LMFDB - Embedded newform 338.3.f.h.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.h.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	0.999167	−	0.0408192i	$-0.0129968\pi$
$5$	4.79174	+	4.79174i	0.958347	+	0.958347i	−0.0408192	+	0.999167i	$0.512997\pi$
$6$	1.11407	−	4.15776i	0.185678	−	0.692960i
$7$	−4.25390	−	1.13983i	−0.607700	−	0.162833i	−0.0581698	−	0.998307i	$-0.518526\pi$
$7$	−4.25390	−	1.13983i	−0.607700	−	0.162833i	−0.549530	+	0.835474i	$0.685193\pi$
$8$	−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	$0.143142\pi$
$11$	3.71800	+	13.8758i	0.338000	+	1.26143i	−0.562580	+	0.826743i	$0.690191\pi$
$12$			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	$0.327316\pi$
$19$	−6.82178	+	25.4592i	−0.359041	+	1.33996i	−0.875322	+	0.483540i	$0.839351\pi$
$20$	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	0.554752	−	0.832016i	$-0.312813\pi$
$31$	−8.59518	−	8.59518i	−0.277264	−	0.277264i	−0.832016	+	0.554752i	$0.812813\pi$
$32$	−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	0.984587	−	0.174898i	$-0.0559596\pi$
$37$	1.64504	+	6.13936i	0.0444605	+	0.165929i	−0.940126	+	0.340827i	$0.889293\pi$
$38$		−	37.2749i		−	0.980919i
$39$		0			0
$40$	−19.1669			−0.479174
$41$	−70.4778	+	18.8845i	−1.71897	+	0.460596i	−0.977595	−	0.210495i	$-0.932492\pi$
$41$	−70.4778	+	18.8845i	−1.71897	+	0.460596i	−0.741375	+	0.671091i	$0.765826\pi$
$42$	−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	−0.620949	−	0.783851i	$-0.713253\pi$
$47$	7.65637	−	7.65637i	0.162902	−	0.162902i	0.783851	+	0.620949i	$0.213253\pi$
$48$	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	−0.0639871	−	0.997951i	$-0.520382\pi$
$59$	−36.4842	−	9.77592i	−0.618377	−	0.165694i	−0.554390	+	0.832257i	$0.687048\pi$
$60$	−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	0.621575	−	0.783355i	$-0.286493\pi$
$67$	103.954	−	27.8544i	1.55155	−	0.415737i	0.929977	+	0.367618i	$0.119827\pi$
$68$	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	−0.969968	−	0.243232i	$-0.921792\pi$
$71$	−0.591796	+	2.20861i	−0.00833516	+	0.0311072i	0.961633	+	0.274339i	$0.0884591\pi$
$72$	0.721445	+	0.193311i	0.0100201	+	0.00268487i
$73$	38.1773	−	38.1773i	0.522977	−	0.522977i	−0.395492	−	0.918469i	$-0.629426\pi$
$73$	38.1773	−	38.1773i	0.522977	−	0.522977i	0.918469	+	0.395492i	$0.129426\pi$
$74$	−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	0.884838	−	0.465898i	$-0.154269\pi$
$83$	34.7720	+	34.7720i	0.418940	+	0.418940i	−0.465898	+	0.884838i	$0.654269\pi$
$84$	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	0.960503	−	0.278271i	$-0.0897614\pi$
$89$	−0.930292	−	3.47190i	−0.0104527	−	0.0390101i	−0.970955	+	0.239261i	$0.923095\pi$
$90$			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	−0.924185	−	0.381945i	$-0.875254\pi$
$97$	6.51404	−	24.3107i	0.0671551	−	0.250626i	0.991340	+	0.131319i	$0.0419211\pi$
$98$	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	0.908213	−	0.418508i	$-0.137447\pi$
$109$	53.3779	+	53.3779i	0.489705	+	0.489705i	−0.418508	+	0.908213i	$0.637447\pi$
$110$	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	0.230381	−	0.973100i	$-0.426003\pi$
$137$	−7.76140	−	2.07966i	−0.0566525	−	0.0151800i	−0.287034	+	0.957920i	$0.592669\pi$
$138$	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	$0.302197\pi$
$149$	−48.9509	+	182.687i	−0.328529	+	1.22609i	−0.910716	+	0.413033i	$0.864469\pi$
$150$	86.9865	+	23.3080i	0.579910	+	0.155386i
$151$	−70.5995	+	70.5995i	−0.467546	+	0.467546i	−0.901119	−	0.433573i	$-0.857253\pi$
$151$	−70.5995	+	70.5995i	−0.467546	+	0.467546i	0.433573	+	0.901119i	$0.357253\pi$
$152$	−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	−0.119000	−	0.992894i	$-0.537969\pi$
$163$	−117.116	−	31.3812i	−0.718504	−	0.192523i	−0.599504	+	0.800372i	$0.704635\pi$
$164$	−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	$-0.735186\pi$
$167$	−76.7939	−	286.599i	−0.459844	−	1.71616i	0.213601	−	0.976921i	$-0.431481\pi$
$168$			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	$0.0393294\pi$
$193$	37.5529	+	140.149i	0.194575	+	0.726163i	−0.797802	+	0.602920i	$0.794004\pi$
$194$			35.5934i			0.183471i
$195$		0			0
$196$	−59.2103			−0.302093
$197$	149.555	−	40.0731i	0.759161	−	0.203417i	0.141583	−	0.989926i	$-0.454781\pi$
$197$	149.555	−	40.0731i	0.759161	−	0.203417i	0.617578	+	0.786510i	$0.288114\pi$
$198$	−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	−0.672535	−	0.740065i	$-0.734795\pi$
$223$	−197.340	+	52.8772i	−0.884935	+	0.237118i	−0.212400	+	0.977183i	$0.568128\pi$
$224$	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	−0.873063	−	0.487608i	$-0.837870\pi$
$227$	28.7917	−	107.452i	0.126836	−	0.473358i	0.999898	+	0.0142503i	$0.00453617\pi$
$228$	−154.980	−	41.5268i	−0.679738	−	0.182135i
$229$	−212.309	+	212.309i	−0.927114	+	0.927114i	−0.997519	−	0.0704045i	$-0.977571\pi$
$229$	−212.309	+	212.309i	−0.927114	+	0.927114i	0.0704045	+	0.997519i	$0.477571\pi$
$230$	−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	0.934544	−	0.355847i	$-0.115808\pi$
$239$	138.309	+	138.309i	0.578698	+	0.578698i	−0.355847	+	0.934544i	$0.615808\pi$
$240$	−21.3533	+	79.6916i	−0.0889721	+	0.332048i
$241$	217.195	+	58.1972i	0.901223	+	0.241482i	0.679541	−	0.733637i	$-0.262179\pi$
$241$	217.195	+	58.1972i	0.901223	+	0.241482i	0.221682	+	0.975119i	$0.428845\pi$
$242$	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	0.953375	−	0.301788i	$-0.0975834\pi$
$271$	−6.27795	−	23.4296i	−0.0231659	−	0.0864562i	−0.976541	+	0.215332i	$0.930917\pi$
$272$		−	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	−0.398731	−	0.917068i	$-0.630549\pi$
$281$	145.653	−	145.653i	0.518337	−	0.518337i	0.917068	+	0.398731i	$0.130549\pi$
$282$	−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	0.0990115	−	0.995086i	$-0.468432\pi$
$293$	−91.6460	−	24.5565i	−0.312785	−	0.0838105i	−0.411797	+	0.911276i	$0.635099\pi$
$294$	−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	−0.276095	−	0.961130i	$-0.589041\pi$
$307$	210.306	−	210.306i	0.685035	−	0.685035i	0.961130	+	0.276095i	$0.0890406\pi$
$308$	−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	0.0968348	−	0.995300i	$-0.469128\pi$
$317$	−284.814	−	284.814i	−0.898466	−	0.898466i	−0.995300	+	0.0968348i	$0.969128\pi$
$318$	−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	$-0.679801\pi$
$331$	116.054	−	433.118i	0.350615	−	1.30851i	0.885914	−	0.463850i	$-0.153532\pi$
$332$	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	$-0.956818\pi$
$349$	−69.9275	−	260.973i	−0.200365	−	0.747774i	0.790447	−	0.612531i	$-0.209848\pi$
$350$			130.302i			0.372291i
$351$		0			0
$352$	−81.2621			−0.230858
$353$	340.955	−	91.3587i	0.965879	−	0.258806i	0.258792	−	0.965933i	$-0.416676\pi$
$353$	340.955	−	91.3587i	0.965879	−	0.258806i	0.707087	+	0.707127i	$0.250009\pi$
$354$	−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	−0.526685	−	0.850060i	$-0.676565\pi$
$359$	116.092	−	116.092i	0.323375	−	0.323375i	0.850060	+	0.526685i	$0.176565\pi$
$360$	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	0.501101	−	0.865389i	$-0.332928\pi$
$379$	518.382	−	138.900i	1.36776	−	0.366491i	0.866661	+	0.498898i	$0.166262\pi$
$380$	−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	$-0.805556\pi$
$383$	67.8074	−	253.061i	0.177043	−	0.660732i	0.996195	−	0.0871559i	$-0.0277778\pi$
$384$	−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	−0.0635986	−	0.997976i	$-0.520258\pi$
$397$	−245.213	−	65.7046i	−0.617664	−	0.165503i	−0.554066	+	0.832473i	$0.686924\pi$
$398$	−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	$0.0264020\pi$
$401$	70.1504	+	261.805i	0.174939	+	0.652880i	−0.821623	+	0.570031i	$0.806931\pi$
$402$		−	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	−0.997717	−	0.0675274i	$-0.978489\pi$
$409$	−40.8612	+	152.496i	−0.0999051	+	0.372851i	0.897812	+	0.440378i	$0.145156\pi$
$410$	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	0.964347	−	0.264642i	$-0.0852538\pi$
$421$	294.576	+	294.576i	0.699704	+	0.699704i	−0.264642	+	0.964347i	$0.585254\pi$
$422$	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	−0.337089	−	0.941473i	$-0.609442\pi$
$431$	−68.2190	+	18.2792i	−0.158281	+	0.0424112i	0.178808	+	0.983884i	$0.442776\pi$
$432$	−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	0.0545000	−	0.998514i	$-0.482643\pi$
$449$	−178.504	−	47.8299i	−0.397558	−	0.106525i	−0.452058	+	0.891988i	$0.649310\pi$
$450$	−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	−0.557803	−	0.829973i	$-0.688356\pi$
$457$	−286.031	+	76.6418i	−0.625889	+	0.167706i	−0.0680852	+	0.997680i	$0.521689\pi$
$458$	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	$0.316806\pi$
$461$	−159.753	+	596.206i	−0.346535	+	1.29329i	−0.890808	+	0.454379i	$0.849861\pi$
$462$	−263.036	−	70.4804i	−0.569343	−	0.152555i
$463$	198.699	−	198.699i	0.429156	−	0.429156i	−0.459185	−	0.888341i	$-0.651858\pi$
$463$	198.699	−	198.699i	0.429156	−	0.429156i	0.888341	+	0.459185i	$0.151858\pi$
$464$	−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	$-0.968010\pi$
$479$	−87.8794	−	327.970i	−0.183464	−	0.684698i	0.811490	−	0.584367i	$-0.198657\pi$
$480$		−	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	−0.999263	−	0.0383927i	$-0.987776\pi$
$487$	−55.8489	+	208.431i	−0.114679	+	0.427990i	0.884583	+	0.466382i	$0.154443\pi$
$488$	−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	0.179002	−	0.983849i	$-0.442713\pi$
$499$	−401.619	−	401.619i	−0.804847	−	0.804847i	−0.983849	+	0.179002i	$0.942713\pi$
$500$	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	−0.648382	−	0.761315i	$-0.724554\pi$
$509$	−422.083	+	113.097i	−0.829239	+	0.222194i	−0.180858	+	0.983509i	$0.557887\pi$
$510$	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	−0.970558	−	0.240867i	$-0.922568\pi$
$541$	−394.763	+	394.763i	−0.729691	+	0.729691i	0.240867	+	0.970558i	$0.422568\pi$
$542$	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	0.978516	−	0.206172i	$-0.0661005\pi$
$557$	15.6018	+	58.2268i	0.0280104	+	0.104536i	−0.950505	+	0.310708i	$0.899434\pi$
$558$		−	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	0.691205	−	0.722659i	$-0.257080\pi$
$577$	−18.1490	−	18.1490i	−0.0314540	−	0.0314540i	−0.722659	+	0.691205i	$0.757080\pi$
$578$	−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	−0.161720	−	0.986837i	$-0.551704\pi$
$587$	112.495	−	30.1430i	0.191644	−	0.0513509i	0.353364	+	0.935486i	$0.385038\pi$
$588$	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	−0.501762	−	0.865006i	$-0.667315\pi$
$593$	215.404	−	215.404i	0.363244	−	0.363244i	0.865006	+	0.501762i	$0.167315\pi$
$594$	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	−0.783578	−	0.621294i	$-0.786607\pi$
$613$	−705.887	+	189.142i	−1.15153	+	0.308551i	−0.367951	+	0.929845i	$0.619941\pi$
$614$	−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	$0.175059\pi$
$617$	−90.7668	+	338.746i	−0.147110	+	0.549021i	−0.999652	+	0.0263636i	$0.991607\pi$
$618$	−72.2087	−	19.3483i	−0.116843	−	0.0313079i
$619$	283.795	−	283.795i	0.458474	−	0.458474i	−0.439680	−	0.898154i	$-0.644908\pi$
$619$	283.795	−	283.795i	0.458474	−	0.458474i	0.898154	+	0.439680i	$0.144908\pi$
$620$	−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	0.988235	−	0.152944i	$-0.0488753\pi$
$631$	1115.36	+	298.859i	1.76760	+	0.473627i	0.779365	+	0.626570i	$0.215542\pi$
$632$	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	−0.968364	−	0.249542i	$-0.919720\pi$
$643$	−3.19272	+	11.9154i	−0.00496535	+	0.0185309i	0.963399	+	0.268073i	$0.0863867\pi$
$644$	−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	$0.187560\pi$
$661$	257.291	+	960.224i	0.389245	+	1.45268i	−0.442119	+	0.896956i	$0.645773\pi$
$662$			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	−0.246959	−	0.969026i	$-0.579431\pi$
$683$	−645.671	−	173.007i	−0.945345	−	0.253304i	−0.698386	+	0.715722i	$0.746098\pi$
$684$	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	0.160620	−	0.987016i	$-0.448651\pi$
$691$	548.121	−	146.869i	0.793229	−	0.212545i	0.632609	+	0.774471i	$0.281984\pi$
$692$	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	0.285730	−	0.958310i	$-0.407764\pi$
$709$	38.3029	+	10.2632i	0.0540239	+	0.0144757i	−0.231706	+	0.972786i	$0.574431\pi$
$710$	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	0.817038	−	0.576584i	$-0.195615\pi$
$733$	176.253	+	176.253i	0.240454	+	0.240454i	−0.576584	+	0.817038i	$0.695615\pi$
$734$	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	$-0.696926\pi$
$739$	−358.434	−	1337.69i	−0.485026	−	1.81014i	0.0949200	−	0.995485i	$-0.469740\pi$
$740$			86.1425i			0.116409i
$741$		0			0
$742$	−210.272			−0.283385
$743$	563.335	−	150.945i	0.758190	−	0.203156i	0.141042	−	0.990004i	$-0.454955\pi$
$743$	563.335	−	150.945i	0.758190	−	0.203156i	0.617148	+	0.786847i	$0.288288\pi$
$744$	−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	−0.401719	−	0.915763i	$-0.631587\pi$
$761$	−918.907	−	246.221i	−1.20750	−	0.323549i	−0.805781	+	0.592214i	$0.798254\pi$
$762$	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	−0.126874	−	0.991919i	$-0.540494\pi$
$769$	199.332	−	53.4110i	0.259210	−	0.0694551i	0.386084	+	0.922464i	$0.373828\pi$
$770$	−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	$-0.823320\pi$
$773$	115.667	−	431.675i	0.149634	−	0.558441i	0.999505	−	0.0314512i	$-0.0100129\pi$
$774$	−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	−0.177585	−	0.984105i	$-0.556828\pi$
$787$	−648.040	−	173.642i	−0.823431	−	0.220638i	−0.645846	+	0.763468i	$0.723495\pi$
$788$	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	0.149193	−	0.988808i	$-0.452332\pi$
$811$	−680.928	−	680.928i	−0.839615	−	0.839615i	−0.988808	+	0.149193i	$0.952332\pi$
$812$	−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	0.575426	−	0.817854i	$-0.304836\pi$
$821$	1217.29	−	326.171i	1.48269	−	0.397285i	0.907260	+	0.420569i	$0.138170\pi$
$822$	−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	−0.393675	−	0.919250i	$-0.628796\pi$
$827$	434.651	−	434.651i	0.525575	−	0.525575i	0.919250	+	0.393675i	$0.128796\pi$
$828$	−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	0.901562	−	0.432649i	$-0.142421\pi$
$839$	1229.99	+	329.574i	1.46601	+	0.392817i	0.564451	+	0.825466i	$0.309088\pi$
$840$	−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	−0.605163	−	0.796102i	$-0.706892\pi$
$853$	162.871	−	162.871i	0.190939	−	0.190939i	0.796102	+	0.605163i	$0.206892\pi$
$854$	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	$0.0203445\pi$
$863$	916.358	+	916.358i	1.06183	+	1.06183i	0.0638705	+	0.997958i	$0.479656\pi$
$864$	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	$-0.741442\pi$
$877$	237.471	−	886.252i	0.270776	−	1.01055i	0.958619	−	0.284691i	$-0.0918909\pi$
$878$	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	$-0.775492\pi$
$929$	206.356	−	770.131i	0.222127	−	0.828990i	0.983535	−	0.180717i	$-0.0578417\pi$
$930$	−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	0.670374	−	0.742023i	$-0.266134\pi$
$941$	−67.4219	−	67.4219i	−0.0716492	−	0.0716492i	−0.742023	+	0.670374i	$0.766134\pi$
$942$	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	$0.251822\pi$
$947$	425.925	+	1589.57i	0.449762	+	1.67853i	−0.253285	+	0.967392i	$0.581511\pi$
$948$		−	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	0.369937	−	0.929057i	$-0.379379\pi$
$967$	−540.669	−	540.669i	−0.559120	−	0.559120i	−0.929057	+	0.369937i	$0.879379\pi$
$968$	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	−0.397108	−	0.917772i	$-0.629986\pi$
$977$	−275.638	+	73.8571i	−0.282127	+	0.0755958i	0.114981	+	0.993368i	$0.463319\pi$
$978$	−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	−0.727663	−	0.685935i	$-0.759394\pi$
$983$	−41.0192	+	41.0192i	−0.0417286	+	0.0417286i	0.685935	+	0.727663i	$0.259394\pi$
$984$	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.h.319.1		8
13.2	odd	12	inner	338.3.f.h.249.1		8
13.3	even	3		26.3.f.b.11.1	✓	8
13.4	even	6		338.3.d.f.99.3		8
13.5	odd	4		26.3.f.b.19.1	yes	8
13.6	odd	12		338.3.d.g.239.3		8
13.7	odd	12		338.3.d.f.239.3		8
13.8	odd	4		338.3.f.i.19.1		8
13.9	even	3		338.3.d.g.99.3		8
13.10	even	6		338.3.f.i.89.1		8
13.11	odd	12		338.3.f.j.249.1		8
13.12	even	2		338.3.f.j.319.1		8
39.5	even	4		234.3.bb.f.19.1		8
39.29	odd	6		234.3.bb.f.37.1		8
52.3	odd	6		208.3.bd.f.193.2		8
52.31	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	13.3	even	3
26.3.f.b.19.1	yes	8	13.5	odd	4
208.3.bd.f.97.2		8	52.31	even	4
208.3.bd.f.193.2		8	52.3	odd	6
234.3.bb.f.19.1		8	39.5	even	4
234.3.bb.f.37.1		8	39.29	odd	6
338.3.d.f.99.3		8	13.4	even	6
338.3.d.f.239.3		8	13.7	odd	12
338.3.d.g.99.3		8	13.9	even	3
338.3.d.g.239.3		8	13.6	odd	12
338.3.f.h.249.1		8	13.2	odd	12	inner
338.3.f.h.319.1		8	1.1	even	1	trivial
338.3.f.i.19.1		8	13.8	odd	4
338.3.f.i.89.1		8	13.10	even	6
338.3.f.j.249.1		8	13.11	odd	12
338.3.f.j.319.1		8	13.12	even	2

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

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Representations

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Database

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