LMFDB - Embedded newform 1183.2.e.i.170.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 $ x^16 + 11x^14 + 85x^12 + 334x^10 + 952x^8 + 1050x^6 + 853x^4 + 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.5
Root			$0.166188 + 0.287846i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.i.508.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.166188 - 0.287846i) q^{2} +(-0.729919 - 1.26426i) q^{3} +(0.944763 + 1.63638i) q^{4} +(0.722811 - 1.25195i) q^{5} -0.485214 q^{6} +(1.36920 + 2.26391i) q^{7} +1.29278 q^{8} +(0.434437 - 0.752468i) q^{9} +O(q^{10})$	\(q+(0.166188 - 0.287846i) q^{2} +(-0.729919 - 1.26426i) q^{3} +(0.944763 + 1.63638i) q^{4} +(0.722811 - 1.25195i) q^{5} -0.485214 q^{6} +(1.36920 + 2.26391i) q^{7} +1.29278 q^{8} +(0.434437 - 0.752468i) q^{9} +(-0.240245 - 0.416116i) q^{10} +(-2.97758 - 5.15732i) q^{11} +(1.37920 - 2.38885i) q^{12} +(0.879201 - 0.0178849i) q^{14} -2.11037 q^{15} +(-1.67468 + 2.90063i) q^{16} +(-2.16436 - 3.74877i) q^{17} +(-0.144396 - 0.250102i) q^{18} +(0.978767 - 1.69527i) q^{19} +2.73154 q^{20} +(1.86276 - 3.38349i) q^{21} -1.97935 q^{22} +(0.270081 - 0.467795i) q^{23} +(-0.943626 - 1.63441i) q^{24} +(1.45509 + 2.52029i) q^{25} -5.64793 q^{27} +(-2.41104 + 4.37939i) q^{28} +7.15857 q^{29} +(-0.350718 + 0.607461i) q^{30} +(-3.05400 - 5.28968i) q^{31} +(1.84941 + 3.20327i) q^{32} +(-4.34678 + 7.52885i) q^{33} -1.43876 q^{34} +(3.82396 - 0.0777879i) q^{35} +1.64176 q^{36} +(4.01441 - 6.95316i) q^{37} +(-0.325318 - 0.563467i) q^{38} +(0.934437 - 1.61849i) q^{40} +7.55362 q^{41} +(-0.664356 - 1.09848i) q^{42} +4.24839 q^{43} +(5.62622 - 9.74489i) q^{44} +(-0.628032 - 1.08778i) q^{45} +(-0.0897684 - 0.155483i) q^{46} +(3.13042 - 5.42204i) q^{47} +4.88953 q^{48} +(-3.25057 + 6.19950i) q^{49} +0.967272 q^{50} +(-3.15961 + 5.47260i) q^{51} +(1.38953 + 2.40673i) q^{53} +(-0.938616 + 1.62573i) q^{54} -8.60891 q^{55} +(1.77008 + 2.92674i) q^{56} -2.85768 q^{57} +(1.18967 - 2.06056i) q^{58} +(-0.425576 - 0.737119i) q^{59} +(-1.99380 - 3.45337i) q^{60} +(-3.38953 + 5.87083i) q^{61} -2.03015 q^{62} +(2.29835 - 0.0467536i) q^{63} -5.46933 q^{64} +(1.44476 + 2.50240i) q^{66} +(-0.493553 - 0.854859i) q^{67} +(4.08961 - 7.08341i) q^{68} -0.788550 q^{69} +(0.613105 - 1.11364i) q^{70} -3.76223 q^{71} +(0.561633 - 0.972777i) q^{72} +(-4.56760 - 7.91131i) q^{73} +(-1.33429 - 2.31106i) q^{74} +(2.12419 - 3.67921i) q^{75} +3.69881 q^{76} +(7.59879 - 13.8024i) q^{77} +(0.0655625 - 0.113558i) q^{79} +(2.42096 + 4.19322i) q^{80} +(2.81922 + 4.88303i) q^{81} +(1.25532 - 2.17428i) q^{82} -2.66812 q^{83} +(7.29653 - 0.148428i) q^{84} -6.25768 q^{85} +(0.706030 - 1.22288i) q^{86} +(-5.22517 - 9.05026i) q^{87} +(-3.84936 - 6.66729i) q^{88} +(4.85869 - 8.41550i) q^{89} -0.417485 q^{90} +1.02065 q^{92} +(-4.45834 + 7.72207i) q^{93} +(-1.04047 - 1.80215i) q^{94} +(-1.41493 - 2.45072i) q^{95} +(2.69983 - 4.67625i) q^{96} -6.58319 q^{97} +(1.24429 + 1.96594i) q^{98} -5.17429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.166188	−	0.287846i	0.117512	−	0.203538i	−0.801269	−	0.598304i	$-0.795841\pi$
$2$	0.166188	−	0.287846i	0.117512	−	0.203538i	0.918781	+	0.394767i	$0.129175\pi$
$3$	−0.729919	−	1.26426i	−0.421419	−	0.729919i	0.574660	−	0.818392i	$-0.305134\pi$
$3$	−0.729919	−	1.26426i	−0.421419	−	0.729919i	−0.996079	+	0.0884737i	$0.971801\pi$
$4$	0.944763	+	1.63638i	0.472382	+	0.818189i
$5$	0.722811	−	1.25195i	0.323251	−	0.559887i	−0.657906	−	0.753100i	$-0.728558\pi$
$5$	0.722811	−	1.25195i	0.323251	−	0.559887i	0.981157	+	0.193213i	$0.0618909\pi$
$6$	−0.485214			−0.198088
$7$	1.36920	+	2.26391i	0.517510	+	0.855677i
$7$	1.36920	+	2.26391i	0.517510	+	0.855677i
$8$	1.29278			0.457068
$9$	0.434437	−	0.752468i	0.144812	−	0.250823i
$10$	−0.240245	−	0.416116i	−0.0759720	−	0.131587i
$11$	−2.97758	−	5.15732i	−0.897774	−	1.55499i	−0.830333	−	0.557267i	$-0.811850\pi$
$11$	−2.97758	−	5.15732i	−0.897774	−	1.55499i	−0.0674405	−	0.997723i	$-0.521483\pi$
$12$	1.37920	−	2.38885i	0.398141	−	0.689600i
$13$		0			0
$13$		0			0
$14$	0.879201	−	0.0178849i	0.234976	−	0.00477994i
$15$	−2.11037			−0.544896
$16$	−1.67468	+	2.90063i	−0.418670	+	0.725159i
$17$	−2.16436	−	3.74877i	−0.524933	−	0.909211i	−0.999578	−	0.0290341i	$-0.990757\pi$
$17$	−2.16436	−	3.74877i	−0.524933	−	0.909211i	0.474645	−	0.880177i	$-0.342576\pi$
$18$	−0.144396	−	0.250102i	−0.0340345	−	0.0589496i
$19$	0.978767	−	1.69527i	0.224545	−	0.388923i	−0.731638	−	0.681693i	$-0.761244\pi$
$19$	0.978767	−	1.69527i	0.224545	−	0.388923i	0.956183	+	0.292771i	$0.0945772\pi$
$20$	2.73154			0.610791
$21$	1.86276	−	3.38349i	0.406486	−	0.738339i
$22$	−1.97935			−0.421998
$23$	0.270081	−	0.467795i	0.0563158	−	0.0975419i	−0.836493	−	0.547977i	$-0.815398\pi$
$23$	0.270081	−	0.467795i	0.0563158	−	0.0975419i	0.892809	+	0.450436i	$0.148731\pi$
$24$	−0.943626	−	1.63441i	−0.192617	−	0.333622i
$25$	1.45509	+	2.52029i	0.291018	+	0.504058i
$26$		0			0
$27$	−5.64793			−1.08694
$28$	−2.41104	+	4.37939i	−0.455644	+	0.827627i
$29$	7.15857			1.32931			0.664656	−	0.747149i	$-0.268578\pi$
$29$	7.15857			1.32931			0.664656	+	0.747149i	$0.268578\pi$
$30$	−0.350718	+	0.607461i	−0.0640320	+	0.110907i
$31$	−3.05400	−	5.28968i	−0.548514	−	0.950055i	−0.998377	−	0.0569568i	$-0.981860\pi$
$31$	−3.05400	−	5.28968i	−0.548514	−	0.950055i	0.449862	−	0.893098i	$-0.351473\pi$
$32$	1.84941	+	3.20327i	0.326932	+	0.566263i
$33$	−4.34678	+	7.52885i	−0.756678	+	1.31060i
$34$	−1.43876			−0.246745
$35$	3.82396	−	0.0777879i	0.646368	−	0.0131486i
$36$	1.64176			0.273627
$37$	4.01441	−	6.95316i	0.659964	−	1.14309i	−0.320660	−	0.947194i	$-0.603905\pi$
$37$	4.01441	−	6.95316i	0.659964	−	1.14309i	0.980624	−	0.195897i	$-0.0627620\pi$
$38$	−0.325318	−	0.563467i	−0.0527736	−	0.0914065i
$39$		0			0
$40$	0.934437	−	1.61849i	0.147748	−	0.255906i
$41$	7.55362			1.17968			0.589839	−	0.807521i	$-0.299191\pi$
$41$	7.55362			1.17968			0.589839	+	0.807521i	$0.299191\pi$
$42$	−0.664356	−	1.09848i	−0.102512	−	0.169499i
$43$	4.24839			0.647873			0.323936	−	0.946079i	$-0.394994\pi$
$43$	4.24839			0.647873			0.323936	+	0.946079i	$0.394994\pi$
$44$	5.62622	−	9.74489i	0.848184	−	1.46910i
$45$	−0.628032	−	1.08778i	−0.0936215	−	0.162157i
$46$	−0.0897684	−	0.155483i	−0.0132356	−	0.0229248i
$47$	3.13042	−	5.42204i	0.456618	−	0.790886i	−0.542161	−	0.840274i	$-0.682394\pi$
$47$	3.13042	−	5.42204i	0.456618	−	0.790886i	0.998780	+	0.0493882i	$0.0157271\pi$
$48$	4.88953			0.705742
$49$	−3.25057	+	6.19950i	−0.464367	+	0.885643i
$50$	0.967272			0.136793
$51$	−3.15961	+	5.47260i	−0.442434	+	0.766317i
$52$		0			0
$53$	1.38953	+	2.40673i	0.190866	+	0.330590i	0.945538	−	0.325513i	$-0.105537\pi$
$53$	1.38953	+	2.40673i	0.190866	+	0.330590i	−0.754671	+	0.656103i	$0.772204\pi$
$54$	−0.938616	+	1.62573i	−0.127729	+	0.221234i
$55$	−8.60891			−1.16082
$56$	1.77008	+	2.92674i	0.236537	+	0.391103i
$57$	−2.85768			−0.378509
$58$	1.18967	−	2.06056i	0.156211	−	0.270565i
$59$	−0.425576	−	0.737119i	−0.0554053	−	0.0959647i	0.836993	−	0.547214i	$-0.184312\pi$
$59$	−0.425576	−	0.737119i	−0.0554053	−	0.0959647i	−0.892398	+	0.451250i	$0.850978\pi$
$60$	−1.99380	−	3.45337i	−0.257399	−	0.445828i
$61$	−3.38953	+	5.87083i	−0.433984	+	0.751683i	−0.997212	−	0.0746187i	$-0.976226\pi$
$61$	−3.38953	+	5.87083i	−0.433984	+	0.751683i	0.563228	+	0.826302i	$0.309559\pi$
$62$	−2.03015			−0.257829
$63$	2.29835	−	0.0467536i	0.289565	−	0.00589039i
$64$	−5.46933			−0.683667
$65$		0			0
$66$	1.44476	+	2.50240i	0.177838	+	0.308025i
$67$	−0.493553	−	0.854859i	−0.0602971	−	0.104438i	0.834301	−	0.551309i	$-0.185871\pi$
$67$	−0.493553	−	0.854859i	−0.0602971	−	0.104438i	−0.894598	+	0.446871i	$0.852538\pi$
$68$	4.08961	−	7.08341i	0.495938	−	0.858990i
$69$	−0.788550			−0.0949302
$70$	0.613105	−	1.11364i	0.0732801	−	0.133105i
$71$	−3.76223			−0.446494			−0.223247	−	0.974762i	$-0.571666\pi$
$71$	−3.76223			−0.446494			−0.223247	+	0.974762i	$0.571666\pi$
$72$	0.561633	−	0.972777i	0.0661891	−	0.114643i
$73$	−4.56760	−	7.91131i	−0.534597	−	0.925949i	−0.999183	−	0.0404208i	$-0.987130\pi$
$73$	−4.56760	−	7.91131i	−0.534597	−	0.925949i	0.464586	−	0.885528i	$-0.346203\pi$
$74$	−1.33429	−	2.31106i	−0.155108	−	0.268655i
$75$	2.12419	−	3.67921i	0.245281	−	0.424839i
$76$	3.69881			0.424283
$77$	7.59879	−	13.8024i	0.865963	−	1.57293i
$78$		0			0
$79$	0.0655625	−	0.113558i	0.00737636	−	0.0127762i	−0.862314	−	0.506375i	$-0.830985\pi$
$79$	0.0655625	−	0.113558i	0.00737636	−	0.0127762i	0.869690	+	0.493598i	$0.164319\pi$
$80$	2.42096	+	4.19322i	0.270671	+	0.468816i
$81$	2.81922	+	4.88303i	0.313246	+	0.542558i
$82$	1.25532	−	2.17428i	0.138627	−	0.240109i
$83$	−2.66812			−0.292865			−0.146432	−	0.989221i	$-0.546779\pi$
$83$	−2.66812			−0.292865			−0.146432	+	0.989221i	$0.546779\pi$
$84$	7.29653	−	0.148428i	0.796117	−	0.0161948i
$85$	−6.25768			−0.678741
$86$	0.706030	−	1.22288i	0.0761331	−	0.131866i
$87$	−5.22517	−	9.05026i	−0.560197	−	0.970290i
$88$	−3.84936	−	6.66729i	−0.410344	−	0.710736i
$89$	4.85869	−	8.41550i	0.515021	−	0.892042i	−0.484828	−	0.874610i	$-0.661118\pi$
$89$	4.85869	−	8.41550i	0.515021	−	0.892042i	0.999848	−	0.0174319i	$-0.00554904\pi$
$90$	−0.417485			−0.0440068
$91$		0			0
$92$	1.02065			0.106410
$93$	−4.45834	+	7.72207i	−0.462308	+	0.800742i
$94$	−1.04047	−	1.80215i	−0.107317	−	0.185878i
$95$	−1.41493	−	2.45072i	−0.145168	−	0.251439i
$96$	2.69983	−	4.67625i	0.275550	−	0.477267i
$97$	−6.58319			−0.668422			−0.334211	−	0.942498i	$-0.608470\pi$
$97$	−6.58319			−0.668422			−0.334211	+	0.942498i	$0.608470\pi$
$98$	1.24429	+	1.96594i	0.125693	+	0.198590i
$99$	−5.17429			−0.520036
$100$	−2.74943	+	4.76215i	−0.274943	+	0.476215i
$101$	0.0354144	+	0.0613396i	0.00352387	+	0.00610352i	0.867782	−	0.496945i	$-0.165545\pi$
$101$	0.0354144	+	0.0613396i	0.00352387	+	0.00610352i	−0.864258	+	0.503049i	$0.832212\pi$
$102$	1.05018	+	1.81896i	0.103983	+	0.180104i
$103$	−3.16910	+	5.48905i	−0.312261	+	0.540852i	−0.978852	−	0.204572i	$-0.934420\pi$
$103$	−3.16910	+	5.48905i	−0.312261	+	0.540852i	0.666590	+	0.745424i	$0.267753\pi$
$104$		0			0
$105$	−2.88953	−	4.77769i	−0.281989	−	0.466255i
$106$	0.923689			0.0897166
$107$	−3.87476	+	6.71129i	−0.374588	+	0.648805i	−0.990265	−	0.139193i	$-0.955549\pi$
$107$	−3.87476	+	6.71129i	−0.374588	+	0.648805i	0.615678	+	0.787998i	$0.288882\pi$
$108$	−5.33596	−	9.24215i	−0.513453	−	0.889326i
$109$	−0.0167811	−	0.0290658i	−0.00160734	−	0.00278400i	0.865221	−	0.501391i	$-0.167178\pi$
$109$	−0.0167811	−	0.0290658i	−0.00160734	−	0.00278400i	−0.866828	+	0.498607i	$0.833845\pi$
$110$	−1.43069	+	2.47804i	−0.136411	+	0.236271i
$111$	−11.7208			−1.11249
$112$	−8.85975	+	0.180227i	−0.837168	+	0.0170298i
$113$	−9.19987			−0.865451			−0.432725	−	0.901526i	$-0.642448\pi$
$113$	−9.19987			−0.865451			−0.432725	+	0.901526i	$0.642448\pi$
$114$	−0.474911	+	0.822571i	−0.0444795	+	0.0770408i
$115$	−0.390435	−	0.676254i	−0.0364083	−	0.0630610i
$116$	6.76315	+	11.7141i	0.627943	+	1.08763i
$117$		0			0
$118$	−0.282902			−0.0260432
$119$	5.52344	−	10.0327i	0.506333	−	0.919699i
$120$	−2.72825			−0.249054
$121$	−12.2320	+	21.1864i	−1.11200	+	1.92603i
$122$	1.12660	+	1.95132i	0.101997	+	0.176664i
$123$	−5.51353	−	9.54971i	−0.497138	−	0.861068i
$124$	5.77061	−	9.99499i	0.518216	−	0.897577i
$125$	11.4351			1.02279
$126$	0.368500	−	0.669340i	0.0328286	−	0.0596296i
$127$	14.3952			1.27737			0.638683	−	0.769470i	$-0.279480\pi$
$127$	14.3952			1.27737			0.638683	+	0.769470i	$0.279480\pi$
$128$	−4.60775	+	7.98085i	−0.407271	+	0.705414i
$129$	−3.10098	−	5.37105i	−0.273026	−	0.472895i
$130$		0			0
$131$	4.73414	−	8.19978i	0.413624	−	0.716418i	−0.581659	−	0.813433i	$-0.697596\pi$
$131$	4.73414	−	8.19978i	0.413624	−	0.716418i	0.995283	+	0.0970151i	$0.0309295\pi$
$132$	−16.4267			−1.42976
$133$	5.17808	−	0.105334i	0.448996	−	0.00913357i
$134$	−0.328090			−0.0283426
$135$	−4.08238	+	7.07090i	−0.351356	+	0.608566i
$136$	−2.79804	−	4.84635i	−0.239930	−	0.415571i
$137$	8.30313	+	14.3814i	0.709384	+	1.22869i	0.965086	+	0.261934i	$0.0843601\pi$
$137$	8.30313	+	14.3814i	0.709384	+	1.22869i	−0.255702	+	0.966756i	$0.582307\pi$
$138$	−0.131047	+	0.226980i	−0.0111555	+	0.0193219i
$139$	18.4778			1.56726			0.783632	−	0.621225i	$-0.213365\pi$
$139$	18.4778			1.56726			0.783632	+	0.621225i	$0.213365\pi$
$140$	3.74003	+	6.18396i	0.316090	+	0.522640i
$141$	−9.13980			−0.769710
$142$	−0.625236	+	1.08294i	−0.0524687	+	0.0908784i
$143$		0			0
$144$	1.45509	+	2.52029i	0.121257	+	0.210024i
$145$	5.17429	−	8.96213i	0.429701	−	0.744264i
$146$	−3.03631			−0.251287
$147$	10.2104	−	0.415577i	0.842140	−	0.0342762i
$148$	15.1707			1.24702
$149$	−1.54040	+	2.66805i	−0.126195	+	0.218575i	−0.922199	−	0.386715i	$-0.873610\pi$
$149$	−1.54040	+	2.66805i	−0.126195	+	0.218575i	0.796005	+	0.605290i	$0.206943\pi$
$150$	−0.706030	−	1.22288i	−0.0576471	−	0.0998477i
$151$	1.27442	+	2.20737i	0.103711	+	0.179633i	0.913211	−	0.407487i	$-0.133595\pi$
$151$	1.27442	+	2.20737i	0.103711	+	0.179633i	−0.809500	+	0.587120i	$0.800262\pi$
$152$	1.26533	−	2.19162i	0.102632	−	0.177764i
$153$	−3.76111			−0.304068
$154$	−2.71013	−	4.48106i	−0.218388	−	0.361095i
$155$	−8.82985			−0.709231
$156$		0			0
$157$	4.70452	+	8.14847i	0.375461	+	0.650318i	0.990396	−	0.138260i	$-0.0441509\pi$
$157$	4.70452	+	8.14847i	0.375461	+	0.650318i	−0.614935	+	0.788578i	$0.710818\pi$
$158$	−0.0217914	−	0.0377438i	−0.00173363	−	0.00300273i
$159$	2.02848	−	3.51344i	0.160869	−	0.278634i
$160$	5.34708			0.422724
$161$	1.42884	−	0.0290658i	0.112608	−	0.00229070i
$162$	1.87408			0.147241
$163$	0.347578	−	0.602023i	0.0272244	−	0.0471541i	−0.852092	−	0.523392i	$-0.824666\pi$
$163$	0.347578	−	0.602023i	0.0272244	−	0.0471541i	0.879317	+	0.476238i	$0.158000\pi$
$164$	7.13638	+	12.3606i	0.557258	+	0.965199i
$165$	6.28380	+	10.8839i	0.489193	+	0.847308i
$166$	−0.443409	+	0.768007i	−0.0344152	+	0.0596089i
$167$	−13.9840			−1.08211			−0.541056	−	0.840986i	$-0.681975\pi$
$167$	−13.9840			−1.08211			−0.541056	+	0.840986i	$0.681975\pi$
$168$	2.40814	−	4.37412i	0.185792	−	0.337471i
$169$		0			0
$170$	−1.03995	+	1.80125i	−0.0797605	+	0.138149i
$171$	−0.850426	−	1.47298i	−0.0650337	−	0.112642i
$172$	4.01372	+	6.95197i	0.306043	+	0.530083i
$173$	2.71824	−	4.70813i	0.206664	−	0.357952i	−0.743998	−	0.668182i	$-0.767073\pi$
$173$	2.71824	−	4.70813i	0.206664	−	0.357952i	0.950662	+	0.310230i	$0.100406\pi$
$174$	−3.47344			−0.263321
$175$	−3.71339	+	6.74497i	−0.280706	+	0.509872i
$176$	19.9460			1.50349
$177$	−0.621272	+	1.07607i	−0.0466976	+	0.0808827i
$178$	−1.61491	−	2.79711i	−0.121043	−	0.209652i
$179$	−2.67912	−	4.64037i	−0.200247	−	0.346838i	0.748361	−	0.663292i	$-0.230841\pi$
$179$	−2.67912	−	4.64037i	−0.200247	−	0.346838i	−0.948608	+	0.316454i	$0.897508\pi$
$180$	1.18668	−	2.05540i	0.0884502	−	0.153200i
$181$	7.54016			0.560456			0.280228	−	0.959933i	$-0.409590\pi$
$181$	7.54016			0.560456			0.280228	+	0.959933i	$0.409590\pi$
$182$		0			0
$183$	9.89632			0.731557
$184$	0.349157	−	0.604757i	0.0257402	−	0.0445833i
$185$	−5.80331	−	10.0516i	−0.426668	−	0.739011i
$186$	1.48184	+	2.56663i	0.108654	+	0.188194i
$187$	−12.8891	+	22.3245i	−0.942543	+	1.63253i
$188$	11.8300			0.862793
$189$	−7.73316	−	12.7864i	−0.562504	−	0.930074i
$190$	−0.940574			−0.0682364
$191$	−6.77316	+	11.7315i	−0.490089	+	0.848859i	−0.999935	−	0.0114067i	$-0.996369\pi$
$191$	−6.77316	+	11.7315i	−0.490089	+	0.848859i	0.509846	+	0.860266i	$0.329702\pi$
$192$	3.99217	+	6.91464i	0.288110	+	0.499021i
$193$	9.27812	+	16.0702i	0.667853	+	1.15676i	0.978503	+	0.206232i	$0.0661200\pi$
$193$	9.27812	+	16.0702i	0.667853	+	1.15676i	−0.310650	+	0.950524i	$0.600547\pi$
$194$	−1.09405	+	1.89494i	−0.0785479	+	0.136049i
$195$		0			0
$196$	−13.2157	+	0.537898i	−0.943982	+	0.0384213i
$197$	2.66812			0.190096			0.0950480	−	0.995473i	$-0.469700\pi$
$197$	2.66812			0.190096			0.0950480	+	0.995473i	$0.469700\pi$
$198$	−0.859903	+	1.48940i	−0.0611106	+	0.105847i
$199$	−10.0999	−	17.4936i	−0.715965	−	1.24009i	−0.962586	−	0.270976i	$-0.912654\pi$
$199$	−10.0999	−	17.4936i	−0.715965	−	1.24009i	0.246621	−	0.969112i	$-0.420680\pi$
$200$	1.88111	+	3.25819i	0.133015	+	0.230389i
$201$	−0.720507	+	1.24795i	−0.0508206	+	0.0880239i
$202$	0.0235418			0.00165639
$203$	9.80152	+	16.2063i	0.687932	+	1.13746i
$204$	−11.9403			−0.835990
$205$	5.45984	−	9.45672i	0.381332	−	0.660486i
$206$	1.05333	+	1.82443i	0.0733891	+	0.127114i
$207$	−0.234667	−	0.406455i	−0.0163105	−	0.0282506i
$208$		0			0
$209$	−11.6574			−0.806361
$210$	−1.85544	+	0.0377438i	−0.128038	+	0.00260457i
$211$	13.1268			0.903683			0.451842	−	0.892098i	$-0.350767\pi$
$211$	13.1268			0.903683			0.451842	+	0.892098i	$0.350767\pi$
$212$	−2.62555	+	4.54758i	−0.180323	+	0.312329i
$213$	2.74612	+	4.75642i	0.188161	+	0.325905i
$214$	1.28788	+	2.23067i	0.0880374	+	0.152485i
$215$	3.07078	−	5.31875i	0.209425	−	0.362736i
$216$	−7.30155			−0.496807
$217$	7.79382	−	14.1566i	0.529079	−	0.961014i
$218$	−0.0111553			−0.000755530
$219$	−6.66795	+	11.5492i	−0.450578	+	0.780424i
$220$	−8.13338	−	14.0874i	−0.548352	−	0.949774i
$221$		0			0
$222$	−1.94785	+	3.37377i	−0.130731	+	0.226433i
$223$	2.22334			0.148886			0.0744428	−	0.997225i	$-0.476282\pi$
$223$	2.22334			0.148886			0.0744428	+	0.997225i	$0.476282\pi$
$224$	−4.71969	+	8.57281i	−0.315348	+	0.572795i
$225$	2.52858			0.168572
$226$	−1.52890	+	2.64814i	−0.101701	+	0.176152i
$227$	13.5523	+	23.4732i	0.899495	+	1.55797i	0.828141	+	0.560520i	$0.189399\pi$
$227$	13.5523	+	23.4732i	0.899495	+	1.55797i	0.0713539	+	0.997451i	$0.477268\pi$
$228$	−2.69983	−	4.67625i	−0.178801	−	0.309692i
$229$	−9.49437	+	16.4447i	−0.627406	+	1.08670i	0.360665	+	0.932696i	$0.382550\pi$
$229$	−9.49437	+	16.4447i	−0.627406	+	1.08670i	−0.988070	+	0.154003i	$0.950783\pi$
$230$	−0.259542			−0.0171137
$231$	−22.9962	+	0.467795i	−1.51304	+	0.0307786i
$232$	9.25447			0.607586
$233$	−10.8700	+	18.8274i	−0.712118	+	1.23343i	0.251942	+	0.967742i	$0.418931\pi$
$233$	−10.8700	+	18.8274i	−0.712118	+	1.23343i	−0.964060	+	0.265683i	$0.914403\pi$
$234$		0			0
$235$	−4.52540	−	7.83822i	−0.295205	−	0.511309i
$236$	0.804137	−	1.39281i	0.0523449	−	0.0906639i
$237$	−0.191421			−0.0124342
$238$	−1.96995	−	3.25722i	−0.127693	−	0.211134i
$239$	−19.9695			−1.29172			−0.645861	−	0.763455i	$-0.723501\pi$
$239$	−19.9695			−1.29172			−0.645861	+	0.763455i	$0.723501\pi$
$240$	3.53420	−	6.12142i	0.228132	−	0.395136i
$241$	1.61524	+	2.79768i	0.104047	+	0.180214i	0.913348	−	0.407179i	$-0.133487\pi$
$241$	1.61524	+	2.79768i	0.104047	+	0.180214i	−0.809302	+	0.587393i	$0.800154\pi$
$242$	4.06560	+	7.04183i	0.261347	+	0.452666i
$243$	−4.35630	+	7.54533i	−0.279456	+	0.484033i
$244$	−12.8092			−0.820025
$245$	5.41188	+	8.55060i	0.345753	+	0.546278i
$246$	−3.66512			−0.233680
$247$		0			0
$248$	−3.94816	−	6.83841i	−0.250708	−	0.434239i
$249$	1.94751	+	3.37319i	0.123419	+	0.213767i
$250$	1.90038	−	3.29155i	0.120190	−	0.208176i
$251$	12.4916			0.788466			0.394233	−	0.919011i	$-0.371010\pi$
$251$	12.4916			0.788466			0.394233	+	0.919011i	$0.371010\pi$
$252$	2.24790	+	3.71680i	0.141605	+	0.234136i
$253$	−3.21675			−0.202236
$254$	2.39230	−	4.14359i	0.150106	−	0.259992i
$255$	4.56760	+	7.91131i	0.286034	+	0.495425i
$256$	−3.93783	−	6.82052i	−0.246114	−	0.426283i
$257$	−2.91379	+	5.04682i	−0.181757	+	0.314812i	−0.942479	−	0.334266i	$-0.891512\pi$
$257$	−2.91379	+	5.04682i	−0.181757	+	0.314812i	0.760722	+	0.649078i	$0.224845\pi$
$258$	−2.06138			−0.128336
$259$	21.2378	−	0.432025i	1.31966	−	0.0268447i
$260$		0			0
$261$	3.10995	−	5.38659i	0.192501	−	0.333422i
$262$	−1.57351	−	2.72540i	−0.0972119	−	0.168376i
$263$	−8.75736	−	15.1682i	−0.540002	−	0.935311i	−0.998903	−	0.0468234i	$-0.985090\pi$
$263$	−8.75736	−	15.1682i	−0.540002	−	0.935311i	0.458901	−	0.888487i	$-0.348243\pi$
$264$	−5.61945	+	9.73316i	−0.345853	+	0.599035i
$265$	4.01746			0.246791
$266$	0.830213	−	1.50799i	0.0509036	−	0.0924609i
$267$	−14.1858			−0.868157
$268$	0.932581	−	1.61528i	0.0569665	−	0.0986688i
$269$	−11.1644	−	19.3372i	−0.680703	−	1.17901i	−0.974767	−	0.223226i	$-0.928341\pi$
$269$	−11.1644	−	19.3372i	−0.680703	−	1.17901i	0.294064	−	0.955786i	$-0.404992\pi$
$270$	1.35688	+	2.35019i	0.0825773	+	0.143028i
$271$	−13.1847	+	22.8366i	−0.800916	+	1.38723i	0.118098	+	0.993002i	$0.462320\pi$
$271$	−13.1847	+	22.8366i	−0.800916	+	1.38723i	−0.919014	+	0.394225i	$0.871013\pi$
$272$	14.4984			0.879097
$273$		0			0
$274$	5.51951			0.333446
$275$	8.66529	−	15.0087i	0.522536	−	0.905060i
$276$	−0.744993	−	1.29037i	−0.0448433	−	0.0776709i
$277$	4.68809	+	8.12001i	0.281680	+	0.487884i	0.971799	−	0.235812i	$-0.0757750\pi$
$277$	4.68809	+	8.12001i	0.281680	+	0.487884i	−0.690119	+	0.723696i	$0.742442\pi$
$278$	3.07078	−	5.31875i	0.184173	−	0.318997i
$279$	−5.30709			−0.317727
$280$	4.94356	−	0.100563i	0.295434	−	0.00600978i
$281$	17.7754			1.06039			0.530195	−	0.847876i	$-0.322119\pi$
$281$	17.7754			1.06039			0.530195	+	0.847876i	$0.322119\pi$
$282$	−1.51892	+	2.63085i	−0.0904505	+	0.156665i
$283$	4.80331	+	8.31958i	0.285527	+	0.494548i	0.972737	−	0.231911i	$-0.0744979\pi$
$283$	4.80331	+	8.31958i	0.285527	+	0.494548i	−0.687210	+	0.726459i	$0.741165\pi$
$284$	−3.55442	−	6.15643i	−0.210916	−	0.365317i
$285$	−2.06556	+	3.57766i	−0.122353	+	0.211922i
$286$		0			0
$287$	10.3424	+	17.1007i	0.610494	+	1.00942i
$288$	3.21380			0.189375
$289$	−0.868875	+	1.50494i	−0.0511103	+	0.0885256i
$290$	−1.71981	−	2.97879i	−0.100990	−	0.174921i
$291$	4.80519	+	8.32284i	0.281685	+	0.487894i
$292$	8.63060	−	14.9486i	0.505067	−	0.874803i
$293$	11.6338			0.679654			0.339827	−	0.940488i	$-0.389631\pi$
$293$	11.6338			0.679654			0.339827	+	0.940488i	$0.389631\pi$
$294$	1.57722	−	3.00808i	0.0919855	−	0.175435i
$295$	−1.23044			−0.0716392
$296$	5.18976	−	8.98892i	0.301648	−	0.522470i
$297$	16.8172	+	29.1282i	0.975830	+	1.69019i
$298$	0.511991	+	0.886795i	0.0296588	+	0.0513706i
$299$		0			0
$300$	8.02744			0.463464
$301$	5.81690	+	9.61796i	0.335281	+	0.554370i
$302$	0.847174			0.0487494
$303$	0.0516993	−	0.0895459i	0.00297005	−	0.00514427i
$304$	3.27825	+	5.67809i	0.188020	+	0.325661i
$305$	4.89997	+	8.48700i	0.280572	+	0.485964i
$306$	−0.625050	+	1.08262i	−0.0357317	+	0.0618892i
$307$	−13.8280			−0.789204			−0.394602	−	0.918852i	$-0.629118\pi$
$307$	−13.8280			−0.789204			−0.394602	+	0.918852i	$0.629118\pi$
$308$	29.7650	−	0.605485i	1.69602	−	0.0345007i
$309$	9.25275			0.526371
$310$	−1.46741	+	2.54163i	−0.0833435	+	0.144355i
$311$	−15.3572	−	26.5994i	−0.870827	−	1.50832i	−0.861143	−	0.508363i	$-0.830251\pi$
$311$	−15.3572	−	26.5994i	−0.870827	−	1.50832i	−0.00968369	−	0.999953i	$-0.503082\pi$
$312$		0			0
$313$	−5.54334	+	9.60135i	−0.313328	+	0.542701i	−0.979081	−	0.203472i	$-0.934777\pi$
$313$	−5.54334	+	9.60135i	−0.313328	+	0.542701i	0.665752	+	0.746173i	$0.268111\pi$
$314$	3.12733			0.176486
$315$	1.60274	−	2.91120i	0.0903042	−	0.164028i
$316$	0.247764			0.0139378
$317$	−11.9417	+	20.6836i	−0.670712	+	1.16171i	0.306991	+	0.951712i	$0.400678\pi$
$317$	−11.9417	+	20.6836i	−0.670712	+	1.16171i	−0.977703	+	0.209994i	$0.932656\pi$
$318$	−0.674218	−	1.16778i	−0.0378083	−	0.0654858i
$319$	−21.3152	−	36.9190i	−1.19342	−	2.06707i
$320$	−3.95329	+	6.84731i	−0.220996	+	0.382776i
$321$	11.3130			0.631433
$322$	0.229089	−	0.416116i	0.0127666	−	0.0231892i
$323$	−8.47360			−0.471484
$324$	−5.32698	+	9.22661i	−0.295944	+	0.512589i
$325$		0			0
$326$	−0.115526	−	0.200098i	−0.00639842	−	0.0110824i
$327$	−0.0244977	+	0.0424313i	−0.00135473	+	0.00234646i
$328$	9.76519			0.539192
$329$	16.5612	−	0.336891i	0.913048	−	0.0185734i
$330$	4.17716			0.229945
$331$	−9.16200	+	15.8690i	−0.503589	+	0.872241i	0.496403	+	0.868092i	$0.334654\pi$
$331$	−9.16200	+	15.8690i	−0.503589	+	0.872241i	−0.999991	+	0.00414903i	$0.998679\pi$
$332$	−2.52075	−	4.36606i	−0.138344	−	0.239619i
$333$	−3.48802	−	6.04142i	−0.191142	−	0.331068i
$334$	−2.32396	+	4.02522i	−0.127162	+	0.220250i
$335$	−1.42698			−0.0779643
$336$	6.69475	+	11.0694i	0.365229	+	0.603888i
$337$	−7.21762			−0.393169			−0.196584	−	0.980487i	$-0.562985\pi$
$337$	−7.21762			−0.393169			−0.196584	+	0.980487i	$0.562985\pi$
$338$		0			0
$339$	6.71516	+	11.6310i	0.364717	+	0.631709i
$340$	−5.91203	−	10.2399i	−0.320625	−	0.555338i
$341$	−18.1870	+	31.5009i	−0.984884	+	1.70587i
$342$	−0.565321			−0.0305691
$343$	−18.4858	+	1.12937i	−0.998139	+	0.0609804i
$344$	5.49224			0.296122
$345$	−0.569972	+	0.987221i	−0.0306863	+	0.0531502i
$346$	−0.903476	−	1.56487i	−0.0485712	−	0.0841277i
$347$	10.5391	+	18.2543i	0.565770	+	0.979942i	0.996978	+	0.0776892i	$0.0247542\pi$
$347$	10.5391	+	18.2543i	0.565770	+	0.979942i	−0.431208	+	0.902253i	$0.641912\pi$
$348$	9.87310	−	17.1007i	0.529254	−	0.916694i
$349$	30.7629			1.64670			0.823350	−	0.567534i	$-0.192102\pi$
$349$	30.7629			1.64670			0.823350	+	0.567534i	$0.192102\pi$
$350$	1.32439	+	2.18982i	0.0707917	+	0.117051i
$351$		0			0
$352$	11.0135	−	19.0760i	0.587022	−	1.01675i
$353$	3.06086	+	5.30157i	0.162913	+	0.282174i	0.935912	−	0.352233i	$-0.114578\pi$
$353$	3.06086	+	5.30157i	0.162913	+	0.282174i	−0.772999	+	0.634407i	$0.781244\pi$
$354$	0.206495	+	0.357660i	0.0109751	+	0.0190094i
$355$	−2.71938	+	4.71010i	−0.144330	+	0.249986i
$356$	18.3613			0.973145
$357$	−16.7156	+	0.340033i	−0.884684	+	0.0179964i
$358$	−1.78095			−0.0941259
$359$	−9.71433	+	16.8257i	−0.512703	+	0.888028i	0.487189	+	0.873297i	$0.338022\pi$
$359$	−9.71433	+	16.8257i	−0.512703	+	0.888028i	−0.999891	+	0.0147308i	$0.995311\pi$
$360$	−0.811909	−	1.40627i	−0.0427914	−	0.0741168i
$361$	7.58403	+	13.1359i	0.399160	+	0.691365i
$362$	1.25308	−	2.17040i	0.0658605	−	0.114074i
$363$	35.7133			1.87446
$364$		0			0
$365$	−13.2060			−0.691235
$366$	1.64465	−	2.84861i	0.0859670	−	0.148899i
$367$	2.70234	+	4.68058i	0.141061	+	0.244324i	0.927896	−	0.372838i	$-0.121615\pi$
$367$	2.70234	+	4.68058i	0.141061	+	0.244324i	−0.786836	+	0.617163i	$0.788282\pi$
$368$	0.904601	+	1.56681i	0.0471556	+	0.0816758i
$369$	3.28158	−	5.68385i	0.170832	−	0.295890i
$370$	−3.85776			−0.200555
$371$	−3.54608	+	6.44106i	−0.184103	+	0.334403i
$372$	−16.8483			−0.873544
$373$	−8.12533	+	14.0735i	−0.420714	+	0.728698i	−0.996009	−	0.0892478i	$-0.971554\pi$
$373$	−8.12533	+	14.0735i	−0.420714	+	0.728698i	0.575296	+	0.817946i	$0.304887\pi$
$374$	4.28401	+	7.42013i	0.221521	+	0.383686i
$375$	−8.34671	−	14.4569i	−0.431022	−	0.746553i
$376$	4.04695	−	7.00952i	0.208706	−	0.361489i
$377$		0			0
$378$	−4.96566	+	0.101013i	−0.255406	+	0.00519553i
$379$	−25.1730			−1.29305			−0.646525	−	0.762893i	$-0.723778\pi$
$379$	−25.1730			−1.29305			−0.646525	+	0.762893i	$0.723778\pi$
$380$	2.67354	−	4.63071i	0.137150	−	0.237550i
$381$	−10.5073	−	18.1992i	−0.538306	−	0.932373i
$382$	2.25123	+	3.89925i	0.115183	+	0.199503i
$383$	1.90719	−	3.30335i	0.0974529	−	0.168793i	−0.813177	−	0.582017i	$-0.802264\pi$
$383$	1.90719	−	3.30335i	0.0974529	−	0.168793i	0.910630	+	0.413223i	$0.135597\pi$
$384$	13.4531			0.686527
$385$	−11.7873	−	19.4898i	−0.600738	−	0.993291i
$386$	6.16764			0.313924
$387$	1.84566	−	3.19677i	0.0938201	−	0.162501i
$388$	−6.21956	−	10.7726i	−0.315750	−	0.546895i
$389$	1.43548	+	2.48632i	0.0727817	+	0.126062i	0.900119	−	0.435643i	$-0.143479\pi$
$389$	1.43548	+	2.48632i	0.0727817	+	0.126062i	−0.827338	+	0.561705i	$0.810146\pi$
$390$		0			0
$391$	−2.33821			−0.118248
$392$	−4.20228	+	8.01461i	−0.212247	+	0.404799i
$393$	−13.8222			−0.697236
$394$	0.443409	−	0.768007i	0.0223386	−	0.0386917i
$395$	−0.0947786	−	0.164161i	−0.00476883	−	0.00825986i
$396$	−4.88848	−	8.46709i	−0.245655	−	0.425487i
$397$	−9.55919	+	16.5570i	−0.479762	+	0.830972i	−0.999731	−	0.0232131i	$-0.992610\pi$
$397$	−9.55919	+	16.5570i	−0.479762	+	0.830972i	0.519968	+	0.854185i	$0.325944\pi$
$398$	−6.71394			−0.336539
$399$	−3.91274	−	6.46953i	−0.195882	−	0.323882i
$400$	−9.74725			−0.487362
$401$	1.49912	−	2.59655i	0.0748625	−	0.129666i	−0.826164	−	0.563430i	$-0.809482\pi$
$401$	1.49912	−	2.59655i	0.0748625	−	0.129666i	0.901026	+	0.433764i	$0.142815\pi$
$402$	0.239479	+	0.414789i	0.0119441	+	0.0206878i
$403$		0			0
$404$	−0.0669165	+	0.115903i	−0.00332922	+	0.00576638i
$405$	8.15104			0.405028
$406$	6.29382	−	0.128030i	0.312357	−	0.00635403i
$407$	−47.8129			−2.37000
$408$	−4.08469	+	7.07489i	−0.202222	+	0.350259i
$409$	−17.0403	−	29.5146i	−0.842587	−	1.45940i	−0.887700	−	0.460422i	$-0.847698\pi$
$409$	−17.0403	−	29.5146i	−0.842587	−	1.45940i	0.0451127	−	0.998982i	$-0.485635\pi$
$410$	−1.81472	−	3.14318i	−0.0896224	−	0.155231i
$411$	12.1212	−	20.9946i	0.597896	−	1.03559i
$412$	−11.9762			−0.590026
$413$	1.08607	−	1.97273i	0.0534421	−	0.0970717i
$414$	−0.155995			−0.00766674
$415$	−1.92855	+	3.34034i	−0.0946687	+	0.163971i
$416$		0			0
$417$	−13.4873	−	23.3606i	−0.660475	−	1.14398i
$418$	−1.93732	+	3.35554i	−0.0947574	+	0.164125i
$419$	34.7759			1.69891			0.849457	−	0.527657i	$-0.176929\pi$
$419$	34.7759			1.69891			0.849457	+	0.527657i	$0.176929\pi$
$420$	5.08819	−	9.24215i	0.248278	−	0.450971i
$421$	24.1400			1.17651			0.588257	−	0.808674i	$-0.299814\pi$
$421$	24.1400			1.17651			0.588257	+	0.808674i	$0.299814\pi$
$422$	2.18151	−	3.77848i	0.106194	−	0.183933i
$423$	−2.71994	−	4.71108i	−0.132248	−	0.229060i
$424$	1.79636	+	3.11138i	0.0872388	+	0.151102i
$425$	6.29866	−	10.9096i	0.305530	−	0.529193i
$426$	1.82549			0.0884451
$427$	−17.9320	+	0.364776i	−0.867789	+	0.0176528i
$428$	−14.6429			−0.707793
$429$		0			0
$430$	−1.02065	−	1.76782i	−0.0492202	−	0.0852519i
$431$	−2.38238	−	4.12641i	−0.114755	−	0.198762i	0.802927	−	0.596078i	$-0.203275\pi$
$431$	−2.38238	−	4.12641i	−0.114755	−	0.198762i	−0.917682	+	0.397316i	$0.869942\pi$
$432$	9.45848	−	16.3826i	0.455071	−	0.788207i
$433$	22.0231			1.05836			0.529181	−	0.848509i	$-0.322499\pi$
$433$	22.0231			1.05836			0.529181	+	0.848509i	$0.322499\pi$
$434$	−2.77968	−	4.59607i	−0.133429	−	0.220618i
$435$	−15.1072			−0.724337
$436$	0.0317084	−	0.0549206i	0.00151856	−	0.00263022i
$437$	−0.528693	−	0.915724i	−0.0252908	−	0.0438050i
$438$	2.21626	+	3.83868i	0.105897	+	0.183419i
$439$	−1.71620	+	2.97254i	−0.0819097	+	0.141872i	−0.904070	−	0.427384i	$-0.859435\pi$
$439$	−1.71620	+	2.97254i	−0.0819097	+	0.141872i	0.822161	+	0.569256i	$0.192769\pi$
$440$	−11.1294			−0.530576
$441$	3.25275	+	5.13924i	0.154893	+	0.244726i
$442$		0			0
$443$	4.35297	−	7.53957i	0.206816	−	0.358216i	−0.743894	−	0.668298i	$-0.767023\pi$
$443$	4.35297	−	7.53957i	0.206816	−	0.358216i	0.950710	+	0.310082i	$0.100357\pi$
$444$	−11.0733	−	19.1796i	−0.525518	−	0.910223i
$445$	−7.02383	−	12.1656i	−0.332962	−	0.576706i
$446$	0.369491	−	0.639977i	0.0174959	−	0.0303038i
$447$	4.49747			0.212723
$448$	−7.48862	−	12.3821i	−0.353804	−	0.584998i
$449$	17.6120			0.831159			0.415580	−	0.909557i	$-0.363579\pi$
$449$	17.6120			0.831159			0.415580	+	0.909557i	$0.363579\pi$
$450$	0.420219	−	0.727841i	0.0198093	−	0.0343107i
$451$	−22.4915	−	38.9564i	−1.05908	−	1.83439i
$452$	−8.69170	−	15.0545i	−0.408823	−	0.708102i
$453$	1.86045	−	3.22240i	0.0874116	−	0.151401i
$454$	9.00887			0.422807
$455$		0			0
$456$	−3.69436			−0.173004
$457$	4.53634	−	7.85717i	0.212201	−	0.367543i	−0.740202	−	0.672384i	$-0.765270\pi$
$457$	4.53634	−	7.85717i	0.212201	−	0.367543i	0.952403	+	0.304842i	$0.0986035\pi$
$458$	3.15570	+	5.46583i	0.147456	+	0.255401i
$459$	12.2241	+	21.1728i	0.570573	+	0.988262i
$460$	0.737738	−	1.27780i	0.0343972	−	0.0595777i
$461$	6.58319			0.306610			0.153305	−	0.988179i	$-0.451008\pi$
$461$	6.58319			0.306610			0.153305	+	0.988179i	$0.451008\pi$
$462$	−3.68704	+	6.69711i	−0.171537	+	0.311578i
$463$	3.47344			0.161424			0.0807121	−	0.996737i	$-0.474281\pi$
$463$	3.47344			0.161424			0.0807121	+	0.996737i	$0.474281\pi$
$464$	−11.9883	+	20.7644i	−0.556544	+	0.963962i
$465$	6.44507	+	11.1632i	0.298883	+	0.517681i
$466$	3.61293	+	6.25777i	0.167366	+	0.289886i
$467$	−14.8927	+	25.7949i	−0.689152	+	1.19365i	0.282960	+	0.959132i	$0.408684\pi$
$467$	−14.8927	+	25.7949i	−0.689152	+	1.19365i	−0.972112	+	0.234515i	$0.924650\pi$
$468$		0			0
$469$	1.25955	−	2.28783i	0.0581606	−	0.105642i
$470$	−3.00826			−0.138761
$471$	6.86783	−	11.8954i	0.316453	−	0.548113i
$472$	−0.550177	−	0.952935i	−0.0253240	−	0.0438624i
$473$	−12.6499	−	21.9103i	−0.581643	−	1.00744i
$474$	−0.0318119	+	0.0550998i	−0.00146117	+	0.00253082i
$475$	5.69677			0.261386
$476$	21.6357	−	0.440118i	0.991671	−	0.0201728i
$477$	2.41465			0.110559
$478$	−3.31869	+	5.74814i	−0.151793	+	0.262914i
$479$	−17.5927	−	30.4715i	−0.803833	−	1.39228i	−0.917076	−	0.398712i	$-0.869457\pi$
$479$	−17.5927	−	30.4715i	−0.803833	−	1.39228i	0.113243	−	0.993567i	$-0.463876\pi$
$480$	−3.90294	−	6.76008i	−0.178144	−	0.308554i
$481$		0			0
$482$	1.07373			0.0489072
$483$	−1.07968	−	1.78520i	−0.0491273	−	0.0812296i
$484$	−46.2252			−2.10115
$485$	−4.75840	+	8.24179i	−0.216068	+	0.374241i
$486$	1.44793	+	2.50788i	0.0656792	+	0.113760i
$487$	0.900769	+	1.56018i	0.0408178	+	0.0706984i	0.885713	−	0.464234i	$-0.153670\pi$
$487$	0.900769	+	1.56018i	0.0408178	+	0.0706984i	−0.844895	+	0.534933i	$0.820337\pi$
$488$	−4.38192	+	7.58971i	−0.198360	+	0.343570i
$489$	−1.01482			−0.0458916
$490$	3.36064	−	0.136782i	0.151818	−	0.00617920i
$491$	−8.19322			−0.369755			−0.184877	−	0.982762i	$-0.559189\pi$
$491$	−8.19322			−0.369755			−0.184877	+	0.982762i	$0.559189\pi$
$492$	10.4180	−	18.0444i	0.469678	−	0.813506i
$493$	−15.4937	−	26.8358i	−0.697800	−	1.20863i
$494$		0			0
$495$	−3.74003	+	6.47792i	−0.168102	+	0.291161i
$496$	20.4579			0.918587
$497$	−5.15125	−	8.51734i	−0.231065	−	0.382055i
$498$	1.29461			0.0580129
$499$	18.2582	−	31.6242i	0.817350	−	1.41569i	−0.0902781	−	0.995917i	$-0.528776\pi$
$499$	18.2582	−	31.6242i	0.817350	−	1.41569i	0.907628	−	0.419775i	$-0.137891\pi$
$500$	10.8035	+	18.7122i	0.483147	+	0.836834i
$501$	10.2072	+	17.6793i	0.456022	+	0.789854i
$502$	2.07596	−	3.59566i	0.0926545	−	0.160482i
$503$	−3.02972			−0.135089			−0.0675443	−	0.997716i	$-0.521516\pi$
$503$	−3.02972			−0.135089			−0.0675443	+	0.997716i	$0.521516\pi$
$504$	2.97127	−	0.0604422i	0.132351	−	0.00269231i
$505$	0.102392			0.00455637
$506$	−0.534585	+	0.925928i	−0.0237652	+	0.0411625i
$507$		0			0
$508$	13.6000	+	23.5559i	0.603404	+	1.04513i
$509$	−14.6724	+	25.4133i	−0.650341	+	1.12642i	0.332699	+	0.943033i	$0.392041\pi$
$509$	−14.6724	+	25.4133i	−0.650341	+	1.12642i	−0.983040	+	0.183391i	$0.941293\pi$
$510$	3.03631			0.134450
$511$	11.6565	−	21.1728i	0.515654	−	0.936630i
$512$	−21.0487			−0.930229
$513$	−5.52800	+	9.57479i	−0.244067	+	0.422737i
$514$	0.968471	+	1.67744i	0.0427174	+	0.0739887i
$515$	4.58133	+	7.93509i	0.201877	+	0.349662i
$516$	5.85938	−	10.1487i	0.257945	−	0.446773i
$517$	−37.2843			−1.63976
$518$	3.40511	−	6.18502i	0.149612	−	0.271754i
$519$	−7.93637			−0.348368
$520$		0			0
$521$	14.8419	+	25.7069i	0.650236	+	1.12624i	0.983066	+	0.183254i	$0.0586632\pi$
$521$	14.8419	+	25.7069i	0.650236	+	1.12624i	−0.332830	+	0.942987i	$0.608003\pi$
$522$	−1.03367	−	1.79037i	−0.0452425	−	0.0783624i
$523$	−10.2864	+	17.8165i	−0.449791	+	0.779062i	−0.998372	−	0.0570361i	$-0.981835\pi$
$523$	−10.2864	+	17.8165i	−0.449791	+	0.779062i	0.548581	+	0.836098i	$0.315168\pi$
$524$	17.8906			0.781553
$525$	11.2379	−	0.228603i	0.490460	−	0.00997704i
$526$	−5.82146			−0.253828
$527$	−13.2199	+	22.8975i	−0.575867	+	0.997431i
$528$	−14.5590	−	25.2168i	−0.633597	−	1.09742i
$529$	11.3541	+	19.6659i	0.493657	+	0.855039i
$530$	0.667652	−	1.15641i	0.0290010	−	0.0502311i
$531$	−0.739544			−0.0320935
$532$	5.06442	+	8.37377i	0.219571	+	0.363049i
$533$		0			0
$534$	−2.35751	+	4.08332i	−0.102019	+	0.176703i
$535$	5.60144	+	9.70198i	0.242171	+	0.419453i
$536$	−0.638057	−	1.10515i	−0.0275599	−	0.0477351i
$537$	−3.91108	+	6.77419i	−0.168775	+	0.292328i
$538$	−7.42151			−0.319964
$539$	41.6516	−	1.69527i	1.79406	−	0.0730206i
$540$	−15.4275			−0.663896
$541$	17.0334	−	29.5027i	0.732324	−	1.26842i	−0.223564	−	0.974689i	$-0.571769\pi$
$541$	17.0334	−	29.5027i	0.732324	−	1.26842i	0.955888	−	0.293732i	$-0.0948974\pi$
$542$	4.38228	+	7.59034i	0.188235	+	0.326033i
$543$	−5.50371	−	9.53270i	−0.236187	−	0.409087i
$544$	8.00555	−	13.8660i	0.343235	−	0.594500i
$545$	−0.0485183			−0.00207830
$546$		0			0
$547$	−0.850931			−0.0363832			−0.0181916	−	0.999835i	$-0.505791\pi$
$547$	−0.850931			−0.0363832			−0.0181916	+	0.999835i	$0.505791\pi$
$548$	−15.6890	+	27.1741i	−0.670200	+	1.16082i
$549$	2.94507	+	5.10102i	0.125693	+	0.217706i
$550$	−2.88013	−	4.98853i	−0.122809	−	0.212712i
$551$	7.00657	−	12.1357i	0.298490	−	0.516999i
$552$	−1.01942			−0.0433895
$553$	0.346853	−	0.00705575i	0.0147497	−	0.000300041i
$554$	3.11641			0.132404
$555$	−8.47189	+	14.6737i	−0.359612	+	0.622866i
$556$	17.4571	+	30.2366i	0.740347	+	1.28232i
$557$	−8.86404	−	15.3530i	−0.375581	−	0.650526i	0.614833	−	0.788658i	$-0.289224\pi$
$557$	−8.86404	−	15.3530i	−0.375581	−	0.650526i	−0.990414	+	0.138132i	$0.955890\pi$
$558$	−0.881972	+	1.52762i	−0.0373369	+	0.0646694i
$559$		0			0
$560$	−6.17829	+	11.2222i	−0.261080	+	0.474224i
$561$	37.6319			1.58882
$562$	2.95405	−	5.11656i	0.124609	−	0.215829i
$563$	12.0903	+	20.9410i	0.509545	+	0.882558i	0.999939	+	0.0110571i	$0.00351966\pi$
$563$	12.0903	+	20.9410i	0.509545	+	0.882558i	−0.490394	+	0.871501i	$0.663147\pi$
$564$	−8.63495	−	14.9562i	−0.363597	−	0.629768i
$565$	−6.64976	+	11.5177i	−0.279758	+	0.484555i
$566$	3.19301			0.134212
$567$	−7.19465	+	13.0683i	−0.302147	+	0.548817i
$568$	−4.86375			−0.204078
$569$	21.3874	−	37.0441i	0.896608	−	1.55297i	0.0648066	−	0.997898i	$-0.479357\pi$
$569$	21.3874	−	37.0441i	0.896608	−	1.55297i	0.831802	−	0.555073i	$-0.187310\pi$
$570$	0.686542	+	1.18913i	0.0287561	+	0.0498070i
$571$	−3.68140	−	6.37637i	−0.154062	−	0.266843i	0.778655	−	0.627452i	$-0.215902\pi$
$571$	−3.68140	−	6.37637i	−0.154062	−	0.266843i	−0.932717	+	0.360609i	$0.882569\pi$
$572$		0			0
$573$	19.7754			0.826131
$574$	6.64115	−	0.135096i	0.277196	−	0.00563878i
$575$	1.57197			0.0655557
$576$	−2.37608	+	4.11550i	−0.0990035	+	0.171479i
$577$	−4.09696	−	7.09615i	−0.170559	−	0.295417i	0.768057	−	0.640382i	$-0.221224\pi$
$577$	−4.09696	−	7.09615i	−0.170559	−	0.295417i	−0.938615	+	0.344965i	$0.887891\pi$
$578$	0.288793	+	0.500204i	0.0120122	+	0.0208057i
$579$	13.5445	−	23.4598i	0.562892	−	0.974957i
$580$	19.5539			0.811932
$581$	−3.65320	−	6.04039i	−0.151560	−	0.250598i
$582$	3.19426			0.132406
$583$	8.27485	−	14.3325i	0.342709	−	0.593590i
$584$	−5.90491	−	10.2276i	−0.244347	−	0.423221i
$585$		0			0
$586$	1.93339	−	3.34874i	0.0798678	−	0.138335i
$587$	−39.1141			−1.61441			−0.807205	−	0.590271i	$-0.799021\pi$
$587$	−39.1141			−1.61441			−0.807205	+	0.590271i	$0.799021\pi$
$588$	10.3265	+	16.3155i	0.425856	+	0.672838i
$589$	−11.9566			−0.492664
$590$	−0.204485	+	0.354178i	−0.00841849	+	0.0145813i
$591$	−1.94751	−	3.37319i	−0.0801100	−	0.138755i
$592$	13.4457	+	23.2886i	0.552615	+	0.957158i
$593$	−0.606691	+	1.05082i	−0.0249138	+	0.0431520i	−0.878213	−	0.478269i	$-0.841264\pi$
$593$	−0.606691	+	1.05082i	−0.0249138	+	0.0431520i	0.853300	+	0.521421i	$0.174598\pi$
$594$	11.1792			0.458689
$595$	−8.56803	−	14.1668i	−0.351255	−	0.580783i
$596$	−5.82125			−0.238448
$597$	−14.7443	+	25.5378i	−0.603442	+	1.04519i
$598$		0			0
$599$	−16.3319	−	28.2877i	−0.667303	−	1.15580i	−0.978655	−	0.205508i	$-0.934115\pi$
$599$	−16.3319	−	28.2877i	−0.667303	−	1.15580i	0.311352	−	0.950295i	$-0.399218\pi$
$600$	2.74612	−	4.75642i	0.112110	−	0.194180i
$601$	2.50114			0.102024			0.0510118	−	0.998698i	$-0.483755\pi$
$601$	2.50114			0.102024			0.0510118	+	0.998698i	$0.483755\pi$
$602$	3.73519	−	0.0759819i	0.152235	−	0.00309679i
$603$	−0.857671			−0.0349271
$604$	−2.40806	+	4.17088i	−0.0979825	+	0.169711i
$605$	17.6828	+	30.6275i	0.718907	+	1.24518i
$606$	−0.0171836	−	0.0297628i	−0.000698035	−	0.00120903i
$607$	−6.32282	+	10.9515i	−0.256635	+	0.444506i	−0.965338	−	0.261001i	$-0.915947\pi$
$607$	−6.32282	+	10.9515i	−0.256635	+	0.444506i	0.708703	+	0.705507i	$0.249281\pi$
$608$	7.24055			0.293643
$609$	13.3347	−	24.2209i	0.540347	−	0.981482i
$610$	3.25726			0.131883
$611$		0			0
$612$	−3.55336	−	6.15460i	−0.143636	−	0.248785i
$613$	10.0140	+	17.3448i	0.404462	+	0.700548i	0.994259	−	0.107003i	$-0.0341256\pi$
$613$	10.0140	+	17.3448i	0.404462	+	0.700548i	−0.589797	+	0.807552i	$0.700792\pi$
$614$	−2.29804	+	3.98032i	−0.0927413	+	0.160633i
$615$	−15.9409			−0.642801
$616$	9.82359	−	17.8435i	0.395804	−	0.718934i
$617$	45.2926			1.82341			0.911705	−	0.410846i	$-0.134767\pi$
$617$	45.2926			1.82341			0.911705	+	0.410846i	$0.134767\pi$
$618$	1.53769	−	2.66336i	0.0618551	−	0.107136i
$619$	−2.21658	−	3.83922i	−0.0890917	−	0.154311i	0.818036	−	0.575167i	$-0.195063\pi$
$619$	−2.21658	−	3.83922i	−0.0890917	−	0.154311i	−0.907127	+	0.420856i	$0.861730\pi$
$620$	−8.34212	−	14.4490i	−0.335028	−	0.580285i
$621$	−1.52540	+	2.64207i	−0.0612122	+	0.106023i
$622$	−10.2087			−0.409332
$623$	25.7045	−	0.522886i	1.02983	−	0.0209490i
$624$		0			0
$625$	0.989985	−	1.71471i	0.0395994	−	0.0685882i
$626$	1.84247	+	3.19125i	0.0736400	+	0.127548i
$627$	8.50897	+	14.7380i	0.339816	+	0.588578i
$628$	−8.88931	+	15.3967i	−0.354722	+	0.614397i
$629$	−34.7544			−1.38575
$630$	−0.571621	−	0.945148i	−0.0227739	−	0.0376556i
$631$	−19.7358			−0.785672			−0.392836	−	0.919609i	$-0.628506\pi$
$631$	−19.7358			−0.785672			−0.392836	+	0.919609i	$0.628506\pi$
$632$	0.0847581	−	0.146805i	0.00337150	−	0.00583961i
$633$	−9.58147	−	16.5956i	−0.380829	−	0.659615i
$634$	3.96912	+	6.87472i	0.157634	+	0.273030i
$635$	10.4050	−	18.0220i	0.412909	−	0.715180i
$636$	7.66574			0.303967
$637$		0			0
$638$	−14.1693			−0.560968
$639$	−1.63445	+	2.83096i	−0.0646580	+	0.111991i
$640$	6.66106	+	11.5373i	0.263302	+	0.456052i
$641$	−19.8213	−	34.3314i	−0.782893	−	1.35601i	−0.930250	−	0.366926i	$-0.880410\pi$
$641$	−19.8213	−	34.3314i	−0.782893	−	1.35601i	0.147357	−	0.989083i	$-0.452923\pi$
$642$	1.88009	−	3.25641i	0.0742012	−	0.128520i
$643$	20.8300			0.821453			0.410727	−	0.911759i	$-0.365275\pi$
$643$	20.8300			0.821453			0.410727	+	0.911759i	$0.365275\pi$
$644$	1.39748	+	2.31066i	0.0550684	+	0.0910529i
$645$	−8.96568			−0.353023
$646$	−1.40821	+	2.43909i	−0.0554052	+	0.0959646i
$647$	7.87206	+	13.6348i	0.309482	+	0.536039i	0.978249	−	0.207433i	$-0.0665109\pi$
$647$	7.87206	+	13.6348i	0.309482	+	0.536039i	−0.668767	+	0.743472i	$0.733178\pi$
$648$	3.64463	+	6.31269i	0.143175	+	0.247986i
$649$	−2.53437	+	4.38966i	−0.0994828	+	0.172309i
$650$		0			0
$651$	−23.5864	+	0.479800i	−0.924426	+	0.0188049i
$652$	1.31352			0.0514413
$653$	13.5132	−	23.4055i	0.528812	−	0.915930i	−0.470623	−	0.882334i	$-0.655971\pi$
$653$	13.5132	−	23.4055i	0.528812	−	0.915930i	0.999436	−	0.0335954i	$-0.0106958\pi$
$654$	0.00814244	+	0.0141031i	0.000318395	+	0.000551476i
$655$	−6.84378	−	11.8538i	−0.267409	−	0.463165i
$656$	−12.6499	+	21.9103i	−0.493896	+	0.855453i
$657$	−7.93734			−0.309665
$658$	2.65529	−	4.82305i	0.103514	−	0.188022i
$659$	−6.79491			−0.264692			−0.132346	−	0.991204i	$-0.542251\pi$
$659$	−6.79491			−0.264692			−0.132346	+	0.991204i	$0.542251\pi$
$660$	−11.8734	+	20.5653i	−0.462172	+	0.800505i
$661$	−3.60263	−	6.23994i	−0.140126	−	0.242705i	0.787418	−	0.616420i	$-0.211417\pi$
$661$	−3.60263	−	6.23994i	−0.140126	−	0.242705i	−0.927544	+	0.373714i	$0.878084\pi$
$662$	3.04522	+	5.27448i	0.118356	+	0.204998i
$663$		0			0
$664$	−3.44930			−0.133859
$665$	3.61090	−	6.55880i	0.140025	−	0.254339i
$666$	−2.31866			−0.0898463
$667$	1.93339	−	3.34874i	0.0748613	−	0.129664i
$668$	−13.2115	−	22.8831i	−0.511170	−	0.885372i
$669$	−1.62285	−	2.81087i	−0.0627432	−	0.108674i
$670$	−0.237147	+	0.410750i	−0.00916178	+	0.0158687i
$671$	40.3703			1.55848
$672$	14.2832	−	0.290552i	0.550987	−	0.0112083i
$673$	8.32130			0.320763			0.160381	−	0.987055i	$-0.448728\pi$
$673$	8.32130			0.320763			0.160381	+	0.987055i	$0.448728\pi$
$674$	−1.19948	+	2.07756i	−0.0462022	+	0.0800246i
$675$	−8.21824	−	14.2344i	−0.316320	−	0.547883i
$676$		0			0
$677$	14.9978	−	25.9770i	0.576413	−	0.998376i	−0.419474	−	0.907767i	$-0.637785\pi$
$677$	14.9978	−	25.9770i	0.576413	−	0.998376i	0.995887	−	0.0906086i	$-0.0288812\pi$
$678$	4.46391			0.171435
$679$	−9.01372	−	14.9037i	−0.345915	−	0.571953i
$680$	−8.08982			−0.310231
$681$	19.7841	−	34.2671i	0.758128	−	1.31312i
$682$	6.04493	+	10.4701i	0.231472	+	0.400922i
$683$	18.0420	+	31.2496i	0.690356	+	1.19573i	0.971721	+	0.236132i	$0.0758796\pi$
$683$	18.0420	+	31.2496i	0.690356	+	1.19573i	−0.281365	+	0.959601i	$0.590787\pi$
$684$	1.60690	−	2.78324i	0.0614415	−	0.106420i
$685$	24.0064			0.917236
$686$	−2.74703	+	5.50874i	−0.104882	+	0.210325i
$687$	27.7205			1.05760
$688$	−7.11470	+	12.3230i	−0.271245	+	0.469811i
$689$		0			0
$690$	0.189445	+	0.328128i	0.00721204	+	0.0124916i
$691$	12.8838	−	22.3155i	0.490124	−	0.848920i	−0.509811	−	0.860286i	$-0.670285\pi$
$691$	12.8838	−	22.3155i	0.490124	−	0.848920i	0.999935	+	0.0113665i	$0.00361814\pi$
$692$	10.2724			0.390497
$693$	−7.08465	−	11.7141i	−0.269123	−	0.444983i
$694$	7.00589			0.265940
$695$	13.3559	−	23.1332i	0.506620	−	0.877491i
$696$	−6.75501	−	11.7000i	−0.256048	−	0.443488i
$697$	−16.3487	−	28.3168i	−0.619252	−	1.07258i
$698$	5.11242	−	8.85496i	0.193508	−	0.335165i
$699$	31.7369			1.20040
$700$	−14.5456	+	0.295890i	−0.549772	+	0.0111836i
$701$	41.7872			1.57828			0.789141	−	0.614213i	$-0.210526\pi$
$701$	41.7872			1.57828			0.789141	+	0.614213i	$0.210526\pi$
$702$		0			0
$703$	−7.85834	−	13.6110i	−0.296383	−	0.513350i
$704$	16.2854	+	28.2071i	0.613778	+	1.06310i
$705$	−6.60635	+	11.4425i	−0.248809	+	0.430951i
$706$	2.03471			0.0765774
$707$	−0.0903778	+	0.164161i	−0.00339901	+	0.00617393i
$708$	−2.34782			−0.0882364
$709$	−0.171924	+	0.297781i	−0.00645673	+	0.0111834i	−0.869236	−	0.494398i	$-0.835389\pi$
$709$	−0.171924	+	0.297781i	−0.00645673	+	0.0111834i	0.862779	+	0.505581i	$0.168722\pi$
$710$	0.903855	+	1.56552i	0.0339211	+	0.0587530i
$711$	−0.0569657	−	0.0986674i	−0.00213638	−	0.00370032i
$712$	6.28124	−	10.8794i	0.235399	−	0.407724i
$713$	−3.29931			−0.123560
$714$	−2.68005	+	4.86802i	−0.100298	+	0.182181i
$715$		0			0
$716$	5.06227	−	8.76810i	0.189186	−	0.327679i
$717$	14.5761	+	25.2466i	0.544356	+	0.942852i
$718$	3.22881	+	5.59246i	0.120498	+	0.208709i
$719$	−4.39005	+	7.60379i	−0.163721	+	0.283574i	−0.936200	−	0.351467i	$-0.885683\pi$
$719$	−4.39005	+	7.60379i	−0.163721	+	0.283574i	0.772479	+	0.635040i	$0.219016\pi$
$720$	4.20702			0.156786
$721$	−16.7659	+	0.341055i	−0.624393	+	0.0127015i
$722$	5.04149			0.187625
$723$	2.35799	−	4.08416i	0.0876946	−	0.151891i
$724$	7.12367	+	12.3386i	0.264749	+	0.458559i
$725$	10.4164	+	18.0416i	0.386854	+	0.670050i
$726$	5.93512	−	10.2799i	0.220273	−	0.381524i
$727$	−17.3658			−0.644064			−0.322032	−	0.946729i	$-0.604366\pi$
$727$	−17.3658			−0.644064			−0.322032	+	0.946729i	$0.604366\pi$
$728$		0			0
$729$	29.6343			1.09757
$730$	−2.19468	+	3.80130i	−0.0812288	+	0.140692i
$731$	−9.19502	−	15.9262i	−0.340090	−	0.589053i
$732$	9.34968	+	16.1941i	0.345574	+	0.598552i
$733$	4.52947	−	7.84528i	0.167300	−	0.289772i	−0.770170	−	0.637839i	$-0.779828\pi$
$733$	4.52947	−	7.84528i	0.167300	−	0.289772i	0.937470	+	0.348067i	$0.113162\pi$
$734$	1.79638			0.0663056
$735$	6.85991	−	13.0833i	0.253032	−	0.482583i
$736$	1.99796			0.0736458
$737$	−2.93919	+	5.09082i	−0.108266	+	0.187523i
$738$	−1.09071	−	1.88917i	−0.0401498	−	0.0695414i
$739$	3.53921	+	6.13010i	0.130192	+	0.225499i	0.923751	−	0.382995i	$-0.125107\pi$
$739$	3.53921	+	6.13010i	0.130192	+	0.225499i	−0.793558	+	0.608494i	$0.791774\pi$
$740$	10.9655	−	18.9928i	0.403100	−	0.698190i
$741$		0			0
$742$	1.26472	+	2.09115i	0.0464292	+	0.0767685i
$743$	−14.6779			−0.538479			−0.269240	−	0.963073i	$-0.586772\pi$
$743$	−14.6779			−0.538479			−0.269240	+	0.963073i	$0.586772\pi$
$744$	−5.76367	+	9.98297i	−0.211306	+	0.365993i
$745$	2.22684	+	3.85699i	0.0815849	+	0.141309i
$746$	2.70066	+	4.67768i	0.0988782	+	0.171262i
$747$	−1.15913	+	2.00768i	−0.0424105	+	0.0734571i
$748$	−48.7085			−1.78096
$749$	−20.4991	+	0.416997i	−0.749020	+	0.0152367i
$750$	−5.54848			−0.202602
$751$	15.8556	−	27.4628i	0.578580	−	1.00213i	−0.417062	−	0.908878i	$-0.636940\pi$
$751$	15.8556	−	27.4628i	0.578580	−	1.00213i	0.995643	−	0.0932523i	$-0.0297263\pi$
$752$	10.4849	+	18.1604i	0.382345	+	0.662241i
$753$	−9.11788	−	15.7926i	−0.332274	−	0.575516i
$754$		0			0
$755$	3.68467			0.134099
$756$	13.6174	−	24.7345i	0.495259	−	0.899585i
$757$	15.5317			0.564510			0.282255	−	0.959339i	$-0.408918\pi$
$757$	15.5317			0.564510			0.282255	+	0.959339i	$0.408918\pi$
$758$	−4.18344	+	7.24593i	−0.151949	+	0.263184i
$759$	2.34797	+	4.06680i	0.0852259	+	0.147616i
$760$	−1.82919	−	3.16825i	−0.0663518	−	0.114925i
$761$	−0.125185	+	0.216826i	−0.00453794	+	0.00785993i	−0.868285	−	0.496065i	$-0.834778\pi$
$761$	−0.125185	+	0.216826i	−0.00453794	+	0.00785993i	0.863748	+	0.503925i	$0.168111\pi$
$762$	−6.98474			−0.253030
$763$	0.0428255	−	0.0777879i	0.00155039	−	0.00281611i
$764$	−25.5961			−0.926036
$765$	−2.71857	+	4.70870i	−0.0982901	+	0.170243i
$766$	−0.633903	−	1.09795i	−0.0229039	−	0.0396706i
$767$		0			0
$768$	−5.74859	+	9.95686i	−0.207435	+	0.359287i
$769$	−24.0146			−0.865988			−0.432994	−	0.901397i	$-0.642543\pi$
$769$	−24.0146			−0.865988			−0.432994	+	0.901397i	$0.642543\pi$
$770$	−7.56896	+	0.153969i	−0.272766	+	0.00554867i
$771$	8.50731			0.306383
$772$	−17.5312	+	30.3650i	−0.630963	+	1.09286i
$773$	−15.2531	−	26.4192i	−0.548616	−	0.950231i	−0.998370	−	0.0570784i	$-0.981821\pi$
$773$	−15.2531	−	26.4192i	−0.548616	−	0.950231i	0.449753	−	0.893153i	$-0.351512\pi$
$774$	−0.613451	−	1.06253i	−0.0220501	−	0.0381918i
$775$	8.88768	−	15.3939i	0.319255	−	0.552966i
$776$	−8.51064			−0.305514
$777$	−16.0481	−	26.5347i	−0.575722	−	0.951928i
$778$	0.954237			0.0342110
$779$	7.39323	−	12.8055i	0.264890	−	0.458803i
$780$		0			0
$781$	11.2023	+	19.4030i	0.400851	+	0.694294i
$782$	−0.388582	+	0.673043i	−0.0138956	+	0.0240680i
$783$	−40.4311			−1.44489
$784$	−12.5388	−	19.8109i	−0.447815	−	0.707532i
$785$	13.6019			0.485473
$786$	−2.29707	+	3.97865i	−0.0819339	+	0.141914i
$787$	−9.92461	−	17.1899i	−0.353774	−	0.612755i	0.633133	−	0.774043i	$-0.281769\pi$
$787$	−9.92461	−	17.1899i	−0.353774	−	0.612755i	−0.986907	+	0.161288i	$0.948435\pi$
$788$	2.52075	+	4.36606i	0.0897978	+	0.155534i
$789$	−12.7843	+	22.1431i	−0.455134	+	0.788315i
$790$	−0.0630042			−0.00224159
$791$	−12.5965	−	20.8277i	−0.447879	−	0.740547i
$792$	−6.68923			−0.237691
$793$		0			0
$794$	3.17724	+	5.50314i	0.112756	+	0.195299i
$795$	−2.93242	−	5.07910i	−0.104002	−	0.180137i
$796$	19.0841	−	33.0546i	0.676418	−	1.17159i
$797$	52.2894			1.85219			0.926093	−	0.377296i	$-0.123146\pi$
$797$	52.2894			1.85219			0.926093	+	0.377296i	$0.123146\pi$
$798$	−2.51248	+	0.0511093i	−0.0889407	+	0.00180925i
$799$	−27.1014			−0.958777
$800$	−5.38210	+	9.32207i	−0.190286	+	0.329585i
$801$	−4.22160	−	7.31202i	−0.149163	−	0.258358i
$802$	−0.498271	−	0.863031i	−0.0175946	−	0.0304747i
$803$	−27.2008	+	47.1131i	−0.959894	+	1.66259i
$804$	−2.72283			−0.0960269
$805$	0.996393	−	1.80984i	0.0351182	−	0.0637884i
$806$		0			0
$807$	−16.2981	+	28.2292i	−0.573722	+	0.993715i
$808$	0.0457832	+	0.0792988i	0.00161065	+	0.00278972i
$809$	1.18230	+	2.04780i	0.0415674	+	0.0719969i	0.886061	−	0.463569i	$-0.153432\pi$
$809$	1.18230	+	2.04780i	0.0415674	+	0.0719969i	−0.844493	+	0.535566i	$0.820098\pi$
$810$	1.35460	−	2.34624i	0.0475959	−	0.0824385i
$811$	23.6646			0.830978			0.415489	−	0.909598i	$-0.363610\pi$
$811$	23.6646			0.830978			0.415489	+	0.909598i	$0.363610\pi$
$812$	−17.2596	+	31.3502i	−0.605693	+	1.10017i
$813$	38.4952			1.35008
$814$	−7.94591	+	13.7627i	−0.278504	+	0.482383i
$815$	−0.502467	−	0.870298i	−0.0176006	−	0.0304852i
$816$	−10.5827	−	18.3297i	−0.370468	−	0.641669i
$817$	4.15818	−	7.20218i	0.145476	−	0.251972i
$818$	−11.3275			−0.396058
$819$		0			0
$820$	20.6330			0.720536
$821$	1.78877	−	3.09823i	0.0624284	−	0.108129i	−0.833122	−	0.553089i	$-0.813449\pi$
$821$	1.78877	−	3.09823i	0.0624284	−	0.108129i	0.895550	+	0.444960i	$0.146782\pi$
$822$	−4.02879	−	6.97808i	−0.140520	−	0.243388i
$823$	14.9711	+	25.9307i	0.521859	+	0.903887i	0.999677	+	0.0254278i	$0.00809478\pi$
$823$	14.9711	+	25.9307i	0.521859	+	0.903887i	−0.477817	+	0.878459i	$0.658572\pi$
$824$	−4.09696	+	7.09615i	−0.142725	+	0.247206i
$825$	−25.2998			−0.880827
$826$	−0.387350	−	0.640464i	−0.0134776	−	0.0222846i
$827$	−9.32620			−0.324304			−0.162152	−	0.986766i	$-0.551843\pi$
$827$	−9.32620			−0.324304			−0.162152	+	0.986766i	$0.551843\pi$
$828$	0.443409	−	0.768007i	0.0154095	−	0.0266901i
$829$	−19.1134	−	33.1054i	−0.663836	−	1.14980i	−0.979599	−	0.200960i	$-0.935594\pi$
$829$	−19.1134	−	33.1054i	−0.663836	−	1.14980i	0.315763	−	0.948838i	$-0.397739\pi$
$830$	0.641002	+	1.11025i	0.0222495	+	0.0385373i
$831$	6.84385	−	11.8539i	0.237411	−	0.411207i
$832$		0			0
$833$	30.2759	−	1.23227i	1.04900	−	0.0426956i
$834$	−8.96568			−0.310456
$835$	−10.1078	+	17.5072i	−0.349794	+	0.605860i
$836$	−11.0135	−	19.0760i	−0.380910	−	0.659756i
$837$	17.2488	+	29.8757i	0.596205	+	1.03266i
$838$	5.77933	−	10.0101i	0.199644	−	0.345793i
$839$	−23.4981			−0.811244			−0.405622	−	0.914041i	$-0.632945\pi$
$839$	−23.4981			−0.811244			−0.405622	+	0.914041i	$0.632945\pi$
$840$	−3.73553	−	6.17652i	−0.128888	−	0.213110i
$841$	22.2451			0.767071
$842$	4.01178	−	6.94860i	0.138255	−	0.239465i
$843$	−12.9746	−	22.4726i	−0.446868	−	0.773998i
$844$	12.4017	+	21.4803i	0.426883	+	0.739384i
$845$		0			0
$846$	−1.80808			−0.0621632
$847$	−64.7121	+	1.31639i	−2.22353	+	0.0452316i
$848$	−9.30806			−0.319640
$849$	7.01205	−	12.1452i	0.240653	−	0.416823i
$850$	−2.09352	−	3.62608i	−0.0718072	−	0.124374i
$851$	−2.16843	−	3.75584i	−0.0743329	−	0.128748i
$852$	−5.18887	+	8.98738i	−0.177768	+	0.307903i
$853$	−40.9295			−1.40140			−0.700700	−	0.713456i	$-0.747129\pi$
$853$	−40.9295			−1.40140			−0.700700	+	0.713456i	$0.747129\pi$
$854$	−2.87508	+	5.22226i	−0.0983830	+	0.178702i
$855$	−2.45879			−0.0840888
$856$	−5.00923	+	8.67624i	−0.171212	+	0.296548i
$857$	5.83099	+	10.0996i	0.199183	+	0.344995i	0.948264	−	0.317484i	$-0.102838\pi$
$857$	5.83099	+	10.0996i	0.199183	+	0.344995i	−0.749081	+	0.662479i	$0.769505\pi$
$858$		0			0
$859$	−14.1388	+	24.4891i	−0.482410	+	0.835559i	−0.999796	−	0.0201934i	$-0.993572\pi$
$859$	−14.1388	+	24.4891i	−0.482410	+	0.835559i	0.517386	+	0.855752i	$0.326905\pi$
$860$	11.6046			0.395715
$861$	14.0705	−	25.5576i	0.479523	−	0.871001i
$862$	−1.58369			−0.0539407
$863$	5.72212	−	9.91101i	0.194783	−	0.337375i	−0.752046	−	0.659110i	$-0.770933\pi$
$863$	5.72212	−	9.91101i	0.194783	−	0.337375i	0.946829	+	0.321736i	$0.104266\pi$
$864$	−10.4453	−	18.0918i	−0.355357	−	0.615496i
$865$	−3.92954	−	6.80617i	−0.133609	−	0.231417i
$866$	3.65996	−	6.33924i	0.124371	−	0.215416i
$867$	2.53683			0.0861553
$868$	30.5289	−	0.621025i	1.03622	−	0.0210790i
$869$	−0.780871			−0.0264892
$870$	−2.51064	+	4.34855i	−0.0851186	+	0.147430i
$871$		0			0
$872$	−0.0216944	−	0.0375757i	−0.000734664	−	0.00127248i
$873$	−2.85998	+	4.95364i	−0.0967958	+	0.167655i
$874$	−0.351449			−0.0118879
$875$	15.6570	+	25.8881i	0.529303	+	0.875177i
$876$	−25.1985			−0.851380
$877$	28.1743	−	48.7993i	0.951378	−	1.64783i	0.208930	−	0.977930i	$-0.433002\pi$
$877$	28.1743	−	48.7993i	0.951378	−	1.64783i	0.742447	−	0.669904i	$-0.233665\pi$
$878$	0.570422	+	0.988000i	0.0192508	+	0.0333434i
$879$	−8.49173	−	14.7081i	−0.286419	−	0.496092i
$880$	14.4172	−	24.9713i	0.486003	−	0.841782i
$881$	−1.16418			−0.0392221			−0.0196111	−	0.999808i	$-0.506243\pi$
$881$	−1.16418			−0.0392221			−0.0196111	+	0.999808i	$0.506243\pi$
$882$	2.01988	−	0.0822115i	0.0680128	−	0.00276821i
$883$	−12.1881			−0.410162			−0.205081	−	0.978745i	$-0.565746\pi$
$883$	−12.1881			−0.410162			−0.205081	+	0.978745i	$0.565746\pi$
$884$		0			0
$885$	0.898123	+	1.55560i	0.0301901	+	0.0522908i
$886$	−1.44682	−	2.50597i	−0.0486069	−	0.0841896i
$887$	−15.3320	+	26.5559i	−0.514799	+	0.891659i	0.485053	+	0.874485i	$0.338800\pi$
$887$	−15.3320	+	26.5559i	−0.514799	+	0.891659i	−0.999853	+	0.0171740i	$0.994533\pi$
$888$	−15.1524			−0.508481
$889$	19.7099	+	32.5894i	0.661049	+	1.09301i
$890$	−4.66910			−0.156509
$891$	16.7889	−	29.0792i	0.562449	−	0.974190i
$892$	2.10053	+	3.63822i	0.0703308	+	0.121817i
$893$	−6.12790	−	10.6138i	−0.205062	−	0.355178i
$894$	0.747424	−	1.29458i	0.0249976	−	0.0432971i
$895$	−7.74598			−0.258920
$896$	−24.3769	+	0.495879i	−0.814374	+	0.0165662i
$897$		0			0
$898$	2.92689	−	5.06952i	0.0976716	−	0.169172i
$899$	−21.8622	−	37.8665i	−0.729147	−	1.26292i
$900$	2.38891	+	4.13771i	0.0796303	+	0.137924i
$901$	6.01486	−	10.4180i	0.200384	−	0.347075i
$902$	−14.9512			−0.497822
$903$	7.91370	−	14.3744i	0.263352	−	0.478350i
$904$	−11.8934			−0.395570
$905$	5.45011	−	9.43987i	0.181168	−	0.313792i
$906$	−0.618368	−	1.07105i	−0.0205439	−	0.0355831i
$907$	5.82396	+	10.0874i	0.193382	+	0.334947i	0.946369	−	0.323088i	$-0.104721\pi$
$907$	5.82396	+	10.0874i	0.193382	+	0.334947i	−0.752987	+	0.658035i	$0.771388\pi$
$908$	−25.6074	+	44.3532i	−0.849810	+	1.47191i
$909$	0.0615414			0.00204120
$910$		0			0
$911$	−26.5833			−0.880743			−0.440371	−	0.897816i	$-0.645153\pi$
$911$	−26.5833			−0.880743			−0.440371	+	0.897816i	$0.645153\pi$
$912$	4.78571	−	8.28909i	0.158471	−	0.274479i
$913$	7.94455	+	13.7604i	0.262926	+	0.455402i
$914$	−1.50777	−	2.61153i	−0.0498725	−	0.0863817i
$915$	7.15316	−	12.3896i	0.236476	−	0.409589i
$916$	−35.8797			−1.18550
$917$	25.0455	−	0.509482i	0.827077	−	0.0168246i
$918$	8.12600			0.268198
$919$	22.8540	−	39.5842i	0.753883	−	1.30576i	−0.192045	−	0.981386i	$-0.561512\pi$
$919$	22.8540	−	39.5842i	0.753883	−	1.30576i	0.945928	−	0.324377i	$-0.105155\pi$
$920$	−0.504748	−	0.874250i	−0.0166411	−	0.0288232i
$921$	10.0933	+	17.4821i	0.332585	+	0.576055i
$922$	1.09405	−	1.89494i	0.0360305	−	0.0624066i
$923$		0			0
$924$	−22.4915	−	37.1886i	−0.739916	−	1.22342i
$925$	23.3653			0.768246
$926$	0.577242	−	0.999813i	0.0189694	−	0.0328559i
$927$	2.75356	+	4.76930i	0.0904386	+	0.156644i
$928$	13.2391	+	22.9308i	0.434595	+	0.752740i
$929$	5.53257	−	9.58268i	0.181518	−	0.314398i	−0.760880	−	0.648893i	$-0.775232\pi$
$929$	5.53257	−	9.58268i	0.181518	−	0.314398i	0.942398	+	0.334495i	$0.108566\pi$
$930$	4.28437			0.140490
$931$	7.32830	+	11.5785i	0.240175	+	0.379469i
$932$	−41.0784			−1.34557
$933$	−22.4190	+	38.8309i	−0.733965	+	1.27127i
$934$	4.94997	+	8.57360i	0.161968	+	0.280537i
$935$	18.6327	+	32.2729i	0.609356	+	1.05544i
$936$		0			0
$937$	−57.6584			−1.88362			−0.941808	−	0.336150i	$-0.890875\pi$
$937$	−57.6584			−1.88362			−0.941808	+	0.336150i	$0.890875\pi$
$938$	−0.449221	−	0.742765i	−0.0146676	−	0.0242521i
$939$	16.1848			0.528170
$940$	8.55086	−	14.8105i	0.278898	−	0.483066i
$941$	8.48723	+	14.7003i	0.276676	+	0.479216i	0.970557	−	0.240874i	$-0.0774339\pi$
$941$	8.48723	+	14.7003i	0.276676	+	0.479216i	−0.693881	+	0.720090i	$0.744101\pi$
$942$	−2.28270	−	3.95375i	−0.0743743	−	0.128820i
$943$	2.04009	−	3.53354i	0.0664345	−	0.115068i
$944$	2.85082			0.0927862
$945$	−21.5975	+	0.439340i	−0.702566	+	0.0142917i
$946$	−8.40904			−0.273401
$947$	8.34808	−	14.4593i	0.271276	−	0.469864i	−0.697913	−	0.716183i	$-0.745888\pi$
$947$	8.34808	−	14.4593i	0.271276	−	0.469864i	0.969189	+	0.246319i	$0.0792210\pi$
$948$	−0.180848	−	0.313238i	−0.00587366	−	0.0101735i
$949$		0			0
$950$	0.946733	−	1.63979i	0.0307161	−	0.0532018i
$951$	34.8658			1.13060
$952$	7.14062	−	12.9702i	0.231429	−	0.420365i
$953$	−18.2473			−0.591089			−0.295545	−	0.955329i	$-0.595501\pi$
$953$	−18.2473			−0.591089			−0.295545	+	0.955329i	$0.595501\pi$
$954$	0.401285	−	0.695046i	0.0129921	−	0.0225029i
$955$	9.79143	+	16.9593i	0.316843	+	0.548789i
$956$	−18.8665	−	32.6777i	−0.610186	−	1.05687i
$957$	−31.1167	+	53.8957i	−1.00586	+	1.74220i
$958$	−11.6948			−0.377841
$959$	−21.1896	+	38.4886i	−0.684248	+	1.24286i
$960$	11.5423			0.372527
$961$	−3.15382	+	5.46257i	−0.101736	+	0.176212i
$962$		0			0
$963$	3.36669	+	5.83127i	0.108490	+	0.187910i
$964$	−3.05204	+	5.28629i	−0.0982996	+	0.170260i
$965$	26.8253			0.863537
$966$	−0.693293	+	0.0141031i	−0.0223063	+	0.000453760i
$967$	−29.5845			−0.951374			−0.475687	−	0.879615i	$-0.657801\pi$
$967$	−29.5845			−0.951374			−0.475687	+	0.879615i	$0.657801\pi$
$968$	−15.8133	+	27.3894i	−0.508258	+	0.880328i
$969$	6.18504	+	10.7128i	0.198692	+	0.344145i
$970$	1.58158	+	2.73937i	0.0507813	+	0.0879558i
$971$	−7.56504	+	13.1030i	−0.242774	+	0.420497i	−0.961503	−	0.274793i	$-0.911391\pi$
$971$	−7.56504	+	13.1030i	−0.242774	+	0.420497i	0.718730	+	0.695290i	$0.244724\pi$
$972$	−16.4627			−0.528040
$973$	25.2998	+	41.8320i	0.811075	+	1.34107i
$974$	0.598787			0.0191864
$975$		0			0
$976$	−11.3528	−	19.6636i	−0.363393	−	0.629415i
$977$	−16.2318	−	28.1143i	−0.519301	−	0.899457i	−0.999748	−	0.0224327i	$-0.992859\pi$
$977$	−16.2318	−	28.1143i	−0.519301	−	0.899457i	0.480447	−	0.877024i	$-0.340474\pi$
$978$	−0.168650	+	0.292110i	−0.00539283	+	0.00934065i
$979$	−57.8686			−1.84949
$980$	−8.87906	+	16.9342i	−0.283631	+	0.540943i
$981$	−0.0291614			−0.000931052
$982$	−1.36161	+	2.35838i	−0.0434508	+	0.0752590i
$983$	22.1473	+	38.3602i	0.706388	+	1.22350i	0.966188	+	0.257838i	$0.0830099\pi$
$983$	22.1473	+	38.3602i	0.706388	+	1.22350i	−0.259800	+	0.965662i	$0.583657\pi$
$984$	−7.12779	−	12.3457i	−0.227226	−	0.393567i
$985$	1.92855	−	3.34034i	0.0614487	−	0.106432i
$986$	−10.2994			−0.328001
$987$	−12.5142	−	20.6917i	−0.398333	−	0.658624i
$988$		0			0
$989$	1.14741	−	1.98737i	0.0364855	−	0.0631948i
$990$	1.24309	+	2.15310i	0.0395081	+	0.0684301i
$991$	4.26058	+	7.37955i	0.135342	+	0.234419i	0.925728	−	0.378190i	$-0.123453\pi$
$991$	4.26058	+	7.37955i	0.135342	+	0.234419i	−0.790386	+	0.612609i	$0.790120\pi$
$992$	11.2962	−	19.5655i	0.358654	−	0.621206i
$993$	26.7500			0.848887
$994$	−3.30775	+	0.0672870i	−0.104916	+	0.00213422i
$995$	−29.2014			−0.925746
$996$	−3.67988	+	6.37374i	−0.116601	+	0.201960i
$997$	3.38953	+	5.87083i	0.107347	+	0.185931i	0.914695	−	0.404145i	$-0.132431\pi$
$997$	3.38953	+	5.87083i	0.107347	+	0.185931i	−0.807347	+	0.590076i	$0.799098\pi$
$998$	−6.06858	−	10.5111i	−0.192098	−	0.332723i
$999$	−22.6731	+	39.2709i	−0.717344	+	1.24248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.i.170.5		16
7.2	even	3		8281.2.a.ck.1.4		8
7.4	even	3	inner	1183.2.e.i.508.5		16
7.5	odd	6		8281.2.a.cj.1.4		8
13.5	odd	4		91.2.r.a.51.4	yes	16
13.8	odd	4		91.2.r.a.51.5	yes	16
13.12	even	2	inner	1183.2.e.i.170.4		16
39.5	even	4		819.2.dl.e.415.5		16
39.8	even	4		819.2.dl.e.415.4		16
91.5	even	12		637.2.c.e.246.5		8
91.12	odd	6		8281.2.a.cj.1.5		8
91.18	odd	12		91.2.r.a.25.5	yes	16
91.25	even	6	inner	1183.2.e.i.508.4		16
91.31	even	12		637.2.r.f.116.5		16
91.34	even	4		637.2.r.f.324.5		16
91.44	odd	12		637.2.c.f.246.5		8
91.47	even	12		637.2.c.e.246.4		8
91.51	even	6		8281.2.a.ck.1.5		8
91.60	odd	12		91.2.r.a.25.4	✓	16
91.73	even	12		637.2.r.f.116.4		16
91.83	even	4		637.2.r.f.324.4		16
91.86	odd	12		637.2.c.f.246.4		8
273.200	even	12		819.2.dl.e.298.4		16
273.242	even	12		819.2.dl.e.298.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.4	✓	16	91.60	odd	12
91.2.r.a.25.5	yes	16	91.18	odd	12
91.2.r.a.51.4	yes	16	13.5	odd	4
91.2.r.a.51.5	yes	16	13.8	odd	4
637.2.c.e.246.4		8	91.47	even	12
637.2.c.e.246.5		8	91.5	even	12
637.2.c.f.246.4		8	91.86	odd	12
637.2.c.f.246.5		8	91.44	odd	12
637.2.r.f.116.4		16	91.73	even	12
637.2.r.f.116.5		16	91.31	even	12
637.2.r.f.324.4		16	91.83	even	4
637.2.r.f.324.5		16	91.34	even	4
819.2.dl.e.298.4		16	273.200	even	12
819.2.dl.e.298.5		16	273.242	even	12
819.2.dl.e.415.4		16	39.8	even	4
819.2.dl.e.415.5		16	39.5	even	4
1183.2.e.i.170.4		16	13.12	even	2	inner
1183.2.e.i.170.5		16	1.1	even	1	trivial
1183.2.e.i.508.4		16	91.25	even	6	inner
1183.2.e.i.508.5		16	7.4	even	3	inner
8281.2.a.cj.1.4		8	7.5	odd	6
8281.2.a.cj.1.5		8	91.12	odd	6
8281.2.a.ck.1.4		8	7.2	even	3
8281.2.a.ck.1.5		8	91.51	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.166188 - 0.287846i) q^{2} +(-0.729919 - 1.26426i) q^{3} +(0.944763 + 1.63638i) q^{4} +(0.722811 - 1.25195i) q^{5} -0.485214 q^{6} +(1.36920 + 2.26391i) q^{7} +1.29278 q^{8} +(0.434437 - 0.752468i) q^{9} +O(q^{10})\)	\(q+(0.166188 - 0.287846i) q^{2} +(-0.729919 - 1.26426i) q^{3} +(0.944763 + 1.63638i) q^{4} +(0.722811 - 1.25195i) q^{5} -0.485214 q^{6} +(1.36920 + 2.26391i) q^{7} +1.29278 q^{8} +(0.434437 - 0.752468i) q^{9} +(-0.240245 - 0.416116i) q^{10} +(-2.97758 - 5.15732i) q^{11} +(1.37920 - 2.38885i) q^{12} +(0.879201 - 0.0178849i) q^{14} -2.11037 q^{15} +(-1.67468 + 2.90063i) q^{16} +(-2.16436 - 3.74877i) q^{17} +(-0.144396 - 0.250102i) q^{18} +(0.978767 - 1.69527i) q^{19} +2.73154 q^{20} +(1.86276 - 3.38349i) q^{21} -1.97935 q^{22} +(0.270081 - 0.467795i) q^{23} +(-0.943626 - 1.63441i) q^{24} +(1.45509 + 2.52029i) q^{25} -5.64793 q^{27} +(-2.41104 + 4.37939i) q^{28} +7.15857 q^{29} +(-0.350718 + 0.607461i) q^{30} +(-3.05400 - 5.28968i) q^{31} +(1.84941 + 3.20327i) q^{32} +(-4.34678 + 7.52885i) q^{33} -1.43876 q^{34} +(3.82396 - 0.0777879i) q^{35} +1.64176 q^{36} +(4.01441 - 6.95316i) q^{37} +(-0.325318 - 0.563467i) q^{38} +(0.934437 - 1.61849i) q^{40} +7.55362 q^{41} +(-0.664356 - 1.09848i) q^{42} +4.24839 q^{43} +(5.62622 - 9.74489i) q^{44} +(-0.628032 - 1.08778i) q^{45} +(-0.0897684 - 0.155483i) q^{46} +(3.13042 - 5.42204i) q^{47} +4.88953 q^{48} +(-3.25057 + 6.19950i) q^{49} +0.967272 q^{50} +(-3.15961 + 5.47260i) q^{51} +(1.38953 + 2.40673i) q^{53} +(-0.938616 + 1.62573i) q^{54} -8.60891 q^{55} +(1.77008 + 2.92674i) q^{56} -2.85768 q^{57} +(1.18967 - 2.06056i) q^{58} +(-0.425576 - 0.737119i) q^{59} +(-1.99380 - 3.45337i) q^{60} +(-3.38953 + 5.87083i) q^{61} -2.03015 q^{62} +(2.29835 - 0.0467536i) q^{63} -5.46933 q^{64} +(1.44476 + 2.50240i) q^{66} +(-0.493553 - 0.854859i) q^{67} +(4.08961 - 7.08341i) q^{68} -0.788550 q^{69} +(0.613105 - 1.11364i) q^{70} -3.76223 q^{71} +(0.561633 - 0.972777i) q^{72} +(-4.56760 - 7.91131i) q^{73} +(-1.33429 - 2.31106i) q^{74} +(2.12419 - 3.67921i) q^{75} +3.69881 q^{76} +(7.59879 - 13.8024i) q^{77} +(0.0655625 - 0.113558i) q^{79} +(2.42096 + 4.19322i) q^{80} +(2.81922 + 4.88303i) q^{81} +(1.25532 - 2.17428i) q^{82} -2.66812 q^{83} +(7.29653 - 0.148428i) q^{84} -6.25768 q^{85} +(0.706030 - 1.22288i) q^{86} +(-5.22517 - 9.05026i) q^{87} +(-3.84936 - 6.66729i) q^{88} +(4.85869 - 8.41550i) q^{89} -0.417485 q^{90} +1.02065 q^{92} +(-4.45834 + 7.72207i) q^{93} +(-1.04047 - 1.80215i) q^{94} +(-1.41493 - 2.45072i) q^{95} +(2.69983 - 4.67625i) q^{96} -6.58319 q^{97} +(1.24429 + 1.96594i) q^{98} -5.17429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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