LMFDB - Embedded newform 961.2.c.h.521.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,12,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.207360000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.1
Root			$1.14412 + 1.98168i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.h.439.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.381966 q^{2} +(-1.14412 - 1.98168i) q^{3} -1.85410 q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.437016 - 0.756934i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.47214 q^{8} +(-1.11803 + 1.93649i) q^{9} +(0.427051 - 0.739674i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(2.12132 + 3.67423i) q^{12} +(-3.43237 + 5.94504i) q^{13} +(0.190983 + 0.330792i) q^{14} -5.11667 q^{15} +3.14590 q^{16} +(-0.270091 - 0.467811i) q^{17} +(-0.427051 + 0.739674i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-2.07295 + 3.59045i) q^{20} +(1.14412 - 1.98168i) q^{21} +(-0.810272 + 1.40343i) q^{22} +6.86474 q^{23} +(1.68430 + 2.91730i) q^{24} +(-1.31105 + 2.27080i) q^{26} -1.74806 q^{27} +(-0.927051 - 1.60570i) q^{28} -3.70246 q^{29} -1.95440 q^{30} +4.14590 q^{32} +9.70820 q^{33} +(-0.103165 - 0.178688i) q^{34} +2.23607 q^{35} +(2.07295 - 3.59045i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(-0.190983 - 0.330792i) q^{38} +15.7082 q^{39} +(-1.64590 + 2.85078i) q^{40} +(-3.73607 + 6.47106i) q^{41} +(0.437016 - 0.756934i) q^{42} +(0.103165 + 0.178688i) q^{43} +(3.93314 - 6.81241i) q^{44} +(2.50000 + 4.33013i) q^{45} +2.62210 q^{46} +3.70820 q^{47} +(-3.59929 - 6.23416i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.618034 + 1.07047i) q^{51} +(6.36396 - 11.0227i) q^{52} +(-2.62210 + 4.54160i) q^{53} -0.667701 q^{54} +(4.74342 + 8.21584i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-1.14412 + 1.98168i) q^{57} -1.41421 q^{58} +(2.97214 + 5.14789i) q^{59} +9.48683 q^{60} +4.44897 q^{61} -2.23607 q^{63} -4.70820 q^{64} +(7.67501 + 13.2935i) q^{65} +3.70820 q^{66} +(-3.00000 + 5.19615i) q^{67} +(0.500776 + 0.867369i) q^{68} +(-7.85410 - 13.6037i) q^{69} +0.854102 q^{70} +(-3.73607 + 6.47106i) q^{71} +(1.64590 - 2.85078i) q^{72} +(-2.12132 + 3.67423i) q^{73} +(-0.810272 - 1.40343i) q^{74} +(0.927051 + 1.60570i) q^{76} -4.24264 q^{77} +6.00000 q^{78} +(5.55369 + 9.61927i) q^{79} +(3.51722 - 6.09201i) q^{80} +(5.35410 + 9.27358i) q^{81} +(-1.42705 + 2.47172i) q^{82} +(-1.58114 + 2.73861i) q^{83} +(-2.12132 + 3.67423i) q^{84} -1.20788 q^{85} +(0.0394057 + 0.0682527i) q^{86} +(4.23607 + 7.33708i) q^{87} +(3.12287 - 5.40897i) q^{88} -5.86319 q^{89} +(0.954915 + 1.65396i) q^{90} -6.86474 q^{91} -12.7279 q^{92} +1.41641 q^{94} -2.23607 q^{95} +(-4.74342 - 8.21584i) q^{96} -7.00000 q^{97} +(1.14590 - 1.98475i) q^{98} +(-4.74342 - 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{2} + 12 q^{4} + 4 q^{7} + 24 q^{8} - 10 q^{10} + 6 q^{14} + 52 q^{16} + 10 q^{18} - 4 q^{19} - 30 q^{20} + 6 q^{28} + 60 q^{32} + 24 q^{33} + 30 q^{36} - 6 q^{38} + 72 q^{39} - 40 q^{40} - 12 q^{41}+ \cdots + 36 q^{98}+O(q^{100}) $ 8 * q + 12 * q^2 + 12 * q^4 + 4 * q^7 + 24 * q^8 - 10 * q^10 + 6 * q^14 + 52 * q^16 + 10 * q^18 - 4 * q^19 - 30 * q^20 + 6 * q^28 + 60 * q^32 + 24 * q^33 + 30 * q^36 - 6 * q^38 + 72 * q^39 - 40 * q^40 - 12 * q^41 + 20 * q^45 - 24 * q^47 + 24 * q^49 + 4 * q^51 + 12 * q^56 - 12 * q^59 + 16 * q^64 - 24 * q^66 - 24 * q^67 - 36 * q^69 - 20 * q^70 - 12 * q^71 + 40 * q^72 - 6 * q^76 + 48 * q^78 - 30 * q^80 + 16 * q^81 + 2 * q^82 + 16 * q^87 + 30 * q^90 - 96 * q^94 - 56 * q^97 + 36 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.381966			0.270091			0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966			0.270091			0.135045	+	0.990839i	$0.456882\pi$
$3$	−1.14412	−	1.98168i	−0.660560	−	1.14412i	−0.980469	−	0.196675i	$-0.936986\pi$
$3$	−1.14412	−	1.98168i	−0.660560	−	1.14412i	0.319909	−	0.947448i	$-0.396348\pi$
$4$	−1.85410			−0.927051
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	1.00000			$0$
$6$	−0.437016	−	0.756934i	−0.178411	−	0.309017i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.47214			−0.520479
$9$	−1.11803	+	1.93649i	−0.372678	+	0.645497i
$10$	0.427051	−	0.739674i	0.135045	−	0.233905i
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$	2.12132	+	3.67423i	0.612372	+	1.06066i
$13$	−3.43237	+	5.94504i	−0.951968	+	1.64886i	−0.210808	+	0.977527i	$0.567610\pi$
$13$	−3.43237	+	5.94504i	−0.951968	+	1.64886i	−0.741159	+	0.671329i	$0.765724\pi$
$14$	0.190983	+	0.330792i	0.0510424	+	0.0884080i
$15$	−5.11667			−1.32112
$16$	3.14590			0.786475
$17$	−0.270091	−	0.467811i	−0.0655066	−	0.113461i	0.831412	−	0.555656i	$-0.187533\pi$
$17$	−0.270091	−	0.467811i	−0.0655066	−	0.113461i	−0.896919	+	0.442196i	$0.854200\pi$
$18$	−0.427051	+	0.739674i	−0.100657	+	0.174343i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.07295	+	3.59045i	−0.463525	+	0.802850i
$21$	1.14412	−	1.98168i	0.249668	−	0.432438i
$22$	−0.810272	+	1.40343i	−0.172751	+	0.299213i
$23$	6.86474			1.43140			0.715698	−	0.698410i	$-0.246109\pi$
$23$	6.86474			1.43140			0.715698	+	0.698410i	$0.246109\pi$
$24$	1.68430	+	2.91730i	0.343807	+	0.595492i
$25$		0			0
$26$	−1.31105	+	2.27080i	−0.257118	+	0.445341i
$27$	−1.74806			−0.336415
$28$	−0.927051	−	1.60570i	−0.175196	−	0.303449i
$29$	−3.70246			−0.687529			−0.343765	−	0.939056i	$-0.611702\pi$
$29$	−3.70246			−0.687529			−0.343765	+	0.939056i	$0.611702\pi$
$30$	−1.95440			−0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	9.70820			1.68998
$34$	−0.103165	−	0.178688i	−0.0176927	−	0.0306447i
$35$	2.23607			0.377964
$36$	2.07295	−	3.59045i	0.345492	−	0.598409i
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	0.637284	−	0.770629i	$-0.280058\pi$
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	−0.986026	+	0.166589i	$0.946725\pi$
$38$	−0.190983	−	0.330792i	−0.0309815	−	0.0536616i
$39$	15.7082			2.51533
$40$	−1.64590	+	2.85078i	−0.260239	+	0.450748i
$41$	−3.73607	+	6.47106i	−0.583476	+	1.01061i	0.411588	+	0.911370i	$0.364974\pi$
$41$	−3.73607	+	6.47106i	−0.583476	+	1.01061i	−0.995064	+	0.0992396i	$0.968359\pi$
$42$	0.437016	−	0.756934i	0.0674330	−	0.116797i
$43$	0.103165	+	0.178688i	0.0157326	+	0.0272496i	0.873785	−	0.486313i	$-0.161659\pi$
$43$	0.103165	+	0.178688i	0.0157326	+	0.0272496i	−0.858052	+	0.513563i	$0.828325\pi$
$44$	3.93314	−	6.81241i	0.592944	−	1.02701i
$45$	2.50000	+	4.33013i	0.372678	+	0.645497i
$46$	2.62210			0.386607
$47$	3.70820			0.540897			0.270449	−	0.962734i	$-0.412828\pi$
$47$	3.70820			0.540897			0.270449	+	0.962734i	$0.412828\pi$
$48$	−3.59929	−	6.23416i	−0.519513	−	0.899823i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	−0.618034	+	1.07047i	−0.0865421	+	0.149895i
$52$	6.36396	−	11.0227i	0.882523	−	1.52857i
$53$	−2.62210	+	4.54160i	−0.360173	+	0.623837i	−0.987989	−	0.154524i	$-0.950616\pi$
$53$	−2.62210	+	4.54160i	−0.360173	+	0.623837i	0.627816	+	0.778361i	$0.283949\pi$
$54$	−0.667701			−0.0908626
$55$	4.74342	+	8.21584i	0.639602	+	1.10782i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$	−1.14412	+	1.98168i	−0.151543	+	0.262480i
$58$	−1.41421			−0.185695
$59$	2.97214	+	5.14789i	0.386939	+	0.670198i	0.992036	−	0.125953i	$-0.0401990\pi$
$59$	2.97214	+	5.14789i	0.386939	+	0.670198i	−0.605097	+	0.796152i	$0.706866\pi$
$60$	9.48683			1.22474
$61$	4.44897			0.569632			0.284816	−	0.958582i	$-0.408067\pi$
$61$	4.44897			0.569632			0.284816	+	0.958582i	$0.408067\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	−4.70820			−0.588525
$65$	7.67501	+	13.2935i	0.951968	+	1.64886i
$66$	3.70820			0.456448
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	0.500776	+	0.867369i	0.0607280	+	0.105184i
$69$	−7.85410	−	13.6037i	−0.945523	−	1.63769i
$70$	0.854102			0.102085
$71$	−3.73607	+	6.47106i	−0.443390	+	0.767973i	−0.997938	−	0.0641777i	$-0.979558\pi$
$71$	−3.73607	+	6.47106i	−0.443390	+	0.767973i	0.554549	+	0.832151i	$0.312891\pi$
$72$	1.64590	−	2.85078i	0.193971	−	0.335968i
$73$	−2.12132	+	3.67423i	−0.248282	+	0.430037i	−0.963049	−	0.269326i	$-0.913199\pi$
$73$	−2.12132	+	3.67423i	−0.248282	+	0.430037i	0.714767	+	0.699362i	$0.246533\pi$
$74$	−0.810272	−	1.40343i	−0.0941922	−	0.163146i
$75$		0			0
$76$	0.927051	+	1.60570i	0.106340	+	0.184186i
$77$	−4.24264			−0.483494
$78$	6.00000			0.679366
$79$	5.55369	+	9.61927i	0.624839	+	1.08225i	0.988572	+	0.150749i	$0.0481686\pi$
$79$	5.55369	+	9.61927i	0.624839	+	1.08225i	−0.363733	+	0.931503i	$0.618498\pi$
$80$	3.51722	−	6.09201i	0.393237	−	0.681107i
$81$	5.35410	+	9.27358i	0.594900	+	1.03040i
$82$	−1.42705	+	2.47172i	−0.157591	+	0.272956i
$83$	−1.58114	+	2.73861i	−0.173553	+	0.300602i	−0.939659	−	0.342111i	$-0.888858\pi$
$83$	−1.58114	+	2.73861i	−0.173553	+	0.300602i	0.766107	+	0.642713i	$0.222191\pi$
$84$	−2.12132	+	3.67423i	−0.231455	+	0.400892i
$85$	−1.20788			−0.131013
$86$	0.0394057	+	0.0682527i	0.00424923	+	0.00735988i
$87$	4.23607	+	7.33708i	0.454154	+	0.786618i
$88$	3.12287	−	5.40897i	0.332899	−	0.576598i
$89$	−5.86319			−0.621496			−0.310748	−	0.950492i	$-0.600580\pi$
$89$	−5.86319			−0.621496			−0.310748	+	0.950492i	$0.600580\pi$
$90$	0.954915	+	1.65396i	0.100657	+	0.174343i
$91$	−6.86474			−0.719620
$92$	−12.7279			−1.32698
$93$		0			0
$94$	1.41641			0.146091
$95$	−2.23607			−0.229416
$96$	−4.74342	−	8.21584i	−0.484123	−	0.838525i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	1.14590	−	1.98475i	0.115753	−	0.200490i
$99$	−4.74342	−	8.21584i	−0.476731	−	0.825723i
$100$		0			0
$101$	−2.23607			−0.222497			−0.111249	−	0.993793i	$-0.535485\pi$
$101$	−2.23607			−0.222497			−0.111249	+	0.993793i	$0.535485\pi$
$102$	−0.236068	+	0.408882i	−0.0233742	+	0.0404853i
$103$	1.35410	−	2.34537i	0.133424	−	0.231097i	−0.791571	−	0.611078i	$-0.790736\pi$
$103$	1.35410	−	2.34537i	0.133424	−	0.231097i	0.924994	+	0.379981i	$0.124070\pi$
$104$	5.05291	−	8.75190i	0.495479	−	0.858195i
$105$	−2.55834	−	4.43117i	−0.249668	−	0.432438i
$106$	−1.00155	+	1.73474i	−0.0972793	+	0.168493i
$107$	3.73607	+	6.47106i	0.361179	+	0.625581i	0.988155	−	0.153458i	$-0.0490409\pi$
$107$	3.73607	+	6.47106i	0.361179	+	0.625581i	−0.626976	+	0.779039i	$0.715708\pi$
$108$	3.24109			0.311874
$109$	−14.7082			−1.40879			−0.704395	−	0.709808i	$-0.748782\pi$
$109$	−14.7082			−1.40879			−0.704395	+	0.709808i	$0.748782\pi$
$110$	1.81182	+	3.13817i	0.172751	+	0.299213i
$111$	−4.85410	+	8.40755i	−0.460731	+	0.798009i
$112$	1.57295	+	2.72443i	0.148630	+	0.257434i
$113$	7.11803	−	12.3288i	0.669608	−	1.15980i	−0.308405	−	0.951255i	$-0.599795\pi$
$113$	7.11803	−	12.3288i	0.669608	−	1.15980i	0.978014	−	0.208541i	$-0.0668713\pi$
$114$	−0.437016	+	0.756934i	−0.0409303	+	0.0708934i
$115$	7.67501	−	13.2935i	0.715698	−	1.23963i
$116$	6.86474			0.637375
$117$	−7.67501	−	13.2935i	−0.709555	−	1.22899i
$118$	1.13525	+	1.96632i	0.104509	+	0.181014i
$119$	0.270091	−	0.467811i	0.0247592	−	0.0428842i
$120$	7.53244			0.687614
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	1.69936			0.153852
$123$	17.0981			1.54168
$124$		0			0
$125$	11.1803			1.00000
$126$	−0.854102			−0.0760895
$127$	−4.74342	−	8.21584i	−0.420910	−	0.729038i	0.575119	−	0.818070i	$-0.304956\pi$
$127$	−4.74342	−	8.21584i	−0.420910	−	0.729038i	−0.996029	+	0.0890323i	$0.971623\pi$
$128$	−10.0902			−0.891853
$129$	0.236068	−	0.408882i	0.0207846	−	0.0360000i
$130$	2.93159	+	5.07767i	0.257118	+	0.445341i
$131$	9.70820	+	16.8151i	0.848210	+	1.46914i	0.882804	+	0.469741i	$0.155653\pi$
$131$	9.70820	+	16.8151i	0.848210	+	1.46914i	−0.0345946	+	0.999401i	$0.511014\pi$
$132$	−18.0000			−1.56670
$133$	0.500000	−	0.866025i	0.0433555	−	0.0750939i
$134$	−1.14590	+	1.98475i	−0.0989905	+	0.171457i
$135$	−1.95440	+	3.38511i	−0.168208	+	0.291344i
$136$	0.397610	+	0.688681i	0.0340948	+	0.0590539i
$137$	−3.43237	+	5.94504i	−0.293247	+	0.507919i	−0.974576	−	0.224059i	$-0.928069\pi$
$137$	−3.43237	+	5.94504i	−0.293247	+	0.507919i	0.681329	+	0.731978i	$0.261403\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	1.00155			0.0849505			0.0424752	−	0.999098i	$-0.486476\pi$
$139$	1.00155			0.0849505			0.0424752	+	0.999098i	$0.486476\pi$
$140$	−4.14590			−0.350392
$141$	−4.24264	−	7.34847i	−0.357295	−	0.618853i
$142$	−1.42705	+	2.47172i	−0.119755	+	0.207423i
$143$	−14.5623	−	25.2227i	−1.21776	−	2.10922i
$144$	−3.51722	+	6.09201i	−0.293102	+	0.507667i
$145$	−4.13948	+	7.16978i	−0.343765	+	0.595418i
$146$	−0.810272	+	1.40343i	−0.0670586	+	0.116149i
$147$	−13.7295			−1.13239
$148$	3.93314	+	6.81241i	0.323302	+	0.559976i
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	−0.998305	−	0.0582028i	$-0.981463\pi$
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	0.448747	−	0.893659i	$-0.351870\pi$
$150$		0			0
$151$	3.03476			0.246965			0.123483	−	0.992347i	$-0.460594\pi$
$151$	3.03476			0.246965			0.123483	+	0.992347i	$0.460594\pi$
$152$	0.736068	+	1.27491i	0.0597030	+	0.103409i
$153$	1.20788			0.0976515
$154$	−1.62054			−0.130587
$155$		0			0
$156$	−29.1246			−2.33184
$157$	−4.70820			−0.375756			−0.187878	−	0.982192i	$-0.560161\pi$
$157$	−4.70820			−0.375756			−0.187878	+	0.982192i	$0.560161\pi$
$158$	2.12132	+	3.67423i	0.168763	+	0.292306i
$159$	12.0000			0.951662
$160$	4.63525	−	8.02850i	0.366449	−	0.634708i
$161$	3.43237	+	5.94504i	0.270509	+	0.468535i
$162$	2.04508	+	3.54219i	0.160677	+	0.278301i
$163$	−12.4164			−0.972528			−0.486264	−	0.873812i	$-0.661641\pi$
$163$	−12.4164			−0.972528			−0.486264	+	0.873812i	$0.661641\pi$
$164$	6.92705	−	11.9980i	0.540912	−	0.936887i
$165$	10.8541	−	18.7999i	0.844991	−	1.46357i
$166$	−0.603941	+	1.04606i	−0.0468749	+	0.0811898i
$167$	3.70246	+	6.41285i	0.286505	+	0.496241i	0.972973	−	0.230919i	$-0.0741732\pi$
$167$	3.70246	+	6.41285i	0.286505	+	0.496241i	−0.686468	+	0.727160i	$0.740840\pi$
$168$	−1.68430	+	2.91730i	−0.129947	+	0.225075i
$169$	−17.0623	−	29.5528i	−1.31249	−	2.27329i
$170$	−0.461370			−0.0353855
$171$	2.23607			0.170996
$172$	−0.191279	−	0.331306i	−0.0145849	−	0.0252618i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	1.61803	+	2.80252i	0.122663	+	0.212458i
$175$		0			0
$176$	−6.67346	+	11.5588i	−0.503031	+	0.871275i
$177$	6.80098	−	11.7796i	0.511193	−	0.885412i
$178$	−2.23954			−0.167860
$179$	−8.21519	−	14.2291i	−0.614032	−	1.06353i	−0.990553	−	0.137127i	$-0.956213\pi$
$179$	−8.21519	−	14.2291i	−0.614032	−	1.06353i	0.376521	−	0.926408i	$-0.377120\pi$
$180$	−4.63525	−	8.02850i	−0.345492	−	0.598409i
$181$	−9.08922	+	15.7430i	−0.675597	+	1.17017i	0.300698	+	0.953720i	$0.402781\pi$
$181$	−9.08922	+	15.7430i	−0.675597	+	1.17017i	−0.976294	+	0.216448i	$0.930553\pi$
$182$	−2.62210			−0.194363
$183$	−5.09017	−	8.81643i	−0.376276	−	0.651729i
$184$	−10.1058			−0.745011
$185$	−9.48683			−0.697486
$186$		0			0
$187$	2.29180			0.167593
$188$	−6.87539			−0.501439
$189$	−0.874032	−	1.51387i	−0.0635765	−	0.110118i
$190$	−0.854102			−0.0619631
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	0.484805	+	0.874622i	$0.338891\pi$
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	−0.999848	+	0.0174580i	$0.994443\pi$
$192$	5.38676	+	9.33015i	0.388756	+	0.673345i
$193$	3.64590	+	6.31488i	0.262437	+	0.454555i	0.966889	−	0.255197i	$-0.0821403\pi$
$193$	3.64590	+	6.31488i	0.262437	+	0.454555i	−0.704452	+	0.709752i	$0.748807\pi$
$194$	−2.67376			−0.191965
$195$	17.5623	−	30.4188i	1.25766	−	2.17834i
$196$	−5.56231	+	9.63420i	−0.397308	+	0.688157i
$197$	3.70246	−	6.41285i	0.263789	−	0.456896i	−0.703456	−	0.710738i	$-0.748361\pi$
$197$	3.70246	−	6.41285i	0.263789	−	0.456896i	0.967246	+	0.253842i	$0.0816943\pi$
$198$	−1.81182	−	3.13817i	−0.128761	−	0.223020i
$199$	7.36551	−	12.7574i	0.522127	−	0.904351i	−0.477541	−	0.878609i	$-0.658472\pi$
$199$	7.36551	−	12.7574i	0.522127	−	0.904351i	0.999669	−	0.0257418i	$-0.00819477\pi$
$200$		0			0
$201$	13.7295			0.968402
$202$	−0.854102			−0.0600944
$203$	−1.85123	−	3.20642i	−0.129931	−	0.225047i
$204$	1.14590	−	1.98475i	0.0802289	−	0.138961i
$205$	8.35410	+	14.4697i	0.583476	+	1.01061i
$206$	0.517221	−	0.895853i	0.0360365	−	0.0624170i
$207$	−7.67501	+	13.2935i	−0.533450	+	0.923963i
$208$	−10.7979	+	18.7025i	−0.748698	+	1.29678i
$209$	4.24264			0.293470
$210$	−0.977198	−	1.69256i	−0.0674330	−	0.116797i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	4.86163	−	8.42060i	0.333898	−	0.578329i
$213$	17.0981			1.17154
$214$	1.42705	+	2.47172i	0.0975512	+	0.168964i
$215$	0.461370			0.0314652
$216$	2.57339			0.175097
$217$		0			0
$218$	−5.61803			−0.380501
$219$	9.70820			0.656020
$220$	−8.79478	−	15.2330i	−0.592944	−	1.02701i
$221$	3.70820			0.249441
$222$	−1.85410	+	3.21140i	−0.124439	+	0.215535i
$223$	10.9010	+	18.8812i	0.729988	+	1.26438i	0.956888	+	0.290458i	$0.0938077\pi$
$223$	10.9010	+	18.8812i	0.729988	+	1.26438i	−0.226900	+	0.973918i	$0.572859\pi$
$224$	2.07295	+	3.59045i	0.138505	+	0.239897i
$225$		0			0
$226$	2.71885	−	4.70918i	0.180855	−	0.313250i
$227$	−7.85410	+	13.6037i	−0.521295	+	0.902910i	0.478398	+	0.878143i	$0.341218\pi$
$227$	−7.85410	+	13.6037i	−0.521295	+	0.902910i	−0.999693	+	0.0247665i	$0.992116\pi$
$228$	2.12132	−	3.67423i	0.140488	−	0.243332i
$229$	−2.12132	−	3.67423i	−0.140181	−	0.242800i	0.787384	−	0.616463i	$-0.211435\pi$
$229$	−2.12132	−	3.67423i	−0.140181	−	0.242800i	−0.927565	+	0.373663i	$0.878102\pi$
$230$	2.93159	−	5.07767i	0.193303	−	0.334811i
$231$	4.85410	+	8.40755i	0.319376	+	0.553176i
$232$	5.45052			0.357844
$233$	−4.52786			−0.296630			−0.148315	−	0.988940i	$-0.547385\pi$
$233$	−4.52786			−0.296630			−0.148315	+	0.988940i	$0.547385\pi$
$234$	−2.93159	−	5.07767i	−0.191644	−	0.331937i
$235$	4.14590	−	7.18091i	0.270449	−	0.468431i
$236$	−5.51064	−	9.54471i	−0.358712	−	0.621308i
$237$	12.7082	−	22.0113i	0.825487	−	1.42978i
$238$	0.103165	−	0.178688i	0.00668723	−	0.0115826i
$239$	8.17578	−	14.1609i	0.528848	−	0.915991i	−0.470587	−	0.882354i	$-0.655958\pi$
$239$	8.17578	−	14.1609i	0.528848	−	0.915991i	0.999434	−	0.0336370i	$-0.0107090\pi$
$240$	−16.0965			−1.03903
$241$	−7.36551	−	12.7574i	−0.474454	−	0.821779i	0.525118	−	0.851030i	$-0.324021\pi$
$241$	−7.36551	−	12.7574i	−0.474454	−	0.821779i	−0.999572	+	0.0292505i	$0.990688\pi$
$242$	−1.33688	−	2.31555i	−0.0859380	−	0.148849i
$243$	9.62940	−	16.6786i	0.617727	−	1.06993i
$244$	−8.24885			−0.528078
$245$	−6.70820	−	11.6190i	−0.428571	−	0.742307i
$246$	6.53089			0.416394
$247$	6.86474			0.436793
$248$		0			0
$249$	7.23607			0.458567
$250$	4.27051			0.270091
$251$	11.8782	+	20.5737i	0.749748	+	1.29860i	0.947943	+	0.318439i	$0.103159\pi$
$251$	11.8782	+	20.5737i	0.749748	+	1.29860i	−0.198195	+	0.980163i	$0.563508\pi$
$252$	4.14590			0.261167
$253$	−14.5623	+	25.2227i	−0.915524	+	1.58573i
$254$	−1.81182	−	3.13817i	−0.113684	−	0.196906i
$255$	1.38197	+	2.39364i	0.0865421	+	0.149895i
$256$	5.56231			0.347644
$257$	−11.9721	+	20.7363i	−0.746801	+	1.29350i	0.202547	+	0.979273i	$0.435078\pi$
$257$	−11.9721	+	20.7363i	−0.746801	+	1.29350i	−0.949348	+	0.314225i	$0.898255\pi$
$258$	0.0901699	−	0.156179i	0.00561374	−	0.00972328i
$259$	2.12132	−	3.67423i	0.131812	−	0.228306i
$260$	−14.2302	−	24.6475i	−0.882523	−	1.52857i
$261$	4.13948	−	7.16978i	0.256227	−	0.443798i
$262$	3.70820	+	6.42280i	0.229094	+	0.396802i
$263$	2.70091			0.166545			0.0832725	−	0.996527i	$-0.473463\pi$
$263$	2.70091			0.166545			0.0832725	+	0.996527i	$0.473463\pi$
$264$	−14.2918			−0.879599
$265$	5.86319	+	10.1553i	0.360173	+	0.623837i
$266$	0.190983	−	0.330792i	0.0117099	−	0.0202822i
$267$	6.70820	+	11.6190i	0.410535	+	0.711068i
$268$	5.56231	−	9.63420i	0.339772	−	0.588502i
$269$	−7.40492	+	12.8257i	−0.451486	+	0.781996i	−0.998479	−	0.0551409i	$-0.982439\pi$
$269$	−7.40492	+	12.8257i	−0.451486	+	0.781996i	0.546993	+	0.837137i	$0.315773\pi$
$270$	−0.746512	+	1.29300i	−0.0454313	+	0.0786893i
$271$	−28.0779			−1.70561			−0.852807	−	0.522227i	$-0.825101\pi$
$271$	−28.0779			−1.70561			−0.852807	+	0.522227i	$0.825101\pi$
$272$	−0.849678	−	1.47169i	−0.0515193	−	0.0892340i
$273$	7.85410	+	13.6037i	0.475352	+	0.823334i
$274$	−1.31105	+	2.27080i	−0.0792033	+	0.137184i
$275$		0			0
$276$	14.5623	+	25.2227i	0.876548	+	1.51823i
$277$	19.5927			1.17721			0.588604	−	0.808421i	$-0.299678\pi$
$277$	19.5927			1.17721			0.588604	+	0.808421i	$0.299678\pi$
$278$	0.382559			0.0229443
$279$		0			0
$280$	−3.29180			−0.196722
$281$	−31.3607			−1.87082			−0.935411	−	0.353563i	$-0.884970\pi$
$281$	−31.3607			−1.87082			−0.935411	+	0.353563i	$0.884970\pi$
$282$	−1.62054	−	2.80687i	−0.0965020	−	0.167146i
$283$	24.0000			1.42665			0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000			1.42665			0.713326	+	0.700832i	$0.247188\pi$
$284$	6.92705	−	11.9980i	0.411045	−	0.711951i
$285$	2.55834	+	4.43117i	0.151543	+	0.262480i
$286$	−5.56231	−	9.63420i	−0.328906	−	0.569682i
$287$	−7.47214			−0.441066
$288$	−4.63525	+	8.02850i	−0.273135	+	0.473084i
$289$	8.35410	−	14.4697i	0.491418	−	0.851161i
$290$	−1.58114	+	2.73861i	−0.0928477	+	0.160817i
$291$	8.00886	+	13.8718i	0.469488	+	0.813176i
$292$	3.93314	−	6.81241i	0.230170	−	0.398666i
$293$	7.85410	+	13.6037i	0.458842	+	0.794737i	0.998900	−	0.0468906i	$-0.0149312\pi$
$293$	7.85410	+	13.6037i	0.458842	+	0.794737i	−0.540058	+	0.841627i	$0.681598\pi$
$294$	−5.24419			−0.305848
$295$	13.2918			0.773878
$296$	3.12287	+	5.40897i	0.181513	+	0.314390i
$297$	3.70820	−	6.42280i	0.215172	−	0.372689i
$298$	−2.56231	−	4.43804i	−0.148430	−	0.257089i
$299$	−23.5623	+	40.8111i	−1.36264	+	2.36017i
$300$		0			0
$301$	−0.103165	+	0.178688i	−0.00594636	+	0.0102994i
$302$	1.15917			0.0667030
$303$	2.55834	+	4.43117i	0.146973	+	0.254564i
$304$	−1.57295	−	2.72443i	−0.0902148	−	0.156257i
$305$	4.97410	−	8.61540i	0.284816	−	0.493316i
$306$	0.461370			0.0263748
$307$	8.06231	+	13.9643i	0.460140	+	0.796986i	0.998968	−	0.0454301i	$-0.0144658\pi$
$307$	8.06231	+	13.9643i	0.460140	+	0.796986i	−0.538827	+	0.842416i	$0.681133\pi$
$308$	7.86629			0.448223
$309$	−6.19704			−0.352537
$310$		0			0
$311$	16.5279			0.937209			0.468605	−	0.883408i	$-0.344757\pi$
$311$	16.5279			0.937209			0.468605	+	0.883408i	$0.344757\pi$
$312$	−23.1246			−1.30917
$313$	10.5034	+	18.1925i	0.593689	+	1.02830i	0.993730	+	0.111803i	$0.0356625\pi$
$313$	10.5034	+	18.1925i	0.593689	+	1.02830i	−0.400041	+	0.916497i	$0.631004\pi$
$314$	−1.79837			−0.101488
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	−10.2971	−	17.8351i	−0.579257	−	1.00330i
$317$	−10.8820	−	18.8481i	−0.611192	−	1.05862i	−0.991040	−	0.133567i	$-0.957357\pi$
$317$	−10.8820	−	18.8481i	−0.611192	−	1.05862i	0.379848	−	0.925049i	$-0.375976\pi$
$318$	4.58359			0.257035
$319$	7.85410	−	13.6037i	0.439745	−	0.761661i
$320$	−5.26393	+	9.11740i	−0.294263	+	0.509678i
$321$	8.54904	−	14.8074i	0.477161	−	0.826467i
$322$	1.31105	+	2.27080i	0.0730619	+	0.126547i
$323$	−0.270091	+	0.467811i	−0.0150283	+	0.0260297i
$324$	−9.92705	−	17.1942i	−0.551503	−	0.955231i
$325$		0			0
$326$	−4.74265			−0.262671
$327$	16.8280	+	29.1469i	0.930590	+	1.61183i
$328$	5.50000	−	9.52628i	0.303687	−	0.526001i
$329$	1.85410	+	3.21140i	0.102220	+	0.177050i
$330$	4.14590	−	7.18091i	0.228224	−	0.395296i
$331$	12.8160	−	22.1980i	0.704433	−	1.22011i	−0.262463	−	0.964942i	$-0.584535\pi$
$331$	12.8160	−	22.1980i	0.704433	−	1.22011i	0.966896	−	0.255172i	$-0.0821320\pi$
$332$	2.93159	−	5.07767i	0.160892	−	0.278673i
$333$	9.48683			0.519875
$334$	1.41421	+	2.44949i	0.0773823	+	0.134030i
$335$	6.70820	+	11.6190i	0.366508	+	0.634811i
$336$	3.59929	−	6.23416i	0.196358	−	0.340101i
$337$	−5.86319			−0.319388			−0.159694	−	0.987167i	$-0.551051\pi$
$337$	−5.86319			−0.319388			−0.159694	+	0.987167i	$0.551051\pi$
$338$	−6.51722	−	11.2882i	−0.354490	−	0.613995i
$339$	−32.5756			−1.76926
$340$	2.23954			0.121456
$341$		0			0
$342$	0.854102			0.0461845
$343$	13.0000			0.701934
$344$	−0.151874	−	0.263053i	−0.00818848	−	0.0141829i
$345$	−35.1246			−1.89105
$346$	−3.43769	+	5.95426i	−0.184812	+	0.320103i
$347$	−12.9192	−	22.3767i	−0.693539	−	1.20124i	−0.970671	−	0.240413i	$-0.922717\pi$
$347$	−12.9192	−	22.3767i	−0.693539	−	1.20124i	0.277132	−	0.960832i	$-0.410616\pi$
$348$	−7.85410	−	13.6037i	−0.421024	−	0.729235i
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	6.00000	−	10.3923i	0.320256	−	0.554700i
$352$	−8.79478	+	15.2330i	−0.468763	+	0.811922i
$353$	−7.94510	−	13.7613i	−0.422875	−	0.732441i	0.573344	−	0.819315i	$-0.305646\pi$
$353$	−7.94510	−	13.7613i	−0.422875	−	0.732441i	−0.996219	+	0.0868735i	$0.972312\pi$
$354$	2.59774	−	4.49942i	0.138068	−	0.239142i
$355$	8.35410	+	14.4697i	0.443390	+	0.767973i
$356$	10.8709			0.576159
$357$	−1.23607			−0.0654197
$358$	−3.13792	−	5.43504i	−0.165844	−	0.287251i
$359$	−4.88197	+	8.45581i	−0.257660	+	0.446281i	−0.965615	−	0.259977i	$-0.916285\pi$
$359$	−4.88197	+	8.45581i	−0.257660	+	0.446281i	0.707954	+	0.706258i	$0.249618\pi$
$360$	−3.68034	−	6.37454i	−0.193971	−	0.335968i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−3.47177	+	6.01329i	−0.182472	+	0.316051i
$363$	−8.00886	+	13.8718i	−0.420356	+	0.728078i
$364$	12.7279			0.667124
$365$	4.74342	+	8.21584i	0.248282	+	0.430037i
$366$	−1.94427	−	3.36758i	−0.101629	−	0.176026i
$367$	6.15763	−	10.6653i	0.321426	−	0.556726i	−0.659357	−	0.751830i	$-0.729171\pi$
$367$	6.15763	−	10.6653i	0.321426	−	0.556726i	0.980782	+	0.195105i	$0.0625046\pi$
$368$	21.5958			1.12576
$369$	−8.35410	−	14.4697i	−0.434897	−	0.753264i
$370$	−3.62365			−0.188384
$371$	−5.24419			−0.272265
$372$		0			0
$373$	−22.7082			−1.17579			−0.587893	−	0.808939i	$-0.700042\pi$
$373$	−22.7082			−1.17579			−0.587893	+	0.808939i	$0.700042\pi$
$374$	0.875388			0.0452652
$375$	−12.7917	−	22.1558i	−0.660560	−	1.14412i
$376$	−5.45898			−0.281525
$377$	12.7082	−	22.0113i	0.654506	−	1.13364i
$378$	−0.333851	−	0.578246i	−0.0171714	−	0.0297418i
$379$	9.70820	+	16.8151i	0.498677	+	0.863734i	0.999999	−	0.00152707i	$-0.000486080\pi$
$379$	9.70820	+	16.8151i	0.498677	+	0.863734i	−0.501322	+	0.865261i	$0.667153\pi$
$380$	4.14590			0.212680
$381$	−10.8541	+	18.7999i	−0.556072	+	0.963146i
$382$	−2.71885	+	4.70918i	−0.139108	+	0.240943i
$383$	9.52624	−	16.4999i	0.486768	−	0.843107i	−0.513116	−	0.858319i	$-0.671509\pi$
$383$	9.52624	−	16.4999i	0.486768	−	0.843107i	0.999884	+	0.0152121i	$0.00484236\pi$
$384$	11.5444	+	19.9955i	0.589122	+	1.02039i
$385$	−4.74342	+	8.21584i	−0.241747	+	0.418718i
$386$	1.39261	+	2.41207i	0.0708819	+	0.122771i
$387$	−0.461370			−0.0234528
$388$	12.9787			0.658894
$389$	−16.8918	−	29.2574i	−0.856446	−	1.48341i	−0.875297	−	0.483585i	$-0.839334\pi$
$389$	−16.8918	−	29.2574i	−0.856446	−	1.48341i	0.0188514	−	0.999822i	$-0.493999\pi$
$390$	6.70820	−	11.6190i	0.339683	−	0.588348i
$391$	−1.85410	−	3.21140i	−0.0937660	−	0.162407i
$392$	−4.41641	+	7.64944i	−0.223062	+	0.386355i
$393$	22.2148	−	38.4771i	1.12059	−	1.94091i
$394$	1.41421	−	2.44949i	0.0712470	−	0.123404i
$395$	24.8369			1.24968
$396$	8.79478	+	15.2330i	0.441954	+	0.765487i
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	0.849362	−	0.527811i	$-0.176987\pi$
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	−0.881779	+	0.471664i	$0.843654\pi$
$398$	2.81338	−	4.87291i	0.141022	−	0.244257i
$399$	−2.28825			−0.114556
$400$		0			0
$401$	−3.70246			−0.184892			−0.0924460	−	0.995718i	$-0.529469\pi$
$401$	−3.70246			−0.184892			−0.0924460	+	0.995718i	$0.529469\pi$
$402$	5.24419			0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	23.9443			1.18980
$406$	−0.707107	−	1.22474i	−0.0350931	−	0.0607831i
$407$	18.0000			0.892227
$408$	0.909830	−	1.57587i	0.0450433	−	0.0780173i
$409$	8.67656	+	15.0282i	0.429028	+	0.743099i	0.996787	−	0.0800961i	$-0.0255227\pi$
$409$	8.67656	+	15.0282i	0.429028	+	0.743099i	−0.567759	+	0.823195i	$0.692189\pi$
$410$	3.19098	+	5.52694i	0.157591	+	0.272956i
$411$	15.7082			0.774829
$412$	−2.51064	+	4.34856i	−0.123691	+	0.214238i
$413$	−2.97214	+	5.14789i	−0.146249	+	0.253311i
$414$	−2.93159	+	5.07767i	−0.144080	+	0.249554i
$415$	3.53553	+	6.12372i	0.173553	+	0.300602i
$416$	−14.2302	+	24.6475i	−0.697695	+	1.20844i
$417$	−1.14590	−	1.98475i	−0.0561149	−	0.0971938i
$418$	1.62054			0.0792634
$419$	−18.5967			−0.908511			−0.454255	−	0.890872i	$-0.650095\pi$
$419$	−18.5967			−0.908511			−0.454255	+	0.890872i	$0.650095\pi$
$420$	4.74342	+	8.21584i	0.231455	+	0.400892i
$421$	0.208204	−	0.360620i	0.0101472	−	0.0175755i	−0.860907	−	0.508762i	$-0.830103\pi$
$421$	0.208204	−	0.360620i	0.0101472	−	0.0175755i	0.871054	+	0.491186i	$0.163437\pi$
$422$	0.954915	+	1.65396i	0.0464845	+	0.0805136i
$423$	−4.14590	+	7.18091i	−0.201580	+	0.349148i
$424$	3.86008	−	6.68586i	0.187462	−	0.324694i
$425$		0			0
$426$	6.53089			0.316422
$427$	2.22449	+	3.85292i	0.107650	+	0.186456i
$428$	−6.92705	−	11.9980i	−0.334832	−	0.579945i
$429$	−33.3221	+	57.7156i	−1.60881	+	2.78654i
$430$	0.176228			0.00849845
$431$	0.0557281	+	0.0965239i	0.00268433	+	0.00464939i	0.867364	−	0.497674i	$-0.165812\pi$
$431$	0.0557281	+	0.0965239i	0.00268433	+	0.00464939i	−0.864680	+	0.502323i	$0.832479\pi$
$432$	−5.49923			−0.264582
$433$	21.5958			1.03783			0.518913	−	0.854827i	$-0.326337\pi$
$433$	21.5958			1.03783			0.518913	+	0.854827i	$0.326337\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	27.2705			1.30602
$437$	−3.43237	−	5.94504i	−0.164192	−	0.284390i
$438$	3.70820			0.177185
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	−6.98295	−	12.0948i	−0.332899	−	0.576598i
$441$	6.70820	+	11.6190i	0.319438	+	0.553283i
$442$	1.41641			0.0673717
$443$	−11.9721	+	20.7363i	−0.568813	+	0.985214i	0.427870	+	0.903840i	$0.359264\pi$
$443$	−11.9721	+	20.7363i	−0.568813	+	0.985214i	−0.996684	+	0.0813735i	$0.974069\pi$
$444$	9.00000	−	15.5885i	0.427121	−	0.739795i
$445$	−6.55524	+	11.3540i	−0.310748	+	0.538232i
$446$	4.16383	+	7.21196i	0.197163	+	0.341496i
$447$	−15.3500	+	26.5870i	−0.726031	+	1.25752i
$448$	−2.35410	−	4.07742i	−0.111221	−	0.192640i
$449$	−42.1900			−1.99107			−0.995534	−	0.0944042i	$-0.969905\pi$
$449$	−42.1900			−1.99107			−0.995534	+	0.0944042i	$0.969905\pi$
$450$		0			0
$451$	−15.8508	−	27.4544i	−0.746385	−	1.29278i
$452$	−13.1976	+	22.8588i	−0.620761	+	1.07519i
$453$	−3.47214	−	6.01392i	−0.163135	−	0.282558i
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$	−7.67501	+	13.2935i	−0.359810	+	0.623209i
$456$	1.68430	−	2.91730i	0.0788748	−	0.136615i
$457$	11.3137			0.529233			0.264616	−	0.964354i	$-0.414755\pi$
$457$	11.3137			0.529233			0.264616	+	0.964354i	$0.414755\pi$
$458$	−0.810272	−	1.40343i	−0.0378615	−	0.0655781i
$459$	0.472136	+	0.817763i	0.0220374	+	0.0381699i
$460$	−14.2302	+	24.6475i	−0.663489	+	1.14920i
$461$	−39.1065			−1.82137			−0.910686	−	0.413100i	$-0.864446\pi$
$461$	−39.1065			−1.82137			−0.910686	+	0.413100i	$0.864446\pi$
$462$	1.85410	+	3.21140i	0.0862606	+	0.149408i
$463$	15.1437			0.703787			0.351893	−	0.936040i	$-0.385538\pi$
$463$	15.1437			0.703787			0.351893	+	0.936040i	$0.385538\pi$
$464$	−11.6476			−0.540724
$465$		0			0
$466$	−1.72949			−0.0801171
$467$	15.6525			0.724310			0.362155	−	0.932118i	$-0.382041\pi$
$467$	15.6525			0.724310			0.362155	+	0.932118i	$0.382041\pi$
$468$	14.2302	+	24.6475i	0.657794	+	1.13933i
$469$	−6.00000			−0.277054
$470$	1.58359	−	2.74286i	0.0730457	−	0.126519i
$471$	5.38676	+	9.33015i	0.248209	+	0.429911i
$472$	−4.37539	−	7.57839i	−0.201394	−	0.348824i
$473$	−0.875388			−0.0402504
$474$	4.85410	−	8.40755i	0.222956	−	0.386172i
$475$		0			0
$476$	−0.500776	+	0.867369i	−0.0229530	+	0.0397558i
$477$	−5.86319	−	10.1553i	−0.268457	−	0.464981i
$478$	3.12287	−	5.40897i	0.142837	−	0.247401i
$479$	−12.7361	−	22.0595i	−0.581926	−	1.00793i	−0.995251	−	0.0973416i	$-0.968966\pi$
$479$	−12.7361	−	22.0595i	−0.581926	−	1.00793i	0.413325	−	0.910583i	$-0.364367\pi$
$480$	−21.2132			−0.968246
$481$	29.1246			1.32797
$482$	−2.81338	−	4.87291i	−0.128146	−	0.221955i
$483$	7.85410	−	13.6037i	0.357374	−	0.618990i
$484$	6.48936	+	11.2399i	0.294971	+	0.510904i
$485$	−7.82624	+	13.5554i	−0.355371	+	0.615521i
$486$	3.67811	−	6.37066i	0.166842	−	0.288979i
$487$	−9.29555	+	16.1004i	−0.421222	+	0.729577i	−0.996059	−	0.0886901i	$-0.971732\pi$
$487$	−9.29555	+	16.1004i	−0.421222	+	0.729577i	0.574838	+	0.818268i	$0.305065\pi$
$488$	−6.54949			−0.296482
$489$	14.2059	+	24.6053i	0.642413	+	1.11269i
$490$	−2.56231	−	4.43804i	−0.115753	−	0.200490i
$491$	4.78282	−	8.28409i	0.215846	−	0.373856i	−0.737688	−	0.675142i	$-0.764083\pi$
$491$	4.78282	−	8.28409i	0.215846	−	0.373856i	0.953534	+	0.301286i	$0.0974158\pi$
$492$	−31.7016			−1.42922
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	2.62210			0.117974
$495$	−21.2132			−0.953463
$496$		0			0
$497$	−7.47214			−0.335171
$498$	2.76393			0.123855
$499$	−9.19239	−	15.9217i	−0.411508	−	0.712752i	0.583547	−	0.812079i	$-0.301664\pi$
$499$	−9.19239	−	15.9217i	−0.411508	−	0.712752i	−0.995055	+	0.0993269i	$0.968331\pi$
$500$	−20.7295			−0.927051
$501$	8.47214	−	14.6742i	0.378507	−	0.655594i
$502$	4.53709	+	7.85846i	0.202500	+	0.350740i
$503$	−1.44427	−	2.50155i	−0.0643969	−	0.111539i	0.832029	−	0.554732i	$-0.187179\pi$
$503$	−1.44427	−	2.50155i	−0.0643969	−	0.111539i	−0.896426	+	0.443193i	$0.853846\pi$
$504$	3.29180			0.146628
$505$	−2.50000	+	4.33013i	−0.111249	+	0.192688i
$506$	−5.56231	+	9.63420i	−0.247275	+	0.428292i
$507$	−39.0427	+	67.6240i	−1.73395	+	3.00329i
$508$	8.79478	+	15.2330i	0.390205	+	0.675855i
$509$	2.39141	−	4.14205i	0.105997	−	0.183593i	−0.808148	−	0.588980i	$-0.799530\pi$
$509$	2.39141	−	4.14205i	0.105997	−	0.183593i	0.914145	+	0.405387i	$0.132863\pi$
$510$	0.527864	+	0.914287i	0.0233742	+	0.0404853i
$511$	−4.24264			−0.187683
$512$	22.3050			0.985749
$513$	0.874032	+	1.51387i	0.0385895	+	0.0668389i
$514$	−4.57295	+	7.92058i	−0.201704	+	0.349362i
$515$	−3.02786	−	5.24441i	−0.133424	−	0.231097i
$516$	−0.437694	+	0.758108i	−0.0192684	+	0.0333739i
$517$	−7.86629	+	13.6248i	−0.345959	+	0.599219i
$518$	0.810272	−	1.40343i	0.0356013	−	0.0616633i
$519$	41.1884			1.80797
$520$	−11.2987	−	19.5698i	−0.495479	−	0.858195i
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	0.680835	−	0.732437i	$-0.261617\pi$
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	−0.974726	+	0.223402i	$0.928284\pi$
$522$	1.58114	−	2.73861i	0.0692046	−	0.119866i
$523$	29.0795			1.27156			0.635779	−	0.771871i	$-0.280679\pi$
$523$	29.0795			1.27156			0.635779	+	0.771871i	$0.280679\pi$
$524$	−18.0000	−	31.1769i	−0.786334	−	1.36197i
$525$		0			0
$526$	1.03165			0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	24.1246			1.04890
$530$	2.23954	+	3.87899i	0.0972793	+	0.168493i
$531$	−13.2918			−0.576815
$532$	−0.927051	+	1.60570i	−0.0401928	+	0.0696159i
$533$	−25.6471	−	44.4221i	−1.11090	−	1.92414i
$534$	2.56231	+	4.43804i	0.110882	+	0.192053i
$535$	16.7082			0.722359
$536$	4.41641	−	7.64944i	0.190760	−	0.330406i
$537$	−18.7984	+	32.5597i	−0.811210	+	1.40506i
$538$	−2.82843	+	4.89898i	−0.121942	+	0.211210i
$539$	12.7279	+	22.0454i	0.548230	+	0.949563i
$540$	3.62365	−	6.27634i	0.155937	−	0.270091i
$541$	13.9164	+	24.1039i	0.598313	+	1.03631i	0.993070	+	0.117523i	$0.0374954\pi$
$541$	13.9164	+	24.1039i	0.598313	+	1.03631i	−0.394757	+	0.918786i	$0.629171\pi$
$542$	−10.7248			−0.460670
$543$	41.5967			1.78509
$544$	−1.11977	−	1.93950i	−0.0480097	−	0.0831552i
$545$	−16.4443	+	28.4823i	−0.704395	+	1.22005i
$546$	3.00000	+	5.19615i	0.128388	+	0.222375i
$547$	12.2082	−	21.1452i	0.521985	−	0.904105i	−0.477688	−	0.878530i	$-0.658525\pi$
$547$	12.2082	−	21.1452i	0.521985	−	0.904105i	0.999673	−	0.0255751i	$-0.00814168\pi$
$548$	6.36396	−	11.0227i	0.271855	−	0.470867i
$549$	−4.97410	+	8.61540i	−0.212289	+	0.367696i
$550$		0			0
$551$	1.85123	+	3.20642i	0.0788650	+	0.136598i
$552$	11.5623	+	20.0265i	0.492124	+	0.852384i
$553$	−5.55369	+	9.61927i	−0.236167	+	0.409053i
$554$	7.48373			0.317953
$555$	10.8541	+	18.7999i	0.460731	+	0.798009i
$556$	−1.85698			−0.0787534
$557$	−23.2951			−0.987046			−0.493523	−	0.869733i	$-0.664291\pi$
$557$	−23.2951			−0.987046			−0.493523	+	0.869733i	$0.664291\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	7.03444			0.297259
$561$	−2.62210	−	4.54160i	−0.110705	−	0.191747i
$562$	−11.9787			−0.505292
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	−0.976133	−	0.217173i	$-0.930316\pi$
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	0.676144	+	0.736770i	$0.263650\pi$
$564$	7.86629	+	13.6248i	0.331230	+	0.573708i
$565$	−15.9164	−	27.5680i	−0.669608	−	1.15980i
$566$	9.16718			0.385325
$567$	−5.35410	+	9.27358i	−0.224851	+	0.389454i
$568$	5.50000	−	9.52628i	0.230775	−	0.399714i
$569$	15.3500	−	26.5870i	0.643506	−	1.11459i	−0.341138	−	0.940013i	$-0.610812\pi$
$569$	15.3500	−	26.5870i	0.643506	−	1.11459i	0.984644	−	0.174572i	$-0.0558543\pi$
$570$	0.977198	+	1.69256i	0.0409303	+	0.0708934i
$571$	−3.43237	+	5.94504i	−0.143640	+	0.248792i	−0.928865	−	0.370419i	$-0.879214\pi$
$571$	−3.43237	+	5.94504i	−0.143640	+	0.248792i	0.785225	+	0.619211i	$0.212547\pi$
$572$	27.0000	+	46.7654i	1.12893	+	1.95536i
$573$	32.5756			1.36087
$574$	−2.85410			−0.119128
$575$		0			0
$576$	5.26393	−	9.11740i	0.219331	−	0.379892i
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	0.988645	+	0.150268i	$0.0480135\pi$
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	−0.364187	+	0.931326i	$0.618653\pi$
$578$	3.19098	−	5.52694i	0.132727	−	0.229891i
$579$	8.34271	−	14.4500i	0.346711	−	0.600521i
$580$	7.67501	−	13.2935i	0.318687	−	0.551983i
$581$	−3.16228			−0.131193
$582$	3.05911	+	5.29854i	0.126804	+	0.219631i
$583$	−11.1246	−	19.2684i	−0.460734	−	0.798015i
$584$	3.12287	−	5.40897i	0.129225	−	0.223825i
$585$	−34.3237			−1.41911
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$	41.1884			1.70003			0.850014	−	0.526760i	$-0.176593\pi$
$587$	41.1884			1.70003			0.850014	+	0.526760i	$0.176593\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	−16.9443			−0.696994
$592$	−6.67346	−	11.5588i	−0.274277	−	0.475062i
$593$	−17.1803			−0.705512			−0.352756	−	0.935715i	$-0.614755\pi$
$593$	−17.1803			−0.705512			−0.352756	+	0.935715i	$0.614755\pi$
$594$	1.41641	−	2.45329i	0.0581159	−	0.100660i
$595$	−0.603941	−	1.04606i	−0.0247592	−	0.0428842i
$596$	12.4377	+	21.5427i	0.509468	+	0.882424i
$597$	−33.7082			−1.37958
$598$	−9.00000	+	15.5885i	−0.368037	+	0.637459i
$599$	−11.9721	+	20.7363i	−0.489168	+	0.847264i	−0.999922	−	0.0124626i	$-0.996033\pi$
$599$	−11.9721	+	20.7363i	−0.489168	+	0.847264i	0.510754	+	0.859727i	$0.329366\pi$
$600$		0			0
$601$	−4.34581	−	7.52716i	−0.177269	−	0.307039i	0.763675	−	0.645601i	$-0.223393\pi$
$601$	−4.34581	−	7.52716i	−0.177269	−	0.307039i	−0.940944	+	0.338562i	$0.890060\pi$
$602$	−0.0394057	+	0.0682527i	−0.00160606	+	0.00278177i
$603$	−6.70820	−	11.6190i	−0.273179	−	0.473160i
$604$	−5.62675			−0.228949
$605$	−15.6525			−0.636364
$606$	0.977198	+	1.69256i	0.0396959	+	0.0687554i
$607$	12.5623	−	21.7586i	0.509888	−	0.883152i	−0.490046	−	0.871697i	$-0.663020\pi$
$607$	12.5623	−	21.7586i	0.509888	−	0.883152i	0.999934	−	0.0114559i	$-0.00364660\pi$
$608$	−2.07295	−	3.59045i	−0.0840692	−	0.145612i
$609$	−4.23607	+	7.33708i	−0.171654	+	0.297314i
$610$	1.89994	−	3.29079i	0.0769262	−	0.133240i
$611$	−12.7279	+	22.0454i	−0.514917	+	0.891862i
$612$	−2.23954			−0.0905279
$613$	18.6792	+	32.3534i	0.754447	+	1.30674i	0.945649	+	0.325189i	$0.105428\pi$
$613$	18.6792	+	32.3534i	0.754447	+	1.30674i	−0.191202	+	0.981551i	$0.561239\pi$
$614$	3.07953	+	5.33390i	0.124280	+	0.215259i
$615$	19.1162	−	33.1103i	0.770841	−	1.33514i
$616$	6.24574			0.251648
$617$	23.5623	+	40.8111i	0.948583	+	1.64299i	0.748414	+	0.663232i	$0.230816\pi$
$617$	23.5623	+	40.8111i	0.948583	+	1.64299i	0.200169	+	0.979761i	$0.435851\pi$
$618$	−2.36706			−0.0952170
$619$	−21.5958			−0.868007			−0.434003	−	0.900911i	$-0.642899\pi$
$619$	−21.5958			−0.868007			−0.434003	+	0.900911i	$0.642899\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	6.31308			0.253132
$623$	−2.93159	−	5.07767i	−0.117452	−	0.203432i
$624$	49.4164			1.97824
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	4.01196	+	6.94891i	0.160350	+	0.277734i
$627$	−4.85410	−	8.40755i	−0.193854	−	0.335765i
$628$	8.72949			0.348345
$629$	−1.14590	+	1.98475i	−0.0456899	+	0.0791373i
$630$	−0.954915	+	1.65396i	−0.0380447	+	0.0658954i
$631$	2.32765	−	4.03161i	0.0926623	−	0.160496i	−0.815968	−	0.578097i	$-0.803796\pi$
$631$	2.32765	−	4.03161i	0.0926623	−	0.160496i	0.908631	+	0.417601i	$0.137129\pi$
$632$	−8.17578	−	14.1609i	−0.325215	−	0.563289i
$633$	5.72061	−	9.90839i	0.227374	−	0.393823i
$634$	−4.15654	−	7.19934i	−0.165077	−	0.285922i
$635$	−21.2132			−0.841820
$636$	−22.2492			−0.882239
$637$	20.5942	+	35.6702i	0.815972	+	1.41331i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	−8.35410	−	14.4697i	−0.330483	−	0.572414i
$640$	−11.2812	+	19.5395i	−0.445927	+	0.772368i
$641$	4.24264	−	7.34847i	0.167574	−	0.290247i	−0.769992	−	0.638053i	$-0.779740\pi$
$641$	4.24264	−	7.34847i	0.167574	−	0.290247i	0.937566	+	0.347806i	$0.113073\pi$
$642$	3.26544	−	5.65591i	0.128877	−	0.223221i
$643$	−23.6290			−0.931836			−0.465918	−	0.884828i	$-0.654276\pi$
$643$	−23.6290			−0.931836			−0.465918	+	0.884828i	$0.654276\pi$
$644$	−6.36396	−	11.0227i	−0.250775	−	0.434355i
$645$	−0.527864	−	0.914287i	−0.0207846	−	0.0360000i
$646$	−0.103165	+	0.178688i	−0.00405899	+	0.00703038i
$647$	19.1313			0.752129			0.376064	−	0.926594i	$-0.377277\pi$
$647$	19.1313			0.752129			0.376064	+	0.926594i	$0.377277\pi$
$648$	−7.88197	−	13.6520i	−0.309633	−	0.536300i
$649$	−25.2194			−0.989948
$650$		0			0
$651$		0			0
$652$	23.0213			0.901583
$653$	−6.65248			−0.260331			−0.130166	−	0.991492i	$-0.541551\pi$
$653$	−6.65248			−0.260331			−0.130166	+	0.991492i	$0.541551\pi$
$654$	6.42772	+	11.1331i	0.251344	+	0.435340i
$655$	43.4164			1.69642
$656$	−11.7533	+	20.3573i	−0.458889	+	0.794819i
$657$	−4.74342	−	8.21584i	−0.185058	−	0.320530i
$658$	0.708204	+	1.22665i	0.0276087	+	0.0478196i
$659$	47.1803			1.83789			0.918943	−	0.394391i	$-0.129045\pi$
$659$	47.1803			1.83789			0.918943	+	0.394391i	$0.129045\pi$
$660$	−20.1246	+	34.8569i	−0.783349	+	1.35680i
$661$	22.9164	−	39.6924i	0.891345	−	1.54385i	0.0530809	−	0.998590i	$-0.483096\pi$
$661$	22.9164	−	39.6924i	0.891345	−	1.54385i	0.838264	−	0.545265i	$-0.183571\pi$
$662$	4.89529	−	8.47889i	0.190261	−	0.329541i
$663$	−4.24264	−	7.34847i	−0.164771	−	0.285391i
$664$	2.32765	−	4.03161i	0.0903304	−	0.156457i
$665$	−1.11803	−	1.93649i	−0.0433555	−	0.0750939i
$666$	3.62365			0.140413
$667$	−25.4164			−0.984127
$668$	−6.86474	−	11.8901i	−0.265605	−	0.460041i
$669$	24.9443	−	43.2047i	0.964401	−	1.67039i
$670$	2.56231	+	4.43804i	0.0989905	+	0.171457i
$671$	−9.43769	+	16.3466i	−0.364338	+	0.631052i
$672$	4.74342	−	8.21584i	0.182981	−	0.316933i
$673$	3.72681	−	6.45503i	0.143658	−	0.248823i	−0.785213	−	0.619225i	$-0.787447\pi$
$673$	3.72681	−	6.45503i	0.143658	−	0.248823i	0.928871	+	0.370402i	$0.120780\pi$
$674$	−2.23954			−0.0862638
$675$		0			0
$676$	31.6353	+	54.7939i	1.21674	+	2.10746i
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	−0.586981	−	0.809601i	$-0.699683\pi$
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	0.994625	+	0.103540i	$0.0330168\pi$
$678$	−12.4428			−0.477862
$679$	−3.50000	−	6.06218i	−0.134318	−	0.232645i
$680$	1.77817			0.0681896
$681$	35.9442			1.37739
$682$		0			0
$683$	−18.8197			−0.720114			−0.360057	−	0.932930i	$-0.617243\pi$
$683$	−18.8197			−0.720114			−0.360057	+	0.932930i	$0.617243\pi$
$684$	−4.14590			−0.158522
$685$	7.67501	+	13.2935i	0.293247	+	0.507919i
$686$	4.96556			0.189586
$687$	−4.85410	+	8.40755i	−0.185196	+	0.320768i
$688$	0.324548	+	0.562134i	0.0123733	+	0.0214312i
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$	−13.4164			−0.510754
$691$	10.7918	−	18.6919i	0.410539	−	0.711075i	−0.584409	−	0.811459i	$-0.698674\pi$
$691$	10.7918	−	18.6919i	0.410539	−	0.711075i	0.994949	+	0.100384i	$0.0320071\pi$
$692$	16.6869	−	28.9026i	0.634341	−	1.09871i
$693$	4.74342	−	8.21584i	0.180187	−	0.312094i
$694$	−4.93470	−	8.54714i	−0.187318	−	0.324445i
$695$	1.11977	−	1.93950i	0.0424752	−	0.0735693i
$696$	−6.23607	−	10.8012i	−0.236378	−	0.409418i
$697$	4.03631			0.152886
$698$	2.29180			0.0867458
$699$	5.18043	+	8.97277i	0.195942	+	0.339381i
$700$		0			0
$701$	−13.8262	−	23.9477i	−0.522210	−	0.904494i	−0.999666	−	0.0258384i	$-0.991774\pi$
$701$	−13.8262	−	23.9477i	−0.522210	−	0.904494i	0.477456	−	0.878655i	$-0.341559\pi$
$702$	2.29180	−	3.96951i	0.0864983	−	0.149819i
$703$	−2.12132	+	3.67423i	−0.0800071	+	0.138576i
$704$	9.98761	−	17.2990i	0.376422	−	0.651982i
$705$	−18.9737			−0.714590
$706$	−3.03476	−	5.25636i	−0.114215	−	0.197826i
$707$	−1.11803	−	1.93649i	−0.0420480	−	0.0728293i
$708$	−12.6097	+	21.8406i	−0.473902	+	0.820822i
$709$	15.7326			0.590849			0.295425	−	0.955366i	$-0.404539\pi$
$709$	15.7326			0.590849			0.295425	+	0.955366i	$0.404539\pi$
$710$	3.19098	+	5.52694i	0.119755	+	0.207423i
$711$	−24.8369			−0.931455
$712$	8.63141			0.323476
$713$		0			0
$714$	−0.472136			−0.0176692
$715$	−65.1246			−2.43552
$716$	15.2318	+	26.3823i	0.569239	+	0.985951i
$717$	−37.4164			−1.39734
$718$	−1.86475	+	3.22983i	−0.0695917	+	0.120536i
$719$	4.55214	+	7.88453i	0.169766	+	0.294043i	0.938338	−	0.345720i	$-0.112365\pi$
$719$	4.55214	+	7.88453i	0.169766	+	0.294043i	−0.768571	+	0.639764i	$0.779032\pi$
$720$	7.86475	+	13.6221i	0.293102	+	0.507667i
$721$	2.70820			0.100859
$722$	3.43769	−	5.95426i	0.127938	−	0.221595i
$723$	−16.8541	+	29.1922i	−0.626811	+	1.08567i
$724$	16.8523	−	29.1891i	0.626312	−	1.08481i
$725$		0			0
$726$	−3.05911	+	5.29854i	−0.113534	+	0.196647i
$727$	1.79180	+	3.10348i	0.0664540	+	0.115102i	0.897338	−	0.441344i	$-0.145498\pi$
$727$	1.79180	+	3.10348i	0.0664540	+	0.115102i	−0.830884	+	0.556446i	$0.812165\pi$
$728$	10.1058			0.374547
$729$	−11.9443			−0.442380
$730$	1.81182	+	3.13817i	0.0670586	+	0.116149i
$731$	0.0557281	−	0.0965239i	0.00206118	−	0.00357006i
$732$	9.43769	+	16.3466i	0.348827	+	0.604186i
$733$	−6.20820	+	10.7529i	−0.229305	+	0.397168i	−0.957602	−	0.288093i	$-0.906979\pi$
$733$	−6.20820	+	10.7529i	−0.229305	+	0.397168i	0.728297	+	0.685261i	$0.240312\pi$
$734$	2.35201	−	4.07379i	0.0868141	−	0.150366i
$735$	−15.3500	+	26.5870i	−0.566194	+	0.980677i
$736$	28.4605			1.04907
$737$	−12.7279	−	22.0454i	−0.468839	−	0.812053i
$738$	−3.19098	−	5.52694i	−0.117462	−	0.203450i
$739$	12.8311	−	22.2241i	0.471999	−	0.817527i	−0.527488	−	0.849563i	$-0.676866\pi$
$739$	12.8311	−	22.2241i	0.471999	−	0.817527i	0.999487	+	0.0320362i	$0.0101992\pi$
$740$	17.5896			0.646605
$741$	−7.85410	−	13.6037i	−0.288528	−	0.499745i
$742$	−2.00310			−0.0735362
$743$	−1.69936			−0.0623433			−0.0311717	−	0.999514i	$-0.509924\pi$
$743$	−1.69936			−0.0623433			−0.0311717	+	0.999514i	$0.509924\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−8.67376			−0.317569
$747$	−3.53553	−	6.12372i	−0.129358	−	0.224055i
$748$	−4.24922			−0.155367
$749$	−3.73607	+	6.47106i	−0.136513	+	0.236447i
$750$	−4.88599	−	8.46278i	−0.178411	−	0.309017i
$751$	−14.7705	−	25.5833i	−0.538984	−	0.933547i	−0.998959	−	0.0456153i	$-0.985475\pi$
$751$	−14.7705	−	25.5833i	−0.538984	−	0.933547i	0.459976	−	0.887932i	$-0.347858\pi$
$752$	11.6656			0.425402
$753$	27.1803	−	47.0777i	0.990507	−	1.71561i
$754$	4.85410	−	8.40755i	0.176776	−	0.306185i
$755$	3.39296	−	5.87678i	0.123483	−	0.213878i
$756$	1.62054	+	2.80687i	0.0589386	+	0.102085i
$757$	9.59000	−	16.6104i	0.348554	−	0.603714i	−0.637438	−	0.770501i	$-0.720006\pi$
$757$	9.59000	−	16.6104i	0.348554	−	0.603714i	0.985993	+	0.166787i	$0.0533393\pi$
$758$	3.70820	+	6.42280i	0.134688	+	0.233287i
$759$	66.6443			2.41903
$760$	3.29180			0.119406
$761$	−1.11977	−	1.93950i	−0.0405916	−	0.0703067i	0.845016	−	0.534741i	$-0.179591\pi$
$761$	−1.11977	−	1.93950i	−0.0405916	−	0.0703067i	−0.885607	+	0.464435i	$0.846258\pi$
$762$	−4.14590	+	7.18091i	−0.150190	+	0.260137i
$763$	−7.35410	−	12.7377i	−0.266236	−	0.461135i
$764$	13.1976	−	22.8588i	0.477471	−	0.827004i
$765$	1.35045	−	2.33905i	0.0488258	−	0.0845687i
$766$	3.63870	−	6.30241i	0.131472	−	0.227715i
$767$	−40.8059			−1.47341
$768$	−6.36396	−	11.0227i	−0.229640	−	0.397748i
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	0.713395	−	0.700762i	$-0.247156\pi$
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	−0.963575	+	0.267438i	$0.913823\pi$
$770$	−1.81182	+	3.13817i	−0.0652936	+	0.113092i
$771$	54.7904			1.97323
$772$	−6.75987	−	11.7084i	−0.243293	−	0.421396i
$773$	−26.9976			−0.971035			−0.485518	−	0.874227i	$-0.661369\pi$
$773$	−26.9976			−0.971035			−0.485518	+	0.874227i	$0.661369\pi$
$774$	−0.176228			−0.00633437
$775$		0			0
$776$	10.3050			0.369926
$777$	−9.70820			−0.348280
$778$	−6.45207	−	11.1753i	−0.231318	−	0.400655i
$779$	7.47214			0.267717
$780$	−32.5623	+	56.3996i	−1.16592	+	2.01943i
$781$	−15.8508	−	27.4544i	−0.567186	−	0.982395i
$782$	−0.708204	−	1.22665i	−0.0253253	−	0.0438647i
$783$	6.47214			0.231295
$784$	9.43769	−	16.3466i	0.337061	−	0.583806i
$785$	−5.26393	+	9.11740i	−0.187878	+	0.325414i
$786$	8.48528	−	14.6969i	0.302660	−	0.524222i
$787$	4.55214	+	7.88453i	0.162266	+	0.281053i	0.935681	−	0.352847i	$-0.114786\pi$
$787$	4.55214	+	7.88453i	0.162266	+	0.281053i	−0.773415	+	0.633900i	$0.781453\pi$
$788$	−6.86474	+	11.8901i	−0.244546	+	0.423566i
$789$	−3.09017	−	5.35233i	−0.110013	−	0.190548i
$790$	9.48683			0.337526
$791$	14.2361			0.506176
$792$	6.98295	+	12.0948i	0.248128	+	0.429771i
$793$	−15.2705	+	26.4493i	−0.542272	+	0.939242i
$794$	−0.246711	−	0.427316i	−0.00875545	−	0.0151649i
$795$	13.4164	−	23.2379i	0.475831	−	0.824163i
$796$	−13.6564	+	23.6536i	−0.484039	+	0.838380i
$797$	−2.62210	+	4.54160i	−0.0928794	+	0.160872i	−0.908722	−	0.417403i	$-0.862940\pi$
$797$	−2.62210	+	4.54160i	−0.0928794	+	0.160872i	0.815842	+	0.578275i	$0.196274\pi$
$798$	−0.874032			−0.0309404
$799$	−1.00155	−	1.73474i	−0.0354323	−	0.0613706i
$800$		0			0
$801$	6.55524	−	11.3540i	0.231618	−	0.401174i
$802$	−1.41421			−0.0499376
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$	−25.4558			−0.897758
$805$	15.3500			0.541017
$806$		0			0
$807$	33.8885			1.19293
$808$	3.29180			0.115805
$809$	11.0286	+	19.1020i	0.387744	+	0.671592i	0.992146	−	0.125088i	$-0.0399212\pi$
$809$	11.0286	+	19.1020i	0.387744	+	0.671592i	−0.604402	+	0.796680i	$0.706588\pi$
$810$	9.14590			0.321354
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	−0.179396	−	0.983777i	$-0.557414\pi$
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	0.941674	−	0.336527i	$-0.109252\pi$
$812$	3.43237	+	5.94504i	0.120453	+	0.208630i
$813$	32.1246	+	55.6415i	1.12666	+	1.95143i
$814$	6.87539			0.240982
$815$	−13.8820	+	24.0443i	−0.486264	+	0.842234i
$816$	−1.94427	+	3.36758i	−0.0680631	+	0.117889i
$817$	0.103165	−	0.178688i	0.00360930	−	0.00625150i
$818$	3.31415	+	5.74028i	0.115877	+	0.200704i
$819$	7.67501	−	13.2935i	0.268187	−	0.464513i
$820$	−15.4894	−	26.8284i	−0.540912	−	0.936887i
$821$	14.3485			0.500765			0.250382	−	0.968147i	$-0.419444\pi$
$821$	14.3485			0.500765			0.250382	+	0.968147i	$0.419444\pi$
$822$	6.00000			0.209274
$823$	−7.46868	−	12.9361i	−0.260342	−	0.450925i	0.705991	−	0.708221i	$-0.250502\pi$
$823$	−7.46868	−	12.9361i	−0.260342	−	0.450925i	−0.966333	+	0.257296i	$0.917169\pi$
$824$	−1.99342	+	3.45271i	−0.0694442	+	0.120281i
$825$		0			0
$826$	−1.13525	+	1.96632i	−0.0395006	+	0.0684170i
$827$	−24.0266	+	41.6153i	−0.835486	+	1.44710i	0.0581481	+	0.998308i	$0.481480\pi$
$827$	−24.0266	+	41.6153i	−0.835486	+	1.44710i	−0.893634	+	0.448796i	$0.851853\pi$
$828$	14.2302	−	24.6475i	0.494535	−	0.856560i
$829$	−5.83308			−0.202591			−0.101296	−	0.994856i	$-0.532299\pi$
$829$	−5.83308			−0.202591			−0.101296	+	0.994856i	$0.532299\pi$
$830$	1.35045	+	2.33905i	0.0468749	+	0.0811898i
$831$	−22.4164	−	38.8264i	−0.777617	−	1.34687i
$832$	16.1603	−	27.9904i	0.560257	−	0.970394i
$833$	−3.24109			−0.112297
$834$	−0.437694	−	0.758108i	−0.0151561	−	0.0262511i
$835$	16.5579			0.573010
$836$	−7.86629			−0.272061
$837$		0			0
$838$	−7.10333			−0.245380
$839$	7.41641			0.256043			0.128021	−	0.991771i	$-0.459137\pi$
$839$	7.41641			0.256043			0.128021	+	0.991771i	$0.459137\pi$
$840$	3.76622	+	6.52328i	0.129947	+	0.225075i
$841$	−15.2918			−0.527303
$842$	0.0795268	−	0.137745i	0.00274068	−	0.00474699i
$843$	35.8805	+	62.1468i	1.23579	+	2.14045i
$844$	−4.63525	−	8.02850i	−0.159552	−	0.276352i
$845$	−76.3050			−2.62497
$846$	−1.58359	+	2.74286i	−0.0544450	+	0.0943015i
$847$	3.50000	−	6.06218i	0.120261	−	0.208299i
$848$	−8.24885	+	14.2874i	−0.283267	+	0.490632i
$849$	−27.4589	−	47.5603i	−0.942389	−	1.63226i
$850$		0			0
$851$	−14.5623	−	25.2227i	−0.499189	−	0.864621i
$852$	−31.7016			−1.08608
$853$	−45.7082			−1.56502			−0.782510	−	0.622639i	$-0.786061\pi$
$853$	−45.7082			−1.56502			−0.782510	+	0.622639i	$0.786061\pi$
$854$	0.849678	+	1.47169i	0.0290754	+	0.0503600i
$855$	2.50000	−	4.33013i	0.0854982	−	0.148087i
$856$	−5.50000	−	9.52628i	−0.187986	−	0.325602i
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$	−12.7279	+	22.0454i	−0.434524	+	0.752618i
$859$	1.82688	−	3.16424i	0.0623322	−	0.107963i	−0.833175	−	0.553009i	$-0.813480\pi$
$859$	1.82688	−	3.16424i	0.0623322	−	0.107963i	0.895507	+	0.445046i	$0.146813\pi$
$860$	−0.855427			−0.0291698
$861$	8.54904	+	14.8074i	0.291351	+	0.504634i
$862$	0.0212862	+	0.0368688i	0.000725012	+	0.00125576i
$863$	−17.6626	+	30.5926i	−0.601243	+	1.04138i	0.391391	+	0.920225i	$0.371994\pi$
$863$	−17.6626	+	30.5926i	−0.601243	+	1.04138i	−0.992633	+	0.121158i	$0.961339\pi$
$864$	−7.24730			−0.246558
$865$	20.1246	+	34.8569i	0.684257	+	1.18517i
$866$	8.24885			0.280307
$867$	−38.2325			−1.29844
$868$		0			0
$869$	−47.1246			−1.59859
$870$	7.23607			0.245326
$871$	−20.5942	−	35.6702i	−0.697808	−	1.20864i
$872$	21.6525			0.733245
$873$	7.82624	−	13.5554i	0.264878	−	0.458782i
$874$	−1.31105	−	2.27080i	−0.0443469	−	0.0768110i
$875$	5.59017	+	9.68246i	0.188982	+	0.327327i
$876$	−18.0000			−0.608164
$877$	7.64590	−	13.2431i	0.258184	−	0.447187i	−0.707572	−	0.706642i	$-0.750209\pi$
$877$	7.64590	−	13.2431i	0.258184	−	0.447187i	0.965755	+	0.259454i	$0.0835427\pi$
$878$	4.77458	−	8.26981i	0.161134	−	0.279092i
$879$	17.9721	−	31.1286i	0.606184	−	1.04994i
$880$	14.9223	+	25.8462i	0.503031	+	0.871275i
$881$	24.8369	−	43.0187i	0.836775	−	1.44934i	−0.0558024	−	0.998442i	$-0.517772\pi$
$881$	24.8369	−	43.0187i	0.836775	−	1.44934i	0.892577	−	0.450895i	$-0.148895\pi$
$882$	2.56231	+	4.43804i	0.0862773	+	0.149437i
$883$	−33.9411			−1.14221			−0.571105	−	0.820877i	$-0.693485\pi$
$883$	−33.9411			−1.14221			−0.571105	+	0.820877i	$0.693485\pi$
$884$	−6.87539			−0.231244
$885$	−15.2074	−	26.3401i	−0.511193	−	0.885412i
$886$	−4.57295	+	7.92058i	−0.153631	+	0.266097i
$887$	9.68034	+	16.7668i	0.325034	+	0.562975i	0.981519	−	0.191363i	$-0.0612909\pi$
$887$	9.68034	+	16.7668i	0.325034	+	0.562975i	−0.656485	+	0.754339i	$0.727958\pi$
$888$	7.14590	−	12.3771i	0.239801	−	0.415347i
$889$	4.74342	−	8.21584i	0.159089	−	0.275550i
$890$	−2.50388	+	4.33685i	−0.0839302	+	0.145371i
$891$	−45.4311			−1.52200
$892$	−20.2117	−	35.0076i	−0.676736	−	1.17214i
$893$	−1.85410	−	3.21140i	−0.0620452	−	0.107465i
$894$	−5.86319	+	10.1553i	−0.196094	+	0.339645i
$895$	−36.7394			−1.22806
$896$	−5.04508	−	8.73834i	−0.168544	−	0.291928i
$897$	107.833			3.60043
$898$	−16.1151			−0.537769
$899$		0			0
$900$		0			0
$901$	2.83282			0.0943748
$902$	−6.05446	−	10.4866i	−0.201592	−	0.349167i
$903$	0.472136			0.0157117
$904$	−10.4787	+	18.1497i	−0.348517	+	0.603649i
$905$	20.3241	+	35.2024i	0.675597	+	1.17017i
$906$	−1.32624	−	2.29711i	−0.0440613	−	0.0763164i
$907$	−55.5410			−1.84421			−0.922105	−	0.386941i	$-0.873532\pi$
$907$	−55.5410			−1.84421			−0.922105	+	0.386941i	$0.873532\pi$
$908$	14.5623	−	25.2227i	0.483267	−	0.837043i
$909$	2.50000	−	4.33013i	0.0829198	−	0.143621i
$910$	−2.93159	+	5.07767i	−0.0971813	+	0.168323i
$911$	−7.09542	−	12.2896i	−0.235082	−	0.407174i	0.724215	−	0.689575i	$-0.242202\pi$
$911$	−7.09542	−	12.2896i	−0.235082	−	0.407174i	−0.959296	+	0.282401i	$0.908869\pi$
$912$	−3.59929	+	6.23416i	−0.119185	+	0.206434i
$913$	−6.70820	−	11.6190i	−0.222009	−	0.384531i
$914$	4.32145			0.142941
$915$	−22.7639			−0.752552
$916$	3.93314	+	6.81241i	0.129955	+	0.225088i
$917$	−9.70820	+	16.8151i	−0.320593	+	0.555284i
$918$	0.180340	+	0.312358i	0.00595210	+	0.0103093i
$919$	−12.2705	+	21.2531i	−0.404767	+	0.701077i	−0.994294	−	0.106672i	$-0.965981\pi$
$919$	−12.2705	+	21.2531i	−0.404767	+	0.701077i	0.589528	+	0.807748i	$0.299314\pi$
$920$	−11.2987	+	19.5698i	−0.372506	+	0.645199i
$921$	18.4485	−	31.9538i	0.607900	−	1.05291i
$922$	−14.9374			−0.491936
$923$	−25.6471	−	44.4221i	−0.844185	−	1.46217i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	5.78437			0.190086
$927$	3.02786	+	5.24441i	0.0994481	+	0.172249i
$928$	−15.3500			−0.503889
$929$	23.2951			0.764288			0.382144	−	0.924103i	$-0.375186\pi$
$929$	23.2951			0.764288			0.382144	+	0.924103i	$0.375186\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	8.39512			0.274991
$933$	−18.9099	−	32.7529i	−0.619083	−	1.07228i
$934$	5.97871			0.195629
$935$	2.56231	−	4.43804i	0.0837964	−	0.145140i
$936$	11.2987	+	19.5698i	0.369308	+	0.639660i
$937$	28.1246	+	48.7133i	0.918791	+	1.59139i	0.801254	+	0.598324i	$0.204167\pi$
$937$	28.1246	+	48.7133i	0.918791	+	1.59139i	0.117537	+	0.993069i	$0.462500\pi$
$938$	−2.29180			−0.0748298
$939$	24.0344	−	41.6289i	0.784334	−	1.35851i
$940$	−7.68692	+	13.3141i	−0.250720	+	0.434259i
$941$	−25.4164	+	44.0226i	−0.828552	+	1.43509i	0.0706217	+	0.997503i	$0.477502\pi$
$941$	−25.4164	+	44.0226i	−0.828552	+	1.43509i	−0.899174	+	0.437591i	$0.855832\pi$
$942$	2.05756	+	3.56380i	0.0670389	+	0.116115i
$943$	−25.6471	+	44.4221i	−0.835185	+	1.44658i
$944$	9.35004	+	16.1947i	0.304318	+	0.527094i
$945$	−3.90879			−0.127153
$946$	−0.334369			−0.0108713
$947$	−1.11977	−	1.93950i	−0.0363876	−	0.0630252i	0.847258	−	0.531181i	$-0.178252\pi$
$947$	−1.11977	−	1.93950i	−0.0363876	−	0.0630252i	−0.883646	+	0.468156i	$0.844918\pi$
$948$	−23.5623	+	40.8111i	−0.765268	+	1.32548i
$949$	−14.5623	−	25.2227i	−0.472712	−	0.818762i
$950$		0			0
$951$	−24.9006	+	43.1291i	−0.807458	+	1.39856i
$952$	−0.397610	+	0.688681i	−0.0128866	+	0.0223203i
$953$	53.4550			1.73158			0.865788	−	0.500411i	$-0.166818\pi$
$953$	53.4550			1.73158			0.865788	+	0.500411i	$0.166818\pi$
$954$	−2.23954	−	3.87899i	−0.0725077	−	0.125587i
$955$	15.9164	+	27.5680i	0.515043	+	0.892080i
$956$	−15.1587	+	26.2557i	−0.490269	+	0.849170i
$957$	−35.9442			−1.16191
$958$	−4.86475	−	8.42599i	−0.157173	−	0.272231i
$959$	−6.86474			−0.221674
$960$	24.0903			0.777512
$961$		0			0
$962$	11.1246			0.358672
$963$	−16.7082			−0.538414
$964$	13.6564	+	23.6536i	0.439843	+	0.761831i
$965$	16.3050			0.524875
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	6.45207	+	11.1753i	0.207485	+	0.359374i	0.950922	−	0.309432i	$-0.100139\pi$
$967$	6.45207	+	11.1753i	0.207485	+	0.359374i	−0.743437	+	0.668806i	$0.766806\pi$
$968$	5.15248	+	8.92435i	0.165607	+	0.286839i
$969$	1.23607			0.0397082
$970$	−2.98936	+	5.17772i	−0.0959825	+	0.166247i
$971$	−9.05573	+	15.6850i	−0.290612	+	0.503355i	−0.973955	−	0.226743i	$-0.927192\pi$
$971$	−9.05573	+	15.6850i	−0.290612	+	0.503355i	0.683342	+	0.730098i	$0.260526\pi$
$972$	−17.8539	+	30.9239i	−0.572664	+	0.991883i
$973$	0.500776	+	0.867369i	0.0160541	+	0.0278066i
$974$	−3.55059	+	6.14979i	−0.113768	+	0.197052i
$975$		0			0
$976$	13.9960			0.448001
$977$	42.4853			1.35922			0.679612	−	0.733571i	$-0.262148\pi$
$977$	42.4853			1.35922			0.679612	+	0.733571i	$0.262148\pi$
$978$	5.42617	+	9.39840i	0.173510	+	0.300528i
$979$	12.4377	−	21.5427i	0.397510	−	0.688508i
$980$	12.4377	+	21.5427i	0.397308	+	0.688157i
$981$	16.4443	−	28.4823i	0.525025	−	0.909370i
$982$	1.82688	−	3.16424i	0.0582979	−	0.100975i
$983$	1.50233	−	2.60211i	0.0479168	−	0.0829943i	−0.841072	−	0.540923i	$-0.818075\pi$
$983$	1.50233	−	2.60211i	0.0479168	−	0.0829943i	0.888989	+	0.457928i	$0.151408\pi$
$984$	−25.1707			−0.802413
$985$	−8.27895	−	14.3396i	−0.263789	−	0.456896i
$986$	0.381966	+	0.661585i	0.0121643	+	0.0210691i
$987$	4.24264	−	7.34847i	0.135045	−	0.233904i
$988$	−12.7279			−0.404929
$989$	0.708204	+	1.22665i	0.0225196	+	0.0390050i
$990$	−8.10272			−0.257521
$991$	−4.44897			−0.141326			−0.0706631	−	0.997500i	$-0.522512\pi$
$991$	−4.44897			−0.141326			−0.0706631	+	0.997500i	$0.522512\pi$
$992$		0			0
$993$	−58.6525			−1.86128
$994$	−2.85410			−0.0905266
$995$	−16.4698	−	28.5265i	−0.522127	−	0.904351i
$996$	−13.4164			−0.425115
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	0.166591	+	0.986026i	$0.446724\pi$
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	−0.937219	+	0.348741i	$0.886609\pi$
$998$	−3.51118	−	6.08154i	−0.111144	−	0.192508i
$999$	3.70820	+	6.42280i	0.117322	+	0.203208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.h.521.1		8
31.2	even	5		961.2.g.i.844.1		16
31.3	odd	30		961.2.d.h.628.1		8
31.4	even	5		961.2.g.p.338.1		16
31.5	even	3	inner	961.2.c.h.439.1		8
31.6	odd	6		961.2.a.h.1.1	✓	4
31.7	even	15		961.2.d.j.388.1		8
31.8	even	5		961.2.g.p.732.2		16
31.9	even	15		961.2.g.p.816.1		16
31.10	even	15		961.2.g.i.547.2		16
31.11	odd	30		961.2.g.p.235.1		16
31.12	odd	30		961.2.d.h.531.1		8
31.13	odd	30		961.2.g.i.846.2		16
31.14	even	15		961.2.d.j.374.1		8
31.15	odd	10		961.2.g.i.448.1		16
31.16	even	5		961.2.g.i.448.2		16
31.17	odd	30		961.2.d.j.374.2		8
31.18	even	15		961.2.g.i.846.1		16
31.19	even	15		961.2.d.h.531.2		8
31.20	even	15		961.2.g.p.235.2		16
31.21	odd	30		961.2.g.i.547.1		16
31.22	odd	30		961.2.g.p.816.2		16
31.23	odd	10		961.2.g.p.732.1		16
31.24	odd	30		961.2.d.j.388.2		8
31.25	even	3		961.2.a.h.1.2	yes	4
31.26	odd	6	inner	961.2.c.h.439.2		8
31.27	odd	10		961.2.g.p.338.2		16
31.28	even	15		961.2.d.h.628.2		8
31.29	odd	10		961.2.g.i.844.2		16
31.30	odd	2	inner	961.2.c.h.521.2		8
93.56	odd	6		8649.2.a.r.1.3		4
93.68	even	6		8649.2.a.r.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.6	odd	6
961.2.a.h.1.2	yes	4	31.25	even	3
961.2.c.h.439.1		8	31.5	even	3	inner
961.2.c.h.439.2		8	31.26	odd	6	inner
961.2.c.h.521.1		8	1.1	even	1	trivial
961.2.c.h.521.2		8	31.30	odd	2	inner
961.2.d.h.531.1		8	31.12	odd	30
961.2.d.h.531.2		8	31.19	even	15
961.2.d.h.628.1		8	31.3	odd	30
961.2.d.h.628.2		8	31.28	even	15
961.2.d.j.374.1		8	31.14	even	15
961.2.d.j.374.2		8	31.17	odd	30
961.2.d.j.388.1		8	31.7	even	15
961.2.d.j.388.2		8	31.24	odd	30
961.2.g.i.448.1		16	31.15	odd	10
961.2.g.i.448.2		16	31.16	even	5
961.2.g.i.547.1		16	31.21	odd	30
961.2.g.i.547.2		16	31.10	even	15
961.2.g.i.844.1		16	31.2	even	5
961.2.g.i.844.2		16	31.29	odd	10
961.2.g.i.846.1		16	31.18	even	15
961.2.g.i.846.2		16	31.13	odd	30
961.2.g.p.235.1		16	31.11	odd	30
961.2.g.p.235.2		16	31.20	even	15
961.2.g.p.338.1		16	31.4	even	5
961.2.g.p.338.2		16	31.27	odd	10
961.2.g.p.732.1		16	31.23	odd	10
961.2.g.p.732.2		16	31.8	even	5
961.2.g.p.816.1		16	31.9	even	15
961.2.g.p.816.2		16	31.22	odd	30
8649.2.a.r.1.3		4	93.56	odd	6
8649.2.a.r.1.4		4	93.68	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} +(-1.14412 - 1.98168i) q^{3} -1.85410 q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.437016 - 0.756934i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.47214 q^{8} +(-1.11803 + 1.93649i) q^{9} +(0.427051 - 0.739674i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(2.12132 + 3.67423i) q^{12} +(-3.43237 + 5.94504i) q^{13} +(0.190983 + 0.330792i) q^{14} -5.11667 q^{15} +3.14590 q^{16} +(-0.270091 - 0.467811i) q^{17} +(-0.427051 + 0.739674i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-2.07295 + 3.59045i) q^{20} +(1.14412 - 1.98168i) q^{21} +(-0.810272 + 1.40343i) q^{22} +6.86474 q^{23} +(1.68430 + 2.91730i) q^{24} +(-1.31105 + 2.27080i) q^{26} -1.74806 q^{27} +(-0.927051 - 1.60570i) q^{28} -3.70246 q^{29} -1.95440 q^{30} +4.14590 q^{32} +9.70820 q^{33} +(-0.103165 - 0.178688i) q^{34} +2.23607 q^{35} +(2.07295 - 3.59045i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(-0.190983 - 0.330792i) q^{38} +15.7082 q^{39} +(-1.64590 + 2.85078i) q^{40} +(-3.73607 + 6.47106i) q^{41} +(0.437016 - 0.756934i) q^{42} +(0.103165 + 0.178688i) q^{43} +(3.93314 - 6.81241i) q^{44} +(2.50000 + 4.33013i) q^{45} +2.62210 q^{46} +3.70820 q^{47} +(-3.59929 - 6.23416i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.618034 + 1.07047i) q^{51} +(6.36396 - 11.0227i) q^{52} +(-2.62210 + 4.54160i) q^{53} -0.667701 q^{54} +(4.74342 + 8.21584i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-1.14412 + 1.98168i) q^{57} -1.41421 q^{58} +(2.97214 + 5.14789i) q^{59} +9.48683 q^{60} +4.44897 q^{61} -2.23607 q^{63} -4.70820 q^{64} +(7.67501 + 13.2935i) q^{65} +3.70820 q^{66} +(-3.00000 + 5.19615i) q^{67} +(0.500776 + 0.867369i) q^{68} +(-7.85410 - 13.6037i) q^{69} +0.854102 q^{70} +(-3.73607 + 6.47106i) q^{71} +(1.64590 - 2.85078i) q^{72} +(-2.12132 + 3.67423i) q^{73} +(-0.810272 - 1.40343i) q^{74} +(0.927051 + 1.60570i) q^{76} -4.24264 q^{77} +6.00000 q^{78} +(5.55369 + 9.61927i) q^{79} +(3.51722 - 6.09201i) q^{80} +(5.35410 + 9.27358i) q^{81} +(-1.42705 + 2.47172i) q^{82} +(-1.58114 + 2.73861i) q^{83} +(-2.12132 + 3.67423i) q^{84} -1.20788 q^{85} +(0.0394057 + 0.0682527i) q^{86} +(4.23607 + 7.33708i) q^{87} +(3.12287 - 5.40897i) q^{88} -5.86319 q^{89} +(0.954915 + 1.65396i) q^{90} -6.86474 q^{91} -12.7279 q^{92} +1.41641 q^{94} -2.23607 q^{95} +(-4.74342 - 8.21584i) q^{96} -7.00000 q^{97} +(1.14590 - 1.98475i) q^{98} +(-4.74342 - 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{2} + 12 q^{4} + 4 q^{7} + 24 q^{8} - 10 q^{10} + 6 q^{14} + 52 q^{16} + 10 q^{18} - 4 q^{19} - 30 q^{20} + 6 q^{28} + 60 q^{32} + 24 q^{33} + 30 q^{36} - 6 q^{38} + 72 q^{39} - 40 q^{40} - 12 q^{41}+ \cdots + 36 q^{98}+O(q^{100}) \) 8 * q + 12 * q^2 + 12 * q^4 + 4 * q^7 + 24 * q^8 - 10 * q^10 + 6 * q^14 + 52 * q^16 + 10 * q^18 - 4 * q^19 - 30 * q^20 + 6 * q^28 + 60 * q^32 + 24 * q^33 + 30 * q^36 - 6 * q^38 + 72 * q^39 - 40 * q^40 - 12 * q^41 + 20 * q^45 - 24 * q^47 + 24 * q^49 + 4 * q^51 + 12 * q^56 - 12 * q^59 + 16 * q^64 - 24 * q^66 - 24 * q^67 - 36 * q^69 - 20 * q^70 - 12 * q^71 + 40 * q^72 - 6 * q^76 + 48 * q^78 - 30 * q^80 + 16 * q^81 + 2 * q^82 + 16 * q^87 + 30 * q^90 - 96 * q^94 - 56 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

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