LMFDB - Embedded newform 338.3.f.j.319.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(19,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.f (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,-6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.2
Root			$3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.319
Dual form			338.3.f.j.249.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(2.38787 - 4.13592i) q^{3} +(1.73205 - 1.00000i) q^{4} +(5.88981 + 5.88981i) q^{5} +(1.74804 - 6.52379i) q^{6} +(0.344179 + 0.0922225i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +(10.2015 + 5.88981i) q^{10} +(0.191720 + 0.715507i) q^{11} -9.55149i q^{12} +0.503913 q^{14} +(38.4239 - 10.2956i) q^{15} +(2.00000 - 3.46410i) q^{16} +(2.49470 - 1.44031i) q^{17} +(-13.8077 - 13.8077i) q^{18} +(-2.81216 + 10.4951i) q^{19} +(16.0913 + 4.31164i) q^{20} +(1.20328 - 1.20328i) q^{21} +(0.523787 + 0.907226i) q^{22} +(-19.8278 - 11.4476i) q^{23} +(-3.49609 - 13.0476i) q^{24} +44.3798i q^{25} -22.9605 q^{27} +(0.688358 - 0.184445i) q^{28} +(-15.2092 + 26.3432i) q^{29} +(48.7195 - 28.1282i) q^{30} +(-14.8631 - 14.8631i) q^{31} +(1.46410 - 5.46410i) q^{32} +(3.41708 + 0.915603i) q^{33} +(2.88063 - 2.88063i) q^{34} +(1.48398 + 2.57032i) q^{35} +(-23.9157 - 13.8077i) q^{36} +(-10.7928 - 40.2792i) q^{37} +15.3659i q^{38} +23.5593 q^{40} +(-24.8893 + 6.66907i) q^{41} +(1.20328 - 2.08414i) q^{42} +(25.3907 - 14.6593i) q^{43} +(1.04757 + 1.04757i) q^{44} +(29.7670 - 111.092i) q^{45} +(-31.2753 - 8.38019i) q^{46} +(-21.2000 + 21.2000i) q^{47} +(-9.55149 - 16.5437i) q^{48} +(-42.3253 - 24.4365i) q^{49} +(16.2441 + 60.6239i) q^{50} -13.7571i q^{51} -85.8410 q^{53} +(-31.3646 + 8.40412i) q^{54} +(-3.08501 + 5.34339i) q^{55} +(0.872803 - 0.503913i) q^{56} +(36.6919 + 36.6919i) q^{57} +(-11.1339 + 41.5524i) q^{58} +(96.6638 + 25.9010i) q^{59} +(56.2565 - 56.2565i) q^{60} +(-7.73202 - 13.3923i) q^{61} +(-25.7437 - 14.8631i) q^{62} +(-1.27338 - 4.75233i) q^{63} -8.00000i q^{64} +5.00295 q^{66} +(67.2315 - 18.0146i) q^{67} +(2.88063 - 4.98939i) q^{68} +(-94.6923 + 54.6706i) q^{69} +(2.96795 + 2.96795i) q^{70} +(-25.2424 + 94.2060i) q^{71} +(-37.7234 - 10.1080i) q^{72} +(-50.9541 + 50.9541i) q^{73} +(-29.4864 - 51.0720i) q^{74} +(183.551 + 105.973i) q^{75} +(5.62432 + 20.9903i) q^{76} +0.263943i q^{77} +105.981 q^{79} +(32.1825 - 8.62328i) q^{80} +(7.30809 - 12.6580i) q^{81} +(-31.5584 + 18.2202i) q^{82} +(27.2221 + 27.2221i) q^{83} +(0.880862 - 3.28742i) q^{84} +(23.1765 + 6.21012i) q^{85} +(29.3186 - 29.3186i) q^{86} +(72.6355 + 125.808i) q^{87} +(1.81445 + 1.04757i) q^{88} +(22.0127 + 82.1525i) q^{89} -162.650i q^{90} -45.7902 q^{92} +(-96.9639 + 25.9814i) q^{93} +(-21.2000 + 36.7195i) q^{94} +(-78.3775 + 45.2513i) q^{95} +(-19.1030 - 19.1030i) q^{96} +(-5.26095 + 19.6341i) q^{97} +(-66.7618 - 17.8888i) q^{98} +(7.23232 - 7.23232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{5} + 6 q^{6} + 8 q^{7} + 16 q^{8} - 42 q^{9} + 18 q^{10} + 24 q^{11} + 20 q^{14} + 126 q^{15} + 16 q^{16} + 42 q^{17} - 84 q^{18} + 68 q^{19} + 12 q^{20} + 102 q^{21} - 42 q^{22} + 36 q^{23}+ \cdots - 252 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^5 + 6 * q^6 + 8 * q^7 + 16 * q^8 - 42 * q^9 + 18 * q^10 + 24 * q^11 + 20 * q^14 + 126 * q^15 + 16 * q^16 + 42 * q^17 - 84 * q^18 + 68 * q^19 + 12 * q^20 + 102 * q^21 - 42 * q^22 + 36 * q^23 - 12 * q^24 + 72 * q^27 + 16 * q^28 - 6 * q^29 + 192 * q^30 - 32 * q^31 - 16 * q^32 + 96 * q^33 + 60 * q^34 - 78 * q^35 + 48 * q^36 - 74 * q^37 - 24 * q^40 + 120 * q^41 + 102 * q^42 + 108 * q^43 - 84 * q^44 + 138 * q^45 - 18 * q^46 - 60 * q^47 - 258 * q^49 + 106 * q^50 - 132 * q^53 - 198 * q^54 - 162 * q^55 + 12 * q^56 + 294 * q^57 - 12 * q^58 + 252 * q^59 + 120 * q^60 + 36 * q^61 + 12 * q^62 - 228 * q^63 + 108 * q^66 - 88 * q^67 + 60 * q^68 - 258 * q^69 - 156 * q^70 - 12 * q^71 - 36 * q^72 - 166 * q^73 - 32 * q^74 - 6 * q^75 - 136 * q^76 - 96 * q^79 + 24 * q^80 - 12 * q^81 + 252 * q^82 + 240 * q^83 - 336 * q^84 - 258 * q^85 - 132 * q^86 + 360 * q^87 + 12 * q^88 + 504 * q^89 - 216 * q^92 - 174 * q^93 - 60 * q^94 - 714 * q^95 + 88 * q^97 - 266 * q^98 - 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	2.38787	−	4.13592i	0.795957	−	1.37864i	−0.126272	−	0.991996i	$-0.540301\pi$
$3$	2.38787	−	4.13592i	0.795957	−	1.37864i	0.922230	−	0.386643i	$-0.126365\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	5.88981	+	5.88981i	1.17796	+	1.17796i	0.980263	+	0.197700i	$0.0633472\pi$
$5$	5.88981	+	5.88981i	1.17796	+	1.17796i	0.197700	+	0.980263i	$0.436653\pi$
$6$	1.74804	−	6.52379i	0.291341	−	1.08730i
$7$	0.344179	+	0.0922225i	0.0491684	+	0.0131746i	0.283319	−	0.959026i	$-0.408564\pi$
$7$	0.344179	+	0.0922225i	0.0491684	+	0.0131746i	−0.234151	+	0.972200i	$0.575231\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−6.90386	−	11.9578i	−0.767096	−	1.32865i
$10$	10.2015	+	5.88981i	1.02015	+	0.588981i
$11$	0.191720	+	0.715507i	0.0174290	+	0.0650461i	0.974093	−	0.226149i	$-0.0726137\pi$
$11$	0.191720	+	0.715507i	0.0174290	+	0.0650461i	−0.956664	+	0.291195i	$0.905947\pi$
$12$		−	9.55149i		−	0.795957i
$13$		0			0
$13$		0			0
$14$	0.503913			0.0359938
$15$	38.4239	−	10.2956i	2.56159	−	0.686377i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	2.49470	−	1.44031i	0.146747	−	0.0847244i	−0.424829	−	0.905274i	$-0.639666\pi$
$17$	2.49470	−	1.44031i	0.146747	−	0.0847244i	0.571576	+	0.820549i	$0.306332\pi$
$18$	−13.8077	−	13.8077i	−0.767096	−	0.767096i
$19$	−2.81216	+	10.4951i	−0.148009	+	0.552375i	0.851594	+	0.524201i	$0.175636\pi$
$19$	−2.81216	+	10.4951i	−0.148009	+	0.552375i	−0.999603	+	0.0281743i	$0.991031\pi$
$20$	16.0913	+	4.31164i	0.804563	+	0.215582i
$21$	1.20328	−	1.20328i	0.0572990	−	0.0572990i
$22$	0.523787	+	0.907226i	0.0238085	+	0.0412376i
$23$	−19.8278	−	11.4476i	−0.862076	−	0.497720i	0.00263083	−	0.999997i	$-0.499163\pi$
$23$	−19.8278	−	11.4476i	−0.862076	−	0.497720i	−0.864707	+	0.502277i	$0.832496\pi$
$24$	−3.49609	−	13.0476i	−0.145670	−	0.543649i
$25$			44.3798i			1.77519i
$26$		0			0
$27$	−22.9605			−0.850388
$28$	0.688358	−	0.184445i	0.0245842	−	0.00658732i
$29$	−15.2092	+	26.3432i	−0.524457	+	0.908386i	0.475138	+	0.879911i	$0.342398\pi$
$29$	−15.2092	+	26.3432i	−0.524457	+	0.908386i	−0.999595	+	0.0284745i	$0.990935\pi$
$30$	48.7195	−	28.1282i	1.62398	−	0.937608i
$31$	−14.8631	−	14.8631i	−0.479456	−	0.479456i	0.425502	−	0.904958i	$-0.360098\pi$
$31$	−14.8631	−	14.8631i	−0.479456	−	0.479456i	−0.904958	+	0.425502i	$0.860098\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	3.41708	+	0.915603i	0.103548	+	0.0277456i
$34$	2.88063	−	2.88063i	0.0847244	−	0.0847244i
$35$	1.48398	+	2.57032i	0.0423993	+	0.0734378i
$36$	−23.9157	−	13.8077i	−0.664325	−	0.383548i
$37$	−10.7928	−	40.2792i	−0.291697	−	1.08863i	−0.943805	−	0.330502i	$-0.892782\pi$
$37$	−10.7928	−	40.2792i	−0.291697	−	1.08863i	0.652108	−	0.758126i	$-0.273885\pi$
$38$			15.3659i			0.404367i
$39$		0			0
$40$	23.5593			0.588981
$41$	−24.8893	+	6.66907i	−0.607056	+	0.162660i	−0.549237	−	0.835667i	$-0.685081\pi$
$41$	−24.8893	+	6.66907i	−0.607056	+	0.162660i	−0.0578194	+	0.998327i	$0.518415\pi$
$42$	1.20328	−	2.08414i	0.0286495	−	0.0496224i
$43$	25.3907	−	14.6593i	0.590480	−	0.340914i	−0.174807	−	0.984603i	$-0.555930\pi$
$43$	25.3907	−	14.6593i	0.590480	−	0.340914i	0.765287	+	0.643689i	$0.222597\pi$
$44$	1.04757	+	1.04757i	0.0238085	+	0.0238085i
$45$	29.7670	−	111.092i	0.661489	−	2.46871i
$46$	−31.2753	−	8.38019i	−0.679898	−	0.182178i
$47$	−21.2000	+	21.2000i	−0.451065	+	0.451065i	−0.895708	−	0.444643i	$-0.853330\pi$
$47$	−21.2000	+	21.2000i	−0.451065	+	0.451065i	0.444643	+	0.895708i	$0.353330\pi$
$48$	−9.55149	−	16.5437i	−0.198989	−	0.344660i
$49$	−42.3253	−	24.4365i	−0.863781	−	0.498704i
$50$	16.2441	+	60.6239i	0.324883	+	1.21248i
$51$		−	13.7571i		−	0.269748i
$52$		0			0
$53$	−85.8410			−1.61964			−0.809821	−	0.586678i	$-0.800436\pi$
$53$	−85.8410			−1.61964			−0.809821	+	0.586678i	$0.800436\pi$
$54$	−31.3646	+	8.40412i	−0.580826	+	0.155632i
$55$	−3.08501	+	5.34339i	−0.0560911	+	0.0971526i
$56$	0.872803	−	0.503913i	0.0155858	−	0.00899844i
$57$	36.6919	+	36.6919i	0.643718	+	0.643718i
$58$	−11.1339	+	41.5524i	−0.191965	+	0.716421i
$59$	96.6638	+	25.9010i	1.63837	+	0.439000i	0.956324	−	0.292309i	$-0.0944237\pi$
$59$	96.6638	+	25.9010i	1.63837	+	0.439000i	0.682046	+	0.731309i	$0.261090\pi$
$60$	56.2565	−	56.2565i	0.937608	−	0.937608i
$61$	−7.73202	−	13.3923i	−0.126754	−	0.219545i	0.795663	−	0.605740i	$-0.207123\pi$
$61$	−7.73202	−	13.3923i	−0.126754	−	0.219545i	−0.922417	+	0.386195i	$0.873789\pi$
$62$	−25.7437	−	14.8631i	−0.415221	−	0.239728i
$63$	−1.27338	−	4.75233i	−0.0202124	−	0.0754338i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	5.00295			0.0758023
$67$	67.2315	−	18.0146i	1.00346	−	0.268875i	0.280563	−	0.959836i	$-0.409479\pi$
$67$	67.2315	−	18.0146i	1.00346	−	0.268875i	0.722893	+	0.690960i	$0.242812\pi$
$68$	2.88063	−	4.98939i	0.0423622	−	0.0733735i
$69$	−94.6923	+	54.6706i	−1.37235	+	0.792328i
$70$	2.96795	+	2.96795i	0.0423993	+	0.0423993i
$71$	−25.2424	+	94.2060i	−0.355527	+	1.32685i	0.524293	+	0.851538i	$0.324330\pi$
$71$	−25.2424	+	94.2060i	−0.355527	+	1.32685i	−0.879820	+	0.475307i	$0.842337\pi$
$72$	−37.7234	−	10.1080i	−0.523936	−	0.140388i
$73$	−50.9541	+	50.9541i	−0.698001	+	0.698001i	−0.963979	−	0.265978i	$-0.914305\pi$
$73$	−50.9541	+	50.9541i	−0.698001	+	0.698001i	0.265978	+	0.963979i	$0.414305\pi$
$74$	−29.4864	−	51.0720i	−0.398465	−	0.690162i
$75$	183.551	+	105.973i	2.44735	+	1.41298i
$76$	5.62432	+	20.9903i	0.0740043	+	0.276188i
$77$			0.263943i			0.00342783i
$78$		0			0
$79$	105.981			1.34153			0.670767	−	0.741669i	$-0.265965\pi$
$79$	105.981			1.34153			0.670767	+	0.741669i	$0.265965\pi$
$80$	32.1825	−	8.62328i	0.402282	−	0.107791i
$81$	7.30809	−	12.6580i	0.0902233	−	0.156271i
$82$	−31.5584	+	18.2202i	−0.384858	+	0.222198i
$83$	27.2221	+	27.2221i	0.327977	+	0.327977i	0.851817	−	0.523840i	$-0.175501\pi$
$83$	27.2221	+	27.2221i	0.327977	+	0.327977i	−0.523840	+	0.851817i	$0.675501\pi$
$84$	0.880862	−	3.28742i	0.0104864	−	0.0391360i
$85$	23.1765	+	6.21012i	0.272664	+	0.0730602i
$86$	29.3186	−	29.3186i	0.340914	−	0.340914i
$87$	72.6355	+	125.808i	0.834891	+	1.44607i
$88$	1.81445	+	1.04757i	0.0206188	+	0.0119043i
$89$	22.0127	+	82.1525i	0.247334	+	0.923061i	0.972196	+	0.234168i	$0.0752365\pi$
$89$	22.0127	+	82.1525i	0.247334	+	0.923061i	−0.724863	+	0.688893i	$0.758097\pi$
$90$		−	162.650i		−	1.80722i
$91$		0			0
$92$	−45.7902			−0.497720
$93$	−96.9639	+	25.9814i	−1.04262	+	0.279370i
$94$	−21.2000	+	36.7195i	−0.225532	+	0.390633i
$95$	−78.3775	+	45.2513i	−0.825026	+	0.476329i
$96$	−19.1030	−	19.1030i	−0.198989	−	0.198989i
$97$	−5.26095	+	19.6341i	−0.0542366	+	0.202414i	−0.987727	−	0.156188i	$-0.950080\pi$
$97$	−5.26095	+	19.6341i	−0.0542366	+	0.202414i	0.933491	+	0.358601i	$0.116746\pi$
$98$	−66.7618	−	17.8888i	−0.681243	−	0.182538i
$99$	7.23232	−	7.23232i	0.0730537	−	0.0730537i
$100$	44.3798	+	76.8681i	0.443798	+	0.768681i
$101$	24.0962	+	13.9119i	0.238576	+	0.137742i	0.614522	−	0.788900i	$-0.289349\pi$
$101$	24.0962	+	13.9119i	0.238576	+	0.137742i	−0.375946	+	0.926642i	$0.622682\pi$
$102$	−5.03546	−	18.7926i	−0.0493673	−	0.184241i
$103$			68.0852i			0.661021i	0.943802	+	0.330511i	$0.107221\pi$
$103$			68.0852i			0.661021i	−0.943802	+	0.330511i	$0.892779\pi$
$104$		0			0
$105$	14.1742			0.134992
$106$	−117.261	+	31.4200i	−1.10624	+	0.296415i
$107$	64.2996	−	111.370i	0.600930	−	1.04084i	−0.391750	−	0.920072i	$-0.628130\pi$
$107$	64.2996	−	111.370i	0.600930	−	1.04084i	0.992680	−	0.120770i	$-0.0385365\pi$
$108$	−39.7687	+	22.9605i	−0.368229	+	0.212597i
$109$	30.5407	+	30.5407i	0.280190	+	0.280190i	0.833185	−	0.552995i	$-0.186515\pi$
$109$	30.5407	+	30.5407i	0.280190	+	0.280190i	−0.552995	+	0.833185i	$0.686515\pi$
$110$	−2.25838	+	8.42840i	−0.0205308	+	0.0766219i
$111$	−192.363	−	51.5436i	−1.73300	−	0.464357i
$112$	1.00783	−	1.00783i	0.00899844	−	0.00899844i
$113$	−23.0706	−	39.9595i	−0.204165	−	0.353624i	0.745701	−	0.666280i	$-0.232115\pi$
$113$	−23.0706	−	39.9595i	−0.204165	−	0.353624i	−0.949866	+	0.312656i	$0.898781\pi$
$114$	63.5522	+	36.6919i	0.557476	+	0.321859i
$115$	−49.3578	−	184.206i	−0.429198	−	1.60179i
$116$			60.8370i			0.524457i
$117$		0			0
$118$	141.526			1.19937
$119$	0.991451	−	0.265659i	0.00833152	−	0.00223243i
$120$	56.2565	−	97.4391i	0.468804	−	0.811992i
$121$	104.314	−	60.2256i	0.862098	−	0.497733i
$122$	−15.4640	−	15.4640i	−0.126754	−	0.126754i
$123$	−31.8498	+	118.865i	−0.258941	+	0.966381i
$124$	−40.6068	−	10.8806i	−0.327474	−	0.0877465i
$125$	−114.143	+	114.143i	−0.913147	+	0.913147i
$126$	−3.47895	−	6.02571i	−0.0276107	−	0.0478231i
$127$	−199.748	−	115.325i	−1.57282	−	0.908067i	−0.995822	−	0.0913210i	$-0.970891\pi$
$127$	−199.748	−	115.325i	−1.57282	−	0.908067i	−0.576997	−	0.816746i	$-0.695776\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$		−	140.018i		−	1.08541i
$130$		0			0
$131$	162.262			1.23864			0.619321	−	0.785138i	$-0.287408\pi$
$131$	162.262			1.23864			0.619321	+	0.785138i	$0.287408\pi$
$132$	6.83416	−	1.83121i	0.0517739	−	0.0138728i
$133$	−1.93577	+	3.35286i	−0.0145547	+	0.0252095i
$134$	85.2462	−	49.2169i	0.636165	−	0.367290i
$135$	−135.233	−	135.233i	−1.00173	−	1.00173i
$136$	2.10877	−	7.87002i	0.0155056	−	0.0578678i
$137$	−99.8210	−	26.7470i	−0.728620	−	0.195233i	−0.124606	−	0.992206i	$-0.539767\pi$
$137$	−99.8210	−	26.7470i	−0.728620	−	0.195233i	−0.604015	+	0.796973i	$0.706433\pi$
$138$	−109.341	+	109.341i	−0.792328	+	0.792328i
$139$	12.7892	+	22.1516i	0.0920087	+	0.159364i	0.908356	−	0.418197i	$-0.137338\pi$
$139$	12.7892	+	22.1516i	0.0920087	+	0.159364i	−0.816348	+	0.577561i	$0.804005\pi$
$140$	5.14064	+	2.96795i	0.0367189	+	0.0211997i
$141$	37.0586	+	138.305i	0.262827	+	0.980883i
$142$			137.927i			0.971318i
$143$		0			0
$144$	−55.2309			−0.383548
$145$	−244.736	+	65.5768i	−1.68784	+	0.452254i
$146$	−50.9541	+	88.2551i	−0.349001	+	0.604487i
$147$	−202.135	+	116.703i	−1.37507	+	0.793895i
$148$	−58.9729	−	58.9729i	−0.398465	−	0.398465i
$149$	−6.96307	+	25.9865i	−0.0467320	+	0.174406i	−0.985347	−	0.170559i	$-0.945443\pi$
$149$	−6.96307	+	25.9865i	−0.0467320	+	0.174406i	0.938615	+	0.344965i	$0.112109\pi$
$150$	289.524	+	77.5778i	1.93016	+	0.517185i
$151$	109.697	−	109.697i	0.726468	−	0.726468i	−0.243446	−	0.969914i	$-0.578278\pi$
$151$	109.697	−	109.697i	0.726468	−	0.726468i	0.969914	+	0.243446i	$0.0782780\pi$
$152$	15.3659	+	26.6146i	0.101092	+	0.175096i
$153$	−34.4461	−	19.8875i	−0.225138	−	0.129983i
$154$	0.0966099	+	0.360553i	0.000627337	+	0.00234125i
$155$		−	175.082i		−	1.12956i
$156$		0			0
$157$	−142.680			−0.908790			−0.454395	−	0.890800i	$-0.650145\pi$
$157$	−142.680			−0.908790			−0.454395	+	0.890800i	$0.650145\pi$
$158$	144.773	−	38.7918i	0.916284	−	0.245518i
$159$	−204.977	+	355.031i	−1.28917	+	2.23290i
$160$	40.8058	−	23.5593i	0.255036	−	0.147245i
$161$	−5.76857	−	5.76857i	−0.0358296	−	0.0358296i
$162$	5.34989	−	19.9661i	0.0330240	−	0.123247i
$163$	25.6588	+	6.87526i	0.157416	+	0.0421795i	0.336666	−	0.941624i	$-0.390701\pi$
$163$	25.6588	+	6.87526i	0.157416	+	0.0421795i	−0.179250	+	0.983804i	$0.557367\pi$
$164$	−36.4405	+	36.4405i	−0.222198	+	0.222198i
$165$	14.7332	+	25.5187i	0.0892922	+	0.154659i
$166$	47.1500	+	27.2221i	0.284036	+	0.163988i
$167$	1.94780	+	7.26931i	0.0116635	+	0.0435288i	0.971512	−	0.236989i	$-0.0761605\pi$
$167$	1.94780	+	7.26931i	0.0116635	+	0.0435288i	−0.959849	+	0.280518i	$0.909494\pi$
$168$		−	4.81312i		−	0.0286495i
$169$		0			0
$170$	33.9327			0.199604
$171$	144.914	−	38.8296i	0.847450	−	0.227074i
$172$	29.3186	−	50.7813i	0.170457	−	0.295240i
$173$	24.9669	−	14.4146i	0.144317	−	0.0833216i	−0.426103	−	0.904675i	$-0.640114\pi$
$173$	24.9669	−	14.4146i	0.144317	−	0.0833216i	0.570420	+	0.821353i	$0.306780\pi$
$174$	145.271	+	145.271i	0.834891	+	0.834891i
$175$	−4.09281	+	15.2746i	−0.0233875	+	0.0872834i
$176$	2.86203	+	0.766878i	0.0162615	+	0.00435726i
$177$	337.945	−	337.945i	1.90929	−	1.90929i
$178$	60.1398	+	104.165i	0.337864	+	0.585197i
$179$	183.682	+	106.049i	1.02616	+	0.592453i	0.915882	−	0.401448i	$-0.131493\pi$
$179$	183.682	+	106.049i	1.02616	+	0.592453i	0.110277	+	0.993901i	$0.464826\pi$
$180$	−59.5340	−	222.184i	−0.330744	−	1.23435i
$181$			112.088i			0.619270i	0.950856	+	0.309635i	$0.100207\pi$
$181$			112.088i			0.619270i	−0.950856	+	0.309635i	$0.899793\pi$
$182$		0			0
$183$	−73.8523			−0.403564
$184$	−62.5506	+	16.7604i	−0.339949	+	0.0910891i
$185$	173.670	−	300.805i	0.938755	−	1.62597i
$186$	−122.945	+	70.9825i	−0.660996	+	0.381626i
$187$	1.50884	+	1.50884i	0.00806865	+	0.00806865i
$188$	−15.5195	+	57.9196i	−0.0825505	+	0.308083i
$189$	−7.90251	−	2.11747i	−0.0418122	−	0.0112036i
$190$	−90.5025	+	90.5025i	−0.476329	+	0.476329i
$191$	−132.524	−	229.538i	−0.693843	−	1.20177i	−0.970569	−	0.240823i	$-0.922583\pi$
$191$	−132.524	−	229.538i	−0.693843	−	1.20177i	0.276726	−	0.960949i	$-0.410751\pi$
$192$	−33.0873	−	19.1030i	−0.172330	−	0.0994947i
$193$	41.2029	+	153.771i	0.213486	+	0.796742i	0.986694	+	0.162589i	$0.0519844\pi$
$193$	41.2029	+	153.771i	0.213486	+	0.796742i	−0.773208	+	0.634153i	$0.781349\pi$
$194$			28.7464i			0.148177i
$195$		0			0
$196$	−97.7461			−0.498704
$197$	290.559	−	77.8551i	1.47492	−	0.395204i	0.570305	−	0.821433i	$-0.306825\pi$
$197$	290.559	−	77.8551i	1.47492	−	0.395204i	0.904615	+	0.426230i	$0.140158\pi$
$198$	7.23232	−	12.5267i	0.0365268	−	0.0632663i
$199$	162.223	−	93.6594i	0.815190	−	0.470650i	−0.0335648	−	0.999437i	$-0.510686\pi$
$199$	162.223	−	93.6594i	0.815190	−	0.470650i	0.848755	+	0.528786i	$0.177353\pi$
$200$	88.7596	+	88.7596i	0.443798	+	0.443798i
$201$	86.0333	−	321.081i	0.428026	−	1.59742i
$202$	38.0081	+	10.1842i	0.188159	+	0.0504170i
$203$	−7.66414	+	7.66414i	−0.0377544	+	0.0377544i
$204$	−13.7571	−	23.8281i	−0.0674370	−	0.116804i
$205$	−185.873	−	107.314i	−0.906697	−	0.523482i
$206$	24.9209	+	93.0061i	0.120975	+	0.451486i
$207$			316.130i			1.52720i
$208$		0			0
$209$	−8.04849			−0.0385095
$210$	19.3623	−	5.18811i	0.0922014	−	0.0247053i
$211$	−84.9065	+	147.062i	−0.402401	+	0.696978i	−0.994015	−	0.109243i	$-0.965157\pi$
$211$	−84.9065	+	147.062i	−0.402401	+	0.696978i	0.591614	+	0.806221i	$0.298491\pi$
$212$	−148.681	+	85.8410i	−0.701325	+	0.404910i
$213$	329.353	+	329.353i	1.54626	+	1.54626i
$214$	47.0705	−	175.670i	0.219956	−	0.820886i
$215$	235.887	+	63.2057i	1.09715	+	0.293980i
$216$	−45.9210	+	45.9210i	−0.212597	+	0.212597i
$217$	−3.74486	−	6.48629i	−0.0172574	−	0.0298907i
$218$	52.8981	+	30.5407i	0.242652	+	0.140095i
$219$	89.0700	+	332.414i	0.406712	+	1.51787i
$220$			12.3400i			0.0560911i
$221$		0			0
$222$	−281.639			−1.26865
$223$	−232.297	+	62.2439i	−1.04169	+	0.279121i	−0.738815	−	0.673909i	$-0.764614\pi$
$223$	−232.297	+	62.2439i	−1.04169	+	0.279121i	−0.302878	+	0.953029i	$0.597947\pi$
$224$	1.00783	−	1.74561i	0.00449922	−	0.00779288i
$225$	530.687	−	306.392i	2.35861	−	1.36174i
$226$	−46.1413	−	46.1413i	−0.204165	−	0.204165i
$227$	23.4180	−	87.3971i	0.103163	−	0.385009i	−0.894967	−	0.446132i	$-0.852801\pi$
$227$	23.4180	−	87.3971i	0.103163	−	0.385009i	0.998130	+	0.0611224i	$0.0194680\pi$
$228$	100.244	+	26.8603i	0.439667	+	0.117808i
$229$	−248.887	+	248.887i	−1.08684	+	1.08684i	−0.0909923	+	0.995852i	$0.529004\pi$
$229$	−248.887	+	248.887i	−1.08684	+	1.08684i	−0.995852	+	0.0909923i	$0.970996\pi$
$230$	−134.848	−	233.563i	−0.586295	−	1.01549i
$231$	1.09165	+	0.630263i	0.00472574	+	0.00272841i
$232$	22.2679	+	83.1049i	0.0959823	+	0.358211i
$233$		−	384.870i		−	1.65180i	−0.563815	−	0.825901i	$-0.690667\pi$
$233$		−	384.870i		−	1.65180i	0.563815	−	0.825901i	$-0.309333\pi$
$234$		0			0
$235$	−249.728			−1.06267
$236$	193.328	−	51.8020i	0.819185	−	0.219500i
$237$	253.069	−	438.329i	1.06780	−	1.84949i
$238$	1.25711	−	0.725793i	0.00528198	−	0.00304955i
$239$	−210.628	−	210.628i	−0.881290	−	0.881290i	0.112375	−	0.993666i	$-0.464154\pi$
$239$	−210.628	−	210.628i	−0.881290	−	0.881290i	−0.993666	+	0.112375i	$0.964154\pi$
$240$	41.1826	−	153.696i	0.171594	−	0.640398i
$241$	−180.960	−	48.4880i	−0.750870	−	0.201195i	−0.136966	−	0.990576i	$-0.543735\pi$
$241$	−180.960	−	48.4880i	−0.750870	−	0.201195i	−0.613904	+	0.789381i	$0.710402\pi$
$242$	120.451	−	120.451i	0.497733	−	0.497733i
$243$	−138.224	−	239.411i	−0.568822	−	0.985228i
$244$	−26.7845	−	15.4640i	−0.109773	−	0.0633772i
$245$	−105.362	−	393.215i	−0.430047	−	1.60496i
$246$			174.030i			0.707440i
$247$		0			0
$248$	−59.4525			−0.239728
$249$	177.591	−	47.5853i	0.713216	−	0.191106i
$250$	−114.143	+	197.702i	−0.456573	+	0.790808i
$251$	87.0514	−	50.2592i	0.346818	−	0.200236i	−0.316465	−	0.948604i	$-0.602496\pi$
$251$	87.0514	−	50.2592i	0.346818	−	0.200236i	0.663283	+	0.748369i	$0.269163\pi$
$252$	−6.95789	−	6.95789i	−0.0276107	−	0.0276107i
$253$	4.38944	−	16.3816i	0.0173496	−	0.0647495i
$254$	−315.073	−	84.4234i	−1.24044	−	0.332376i
$255$	81.0270	−	81.0270i	0.317753	−	0.317753i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	60.1930	+	34.7524i	0.234214	+	0.135223i	0.612515	−	0.790459i	$-0.290158\pi$
$257$	60.1930	+	34.7524i	0.234214	+	0.135223i	−0.378301	+	0.925683i	$0.623491\pi$
$258$	−51.2502	−	191.268i	−0.198644	−	0.741350i
$259$		−	14.8586i		−	0.0573691i
$260$		0			0
$261$	420.010			1.60924
$262$	221.654	−	59.3920i	0.846008	−	0.226687i
$263$	−129.589	+	224.455i	−0.492735	+	0.853441i	−0.999965	−	0.00836922i	$-0.997336\pi$
$263$	−129.589	+	224.455i	−0.492735	+	0.853441i	0.507230	+	0.861810i	$0.330669\pi$
$264$	8.66536	−	5.00295i	0.0328233	−	0.0189506i
$265$	−505.587	−	505.587i	−1.90788	−	1.90788i
$266$	−1.41708	+	5.28863i	−0.00532739	+	0.0198821i
$267$	392.339	+	105.127i	1.46943	+	0.393734i
$268$	98.4338	−	98.4338i	0.367290	−	0.367290i
$269$	−21.0056	−	36.3828i	−0.0780878	−	0.135252i	0.824337	−	0.566099i	$-0.191548\pi$
$269$	−21.0056	−	36.3828i	−0.0780878	−	0.135252i	−0.902425	+	0.430847i	$0.858215\pi$
$270$	−234.230	−	135.233i	−0.867520	−	0.500863i
$271$	−81.5504	−	304.350i	−0.300924	−	1.12306i	−0.936398	−	0.350941i	$-0.885862\pi$
$271$	−81.5504	−	304.350i	−0.300924	−	1.12306i	0.635474	−	0.772122i	$-0.280805\pi$
$272$		−	11.5225i		−	0.0423622i
$273$		0			0
$274$	−146.148			−0.533387
$275$	−31.7540	+	8.50847i	−0.115469	+	0.0309399i
$276$	−109.341	+	189.385i	−0.396164	+	0.686176i
$277$	164.261	−	94.8364i	0.593001	−	0.342370i	−0.173282	−	0.984872i	$-0.555437\pi$
$277$	164.261	−	94.8364i	0.593001	−	0.342370i	0.766283	+	0.642503i	$0.222104\pi$
$278$	25.5784	+	25.5784i	0.0920087	+	0.0920087i
$279$	−75.1180	+	280.344i	−0.269240	+	1.00482i
$280$	8.10860	+	2.17269i	0.0289593	+	0.00775961i
$281$	32.8661	−	32.8661i	0.116961	−	0.116961i	−0.646204	−	0.763165i	$-0.723644\pi$
$281$	32.8661	−	32.8661i	0.116961	−	0.116961i	0.763165	+	0.646204i	$0.223644\pi$
$282$	101.246	+	175.363i	0.359028	+	0.621855i
$283$	−456.365	−	263.482i	−1.61260	−	0.931033i	−0.988766	−	0.149474i	$-0.952242\pi$
$283$	−456.365	−	263.482i	−1.61260	−	0.931033i	−0.623831	−	0.781559i	$-0.714425\pi$
$284$	50.4849	+	188.412i	0.177764	+	0.663423i
$285$			432.217i			1.51655i
$286$		0			0
$287$	−9.18141			−0.0319910
$288$	−75.4468	+	20.2159i	−0.261968	+	0.0701942i
$289$	−140.351	+	243.095i	−0.485644	+	0.841159i
$290$	−310.313	+	179.159i	−1.07004	+	0.617791i
$291$	68.6426	+	68.6426i	0.235885	+	0.235885i
$292$	−37.3010	+	139.209i	−0.127743	+	0.476744i
$293$	132.277	+	35.4435i	0.451457	+	0.120968i	0.477381	−	0.878696i	$-0.341586\pi$
$293$	132.277	+	35.4435i	0.451457	+	0.120968i	−0.0259239	+	0.999664i	$0.508253\pi$
$294$	−233.405	+	233.405i	−0.793895	+	0.793895i
$295$	416.780	+	721.884i	1.41281	+	2.44706i
$296$	−102.144	−	58.9729i	−0.345081	−	0.199233i
$297$	−4.40197	−	16.4284i	−0.0148215	−	0.0553144i
$298$			38.0469i			0.127674i
$299$		0			0
$300$	423.893			1.41298
$301$	10.0908	−	2.70383i	0.0335244	−	0.00898283i
$302$	109.697	−	190.000i	0.363234	−	0.629140i
$303$	115.077	−	66.4398i	0.379792	−	0.219273i
$304$	30.7319	+	30.7319i	0.101092	+	0.101092i
$305$	33.3377	−	124.418i	0.109304	−	0.407928i
$306$	−54.3336	−	14.5586i	−0.177561	−	0.0475772i
$307$	306.038	−	306.038i	0.996866	−	0.996866i	−0.00312957	−	0.999995i	$-0.500996\pi$
$307$	306.038	−	306.038i	0.996866	−	0.996866i	0.999995	+	0.00312957i	$0.000996174\pi$
$308$	0.263943	+	0.457163i	0.000856959	+	0.00148430i
$309$	281.595	+	162.579i	0.911309	+	0.526145i
$310$	−64.0845	−	239.167i	−0.206724	−	0.771505i
$311$			138.274i			0.444611i	0.974977	+	0.222305i	$0.0713582\pi$
$311$			138.274i			0.444611i	−0.974977	+	0.222305i	$0.928642\pi$
$312$		0			0
$313$	525.434			1.67870			0.839352	−	0.543589i	$-0.182935\pi$
$313$	525.434			1.67870			0.839352	+	0.543589i	$0.182935\pi$
$314$	−194.905	+	52.2245i	−0.620715	+	0.166320i
$315$	20.4903	−	35.4903i	0.0650487	−	0.112668i
$316$	183.565	−	105.981i	0.580901	−	0.335383i
$317$	−24.3899	−	24.3899i	−0.0769397	−	0.0769397i	0.667590	−	0.744529i	$-0.267326\pi$
$317$	−24.3899	−	24.3899i	−0.0769397	−	0.0769397i	−0.744529	+	0.667590i	$0.767326\pi$
$318$	−150.054	+	560.008i	−0.471867	+	1.76103i
$319$	−21.7646	−	5.83182i	−0.0682277	−	0.0182816i
$320$	47.1185	−	47.1185i	0.147245	−	0.147245i
$321$	−307.078	−	531.875i	−0.956630	−	1.65693i
$322$	−9.99146	−	5.76857i	−0.0310294	−	0.0179148i
$323$	8.10079	+	30.2326i	0.0250799	+	0.0935993i
$324$		−	29.2323i		−	0.0902233i
$325$		0			0
$326$	37.5671			0.115237
$327$	199.241	−	53.3865i	0.609300	−	0.163261i
$328$	−36.4405	+	63.1167i	−0.111099	+	0.192429i
$329$	−9.25172	+	5.34148i	−0.0281207	+	0.0162355i
$330$	29.4664	+	29.4664i	0.0892922	+	0.0892922i
$331$	−5.73931	+	21.4194i	−0.0173393	+	0.0647111i	−0.974053	−	0.226318i	$-0.927331\pi$
$331$	−5.73931	+	21.4194i	−0.0173393	+	0.0647111i	0.956714	+	0.291029i	$0.0939977\pi$
$332$	74.3720	+	19.9279i	0.224012	+	0.0600239i
$333$	−407.141	+	407.141i	−1.22264	+	1.22264i
$334$	5.32150	+	9.21711i	0.0159326	+	0.0275961i
$335$	502.084	+	289.878i	1.49876	+	0.865308i
$336$	−1.76172	−	6.57484i	−0.00524322	−	0.0195680i
$337$		−	544.688i		−	1.61629i	−0.588987	−	0.808143i	$-0.700473\pi$
$337$		−	544.688i		−	1.61629i	0.588987	−	0.808143i	$-0.299527\pi$
$338$		0			0
$339$	−220.359			−0.650026
$340$	46.3530	−	12.4202i	0.136332	−	0.0365301i
$341$	7.78512	−	13.4842i	0.0228303	−	0.0395432i
$342$	183.744	−	106.084i	0.537262	−	0.310188i
$343$	−24.6597	−	24.6597i	−0.0718943	−	0.0718943i
$344$	21.4627	−	80.0999i	0.0623916	−	0.232849i
$345$	−879.719	−	235.720i	−2.54991	−	0.683247i
$346$	28.8293	−	28.8293i	0.0833216	−	0.0833216i
$347$	320.301	+	554.777i	0.923057	+	1.59878i	0.794657	+	0.607059i	$0.207651\pi$
$347$	320.301	+	554.777i	0.923057	+	1.59878i	0.128400	+	0.991722i	$0.459016\pi$
$348$	251.617	+	145.271i	0.723036	+	0.417445i
$349$	−15.6551	−	58.4257i	−0.0448571	−	0.167409i	0.939864	−	0.341550i	$-0.110952\pi$
$349$	−15.6551	−	58.4257i	−0.0448571	−	0.167409i	−0.984721	+	0.174141i	$0.944285\pi$
$350$			22.3635i			0.0638958i
$351$		0			0
$352$	4.19030			0.0119043
$353$	−283.357	+	75.9253i	−0.802711	+	0.215086i	−0.636774	−	0.771051i	$-0.719732\pi$
$353$	−283.357	+	75.9253i	−0.802711	+	0.215086i	−0.165937	+	0.986136i	$0.553065\pi$
$354$	337.945	−	585.338i	0.954647	−	1.65350i
$355$	−703.529	+	406.183i	−1.98177	+	1.14418i
$356$	120.280	+	120.280i	0.337864	+	0.337864i
$357$	1.26872	−	4.73492i	0.00355383	−	0.0132631i
$358$	289.732	+	77.6333i	0.809306	+	0.216853i
$359$	118.752	−	118.752i	0.330785	−	0.330785i	−0.522099	−	0.852885i	$-0.674851\pi$
$359$	118.752	−	118.752i	0.330785	−	0.330785i	0.852885	+	0.522099i	$0.174851\pi$
$360$	−162.650	−	281.718i	−0.451805	−	0.782550i
$361$	210.396	+	121.472i	0.582813	+	0.336487i
$362$	41.0270	+	153.115i	0.113334	+	0.422969i
$363$		−	575.245i		−	1.58470i
$364$		0			0
$365$	−600.220			−1.64444
$366$	−100.884	+	27.0318i	−0.275640	+	0.0738574i
$367$	51.1578	−	88.6080i	0.139395	−	0.241439i	−0.787873	−	0.615838i	$-0.788818\pi$
$367$	51.1578	−	88.6080i	0.139395	−	0.241439i	0.927268	+	0.374399i	$0.122151\pi$
$368$	−79.3110	+	45.7902i	−0.215519	+	0.124430i
$369$	251.580	+	251.580i	0.681789	+	0.681789i
$370$	127.135	−	474.474i	0.343608	−	1.28236i
$371$	−29.5447	−	7.91647i	−0.0796352	−	0.0213382i
$372$	−141.965	+	141.965i	−0.381626	+	0.381626i
$373$	−302.308	−	523.613i	−0.810477	−	1.40379i	−0.912530	−	0.409009i	$-0.865875\pi$
$373$	−302.308	−	523.613i	−0.810477	−	1.40379i	0.102053	−	0.994779i	$-0.467459\pi$
$374$	2.61338	+	1.50884i	0.00698765	+	0.00403432i
$375$	199.528	+	744.647i	0.532073	+	1.98573i
$376$			84.8001i			0.225532i
$377$		0			0
$378$	−11.5701			−0.0306087
$379$	−370.655	+	99.3166i	−0.977980	+	0.262049i	−0.712194	−	0.701983i	$-0.752298\pi$
$379$	−370.655	+	99.3166i	−0.977980	+	0.262049i	−0.265787	+	0.964032i	$0.585632\pi$
$380$	−90.5025	+	156.755i	−0.238165	+	0.412513i
$381$	−953.945	+	550.760i	−2.50379	+	1.44557i
$382$	−265.048	−	265.048i	−0.693843	−	0.693843i
$383$	106.035	−	395.727i	0.276853	−	1.03323i	−0.677736	−	0.735305i	$-0.737039\pi$
$383$	106.035	−	395.727i	0.276853	−	1.03323i	0.954589	−	0.297925i	$-0.0962945\pi$
$384$	−52.1903	−	13.9843i	−0.135912	−	0.0364176i
$385$	−1.55458	+	1.55458i	−0.00403786	+	0.00403786i
$386$	112.568	+	194.974i	0.291628	+	0.505114i
$387$	−350.587	−	202.412i	−0.905910	−	0.523027i
$388$	10.5219	+	39.2682i	0.0271183	+	0.101207i
$389$		−	43.6909i		−	0.112316i	−0.998422	−	0.0561579i	$-0.982115\pi$
$389$		−	43.6909i		−	0.112316i	0.998422	−	0.0561579i	$-0.0178850\pi$
$390$		0			0
$391$	−65.9523			−0.168676
$392$	−133.524	+	35.7775i	−0.340621	+	0.0912692i
$393$	387.461	−	671.102i	0.985906	−	1.70764i
$394$	368.414	−	212.704i	0.935062	−	0.539858i
$395$	624.209	+	624.209i	1.58028	+	1.58028i
$396$	5.29442	−	19.7591i	0.0133698	−	0.0498966i
$397$	−264.715	−	70.9301i	−0.666788	−	0.178665i	−0.0904803	−	0.995898i	$-0.528840\pi$
$397$	−264.715	−	70.9301i	−0.666788	−	0.178665i	−0.576307	+	0.817233i	$0.695507\pi$
$398$	187.319	−	187.319i	0.470650	−	0.470650i
$399$	9.24476	+	16.0124i	0.0231698	+	0.0401313i
$400$	153.736	+	88.7596i	0.384340	+	0.221899i
$401$	23.0664	+	86.0849i	0.0575222	+	0.214676i	0.988704	−	0.149878i	$-0.0478882\pi$
$401$	23.0664	+	86.0849i	0.0575222	+	0.214676i	−0.931182	+	0.364554i	$0.881221\pi$
$402$		−	470.095i		−	1.16939i
$403$		0			0
$404$	55.6477			0.137742
$405$	117.596	−	31.5099i	0.290361	−	0.0778021i
$406$	−7.66414	+	13.2747i	−0.0188772	+	0.0326962i
$407$	26.7509	−	15.4446i	0.0657270	−	0.0379475i
$408$	−27.5143	−	27.5143i	−0.0674370	−	0.0674370i
$409$	−188.970	+	705.246i	−0.462030	+	1.72432i	0.204525	+	0.978861i	$0.434435\pi$
$409$	−188.970	+	705.246i	−0.462030	+	1.72432i	−0.666554	+	0.745456i	$0.732232\pi$
$410$	−293.187	−	78.5591i	−0.715089	−	0.191608i
$411$	−348.983	+	348.983i	−0.849107	+	0.849107i
$412$	68.0852	+	117.927i	0.165255	+	0.286231i
$413$	30.8810	+	17.8291i	0.0747724	+	0.0431699i
$414$	115.711	+	431.841i	0.279496	+	1.04309i
$415$			320.666i			0.772688i
$416$		0			0
$417$	122.156			0.292940
$418$	−10.9944	+	2.94595i	−0.0263025	+	0.00704773i
$419$	−130.487	+	226.011i	−0.311426	+	0.539405i	−0.978671	−	0.205433i	$-0.934140\pi$
$419$	−130.487	+	226.011i	−0.311426	+	0.539405i	0.667246	+	0.744838i	$0.267473\pi$
$420$	24.5504	−	14.1742i	0.0584533	−	0.0337480i
$421$	103.038	+	103.038i	0.244745	+	0.244745i	0.818810	−	0.574065i	$-0.194634\pi$
$421$	103.038	+	103.038i	0.244745	+	0.244745i	−0.574065	+	0.818810i	$0.694634\pi$
$422$	−62.1559	+	231.969i	−0.147289	+	0.549690i
$423$	399.869	+	107.145i	0.945316	+	0.253297i
$424$	−171.682	+	171.682i	−0.404910	+	0.404910i
$425$	63.9208	+	110.714i	0.150402	+	0.260504i
$426$	570.455	+	329.353i	1.33910	+	0.773128i
$427$	−1.42613	−	5.32240i	−0.00333989	−	0.0124646i
$428$		−	257.198i		−	0.600930i
$429$		0			0
$430$	345.362			0.803168
$431$	−131.588	+	35.2588i	−0.305308	+	0.0818069i	−0.408220	−	0.912883i	$-0.633850\pi$
$431$	−131.588	+	35.2588i	−0.305308	+	0.0818069i	0.102913	+	0.994690i	$0.467184\pi$
$432$	−45.9210	+	79.5375i	−0.106299	+	0.184114i
$433$	−174.382	+	100.679i	−0.402729	+	0.232516i	−0.687661	−	0.726032i	$-0.741362\pi$
$433$	−174.382	+	100.679i	−0.402729	+	0.232516i	0.284932	+	0.958548i	$0.408029\pi$
$434$	−7.48972	−	7.48972i	−0.0172574	−	0.0172574i
$435$	−313.178	+	1168.80i	−0.719950	+	2.68689i
$436$	83.4388	+	22.3574i	0.191373	+	0.0512783i
$437$	175.902	−	175.902i	0.402523	−	0.402523i
$438$	243.344	+	421.484i	0.555579	+	0.962291i
$439$	64.3905	+	37.1759i	0.146675	+	0.0846830i	0.571542	−	0.820573i	$-0.306346\pi$
$439$	64.3905	+	37.1759i	0.146675	+	0.0846830i	−0.424866	+	0.905256i	$0.639679\pi$
$440$	4.51677	+	16.8568i	0.0102654	+	0.0383109i
$441$			674.826i			1.53022i
$442$		0			0
$443$	130.644			0.294908			0.147454	−	0.989069i	$-0.452892\pi$
$443$	130.644			0.294908			0.147454	+	0.989069i	$0.452892\pi$
$444$	−384.726	+	103.087i	−0.866501	+	0.232178i
$445$	−354.212	+	613.513i	−0.795982	+	1.37868i
$446$	−294.541	+	170.054i	−0.660407	+	0.381286i
$447$	90.8512	+	90.8512i	0.203246	+	0.203246i
$448$	0.737780	−	2.75343i	0.00164683	−	0.00614605i
$449$	696.251	+	186.560i	1.55067	+	0.415501i	0.929695	−	0.368330i	$-0.120070\pi$
$449$	696.251	+	186.560i	1.55067	+	0.415501i	0.620975	+	0.783831i	$0.286737\pi$
$450$	612.784	−	612.784i	1.36174	−	1.36174i
$451$	−9.54353	−	16.5299i	−0.0211608	−	0.0366516i
$452$	−79.9190	−	46.1413i	−0.176812	−	0.102082i
$453$	−191.755	−	715.638i	−0.423299	−	1.57977i
$454$		−	127.958i		−	0.281846i
$455$		0			0
$456$	146.768			0.321859
$457$	−350.261	+	93.8520i	−0.766434	+	0.205365i	−0.620796	−	0.783972i	$-0.713190\pi$
$457$	−350.261	+	93.8520i	−0.766434	+	0.205365i	−0.145639	+	0.989338i	$0.546524\pi$
$458$	−248.887	+	431.085i	−0.543422	+	0.941234i
$459$	−57.2795	+	33.0703i	−0.124792	+	0.0720486i
$460$	−269.696	−	269.696i	−0.586295	−	0.586295i
$461$	223.937	−	835.746i	0.485765	−	1.81290i	−0.0908282	−	0.995867i	$-0.528951\pi$
$461$	223.937	−	835.746i	0.485765	−	1.81290i	0.576593	−	0.817032i	$-0.304382\pi$
$462$	1.72191	+	0.461384i	0.00372708	+	0.000998667i
$463$	−163.492	+	163.492i	−0.353114	+	0.353114i	−0.861267	−	0.508153i	$-0.830328\pi$
$463$	−163.492	+	163.492i	−0.353114	+	0.353114i	0.508153	+	0.861267i	$0.330328\pi$
$464$	60.8370	+	105.373i	0.131114	+	0.227096i
$465$	−724.125	−	418.074i	−1.55726	−	0.899083i
$466$	−140.872	−	525.742i	−0.302301	−	1.12820i
$467$			242.866i			0.520056i	0.965601	+	0.260028i	$0.0837318\pi$
$467$			242.866i			0.520056i	−0.965601	+	0.260028i	$0.916268\pi$
$468$		0			0
$469$	24.8010			0.0528807
$470$	−341.135	+	91.4070i	−0.725820	+	0.194483i
$471$	−340.702	+	590.113i	−0.723358	+	1.25289i
$472$	245.130	−	141.526i	0.519342	−	0.299842i
$473$	15.3567	+	15.3567i	0.0324666	+	0.0324666i
$474$	185.260	−	691.398i	0.390843	−	1.45865i
$475$	−465.772	−	124.803i	−0.980572	−	0.262744i
$476$	1.45159	−	1.45159i	0.00304955	−	0.00304955i
$477$	592.635	+	1026.47i	1.24242	+	2.15194i
$478$	−364.819	−	210.628i	−0.763220	−	0.440645i
$479$	57.8547	+	215.917i	0.120782	+	0.450766i	0.999654	−	0.0262919i	$-0.00836994\pi$
$479$	57.8547	+	215.917i	0.120782	+	0.450766i	−0.878872	+	0.477058i	$0.841703\pi$
$480$		−	225.026i		−	0.468804i
$481$		0			0
$482$	−264.943			−0.549675
$483$	−37.6329	+	10.0837i	−0.0779150	+	0.0208773i
$484$	120.451	−	208.628i	0.248866	−	0.431049i
$485$	−146.627	+	84.6553i	−0.302324	+	0.174547i
$486$	−276.447	−	276.447i	−0.568822	−	0.568822i
$487$	5.58396	−	20.8396i	0.0114660	−	0.0427918i	−0.959956	−	0.280151i	$-0.909615\pi$
$487$	5.58396	−	20.8396i	0.0114660	−	0.0427918i	0.971422	+	0.237360i	$0.0762820\pi$
$488$	−42.2485	−	11.3205i	−0.0865749	−	0.0231977i
$489$	89.7055	−	89.7055i	0.183447	−	0.183447i
$490$	−287.853	−	498.576i	−0.587455	−	1.01750i
$491$	50.4972	+	29.1546i	0.102846	+	0.0593780i	0.550541	−	0.834808i	$-0.314422\pi$
$491$	50.4972	+	29.1546i	0.102846	+	0.0593780i	−0.447695	+	0.894186i	$0.647755\pi$
$492$	63.6995	+	237.730i	0.129471	+	0.483191i
$493$			87.6244i			0.177737i
$494$		0			0
$495$	85.1940			0.172109
$496$	−81.2137	+	21.7611i	−0.163737	+	0.0438733i
$497$	−17.3758	+	30.0958i	−0.0349614	+	0.0605549i
$498$	225.176	−	130.006i	0.452161	−	0.261055i
$499$	−625.494	−	625.494i	−1.25350	−	1.25350i	−0.954142	−	0.299353i	$-0.903229\pi$
$499$	−625.494	−	625.494i	−1.25350	−	1.25350i	−0.299353	−	0.954142i	$-0.596771\pi$
$500$	−83.5587	+	311.845i	−0.167117	+	0.623691i
$501$	34.7163	+	9.30221i	0.0692941	+	0.0185673i
$502$	100.518	−	100.518i	0.200236	−	0.200236i
$503$	5.25707	+	9.10551i	0.0104514	+	0.0181024i	0.871204	−	0.490921i	$-0.163340\pi$
$503$	5.25707	+	9.10551i	0.0104514	+	0.0181024i	−0.860752	+	0.509024i	$0.830006\pi$
$504$	−12.0514	−	6.95789i	−0.0239116	−	0.0138053i
$505$	59.9832	+	223.860i	0.118779	+	0.443288i
$506$		−	23.9843i		−	0.0473999i
$507$		0			0
$508$	−461.298			−0.908067
$509$	98.4183	−	26.3711i	0.193356	−	0.0518097i	−0.160841	−	0.986980i	$-0.551421\pi$
$509$	98.4183	−	26.3711i	0.193356	−	0.0518097i	0.354198	+	0.935171i	$0.384754\pi$
$510$	81.0270	−	140.343i	0.158876	−	0.275182i
$511$	−22.2364	+	12.8382i	−0.0435155	+	0.0251237i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	64.5686	−	240.973i	0.125865	−	0.469734i
$514$	94.9454	+	25.4405i	0.184719	+	0.0494952i
$515$	−401.009	+	401.009i	−0.778658	+	0.778658i
$516$	−140.018	−	242.518i	−0.271353	−	0.469997i
$517$	−19.2332	−	11.1043i	−0.0372016	−	0.0214784i
$518$	−5.43862	−	20.2972i	−0.0104993	−	0.0391838i
$519$		−	137.681i		−	0.265282i
$520$		0			0
$521$	170.985			0.328185			0.164093	−	0.986445i	$-0.447530\pi$
$521$	170.985			0.328185			0.164093	+	0.986445i	$0.447530\pi$
$522$	573.745	−	153.734i	1.09913	−	0.294510i
$523$	417.695	−	723.469i	0.798652	−	1.38331i	−0.121842	−	0.992549i	$-0.538880\pi$
$523$	417.695	−	723.469i	0.798652	−	1.38331i	0.920494	−	0.390756i	$-0.127786\pi$
$524$	281.046	−	162.262i	0.536347	−	0.309660i
$525$	53.4013	+	53.4013i	0.101717	+	0.101717i
$526$	−94.8659	+	354.044i	−0.180353	+	0.673088i
$527$	−58.4866	−	15.6714i	−0.110980	−	0.0297371i
$528$	10.0059	−	10.0059i	0.0189506	−	0.0189506i
$529$	−2.40684	−	4.16878i	−0.00454980	−	0.00788048i
$530$	−875.703	−	505.587i	−1.65227	−	0.953938i
$531$	−357.634	−	1334.71i	−0.673510	−	2.51357i
$532$			7.74309i			0.0145547i
$533$		0			0
$534$	574.424			1.07570
$535$	1034.66	−	277.237i	1.93395	−	0.518199i
$536$	98.4338	−	170.492i	0.183645	−	0.318083i
$537$	877.220	−	506.463i	1.63356	−	0.943135i
$538$	−42.0112	−	42.0112i	−0.0780878	−	0.0780878i
$539$	9.36991	−	34.9690i	0.0173839	−	0.0648775i
$540$	−369.463	−	98.9974i	−0.684191	−	0.183329i
$541$	−503.966	+	503.966i	−0.931545	+	0.931545i	−0.997803	−	0.0662572i	$-0.978894\pi$
$541$	−503.966	+	503.966i	−0.931545	+	0.931545i	0.0662572	+	0.997803i	$0.478894\pi$
$542$	−222.800	−	385.900i	−0.411070	−	0.711993i
$543$	463.586	+	267.651i	0.853749	+	0.492912i
$544$	−4.21753	−	15.7400i	−0.00775282	−	0.0289339i
$545$			359.758i			0.660107i
$546$		0			0
$547$	−249.081			−0.455359			−0.227680	−	0.973736i	$-0.573114\pi$
$547$	−249.081			−0.455359			−0.227680	+	0.973736i	$0.573114\pi$
$548$	−199.642	+	53.4939i	−0.364310	+	0.0976166i
$549$	−106.762	+	184.917i	−0.194466	+	0.336824i
$550$	−40.2625	+	23.2456i	−0.0732046	+	0.0422647i
$551$	−233.704	−	233.704i	−0.424146	−	0.424146i
$552$	−80.0433	+	298.726i	−0.145006	+	0.541170i
$553$	36.4765	+	9.77384i	0.0659611	+	0.0176742i
$554$	189.673	−	189.673i	0.342370	−	0.342370i
$555$	−829.402	−	1436.57i	−1.49442	−	2.58841i
$556$	44.3031	+	25.5784i	0.0796819	+	0.0460044i
$557$	169.408	+	632.239i	0.304144	+	1.13508i	0.933680	+	0.358109i	$0.116578\pi$
$557$	169.408	+	632.239i	0.304144	+	1.13508i	−0.629536	+	0.776971i	$0.716755\pi$
$558$			410.452i			0.735577i
$559$		0			0
$560$	11.8718			0.0211997
$561$	9.84333	−	2.63751i	0.0175460	−	0.00470145i
$562$	32.8661	−	56.9258i	0.0584806	−	0.101291i
$563$	828.273	−	478.204i	1.47118	−	0.849385i	0.471702	−	0.881758i	$-0.343640\pi$
$563$	828.273	−	478.204i	1.47118	−	0.849385i	0.999476	+	0.0323732i	$0.0103065\pi$
$564$	202.492	+	202.492i	0.359028	+	0.359028i
$565$	99.4723	−	371.236i	0.176057	−	0.657055i
$566$	−719.847	−	192.883i	−1.27182	−	0.340782i
$567$	3.68264	−	3.68264i	0.00649495	−	0.00649495i
$568$	137.927	+	238.897i	0.242830	+	0.420593i
$569$	281.681	+	162.629i	0.495046	+	0.285815i	0.726666	−	0.686991i	$-0.241069\pi$
$569$	281.681	+	162.629i	0.495046	+	0.285815i	−0.231619	+	0.972807i	$0.574402\pi$
$570$	158.202	+	590.419i	0.277548	+	1.03582i
$571$			218.946i			0.383442i	0.981449	+	0.191721i	$0.0614069\pi$
$571$			218.946i			0.383442i	−0.981449	+	0.191721i	$0.938593\pi$
$572$		0			0
$573$	−1265.80			−2.20908
$574$	−12.5420	+	3.36063i	−0.0218502	+	0.00585475i
$575$	508.040	−	879.951i	0.883548	−	1.53035i
$576$	−95.6628	+	55.2309i	−0.166081	+	0.0958870i
$577$	478.578	+	478.578i	0.829425	+	0.829425i	0.987437	−	0.158012i	$-0.0505084\pi$
$577$	478.578	+	478.578i	0.829425	+	0.829425i	−0.158012	+	0.987437i	$0.550508\pi$
$578$	−102.744	+	383.446i	−0.177758	+	0.663401i
$579$	734.372	+	196.774i	1.26834	+	0.339852i
$580$	−358.319	+	358.319i	−0.617791	+	0.617791i
$581$	6.85877	+	11.8797i	0.0118051	+	0.0204471i
$582$	118.892	+	68.6426i	0.204283	+	0.117943i
$583$	−16.4574	−	61.4198i	−0.0282288	−	0.105351i
$584$			203.816i			0.349001i
$585$		0			0
$586$	193.667			0.330490
$587$	239.510	−	64.1765i	0.408024	−	0.109330i	−0.0489685	−	0.998800i	$-0.515593\pi$
$587$	239.510	−	64.1765i	0.408024	−	0.109330i	0.456992	+	0.889471i	$0.348927\pi$
$588$	−233.405	+	404.269i	−0.396947	+	0.687533i
$589$	197.788	−	114.193i	0.335803	−	0.193876i
$590$	833.560	+	833.560i	1.41281	+	1.41281i
$591$	371.816	−	1387.64i	0.629130	−	2.34795i
$592$	−161.117	−	43.1711i	−0.272157	−	0.0729242i
$593$	107.905	−	107.905i	0.181964	−	0.181964i	−0.610247	−	0.792211i	$-0.708930\pi$
$593$	107.905	−	107.905i	0.181964	−	0.181964i	0.792211	+	0.610247i	$0.208930\pi$
$594$	−12.0264	−	20.8304i	−0.0202465	−	0.0350679i
$595$	7.40414	+	4.27478i	0.0124439	+	0.00718451i
$596$	13.9261	+	51.9730i	0.0233660	+	0.0872031i
$597$		−	894.587i		−	1.49847i
$598$		0			0
$599$	788.030			1.31558			0.657788	−	0.753203i	$-0.271492\pi$
$599$	788.030			1.31558			0.657788	+	0.753203i	$0.271492\pi$
$600$	579.049	−	155.156i	0.965081	−	0.258593i
$601$	−191.526	+	331.733i	−0.318679	+	0.551968i	−0.980213	−	0.197947i	$-0.936573\pi$
$601$	−191.526	+	331.733i	−0.318679	+	0.551968i	0.661534	+	0.749915i	$0.269906\pi$
$602$	12.7947	−	7.38701i	0.0212536	−	0.0122708i
$603$	−679.574	−	679.574i	−1.12699	−	1.12699i
$604$	80.3035	−	299.697i	0.132953	−	0.496187i
$605$	969.107	+	259.671i	1.60183	+	0.429209i
$606$	132.880	−	132.880i	0.219273	−	0.219273i
$607$	−118.890	−	205.923i	−0.195865	−	0.339248i	0.751319	−	0.659939i	$-0.229418\pi$
$607$	−118.890	−	205.923i	−0.195865	−	0.339248i	−0.947184	+	0.320692i	$0.896085\pi$
$608$	53.2292	+	30.7319i	0.0875480	+	0.0505459i
$609$	13.3972	+	49.9992i	0.0219988	+	0.0821005i
$610$		−	182.161i		−	0.298624i
$611$		0			0
$612$	−79.5499			−0.129983
$613$	423.210	−	113.399i	0.690391	−	0.184990i	0.103468	−	0.994633i	$-0.467006\pi$
$613$	423.210	−	113.399i	0.690391	−	0.184990i	0.586923	+	0.809643i	$0.300339\pi$
$614$	306.038	−	530.073i	0.498433	−	0.863311i
$615$	−887.681	+	512.503i	−1.44338	+	0.833338i
$616$	0.527886	+	0.527886i	0.000856959	+	0.000856959i
$617$	−29.9483	+	111.769i	−0.0485386	+	0.181149i	−0.985939	−	0.167104i	$-0.946558\pi$
$617$	−29.9483	+	111.769i	−0.0485386	+	0.181149i	0.937401	+	0.348253i	$0.113225\pi$
$618$	444.173	+	119.016i	0.718727	+	0.192582i
$619$	471.622	−	471.622i	0.761910	−	0.761910i	−0.214757	−	0.976667i	$-0.568896\pi$
$619$	471.622	−	471.622i	0.761910	−	0.761910i	0.976667	+	0.214757i	$0.0688961\pi$
$620$	−175.082	−	303.251i	−0.282390	−	0.489115i
$621$	455.255	+	262.841i	0.733099	+	0.423255i
$622$	50.6118	+	188.886i	0.0813694	+	0.303675i
$623$			30.3052i			0.0486440i
$624$		0			0
$625$	−235.071			−0.376114
$626$	717.756	−	192.322i	1.14658	−	0.307224i
$627$	−19.2188	+	33.2879i	−0.0306519	+	0.0530907i
$628$	−247.129	+	142.680i	−0.393518	+	0.227197i
$629$	−84.9395	−	84.9395i	−0.135039	−	0.135039i
$630$	15.0000	−	55.9807i	0.0238095	−	0.0888582i
$631$	−822.277	−	220.328i	−1.30313	−	0.349173i	−0.460499	−	0.887660i	$-0.652330\pi$
$631$	−822.277	−	220.328i	−1.30313	−	0.349173i	−0.842634	+	0.538487i	$0.818996\pi$
$632$	211.962	−	211.962i	0.335383	−	0.335383i
$633$	405.492	+	702.333i	0.640588	+	1.10953i
$634$	−42.2445	−	24.3899i	−0.0666318	−	0.0384699i
$635$	−497.238	−	1855.72i	−0.783052	−	2.92239i
$636$			819.909i			1.28917i
$637$		0			0
$638$	−31.8657			−0.0499462
$639$	1300.77	−	348.541i	2.03564	−	0.545447i
$640$	47.1185	−	81.6116i	0.0736227	−	0.127518i
$641$	−25.2926	+	14.6027i	−0.0394580	+	0.0227811i	−0.519599	−	0.854410i	$-0.673919\pi$
$641$	−25.2926	+	14.6027i	−0.0394580	+	0.0227811i	0.480141	+	0.877191i	$0.340585\pi$
$642$	−614.156	−	614.156i	−0.956630	−	0.956630i
$643$	52.8962	−	197.411i	0.0822648	−	0.307016i	−0.912517	−	0.409038i	$-0.865864\pi$
$643$	52.8962	−	197.411i	0.0822648	−	0.307016i	0.994782	+	0.102022i	$0.0325311\pi$
$644$	−15.7600	−	4.22289i	−0.0244721	−	0.00655728i
$645$	824.681	−	824.681i	1.27857	−	1.27857i
$646$	22.1318	+	38.3334i	0.0342597	+	0.0593396i
$647$	915.647	+	528.649i	1.41522	+	0.817077i	0.995874	−	0.0907495i	$-0.0289263\pi$
$647$	915.647	+	528.649i	1.41522	+	0.817077i	0.419345	+	0.907827i	$0.362260\pi$
$648$	−10.6998	−	39.9321i	−0.0165120	−	0.0616237i
$649$			74.1294i			0.114221i
$650$		0			0
$651$	−35.7690			−0.0549447
$652$	51.3177	−	13.7505i	0.0787081	−	0.0210898i
$653$	−38.0505	+	65.9054i	−0.0582703	+	0.100927i	−0.893689	−	0.448687i	$-0.851892\pi$
$653$	−38.0505	+	65.9054i	−0.0582703	+	0.100927i	0.835419	+	0.549614i	$0.185225\pi$
$654$	252.628	−	145.855i	0.386281	−	0.223019i
$655$	955.693	+	955.693i	1.45907	+	1.45907i
$656$	−26.6763	+	99.5572i	−0.0406650	+	0.151764i
$657$	961.081	+	257.521i	1.46283	+	0.391965i
$658$	−10.6830	+	10.6830i	−0.0162355	+	0.0162355i
$659$	421.818	+	730.610i	0.640087	+	1.10866i	0.985413	+	0.170181i	$0.0544352\pi$
$659$	421.818	+	730.610i	0.640087	+	1.10866i	−0.345325	+	0.938483i	$0.612231\pi$
$660$	51.0374	+	29.4664i	0.0773293	+	0.0446461i
$661$	216.792	+	809.079i	0.327976	+	1.22402i	0.911286	+	0.411773i	$0.135090\pi$
$661$	216.792	+	809.079i	0.327976	+	1.22402i	−0.583311	+	0.812249i	$0.698243\pi$
$662$			31.3602i			0.0473718i
$663$		0			0
$664$	108.888			0.163988
$665$	−31.1491	+	8.34636i	−0.0468407	+	0.0125509i
$666$	−407.141	+	705.188i	−0.611322	+	1.05884i
$667$	603.130	−	348.218i	0.904244	−	0.522065i
$668$	10.6430	+	10.6430i	0.0159326	+	0.0159326i
$669$	−297.261	+	1109.39i	−0.444336	+	1.65829i
$670$	791.962	+	212.206i	1.18203	+	0.316725i
$671$	8.09987	−	8.09987i	0.0120713	−	0.0120713i
$672$	−4.81312	−	8.33656i	−0.00716238	−	0.0124056i
$673$	−334.718	−	193.250i	−0.497353	−	0.287147i	0.230267	−	0.973128i	$-0.426040\pi$
$673$	−334.718	−	193.250i	−0.497353	−	0.287147i	−0.727620	+	0.685981i	$0.759373\pi$
$674$	−199.370	−	744.058i	−0.295801	−	1.10394i
$675$		−	1018.98i		−	1.50960i
$676$		0			0
$677$	328.683			0.485500			0.242750	−	0.970089i	$-0.421951\pi$
$677$	328.683			0.485500			0.242750	+	0.970089i	$0.421951\pi$
$678$	−301.016	+	80.6570i	−0.443976	+	0.118963i
$679$	−3.62141	+	6.27247i	−0.00533345	+	0.00923781i
$680$	58.7732	−	33.9327i	0.0864312	−	0.0499011i
$681$	−305.548	−	305.548i	−0.448675	−	0.448675i
$682$	5.69910	−	21.2693i	0.00835646	−	0.0311867i
$683$	−780.775	−	209.208i	−1.14316	−	0.306308i	−0.362936	−	0.931814i	$-0.618226\pi$
$683$	−780.775	−	209.208i	−1.14316	−	0.306308i	−0.780219	+	0.625506i	$0.784892\pi$
$684$	212.169	−	212.169i	0.310188	−	0.310188i
$685$	−430.392	−	745.462i	−0.628310	−	1.08827i
$686$	−42.7119	−	24.6597i	−0.0622623	−	0.0359471i
$687$	435.066	+	1623.69i	0.633283	+	2.36345i
$688$		−	117.274i		−	0.170457i
$689$		0			0
$690$	−1288.00			−1.86666
$691$	−779.206	+	208.788i	−1.12765	+	0.302153i	−0.773975	−	0.633216i	$-0.781735\pi$
$691$	−779.206	+	208.788i	−1.12765	+	0.302153i	−0.353674	+	0.935369i	$0.615068\pi$
$692$	28.8293	−	49.9338i	0.0416608	−	0.0721586i
$693$	3.15619	−	1.82223i	0.00455439	−	0.00262948i
$694$	640.601	+	640.601i	0.923057	+	0.923057i
$695$	−55.1425	+	205.795i	−0.0793417	+	0.296107i
$696$	396.888	+	106.346i	0.570241	+	0.152796i
$697$	−52.4857	+	52.4857i	−0.0753023	+	0.0753023i
$698$	−42.7706	−	74.0809i	−0.0612759	−	0.106133i
$699$	−1591.79	−	919.020i	−2.27724	−	1.31476i
$700$	8.18563	+	30.5492i	0.0116938	+	0.0436417i
$701$			1080.31i			1.54110i	0.637378	+	0.770552i	$0.280019\pi$
$701$			1080.31i			1.54110i	−0.637378	+	0.770552i	$0.719981\pi$
$702$		0			0
$703$	453.087			0.644505
$704$	5.72406	−	1.53376i	0.00813076	−	0.00217863i
$705$	−596.320	+	1032.86i	−0.845843	+	1.46504i
$706$	−359.282	+	207.432i	−0.508898	+	0.293813i
$707$	7.01040	+	7.01040i	0.00991570	+	0.00991570i
$708$	247.393	−	923.283i	0.349425	−	1.30407i
$709$	762.964	+	204.436i	1.07611	+	0.288343i	0.753002	−	0.658018i	$-0.228605\pi$
$709$	762.964	+	204.436i	1.07611	+	0.288343i	0.323110	+	0.946361i	$0.395272\pi$
$710$	−812.365	+	812.365i	−1.14418	+	1.14418i
$711$	−731.679	−	1267.31i	−1.02908	−	1.78243i
$712$	208.330	+	120.280i	0.292599	+	0.168932i
$713$	124.556	+	464.849i	0.174693	+	0.651962i
$714$		−	6.93240i		−	0.00970925i
$715$		0			0
$716$	424.196			0.592453
$717$	−1374.10	+	368.188i	−1.91645	+	0.513511i
$718$	118.752	−	205.684i	0.165393	−	0.286469i
$719$	700.700	−	404.550i	0.974548	−	0.562656i	0.0739286	−	0.997264i	$-0.476446\pi$
$719$	700.700	−	404.550i	0.974548	−	0.562656i	0.900620	+	0.434608i	$0.143113\pi$
$720$	−325.300	−	325.300i	−0.451805	−	0.451805i
$721$	−6.27898	+	23.4335i	−0.00870871	+	0.0325014i
$722$	331.868	+	88.9237i	0.459650	+	0.123163i
$723$	−632.651	+	632.651i	−0.875036	+	0.875036i
$724$	112.088	+	194.142i	0.154817	+	0.268152i
$725$	−1169.11	−	674.983i	−1.61256	−	0.931011i
$726$	−210.554	−	785.799i	−0.290019	−	1.08237i
$727$			1368.53i			1.88243i	0.337808	+	0.941215i	$0.390315\pi$
$727$			1368.53i			1.88243i	−0.337808	+	0.941215i	$0.609685\pi$
$728$		0			0
$729$	−1188.70			−1.63059
$730$	−819.916	+	219.696i	−1.12317	+	0.300953i
$731$	42.2280	−	73.1410i	0.0577674	−	0.100056i
$732$	−127.916	+	73.8523i	−0.174749	+	0.100891i
$733$	−204.408	−	204.408i	−0.278865	−	0.278865i	0.553791	−	0.832656i	$-0.313181\pi$
$733$	−204.408	−	204.408i	−0.278865	−	0.278865i	−0.832656	+	0.553791i	$0.813181\pi$
$734$	37.4501	−	139.766i	0.0510220	−	0.190417i
$735$	−1877.89	−	503.180i	−2.55496	−	0.684598i
$736$	−91.5805	+	91.5805i	−0.124430	+	0.124430i
$737$	25.7792	+	44.6509i	0.0349786	+	0.0605846i
$738$	435.749	+	251.580i	0.590446	+	0.340894i
$739$	62.8090	+	234.406i	0.0849918	+	0.317194i	0.995313	−	0.0967096i	$-0.0308318\pi$
$739$	62.8090	+	234.406i	0.0849918	+	0.317194i	−0.910321	+	0.413903i	$0.864165\pi$
$740$		−	694.678i		−	0.938755i
$741$		0			0
$742$	−43.2564			−0.0582970
$743$	87.1920	−	23.3630i	0.117351	−	0.0314442i	−0.199665	−	0.979864i	$-0.563986\pi$
$743$	87.1920	−	23.3630i	0.117351	−	0.0314442i	0.317017	+	0.948420i	$0.397319\pi$
$744$	−141.965	+	245.891i	−0.190813	+	0.330498i
$745$	−194.067	+	112.045i	−0.260493	+	0.150395i
$746$	−604.616	−	604.616i	−0.810477	−	0.810477i
$747$	137.580	−	513.454i	0.184176	−	0.687355i
$748$	4.12222	+	1.10455i	0.00551099	+	0.00147666i
$749$	32.4014	−	32.4014i	0.0432595	−	0.0432595i
$750$	545.119	+	944.174i	0.726826	+	1.25890i
$751$	−339.714	−	196.134i	−0.452349	−	0.261164i	0.256473	−	0.966552i	$-0.417440\pi$
$751$	−339.714	−	196.134i	−0.452349	−	0.261164i	−0.708822	+	0.705387i	$0.750773\pi$
$752$	31.0390	+	115.839i	0.0412753	+	0.154041i
$753$		−	480.050i		−	0.637516i
$754$		0			0
$755$	1292.19			1.71150
$756$	−15.8050	+	4.23494i	−0.0209061	+	0.00560178i
$757$	178.827	−	309.738i	0.236232	−	0.409165i	−0.723398	−	0.690431i	$-0.757421\pi$
$757$	178.827	−	309.738i	0.236232	−	0.409165i	0.959630	+	0.281266i	$0.0907542\pi$
$758$	−469.971	+	271.338i	−0.620015	+	0.357966i
$759$	−57.2715	−	57.2715i	−0.0754566	−	0.0754566i
$760$	−66.2524	+	247.257i	−0.0871743	+	0.325339i
$761$	−805.649	−	215.873i	−1.05867	−	0.283670i	−0.312841	−	0.949806i	$-0.601281\pi$
$761$	−805.649	−	215.873i	−1.05867	−	0.283670i	−0.745831	+	0.666135i	$0.767947\pi$
$762$	−1101.52	+	1101.52i	−1.44557	+	1.44557i
$763$	7.69493	+	13.3280i	0.0100851	+	0.0174679i
$764$	−459.077	−	265.048i	−0.600886	−	0.346922i
$765$	−85.7476	−	320.015i	−0.112088	−	0.418320i
$766$		−	579.385i		−	0.756377i
$767$		0			0
$768$	−76.4119			−0.0994947
$769$	805.575	−	215.853i	1.04756	−	0.280693i	0.306318	−	0.951929i	$-0.400903\pi$
$769$	805.575	−	215.853i	1.04756	−	0.280693i	0.741244	+	0.671236i	$0.234236\pi$
$770$	−1.55458	+	2.69260i	−0.00201893	+	0.00349689i
$771$	287.466	−	165.969i	0.372849	−	0.215264i
$772$	225.137	+	225.137i	0.291628	+	0.291628i
$773$	−231.816	+	865.148i	−0.299891	+	1.11921i	0.637364	+	0.770563i	$0.280025\pi$
$773$	−231.816	+	865.148i	−0.299891	+	1.11921i	−0.937255	+	0.348645i	$0.886642\pi$
$774$	−552.999	−	148.176i	−0.714469	−	0.191441i
$775$	659.623	−	659.623i	0.851126	−	0.851126i
$776$	28.7464	+	49.7901i	0.0370443	+	0.0641626i
$777$	−61.4539	−	35.4804i	−0.0790912	−	0.0456633i
$778$	−15.9920	−	59.6828i	−0.0205552	−	0.0767132i
$779$		−	279.971i		−	0.359398i
$780$		0			0
$781$	−72.2445			−0.0925026
$782$	−90.0925	+	24.1402i	−0.115208	+	0.0308699i
$783$	349.212	−	604.852i	0.445992	−	0.772481i
$784$	−169.301	+	97.7461i	−0.215945	+	0.124676i
$785$	−840.359	−	840.359i	−1.07052	−	1.07052i
$786$	283.641	−	1058.56i	0.360867	−	1.34677i
$787$	915.976	+	245.435i	1.16388	+	0.311861i	0.788516	−	0.615015i	$-0.210850\pi$
$787$	915.976	+	245.435i	1.16388	+	0.311861i	0.375367	+	0.926876i	$0.377517\pi$
$788$	425.408	−	425.408i	0.539858	−	0.539858i
$789$	618.885	+	1071.94i	0.784391	+	1.35861i
$790$	1081.16	+	624.209i	1.36856	+	0.790138i
$791$	−4.25526	−	15.8809i	−0.00537960	−	0.0200769i
$792$		−	28.9293i		−	0.0365268i
$793$		0			0
$794$	−387.569			−0.488122
$795$	−3298.34	+	883.789i	−4.14886	+	1.11168i
$796$	187.319	−	324.446i	0.235325	−	0.407595i
$797$	332.978	−	192.245i	0.417789	−	0.241210i	−0.276342	−	0.961059i	$-0.589122\pi$
$797$	332.978	−	192.245i	0.417789	−	0.241210i	0.694131	+	0.719849i	$0.255789\pi$
$798$	18.4895	+	18.4895i	0.0231698	+	0.0231698i
$799$	−22.3530	+	83.4224i	−0.0279762	+	0.104408i
$800$	242.496	+	64.9765i	0.303120	+	0.0812207i
$801$	830.394	−	830.394i	1.03670	−	1.03670i
$802$	63.0185	+	109.151i	0.0785767	+	0.136099i
$803$	−46.2269	−	26.6891i	−0.0575677	−	0.0332367i
$804$	−172.067	−	642.161i	−0.214013	−	0.798708i
$805$		−	67.9516i		−	0.0844119i
$806$		0			0
$807$	−200.635			−0.248618
$808$	76.0162	−	20.3685i	0.0940794	−	0.0252085i
$809$	−7.78898	+	13.4909i	−0.00962791	+	0.0166760i	−0.870799	−	0.491639i	$-0.836398\pi$
$809$	−7.78898	+	13.4909i	−0.00962791	+	0.0166760i	0.861171	+	0.508315i	$0.169731\pi$
$810$	149.106	−	86.0865i	0.184082	−	0.106280i
$811$	488.921	+	488.921i	0.602861	+	0.602861i	0.941071	−	0.338209i	$-0.109821\pi$
$811$	488.921	+	488.921i	0.602861	+	0.602861i	−0.338209	+	0.941071i	$0.609821\pi$
$812$	−5.61054	+	20.9388i	−0.00690953	+	0.0257867i
$813$	−1453.50	−	389.464i	−1.78782	−	0.479045i
$814$	30.8893	−	30.8893i	0.0379475	−	0.0379475i
$815$	110.632	+	191.620i	0.135744	+	0.235116i
$816$	−47.6561	−	27.5143i	−0.0584021	−	0.0337185i
$817$	82.4487	+	307.703i	0.100916	+	0.376625i
$818$			1032.55i			1.26229i
$819$		0			0
$820$	−429.255			−0.523482
$821$	−382.310	+	102.440i	−0.465664	+	0.124774i	−0.484019	−	0.875057i	$-0.660824\pi$
$821$	−382.310	+	102.440i	−0.465664	+	0.124774i	0.0183556	+	0.999832i	$0.494157\pi$
$822$	−348.983	+	604.456i	−0.424553	+	0.735348i
$823$	−397.982	+	229.775i	−0.483575	+	0.279192i	−0.721905	−	0.691992i	$-0.756733\pi$
$823$	−397.982	+	229.775i	−0.483575	+	0.279192i	0.238330	+	0.971184i	$0.423400\pi$
$824$	136.170	+	136.170i	0.165255	+	0.165255i
$825$	−40.6343	+	151.649i	−0.0492537	+	0.183817i
$826$	48.7101	+	13.0518i	0.0589711	+	0.0158013i
$827$	−1019.38	+	1019.38i	−1.23263	+	1.23263i	−0.269678	+	0.962951i	$0.586917\pi$
$827$	−1019.38	+	1019.38i	−1.23263	+	1.23263i	−0.962951	+	0.269678i	$0.913083\pi$
$828$	316.130	+	547.552i	0.381799	+	0.661295i
$829$	118.994	+	68.7010i	0.143539	+	0.0828722i	0.570049	−	0.821610i	$-0.306924\pi$
$829$	118.994	+	68.7010i	0.143539	+	0.0828722i	−0.426511	+	0.904483i	$0.640257\pi$
$830$	117.372	+	438.037i	0.141412	+	0.527756i
$831$		−	905.828i		−	1.09005i
$832$		0			0
$833$	−140.785			−0.169010
$834$	166.868	−	44.7122i	0.200082	−	0.0536118i
$835$	−31.3426	+	54.2870i	−0.0375361	+	0.0650144i
$836$	−13.9404	+	8.04849i	−0.0166751	+	0.00962738i
$837$	341.265	+	341.265i	0.407724	+	0.407724i
$838$	−95.5233	+	356.498i	−0.113990	+	0.425415i
$839$	−522.627	−	140.038i	−0.622917	−	0.166910i	−0.0664636	−	0.997789i	$-0.521172\pi$
$839$	−522.627	−	140.038i	−0.622917	−	0.166910i	−0.556454	+	0.830879i	$0.687838\pi$
$840$	28.3484	−	28.3484i	0.0337480	−	0.0337480i
$841$	−42.1426	−	72.9930i	−0.0501101	−	0.0867932i
$842$	178.467	+	103.038i	0.211956	+	0.122373i
$843$	−57.4514	−	214.412i	−0.0681511	−	0.254344i
$844$			339.626i			0.402401i
$845$		0			0
$846$	585.449			0.692020
$847$	41.4568	−	11.1083i	0.0489454	−	0.0131149i
$848$	−171.682	+	297.362i	−0.202455	+	0.350663i
$849$	−2179.48	+	1258.32i	−2.56712	+	1.48213i
$850$	127.842	+	127.842i	0.150402	+	0.150402i
$851$	−247.102	+	922.197i	−0.290367	+	1.08366i
$852$	899.808	+	241.103i	1.05611	+	0.282984i
$853$	549.575	−	549.575i	0.644285	−	0.644285i	−0.307321	−	0.951606i	$-0.599433\pi$
$853$	549.575	−	549.575i	0.644285	−	0.644285i	0.951606	+	0.307321i	$0.0994325\pi$
$854$	−3.89626	−	6.74853i	−0.00456237	−	0.00790226i
$855$	1082.21	+	624.817i	1.26575	+	0.730780i
$856$	−94.1411	−	351.339i	−0.109978	−	0.410443i
$857$		−	908.454i		−	1.06004i	−0.847985	−	0.530020i	$-0.822184\pi$
$857$		−	908.454i		−	1.06004i	0.847985	−	0.530020i	$-0.177816\pi$
$858$		0			0
$859$	−383.134			−0.446023			−0.223012	−	0.974816i	$-0.571589\pi$
$859$	−383.134			−0.446023			−0.223012	+	0.974816i	$0.571589\pi$
$860$	471.773	−	126.411i	0.548574	−	0.146990i
$861$	−21.9240	+	37.9735i	−0.0254634	+	0.0441040i
$862$	−166.846	+	96.3288i	−0.193557	+	0.111750i
$863$	320.195	+	320.195i	0.371026	+	0.371026i	0.867851	−	0.496825i	$-0.165501\pi$
$863$	320.195	+	320.195i	0.371026	+	0.371026i	−0.496825	+	0.867851i	$0.665501\pi$
$864$	−33.6165	+	125.458i	−0.0389080	+	0.145207i
$865$	231.950	+	62.1508i	0.268150	+	0.0718506i
$866$	−201.358	+	201.358i	−0.232516	+	0.232516i
$867$	670.280	+	1160.96i	0.773103	+	1.33905i
$868$	−12.9726	−	7.48972i	−0.0149454	−	0.00862871i
$869$	20.3186	+	75.8302i	0.0233816	+	0.0872615i
$870$			1711.24i			1.96694i
$871$		0			0
$872$	122.163			0.140095
$873$	271.103	−	72.6417i	0.310541	−	0.0832093i
$874$	175.902	−	304.672i	0.201261	−	0.348595i
$875$	−49.8123	+	28.7591i	−0.0569283	+	0.0328676i
$876$	486.687	+	486.687i	0.555579	+	0.555579i
$877$	−391.203	+	1459.99i	−0.446069	+	1.66475i	0.267029	+	0.963689i	$0.413958\pi$
$877$	−391.203	+	1459.99i	−0.446069	+	1.66475i	−0.713098	+	0.701064i	$0.752709\pi$
$878$	101.566	+	27.2146i	0.115679	+	0.0309961i
$879$	462.452	−	462.452i	0.526111	−	0.526111i
$880$	12.3400	+	21.3736i	0.0140228	+	0.0242882i
$881$	1005.27	+	580.392i	1.14105	+	0.658788i	0.946691	−	0.322142i	$-0.104403\pi$
$881$	1005.27	+	580.392i	1.14105	+	0.658788i	0.194363	+	0.980930i	$0.437736\pi$
$882$	247.003	+	921.829i	0.280049	+	1.04516i
$883$		−	1327.78i		−	1.50371i	−0.659328	−	0.751856i	$-0.729159\pi$
$883$		−	1327.78i		−	1.50371i	0.659328	−	0.751856i	$-0.270841\pi$
$884$		0			0
$885$	3980.87			4.49815
$886$	178.463	−	47.8191i	0.201426	−	0.0539719i
$887$	−248.628	+	430.636i	−0.280302	+	0.485497i	−0.971459	−	0.237207i	$-0.923768\pi$
$887$	−248.628	+	430.636i	−0.280302	+	0.485497i	0.691157	+	0.722704i	$0.257101\pi$
$888$	−487.814	+	281.639i	−0.549340	+	0.317161i
$889$	−58.1135	−	58.1135i	−0.0653695	−	0.0653695i
$890$	−259.301	+	967.725i	−0.291350	+	1.08733i
$891$	10.4580	+	2.80221i	0.0117373	+	0.00314501i
$892$	−340.107	+	340.107i	−0.381286	+	0.381286i
$893$	−162.879	−	282.115i	−0.182396	−	0.315918i
$894$	157.359	+	90.8512i	0.176017	+	0.101623i
$895$	457.246	+	1706.46i	0.510889	+	1.90666i
$896$		−	4.03130i		−	0.00449922i
$897$		0			0
$898$	1019.38			1.13517
$899$	617.599	−	165.485i	0.686985	−	0.184077i
$900$	612.784	−	1061.37i	0.680871	−	1.17930i
$901$	−214.147	+	123.638i	−0.237677	+	0.137223i
$902$	−19.0871	−	19.0871i	−0.0211608	−	0.0211608i
$903$	12.9128	−	48.1913i	0.0142999	−	0.0533680i
$904$	−126.060	−	33.7778i	−0.139447	−	0.0373648i
$905$	−660.176	+	660.176i	−0.729477	+	0.729477i
$906$	−523.883	−	907.392i	−0.578237	−	1.00154i
$907$	837.965	+	483.799i	0.923886	+	0.533406i	0.884873	−	0.465833i	$-0.154245\pi$
$907$	837.965	+	483.799i	0.923886	+	0.533406i	0.0390135	+	0.999239i	$0.487578\pi$
$908$	−46.8360	−	174.794i	−0.0515814	−	0.192505i
$909$		−	384.184i		−	0.422645i
$910$		0			0
$911$	−760.079			−0.834335			−0.417168	−	0.908830i	$-0.636977\pi$
$911$	−760.079			−0.834335			−0.417168	+	0.908830i	$0.636977\pi$
$912$	200.488	−	53.7207i	0.219834	−	0.0589042i
$913$	−14.2586	+	24.6966i	−0.0156173	+	0.0270499i
$914$	−444.113	+	256.408i	−0.485900	+	0.280534i
$915$	−434.976	−	434.976i	−0.475384	−	0.475384i
$916$	−182.198	+	679.973i	−0.198906	+	0.742328i
$917$	55.8472	+	14.9642i	0.0609020	+	0.0163187i
$918$	−66.1406	+	66.1406i	−0.0720486	+	0.0720486i
$919$	−208.249	−	360.698i	−0.226604	−	0.392490i	0.730195	−	0.683238i	$-0.239429\pi$
$919$	−208.249	−	360.698i	−0.226604	−	0.392490i	−0.956800	+	0.290748i	$0.906096\pi$
$920$	−467.127	−	269.696i	−0.507747	−	0.293148i
$921$	−534.967	−	1996.53i	−0.580855	−	2.16778i
$922$		−	1223.62i		−	1.32713i
$923$		0			0
$924$	2.52105			0.00272841
$925$	1787.58	−	478.982i	1.93252	−	0.517818i
$926$	−163.492	+	283.176i	−0.176557	+	0.305806i
$927$	814.152	−	470.051i	0.878265	−	0.507067i
$928$	121.674	+	121.674i	0.131114	+	0.131114i
$929$	108.175	−	403.716i	0.116443	−	0.434571i	−0.882948	−	0.469471i	$-0.844445\pi$
$929$	108.175	−	403.716i	0.116443	−	0.434571i	0.999391	+	0.0349002i	$0.0111113\pi$
$930$	−1142.20	−	306.051i	−1.22817	−	0.329087i
$931$	375.490	−	375.490i	0.403319	−	0.403319i
$932$	−384.870	−	666.614i	−0.412950	−	0.715251i
$933$	571.890	+	330.181i	0.612958	+	0.353891i
$934$	88.8952	+	331.761i	0.0951769	+	0.355205i
$935$			17.7735i			0.0190091i
$936$		0			0
$937$	−140.819			−0.150287			−0.0751436	−	0.997173i	$-0.523942\pi$
$937$	−140.819			−0.150287			−0.0751436	+	0.997173i	$0.523942\pi$
$938$	33.8788	−	9.07781i	0.0361182	−	0.00967783i
$939$	1254.67	−	2173.15i	1.33618	−	2.31432i
$940$	−432.542	+	249.728i	−0.460151	+	0.265669i
$941$	−1032.31	−	1032.31i	−1.09704	−	1.09704i	−0.994756	−	0.102281i	$-0.967386\pi$
$941$	−1032.31	−	1032.31i	−1.09704	−	1.09704i	−0.102281	−	0.994756i	$-0.532614\pi$
$942$	−249.411	+	930.814i	−0.264767	+	0.988125i
$943$	569.843	+	152.689i	0.604288	+	0.161918i
$944$	283.051	−	283.051i	0.299842	−	0.299842i
$945$	−34.0728	−	59.0158i	−0.0360559	−	0.0624506i
$946$	26.5986	+	15.3567i	0.0281169	+	0.0162333i
$947$	125.045	+	466.674i	0.132043	+	0.492792i	0.999993	−	0.00386092i	$-0.00122897\pi$
$947$	125.045	+	466.674i	0.132043	+	0.492792i	−0.867949	+	0.496653i	$0.834562\pi$
$948$		−	1012.28i		−	1.06780i
$949$		0			0
$950$	−681.937			−0.717829
$951$	−159.114	+	42.6346i	−0.167313	+	0.0448313i
$952$	1.45159	−	2.51422i	0.00152477	−	0.00264099i
$953$	−742.996	+	428.969i	−0.779639	+	0.450125i	−0.836302	−	0.548269i	$-0.815287\pi$
$953$	−742.996	+	428.969i	−0.779639	+	0.450125i	0.0566633	+	0.998393i	$0.481954\pi$
$954$	1185.27	+	1185.27i	1.24242	+	1.24242i
$955$	571.396	−	2132.48i	0.598321	−	2.23296i
$956$	−575.448	−	154.191i	−0.601933	−	0.161287i
$957$	−76.0911	+	76.0911i	−0.0795100	+	0.0795100i
$958$	158.062	+	273.772i	0.164992	+	0.285774i
$959$	−31.8896	−	18.4115i	−0.0332530	−	0.0191986i
$960$	−82.3652	−	307.391i	−0.0857971	−	0.320199i
$961$		−	519.175i		−	0.540244i
$962$		0			0
$963$	−1775.66			−1.84389
$964$	−361.919	+	96.9760i	−0.375435	+	0.100598i
$965$	−663.006	+	1148.36i	−0.687053	+	1.19001i
$966$	−47.7166	+	27.5492i	−0.0493961	+	0.0285189i
$967$	911.551	+	911.551i	0.942658	+	0.942658i	0.998443	−	0.0557845i	$-0.0177660\pi$
$967$	911.551	+	911.551i	0.942658	+	0.942658i	−0.0557845	+	0.998443i	$0.517766\pi$
$968$	88.1765	−	329.079i	0.0910914	−	0.339958i
$969$	144.383	+	38.6873i	0.149002	+	0.0399250i
$970$	−169.311	+	169.311i	−0.174547	+	0.174547i
$971$	−537.004	−	930.119i	−0.553043	−	0.957898i	−0.998053	−	0.0623725i	$-0.980133\pi$
$971$	−537.004	−	930.119i	−0.553043	−	0.957898i	0.445010	−	0.895525i	$-0.353200\pi$
$972$	−478.821	−	276.447i	−0.492614	−	0.284411i
$973$	2.35891	+	8.80355i	0.00242436	+	0.00904785i
$974$		−	30.5113i		−	0.0313258i
$975$		0			0
$976$	−61.8562			−0.0633772
$977$	−767.374	+	205.617i	−0.785439	+	0.210458i	−0.629181	−	0.777258i	$-0.716610\pi$
$977$	−767.374	+	205.617i	−0.785439	+	0.210458i	−0.156258	+	0.987716i	$0.549943\pi$
$978$	89.7055	−	155.375i	0.0917234	−	0.158870i
$979$	−54.5604	+	31.5005i	−0.0557307	+	0.0321762i
$980$	−575.706	−	575.706i	−0.587455	−	0.587455i
$981$	154.352	−	576.050i	0.157342	−	0.587207i
$982$	79.6518	+	21.3426i	0.0811118	+	0.0217339i
$983$	1275.63	−	1275.63i	1.29769	−	1.29769i	0.367773	−	0.929916i	$-0.380120\pi$
$983$	1275.63	−	1275.63i	1.29769	−	1.29769i	0.929916	−	0.367773i	$-0.119880\pi$
$984$	174.030	+	301.429i	0.176860	+	0.306331i
$985$	2169.89	+	1252.79i	2.20294	+	1.27187i
$986$	32.0728	+	119.697i	0.0325281	+	0.121397i
$987$			51.0191i			0.0516911i
$988$		0			0
$989$	−671.253			−0.678719
$990$	116.377	−	31.1832i	0.117553	−	0.0314981i
$991$	564.667	−	978.032i	0.569795	−	0.986914i	−0.426791	−	0.904350i	$-0.640356\pi$
$991$	564.667	−	978.032i	0.569795	−	0.986914i	0.996586	−	0.0825637i	$-0.0263108\pi$
$992$	−102.975	+	59.4525i	−0.103805	+	0.0599320i
$993$	74.8840	+	74.8840i	0.0754119	+	0.0754119i
$994$	−12.7200	+	47.4716i	−0.0127968	+	0.0477582i
$995$	1507.10	+	403.826i	1.51467	+	0.405855i
$996$	260.011	−	260.011i	0.261055	−	0.261055i
$997$	3.57219	+	6.18721i	0.00358294	+	0.00620583i	0.867811	−	0.496894i	$-0.165526\pi$
$997$	3.57219	+	6.18721i	0.00358294	+	0.00620583i	−0.864228	+	0.503100i	$0.832193\pi$
$998$	−1083.39	−	625.494i	−1.08556	−	0.626748i
$999$	247.808	+	924.830i	0.248056	+	0.925756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.j.319.2		8
13.2	odd	12	inner	338.3.f.j.249.2		8
13.3	even	3		338.3.f.i.89.2		8
13.4	even	6		338.3.d.g.99.1		8
13.5	odd	4		338.3.f.i.19.2		8
13.6	odd	12		338.3.d.f.239.1		8
13.7	odd	12		338.3.d.g.239.1		8
13.8	odd	4		26.3.f.b.19.2	yes	8
13.9	even	3		338.3.d.f.99.1		8
13.10	even	6		26.3.f.b.11.2	✓	8
13.11	odd	12		338.3.f.h.249.2		8
13.12	even	2		338.3.f.h.319.2		8
39.8	even	4		234.3.bb.f.19.2		8
39.23	odd	6		234.3.bb.f.37.2		8
52.23	odd	6		208.3.bd.f.193.1		8
52.47	even	4		208.3.bd.f.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.2	✓	8	13.10	even	6
26.3.f.b.19.2	yes	8	13.8	odd	4
208.3.bd.f.97.1		8	52.47	even	4
208.3.bd.f.193.1		8	52.23	odd	6
234.3.bb.f.19.2		8	39.8	even	4
234.3.bb.f.37.2		8	39.23	odd	6
338.3.d.f.99.1		8	13.9	even	3
338.3.d.f.239.1		8	13.6	odd	12
338.3.d.g.99.1		8	13.4	even	6
338.3.d.g.239.1		8	13.7	odd	12
338.3.f.h.249.2		8	13.11	odd	12
338.3.f.h.319.2		8	13.12	even	2
338.3.f.i.19.2		8	13.5	odd	4
338.3.f.i.89.2		8	13.3	even	3
338.3.f.j.249.2		8	13.2	odd	12	inner
338.3.f.j.319.2		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(2.38787 - 4.13592i) q^{3} +(1.73205 - 1.00000i) q^{4} +(5.88981 + 5.88981i) q^{5} +(1.74804 - 6.52379i) q^{6} +(0.344179 + 0.0922225i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +(10.2015 + 5.88981i) q^{10} +(0.191720 + 0.715507i) q^{11} -9.55149i q^{12} +0.503913 q^{14} +(38.4239 - 10.2956i) q^{15} +(2.00000 - 3.46410i) q^{16} +(2.49470 - 1.44031i) q^{17} +(-13.8077 - 13.8077i) q^{18} +(-2.81216 + 10.4951i) q^{19} +(16.0913 + 4.31164i) q^{20} +(1.20328 - 1.20328i) q^{21} +(0.523787 + 0.907226i) q^{22} +(-19.8278 - 11.4476i) q^{23} +(-3.49609 - 13.0476i) q^{24} +44.3798i q^{25} -22.9605 q^{27} +(0.688358 - 0.184445i) q^{28} +(-15.2092 + 26.3432i) q^{29} +(48.7195 - 28.1282i) q^{30} +(-14.8631 - 14.8631i) q^{31} +(1.46410 - 5.46410i) q^{32} +(3.41708 + 0.915603i) q^{33} +(2.88063 - 2.88063i) q^{34} +(1.48398 + 2.57032i) q^{35} +(-23.9157 - 13.8077i) q^{36} +(-10.7928 - 40.2792i) q^{37} +15.3659i q^{38} +23.5593 q^{40} +(-24.8893 + 6.66907i) q^{41} +(1.20328 - 2.08414i) q^{42} +(25.3907 - 14.6593i) q^{43} +(1.04757 + 1.04757i) q^{44} +(29.7670 - 111.092i) q^{45} +(-31.2753 - 8.38019i) q^{46} +(-21.2000 + 21.2000i) q^{47} +(-9.55149 - 16.5437i) q^{48} +(-42.3253 - 24.4365i) q^{49} +(16.2441 + 60.6239i) q^{50} -13.7571i q^{51} -85.8410 q^{53} +(-31.3646 + 8.40412i) q^{54} +(-3.08501 + 5.34339i) q^{55} +(0.872803 - 0.503913i) q^{56} +(36.6919 + 36.6919i) q^{57} +(-11.1339 + 41.5524i) q^{58} +(96.6638 + 25.9010i) q^{59} +(56.2565 - 56.2565i) q^{60} +(-7.73202 - 13.3923i) q^{61} +(-25.7437 - 14.8631i) q^{62} +(-1.27338 - 4.75233i) q^{63} -8.00000i q^{64} +5.00295 q^{66} +(67.2315 - 18.0146i) q^{67} +(2.88063 - 4.98939i) q^{68} +(-94.6923 + 54.6706i) q^{69} +(2.96795 + 2.96795i) q^{70} +(-25.2424 + 94.2060i) q^{71} +(-37.7234 - 10.1080i) q^{72} +(-50.9541 + 50.9541i) q^{73} +(-29.4864 - 51.0720i) q^{74} +(183.551 + 105.973i) q^{75} +(5.62432 + 20.9903i) q^{76} +0.263943i q^{77} +105.981 q^{79} +(32.1825 - 8.62328i) q^{80} +(7.30809 - 12.6580i) q^{81} +(-31.5584 + 18.2202i) q^{82} +(27.2221 + 27.2221i) q^{83} +(0.880862 - 3.28742i) q^{84} +(23.1765 + 6.21012i) q^{85} +(29.3186 - 29.3186i) q^{86} +(72.6355 + 125.808i) q^{87} +(1.81445 + 1.04757i) q^{88} +(22.0127 + 82.1525i) q^{89} -162.650i q^{90} -45.7902 q^{92} +(-96.9639 + 25.9814i) q^{93} +(-21.2000 + 36.7195i) q^{94} +(-78.3775 + 45.2513i) q^{95} +(-19.1030 - 19.1030i) q^{96} +(-5.26095 + 19.6341i) q^{97} +(-66.7618 - 17.8888i) q^{98} +(7.23232 - 7.23232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{5} + 6 q^{6} + 8 q^{7} + 16 q^{8} - 42 q^{9} + 18 q^{10} + 24 q^{11} + 20 q^{14} + 126 q^{15} + 16 q^{16} + 42 q^{17} - 84 q^{18} + 68 q^{19} + 12 q^{20} + 102 q^{21} - 42 q^{22} + 36 q^{23}+ \cdots - 252 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^5 + 6 * q^6 + 8 * q^7 + 16 * q^8 - 42 * q^9 + 18 * q^10 + 24 * q^11 + 20 * q^14 + 126 * q^15 + 16 * q^16 + 42 * q^17 - 84 * q^18 + 68 * q^19 + 12 * q^20 + 102 * q^21 - 42 * q^22 + 36 * q^23 - 12 * q^24 + 72 * q^27 + 16 * q^28 - 6 * q^29 + 192 * q^30 - 32 * q^31 - 16 * q^32 + 96 * q^33 + 60 * q^34 - 78 * q^35 + 48 * q^36 - 74 * q^37 - 24 * q^40 + 120 * q^41 + 102 * q^42 + 108 * q^43 - 84 * q^44 + 138 * q^45 - 18 * q^46 - 60 * q^47 - 258 * q^49 + 106 * q^50 - 132 * q^53 - 198 * q^54 - 162 * q^55 + 12 * q^56 + 294 * q^57 - 12 * q^58 + 252 * q^59 + 120 * q^60 + 36 * q^61 + 12 * q^62 - 228 * q^63 + 108 * q^66 - 88 * q^67 + 60 * q^68 - 258 * q^69 - 156 * q^70 - 12 * q^71 - 36 * q^72 - 166 * q^73 - 32 * q^74 - 6 * q^75 - 136 * q^76 - 96 * q^79 + 24 * q^80 - 12 * q^81 + 252 * q^82 + 240 * q^83 - 336 * q^84 - 258 * q^85 - 132 * q^86 + 360 * q^87 + 12 * q^88 + 504 * q^89 - 216 * q^92 - 174 * q^93 - 60 * q^94 - 714 * q^95 + 88 * q^97 - 266 * q^98 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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