LMFDB - Embedded newform 425.3.t.b.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,-8,8,0,0,8,-8,-8,0,40,-32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
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			249.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.249
Dual form			425.3.t.b.99.1

$q$-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} +(-1.37529 + 0.273561i) q^{3} +(2.78950 + 2.78950i) q^{4} +(-0.0641865 + 0.322688i) q^{6} +(3.98841 + 5.96908i) q^{7} +(1.72225 - 0.713379i) q^{8} +(-6.49834 + 2.69170i) q^{9} +(12.8888 + 2.56374i) q^{11} +(-4.59946 - 3.07326i) q^{12} +(-5.20259 - 5.20259i) q^{13} +(1.65205 - 0.328614i) q^{14} +15.3424i q^{16} +(-16.9919 - 0.525274i) q^{17} +1.65035i q^{18} +(22.2860 + 9.23114i) q^{19} +(-7.11811 - 7.11811i) q^{21} +(1.71303 - 2.56374i) q^{22} +(-31.4606 - 6.25790i) q^{23} +(-2.17343 + 1.45224i) q^{24} +(-1.59492 + 0.660638i) q^{26} +(18.6939 - 12.4909i) q^{27} +(-5.52507 + 27.7764i) q^{28} +(-21.4682 + 32.1294i) q^{29} +(10.5189 - 2.09235i) q^{31} +(10.2148 + 4.23111i) q^{32} -18.4271 q^{33} +(-1.63957 + 3.63621i) q^{34} +(-25.6356 - 10.6186i) q^{36} +(11.9474 - 2.37648i) q^{37} +(4.00212 - 4.00212i) q^{38} +(8.57827 + 5.73181i) q^{39} +(-30.0989 + 20.1114i) q^{41} +(-2.18215 + 0.903876i) q^{42} +(12.1240 + 29.2698i) q^{43} +(28.8017 + 43.1047i) q^{44} +(-4.18140 + 6.25790i) q^{46} +(28.8242 + 28.8242i) q^{47} +(-4.19709 - 21.1002i) q^{48} +(-0.970996 + 2.34419i) q^{49} +(23.5124 - 3.92592i) q^{51} -29.0252i q^{52} +(-22.2872 + 53.8061i) q^{53} +(-1.02915 - 5.17389i) q^{54} +(11.1272 + 7.43499i) q^{56} +(-33.1748 - 6.59888i) q^{57} +(5.03714 + 7.53862i) q^{58} +(1.99047 + 4.80542i) q^{59} +(25.4584 + 38.1012i) q^{61} +(0.490934 - 2.46809i) q^{62} +(-41.9850 - 28.0535i) q^{63} +(-41.5605 + 41.5605i) q^{64} +(-1.65457 + 3.99449i) q^{66} -59.2116 q^{67} +(-45.9336 - 48.8641i) q^{68} +44.9792 q^{69} +(-7.79189 - 39.1725i) q^{71} +(-9.27155 + 9.27155i) q^{72} +(6.57431 - 9.83914i) q^{73} +(0.557600 - 2.80324i) q^{74} +(36.4164 + 87.9169i) q^{76} +(36.1026 + 87.1593i) q^{77} +(2.01275 - 1.34487i) q^{78} +(114.454 + 22.7663i) q^{79} +(22.4701 - 22.4701i) q^{81} +(1.65702 + 8.33042i) q^{82} +(94.6362 + 39.1996i) q^{83} -39.7119i q^{84} +7.43351 q^{86} +(20.7355 - 50.0599i) q^{87} +(24.0266 - 4.77918i) q^{88} +(-103.152 - 103.152i) q^{89} +(10.3046 - 51.8047i) q^{91} +(-70.3029 - 105.216i) q^{92} +(-13.8942 + 5.75515i) q^{93} +(8.83643 - 3.66017i) q^{94} +(-15.2057 - 3.02461i) q^{96} +(110.088 + 73.5583i) q^{97} +(0.420971 + 0.420971i) q^{98} +(-90.6564 + 18.0327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{7} - 8 q^{8} - 8 q^{9} + 40 q^{11} - 32 q^{12} - 16 q^{14} - 64 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 24 q^{24} + 112 q^{27} - 8 q^{28} - 24 q^{29}+ \cdots - 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^7 - 8 * q^8 - 8 * q^9 + 40 * q^11 - 32 * q^12 - 16 * q^14 - 64 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 24 * q^24 + 112 * q^27 - 8 * q^28 - 24 * q^29 + 32 * q^31 - 16 * q^32 + 16 * q^33 - 64 * q^34 - 104 * q^36 + 56 * q^37 - 8 * q^38 + 72 * q^39 + 88 * q^42 - 48 * q^43 + 96 * q^44 + 80 * q^47 + 16 * q^48 - 8 * q^49 - 176 * q^51 + 88 * q^53 - 208 * q^54 + 72 * q^56 - 168 * q^57 - 96 * q^58 - 8 * q^59 + 264 * q^61 - 96 * q^62 - 16 * q^63 + 120 * q^64 + 8 * q^66 - 32 * q^67 + 120 * q^68 + 208 * q^69 + 32 * q^71 + 24 * q^72 - 240 * q^73 - 176 * q^74 - 80 * q^76 + 120 * q^77 + 96 * q^79 - 224 * q^81 - 352 * q^82 + 504 * q^83 + 288 * q^86 - 216 * q^87 + 24 * q^88 - 288 * q^89 - 24 * q^91 - 72 * q^92 - 248 * q^93 + 8 * q^94 + 328 * q^96 + 280 * q^97 + 16 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$

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	−0.899841	−	0.436218i	$-0.856318\pi$
$2$	0.0897902	−	0.216773i	0.0448951	−	0.108386i	0.944736	+	0.327831i	$0.106318\pi$
$3$	−1.37529	+	0.273561i	−0.458428	+	0.0911871i	−0.418902	−	0.908031i	$-0.637585\pi$
$3$	−1.37529	+	0.273561i	−0.458428	+	0.0911871i	−0.0395264	+	0.999219i	$0.512585\pi$
$4$	2.78950	+	2.78950i	0.697375	+	0.697375i
$5$		0			0
$5$		0			0
$6$	−0.0641865	+	0.322688i	−0.0106978	+	0.0537813i
$7$	3.98841	+	5.96908i	0.569773	+	0.852726i	0.998719	−	0.0506046i	$-0.0161148\pi$
$7$	3.98841	+	5.96908i	0.569773	+	0.852726i	−0.428946	+	0.903330i	$0.641115\pi$
$8$	1.72225	−	0.713379i	0.215281	−	0.0891723i
$9$	−6.49834	+	2.69170i	−0.722038	+	0.299078i
$10$		0			0
$11$	12.8888	+	2.56374i	1.17171	+	0.233067i	0.742315	−	0.670052i	$-0.233728\pi$
$11$	12.8888	+	2.56374i	1.17171	+	0.233067i	0.429392	+	0.903118i	$0.358728\pi$
$12$	−4.59946	−	3.07326i	−0.383288	−	0.256105i
$13$	−5.20259	−	5.20259i	−0.400199	−	0.400199i	0.478104	−	0.878303i	$-0.341324\pi$
$13$	−5.20259	−	5.20259i	−0.400199	−	0.400199i	−0.878303	+	0.478104i	$0.841324\pi$
$14$	1.65205	−	0.328614i	0.118004	−	0.0234724i
$15$		0			0
$16$			15.3424i			0.958900i
$17$	−16.9919	−	0.525274i	−0.999523	−	0.0308985i
$17$	−16.9919	−	0.525274i	−0.999523	−	0.0308985i
$18$			1.65035i			0.0916862i
$19$	22.2860	+	9.23114i	1.17295	+	0.485850i	0.882165	−	0.470940i	$-0.156085\pi$
$19$	22.2860	+	9.23114i	1.17295	+	0.485850i	0.290780	+	0.956790i	$0.406085\pi$
$20$		0			0
$21$	−7.11811	−	7.11811i	−0.338958	−	0.338958i
$22$	1.71303	−	2.56374i	0.0778651	−	0.116533i
$23$	−31.4606	−	6.25790i	−1.36785	−	0.272083i	−0.544094	−	0.839024i	$-0.683127\pi$
$23$	−31.4606	−	6.25790i	−1.36785	−	0.272083i	−0.823758	+	0.566941i	$0.808127\pi$
$24$	−2.17343	+	1.45224i	−0.0905596	+	0.0605100i
$25$		0			0
$26$	−1.59492	+	0.660638i	−0.0613431	+	0.0254091i
$27$	18.6939	−	12.4909i	0.692368	−	0.462625i
$28$	−5.52507	+	27.7764i	−0.197324	+	0.992015i
$29$	−21.4682	+	32.1294i	−0.740282	+	1.10791i	0.249920	+	0.968266i	$0.419596\pi$
$29$	−21.4682	+	32.1294i	−0.740282	+	1.10791i	−0.990202	+	0.139644i	$0.955404\pi$
$30$		0			0
$31$	10.5189	−	2.09235i	0.339321	−	0.0674951i	−0.0224889	−	0.999747i	$-0.507159\pi$
$31$	10.5189	−	2.09235i	0.339321	−	0.0674951i	0.361810	+	0.932252i	$0.382159\pi$
$32$	10.2148	+	4.23111i	0.319213	+	0.132222i
$33$	−18.4271			−0.558396
$34$	−1.63957	+	3.63621i	−0.0482226	+	0.106947i
$35$		0			0
$36$	−25.6356	−	10.6186i	−0.712100	−	0.294962i
$37$	11.9474	−	2.37648i	0.322901	−	0.0642291i	−0.0309782	−	0.999520i	$-0.509862\pi$
$37$	11.9474	−	2.37648i	0.322901	−	0.0642291i	0.353880	+	0.935291i	$0.384862\pi$
$38$	4.00212	−	4.00212i	0.105319	−	0.105319i
$39$	8.57827	+	5.73181i	0.219956	+	0.146970i
$40$		0			0
$41$	−30.0989	+	20.1114i	−0.734119	+	0.490522i	−0.865562	−	0.500801i	$-0.833039\pi$
$41$	−30.0989	+	20.1114i	−0.734119	+	0.490522i	0.131444	+	0.991324i	$0.458039\pi$
$42$	−2.18215	+	0.903876i	−0.0519559	+	0.0215209i
$43$	12.1240	+	29.2698i	0.281952	+	0.680693i	0.999881	−	0.0154234i	$-0.00490963\pi$
$43$	12.1240	+	29.2698i	0.281952	+	0.680693i	−0.717929	+	0.696117i	$0.754910\pi$
$44$	28.8017	+	43.1047i	0.654583	+	0.979653i
$45$		0			0
$46$	−4.18140	+	6.25790i	−0.0908999	+	0.136041i
$47$	28.8242	+	28.8242i	0.613281	+	0.613281i	0.943800	−	0.330518i	$-0.107224\pi$
$47$	28.8242	+	28.8242i	0.613281	+	0.613281i	−0.330518	+	0.943800i	$0.607224\pi$
$48$	−4.19709	−	21.1002i	−0.0874393	−	0.439587i
$49$	−0.970996	+	2.34419i	−0.0198162	+	0.0478406i
$50$		0			0
$51$	23.5124	−	3.92592i	0.461027	−	0.0769788i
$52$		−	29.0252i		−	0.558177i
$53$	−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	$0.939846\pi$
$54$	−1.02915	−	5.17389i	−0.0190584	−	0.0958128i
$55$		0			0
$56$	11.1272	+	7.43499i	0.198701	+	0.132768i
$57$	−33.1748	−	6.59888i	−0.582015	−	0.115770i
$58$	5.03714	+	7.53862i	0.0868473	+	0.129976i
$59$	1.99047	+	4.80542i	0.0337368	+	0.0814478i	0.939850	−	0.341588i	$-0.110965\pi$
$59$	1.99047	+	4.80542i	0.0337368	+	0.0814478i	−0.906113	+	0.423035i	$0.860965\pi$
$60$		0			0
$61$	25.4584	+	38.1012i	0.417351	+	0.624611i	0.979265	−	0.202586i	$-0.0649345\pi$
$61$	25.4584	+	38.1012i	0.417351	+	0.624611i	−0.561913	+	0.827196i	$0.689934\pi$
$62$	0.490934	−	2.46809i	0.00791829	−	0.0398079i
$63$	−41.9850	−	28.0535i	−0.666429	−	0.445294i
$64$	−41.5605	+	41.5605i	−0.649382	+	0.649382i
$65$		0			0
$66$	−1.65457	+	3.99449i	−0.0250693	+	0.0605225i
$67$	−59.2116			−0.883755			−0.441877	−	0.897075i	$-0.645687\pi$
$67$	−59.2116			−0.883755			−0.441877	+	0.897075i	$0.645687\pi$
$68$	−45.9336	−	48.8641i	−0.675494	−	0.718590i
$69$	44.9792			0.651873
$70$		0			0
$71$	−7.79189	−	39.1725i	−0.109745	−	0.551725i	−0.996063	−	0.0886482i	$-0.971745\pi$
$71$	−7.79189	−	39.1725i	−0.109745	−	0.551725i	0.886318	−	0.463077i	$-0.153255\pi$
$72$	−9.27155	+	9.27155i	−0.128772	+	0.128772i
$73$	6.57431	−	9.83914i	0.0900590	−	0.134783i	−0.783705	−	0.621134i	$-0.786672\pi$
$73$	6.57431	−	9.83914i	0.0900590	−	0.134783i	0.873764	+	0.486351i	$0.161672\pi$
$74$	0.557600	−	2.80324i	0.00753514	−	0.0378817i
$75$		0			0
$76$	36.4164	+	87.9169i	0.479163	+	1.15680i
$77$	36.1026	+	87.1593i	0.468865	+	1.13194i
$78$	2.01275	−	1.34487i	0.0258044	−	0.0172420i
$79$	114.454	+	22.7663i	1.44879	+	0.288181i	0.855915	−	0.517116i	$-0.172994\pi$
$79$	114.454	+	22.7663i	1.44879	+	0.288181i	0.592871	+	0.805298i	$0.297994\pi$
$80$		0			0
$81$	22.4701	−	22.4701i	0.277408	−	0.277408i
$82$	1.65702	+	8.33042i	0.0202076	+	0.101591i
$83$	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
$88$	24.0266	−	4.77918i	0.273029	−	0.0543089i
$89$	−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			0
$91$	10.3046	−	51.8047i	0.113237	−	0.569282i
$92$	−70.3029	−	105.216i	−0.764162	−	1.14365i
$93$	−13.8942	+	5.75515i	−0.149400	+	0.0618833i
$94$	8.83643	−	3.66017i	0.0940046	−	0.0389380i
$95$		0			0
$96$	−15.2057	−	3.02461i	−0.158393	−	0.0315064i
$97$	110.088	+	73.5583i	1.13492	+	0.758333i	0.973530	−	0.228557i	$-0.0734009\pi$
$97$	110.088	+	73.5583i	1.13492	+	0.758333i	0.161394	+	0.986890i	$0.448401\pi$
$98$	0.420971	+	0.420971i	0.00429562	+	0.00429562i
$99$	−90.6564	+	18.0327i	−0.915722	+	0.182148i
$100$		0			0
$101$		−	124.860i		−	1.23624i	−0.786085	−	0.618119i	$-0.787895\pi$
$101$		−	124.860i		−	1.23624i	0.786085	−	0.618119i	$-0.212105\pi$
$102$	1.26015	−	5.44935i	0.0123544	−	0.0534250i
$103$		−	87.0352i		−	0.845002i	−0.906362	−	0.422501i	$-0.861152\pi$
$103$		−	87.0352i		−	0.845002i	0.906362	−	0.422501i	$-0.138848\pi$
$104$	−12.6716	−	5.24873i	−0.121842	−	0.0504686i
$105$		0			0
$106$	9.66253	+	9.66253i	0.0911560	+	0.0911560i
$107$	28.5619	−	42.7459i	0.266933	−	0.399494i	−0.673653	−	0.739047i	$-0.735276\pi$
$107$	28.5619	−	42.7459i	0.266933	−	0.399494i	0.940587	+	0.339553i	$0.110276\pi$
$108$	86.9900	+	17.3034i	0.805463	+	0.160217i
$109$	25.0665	−	16.7489i	0.229968	−	0.153660i	−0.435248	−	0.900310i	$-0.643339\pi$
$109$	25.0665	−	16.7489i	0.229968	−	0.153660i	0.665216	+	0.746651i	$0.268339\pi$
$110$		0			0
$111$	−15.7809	+	6.53667i	−0.142170	+	0.0588889i
$112$	−91.5800	+	61.1918i	−0.817679	+	0.546355i
$113$	19.8625	−	99.8557i	0.175775	−	0.883678i	−0.787737	−	0.616012i	$-0.788747\pi$
$113$	19.8625	−	99.8557i	0.175775	−	0.883678i	0.963512	−	0.267667i	$-0.0862526\pi$
$114$	−4.40923	+	6.59888i	−0.0386775	+	0.0578850i
$115$		0			0
$116$	−149.510	+	29.7395i	−1.28888	+	0.256375i
$117$	47.8120	+	19.8044i	0.408649	+	0.169268i
$118$	1.22041			0.0103425
$119$	−64.6352	−	103.521i	−0.543153	−	0.869924i
$120$		0			0
$121$	47.7582	+	19.7821i	0.394696	+	0.163488i
$122$	10.5452	−	2.09758i	0.0864363	−	0.0171933i
$123$	35.8928	−	35.8928i	0.291812	−	0.291812i
$124$	35.1792	+	23.5060i	0.283703	+	0.189564i
$125$		0			0
$126$	−9.85108	+	6.58228i	−0.0781832	+	0.0522403i
$127$	−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
$129$	−24.6810	−	36.9377i	−0.191325	−	0.286339i
$130$		0			0
$131$	31.3353	−	46.8966i	0.239201	−	0.357989i	−0.692374	−	0.721539i	$-0.743435\pi$
$131$	31.3353	−	46.8966i	0.239201	−	0.357989i	0.931575	+	0.363549i	$0.118435\pi$
$132$	−51.4023	−	51.4023i	−0.389411	−	0.389411i
$133$	33.7841	+	169.844i	0.254016	+	1.27702i
$134$	−5.31662	+	12.8355i	−0.0396763	+	0.0957870i
$135$		0			0
$136$	−29.6390	+	11.2170i	−0.217934	+	0.0824779i
$137$		−	167.615i		−	1.22347i	−0.791065	−	0.611733i	$-0.790473\pi$
$137$		−	167.615i		−	1.22347i	0.791065	−	0.611733i	$-0.209527\pi$
$138$	4.03869	−	9.75027i	0.0292659	−	0.0706541i
$139$	−18.7153	−	94.0884i	−0.134643	−	0.676895i	−0.987861	−	0.155341i	$-0.950353\pi$
$139$	−18.7153	−	94.0884i	−0.134643	−	0.676895i	0.853218	−	0.521554i	$-0.174647\pi$
$140$		0			0
$141$	−47.5267	−	31.7563i	−0.337069	−	0.225222i
$142$	−9.19117	−	1.82824i	−0.0647265	−	0.0128749i
$143$	−53.7169	−	80.3930i	−0.375642	−	0.562189i
$144$	−41.2972	−	99.7001i	−0.286786	−	0.692362i
$145$		0			0
$146$	−1.54255	−	2.30859i	−0.0105654	−	0.0158123i
$147$	0.694116	−	3.48956i	0.00472188	−	0.0237385i
$148$	39.9563	+	26.6979i	0.269975	+	0.180392i
$149$	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	$0.0940930\pi$
$150$		0			0
$151$	34.9619	−	84.4056i	0.231536	−	0.558977i	−0.764822	−	0.644241i	$-0.777173\pi$
$151$	34.9619	−	84.4056i	0.231536	−	0.558977i	0.996358	+	0.0852638i	$0.0271733\pi$
$152$	44.9672			0.295837
$153$	111.833	−	42.3237i	0.730934	−	0.276625i
$154$	22.1354			0.143737
$155$		0			0
$156$	7.94018	+	39.9180i	0.0508986	+	0.255884i
$157$	−70.4744	+	70.4744i	−0.448882	+	0.448882i	−0.894983	−	0.446101i	$-0.852812\pi$
$157$	−70.4744	+	70.4744i	−0.448882	+	0.448882i	0.446101	+	0.894983i	$0.352812\pi$
$158$	15.2120	−	22.7663i	0.0962784	−	0.144091i
$159$	15.9320	−	80.0957i	0.100201	−	0.503747i
$160$		0			0
$161$	−88.1239	−	212.750i	−0.547353	−	1.32143i
$162$	−2.85331	−	6.88849i	−0.0176130	−	0.0425216i
$163$	−46.9226	+	31.3527i	−0.287869	+	0.192348i	−0.691117	−	0.722743i	$-0.742881\pi$
$163$	−46.9226	+	31.3527i	−0.287869	+	0.192348i	0.403248	+	0.915091i	$0.367881\pi$
$164$	−140.062	−	27.8600i	−0.854034	−	0.169878i
$165$		0			0
$166$	16.9948	−	16.9948i	0.102378	−	0.102378i
$167$	49.7011	+	249.864i	0.297611	+	1.49619i	0.783070	+	0.621933i	$0.213653\pi$
$167$	49.7011	+	249.864i	0.297611	+	1.49619i	−0.485459	+	0.874260i	$0.661347\pi$
$168$	−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
$173$	258.425	−	51.4039i	1.49379	−	0.297133i	0.620448	−	0.784247i	$-0.286951\pi$
$173$	258.425	−	51.4039i	1.49379	−	0.297133i	0.873338	+	0.487115i	$0.161951\pi$
$174$	−8.98979	−	8.98979i	−0.0516654	−	0.0516654i
$175$		0			0
$176$	−39.3338	+	197.745i	−0.223488	+	1.12355i
$177$	−4.05204	−	6.06431i	−0.0228929	−	0.0342616i
$178$	−31.6227	+	13.0985i	−0.177655	+	0.0735873i
$179$	−86.3029	+	35.7478i	−0.482139	+	0.199708i	−0.610496	−	0.792020i	$-0.709030\pi$
$179$	−86.3029	+	35.7478i	−0.482139	+	0.199708i	0.128357	+	0.991728i	$0.459030\pi$
$180$		0			0
$181$	337.126	+	67.0585i	1.86257	+	0.370489i	0.992481	−	0.122400i	$-0.0390590\pi$
$181$	337.126	+	67.0585i	1.86257	+	0.370489i	0.870092	+	0.492889i	$0.164059\pi$
$182$	−10.3046	−	6.88531i	−0.0566187	−	0.0378314i
$183$	−45.4356	−	45.4356i	−0.248282	−	0.248282i
$184$	−58.6472	+	11.6657i	−0.318735	+	0.0634003i
$185$		0			0
$186$			3.52863i			0.0189711i
$187$	−217.658	−	50.3328i	−1.16395	−	0.269159i
$188$			160.810i			0.855373i
$189$	149.118	+	61.7668i	0.788985	+	0.326808i
$190$		0			0
$191$	26.0458	+	26.0458i	0.136365	+	0.136365i	0.771995	−	0.635629i	$-0.219259\pi$
$191$	26.0458	+	26.0458i	0.136365	+	0.136365i	−0.635629	+	0.771995i	$0.719259\pi$
$192$	45.7882	−	68.5269i	0.238480	−	0.356911i
$193$	23.0442	+	4.58379i	0.119400	+	0.0237502i	0.254429	−	0.967092i	$-0.418113\pi$
$193$	23.0442	+	4.58379i	0.119400	+	0.0237502i	−0.135028	+	0.990842i	$0.543113\pi$
$194$	25.8302	−	17.2592i	0.133145	−	0.0889650i
$195$		0			0
$196$	−9.24771	+	3.83053i	−0.0471822	+	0.0195435i
$197$	91.2382	−	60.9634i	0.463138	−	0.309459i	−0.302020	−	0.953302i	$-0.597661\pi$
$197$	91.2382	−	60.9634i	0.463138	−	0.309459i	0.765158	+	0.643843i	$0.222661\pi$
$198$	−4.23107	+	21.2710i	−0.0213690	+	0.107429i
$199$	−88.0694	+	131.805i	−0.442560	+	0.662337i	−0.983952	−	0.178433i	$-0.942897\pi$
$199$	−88.0694	+	131.805i	−0.442560	+	0.662337i	0.541393	+	0.840770i	$0.317897\pi$
$200$		0			0
$201$	81.4328	−	16.1980i	0.405138	−	0.0805870i
$202$	−27.0663	−	11.2112i	−0.133991	−	0.0555010i
$203$	−277.407			−1.36654
$204$	76.5391	+	54.6364i	0.375192	+	0.267826i
$205$		0			0
$206$	−18.8669	−	7.81491i	−0.0915867	−	0.0379364i
$207$	221.286	−	44.0166i	1.06902	−	0.212640i
$208$	79.8202	−	79.8202i	0.383751	−	0.383751i
$209$	263.572	+	176.113i	1.26111	+	0.842648i
$210$		0			0
$211$	−87.4788	+	58.4515i	−0.414592	+	0.277021i	−0.745323	−	0.666704i	$-0.767705\pi$
$211$	−87.4788	+	58.4515i	−0.414592	+	0.277021i	0.330731	+	0.943725i	$0.392705\pi$
$212$	−212.262	+	87.9220i	−1.00124	+	0.414726i
$213$	21.4322	+	51.7418i	0.100620	+	0.242919i
$214$	−6.70156	−	10.0296i	−0.0313157	−	0.0468673i
$215$		0			0
$216$	23.2849	−	34.8482i	0.107800	−	0.161334i
$217$	54.4433	+	54.4433i	0.250891	+	0.250891i
$218$	−1.37998	−	6.93762i	−0.00633017	−	0.0318239i
$219$	−6.34994	+	15.3301i	−0.0289952	+	0.0700005i
$220$		0			0
$221$	85.6690	+	91.1345i	0.387642	+	0.412373i
$222$			4.00780i			0.0180531i
$223$	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	$0.0306393\pi$
$224$	15.4850	+	77.8484i	0.0691295	+	0.347538i
$225$		0			0
$226$	−19.8625	−	13.2717i	−0.0878873	−	0.0587244i
$227$	332.574	+	66.1531i	1.46509	+	0.291424i	0.862267	−	0.506455i	$-0.169044\pi$
$227$	332.574	+	66.1531i	1.46509	+	0.291424i	0.602819	+	0.797878i	$0.294044\pi$
$228$	−74.1336	−	110.949i	−0.325147	−	0.486617i
$229$	−11.8762	−	28.6716i	−0.0518610	−	0.125204i	0.895826	−	0.444406i	$-0.146585\pi$
$229$	−11.8762	−	28.6716i	−0.0518610	−	0.125204i	−0.947687	+	0.319202i	$0.896585\pi$
$230$		0			0
$231$	−73.4948	−	109.993i	−0.318159	−	0.476159i
$232$	−14.0531	+	70.6497i	−0.0605737	+	0.304525i
$233$	206.318	+	137.858i	0.885487	+	0.591663i	0.913001	−	0.407958i	$-0.133759\pi$
$233$	206.318	+	137.858i	0.885487	+	0.591663i	−0.0275138	+	0.999621i	$0.508759\pi$
$234$	8.58610	−	8.58610i	0.0366927	−	0.0366927i
$235$		0			0
$236$	−7.85230	+	18.9571i	−0.0332725	+	0.0803268i
$237$	−163.635			−0.690443
$238$	−28.2441	+	4.71599i	−0.118673	+	0.0198151i
$239$	−183.058			−0.765931			−0.382966	−	0.923763i	$-0.625097\pi$
$239$	−183.058			−0.765931			−0.382966	+	0.923763i	$0.625097\pi$
$240$		0			0
$241$	64.1856	+	322.683i	0.266330	+	1.33893i	0.849931	+	0.526893i	$0.176643\pi$
$241$	64.1856	+	322.683i	0.266330	+	1.33893i	−0.583601	+	0.812041i	$0.698357\pi$
$242$	8.57644	−	8.57644i	0.0354398	−	0.0354398i
$243$	−137.174	+	205.295i	−0.564501	+	0.844836i
$244$	−35.2671	+	177.300i	−0.144537	+	0.726638i
$245$		0			0
$246$	−4.55776	−	11.0034i	−0.0185275	−	0.0447293i
$247$	−67.9188	−	163.970i	−0.274975	−	0.663848i
$248$	16.6236	−	11.1075i	0.0670306	−	0.0447884i
$249$	−140.875	−	28.0218i	−0.565764	−	0.112537i
$250$		0			0
$251$	157.200	−	157.200i	0.626293	−	0.626293i	−0.320840	−	0.947133i	$-0.603965\pi$
$251$	157.200	−	157.200i	0.626293	−	0.626293i	0.947133	+	0.320840i	$0.103965\pi$
$252$	−38.8620	−	195.372i	−0.154214	−	0.775287i
$253$	−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	−0.777314	−	0.629113i	$-0.783418\pi$
$257$	55.8153	−	134.750i	0.217180	−	0.524320i	0.994494	+	0.104794i	$0.0334182\pi$
$258$	−10.2232	+	2.03352i	−0.0396248	+	0.00788186i
$259$	61.8363	+	61.8363i	0.238750	+	0.238750i
$260$		0			0
$261$	53.0248	−	266.574i	0.203160	−	1.02136i
$262$	−7.35230	−	11.0035i	−0.0280622	−	0.0419981i
$263$	0.704127	−	0.291659i	0.00267729	−	0.00110897i	−0.381344	−	0.924433i	$-0.624539\pi$
$263$	0.704127	−	0.291659i	0.00267729	−	0.00110897i	0.384022	+	0.923324i	$0.374539\pi$
$264$	−31.7360	+	13.1455i	−0.120212	+	0.0497935i
$265$		0			0
$266$	39.8511	+	7.92687i	0.149816	+	0.0298003i
$267$	170.082	+	113.645i	0.637012	+	0.425638i
$268$	−165.171	−	165.171i	−0.616308	−	0.616308i
$269$	242.322	−	48.2008i	0.900825	−	0.179185i	0.277111	−	0.960838i	$-0.410623\pi$
$269$	242.322	−	48.2008i	0.900825	−	0.179185i	0.623714	+	0.781653i	$0.285623\pi$
$270$		0			0
$271$		−	136.078i		−	0.502133i	−0.967970	−	0.251066i	$-0.919219\pi$
$271$		−	136.078i		−	0.502133i	0.967970	−	0.251066i	$-0.0807812\pi$
$272$	8.05896	−	260.696i	0.0296285	−	0.958442i
$273$			74.0652i			0.271301i
$274$	−36.3343	−	15.0502i	−0.132607	−	0.0549276i
$275$		0			0
$276$	125.470	+	125.470i	0.454600	+	0.454600i
$277$	−63.3196	+	94.7644i	−0.228590	+	0.342110i	−0.927979	−	0.372631i	$-0.878456\pi$
$277$	−63.3196	+	94.7644i	−0.228590	+	0.342110i	0.699389	+	0.714741i	$0.253456\pi$
$278$	−22.0762	−	4.39124i	−0.0794110	−	0.0157958i
$279$	−62.7237	+	41.9106i	−0.224816	+	0.150217i
$280$		0			0
$281$	−215.842	+	89.4048i	−0.768122	+	0.318167i	−0.732112	−	0.681185i	$-0.761465\pi$
$281$	−215.842	+	89.4048i	−0.768122	+	0.318167i	−0.0360106	+	0.999351i	$0.511465\pi$
$282$	−11.1513	+	7.45109i	−0.0395438	+	0.0264223i
$283$	74.1716	−	372.886i	0.262091	−	1.31762i	−0.595529	−	0.803334i	$-0.703057\pi$
$283$	74.1716	−	372.886i	0.262091	−	1.31762i	0.857620	−	0.514285i	$-0.171943\pi$
$284$	87.5362	−	131.007i	0.308226	−	0.461293i
$285$		0			0
$286$	−22.2503	+	4.42585i	−0.0777981	+	0.0154750i
$287$	−240.093	−	99.4499i	−0.836562	−	0.346515i
$288$	−77.7682			−0.270028
$289$	288.448	+	17.8508i	0.998091	+	0.0617674i
$290$		0			0
$291$	−171.525	−	71.0479i	−0.589432	−	0.244151i
$292$	45.7853	−	9.10726i	0.156799	−	0.0311893i
$293$	−251.716	+	251.716i	−0.859100	+	0.859100i	−0.991232	−	0.132132i	$-0.957818\pi$
$293$	−251.716	+	251.716i	−0.859100	+	0.859100i	0.132132	+	0.991232i	$0.457818\pi$
$294$	−0.694116	−	0.463794i	−0.00236094	−	0.00157753i
$295$		0			0
$296$	18.8810	−	12.6159i	0.0637871	−	0.0426212i
$297$	272.965	−	113.066i	0.919074	−	0.380693i
$298$	−12.5880	−	30.3900i	−0.0422415	−	0.101980i
$299$	131.119	+	196.234i	0.438526	+	0.656300i
$300$		0			0
$301$	−126.359	+	189.109i	−0.419796	+	0.628269i
$302$	−15.1576	−	15.1576i	−0.0501907	−	0.0501907i
$303$	34.1569	+	171.718i	0.112729	+	0.566727i
$304$	−141.628	+	341.920i	−0.465881	+	1.12474i
$305$		0			0
$306$	0.866887	−	28.0426i	0.00283296	−	0.0916424i
$307$			209.760i			0.683259i	0.939835	+	0.341629i	$0.110979\pi$
$307$			209.760i			0.683259i	−0.939835	+	0.341629i	$0.889021\pi$
$308$	−142.423	+	343.839i	−0.462411	+	1.11636i
$309$	23.8095	+	119.698i	0.0770533	+	0.387373i
$310$		0			0
$311$	−3.28771	−	2.19678i	−0.0105714	−	0.00706359i	0.550273	−	0.834985i	$-0.314524\pi$
$311$	−3.28771	−	2.19678i	−0.0105714	−	0.00706359i	−0.560845	+	0.827921i	$0.689524\pi$
$312$	18.8629	+	3.75206i	0.0604579	+	0.0120258i
$313$	252.697	+	378.187i	0.807337	+	1.20827i	0.974953	+	0.222413i	$0.0713933\pi$
$313$	252.697	+	378.187i	0.807337	+	1.20827i	−0.167615	+	0.985852i	$0.553607\pi$
$314$	8.94902	+	21.6049i	0.0285001	+	0.0688053i
$315$		0			0
$316$	255.763	+	382.776i	0.809376	+	1.21132i
$317$	−0.232495	+	1.16883i	−0.000733423	+	0.00368717i	−0.981150	−	0.193246i	$-0.938098\pi$
$317$	−0.232495	+	1.16883i	−0.000733423	+	0.00368717i	0.980417	+	0.196934i	$0.0630983\pi$
$318$	−15.9320	−	10.6454i	−0.0501007	−	0.0334762i
$319$	−359.070	+	359.070i	−1.12561	+	1.12561i
$320$		0			0
$321$	−27.5871	+	66.6012i	−0.0859412	+	0.207480i
$322$	−54.0311			−0.167798
$323$	−373.831	−	168.561i	−1.15737	−	0.521860i
$324$	125.361			0.386915
$325$		0			0
$326$	2.58322	+	12.9867i	0.00792397	+	0.0398365i
$327$	−29.8917	+	29.8917i	−0.0914120	+	0.0914120i
$328$	−37.4907	+	56.1087i	−0.114301	+	0.171063i
$329$	−57.0912	+	287.017i	−0.173529	+	0.872391i
$330$		0			0
$331$	186.788	+	450.945i	0.564313	+	1.36237i	0.906287	+	0.422662i	$0.138904\pi$
$331$	186.788	+	450.945i	0.564313	+	1.36237i	−0.341975	+	0.939709i	$0.611096\pi$
$332$	154.640	+	373.335i	0.465784	+	1.12450i
$333$	−71.2412	+	47.6019i	−0.213938	+	0.142949i
$334$	58.6264	+	11.6615i	0.175528	+	0.0349147i
$335$		0			0
$336$	109.209	−	109.209i	0.325027	−	0.325027i
$337$	17.5925	+	88.4436i	0.0522033	+	0.262444i	0.998069	−	0.0621144i	$-0.0197844\pi$
$337$	17.5925	+	88.4436i	0.0522033	+	0.262444i	−0.945866	+	0.324558i	$0.894784\pi$
$338$	−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
$343$	327.144	−	65.0730i	0.953773	−	0.189717i
$344$	41.7609	+	41.7609i	0.121398	+	0.121398i
$345$		0			0
$346$	12.0611	−	60.6351i	0.0348586	−	0.175246i
$347$	−98.2806	−	147.087i	−0.283229	−	0.423883i	0.662389	−	0.749160i	$-0.269542\pi$
$347$	−98.2806	−	147.087i	−0.283229	−	0.423883i	−0.945619	+	0.325277i	$0.894542\pi$
$348$	197.484	−	81.8005i	0.567482	−	0.235059i
$349$	277.045	−	114.756i	0.793826	−	0.328813i	0.0513451	−	0.998681i	$-0.483649\pi$
$349$	277.045	−	114.756i	0.793826	−	0.328813i	0.742481	+	0.669868i	$0.233649\pi$
$350$		0			0
$351$	−162.242	−	32.2719i	−0.462227	−	0.0919427i
$352$	120.809	+	80.7219i	0.343207	+	0.229324i
$353$	−213.143	−	213.143i	−0.603804	−	0.603804i	0.337516	−	0.941320i	$-0.390413\pi$
$353$	−213.143	−	213.143i	−0.603804	−	0.603804i	−0.941320	+	0.337516i	$0.890413\pi$
$354$	−1.67841	+	0.333857i	−0.00474127	+	0.000943098i
$355$		0			0
$356$		−	575.486i		−	1.61653i
$357$	117.211	+	124.689i	0.328323	+	0.349269i
$358$			21.9179i			0.0612232i
$359$	−319.178	−	132.208i	−0.889074	−	0.368266i	−0.109065	−	0.994035i	$-0.534786\pi$
$359$	−319.178	−	132.208i	−0.889074	−	0.368266i	−0.780009	+	0.625768i	$0.784786\pi$
$360$		0			0
$361$	156.184	+	156.184i	0.432643	+	0.432643i
$362$	44.8070	−	67.0585i	0.123776	−	0.185244i
$363$	−71.0927	−	14.1412i	−0.195848	−	0.0389565i
$364$	173.254	−	115.765i	0.475972	−	0.318034i
$365$		0			0
$366$	−13.9289	+	5.76953i	−0.0380571	+	0.0157638i
$367$	−413.881	+	276.546i	−1.12774	+	0.753533i	−0.972166	−	0.234292i	$-0.924723\pi$
$367$	−413.881	+	276.546i	−1.12774	+	0.753533i	−0.155575	+	0.987824i	$0.549723\pi$
$368$	96.0112	−	482.681i	0.260900	−	1.31163i
$369$	141.459	−	211.708i	0.383357	−	0.573735i
$370$		0			0
$371$	−410.064	+	81.5668i	−1.10529	+	0.219857i
$372$	−54.8117	−	22.7038i	−0.147343	−	0.0610316i
$373$	−187.052			−0.501479			−0.250740	−	0.968055i	$-0.580674\pi$
$373$	−187.052			−0.501479			−0.250740	+	0.968055i	$0.580674\pi$
$374$	−30.4543	+	42.6629i	−0.0814287	+	0.114072i
$375$		0			0
$376$	70.2050	+	29.0799i	0.186715	+	0.0773401i
$377$	278.846	−	55.4659i	0.739644	−	0.147124i
$378$	26.7787	−	26.7787i	0.0708431	−	0.0708431i
$379$	−65.2279	−	43.5839i	−0.172105	−	0.114997i	0.466534	−	0.884503i	$-0.345502\pi$
$379$	−65.2279	−	43.5839i	−0.172105	−	0.114997i	−0.638640	+	0.769506i	$0.720502\pi$
$380$		0			0
$381$	21.7389	−	14.5255i	0.0570575	−	0.0381246i
$382$	7.98468	−	3.30736i	0.0209023	−	0.00865801i
$383$	172.808	+	417.194i	0.451195	+	1.08928i	0.971868	+	0.235525i	$0.0756808\pi$
$383$	172.808	+	417.194i	0.451195	+	1.08928i	−0.520674	+	0.853756i	$0.674319\pi$
$384$	−45.1969	−	67.6419i	−0.117700	−	0.176151i
$385$		0			0
$386$	3.06279	−	4.58379i	0.00793468	−	0.0118751i
$387$	−157.571	−	157.571i	−0.407161	−	0.407161i
$388$	101.899	+	512.280i	0.262626	+	1.32031i
$389$	41.7745	−	100.853i	0.107390	−	0.259261i	−0.861045	−	0.508528i	$-0.830190\pi$
$389$	41.7745	−	100.853i	0.107390	−	0.259261i	0.968435	+	0.249267i	$0.0801897\pi$
$390$		0			0
$391$	531.288	+	122.859i	1.35879	+	0.314217i
$392$			4.72997i			0.0120662i
$393$	−30.2659	+	73.0684i	−0.0770125	+	0.185925i
$394$	−5.02291	−	25.2519i	−0.0127485	−	0.0640910i
$395$		0			0
$396$	−303.188	−	202.584i	−0.765627	−	0.511575i
$397$	−562.982	−	111.984i	−1.41809	−	0.282076i	−0.574255	−	0.818676i	$-0.694708\pi$
$397$	−562.982	−	111.984i	−1.41809	−	0.282076i	−0.843837	+	0.536600i	$0.819708\pi$
$398$	20.6640	+	30.9258i	0.0519196	+	0.0777031i
$399$	−92.9256	−	224.342i	−0.232896	−	0.562261i
$400$		0			0
$401$	−159.774	−	239.118i	−0.398438	−	0.596304i	0.576956	−	0.816775i	$-0.304241\pi$
$401$	−159.774	−	239.118i	−0.398438	−	0.596304i	−0.975394	+	0.220471i	$0.929241\pi$
$402$	3.80059	−	19.1068i	0.00945420	−	0.0475295i
$403$	−65.6113	−	43.8401i	−0.162807	−	0.108784i
$404$	348.297	−	348.297i	0.862121	−	0.862121i
$405$		0			0
$406$	−24.9084	+	60.1342i	−0.0613508	+	0.148114i
$407$	160.079			0.393315
$408$	37.6935	−	23.5346i	0.0923860	−	0.0576829i
$409$	−208.584			−0.509985			−0.254992	−	0.966943i	$-0.582073\pi$
$409$	−208.584			−0.509985			−0.254992	+	0.966943i	$0.582073\pi$
$410$		0			0
$411$	45.8529	+	230.518i	0.111564	+	0.560871i
$412$	242.785	−	242.785i	0.589283	−	0.589283i
$413$	−20.7451	+	31.0473i	−0.0502303	+	0.0751750i
$414$	10.3277	−	51.9211i	0.0249462	−	0.125413i
$415$		0			0
$416$	−31.1307	−	75.1561i	−0.0748334	−	0.180664i
$417$	51.4779	+	124.279i	0.123448	+	0.298030i
$418$	61.8428	−	41.3220i	0.147949	−	0.0988565i
$419$	−134.936	−	26.8405i	−0.322043	−	0.0640584i	0.0314214	−	0.999506i	$-0.489997\pi$
$419$	−134.936	−	26.8405i	−0.322043	−	0.0640584i	−0.353465	+	0.935448i	$0.614997\pi$
$420$		0			0
$421$	198.240	−	198.240i	0.470880	−	0.470880i	−0.431320	−	0.902199i	$-0.641952\pi$
$421$	198.240	−	198.240i	0.470880	−	0.470880i	0.902199	+	0.431320i	$0.141952\pi$
$422$	4.81595	+	24.2114i	0.0114122	+	0.0573730i
$423$	−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
$428$	198.913	−	39.5662i	0.464750	−	0.0924445i
$429$	95.8684	+	95.8684i	0.223470	+	0.223470i
$430$		0			0
$431$	−60.0816	+	302.051i	−0.139400	+	0.700814i	0.846354	+	0.532621i	$0.178793\pi$
$431$	−60.0816	+	302.051i	−0.139400	+	0.700814i	−0.985754	+	0.168192i	$0.946207\pi$
$432$	191.640	+	286.810i	0.443611	+	0.663911i
$433$	471.035	−	195.109i	1.08784	−	0.450598i	0.234587	−	0.972095i	$-0.424626\pi$
$433$	471.035	−	195.109i	1.08784	−	0.450598i	0.853253	+	0.521497i	$0.174626\pi$
$434$	16.6903	−	6.91334i	0.0384569	−	0.0159294i
$435$		0			0
$436$	116.644	+	23.2019i	0.267532	+	0.0532154i
$437$	−643.362	−	429.881i	−1.47222	−	0.983709i
$438$	2.75299	+	2.75299i	0.00628536	+	0.00628536i
$439$	104.675	−	20.8211i	0.238439	−	0.0474284i	−0.0744244	−	0.997227i	$-0.523712\pi$
$439$	104.675	−	20.8211i	0.238439	−	0.0474284i	0.312863	+	0.949798i	$0.398712\pi$
$440$		0			0
$441$		−	17.8470i		−	0.0404694i
$442$	27.4477	−	10.3877i	0.0620989	−	0.0235016i
$443$		−	384.320i		−	0.867539i	−0.901024	−	0.433769i	$-0.857183\pi$
$443$		−	384.320i		−	0.867539i	0.901024	−	0.433769i	$-0.142817\pi$
$444$	−62.2548	−	25.7868i	−0.140214	−	0.0580784i
$445$		0			0
$446$	−21.6158	−	21.6158i	−0.0484659	−	0.0484659i
$447$	−109.215	+	163.452i	−0.244330	+	0.365665i
$448$	−413.838	−	82.3175i	−0.923746	−	0.183744i
$449$	−33.3516	+	22.2848i	−0.0742797	+	0.0496321i	−0.592156	−	0.805824i	$-0.701723\pi$
$449$	−33.3516	+	22.2848i	−0.0742797	+	0.0496321i	0.517876	+	0.855456i	$0.326723\pi$
$450$		0			0
$451$	−439.498	+	182.046i	−0.974496	+	0.403649i
$452$	333.954	−	223.141i	0.738836	−	0.493674i
$453$	−24.9925	+	125.646i	−0.0551712	+	0.277364i
$454$	44.2021	−	66.1531i	0.0973615	−	0.145712i
$455$		0			0
$456$	−61.8428	+	12.3013i	−0.135620	+	0.0269765i
$457$	23.3696	+	9.67999i	0.0511369	+	0.0211816i	0.408105	−	0.912935i	$-0.366190\pi$
$457$	23.3696	+	9.67999i	0.0511369	+	0.0211816i	−0.356968	+	0.934116i	$0.616190\pi$
$458$	−7.28159			−0.0158987
$459$	−324.206	+	202.424i	−0.706331	+	0.441011i
$460$		0			0
$461$	−614.740	−	254.634i	−1.33349	−	0.552351i	−0.401843	−	0.915708i	$-0.631630\pi$
$461$	−614.740	−	254.634i	−1.33349	−	0.552351i	−0.931650	+	0.363358i	$0.881630\pi$
$462$	−30.4425	+	6.05539i	−0.0658929	+	0.0131069i
$463$	589.351	−	589.351i	1.27290	−	1.27290i	0.328335	−	0.944561i	$-0.393512\pi$
$463$	589.351	−	589.351i	1.27290	−	1.27290i	0.944561	−	0.328335i	$-0.106488\pi$
$464$	−492.942	−	329.373i	−1.06237	−	0.709856i
$465$		0			0
$466$	48.4091	−	32.3460i	0.103882	−	0.0694119i
$467$	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
$469$	−236.160	−	353.439i	−0.503540	−	0.753601i
$470$		0			0
$471$	77.6434	−	116.202i	0.164848	−	0.246712i
$472$	6.85617	+	6.85617i	0.0145258	+	0.0145258i
$473$	81.2228	+	408.334i	0.171718	+	0.863286i
$474$	−14.6928	+	35.4716i	−0.0309975	+	0.0748346i
$475$		0			0
$476$	108.472	−	469.071i	0.227881	−	0.985444i
$477$		−	409.641i		−	0.858787i
$478$	−16.4368	+	39.6819i	−0.0343866	+	0.0830165i
$479$	−73.5553	−	369.788i	−0.153560	−	0.771999i	−0.978414	−	0.206653i	$-0.933743\pi$
$479$	−73.5553	−	369.788i	−0.153560	−	0.771999i	0.824854	−	0.565346i	$-0.191257\pi$
$480$		0			0
$481$	−74.5210	−	49.7933i	−0.154929	−	0.103520i
$482$	75.7121	+	15.0601i	0.157079	+	0.0312450i
$483$	179.396	+	268.485i	0.371420	+	0.555869i
$484$	78.0393	+	188.404i	0.161238	+	0.389263i
$485$		0			0
$486$	32.1855	+	48.1690i	0.0662253	+	0.0991132i
$487$	102.711	−	516.361i	0.210905	−	1.06029i	−0.719706	−	0.694279i	$-0.755724\pi$
$487$	102.711	−	516.361i	0.210905	−	1.06029i	0.930611	−	0.366010i	$-0.119276\pi$
$488$	71.0264	+	47.4583i	0.145546	+	0.0972506i
$489$	55.9551	−	55.9551i	0.114428	−	0.114428i
$490$		0			0
$491$	236.144	−	570.101i	0.480944	−	1.16110i	−0.478217	−	0.878242i	$-0.658717\pi$
$491$	236.144	−	570.101i	0.480944	−	1.16110i	0.959161	−	0.282860i	$-0.0912833\pi$
$492$	200.246			0.407004
$493$	381.661	−	534.662i	0.774161	−	1.08451i
$494$	−41.6428			−0.0842971
$495$		0			0
$496$	32.1016	+	161.386i	0.0647210	+	0.325375i
$497$	202.746	−	202.746i	0.407941	−	0.407941i
$498$	−18.7236	+	28.0218i	−0.0375976	+	0.0562687i
$499$	162.431	−	816.596i	0.325513	−	1.63647i	−0.378016	−	0.925799i	$-0.623393\pi$
$499$	162.431	−	816.596i	0.325513	−	1.63647i	0.703529	−	0.710667i	$-0.251607\pi$
$500$		0			0
$501$	−136.706	−	330.038i	−0.272867	−	0.658759i
$502$	−19.9616	−	48.1916i	−0.0397641	−	0.0959991i
$503$	194.100	−	129.694i	0.385885	−	0.257840i	−0.347463	−	0.937694i	$-0.612957\pi$
$503$	194.100	−	129.694i	0.385885	−	0.257840i	0.733348	+	0.679854i	$0.237957\pi$
$504$	−92.3214	−	18.3639i	−0.183177	−	0.0364363i
$505$		0			0
$506$	−69.9367	+	69.9367i	−0.138215	+	0.138215i
$507$	31.4229	+	157.974i	0.0619782	+	0.311585i
$508$	−67.9562	−	28.1484i	−0.133772	−	0.0554102i
$509$		−	195.683i		−	0.384447i	−0.981351	−	0.192223i	$-0.938430\pi$
$509$		−	195.683i		−	0.384447i	0.981351	−	0.192223i	$-0.0615698\pi$
$510$		0			0
$511$	84.9517			0.166246
$512$	−108.695	+	262.413i	−0.212295	+	0.512526i
$513$	531.917	−	105.805i	1.03688	−	0.206247i
$514$	−24.1985	−	24.1985i	−0.0470788	−	0.0470788i
$515$		0			0
$516$	34.1901	−	171.885i	0.0662599	−	0.333111i
$517$	297.611	+	445.406i	0.575650	+	0.861521i
$518$	18.9567	−	7.85213i	0.0365960	−	0.0151586i
$519$	−341.346	+	141.390i	−0.657699	+	0.272428i
$520$		0			0
$521$	968.815	+	192.709i	1.85953	+	0.369883i	0.991868	−	0.127272i	$-0.0406220\pi$
$521$	968.815	+	192.709i	1.85953	+	0.369883i	0.867662	+	0.497155i	$0.165622\pi$
$522$	−53.0248	−	35.4300i	−0.101580	−	0.0678736i
$523$	−326.381	−	326.381i	−0.624055	−	0.624055i	0.322511	−	0.946566i	$-0.395473\pi$
$523$	−326.381	−	326.381i	−0.624055	−	0.624055i	−0.946566	+	0.322511i	$0.895473\pi$
$524$	218.228	−	43.4082i	0.416466	−	0.0828401i
$525$		0			0
$526$		−	0.178824i		−	0.000339969i
$527$	−179.836	+	30.0276i	−0.341244	+	0.0569784i
$528$		−	282.716i		−	0.535446i
$529$	461.876	+	191.315i	0.873111	+	0.361655i
$530$		0			0
$531$	−25.8695	−	25.8695i	−0.0487185	−	0.0487185i
$532$	−379.540	+	568.021i	−0.713420	+	1.06771i
$533$	261.223	+	51.9606i	0.490100	+	0.0974870i
$534$	39.9069	−	26.6650i	0.0747321	−	0.0499344i
$535$		0			0
$536$	−101.977	+	42.2403i	−0.190256	+	0.0788065i
$537$	108.912	−	72.7726i	0.202815	−	0.135517i
$538$	11.3095	−	56.8567i	0.0210214	−	0.105682i
$539$	−18.5248	+	27.7244i	−0.0343689	+	0.0514367i
$540$		0			0
$541$	−388.337	+	77.2451i	−0.717814	+	0.142782i	−0.540466	−	0.841366i	$-0.681752\pi$
$541$	−388.337	+	77.2451i	−0.717814	+	0.142782i	−0.177348	+	0.984148i	$0.556752\pi$
$542$	−29.4980	−	12.2185i	−0.0544244	−	0.0225433i
$543$	−481.989			−0.887640
$544$	−171.346	−	77.2601i	−0.314975	−	0.142022i
$545$		0			0
$546$	16.0553	+	6.65033i	0.0294053	+	0.0121801i
$547$	−243.007	+	48.3371i	−0.444254	+	0.0883677i	−0.412148	−	0.911117i	$-0.635221\pi$
$547$	−243.007	+	48.3371i	−0.444254	+	0.0883677i	−0.0321060	+	0.999484i	$0.510221\pi$
$548$	467.561	−	467.561i	0.853214	−	0.853214i
$549$	−267.995	−	179.068i	−0.488151	−	0.326172i
$550$		0			0
$551$	−775.030	+	517.858i	−1.40659	+	0.939852i
$552$	77.4654	−	32.0872i	0.140336	−	0.0581290i
$553$	320.596	+	773.987i	0.579740	+	1.39962i
$554$	14.8569	+	22.2349i	0.0268174	+	0.0401351i
$555$		0			0
$556$	210.253	−	314.666i	0.378153	−	0.565946i
$557$	−64.5724	−	64.5724i	−0.115929	−	0.115929i	0.646763	−	0.762691i	$-0.276122\pi$
$557$	−64.5724	−	64.5724i	−0.115929	−	0.115929i	−0.762691	+	0.646763i	$0.776122\pi$
$558$	3.45311	+	17.3600i	0.00618837	+	0.0311110i
$559$	89.2028	−	215.355i	0.159576	−	0.385250i
$560$		0			0
$561$	313.111	+	9.67926i	0.558130	+	0.0172536i
$562$			54.8164i			0.0975381i
$563$	−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	$0.211210\pi$
$564$	−43.9914	−	221.160i	−0.0779990	−	0.392128i
$565$		0			0
$566$	−74.1716	−	49.5599i	−0.131045	−	0.0875617i
$567$	223.746	+	44.5058i	0.394613	+	0.0784934i
$568$	−41.3644	−	61.9062i	−0.0728246	−	0.108990i
$569$	52.8038	+	127.480i	0.0928010	+	0.224042i	0.963464	−	0.267839i	$-0.0863096\pi$
$569$	52.8038	+	127.480i	0.0928010	+	0.224042i	−0.870663	+	0.491881i	$0.836310\pi$
$570$		0			0
$571$	−59.2021	−	88.6021i	−0.103681	−	0.155170i	0.776001	−	0.630731i	$-0.217245\pi$
$571$	−59.2021	−	88.6021i	−0.103681	−	0.155170i	−0.879683	+	0.475561i	$0.842245\pi$
$572$	74.4130	−	374.099i	0.130093	−	0.654020i
$573$	−42.9455	−	28.6953i	−0.0749486	−	0.0500790i
$574$	−43.1161	+	43.1161i	−0.0751151	+	0.0751151i
$575$		0			0
$576$	158.206	−	381.943i	0.274663	−	0.663095i
$577$	−661.008			−1.14559			−0.572797	−	0.819697i	$-0.694142\pi$
$577$	−661.008			−1.14559			−0.572797	+	0.819697i	$0.694142\pi$
$578$	29.7694	−	60.9249i	0.0515041	−	0.105406i
$579$	−32.9464			−0.0569022
$580$		0			0
$581$	143.463	+	721.235i	0.246923	+	1.24137i
$582$	−30.8025	+	30.8025i	−0.0529252	+	0.0529252i
$583$	−425.200	+	636.356i	−0.729331	+	1.09152i
$584$	4.30355	−	21.6354i	0.00736910	−	0.0370469i
$585$		0			0
$586$	31.9636	+	77.1669i	0.0545453	+	0.131684i
$587$	−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	$0.924394\pi$
$588$	11.6704	−	7.79788i	0.0198475	−	0.0132617i
$589$	253.739	+	50.4719i	0.430797	+	0.0856909i
$590$		0			0
$591$	−108.801	+	108.801i	−0.184097	+	0.184097i
$592$	36.4608	+	183.301i	0.0615893	+	0.309630i
$593$	−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
$598$	54.3114	−	10.8032i	0.0908217	−	0.0180656i
$599$	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	$0.645451\pi$
$600$		0			0
$601$	−16.5544	+	83.2246i	−0.0275448	+	0.138477i	−0.992111	−	0.125365i	$-0.959990\pi$
$601$	−16.5544	+	83.2246i	−0.0275448	+	0.138477i	0.964566	+	0.263842i	$0.0849898\pi$
$602$	29.6479	+	44.3712i	0.0492490	+	0.0737063i
$603$	384.777	−	159.380i	0.638105	−	0.264312i
$604$	332.976	−	137.923i	0.551284	−	0.228349i
$605$		0			0
$606$	40.2908	+	8.01433i	0.0664864	+	0.0132250i
$607$	−280.869	−	187.671i	−0.462717	−	0.309178i	0.302271	−	0.953222i	$-0.402255\pi$
$607$	−280.869	−	187.671i	−0.462717	−	0.309178i	−0.764988	+	0.644044i	$0.777255\pi$
$608$	188.589	+	188.589i	0.310179	+	0.310179i
$609$	381.514	−	75.8878i	0.626459	−	0.124610i
$610$		0			0
$611$		−	299.921i		−	0.490869i
$612$	430.020	+	193.896i	0.702647	+	0.316824i
$613$			770.822i			1.25746i	0.777624	+	0.628729i	$0.216425\pi$
$613$			770.822i			1.25746i	−0.777624	+	0.628729i	$0.783575\pi$
$614$	45.4704	+	18.8344i	0.0740560	+	0.0306750i
$615$		0			0
$616$	124.355	+	124.355i	0.201875	+	0.201875i
$617$	−547.640	+	819.601i	−0.887584	+	1.32836i	0.0564117	+	0.998408i	$0.482034\pi$
$617$	−547.640	+	819.601i	−0.887584	+	1.32836i	−0.943996	+	0.329956i	$0.892966\pi$
$618$	28.0852	+	5.58649i	0.0454453	+	0.00903962i
$619$	−470.818	+	314.591i	−0.760611	+	0.508224i	−0.874356	−	0.485286i	$-0.838716\pi$
$619$	−470.818	+	314.591i	−0.760611	+	0.508224i	0.113744	+	0.993510i	$0.463716\pi$
$620$		0			0
$621$	−666.289	+	275.986i	−1.07293	+	0.444422i
$622$	−0.771405	+	0.515436i	−0.00124020	+	0.000828676i
$623$	204.310	−	1027.14i	0.327946	−	1.64870i
$624$	−87.9398	+	131.611i	−0.140929	+	0.210915i
$625$		0			0
$626$	104.670	−	20.8202i	0.167205	−	0.0332591i
$627$	−410.665	−	170.103i	−0.654968	−	0.271297i
$628$	−393.177			−0.626078
$629$	−204.256	+	34.1052i	−0.324732	+	0.0542213i
$630$		0			0
$631$	133.777	+	55.4123i	0.212008	+	0.0878166i	0.486160	−	0.873870i	$-0.338397\pi$
$631$	133.777	+	55.4123i	0.212008	+	0.0878166i	−0.274152	+	0.961686i	$0.588397\pi$
$632$	213.359	−	42.4398i	0.337594	−	0.0671516i
$633$	104.318	−	104.318i	0.164800	−	0.164800i
$634$	0.232495	+	0.155348i	0.000366712	+	0.000245029i
$635$		0			0
$636$	267.869	−	178.985i	0.421178	−	0.281422i
$637$	17.2475	−	7.14417i	0.0270762	−	0.0112153i
$638$	45.5956	+	110.077i	0.0714664	+	0.172535i
$639$	156.075	+	233.583i	0.244249	+	0.365544i
$640$		0			0
$641$	−465.702	+	696.973i	−0.726525	+	1.08732i	0.265844	+	0.964016i	$0.414349\pi$
$641$	−465.702	+	696.973i	−0.726525	+	1.08732i	−0.992369	+	0.123305i	$0.960651\pi$
$642$	11.9603	+	11.9603i	0.0186297	+	0.0186297i
$643$	−4.77116	−	23.9863i	−0.00742016	−	0.0373037i	0.976898	−	0.213707i	$-0.0685537\pi$
$643$	−4.77116	−	23.9863i	−0.00742016	−	0.0373037i	−0.984318	+	0.176403i	$0.943554\pi$
$644$	347.644	−	839.287i	0.539820	−	1.30324i
$645$		0			0
$646$	−70.1058	+	65.9014i	−0.108523	+	0.102015i
$647$			1125.85i			1.74011i	0.492957	+	0.870054i	$0.335916\pi$
$647$			1125.85i			1.74011i	−0.492957	+	0.870054i	$0.664084\pi$
$648$	22.6694	−	54.7287i	0.0349836	−	0.0844579i
$649$	13.3349	+	67.0390i	0.0205468	+	0.103296i
$650$		0			0
$651$	−89.7686	−	59.9815i	−0.137893	−	0.0921374i
$652$	−218.349	−	43.4323i	−0.334891	−	0.0666139i
$653$	116.204	+	173.912i	0.177954	+	0.266327i	0.909714	−	0.415235i	$-0.136301\pi$
$653$	116.204	+	173.912i	0.177954	+	0.266327i	−0.731760	+	0.681563i	$0.761301\pi$
$654$	3.79573	+	9.16369i	0.00580386	+	0.0140118i
$655$		0			0
$656$	−308.557	−	461.789i	−0.470362	−	0.703946i
$657$	−16.2380	+	81.6342i	−0.0247154	+	0.124253i
$658$	57.0912	+	38.1471i	0.0867647	+	0.0579743i
$659$	−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	$0.936544\pi$
$660$		0			0
$661$	232.630	−	561.618i	0.351936	−	0.849649i	−0.644445	−	0.764651i	$-0.722911\pi$
$661$	232.630	−	561.618i	0.351936	−	0.849649i	0.996381	−	0.0849986i	$-0.0270886\pi$
$662$	114.524			0.172997
$663$	−142.750	−	101.900i	−0.215309	−	0.153696i
$664$	190.951			0.287577
$665$		0			0
$666$	3.92202	+	19.7173i	0.00588892	+	0.0296056i
$667$	876.464	−	876.464i	1.31404	−	1.31404i
$668$	−558.355	+	835.637i	−0.835861	+	1.25095i
$669$	−35.6411	+	179.180i	−0.0532752	+	0.267832i
$670$		0			0
$671$	230.446	+	556.347i	0.343437	+	0.829131i
$672$	−42.5926	−	102.828i	−0.0633819	−	0.153017i
$673$	−637.906	+	426.235i	−0.947855	+	0.633336i	−0.930414	−	0.366511i	$-0.880552\pi$
$673$	−637.906	+	426.235i	−0.947855	+	0.633336i	−0.0174414	+	0.999848i	$0.505552\pi$
$674$	20.7518	+	4.12779i	0.0307890	+	0.00612431i
$675$		0			0
$676$	320.419	−	320.419i	0.473993	−	0.473993i
$677$	−139.703	−	702.334i	−0.206356	−	1.03742i	−0.935572	−	0.353137i	$-0.885115\pi$
$677$	−139.703	−	702.334i	−0.206356	−	1.03742i	0.729216	−	0.684284i	$-0.239885\pi$
$678$	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
$683$	1212.71	−	241.224i	1.77557	−	0.353182i	0.804864	−	0.593460i	$-0.202238\pi$
$683$	1212.71	−	241.224i	1.77557	−	0.353182i	0.970704	+	0.240277i	$0.0772384\pi$
$684$	−473.292	−	473.292i	−0.691948	−	0.691948i
$685$		0			0
$686$	15.2683	−	76.7588i	0.0222570	−	0.111893i
$687$	24.1766	+	36.1828i	0.0351915	+	0.0526678i
$688$	−449.069	+	186.010i	−0.652717	+	0.270364i
$689$	395.882	−	163.980i	0.574575	−	0.237997i
$690$		0			0
$691$	−229.781	−	45.7063i	−0.332534	−	0.0661451i	0.0259995	−	0.999662i	$-0.491723\pi$
$691$	−229.781	−	45.7063i	−0.332534	−	0.0661451i	−0.358534	+	0.933517i	$0.616723\pi$
$692$	864.268	+	577.485i	1.24894	+	0.834516i
$693$	−469.214	−	469.214i	−0.677076	−	0.677076i
$694$	−40.7092	+	8.09756i	−0.0586587	+	0.0116680i
$695$		0			0
$696$		−	101.008i		−	0.145126i
$697$	522.000	−	325.921i	0.748925	−	0.467605i
$698$		−	70.3598i		−	0.100802i
$699$	−321.459	−	133.153i	−0.459884	−	0.190490i
$700$		0			0
$701$	375.122	+	375.122i	0.535124	+	0.535124i	0.922093	−	0.386968i	$-0.126478\pi$
$701$	375.122	+	375.122i	0.535124	+	0.535124i	−0.386968	+	0.922093i	$0.626478\pi$
$702$	−21.5634	+	32.2719i	−0.0307171	+	0.0459713i
$703$	288.196	+	57.3257i	0.409951	+	0.0815444i
$704$	−642.213	+	429.113i	−0.912235	+	0.609536i
$705$		0			0
$706$	−65.3416	+	27.0654i	−0.0925519	+	0.0383363i
$707$	745.300	−	497.993i	1.05417	−	0.704375i
$708$	5.61322	−	28.2196i	0.00792827	−	0.0398581i
$709$	90.0264	−	134.734i	0.126977	−	0.190034i	−0.762534	−	0.646948i	$-0.776045\pi$
$709$	90.0264	−	134.734i	0.126977	−	0.190034i	0.889511	+	0.456914i	$0.151045\pi$
$710$		0			0
$711$	−805.042	+	160.133i	−1.13227	+	0.225222i
$712$	−251.240	−	104.067i	−0.352866	−	0.146162i
$713$	−344.026			−0.482505
$714$	37.5536	−	14.2123i	0.0525961	−	0.0199052i
$715$		0			0
$716$	−340.460	−	141.023i	−0.475503	−	0.196960i
$717$	251.756	−	50.0775i	0.351125	−	0.0698430i
$718$	−57.3180	+	57.3180i	−0.0798301	+	0.0798301i
$719$	257.072	+	171.770i	0.357541	+	0.238901i	0.721347	−	0.692573i	$-0.243523\pi$
$719$	257.072	+	171.770i	0.357541	+	0.238901i	−0.363807	+	0.931474i	$0.618523\pi$
$720$		0			0
$721$	519.520	−	347.132i	0.720555	−	0.481459i
$722$	47.8803	−	19.8327i	0.0663162	−	0.0274691i
$723$	−176.547	−	426.223i	−0.244187	−	0.589519i
$724$	753.352	+	1127.47i	1.04054	+	1.55728i
$725$		0			0
$726$	−9.44887	+	14.1412i	−0.0130150	+	0.0194783i
$727$	−114.563	−	114.563i	−0.157583	−	0.157583i	0.623912	−	0.781495i	$-0.285542\pi$
$727$	−114.563	−	114.563i	−0.157583	−	0.157583i	−0.781495	+	0.623912i	$0.785542\pi$
$728$	−19.2093	−	96.5716i	−0.0263864	−	0.132653i
$729$	23.0458	−	55.6376i	0.0316129	−	0.0763204i
$730$		0			0
$731$	−190.634	−	503.718i	−0.260785	−	0.689080i
$732$		−	253.485i		−	0.346291i
$733$	−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	$0.756389\pi$
$734$	22.7853	+	114.549i	0.0310426	+	0.156062i
$735$		0			0
$736$	−294.886	−	197.037i	−0.400660	−	0.267713i
$737$	−763.164	−	151.803i	−1.03550	−	0.205974i
$738$	−33.1909	−	49.6737i	−0.0449741	−	0.0673086i
$739$	180.353	+	435.411i	0.244050	+	0.589190i	0.997678	−	0.0681123i	$-0.0216976\pi$
$739$	180.353	+	435.411i	0.244050	+	0.589190i	−0.753627	+	0.657302i	$0.771698\pi$
$740$		0			0
$741$	138.264	+	206.926i	0.186591	+	0.279253i
$742$	−19.1383	+	96.2146i	−0.0257928	+	0.129669i
$743$	−1006.79	−	672.718i	−1.35504	−	0.905408i	−0.355467	−	0.934689i	$-0.615678\pi$
$743$	−1006.79	−	672.718i	−1.35504	−	0.905408i	−0.999571	+	0.0292810i	$0.990678\pi$
$744$	−19.8236	+	19.8236i	−0.0266446	+	0.0266446i
$745$		0			0
$746$	−16.7954	+	40.5477i	−0.0225140	+	0.0543535i
$747$	−720.492			−0.964514
$748$	−466.753	−	747.560i	−0.624001	−	0.999411i
$749$	369.070			0.492750
$750$		0			0
$751$	260.251	+	1308.37i	0.346539	+	1.74217i	0.623992	+	0.781431i	$0.285510\pi$
$751$	260.251	+	1308.37i	0.346539	+	1.74217i	−0.277453	+	0.960739i	$0.589490\pi$
$752$	−442.232	+	442.232i	−0.588075	+	0.588075i
$753$	−173.191	+	259.198i	−0.230001	+	0.344220i
$754$	13.0141	−	65.4265i	0.0172601	−	0.0867725i
$755$		0			0
$756$	243.667	+	588.263i	0.322310	+	0.778126i
$757$	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	$0.752995\pi$
$758$	−15.3046	+	10.2262i	−0.0201908	+	0.0134911i
$759$	579.727	+	115.315i	0.763804	+	0.151930i
$760$		0			0
$761$	375.368	−	375.368i	0.493256	−	0.493256i	−0.416075	−	0.909330i	$-0.636594\pi$
$761$	375.368	−	375.368i	0.493256	−	0.493256i	0.909330	+	0.416075i	$0.136594\pi$
$762$	−1.19679	−	6.01665i	−0.00157059	−	0.00789587i
$763$	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
$768$	304.611	−	60.5908i	0.396628	−	0.0788943i
$769$	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	$0.616427\pi$
$770$		0			0
$771$	−39.8996	+	200.589i	−0.0517505	+	0.260167i
$772$	51.4954	+	77.0684i	0.0667039	+	0.0998295i
$773$	−966.801	+	400.462i	−1.25071	+	0.518062i	−0.907047	−	0.421029i	$-0.861669\pi$
$773$	−966.801	+	400.462i	−1.25071	+	0.518062i	−0.343666	+	0.939092i	$0.611669\pi$
$774$	−48.3055	+	20.0088i	−0.0624102	+	0.0258511i
$775$		0			0
$776$	242.073	+	48.1514i	0.311950	+	0.0620507i
$777$	−101.959	−	68.1266i	−0.131221	−	0.0876790i
$778$	−18.1112	−	18.1112i	−0.0232791	−	0.0232791i
$779$	−856.433	+	170.355i	−1.09940	+	0.218684i
$780$		0			0
$781$		−	524.862i		−	0.672038i
$782$	74.3369	−	104.137i	0.0950600	−	0.133168i
$783$			868.781i			1.10955i
$784$	−35.9655	−	14.8974i	−0.0458744	−	0.0190018i
$785$		0			0
$786$	13.1216	+	13.1216i	0.0166942	+	0.0166942i
$787$	413.767	−	619.246i	0.525752	−	0.786844i	−0.469627	−	0.882865i	$-0.655612\pi$
$787$	413.767	−	619.246i	0.525752	−	0.786844i	0.995379	+	0.0960208i	$0.0306115\pi$
$788$	424.566	+	84.4515i	0.538790	+	0.107172i
$789$	−0.888589	+	0.593736i	−0.00112622	+	0.000752517i
$790$		0			0
$791$	675.266	−	279.704i	0.853687	−	0.353609i
$792$	−143.269	+	95.7291i	−0.180895	+	0.120870i
$793$	65.7753	−	330.675i	0.0829449	−	0.416992i
$794$	−74.8254	+	111.984i	−0.0942386	+	0.141038i
$795$		0			0
$796$	−613.340	+	122.001i	−0.770527	+	0.153267i
$797$	−170.291	−	70.5367i	−0.213665	−	0.0885028i	0.273284	−	0.961933i	$-0.411890\pi$
$797$	−170.291	−	70.5367i	−0.213665	−	0.0885028i	−0.486949	+	0.873431i	$0.661890\pi$
$798$	−56.9751			−0.0713974
$799$	−474.637	−	504.918i	−0.594039	−	0.631938i
$800$		0			0
$801$	947.974	+	392.663i	1.18349	+	0.490217i
$802$	−66.1804	+	13.1641i	−0.0825192	+	0.0164141i
$803$	109.960	−	109.960i	0.136936	−	0.136936i
$804$	272.341	+	181.972i	0.338733	+	0.226334i
$805$		0			0
$806$	−15.3946	+	10.2863i	−0.0191000	+	0.0127622i
$807$	−320.076	+	132.580i	−0.396624	+	0.164287i
$808$	−89.0725	−	215.040i	−0.110238	−	0.266139i
$809$	−455.902	−	682.305i	−0.563538	−	0.843393i	0.434830	−	0.900513i	$-0.356809\pi$
$809$	−455.902	−	682.305i	−0.563538	−	0.843393i	−0.998367	+	0.0571191i	$0.981809\pi$
$810$		0			0
$811$	−289.106	+	432.678i	−0.356481	+	0.533511i	−0.965757	−	0.259446i	$-0.916460\pi$
$811$	−289.106	+	432.678i	−0.356481	+	0.533511i	0.609277	+	0.792958i	$0.291460\pi$
$812$	−773.826	−	773.826i	−0.952988	−	0.952988i
$813$	37.2257	+	187.146i	0.0457880	+	0.230192i
$814$	14.3736	−	34.7008i	0.0176579	−	0.0426300i
$815$		0			0
$816$	60.2330	+	360.736i	0.0738150	+	0.442079i
$817$			764.224i			0.935402i
$818$	−18.7288	+	45.2153i	−0.0228958	+	0.0552754i
$819$	72.4800	+	364.382i	0.0884982	+	0.444910i
$820$		0			0
$821$	−624.614	−	417.354i	−0.760797	−	0.508348i	0.113620	−	0.993524i	$-0.463755\pi$
$821$	−624.614	−	417.354i	−0.760797	−	0.508348i	−0.874416	+	0.485176i	$0.838755\pi$
$822$	54.0872	+	10.7586i	0.0657995	+	0.0130883i
$823$	−662.320	−	991.232i	−0.804763	−	1.20441i	−0.975696	−	0.219130i	$-0.929678\pi$
$823$	−662.320	−	991.232i	−0.804763	−	1.20441i	0.170933	−	0.985283i	$-0.445322\pi$
$824$	−62.0890	−	149.896i	−0.0753508	−	0.181913i
$825$		0			0
$826$	4.86749	+	7.28472i	0.00589285	+	0.00881927i
$827$	24.2442	−	121.884i	0.0293158	−	0.147380i	−0.963355	−	0.268229i	$-0.913562\pi$
$827$	24.2442	−	121.884i	0.0293158	−	0.147380i	0.992671	+	0.120849i	$0.0385616\pi$
$828$	740.062	+	494.493i	0.893794	+	0.597214i
$829$	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	$0.0144652\pi$
$830$		0			0
$831$	61.1586	−	147.650i	0.0735964	−	0.177677i
$832$	432.444			0.519764
$833$	17.7304	−	39.3222i	0.0212850	−	0.0472055i
$834$	31.5624			0.0378446
$835$		0			0
$836$	243.967	+	1226.50i	0.291826	+	1.46711i
$837$	170.505	−	170.505i	0.203710	−	0.203710i
$838$	−17.9342	+	26.8405i	−0.0214012	+	0.0320292i
$839$	−234.514	+	1178.98i	−0.279516	+	1.40522i	0.544551	+	0.838728i	$0.316700\pi$
$839$	−234.514	+	1178.98i	−0.279516	+	1.40522i	−0.824067	+	0.566493i	$0.808300\pi$
$840$		0			0
$841$	−249.579	−	602.536i	−0.296764	−	0.716452i
$842$	−25.1731	−	60.7731i	−0.0298967	−	0.0721771i
$843$	272.387	−	182.003i	0.323116	−	0.215899i
$844$	−407.072	−	80.9718i	−0.482313	−	0.0959381i
$845$		0			0
$846$	−47.5701	+	47.5701i	−0.0562294	+	0.0562294i
$847$	72.3984	+	363.972i	0.0854763	+	0.429718i
$848$	−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
$853$	1501.74	−	298.716i	1.76054	−	0.350194i	0.794242	−	0.607602i	$-0.207868\pi$
$853$	1501.74	−	298.716i	1.76054	−	0.350194i	0.966303	+	0.257408i	$0.0828685\pi$
$854$	54.5793	+	54.5793i	0.0639102	+	0.0639102i
$855$		0			0
$856$	18.6967	−	93.9944i	0.0218419	−	0.109807i
$857$	342.009	+	511.852i	0.399077	+	0.597260i	0.975529	−	0.219870i	$-0.0705634\pi$
$857$	342.009	+	511.852i	0.399077	+	0.597260i	−0.576453	+	0.817131i	$0.695563\pi$
$858$	29.3897	−	12.1736i	0.0342537	−	0.0141884i
$859$	161.984	−	67.0958i	0.188572	−	0.0781092i	−0.286399	−	0.958110i	$-0.592458\pi$
$859$	161.984	−	67.0958i	0.188572	−	0.0781092i	0.474972	+	0.880001i	$0.342458\pi$
$860$		0			0
$861$	357.402	+	71.0918i	0.415102	+	0.0825688i
$862$	60.0816	+	40.1452i	0.0697002	+	0.0465722i
$863$	−551.248	−	551.248i	−0.638758	−	0.638758i	0.311491	−	0.950249i	$-0.399172\pi$
$863$	−551.248	−	551.248i	−0.638758	−	0.638758i	−0.950249	+	0.311491i	$0.899172\pi$
$864$	243.805	−	48.4959i	0.282182	−	0.0561295i
$865$		0			0
$866$		−	119.626i		−	0.138137i
$867$	−401.582	+	54.3583i	−0.463186	+	0.0626970i
$868$			303.739i			0.349930i
$869$	1416.81	+	586.860i	1.63039	+	0.675328i
$870$		0			0
$871$	308.053	+	308.053i	0.353678	+	0.353678i
$872$	31.2224	−	46.7276i	0.0358055	−	0.0535867i
$873$	−913.384	−	181.683i	−1.04626	−	0.208114i
$874$	−150.954	+	100.864i	−0.172716	+	0.115405i
$875$		0			0
$876$	−60.4765	+	25.0502i	−0.0690371	+	0.0285961i
$877$	−932.115	+	622.820i	−1.06285	+	0.710171i	−0.958708	−	0.284392i	$-0.908208\pi$
$877$	−932.115	+	622.820i	−1.06285	+	0.710171i	−0.104137	+	0.994563i	$0.533208\pi$
$878$	4.88531	−	24.5601i	0.00556413	−	0.0279728i
$879$	277.322	−	415.041i	0.315497	−	0.472175i
$880$		0			0
$881$	890.772	−	177.186i	1.01109	−	0.201119i	0.338370	−	0.941013i	$-0.390125\pi$
$881$	890.772	−	177.186i	1.01109	−	0.201119i	0.672723	+	0.739895i	$0.265125\pi$
$882$	−3.86874	−	1.60248i	−0.00438633	−	0.00181688i
$883$	−1050.48			−1.18967			−0.594837	−	0.803846i	$-0.702783\pi$
$883$	−1050.48			−1.18967			−0.594837	+	0.803846i	$0.702783\pi$
$884$	−15.2462	+	493.193i	−0.0172468	+	0.557911i
$885$		0			0
$886$	−83.3100	−	34.5082i	−0.0940294	−	0.0389483i
$887$	886.081	−	176.252i	0.998964	−	0.198706i	0.331586	−	0.943425i	$-0.392416\pi$
$887$	886.081	−	176.252i	0.998964	−	0.198706i	0.667378	+	0.744719i	$0.267416\pi$
$888$	−22.5155	+	22.5155i	−0.0253553	+	0.0253553i
$889$	−111.296	−	74.3657i	−0.125192	−	0.0836509i
$890$		0			0
$891$	347.219	−	232.004i	0.389696	−	0.260386i
$892$	474.846	−	196.688i	0.532339	−	0.220502i
$893$	376.295	+	908.455i	0.421382	+	1.01731i
$894$	25.6256	+	38.3514i	0.0286639	+	0.0428986i
$895$		0			0
$896$	−231.393	+	346.304i	−0.258251	+	0.386500i
$897$	−234.008	−	234.008i	−0.260879	−	0.260879i
$898$	1.83609	+	9.23067i	0.00204465	+	0.0102791i
$899$	−158.597	+	382.886i	−0.176414	+	0.425902i
$900$		0			0
$901$	406.965	−	902.561i	0.451682	−	1.00173i
$902$			111.617i			0.123744i
$903$	122.046	−	294.645i	0.135156	−	0.326296i
$904$	−37.0267	−	186.146i	−0.0409587	−	0.205913i
$905$		0			0
$906$	24.9925	+	16.6995i	0.0275856	+	0.0184321i
$907$	1293.65	+	257.323i	1.42630	+	0.283708i	0.847080	−	0.531465i	$-0.178358\pi$
$907$	1293.65	+	257.323i	1.42630	+	0.283708i	0.579217	+	0.815173i	$0.303358\pi$
$908$	743.182	+	1112.25i	0.818482	+	1.22494i
$909$	336.086	+	811.383i	0.369731	+	0.892611i
$910$		0			0
$911$	414.003	+	619.599i	0.454449	+	0.680130i	0.985972	−	0.166914i	$-0.0533801\pi$
$911$	414.003	+	619.599i	0.454449	+	0.680130i	−0.531523	+	0.847044i	$0.678380\pi$
$912$	101.243	−	508.981i	0.111012	−	0.558094i
$913$	1119.25	+	747.856i	1.22590	+	0.819120i
$914$	4.19671	−	4.19671i	0.00459159	−	0.00459159i
$915$		0			0
$916$	46.8509	−	113.108i	0.0511472	−	0.123480i
$917$	404.908			0.441557
$918$	14.7695	+	88.4548i	0.0160888	+	0.0963560i
$919$	−682.519			−0.742676			−0.371338	−	0.928498i	$-0.621101\pi$
$919$	−682.519			−0.742676			−0.371338	+	0.928498i	$0.621101\pi$
$920$		0			0
$921$	−57.3823	−	288.481i	−0.0623044	−	0.313225i
$922$	−110.395	+	110.395i	−0.119735	+	0.119735i
$923$	−163.260	+	244.336i	−0.176880	+	0.264720i
$924$	101.811	−	511.838i	0.110185	−	0.553937i
$925$		0			0
$926$	−74.8373	−	180.673i	−0.0808178	−	0.195111i
$927$	234.273	+	565.584i	0.252721	+	0.610123i
$928$	−355.236	+	237.361i	−0.382798	+	0.255777i
$929$	−759.942	−	151.162i	−0.818021	−	0.162715i	−0.231694	−	0.972789i	$-0.574427\pi$
$929$	−759.942	−	151.162i	−0.818021	−	0.162715i	−0.586327	+	0.810074i	$0.699427\pi$
$930$		0			0
$931$	−43.2791	+	43.2791i	−0.0464867	+	0.0464867i
$932$	190.972	+	960.079i	0.204905	+	1.03013i
$933$	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	−0.955302	−	0.295632i	$-0.904470\pi$
$937$	−66.3005	+	160.063i	−0.0707582	+	0.170825i	0.884544	+	0.466457i	$0.154470\pi$
$938$	−97.8207	+	19.4578i	−0.104287	+	0.0207439i
$939$	−450.987	−	450.987i	−0.480285	−	0.480285i
$940$		0			0
$941$	−109.163	+	548.798i	−0.116007	+	0.583207i	0.878430	+	0.477872i	$0.158592\pi$
$941$	−109.163	+	548.798i	−0.116007	+	0.583207i	−0.994437	+	0.105335i	$0.966408\pi$
$942$	−18.2177	−	27.2647i	−0.0193394	−	0.0289435i
$943$	1072.78	−	444.362i	1.13763	−	0.471221i
$944$	−73.7267	+	30.5386i	−0.0781003	+	0.0323502i
$945$		0			0
$946$	95.8088	+	19.0576i	0.101278	+	0.0201454i
$947$	−1131.96	−	756.351i	−1.19531	−	0.798681i	−0.211410	−	0.977398i	$-0.567805\pi$
$947$	−1131.96	−	756.351i	−1.19531	−	0.798681i	−0.983901	+	0.178717i	$0.942805\pi$
$948$	−456.460	−	456.460i	−0.481498	−	0.481498i
$949$	−85.3924	+	16.9856i	−0.0899814	+	0.0178984i
$950$		0			0
$951$		−	1.67108i		−	0.00175718i
$952$	−185.167	−	132.179i	−0.194504	−	0.138844i
$953$		−	553.052i		−	0.580328i	−0.956977	−	0.290164i	$-0.906290\pi$
$953$		−	553.052i		−	0.580328i	0.956977	−	0.290164i	$-0.0937098\pi$
$954$	−88.7991	−	36.7818i	−0.0930808	−	0.0385553i
$955$		0			0
$956$	−510.639	−	510.639i	−0.534141	−	0.534141i
$957$	395.596	−	592.051i	0.413371	−	0.618653i
$958$	−86.7644	−	17.2585i	−0.0905683	−	0.0180152i
$959$	1000.51	−	668.516i	1.04328	−	0.697097i
$960$		0			0
$961$	−781.578	+	323.740i	−0.813297	+	0.336878i
$962$	−17.4851	+	11.6832i	−0.0181758	+	0.0121447i
$963$	−70.5457	+	354.657i	−0.0732562	+	0.368284i
$964$	−721.078	+	1079.17i	−0.748006	+	1.11947i
$965$		0			0
$966$	74.3081	−	14.7808i	0.0769235	−	0.0153010i
$967$	681.241	+	282.179i	0.704490	+	0.291809i	0.706022	−	0.708190i	$-0.250488\pi$
$967$	681.241	+	282.179i	0.704490	+	0.291809i	−0.00153265	+	0.999999i	$0.500488\pi$
$968$	96.3636			0.0995491
$969$	560.237	+	129.553i	0.578160	+	0.133698i
$970$		0			0
$971$	−1570.52	−	650.532i	−1.61743	−	0.669961i	−0.623688	−	0.781673i	$-0.714367\pi$
$971$	−1570.52	−	650.532i	−1.61743	−	0.669961i	−0.993741	+	0.111712i	$0.964367\pi$
$972$	−955.316	+	190.024i	−0.982836	+	0.195498i
$973$	486.976	−	486.976i	0.500490	−	0.500490i
$974$	−102.711	−	68.6290i	−0.105452	−	0.0704610i
$975$		0			0
$976$	−584.564	+	390.593i	−0.598939	+	0.400198i
$977$	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
$979$	−1065.05	−	1593.96i	−1.08790	−	1.62815i
$980$		0			0
$981$	−117.808	+	176.311i	−0.120089	+	0.179726i
$982$	−102.379	−	102.379i	−0.104256	−	0.104256i
$983$	238.411	+	1198.57i	0.242534	+	1.21930i	0.889555	+	0.456828i	$0.151015\pi$
$983$	238.411	+	1198.57i	0.242534	+	1.21930i	−0.647021	+	0.762472i	$0.723985\pi$
$984$	36.2112	−	87.4215i	0.0368000	−	0.0888430i
$985$		0			0
$986$	−81.6307	−	130.741i	−0.0827898	−	0.132598i
$987$		−	410.348i		−	0.415753i
$988$	267.936	−	646.855i	0.271190	−	0.654711i
$989$	−198.259	−	996.716i	−0.200464	−	1.00780i
$990$		0			0
$991$	−1202.45	−	803.454i	−1.21337	−	0.810750i	−0.226780	−	0.973946i	$-0.572820\pi$
$991$	−1202.45	−	803.454i	−1.21337	−	0.810750i	−0.986594	+	0.163196i	$0.947820\pi$
$992$	116.302	+	23.1339i	0.117240	+	0.0233205i
$993$	−380.247	−	569.080i	−0.382928	−	0.573092i
$994$	−25.7453	−	62.1546i	−0.0259007	−	0.0625297i
$995$		0			0
$996$	−314.804	−	471.138i	−0.316069	−	0.473030i
$997$	167.876	−	843.968i	0.168381	−	0.846508i	−0.800567	−	0.599243i	$-0.795468\pi$
$997$	167.876	−	843.968i	0.168381	−	0.846508i	0.968948	−	0.247265i	$-0.0795317\pi$
$998$	−162.431	−	108.533i	−0.162757	−	0.108751i
$999$	193.659	−	193.659i	0.193852	−	0.193852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.b.249.1		8
5.2	odd	4		17.3.e.b.11.1	✓	8
5.3	odd	4		425.3.u.a.351.1		8
5.4	even	2		425.3.t.d.249.1		8
15.2	even	4		153.3.p.a.28.1		8
17.14	odd	16		425.3.t.d.99.1		8
20.7	even	4		272.3.bh.b.113.1		8
85.2	odd	8		289.3.e.n.214.1		8
85.7	even	16		289.3.e.n.131.1		8
85.12	even	16		289.3.e.h.224.1		8
85.14	odd	16	inner	425.3.t.b.99.1		8
85.22	even	16		289.3.e.f.224.1		8
85.27	even	16		289.3.e.j.131.1		8
85.32	odd	8		289.3.e.j.214.1		8
85.37	even	16		289.3.e.g.65.1		8
85.42	odd	8		289.3.e.a.75.1		8
85.47	odd	4		289.3.e.f.40.1		8
85.48	even	16		425.3.u.a.201.1		8
85.57	even	16		289.3.e.a.158.1		8
85.62	even	16		289.3.e.e.158.1		8
85.67	odd	4		289.3.e.g.249.1		8
85.72	odd	4		289.3.e.h.40.1		8
85.77	odd	8		289.3.e.e.75.1		8
85.82	even	16		17.3.e.b.14.1	yes	8
255.167	odd	16		153.3.p.a.82.1		8
340.167	odd	16		272.3.bh.b.65.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.11.1	✓	8	5.2	odd	4
17.3.e.b.14.1	yes	8	85.82	even	16
153.3.p.a.28.1		8	15.2	even	4
153.3.p.a.82.1		8	255.167	odd	16
272.3.bh.b.65.1		8	340.167	odd	16
272.3.bh.b.113.1		8	20.7	even	4
289.3.e.a.75.1		8	85.42	odd	8
289.3.e.a.158.1		8	85.57	even	16
289.3.e.e.75.1		8	85.77	odd	8
289.3.e.e.158.1		8	85.62	even	16
289.3.e.f.40.1		8	85.47	odd	4
289.3.e.f.224.1		8	85.22	even	16
289.3.e.g.65.1		8	85.37	even	16
289.3.e.g.249.1		8	85.67	odd	4
289.3.e.h.40.1		8	85.72	odd	4
289.3.e.h.224.1		8	85.12	even	16
289.3.e.j.131.1		8	85.27	even	16
289.3.e.j.214.1		8	85.32	odd	8
289.3.e.n.131.1		8	85.7	even	16
289.3.e.n.214.1		8	85.2	odd	8
425.3.t.b.99.1		8	85.14	odd	16	inner
425.3.t.b.249.1		8	1.1	even	1	trivial
425.3.t.d.99.1		8	17.14	odd	16
425.3.t.d.249.1		8	5.4	even	2
425.3.u.a.201.1		8	85.48	even	16
425.3.u.a.351.1		8	5.3	odd	4

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0897902 - 0.216773i) q^{2} +(-1.37529 + 0.273561i) q^{3} +(2.78950 + 2.78950i) q^{4} +(-0.0641865 + 0.322688i) q^{6} +(3.98841 + 5.96908i) q^{7} +(1.72225 - 0.713379i) q^{8} +(-6.49834 + 2.69170i) q^{9} +(12.8888 + 2.56374i) q^{11} +(-4.59946 - 3.07326i) q^{12} +(-5.20259 - 5.20259i) q^{13} +(1.65205 - 0.328614i) q^{14} +15.3424i q^{16} +(-16.9919 - 0.525274i) q^{17} +1.65035i q^{18} +(22.2860 + 9.23114i) q^{19} +(-7.11811 - 7.11811i) q^{21} +(1.71303 - 2.56374i) q^{22} +(-31.4606 - 6.25790i) q^{23} +(-2.17343 + 1.45224i) q^{24} +(-1.59492 + 0.660638i) q^{26} +(18.6939 - 12.4909i) q^{27} +(-5.52507 + 27.7764i) q^{28} +(-21.4682 + 32.1294i) q^{29} +(10.5189 - 2.09235i) q^{31} +(10.2148 + 4.23111i) q^{32} -18.4271 q^{33} +(-1.63957 + 3.63621i) q^{34} +(-25.6356 - 10.6186i) q^{36} +(11.9474 - 2.37648i) q^{37} +(4.00212 - 4.00212i) q^{38} +(8.57827 + 5.73181i) q^{39} +(-30.0989 + 20.1114i) q^{41} +(-2.18215 + 0.903876i) q^{42} +(12.1240 + 29.2698i) q^{43} +(28.8017 + 43.1047i) q^{44} +(-4.18140 + 6.25790i) q^{46} +(28.8242 + 28.8242i) q^{47} +(-4.19709 - 21.1002i) q^{48} +(-0.970996 + 2.34419i) q^{49} +(23.5124 - 3.92592i) q^{51} -29.0252i q^{52} +(-22.2872 + 53.8061i) q^{53} +(-1.02915 - 5.17389i) q^{54} +(11.1272 + 7.43499i) q^{56} +(-33.1748 - 6.59888i) q^{57} +(5.03714 + 7.53862i) q^{58} +(1.99047 + 4.80542i) q^{59} +(25.4584 + 38.1012i) q^{61} +(0.490934 - 2.46809i) q^{62} +(-41.9850 - 28.0535i) q^{63} +(-41.5605 + 41.5605i) q^{64} +(-1.65457 + 3.99449i) q^{66} -59.2116 q^{67} +(-45.9336 - 48.8641i) q^{68} +44.9792 q^{69} +(-7.79189 - 39.1725i) q^{71} +(-9.27155 + 9.27155i) q^{72} +(6.57431 - 9.83914i) q^{73} +(0.557600 - 2.80324i) q^{74} +(36.4164 + 87.9169i) q^{76} +(36.1026 + 87.1593i) q^{77} +(2.01275 - 1.34487i) q^{78} +(114.454 + 22.7663i) q^{79} +(22.4701 - 22.4701i) q^{81} +(1.65702 + 8.33042i) q^{82} +(94.6362 + 39.1996i) q^{83} -39.7119i q^{84} +7.43351 q^{86} +(20.7355 - 50.0599i) q^{87} +(24.0266 - 4.77918i) q^{88} +(-103.152 - 103.152i) q^{89} +(10.3046 - 51.8047i) q^{91} +(-70.3029 - 105.216i) q^{92} +(-13.8942 + 5.75515i) q^{93} +(8.83643 - 3.66017i) q^{94} +(-15.2057 - 3.02461i) q^{96} +(110.088 + 73.5583i) q^{97} +(0.420971 + 0.420971i) q^{98} +(-90.6564 + 18.0327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{7} - 8 q^{8} - 8 q^{9} + 40 q^{11} - 32 q^{12} - 16 q^{14} - 64 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 24 q^{24} + 112 q^{27} - 8 q^{28} - 24 q^{29}+ \cdots - 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^7 - 8 * q^8 - 8 * q^9 + 40 * q^11 - 32 * q^12 - 16 * q^14 - 64 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 24 * q^24 + 112 * q^27 - 8 * q^28 - 24 * q^29 + 32 * q^31 - 16 * q^32 + 16 * q^33 - 64 * q^34 - 104 * q^36 + 56 * q^37 - 8 * q^38 + 72 * q^39 + 88 * q^42 - 48 * q^43 + 96 * q^44 + 80 * q^47 + 16 * q^48 - 8 * q^49 - 176 * q^51 + 88 * q^53 - 208 * q^54 + 72 * q^56 - 168 * q^57 - 96 * q^58 - 8 * q^59 + 264 * q^61 - 96 * q^62 - 16 * q^63 + 120 * q^64 + 8 * q^66 - 32 * q^67 + 120 * q^68 + 208 * q^69 + 32 * q^71 + 24 * q^72 - 240 * q^73 - 176 * q^74 - 80 * q^76 + 120 * q^77 + 96 * q^79 - 224 * q^81 - 352 * q^82 + 504 * q^83 + 288 * q^86 - 216 * q^87 + 24 * q^88 - 288 * q^89 - 24 * q^91 - 72 * q^92 - 248 * q^93 + 8 * q^94 + 328 * q^96 + 280 * q^97 + 16 * q^98 - 136 * q^99

Introduction

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