LMFDB - Embedded newform 1183.2.e.i.508.3

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			508.3
Root			$-0.536527 + 0.929293i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.i.170.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +O(q^{10})$	\(q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +(0.335561 - 0.581209i) q^{10} +(-0.354260 + 0.613597i) q^{11} +(-1.03159 - 1.78676i) q^{12} +(-1.53159 + 2.39047i) q^{14} +1.52068 q^{15} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(-1.56222 + 2.70585i) q^{18} +(-2.60138 - 4.50573i) q^{19} +0.530712 q^{20} +(-6.42602 - 0.297185i) q^{21} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(-3.71598 + 6.43627i) q^{24} +(2.30442 - 3.99137i) q^{25} +0.214623 q^{27} +(-2.24266 - 0.103717i) q^{28} -6.59711 q^{29} +(-0.815886 - 1.41316i) q^{30} +(-2.19530 + 3.80238i) q^{31} +(-2.20741 + 3.82335i) q^{32} +(0.861351 + 1.49190i) q^{33} -3.58737 q^{34} +(0.892689 - 1.39329i) q^{35} -2.47076 q^{36} +(0.211704 + 0.366683i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} +5.01604 q^{41} +(3.17157 + 6.13111i) q^{42} -11.2059 q^{43} +(0.300609 + 0.520670i) q^{44} +(0.910544 - 1.57711i) q^{45} +(2.37757 - 4.11807i) q^{46} +(4.03635 + 6.99116i) q^{47} +3.84855 q^{48} +(-4.04458 + 5.71326i) q^{49} -4.94553 q^{50} +(-4.06426 - 7.03950i) q^{51} +(0.348553 - 0.603712i) q^{53} +(-0.115151 - 0.199447i) q^{54} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} -12.6500 q^{57} +(3.53953 + 6.13065i) q^{58} +(4.93159 - 8.54177i) q^{59} +(0.645188 - 1.11750i) q^{60} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} +(-4.15596 + 6.48654i) q^{63} +7.90305 q^{64} +(0.924277 - 1.60089i) q^{66} +(5.21041 - 9.02470i) q^{67} +(-1.41841 - 2.45676i) q^{68} +10.7745 q^{69} +(-1.77373 - 0.0820297i) q^{70} +14.0876 q^{71} +(4.45007 + 7.70775i) q^{72} +(-2.54191 + 4.40273i) q^{73} +(0.227170 - 0.393471i) q^{74} +(-5.60297 - 9.70463i) q^{75} -4.41482 q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(-0.494983 + 0.857336i) q^{80} +(4.62851 - 8.01682i) q^{81} +(-2.69124 - 4.66137i) q^{82} -10.2035 q^{83} +(-2.94480 + 4.59619i) q^{84} +2.09090 q^{85} +(6.01230 + 10.4136i) q^{86} +(-8.02012 + 13.8913i) q^{87} +(1.08285 - 1.87555i) q^{88} +(-6.68955 - 11.5866i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(5.33767 + 9.24512i) q^{93} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +(5.36711 + 9.29610i) q^{96} +0.202023 q^{97} +(7.47932 + 0.693276i) q^{98} +2.06302 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 $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.536527	−	0.929293i	−0.379382	−	0.657109i	0.611590	−	0.791175i	$-0.290530\pi$
$2$	−0.536527	−	0.929293i	−0.379382	−	0.657109i	−0.990972	+	0.134065i	$0.957197\pi$
$3$	1.21570	−	2.10566i	0.701886	−	1.21570i	−0.265918	−	0.963996i	$-0.585675\pi$
$3$	1.21570	−	2.10566i	0.701886	−	1.21570i	0.967804	−	0.251707i	$-0.0809918\pi$
$4$	0.424277	−	0.734868i	0.212138	−	0.367434i
$5$	0.312716	+	0.541640i	0.139851	+	0.242229i	0.927440	−	0.373972i	$-0.122004\pi$
$5$	0.312716	+	0.541640i	0.139851	+	0.242229i	−0.787589	+	0.616201i	$0.788671\pi$
$6$	−2.60903			−1.06513
$7$	−1.21561	−	2.34996i	−0.459458	−	0.888200i
$7$	−1.21561	−	2.34996i	−0.459458	−	0.888200i
$8$	−3.05665			−1.08069
$9$	−1.45586	−	2.52163i	−0.485288	−	0.840544i
$10$	0.335561	−	0.581209i	0.106114	−	0.183795i
$11$	−0.354260	+	0.613597i	−0.106814	+	0.185006i	−0.914478	−	0.404636i	$-0.867398\pi$
$11$	−0.354260	+	0.613597i	−0.106814	+	0.185006i	0.807664	+	0.589643i	$0.200731\pi$
$12$	−1.03159	−	1.78676i	−0.297794	−	0.515794i
$13$		0			0
$13$		0			0
$14$	−1.53159	+	2.39047i	−0.409334	+	0.638881i
$15$	1.52068			0.392637
$16$	0.791426	+	1.37079i	0.197856	+	0.342697i
$17$	1.67157	−	2.89524i	0.405414	−	0.702199i	−0.588955	−	0.808166i	$-0.700461\pi$
$17$	1.67157	−	2.89524i	0.405414	−	0.702199i	0.994370	+	0.105967i	$0.0337939\pi$
$18$	−1.56222	+	2.70585i	−0.368219	+	0.637775i
$19$	−2.60138	−	4.50573i	−0.596798	−	1.03368i	−0.993290	−	0.115646i	$-0.963106\pi$
$19$	−2.60138	−	4.50573i	−0.596798	−	1.03368i	0.396492	−	0.918038i	$-0.370227\pi$
$20$	0.530712			0.118671
$21$	−6.42602	−	0.297185i	−1.40227	−	0.0648510i
$22$	0.760282			0.162093
$23$	2.21570	+	3.83771i	0.462006	+	0.800218i	0.999061	−	0.0433296i	$-0.0137966\pi$
$23$	2.21570	+	3.83771i	0.462006	+	0.800218i	−0.537055	+	0.843547i	$0.680463\pi$
$24$	−3.71598	+	6.43627i	−0.758522	+	1.31380i
$25$	2.30442	−	3.99137i	0.460883	−	0.798274i
$26$		0			0
$27$	0.214623			0.0413042
$28$	−2.24266	−	0.103717i	−0.423824	−	0.0196006i
$29$	−6.59711			−1.22505			−0.612526	−	0.790450i	$-0.709847\pi$
$29$	−6.59711			−1.22505			−0.612526	+	0.790450i	$0.709847\pi$
$30$	−0.815886	−	1.41316i	−0.148960	−	0.258006i
$31$	−2.19530	+	3.80238i	−0.394288	+	0.682927i	−0.993010	−	0.118030i	$-0.962342\pi$
$31$	−2.19530	+	3.80238i	−0.394288	+	0.682927i	0.598722	+	0.800957i	$0.295675\pi$
$32$	−2.20741	+	3.82335i	−0.390219	+	0.675879i
$33$	0.861351	+	1.49190i	0.149942	+	0.259707i
$34$	−3.58737			−0.615228
$35$	0.892689	−	1.39329i	0.150892	−	0.235509i
$36$	−2.47076			−0.411793
$37$	0.211704	+	0.366683i	0.0348040	+	0.0602823i	0.882903	−	0.469556i	$-0.155586\pi$
$37$	0.211704	+	0.366683i	0.0348040	+	0.0602823i	−0.848099	+	0.529838i	$0.822253\pi$
$38$	−2.79143	+	4.83489i	−0.452829	+	0.784323i
$39$		0			0
$40$	−0.955864	−	1.65561i	−0.151135	−	0.261774i
$41$	5.01604			0.783374			0.391687	−	0.920099i	$-0.371892\pi$
$41$	5.01604			0.783374			0.391687	+	0.920099i	$0.371892\pi$
$42$	3.17157	+	6.13111i	0.489383	+	0.946050i
$43$	−11.2059			−1.70889			−0.854445	−	0.519542i	$-0.826103\pi$
$43$	−11.2059			−1.70889			−0.854445	+	0.519542i	$0.826103\pi$
$44$	0.300609	+	0.520670i	0.0453185	+	0.0784939i
$45$	0.910544	−	1.57711i	0.135736	−	0.235101i
$46$	2.37757	−	4.11807i	0.350554	−	0.607177i
$47$	4.03635	+	6.99116i	0.588762	+	1.01977i	0.994395	+	0.105729i	$0.0337177\pi$
$47$	4.03635	+	6.99116i	0.588762	+	1.01977i	−0.405633	+	0.914036i	$0.632949\pi$
$48$	3.84855			0.555491
$49$	−4.04458	+	5.71326i	−0.577797	+	0.816180i
$50$	−4.94553			−0.699404
$51$	−4.06426	−	7.03950i	−0.569110	−	0.985727i
$52$		0			0
$53$	0.348553	−	0.603712i	0.0478774	−	0.0829262i	−0.841094	−	0.540890i	$-0.818088\pi$
$53$	0.348553	−	0.603712i	0.0478774	−	0.0829262i	0.888971	+	0.457964i	$0.151421\pi$
$54$	−0.115151	−	0.199447i	−0.0156701	−	0.0271414i
$55$	−0.443132			−0.0597519
$56$	3.71570	+	7.18300i	0.496532	+	0.959869i
$57$	−12.6500			−1.67554
$58$	3.53953	+	6.13065i	0.464763	+	0.804993i
$59$	4.93159	−	8.54177i	0.642039	−	1.11204i	−0.342938	−	0.939358i	$-0.611422\pi$
$59$	4.93159	−	8.54177i	0.642039	−	1.11204i	0.984977	−	0.172686i	$-0.0552445\pi$
$60$	0.645188	−	1.11750i	0.0832934	−	0.144268i
$61$	−2.34855	−	4.06781i	−0.300701	−	0.520830i	0.675594	−	0.737274i	$-0.263887\pi$
$61$	−2.34855	−	4.06781i	−0.300701	−	0.520830i	−0.976295	+	0.216444i	$0.930554\pi$
$62$	4.71136			0.598344
$63$	−4.15596	+	6.48654i	−0.523601	+	0.817227i
$64$	7.90305			0.987881
$65$		0			0
$66$	0.924277	−	1.60089i	0.113771	−	0.197056i
$67$	5.21041	−	9.02470i	0.636553	−	1.10254i	−0.349631	−	0.936888i	$-0.613693\pi$
$67$	5.21041	−	9.02470i	0.636553	−	1.10254i	0.986184	−	0.165655i	$-0.0529738\pi$
$68$	−1.41841	−	2.45676i	−0.172008	−	0.297926i
$69$	10.7745			1.29710
$70$	−1.77373	−	0.0820297i	−0.212001	−	0.00980443i
$71$	14.0876			1.67189			0.835946	−	0.548812i	$-0.184920\pi$
$71$	14.0876			1.67189			0.835946	+	0.548812i	$0.184920\pi$
$72$	4.45007	+	7.70775i	0.524446	+	0.908368i
$73$	−2.54191	+	4.40273i	−0.297509	+	0.515300i	−0.975565	−	0.219710i	$-0.929489\pi$
$73$	−2.54191	+	4.40273i	−0.297509	+	0.515300i	0.678057	+	0.735010i	$0.262822\pi$
$74$	0.227170	−	0.393471i	0.0264080	−	0.0457400i
$75$	−5.60297	−	9.70463i	−0.646975	−	1.12059i
$76$	−4.41482			−0.506415
$77$	1.87257	+	0.0866008i	0.213399	+	0.00986908i
$78$		0			0
$79$	1.95586	+	3.38766i	0.220052	+	0.381141i	0.954823	−	0.297174i	$-0.0960440\pi$
$79$	1.95586	+	3.38766i	0.220052	+	0.381141i	−0.734772	+	0.678315i	$0.762711\pi$
$80$	−0.494983	+	0.857336i	−0.0553408	+	0.0958530i
$81$	4.62851	−	8.01682i	0.514279	−	0.890757i
$82$	−2.69124	−	4.66137i	−0.297198	−	0.514762i
$83$	−10.2035			−1.11998			−0.559990	−	0.828499i	$-0.689195\pi$
$83$	−10.2035			−1.11998			−0.559990	+	0.828499i	$0.689195\pi$
$84$	−2.94480	+	4.59619i	−0.321304	+	0.501486i
$85$	2.09090			0.226790
$86$	6.01230	+	10.4136i	0.648323	+	1.12293i
$87$	−8.02012	+	13.8913i	−0.859847	+	1.48930i
$88$	1.08285	−	1.87555i	0.115432	−	0.199935i
$89$	−6.68955	−	11.5866i	−0.709090	−	1.22818i	−0.965195	−	0.261532i	$-0.915772\pi$
$89$	−6.68955	−	11.5866i	−0.709090	−	1.22818i	0.256104	−	0.966649i	$-0.417561\pi$
$90$	−1.95413			−0.205983
$91$		0			0
$92$	3.76028			0.392036
$93$	5.33767	+	9.24512i	0.553491	+	0.958674i
$94$	4.33122	−	7.50190i	0.446731	−	0.773761i
$95$	1.62699	−	2.81802i	0.166925	−	0.289123i
$96$	5.36711	+	9.29610i	0.547778	+	0.948780i
$97$	0.202023			0.0205123			0.0102562	−	0.999947i	$-0.496735\pi$
$97$	0.202023			0.0205123			0.0102562	+	0.999947i	$0.496735\pi$
$98$	7.47932	+	0.693276i	0.755526	+	0.0700315i
$99$	2.06302			0.207341
$100$	−1.95542	−	3.38689i	−0.195542	−	0.338689i
$101$	8.66723	−	15.0121i	0.862421	−	1.49376i	−0.00716374	−	0.999974i	$-0.502280\pi$
$101$	8.66723	−	15.0121i	0.862421	−	1.49376i	0.869585	−	0.493783i	$-0.164386\pi$
$102$	−4.36117	+	7.55377i	−0.431820	+	0.747934i
$103$	5.40739	+	9.36587i	0.532806	+	0.922847i	0.999266	+	0.0383047i	$0.0121957\pi$
$103$	5.40739	+	9.36587i	0.532806	+	0.922847i	−0.466460	+	0.884542i	$0.654471\pi$
$104$		0			0
$105$	−1.84855	−	3.57353i	−0.180400	−	0.348740i
$106$	−0.748033			−0.0726554
$107$	3.05839	+	5.29729i	0.295666	+	0.512108i	0.975140	−	0.221592i	$-0.0711252\pi$
$107$	3.05839	+	5.29729i	0.295666	+	0.512108i	−0.679474	+	0.733700i	$0.737792\pi$
$108$	0.0910594	−	0.157720i	0.00876220	−	0.0151766i
$109$	5.69958	−	9.87196i	0.545921	−	0.945563i	−0.452628	−	0.891700i	$-0.649513\pi$
$109$	5.69958	−	9.87196i	0.545921	−	0.945563i	0.998548	−	0.0538629i	$-0.0171534\pi$
$110$	0.237752	+	0.411799i	0.0226688	+	0.0392635i
$111$	1.02948			0.0977137
$112$	2.25923	−	3.52616i	0.213477	−	0.333191i
$113$	−0.923456			−0.0868714			−0.0434357	−	0.999056i	$-0.513830\pi$
$113$	−0.923456			−0.0868714			−0.0434357	+	0.999056i	$0.513830\pi$
$114$	6.78709	+	11.7556i	0.635669	+	1.10101i
$115$	−1.38577	+	2.40023i	−0.129224	+	0.223822i
$116$	−2.79900	+	4.84801i	−0.259880	+	0.450126i
$117$		0			0
$118$	−10.5837			−0.974312
$119$	−8.83566	−	0.408623i	−0.809963	−	0.0374584i
$120$	−4.64819			−0.424319
$121$	5.24900	+	9.09153i	0.477182	+	0.826503i
$122$	−2.52013	+	4.36499i	−0.228162	+	0.395187i
$123$	6.09801	−	10.5621i	0.549839	−	0.952349i
$124$	1.86283	+	3.22652i	0.167287	+	0.289750i
$125$	6.00967			0.537521
$126$	8.25768	+	0.381893i	0.735652	+	0.0340218i
$127$	−8.50972			−0.755116			−0.377558	−	0.925986i	$-0.623236\pi$
$127$	−8.50972			−0.755116			−0.377558	+	0.925986i	$0.623236\pi$
$128$	0.174618	+	0.302447i	0.0154342	+	0.0267328i
$129$	−13.6231	+	23.5959i	−1.19945	+	2.07750i
$130$		0			0
$131$	3.50152	+	6.06482i	0.305930	+	0.529885i	0.977468	−	0.211084i	$-0.0676995\pi$
$131$	3.50152	+	6.06482i	0.305930	+	0.529885i	−0.671538	+	0.740970i	$0.734366\pi$
$132$	1.46180			0.127234
$133$	−7.42599	+	11.5903i	−0.643915	+	1.00501i
$134$	−11.1821			−0.965988
$135$	0.0671160	+	0.116248i	0.00577642	+	0.0100051i
$136$	−5.10940	+	8.84974i	−0.438128	+	0.758859i
$137$	−3.10847	+	5.38403i	−0.265575	+	0.459989i	−0.967714	−	0.252051i	$-0.918895\pi$
$137$	−3.10847	+	5.38403i	−0.265575	+	0.459989i	0.702139	+	0.712040i	$0.252228\pi$
$138$	−5.78084	−	10.0127i	−0.492097	−	0.852338i
$139$	6.53140			0.553986			0.276993	−	0.960872i	$-0.410662\pi$
$139$	6.53140			0.553986			0.276993	+	0.960872i	$0.410662\pi$
$140$	−0.645140	−	1.24715i	−0.0545242	−	0.105403i
$141$	19.6280			1.65297
$142$	−7.55839	−	13.0915i	−0.634286	−	1.09862i
$143$		0			0
$144$	2.30442	−	3.99137i	0.192035	−	0.332614i
$145$	−2.06302	−	3.57326i	−0.171325	−	0.296743i
$146$	5.45523			0.451478
$147$	7.11317	+	15.4621i	0.586685	+	1.27529i
$148$	0.359285			0.0295330
$149$	−1.84869	−	3.20203i	−0.151451	−	0.262320i	0.780310	−	0.625393i	$-0.215061\pi$
$149$	−1.84869	−	3.20203i	−0.151451	−	0.262320i	−0.931761	+	0.363072i	$0.881728\pi$
$150$	−6.01230	+	10.4136i	−0.490902	+	0.850267i
$151$	−2.43887	+	4.22425i	−0.198473	+	0.343764i	−0.948033	−	0.318171i	$-0.896931\pi$
$151$	−2.43887	+	4.22425i	−0.198473	+	0.343764i	0.749561	+	0.661935i	$0.230265\pi$
$152$	7.95152	+	13.7724i	0.644954	+	1.11709i
$153$	−9.73430			−0.786971
$154$	−0.924207	−	1.78663i	−0.0744747	−	0.143971i
$155$	−2.74603			−0.220566
$156$		0			0
$157$	4.75984	−	8.24428i	0.379876	−	0.657965i	−0.611168	−	0.791501i	$-0.709300\pi$
$157$	4.75984	−	8.24428i	0.379876	−	0.657965i	0.991044	+	0.133536i	$0.0426332\pi$
$158$	2.09875	−	3.63514i	0.166968	−	0.289196i
$159$	−0.847473	−	1.46787i	−0.0672090	−	0.116409i
$160$	−2.76117			−0.218290
$161$	6.32501	−	9.87196i	0.498481	−	0.778020i
$162$	−9.93329			−0.780433
$163$	−11.8544	−	20.5325i	−0.928511	−	1.60823i	−0.785815	−	0.618461i	$-0.787756\pi$
$163$	−11.8544	−	20.5325i	−0.928511	−	1.60823i	−0.142696	−	0.989767i	$-0.545577\pi$
$164$	2.12819	−	3.68613i	0.166184	−	0.287838i
$165$	−0.538716	+	0.933084i	−0.0419390	+	0.0726405i
$166$	5.47446	+	9.48204i	0.424901	+	0.735949i
$167$	−1.13193			−0.0875914			−0.0437957	−	0.999041i	$-0.513945\pi$
$167$	−1.13193			−0.0875914			−0.0437957	+	0.999041i	$0.513945\pi$
$168$	19.6421	+	0.908391i	1.51542	+	0.0700839i
$169$		0			0
$170$	−1.12183	−	1.94306i	−0.0860402	−	0.149026i
$171$	−7.57452	+	13.1195i	−0.579238	+	1.00327i
$172$	−4.75442	+	8.23489i	−0.362521	+	0.627905i
$173$	−5.99458	−	10.3829i	−0.455760	−	0.789399i	0.542972	−	0.839751i	$-0.317299\pi$
$173$	−5.99458	−	10.3829i	−0.455760	−	0.789399i	−0.998732	+	0.0503522i	$0.983966\pi$
$174$	17.2121			1.30484
$175$	−12.1808	−	0.563327i	−0.920783	−	0.0425835i
$176$	−1.12148			−0.0845350
$177$	−11.9907	−	20.7685i	−0.901276	−	1.56106i
$178$	−7.17825	+	12.4331i	−0.538033	+	0.931900i
$179$	−4.73538	+	8.20192i	−0.353939	+	0.613040i	−0.986936	−	0.161114i	$-0.948491\pi$
$179$	−4.73538	+	8.20192i	−0.353939	+	0.613040i	0.632997	+	0.774154i	$0.281825\pi$
$180$	−0.772645	−	1.33826i	−0.0575896	−	0.0997480i
$181$	11.4314			0.849690			0.424845	−	0.905266i	$-0.360329\pi$
$181$	11.4314			0.849690			0.424845	+	0.905266i	$0.360329\pi$
$182$		0			0
$183$	−11.4206			−0.844233
$184$	−6.77264	−	11.7305i	−0.499285	−	0.864788i
$185$	−0.132407	+	0.229335i	−0.00973473	+	0.0168611i
$186$	5.72761	−	9.92052i	0.419969	−	0.727408i
$187$	1.18434	+	2.05134i	0.0866075	+	0.150009i
$188$	6.85011			0.499595
$189$	−0.260898	−	0.504354i	−0.0189775	−	0.0366864i
$190$	−3.49169			−0.253314
$191$	−7.84377	−	13.5858i	−0.567555	−	0.983034i	−0.996807	−	0.0798496i	$-0.974556\pi$
$191$	−7.84377	−	13.5858i	−0.567555	−	0.983034i	0.429252	−	0.903185i	$-0.358777\pi$
$192$	9.60776	−	16.6411i	0.693380	−	1.20097i
$193$	11.5036	−	19.9248i	0.828045	−	1.43422i	−0.0715256	−	0.997439i	$-0.522787\pi$
$193$	11.5036	−	19.9248i	0.828045	−	1.43422i	0.899570	−	0.436776i	$-0.143880\pi$
$194$	−0.108391	−	0.187739i	−0.00778202	−	0.0134788i
$195$		0			0
$196$	2.48248	+	5.39624i	0.177320	+	0.385446i
$197$	10.2035			0.726970			0.363485	−	0.931600i	$-0.381587\pi$
$197$	10.2035			0.726970			0.363485	+	0.931600i	$0.381587\pi$
$198$	−1.10687	−	1.91715i	−0.0786616	−	0.136246i
$199$	−5.96173	+	10.3260i	−0.422616	+	0.731992i	−0.996194	−	0.0871586i	$-0.972221\pi$
$199$	−5.96173	+	10.3260i	−0.422616	+	0.731992i	0.573579	+	0.819150i	$0.305555\pi$
$200$	−7.04381	+	12.2002i	−0.498072	+	0.862687i
$201$	−12.6686	−	21.9427i	−0.893576	−	1.54772i
$202$	−18.6008			−1.30875
$203$	8.01952	+	15.5029i	0.562860	+	1.08809i
$204$	−6.89747			−0.482920
$205$	1.56860	+	2.71689i	0.109555	+	0.189756i
$206$	5.80243	−	10.0501i	0.404274	−	0.700223i
$207$	6.45152	−	11.1744i	0.448412	−	0.776672i
$208$		0			0
$209$	3.68627			0.254984
$210$	−2.32905	+	3.63514i	−0.160720	+	0.250849i
$211$	−15.5893			−1.07321			−0.536606	−	0.843833i	$-0.680294\pi$
$211$	−15.5893			−1.07321			−0.536606	+	0.843833i	$0.680294\pi$
$212$	−0.295766	−	0.512281i	−0.0203133	−	0.0351836i
$213$	17.1263	−	29.6637i	1.17348	−	2.03252i
$214$	3.28182	−	5.68428i	0.224341	−	0.388570i
$215$	−3.50428	−	6.06959i	−0.238990	−	0.413942i
$216$	−0.656028			−0.0446370
$217$	11.6041	+	0.536653i	0.787734	+	0.0364304i
$218$	−12.2319			−0.828451
$219$	6.18042	+	10.7048i	0.417634	+	0.723364i
$220$	−0.188010	+	0.325643i	−0.0126757	+	0.0219549i
$221$		0			0
$222$	−0.552343	−	0.956687i	−0.0370709	−	0.0642086i
$223$	−6.76662			−0.453126			−0.226563	−	0.973996i	$-0.572749\pi$
$223$	−6.76662			−0.453126			−0.226563	+	0.973996i	$0.572749\pi$
$224$	11.6680	+	0.539613i	0.779604	+	0.0360544i
$225$	−13.4197			−0.894645
$226$	0.495459	+	0.858161i	0.0329575	+	0.0570840i
$227$	−8.41225	+	14.5704i	−0.558340	+	0.967074i	0.439295	+	0.898343i	$0.355228\pi$
$227$	−8.41225	+	14.5704i	−0.558340	+	0.967074i	−0.997635	+	0.0687311i	$0.978105\pi$
$228$	−5.36711	+	9.29610i	−0.355445	+	0.615650i
$229$	−5.51286	−	9.54855i	−0.364300	−	0.630986i	0.624364	−	0.781134i	$-0.285358\pi$
$229$	−5.51286	−	9.54855i	−0.364300	−	0.630986i	−0.988664	+	0.150148i	$0.952025\pi$
$230$	2.97402			0.196101
$231$	2.45884	−	3.83771i	0.161780	−	0.252503i
$232$	20.1651			1.32390
$233$	−8.67743	−	15.0298i	−0.568477	−	0.984632i	−0.996717	−	0.0809664i	$-0.974199\pi$
$233$	−8.67743	−	15.0298i	−0.568477	−	0.984632i	0.428239	−	0.903665i	$-0.359134\pi$
$234$		0			0
$235$	−2.52446	+	4.37249i	−0.164678	+	0.285230i
$236$	−4.18472	−	7.24814i	−0.272402	−	0.471814i
$237$	9.51100			0.617806
$238$	4.36084	+	8.43015i	0.282671	+	0.546445i
$239$	19.7223			1.27573			0.637865	−	0.770148i	$-0.279818\pi$
$239$	19.7223			1.27573			0.637865	+	0.770148i	$0.279818\pi$
$240$	1.20350	+	2.08453i	0.0776858	+	0.134556i
$241$	−1.39206	+	2.41112i	−0.0896706	+	0.155314i	−0.907372	−	0.420329i	$-0.861915\pi$
$241$	−1.39206	+	2.41112i	−0.0896706	+	0.155314i	0.817701	+	0.575643i	$0.195248\pi$
$242$	5.63246	−	9.75571i	0.362069	−	0.627121i
$243$	−10.9318	−	18.9345i	−0.701278	−	1.21465i
$244$	−3.98574			−0.255161
$245$	−4.35934	−	0.404077i	−0.278508	−	0.0258155i
$246$	−13.0870			−0.834397
$247$		0			0
$248$	6.71028	−	11.6226i	0.426103	−	0.738033i
$249$	−12.4044	+	21.4851i	−0.786098	+	1.36156i
$250$	−3.22435	−	5.58475i	−0.203926	−	0.353210i
$251$	23.5608			1.48714			0.743572	−	0.668655i	$-0.233130\pi$
$251$	23.5608			1.48714			0.743572	+	0.668655i	$0.233130\pi$
$252$	3.00348	+	5.80617i	0.189201	+	0.365754i
$253$	−3.13974			−0.197394
$254$	4.56570	+	7.90803i	0.286478	+	0.496194i
$255$	2.54191	−	4.40273i	0.159181	−	0.275709i
$256$	8.09042	−	14.0130i	0.505651	−	0.875814i
$257$	1.71615	+	2.97245i	0.107050	+	0.185417i	0.914574	−	0.404419i	$-0.132526\pi$
$257$	1.71615	+	2.97245i	0.107050	+	0.185417i	−0.807524	+	0.589835i	$0.799193\pi$
$258$	29.2367			1.82019
$259$	0.604338	−	0.943239i	0.0375517	−	0.0586100i
$260$		0			0
$261$	9.60450	+	16.6355i	0.594503	+	1.02971i
$262$	3.75733	−	6.50788i	0.232128	−	0.402058i
$263$	10.7245	−	18.5754i	0.661303	−	1.14541i	−0.318970	−	0.947765i	$-0.603337\pi$
$263$	10.7245	−	18.5754i	0.661303	−	1.14541i	0.980273	−	0.197646i	$-0.0633298\pi$
$264$	−2.63285	−	4.56023i	−0.162041	−	0.280663i
$265$	0.435992			0.0267828
$266$	14.7551	+	0.682378i	0.904691	+	0.0418393i
$267$	−32.5300			−1.99080
$268$	−4.42131	−	7.65794i	−0.270075	−	0.467783i
$269$	−7.32843	+	12.6932i	−0.446822	+	0.773919i	−0.998177	−	0.0603517i	$-0.980778\pi$
$269$	−7.32843	+	12.6932i	−0.446822	+	0.773919i	0.551355	+	0.834271i	$0.314111\pi$
$270$	0.0720191	−	0.124741i	0.00438294	−	0.00759148i
$271$	1.02183	+	1.76986i	0.0620717	+	0.107511i	0.895391	−	0.445280i	$-0.146896\pi$
$271$	1.02183	+	1.76986i	0.0620717	+	0.107511i	−0.833320	+	0.552792i	$0.813563\pi$
$272$	5.29168			0.320856
$273$		0			0
$274$	6.67112			0.403017
$275$	1.63273	+	2.82797i	0.0984572	+	0.170533i
$276$	4.57138	−	7.91787i	0.275165	−	0.476600i
$277$	2.71678	−	4.70560i	0.163236	−	0.282732i	−0.772792	−	0.634660i	$-0.781140\pi$
$277$	2.71678	−	4.70560i	0.163236	−	0.282732i	0.936027	+	0.351927i	$0.114474\pi$
$278$	−3.50428	−	6.06959i	−0.210173	−	0.364030i
$279$	12.7843			0.765373
$280$	−2.72864	+	4.25881i	−0.163067	+	0.254513i
$281$	20.2356			1.20715			0.603577	−	0.797305i	$-0.293742\pi$
$281$	20.2356			1.20715			0.603577	+	0.797305i	$0.293742\pi$
$282$	−10.5310	−	18.2401i	−0.627109	−	1.08618i
$283$	−0.867593	+	1.50272i	−0.0515731	+	0.0893272i	−0.890659	−	0.454671i	$-0.849757\pi$
$283$	−0.867593	+	1.50272i	−0.0515731	+	0.0893272i	0.839086	+	0.543998i	$0.183090\pi$
$284$	5.97704	−	10.3525i	0.354672	−	0.614310i
$285$	−3.95586	−	6.85176i	−0.234325	−	0.405863i
$286$		0			0
$287$	−6.09755	−	11.7875i	−0.359927	−	0.695792i
$288$	12.8548			0.757474
$289$	2.91173	+	5.04326i	0.171278	+	0.296662i
$290$	−2.21373	+	3.83430i	−0.129995	+	0.225158i
$291$	0.245600	−	0.425392i	0.0143973	−	0.0249369i
$292$	2.15695	+	3.73595i	0.126226	+	0.218630i
$293$	27.2441			1.59162			0.795810	−	0.605547i	$-0.207046\pi$
$293$	27.2441			1.59162			0.795810	+	0.605547i	$0.207046\pi$
$294$	10.5524	−	14.9061i	0.615430	−	0.869340i
$295$	6.16875			0.359159
$296$	−0.647107	−	1.12082i	−0.0376123	−	0.0651465i
$297$	−0.0760324	+	0.131692i	−0.00441185	+	0.00764154i
$298$	−1.98375	+	3.43595i	−0.114915	+	0.199039i
$299$		0			0
$300$	−9.50884			−0.548993
$301$	13.6221	+	26.3335i	0.785163	+	1.51784i
$302$	5.23409			0.301188
$303$	−21.0735	−	36.5004i	−1.21064	−	2.09690i
$304$	4.11760	−	7.13190i	0.236161	−	0.409042i
$305$	1.46886	−	2.54414i	0.0841067	−	0.145677i
$306$	5.22272	+	9.04601i	0.298563	+	0.517126i
$307$	12.7138			0.725612			0.362806	−	0.931865i	$-0.381819\pi$
$307$	12.7138			0.725612			0.362806	+	0.931865i	$0.381819\pi$
$308$	0.858127	−	1.33935i	0.0488963	−	0.0763165i
$309$	26.2951			1.49588
$310$	1.47332	+	2.55186i	0.0836788	+	0.144936i
$311$	−4.80939	+	8.33011i	−0.272716	+	0.472357i	−0.969556	−	0.244869i	$-0.921255\pi$
$311$	−4.80939	+	8.33011i	−0.272716	+	0.472357i	0.696841	+	0.717226i	$0.254588\pi$
$312$		0			0
$313$	4.51273	+	7.81628i	0.255075	+	0.441802i	0.964916	−	0.262559i	$-0.0845666\pi$
$313$	4.51273	+	7.81628i	0.255075	+	0.441802i	−0.709841	+	0.704362i	$0.751233\pi$
$314$	−10.2151			−0.576473
$315$	−4.81300	−	0.222587i	−0.271182	−	0.0125414i
$316$	3.31931			0.186726
$317$	−12.3131	−	21.3269i	−0.691572	−	1.19784i	−0.971323	−	0.237766i	$-0.923585\pi$
$317$	−12.3131	−	21.3269i	−0.691572	−	1.19784i	0.279750	−	0.960073i	$-0.409748\pi$
$318$	−0.909386	+	1.57510i	−0.0509958	+	0.0883273i
$319$	2.33709	−	4.04797i	0.130852	−	0.226643i
$320$	2.47141	+	4.28061i	0.138156	+	0.239293i
$321$	14.8724			0.830095
$322$	−12.5675	−	0.581209i	−0.700359	−	0.0323895i
$323$	−17.3935			−0.967802
$324$	−3.92754	−	6.80269i	−0.218196	−	0.377927i
$325$		0			0
$326$	−12.7205	+	22.0325i	−0.704521	+	1.22027i
$327$	−13.8580	−	24.0027i	−0.766348	−	1.32735i
$328$	−15.3323			−0.846584
$329$	11.5223	−	17.9838i	0.635244	−	0.991477i
$330$	1.15614			0.0636436
$331$	−6.58591	−	11.4071i	−0.361994	−	0.626993i	0.626295	−	0.779586i	$-0.284571\pi$
$331$	−6.58591	−	11.4071i	−0.361994	−	0.626993i	−0.988289	+	0.152594i	$0.951237\pi$
$332$	−4.32911	+	7.49823i	−0.237591	+	0.411519i
$333$	0.616426	−	1.06768i	0.0337799	−	0.0585085i
$334$	0.607311	+	1.05189i	0.0332306	+	0.0575571i
$335$	6.51752			0.356090
$336$	−4.67834	−	9.04393i	−0.255225	−	0.493387i
$337$	−17.0307			−0.927720			−0.463860	−	0.885909i	$-0.653536\pi$
$337$	−17.0307			−0.927720			−0.463860	+	0.885909i	$0.653536\pi$
$338$		0			0
$339$	−1.12265	+	1.94448i	−0.0609738	+	0.105610i
$340$	0.887121	−	1.53654i	0.0481109	−	0.0833305i
$341$	−1.55542	−	2.69406i	−0.0842306	−	0.145892i
$342$	16.2558			0.879010
$343$	18.3425	+	2.55948i	0.990405	+	0.138199i
$344$	34.2527			1.84678
$345$	3.36937	+	5.83592i	0.181401	+	0.314195i
$346$	−6.43251	+	11.1414i	−0.345814	+	0.598968i
$347$	−0.229959	+	0.398300i	−0.0123448	+	0.0213819i	−0.872132	−	0.489271i	$-0.837263\pi$
$347$	−0.229959	+	0.398300i	−0.0123448	+	0.0213819i	0.859787	+	0.510653i	$0.170596\pi$
$348$	6.80550	+	11.7875i	0.364813	+	0.631875i
$349$	−6.87822			−0.368183			−0.184091	−	0.982909i	$-0.558934\pi$
$349$	−6.87822			−0.368183			−0.184091	+	0.982909i	$0.558934\pi$
$350$	6.01184	+	11.6218i	0.321347	+	0.621210i
$351$		0			0
$352$	−1.56400	−	2.70892i	−0.0833613	−	0.144386i
$353$	−0.766631	+	1.32784i	−0.0408036	+	0.0706740i	−0.885706	−	0.464247i	$-0.846325\pi$
$353$	−0.766631	+	1.32784i	−0.0408036	+	0.0706740i	0.844902	+	0.534921i	$0.179658\pi$
$354$	−12.8667	+	22.2857i	−0.683856	+	1.18447i
$355$	4.40542	+	7.63041i	0.233815	+	0.404980i
$356$	−11.3529			−0.601701
$357$	−11.6019	+	18.1081i	−0.614040	+	0.958383i
$358$	10.1626			0.537112
$359$	13.6034	+	23.5617i	0.717959	+	1.24354i	0.961807	+	0.273728i	$0.0882568\pi$
$359$	13.6034	+	23.5617i	0.717959	+	1.24354i	−0.243848	+	0.969813i	$0.578410\pi$
$360$	−2.78322	+	4.82068i	−0.146688	+	0.254072i
$361$	−4.03438	+	6.98774i	−0.212336	+	0.367776i
$362$	−6.13326	−	10.6231i	−0.322357	−	0.558339i
$363$	25.5249			1.33971
$364$		0			0
$365$	−3.17959			−0.166427
$366$	6.12745	+	10.6131i	0.320287	+	0.554753i
$367$	−13.4907	+	23.3666i	−0.704208	+	1.21972i	0.262769	+	0.964859i	$0.415364\pi$
$367$	−13.4907	+	23.3666i	−0.704208	+	1.21972i	−0.966977	+	0.254865i	$0.917969\pi$
$368$	−3.50713	+	6.07452i	−0.182822	+	0.316656i
$369$	−7.30267	−	12.6486i	−0.380162	−	0.658460i
$370$	0.284159			0.0147727
$371$	−1.84240	−	0.0852056i	−0.0956526	−	0.00442365i
$372$	9.05859			0.469666
$373$	−1.98619	−	3.44018i	−0.102841	−	0.178126i	0.810013	−	0.586412i	$-0.199460\pi$
$373$	−1.98619	−	3.44018i	−0.102841	−	0.178126i	−0.912854	+	0.408286i	$0.866127\pi$
$374$	1.27086	−	2.20120i	0.0657147	−	0.113821i
$375$	7.30597	−	12.6543i	0.377279	−	0.653466i
$376$	−12.3377	−	21.3695i	−0.636269	−	1.10205i
$377$		0			0
$378$	−0.328714	+	0.513050i	−0.0169072	+	0.0263885i
$379$	−11.4059			−0.585884			−0.292942	−	0.956130i	$-0.594634\pi$
$379$	−11.4059			−0.585884			−0.292942	+	0.956130i	$0.594634\pi$
$380$	−1.38058	−	2.39124i	−0.0708225	−	0.122668i
$381$	−10.3453	+	17.9186i	−0.530005	+	0.917996i
$382$	−8.41680	+	14.5783i	−0.430641	+	0.745892i
$383$	11.8960	+	20.6044i	0.607856	+	1.05284i	0.991593	+	0.129395i	$0.0413036\pi$
$383$	11.8960	+	20.6044i	0.607856	+	1.05284i	−0.383737	+	0.923442i	$0.625363\pi$
$384$	0.849134			0.0433322
$385$	0.538676	+	1.04134i	0.0274535	+	0.0530716i
$386$	−24.6879			−1.25658
$387$	16.3143	+	28.2573i	0.829304	+	1.43640i
$388$	0.0857137	−	0.148460i	0.00435145	−	0.00753694i
$389$	14.2055	−	24.6046i	0.720247	−	1.24751i	−0.240653	−	0.970611i	$-0.577362\pi$
$389$	14.2055	−	24.6046i	0.720247	−	1.24751i	0.960901	−	0.276894i	$-0.0893051\pi$
$390$		0			0
$391$	14.8148			0.749216
$392$	12.3629	−	17.4635i	0.624420	−	0.882038i
$393$	17.0272			0.858911
$394$	−5.47446	−	9.48204i	−0.275799	−	0.477698i
$395$	−1.22326	+	2.11875i	−0.0615489	+	0.106606i
$396$	0.875291	−	1.51605i	0.0439850	−	0.0761843i
$397$	4.92956	+	8.53825i	0.247408	+	0.428522i	0.962806	−	0.270195i	$-0.0870880\pi$
$397$	4.92956	+	8.53825i	0.247408	+	0.428522i	−0.715398	+	0.698717i	$0.753755\pi$
$398$	12.7945			0.641332
$399$	15.3775	+	29.7270i	0.769838	+	1.48821i
$400$	7.29510			0.364755
$401$	−6.30971	−	10.9287i	−0.315092	−	0.545756i	0.664365	−	0.747408i	$-0.268702\pi$
$401$	−6.30971	−	10.9287i	−0.315092	−	0.545756i	−0.979457	+	0.201653i	$0.935369\pi$
$402$	−13.5941	+	23.5457i	−0.678013	+	1.17435i
$403$		0			0
$404$	−7.35460	−	12.7385i	−0.365905	−	0.633766i
$405$	5.78964			0.287689
$406$	10.1041	−	15.7702i	0.501456	−	0.782663i
$407$	−0.299994			−0.0148701
$408$	12.4230	+	21.5173i	0.615031	+	1.06527i
$409$	9.02867	−	15.6381i	0.446439	−	0.773255i	−0.551712	−	0.834035i	$-0.686025\pi$
$409$	9.02867	−	15.6381i	0.446439	−	0.773255i	0.998151	+	0.0607793i	$0.0193586\pi$
$410$	1.68319	−	2.91537i	0.0831268	−	0.143980i
$411$	7.55795	+	13.0908i	0.372806	+	0.645720i
$412$	9.17691			0.452114
$413$	−26.0677	−	1.20555i	−1.28271	−	0.0593214i
$414$	−13.8457			−0.680478
$415$	−3.19080	−	5.52663i	−0.156630	−	0.271291i
$416$		0			0
$417$	7.94024	−	13.7529i	0.388835	−	0.673483i
$418$	−1.97778	−	3.42562i	−0.0967366	−	0.167553i
$419$	14.2805			0.697647			0.348823	−	0.937188i	$-0.386581\pi$
$419$	14.2805			0.697647			0.348823	+	0.937188i	$0.386581\pi$
$420$	−3.41037	−	0.157720i	−0.166409	−	0.00769593i
$421$	4.27439			0.208321			0.104160	−	0.994561i	$-0.466784\pi$
$421$	4.27439			0.208321			0.104160	+	0.994561i	$0.466784\pi$
$422$	8.36410	+	14.4870i	0.407158	+	0.705218i
$423$	11.7527	−	20.3564i	0.571438	−	0.989760i
$424$	−1.06541	+	1.84534i	−0.0517407	+	0.0896175i
$425$	−7.70398	−	13.3437i	−0.373698	−	0.647263i
$426$	−36.7550			−1.78079
$427$	−6.70425	+	10.4639i	−0.324441	+	0.506382i
$428$	5.19042			0.250888
$429$		0			0
$430$	−3.76028	+	6.51300i	−0.181337	+	0.314085i
$431$	−7.30335	+	12.6498i	−0.351790	+	0.609318i	−0.986563	−	0.163381i	$-0.947760\pi$
$431$	−7.30335	+	12.6498i	−0.351790	+	0.609318i	0.634773	+	0.772698i	$0.281094\pi$
$432$	0.169858	+	0.294203i	0.00817230	+	0.0141548i
$433$	−28.0099			−1.34607			−0.673035	−	0.739611i	$-0.735009\pi$
$433$	−28.0099			−1.34607			−0.673035	+	0.739611i	$0.735009\pi$
$434$	−5.72718	−	11.0715i	−0.274914	−	0.531449i
$435$	−10.0321			−0.481001
$436$	−4.83640	−	8.37688i	−0.231621	−	0.401180i
$437$	11.5278	−	19.9667i	0.551448	−	0.955137i
$438$	6.63193	−	11.4868i	0.316886	−	0.548863i
$439$	−8.53872	−	14.7895i	−0.407531	−	0.705864i	0.587082	−	0.809528i	$-0.300277\pi$
$439$	−8.53872	−	14.7895i	−0.407531	−	0.705864i	−0.994612	+	0.103664i	$0.966943\pi$
$440$	1.35450			0.0645733
$441$	20.2951	+	1.88120i	0.966433	+	0.0895810i
$442$		0			0
$443$	−6.90783	−	11.9647i	−0.328201	−	0.568461i	0.653954	−	0.756534i	$-0.273109\pi$
$443$	−6.90783	−	11.9647i	−0.328201	−	0.568461i	−0.982155	+	0.188073i	$0.939776\pi$
$444$	0.436783	−	0.756531i	0.0207288	−	0.0359034i
$445$	4.18386	−	7.24665i	0.198334	−	0.343524i
$446$	3.63048	+	6.28817i	0.171908	+	0.297754i
$447$	−8.98984			−0.425205
$448$	−9.60703	−	18.5718i	−0.453890	−	0.877436i
$449$	32.6410			1.54042			0.770211	−	0.637789i	$-0.220151\pi$
$449$	32.6410			1.54042			0.770211	+	0.637789i	$0.220151\pi$
$450$	7.20003	+	12.4708i	0.339412	+	0.587880i
$451$	−1.77698	+	3.07783i	−0.0836749	+	0.144929i
$452$	−0.391801	+	0.678619i	−0.0184287	+	0.0319195i
$453$	5.92988	+	10.2709i	0.278610	+	0.482567i
$454$	18.0536			0.847298
$455$		0			0
$456$	38.6667			1.81074
$457$	1.58517	+	2.74559i	0.0741511	+	0.128433i	0.900717	−	0.434407i	$-0.143042\pi$
$457$	1.58517	+	2.74559i	0.0741511	+	0.128433i	−0.826566	+	0.562840i	$0.809709\pi$
$458$	−5.91560	+	10.2461i	−0.276418	+	0.478769i
$459$	0.358756	−	0.621384i	0.0167453	−	0.0290037i
$460$	1.17590	+	2.03672i	0.0548266	+	0.0949625i
$461$	−0.202023			−0.00940915			−0.00470458	−	0.999989i	$-0.501498\pi$
$461$	−0.202023			−0.00940915			−0.00470458	+	0.999989i	$0.501498\pi$
$462$	−4.88559	−	0.225944i	−0.227298	−	0.0105119i
$463$	−17.2121			−0.799912			−0.399956	−	0.916534i	$-0.630975\pi$
$463$	−17.2121			−0.799912			−0.399956	+	0.916534i	$0.630975\pi$
$464$	−5.22112	−	9.04325i	−0.242384	−	0.419822i
$465$	−3.33835	+	5.78219i	−0.154812	+	0.268143i
$466$	−9.31136	+	16.1277i	−0.431340	+	0.747103i
$467$	0.0955845	+	0.165557i	0.00442312	+	0.00766108i	0.868228	−	0.496165i	$-0.165259\pi$
$467$	0.0955845	+	0.165557i	0.00442312	+	0.00766108i	−0.863805	+	0.503826i	$0.831925\pi$
$468$		0			0
$469$	−27.5415	−	1.27371i	−1.27175	−	0.0588146i
$470$	5.41777			0.249903
$471$	−11.5731	−	20.0452i	−0.533260	−	0.923633i
$472$	−15.0742	+	26.1092i	−0.693845	+	1.20177i
$473$	3.96982	−	6.87593i	0.182533	−	0.316156i
$474$	−5.10291	−	8.83850i	−0.234384	−	0.405966i
$475$	−23.9787			−1.10022
$476$	−4.04905	+	6.31968i	−0.185588	+	0.289662i
$477$	−2.02978			−0.0929374
$478$	−10.5816	−	18.3278i	−0.483989	−	0.838294i
$479$	−10.7392	+	18.6009i	−0.490688	+	0.849897i	−0.999943	−	0.0107189i	$-0.996588\pi$
$479$	−10.7392	+	18.6009i	−0.490688	+	0.849897i	0.509254	+	0.860616i	$0.329921\pi$
$480$	−3.35676	+	5.81408i	−0.153214	+	0.265375i
$481$		0			0
$482$	2.98752			0.136078
$483$	−13.0976	−	25.3197i	−0.595964	−	1.15209i
$484$	8.90811			0.404914
$485$	0.0631758	+	0.109424i	0.00286867	+	0.00496868i
$486$	−11.7305	+	20.3178i	−0.532105	+	0.921633i
$487$	−9.52422	+	16.4964i	−0.431584	+	0.747525i	−0.997010	−	0.0772740i	$-0.975378\pi$
$487$	−9.52422	+	16.4964i	−0.431584	+	0.747525i	0.565426	+	0.824799i	$0.308712\pi$
$488$	7.17871	+	12.4339i	0.324965	+	0.562856i
$489$	−57.6458			−2.60684
$490$	1.96340	+	4.26790i	0.0886973	+	0.192804i
$491$	35.7559			1.61364			0.806821	−	0.590796i	$-0.201186\pi$
$491$	35.7559			1.61364			0.806821	+	0.590796i	$0.201186\pi$
$492$	−5.17448	−	8.96247i	−0.233284	−	0.404059i
$493$	−11.0275	+	19.1002i	−0.496654	+	0.860230i
$494$		0			0
$495$	0.645140	+	1.11741i	0.0289969	+	0.0502240i
$496$	−6.94968			−0.312050
$497$	−17.1251	−	33.1053i	−0.768164	−	1.48497i
$498$	26.6213			1.19293
$499$	−8.84457	−	15.3192i	−0.395937	−	0.685784i	0.597283	−	0.802031i	$-0.296247\pi$
$499$	−8.84457	−	15.3192i	−0.395937	−	0.685784i	−0.993220	+	0.116247i	$0.962914\pi$
$500$	2.54976	−	4.41632i	0.114029	−	0.197504i
$501$	−1.37609	+	2.38346i	−0.0614792	+	0.106485i
$502$	−12.6410	−	21.8949i	−0.564196	−	0.977217i
$503$	11.3305			0.505203			0.252601	−	0.967570i	$-0.418714\pi$
$503$	11.3305			0.505203			0.252601	+	0.967570i	$0.418714\pi$
$504$	12.7033	−	19.8271i	0.565851	−	0.883169i
$505$	10.8415			0.482441
$506$	1.68456	+	2.91774i	0.0748878	+	0.129709i
$507$		0			0
$508$	−3.61048	+	6.25353i	−0.160189	+	0.277455i
$509$	9.67569	+	16.7588i	0.428868	+	0.742821i	0.996773	−	0.0802734i	$-0.0255793\pi$
$509$	9.67569	+	16.7588i	0.428868	+	0.742821i	−0.567905	+	0.823094i	$0.692246\pi$
$510$	−5.45523			−0.241562
$511$	13.4362	+	0.621384i	0.594382	+	0.0274884i
$512$	−16.6645			−0.736472
$513$	−0.558316	−	0.967032i	−0.0246502	−	0.0426955i
$514$	1.84152	−	3.18961i	0.0812259	−	0.140687i
$515$	−3.38195	+	5.85772i	−0.149027	+	0.258122i
$516$	11.5599	+	20.0224i	0.508897	+	0.881435i
$517$	−5.71967			−0.251551
$518$	−1.20079	−	0.0555330i	−0.0527597	−	0.00243998i
$519$	−29.1505			−1.27957
$520$		0			0
$521$	3.85550	−	6.67791i	0.168912	−	0.292565i	−0.769125	−	0.639098i	$-0.779308\pi$
$521$	3.85550	−	6.67791i	0.168912	−	0.292565i	0.938038	+	0.346533i	$0.112641\pi$
$522$	10.3062	−	17.8508i	0.451088	−	0.781307i
$523$	17.5251	+	30.3543i	0.766317	+	1.32730i	0.939547	+	0.342419i	$0.111246\pi$
$523$	17.5251	+	30.3543i	0.766317	+	1.32730i	−0.173230	+	0.984881i	$0.555420\pi$
$524$	5.94246			0.259597
$525$	−15.9944	+	24.9638i	−0.698054	+	1.08951i
$526$	−23.0160			−1.00355
$527$	7.33919	+	12.7119i	0.319700	+	0.553737i
$528$	−1.36339	+	2.36146i	−0.0593339	+	0.102769i
$529$	1.68133	−	2.91214i	0.0731011	−	0.126615i
$530$	−0.233922	−	0.405165i	−0.0101609	−	0.0175992i
$531$	−28.7189			−1.24630
$532$	5.36671	+	10.3746i	0.232676	+	0.449797i
$533$		0			0
$534$	17.4532	+	30.2299i	0.755275	+	1.30818i
$535$	−1.91282	+	3.31309i	−0.0826982	+	0.143238i
$536$	−15.9264	+	27.5854i	−0.687917	+	1.19151i
$537$	11.5136	+	19.9422i	0.496849	+	0.860568i
$538$	15.7276			0.678066
$539$	−2.07281	−	4.50573i	−0.0892821	−	0.194075i
$540$	0.113903			0.00490160
$541$	−6.06674	−	10.5079i	−0.260829	−	0.451770i	0.705633	−	0.708577i	$-0.250663\pi$
$541$	−6.06674	−	10.5079i	−0.260829	−	0.451770i	−0.966463	+	0.256807i	$0.917329\pi$
$542$	1.09648	−	1.89916i	0.0470978	−	0.0815758i
$543$	13.8972	−	24.0706i	0.596385	−	1.03297i
$544$	7.37967	+	12.7820i	0.316401	+	0.548022i
$545$	7.12940			0.305390
$546$		0			0
$547$	−5.12546			−0.219149			−0.109575	−	0.993979i	$-0.534949\pi$
$547$	−5.12546			−0.219149			−0.109575	+	0.993979i	$0.534949\pi$
$548$	2.63770	+	4.56864i	0.112677	+	0.195162i
$549$	−6.83835	+	11.8444i	−0.291854	+	0.505505i
$550$	1.75201	−	3.03457i	0.0747058	−	0.129394i
$551$	17.1616	+	29.7248i	0.731109	+	1.26632i
$552$	−32.9340			−1.40177
$553$	5.58327	−	8.71427i	0.237425	−	0.370568i
$554$	−5.83051			−0.247715
$555$	0.321934	+	0.557606i	0.0136653	+	0.0236691i
$556$	2.77112	−	4.79972i	0.117522	−	0.203554i
$557$	−18.7793	+	32.5267i	−0.795705	+	1.37820i	0.126686	+	0.991943i	$0.459566\pi$
$557$	−18.7793	+	32.5267i	−0.795705	+	1.37820i	−0.922391	+	0.386258i	$0.873767\pi$
$558$	−6.85911	−	11.8803i	−0.290369	−	0.502934i
$559$		0			0
$560$	2.61641	+	0.121001i	0.110563	+	0.00511323i
$561$	5.75922			0.243154
$562$	−10.8569	−	18.8048i	−0.457973	−	0.793232i
$563$	−14.3504	+	24.8557i	−0.604799	+	1.04754i	0.387284	+	0.921960i	$0.373413\pi$
$563$	−14.3504	+	24.8557i	−0.604799	+	1.04754i	−0.992083	+	0.125583i	$0.959920\pi$
$564$	8.32769	−	14.4240i	0.350659	−	0.607359i
$565$	−0.288779	−	0.500180i	−0.0121490	−	0.0210428i
$566$	1.86195			0.0782636
$567$	−24.4656	−	1.13146i	−1.02746	−	0.0475170i
$568$	−43.0610			−1.80680
$569$	−8.97417	−	15.5437i	−0.376217	−	0.651627i	0.614291	−	0.789079i	$-0.289442\pi$
$569$	−8.97417	−	15.5437i	−0.376217	−	0.651627i	−0.990508	+	0.137452i	$0.956109\pi$
$570$	−4.24486	+	7.35231i	−0.177798	+	0.307955i
$571$	−8.91370	+	15.4390i	−0.373027	+	0.646101i	−0.990030	−	0.140860i	$-0.955013\pi$
$571$	−8.91370	+	15.4390i	−0.373027	+	0.646101i	0.617003	+	0.786961i	$0.288347\pi$
$572$		0			0
$573$	−38.1428			−1.59344
$574$	−7.68250	+	11.9907i	−0.320662	+	0.500483i
$575$	20.4236			0.851724
$576$	−11.5058	−	19.9286i	−0.479407	−	0.830357i
$577$	−16.5285	+	28.6282i	−0.688091	+	1.19181i	0.284363	+	0.958717i	$0.408218\pi$
$577$	−16.5285	+	28.6282i	−0.688091	+	1.19181i	−0.972455	+	0.233092i	$0.925116\pi$
$578$	3.12445	−	5.41170i	0.129960	−	0.225097i
$579$	−27.9698	−	48.4451i	−1.16239	−	2.01331i
$580$	−3.50117			−0.145378
$581$	12.4035	+	23.9778i	0.514584	+	0.994766i
$582$	−0.527085			−0.0218484
$583$	0.246957	+	0.427742i	0.0102279	+	0.0177153i
$584$	7.76975	−	13.4576i	0.321515	−	0.556880i
$585$		0			0
$586$	−14.6172	−	25.3178i	−0.603832	−	1.04587i
$587$	14.7295			0.607953			0.303976	−	0.952680i	$-0.401686\pi$
$587$	14.7295			0.607953			0.303976	+	0.952680i	$0.401686\pi$
$588$	14.3806	+	1.33297i	0.593045	+	0.0549708i
$589$	22.8433			0.941241
$590$	−3.30970	−	5.73258i	−0.136258	−	0.236006i
$591$	12.4044	−	21.4851i	0.510250	−	0.883779i
$592$	−0.335097	+	0.580404i	−0.0137724	+	0.0238545i
$593$	4.60494	+	7.97598i	0.189102	+	0.327534i	0.944951	−	0.327212i	$-0.106109\pi$
$593$	4.60494	+	7.97598i	0.189102	+	0.327534i	−0.755849	+	0.654746i	$0.772776\pi$
$594$	0.163174			0.00669510
$595$	−2.54172	−	4.91353i	−0.104201	−	0.201435i
$596$	−3.13743			−0.128514
$597$	14.4954	+	25.1067i	0.593256	+	1.02755i
$598$		0			0
$599$	5.28727	−	9.15782i	0.216032	−	0.374178i	−0.737559	−	0.675282i	$-0.764022\pi$
$599$	5.28727	−	9.15782i	0.216032	−	0.374178i	0.953591	+	0.301104i	$0.0973551\pi$
$600$	17.1263	+	29.6637i	0.699180	+	1.21102i
$601$	4.08916			0.166800			0.0834001	−	0.996516i	$-0.473422\pi$
$601$	4.08916			0.166800			0.0834001	+	0.996516i	$0.473422\pi$
$602$	17.1629	−	26.7875i	0.699507	−	1.09178i
$603$	−30.3426			−1.23565
$604$	2.06951	+	3.58450i	0.0842072	+	0.145851i
$605$	−3.28289	+	5.68613i	−0.133469	+	0.231174i
$606$	−22.6131	+	39.1670i	−0.918593	+	1.59105i
$607$	−1.80353	−	3.12380i	−0.0732030	−	0.126791i	0.827100	−	0.562054i	$-0.189989\pi$
$607$	−1.80353	−	3.12380i	−0.0732030	−	0.126791i	−0.900303	+	0.435263i	$0.856655\pi$
$608$	22.9693			0.931527
$609$	42.3932	+	1.96056i	1.71786	+	0.0794459i
$610$	−3.15233			−0.127634
$611$		0			0
$612$	−4.13003	+	7.15343i	−0.166947	+	0.289160i
$613$	19.2422	−	33.3285i	0.777186	−	1.34613i	−0.156371	−	0.987698i	$-0.549980\pi$
$613$	19.2422	−	33.3285i	0.777186	−	1.34613i	0.933557	−	0.358428i	$-0.116687\pi$
$614$	−6.82128	−	11.8148i	−0.275284	−	0.476806i
$615$	7.62778			0.307582
$616$	−5.72379	−	0.264709i	−0.230618	−	0.0106654i
$617$	−3.09503			−0.124601			−0.0623007	−	0.998057i	$-0.519844\pi$
$617$	−3.09503			−0.124601			−0.0623007	+	0.998057i	$0.519844\pi$
$618$	−14.1080	−	24.4359i	−0.567509	−	0.982954i
$619$	−6.13462	+	10.6255i	−0.246571	+	0.427074i	−0.962572	−	0.271025i	$-0.912637\pi$
$619$	−6.13462	+	10.6255i	−0.246571	+	0.427074i	0.716001	+	0.698099i	$0.245971\pi$
$620$	−1.16507	+	2.01797i	−0.0467905	+	0.0810435i
$621$	0.475540	+	0.823660i	0.0190828	+	0.0330523i
$622$	10.3215			0.413854
$623$	−19.0962	+	29.8050i	−0.765073	+	1.19411i
$624$		0			0
$625$	−9.64277	−	16.7018i	−0.385711	−	0.668071i
$626$	4.84241	−	8.38730i	0.193542	−	0.335224i
$627$	4.48140	−	7.76202i	0.178970	−	0.309985i
$628$	−4.03897	−	6.99571i	−0.161173	−	0.279159i
$629$	1.41551			0.0564402
$630$	2.37546	+	4.59211i	0.0946406	+	0.182954i
$631$	−5.31780			−0.211698			−0.105849	−	0.994382i	$-0.533756\pi$
$631$	−5.31780			−0.211698			−0.105849	+	0.994382i	$0.533756\pi$
$632$	−5.97840	−	10.3549i	−0.237808	−	0.411896i
$633$	−18.9520	+	32.8258i	−0.753273	+	1.30471i
$634$	−13.2126	+	22.8849i	−0.524740	+	0.908877i
$635$	−2.66113	−	4.60921i	−0.105604	−	0.182911i
$636$	−1.43825			−0.0570304
$637$		0			0
$638$	−5.01566			−0.198572
$639$	−20.5097	−	35.5238i	−0.811349	−	1.40530i
$640$	−0.109212	+	0.189160i	−0.00431697	+	0.00747721i
$641$	−6.09521	+	10.5572i	−0.240746	+	0.416985i	−0.960927	−	0.276801i	$-0.910726\pi$
$641$	−6.09521	+	10.5572i	−0.240746	+	0.416985i	0.720181	+	0.693787i	$0.244059\pi$
$642$	−7.97944	−	13.8208i	−0.314923	−	0.545463i
$643$	−18.9733			−0.748235			−0.374117	−	0.927381i	$-0.622054\pi$
$643$	−18.9733			−0.748235			−0.374117	+	0.927381i	$0.622054\pi$
$644$	−4.57104	−	8.83649i	−0.180124	−	0.348207i
$645$	−17.0406			−0.670974
$646$	9.33211	+	16.1637i	0.367167	+	0.635952i
$647$	−9.85587	+	17.0709i	−0.387474	+	0.671125i	−0.992109	−	0.125378i	$-0.959986\pi$
$647$	−9.85587	+	17.0709i	−0.387474	+	0.671125i	0.604635	+	0.796503i	$0.293319\pi$
$648$	−14.1478	+	24.5046i	−0.555776	+	0.962633i
$649$	3.49414	+	6.05202i	0.137157	+	0.237563i
$650$		0			0
$651$	15.2371	−	23.7818i	0.597188	−	0.932080i
$652$	−20.1182			−0.787891
$653$	10.1986	+	17.6645i	0.399103	+	0.691267i	0.993616	−	0.112819i	$-0.0359882\pi$
$653$	10.1986	+	17.6645i	0.399103	+	0.691267i	−0.594512	+	0.804087i	$0.702655\pi$
$654$	−14.8704	+	25.7563i	−0.581478	+	1.00715i
$655$	−2.18996	+	3.79313i	−0.0855690	+	0.148210i
$656$	3.96982	+	6.87593i	0.154996	+	0.268460i
$657$	14.8027			0.577510
$658$	−22.8942	−	1.05879i	−0.892509	−	0.0412759i
$659$	32.6628			1.27236			0.636181	−	0.771540i	$-0.280513\pi$
$659$	32.6628			1.27236			0.636181	+	0.771540i	$0.280513\pi$
$660$	0.457129	+	0.791771i	0.0177937	+	0.0308196i
$661$	4.86846	−	8.43242i	0.189361	−	0.327983i	−0.755676	−	0.654945i	$-0.772692\pi$
$661$	4.86846	−	8.43242i	0.189361	−	0.327983i	0.945037	+	0.326962i	$0.106025\pi$
$662$	−7.06704	+	12.2405i	−0.274668	+	0.475740i
$663$		0			0
$664$	31.1886			1.21035
$665$	−8.60002	−	0.397725i	−0.333494	−	0.0154231i
$666$	−1.32292			−0.0512620
$667$	−14.6172	−	25.3178i	−0.565981	−	0.980308i
$668$	−0.480251	+	0.831819i	−0.0185815	+	0.0321841i
$669$	−8.22620	+	14.2482i	−0.318043	+	0.550867i
$670$	−3.49683	−	6.05668i	−0.135094	−	0.233990i
$671$	3.32800			0.128476
$672$	15.3211	−	23.9129i	0.591025	−	0.922461i
$673$	39.4512			1.52073			0.760367	−	0.649494i	$-0.225019\pi$
$673$	39.4512			1.52073			0.760367	+	0.649494i	$0.225019\pi$
$674$	9.13742	+	15.8265i	0.351960	+	0.609613i
$675$	0.494581	−	0.856639i	0.0190364	−	0.0329720i
$676$		0			0
$677$	24.3169	+	42.1182i	0.934576	+	1.61873i	0.775389	+	0.631484i	$0.217554\pi$
$677$	24.3169	+	42.1182i	0.934576	+	1.61873i	0.159187	+	0.987248i	$0.449113\pi$
$678$	2.40932			0.0925296
$679$	−0.245582	−	0.474745i	−0.00942455	−	0.0182191i
$680$	−6.39117			−0.245090
$681$	20.4536	+	35.4266i	0.783783	+	1.35755i
$682$	−1.66905	+	2.89088i	−0.0639112	+	0.110697i
$683$	−2.85387	+	4.94304i	−0.109200	+	0.189140i	−0.915446	−	0.402440i	$-0.868162\pi$
$683$	−2.85387	+	4.94304i	−0.109200	+	0.189140i	0.806246	+	0.591580i	$0.201496\pi$
$684$	6.42738	+	11.1326i	0.245757	+	0.425664i
$685$	−3.88828			−0.148563
$686$	−7.46278	−	18.4188i	−0.284930	−	0.703234i
$687$	−26.8080			−1.02279
$688$	−8.86867	−	15.3610i	−0.338115	−	0.585632i
$689$		0			0
$690$	3.61552	−	6.26226i	0.137640	−	0.238400i
$691$	20.8866	+	36.1766i	0.794563	+	1.37622i	0.923116	+	0.384521i	$0.125633\pi$
$691$	20.8866	+	36.1766i	0.794563	+	1.37622i	−0.128553	+	0.991703i	$0.541033\pi$
$692$	−10.1734			−0.386736
$693$	−2.50783	−	4.84801i	−0.0952646	−	0.184161i
$694$	0.493517			0.0187336
$695$	2.04247	+	3.53767i	0.0774754	+	0.134191i
$696$	24.5147	−	42.4608i	0.929228	−	1.60947i
$697$	8.38464	−	14.5226i	0.317591	−	0.550084i
$698$	3.69035	+	6.39188i	0.139682	+	0.241936i
$699$	−42.1967			−1.59603
$700$	−5.58200	+	8.71229i	−0.210980	+	0.329294i
$701$	−22.4361			−0.847399			−0.423700	−	0.905803i	$-0.639269\pi$
$701$	−22.4361			−0.847399			−0.423700	+	0.905803i	$0.639269\pi$
$702$		0			0
$703$	1.10145	−	1.90776i	0.0415419	−	0.0719527i
$704$	−2.79974	+	4.84929i	−0.105519	+	0.182764i
$705$	6.13798	+	10.6313i	0.231170	+	0.400398i
$706$	1.64527			0.0619207
$707$	−45.8137	−	2.11875i	−1.72300	−	0.0796837i
$708$	−20.3495			−0.764780
$709$	14.3734	+	24.8955i	0.539804	+	0.934969i	0.998914	+	0.0465891i	$0.0148351\pi$
$709$	14.3734	+	24.8955i	0.539804	+	0.934969i	−0.459110	+	0.888380i	$0.651832\pi$
$710$	4.72726	−	8.18785i	0.177411	−	0.307285i
$711$	5.69495	−	9.86394i	0.213577	−	0.369927i
$712$	20.4476	+	35.4163i	0.766307	+	1.32728i
$713$	−19.4566			−0.728654
$714$	23.0525	+	1.06611i	0.862718	+	0.0398982i
$715$		0			0
$716$	4.01822	+	6.95976i	0.150168	+	0.260098i
$717$	23.9765	−	41.5284i	0.895417	−	1.55091i
$718$	14.5972	−	25.2830i	0.544762	−	0.943555i
$719$	2.10450	+	3.64509i	0.0784844	+	0.135939i	0.902596	−	0.430488i	$-0.141659\pi$
$719$	2.10450	+	3.64509i	0.0784844	+	0.135939i	−0.824112	+	0.566427i	$0.808325\pi$
$720$	2.88251			0.107425
$721$	15.4361	−	24.0924i	0.574870	−	0.897247i
$722$	8.65821			0.322225
$723$	3.38467	+	5.86242i	0.125877	+	0.218026i
$724$	4.85008	−	8.40058i	0.180252	−	0.312205i
$725$	−15.2025	+	26.3315i	−0.564606	+	0.977927i
$726$	−13.6948	−	23.7201i	−0.508262	−	0.880335i
$727$	43.4680			1.61214			0.806070	−	0.591820i	$-0.201591\pi$
$727$	43.4680			1.61214			0.806070	+	0.591820i	$0.201591\pi$
$728$		0			0
$729$	−25.3884			−0.940312
$730$	1.70594	+	2.95477i	0.0631396	+	0.109361i
$731$	−18.7315	+	32.4439i	−0.692809	+	1.19998i
$732$	−4.84548	+	8.39261i	−0.179094	+	0.310200i
$733$	4.54710	+	7.87581i	0.167951	+	0.290900i	0.937699	−	0.347448i	$-0.112952\pi$
$733$	4.54710	+	7.87581i	0.167951	+	0.290900i	−0.769748	+	0.638348i	$0.779618\pi$
$734$	28.9525			1.06866
$735$	−6.15050	+	8.68803i	−0.226865	+	0.320463i
$736$	−19.5639			−0.721133
$737$	3.69169	+	6.39419i	0.135985	+	0.235533i
$738$	−7.83617	+	13.5726i	−0.288453	+	0.499616i
$739$	4.80433	−	8.32135i	0.176730	−	0.306106i	−0.764028	−	0.645183i	$-0.776781\pi$
$739$	4.80433	−	8.32135i	0.176730	−	0.306106i	0.940759	+	0.339077i	$0.110115\pi$
$740$	0.112354	+	0.194603i	0.00413022	+	0.00715375i
$741$		0			0
$742$	0.909317	+	1.75784i	0.0333821	+	0.0645325i
$743$	−32.1771			−1.18046			−0.590231	−	0.807234i	$-0.700964\pi$
$743$	−32.1771			−1.18046			−0.590231	+	0.807234i	$0.700964\pi$
$744$	−16.3154	−	28.2591i	−0.598152	−	1.03603i
$745$	1.15623	−	2.00265i	0.0423610	−	0.0733714i
$746$	−2.13129	+	3.69150i	−0.0780320	+	0.135155i
$747$	14.8549	+	25.7295i	0.543513	+	0.941392i
$748$	2.00995			0.0734911
$749$	8.73058	−	13.6265i	0.319008	−	0.497903i
$750$	−15.6794			−0.572531
$751$	−3.89892	−	6.75313i	−0.142274	−	0.246425i	0.786079	−	0.618126i	$-0.212108\pi$
$751$	−3.89892	−	6.75313i	−0.142274	−	0.246425i	−0.928352	+	0.371701i	$0.878775\pi$
$752$	−6.38894	+	11.0660i	−0.232981	+	0.403534i
$753$	28.6429	−	49.6110i	1.04381	−	1.80793i
$754$		0			0
$755$	−3.05070			−0.111026
$756$	−0.481327	−	0.0222599i	−0.0175057	−	0.000809586i
$757$	17.9970			0.654110			0.327055	−	0.945005i	$-0.393944\pi$
$757$	17.9970			0.654110			0.327055	+	0.945005i	$0.393944\pi$
$758$	6.11960	+	10.5995i	0.222274	+	0.384990i
$759$	−3.81699	+	6.61123i	−0.138548	+	0.239972i
$760$	−4.97314	+	8.61373i	−0.180395	+	0.312453i
$761$	20.3395	+	35.2290i	0.737306	+	1.27705i	0.953704	+	0.300746i	$0.0972358\pi$
$761$	20.3395	+	35.2290i	0.737306	+	1.27705i	−0.216398	+	0.976305i	$0.569431\pi$
$762$	22.2021			0.804299
$763$	−30.1271	−	1.39329i	−1.09068	−	0.0504406i
$764$	−13.3117			−0.481601
$765$	−3.04407	−	5.27248i	−0.110059	−	0.190627i
$766$	12.7650	−	22.1097i	0.461220	−	0.798856i
$767$		0			0
$768$	−19.6711	−	34.0713i	−0.709819	−	1.22944i
$769$	39.3098			1.41755			0.708774	−	0.705435i	$-0.249248\pi$
$769$	39.3098			1.41755			0.708774	+	0.705435i	$0.249248\pi$
$770$	0.678695	−	1.05929i	0.0244585	−	0.0381743i
$771$	8.34529			0.300548
$772$	−9.76138	−	16.9072i	−0.351320	−	0.608504i
$773$	−6.73679	+	11.6685i	−0.242306	+	0.419685i	−0.961371	−	0.275257i	$-0.911237\pi$
$773$	−6.73679	+	11.6685i	−0.242306	+	0.419685i	0.719065	+	0.694943i	$0.244570\pi$
$774$	17.5062	−	30.3216i	0.629247	−	1.08989i
$775$	10.1178	+	17.5245i	0.363442	+	0.629500i
$776$	−0.617515			−0.0221675
$777$	−1.25144	−	2.41923i	−0.0448953	−	0.0867893i
$778$	−30.4866			−1.09300
$779$	−13.0486	−	22.6009i	−0.467516	−	0.809761i
$780$		0			0
$781$	−4.99068	+	8.64412i	−0.178581	+	0.309311i
$782$	−7.94854	−	13.7673i	−0.284239	−	0.492316i
$783$	−1.41589			−0.0505998
$784$	−11.0327	−	1.02264i	−0.394024	−	0.0365230i
$785$	5.95391			0.212504
$786$	−9.13558	−	15.8233i	−0.325855	−	0.564398i
$787$	−19.9145	+	34.4930i	−0.709877	+	1.22954i	0.255026	+	0.966934i	$0.417916\pi$
$787$	−19.9145	+	34.4930i	−0.709877	+	1.22954i	−0.964903	+	0.262608i	$0.915417\pi$
$788$	4.32911	−	7.49823i	0.154218	−	0.267114i
$789$	−26.0757	−	45.1644i	−0.928319	−	1.60790i
$790$	2.62525			0.0934022
$791$	1.12256	+	2.17008i	0.0399137	+	0.0771592i
$792$	−6.30594			−0.224072
$793$		0			0
$794$	5.28969	−	9.16201i	0.187724	−	0.325148i
$795$	0.530037	−	0.918051i	0.0187985	−	0.0325599i
$796$	5.05884	+	8.76217i	0.179306	+	0.310567i
$797$	−21.2530			−0.752821			−0.376410	−	0.926453i	$-0.622842\pi$
$797$	−21.2530			−0.752821			−0.376410	+	0.926453i	$0.622842\pi$
$798$	19.3746	−	30.2396i	0.685854	−	1.07047i
$799$	26.9881			0.954770
$800$	10.1736	+	17.6212i	0.359691	+	0.623003i
$801$	−19.4781	+	33.7371i	−0.688226	+	1.19204i
$802$	−6.77067	+	11.7271i	−0.239081	+	0.414100i
$803$	−1.80100	−	3.11942i	−0.0635559	−	0.110082i
$804$	−21.5000			−0.758246
$805$	7.32498	+	0.338759i	0.258172	+	0.0119397i
$806$		0			0
$807$	17.8184	+	30.8624i	0.627237	+	1.08641i
$808$	−26.4927	+	45.8867i	−0.932010	+	1.61429i
$809$	−10.7088	+	18.5481i	−0.376500	+	0.652117i	−0.990550	−	0.137150i	$-0.956206\pi$
$809$	−10.7088	+	18.5481i	−0.376500	+	0.652117i	0.614050	+	0.789267i	$0.289539\pi$
$810$	−3.10630	−	5.38027i	−0.109144	−	0.189043i
$811$	−11.0116			−0.386669			−0.193335	−	0.981133i	$-0.561930\pi$
$811$	−11.0116			−0.386669			−0.193335	+	0.981133i	$0.561930\pi$
$812$	14.7951	+	0.684230i	0.519206	+	0.0240118i
$813$	4.96896			0.174269
$814$	0.160955	+	0.278782i	0.00564147	+	0.00977131i
$815$	7.41414	−	12.8417i	0.259706	−	0.449824i
$816$	6.43311	−	11.1425i	0.225204	−	0.390065i
$817$	29.1509	+	50.4909i	1.01986	+	1.76645i
$818$	−19.3765			−0.677484
$819$		0			0
$820$	2.66207			0.0929636
$821$	19.3342	+	33.4879i	0.674769	+	1.16873i	0.976536	+	0.215353i	$0.0690902\pi$
$821$	19.3342	+	33.4879i	0.674769	+	1.16873i	−0.301767	+	0.953382i	$0.597576\pi$
$822$	8.11010	−	14.0471i	0.282872	−	0.489949i
$823$	10.2283	−	17.7160i	0.356537	−	0.617540i	−0.630843	−	0.775911i	$-0.717291\pi$
$823$	10.2283	−	17.7160i	0.356537	−	0.617540i	0.987380	+	0.158371i	$0.0506241\pi$
$824$	−16.5285	−	28.6282i	−0.575798	−	0.997312i
$825$	7.93965			0.276423
$826$	12.8657	+	24.8713i	0.447655	+	0.865384i
$827$	27.3451			0.950881			0.475440	−	0.879748i	$-0.342289\pi$
$827$	27.3451			0.950881			0.475440	+	0.879748i	$0.342289\pi$
$828$	−5.47446	−	9.48204i	−0.190251	−	0.329524i
$829$	12.5043	−	21.6581i	0.434292	−	0.752217i	−0.562945	−	0.826494i	$-0.690332\pi$
$829$	12.5043	−	21.6581i	0.434292	−	0.752217i	0.997238	+	0.0742776i	$0.0236651\pi$
$830$	−3.42390	+	5.93037i	−0.118845	+	0.205846i
$831$	−6.60560	−	11.4412i	−0.229146	−	0.396892i
$832$		0			0
$833$	9.78048	+	21.2601i	0.338873	+	0.736620i
$834$	−17.0406			−0.590069
$835$	−0.353972	−	0.613098i	−0.0122497	−	0.0212171i
$836$	1.56400	−	2.70892i	0.0540920	−	0.0936900i
$837$	−0.471162	+	0.816077i	−0.0162857	+	0.0282077i
$838$	−7.66187	−	13.2707i	−0.264675	−	0.458430i
$839$	8.76981			0.302768			0.151384	−	0.988475i	$-0.451627\pi$
$839$	8.76981			0.302768			0.151384	+	0.988475i	$0.451627\pi$
$840$	5.65039	+	10.9230i	0.194957	+	0.376880i
$841$	14.5218			0.500753
$842$	−2.29333	−	3.97216i	−0.0790332	−	0.136890i
$843$	24.6004	−	42.6092i	0.847284	−	1.46754i
$844$	−6.61418	+	11.4561i	−0.227669	+	0.394335i
$845$		0			0
$846$	−25.2227			−0.867174
$847$	14.9840	−	23.3867i	0.514855	−	0.803576i
$848$	1.10342			0.0378914
$849$	2.10947	+	3.65371i	0.0723968	+	0.125395i
$850$	−8.26679	+	14.3185i	−0.283549	+	0.491120i
$851$	−0.938148	+	1.62492i	−0.0321593	+	0.0557015i
$852$	−14.5326	−	25.1712i	−0.497879	−	0.862352i
$853$	19.8232			0.678734			0.339367	−	0.940654i	$-0.389787\pi$
$853$	19.8232			0.678734			0.339367	+	0.940654i	$0.389787\pi$
$854$	13.3210	+	0.616058i	0.455836	+	0.0210811i
$855$	−9.47469			−0.324028
$856$	−9.34845	−	16.1920i	−0.319523	−	0.553431i
$857$	1.33518	−	2.31261i	0.0456090	−	0.0789972i	−0.842320	−	0.538978i	$-0.818810\pi$
$857$	1.33518	−	2.31261i	0.0456090	−	0.0789972i	0.887929	+	0.459981i	$0.152144\pi$
$858$		0			0
$859$	19.4798	+	33.7401i	0.664644	+	1.15120i	0.979382	+	0.202018i	$0.0647500\pi$
$859$	19.4798	+	33.7401i	0.664644	+	1.15120i	−0.314738	+	0.949179i	$0.601917\pi$
$860$	−5.94713			−0.202795
$861$	−32.2332	−	1.49069i	−1.09850	−	0.0508026i
$862$	15.6738			0.533851
$863$	12.3988	+	21.4754i	0.422060	+	0.731030i	0.996141	−	0.0877689i	$-0.0279737\pi$
$863$	12.3988	+	21.4754i	0.422060	+	0.731030i	−0.574081	+	0.818799i	$0.694640\pi$
$864$	−0.473761	+	0.820578i	−0.0161177	+	0.0279166i
$865$	3.74920	−	6.49381i	0.127477	−	0.220796i
$866$	15.0281	+	26.0294i	0.510675	+	0.884514i
$867$	14.1592			0.480871
$868$	5.31770	−	8.29976i	0.180494	−	0.281712i
$869$	−2.77154			−0.0940181
$870$	5.38249	+	9.32274i	0.182483	+	0.316070i
$871$		0			0
$872$	−17.4216	+	30.1752i	−0.589971	+	1.02186i
$873$	−0.294118	−	0.509428i	−0.00995439	−	0.0172415i
$874$	−24.7399			−0.836839
$875$	−7.30542	−	14.1225i	−0.246968	−	0.477426i
$876$	10.4888			0.354385
$877$	−0.989201	−	1.71335i	−0.0334029	−	0.0578556i	0.848841	−	0.528649i	$-0.177301\pi$
$877$	−0.989201	−	1.71335i	−0.0334029	−	0.0578556i	−0.882244	+	0.470793i	$0.843968\pi$
$878$	−9.16251	+	15.8699i	−0.309220	+	0.535584i
$879$	33.1208	−	57.3668i	1.11714	−	1.93494i
$880$	−0.350706	−	0.607440i	−0.0118223	−	0.0204768i
$881$	17.1466			0.577683			0.288841	−	0.957377i	$-0.406730\pi$
$881$	17.1466			0.577683			0.288841	+	0.957377i	$0.406730\pi$
$882$	−9.14069	−	19.8694i	−0.307783	−	0.669038i
$883$	−10.2168			−0.343822			−0.171911	−	0.985112i	$-0.554994\pi$
$883$	−10.2168			−0.343822			−0.171911	+	0.985112i	$0.554994\pi$
$884$		0			0
$885$	7.49936	−	12.9893i	0.252088	−	0.436630i
$886$	−7.41248	+	12.8388i	−0.249027	+	0.431328i
$887$	−25.4965	−	44.1613i	−0.856090	−	1.48279i	−0.875630	−	0.482983i	$-0.839553\pi$
$887$	−25.4965	−	44.1613i	−0.856090	−	1.48279i	0.0195395	−	0.999809i	$-0.493780\pi$
$888$	−3.14676			−0.105598
$889$	10.3445	+	19.9975i	0.346944	+	0.670694i
$890$	−8.97901			−0.300977
$891$	3.27940	+	5.68008i	0.109864	+	0.190290i
$892$	−2.87092	+	4.97258i	−0.0961255	+	0.166494i
$893$	21.0002	−	36.3733i	0.702743	−	1.21719i
$894$	4.82329	+	8.35419i	0.161315	+	0.279406i
$895$	−5.92331			−0.197995
$896$	0.498470	−	0.778003i	0.0166527	−	0.0259913i
$897$		0			0
$898$	−17.5128	−	30.3330i	−0.584409	−	1.01223i
$899$	14.4827	−	25.0847i	0.483024	−	0.836621i
$900$	−5.69365	+	9.86170i	−0.189788	+	0.328723i
$901$	−1.16526	−	2.01829i	−0.0388204	−	0.0672389i
$902$	3.81360			0.126979
$903$	72.0097	+	3.33024i	2.39633	+	0.110823i
$904$	2.82268			0.0938811
$905$	3.57478	+	6.19170i	0.118830	+	0.205819i
$906$	6.36309	−	11.0212i	0.211400	−	0.366155i
$907$	2.89269	−	5.01028i	0.0960501	−	0.166364i	−0.813996	−	0.580870i	$-0.802712\pi$
$907$	2.89269	−	5.01028i	0.0960501	−	0.166364i	0.910046	+	0.414506i	$0.136046\pi$
$908$	7.13824	+	12.3638i	0.236891	+	0.410307i
$909$	−50.4732			−1.67409
$910$		0			0
$911$	−1.70706			−0.0565573			−0.0282787	−	0.999600i	$-0.509003\pi$
$911$	−1.70706			−0.0565573			−0.0282787	+	0.999600i	$0.509003\pi$
$912$	−10.0116	−	17.3405i	−0.331516	−	0.574202i
$913$	3.61470	−	6.26084i	0.119629	−	0.207204i
$914$	1.70097	−	2.94617i	0.0562632	−	0.0974507i
$915$	−3.57139	−	6.18583i	−0.118067	−	0.204497i
$916$	−9.35590			−0.309128
$917$	9.99556	−	15.6009i	0.330082	−	0.515187i
$918$	−0.769931			−0.0254115
$919$	−18.6025	−	32.2205i	−0.613640	−	1.06286i	−0.990622	−	0.136634i	$-0.956371\pi$
$919$	−18.6025	−	32.2205i	−0.613640	−	1.06286i	0.376982	−	0.926221i	$-0.376962\pi$
$920$	4.23582	−	7.33666i	0.139651	−	0.241882i
$921$	15.4561	−	26.7708i	0.509297	−	0.882128i
$922$	0.108391	+	0.187739i	0.00356967	+	0.00618284i
$923$		0			0
$924$	−1.77698	−	3.43517i	−0.0584585	−	0.113009i
$925$	1.95142			0.0641623
$926$	9.23474	+	15.9950i	0.303472	+	0.525630i
$927$	15.7449	−	27.2709i	0.517129	−	0.895693i
$928$	14.5625	−	25.2230i	0.478038	−	0.827987i
$929$	9.95229	+	17.2379i	0.326524	+	0.565556i	0.981820	−	0.189816i	$-0.0607893\pi$
$929$	9.95229	+	17.2379i	0.326524	+	0.565556i	−0.655296	+	0.755373i	$0.727456\pi$
$930$	7.16447			0.234932
$931$	36.2639	+	3.36139i	1.18850	+	0.110165i
$932$	−14.7265			−0.482383
$933$	11.6936	+	20.2539i	0.382831	+	0.663082i
$934$	0.102567	−	0.177652i	0.00335611	−	0.00581295i
$935$	−0.740724	+	1.28297i	−0.0242243	+	0.0419577i
$936$		0			0
$937$	7.16949			0.234217			0.117109	−	0.993119i	$-0.462637\pi$
$937$	7.16949			0.234217			0.117109	+	0.993119i	$0.462637\pi$
$938$	13.5931	+	26.2775i	0.443831	+	0.857990i
$939$	21.9446			0.716134
$940$	2.14214	+	3.71029i	0.0698688	+	0.121016i
$941$	1.53036	−	2.65066i	0.0498883	−	0.0864091i	−0.840003	−	0.542582i	$-0.817447\pi$
$941$	1.53036	−	2.65066i	0.0498883	−	0.0864091i	0.889891	+	0.456173i	$0.150780\pi$
$942$	−12.4186	+	21.5096i	−0.404619	+	0.700820i
$943$	11.1140	+	19.2501i	0.361923	+	0.626869i
$944$	15.6120			0.508126
$945$	0.191591	−	0.299032i	0.00623247	−	0.00972752i
$946$	−8.51968			−0.276999
$947$	−22.1028	−	38.2832i	−0.718244	−	1.24404i	−0.961695	−	0.274122i	$-0.911613\pi$
$947$	−22.1028	−	38.2832i	−0.718244	−	1.24404i	0.243451	−	0.969913i	$-0.421721\pi$
$948$	4.03529	−	6.98933i	0.131060	−	0.227003i
$949$		0			0
$950$	12.8652	+	22.2832i	0.417403	+	0.722963i
$951$	−59.8762			−1.94162
$952$	27.0075	+	1.24902i	0.875320	+	0.0404810i
$953$	−13.7002			−0.443791			−0.221896	−	0.975070i	$-0.571224\pi$
$953$	−13.7002			−0.443791			−0.221896	+	0.975070i	$0.571224\pi$
$954$	1.08903	+	1.88626i	0.0352588	+	0.0610700i
$955$	4.90574	−	8.49700i	0.158746	−	0.274956i
$956$	8.36771	−	14.4933i	0.270631	−	0.468747i
$957$	−5.68242	−	9.84225i	−0.183687	−	0.318155i
$958$	23.0476			0.744634
$959$	16.4309	+	0.759882i	0.530582	+	0.0245379i
$960$	12.0180			0.387879
$961$	5.86129	+	10.1520i	0.189074	+	0.327485i
$962$		0			0
$963$	8.90521	−	15.4243i	0.286966	−	0.497040i
$964$	1.18124	+	2.04597i	0.0380451	+	0.0658961i
$965$	14.3894			0.463211
$966$	−16.5022	+	25.7563i	−0.530948	+	0.828694i
$967$	43.9429			1.41311			0.706554	−	0.707659i	$-0.250249\pi$
$967$	43.9429			1.41311			0.706554	+	0.707659i	$0.250249\pi$
$968$	−16.0444	−	27.7897i	−0.515686	−	0.893194i
$969$	−21.1454	+	36.6248i	−0.679287	+	1.17656i
$970$	0.0677912	−	0.117418i	0.00217664	−	0.00377006i
$971$	10.6585	+	18.4611i	0.342049	+	0.592446i	0.984813	−	0.173618i	$-0.0555458\pi$
$971$	10.6585	+	18.4611i	0.342049	+	0.592446i	−0.642764	+	0.766064i	$0.722212\pi$
$972$	−18.5525			−0.595072
$973$	−7.93965	−	15.3485i	−0.254533	−	0.492050i
$974$	20.4400			0.654941
$975$		0			0
$976$	3.71741	−	6.43874i	0.118991	−	0.206099i
$977$	−8.22330	+	14.2432i	−0.263087	+	0.455679i	−0.967061	−	0.254547i	$-0.918074\pi$
$977$	−8.22330	+	14.2432i	−0.263087	+	0.455679i	0.703974	+	0.710226i	$0.251407\pi$
$978$	30.9286	+	53.5699i	0.988987	+	1.71298i
$979$	9.47937			0.302962
$980$	−2.14651	+	3.03210i	−0.0685677	+	0.0968568i
$981$	−33.1913			−1.05972
$982$	−19.1840	−	33.2277i	−0.612187	−	1.06034i
$983$	5.85521	−	10.1415i	0.186752	−	0.323464i	−0.757413	−	0.652936i	$-0.773537\pi$
$983$	5.85521	−	10.1415i	0.186752	−	0.323464i	0.944166	+	0.329471i	$0.106871\pi$
$984$	−18.6395	+	32.2846i	−0.594206	+	1.02919i
$985$	3.19080	+	5.52663i	0.101667	+	0.176093i
$986$	23.6662			0.753687
$987$	−23.8600	−	46.1249i	−0.759472	−	1.46817i
$988$		0			0
$989$	−24.8290	−	43.0051i	−0.789517	−	1.36748i
$990$	0.692270	−	1.19905i	0.0220018	−	0.0381082i
$991$	15.6873	−	27.1713i	0.498325	−	0.863124i	−0.501673	−	0.865057i	$-0.667282\pi$
$991$	15.6873	−	27.1713i	0.498325	−	0.863124i	0.999998	+	0.00193305i	$0.000615311\pi$
$992$	−9.69187	−	16.7868i	−0.307717	−	0.532982i
$993$	−32.0260			−1.01632
$994$	−21.5764	+	33.6761i	−0.684362	+	1.06814i
$995$	−7.45731			−0.236413
$996$	10.5258	+	18.2312i	0.333523	+	0.577679i
$997$	2.34855	−	4.06781i	0.0743794	−	0.128829i	−0.826437	−	0.563029i	$-0.809636\pi$
$997$	2.34855	−	4.06781i	0.0743794	−	0.128829i	0.900816	+	0.434201i	$0.142969\pi$
$998$	−9.49071	+	16.4384i	−0.300423	+	0.520348i
$999$	0.0454366	+	0.0786985i	0.00143755	+	0.00248991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.i.508.3		16
7.2	even	3	inner	1183.2.e.i.170.3		16
7.3	odd	6		8281.2.a.cj.1.6		8
7.4	even	3		8281.2.a.ck.1.6		8
13.5	odd	4		91.2.r.a.25.3	✓	16
13.8	odd	4		91.2.r.a.25.6	yes	16
13.12	even	2	inner	1183.2.e.i.508.6		16
39.5	even	4		819.2.dl.e.298.6		16
39.8	even	4		819.2.dl.e.298.3		16
91.5	even	12		637.2.r.f.324.6		16
91.18	odd	12		637.2.c.f.246.3		8
91.25	even	6		8281.2.a.ck.1.3		8
91.31	even	12		637.2.c.e.246.3		8
91.34	even	4		637.2.r.f.116.6		16
91.38	odd	6		8281.2.a.cj.1.3		8
91.44	odd	12		91.2.r.a.51.6	yes	16
91.47	even	12		637.2.r.f.324.3		16
91.51	even	6	inner	1183.2.e.i.170.6		16
91.60	odd	12		637.2.c.f.246.6		8
91.73	even	12		637.2.c.e.246.6		8
91.83	even	4		637.2.r.f.116.3		16
91.86	odd	12		91.2.r.a.51.3	yes	16
273.44	even	12		819.2.dl.e.415.3		16
273.86	even	12		819.2.dl.e.415.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.3	✓	16	13.5	odd	4
91.2.r.a.25.6	yes	16	13.8	odd	4
91.2.r.a.51.3	yes	16	91.86	odd	12
91.2.r.a.51.6	yes	16	91.44	odd	12
637.2.c.e.246.3		8	91.31	even	12
637.2.c.e.246.6		8	91.73	even	12
637.2.c.f.246.3		8	91.18	odd	12
637.2.c.f.246.6		8	91.60	odd	12
637.2.r.f.116.3		16	91.83	even	4
637.2.r.f.116.6		16	91.34	even	4
637.2.r.f.324.3		16	91.47	even	12
637.2.r.f.324.6		16	91.5	even	12
819.2.dl.e.298.3		16	39.8	even	4
819.2.dl.e.298.6		16	39.5	even	4
819.2.dl.e.415.3		16	273.44	even	12
819.2.dl.e.415.6		16	273.86	even	12
1183.2.e.i.170.3		16	7.2	even	3	inner
1183.2.e.i.170.6		16	91.51	even	6	inner
1183.2.e.i.508.3		16	1.1	even	1	trivial
1183.2.e.i.508.6		16	13.12	even	2	inner
8281.2.a.cj.1.3		8	91.38	odd	6
8281.2.a.cj.1.6		8	7.3	odd	6
8281.2.a.ck.1.3		8	91.25	even	6
8281.2.a.ck.1.6		8	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +O(q^{10})\)	\(q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +(0.335561 - 0.581209i) q^{10} +(-0.354260 + 0.613597i) q^{11} +(-1.03159 - 1.78676i) q^{12} +(-1.53159 + 2.39047i) q^{14} +1.52068 q^{15} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(-1.56222 + 2.70585i) q^{18} +(-2.60138 - 4.50573i) q^{19} +0.530712 q^{20} +(-6.42602 - 0.297185i) q^{21} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(-3.71598 + 6.43627i) q^{24} +(2.30442 - 3.99137i) q^{25} +0.214623 q^{27} +(-2.24266 - 0.103717i) q^{28} -6.59711 q^{29} +(-0.815886 - 1.41316i) q^{30} +(-2.19530 + 3.80238i) q^{31} +(-2.20741 + 3.82335i) q^{32} +(0.861351 + 1.49190i) q^{33} -3.58737 q^{34} +(0.892689 - 1.39329i) q^{35} -2.47076 q^{36} +(0.211704 + 0.366683i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} +5.01604 q^{41} +(3.17157 + 6.13111i) q^{42} -11.2059 q^{43} +(0.300609 + 0.520670i) q^{44} +(0.910544 - 1.57711i) q^{45} +(2.37757 - 4.11807i) q^{46} +(4.03635 + 6.99116i) q^{47} +3.84855 q^{48} +(-4.04458 + 5.71326i) q^{49} -4.94553 q^{50} +(-4.06426 - 7.03950i) q^{51} +(0.348553 - 0.603712i) q^{53} +(-0.115151 - 0.199447i) q^{54} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} -12.6500 q^{57} +(3.53953 + 6.13065i) q^{58} +(4.93159 - 8.54177i) q^{59} +(0.645188 - 1.11750i) q^{60} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} +(-4.15596 + 6.48654i) q^{63} +7.90305 q^{64} +(0.924277 - 1.60089i) q^{66} +(5.21041 - 9.02470i) q^{67} +(-1.41841 - 2.45676i) q^{68} +10.7745 q^{69} +(-1.77373 - 0.0820297i) q^{70} +14.0876 q^{71} +(4.45007 + 7.70775i) q^{72} +(-2.54191 + 4.40273i) q^{73} +(0.227170 - 0.393471i) q^{74} +(-5.60297 - 9.70463i) q^{75} -4.41482 q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(-0.494983 + 0.857336i) q^{80} +(4.62851 - 8.01682i) q^{81} +(-2.69124 - 4.66137i) q^{82} -10.2035 q^{83} +(-2.94480 + 4.59619i) q^{84} +2.09090 q^{85} +(6.01230 + 10.4136i) q^{86} +(-8.02012 + 13.8913i) q^{87} +(1.08285 - 1.87555i) q^{88} +(-6.68955 - 11.5866i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(5.33767 + 9.24512i) q^{93} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +(5.36711 + 9.29610i) q^{96} +0.202023 q^{97} +(7.47932 + 0.693276i) q^{98} +2.06302 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

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Database

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