LMFDB - Embedded newform 289.3.e.j.214.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,-8,8,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			214.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.214
Dual form			289.3.e.j.131.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0897902 + 0.216773i) q^{2} +(-1.16591 - 0.779037i) q^{3} +(2.78950 + 2.78950i) q^{4} +(-0.338093 + 0.0672509i) q^{5} +(0.273561 - 0.182788i) q^{6} +(-7.04101 - 1.40054i) q^{7} +(-1.72225 + 0.713379i) q^{8} +(-2.69170 - 6.49834i) q^{9} +(0.0157793 - 0.0793278i) q^{10} +(-7.30090 - 10.9266i) q^{11} +(-1.07918 - 5.42543i) q^{12} +(5.20259 - 5.20259i) q^{13} +(0.935813 - 1.40054i) q^{14} +(0.446577 + 0.184978i) q^{15} +15.3424i q^{16} +1.65035 q^{18} +(9.23114 - 22.2860i) q^{19} +(-1.13071 - 0.755514i) q^{20} +(7.11811 + 7.11811i) q^{21} +(3.02413 - 0.601537i) q^{22} +(26.6710 - 17.8210i) q^{23} +(2.56374 + 0.509959i) q^{24} +(-22.9872 + 9.52161i) q^{25} +(0.660638 + 1.59492i) q^{26} +(-4.38621 + 22.0510i) q^{27} +(-15.7341 - 23.5477i) q^{28} +(-7.53862 - 37.8992i) q^{29} +(-0.0801965 + 0.0801965i) q^{30} +(-5.95850 + 8.91753i) q^{31} +(-10.2148 - 4.23111i) q^{32} +18.4271i q^{33} +2.47470 q^{35} +(10.6186 - 25.6356i) q^{36} +(-10.1285 - 6.76763i) q^{37} +(4.00212 + 4.00212i) q^{38} +(-10.1188 + 2.01275i) q^{39} +(0.534305 - 0.357011i) q^{40} +(-35.5040 - 7.06219i) q^{41} +(-2.18215 + 0.903876i) q^{42} +(-12.1240 - 29.2698i) q^{43} +(10.1138 - 50.8455i) q^{44} +(1.34706 + 2.01603i) q^{45} +(1.46831 + 7.38170i) q^{46} +(28.8242 - 28.8242i) q^{47} +(11.9523 - 17.8879i) q^{48} +(2.34419 + 0.970996i) q^{49} -5.83795i q^{50} +29.0252 q^{52} +(-22.2872 + 53.8061i) q^{53} +(-4.38621 - 2.93077i) q^{54} +(3.20321 + 3.20321i) q^{55} +(13.1255 - 2.61082i) q^{56} +(-28.1243 + 18.7920i) q^{57} +(8.89241 + 1.76881i) q^{58} +(-4.80542 + 1.99047i) q^{59} +(0.729730 + 1.76172i) q^{60} +(-8.93981 + 44.9435i) q^{61} +(-1.39806 - 2.09235i) q^{62} +(9.85108 + 49.5247i) q^{63} +(-41.5605 + 41.5605i) q^{64} +(-1.40908 + 2.10884i) q^{65} +(-3.99449 - 1.65457i) q^{66} -59.2116i q^{67} -44.9792 q^{69} +(-0.222204 + 0.536448i) q^{70} +(33.2088 + 22.1894i) q^{71} +(9.27155 + 9.27155i) q^{72} +(-11.6061 + 2.30859i) q^{73} +(2.37648 - 1.58791i) q^{74} +(34.2187 + 6.80652i) q^{75} +(87.9169 - 36.4164i) q^{76} +(36.1026 + 87.1593i) q^{77} +(0.472257 - 2.37420i) q^{78} +(64.8330 + 97.0295i) q^{79} +(-1.03179 - 5.18716i) q^{80} +(-22.4701 + 22.4701i) q^{81} +(4.71881 - 7.06219i) q^{82} +(94.6362 + 39.1996i) q^{83} +39.7119i q^{84} +7.43351 q^{86} +(-20.7355 + 50.0599i) q^{87} +(20.3687 + 13.6100i) q^{88} +(-103.152 - 103.152i) q^{89} +(-0.557973 + 0.110988i) q^{90} +(-43.9179 + 29.3450i) q^{91} +(124.110 + 24.6871i) q^{92} +(13.8942 - 5.75515i) q^{93} +(3.66017 + 8.83643i) q^{94} +(-1.62224 + 8.15553i) q^{95} +(8.61336 + 12.8908i) q^{96} +(25.8302 + 129.857i) q^{97} +(-0.420971 + 0.420971i) q^{98} +(-51.3527 + 76.8548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 16 q^{5} - 8 q^{7} + 8 q^{8} - 56 q^{9} + 48 q^{10} - 24 q^{11} - 24 q^{12} + 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} - 48 q^{20} + 64 q^{21} + 16 q^{22} + 104 q^{23}+ \cdots - 120 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 16 * q^5 - 8 * q^7 + 8 * q^8 - 56 * q^9 + 48 * q^10 - 24 * q^11 - 24 * q^12 + 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 - 48 * q^20 + 64 * q^21 + 16 * q^22 + 104 * q^23 - 136 * q^25 + 40 * q^26 - 32 * q^27 - 168 * q^30 - 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 - 48 * q^37 - 8 * q^38 + 96 * q^39 - 8 * q^40 - 208 * q^41 + 88 * q^42 + 48 * q^43 + 56 * q^44 - 48 * q^45 + 80 * q^46 + 80 * q^47 + 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 - 32 * q^54 + 8 * q^55 + 8 * q^56 - 40 * q^57 + 120 * q^58 - 40 * q^59 - 96 * q^60 + 16 * q^61 - 256 * q^62 - 96 * q^63 + 120 * q^64 + 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 + 328 * q^71 - 24 * q^72 - 160 * q^73 - 168 * q^74 + 264 * q^75 + 192 * q^76 + 120 * q^77 + 168 * q^78 + 352 * q^79 + 328 * q^80 + 224 * q^81 - 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 + 56 * q^88 - 288 * q^89 - 392 * q^90 - 32 * q^91 + 200 * q^92 + 248 * q^93 + 72 * q^94 - 800 * q^95 + 408 * q^96 - 504 * q^97 - 16 * q^98 - 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.0897902	+	0.216773i	−0.0448951	+	0.108386i	−0.944736	−	0.327831i	$-0.893682\pi$
$2$	−0.0897902	+	0.216773i	−0.0448951	+	0.108386i	0.899841	+	0.436218i	$0.143682\pi$
$3$	−1.16591	−	0.779037i	−0.388637	−	0.259679i	0.345867	−	0.938284i	$-0.387585\pi$
$3$	−1.16591	−	0.779037i	−0.388637	−	0.259679i	−0.734504	+	0.678605i	$0.762585\pi$
$4$	2.78950	+	2.78950i	0.697375	+	0.697375i
$5$	−0.338093	+	0.0672509i	−0.0676186	+	0.0134502i	−0.228784	−	0.973477i	$-0.573475\pi$
$5$	−0.338093	+	0.0672509i	−0.0676186	+	0.0134502i	0.161165	+	0.986927i	$0.448475\pi$
$6$	0.273561	−	0.182788i	0.0455935	−	0.0304646i
$7$	−7.04101	−	1.40054i	−1.00586	−	0.200078i	−0.335441	−	0.942061i	$-0.608885\pi$
$7$	−7.04101	−	1.40054i	−1.00586	−	0.200078i	−0.670418	+	0.741984i	$0.733885\pi$
$8$	−1.72225	+	0.713379i	−0.215281	+	0.0891723i
$9$	−2.69170	−	6.49834i	−0.299078	−	0.722038i
$10$	0.0157793	−	0.0793278i	0.00157793	−	0.00793278i
$11$	−7.30090	−	10.9266i	−0.663718	−	0.993325i	−0.998694	−	0.0510977i	$-0.983728\pi$
$11$	−7.30090	−	10.9266i	−0.663718	−	0.993325i	0.334975	−	0.942227i	$-0.391272\pi$
$12$	−1.07918	−	5.42543i	−0.0899321	−	0.452119i
$13$	5.20259	−	5.20259i	0.400199	−	0.400199i	−0.478104	−	0.878303i	$-0.658676\pi$
$13$	5.20259	−	5.20259i	0.400199	−	0.400199i	0.878303	+	0.478104i	$0.158676\pi$
$14$	0.935813	−	1.40054i	0.0668438	−	0.100039i
$15$	0.446577	+	0.184978i	0.0297718	+	0.0123319i
$16$			15.3424i			0.958900i
$17$		0			0
$17$		0			0
$18$	1.65035			0.0916862
$19$	9.23114	−	22.2860i	0.485850	−	1.17295i	−0.470940	−	0.882165i	$-0.656085\pi$
$19$	9.23114	−	22.2860i	0.485850	−	1.17295i	0.956790	−	0.290780i	$-0.0939147\pi$
$20$	−1.13071	−	0.755514i	−0.0565353	−	0.0377757i
$21$	7.11811	+	7.11811i	0.338958	+	0.338958i
$22$	3.02413	−	0.601537i	0.137461	−	0.0273426i
$23$	26.6710	−	17.8210i	1.15961	−	0.774826i	0.181597	−	0.983373i	$-0.441873\pi$
$23$	26.6710	−	17.8210i	1.15961	−	0.774826i	0.978012	+	0.208547i	$0.0668734\pi$
$24$	2.56374	+	0.509959i	0.106822	+	0.0212483i
$25$	−22.9872	+	9.52161i	−0.919488	+	0.380864i
$26$	0.660638	+	1.59492i	0.0254091	+	0.0613431i
$27$	−4.38621	+	22.0510i	−0.162452	+	0.816703i
$28$	−15.7341	−	23.5477i	−0.561931	−	0.840989i
$29$	−7.53862	−	37.8992i	−0.259952	−	1.30687i	−0.861388	−	0.507948i	$-0.830404\pi$
$29$	−7.53862	−	37.8992i	−0.259952	−	1.30687i	0.601436	−	0.798921i	$-0.294596\pi$
$30$	−0.0801965	+	0.0801965i	−0.00267322	+	0.00267322i
$31$	−5.95850	+	8.91753i	−0.192210	+	0.287662i	−0.915040	−	0.403364i	$-0.867841\pi$
$31$	−5.95850	+	8.91753i	−0.192210	+	0.287662i	0.722830	+	0.691026i	$0.242841\pi$
$32$	−10.2148	−	4.23111i	−0.319213	−	0.132222i
$33$			18.4271i			0.558396i
$34$		0			0
$35$	2.47470			0.0707058
$36$	10.6186	−	25.6356i	0.294962	−	0.712100i
$37$	−10.1285	−	6.76763i	−0.273743	−	0.182909i	0.411120	−	0.911581i	$-0.365138\pi$
$37$	−10.1285	−	6.76763i	−0.273743	−	0.182909i	−0.684863	+	0.728672i	$0.740138\pi$
$38$	4.00212	+	4.00212i	0.105319	+	0.105319i
$39$	−10.1188	+	2.01275i	−0.259455	+	0.0516089i
$40$	0.534305	−	0.357011i	0.0133576	−	0.00892528i
$41$	−35.5040	−	7.06219i	−0.865952	−	0.172249i	−0.257925	−	0.966165i	$-0.583039\pi$
$41$	−35.5040	−	7.06219i	−0.865952	−	0.172249i	−0.608027	+	0.793916i	$0.708039\pi$
$42$	−2.18215	+	0.903876i	−0.0519559	+	0.0215209i
$43$	−12.1240	−	29.2698i	−0.281952	−	0.680693i	0.717929	−	0.696117i	$-0.245090\pi$
$43$	−12.1240	−	29.2698i	−0.281952	−	0.680693i	−0.999881	+	0.0154234i	$0.995090\pi$
$44$	10.1138	−	50.8455i	0.229859	−	1.15558i
$45$	1.34706	+	2.01603i	0.0299348	+	0.0448006i
$46$	1.46831	+	7.38170i	0.0319198	+	0.160472i
$47$	28.8242	−	28.8242i	0.613281	−	0.613281i	−0.330518	−	0.943800i	$-0.607224\pi$
$47$	28.8242	−	28.8242i	0.613281	−	0.613281i	0.943800	+	0.330518i	$0.107224\pi$
$48$	11.9523	−	17.8879i	0.249006	−	0.372664i
$49$	2.34419	+	0.970996i	0.0478406	+	0.0198162i
$50$		−	5.83795i		−	0.116759i
$51$		0			0
$52$	29.0252			0.558177
$53$	−22.2872	+	53.8061i	−0.420514	+	1.01521i	0.561682	+	0.827353i	$0.310154\pi$
$53$	−22.2872	+	53.8061i	−0.420514	+	1.01521i	−0.982196	+	0.187857i	$0.939846\pi$
$54$	−4.38621	−	2.93077i	−0.0812262	−	0.0542736i
$55$	3.20321	+	3.20321i	0.0582401	+	0.0582401i
$56$	13.1255	−	2.61082i	0.234384	−	0.0466218i
$57$	−28.1243	+	18.7920i	−0.493408	+	0.329685i
$58$	8.89241	+	1.76881i	0.153317	+	0.0304967i
$59$	−4.80542	+	1.99047i	−0.0814478	+	0.0337368i	−0.423035	−	0.906113i	$-0.639035\pi$
$59$	−4.80542	+	1.99047i	−0.0814478	+	0.0337368i	0.341588	+	0.939850i	$0.389035\pi$
$60$	0.729730	+	1.76172i	0.0121622	+	0.0293621i
$61$	−8.93981	+	44.9435i	−0.146554	+	0.736778i	0.835694	+	0.549195i	$0.185066\pi$
$61$	−8.93981	+	44.9435i	−0.146554	+	0.736778i	−0.982249	+	0.187584i	$0.939934\pi$
$62$	−1.39806	−	2.09235i	−0.0225494	−	0.0337475i
$63$	9.85108	+	49.5247i	0.156366	+	0.786107i
$64$	−41.5605	+	41.5605i	−0.649382	+	0.649382i
$65$	−1.40908	+	2.10884i	−0.0216782	+	0.0324436i
$66$	−3.99449	−	1.65457i	−0.0605225	−	0.0250693i
$67$		−	59.2116i		−	0.883755i	−0.897075	−	0.441877i	$-0.854313\pi$
$67$		−	59.2116i		−	0.883755i	0.897075	−	0.441877i	$-0.145687\pi$
$68$		0			0
$69$	−44.9792			−0.651873
$70$	−0.222204	+	0.536448i	−0.00317435	+	0.00766355i
$71$	33.2088	+	22.1894i	0.467730	+	0.312527i	0.767007	−	0.641639i	$-0.221745\pi$
$71$	33.2088	+	22.1894i	0.467730	+	0.312527i	−0.299277	+	0.954166i	$0.596745\pi$
$72$	9.27155	+	9.27155i	0.128772	+	0.128772i
$73$	−11.6061	+	2.30859i	−0.158987	+	0.0316245i	−0.273942	−	0.961746i	$-0.588328\pi$
$73$	−11.6061	+	2.30859i	−0.158987	+	0.0316245i	0.114955	+	0.993371i	$0.463328\pi$
$74$	2.37648	−	1.58791i	0.0321145	−	0.0214583i
$75$	34.2187	+	6.80652i	0.456249	+	0.0907537i
$76$	87.9169	−	36.4164i	1.15680	−	0.479163i
$77$	36.1026	+	87.1593i	0.468865	+	1.13194i
$78$	0.472257	−	2.37420i	0.00605457	−	0.0304384i
$79$	64.8330	+	97.0295i	0.820671	+	1.22822i	0.970880	+	0.239567i	$0.0770056\pi$
$79$	64.8330	+	97.0295i	0.820671	+	1.22822i	−0.150208	+	0.988654i	$0.547994\pi$
$80$	−1.03179	−	5.18716i	−0.0128974	−	0.0648395i
$81$	−22.4701	+	22.4701i	−0.277408	+	0.277408i
$82$	4.71881	−	7.06219i	0.0575464	−	0.0861243i
$83$	94.6362	+	39.1996i	1.14019	+	0.472284i	0.871234	−	0.490867i	$-0.163320\pi$
$83$	94.6362	+	39.1996i	1.14019	+	0.472284i	0.268960	+	0.963151i	$0.413320\pi$
$84$			39.7119i			0.472761i
$85$		0			0
$86$	7.43351			0.0864362
$87$	−20.7355	+	50.0599i	−0.238339	+	0.575402i
$88$	20.3687	+	13.6100i	0.231463	+	0.154659i
$89$	−103.152	−	103.152i	−1.15901	−	1.15901i	−0.984688	−	0.174326i	$-0.944225\pi$
$89$	−103.152	−	103.152i	−1.15901	−	1.15901i	−0.174326	−	0.984688i	$-0.555775\pi$
$90$	−0.557973	+	0.110988i	−0.00619970	+	0.00123320i
$91$	−43.9179	+	29.3450i	−0.482614	+	0.322473i
$92$	124.110	+	24.6871i	1.34903	+	0.268338i
$93$	13.8942	−	5.75515i	0.149400	−	0.0618833i
$94$	3.66017	+	8.83643i	0.0389380	+	0.0940046i
$95$	−1.62224	+	8.15553i	−0.0170762	+	0.0858477i
$96$	8.61336	+	12.8908i	0.0897225	+	0.134279i
$97$	25.8302	+	129.857i	0.266291	+	1.33874i	0.850004	+	0.526775i	$0.176599\pi$
$97$	25.8302	+	129.857i	0.266291	+	1.33874i	−0.583713	+	0.811960i	$0.698401\pi$
$98$	−0.420971	+	0.420971i	−0.00429562	+	0.00429562i
$99$	−51.3527	+	76.8548i	−0.518715	+	0.776311i
$100$	−90.6833	−	37.5623i	−0.906833	−	0.375623i
$101$		−	124.860i		−	1.23624i	−0.786085	−	0.618119i	$-0.787895\pi$
$101$		−	124.860i		−	1.23624i	0.786085	−	0.618119i	$-0.212105\pi$
$102$		0			0
$103$	−87.0352			−0.845002			−0.422501	−	0.906362i	$-0.638848\pi$
$103$	−87.0352			−0.845002			−0.422501	+	0.906362i	$0.638848\pi$
$104$	−5.24873	+	12.6716i	−0.0504686	+	0.121842i
$105$	−2.88528	−	1.92789i	−0.0274789	−	0.0183608i
$106$	−9.66253	−	9.66253i	−0.0911560	−	0.0911560i
$107$	50.4222	−	10.0296i	0.471236	−	0.0937346i	0.0462407	−	0.998930i	$-0.485276\pi$
$107$	50.4222	−	10.0296i	0.471236	−	0.0937346i	0.424995	+	0.905196i	$0.360276\pi$
$108$	−73.7466	+	49.2759i	−0.682838	+	0.456258i
$109$	−29.5679	−	5.88143i	−0.271265	−	0.0539580i	0.0575831	−	0.998341i	$-0.481661\pi$
$109$	−29.5679	−	5.88143i	−0.271265	−	0.0539580i	−0.328849	+	0.944383i	$0.606661\pi$
$110$	−0.981984	+	0.406751i	−0.00892713	+	0.00369774i
$111$	6.53667	+	15.7809i	0.0588889	+	0.142170i
$112$	21.4877	−	108.026i	0.191854	−	0.964518i
$113$	56.5637	+	84.6535i	0.500564	+	0.749146i	0.992600	−	0.121428i	$-0.0387474\pi$
$113$	56.5637	+	84.6535i	0.500564	+	0.749146i	−0.492037	+	0.870575i	$0.663747\pi$
$114$	−1.54832	−	7.78392i	−0.0135817	−	0.0682800i
$115$	−7.81881	+	7.81881i	−0.0679896	+	0.0679896i
$116$	84.6908	−	126.749i	0.730093	−	1.09266i
$117$	−47.8120	−	19.8044i	−0.408649	−	0.169268i
$118$		−	1.22041i		−	0.0103425i
$119$		0			0
$120$	−0.901076			−0.00750897
$121$	−19.7821	+	47.7582i	−0.163488	+	0.394696i
$122$	−8.93981	−	5.97339i	−0.0732772	−	0.0489622i
$123$	35.8928	+	35.8928i	0.291812	+	0.291812i
$124$	−41.4967	+	8.25420i	−0.334651	+	0.0665661i
$125$	14.2970	−	9.55296i	0.114376	−	0.0764237i
$126$	−11.6201	−	2.31139i	−0.0922234	−	0.0183444i
$127$	−17.2261	+	7.13530i	−0.135639	+	0.0561835i	−0.449470	−	0.893295i	$-0.648387\pi$
$127$	−17.2261	+	7.13530i	−0.135639	+	0.0561835i	0.313832	+	0.949479i	$0.398387\pi$
$128$	−22.2019	−	53.6001i	−0.173452	−	0.418751i
$129$	−8.66681	+	43.5710i	−0.0671846	+	0.337760i
$130$	−0.330617	−	0.494803i	−0.00254321	−	0.00380618i
$131$	−11.0035	−	55.3183i	−0.0839962	−	0.422277i	−0.999787	−	0.0206226i	$-0.993435\pi$
$131$	−11.0035	−	55.3183i	−0.0839962	−	0.422277i	0.915791	−	0.401655i	$-0.131565\pi$
$132$	−51.4023	+	51.4023i	−0.389411	+	0.389411i
$133$	−96.2090	+	143.987i	−0.723376	+	1.08261i
$134$	12.8355	+	5.31662i	0.0957870	+	0.0396763i
$135$		−	7.75026i		−	0.0574094i
$136$		0			0
$137$	167.615			1.22347			0.611733	−	0.791065i	$-0.290473\pi$
$137$	167.615			1.22347			0.611733	+	0.791065i	$0.290473\pi$
$138$	4.03869	−	9.75027i	0.0292659	−	0.0706541i
$139$	−79.7643	−	53.2968i	−0.573844	−	0.383430i	0.234522	−	0.972111i	$-0.424647\pi$
$139$	−79.7643	−	53.2968i	−0.573844	−	0.383430i	−0.808366	+	0.588681i	$0.799647\pi$
$140$	6.90319	+	6.90319i	0.0493085	+	0.0493085i
$141$	−56.0616	+	11.1513i	−0.397600	+	0.0790875i
$142$	−7.79189	+	5.20638i	−0.0548725	+	0.0366646i
$143$	−94.8300	−	18.8629i	−0.663147	−	0.131908i
$144$	99.7001	−	41.2972i	0.692362	−	0.286786i
$145$	5.09751	+	12.3065i	0.0351552	+	0.0848723i
$146$	0.541672	−	2.72317i	0.00371008	−	0.0186518i
$147$	−1.97668	−	2.95830i	−0.0134468	−	0.0201245i
$148$	−9.37507	−	47.1317i	−0.0633451	−	0.318457i
$149$	99.1314	−	99.1314i	0.665311	−	0.665311i	−0.291316	−	0.956627i	$-0.594093\pi$
$149$	99.1314	−	99.1314i	0.665311	−	0.665311i	0.956627	+	0.291316i	$0.0940930\pi$
$150$	−4.54797	+	6.80652i	−0.0303198	+	0.0453768i
$151$	84.4056	+	34.9619i	0.558977	+	0.231536i	0.644241	−	0.764822i	$-0.277173\pi$
$151$	84.4056	+	34.9619i	0.558977	+	0.231536i	−0.0852638	+	0.996358i	$0.527173\pi$
$152$			44.9672i			0.295837i
$153$		0			0
$154$	−22.1354			−0.143737
$155$	1.41482	−	3.41567i	0.00912785	−	0.0220366i
$156$	−33.8408	−	22.6117i	−0.216928	−	0.144947i
$157$	70.4744	+	70.4744i	0.448882	+	0.448882i	0.894983	−	0.446101i	$-0.147188\pi$
$157$	70.4744	+	70.4744i	0.448882	+	0.448882i	−0.446101	+	0.894983i	$0.647188\pi$
$158$	−26.8547	+	5.34174i	−0.169967	+	0.0338085i
$159$	67.9019	−	45.3706i	0.427056	−	0.285350i
$160$	3.73810	+	0.743555i	0.0233631	+	0.00464722i
$161$	−212.750	+	88.1239i	−1.32143	+	0.547353i
$162$	−2.85331	−	6.88849i	−0.0176130	−	0.0425216i
$163$	−11.0096	+	55.3490i	−0.0675435	+	0.339564i	−0.999750	−	0.0223629i	$-0.992881\pi$
$163$	−11.0096	+	55.3490i	−0.0675435	+	0.339564i	0.932206	+	0.361927i	$0.117881\pi$
$164$	−79.3385	−	118.738i	−0.483771	−	0.724015i
$165$	−1.23924	−	6.23007i	−0.00751053	−	0.0377580i
$166$	−16.9948	+	16.9948i	−0.102378	+	0.102378i
$167$	141.537	−	211.825i	0.847525	−	1.26841i	−0.113941	−	0.993488i	$-0.536347\pi$
$167$	141.537	−	211.825i	0.847525	−	1.26841i	0.961466	−	0.274924i	$-0.0886526\pi$
$168$	−17.3371	−	7.18125i	−0.103197	−	0.0427455i
$169$			114.866i			0.679682i
$170$		0			0
$171$	−169.669			−0.992218
$172$	47.8284	−	115.468i	0.278072	−	0.671325i
$173$	219.082	+	146.386i	1.26637	+	0.846162i	0.993270	−	0.115823i	$-0.0369507\pi$
$173$	219.082	+	146.386i	1.26637	+	0.846162i	0.273101	+	0.961985i	$0.411951\pi$
$174$	−8.98979	−	8.98979i	−0.0516654	−	0.0516654i
$175$	175.189	−	34.8472i	1.00108	−	0.199127i
$176$	167.640	−	112.013i	0.952499	−	0.636439i
$177$	7.15334	+	1.42289i	0.0404144	+	0.00803892i
$178$	31.6227	−	13.0985i	0.177655	−	0.0735873i
$179$	−35.7478	−	86.3029i	−0.199708	−	0.482139i	0.792020	−	0.610496i	$-0.209030\pi$
$179$	−35.7478	−	86.3029i	−0.199708	−	0.482139i	−0.991728	+	0.128357i	$0.959030\pi$
$180$	−1.86606	+	9.38134i	−0.0103670	+	0.0521185i
$181$	−190.966	−	285.801i	−1.05506	−	1.57901i	−0.788340	−	0.615240i	$-0.789059\pi$
$181$	−190.966	−	285.801i	−1.05506	−	1.57901i	−0.266723	−	0.963773i	$-0.585941\pi$
$182$	−2.41780	−	12.1551i	−0.0132846	−	0.0667863i
$183$	45.4356	−	45.4356i	0.248282	−	0.248282i
$184$	−33.2210	+	49.7187i	−0.180549	+	0.270210i
$185$	3.87950	+	1.60694i	0.0209703	+	0.00868616i
$186$			3.52863i			0.0189711i
$187$		0			0
$188$	160.810			0.855373
$189$	61.7668	−	149.118i	0.326808	−	0.788985i
$190$	−1.62224	−	1.08394i	−0.00853808	−	0.00570496i
$191$	−26.0458	−	26.0458i	−0.136365	−	0.136365i	0.635629	−	0.771995i	$-0.280741\pi$
$191$	−26.0458	−	26.0458i	−0.136365	−	0.136365i	−0.771995	+	0.635629i	$0.780741\pi$
$192$	80.8329	−	16.0787i	0.421005	−	0.0837431i
$193$	−19.5360	+	13.0535i	−0.101223	+	0.0676348i	−0.605151	−	0.796110i	$-0.706887\pi$
$193$	−19.5360	+	13.0535i	−0.101223	+	0.0676348i	0.503929	+	0.863745i	$0.331887\pi$
$194$	−30.4688	−	6.06063i	−0.157056	−	0.0312403i
$195$	3.28572	−	1.36099i	0.0168499	−	0.00697944i
$196$	3.83053	+	9.24771i	0.0195435	+	0.0471822i
$197$	−21.4075	+	107.623i	−0.108668	+	0.546308i	0.887646	+	0.460526i	$0.152339\pi$
$197$	−21.4075	+	107.623i	−0.108668	+	0.546308i	−0.996314	+	0.0857828i	$0.972661\pi$
$198$	−12.0491	−	18.0327i	−0.0608538	−	0.0910742i
$199$	−30.9258	−	155.475i	−0.155406	−	0.781280i	−0.977336	−	0.211692i	$-0.932103\pi$
$199$	−30.9258	−	155.475i	−0.155406	−	0.781280i	0.821930	−	0.569588i	$-0.192897\pi$
$200$	32.7972	−	32.7972i	0.163986	−	0.163986i
$201$	−46.1280	+	69.0354i	−0.229492	+	0.343460i
$202$	27.0663	+	11.2112i	0.133991	+	0.0555010i
$203$			277.407i			1.36654i
$204$		0			0
$205$	12.4786			0.0608713
$206$	7.81491	−	18.8669i	0.0379364	−	0.0915867i
$207$	−187.597	−	125.349i	−0.906267	−	0.605548i
$208$	79.8202	+	79.8202i	0.383751	+	0.383751i
$209$	−310.905	+	61.8428i	−1.48758	+	0.295899i
$210$	0.676983	−	0.452346i	0.00322373	−	0.00215403i
$211$	−103.188	−	20.5254i	−0.489044	−	0.0972769i	−0.0555921	−	0.998454i	$-0.517705\pi$
$211$	−103.188	−	20.5254i	−0.489044	−	0.0972769i	−0.433452	+	0.901177i	$0.642705\pi$
$212$	−212.262	+	87.9220i	−1.00124	+	0.414726i
$213$	−21.4322	−	51.7418i	−0.100620	−	0.242919i
$214$	−2.35328	+	11.8307i	−0.0109966	+	0.0552837i
$215$	6.06745	+	9.08057i	0.0282207	+	0.0422352i
$216$	−8.17655	−	41.1063i	−0.0378544	−	0.190307i
$217$	54.4433	−	54.4433i	0.250891	−	0.250891i
$218$	3.92984	−	5.88143i	0.0180268	−	0.0269790i
$219$	15.3301	+	6.34994i	0.0700005	+	0.0289952i
$220$			17.8707i			0.0812304i
$221$		0			0
$222$	−4.00780			−0.0180531
$223$	49.8581	−	120.368i	0.223579	−	0.539768i	−0.771792	−	0.635875i	$-0.780639\pi$
$223$	49.8581	−	120.368i	0.223579	−	0.539768i	0.995371	+	0.0961075i	$0.0306393\pi$
$224$	65.9967	+	44.0976i	0.294628	+	0.196864i
$225$	123.749	+	123.749i	0.549997	+	0.549997i
$226$	−23.4294	+	4.66041i	−0.103670	+	0.0206213i
$227$	281.943	−	188.388i	1.24204	−	0.829904i	0.251597	−	0.967832i	$-0.419044\pi$
$227$	281.943	−	188.388i	1.24204	−	0.829904i	0.990442	+	0.137928i	$0.0440443\pi$
$228$	−130.873	−	26.0323i	−0.574004	−	0.114177i
$229$	28.6716	−	11.8762i	0.125204	−	0.0518610i	−0.319202	−	0.947687i	$-0.603415\pi$
$229$	28.6716	−	11.8762i	0.125204	−	0.0518610i	0.444406	+	0.895826i	$0.353415\pi$
$230$	−0.992852	−	2.39696i	−0.00431675	−	0.0104216i
$231$	25.8079	−	129.745i	0.111723	−	0.561668i
$232$	40.0199	+	59.8939i	0.172499	+	0.258164i
$233$	−48.4091	−	243.369i	−0.207765	−	1.04450i	−0.934059	−	0.357119i	$-0.883759\pi$
$233$	−48.4091	−	243.369i	−0.207765	−	1.04450i	0.726294	−	0.687384i	$-0.241241\pi$
$234$	8.58610	−	8.58610i	0.0366927	−	0.0366927i
$235$	−7.80681	+	11.6837i	−0.0332205	+	0.0497180i
$236$	−18.9571	−	7.85230i	−0.0803268	−	0.0332725i
$237$		−	163.635i		−	0.690443i
$238$		0			0
$239$	183.058			0.765931			0.382966	−	0.923763i	$-0.374903\pi$
$239$	183.058			0.765931			0.382966	+	0.923763i	$0.374903\pi$
$240$	−2.83801	+	6.85157i	−0.0118250	+	0.0285482i
$241$	−273.557	−	182.785i	−1.13509	−	0.758445i	−0.161531	−	0.986868i	$-0.551643\pi$
$241$	−273.557	−	182.785i	−1.13509	−	0.758445i	−0.973562	+	0.228423i	$0.926643\pi$
$242$	−8.57644	−	8.57644i	−0.0354398	−	0.0354398i
$243$	242.162	−	48.1690i	0.996551	−	0.198226i
$244$	−150.307	+	100.432i	−0.616014	+	0.411607i
$245$	−0.857855	−	0.170638i	−0.00350145	−	0.000696482i
$246$	−11.0034	+	4.55776i	−0.0447293	+	0.0185275i
$247$	−67.9188	−	163.970i	−0.274975	−	0.663848i
$248$	3.90045	−	19.6089i	0.0157276	−	0.0790680i
$249$	−79.7994	−	119.428i	−0.320480	−	0.479631i
$250$	0.787089	+	3.95697i	0.00314836	+	0.0158279i
$251$	−157.200	+	157.200i	−0.626293	+	0.626293i	−0.947133	−	0.320840i	$-0.896035\pi$
$251$	−157.200	+	157.200i	−0.626293	+	0.626293i	0.320840	+	0.947133i	$0.396035\pi$
$252$	−110.670	+	165.629i	−0.439165	+	0.657257i
$253$	−389.445	−	161.313i	−1.53931	−	0.637602i
$254$		−	4.37484i		−	0.0172238i
$255$		0			0
$256$	−221.489			−0.865191
$257$	−55.8153	+	134.750i	−0.217180	+	0.524320i	−0.994494	−	0.104794i	$-0.966582\pi$
$257$	−55.8153	+	134.750i	−0.217180	+	0.524320i	0.777314	+	0.629113i	$0.216582\pi$
$258$	−8.66681	−	5.79098i	−0.0335923	−	0.0224456i
$259$	61.8363	+	61.8363i	0.238750	+	0.238750i
$260$	−9.81323	+	1.95197i	−0.0377432	+	0.00750758i
$261$	−225.990	+	151.002i	−0.865863	+	0.578551i
$262$	12.9795	+	2.58179i	0.0495401	+	0.00985415i
$263$	−0.704127	+	0.291659i	−0.00267729	+	0.00110897i	−0.384022	−	0.923324i	$-0.625461\pi$
$263$	−0.704127	+	0.291659i	−0.00267729	+	0.00110897i	0.381344	+	0.924433i	$0.375461\pi$
$264$	−13.1455	−	31.7360i	−0.0497935	−	0.120212i
$265$	3.91665	−	19.6903i	0.0147798	−	0.0743031i
$266$	−22.5738	−	33.7841i	−0.0848640	−	0.127008i
$267$	39.9069	+	200.626i	0.149464	+	0.751407i
$268$	165.171	−	165.171i	0.616308	−	0.616308i
$269$	137.264	−	205.431i	0.510276	−	0.763682i	−0.483468	−	0.875362i	$-0.660623\pi$
$269$	137.264	−	205.431i	0.510276	−	0.763682i	0.993744	+	0.111680i	$0.0356231\pi$
$270$	1.68005	+	0.695898i	0.00622239	+	0.00257740i
$271$		−	136.078i		−	0.502133i	−0.967970	−	0.251066i	$-0.919219\pi$
$271$		−	136.078i		−	0.502133i	0.967970	−	0.251066i	$-0.0807812\pi$
$272$		0			0
$273$	74.0652			0.271301
$274$	−15.0502	+	36.3343i	−0.0549276	+	0.132607i
$275$	271.866	+	181.655i	0.988603	+	0.660563i
$276$	−125.470	−	125.470i	−0.454600	−	0.454600i
$277$	−111.782	+	22.2349i	−0.403546	+	0.0802703i	−0.392690	−	0.919671i	$-0.628456\pi$
$277$	−111.782	+	22.2349i	−0.403546	+	0.0802703i	−0.0108557	+	0.999941i	$0.503456\pi$
$278$	18.7153	−	12.5052i	0.0673214	−	0.0449827i
$279$	73.9877	+	14.7171i	0.265189	+	0.0527493i
$280$	−4.26205	+	1.76540i	−0.0152216	+	0.00630500i
$281$	89.4048	+	215.842i	0.318167	+	0.768122i	0.999351	+	0.0360106i	$0.0114650\pi$
$281$	89.4048	+	215.842i	0.318167	+	0.768122i	−0.681185	+	0.732112i	$0.738535\pi$
$282$	2.61647	−	13.1539i	0.00927828	−	0.0466450i
$283$	211.223	+	316.118i	0.746371	+	1.11702i	0.989145	+	0.146940i	$0.0469425\pi$
$283$	211.223	+	316.118i	0.746371	+	1.11702i	−0.242774	+	0.970083i	$0.578057\pi$
$284$	30.7386	+	154.533i	0.108235	+	0.544132i
$285$	8.24484	−	8.24484i	0.0289293	−	0.0289293i
$286$	12.6038	−	18.8629i	0.0440691	−	0.0659540i
$287$	240.093	+	99.4499i	0.836562	+	0.346515i
$288$			77.7682i			0.270028i
$289$		0			0
$290$	−3.12542			−0.0107773
$291$	71.0479	−	171.525i	0.244151	−	0.589432i
$292$	−38.8149	−	25.9353i	−0.132928	−	0.0888195i
$293$	−251.716	−	251.716i	−0.859100	−	0.859100i	0.132132	−	0.991232i	$-0.457818\pi$
$293$	−251.716	−	251.716i	−0.859100	−	0.859100i	−0.991232	+	0.132132i	$0.957818\pi$
$294$	0.818766	−	0.162863i	0.00278492	−	0.000553955i
$295$	1.49082	−	0.996133i	0.00505362	−	0.00337672i
$296$	22.2716	+	4.43010i	0.0752420	+	0.0149666i
$297$	272.965	−	113.066i	0.919074	−	0.380693i
$298$	12.5880	+	30.3900i	0.0422415	+	0.101980i
$299$	46.0429	−	231.474i	0.153990	−	0.774159i
$300$	76.4663	+	114.440i	0.254888	+	0.381466i
$301$	44.3712	+	223.069i	0.147413	+	0.741093i
$302$	−15.1576	+	15.1576i	−0.0501907	+	0.0501907i
$303$	−97.2705	+	145.576i	−0.321025	+	0.480448i
$304$	341.920	+	141.628i	1.12474	+	0.465881i
$305$		−	15.7963i		−	0.0517911i
$306$		0			0
$307$	−209.760			−0.683259			−0.341629	−	0.939835i	$-0.610979\pi$
$307$	−209.760			−0.683259			−0.341629	+	0.939835i	$0.610979\pi$
$308$	−142.423	+	343.839i	−0.462411	+	1.11636i
$309$	101.475	+	67.8036i	0.328399	+	0.219429i
$310$	0.613387	+	0.613387i	0.00197867	+	0.00197867i
$311$	−3.87811	+	0.771405i	−0.0124698	+	0.00248040i	−0.201321	−	0.979525i	$-0.564524\pi$
$311$	−3.87811	+	0.771405i	−0.0124698	+	0.00248040i	0.188851	+	0.982006i	$0.439524\pi$
$312$	15.9912	−	10.6850i	0.0512537	−	0.0342466i
$313$	446.102	+	88.7352i	1.42525	+	0.283499i	0.846665	−	0.532126i	$-0.178607\pi$
$313$	446.102	+	88.7352i	1.42525	+	0.283499i	0.578581	+	0.815625i	$0.303607\pi$
$314$	−21.6049	+	8.94902i	−0.0688053	+	0.0285001i
$315$	−6.66116	−	16.0815i	−0.0211466	−	0.0510523i
$316$	−89.8120	+	451.515i	−0.284215	+	1.42885i
$317$	0.662090	+	0.990888i	0.00208861	+	0.00312583i	0.832512	−	0.554006i	$-0.186902\pi$
$317$	0.662090	+	0.990888i	0.00208861	+	0.00312583i	−0.830424	+	0.557132i	$0.811902\pi$
$318$	3.73818	+	18.7931i	0.0117553	+	0.0590978i
$319$	−359.070	+	359.070i	−1.12561	+	1.12561i
$320$	11.2563	−	16.8463i	0.0351760	−	0.0526447i
$321$	−66.6012	−	27.5871i	−0.207480	−	0.0859412i
$322$		−	54.0311i		−	0.167798i
$323$		0			0
$324$	−125.361			−0.386915
$325$	−70.0559	+	169.130i	−0.215557	+	0.520400i
$326$	−11.0096	−	7.35638i	−0.0337718	−	0.0225656i
$327$	29.8917	+	29.8917i	0.0914120	+	0.0914120i
$328$	66.1848	−	13.1650i	0.201783	−	0.0401371i
$329$	−243.321	+	162.582i	−0.739578	+	0.494170i
$330$	1.46178	+	0.290766i	0.00442964	+	0.000881109i
$331$	450.945	−	186.788i	1.36237	−	0.564313i	0.422662	−	0.906287i	$-0.361096\pi$
$331$	450.945	−	186.788i	1.36237	−	0.564313i	0.939709	+	0.341975i	$0.111096\pi$
$332$	154.640	+	373.335i	0.465784	+	1.12450i
$333$	−16.7155	+	84.0347i	−0.0501968	+	0.252357i
$334$	33.2092	+	49.7011i	0.0994288	+	0.148806i
$335$	3.98203	+	20.0190i	0.0118867	+	0.0597583i
$336$	−109.209	+	109.209i	−0.325027	+	0.325027i
$337$	50.0993	−	74.9788i	0.148662	−	0.222489i	−0.749663	−	0.661820i	$-0.769784\pi$
$337$	50.0993	−	74.9788i	0.148662	−	0.222489i	0.898325	+	0.439331i	$0.144784\pi$
$338$	−24.8999	−	10.3139i	−0.0736682	−	0.0305144i
$339$		−	142.764i		−	0.421132i
$340$		0			0
$341$	140.940			0.413315
$342$	15.2346	−	36.7797i	0.0445457	−	0.107543i
$343$	277.339	+	185.312i	0.808570	+	0.540269i
$344$	41.7609	+	41.7609i	0.121398	+	0.121398i
$345$	15.2072	−	3.02489i	0.0440787	−	0.00876781i
$346$	−51.4039	+	34.3470i	−0.148566	+	0.0992688i
$347$	173.501	+	34.5116i	0.500004	+	0.0994570i	0.438648	−	0.898659i	$-0.355458\pi$
$347$	173.501	+	34.5116i	0.500004	+	0.0994570i	0.0613560	+	0.998116i	$0.480458\pi$
$348$	−197.484	+	81.8005i	−0.567482	+	0.235059i
$349$	114.756	+	277.045i	0.328813	+	0.793826i	0.998681	+	0.0513451i	$0.0163509\pi$
$349$	114.756	+	277.045i	0.328813	+	0.793826i	−0.669868	+	0.742481i	$0.733649\pi$
$350$	−8.17630	+	41.1050i	−0.0233609	+	0.117443i
$351$	91.9025	+	137.542i	0.261831	+	0.391857i
$352$	28.3458	+	142.504i	0.0805277	+	0.404840i
$353$	213.143	−	213.143i	0.603804	−	0.603804i	−0.337516	−	0.941320i	$-0.609587\pi$
$353$	213.143	−	213.143i	0.603804	−	0.603804i	0.941320	+	0.337516i	$0.109587\pi$
$354$	−0.950743	+	1.42289i	−0.00268572	+	0.00401946i
$355$	−12.7199	−	5.26877i	−0.0358308	−	0.0148416i
$356$		−	575.486i		−	1.61653i
$357$		0			0
$358$	21.9179			0.0612232
$359$	−132.208	+	319.178i	−0.368266	+	0.889074i	0.625768	+	0.780009i	$0.284786\pi$
$359$	−132.208	+	319.178i	−0.368266	+	0.889074i	−0.994035	+	0.109065i	$0.965214\pi$
$360$	−3.75817	−	2.51113i	−0.0104394	−	0.00697536i
$361$	−156.184	−	156.184i	−0.432643	−	0.432643i
$362$	79.1009	−	15.7341i	0.218511	−	0.0434645i
$363$	60.2695	−	40.2708i	0.166032	−	0.110939i
$364$	−204.367	−	40.6511i	−0.561447	−	0.111679i
$365$	3.76867	−	1.56104i	0.0103251	−	0.00427681i
$366$	5.76953	+	13.9289i	0.0157638	+	0.0380571i
$367$	97.1102	−	488.206i	0.264605	−	1.33026i	−0.588489	−	0.808505i	$-0.700277\pi$
$367$	97.1102	−	488.206i	0.264605	−	1.33026i	0.853095	−	0.521756i	$-0.174723\pi$
$368$	273.417	+	409.197i	0.742981	+	1.11195i
$369$	49.6737	+	249.727i	0.134617	+	0.676766i
$370$	−0.696682	+	0.696682i	−0.00188292	+	0.00188292i
$371$	232.283	−	347.635i	0.626098	−	0.937022i
$372$	54.8117	+	22.7038i	0.147343	+	0.0610316i
$373$			187.052i			0.501479i	0.968055	+	0.250740i	$0.0806738\pi$
$373$			187.052i			0.501479i	−0.968055	+	0.250740i	$0.919326\pi$
$374$		0			0
$375$	−24.1111			−0.0642964
$376$	−29.0799	+	70.2050i	−0.0773401	+	0.186715i
$377$	−236.394	−	157.954i	−0.627040	−	0.418975i
$378$	26.7787	+	26.7787i	0.0708431	+	0.0708431i
$379$	76.9416	−	15.3046i	0.203012	−	0.0403816i	−0.0925366	−	0.995709i	$-0.529498\pi$
$379$	76.9416	−	15.3046i	0.203012	−	0.0403816i	0.295549	+	0.955328i	$0.404498\pi$
$380$	−27.2751	+	18.2246i	−0.0717765	+	0.0479595i
$381$	25.6428	+	5.10067i	0.0673039	+	0.0133876i
$382$	7.98468	−	3.30736i	0.0209023	−	0.00865801i
$383$	−172.808	−	417.194i	−0.451195	−	1.08928i	−0.971868	−	0.235525i	$-0.924319\pi$
$383$	−172.808	−	417.194i	−0.451195	−	1.08928i	0.520674	−	0.853756i	$-0.325681\pi$
$384$	−15.8710	+	79.7891i	−0.0413308	+	0.207784i
$385$	−18.0676	−	27.0400i	−0.0469288	−	0.0702338i
$386$	−1.07551	−	5.40694i	−0.00278629	−	0.0140076i
$387$	−157.571	+	157.571i	−0.407161	+	0.407161i
$388$	−290.183	+	434.290i	−0.747895	+	1.11930i
$389$	−100.853	−	41.7745i	−0.259261	−	0.107390i	0.249267	−	0.968435i	$-0.419810\pi$
$389$	−100.853	−	41.7745i	−0.259261	−	0.107390i	−0.508528	+	0.861045i	$0.669810\pi$
$390$			0.834459i			0.00213964i
$391$		0			0
$392$	−4.72997			−0.0120662
$393$	−30.2659	+	73.0684i	−0.0770125	+	0.185925i
$394$	−21.4075	−	14.3040i	−0.0543338	−	0.0363047i
$395$	−28.4449	−	28.4449i	−0.0720125	−	0.0720125i
$396$	−357.635	+	71.1380i	−0.903118	+	0.179641i
$397$	−477.273	+	318.904i	−1.20220	+	0.803284i	−0.984951	−	0.172832i	$-0.944708\pi$
$397$	−477.273	+	318.904i	−1.20220	+	0.803284i	−0.217249	+	0.976116i	$0.569708\pi$
$398$	36.4795	+	7.25623i	0.0916571	+	0.0182317i
$399$	224.342	−	92.9256i	0.562261	−	0.232896i
$400$	−146.084	−	352.679i	−0.365211	−	0.881697i
$401$	56.1050	−	282.059i	0.139913	−	0.703389i	−0.845604	−	0.533811i	$-0.820759\pi$
$401$	56.1050	−	282.059i	0.139913	−	0.703389i	0.985517	−	0.169578i	$-0.0542405\pi$
$402$	−10.8232	−	16.1980i	−0.0269233	−	0.0402935i
$403$	15.3946	+	77.3938i	0.0382000	+	0.192044i
$404$	348.297	−	348.297i	0.862121	−	0.862121i
$405$	6.08584	−	9.10811i	0.0150268	−	0.0224892i
$406$	−60.1342	−	24.9084i	−0.148114	−	0.0613508i
$407$			160.079i			0.393315i
$408$		0			0
$409$	208.584			0.509985			0.254992	−	0.966943i	$-0.417927\pi$
$409$	208.584			0.509985			0.254992	+	0.966943i	$0.417927\pi$
$410$	−1.12046	+	2.70502i	−0.00273282	+	0.00659761i
$411$	−195.424	−	130.578i	−0.475484	−	0.317708i
$412$	−242.785	−	242.785i	−0.589283	−	0.589283i
$413$	36.6228	−	7.28472i	0.0886750	−	0.0176385i
$414$	44.0166	−	29.4109i	0.106320	−	0.0710409i
$415$	−34.6320	−	6.88874i	−0.0834507	−	0.0165994i
$416$	−75.1561	+	31.1307i	−0.180664	+	0.0748334i
$417$	51.4779	+	124.279i	0.123448	+	0.298030i
$418$	14.5104	−	72.9486i	0.0347138	−	0.174518i
$419$	−76.4352	−	114.393i	−0.182423	−	0.273015i	0.728976	−	0.684539i	$-0.239997\pi$
$419$	−76.4352	−	114.393i	−0.182423	−	0.273015i	−0.911399	+	0.411524i	$0.864997\pi$
$420$	−2.67066	−	13.4263i	−0.00635872	−	0.0319675i
$421$	−198.240	+	198.240i	−0.470880	+	0.470880i	−0.902199	−	0.431320i	$-0.858048\pi$
$421$	−198.240	+	198.240i	−0.470880	+	0.470880i	0.431320	+	0.902199i	$0.358048\pi$
$422$	13.7147	−	20.5254i	0.0324992	−	0.0486385i
$423$	−264.896	−	109.723i	−0.626231	−	0.259393i
$424$		−	108.567i		−	0.256054i
$425$		0			0
$426$	13.1406			0.0308465
$427$	125.891	−	303.927i	0.294826	−	0.711773i
$428$	168.630	+	112.675i	0.393996	+	0.263260i
$429$	95.8684	+	95.8684i	0.223470	+	0.223470i
$430$	−2.51322	+	0.499910i	−0.00584469	+	0.00116258i
$431$	256.066	−	171.098i	0.594121	−	0.396979i	−0.221842	−	0.975083i	$-0.571207\pi$
$431$	256.066	−	171.098i	0.594121	−	0.396979i	0.815963	+	0.578104i	$0.196207\pi$
$432$	−338.315	−	67.2950i	−0.783137	−	0.155776i
$433$	−471.035	+	195.109i	−1.08784	+	0.450598i	−0.853253	−	0.521497i	$-0.825374\pi$
$433$	−471.035	+	195.109i	−1.08784	+	0.450598i	−0.234587	+	0.972095i	$0.575374\pi$
$434$	6.91334	+	16.6903i	0.0159294	+	0.0384569i
$435$	3.64396	−	18.3194i	0.00837691	−	0.0421136i
$436$	−66.0735	−	98.8859i	−0.151545	−	0.226803i
$437$	−150.954	−	758.897i	−0.345433	−	1.73661i
$438$	−2.75299	+	2.75299i	−0.00628536	+	0.00628536i
$439$	59.2933	−	88.7388i	0.135065	−	0.202138i	−0.757772	−	0.652520i	$-0.773712\pi$
$439$	59.2933	−	88.7388i	0.135065	−	0.202138i	0.892836	+	0.450381i	$0.148712\pi$
$440$	−7.80181	−	3.23162i	−0.0177314	−	0.00734458i
$441$		−	17.8470i		−	0.0404694i
$442$		0			0
$443$	−384.320			−0.867539			−0.433769	−	0.901024i	$-0.642817\pi$
$443$	−384.320			−0.867539			−0.433769	+	0.901024i	$0.642817\pi$
$444$	−25.7868	+	62.2548i	−0.0580784	+	0.140214i
$445$	41.8121	+	27.9380i	0.0939599	+	0.0627820i
$446$	21.6158	+	21.6158i	0.0484659	+	0.0484659i
$447$	−192.805	+	38.3514i	−0.431332	+	0.0857972i
$448$	350.835	−	234.420i	0.783114	−	0.523260i
$449$	39.3409	+	7.82538i	0.0876189	+	0.0174285i	0.238705	−	0.971092i	$-0.423277\pi$
$449$	39.3409	+	7.82538i	0.0876189	+	0.0174285i	−0.151086	+	0.988521i	$0.548277\pi$
$450$	−37.9370	+	15.7140i	−0.0843044	+	0.0349200i
$451$	182.046	+	439.498i	0.403649	+	0.974496i
$452$	−78.3566	+	393.925i	−0.173355	+	0.871516i
$453$	−71.1727	−	106.518i	−0.157114	−	0.235138i
$454$	15.5217	+	78.0330i	0.0341888	+	0.171879i
$455$	12.8749	−	12.8749i	0.0282964	−	0.0282964i
$456$	35.0311	−	52.4278i	0.0768227	−	0.114973i
$457$	−23.3696	−	9.67999i	−0.0511369	−	0.0211816i	0.356968	−	0.934116i	$-0.383810\pi$
$457$	−23.3696	−	9.67999i	−0.0511369	−	0.0211816i	−0.408105	+	0.912935i	$0.633810\pi$
$458$			7.28159i			0.0158987i
$459$		0			0
$460$	−43.6211			−0.0948285
$461$	254.634	−	614.740i	0.552351	−	1.33349i	−0.363358	−	0.931650i	$-0.618370\pi$
$461$	254.634	−	614.740i	0.552351	−	1.33349i	0.915708	−	0.401843i	$-0.131630\pi$
$462$	25.8079	+	17.2443i	0.0558613	+	0.0373253i
$463$	589.351	+	589.351i	1.27290	+	1.27290i	0.944561	+	0.328335i	$0.106488\pi$
$463$	589.351	+	589.351i	1.27290	+	1.27290i	0.328335	+	0.944561i	$0.393512\pi$
$464$	581.465	−	115.661i	1.25316	−	0.249268i
$465$	−4.31048	+	2.88017i	−0.00926985	+	0.00619392i
$466$	57.1025	+	11.3584i	0.122538	+	0.0243742i
$467$	249.292	−	103.260i	0.533816	−	0.221114i	−0.0994577	−	0.995042i	$-0.531711\pi$
$467$	249.292	−	103.260i	0.533816	−	0.221114i	0.633274	+	0.773928i	$0.281711\pi$
$468$	−78.1272	−	188.616i	−0.166938	−	0.403025i
$469$	−82.9284	+	416.909i	−0.176820	+	0.888932i
$470$	−1.83174	−	2.74139i	−0.00389731	−	0.00583274i
$471$	−27.2647	−	137.069i	−0.0578869	−	0.291017i
$472$	6.85617	−	6.85617i	0.0145258	−	0.0145258i
$473$	−231.303	+	346.169i	−0.489012	+	0.731859i
$474$	35.4716	+	14.6928i	0.0748346	+	0.0309975i
$475$			600.187i			1.26355i
$476$		0			0
$477$	409.641			0.858787
$478$	−16.4368	+	39.6819i	−0.0343866	+	0.0830165i
$479$	−313.491	−	209.468i	−0.654469	−	0.437302i	0.183500	−	0.983020i	$-0.441257\pi$
$479$	−313.491	−	209.468i	−0.654469	−	0.437302i	−0.837969	+	0.545717i	$0.816257\pi$
$480$	−3.77904	−	3.77904i	−0.00787299	−	0.00787299i
$481$	−87.9035	+	17.4851i	−0.182751	+	0.0363515i
$482$	64.1856	−	42.8875i	0.133165	−	0.0889782i
$483$	316.699	+	62.9954i	0.655692	+	0.130425i
$484$	−188.404	+	78.0393i	−0.389263	+	0.161238i
$485$	−17.4660	−	42.1668i	−0.0360125	−	0.0869418i
$486$	−11.3020	+	56.8192i	−0.0232552	+	0.116912i
$487$	−292.495	−	437.749i	−0.600605	−	0.898869i	0.399233	−	0.916849i	$-0.369276\pi$
$487$	−292.495	−	437.749i	−0.600605	−	0.898869i	−0.999838	+	0.0179801i	$0.994276\pi$
$488$	−16.6651	−	83.7813i	−0.0341499	−	0.171683i
$489$	55.9551	−	55.9551i	0.114428	−	0.114428i
$490$	0.114017	−	0.170638i	0.000232687	−	0.000348241i
$491$	570.101	+	236.144i	1.16110	+	0.480944i	0.878242	−	0.478217i	$-0.158717\pi$
$491$	570.101	+	236.144i	1.16110	+	0.480944i	0.282860	+	0.959161i	$0.408717\pi$
$492$			200.246i			0.407004i
$493$		0			0
$494$	41.6428			0.0842971
$495$	12.1935	−	29.4376i	0.0246332	−	0.0594699i
$496$	−136.816	−	91.4177i	−0.275839	−	0.184310i
$497$	−202.746	−	202.746i	−0.407941	−	0.407941i
$498$	33.0540	−	6.57485i	0.0663735	−	0.0132025i
$499$	692.277	−	462.565i	1.38733	−	0.926983i	0.387341	−	0.921936i	$-0.373393\pi$
$499$	692.277	−	462.565i	1.38733	−	0.926983i	0.999987	−	0.00504699i	$-0.00160651\pi$
$500$	66.5295	+	13.2335i	0.133059	+	0.0264671i
$501$	−330.038	+	136.706i	−0.658759	+	0.272867i
$502$	−19.9616	−	48.1916i	−0.0397641	−	0.0959991i
$503$	45.5423	−	228.957i	0.0905414	−	0.455182i	−0.908743	−	0.417356i	$-0.862957\pi$
$503$	45.5423	−	228.957i	0.0905414	−	0.455182i	0.999284	−	0.0378261i	$-0.0120433\pi$
$504$	−52.2959	−	78.2663i	−0.103762	−	0.155290i
$505$	8.39695	+	42.2143i	0.0166276	+	0.0835927i
$506$	69.9367	−	69.9367i	0.138215	−	0.138215i
$507$	89.4850	−	133.924i	0.176499	−	0.264149i
$508$	−67.9562	−	28.1484i	−0.133772	−	0.0554102i
$509$			195.683i			0.384447i	0.981351	+	0.192223i	$0.0615698\pi$
$509$			195.683i			0.384447i	−0.981351	+	0.192223i	$0.938430\pi$
$510$		0			0
$511$	84.9517			0.166246
$512$	108.695	−	262.413i	0.212295	−	0.512526i
$513$	450.938	+	301.307i	0.879021	+	0.587343i
$514$	−24.1985	−	24.1985i	−0.0470788	−	0.0470788i
$515$	29.4260	−	5.85319i	0.0571379	−	0.0113654i
$516$	−145.717	+	97.3652i	−0.282398	+	0.188692i
$517$	−525.392	−	104.507i	−1.01623	−	0.202141i
$518$	−18.9567	+	7.85213i	−0.0365960	+	0.0151586i
$519$	−141.390	−	341.346i	−0.272428	−	0.657699i
$520$	0.922386	−	4.63715i	0.00177382	−	0.00891759i
$521$	−548.790	−	821.322i	−1.05334	−	1.57643i	−0.791351	−	0.611362i	$-0.790622\pi$
$521$	−548.790	−	821.322i	−1.05334	−	1.57643i	−0.261988	−	0.965071i	$-0.584378\pi$
$522$	−12.4414	−	62.5470i	−0.0238341	−	0.119822i
$523$	326.381	−	326.381i	0.624055	−	0.624055i	−0.322511	−	0.946566i	$-0.604527\pi$
$523$	326.381	−	326.381i	0.624055	−	0.624055i	0.946566	+	0.322511i	$0.104527\pi$
$524$	123.616	−	185.005i	0.235909	−	0.353062i
$525$	−231.401	−	95.8496i	−0.440765	−	0.182571i
$526$		−	0.178824i		−	0.000339969i
$527$		0			0
$528$	−282.716			−0.535446
$529$	191.315	−	461.876i	0.361655	−	0.873111i
$530$	3.91665	+	2.61702i	0.00738990	+	0.00493778i
$531$	25.8695	+	25.8695i	0.0487185	+	0.0487185i
$532$	−670.027	+	133.277i	−1.25945	+	0.250520i
$533$	−221.454	+	147.971i	−0.415487	+	0.277619i
$534$	−47.0734	−	9.36349i	−0.0881525	−	0.0175346i
$535$	−16.3729	+	6.78188i	−0.0306035	+	0.0126764i
$536$	42.2403	+	101.977i	0.0788065	+	0.190256i
$537$	−25.5543	+	128.470i	−0.0475872	+	0.239237i
$538$	32.2067	+	48.2008i	0.0598638	+	0.0895926i
$539$	−6.50505	−	32.7031i	−0.0120687	−	0.0606737i
$540$	21.6194	−	21.6194i	0.0400358	−	0.0400358i
$541$	219.975	−	329.217i	0.406609	−	0.608533i	−0.570494	−	0.821302i	$-0.693248\pi$
$541$	219.975	−	329.217i	0.406609	−	0.608533i	0.977103	+	0.212769i	$0.0682481\pi$
$542$	29.4980	+	12.2185i	0.0544244	+	0.0225433i
$543$			481.989i			0.887640i
$544$		0			0
$545$	10.3922			0.0190683
$546$	−6.65033	+	16.0553i	−0.0121801	+	0.0294053i
$547$	206.011	+	137.652i	0.376621	+	0.251650i	0.729445	−	0.684040i	$-0.239779\pi$
$547$	206.011	+	137.652i	0.376621	+	0.251650i	−0.352824	+	0.935690i	$0.614779\pi$
$548$	467.561	+	467.561i	0.853214	+	0.853214i
$549$	316.121	−	62.8805i	0.575813	−	0.114536i
$550$	−63.7887	+	42.6223i	−0.115980	+	0.0774950i
$551$	−914.210	−	181.848i	−1.65918	−	0.330032i
$552$	77.4654	−	32.0872i	0.140336	−	0.0581290i
$553$	−320.596	−	773.987i	−0.579740	−	1.39962i
$554$	5.21704	−	26.2278i	0.00941704	−	0.0473426i
$555$	−3.27128	−	4.89582i	−0.00589420	−	0.00882130i
$556$	−73.8310	−	371.174i	−0.132790	−	0.667578i
$557$	−64.5724	+	64.5724i	−0.115929	+	0.115929i	−0.762691	−	0.646763i	$-0.776122\pi$
$557$	−64.5724	+	64.5724i	−0.115929	+	0.115929i	0.646763	+	0.762691i	$0.276122\pi$
$558$	−9.83363	+	14.7171i	−0.0176230	+	0.0263747i
$559$	−215.355	−	89.2028i	−0.385250	−	0.159576i
$560$			37.9679i			0.0677998i
$561$		0			0
$562$	−54.8164			−0.0975381
$563$	−115.282	+	278.316i	−0.204764	+	0.494345i	−0.992584	−	0.121561i	$-0.961210\pi$
$563$	−115.282	+	278.316i	−0.204764	+	0.494345i	0.787819	+	0.615906i	$0.211210\pi$
$564$	−187.490	−	125.277i	−0.332430	−	0.222122i
$565$	−24.8168	−	24.8168i	−0.0439236	−	0.0439236i
$566$	−87.4914	+	17.4031i	−0.154578	+	0.0307476i
$567$	189.682	−	126.742i	0.334537	−	0.223530i
$568$	−73.0233	−	14.5252i	−0.128562	−	0.0255726i
$569$	−127.480	+	52.8038i	−0.224042	+	0.0928010i	−0.491881	−	0.870663i	$-0.663690\pi$
$569$	−127.480	+	52.8038i	−0.224042	+	0.0928010i	0.267839	+	0.963464i	$0.413690\pi$
$570$	1.04695	+	2.52756i	0.00183676	+	0.00443432i
$571$	20.7890	−	104.513i	0.0364080	−	0.183036i	−0.958302	−	0.285757i	$-0.907755\pi$
$571$	20.7890	−	104.513i	0.0364080	−	0.183036i	0.994710	+	0.102721i	$0.0327550\pi$
$572$	−211.910	−	317.146i	−0.370472	−	0.554451i
$573$	10.0764	+	50.6577i	0.0175854	+	0.0884079i
$574$	−43.1161	+	43.1161i	−0.0751151	+	0.0751151i
$575$	−443.407	+	663.606i	−0.771143	+	1.15410i
$576$	381.943	+	158.206i	0.663095	+	0.274663i
$577$		−	661.008i		−	1.14559i	−0.819697	−	0.572797i	$-0.805858\pi$
$577$		−	661.008i		−	1.14559i	0.819697	−	0.572797i	$-0.194142\pi$
$578$		0			0
$579$	32.9464			0.0569022
$580$	−20.1094	+	48.5484i	−0.0346714	+	0.0837042i
$581$	−611.433	−	408.547i	−1.05238	−	0.703178i
$582$	30.8025	+	30.8025i	0.0529252	+	0.0529252i
$583$	750.634	−	149.310i	1.28754	−	0.256107i
$584$	18.3416	−	12.2555i	0.0314069	−	0.0209854i
$585$	17.4968	+	3.48032i	0.0299090	+	0.00594927i
$586$	77.1669	−	31.9636i	0.131684	−	0.0545453i
$587$	−69.4359	−	167.633i	−0.118289	−	0.285576i	0.853634	−	0.520873i	$-0.174394\pi$
$587$	−69.4359	−	167.633i	−0.118289	−	0.285576i	−0.971923	+	0.235297i	$0.924394\pi$
$588$	2.73825	−	13.7661i	0.00465689	−	0.0234118i
$589$	143.732	+	215.110i	0.244027	+	0.365212i
$590$	0.0820736	+	0.412612i	0.000139108	+	0.000699342i
$591$	108.801	−	108.801i	0.184097	−	0.184097i
$592$	103.832	−	155.395i	0.175391	−	0.262492i
$593$	−508.710	−	210.715i	−0.857859	−	0.355337i	−0.0899889	−	0.995943i	$-0.528683\pi$
$593$	−508.710	−	210.715i	−0.857859	−	0.355337i	−0.767870	+	0.640606i	$0.778683\pi$
$594$			69.3236i			0.116706i
$595$		0			0
$596$	553.054			0.927943
$597$	−85.0637	+	205.362i	−0.142485	+	0.343990i
$598$	46.0429	+	30.7649i	0.0769949	+	0.0514463i
$599$	273.259	+	273.259i	0.456191	+	0.456191i	0.897403	−	0.441212i	$-0.145451\pi$
$599$	273.259	+	273.259i	0.456191	+	0.456191i	−0.441212	+	0.897403i	$0.645451\pi$
$600$	−63.7887	+	12.6884i	−0.106315	+	0.0211473i
$601$	70.5544	−	47.1429i	0.117395	−	0.0784408i	−0.495487	−	0.868616i	$-0.665010\pi$
$601$	70.5544	−	47.1429i	0.117395	−	0.0784408i	0.612882	+	0.790175i	$0.290010\pi$
$602$	−52.3394	−	10.4110i	−0.0869425	−	0.0172939i
$603$	−384.777	+	159.380i	−0.638105	+	0.264312i
$604$	137.923	+	332.976i	0.228349	+	0.551284i
$605$	3.47641	−	17.4771i	0.00574613	−	0.0288877i
$606$	−22.8229	−	34.1569i	−0.0376615	−	0.0563645i
$607$	−65.9013	−	331.308i	−0.108569	−	0.545812i	−0.996336	−	0.0855204i	$-0.972745\pi$
$607$	−65.9013	−	331.308i	−0.108569	−	0.545812i	0.887768	−	0.460292i	$-0.152255\pi$
$608$	−188.589	+	188.589i	−0.310179	+	0.310179i
$609$	216.110	−	323.432i	0.354861	−	0.531086i
$610$	3.42421	+	1.41835i	0.00561345	+	0.00232517i
$611$		−	299.921i		−	0.490869i
$612$		0			0
$613$	770.822			1.25746			0.628729	−	0.777624i	$-0.283575\pi$
$613$	770.822			1.25746			0.628729	+	0.777624i	$0.283575\pi$
$614$	18.8344	−	45.4704i	0.0306750	−	0.0740560i
$615$	−14.5489	−	9.72129i	−0.0236568	−	0.0158070i
$616$	−124.355	−	124.355i	−0.201875	−	0.201875i
$617$	−966.785	+	192.305i	−1.56691	+	0.311678i	−0.900821	−	0.434192i	$-0.857034\pi$
$617$	−966.785	+	192.305i	−1.56691	+	0.311678i	−0.666092	+	0.745870i	$0.732034\pi$
$618$	−23.8095	+	15.9090i	−0.0385266	+	0.0257427i
$619$	555.368	+	110.470i	0.897202	+	0.178465i	0.622088	−	0.782947i	$-0.286284\pi$
$619$	555.368	+	110.470i	0.897202	+	0.178465i	0.275114	+	0.961412i	$0.411284\pi$
$620$	13.4746	−	5.58138i	0.0217333	−	0.00900222i
$621$	275.986	+	666.289i	0.444422	+	1.07293i
$622$	0.180997	−	0.909934i	0.000290992	−	0.00146292i
$623$	581.827	+	870.765i	0.933911	+	1.39770i
$624$	−30.8803	−	155.246i	−0.0494877	−	0.248792i
$625$	435.650	−	435.650i	0.697040	−	0.697040i
$626$	−59.2910	+	88.7352i	−0.0947140	+	0.141750i
$627$	410.665	+	170.103i	0.654968	+	0.271297i
$628$			393.177i			0.626078i
$629$		0			0
$630$	4.08413			0.00648275
$631$	−55.4123	+	133.777i	−0.0878166	+	0.212008i	−0.961686	−	0.274152i	$-0.911603\pi$
$631$	−55.4123	+	133.777i	−0.0878166	+	0.212008i	0.873870	+	0.486160i	$0.161603\pi$
$632$	−180.877	−	120.858i	−0.286198	−	0.191232i
$633$	104.318	+	104.318i	0.164800	+	0.164800i
$634$	−0.274247	+	0.0545511i	−0.000432566	+	8.60427e-5i
$635$	5.34418	−	3.57087i	0.00841604	−	0.00562342i
$636$	315.973	+	62.8510i	0.496814	+	0.0988224i
$637$	17.2475	−	7.14417i	0.0270762	−	0.0112153i
$638$	−45.5956	−	110.077i	−0.0714664	−	0.172535i
$639$	54.8063	−	275.530i	0.0857688	−	0.431189i
$640$	11.1110	+	16.6287i	0.0173609	+	0.0259824i
$641$	163.533	+	822.135i	0.255121	+	1.28258i	0.869643	+	0.493682i	$0.164349\pi$
$641$	163.533	+	822.135i	0.255121	+	1.28258i	−0.614521	+	0.788900i	$0.710651\pi$
$642$	11.9603	−	11.9603i	0.0186297	−	0.0186297i
$643$	13.5871	−	20.3346i	0.0211308	−	0.0316245i	−0.820754	−	0.571282i	$-0.806446\pi$
$643$	13.5871	−	20.3346i	0.0211308	−	0.0316245i	0.841885	+	0.539657i	$0.181446\pi$
$644$	−839.287	−	347.644i	−1.30324	−	0.539820i
$645$		−	15.3139i		−	0.0237425i
$646$		0			0
$647$	−1125.85			−1.74011			−0.870054	−	0.492957i	$-0.835916\pi$
$647$	−1125.85			−1.74011			−0.870054	+	0.492957i	$0.835916\pi$
$648$	22.6694	−	54.7287i	0.0349836	−	0.0844579i
$649$	56.8329	+	37.9745i	0.0875700	+	0.0585124i
$650$	−30.3724	−	30.3724i	−0.0467268	−	0.0467268i
$651$	−105.889	+	21.0627i	−0.162656	+	0.0323544i
$652$	−185.107	+	123.685i	−0.283907	+	0.189700i
$653$	205.143	+	40.8055i	0.314155	+	0.0624892i	0.349649	−	0.936881i	$-0.386301\pi$
$653$	205.143	+	40.8055i	0.314155	+	0.0624892i	−0.0354948	+	0.999370i	$0.511301\pi$
$654$	−9.16369	+	3.79573i	−0.0140118	+	0.00580386i
$655$	7.44042	+	17.9628i	0.0113594	+	0.0274240i
$656$	108.351	−	544.717i	0.165169	−	0.830361i
$657$	46.2421	+	69.2061i	0.0703836	+	0.105337i
$658$	−13.3955	−	67.3436i	−0.0203579	−	0.102346i
$659$	−776.454	+	776.454i	−1.17823	+	1.17823i	−0.198036	+	0.980195i	$0.563456\pi$
$659$	−776.454	+	776.454i	−1.17823	+	1.17823i	−0.980195	+	0.198036i	$0.936544\pi$
$660$	13.9219	−	20.8356i	0.0210938	−	0.0315691i
$661$	561.618	+	232.630i	0.849649	+	0.351936i	0.764651	−	0.644445i	$-0.222911\pi$
$661$	561.618	+	232.630i	0.849649	+	0.351936i	0.0849986	+	0.996381i	$0.472911\pi$
$662$			114.524i			0.172997i
$663$		0			0
$664$	−190.951			−0.287577
$665$	22.8444	−	55.1512i	0.0343524	−	0.0829341i
$666$	−16.7155	−	11.1690i	−0.0250984	−	0.0167702i
$667$	−876.464	−	876.464i	−1.31404	−	1.31404i
$668$	985.701	−	196.068i	1.47560	−	0.293515i
$669$	−151.901	+	101.497i	−0.227057	+	0.151715i
$670$	−4.69713	−	0.934317i	−0.00701064	−	0.00139450i
$671$	556.347	−	230.446i	0.829131	−	0.343437i
$672$	−42.5926	−	102.828i	−0.0633819	−	0.153017i
$673$	−149.674	+	752.462i	−0.222398	+	1.11807i	0.694666	+	0.719332i	$0.255552\pi$
$673$	−149.674	+	752.462i	−0.222398	+	1.11807i	−0.917064	+	0.398739i	$0.869448\pi$
$674$	11.7549	+	17.5925i	0.0174406	+	0.0261017i
$675$	−109.134	−	548.654i	−0.161680	−	0.812821i
$676$	−320.419	+	320.419i	−0.473993	+	0.473993i
$677$	−397.840	+	595.410i	−0.587651	+	0.879483i	−0.999495	−	0.0317720i	$-0.989885\pi$
$677$	−397.840	+	595.410i	−0.587651	+	0.879483i	0.411844	+	0.911254i	$0.364885\pi$
$678$	30.9473	+	12.8188i	0.0456449	+	0.0189068i
$679$		−	950.503i		−	1.39986i
$680$		0			0
$681$	−475.482			−0.698211
$682$	−12.6551	+	30.5520i	−0.0185558	+	0.0447977i
$683$	1028.09	+	686.947i	1.50525	+	1.00578i	0.988764	+	0.149485i	$0.0477616\pi$
$683$	1028.09	+	686.947i	1.50525	+	1.00578i	0.516490	+	0.856293i	$0.327238\pi$
$684$	−473.292	−	473.292i	−0.691948	−	0.691948i
$685$	−56.6694	+	11.2722i	−0.0827290	+	0.0164558i
$686$	−65.0730	+	43.4804i	−0.0948586	+	0.0633825i
$687$	−42.6805	−	8.48968i	−0.0621259	−	0.0123576i
$688$	449.069	−	186.010i	0.652717	−	0.270364i
$689$	163.980	+	395.882i	0.237997	+	0.574575i
$690$	−0.709740	+	3.56811i	−0.00102861	+	0.00517117i
$691$	130.161	+	194.799i	0.188365	+	0.281909i	0.913618	−	0.406575i	$-0.133277\pi$
$691$	130.161	+	194.799i	0.188365	+	0.281909i	−0.725252	+	0.688483i	$0.758277\pi$
$692$	202.786	+	1019.47i	0.293043	+	1.47323i
$693$	469.214	−	469.214i	0.677076	−	0.677076i
$694$	−23.0599	+	34.5116i	−0.0332275	+	0.0497285i
$695$	30.5520	+	12.6551i	0.0439597	+	0.0182087i
$696$		−	101.008i		−	0.145126i
$697$		0			0
$698$	−70.3598			−0.100802
$699$	−133.153	+	321.459i	−0.190490	+	0.459884i
$700$	585.894	+	391.482i	0.836992	+	0.559260i
$701$	−375.122	−	375.122i	−0.535124	−	0.535124i	0.386968	−	0.922093i	$-0.373522\pi$
$701$	−375.122	−	375.122i	−0.535124	−	0.535124i	−0.922093	+	0.386968i	$0.873522\pi$
$702$	−38.0673	+	7.57205i	−0.0542269	+	0.0107864i
$703$	−244.321	+	163.250i	−0.347540	+	0.232219i
$704$	757.542	+	150.685i	1.07605	+	0.214041i
$705$	18.2041	−	7.54038i	0.0258214	−	0.0106956i
$706$	27.0654	+	65.3416i	0.0383363	+	0.0925519i
$707$	−174.872	+	879.141i	−0.247344	+	1.24348i
$708$	15.9851	+	23.9234i	0.0225778	+	0.0337901i
$709$	31.6131	+	158.930i	0.0445882	+	0.224160i	0.996654	−	0.0817322i	$-0.0260452\pi$
$709$	31.6131	+	158.930i	0.0445882	+	0.224160i	−0.952066	+	0.305892i	$0.901045\pi$
$710$	2.28425	−	2.28425i	0.00321726	−	0.00321726i
$711$	456.020	−	682.482i	0.641378	−	0.959890i
$712$	251.240	+	104.067i	0.352866	+	0.146162i
$713$			344.026i			0.482505i
$714$		0			0
$715$	33.3299			0.0466153
$716$	141.023	−	340.460i	0.196960	−	0.475503i
$717$	−213.429	−	142.609i	−0.297669	−	0.198896i
$718$	−57.3180	−	57.3180i	−0.0798301	−	0.0798301i
$719$	−303.237	+	60.3176i	−0.421748	+	0.0838909i	−0.401402	−	0.915902i	$-0.631477\pi$
$719$	−303.237	+	60.3176i	−0.421748	+	0.0838909i	−0.0203463	+	0.999793i	$0.506477\pi$
$720$	−30.9307	+	20.6672i	−0.0429592	+	0.0287045i
$721$	612.816	+	121.897i	0.849952	+	0.169066i
$722$	47.8803	−	19.8327i	0.0663162	−	0.0274691i
$723$	176.547	+	426.223i	0.244187	+	0.589519i
$724$	264.542	−	1329.94i	0.365390	−	1.83694i
$725$	534.153	+	799.417i	0.736763	+	1.10264i
$726$	3.31800	+	16.6807i	0.00457025	+	0.0229762i
$727$	−114.563	+	114.563i	−0.157583	+	0.157583i	−0.781495	−	0.623912i	$-0.785542\pi$
$727$	−114.563	+	114.563i	−0.157583	+	0.157583i	0.623912	+	0.781495i	$0.285542\pi$
$728$	54.7034	−	81.8695i	0.0751421	−	0.112458i
$729$	−55.6376	−	23.0458i	−0.0763204	−	0.0316129i
$730$			0.957112i			0.00131111i
$731$		0			0
$732$	253.485			0.346291
$733$	−513.896	+	1240.65i	−0.701086	+	1.69257i	0.0200698	+	0.999799i	$0.493611\pi$
$733$	−513.896	+	1240.65i	−0.701086	+	1.69257i	−0.721156	+	0.692773i	$0.756389\pi$
$734$	97.1102	+	64.8870i	0.132303	+	0.0884019i
$735$	0.867249	+	0.867249i	0.00117993	+	0.00117993i
$736$	−347.842	+	69.1900i	−0.472611	+	0.0940082i
$737$	−646.980	+	432.298i	−0.877856	+	0.586564i
$738$	−58.5941	−	11.6551i	−0.0793959	−	0.0157928i
$739$	−435.411	+	180.353i	−0.589190	+	0.244050i	−0.657302	−	0.753627i	$-0.728302\pi$
$739$	−435.411	+	180.353i	−0.589190	+	0.244050i	0.0681123	+	0.997678i	$0.478302\pi$
$740$	6.33929	+	15.3044i	0.00856661	+	0.0206816i
$741$	−48.5517	+	244.086i	−0.0655219	+	0.329401i
$742$	54.5012	+	81.5668i	0.0734517	+	0.109928i
$743$	236.227	+	1187.59i	0.317937	+	1.59838i	0.727508	+	0.686099i	$0.240678\pi$
$743$	236.227	+	1187.59i	0.317937	+	1.59838i	−0.409571	+	0.912278i	$0.634322\pi$
$744$	−19.8236	+	19.8236i	−0.0266446	+	0.0266446i
$745$	−26.8490	+	40.1823i	−0.0360389	+	0.0539360i
$746$	−40.5477	−	16.7954i	−0.0543535	−	0.0225140i
$747$		−	720.492i		−	0.964514i
$748$		0			0
$749$	−369.070			−0.492750
$750$	2.16495	−	5.22664i	0.00288659	−	0.00696885i
$751$	−1109.18	−	741.132i	−1.47694	−	0.986860i	−0.993784	−	0.111326i	$-0.964490\pi$
$751$	−1109.18	−	741.132i	−1.47694	−	0.986860i	−0.483156	−	0.875534i	$-0.660510\pi$
$752$	442.232	+	442.232i	0.588075	+	0.588075i
$753$	305.745	−	60.8164i	0.406036	−	0.0807655i
$754$	55.4659	−	37.0611i	0.0735622	−	0.0491527i
$755$	−30.8882	−	6.14404i	−0.0409115	−	0.00813780i
$756$	588.263	−	243.667i	0.778126	−	0.322310i
$757$	216.673	+	523.096i	0.286226	+	0.691011i	0.999956	−	0.00941009i	$-0.00299537\pi$
$757$	216.673	+	523.096i	0.286226	+	0.691011i	−0.713729	+	0.700422i	$0.752995\pi$
$758$	−3.59097	+	18.0530i	−0.00473743	+	0.0238167i
$759$	328.389	+	491.469i	0.432660	+	0.647521i
$760$	−3.02409	−	15.2031i	−0.00397906	−	0.0200041i
$761$	−375.368	+	375.368i	−0.493256	+	0.493256i	−0.909330	−	0.416075i	$-0.863406\pi$
$761$	−375.368	+	375.368i	−0.493256	+	0.493256i	0.416075	+	0.909330i	$0.363406\pi$
$762$	−3.40816	+	5.10067i	−0.00447265	+	0.00669379i
$763$	199.951	+	82.8224i	0.262059	+	0.108548i
$764$		−	145.309i		−	0.190196i
$765$		0			0
$766$	105.953			0.138320
$767$	−14.6450	+	35.3562i	−0.0190939	+	0.0460968i
$768$	258.236	+	172.548i	0.336245	+	0.224672i
$769$	443.086	+	443.086i	0.576185	+	0.576185i	0.933850	−	0.357665i	$-0.116427\pi$
$769$	443.086	+	443.086i	0.576185	+	0.576185i	−0.357665	+	0.933850i	$0.616427\pi$
$770$	7.48383	−	1.48863i	0.00971926	−	0.00193328i
$771$	170.051	−	113.624i	0.220559	−	0.147373i
$772$	−90.9083	−	18.0828i	−0.117757	−	0.0234233i
$773$	966.801	−	400.462i	1.25071	−	0.518062i	0.343666	−	0.939092i	$-0.388331\pi$
$773$	966.801	−	400.462i	1.25071	−	0.518062i	0.907047	+	0.421029i	$0.138331\pi$
$774$	−20.0088	−	48.3055i	−0.0258511	−	0.0624102i
$775$	52.0601	−	261.724i	0.0671743	−	0.337708i
$776$	−137.123	−	205.220i	−0.176706	−	0.264458i
$777$	−23.9229	−	120.268i	−0.0307888	−	0.154786i
$778$	18.1112	−	18.1112i	0.0232791	−	0.0232791i
$779$	−485.131	+	726.049i	−0.622761	+	0.932027i
$780$	12.9620	+	5.36904i	0.0166180	+	0.00688338i
$781$		−	524.862i		−	0.672038i
$782$		0			0
$783$	868.781			1.10955
$784$	−14.8974	+	35.9655i	−0.0190018	+	0.0458744i
$785$	−28.5664	−	19.0875i	−0.0363903	−	0.0243152i
$786$	−13.1216	−	13.1216i	−0.0166942	−	0.0166942i
$787$	730.451	−	145.296i	0.928146	−	0.184620i	0.292204	−	0.956356i	$-0.405612\pi$
$787$	730.451	−	145.296i	0.928146	−	0.184620i	0.635942	+	0.771736i	$0.280612\pi$
$788$	−359.930	+	240.497i	−0.456764	+	0.305200i
$789$	1.04816	+	0.208492i	0.00132847	+	0.000264249i
$790$	8.72016	−	3.61201i	0.0110382	−	0.00457216i
$791$	−279.704	−	675.266i	−0.353609	−	0.853687i
$792$	33.6156	−	168.997i	0.0424439	−	0.213380i
$793$	187.312	+	280.332i	0.236207	+	0.353509i
$794$	−26.2752	−	132.094i	−0.0330922	−	0.166366i
$795$	−19.9059	+	19.9059i	−0.0250389	+	0.0250389i
$796$	347.429	−	519.964i	0.436469	−	0.653221i
$797$	170.291	+	70.5367i	0.213665	+	0.0885028i	0.486949	−	0.873431i	$-0.338110\pi$
$797$	170.291	+	70.5367i	0.213665	+	0.0885028i	−0.273284	+	0.961933i	$0.588110\pi$
$798$			56.9751i			0.0713974i
$799$		0			0
$800$	275.097			0.343871
$801$	−392.663	+	947.974i	−0.490217	+	1.18349i
$802$	56.1050	+	37.4882i	0.0699564	+	0.0467434i
$803$	109.960	+	109.960i	0.136936	+	0.136936i
$804$	−321.248	+	63.9002i	−0.399562	+	0.0794779i
$805$	66.0029	−	44.1017i	0.0819911	−	0.0547847i
$806$	−18.1592	−	3.61208i	−0.0225300	−	0.00448149i
$807$	−320.076	+	132.580i	−0.396624	+	0.164287i
$808$	89.0725	+	215.040i	0.110238	+	0.266139i
$809$	−160.091	+	804.834i	−0.197888	+	0.994850i	0.746342	+	0.665563i	$0.231809\pi$
$809$	−160.091	+	804.834i	−0.197888	+	0.994850i	−0.944230	+	0.329287i	$0.893191\pi$
$810$	1.42794	+	2.13706i	0.00176289	+	0.00263835i
$811$	101.521	+	510.378i	0.125179	+	0.629319i	0.991529	+	0.129882i	$0.0414599\pi$
$811$	101.521	+	510.378i	0.125179	+	0.629319i	−0.866350	+	0.499437i	$0.833540\pi$
$812$	−773.826	+	773.826i	−0.952988	+	0.952988i
$813$	−106.010	+	158.655i	−0.130393	+	0.195147i
$814$	−34.7008	−	14.3736i	−0.0426300	−	0.0176579i
$815$		−	19.4535i		−	0.0238693i
$816$		0			0
$817$	−764.224			−0.935402
$818$	−18.7288	+	45.2153i	−0.0228958	+	0.0552754i
$819$	308.908	+	206.406i	0.377177	+	0.252021i
$820$	34.8091	+	34.8091i	0.0424501	+	0.0424501i
$821$	−736.782	+	146.555i	−0.897421	+	0.178508i	−0.622186	−	0.782869i	$-0.713755\pi$
$821$	−736.782	+	146.555i	−0.897421	+	0.178508i	−0.275234	+	0.961377i	$0.588755\pi$
$822$	45.8529	−	30.6379i	0.0557821	−	0.0372724i
$823$	−1169.24	−	232.576i	−1.42070	−	0.282595i	−0.575832	−	0.817568i	$-0.695322\pi$
$823$	−1169.24	−	232.576i	−1.42070	−	0.282595i	−0.844869	+	0.534973i	$0.820322\pi$
$824$	149.896	−	62.0890i	0.181913	−	0.0753508i
$825$	−175.455	−	423.587i	−0.212673	−	0.513439i
$826$	−1.70924	+	8.59291i	−0.00206929	+	0.0104030i
$827$	−69.0415	−	103.328i	−0.0834843	−	0.124943i	0.787377	−	0.616471i	$-0.211438\pi$
$827$	−69.0415	−	103.328i	−0.0834843	−	0.124943i	−0.870862	+	0.491528i	$0.836438\pi$
$828$	−173.643	−	872.962i	−0.209714	−	1.05430i
$829$	790.484	−	790.484i	0.953540	−	0.953540i	−0.0454281	−	0.998968i	$-0.514465\pi$
$829$	790.484	−	790.484i	0.953540	−	0.953540i	0.998968	+	0.0454281i	$0.0144652\pi$
$830$	4.60291	−	6.88874i	0.00554567	−	0.00829969i
$831$	147.650	+	61.1586i	0.177677	+	0.0735964i
$832$			432.444i			0.519764i
$833$		0			0
$834$	−31.5624			−0.0378446
$835$	−33.6072	+	81.1349i	−0.0402481	+	0.0971676i
$836$	−1039.78	−	694.758i	−1.24375	−	0.831050i
$837$	−170.505	−	170.505i	−0.203710	−	0.203710i
$838$	31.6605	−	6.29767i	0.0377810	−	0.00751512i
$839$	−999.491	+	667.839i	−1.19129	+	0.795994i	−0.983274	−	0.182132i	$-0.941700\pi$
$839$	−999.491	+	667.839i	−1.19129	+	0.795994i	−0.208015	+	0.978126i	$0.566700\pi$
$840$	6.34449	+	1.26200i	0.00755296	+	0.00150238i
$841$	−602.536	+	249.579i	−0.716452	+	0.296764i
$842$	−25.1731	−	60.7731i	−0.0298967	−	0.0721771i
$843$	63.9110	−	321.303i	0.0758138	−	0.381142i
$844$	−230.588	−	345.099i	−0.273209	−	0.408886i
$845$	−7.72485	−	38.8355i	−0.00914184	−	0.0459591i
$846$	47.5701	−	47.5701i	0.0562294	−	0.0562294i
$847$	206.173	−	308.560i	0.243416	−	0.364298i
$848$	−825.515	−	341.940i	−0.973485	−	0.403231i
$849$		−	533.115i		−	0.627933i
$850$		0			0
$851$	−390.743			−0.459157
$852$	84.5487	−	204.119i	0.0992356	−	0.239576i
$853$	1273.12	+	850.670i	1.49252	+	0.997268i	0.991253	+	0.131974i	$0.0421315\pi$
$853$	1273.12	+	850.670i	1.49252	+	0.997268i	0.501264	+	0.865294i	$0.332868\pi$
$854$	54.5793	+	54.5793i	0.0639102	+	0.0639102i
$855$	57.3640	−	11.4104i	0.0670924	−	0.0133455i
$856$	−79.6846	+	53.2436i	−0.0930895	+	0.0622004i
$857$	−603.771	−	120.097i	−0.704516	−	0.140137i	−0.170185	−	0.985412i	$-0.554437\pi$
$857$	−603.771	−	120.097i	−0.704516	−	0.140137i	−0.534331	+	0.845275i	$0.679437\pi$
$858$	−29.3897	+	12.1736i	−0.0342537	+	0.0141884i
$859$	67.0958	+	161.984i	0.0781092	+	0.188572i	0.958110	−	0.286399i	$-0.0924584\pi$
$859$	67.0958	+	161.984i	0.0781092	+	0.188572i	−0.880001	+	0.474972i	$0.842458\pi$
$860$	−8.40512	+	42.2554i	−0.00977339	+	0.0491342i
$861$	−202.452	−	302.991i	−0.235136	−	0.351906i
$862$	14.0971	+	70.8711i	0.0163540	+	0.0822170i
$863$	551.248	−	551.248i	0.638758	−	0.638758i	−0.311491	−	0.950249i	$-0.600828\pi$
$863$	551.248	−	551.248i	0.638758	−	0.638758i	0.950249	+	0.311491i	$0.100828\pi$
$864$	138.105	−	206.688i	0.159843	−	0.239222i
$865$	−83.9147	−	34.7586i	−0.0970113	−	0.0401834i
$866$		−	119.626i		−	0.138137i
$867$		0			0
$868$	303.739			0.349930
$869$	586.860	−	1416.81i	0.675328	−	1.63039i
$870$	3.64396	+	2.43481i	0.00418846	+	0.00279864i
$871$	−308.053	−	308.053i	−0.353678	−	0.353678i
$872$	55.1190	−	10.9639i	0.0632099	−	0.0125732i
$873$	774.330	−	517.391i	0.886976	−	0.592658i
$874$	178.062	+	35.4188i	0.203733	+	0.0405250i
$875$	−114.045	+	47.2389i	−0.130337	+	0.0539873i
$876$	25.0502	+	60.4765i	0.0285961	+	0.0690371i
$877$	218.705	−	1099.51i	0.249379	−	1.25371i	−0.629626	−	0.776899i	$-0.716792\pi$
$877$	218.705	−	1099.51i	0.249379	−	1.25371i	0.879005	−	0.476813i	$-0.158208\pi$
$878$	13.9122	+	20.8211i	0.0158453	+	0.0237142i
$879$	97.3825	+	489.575i	0.110788	+	0.556968i
$880$	−49.1449	+	49.1449i	−0.0558464	+	0.0558464i
$881$	−504.582	+	755.160i	−0.572738	+	0.857163i	−0.998871	−	0.0474975i	$-0.984875\pi$
$881$	−504.582	+	755.160i	−0.572738	+	0.857163i	0.426133	+	0.904660i	$0.359875\pi$
$882$	3.86874	+	1.60248i	0.00438633	+	0.00181688i
$883$			1050.48i			1.18967i	0.803846	+	0.594837i	$0.202783\pi$
$883$			1050.48i			1.18967i	−0.803846	+	0.594837i	$0.797217\pi$
$884$		0			0
$885$	−2.51419			−0.00284089
$886$	34.5082	−	83.3100i	0.0389483	−	0.0940294i
$887$	−751.183	−	501.925i	−0.846881	−	0.565868i	0.0546880	−	0.998503i	$-0.482584\pi$
$887$	−751.183	−	501.925i	−0.846881	−	0.565868i	−0.901569	+	0.432636i	$0.857584\pi$
$888$	−22.5155	−	22.5155i	−0.0253553	−	0.0253553i
$889$	131.283	−	26.1138i	0.147675	−	0.0293743i
$890$	−9.81051	+	6.55518i	−0.0110230	+	0.00736537i
$891$	409.573	+	81.4691i	0.459678	+	0.0914355i
$892$	474.846	−	196.688i	0.532339	−	0.220502i
$893$	−376.295	−	908.455i	−0.421382	−	1.01731i
$894$	8.99850	−	45.2385i	0.0100654	−	0.0506024i
$895$	17.8900	+	26.7743i	0.0199889	+	0.0299155i
$896$	81.2545	+	408.494i	0.0906858	+	0.455908i
$897$	−234.008	+	234.008i	−0.260879	+	0.260879i
$898$	−5.22875	+	7.82538i	−0.00582267	+	0.00871424i
$899$	382.886	+	158.597i	0.425902	+	0.176414i
$900$			690.397i			0.767108i
$901$		0			0
$902$	−111.617			−0.123744
$903$	122.046	−	294.645i	0.135156	−	0.326296i
$904$	−157.807	−	105.443i	−0.174565	−	0.116641i
$905$	83.7848	+	83.7848i	0.0925799	+	0.0925799i
$906$	29.4807	−	5.86408i	0.0325394	−	0.00647249i
$907$	1096.70	−	732.795i	1.20916	−	0.807933i	0.223174	−	0.974779i	$-0.428358\pi$
$907$	1096.70	−	732.795i	1.20916	−	0.807933i	0.985983	+	0.166846i	$0.0533583\pi$
$908$	1311.99	+	260.971i	1.44492	+	0.287413i
$909$	−811.383	+	336.086i	−0.892611	+	0.369731i
$910$	1.63488	+	3.94696i	0.00179657	+	0.00433731i
$911$	−145.378	+	730.867i	−0.159581	+	0.802268i	0.815213	+	0.579161i	$0.196620\pi$
$911$	−145.378	+	730.867i	−0.159581	+	0.802268i	−0.974794	+	0.223107i	$0.928380\pi$
$912$	−288.315	−	431.494i	−0.316135	−	0.473129i
$913$	−262.612	−	1320.24i	−0.287637	−	1.44605i
$914$	4.19671	−	4.19671i	0.00459159	−	0.00459159i
$915$	−12.3059	+	18.4171i	−0.0134491	+	0.0201279i
$916$	113.108	+	46.8509i	0.123480	+	0.0511472i
$917$			404.908i			0.441557i
$918$		0			0
$919$	682.519			0.742676			0.371338	−	0.928498i	$-0.378899\pi$
$919$	682.519			0.742676			0.371338	+	0.928498i	$0.378899\pi$
$920$	7.88816	−	19.0437i	0.00857408	−	0.0206997i
$921$	244.562	+	163.411i	0.265540	+	0.177428i
$922$	110.395	+	110.395i	0.119735	+	0.119735i
$923$	288.214	−	57.3294i	0.312258	−	0.0621120i
$924$	433.915	−	289.933i	0.469605	−	0.313780i
$925$	297.264	+	59.1295i	0.321367	+	0.0639238i
$926$	−180.673	+	74.8373i	−0.195111	+	0.0808178i
$927$	234.273	+	565.584i	0.252721	+	0.610123i
$928$	−83.3502	+	419.030i	−0.0898170	+	0.451541i
$929$	−430.472	−	644.248i	−0.463372	−	0.693485i	0.524033	−	0.851698i	$-0.324427\pi$
$929$	−430.472	−	644.248i	−0.463372	−	0.693485i	−0.987405	+	0.158213i	$0.949427\pi$
$930$	−0.237304	−	1.19301i	−0.000255165	−	0.00128280i
$931$	43.2791	−	43.2791i	0.0464867	−	0.0464867i
$932$	543.841	−	813.915i	0.583520	−	0.873300i
$933$	5.12249	+	2.12180i	0.00549034	+	0.00227417i
$934$			63.3115i			0.0677853i
$935$		0			0
$936$	96.4721			0.103069
$937$	66.3005	−	160.063i	0.0707582	−	0.170825i	−0.884544	−	0.466457i	$-0.845530\pi$
$937$	66.3005	−	160.063i	0.0707582	−	0.170825i	0.955302	+	0.295632i	$0.0955301\pi$
$938$	−82.9284	−	55.4110i	−0.0884098	−	0.0590736i
$939$	−450.987	−	450.987i	−0.480285	−	0.480285i
$940$	−54.3688	+	10.8146i	−0.0578392	+	0.0115049i
$941$	465.248	−	310.869i	0.494419	−	0.330360i	−0.283237	−	0.959050i	$-0.591408\pi$
$941$	465.248	−	310.869i	0.494419	−	0.330360i	0.777656	+	0.628690i	$0.216408\pi$
$942$	32.1609	+	6.39721i	0.0341411	+	0.00679109i
$943$	−1072.78	+	444.362i	−1.13763	+	0.471221i
$944$	−30.5386	−	73.7267i	−0.0323502	−	0.0781003i
$945$	−10.8546	+	54.5697i	−0.0114863	+	0.0577457i
$946$	−54.2713	−	81.2228i	−0.0573693	−	0.0858592i
$947$	−265.595	−	1335.24i	−0.280459	−	1.40996i	−0.822095	−	0.569351i	$-0.807195\pi$
$947$	−265.595	−	1335.24i	−0.280459	−	1.40996i	0.541635	−	0.840614i	$-0.317805\pi$
$948$	456.460	−	456.460i	0.481498	−	0.481498i
$949$	−48.3709	+	72.3922i	−0.0509704	+	0.0762826i
$950$	−130.104	−	53.8909i	−0.136952	−	0.0567273i
$951$		−	1.67108i		−	0.00175718i
$952$		0			0
$953$	−553.052			−0.580328			−0.290164	−	0.956977i	$-0.593710\pi$
$953$	−553.052			−0.580328			−0.290164	+	0.956977i	$0.593710\pi$
$954$	−36.7818	+	88.7991i	−0.0385553	+	0.0930808i
$955$	10.5575	+	7.05430i	0.0110550	+	0.00738670i
$956$	510.639	+	510.639i	0.534141	+	0.534141i
$957$	698.371	−	138.915i	0.729751	−	0.145156i
$958$	73.5553	−	49.1481i	0.0767801	−	0.0513028i
$959$	−1180.18	−	234.752i	−1.23063	−	0.244788i
$960$	−26.2478	+	10.8722i	−0.0273414	+	0.0113252i
$961$	323.740	+	781.578i	0.336878	+	0.813297i
$962$	4.10258	−	20.6251i	0.00426464	−	0.0214398i
$963$	−200.897	−	300.664i	−0.208616	−	0.312216i
$964$	−253.209	−	1272.97i	−0.262665	−	1.32051i
$965$	5.72712	−	5.72712i	0.00593483	−	0.00593483i
$966$	−42.0922	+	62.9954i	−0.0435737	+	0.0652126i
$967$	−681.241	−	282.179i	−0.704490	−	0.291809i	0.00153265	−	0.999999i	$-0.499512\pi$
$967$	−681.241	−	282.179i	−0.704490	−	0.291809i	−0.706022	+	0.708190i	$0.749512\pi$
$968$		−	96.3636i		−	0.0995491i
$969$		0			0
$970$	10.7089			0.0110401
$971$	650.532	−	1570.52i	0.669961	−	1.61743i	−0.111712	−	0.993741i	$-0.535633\pi$
$971$	650.532	−	1570.52i	0.669961	−	1.61743i	0.781673	−	0.623688i	$-0.214367\pi$
$972$	809.878	+	541.143i	0.833208	+	0.556732i
$973$	486.976	+	486.976i	0.500490	+	0.500490i
$974$	121.155	−	24.0993i	0.124389	−	0.0247426i
$975$	213.437	−	142.614i	0.218910	−	0.146271i
$976$	−689.541	−	137.158i	−0.706497	−	0.140531i
$977$	112.483	−	46.5920i	0.115131	−	0.0476888i	−0.324374	−	0.945929i	$-0.605154\pi$
$977$	112.483	−	46.5920i	0.115131	−	0.0476888i	0.439505	+	0.898240i	$0.355154\pi$
$978$	7.10532	+	17.1538i	0.00726515	+	0.0175396i
$979$	−373.996	+	1880.20i	−0.382018	+	1.92054i
$980$	−1.91699	−	2.86898i	−0.00195611	−	0.00292753i
$981$	41.3685	+	207.974i	0.0421697	+	0.212002i
$982$	−102.379	+	102.379i	−0.104256	+	0.104256i
$983$	−678.937	+	1016.10i	−0.690678	+	1.03367i	0.305984	+	0.952037i	$0.401015\pi$
$983$	−678.937	+	1016.10i	−0.690678	+	1.03367i	−0.996662	+	0.0816362i	$0.973985\pi$
$984$	−87.4215	−	36.2112i	−0.0888430	−	0.0368000i
$985$		−	37.8262i		−	0.0384022i
$986$		0			0
$987$	410.348			0.415753
$988$	267.936	−	646.855i	0.271190	−	0.654711i
$989$	−844.975	−	564.594i	−0.854373	−	0.570874i
$990$	5.28642	+	5.28642i	0.00533981	+	0.00533981i
$991$	−1418.39	+	282.135i	−1.43127	+	0.284698i	−0.849042	−	0.528326i	$-0.822820\pi$
$991$	−1418.39	+	282.135i	−1.43127	+	0.284698i	−0.582230	+	0.813024i	$0.697820\pi$
$992$	98.5960	−	65.8797i	0.0993911	−	0.0664110i
$993$	−671.276	−	133.525i	−0.676008	−	0.134466i
$994$	62.1546	−	25.7453i	0.0625297	−	0.0259007i
$995$	20.9116	+	50.4851i	0.0210167	+	0.0507388i
$996$	110.545	−	555.745i	0.110989	−	0.557977i
$997$	−478.070	−	715.482i	−0.479508	−	0.717635i	0.510307	−	0.859992i	$-0.329532\pi$
$997$	−478.070	−	715.482i	−0.479508	−	0.717635i	−0.989815	+	0.142357i	$0.954532\pi$
$998$	38.1117	+	191.601i	0.0381881	+	0.191985i
$999$	193.659	−	193.659i	0.193852	−	0.193852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.j.214.1		8
17.2	even	8		289.3.e.f.40.1		8
17.3	odd	16		289.3.e.e.158.1		8
17.4	even	4		289.3.e.e.75.1		8
17.5	odd	16		289.3.e.n.131.1		8
17.6	odd	16		289.3.e.f.224.1		8
17.7	odd	16		289.3.e.g.65.1		8
17.8	even	8		17.3.e.b.11.1	✓	8
17.9	even	8		289.3.e.g.249.1		8
17.10	odd	16		17.3.e.b.14.1	yes	8
17.11	odd	16		289.3.e.h.224.1		8
17.12	odd	16	inner	289.3.e.j.131.1		8
17.13	even	4		289.3.e.a.75.1		8
17.14	odd	16		289.3.e.a.158.1		8
17.15	even	8		289.3.e.h.40.1		8
17.16	even	2		289.3.e.n.214.1		8
51.8	odd	8		153.3.p.a.28.1		8
51.44	even	16		153.3.p.a.82.1		8
68.27	even	16		272.3.bh.b.65.1		8
68.59	odd	8		272.3.bh.b.113.1		8
85.8	odd	8		425.3.t.b.249.1		8
85.27	even	16		425.3.t.b.99.1		8
85.42	odd	8		425.3.t.d.249.1		8
85.44	odd	16		425.3.u.a.201.1		8
85.59	even	8		425.3.u.a.351.1		8
85.78	even	16		425.3.t.d.99.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.11.1	✓	8	17.8	even	8
17.3.e.b.14.1	yes	8	17.10	odd	16
153.3.p.a.28.1		8	51.8	odd	8
153.3.p.a.82.1		8	51.44	even	16
272.3.bh.b.65.1		8	68.27	even	16
272.3.bh.b.113.1		8	68.59	odd	8
289.3.e.a.75.1		8	17.13	even	4
289.3.e.a.158.1		8	17.14	odd	16
289.3.e.e.75.1		8	17.4	even	4
289.3.e.e.158.1		8	17.3	odd	16
289.3.e.f.40.1		8	17.2	even	8
289.3.e.f.224.1		8	17.6	odd	16
289.3.e.g.65.1		8	17.7	odd	16
289.3.e.g.249.1		8	17.9	even	8
289.3.e.h.40.1		8	17.15	even	8
289.3.e.h.224.1		8	17.11	odd	16
289.3.e.j.131.1		8	17.12	odd	16	inner
289.3.e.j.214.1		8	1.1	even	1	trivial
289.3.e.n.131.1		8	17.5	odd	16
289.3.e.n.214.1		8	17.16	even	2
425.3.t.b.99.1		8	85.27	even	16
425.3.t.b.249.1		8	85.8	odd	8
425.3.t.d.99.1		8	85.78	even	16
425.3.t.d.249.1		8	85.42	odd	8
425.3.u.a.201.1		8	85.44	odd	16
425.3.u.a.351.1		8	85.59	even	8

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0897902 + 0.216773i) q^{2} +(-1.16591 - 0.779037i) q^{3} +(2.78950 + 2.78950i) q^{4} +(-0.338093 + 0.0672509i) q^{5} +(0.273561 - 0.182788i) q^{6} +(-7.04101 - 1.40054i) q^{7} +(-1.72225 + 0.713379i) q^{8} +(-2.69170 - 6.49834i) q^{9} +(0.0157793 - 0.0793278i) q^{10} +(-7.30090 - 10.9266i) q^{11} +(-1.07918 - 5.42543i) q^{12} +(5.20259 - 5.20259i) q^{13} +(0.935813 - 1.40054i) q^{14} +(0.446577 + 0.184978i) q^{15} +15.3424i q^{16} +1.65035 q^{18} +(9.23114 - 22.2860i) q^{19} +(-1.13071 - 0.755514i) q^{20} +(7.11811 + 7.11811i) q^{21} +(3.02413 - 0.601537i) q^{22} +(26.6710 - 17.8210i) q^{23} +(2.56374 + 0.509959i) q^{24} +(-22.9872 + 9.52161i) q^{25} +(0.660638 + 1.59492i) q^{26} +(-4.38621 + 22.0510i) q^{27} +(-15.7341 - 23.5477i) q^{28} +(-7.53862 - 37.8992i) q^{29} +(-0.0801965 + 0.0801965i) q^{30} +(-5.95850 + 8.91753i) q^{31} +(-10.2148 - 4.23111i) q^{32} +18.4271i q^{33} +2.47470 q^{35} +(10.6186 - 25.6356i) q^{36} +(-10.1285 - 6.76763i) q^{37} +(4.00212 + 4.00212i) q^{38} +(-10.1188 + 2.01275i) q^{39} +(0.534305 - 0.357011i) q^{40} +(-35.5040 - 7.06219i) q^{41} +(-2.18215 + 0.903876i) q^{42} +(-12.1240 - 29.2698i) q^{43} +(10.1138 - 50.8455i) q^{44} +(1.34706 + 2.01603i) q^{45} +(1.46831 + 7.38170i) q^{46} +(28.8242 - 28.8242i) q^{47} +(11.9523 - 17.8879i) q^{48} +(2.34419 + 0.970996i) q^{49} -5.83795i q^{50} +29.0252 q^{52} +(-22.2872 + 53.8061i) q^{53} +(-4.38621 - 2.93077i) q^{54} +(3.20321 + 3.20321i) q^{55} +(13.1255 - 2.61082i) q^{56} +(-28.1243 + 18.7920i) q^{57} +(8.89241 + 1.76881i) q^{58} +(-4.80542 + 1.99047i) q^{59} +(0.729730 + 1.76172i) q^{60} +(-8.93981 + 44.9435i) q^{61} +(-1.39806 - 2.09235i) q^{62} +(9.85108 + 49.5247i) q^{63} +(-41.5605 + 41.5605i) q^{64} +(-1.40908 + 2.10884i) q^{65} +(-3.99449 - 1.65457i) q^{66} -59.2116i q^{67} -44.9792 q^{69} +(-0.222204 + 0.536448i) q^{70} +(33.2088 + 22.1894i) q^{71} +(9.27155 + 9.27155i) q^{72} +(-11.6061 + 2.30859i) q^{73} +(2.37648 - 1.58791i) q^{74} +(34.2187 + 6.80652i) q^{75} +(87.9169 - 36.4164i) q^{76} +(36.1026 + 87.1593i) q^{77} +(0.472257 - 2.37420i) q^{78} +(64.8330 + 97.0295i) q^{79} +(-1.03179 - 5.18716i) q^{80} +(-22.4701 + 22.4701i) q^{81} +(4.71881 - 7.06219i) q^{82} +(94.6362 + 39.1996i) q^{83} +39.7119i q^{84} +7.43351 q^{86} +(-20.7355 + 50.0599i) q^{87} +(20.3687 + 13.6100i) q^{88} +(-103.152 - 103.152i) q^{89} +(-0.557973 + 0.110988i) q^{90} +(-43.9179 + 29.3450i) q^{91} +(124.110 + 24.6871i) q^{92} +(13.8942 - 5.75515i) q^{93} +(3.66017 + 8.83643i) q^{94} +(-1.62224 + 8.15553i) q^{95} +(8.61336 + 12.8908i) q^{96} +(25.8302 + 129.857i) q^{97} +(-0.420971 + 0.420971i) q^{98} +(-51.3527 + 76.8548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 16 q^{5} - 8 q^{7} + 8 q^{8} - 56 q^{9} + 48 q^{10} - 24 q^{11} - 24 q^{12} + 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} - 48 q^{20} + 64 q^{21} + 16 q^{22} + 104 q^{23}+ \cdots - 120 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 16 * q^5 - 8 * q^7 + 8 * q^8 - 56 * q^9 + 48 * q^10 - 24 * q^11 - 24 * q^12 + 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 - 48 * q^20 + 64 * q^21 + 16 * q^22 + 104 * q^23 - 136 * q^25 + 40 * q^26 - 32 * q^27 - 168 * q^30 - 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 - 48 * q^37 - 8 * q^38 + 96 * q^39 - 8 * q^40 - 208 * q^41 + 88 * q^42 + 48 * q^43 + 56 * q^44 - 48 * q^45 + 80 * q^46 + 80 * q^47 + 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 - 32 * q^54 + 8 * q^55 + 8 * q^56 - 40 * q^57 + 120 * q^58 - 40 * q^59 - 96 * q^60 + 16 * q^61 - 256 * q^62 - 96 * q^63 + 120 * q^64 + 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 + 328 * q^71 - 24 * q^72 - 160 * q^73 - 168 * q^74 + 264 * q^75 + 192 * q^76 + 120 * q^77 + 168 * q^78 + 352 * q^79 + 328 * q^80 + 224 * q^81 - 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 + 56 * q^88 - 288 * q^89 - 392 * q^90 - 32 * q^91 + 200 * q^92 + 248 * q^93 + 72 * q^94 - 800 * q^95 + 408 * q^96 - 504 * q^97 - 16 * q^98 - 120 * q^99

Introduction

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