569	+	1.31561i
$298$	−9.73607	+	16.8634i	−0.563995	+	0.976868i
$299$	3.21885	+	5.57521i	0.186151	+	0.322423i
$300$	−1.50000	−	2.59808i	−0.0866025	−	0.150000i
$301$	3.57295	+	6.18853i	0.205941	+	0.356701i
$302$	29.9443			1.72310
$303$	4.61803	−	7.99867i	0.265299	−	0.459512i
$304$	12.1353	−	21.0189i	0.696005	−	1.20552i
$305$	2.09017	+	3.62028i	0.119683	+	0.207297i
$306$	13.7082			0.783646
$307$	2.54508	−	4.40822i	0.145256	−	0.251590i	−0.784213	−	0.620492i	$-0.786933\pi$
$307$	2.54508	−	4.40822i	0.145256	−	0.251590i	0.929468	+	0.368902i	$0.120266\pi$
$308$	−9.70820			−0.553176
$309$	6.85410			0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	−4.14590			−0.234715
$313$	1.61803	−	2.80252i	0.0914567	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$313$	1.61803	−	2.80252i	0.0914567	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$314$	−6.00000			−0.338600
$315$	−1.14590	−	1.98475i	−0.0645640	−	0.111828i
$316$		0			0
$317$	4.94427	−	8.56373i	0.277698	−	0.480987i	−0.693114	−	0.720828i	$-0.743762\pi$
$317$	4.94427	−	8.56373i	0.277698	−	0.480987i	0.970812	+	0.239841i	$0.0770952\pi$
$318$	−1.14590			−0.0642588
$319$	−16.7082	−	28.9395i	−0.935480	−	1.62030i
$320$	0.809017	+	1.40126i	0.0452254	+	0.0783327i
$321$	−5.04508	−	8.73834i	−0.281589	−	0.487727i
$322$	−8.42705	+	14.5961i	−0.469621	+	0.813408i
$323$	10.5902	+	18.3427i	0.589253	+	1.02062i
$324$	−0.309017	+	0.535233i	−0.0171676	+	0.0297352i
$325$	9.00000			0.499230
$326$	1.14590			0.0634654
$327$	9.20820	−	15.9491i	0.509215	−	0.881986i
$328$	−2.76393	−	4.78727i	−0.152613	−	0.264333i
$329$	8.42705	−	14.5961i	0.464598	−	0.804708i
$330$	1.61803	+	2.80252i	0.0890698	+	0.154273i
$331$	11.1353	+	19.2868i	0.612049	+	1.06010i	0.990895	+	0.134640i	$0.0429878\pi$
$331$	11.1353	+	19.2868i	0.612049	+	1.06010i	−0.378846	+	0.925460i	$0.623679\pi$
$332$	−2.19098	−	3.79489i	−0.120246	−	0.208272i
$333$	8.47214			0.464270
$334$	3.85410	−	6.67550i	0.210887	−	0.365267i
$335$	0.0450850	−	0.0780895i	0.00246326	−	0.00426648i
$336$	−7.28115	−	12.6113i	−0.397219	−	0.688004i
$337$	−27.9787			−1.52410			−0.762049	−	0.647520i	$-0.775806\pi$
$337$	−27.9787			−1.52410			−0.762049	+	0.647520i	$0.775806\pi$
$338$	7.73607	−	13.3993i	0.420787	−	0.728824i
$339$	−4.85410			−0.263639
$340$	1.00000			0.0542326
$341$		0			0
$342$	−16.1803			−0.874933
$343$	−15.0000			−0.809924
$344$	−2.66312	+	4.61266i	−0.143586	+	0.248698i
$345$	1.32624			0.0714022
$346$	−9.78115	−	16.9415i	−0.525838	−	0.910778i
$347$	16.0623	−	27.8207i	0.862270	−	1.49350i	−0.00746305	−	0.999972i	$-0.502376\pi$
$347$	16.0623	−	27.8207i	0.862270	−	1.49350i	0.869733	−	0.493523i	$-0.164291\pi$
$348$	−1.97214	+	3.41584i	−0.105718	+	0.183108i
$349$	−3.29180			−0.176206			−0.0881029	−	0.996111i	$-0.528080\pi$
$349$	−3.29180			−0.176206			−0.0881029	+	0.996111i	$0.528080\pi$
$350$	11.7812	+	20.4056i	0.629729	+	1.09072i
$351$	4.63525	+	8.02850i	0.247412	+	0.428529i
$352$	−8.85410	−	15.3358i	−0.471925	−	0.817398i
$353$	17.3090	−	29.9801i	0.921266	−	1.59568i	0.123807	−	0.992306i	$-0.460490\pi$
$353$	17.3090	−	29.9801i	0.921266	−	1.59568i	0.797459	−	0.603373i	$-0.206177\pi$
$354$	0.427051	+	0.739674i	0.0226975	+	0.0393132i
$355$	−2.11803	+	3.66854i	−0.112414	+	0.194706i
$356$	−5.32624			−0.282290
$357$	12.7082			0.672589
$358$	3.88197	−	6.72376i	0.205168	−	0.355362i
$359$	4.83688	+	8.37772i	0.255281	+	0.442159i	0.964972	−	0.262354i	$-0.0844987\pi$
$359$	4.83688	+	8.37772i	0.255281	+	0.442159i	−0.709691	+	0.704513i	$0.751165\pi$
$360$	0.854102	−	1.47935i	0.0450151	−	0.0779685i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−13.7533	−	23.8214i	−0.722857	−	1.25202i
$363$	8.20820	+	14.2170i	0.430819	+	0.746200i
$364$	−3.43769			−0.180184
$365$	2.20820	−	3.82472i	0.115583	−	0.200195i
$366$	8.85410	−	15.3358i	0.462811	−	0.801613i
$367$	1.36475	+	2.36381i	0.0712391	+	0.123390i	0.899445	−	0.437035i	$-0.143971\pi$
$367$	1.36475	+	2.36381i	0.0712391	+	0.123390i	−0.828206	+	0.560425i	$0.810638\pi$
$368$	−16.8541			−0.878581
$369$	−2.47214	+	4.28187i	−0.128694	+	0.222905i
$370$	2.61803			0.136105
$371$	2.12461			0.110304
$372$		0			0
$373$	−31.6525			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$373$	−31.6525			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$374$	35.8885			1.85575
$375$	1.88197	−	3.25966i	0.0971843	−	0.168328i
$376$	12.5623			0.647851
$377$	−5.91641	−	10.2475i	−0.304711	−	0.527774i
$378$	−12.1353	+	21.0189i	−0.624170	+	1.08109i
$379$	−4.20820	+	7.28882i	−0.216161	+	0.374402i	−0.953631	−	0.300978i	$-0.902687\pi$
$379$	−4.20820	+	7.28882i	−0.216161	+	0.374402i	0.737470	+	0.675380i	$0.236020\pi$
$380$	−1.18034			−0.0605502
$381$	2.88197	+	4.99171i	0.147648	+	0.255733i
$382$	3.97214	+	6.87994i	0.203232	+	0.352008i
$383$	5.07295	+	8.78661i	0.259216	+	0.448975i	0.966032	−	0.258422i	$-0.0832027\pi$
$383$	5.07295	+	8.78661i	0.259216	+	0.448975i	−0.706816	+	0.707397i	$0.749869\pi$
$384$	6.80902	−	11.7936i	0.347471	−	0.601838i
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$	3.73607	−	6.47106i	0.190161	−	0.329368i
$387$	4.76393			0.242164
$388$	−11.5623			−0.586987
$389$	−14.5344	+	25.1744i	−0.736925	+	1.27639i	0.216948	+	0.976183i	$0.430390\pi$
$389$	−14.5344	+	25.1744i	−0.736925	+	1.27639i	−0.953873	+	0.300209i	$0.902944\pi$
$390$	0.572949	+	0.992377i	0.0290124	+	0.0502510i
$391$	7.35410	−	12.7377i	0.371913	−	0.644172i
$392$	2.23607	+	3.87298i	0.112938	+	0.195615i
$393$	−5.54508	−	9.60437i	−0.279713	−	0.484476i
$394$	8.42705	+	14.5961i	0.424549	+	0.735340i
$395$		0			0
$396$	−3.23607	+	5.60503i	−0.162619	+	0.281664i
$397$	−14.8541	+	25.7281i	−0.745506	+	1.29125i	0.204452	+	0.978877i	$0.434459\pi$
$397$	−14.8541	+	25.7281i	−0.745506	+	1.29125i	−0.949958	+	0.312378i	$0.898875\pi$
$398$	10.7533	+	18.6252i	0.539014	+	0.933599i
$399$	−15.0000			−0.750939
$400$	−11.7812	+	20.4056i	−0.589058	+	1.02028i
$401$	23.8328			1.19015			0.595077	−	0.803669i	$-0.297122\pi$
$401$	23.8328			1.19015			0.595077	+	0.803669i	$0.297122\pi$
$402$	−0.381966			−0.0190507
$403$		0			0
$404$	5.70820			0.283994
$405$	−0.381966			−0.0189800
$406$	15.4894	−	26.8284i	0.768724	−	1.33147i
$407$	22.1803			1.09944
$408$	4.73607	+	8.20311i	0.234470	+	0.406114i
$409$	−8.09017	+	14.0126i	−0.400033	+	0.692878i	−0.993729	−	0.111811i	$-0.964335\pi$
$409$	−8.09017	+	14.0126i	−0.400033	+	0.692878i	0.593696	+	0.804689i	$0.297668\pi$
$410$	−0.763932	+	1.32317i	−0.0377279	+	0.0653467i
$411$	−2.47214			−0.121941
$412$	2.11803	+	3.66854i	0.104348	+	0.180736i
$413$	−0.791796	−	1.37143i	−0.0389617	−	0.0674837i
$414$	5.61803	+	9.73072i	0.276111	+	0.478239i
$415$	1.35410	−	2.34537i	0.0664703	−	0.115130i
$416$	−3.13525	−	5.43042i	−0.153719	−	0.266248i
$417$	−0.427051	+	0.739674i	−0.0209128	+	0.0362220i
$418$	−42.3607			−2.07193
$419$	−4.47214			−0.218478			−0.109239	−	0.994016i	$-0.534841\pi$
$419$	−4.47214			−0.218478			−0.109239	+	0.994016i	$0.534841\pi$
$420$	−0.354102	+	0.613323i	−0.0172784	+	0.0299271i
$421$	−9.61803	−	16.6589i	−0.468754	−	0.811906i	0.530608	−	0.847617i	$-0.321964\pi$
$421$	−9.61803	−	16.6589i	−0.468754	−	0.811906i	−0.999362	+	0.0357112i	$0.988630\pi$
$422$	6.47214	−	11.2101i	0.315059	−	0.545698i
$423$	−5.61803	−	9.73072i	−0.273158	−	0.473124i
$424$	0.791796	+	1.37143i	0.0384530	+	0.0666026i
$425$	−10.2812	−	17.8075i	−0.498709	−	0.863790i
$426$	17.9443			0.869403
$427$	−16.4164	+	28.4341i	−0.794446	+	1.37602i
$428$	3.11803	−	5.40059i	0.150716	−	0.261048i
$429$	4.85410	+	8.40755i	0.234358	+	0.405920i
$430$	1.47214			0.0709927
$431$	−12.3820	+	21.4462i	−0.596418	+	1.03303i	0.396927	+	0.917850i	$0.370077\pi$
$431$	−12.3820	+	21.4462i	−0.596418	+	1.03303i	−0.993345	+	0.115177i	$0.963257\pi$
$432$	−24.2705			−1.16772
$433$	27.4164			1.31755			0.658774	−	0.752341i	$-0.271075\pi$
$433$	27.4164			1.31755			0.658774	+	0.752341i	$0.271075\pi$
$434$		0			0
$435$	−2.43769			−0.116878
$436$	11.3820			0.545097
$437$	−8.68034	+	15.0348i	−0.415237	+	0.719212i
$438$	−18.7082			−0.893913
$439$	5.91641	+	10.2475i	0.282375	+	0.489087i	0.971969	−	0.235108i	$-0.0755445\pi$
$439$	5.91641	+	10.2475i	0.282375	+	0.489087i	−0.689594	+	0.724196i	$0.742211\pi$
$440$	2.23607	−	3.87298i	0.106600	−	0.184637i
$441$	2.00000	−	3.46410i	0.0952381	−	0.164957i
$442$	12.7082			0.604468
$443$	0.437694	+	0.758108i	0.0207955	+	0.0360188i	0.876236	−	0.481882i	$-0.160047\pi$
$443$	0.437694	+	0.758108i	0.0207955	+	0.0360188i	−0.855440	+	0.517901i	$0.826713\pi$
$444$	−1.30902	−	2.26728i	−0.0621232	−	0.107601i
$445$	−1.64590	−	2.85078i	−0.0780230	−	0.135140i
$446$	10.2812	−	17.8075i	0.486827	−	0.843209i
$447$	6.01722	+	10.4221i	0.284605	+	0.492950i
$448$	−6.35410	+	11.0056i	−0.300203	+	0.519967i
$449$	−34.0689			−1.60781			−0.803905	−	0.594758i	$-0.797248\pi$
$449$	−34.0689			−1.60781			−0.803905	+	0.594758i	$0.797248\pi$
$450$	15.7082			0.740492
$451$	−6.47214	+	11.2101i	−0.304761	+	0.527862i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	9.25329	−	16.0272i	0.434757	−	0.753022i
$454$	−17.5902	−	30.4671i	−0.825548	−	1.42989i
$455$	−1.06231	−	1.83997i	−0.0498017	−	0.0862590i
$456$	−5.59017	−	9.68246i	−0.261784	−	0.453423i
$457$	26.7426			1.25097			0.625484	−	0.780237i	$-0.284902\pi$
$457$	26.7426			1.25097			0.625484	+	0.780237i	$0.284902\pi$
$458$	2.23607	−	3.87298i	0.104485	−	0.180973i
$459$	10.5902	−	18.3427i	0.494307	−	0.856164i
$460$	0.409830	+	0.709846i	0.0191084	+	0.0330968i
$461$	−31.7426			−1.47840			−0.739201	−	0.673485i	$-0.764797\pi$
$461$	−31.7426			−1.47840			−0.739201	+	0.673485i	$0.764797\pi$
$462$	−12.7082	+	22.0113i	−0.591239	+	1.02406i
$463$	9.12461			0.424057			0.212028	−	0.977264i	$-0.431993\pi$
$463$	9.12461			0.424057			0.212028	+	0.977264i	$0.431993\pi$
$464$	30.9787			1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	38.7771			1.79439			0.897195	−	0.441635i	$-0.145601\pi$
$467$	38.7771			1.79439			0.897195	+	0.441635i	$0.145601\pi$
$468$	−1.14590	+	1.98475i	−0.0529692	+	0.0917453i
$469$	0.708204			0.0327018
$470$	−1.73607	−	3.00696i	−0.0800788	−	0.138701i
$471$	−1.85410	+	3.21140i	−0.0854325	+	0.147973i
$472$	0.590170	−	1.02220i	0.0271648	−	0.0470508i
$473$	12.4721			0.573469
$474$		0			0
$475$	12.1353	+	21.0189i	0.556804	+	0.964412i
$476$	3.92705	+	6.80185i	0.179996	+	0.311762i
$477$	0.708204	−	1.22665i	0.0324264	−	0.0561642i
$478$	−10.8541	−	18.7999i	−0.496455	−	0.859885i
$479$	−4.47214	+	7.74597i	−0.204337	+	0.353922i	−0.949921	−	0.312489i	$-0.898837\pi$
$479$	−4.47214	+	7.74597i	−0.204337	+	0.353922i	0.745584	+	0.666411i	$0.232171\pi$
$480$	−1.29180			−0.0589622
$481$	7.85410			0.358116
$482$	14.1353	−	24.4830i	0.643843	−	1.11517i
$483$	5.20820	+	9.02087i	0.236981	+	0.410464i
$484$	−5.07295	+	8.78661i	−0.230589	+	0.399391i
$485$	−3.57295	−	6.18853i	−0.162239	−	0.281007i
$486$	12.9443	+	22.4201i	0.587164	+	1.01700i
$487$	20.9615	+	36.3064i	0.949856	+	1.64520i	0.745724	+	0.666255i	$0.232104\pi$
$487$	20.9615	+	36.3064i	0.949856	+	1.64520i	0.204132	+	0.978943i	$0.434563\pi$
$488$	−24.4721			−1.10780
$489$	0.354102	−	0.613323i	0.0160130	−	0.0277354i
$490$	0.618034	−	1.07047i	0.0279199	−	0.0483587i
$491$	−10.7984	−	18.7033i	−0.487324	−	0.844070i	0.512570	−	0.858645i	$-0.328694\pi$
$491$	−10.7984	−	18.7033i	−0.487324	−	0.844070i	−0.999894	+	0.0145759i	$0.995360\pi$
$492$	1.52786			0.0688814
$493$	−13.5172	+	23.4125i	−0.608785	+	1.05445i
$494$	−15.0000			−0.674882
$495$	−4.00000			−0.179787
$496$		0			0
$497$	−33.2705			−1.49239
$498$	−11.4721			−0.514079
$499$	−5.42705	+	9.39993i	−0.242948	+	0.420799i	−0.961553	−	0.274620i	$-0.911448\pi$
$499$	−5.42705	+	9.39993i	−0.242948	+	0.420799i	0.718605	+	0.695419i	$0.244781\pi$
$500$	2.32624			0.104033
$501$	−2.38197	−	4.12569i	−0.106418	−	0.184322i
$502$	13.7082	−	23.7433i	0.611827	−	1.05972i
$503$	−9.92705	+	17.1942i	−0.442625	+	0.766650i	−0.997883	−	0.0650285i	$-0.979286\pi$
$503$	−9.92705	+	17.1942i	−0.442625	+	0.766650i	0.555258	+	0.831678i	$0.312619\pi$
$504$	13.4164			0.597614
$505$	1.76393	+	3.05522i	0.0784939	+	0.135956i
$506$	14.7082	+	25.4754i	0.653859	+	1.13252i
$507$	−4.78115	−	8.28120i	−0.212338	−	0.367781i
$508$	−1.78115	+	3.08505i	−0.0790259	+	0.136877i
$509$	6.54508	+	11.3364i	0.290106	+	0.502478i	0.973835	−	0.227258i	$-0.0729762\pi$
$509$	6.54508	+	11.3364i	0.290106	+	0.502478i	−0.683729	+	0.729736i	$0.739643\pi$
$510$	1.30902	−	2.26728i	0.0579642	−	0.100397i
$511$	34.6869			1.53446
$512$	−5.29180			−0.233867
$513$	−12.5000	+	21.6506i	−0.551888	+	0.955899i
$514$	20.5623	+	35.6150i	0.906964	+	1.57091i
$515$	−1.30902	+	2.26728i	−0.0576822	+	0.0999085i
$516$	−0.736068	−	1.27491i	−0.0324036	−	0.0561247i
$517$	−14.7082	−	25.4754i	−0.646866	−	1.12040i
$518$	10.2812	+	17.8075i	0.451728	+	0.782416i
$519$	−12.0902			−0.530700
$520$	0.791796	−	1.37143i	0.0347226	−	0.0601412i
$521$	13.5344	−	23.4423i	0.592955	−	1.02703i	−0.400877	−	0.916132i	$-0.631295\pi$
$521$	13.5344	−	23.4423i	0.592955	−	1.02703i	0.993832	−	0.110896i	$-0.0353720\pi$
$522$	−10.3262	−	17.8856i	−0.451967	−	0.782830i
$523$	−6.12461			−0.267811			−0.133905	−	0.990994i	$-0.542752\pi$
$523$	−6.12461			−0.267811			−0.133905	+	0.990994i	$0.542752\pi$
$524$	3.42705	−	5.93583i	0.149711	−	0.259308i
$525$	14.5623			0.635551
$526$	22.3262			0.973470
$527$		0			0
$528$	−25.4164			−1.10611
$529$	−10.9443			−0.475838
$530$	0.218847	−	0.379054i	0.00950611	−	0.0164651i
$531$	−1.05573			−0.0458147
$532$	−4.63525	−	8.02850i	−0.200964	−	0.348079i
$533$	−2.29180	+	3.96951i	−0.0992687	+	0.171938i
$534$	−6.97214	+	12.0761i	−0.301714	+	0.522584i
$535$	3.85410			0.166627
$536$	0.263932	+	0.457144i	0.0114001	+	0.0197456i
$537$	−2.39919	−	4.15551i	−0.103533	−	0.179324i
$538$	2.92705	+	5.06980i	0.126194	+	0.218575i
$539$	5.23607	−	9.06914i	0.225533	−	0.390635i
$540$	0.590170	+	1.02220i	0.0253969	+	0.0439887i
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	−0.999520	−	0.0309841i	$-0.990136\pi$
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	0.526593	+	0.850118i	$0.323469\pi$
$542$	−17.0902			−0.734086
$543$	−17.0000			−0.729540
$544$	−7.16312	+	12.4069i	−0.307116	+	0.531941i
$545$	3.51722	+	6.09201i	0.150661	+	0.260953i
$546$	−4.50000	+	7.79423i	−0.192582	+	0.333562i
$547$	5.14590	+	8.91296i	0.220023	+	0.381091i	0.954815	−	0.297202i	$-0.0960535\pi$
$547$	5.14590	+	8.91296i	0.220023	+	0.381091i	−0.734792	+	0.678293i	$0.762720\pi$
$548$	−0.763932	−	1.32317i	−0.0326336	−	0.0565230i
$549$	10.9443	+	18.9560i	0.467090	+	0.809024i
$550$	41.1246			1.75356
$551$	15.9549	−	27.6347i	0.679702	−	1.17728i
$552$	−3.88197	+	6.72376i	−0.165227	+	0.286182i
$553$		0			0
$554$	−3.76393			−0.159914
$555$	0.809017	−	1.40126i	0.0343409	−	0.0594801i
$556$	−0.527864			−0.0223864
$557$	0.111456			0.00472255			0.00236127	−	0.999997i	$-0.499248\pi$
$557$	0.111456			0.00472255			0.00236127	+	0.999997i	$0.499248\pi$
$558$		0			0
$559$	4.41641			0.186794
$560$	5.56231			0.235050
$561$	11.0902	−	19.2087i	0.468227	−	0.810994i
$562$	−16.2361			−0.684877
$563$	−5.78115	−	10.0133i	−0.243647	−	0.422008i	0.718104	−	0.695936i	$-0.245010\pi$
$563$	−5.78115	−	10.0133i	−0.243647	−	0.422008i	−0.961750	+	0.273928i	$0.911677\pi$
$564$	−1.73607	+	3.00696i	−0.0731016	+	0.126616i
$565$	0.927051	−	1.60570i	0.0390013	−	0.0675523i
$566$	−21.9443			−0.922387
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$	−12.3992	−	21.4760i	−0.520258	−	0.901114i
$569$	−12.2361	−	21.1935i	−0.512963	−	0.888477i	−0.999887	−	0.0150332i	$-0.995215\pi$
$569$	−12.2361	−	21.1935i	−0.512963	−	0.888477i	0.486924	−	0.873444i	$-0.338119\pi$
$570$	−1.54508	+	2.67617i	−0.0647165	+	0.112092i
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	0.783450	−	0.621455i	$-0.213458\pi$
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	−0.929921	+	0.367760i	$0.880125\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$	4.90983			0.205111
$574$	−12.0000			−0.500870
$575$	8.42705	−	14.5961i	0.351432	−	0.608699i
$576$	4.23607	+	7.33708i	0.176503	+	0.305712i
$577$	3.98936	−	6.90977i	0.166079	−	0.287657i	−0.770959	−	0.636885i	$-0.780223\pi$
$577$	3.98936	−	6.90977i	0.166079	−	0.287657i	0.937038	+	0.349227i	$0.113556\pi$
$578$	−0.763932	−	1.32317i	−0.0317754	−	0.0550366i
$579$	−2.30902	−	3.99933i	−0.0959595	−	0.166207i
$580$	−0.753289	−	1.30473i	−0.0312786	−	0.0541762i
$581$	21.2705			0.882449
$582$	−15.1353	+	26.2150i	−0.627377	+	1.08665i
$583$	1.85410	−	3.21140i	0.0767891	−	0.133003i
$584$	12.9271	+	22.3903i	0.534925	+	0.926518i
$585$	−1.41641			−0.0585613
$586$	3.04508	−	5.27424i	0.125791	−	0.217877i
$587$	−40.0132			−1.65152			−0.825760	−	0.564022i	$-0.809253\pi$
$587$	−40.0132			−1.65152			−0.825760	+	0.564022i	$0.809253\pi$
$588$	−1.23607			−0.0509746
$589$		0			0
$590$	−0.326238			−0.0134310
$591$	10.4164			0.428474
$592$	−10.2812	+	17.8075i	−0.422553	+	0.731883i
$593$	41.8885			1.72016			0.860078	−	0.510162i	$-0.170415\pi$
$593$	41.8885			1.72016			0.860078	+	0.510162i	$0.170415\pi$
$594$	21.1803	+	36.6854i	0.869040	+	1.50522i
$595$	−2.42705	+	4.20378i	−0.0994994	+	0.172338i
$596$	−3.71885	+	6.44123i	−0.152330	+	0.263843i
$597$	13.2918			0.543997
$598$	5.20820	+	9.02087i	0.212979	+	0.368891i
$599$	−2.60081	−	4.50474i	−0.106266	−	0.184059i	0.807989	−	0.589198i	$-0.200556\pi$
$599$	−2.60081	−	4.50474i	−0.106266	−	0.184059i	−0.914255	+	0.405140i	$0.867223\pi$
$600$	5.42705	+	9.39993i	0.221558	+	0.383750i
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	−0.998302	−	0.0582563i	$-0.981446\pi$
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	0.549602	+	0.835426i	$0.314779\pi$
$602$	5.78115	+	10.0133i	0.235622	+	0.408110i
$603$	0.236068	−	0.408882i	0.00961343	−	0.0166510i
$604$	11.4377			0.465393
$605$	−6.27051			−0.254932
$606$	7.47214	−	12.9421i	0.303535	−	0.525738i
$607$	−0.708204	−	1.22665i	−0.0287451	−	0.0497880i	0.851295	−	0.524687i	$-0.175818\pi$
$607$	−0.708204	−	1.22665i	−0.0287451	−	0.0497880i	−0.880040	+	0.474899i	$0.842484\pi$
$608$	8.45492	−	14.6443i	0.342892	−	0.593907i
$609$	−9.57295	−	16.5808i	−0.387915	−	0.671889i
$610$	3.38197	+	5.85774i	0.136932	+	0.237173i
$611$	−5.20820	−	9.02087i	−0.210701	−	0.364945i
$612$	5.23607			0.211656
$613$	−21.4721	+	37.1908i	−0.867251	+	1.50212i	−0.00245723	+	0.999997i	$0.500782\pi$
$613$	−21.4721	+	37.1908i	−0.867251	+	1.50212i	−0.864794	+	0.502127i	$0.832551\pi$
$614$	4.11803	−	7.13264i	0.166190	−	0.287850i
$615$	0.472136	+	0.817763i	0.0190384	+	0.0329754i
$616$	35.1246			1.41521
$617$	4.88197	−	8.45581i	0.196541	−	0.340418i	−0.750864	−	0.660457i	$-0.770363\pi$
$617$	4.88197	−	8.45581i	0.196541	−	0.340418i	0.947404	+	0.320039i	$0.103696\pi$
$618$	11.0902			0.446112
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	17.3607			0.696660
$622$	12.1803			0.488387
$623$	12.9271	−	22.3903i	0.517911	−	0.897049i
$624$	−9.00000			−0.360288
$625$	−11.4164	−	19.7738i	−0.456656	−	0.790952i
$626$	2.61803	−	4.53457i	0.104638	−	0.181238i
$627$	−13.0902	+	22.6728i	−0.522771	+	0.905466i
$628$	−2.29180			−0.0914526
$629$	−8.97214	−	15.5402i	−0.357742	−	0.619628i
$630$	−1.85410	−	3.21140i	−0.0738692	−	0.127945i
$631$	21.1353	+	36.6073i	0.841381	+	1.45732i	0.888727	+	0.458436i	$0.151590\pi$
$631$	21.1353	+	36.6073i	0.841381	+	1.45732i	−0.0473460	+	0.998879i	$0.515076\pi$
$632$		0			0
$633$	−4.00000	−	6.92820i	−0.158986	−	0.275371i
$634$	8.00000	−	13.8564i	0.317721	−	0.550308i
$635$	−2.20163			−0.0873689
$636$	−0.437694			−0.0173557
$637$	1.85410	−	3.21140i	0.0734622	−	0.127240i
$638$	−27.0344	−	46.8250i	−1.07030	−	1.85382i
$639$	−11.0902	+	19.2087i	−0.438720	+	0.759886i
$640$	2.60081	+	4.50474i	0.102806	+	0.178065i
$641$	14.9549	+	25.9027i	0.590684	+	1.02309i	0.994141	+	0.108095i	$0.0344752\pi$
$641$	14.9549	+	25.9027i	0.590684	+	1.02309i	−0.403457	+	0.914999i	$0.632191\pi$
$642$	−8.16312	−	14.1389i	−0.322173	−	0.558019i
$643$	14.8541			0.585789			0.292894	−	0.956145i	$-0.405382\pi$
$643$	14.8541			0.585789			0.292894	+	0.956145i	$0.405382\pi$
$644$	−3.21885	+	5.57521i	−0.126840	+	0.219694i
$645$	0.454915	−	0.787936i	0.0179123	−	0.0310249i
$646$	17.1353	+	29.6791i	0.674178	+	1.16771i
$647$	5.88854			0.231503			0.115751	−	0.993278i	$-0.463072\pi$
$647$	5.88854			0.231503			0.115751	+	0.993278i	$0.463072\pi$
$648$	1.11803	−	1.93649i	0.0439205	−	0.0760726i
$649$	−2.76393			−0.108494
$650$	14.5623			0.571181
$651$		0			0
$652$	0.437694			0.0171414
$653$	8.34752			0.326664			0.163332	−	0.986571i	$-0.447776\pi$
$653$	8.34752			0.326664			0.163332	+	0.986571i	$0.447776\pi$
$654$	14.8992	−	25.8061i	0.582604	−	1.00910i
$655$	4.23607			0.165517
$656$	−6.00000	−	10.3923i	−0.234261	−	0.405751i
$657$	11.5623	−	20.0265i	0.451089	−	0.781308i
$658$	13.6353	−	23.6170i	0.531558	−	0.920685i
$659$	−37.6869			−1.46807			−0.734037	−	0.679110i	$-0.762366\pi$
$659$	−37.6869			−1.46807			−0.734037	+	0.679110i	$0.762366\pi$
$660$	0.618034	+	1.07047i	0.0240569	+	0.0416678i
$661$	7.19098	+	12.4551i	0.279697	+	0.484449i	0.971309	−	0.237820i	$-0.0764327\pi$
$661$	7.19098	+	12.4551i	0.279697	+	0.484449i	−0.691613	+	0.722269i	$0.743099\pi$
$662$	18.0172	+	31.2067i	0.700259	+	1.21288i
$663$	3.92705	−	6.80185i	0.152514	−	0.264162i
$664$	7.92705	+	13.7301i	0.307629	+	0.532829i
$665$	2.86475	−	4.96188i	0.111090	−	0.192414i
$666$	13.7082			0.531182
$667$	−22.1591			−0.858002
$668$	1.47214	−	2.54981i	0.0569587	−	0.0986553i
$669$	−6.35410	−	11.0056i	−0.245664	−	0.425502i
$670$	0.0729490	−	0.126351i	0.00281827	−	0.00488138i
$671$	28.6525	+	49.6275i	1.10612	+	1.91585i
$672$	−5.07295	−	8.78661i	−0.195693	−	0.338951i
$673$	−11.2082	−	19.4132i	−0.432045	−	0.748323i	0.565005	−	0.825088i	$-0.308874\pi$
$673$	−11.2082	−	19.4132i	−0.432045	−	0.748323i	−0.997049	+	0.0767646i	$0.975541\pi$
$674$	−45.2705			−1.74375
$675$	12.1353	−	21.0189i	0.467086	−	0.809017i
$676$	2.95492	−	5.11806i	0.113651	−	0.196849i
$677$	1.32624	+	2.29711i	0.0509715	+	0.0882852i	0.890385	−	0.455207i	$-0.150435\pi$
$677$	1.32624	+	2.29711i	0.0509715	+	0.0882852i	−0.839414	+	0.543493i	$0.817102\pi$
$678$	−7.85410			−0.301635
$679$	28.0623	−	48.6053i	1.07693	−	1.86530i
$680$	−3.61803			−0.138745
$681$	−21.7426			−0.833180
$682$		0			0
$683$	27.9443			1.06926			0.534629	−	0.845087i	$-0.320451\pi$
$683$	27.9443			1.06926			0.534629	+	0.845087i	$0.320451\pi$
$684$	−6.18034			−0.236311
$685$	0.472136	−	0.817763i	0.0180394	−	0.0312451i
$686$	−24.2705			−0.926652
$687$	−1.38197	−	2.39364i	−0.0527253	−	0.0913229i
$688$	−5.78115	+	10.0133i	−0.220404	+	0.381752i
$689$	0.656541	−	1.13716i	0.0250122	−	0.0433224i
$690$	2.14590			0.0816929
$691$	24.9164	+	43.1565i	0.947865	+	1.64175i	0.749911	+	0.661539i	$0.230096\pi$
$691$	24.9164	+	43.1565i	0.947865	+	1.64175i	0.197954	+	0.980211i	$0.436570\pi$
$692$	−3.73607	−	6.47106i	−0.142024	−	0.245993i
$693$	−15.7082	−	27.2074i	−0.596705	−	1.03352i
$694$	25.9894	−	45.0149i	0.986542	−	1.70874i
$695$	−0.163119	−	0.282530i	−0.00618745	−	0.0107170i
$696$	7.13525	−	12.3586i	0.270461	−	0.468452i
$697$	10.4721			0.396660
$698$	−5.32624			−0.201601
$699$	−2.89919	+	5.02154i	−0.109657	+	0.189932i
$700$	4.50000	+	7.79423i	0.170084	+	0.294594i
$701$	0.482779	−	0.836198i	0.0182343	−	0.0315828i	−0.856764	−	0.515708i	$-0.827529\pi$
$701$	0.482779	−	0.836198i	0.0182343	−	0.0315828i	0.874999	+	0.484125i	$0.160862\pi$
$702$	7.50000	+	12.9904i	0.283069	+	0.490290i
$703$	10.5902	+	18.3427i	0.399416	+	0.691809i
$704$	11.0902	+	19.2087i	0.417977	+	0.723957i
$705$	−2.14590			−0.0808192
$706$	28.0066	−	48.5088i	1.05404	−	1.82565i
$707$	−13.8541	+	23.9960i	−0.521037	+	0.902463i
$708$	0.163119	+	0.282530i	0.00613039	+	0.0106181i
$709$	10.8541			0.407634			0.203817	−	0.979009i	$-0.434665\pi$
$709$	10.8541			0.407634			0.203817	+	0.979009i	$0.434665\pi$
$710$	−3.42705	+	5.93583i	−0.128615	+	0.222768i
$711$		0			0
$712$	19.2705			0.722193
$713$		0			0
$714$	20.5623			0.769525
$715$	−3.70820			−0.138679
$716$	1.48278	−	2.56825i	0.0554141	−	0.0959800i
$717$	−13.4164			−0.501045
$718$	7.82624	+	13.5554i	0.292073	+	0.505885i
$719$	21.8090	−	37.7743i	0.813339	−	1.40874i	−0.0971753	−	0.995267i	$-0.530981\pi$
$719$	21.8090	−	37.7743i	0.813339	−	1.40874i	0.910514	−	0.413477i	$-0.135686\pi$
$720$	1.85410	−	3.21140i	0.0690983	−	0.119682i
$721$	−20.5623			−0.765780
$722$	−4.85410	−	8.40755i	−0.180651	−	0.312897i
$723$	−8.73607	−	15.1313i	−0.324898	−	0.562740i
$724$	−5.25329	−	9.09896i	−0.195237	−	0.338160i
$725$	−15.4894	+	26.8284i	−0.575260	+	0.996380i
$726$	13.2812	+	23.0036i	0.492910	+	0.853745i
$727$	−14.9164	+	25.8360i	−0.553219	+	0.958203i	0.444821	+	0.895620i	$0.353267\pi$
$727$	−14.9164	+	25.8360i	−0.553219	+	0.958203i	−0.998040	+	0.0625837i	$0.980066\pi$
$728$	12.4377			0.460972
$729$	13.0000			0.481481
$730$	3.57295	−	6.18853i	0.132241	−	0.229048i
$731$	−5.04508	−	8.73834i	−0.186599	−	0.323199i
$732$	3.38197	−	5.85774i	0.125001	−	0.216508i
$733$	−5.02786	−	8.70852i	−0.185708	−	0.321656i	0.758107	−	0.652131i	$-0.226125\pi$
$733$	−5.02786	−	8.70852i	−0.185708	−	0.321656i	−0.943815	+	0.330474i	$0.892791\pi$
$734$	2.20820	+	3.82472i	0.0815063	+	0.141173i
$735$	−0.381966	−	0.661585i	−0.0140890	−	0.0244029i
$736$	−11.7426			−0.432840
$737$	0.618034	−	1.07047i	0.0227656	−	0.0394311i
$738$	−4.00000	+	6.92820i	−0.147242	+	0.255031i
$739$	−4.14590	−	7.18091i	−0.152509	−	0.264154i	0.779640	−	0.626228i	$-0.215402\pi$
$739$	−4.14590	−	7.18091i	−0.152509	−	0.264154i	−0.932149	+	0.362074i	$0.882069\pi$
$740$	1.00000			0.0367607
$741$	−4.63525	+	8.02850i	−0.170280	+	0.294934i
$742$	3.43769			0.126202
$743$	−23.5623			−0.864417			−0.432209	−	0.901774i	$-0.642266\pi$
$743$	−23.5623			−0.864417			−0.432209	+	0.901774i	$0.642266\pi$
$744$		0			0
$745$	−4.59675			−0.168412
$746$	−51.2148			−1.87511
$747$	7.09017	−	12.2805i	0.259416	−	0.449321i
$748$	13.7082			0.501222
$749$	15.1353	+	26.2150i	0.553030	+	0.957876i
$750$	3.04508	−	5.27424i	0.111191	−	0.192588i
$751$	−6.91641	+	11.9796i	−0.252383	+	0.437141i	−0.964182	−	0.265243i	$-0.914548\pi$
$751$	−6.91641	+	11.9796i	−0.252383	+	0.437141i	0.711798	+	0.702384i	$0.247881\pi$
$752$	27.2705			0.994453
$753$	−8.47214	−	14.6742i	−0.308742	−	0.534756i
$754$	−9.57295	−	16.5808i	−0.348626	−	0.603838i
$755$	3.53444	+	6.12183i	0.128632	+	0.222796i
$756$	−4.63525	+	8.02850i	−0.168583	+	0.291994i
$757$	−1.43769	−	2.49016i	−0.0522539	−	0.0905064i	0.838715	−	0.544570i	$-0.183307\pi$
$757$	−1.43769	−	2.49016i	−0.0522539	−	0.0905064i	−0.890969	+	0.454064i	$0.849974\pi$
$758$	−6.80902	+	11.7936i	−0.247315	+	0.428362i
$759$	18.1803			0.659905
$760$	4.27051			0.154908
$761$	17.2533	−	29.8836i	0.625431	−	1.08328i	−0.363026	−	0.931779i	$-0.618256\pi$
$761$	17.2533	−	29.8836i	0.625431	−	1.08328i	0.988457	−	0.151500i	$-0.0484103\pi$
$762$	4.66312	+	8.07676i	0.168927	+	0.292590i
$763$	−27.6246	+	47.8472i	−1.00008	+	1.73219i
$764$	1.51722	+	2.62790i	0.0548911	+	0.0950742i
$765$	1.61803	+	2.80252i	0.0585001	+	0.101325i
$766$	8.20820	+	14.2170i	0.296574	+	0.513682i
$767$	−0.978714			−0.0353393
$768$	6.78115	−	11.7453i	0.244694	−	0.423822i
$769$	5.62868	−	9.74915i	0.202975	−	0.351564i	−0.746510	−	0.665374i	$-0.768272\pi$
$769$	5.62868	−	9.74915i	0.202975	−	0.351564i	0.949486	+	0.313810i	$0.101606\pi$
$770$	−4.85410	−	8.40755i	−0.174930	−	0.302987i
$771$	25.4164			0.915350
$772$	1.42705	−	2.47172i	0.0513607	−	0.0889593i
$773$	−7.90983			−0.284497			−0.142248	−	0.989831i	$-0.545433\pi$
$773$	−7.90983			−0.284497			−0.142248	+	0.989831i	$0.545433\pi$
$774$	7.70820			0.277066
$775$		0			0
$776$	41.8328			1.50171
$777$	12.7082			0.455904
$778$	−23.5172	+	40.7330i	−0.843133	+	1.46035i
$779$	−12.3607			−0.442867
$780$	0.218847	+	0.379054i	0.00783598	+	0.0135723i
$781$	−29.0344	+	50.2891i	−1.03893	+	1.79949i
$782$	11.8992	−	20.6100i	0.425514	−	0.737012i
$783$	−31.9098			−1.14036
$784$	4.85410	+	8.40755i	0.173361	+	0.300270i
$785$	−0.708204	−	1.22665i	−0.0252769	−	0.0437808i
$786$	−8.97214	−	15.5402i	−0.320025	−	0.554300i
$787$	−22.3541	+	38.7184i	−0.796838	+	1.38016i	0.124828	+	0.992178i	$0.460162\pi$
$787$	−22.3541	+	38.7184i	−0.796838	+	1.38016i	−0.921666	+	0.387985i	$0.873171\pi$
$788$	3.21885	+	5.57521i	0.114667	+	0.198609i
$789$	6.89919	−	11.9497i	0.245618	−	0.425422i
$790$		0			0
$791$	14.5623			0.517776
$792$	11.7082	−	20.2792i	0.416033	−	0.720590i
$793$	10.1459	+	17.5732i	0.360291	+	0.624043i
$794$	−24.0344	+	41.6289i	−0.852950	+	1.47735i
$795$	−0.135255	−	0.234268i	−0.00479700	−	0.00830864i
$796$	4.10739	+	7.11421i	0.145583	+	0.252156i
$797$	−13.4721	−	23.3344i	−0.477208	−	0.826548i	0.522451	−	0.852669i	$-0.325018\pi$
$797$	−13.4721	−	23.3344i	−0.477208	−	0.826548i	−0.999659	+	0.0261215i	$0.991684\pi$
$798$	−24.2705			−0.859167
$799$	−11.8992	+	20.6100i	−0.420963	+	0.729129i
$800$	−8.20820	+	14.2170i	−0.290204	+	0.502648i
$801$	−8.61803	−	14.9269i	−0.304503	−	0.527415i
$802$	38.5623			1.36168
$803$	30.2705	−	52.4301i	1.06822	−	1.85022i
$804$	−0.145898			−0.00514543
$805$	−3.97871			−0.140231
$806$		0			0
$807$	3.61803			0.127361
$808$	−20.6525			−0.726552
$809$	−15.1008	+	26.1554i	−0.530916	+	0.919574i	0.468433	+	0.883499i	$0.344819\pi$
$809$	−15.1008	+	26.1554i	−0.530916	+	0.919574i	−0.999349	+	0.0360749i	$0.988515\pi$
$810$	−0.618034			−0.0217155
$811$	14.3885	+	24.9217i	0.505250	+	0.875119i	0.999982	+	0.00607295i	$0.00193309\pi$
$811$	14.3885	+	24.9217i	0.505250	+	0.875119i	−0.494731	+	0.869046i	$0.664734\pi$
$812$	5.91641	−	10.2475i	0.207625	−	0.359617i
$813$	−5.28115	+	9.14723i	−0.185218	+	0.320807i
$814$	35.8885			1.25789
$815$	0.135255	+	0.234268i	0.00473777	+	0.00820606i
$816$	10.2812	+	17.8075i	0.359912	+	0.623386i
$817$	5.95492	+	10.3142i	0.208336	+	0.360849i
$818$	−13.0902	+	22.6728i	−0.457687	+	0.792737i
$819$	−5.56231	−	9.63420i	−0.194363	−	0.336646i
$820$	−0.291796	+	0.505406i	−0.0101900	+	0.0176495i
$821$	−23.5279			−0.821128			−0.410564	−	0.911832i	$-0.634668\pi$
$821$	−23.5279			−0.821128			−0.410564	+	0.911832i	$0.634668\pi$
$822$	−4.00000			−0.139516
$823$	−17.0623	+	29.5528i	−0.594755	+	1.03015i	0.398827	+	0.917026i	$0.369417\pi$
$823$	−17.0623	+	29.5528i	−0.594755	+	1.03015i	−0.993581	+	0.113119i	$0.963916\pi$
$824$	−7.66312	−	13.2729i	−0.266957	−	0.462384i
$825$	12.7082	−	22.0113i	0.442443	−	0.766334i
$826$	−1.28115	−	2.21902i	−0.0445770	−	0.0772097i
$827$	−9.16312	−	15.8710i	−0.318633	−	0.551888i	0.661570	−	0.749883i	$-0.269890\pi$
$827$	−9.16312	−	15.8710i	−0.318633	−	0.551888i	−0.980203	+	0.197995i	$0.936557\pi$
$828$	2.14590	+	3.71680i	0.0745751	+	0.129168i
$829$	−8.29180			−0.287986			−0.143993	−	0.989579i	$-0.545994\pi$
$829$	−8.29180			−0.287986			−0.143993	+	0.989579i	$0.545994\pi$
$830$	2.19098	−	3.79489i	0.0760501	−	0.131723i
$831$	−1.16312	+	2.01458i	−0.0403481	+	0.0698850i
$832$	3.92705	+	6.80185i	0.136146	+	0.235812i
$833$	−8.47214			−0.293542
$834$	−0.690983	+	1.19682i	−0.0239268	+	0.0414424i
$835$	1.81966			0.0629719
$836$	−16.1803			−0.559609
$837$		0			0
$838$	−7.23607			−0.249966
$839$	−11.1803			−0.385988			−0.192994	−	0.981200i	$-0.561820\pi$
$839$	−11.1803			−0.385988			−0.192994	+	0.981200i	$0.561820\pi$
$840$	1.28115	−	2.21902i	0.0442040	−	0.0765635i
$841$	11.7295			0.404465
$842$	−15.5623	−	26.9547i	−0.536312	−	0.928920i
$843$	−5.01722	+	8.69008i	−0.172802	+	0.299302i
$844$	2.47214	−	4.28187i	0.0850944	−	0.147388i
$845$	3.65248			0.125649
$846$	−9.09017	−	15.7446i	−0.312526	−	0.541312i
$847$	−24.6246	−	42.6511i	−0.846112	−	1.46551i
$848$	1.71885	+	2.97713i	0.0590255	+	0.102235i
$849$	−6.78115	+	11.7453i	−0.232729	+	0.403098i
$850$	−16.6353	−	28.8131i	−0.570585	−	0.988281i
$851$	7.35410	−	12.7377i	0.252095	−	0.436642i
$852$	6.85410			0.234818
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$	−26.5623	+	46.0073i	−0.908943	+	1.57434i
$855$	−1.90983	−	3.30792i	−0.0653148	−	0.113129i
$856$	−11.2812	+	19.5395i	−0.385582	+	0.667847i
$857$	−7.09017	−	12.2805i	−0.242196	−	0.419495i	0.719144	−	0.694861i	$-0.244534\pi$
$857$	−7.09017	−	12.2805i	−0.242196	−	0.419495i	−0.961339	+	0.275366i	$0.911201\pi$
$858$	7.85410	+	13.6037i	0.268135	+	0.464423i
$859$	−28.3541	−	49.1107i	−0.967429	−	1.67564i	−0.702941	−	0.711248i	$-0.748130\pi$
$859$	−28.3541	−	49.1107i	−0.967429	−	1.67564i	−0.264488	−	0.964389i	$-0.585203\pi$
$860$	0.562306			0.0191745
$861$	−3.70820	+	6.42280i	−0.126375	+	0.218888i
$862$	−20.0344	+	34.7007i	−0.682376	+	1.18191i
$863$	−20.2533	−	35.0797i	−0.689430	−	1.19413i	−0.972023	−	0.234888i	$-0.924528\pi$
$863$	−20.2533	−	35.0797i	−0.689430	−	1.19413i	0.282593	−	0.959240i	$-0.408806\pi$
$864$	−16.9098			−0.575284
$865$	2.30902	−	3.99933i	0.0785089	−	0.135981i
$866$	44.3607			1.50744
$867$	−0.944272			−0.0320692
$868$		0			0
$869$		0			0
$870$	−3.94427			−0.133723
$871$	0.218847	−	0.379054i	0.00741535	−	0.0128438i
$872$	−41.1803			−1.39454
$873$	−18.7082	−	32.4036i	−0.633177	−	1.09669i
$874$	−14.0451	+	24.3268i	−0.475082	+	0.822866i
$875$	−5.64590	+	9.77898i	−0.190866	+	0.330590i
$876$	−7.14590			−0.241438
$877$	−14.8541	−	25.7281i	−0.501587	−	0.868775i	−0.999998	−	0.00183392i	$-0.999416\pi$
$877$	−14.8541	−	25.7281i	−0.501587	−	0.868775i	0.498411	−	0.866941i	$-0.333917\pi$
$878$	9.57295	+	16.5808i	0.323071	+	0.559576i
$879$	−1.88197	−	3.25966i	−0.0634771	−	0.109946i
$880$	4.85410	−	8.40755i	0.163632	−	0.283418i
$881$	−14.6803	−	25.4271i	−0.494593	−	0.856661i	0.505387	−	0.862893i	$-0.331350\pi$
$881$	−14.6803	−	25.4271i	−0.494593	−	0.856661i	−0.999981	+	0.00623200i	$0.998016\pi$
$882$	3.23607	−	5.60503i	0.108964	−	0.188731i
$883$	−1.00000			−0.0336527			−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000			−0.0336527			−0.0168263	+	0.999858i	$0.505356\pi$
$884$	4.85410			0.163261
$885$	−0.100813	+	0.174613i	−0.00338879	+	0.00586956i
$886$	0.708204	+	1.22665i	0.0237926	+	0.0412100i
$887$	24.0517	−	41.6587i	0.807576	−	1.39876i	−0.106963	−	0.994263i	$-0.534112\pi$
$887$	24.0517	−	41.6587i	0.807576	−	1.39876i	0.914538	−	0.404499i	$-0.132554\pi$
$888$	4.73607	+	8.20311i	0.158932	+	0.275278i
$889$	−8.64590	−	14.9751i	−0.289974	−	0.502250i
$890$	−2.66312	−	4.61266i	−0.0892680	−	0.154617i
$891$	−5.23607			−0.175415
$892$	3.92705	−	6.80185i	0.131487	−	0.227743i
$893$	14.0451	−	24.3268i	0.470001	−	0.814065i
$894$	9.73607	+	16.8634i	0.325623	+	0.563995i
$895$	1.83282			0.0612643
$896$	−20.4271	+	35.3807i	−0.682420	+	1.18199i
$897$	6.43769			0.214948
$898$	−55.1246			−1.83953
$899$		0			0
$900$	6.00000			0.200000
$901$	−3.00000			−0.0999445
$902$	−10.4721	+	18.1383i	−0.348684	+	0.603938i
$903$	7.14590			0.237801
$904$	5.42705	+	9.39993i	0.180501	+	0.312637i
$905$	3.24671	−	5.62347i	0.107924	−	0.186930i
$906$	14.9721	−	25.9325i	0.497416	−	0.861550i
$907$	−11.9230			−0.395896			−0.197948	−	0.980212i	$-0.563428\pi$
$907$	−11.9230			−0.395896			−0.197948	+	0.980212i	$0.563428\pi$
$908$	−6.71885	−	11.6374i	−0.222973	−	0.386200i
$909$	9.23607	+	15.9973i	0.306341	+	0.530598i
$910$	−1.71885	−	2.97713i	−0.0569792	−	0.0986909i
$911$	7.09017	−	12.2805i	0.234908	−	0.406872i	−0.724338	−	0.689445i	$-0.757855\pi$
$911$	7.09017	−	12.2805i	0.234908	−	0.406872i	0.959246	+	0.282573i	$0.0911878\pi$
$912$	−12.1353	−	21.0189i	−0.401838	−	0.696005i
$913$	18.5623	−	32.1509i	0.614323	−	1.06404i
$914$	43.2705			1.43126
$915$	4.18034			0.138198
$916$	0.854102	−	1.47935i	0.0282203	−	0.0488790i
$917$	16.6353	+	28.8131i	0.549345	+	0.951493i
$918$	17.1353	−	29.6791i	0.565548	−	0.979557i
$919$	−25.0623	−	43.4092i	−0.826729	−	1.43194i	−0.900591	−	0.434668i	$-0.856866\pi$
$919$	−25.0623	−	43.4092i	−0.826729	−	1.43194i	0.0738614	−	0.997269i	$-0.476468\pi$
$920$	−1.48278	−	2.56825i	−0.0488858	−	0.0846727i
$921$	−2.54508	−	4.40822i	−0.0838634	−	0.145256i
$922$	−51.3607			−1.69147
$923$	−10.2812	+	17.8075i	−0.338408	+	0.586140i
$924$	−4.85410	+	8.40755i	−0.159688	+	0.276588i
$925$	−10.2812	−	17.8075i	−0.338042	−	0.585506i
$926$	14.7639			0.485173
$927$	−6.85410	+	11.8717i	−0.225118	+	0.389916i
$928$	21.5836			0.708516
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−3.58359			−0.117384
$933$	3.76393	−	6.51932i	0.123226	−	0.213433i
$934$	62.7426			2.05300
$935$	4.23607	+	7.33708i	0.138534	+	0.239948i
$936$	4.14590	−	7.18091i	0.135513	−	0.234715i
$937$	22.2426	−	38.5254i	0.726636	−	1.25857i	−0.231662	−	0.972796i	$-0.574416\pi$
$937$	22.2426	−	38.5254i	0.726636	−	1.25857i	0.958297	−	0.285773i	$-0.0922504\pi$
$938$	1.14590			0.0374149
$939$	−1.61803	−	2.80252i	−0.0528025	−	0.0914567i
$940$	−0.663119	−	1.14856i	−0.0216286	−	0.0374618i
$941$	−27.7082	−	47.9920i	−0.903262	−	1.56450i	−0.823234	−	0.567702i	$-0.807832\pi$
$941$	−27.7082	−	47.9920i	−0.903262	−	1.56450i	−0.0800278	−	0.996793i	$-0.525501\pi$
$942$	−3.00000	+	5.19615i	−0.0977453	+	0.169300i
$943$	4.29180	+	7.43361i	0.139760	+	0.242072i
$944$	1.28115	−	2.21902i	0.0416980	−	0.0722230i
$945$	−5.72949			−0.186380
$946$	20.1803			0.656119
$947$	18.0344	−	31.2366i	0.586041	−	1.01505i	−0.408704	−	0.912667i	$-0.634019\pi$
$947$	18.0344	−	31.2366i	0.586041	−	1.01505i	0.994745	−	0.102385i	$-0.0326474\pi$
$948$		0			0
$949$	10.7188	−	18.5656i	0.347948	−	0.602664i
$950$	19.6353	+	34.0093i	0.637052	+	1.10341i
$951$	−4.94427	−	8.56373i	−0.160329	−	0.277698i
$952$	−14.2082	−	24.6093i	−0.460491	−	0.797593i
$953$	−9.21478			−0.298496			−0.149248	−	0.988800i	$-0.547685\pi$
$953$	−9.21478			−0.298496			−0.149248	+	0.988800i	$0.547685\pi$
$954$	1.14590	−	1.98475i	0.0370998	−	0.0642588i
$955$	−0.937694	+	1.62413i	−0.0303431	+	0.0525557i
$956$	−4.14590	−	7.18091i	−0.134088	−	0.232247i
$957$	−33.4164			−1.08020
$958$	−7.23607	+	12.5332i	−0.233787	+	0.404931i
$959$	7.41641			0.239488
$960$	1.61803			0.0522218
$961$		0			0
$962$	12.7082			0.409729
$963$	20.1803			0.650302
$964$	5.39919	−	9.35167i	0.173896	−	0.301197i
$965$	1.76393			0.0567830
$966$	8.42705	+	14.5961i	0.271136	+	0.469621i
$967$	−6.17376	+	10.6933i	−0.198535	+	0.343872i	−0.948054	−	0.318111i	$-0.896952\pi$
$967$	−6.17376	+	10.6933i	−0.198535	+	0.343872i	0.749519	+	0.661983i	$0.230285\pi$
$968$	18.3541	−	31.7902i	0.589923	−	1.02178i
$969$	21.1803			0.680411
$970$	−5.78115	−	10.0133i	−0.185622	−	0.321506i
$971$	0.218847	+	0.379054i	0.00702314	+	0.0121644i	0.869516	−	0.493905i	$-0.164431\pi$
$971$	0.218847	+	0.379054i	0.00702314	+	0.0121644i	−0.862492	+	0.506070i	$0.831098\pi$
$972$	4.94427	+	8.56373i	0.158588	+	0.274682i
$973$	1.28115	−	2.21902i	0.0410719	−	0.0711386i
$974$	33.9164	+	58.7449i	1.08675	+	1.88231i
$975$	4.50000	−	7.79423i	0.144115	−	0.249615i
$976$	−53.1246			−1.70048
$977$	52.0689			1.66583			0.832916	−	0.553400i	$-0.186670\pi$
$977$	52.0689			1.66583			0.832916	+	0.553400i	$0.186670\pi$
$978$	0.572949	−	0.992377i	0.0183209	−	0.0317327i
$979$	−22.5623	−	39.0791i	−0.721094	−	1.24897i
$980$	0.236068	−	0.408882i	0.00754091	−	0.0130612i
$981$	18.4164	+	31.8982i	0.587991	+	1.01843i
$982$	−17.4721	−	30.2626i	−0.557558	−	0.965719i
$983$	4.01722	+	6.95803i	0.128129	+	0.221927i	0.922952	−	0.384915i	$-0.125769\pi$
$983$	4.01722	+	6.95803i	0.128129	+	0.221927i	−0.794822	+	0.606842i	$0.792436\pi$
$984$	−5.52786			−0.176222
$985$	−1.98936	+	3.44567i	−0.0633862	+	0.109788i
$986$	−21.8713	+	37.8822i	−0.696525	+	1.20642i
$987$	−8.42705	−	14.5961i	−0.268236	−	0.464598i
$988$	−5.72949			−0.182279
$989$	4.13525	−	7.16247i	0.131493	−	0.227753i
$990$	−6.47214			−0.205698
$991$	16.2705			0.516850			0.258425	−	0.966031i	$-0.416797\pi$
$991$	16.2705			0.516850			0.258425	+	0.966031i	$0.416797\pi$
$992$		0			0
$993$	22.2705			0.706733
$994$	−53.8328			−1.70747
$995$	−2.53851	+	4.39682i	−0.0804761	+	0.139389i
$996$	−4.38197			−0.138848
$997$	−26.6246	−	46.1152i	−0.843210	−	1.46048i	−0.887167	−	0.461449i	$-0.847330\pi$
$997$	−26.6246	−	46.1152i	−0.843210	−	1.46048i	0.0439568	−	0.999033i	$-0.486004\pi$
$998$	−8.78115	+	15.2094i	−0.277963	+	0.481445i
$999$	10.5902	−	18.3427i	0.335058	−	0.580338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.f.439.2		4
31.2	even	5		961.2.g.f.547.1		8
31.3	odd	30		961.2.g.g.448.1		8
31.4	even	5		961.2.g.b.235.1		8
31.5	even	3		961.2.a.d.1.2		2
31.6	odd	6		961.2.c.d.521.2		4
31.7	even	15		961.2.g.b.338.1		8
31.8	even	5		961.2.g.b.816.1		8
31.9	even	15		31.2.d.a.2.1	✓	4
31.10	even	15		961.2.d.f.531.1		4
31.11	odd	30		961.2.d.b.388.1		4
31.12	odd	30		961.2.g.g.844.1		8
31.13	odd	30		961.2.d.e.628.1		4
31.14	even	15		961.2.g.b.732.1		8
31.15	odd	10		961.2.g.g.846.1		8
31.16	even	5		961.2.g.f.846.1		8
31.17	odd	30		961.2.g.c.732.1		8
31.18	even	15		961.2.d.f.628.1		4
31.19	even	15		961.2.g.f.844.1		8
31.20	even	15		31.2.d.a.16.1	yes	4
31.21	odd	30		961.2.d.e.531.1		4
31.22	odd	30		961.2.d.b.374.1		4
31.23	odd	10		961.2.g.c.816.1		8
31.24	odd	30		961.2.g.c.338.1		8
31.25	even	3	inner	961.2.c.f.521.2		4
31.26	odd	6		961.2.a.e.1.2		2
31.27	odd	10		961.2.g.c.235.1		8
31.28	even	15		961.2.g.f.448.1		8
31.29	odd	10		961.2.g.g.547.1		8
31.30	odd	2		961.2.c.d.439.2		4
93.5	odd	6		8649.2.a.g.1.1		2
93.20	odd	30		279.2.i.a.109.1		4
93.26	even	6		8649.2.a.f.1.1		2
93.71	odd	30		279.2.i.a.64.1		4
124.51	odd	30		496.2.n.b.481.1		4
124.71	odd	30		496.2.n.b.33.1		4
155.9	even	30		775.2.k.c.126.1		4
155.82	odd	60		775.2.bf.a.574.1		8
155.102	odd	60		775.2.bf.a.374.2		8
155.113	odd	60		775.2.bf.a.574.2		8
155.133	odd	60		775.2.bf.a.374.1		8
155.144	even	30		775.2.k.c.326.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.2.1	✓	4	31.9	even	15
31.2.d.a.16.1	yes	4	31.20	even	15
279.2.i.a.64.1		4	93.71	odd	30
279.2.i.a.109.1		4	93.20	odd	30
496.2.n.b.33.1		4	124.71	odd	30
496.2.n.b.481.1		4	124.51	odd	30
775.2.k.c.126.1		4	155.9	even	30
775.2.k.c.326.1		4	155.144	even	30
775.2.bf.a.374.1		8	155.133	odd	60
775.2.bf.a.374.2		8	155.102	odd	60
775.2.bf.a.574.1		8	155.82	odd	60
775.2.bf.a.574.2		8	155.113	odd	60
961.2.a.d.1.2		2	31.5	even	3
961.2.a.e.1.2		2	31.26	odd	6
961.2.c.d.439.2		4	31.30	odd	2
961.2.c.d.521.2		4	31.6	odd	6
961.2.c.f.439.2		4	1.1	even	1	trivial
961.2.c.f.521.2		4	31.25	even	3	inner
961.2.d.b.374.1		4	31.22	odd	30
961.2.d.b.388.1		4	31.11	odd	30
961.2.d.e.531.1		4	31.21	odd	30
961.2.d.e.628.1		4	31.13	odd	30
961.2.d.f.531.1		4	31.10	even	15
961.2.d.f.628.1		4	31.18	even	15
961.2.g.b.235.1		8	31.4	even	5
961.2.g.b.338.1		8	31.7	even	15
961.2.g.b.732.1		8	31.14	even	15
961.2.g.b.816.1		8	31.8	even	5
961.2.g.c.235.1		8	31.27	odd	10
961.2.g.c.338.1		8	31.24	odd	30
961.2.g.c.732.1		8	31.17	odd	30
961.2.g.c.816.1		8	31.23	odd	10
961.2.g.f.448.1		8	31.28	even	15
961.2.g.f.547.1		8	31.2	even	5
961.2.g.f.844.1		8	31.19	even	15
961.2.g.f.846.1		8	31.16	even	5
961.2.g.g.448.1		8	31.3	odd	30
961.2.g.g.547.1		8	31.29	odd	10
961.2.g.g.844.1		8	31.12	odd	30
961.2.g.g.846.1		8	31.15	odd	10
8649.2.a.f.1.1		2	93.26	even	6
8649.2.a.g.1.1		2	93.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +(0.500000 - 0.866025i) q^{3} +0.618034 q^{4} +(0.190983 + 0.330792i) q^{5} +(0.809017 - 1.40126i) q^{6} +(-1.50000 + 2.59808i) q^{7} -2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.309017 + 0.535233i) q^{10} +(2.61803 + 4.53457i) q^{11} +(0.309017 - 0.535233i) q^{12} +(0.927051 + 1.60570i) q^{13} +(-2.42705 + 4.20378i) q^{14} +0.381966 q^{15} -4.85410 q^{16} +(2.11803 - 3.66854i) q^{17} +(1.61803 + 2.80252i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.118034 + 0.204441i) q^{20} +(1.50000 + 2.59808i) q^{21} +(4.23607 + 7.33708i) q^{22} +3.47214 q^{23} +(-1.11803 + 1.93649i) q^{24} +(2.42705 - 4.20378i) q^{25} +(1.50000 + 2.59808i) q^{26} +5.00000 q^{27} +(-0.927051 + 1.60570i) q^{28} -6.38197 q^{29} +0.618034 q^{30} -3.38197 q^{32} +5.23607 q^{33} +(3.42705 - 5.93583i) q^{34} -1.14590 q^{35} +(0.618034 + 1.07047i) q^{36} +(2.11803 - 3.66854i) q^{37} +(-4.04508 + 7.00629i) q^{38} +1.85410 q^{39} +(-0.427051 - 0.739674i) q^{40} +(1.23607 + 2.14093i) q^{41} +(2.42705 + 4.20378i) q^{42} +(1.19098 - 2.06284i) q^{43} +(1.61803 + 2.80252i) q^{44} +(-0.381966 + 0.661585i) q^{45} +5.61803 q^{46} -5.61803 q^{47} +(-2.42705 + 4.20378i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(3.92705 - 6.80185i) q^{50} +(-2.11803 - 3.66854i) q^{51} +(0.572949 + 0.992377i) q^{52} +(-0.354102 - 0.613323i) q^{53} +8.09017 q^{54} +(-1.00000 + 1.73205i) q^{55} +(3.35410 - 5.80948i) q^{56} +(2.50000 + 4.33013i) q^{57} -10.3262 q^{58} +(-0.263932 + 0.457144i) q^{59} +0.236068 q^{60} +10.9443 q^{61} -6.00000 q^{63} +4.23607 q^{64} +(-0.354102 + 0.613323i) q^{65} +8.47214 q^{66} +(-0.118034 - 0.204441i) q^{67} +(1.30902 - 2.26728i) q^{68} +(1.73607 - 3.00696i) q^{69} -1.85410 q^{70} +(5.54508 + 9.60437i) q^{71} +(-2.23607 - 3.87298i) q^{72} +(-5.78115 - 10.0133i) q^{73} +(3.42705 - 5.93583i) q^{74} +(-2.42705 - 4.20378i) q^{75} +(-1.54508 + 2.67617i) q^{76} -15.7082 q^{77} +3.00000 q^{78} +(-0.927051 - 1.60570i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +(-3.54508 - 6.14027i) q^{83} +(0.927051 + 1.60570i) q^{84} +1.61803 q^{85} +(1.92705 - 3.33775i) q^{86} +(-3.19098 + 5.52694i) q^{87} +(-5.85410 - 10.1396i) q^{88} -8.61803 q^{89} +(-0.618034 + 1.07047i) q^{90} -5.56231 q^{91} +2.14590 q^{92} -9.09017 q^{94} -1.90983 q^{95} +(-1.69098 + 2.92887i) q^{96} -18.7082 q^{97} +(-1.61803 - 2.80252i) q^{98} +(-5.23607 + 9.06914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 3 q^{5} + q^{6} - 6 q^{7} + 4 q^{9} - q^{10} + 6 q^{11} - q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 6 q^{21}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 3 * q^5 + q^6 - 6 * q^7 + 4 * q^9 - q^10 + 6 * q^11 - q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 + 6 * q^21 + 8 * q^22 - 4 * q^23 + 3 * q^25 + 6 * q^26 + 20 * q^27 + 3 * q^28 - 30 * q^29 - 2 * q^30 - 18 * q^32 + 12 * q^33 + 7 * q^34 - 18 * q^35 - 2 * q^36 + 4 * q^37 - 5 * q^38 - 6 * q^39 + 5 * q^40 - 4 * q^41 + 3 * q^42 + 7 * q^43 + 2 * q^44 - 6 * q^45 + 18 * q^46 - 18 * q^47 - 3 * q^48 - 4 * q^49 + 9 * q^50 - 4 * q^51 + 9 * q^52 + 12 * q^53 + 10 * q^54 - 4 * q^55 + 10 * q^57 - 10 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 - 24 * q^63 + 8 * q^64 + 12 * q^65 + 16 * q^66 + 4 * q^67 + 3 * q^68 - 2 * q^69 + 6 * q^70 + 11 * q^71 - 3 * q^73 + 7 * q^74 - 3 * q^75 + 5 * q^76 - 36 * q^77 + 12 * q^78 + 3 * q^80 - 2 * q^81 + 8 * q^82 - 3 * q^83 - 3 * q^84 + 2 * q^85 + q^86 - 15 * q^87 - 10 * q^88 - 30 * q^89 + 2 * q^90 + 18 * q^91 + 22 * q^92 - 14 * q^94 - 30 * q^95 - 9 * q^96 - 48 * q^97 - 2 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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