LMFDB - Embedded newform 338.3.f.j.319.1

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			319.1
Root			$-3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.319
Dual form			338.3.f.j.249.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(-1.52185 + 2.63592i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.79174 - 4.79174i) q^{5} +(-1.11407 + 4.15776i) q^{6} +(4.25390 + 1.13983i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +(-8.29953 - 4.79174i) q^{10} +(-3.71800 - 13.8758i) q^{11} +6.08739i q^{12} +6.22814 q^{14} +(19.9229 - 5.33833i) q^{15} +(2.00000 - 3.46410i) q^{16} +(20.9957 - 12.1219i) q^{17} +(-0.264067 - 0.264067i) q^{18} +(6.82178 - 25.4592i) q^{19} +(-13.0913 - 3.50779i) q^{20} +(-9.47827 + 9.47827i) q^{21} +(-10.1578 - 17.5938i) q^{22} +(5.44507 + 3.14371i) q^{23} +(2.22814 + 8.31552i) q^{24} +20.9215i q^{25} -26.5895 q^{27} +(8.50779 - 2.27966i) q^{28} +(11.1112 - 19.2451i) q^{29} +(25.2612 - 14.5846i) q^{30} +(8.59518 + 8.59518i) q^{31} +(1.46410 - 5.46410i) q^{32} +(42.2336 + 11.3164i) q^{33} +(24.2437 - 24.2437i) q^{34} +(-14.9218 - 25.8453i) q^{35} +(-0.457378 - 0.264067i) q^{36} +(-1.64504 - 6.13936i) q^{37} -37.2749i q^{38} -19.1669 q^{40} +(70.4778 - 18.8845i) q^{41} +(-9.47827 + 16.4168i) q^{42} +(-26.9695 + 15.5708i) q^{43} +(-20.3155 - 20.3155i) q^{44} +(-0.463147 + 1.72849i) q^{45} +(8.58878 + 2.30136i) q^{46} +(-7.65637 + 7.65637i) q^{47} +(6.08739 + 10.5437i) q^{48} +(-25.6388 - 14.8026i) q^{49} +(7.65779 + 28.5793i) q^{50} +73.7905i q^{51} -33.7616 q^{53} +(-36.3219 + 9.73243i) q^{54} +(-48.6733 + 84.3047i) q^{55} +(10.7875 - 6.22814i) q^{56} +(56.7267 + 56.7267i) q^{57} +(8.13394 - 30.3563i) q^{58} +(36.4842 + 9.77592i) q^{59} +(29.1692 - 29.1692i) q^{60} +(11.5359 + 19.9807i) q^{61} +(14.8873 + 8.59518i) q^{62} +(-0.300991 - 1.12332i) q^{63} -8.00000i q^{64} +61.8342 q^{66} +(-103.954 + 27.8544i) q^{67} +(24.2437 - 41.9914i) q^{68} +(-16.5731 + 9.56849i) q^{69} +(-29.8436 - 29.8436i) q^{70} +(0.591796 - 2.20861i) q^{71} +(-0.721445 - 0.193311i) q^{72} +(-38.1773 + 38.1773i) q^{73} +(-4.49432 - 7.78440i) q^{74} +(-55.1473 - 31.8393i) q^{75} +(-13.6436 - 50.9185i) q^{76} -63.2639i q^{77} -19.1299 q^{79} +(-26.1825 + 7.01559i) q^{80} +(41.6534 - 72.1459i) q^{81} +(89.3622 - 51.5933i) q^{82} +(-34.7720 - 34.7720i) q^{83} +(-6.93858 + 25.8951i) q^{84} +(-158.691 - 42.5210i) q^{85} +(-31.1417 + 31.1417i) q^{86} +(33.8190 + 58.5762i) q^{87} +(-35.1875 - 20.3155i) q^{88} +(0.930292 + 3.47190i) q^{89} +2.53068i q^{90} +12.5748 q^{92} +(-35.7367 + 9.57562i) q^{93} +(-7.65637 + 13.2612i) q^{94} +(-154.682 + 89.3058i) q^{95} +(12.1748 + 12.1748i) q^{96} +(-6.51404 + 24.3107i) q^{97} +(-40.4414 - 10.8362i) q^{98} +(-2.68233 + 2.68233i) 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
$3$	−1.52185	+	2.63592i	−0.507282	+	0.878639i	0.492682	+	0.870209i	$0.336016\pi$
$3$	−1.52185	+	2.63592i	−0.507282	+	0.878639i	−0.999964	+	0.00842924i	$0.997317\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−4.79174	−	4.79174i	−0.958347	−	0.958347i	0.0408192	−	0.999167i	$-0.487003\pi$
$5$	−4.79174	−	4.79174i	−0.958347	−	0.958347i	−0.999167	+	0.0408192i	$0.987003\pi$
$6$	−1.11407	+	4.15776i	−0.185678	+	0.692960i
$7$	4.25390	+	1.13983i	0.607700	+	0.162833i	0.549530	−	0.835474i	$-0.314807\pi$
$7$	4.25390	+	1.13983i	0.607700	+	0.162833i	0.0581698	+	0.998307i	$0.481474\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−0.132034	−	0.228689i	−0.0146704	−	0.0254099i
$10$	−8.29953	−	4.79174i	−0.829953	−	0.479174i
$11$	−3.71800	−	13.8758i	−0.338000	−	1.26143i	−0.900580	−	0.434690i	$-0.856858\pi$
$11$	−3.71800	−	13.8758i	−0.338000	−	1.26143i	0.562580	−	0.826743i	$-0.309809\pi$
$12$			6.08739i			0.507282i
$13$		0			0
$13$		0			0
$14$	6.22814			0.444867
$15$	19.9229	−	5.33833i	1.32819	−	0.355888i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	20.9957	−	12.1219i	1.23504	−	0.713051i	0.266964	−	0.963707i	$-0.413980\pi$
$17$	20.9957	−	12.1219i	1.23504	−	0.713051i	0.968076	+	0.250656i	$0.0806462\pi$
$18$	−0.264067	−	0.264067i	−0.0146704	−	0.0146704i
$19$	6.82178	−	25.4592i	0.359041	−	1.33996i	−0.516281	−	0.856419i	$-0.672684\pi$
$19$	6.82178	−	25.4592i	0.359041	−	1.33996i	0.875322	−	0.483540i	$-0.160649\pi$
$20$	−13.0913	−	3.50779i	−0.654563	−	0.175390i
$21$	−9.47827	+	9.47827i	−0.451346	+	0.451346i
$22$	−10.1578	−	17.5938i	−0.461716	−	0.799716i
$23$	5.44507	+	3.14371i	0.236742	+	0.136683i	0.613678	−	0.789556i	$-0.289689\pi$
$23$	5.44507	+	3.14371i	0.236742	+	0.136683i	−0.376936	+	0.926239i	$0.623022\pi$
$24$	2.22814	+	8.31552i	0.0928391	+	0.346480i
$25$			20.9215i			0.836859i
$26$		0			0
$27$	−26.5895			−0.984796
$28$	8.50779	−	2.27966i	0.303850	−	0.0814163i
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	−0.608366	−	0.793657i	$-0.708175\pi$
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	0.991510	+	0.130032i	$0.0415080\pi$
$30$	25.2612	−	14.5846i	0.842041	−	0.486153i
$31$	8.59518	+	8.59518i	0.277264	+	0.277264i	0.832016	−	0.554752i	$-0.187187\pi$
$31$	8.59518	+	8.59518i	0.277264	+	0.277264i	−0.554752	+	0.832016i	$0.687187\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	42.2336	+	11.3164i	1.27980	+	0.342923i
$34$	24.2437	−	24.2437i	0.713051	−	0.713051i
$35$	−14.9218	−	25.8453i	−0.426337	−	0.738438i
$36$	−0.457378	−	0.264067i	−0.0127049	−	0.00733521i
$37$	−1.64504	−	6.13936i	−0.0444605	−	0.165929i	0.940126	−	0.340827i	$-0.110707\pi$
$37$	−1.64504	−	6.13936i	−0.0444605	−	0.165929i	−0.984587	+	0.174898i	$0.944040\pi$
$38$		−	37.2749i		−	0.980919i
$39$		0			0
$40$	−19.1669			−0.479174
$41$	70.4778	−	18.8845i	1.71897	−	0.460596i	0.741375	−	0.671091i	$-0.234174\pi$
$41$	70.4778	−	18.8845i	1.71897	−	0.460596i	0.977595	+	0.210495i	$0.0675075\pi$
$42$	−9.47827	+	16.4168i	−0.225673	+	0.390877i
$43$	−26.9695	+	15.5708i	−0.627197	+	0.362113i	−0.779666	−	0.626196i	$-0.784611\pi$
$43$	−26.9695	+	15.5708i	−0.627197	+	0.362113i	0.152468	+	0.988308i	$0.451278\pi$
$44$	−20.3155	−	20.3155i	−0.461716	−	0.461716i
$45$	−0.463147	+	1.72849i	−0.0102922	+	0.0384109i
$46$	8.58878	+	2.30136i	0.186713	+	0.0500295i
$47$	−7.65637	+	7.65637i	−0.162902	+	0.162902i	−0.783851	−	0.620949i	$-0.786747\pi$
$47$	−7.65637	+	7.65637i	−0.162902	+	0.162902i	0.620949	+	0.783851i	$0.286747\pi$
$48$	6.08739	+	10.5437i	0.126821	+	0.219660i
$49$	−25.6388	−	14.8026i	−0.523241	−	0.302093i
$50$	7.65779	+	28.5793i	0.153156	+	0.571585i
$51$			73.7905i			1.44687i
$52$		0			0
$53$	−33.7616			−0.637010			−0.318505	−	0.947921i	$-0.603181\pi$
$53$	−33.7616			−0.637010			−0.318505	+	0.947921i	$0.603181\pi$
$54$	−36.3219	+	9.73243i	−0.672628	+	0.180230i
$55$	−48.6733	+	84.3047i	−0.884969	+	1.53281i
$56$	10.7875	−	6.22814i	0.192633	−	0.111217i
$57$	56.7267	+	56.7267i	0.995205	+	0.995205i
$58$	8.13394	−	30.3563i	0.140240	−	0.523384i
$59$	36.4842	+	9.77592i	0.618377	+	0.165694i	0.554390	−	0.832257i	$-0.312952\pi$
$59$	36.4842	+	9.77592i	0.618377	+	0.165694i	0.0639871	+	0.997951i	$0.479618\pi$
$60$	29.1692	−	29.1692i	0.486153	−	0.486153i
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	0.944955	−	0.327201i	$-0.106106\pi$
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	−0.755842	+	0.654754i	$0.772772\pi$
$62$	14.8873	+	8.59518i	0.240118	+	0.138632i
$63$	−0.300991	−	1.12332i	−0.00477764	−	0.0178304i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	61.8342			0.936882
$67$	−103.954	+	27.8544i	−1.55155	+	0.415737i	−0.929977	−	0.367618i	$-0.880173\pi$
$67$	−103.954	+	27.8544i	−1.55155	+	0.415737i	−0.621575	+	0.783355i	$0.713507\pi$
$68$	24.2437	−	41.9914i	0.356525	−	0.617520i
$69$	−16.5731	+	9.56849i	−0.240190	+	0.138674i
$70$	−29.8436	−	29.8436i	−0.426337	−	0.426337i
$71$	0.591796	−	2.20861i	0.00833516	−	0.0311072i	−0.961633	−	0.274339i	$-0.911541\pi$
$71$	0.591796	−	2.20861i	0.00833516	−	0.0311072i	0.969968	+	0.243232i	$0.0782076\pi$
$72$	−0.721445	−	0.193311i	−0.0100201	−	0.00268487i
$73$	−38.1773	+	38.1773i	−0.522977	+	0.522977i	−0.918469	−	0.395492i	$-0.870574\pi$
$73$	−38.1773	+	38.1773i	−0.522977	+	0.522977i	0.395492	+	0.918469i	$0.370574\pi$
$74$	−4.49432	−	7.78440i	−0.0607341	−	0.105195i
$75$	−55.1473	−	31.8393i	−0.735297	−	0.424524i
$76$	−13.6436	−	50.9185i	−0.179521	−	0.669980i
$77$		−	63.2639i		−	0.821610i
$78$		0			0
$79$	−19.1299			−0.242150			−0.121075	−	0.992643i	$-0.538634\pi$
$79$	−19.1299			−0.242150			−0.121075	+	0.992643i	$0.538634\pi$
$80$	−26.1825	+	7.01559i	−0.327282	+	0.0876949i
$81$	41.6534	−	72.1459i	0.514240	−	0.890690i
$82$	89.3622	−	51.5933i	1.08978	−	0.629187i
$83$	−34.7720	−	34.7720i	−0.418940	−	0.418940i	0.465898	−	0.884838i	$-0.345731\pi$
$83$	−34.7720	−	34.7720i	−0.418940	−	0.418940i	−0.884838	+	0.465898i	$0.845731\pi$
$84$	−6.93858	+	25.8951i	−0.0826021	+	0.308275i
$85$	−158.691	−	42.5210i	−1.86695	−	0.500247i
$86$	−31.1417	+	31.1417i	−0.362113	+	0.362113i
$87$	33.8190	+	58.5762i	0.388724	+	0.673290i
$88$	−35.1875	−	20.3155i	−0.399858	−	0.230858i
$89$	0.930292	+	3.47190i	0.0104527	+	0.0390101i	0.970955	−	0.239261i	$-0.0769052\pi$
$89$	0.930292	+	3.47190i	0.0104527	+	0.0390101i	−0.960503	+	0.278271i	$0.910239\pi$
$90$			2.53068i			0.0281187i
$91$		0			0
$92$	12.5748			0.136683
$93$	−35.7367	+	9.57562i	−0.384266	+	0.102964i
$94$	−7.65637	+	13.2612i	−0.0814508	+	0.141077i
$95$	−154.682	+	89.3058i	−1.62823	+	0.940061i
$96$	12.1748	+	12.1748i	0.126821	+	0.126821i
$97$	−6.51404	+	24.3107i	−0.0671551	+	0.250626i	−0.991340	−	0.131319i	$-0.958079\pi$
$97$	−6.51404	+	24.3107i	−0.0671551	+	0.250626i	0.924185	+	0.381945i	$0.124746\pi$
$98$	−40.4414	−	10.8362i	−0.412667	−	0.110574i
$99$	−2.68233	+	2.68233i	−0.0270943	+	0.0270943i
$100$	20.9215	+	36.2371i	0.209215	+	0.362371i
$101$	131.473	+	75.9060i	1.30171	+	0.751545i	0.980698	−	0.195529i	$-0.0626425\pi$
$101$	131.473	+	75.9060i	1.30171	+	0.751545i	0.321016	+	0.947074i	$0.395976\pi$
$102$	27.0092	+	100.800i	0.264796	+	0.988232i
$103$		−	17.3672i		−	0.168614i	−0.996440	−	0.0843069i	$-0.973132\pi$
$103$		−	17.3672i		−	0.168614i	0.996440	−	0.0843069i	$-0.0268676\pi$
$104$		0			0
$105$	90.8347			0.865093
$106$	−46.1191	+	12.3576i	−0.435086	+	0.116581i
$107$	−26.5964	+	46.0662i	−0.248564	+	0.430526i	−0.963128	−	0.269045i	$-0.913292\pi$
$107$	−26.5964	+	46.0662i	−0.248564	+	0.430526i	0.714564	+	0.699571i	$0.246625\pi$
$108$	−46.0544	+	26.5895i	−0.426429	+	0.246199i
$109$	−53.3779	−	53.3779i	−0.489705	−	0.489705i	0.418508	−	0.908213i	$-0.362553\pi$
$109$	−53.3779	−	53.3779i	−0.489705	−	0.489705i	−0.908213	+	0.418508i	$0.862553\pi$
$110$	−35.6313	+	132.978i	−0.323921	+	1.20889i
$111$	18.6863	+	5.00699i	0.168345	+	0.0451080i
$112$	12.4563	−	12.4563i	0.111217	−	0.111217i
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	0.774680	−	0.632354i	$-0.217911\pi$
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	−0.934974	+	0.354715i	$0.884578\pi$
$114$	98.2535	+	56.7267i	0.861873	+	0.497603i
$115$	−11.0275	−	41.1552i	−0.0958912	−	0.357871i
$116$		−	44.4447i		−	0.383144i
$117$		0			0
$118$	53.4166			0.452683
$119$	103.130	−	27.6337i	0.866641	−	0.232216i
$120$	29.1692	−	50.5225i	0.243076	−	0.421020i
$121$	−73.9242	+	42.6801i	−0.610943	+	0.352728i
$122$	23.0717	+	23.0717i	0.189113	+	0.189113i
$123$	−57.4785	+	214.513i	−0.467305	+	1.74401i
$124$	23.4825	+	6.29211i	0.189375	+	0.0507428i
$125$	−19.5432	+	19.5432i	−0.156346	+	0.156346i
$126$	−0.822324	−	1.42431i	−0.00652638	−	0.0113040i
$127$	115.255	+	66.5425i	0.907520	+	0.523957i	0.879632	−	0.475654i	$-0.157789\pi$
$127$	115.255	+	66.5425i	0.907520	+	0.523957i	0.0278874	+	0.999611i	$0.491122\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$		−	94.7857i		−	0.734773i
$130$		0			0
$131$	38.2739			0.292167			0.146083	−	0.989272i	$-0.453333\pi$
$131$	38.2739			0.292167			0.146083	+	0.989272i	$0.453333\pi$
$132$	84.4671	−	22.6329i	0.639902	−	0.171461i
$133$	58.0383	−	100.525i	0.436378	−	0.755829i
$134$	−131.808	+	76.0996i	−0.983644	+	0.567907i
$135$	127.410	+	127.410i	0.943777	+	0.943777i
$136$	17.7476	−	66.2351i	0.130497	−	0.487023i
$137$	7.76140	+	2.07966i	0.0566525	+	0.0151800i	0.287034	−	0.957920i	$-0.407331\pi$
$137$	7.76140	+	2.07966i	0.0566525	+	0.0151800i	−0.230381	+	0.973100i	$0.573997\pi$
$138$	−19.1370	+	19.1370i	−0.138674	+	0.138674i
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.854012	+	0.520253i	$0.174162\pi$
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.0235463	+	0.999723i	$0.492504\pi$
$140$	−51.6906	−	29.8436i	−0.369219	−	0.213169i
$141$	−8.52973	−	31.8334i	−0.0604945	−	0.225769i
$142$		−	3.23364i		−	0.0227721i
$143$		0			0
$144$	−1.05627			−0.00733521
$145$	−145.459	+	38.9757i	−1.00317	+	0.268798i
$146$	−38.1773	+	66.1251i	−0.261488	+	0.452911i
$147$	78.0367	−	45.0545i	0.530862	−	0.306493i
$148$	−8.98865	−	8.98865i	−0.0607341	−	0.0607341i
$149$	48.9509	−	182.687i	0.328529	−	1.22609i	−0.582187	−	0.813055i	$-0.697803\pi$
$149$	48.9509	−	182.687i	0.328529	−	1.22609i	0.910716	−	0.413033i	$-0.135531\pi$
$150$	−86.9865	−	23.3080i	−0.579910	−	0.155386i
$151$	70.5995	−	70.5995i	0.467546	−	0.467546i	−0.433573	−	0.901119i	$-0.642747\pi$
$151$	70.5995	−	70.5995i	0.467546	−	0.467546i	0.901119	+	0.433573i	$0.142747\pi$
$152$	−37.2749	−	64.5620i	−0.245230	−	0.424750i
$153$	−5.54428	−	3.20099i	−0.0362371	−	0.0209215i
$154$	−23.1562	−	86.4202i	−0.150365	−	0.561170i
$155$		−	82.3717i		−	0.531430i
$156$		0			0
$157$	176.794			1.12608			0.563038	−	0.826431i	$-0.309632\pi$
$157$	176.794			1.12608			0.563038	+	0.826431i	$0.309632\pi$
$158$	−26.1319	+	7.00202i	−0.165392	+	0.0443166i
$159$	51.3799	−	88.9926i	0.323144	−	0.559702i
$160$	−33.1981	+	19.1669i	−0.207488	+	0.119793i
$161$	19.5795	+	19.5795i	0.121612	+	0.121612i
$162$	30.4924	−	113.799i	0.188225	−	0.702465i
$163$	117.116	+	31.3812i	0.718504	+	0.192523i	0.599504	−	0.800372i	$-0.295365\pi$
$163$	117.116	+	31.3812i	0.718504	+	0.192523i	0.119000	+	0.992894i	$0.462031\pi$
$164$	103.187	−	103.187i	0.629187	−	0.629187i
$165$	−148.147	−	256.598i	−0.897858	−	1.55514i
$166$	−60.2269	−	34.7720i	−0.362813	−	0.209470i
$167$	76.7939	+	286.599i	0.459844	+	1.71616i	0.673444	+	0.739238i	$0.264814\pi$
$167$	76.7939	+	286.599i	0.459844	+	1.71616i	−0.213601	+	0.976921i	$0.568519\pi$
$168$			37.9131i			0.225673i
$169$		0			0
$170$	−232.339			−1.36670
$171$	−6.72295	+	1.80141i	−0.0393155	+	0.0105346i
$172$	−31.1417	+	53.9390i	−0.181056	+	0.313599i
$173$	241.179	−	139.245i	1.39410	−	0.804884i	0.400334	−	0.916369i	$-0.368894\pi$
$173$	241.179	−	139.245i	1.39410	−	0.804884i	0.993766	+	0.111485i	$0.0355608\pi$
$174$	67.6380	+	67.6380i	0.388724	+	0.388724i
$175$	−23.8469	+	88.9978i	−0.136268	+	0.508559i
$176$	−55.5030	−	14.8720i	−0.315358	−	0.0845000i
$177$	−81.2919	+	81.2919i	−0.459276	+	0.459276i
$178$	2.54160	+	4.40219i	0.0142787	+	0.0247314i
$179$	−68.2036	−	39.3774i	−0.381026	−	0.219985i	0.297239	−	0.954803i	$-0.403934\pi$
$179$	−68.2036	−	39.3774i	−0.381026	−	0.219985i	−0.678264	+	0.734818i	$0.737268\pi$
$180$	0.926294	+	3.45698i	0.00514608	+	0.0192054i
$181$			200.758i			1.10916i	0.832130	+	0.554581i	$0.187121\pi$
$181$			200.758i			1.10916i	−0.832130	+	0.554581i	$0.812879\pi$
$182$		0			0
$183$	−70.2233			−0.383734
$184$	17.1776	−	4.60271i	0.0933563	−	0.0250147i
$185$	−21.5356	+	37.3008i	−0.116409	+	0.201626i
$186$	−45.3123	+	26.1611i	−0.243615	+	0.140651i
$187$	−246.262	−	246.262i	−1.31691	−	1.31691i
$188$	−5.60485	+	20.9176i	−0.0298131	+	0.111264i
$189$	−113.109	−	30.3075i	−0.598460	−	0.160357i
$190$	−178.612	+	178.612i	−0.940061	+	0.940061i
$191$	−20.2650	−	35.1001i	−0.106100	−	0.183770i	0.808087	−	0.589063i	$-0.200503\pi$
$191$	−20.2650	−	35.1001i	−0.106100	−	0.183770i	−0.914187	+	0.405293i	$0.867170\pi$
$192$	21.0873	+	12.1748i	0.109830	+	0.0634103i
$193$	−37.5529	−	140.149i	−0.194575	−	0.726163i	−0.992377	−	0.123243i	$-0.960671\pi$
$193$	−37.5529	−	140.149i	−0.194575	−	0.726163i	0.797802	−	0.602920i	$-0.205996\pi$
$194$			35.5934i			0.183471i
$195$		0			0
$196$	−59.2103			−0.302093
$197$	−149.555	+	40.0731i	−0.759161	+	0.203417i	−0.617578	−	0.786510i	$-0.711886\pi$
$197$	−149.555	+	40.0731i	−0.759161	+	0.203417i	−0.141583	+	0.989926i	$0.545219\pi$
$198$	−2.68233	+	4.64594i	−0.0135471	+	0.0234643i
$199$	225.470	−	130.175i	1.13302	−	0.654147i	0.188324	−	0.982107i	$-0.439695\pi$
$199$	225.470	−	130.175i	1.13302	−	0.654147i	0.944691	+	0.327960i	$0.106361\pi$
$200$	41.8430	+	41.8430i	0.209215	+	0.209215i
$201$	84.7802	−	316.404i	0.421792	−	1.57415i
$202$	207.379	+	55.5671i	1.02663	+	0.275084i
$203$	69.2019	−	69.2019i	0.340896	−	0.340896i
$204$	73.7905	+	127.809i	0.361718	+	0.626514i
$205$	−428.200	−	247.221i	−2.08878	−	1.20596i
$206$	−6.35684	−	23.7241i	−0.0308585	−	0.115165i
$207$		−	1.66030i		−	0.00802079i
$208$		0			0
$209$	−378.630			−1.81162
$210$	124.083	−	33.2478i	0.590869	−	0.158323i
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.352831	+	0.935687i	$0.614781\pi$
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.633913	+	0.773404i	$0.718552\pi$
$212$	−58.4767	+	33.7616i	−0.275834	+	0.159253i
$213$	4.92110	+	4.92110i	0.0231037	+	0.0231037i
$214$	−19.4699	+	72.6626i	−0.0909808	+	0.339545i
$215$	203.842	+	54.6193i	0.948103	+	0.254043i
$216$	−53.1790	+	53.1790i	−0.246199	+	0.246199i
$217$	26.7660	+	46.3600i	0.123346	+	0.213641i
$218$	−92.4532	−	53.3779i	−0.424097	−	0.244853i
$219$	−42.5322	−	158.732i	−0.194211	−	0.724805i
$220$			194.693i			0.884969i
$221$		0			0
$222$	27.3587			0.123237
$223$	197.340	−	52.8772i	0.884935	−	0.237118i	0.212400	−	0.977183i	$-0.431872\pi$
$223$	197.340	−	52.8772i	0.884935	−	0.237118i	0.672535	+	0.740065i	$0.265205\pi$
$224$	12.4563	−	21.5749i	0.0556084	−	0.0963165i
$225$	4.78451	−	2.76234i	0.0212645	−	0.0122771i
$226$	−36.2266	−	36.2266i	−0.160295	−	0.160295i
$227$	−28.7917	+	107.452i	−0.126836	+	0.473358i	−0.999898	−	0.0142503i	$-0.995464\pi$
$227$	−28.7917	+	107.452i	−0.126836	+	0.473358i	0.873063	+	0.487608i	$0.162130\pi$
$228$	154.980	+	41.5268i	0.679738	+	0.182135i
$229$	212.309	−	212.309i	0.927114	−	0.927114i	−0.0704045	−	0.997519i	$-0.522429\pi$
$229$	212.309	−	212.309i	0.927114	−	0.927114i	0.997519	+	0.0704045i	$0.0224290\pi$
$230$	−30.1277	−	52.1826i	−0.130990	−	0.226881i
$231$	166.758	+	96.2780i	0.721898	+	0.416788i
$232$	−16.2679	−	60.7126i	−0.0701202	−	0.261692i
$233$			46.5826i			0.199925i	0.994991	+	0.0999627i	$0.0318723\pi$
$233$			46.5826i			0.199925i	−0.994991	+	0.0999627i	$0.968128\pi$
$234$		0			0
$235$	73.3746			0.312233
$236$	72.9685	−	19.5518i	0.309188	−	0.0828468i
$237$	29.1127	−	50.4247i	0.122839	−	0.212763i
$238$	130.764	−	75.4966i	0.549429	−	0.317213i
$239$	−138.309	−	138.309i	−0.578698	−	0.578698i	0.355847	−	0.934544i	$-0.384192\pi$
$239$	−138.309	−	138.309i	−0.578698	−	0.578698i	−0.934544	+	0.355847i	$0.884192\pi$
$240$	21.3533	−	79.6916i	0.0889721	−	0.332048i
$241$	−217.195	−	58.1972i	−0.901223	−	0.241482i	−0.221682	−	0.975119i	$-0.571155\pi$
$241$	−217.195	−	58.1972i	−0.901223	−	0.241482i	−0.679541	+	0.733637i	$0.737821\pi$
$242$	−85.3603	+	85.3603i	−0.352728	+	0.352728i
$243$	7.12754	+	12.3453i	0.0293314	+	0.0508035i
$244$	39.9614	+	23.0717i	0.163776	+	0.0945563i
$245$	51.9244	+	193.784i	0.211936	+	0.790957i
$246$			314.068i			1.27670i
$247$		0			0
$248$	34.3807			0.138632
$249$	144.574	−	38.7384i	0.580618	−	0.155576i
$250$	−19.5432	+	33.8498i	−0.0781728	+	0.135399i
$251$	−3.02255	+	1.74507i	−0.0120420	+	0.00695247i	−0.506009	−	0.862528i	$-0.668880\pi$
$251$	−3.02255	+	1.74507i	−0.0120420	+	0.00695247i	0.493967	+	0.869481i	$0.335546\pi$
$252$	−1.64465	−	1.64465i	−0.00652638	−	0.00652638i
$253$	23.3766	−	87.2427i	0.0923977	−	0.344833i
$254$	181.798	+	48.7125i	0.715738	+	0.191781i
$255$	353.584	−	353.584i	1.38661	−	1.38661i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	160.572	+	92.7065i	0.624795	+	0.360726i	0.778734	−	0.627355i	$-0.215862\pi$
$257$	160.572	+	92.7065i	0.624795	+	0.360726i	−0.153938	+	0.988080i	$0.549196\pi$
$258$	−34.6940	−	129.480i	−0.134473	−	0.501859i
$259$		−	27.9913i		−	0.108074i
$260$		0			0
$261$	−5.86820			−0.0224835
$262$	52.2831	−	14.0092i	0.199554	−	0.0534703i
$263$	93.6758	−	162.251i	0.356182	−	0.616925i	−0.631138	−	0.775671i	$-0.717412\pi$
$263$	93.6758	−	162.251i	0.356182	−	0.616925i	0.987319	+	0.158746i	$0.0507451\pi$
$264$	107.100	−	61.8342i	0.405682	−	0.234221i
$265$	161.776	+	161.776i	0.610477	+	0.610477i
$266$	42.4870	−	158.564i	0.159726	−	0.596104i
$267$	−10.5674	−	2.83152i	−0.0395782	−	0.0106050i
$268$	−152.199	+	152.199i	−0.567907	+	0.567907i
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	−0.985559	−	0.169334i	$-0.945838\pi$
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	0.346132	−	0.938186i	$-0.387495\pi$
$270$	220.680	+	127.410i	0.817335	+	0.471888i
$271$	6.27795	+	23.4296i	0.0231659	+	0.0864562i	0.976541	−	0.215332i	$-0.0690832\pi$
$271$	6.27795	+	23.4296i	0.0231659	+	0.0864562i	−0.953375	+	0.301788i	$0.902417\pi$
$272$		−	96.9749i		−	0.356525i
$273$		0			0
$274$	11.3635			0.0414725
$275$	290.301	−	77.7860i	1.05564	−	0.282858i
$276$	−19.1370	+	33.1462i	−0.0693369	+	0.120095i
$277$	428.588	−	247.446i	1.54725	−	0.893306i	0.548901	−	0.835888i	$-0.315047\pi$
$277$	428.588	−	247.446i	1.54725	−	0.893306i	0.998350	−	0.0574180i	$-0.0182868\pi$
$278$	243.961	+	243.961i	0.877558	+	0.877558i
$279$	0.830770	−	3.10048i	0.00297767	−	0.0111128i
$280$	−81.5342	−	21.8470i	−0.291194	−	0.0780251i
$281$	−145.653	+	145.653i	−0.518337	+	0.518337i	−0.917068	−	0.398731i	$-0.869451\pi$
$281$	−145.653	+	145.653i	−0.518337	+	0.518337i	0.398731	+	0.917068i	$0.369451\pi$
$282$	−23.3036	−	40.3631i	−0.0826370	−	0.143132i
$283$	−372.577	−	215.107i	−1.31653	−	0.760096i	−0.333357	−	0.942801i	$-0.608182\pi$
$283$	−372.577	−	215.107i	−1.31653	−	0.760096i	−0.983168	+	0.182704i	$0.941515\pi$
$284$	−1.18359	−	4.41723i	−0.00416758	−	0.0155536i
$285$		−	543.639i		−	1.90750i
$286$		0			0
$287$	321.330			1.11962
$288$	−1.44289	+	0.386621i	−0.00501004	+	0.00134244i
$289$	149.379	−	258.732i	0.516883	−	0.895267i
$290$	−184.435	+	106.484i	−0.635983	+	0.367185i
$291$	−54.1677	−	54.1677i	−0.186143	−	0.186143i
$292$	−27.9477	+	104.302i	−0.0957114	+	0.357200i
$293$	91.6460	+	24.5565i	0.312785	+	0.0838105i	0.411797	−	0.911276i	$-0.364901\pi$
$293$	91.6460	+	24.5565i	0.312785	+	0.0838105i	−0.0990115	+	0.995086i	$0.531568\pi$
$294$	90.1090	−	90.1090i	0.306493	−	0.306493i
$295$	−127.979	−	221.667i	−0.433828	−	0.751412i
$296$	−15.5688	−	8.98865i	−0.0525973	−	0.0303671i
$297$	98.8597	+	368.950i	0.332861	+	1.24225i
$298$		−	267.473i		−	0.897559i
$299$		0			0
$300$	−127.357			−0.424524
$301$	−132.474	+	35.4962i	−0.440111	+	0.117927i
$302$	70.5995	−	122.282i	0.233773	−	0.404907i
$303$	−400.164	+	231.035i	−1.32067	+	0.762490i
$304$	−74.5498	−	74.5498i	−0.245230	−	0.245230i
$305$	40.4655	−	151.019i	0.132674	−	0.495145i
$306$	−8.74526	−	2.34329i	−0.0285793	−	0.00765780i
$307$	−210.306	+	210.306i	−0.685035	+	0.685035i	−0.961130	−	0.276095i	$-0.910959\pi$
$307$	−210.306	+	210.306i	−0.685035	+	0.685035i	0.276095	+	0.961130i	$0.410959\pi$
$308$	−63.2639	−	109.576i	−0.205402	−	0.355767i
$309$	45.7785	+	26.4302i	0.148151	+	0.0855347i
$310$	−30.1501	−	112.522i	−0.0972585	−	0.362974i
$311$			246.623i			0.793001i	0.918035	+	0.396500i	$0.129775\pi$
$311$			246.623i			0.793001i	−0.918035	+	0.396500i	$0.870225\pi$
$312$		0			0
$313$	−118.526			−0.378679			−0.189339	−	0.981912i	$-0.560635\pi$
$313$	−118.526			−0.378679			−0.189339	+	0.981912i	$0.560635\pi$
$314$	241.505	−	64.7111i	0.769125	−	0.206086i
$315$	−3.94036	+	6.82490i	−0.0125091	+	0.0216664i
$316$	−33.1339	+	19.1299i	−0.104854	+	0.0605376i
$317$	284.814	+	284.814i	0.898466	+	0.898466i	0.995300	−	0.0968348i	$-0.0308718\pi$
$317$	284.814	+	284.814i	0.898466	+	0.898466i	−0.0968348	+	0.995300i	$0.530872\pi$
$318$	37.6127	−	140.372i	0.118279	−	0.441423i
$319$	−308.352	−	82.6227i	−0.966621	−	0.259005i
$320$	−38.3339	+	38.3339i	−0.119793	+	0.119793i
$321$	−80.9512	−	140.212i	−0.252184	−	0.436796i
$322$	33.9126	+	19.5795i	0.105319	+	0.0608058i
$323$	−165.385	−	617.227i	−0.512029	−	1.91092i
$324$		−	166.614i		−	0.514240i
$325$		0			0
$326$	171.470			0.525981
$327$	221.933	−	59.4666i	0.678693	−	0.181855i
$328$	103.187	−	178.724i	0.314593	−	0.544892i
$329$	−41.2964	+	23.8425i	−0.125521	+	0.0724695i
$330$	−296.293	−	296.293i	−0.897858	−	0.897858i
$331$	−116.054	+	433.118i	−0.350615	+	1.30851i	0.535299	+	0.844663i	$0.320199\pi$
$331$	−116.054	+	433.118i	−0.350615	+	1.30851i	−0.885914	+	0.463850i	$0.846468\pi$
$332$	−94.9990	−	25.4549i	−0.286141	−	0.0766714i
$333$	−1.18680	+	1.18680i	−0.00356398	+	0.00356398i
$334$	209.805	+	363.392i	0.628158	+	1.08800i
$335$	631.591	+	364.649i	1.88535	+	1.08850i
$336$	13.8772	+	51.7902i	0.0413010	+	0.154138i
$337$			474.455i			1.40788i	0.710260	+	0.703939i	$0.248577\pi$
$337$			474.455i			1.40788i	−0.710260	+	0.703939i	$0.751423\pi$
$338$		0			0
$339$	110.263			0.325259
$340$	−317.381	+	85.0420i	−0.933474	+	0.250124i
$341$	87.3078	−	151.222i	0.256035	−	0.443465i
$342$	−8.52436	+	4.92154i	−0.0249250	+	0.0143905i
$343$	−244.782	−	244.782i	−0.713650	−	0.713650i
$344$	−22.7973	+	85.0807i	−0.0662712	+	0.247328i
$345$	125.264	+	33.5643i	0.363083	+	0.0972878i
$346$	278.490	−	278.490i	0.804884	−	0.804884i
$347$	266.818	+	462.142i	0.768927	+	1.33182i	0.938145	+	0.346242i	$0.112543\pi$
$347$	266.818	+	462.142i	0.768927	+	1.33182i	−0.169218	+	0.985579i	$0.554124\pi$
$348$	117.152	+	67.6380i	0.336645	+	0.194362i
$349$	69.9275	+	260.973i	0.200365	+	0.747774i	0.990812	+	0.135244i	$0.0431817\pi$
$349$	69.9275	+	260.973i	0.200365	+	0.747774i	−0.790447	+	0.612531i	$0.790152\pi$
$350$			130.302i			0.372291i
$351$		0			0
$352$	−81.2621			−0.230858
$353$	−340.955	+	91.3587i	−0.965879	+	0.258806i	−0.707087	−	0.707127i	$-0.749991\pi$
$353$	−340.955	+	91.3587i	−0.965879	+	0.258806i	−0.258792	+	0.965933i	$0.583324\pi$
$354$	−81.2919	+	140.802i	−0.229638	+	0.397745i
$355$	−13.4188	+	7.74736i	−0.0377995	+	0.0218236i
$356$	5.08321	+	5.08321i	0.0142787	+	0.0142787i
$357$	−84.1085	+	313.897i	−0.235598	+	0.879263i
$358$	−107.581	−	28.8262i	−0.300505	−	0.0805202i
$359$	−116.092	+	116.092i	−0.323375	+	0.323375i	−0.850060	−	0.526685i	$-0.823435\pi$
$359$	−116.092	+	116.092i	−0.323375	+	0.323375i	0.526685	+	0.850060i	$0.323435\pi$
$360$	2.53068	+	4.38327i	0.00702967	+	0.0121758i
$361$	−289.001	−	166.855i	−0.800556	−	0.462201i
$362$	73.4826	+	274.241i	0.202991	+	0.757572i
$363$		−	259.810i		−	0.715731i
$364$		0			0
$365$	365.871			1.00239
$366$	−95.9268	+	25.7035i	−0.262095	+	0.0702282i
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.160497	+	0.987036i	$0.551310\pi$
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.774550	+	0.632513i	$0.782024\pi$
$368$	21.7803	−	12.5748i	0.0591855	−	0.0341708i
$369$	−13.6241	−	13.6241i	−0.0369217	−	0.0369217i
$370$	−15.7652	+	58.8364i	−0.0426086	+	0.159017i
$371$	−143.618	−	38.4824i	−0.387111	−	0.103726i
$372$	−52.3222	+	52.3222i	−0.140651	+	0.140651i
$373$	308.636	+	534.572i	0.827441	+	1.43317i	0.900039	+	0.435809i	$0.143538\pi$
$373$	308.636	+	534.572i	0.827441	+	1.43317i	−0.0725981	+	0.997361i	$0.523129\pi$
$374$	−426.538	−	246.262i	−1.14048	−	0.658455i
$375$	−21.7725	−	81.2560i	−0.0580599	−	0.216683i
$376$			30.6255i			0.0814508i
$377$		0			0
$378$	−165.603			−0.438103
$379$	−518.382	+	138.900i	−1.36776	+	0.366491i	−0.866661	−	0.498898i	$-0.833738\pi$
$379$	−518.382	+	138.900i	−1.36776	+	0.366491i	−0.501101	+	0.865389i	$0.667072\pi$
$380$	−178.612	+	309.364i	−0.470030	+	0.814116i
$381$	−350.801	+	202.535i	−0.920737	+	0.531588i
$382$	−40.5301	−	40.5301i	−0.106100	−	0.106100i
$383$	−67.8074	+	253.061i	−0.177043	+	0.660732i	0.819152	+	0.573577i	$0.194444\pi$
$383$	−67.8074	+	253.061i	−0.177043	+	0.660732i	−0.996195	+	0.0871559i	$0.972222\pi$
$384$	33.2621	+	8.91255i	0.0866200	+	0.0232098i
$385$	−303.144	+	303.144i	−0.787387	+	0.787387i
$386$	−102.596	−	177.702i	−0.265794	−	0.460369i
$387$	7.12176	+	4.11175i	0.0184025	+	0.0106247i
$388$	13.0281	+	48.6215i	0.0335775	+	0.125313i
$389$		−	184.591i		−	0.474527i	−0.971445	−	0.237264i	$-0.923749\pi$
$389$		−	184.591i		−	0.474527i	0.971445	−	0.237264i	$-0.0762505\pi$
$390$		0			0
$391$	152.431			0.389848
$392$	−80.8828	+	21.6725i	−0.206334	+	0.0552869i
$393$	−58.2469	+	100.887i	−0.148211	+	0.256709i
$394$	−189.628	+	109.482i	−0.481289	+	0.277872i
$395$	91.6653	+	91.6653i	0.232064	+	0.232064i
$396$	−1.96360	+	7.32827i	−0.00495860	+	0.0185057i
$397$	245.213	+	65.7046i	0.617664	+	0.165503i	0.554066	−	0.832473i	$-0.313076\pi$
$397$	245.213	+	65.7046i	0.617664	+	0.165503i	0.0635986	+	0.997976i	$0.479742\pi$
$398$	260.350	−	260.350i	0.654147	−	0.654147i
$399$	176.651	+	305.968i	0.442734	+	0.766838i
$400$	72.4741	+	41.8430i	0.181185	+	0.104607i
$401$	−70.1504	−	261.805i	−0.174939	−	0.652880i	−0.996562	−	0.0828492i	$-0.973598\pi$
$401$	−70.1504	−	261.805i	−0.174939	−	0.652880i	0.821623	−	0.570031i	$-0.193069\pi$
$402$		−	463.248i		−	1.15236i
$403$		0			0
$404$	303.624			0.751545
$405$	−545.296	+	146.112i	−1.34641	+	0.360770i
$406$	69.2019	−	119.861i	0.170448	−	0.295225i
$407$	−79.0721	+	45.6523i	−0.194280	+	0.112168i
$408$	147.581	+	147.581i	0.361718	+	0.361718i
$409$	40.8612	−	152.496i	0.0999051	−	0.372851i	−0.897812	−	0.440378i	$-0.854844\pi$
$409$	40.8612	−	152.496i	0.0999051	−	0.372851i	0.997717	+	0.0675274i	$0.0215110\pi$
$410$	−675.422	−	180.979i	−1.64737	−	0.441411i
$411$	−17.2935	+	17.2935i	−0.0420766	+	0.0420766i
$412$	−17.3672	−	30.0809i	−0.0421534	−	0.0730119i
$413$	144.057	+	83.1715i	0.348807	+	0.201384i
$414$	−0.607713	−	2.26802i	−0.00146791	−	0.00547830i
$415$			333.237i			0.802980i
$416$		0			0
$417$	−742.543			−1.78068
$418$	−517.218	+	138.588i	−1.23736	+	0.331550i
$419$	326.238	−	565.061i	0.778611	−	1.34859i	−0.154132	−	0.988050i	$-0.549258\pi$
$419$	326.238	−	565.061i	0.778611	−	1.34859i	0.932743	−	0.360543i	$-0.117409\pi$
$420$	157.330	−	90.8347i	0.374596	−	0.216273i
$421$	−294.576	−	294.576i	−0.699704	−	0.699704i	0.264642	−	0.964347i	$-0.414746\pi$
$421$	−294.576	−	294.576i	−0.699704	−	0.699704i	−0.964347	+	0.264642i	$0.914746\pi$
$422$	−152.415	+	568.821i	−0.361173	+	1.34792i
$423$	2.76183	+	0.740029i	0.00652914	+	0.00174948i
$424$	−67.5231	+	67.5231i	−0.159253	+	0.159253i
$425$	253.607	+	439.261i	0.596723	+	1.03355i
$426$	8.52359	+	4.92110i	0.0200084	+	0.0115519i
$427$	26.2978	+	98.1448i	0.0615874	+	0.229847i
$428$			106.385i			0.248564i
$429$		0			0
$430$	298.445			0.694059
$431$	68.2190	−	18.2792i	0.158281	−	0.0424112i	−0.178808	−	0.983884i	$-0.557224\pi$
$431$	68.2190	−	18.2792i	0.158281	−	0.0424112i	0.337089	+	0.941473i	$0.390558\pi$
$432$	−53.1790	+	92.1087i	−0.123100	+	0.213215i
$433$	−404.363	+	233.459i	−0.933864	+	0.539167i	−0.888032	−	0.459782i	$-0.847927\pi$
$433$	−404.363	+	233.459i	−0.933864	+	0.539167i	−0.0458326	+	0.998949i	$0.514594\pi$
$434$	53.5320	+	53.5320i	0.123346	+	0.123346i
$435$	118.630	−	442.734i	0.272713	−	1.01778i
$436$	−145.831	−	39.0753i	−0.334475	−	0.0896223i
$437$	117.182	−	117.182i	0.268150	−	0.268150i
$438$	−116.200	−	201.264i	−0.265297	−	0.459508i
$439$	−103.577	−	59.8002i	−0.235938	−	0.136219i	0.377370	−	0.926063i	$-0.376828\pi$
$439$	−103.577	−	59.8002i	−0.235938	−	0.136219i	−0.613309	+	0.789843i	$0.710162\pi$
$440$	71.2627	+	265.956i	0.161961	+	0.604445i
$441$			7.81775i			0.0177273i
$442$		0			0
$443$	−56.7213			−0.128039			−0.0640195	−	0.997949i	$-0.520392\pi$
$443$	−56.7213			−0.128039			−0.0640195	+	0.997949i	$0.520392\pi$
$444$	37.3727	−	10.0140i	0.0841727	−	0.0225540i
$445$	12.1787	−	21.0941i	0.0273679	−	0.0474025i
$446$	250.218	−	144.463i	0.561026	−	0.323909i
$447$	407.052	+	407.052i	0.910631	+	0.910631i
$448$	9.11863	−	34.0312i	0.0203541	−	0.0759625i
$449$	178.504	+	47.8299i	0.397558	+	0.106525i	0.452058	−	0.891988i	$-0.350690\pi$
$449$	178.504	+	47.8299i	0.397558	+	0.106525i	−0.0545000	+	0.998514i	$0.517357\pi$
$450$	5.52468	−	5.52468i	0.0122771	−	0.0122771i
$451$	−524.072	−	907.720i	−1.16202	−	2.01268i
$452$	−62.7464	−	36.2266i	−0.138819	−	0.0801474i
$453$	78.6527	+	293.536i	0.173626	+	0.647982i
$454$			157.321i			0.346522i
$455$		0			0
$456$	226.907			0.497603
$457$	286.031	−	76.6418i	0.625889	−	0.167706i	0.0680852	−	0.997680i	$-0.478311\pi$
$457$	286.031	−	76.6418i	0.625889	−	0.167706i	0.557803	+	0.829973i	$0.311644\pi$
$458$	212.309	−	367.730i	0.463557	−	0.802904i
$459$	−558.265	+	322.314i	−1.21626	+	0.702210i
$460$	−60.2553	−	60.2553i	−0.130990	−	0.130990i
$461$	159.753	−	596.206i	0.346535	−	1.29329i	−0.544273	−	0.838908i	$-0.683194\pi$
$461$	159.753	−	596.206i	0.346535	−	1.29329i	0.890808	−	0.454379i	$-0.150139\pi$
$462$	263.036	+	70.4804i	0.569343	+	0.152555i
$463$	−198.699	+	198.699i	−0.429156	+	0.429156i	−0.888341	−	0.459185i	$-0.848142\pi$
$463$	−198.699	+	198.699i	−0.429156	+	0.429156i	0.459185	+	0.888341i	$0.348142\pi$
$464$	−44.4447	−	76.9805i	−0.0957860	−	0.165906i
$465$	217.125	+	125.357i	0.466935	+	0.269585i
$466$	17.0504	+	63.6330i	0.0365889	+	0.136552i
$467$		−	522.015i		−	1.11781i	−0.829233	−	0.558903i	$-0.811223\pi$
$467$		−	522.015i		−	1.11781i	0.829233	−	0.558903i	$-0.188777\pi$
$468$		0			0
$469$	−473.959			−1.01057
$470$	100.232	−	26.8570i	0.213259	−	0.0571425i
$471$	−269.053	+	466.014i	−0.571239	+	0.989414i
$472$	92.5203	−	53.4166i	0.196018	−	0.113171i
$473$	316.330	+	316.330i	0.668773	+	0.668773i
$474$	21.3120	−	79.5374i	0.0449620	−	0.167801i
$475$	532.645	+	142.722i	1.12136	+	0.300467i
$476$	150.993	−	150.993i	0.317213	−	0.317213i
$477$	4.45766	+	7.72090i	0.00934520	+	0.0161864i
$478$	−239.558	−	138.309i	−0.501167	−	0.289349i
$479$	87.8794	+	327.970i	0.183464	+	0.684698i	0.994954	+	0.100331i	$0.0319903\pi$
$479$	87.8794	+	327.970i	0.183464	+	0.684698i	−0.811490	+	0.584367i	$0.801343\pi$
$480$		−	116.677i		−	0.243076i
$481$		0			0
$482$	−317.995			−0.659741
$483$	−81.4067	+	21.8129i	−0.168544	+	0.0451612i
$484$	−85.3603	+	147.848i	−0.176364	+	0.305472i
$485$	147.704	−	85.2771i	0.304545	−	0.175829i
$486$	14.2551	+	14.2551i	0.0293314	+	0.0293314i
$487$	55.8489	−	208.431i	0.114679	−	0.427990i	−0.884583	−	0.466382i	$-0.845557\pi$
$487$	55.8489	−	208.431i	0.114679	−	0.427990i	0.999263	+	0.0383927i	$0.0122238\pi$
$488$	63.0332	+	16.8897i	0.129166	+	0.0346100i
$489$	−260.951	+	260.951i	−0.533642	+	0.533642i
$490$	141.860	+	245.709i	0.289510	+	0.501447i
$491$	480.847	+	277.617i	0.979322	+	0.565412i	0.902065	−	0.431600i	$-0.142051\pi$
$491$	480.847	+	277.617i	0.979322	+	0.565412i	0.0772564	+	0.997011i	$0.475384\pi$
$492$	114.957	+	429.025i	0.233652	+	0.872003i
$493$		−	538.753i		−	1.09280i
$494$		0			0
$495$	25.7061			0.0519315
$496$	46.9649	−	12.5842i	0.0946874	−	0.0253714i
$497$	5.03488	−	8.72067i	0.0101305	−	0.0175466i
$498$	183.312	−	105.835i	0.368097	−	0.212521i
$499$	401.619	+	401.619i	0.804847	+	0.804847i	0.983849	−	0.179002i	$-0.0572868\pi$
$499$	401.619	+	401.619i	0.804847	+	0.804847i	−0.179002	+	0.983849i	$0.557287\pi$
$500$	−14.3066	+	53.3930i	−0.0286132	+	0.106786i
$501$	−872.318	−	233.737i	−1.74115	−	0.466541i
$502$	−3.49014	+	3.49014i	−0.00695247	+	0.00695247i
$503$	196.833	+	340.925i	0.391319	+	0.677784i	0.992624	−	0.121236i	$-0.0386857\pi$
$503$	196.833	+	340.925i	0.391319	+	0.677784i	−0.601305	+	0.799020i	$0.705352\pi$
$504$	−2.84861	−	1.64465i	−0.00565201	−	0.00326319i
$505$	−266.263	−	993.706i	−0.527253	−	1.96773i
$506$		−	127.732i		−	0.252435i
$507$		0			0
$508$	266.170			0.523957
$509$	422.083	−	113.097i	0.829239	−	0.222194i	0.180858	−	0.983509i	$-0.442113\pi$
$509$	422.083	−	113.097i	0.829239	−	0.222194i	0.648382	+	0.761315i	$0.275446\pi$
$510$	353.584	−	612.426i	0.693303	−	1.20084i
$511$	−205.918	+	118.887i	−0.402971	+	0.232655i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−181.388	+	676.948i	−0.353582	+	1.31959i
$514$	253.279	+	67.8659i	0.492761	+	0.132035i
$515$	−83.2191	+	83.2191i	−0.161591	+	0.161591i
$516$	−94.7857	−	164.174i	−0.183693	−	0.318166i
$517$	134.704	+	77.7716i	0.260550	+	0.150429i
$518$	−10.2455	−	38.2368i	−0.0197790	−	0.0738162i
$519$			847.638i			1.63321i
$520$		0			0
$521$	947.876			1.81934			0.909669	−	0.415333i	$-0.136335\pi$
$521$	947.876			1.81934			0.909669	+	0.415333i	$0.136335\pi$
$522$	−8.01611	+	2.14791i	−0.0153565	+	0.00411477i
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	−0.793258	−	0.608886i	$-0.791617\pi$
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	0.923940	+	0.382538i	$0.124950\pi$
$524$	66.2923	−	38.2739i	0.126512	−	0.0730417i
$525$	−198.299	−	198.299i	−0.377713	−	0.377713i
$526$	68.5754	−	255.927i	0.130372	−	0.486553i
$527$	284.651	+	76.2721i	0.540135	+	0.144729i
$528$	123.668	−	123.668i	0.234221	−	0.234221i
$529$	−244.734	−	423.892i	−0.462635	−	0.801308i
$530$	280.205	+	161.776i	0.528689	+	0.305239i
$531$	−2.58150	−	9.63430i	−0.00486159	−	0.0181437i
$532$		−	232.153i		−	0.436378i
$533$		0			0
$534$	−15.4717			−0.0289733
$535$	348.180	−	93.2946i	0.650804	−	0.174382i
$536$	−152.199	+	263.617i	−0.283954	+	0.491822i
$537$	207.591	−	119.853i	0.386575	−	0.223189i
$538$	−344.012	−	344.012i	−0.639427	−	0.639427i
$539$	−110.072	+	410.794i	−0.204215	+	0.762141i
$540$	348.090	+	93.2705i	0.644612	+	0.172723i
$541$	394.763	−	394.763i	0.729691	−	0.729691i	−0.240867	−	0.970558i	$-0.577432\pi$
$541$	394.763	−	394.763i	0.729691	−	0.729691i	0.970558	+	0.240867i	$0.0774318\pi$
$542$	17.1517	+	29.7076i	0.0316452	+	0.0548110i
$543$	−529.182	−	305.523i	−0.974552	−	0.562658i
$544$	−35.4953	−	132.470i	−0.0652487	−	0.243511i
$545$			511.545i			0.938616i
$546$		0			0
$547$	−716.303			−1.30951			−0.654756	−	0.755840i	$-0.727229\pi$
$547$	−716.303			−1.30951			−0.654756	+	0.755840i	$0.727229\pi$
$548$	15.5228	−	4.15932i	0.0283263	−	0.00759000i
$549$	3.04625	−	5.27625i	0.00554872	−	0.00961066i
$550$	368.087	−	212.515i	0.669250	−	0.386392i
$551$	−414.168	−	414.168i	−0.751666	−	0.751666i
$552$	−14.0092	+	52.2832i	−0.0253791	+	0.0947159i
$553$	−81.3765	−	21.8048i	−0.147155	−	0.0394300i
$554$	494.891	−	494.891i	0.893306	−	0.893306i
$555$	−65.5478	−	113.532i	−0.118104	−	0.204562i
$556$	422.553	+	243.961i	0.759988	+	0.438779i
$557$	−15.6018	−	58.2268i	−0.0280104	−	0.104536i	0.950505	−	0.310708i	$-0.100566\pi$
$557$	−15.6018	−	58.2268i	−0.0280104	−	0.104536i	−0.978516	+	0.206172i	$0.933899\pi$
$558$		−	4.53941i		−	0.00813515i
$559$		0			0
$560$	−119.374			−0.213169
$561$	1023.90	−	274.353i	1.82513	−	0.489043i
$562$	−145.653	+	252.278i	−0.259168	+	0.448893i
$563$	233.194	−	134.635i	0.414199	−	0.239138i	−0.278393	−	0.960467i	$-0.589802\pi$
$563$	233.194	−	134.635i	0.414199	−	0.239138i	0.692592	+	0.721329i	$0.256469\pi$
$564$	−46.6073	−	46.6073i	−0.0826370	−	0.0826370i
$565$	−63.5378	+	237.126i	−0.112456	+	0.419693i
$566$	−587.684	−	157.469i	−1.03831	−	0.278215i
$567$	259.423	−	259.423i	0.457537	−	0.457537i
$568$	−3.23364	−	5.60082i	−0.00569302	−	0.00986060i
$569$	−232.943	−	134.490i	−0.409390	−	0.236361i	0.281138	−	0.959667i	$-0.409288\pi$
$569$	−232.943	−	134.490i	−0.409390	−	0.236361i	−0.690528	+	0.723306i	$0.742622\pi$
$570$	−198.986	−	742.624i	−0.349097	−	1.30285i
$571$			328.719i			0.575689i	0.957677	+	0.287845i	$0.0929387\pi$
$571$			328.719i			0.575689i	−0.957677	+	0.287845i	$0.907061\pi$
$572$		0			0
$573$	123.361			0.215290
$574$	438.945	−	117.615i	0.764713	−	0.204904i
$575$	−65.7711	+	113.919i	−0.114384	+	0.198120i
$576$	−1.82951	+	1.05627i	−0.00317624	+	0.00183380i
$577$	18.1490	+	18.1490i	0.0314540	+	0.0314540i	0.722659	−	0.691205i	$-0.242920\pi$
$577$	18.1490	+	18.1490i	0.0314540	+	0.0314540i	−0.691205	+	0.722659i	$0.742920\pi$
$578$	109.353	−	408.111i	0.189192	−	0.706075i
$579$	426.572	+	114.300i	0.736739	+	0.197409i
$580$	−212.967	+	212.967i	−0.367185	+	0.367185i
$581$	−108.283	−	187.551i	−0.186373	−	0.322807i
$582$	−93.8212	−	54.1677i	−0.161205	−	0.0930716i
$583$	125.525	+	468.467i	0.215309	+	0.803546i
$584$			152.709i			0.261488i
$585$		0			0
$586$	134.179			0.228975
$587$	−112.495	+	30.1430i	−0.191644	+	0.0513509i	−0.353364	−	0.935486i	$-0.614962\pi$
$587$	−112.495	+	30.1430i	−0.191644	+	0.0513509i	0.161720	+	0.986837i	$0.448296\pi$
$588$	90.1090	−	156.073i	0.153247	−	0.265431i
$589$	277.461	−	160.192i	0.471072	−	0.271973i
$590$	−255.958	−	255.958i	−0.433828	−	0.433828i
$591$	121.970	−	455.199i	0.206379	−	0.770218i
$592$	−24.5574	−	6.58015i	−0.0414822	−	0.0111151i
$593$	−215.404	+	215.404i	−0.363244	+	0.363244i	−0.865006	−	0.501762i	$-0.832685\pi$
$593$	−215.404	+	215.404i	−0.363244	+	0.363244i	0.501762	+	0.865006i	$0.332685\pi$
$594$	270.090	+	467.809i	0.454697	+	0.787558i
$595$	−626.587	−	361.760i	−1.05309	−	0.608000i
$596$	−97.9017	−	365.374i	−0.164265	−	0.613044i
$597$			792.427i			1.32735i
$598$		0			0
$599$	−657.704			−1.09800			−0.549002	−	0.835821i	$-0.684992\pi$
$599$	−657.704			−1.09800			−0.549002	+	0.835821i	$0.684992\pi$
$600$	−173.973	+	46.6159i	−0.289955	+	0.0776932i
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	−0.963211	−	0.268747i	$-0.913390\pi$
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	0.714347	+	0.699791i	$0.246724\pi$
$602$	−167.970	+	96.9774i	−0.279019	+	0.161092i
$603$	20.0954	+	20.0954i	0.0333257	+	0.0333257i
$604$	51.6824	−	192.881i	0.0855669	−	0.319340i
$605$	558.737	+	149.713i	0.923532	+	0.247460i
$606$	−462.069	+	462.069i	−0.762490	+	0.762490i
$607$	355.980	+	616.576i	0.586459	+	1.01578i	0.994692	+	0.102898i	$0.0328116\pi$
$607$	355.980	+	616.576i	0.586459	+	1.01578i	−0.408233	+	0.912878i	$0.633855\pi$
$608$	−129.124	−	74.5498i	−0.212375	−	0.122615i
$609$	77.0957	+	287.725i	0.126594	+	0.472455i
$610$		−	221.107i		−	0.362471i
$611$		0			0
$612$	−12.8040			−0.0209215
$613$	705.887	−	189.142i	1.15153	−	0.308551i	0.367951	−	0.929845i	$-0.380059\pi$
$613$	705.887	−	189.142i	1.15153	−	0.308551i	0.783578	+	0.621294i	$0.213393\pi$
$614$	−210.306	+	364.260i	−0.342517	+	0.593257i
$615$	1303.31	−	752.466i	2.11920	−	1.22352i
$616$	−126.528	−	126.528i	−0.205402	−	0.205402i
$617$	90.7668	−	338.746i	0.147110	−	0.549021i	−0.852543	−	0.522658i	$-0.824941\pi$
$617$	90.7668	−	338.746i	0.147110	−	0.549021i	0.999652	−	0.0263636i	$-0.00839276\pi$
$618$	72.2087	+	19.3483i	0.116843	+	0.0313079i
$619$	−283.795	+	283.795i	−0.458474	+	0.458474i	−0.898154	−	0.439680i	$-0.855092\pi$
$619$	−283.795	+	283.795i	−0.458474	+	0.458474i	0.439680	+	0.898154i	$0.355092\pi$
$620$	−82.3717	−	142.672i	−0.132858	−	0.230116i
$621$	−144.782	−	83.5897i	−0.233143	−	0.134605i
$622$	90.2704	+	336.894i	0.145129	+	0.541630i
$623$			15.8295i			0.0254084i
$624$		0			0
$625$	710.329			1.13653
$626$	−161.910	+	43.3837i	−0.258642	+	0.0693030i
$627$	576.216	−	998.036i	0.919005	−	1.59176i
$628$	306.216	−	176.794i	0.487606	−	0.281519i
$629$	−108.959	−	108.959i	−0.173226	−	0.173226i
$630$	−2.88454	+	10.7653i	−0.00457864	+	0.0170877i
$631$	−1115.36	−	298.859i	−1.76760	−	0.473627i	−0.779365	−	0.626570i	$-0.784458\pi$
$631$	−1115.36	−	298.859i	−1.76760	−	0.473627i	−0.988235	+	0.152944i	$0.951125\pi$
$632$	−38.2597	+	38.2597i	−0.0605376	+	0.0605376i
$633$	−633.706	−	1097.61i	−1.00112	−	1.73398i
$634$	493.312	+	284.814i	0.778094	+	0.449233i
$635$	−233.417	−	871.126i	−0.367587	−	1.37185i
$636$		−	205.520i		−	0.323144i
$637$		0			0
$638$	−451.459			−0.707615
$639$	−0.583223	+	0.156274i	−0.000912712	+	0.000244560i
$640$	−38.3339	+	66.3963i	−0.0598967	+	0.103744i
$641$	−225.174	+	130.005i	−0.351286	+	0.202815i	−0.665252	−	0.746619i	$-0.731676\pi$
$641$	−225.174	+	130.005i	−0.351286	+	0.202815i	0.313965	+	0.949434i	$0.398342\pi$
$642$	−161.902	−	161.902i	−0.252184	−	0.252184i
$643$	3.19272	−	11.9154i	0.00496535	−	0.0185309i	−0.963399	−	0.268073i	$-0.913613\pi$
$643$	3.19272	−	11.9154i	0.00496535	−	0.0185309i	0.968364	+	0.249542i	$0.0802800\pi$
$644$	53.4921	+	14.3332i	0.0830622	+	0.0222565i
$645$	−454.188	+	454.188i	−0.704168	+	0.704168i
$646$	−451.841	−	782.612i	−0.699445	−	1.21147i
$647$	−822.864	−	475.081i	−1.27182	−	0.734283i	−0.296486	−	0.955037i	$-0.595815\pi$
$647$	−822.864	−	475.081i	−1.27182	−	0.734283i	−0.975329	+	0.220755i	$0.929148\pi$
$648$	−60.9849	−	227.599i	−0.0941124	−	0.351232i
$649$		−	542.593i		−	0.836045i
$650$		0			0
$651$	−162.935			−0.250284
$652$	234.232	−	62.7624i	0.359252	−	0.0962613i
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	−0.997147	−	0.0754792i	$-0.975951\pi$
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	0.563941	+	0.825815i	$0.309285\pi$
$654$	281.399	−	162.466i	0.430274	−	0.248419i
$655$	−183.398	−	183.398i	−0.279997	−	0.279997i
$656$	75.5378	−	281.911i	0.115149	−	0.429742i
$657$	13.7714	+	3.69004i	0.0209611	+	0.00561650i
$658$	−47.6849	+	47.6849i	−0.0724695	+	0.0724695i
$659$	−190.174	−	329.390i	−0.288579	−	0.499833i	0.684892	−	0.728645i	$-0.259849\pi$
$659$	−190.174	−	329.390i	−0.288579	−	0.499833i	−0.973471	+	0.228811i	$0.926516\pi$
$660$	−513.195	−	296.293i	−0.777568	−	0.448929i
$661$	−257.291	−	960.224i	−0.389245	−	1.45268i	−0.831364	−	0.555728i	$-0.812440\pi$
$661$	−257.291	−	960.224i	−0.389245	−	1.45268i	0.442119	−	0.896956i	$-0.354227\pi$
$662$			634.128i			0.957898i
$663$		0			0
$664$	−139.088			−0.209470
$665$	−759.795	+	203.586i	−1.14255	+	0.306145i
$666$	−1.18680	+	2.05561i	−0.00178199	+	0.00308650i
$667$	121.002	−	69.8606i	0.181413	−	0.104739i
$668$	419.609	+	419.609i	0.628158	+	0.628158i
$669$	−160.942	+	600.644i	−0.240571	+	0.897823i
$670$	996.240	+	266.942i	1.48693	+	0.398420i
$671$	234.357	−	234.357i	0.349266	−	0.349266i
$672$	37.9131	+	65.6674i	0.0564183	+	0.0977193i
$673$	548.632	+	316.753i	0.815204	+	0.470658i	0.848760	−	0.528779i	$-0.177350\pi$
$673$	548.632	+	316.753i	0.815204	+	0.470658i	−0.0335560	+	0.999437i	$0.510683\pi$
$674$	173.663	+	648.117i	0.257660	+	0.961599i
$675$		−	556.292i		−	0.824136i
$676$		0			0
$677$	−221.745			−0.327540			−0.163770	−	0.986499i	$-0.552366\pi$
$677$	−221.745			−0.327540			−0.163770	+	0.986499i	$0.552366\pi$
$678$	150.622	−	40.3590i	0.222156	−	0.0595265i
$679$	−55.4201	+	95.9905i	−0.0816202	+	0.141370i
$680$	−402.423	+	232.339i	−0.591799	+	0.341675i
$681$	−239.418	−	239.418i	−0.351569	−	0.351569i
$682$	63.9137	−	238.529i	0.0937152	−	0.349750i
$683$	645.671	+	173.007i	0.945345	+	0.253304i	0.698386	−	0.715722i	$-0.253902\pi$
$683$	645.671	+	173.007i	0.945345	+	0.253304i	0.246959	+	0.969026i	$0.420569\pi$
$684$	−9.84309	+	9.84309i	−0.0143905	+	0.0143905i
$685$	−27.2254	−	47.1558i	−0.0397451	−	0.0688405i
$686$	−423.975	−	244.782i	−0.618039	−	0.356825i
$687$	236.527	+	882.731i	0.344290	+	1.28491i
$688$			124.567i			0.181056i
$689$		0			0
$690$	183.399			0.265795
$691$	−548.121	+	146.869i	−0.793229	+	0.212545i	−0.632609	−	0.774471i	$-0.718016\pi$
$691$	−548.121	+	146.869i	−0.793229	+	0.212545i	−0.160620	+	0.987016i	$0.551349\pi$
$692$	278.490	−	482.359i	0.402442	−	0.697050i
$693$	−14.4678	+	8.35297i	−0.0208770	+	0.0120534i
$694$	533.636	+	533.636i	0.768927	+	0.768927i
$695$	427.883	−	1596.88i	0.615659	−	2.29767i
$696$	184.790	+	49.5145i	0.265504	+	0.0711415i
$697$	1250.81	−	1250.81i	1.79457	−	1.79457i
$698$	191.046	+	330.901i	0.273704	+	0.474070i
$699$	−122.788	−	70.8916i	−0.175662	−	0.101419i
$700$	47.6938	+	177.996i	0.0681340	+	0.254280i
$701$			597.453i			0.852287i	0.904656	+	0.426143i	$0.140128\pi$
$701$			597.453i			0.852287i	−0.904656	+	0.426143i	$0.859872\pi$
$702$		0			0
$703$	−167.526			−0.238301
$704$	−111.006	+	29.7440i	−0.157679	+	0.0422500i
$705$	−111.665	+	193.409i	−0.158390	+	0.274339i
$706$	−432.314	+	249.596i	−0.612342	+	0.353536i
$707$	472.753	+	472.753i	0.668675	+	0.668675i
$708$	−59.5098	+	222.094i	−0.0840534	+	0.313692i
$709$	−38.3029	−	10.2632i	−0.0540239	−	0.0144757i	0.231706	−	0.972786i	$-0.425569\pi$
$709$	−38.3029	−	10.2632i	−0.0540239	−	0.0144757i	−0.285730	+	0.958310i	$0.592236\pi$
$710$	−15.4947	+	15.4947i	−0.0218236	+	0.0218236i
$711$	2.52579	+	4.37479i	0.00355244	+	0.00615301i
$712$	8.80437	+	5.08321i	0.0123657	+	0.00713934i
$713$	19.7806	+	73.8221i	0.0277427	+	0.103537i
$714$			459.577i			0.643666i
$715$		0			0
$716$	−157.509			−0.219985
$717$	575.055	−	154.085i	0.802029	−	0.214903i
$718$	−116.092	+	201.077i	−0.161688	+	0.280051i
$719$	864.778	−	499.280i	1.20275	−	0.694409i	0.241585	−	0.970380i	$-0.422333\pi$
$719$	864.778	−	499.280i	1.20275	−	0.694409i	0.961166	+	0.275971i	$0.0889993\pi$
$720$	5.06137	+	5.06137i	0.00702967	+	0.00702967i
$721$	19.7956	−	73.8783i	0.0274558	−	0.102466i
$722$	−455.855	−	122.146i	−0.631379	−	0.169177i
$723$	483.940	−	483.940i	0.669350	−	0.669350i
$724$	200.758	+	347.724i	0.277290	+	0.480281i
$725$	402.636	+	232.462i	0.555360	+	0.320638i
$726$	−95.0972	−	354.908i	−0.130988	−	0.488854i
$727$		−	685.178i		−	0.942473i	−0.882007	−	0.471237i	$-0.843808\pi$
$727$		−	685.178i		−	0.942473i	0.882007	−	0.471237i	$-0.156192\pi$
$728$		0			0
$729$	706.374			0.968963
$730$	499.789	−	133.918i	0.684643	−	0.183450i
$731$	−377.495	+	653.841i	−0.516409	+	0.894447i
$732$	−121.630	+	70.2233i	−0.166162	+	0.0959334i
$733$	−176.253	−	176.253i	−0.240454	−	0.240454i	0.576584	−	0.817038i	$-0.304385\pi$
$733$	−176.253	−	176.253i	−0.240454	−	0.240454i	−0.817038	+	0.576584i	$0.804385\pi$
$734$	−251.212	+	937.537i	−0.342251	+	1.27730i
$735$	−589.820	−	158.042i	−0.802477	−	0.215023i
$736$	25.1497	−	25.1497i	0.0341708	−	0.0341708i
$737$	773.001	+	1338.88i	1.04885	+	1.81666i
$738$	−23.5976	−	13.6241i	−0.0319751	−	0.0184608i
$739$	358.434	+	1337.69i	0.485026	+	1.81014i	0.579946	+	0.814655i	$0.303074\pi$
$739$	358.434	+	1337.69i	0.485026	+	1.81014i	−0.0949200	+	0.995485i	$0.530260\pi$
$740$			86.1425i			0.116409i
$741$		0			0
$742$	−210.272			−0.283385
$743$	−563.335	+	150.945i	−0.758190	+	0.203156i	−0.617148	−	0.786847i	$-0.711712\pi$
$743$	−563.335	+	150.945i	−0.758190	+	0.203156i	−0.141042	+	0.990004i	$0.545045\pi$
$744$	−52.3222	+	90.6247i	−0.0703255	+	0.121807i
$745$	−1109.95	+	640.829i	−1.48986	+	0.860173i
$746$	617.271	+	617.271i	0.827441	+	0.827441i
$747$	−3.36090	+	12.5431i	−0.00449920	+	0.0167912i
$748$	−672.800	−	180.276i	−0.899466	−	0.241011i
$749$	−165.646	+	165.646i	−0.221156	+	0.221156i
$750$	−59.4835	−	103.028i	−0.0793113	−	0.137371i
$751$	1012.32	+	584.461i	1.34796	+	0.778244i	0.987960	−	0.154709i	$-0.0494441\pi$
$751$	1012.32	+	584.461i	1.34796	+	0.778244i	0.359998	+	0.932953i	$0.382777\pi$
$752$	11.2097	+	41.8352i	0.0149065	+	0.0556319i
$753$		−	10.6229i		−	0.0141075i
$754$		0			0
$755$	−676.588			−0.896143
$756$	−226.218	+	60.6149i	−0.299230	+	0.0801785i
$757$	561.343	−	972.275i	0.741537	−	1.28438i	−0.210259	−	0.977646i	$-0.567431\pi$
$757$	561.343	−	972.275i	0.741537	−	1.28438i	0.951796	−	0.306733i	$-0.0992360\pi$
$758$	−657.282	+	379.482i	−0.867126	+	0.500636i
$759$	194.389	+	194.389i	0.256112	+	0.256112i
$760$	−130.753	+	487.976i	−0.172043	+	0.642073i
$761$	918.907	+	246.221i	1.20750	+	0.323549i	0.805781	−	0.592214i	$-0.201746\pi$
$761$	918.907	+	246.221i	1.20750	+	0.323549i	0.401719	+	0.915763i	$0.368413\pi$
$762$	−405.070	+	405.070i	−0.531588	+	0.531588i
$763$	−166.222	−	287.906i	−0.217854	−	0.377334i
$764$	−70.2001	−	40.5301i	−0.0918850	−	0.0530498i
$765$	11.2284	+	41.9050i	0.0146777	+	0.0547778i
$766$			370.506i			0.483690i
$767$		0			0
$768$	48.6991			0.0634103
$769$	−199.332	+	53.4110i	−0.259210	+	0.0694551i	−0.386084	−	0.922464i	$-0.626172\pi$
$769$	−199.332	+	53.4110i	−0.259210	+	0.0694551i	0.126874	+	0.991919i	$0.459506\pi$
$770$	−303.144	+	525.061i	−0.393694	+	0.681898i
$771$	−488.733	+	282.170i	−0.633895	+	0.365979i
$772$	−205.193	−	205.193i	−0.265794	−	0.265794i
$773$	−115.667	+	431.675i	−0.149634	+	0.558441i	0.849871	+	0.526990i	$0.176680\pi$
$773$	−115.667	+	431.675i	−0.149634	+	0.558441i	−0.999505	+	0.0314512i	$0.989987\pi$
$774$	11.2335	+	3.01001i	0.0145136	+	0.00388890i
$775$	−179.824	+	179.824i	−0.232031	+	0.232031i
$776$	35.5934	+	61.6496i	0.0458678	+	0.0794453i
$777$	73.7826	+	42.5984i	0.0949583	+	0.0548242i
$778$	−67.5651	−	252.156i	−0.0868445	−	0.324108i
$779$		−	1923.14i		−	2.46872i
$780$		0			0
$781$	−32.8465			−0.0420570
$782$	208.224	−	55.7934i	0.266271	−	0.0713471i
$783$	−295.441	+	511.718i	−0.377319	+	0.653535i
$784$	−102.555	+	59.2103i	−0.130810	+	0.0755233i
$785$	−847.151	−	847.151i	−1.07917	−	1.07917i
$786$	−42.6397	+	159.134i	−0.0542490	+	0.202460i
$787$	648.040	+	173.642i	0.823431	+	0.220638i	0.645846	−	0.763468i	$-0.276505\pi$
$787$	648.040	+	173.642i	0.823431	+	0.220638i	0.177585	+	0.984105i	$0.443172\pi$
$788$	−218.963	+	218.963i	−0.277872	+	0.277872i
$789$	285.120	+	493.843i	0.361369	+	0.625910i
$790$	158.769	+	91.6653i	0.200973	+	0.116032i
$791$	−41.2921	−	154.104i	−0.0522025	−	0.194822i
$792$			10.7293i			0.0135471i
$793$		0			0
$794$	359.016			0.452162
$795$	−672.628	+	180.230i	−0.846073	+	0.226705i
$796$	260.350	−	450.940i	0.327073	−	0.566508i
$797$	207.230	−	119.644i	0.260013	−	0.150118i	−0.364328	−	0.931271i	$-0.618701\pi$
$797$	207.230	−	119.644i	0.260013	−	0.150118i	0.624340	+	0.781152i	$0.285368\pi$
$798$	353.302	+	353.302i	0.442734	+	0.442734i
$799$	−67.9413	+	253.560i	−0.0850329	+	0.317347i
$800$	114.317	+	30.6312i	0.142896	+	0.0382890i
$801$	0.671155	−	0.671155i	0.000837896	−	0.000837896i
$802$	−191.654	−	331.955i	−0.238971	−	0.413909i
$803$	671.683	+	387.796i	0.836466	+	0.482934i
$804$	−169.560	−	632.808i	−0.210896	−	0.787075i
$805$		−	187.639i		−	0.233092i
$806$		0			0
$807$	1047.07			1.29748
$808$	414.758	−	111.134i	0.513315	−	0.137542i
$809$	−234.046	+	405.380i	−0.289303	+	0.501088i	−0.973644	−	0.228075i	$-0.926757\pi$
$809$	−234.046	+	405.380i	−0.289303	+	0.501088i	0.684340	+	0.729163i	$0.260090\pi$
$810$	−691.408	+	399.185i	−0.853590	+	0.492820i
$811$	680.928	+	680.928i	0.839615	+	0.839615i	0.988808	−	0.149193i	$-0.0476675\pi$
$811$	680.928	+	680.928i	0.839615	+	0.839615i	−0.149193	+	0.988808i	$0.547668\pi$
$812$	50.6593	−	189.063i	0.0623883	−	0.232836i
$813$	−71.3126	−	19.1082i	−0.0877154	−	0.0235033i
$814$	−91.3046	+	91.3046i	−0.112168	+	0.112168i
$815$	−410.819	−	711.560i	−0.504073	−	0.873080i
$816$	255.618	+	147.581i	0.313257	+	0.180859i
$817$	212.442	+	792.843i	0.260027	+	0.970433i
$818$		−	223.270i		−	0.272946i
$819$		0			0
$820$	−988.886			−1.20596
$821$	−1217.29	+	326.171i	−1.48269	+	0.397285i	−0.907260	−	0.420569i	$-0.861830\pi$
$821$	−1217.29	+	326.171i	−1.48269	+	0.397285i	−0.575426	+	0.817854i	$0.695164\pi$
$822$	−17.2935	+	29.9532i	−0.0210383	+	0.0364394i
$823$	−499.204	+	288.216i	−0.606566	+	0.350201i	−0.771620	−	0.636083i	$-0.780553\pi$
$823$	−499.204	+	288.216i	−0.606566	+	0.350201i	0.165054	+	0.986285i	$0.447220\pi$
$824$	−34.7344	−	34.7344i	−0.0421534	−	0.0421534i
$825$	−236.757	+	883.589i	−0.286978	+	1.07102i
$826$	227.229	+	60.8858i	0.275095	+	0.0737116i
$827$	−434.651	+	434.651i	−0.525575	+	0.525575i	−0.919250	−	0.393675i	$-0.871204\pi$
$827$	−434.651	+	434.651i	−0.525575	+	0.525575i	0.393675	+	0.919250i	$0.371204\pi$
$828$	−1.66030	−	2.87573i	−0.00200520	−	0.00347310i
$829$	109.340	+	63.1272i	0.131893	+	0.0761486i	0.564495	−	0.825437i	$-0.309071\pi$
$829$	109.340	+	63.1272i	0.131893	+	0.0761486i	−0.432602	+	0.901585i	$0.642404\pi$
$830$	121.973	+	455.210i	0.146956	+	0.548446i
$831$			1506.30i			1.81263i
$832$		0			0
$833$	−717.739			−0.861632
$834$	−1014.33	+	271.790i	−1.21623	+	0.325887i
$835$	1005.33	−	1741.28i	1.20399	−	2.08537i
$836$	−655.806	+	378.630i	−0.784457	+	0.452906i
$837$	−228.542	−	228.542i	−0.273048	−	0.273048i
$838$	238.823	−	891.299i	0.284991	−	1.06360i
$839$	−1229.99	−	329.574i	−1.46601	−	0.392817i	−0.564451	−	0.825466i	$-0.690912\pi$
$839$	−1229.99	−	329.574i	−1.46601	−	0.392817i	−0.901562	+	0.432649i	$0.857579\pi$
$840$	181.669	−	181.669i	0.216273	−	0.216273i
$841$	173.584	+	300.656i	0.206401	+	0.357498i
$842$	−510.220	−	294.576i	−0.605962	−	0.349852i
$843$	−162.267	−	605.589i	−0.192488	−	0.718374i
$844$			832.812i			0.986744i
$845$		0			0
$846$	4.04360			0.00477966
$847$	−363.114	+	97.2960i	−0.428706	+	0.114871i
$848$	−67.5231	+	116.953i	−0.0796263	+	0.137917i
$849$	1134.01	−	654.720i	1.33570	−	0.771166i
$850$	507.215	+	507.215i	0.596723	+	0.596723i
$851$	10.3430	−	38.6007i	0.0121540	−	0.0453593i
$852$	13.4447	+	3.60249i	0.0157801	+	0.00422828i
$853$	−162.871	+	162.871i	−0.190939	+	0.190939i	−0.796102	−	0.605163i	$-0.793108\pi$
$853$	−162.871	+	162.871i	−0.190939	+	0.190939i	0.605163	+	0.796102i	$0.293108\pi$
$854$	71.8470	+	124.443i	0.0841299	+	0.145717i
$855$	40.8465	+	23.5827i	0.0477737	+	0.0275822i
$856$	38.9398	+	145.325i	0.0454904	+	0.169772i
$857$		−	1077.67i		−	1.25750i	−0.777609	−	0.628748i	$-0.783568\pi$
$857$		−	1077.67i		−	1.25750i	0.777609	−	0.628748i	$-0.216432\pi$
$858$		0			0
$859$	654.044			0.761402			0.380701	−	0.924698i	$-0.375683\pi$
$859$	654.044			0.761402			0.380701	+	0.924698i	$0.375683\pi$
$860$	407.684	−	109.239i	0.474051	−	0.127022i
$861$	−489.015	+	846.999i	−0.567962	+	0.983739i
$862$	86.4982	−	49.9398i	0.100346	−	0.0579348i
$863$	−916.358	−	916.358i	−1.06183	−	1.06183i	−0.997958	−	0.0638705i	$-0.979656\pi$
$863$	−916.358	−	916.358i	−1.06183	−	1.06183i	−0.0638705	−	0.997958i	$-0.520344\pi$
$864$	−38.9297	+	145.288i	−0.0450576	+	0.168157i
$865$	−1822.89	−	488.443i	−2.10739	−	0.564674i
$866$	−466.918	+	466.918i	−0.539167	+	0.539167i
$867$	454.664	+	787.502i	0.524411	+	0.908306i
$868$	92.7201	+	53.5320i	0.106820	+	0.0616728i
$869$	71.1248	+	265.441i	0.0818468	+	0.305456i
$870$		−	648.207i		−	0.745066i
$871$		0			0
$872$	−213.512			−0.244853
$873$	6.41967	−	1.72015i	0.00735358	−	0.00197039i
$874$	117.182	−	202.964i	0.134075	−	0.232225i
$875$	−105.411	+	60.8589i	−0.120469	+	0.0695530i
$876$	−232.400	−	232.400i	−0.265297	−	0.265297i
$877$	−237.471	+	886.252i	−0.270776	+	1.01055i	0.687843	+	0.725859i	$0.258558\pi$
$877$	−237.471	+	886.252i	−0.270776	+	1.01055i	−0.958619	+	0.284691i	$0.908109\pi$
$878$	−163.377	−	43.7768i	−0.186079	−	0.0498597i
$879$	−204.200	+	204.200i	−0.232309	+	0.232309i
$880$	194.693	+	337.219i	0.221242	+	0.383203i
$881$	−837.311	−	483.422i	−0.950410	−	0.548719i	−0.0572017	−	0.998363i	$-0.518218\pi$
$881$	−837.311	−	483.422i	−0.950410	−	0.548719i	−0.893208	+	0.449643i	$0.851551\pi$
$882$	2.86150	+	10.6793i	0.00324433	+	0.0121080i
$883$		−	1129.48i		−	1.27914i	−0.768731	−	0.639572i	$-0.779112\pi$
$883$		−	1129.48i		−	1.27914i	0.768731	−	0.639572i	$-0.220888\pi$
$884$		0			0
$885$	779.059			0.880293
$886$	−77.4827	+	20.7614i	−0.0874523	+	0.0234328i
$887$	827.477	−	1433.23i	0.932894	−	1.61582i	0.154547	−	0.987985i	$-0.450608\pi$
$887$	827.477	−	1433.23i	0.932894	−	1.61582i	0.778347	−	0.627834i	$-0.216058\pi$
$888$	47.3866	−	27.3587i	0.0533633	−	0.0308093i
$889$	414.436	+	414.436i	0.466182	+	0.466182i
$890$	8.91542	−	33.2728i	0.0100173	−	0.0373852i
$891$	−1155.95	−	309.735i	−1.29736	−	0.347626i
$892$	288.926	−	288.926i	0.323909	−	0.323909i
$893$	142.695	+	247.155i	0.159793	+	0.276770i
$894$	705.035	+	407.052i	0.788630	+	0.455316i
$895$	138.128	+	515.500i	0.154333	+	0.575977i
$896$		−	49.8251i		−	0.0556084i
$897$		0			0
$898$	261.348			0.291033
$899$	260.918	−	69.9127i	0.290231	−	0.0777672i
$900$	5.52468	−	9.56903i	0.00613853	−	0.0106323i
$901$	−708.847	+	409.253i	−0.786733	+	0.454221i
$902$	−1048.14	−	1048.14i	−1.16202	−	1.16202i
$903$	108.039	−	403.209i	0.119645	−	0.446521i
$904$	−98.9730	−	26.5197i	−0.109483	−	0.0293360i
$905$	961.981	−	961.981i	1.06296	−	1.06296i
$906$	214.883	+	372.188i	0.237178	+	0.410804i
$907$	−386.408	−	223.093i	−0.426029	−	0.245968i	0.271625	−	0.962403i	$-0.412439\pi$
$907$	−386.408	−	223.093i	−0.426029	−	0.245968i	−0.697653	+	0.716435i	$0.745772\pi$
$908$	57.5835	+	214.904i	0.0634179	+	0.236679i
$909$		−	40.0886i		−	0.0441019i
$910$		0			0
$911$	1639.85			1.80005			0.900025	−	0.435838i	$-0.143548\pi$
$911$	1639.85			1.80005			0.900025	+	0.435838i	$0.143548\pi$
$912$	309.960	−	83.0536i	0.339869	−	0.0910676i
$913$	−353.206	+	611.771i	−0.386863	+	0.670067i
$914$	362.673	−	209.389i	0.396797	−	0.229091i
$915$	336.491	+	336.491i	0.367750	+	0.367750i
$916$	155.421	−	580.039i	0.169674	−	0.633231i
$917$	162.813	+	43.6256i	0.177550	+	0.0475743i
$918$	−644.629	+	644.629i	−0.702210	+	0.702210i
$919$	−595.311	−	1031.11i	−0.647782	−	1.12199i	−0.983652	−	0.180082i	$-0.942364\pi$
$919$	−595.311	−	1031.11i	−0.647782	−	1.12199i	0.335870	−	0.941908i	$-0.390970\pi$
$920$	−104.365	−	60.2553i	−0.113441	−	0.0654949i
$921$	−234.295	−	874.401i	−0.254392	−	0.949404i
$922$		−	872.906i		−	0.946752i
$923$		0			0
$924$	385.112			0.416788
$925$	128.445	−	34.4166i	0.138859	−	0.0372071i
$926$	−198.699	+	344.157i	−0.214578	+	0.371660i
$927$	−3.97169	+	2.29306i	−0.00428446	+	0.00247363i
$928$	−88.8894	−	88.8894i	−0.0957860	−	0.0957860i
$929$	−206.356	+	770.131i	−0.222127	+	0.828990i	0.761408	+	0.648273i	$0.224508\pi$
$929$	−206.356	+	770.131i	−0.222127	+	0.828990i	−0.983535	+	0.180717i	$0.942158\pi$
$930$	342.482	+	91.7677i	0.368260	+	0.0986750i
$931$	−551.765	+	551.765i	−0.592658	+	0.592658i
$932$	46.5826	+	80.6834i	0.0499813	+	0.0865702i
$933$	−650.078	−	375.323i	−0.696761	−	0.402275i
$934$	−191.071	−	713.086i	−0.204573	−	0.763475i
$935$			2360.05i			2.52411i
$936$		0			0
$937$	406.611			0.433950			0.216975	−	0.976177i	$-0.430381\pi$
$937$	406.611			0.433950			0.216975	+	0.976177i	$0.430381\pi$
$938$	−647.440	+	173.481i	−0.690234	+	0.184948i
$939$	180.379	−	312.426i	0.192097	−	0.332722i
$940$	127.089	−	73.3746i	0.135201	−	0.0780581i
$941$	67.4219	+	67.4219i	0.0716492	+	0.0716492i	0.742023	−	0.670374i	$-0.233866\pi$
$941$	67.4219	+	67.4219i	0.0716492	+	0.0716492i	−0.670374	+	0.742023i	$0.733866\pi$
$942$	−196.961	+	735.068i	−0.209088	+	0.780327i
$943$	443.123	+	118.735i	0.469908	+	0.125911i
$944$	106.833	−	106.833i	0.113171	−	0.113171i
$945$	396.763	+	687.214i	0.419855	+	0.727210i
$946$	547.899	+	316.330i	0.579175	+	0.334387i
$947$	−425.925	−	1589.57i	−0.449762	−	1.67853i	−0.703047	−	0.711143i	$-0.748178\pi$
$947$	−425.925	−	1589.57i	−0.449762	−	1.67853i	0.253285	−	0.967392i	$-0.418489\pi$
$948$		−	116.451i		−	0.122839i
$949$		0			0
$950$	779.846			0.820891
$951$	−1184.19	+	317.302i	−1.24520	+	0.333651i
$952$	150.993	−	261.528i	0.158606	−	0.274714i
$953$	807.423	−	466.166i	0.847243	−	0.489156i	−0.0124765	−	0.999922i	$-0.503971\pi$
$953$	807.423	−	466.166i	0.847243	−	0.489156i	0.859720	+	0.510766i	$0.170638\pi$
$954$	8.91532	+	8.91532i	0.00934520	+	0.00934520i
$955$	−71.0856	+	265.295i	−0.0744351	+	0.277796i
$956$	−377.866	−	101.249i	−0.395258	−	0.105909i
$957$	687.051	−	687.051i	0.717921	−	0.717921i
$958$	240.091	+	415.850i	0.250617	+	0.434081i
$959$	30.6457	+	17.6933i	0.0319559	+	0.0184498i
$960$	−42.7066	−	159.383i	−0.0444860	−	0.166024i
$961$		−	813.246i		−	0.846249i
$962$		0			0
$963$	14.0465			0.0145862
$964$	−434.389	+	116.394i	−0.450611	+	0.120741i
$965$	−491.615	+	851.503i	−0.509446	+	0.882386i
$966$	−103.220	+	59.5939i	−0.106853	+	0.0616914i
$967$	540.669	+	540.669i	0.559120	+	0.559120i	0.929057	−	0.369937i	$-0.120621\pi$
$967$	540.669	+	540.669i	0.559120	+	0.559120i	−0.369937	+	0.929057i	$0.620621\pi$
$968$	−62.4880	+	233.209i	−0.0645538	+	0.240918i
$969$	1878.65	+	503.382i	1.93875	+	0.519486i
$970$	170.554	−	170.554i	0.175829	−	0.175829i
$971$	−848.378	−	1469.43i	−0.873716	−	1.51332i	−0.858124	−	0.513442i	$-0.828370\pi$
$971$	−848.378	−	1469.43i	−0.873716	−	1.51332i	−0.0155919	−	0.999878i	$-0.504963\pi$
$972$	24.6905	+	14.2551i	0.0254018	+	0.0146657i
$973$	278.074	+	1037.79i	0.285790	+	1.06658i
$974$		−	305.164i		−	0.313310i
$975$		0			0
$976$	92.2869			0.0945563
$977$	275.638	−	73.8571i	0.282127	−	0.0755958i	−0.114981	−	0.993368i	$-0.536681\pi$
$977$	275.638	−	73.8571i	0.282127	−	0.0755958i	0.397108	+	0.917772i	$0.370014\pi$
$978$	−260.951	+	451.980i	−0.266821	+	0.462148i
$979$	44.7164	−	25.8170i	0.0456756	−	0.0263708i
$980$	283.720	+	283.720i	0.289510	+	0.289510i
$981$	−5.15926	+	19.2546i	−0.00525918	+	0.0196275i
$982$	758.464	+	203.230i	0.772367	+	0.206955i
$983$	41.0192	−	41.0192i	0.0417286	−	0.0417286i	−0.685935	−	0.727663i	$-0.740606\pi$
$983$	41.0192	−	41.0192i	0.0417286	−	0.0417286i	0.727663	+	0.685935i	$0.240606\pi$
$984$	314.068	+	543.982i	0.319175	+	0.552827i
$985$	908.647	+	524.607i	0.922484	+	0.532596i
$986$	−197.197	−	735.950i	−0.199997	−	0.746399i
$987$		−	145.138i		−	0.147050i
$988$		0			0
$989$	−195.801			−0.197979
$990$	35.1151	−	9.40908i	0.0354698	−	0.00950412i
$991$	−188.074	+	325.754i	−0.189782	+	0.328712i	−0.945178	−	0.326557i	$-0.894111\pi$
$991$	−188.074	+	325.754i	−0.189782	+	0.328712i	0.755395	+	0.655269i	$0.227445\pi$
$992$	59.5492	−	34.3807i	0.0600294	−	0.0346580i
$993$	−965.046	−	965.046i	−0.971849	−	0.971849i
$994$	3.68579	−	13.7556i	0.00370804	−	0.0138386i
$995$	−1704.16	−	456.628i	−1.71272	−	0.458922i
$996$	211.671	−	211.671i	0.212521	−	0.212521i
$997$	722.549	+	1251.49i	0.724724	+	1.25526i	0.959088	+	0.283109i	$0.0913659\pi$
$997$	722.549	+	1251.49i	0.724724	+	1.25526i	−0.234364	+	0.972149i	$0.575301\pi$
$998$	695.624	+	401.619i	0.697018	+	0.402424i
$999$	43.7407	+	163.243i	0.0437845	+	0.163406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.j.319.1		8
13.2	odd	12	inner	338.3.f.j.249.1		8
13.3	even	3		338.3.f.i.89.1		8
13.4	even	6		338.3.d.g.99.3		8
13.5	odd	4		338.3.f.i.19.1		8
13.6	odd	12		338.3.d.f.239.3		8
13.7	odd	12		338.3.d.g.239.3		8
13.8	odd	4		26.3.f.b.19.1	yes	8
13.9	even	3		338.3.d.f.99.3		8
13.10	even	6		26.3.f.b.11.1	✓	8
13.11	odd	12		338.3.f.h.249.1		8
13.12	even	2		338.3.f.h.319.1		8
39.8	even	4		234.3.bb.f.19.1		8
39.23	odd	6		234.3.bb.f.37.1		8
52.23	odd	6		208.3.bd.f.193.2		8
52.47	even	4		208.3.bd.f.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.1	✓	8	13.10	even	6
26.3.f.b.19.1	yes	8	13.8	odd	4
208.3.bd.f.97.2		8	52.47	even	4
208.3.bd.f.193.2		8	52.23	odd	6
234.3.bb.f.19.1		8	39.8	even	4
234.3.bb.f.37.1		8	39.23	odd	6
338.3.d.f.99.3		8	13.9	even	3
338.3.d.f.239.3		8	13.6	odd	12
338.3.d.g.99.3		8	13.4	even	6
338.3.d.g.239.3		8	13.7	odd	12
338.3.f.h.249.1		8	13.11	odd	12
338.3.f.h.319.1		8	13.12	even	2
338.3.f.i.19.1		8	13.5	odd	4
338.3.f.i.89.1		8	13.3	even	3
338.3.f.j.249.1		8	13.2	odd	12	inner
338.3.f.j.319.1		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} +(-1.52185 + 2.63592i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.79174 - 4.79174i) q^{5} +(-1.11407 + 4.15776i) q^{6} +(4.25390 + 1.13983i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +(-8.29953 - 4.79174i) q^{10} +(-3.71800 - 13.8758i) q^{11} +6.08739i q^{12} +6.22814 q^{14} +(19.9229 - 5.33833i) q^{15} +(2.00000 - 3.46410i) q^{16} +(20.9957 - 12.1219i) q^{17} +(-0.264067 - 0.264067i) q^{18} +(6.82178 - 25.4592i) q^{19} +(-13.0913 - 3.50779i) q^{20} +(-9.47827 + 9.47827i) q^{21} +(-10.1578 - 17.5938i) q^{22} +(5.44507 + 3.14371i) q^{23} +(2.22814 + 8.31552i) q^{24} +20.9215i q^{25} -26.5895 q^{27} +(8.50779 - 2.27966i) q^{28} +(11.1112 - 19.2451i) q^{29} +(25.2612 - 14.5846i) q^{30} +(8.59518 + 8.59518i) q^{31} +(1.46410 - 5.46410i) q^{32} +(42.2336 + 11.3164i) q^{33} +(24.2437 - 24.2437i) q^{34} +(-14.9218 - 25.8453i) q^{35} +(-0.457378 - 0.264067i) q^{36} +(-1.64504 - 6.13936i) q^{37} -37.2749i q^{38} -19.1669 q^{40} +(70.4778 - 18.8845i) q^{41} +(-9.47827 + 16.4168i) q^{42} +(-26.9695 + 15.5708i) q^{43} +(-20.3155 - 20.3155i) q^{44} +(-0.463147 + 1.72849i) q^{45} +(8.58878 + 2.30136i) q^{46} +(-7.65637 + 7.65637i) q^{47} +(6.08739 + 10.5437i) q^{48} +(-25.6388 - 14.8026i) q^{49} +(7.65779 + 28.5793i) q^{50} +73.7905i q^{51} -33.7616 q^{53} +(-36.3219 + 9.73243i) q^{54} +(-48.6733 + 84.3047i) q^{55} +(10.7875 - 6.22814i) q^{56} +(56.7267 + 56.7267i) q^{57} +(8.13394 - 30.3563i) q^{58} +(36.4842 + 9.77592i) q^{59} +(29.1692 - 29.1692i) q^{60} +(11.5359 + 19.9807i) q^{61} +(14.8873 + 8.59518i) q^{62} +(-0.300991 - 1.12332i) q^{63} -8.00000i q^{64} +61.8342 q^{66} +(-103.954 + 27.8544i) q^{67} +(24.2437 - 41.9914i) q^{68} +(-16.5731 + 9.56849i) q^{69} +(-29.8436 - 29.8436i) q^{70} +(0.591796 - 2.20861i) q^{71} +(-0.721445 - 0.193311i) q^{72} +(-38.1773 + 38.1773i) q^{73} +(-4.49432 - 7.78440i) q^{74} +(-55.1473 - 31.8393i) q^{75} +(-13.6436 - 50.9185i) q^{76} -63.2639i q^{77} -19.1299 q^{79} +(-26.1825 + 7.01559i) q^{80} +(41.6534 - 72.1459i) q^{81} +(89.3622 - 51.5933i) q^{82} +(-34.7720 - 34.7720i) q^{83} +(-6.93858 + 25.8951i) q^{84} +(-158.691 - 42.5210i) q^{85} +(-31.1417 + 31.1417i) q^{86} +(33.8190 + 58.5762i) q^{87} +(-35.1875 - 20.3155i) q^{88} +(0.930292 + 3.47190i) q^{89} +2.53068i q^{90} +12.5748 q^{92} +(-35.7367 + 9.57562i) q^{93} +(-7.65637 + 13.2612i) q^{94} +(-154.682 + 89.3058i) q^{95} +(12.1748 + 12.1748i) q^{96} +(-6.51404 + 24.3107i) q^{97} +(-40.4414 - 10.8362i) q^{98} +(-2.68233 + 2.68233i) 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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