LMFDB - Embedded newform 230.3.f.a.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.5
Root			$-0.0649756 + 0.0649756i$ of defining polynomial
Character	$\chi$	$=$	230.47
Dual form			230.3.f.a.93.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.0649756 + 0.0649756i) q^{3} +2.00000i q^{4} +(-4.95703 - 0.654141i) q^{5} +0.129951 q^{6} +(-3.31044 - 3.31044i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.99156i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.0649756 + 0.0649756i) q^{3} +2.00000i q^{4} +(-4.95703 - 0.654141i) q^{5} +0.129951 q^{6} +(-3.31044 - 3.31044i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.99156i q^{9} +(4.30288 + 5.61117i) q^{10} +11.2959 q^{11} +(-0.129951 - 0.129951i) q^{12} +(6.07959 - 6.07959i) q^{13} +6.62087i q^{14} +(0.364589 - 0.279583i) q^{15} -4.00000 q^{16} +(18.2517 + 18.2517i) q^{17} +(8.99156 - 8.99156i) q^{18} +22.9272i q^{19} +(1.30828 - 9.91405i) q^{20} +0.430195 q^{21} +(-11.2959 - 11.2959i) q^{22} +(-3.39116 + 3.39116i) q^{23} +0.259903i q^{24} +(24.1442 + 6.48519i) q^{25} -12.1592 q^{26} +(-1.16901 - 1.16901i) q^{27} +(6.62087 - 6.62087i) q^{28} +24.1743i q^{29} +(-0.644172 - 0.0850065i) q^{30} +1.45528 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.733956 + 0.733956i) q^{33} -36.5034i q^{34} +(14.2444 + 18.5754i) q^{35} -17.9831 q^{36} +(3.02520 + 3.02520i) q^{37} +(22.9272 - 22.9272i) q^{38} +0.790050i q^{39} +(-11.2223 + 8.60577i) q^{40} +46.8844 q^{41} +(-0.430195 - 0.430195i) q^{42} +(48.4158 - 48.4158i) q^{43} +22.5917i q^{44} +(5.88175 - 44.5714i) q^{45} +6.78233 q^{46} +(9.42035 + 9.42035i) q^{47} +(0.259903 - 0.259903i) q^{48} -27.0820i q^{49} +(-17.6590 - 30.6294i) q^{50} -2.37183 q^{51} +(12.1592 + 12.1592i) q^{52} +(-69.3124 + 69.3124i) q^{53} +2.33803i q^{54} +(-55.9939 - 7.38909i) q^{55} -13.2417 q^{56} +(-1.48971 - 1.48971i) q^{57} +(24.1743 - 24.1743i) q^{58} +92.6123i q^{59} +(0.559165 + 0.729178i) q^{60} -113.348 q^{61} +(-1.45528 - 1.45528i) q^{62} +(29.7660 - 29.7660i) q^{63} -8.00000i q^{64} +(-34.1136 + 26.1598i) q^{65} +1.46791 q^{66} +(-6.74683 - 6.74683i) q^{67} +(-36.5034 + 36.5034i) q^{68} -0.440686i q^{69} +(4.33099 - 32.8198i) q^{70} -26.7478 q^{71} +(17.9831 + 17.9831i) q^{72} +(33.5695 - 33.5695i) q^{73} -6.05040i q^{74} +(-1.99016 + 1.14741i) q^{75} -45.8543 q^{76} +(-37.3942 - 37.3942i) q^{77} +(0.790050 - 0.790050i) q^{78} +55.9899i q^{79} +(19.8281 + 2.61657i) q^{80} -80.7721 q^{81} +(-46.8844 - 46.8844i) q^{82} +(77.9157 - 77.9157i) q^{83} +0.860391i q^{84} +(-78.5349 - 102.413i) q^{85} -96.8315 q^{86} +(-1.57074 - 1.57074i) q^{87} +(22.5917 - 22.5917i) q^{88} +81.5042i q^{89} +(-50.4531 + 38.6896i) q^{90} -40.2522 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-0.0945580 + 0.0945580i) q^{93} -18.8407i q^{94} +(14.9976 - 113.650i) q^{95} -0.519805 q^{96} +(2.69032 + 2.69032i) q^{97} +(-27.0820 + 27.0820i) q^{98} +101.567i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−0.0649756	+	0.0649756i	−0.0216585	+	0.0216585i	−0.717853	−	0.696195i	$-0.754875\pi$
$3$	−0.0649756	+	0.0649756i	−0.0216585	+	0.0216585i	0.696195	+	0.717853i	$0.254875\pi$
$4$			2.00000i			0.500000i
$5$	−4.95703	−	0.654141i	−0.991405	−	0.130828i
$5$	−4.95703	−	0.654141i	−0.991405	−	0.130828i
$6$	0.129951			0.0216585
$7$	−3.31044	−	3.31044i	−0.472919	−	0.472919i	0.429939	−	0.902858i	$-0.358535\pi$
$7$	−3.31044	−	3.31044i	−0.472919	−	0.472919i	−0.902858	+	0.429939i	$0.858535\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			8.99156i			0.999062i
$10$	4.30288	+	5.61117i	0.430288	+	0.561117i
$11$	11.2959			1.02690			0.513448	−	0.858120i	$-0.328368\pi$
$11$	11.2959			1.02690			0.513448	+	0.858120i	$0.328368\pi$
$12$	−0.129951	−	0.129951i	−0.0108293	−	0.0108293i
$13$	6.07959	−	6.07959i	0.467661	−	0.467661i	−0.433495	−	0.901156i	$-0.642720\pi$
$13$	6.07959	−	6.07959i	0.467661	−	0.467661i	0.901156	+	0.433495i	$0.142720\pi$
$14$			6.62087i			0.472919i
$15$	0.364589	−	0.279583i	0.0243059	−	0.0186388i
$16$	−4.00000			−0.250000
$17$	18.2517	+	18.2517i	1.07363	+	1.07363i	0.997065	+	0.0765647i	$0.0243952\pi$
$17$	18.2517	+	18.2517i	1.07363	+	1.07363i	0.0765647	+	0.997065i	$0.475605\pi$
$18$	8.99156	−	8.99156i	0.499531	−	0.499531i
$19$			22.9272i			1.20669i	0.797479	+	0.603346i	$0.206166\pi$
$19$			22.9272i			1.20669i	−0.797479	+	0.603346i	$0.793834\pi$
$20$	1.30828	−	9.91405i	0.0654141	−	0.495703i
$21$	0.430195			0.0204855
$22$	−11.2959	−	11.2959i	−0.513448	−	0.513448i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			0.259903i			0.0108293i
$25$	24.1442	+	6.48519i	0.965768	+	0.259408i
$26$	−12.1592			−0.467661
$27$	−1.16901	−	1.16901i	−0.0432968	−	0.0432968i
$28$	6.62087	−	6.62087i	0.236460	−	0.236460i
$29$			24.1743i			0.833597i	0.908999	+	0.416799i	$0.136848\pi$
$29$			24.1743i			0.833597i	−0.908999	+	0.416799i	$0.863152\pi$
$30$	−0.644172	−	0.0850065i	−0.0214724	−	0.00283355i
$31$	1.45528			0.0469447			0.0234723	−	0.999724i	$-0.492528\pi$
$31$	1.45528			0.0469447			0.0234723	+	0.999724i	$0.492528\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−0.733956	+	0.733956i	−0.0222411	+	0.0222411i
$34$		−	36.5034i		−	1.07363i
$35$	14.2444	+	18.5754i	0.406983	+	0.530726i
$36$	−17.9831			−0.499531
$37$	3.02520	+	3.02520i	0.0817622	+	0.0817622i	0.746805	−	0.665043i	$-0.231587\pi$
$37$	3.02520	+	3.02520i	0.0817622	+	0.0817622i	−0.665043	+	0.746805i	$0.731587\pi$
$38$	22.9272	−	22.9272i	0.603346	−	0.603346i
$39$			0.790050i			0.0202577i
$40$	−11.2223	+	8.60577i	−0.280558	+	0.215144i
$41$	46.8844			1.14352			0.571762	−	0.820420i	$-0.306260\pi$
$41$	46.8844			1.14352			0.571762	+	0.820420i	$0.306260\pi$
$42$	−0.430195	−	0.430195i	−0.0102427	−	0.0102427i
$43$	48.4158	−	48.4158i	1.12595	−	1.12595i	0.135118	−	0.990829i	$-0.456858\pi$
$43$	48.4158	−	48.4158i	1.12595	−	1.12595i	0.990829	−	0.135118i	$-0.0431415\pi$
$44$			22.5917i			0.513448i
$45$	5.88175	−	44.5714i	0.130706	−	0.990475i
$46$	6.78233			0.147442
$47$	9.42035	+	9.42035i	0.200433	+	0.200433i	0.800185	−	0.599753i	$-0.204734\pi$
$47$	9.42035	+	9.42035i	0.200433	+	0.200433i	−0.599753	+	0.800185i	$0.704734\pi$
$48$	0.259903	−	0.259903i	0.00541464	−	0.00541464i
$49$		−	27.0820i		−	0.552695i
$50$	−17.6590	−	30.6294i	−0.353180	−	0.612588i
$51$	−2.37183			−0.0465065
$52$	12.1592	+	12.1592i	0.233830	+	0.233830i
$53$	−69.3124	+	69.3124i	−1.30778	+	1.30778i	−0.384768	+	0.923013i	$0.625719\pi$
$53$	−69.3124	+	69.3124i	−1.30778	+	1.30778i	−0.923013	+	0.384768i	$0.874281\pi$
$54$			2.33803i			0.0432968i
$55$	−55.9939	−	7.38909i	−1.01807	−	0.134347i
$56$	−13.2417			−0.236460
$57$	−1.48971	−	1.48971i	−0.0261352	−	0.0261352i
$58$	24.1743	−	24.1743i	0.416799	−	0.416799i
$59$			92.6123i			1.56970i	0.619686	+	0.784850i	$0.287260\pi$
$59$			92.6123i			1.56970i	−0.619686	+	0.784850i	$0.712740\pi$
$60$	0.559165	+	0.729178i	0.00931942	+	0.0121530i
$61$	−113.348			−1.85816			−0.929080	−	0.369878i	$-0.879400\pi$
$61$	−113.348			−1.85816			−0.929080	+	0.369878i	$0.879400\pi$
$62$	−1.45528	−	1.45528i	−0.0234723	−	0.0234723i
$63$	29.7660	−	29.7660i	0.472476	−	0.472476i
$64$		−	8.00000i		−	0.125000i
$65$	−34.1136	+	26.1598i	−0.524824	+	0.402458i
$66$	1.46791			0.0222411
$67$	−6.74683	−	6.74683i	−0.100699	−	0.100699i	0.654962	−	0.755661i	$-0.272684\pi$
$67$	−6.74683	−	6.74683i	−0.100699	−	0.100699i	−0.755661	+	0.654962i	$0.772684\pi$
$68$	−36.5034	+	36.5034i	−0.536815	+	0.536815i
$69$		−	0.440686i		−	0.00638676i
$70$	4.33099	−	32.8198i	0.0618712	−	0.468855i
$71$	−26.7478			−0.376730			−0.188365	−	0.982099i	$-0.560319\pi$
$71$	−26.7478			−0.376730			−0.188365	+	0.982099i	$0.560319\pi$
$72$	17.9831	+	17.9831i	0.249765	+	0.249765i
$73$	33.5695	−	33.5695i	0.459856	−	0.459856i	−0.438752	−	0.898608i	$-0.644579\pi$
$73$	33.5695	−	33.5695i	0.459856	−	0.459856i	0.898608	+	0.438752i	$0.144579\pi$
$74$		−	6.05040i		−	0.0817622i
$75$	−1.99016	+	1.14741i	−0.0265355	+	0.0152987i
$76$	−45.8543			−0.603346
$77$	−37.3942	−	37.3942i	−0.485639	−	0.485639i
$78$	0.790050	−	0.790050i	0.0101289	−	0.0101289i
$79$			55.9899i			0.708733i	0.935107	+	0.354367i	$0.115304\pi$
$79$			55.9899i			0.708733i	−0.935107	+	0.354367i	$0.884696\pi$
$80$	19.8281	+	2.61657i	0.247851	+	0.0327071i
$81$	−80.7721			−0.997186
$82$	−46.8844	−	46.8844i	−0.571762	−	0.571762i
$83$	77.9157	−	77.9157i	0.938743	−	0.938743i	−0.0594862	−	0.998229i	$-0.518946\pi$
$83$	77.9157	−	77.9157i	0.938743	−	0.938743i	0.998229	+	0.0594862i	$0.0189462\pi$
$84$			0.860391i			0.0102427i
$85$	−78.5349	−	102.413i	−0.923940	−	1.20486i
$86$	−96.8315			−1.12595
$87$	−1.57074	−	1.57074i	−0.0180545	−	0.0180545i
$88$	22.5917	−	22.5917i	0.256724	−	0.256724i
$89$			81.5042i			0.915778i	0.889009	+	0.457889i	$0.151394\pi$
$89$			81.5042i			0.915778i	−0.889009	+	0.457889i	$0.848606\pi$
$90$	−50.4531	+	38.6896i	−0.560590	+	0.429885i
$91$	−40.2522			−0.442332
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−0.0945580	+	0.0945580i	−0.00101675	+	0.00101675i
$94$		−	18.8407i		−	0.200433i
$95$	14.9976	−	113.650i	0.157869	−	1.19632i
$96$	−0.519805			−0.00541464
$97$	2.69032	+	2.69032i	0.0277352	+	0.0277352i	0.720838	−	0.693103i	$-0.243757\pi$
$97$	2.69032	+	2.69032i	0.0277352	+	0.0277352i	−0.693103	+	0.720838i	$0.743757\pi$
$98$	−27.0820	+	27.0820i	−0.276347	+	0.276347i
$99$			101.567i			1.02593i
$100$	−12.9704	+	48.2884i	−0.129704	+	0.482884i
$101$	32.0918			0.317740			0.158870	−	0.987299i	$-0.449215\pi$
$101$	32.0918			0.317740			0.158870	+	0.987299i	$0.449215\pi$
$102$	2.37183	+	2.37183i	0.0232533	+	0.0232533i
$103$	23.0915	−	23.0915i	0.224189	−	0.224189i	−0.586071	−	0.810260i	$-0.699326\pi$
$103$	23.0915	−	23.0915i	0.224189	−	0.224189i	0.810260	+	0.586071i	$0.199326\pi$
$104$		−	24.3184i		−	0.233830i
$105$	−2.13249	−	0.281409i	−0.0203094	−	0.00268008i
$106$	138.625			1.30778
$107$	−0.772222	−	0.772222i	−0.00721703	−	0.00721703i	0.703489	−	0.710706i	$-0.251624\pi$
$107$	−0.772222	−	0.772222i	−0.00721703	−	0.00721703i	−0.710706	+	0.703489i	$0.751624\pi$
$108$	2.33803	−	2.33803i	0.0216484	−	0.0216484i
$109$			17.8026i			0.163326i	0.996660	+	0.0816632i	$0.0260232\pi$
$109$			17.8026i			0.163326i	−0.996660	+	0.0816632i	$0.973977\pi$
$110$	48.6048	+	63.3830i	0.441862	+	0.576209i
$111$	−0.393129			−0.00354170
$112$	13.2417	+	13.2417i	0.118230	+	0.118230i
$113$	−50.2540	+	50.2540i	−0.444726	+	0.444726i	−0.893597	−	0.448871i	$-0.851826\pi$
$113$	−50.2540	+	50.2540i	−0.444726	+	0.444726i	0.448871	+	0.893597i	$0.351826\pi$
$114$			2.97941i			0.0261352i
$115$	19.0284	−	14.5918i	0.165464	−	0.126885i
$116$	−48.3486			−0.416799
$117$	54.6650	+	54.6650i	0.467222	+	0.467222i
$118$	92.6123	−	92.6123i	0.784850	−	0.784850i
$119$		−	120.842i		−	1.01548i
$120$	0.170013	−	1.28834i	0.00141678	−	0.0107362i
$121$	6.59659			0.0545172
$122$	113.348	+	113.348i	0.929080	+	0.929080i
$123$	−3.04635	+	3.04635i	−0.0247671	+	0.0247671i
$124$			2.91057i			0.0234723i
$125$	−115.441	−	47.9410i	−0.923529	−	0.383528i
$126$	−59.5319			−0.472476
$127$	24.9970	+	24.9970i	0.196827	+	0.196827i	0.798638	−	0.601811i	$-0.205554\pi$
$127$	24.9970	+	24.9970i	0.196827	+	0.196827i	−0.601811	+	0.798638i	$0.705554\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			6.29169i			0.0487728i
$130$	60.2734	+	7.95382i	0.463641	+	0.0611832i
$131$	193.717			1.47876			0.739378	−	0.673291i	$-0.235120\pi$
$131$	193.717			1.47876			0.739378	+	0.673291i	$0.235120\pi$
$132$	−1.46791	−	1.46791i	−0.0111205	−	0.0111205i
$133$	75.8989	−	75.8989i	0.570668	−	0.570668i
$134$			13.4937i			0.100699i
$135$	5.03013	+	6.55953i	0.0372602	+	0.0485891i
$136$	73.0068			0.536815
$137$	83.2274	+	83.2274i	0.607499	+	0.607499i	0.942292	−	0.334792i	$-0.108666\pi$
$137$	83.2274	+	83.2274i	0.607499	+	0.607499i	−0.334792	+	0.942292i	$0.608666\pi$
$138$	−0.440686	+	0.440686i	−0.00319338	+	0.00319338i
$139$		−	144.121i		−	1.03684i	−0.855126	−	0.518420i	$-0.826521\pi$
$139$		−	144.121i		−	1.03684i	0.855126	−	0.518420i	$-0.173479\pi$
$140$	−37.1508	+	28.4888i	−0.265363	+	0.203492i
$141$	−1.22419			−0.00868217
$142$	26.7478	+	26.7478i	0.188365	+	0.188365i
$143$	68.6742	−	68.6742i	0.480239	−	0.480239i
$144$		−	35.9662i		−	0.249765i
$145$	15.8134	−	119.833i	0.109058	−	0.826432i
$146$	−67.1390			−0.459856
$147$	1.75967	+	1.75967i	0.0119706	+	0.0119706i
$148$	−6.05040	+	6.05040i	−0.0408811	+	0.0408811i
$149$			224.861i			1.50913i	0.656224	+	0.754567i	$0.272153\pi$
$149$			224.861i			1.50913i	−0.656224	+	0.754567i	$0.727847\pi$
$150$	3.13757	+	0.842759i	0.0209171	+	0.00561839i
$151$	248.329			1.64457			0.822283	−	0.569079i	$-0.192700\pi$
$151$	248.329			1.64457			0.822283	+	0.569079i	$0.192700\pi$
$152$	45.8543	+	45.8543i	0.301673	+	0.301673i
$153$	−164.111	+	164.111i	−1.07262	+	1.07262i
$154$			74.7885i			0.485639i
$155$	−7.21388	−	0.951962i	−0.0465412	−	0.00614169i
$156$	−1.58010			−0.0101289
$157$	−154.022	−	154.022i	−0.981033	−	0.981033i	0.0187908	−	0.999823i	$-0.494018\pi$
$157$	−154.022	−	154.022i	−0.981033	−	0.981033i	−0.999823	+	0.0187908i	$0.994018\pi$
$158$	55.9899	−	55.9899i	0.354367	−	0.354367i
$159$		−	9.00724i		−	0.0566493i
$160$	−17.2115	−	22.4447i	−0.107572	−	0.140279i
$161$	22.4525			0.139456
$162$	80.7721	+	80.7721i	0.498593	+	0.498593i
$163$	−0.742426	+	0.742426i	−0.00455476	+	0.00455476i	−0.709380	−	0.704826i	$-0.751025\pi$
$163$	−0.742426	+	0.742426i	−0.00455476	+	0.00455476i	0.704826	+	0.709380i	$0.251025\pi$
$164$			93.7689i			0.571762i
$165$	4.11835	−	3.15813i	0.0249597	−	0.0191402i
$166$	−155.831			−0.938743
$167$	115.646	+	115.646i	0.692492	+	0.692492i	0.962780	−	0.270288i	$-0.0871189\pi$
$167$	115.646	+	115.646i	0.692492	+	0.692492i	−0.270288	+	0.962780i	$0.587119\pi$
$168$	0.860391	−	0.860391i	0.00512137	−	0.00512137i
$169$			95.0772i			0.562587i
$170$	−23.8784	+	180.948i	−0.140461	+	1.06440i
$171$	−206.151			−1.20556
$172$	96.8315	+	96.8315i	0.562974	+	0.562974i
$173$	135.671	−	135.671i	0.784224	−	0.784224i	−0.196317	−	0.980541i	$-0.562898\pi$
$173$	135.671	−	135.671i	0.784224	−	0.784224i	0.980541	+	0.196317i	$0.0628980\pi$
$174$			3.14148i			0.0180545i
$175$	−58.4590	−	101.397i	−0.334051	−	0.579409i
$176$	−45.1835			−0.256724
$177$	−6.01754	−	6.01754i	−0.0339974	−	0.0339974i
$178$	81.5042	−	81.5042i	0.457889	−	0.457889i
$179$		−	317.529i		−	1.77390i	−0.461861	−	0.886952i	$-0.652818\pi$
$179$		−	317.529i		−	1.77390i	0.461861	−	0.886952i	$-0.347182\pi$
$180$	89.1427	+	11.7635i	0.495237	+	0.0653528i
$181$	39.6540			0.219083			0.109541	−	0.993982i	$-0.465062\pi$
$181$	39.6540			0.219083			0.109541	+	0.993982i	$0.465062\pi$
$182$	40.2522	+	40.2522i	0.221166	+	0.221166i
$183$	7.36485	−	7.36485i	0.0402451	−	0.0402451i
$184$			13.5647i			0.0737210i
$185$	−13.0171	−	16.9749i	−0.0703626	−	0.0917562i
$186$	0.189116			0.00101675
$187$	206.169	+	206.169i	1.10251	+	1.10251i
$188$	−18.8407	+	18.8407i	−0.100216	+	0.100216i
$189$			7.73988i			0.0409518i
$190$	−128.648	+	98.6529i	−0.677095	+	0.519226i
$191$	106.653			0.558395			0.279197	−	0.960234i	$-0.409932\pi$
$191$	106.653			0.558395			0.279197	+	0.960234i	$0.409932\pi$
$192$	0.519805	+	0.519805i	0.00270732	+	0.00270732i
$193$	−141.080	+	141.080i	−0.730985	+	0.730985i	−0.970815	−	0.239830i	$-0.922908\pi$
$193$	−141.080	+	141.080i	−0.730985	+	0.730985i	0.239830	+	0.970815i	$0.422908\pi$
$194$		−	5.38063i		−	0.0277352i
$195$	0.516805	−	3.91630i	0.00265028	−	0.0200836i
$196$	54.1641			0.276347
$197$	−126.726	−	126.726i	−0.643281	−	0.643281i	0.308080	−	0.951361i	$-0.400314\pi$
$197$	−126.726	−	126.726i	−0.643281	−	0.643281i	−0.951361	+	0.308080i	$0.900314\pi$
$198$	101.567	−	101.567i	0.512967	−	0.512967i
$199$		−	96.1858i		−	0.483346i	−0.970358	−	0.241673i	$-0.922304\pi$
$199$		−	96.1858i		−	0.483346i	0.970358	−	0.241673i	$-0.0776961\pi$
$200$	61.2588	−	35.3180i	0.306294	−	0.176590i
$201$	0.876759			0.00436198
$202$	−32.0918	−	32.0918i	−0.158870	−	0.158870i
$203$	80.0275	−	80.0275i	0.394224	−	0.394224i
$204$		−	4.74366i		−	0.0232533i
$205$	−232.407	−	30.6691i	−1.13369	−	0.149605i
$206$	−46.1830			−0.224189
$207$	−30.4919	−	30.4919i	−0.147304	−	0.147304i
$208$	−24.3184	+	24.3184i	−0.116915	+	0.116915i
$209$			258.982i			1.23915i
$210$	1.85108	+	2.41390i	0.00881467	+	0.0114948i
$211$	380.514			1.80338			0.901692	−	0.432379i	$-0.142326\pi$
$211$	380.514			1.80338			0.901692	+	0.432379i	$0.142326\pi$
$212$	−138.625	−	138.625i	−0.653891	−	0.653891i
$213$	1.73796	−	1.73796i	0.00815943	−	0.00815943i
$214$			1.54444i			0.00721703i
$215$	−271.669	+	208.327i	−1.26358	+	0.968965i
$216$	−4.67605			−0.0216484
$217$	−4.81763	−	4.81763i	−0.0222010	−	0.0222010i
$218$	17.8026	−	17.8026i	0.0816632	−	0.0816632i
$219$			4.36240i			0.0199196i
$220$	14.7782	−	111.988i	0.0671736	−	0.509035i
$221$	221.926			1.00419
$222$	0.393129	+	0.393129i	0.00177085	+	0.00177085i
$223$	−60.6308	+	60.6308i	−0.271887	+	0.271887i	−0.829859	−	0.557973i	$-0.811579\pi$
$223$	−60.6308	+	60.6308i	−0.271887	+	0.271887i	0.557973	+	0.829859i	$0.311579\pi$
$224$		−	26.4835i		−	0.118230i
$225$	−58.3119	+	217.094i	−0.259164	+	0.964862i
$226$	100.508			0.444726
$227$	−234.946	−	234.946i	−1.03501	−	1.03501i	−0.999365	−	0.0356411i	$-0.988653\pi$
$227$	−234.946	−	234.946i	−1.03501	−	1.03501i	−0.0356411	−	0.999365i	$-0.511347\pi$
$228$	2.97941	−	2.97941i	0.0130676	−	0.0130676i
$229$		−	338.701i		−	1.47905i	−0.673132	−	0.739523i	$-0.735051\pi$
$229$		−	338.701i		−	1.47905i	0.673132	−	0.739523i	$-0.264949\pi$
$230$	−33.6202	−	4.43660i	−0.146175	−	0.0192896i
$231$	4.85943			0.0210365
$232$	48.3486	+	48.3486i	0.208399	+	0.208399i
$233$	−194.995	+	194.995i	−0.836888	+	0.836888i	−0.988448	−	0.151560i	$-0.951570\pi$
$233$	−194.995	+	194.995i	−0.836888	+	0.836888i	0.151560	+	0.988448i	$0.451570\pi$
$234$		−	109.330i		−	0.467222i
$235$	−40.5347	−	52.8591i	−0.172488	−	0.224932i
$236$	−185.225			−0.784850
$237$	−3.63798	−	3.63798i	−0.0153501	−	0.0153501i
$238$	−120.842	+	120.842i	−0.507740	+	0.507740i
$239$			197.284i			0.825457i	0.910854	+	0.412728i	$0.135424\pi$
$239$			197.284i			0.825457i	−0.910854	+	0.412728i	$0.864576\pi$
$240$	−1.45836	+	1.11833i	−0.00607649	+	0.00465971i
$241$	−95.2497			−0.395227			−0.197613	−	0.980280i	$-0.563319\pi$
$241$	−95.2497			−0.395227			−0.197613	+	0.980280i	$0.563319\pi$
$242$	−6.59659	−	6.59659i	−0.0272586	−	0.0272586i
$243$	15.7693	−	15.7693i	0.0648944	−	0.0648944i
$244$		−	226.696i		−	0.929080i
$245$	−17.7155	+	134.246i	−0.0723081	+	0.547944i
$246$	6.09269			0.0247671
$247$	139.388	+	139.388i	0.564323	+	0.564323i
$248$	2.91057	−	2.91057i	0.0117362	−	0.0117362i
$249$			10.1252i			0.0406636i
$250$	67.5002	+	163.382i	0.270001	+	0.653529i
$251$	−287.374			−1.14492			−0.572459	−	0.819934i	$-0.694010\pi$
$251$	−287.374			−1.14492			−0.572459	+	0.819934i	$0.694010\pi$
$252$	59.5319	+	59.5319i	0.236238	+	0.236238i
$253$	−38.3061	+	38.3061i	−0.151408	+	0.151408i
$254$		−	49.9940i		−	0.196827i
$255$	11.7572	+	1.55151i	0.0461068	+	0.00608436i
$256$	16.0000			0.0625000
$257$	−127.591	−	127.591i	−0.496465	−	0.496465i	0.413871	−	0.910336i	$-0.364176\pi$
$257$	−127.591	−	127.591i	−0.496465	−	0.496465i	−0.910336	+	0.413871i	$0.864176\pi$
$258$	6.29169	−	6.29169i	0.0243864	−	0.0243864i
$259$		−	20.0295i		−	0.0773338i
$260$	−52.3195	−	68.2272i	−0.201229	−	0.262412i
$261$	−217.365			−0.832815
$262$	−193.717	−	193.717i	−0.739378	−	0.739378i
$263$	−289.451	+	289.451i	−1.10057	+	1.10057i	−0.106233	+	0.994341i	$0.533879\pi$
$263$	−289.451	+	289.451i	−1.10057	+	1.10057i	−0.994341	+	0.106233i	$0.966121\pi$
$264$			2.93582i			0.0111205i
$265$	388.924	−	298.243i	1.46764	−	1.12545i
$266$	−151.798			−0.570668
$267$	−5.29579	−	5.29579i	−0.0198344	−	0.0198344i
$268$	13.4937	−	13.4937i	0.0503494	−	0.0503494i
$269$		−	336.736i		−	1.25181i	−0.779901	−	0.625903i	$-0.784731\pi$
$269$		−	336.736i		−	1.25181i	0.779901	−	0.625903i	$-0.215269\pi$
$270$	1.52940	−	11.5897i	0.00566444	−	0.0429246i
$271$	201.995			0.745370			0.372685	−	0.927958i	$-0.378437\pi$
$271$	201.995			0.745370			0.372685	+	0.927958i	$0.378437\pi$
$272$	−73.0068	−	73.0068i	−0.268407	−	0.268407i
$273$	2.61541	−	2.61541i	0.00958026	−	0.00958026i
$274$		−	166.455i		−	0.607499i
$275$	272.730	+	73.2558i	0.991744	+	0.266385i
$276$	0.881373			0.00319338
$277$	−231.622	−	231.622i	−0.836182	−	0.836182i	0.152172	−	0.988354i	$-0.451373\pi$
$277$	−231.622	−	231.622i	−0.836182	−	0.836182i	−0.988354	+	0.152172i	$0.951373\pi$
$278$	−144.121	+	144.121i	−0.518420	+	0.518420i
$279$			13.0853i			0.0469006i
$280$	65.6396	+	8.66197i	0.234427	+	0.0309356i
$281$	−14.7060			−0.0523347			−0.0261673	−	0.999658i	$-0.508330\pi$
$281$	−14.7060			−0.0523347			−0.0261673	+	0.999658i	$0.508330\pi$
$282$	1.22419	+	1.22419i	0.00434109	+	0.00434109i
$283$	−203.571	+	203.571i	−0.719334	+	0.719334i	−0.968469	−	0.249135i	$-0.919854\pi$
$283$	−203.571	+	203.571i	−0.719334	+	0.719334i	0.249135	+	0.968469i	$0.419854\pi$
$284$		−	53.4957i		−	0.188365i
$285$	6.41003	+	8.35899i	0.0224913	+	0.0293298i
$286$	−137.348			−0.480239
$287$	−155.208	−	155.208i	−0.540794	−	0.540794i
$288$	−35.9662	+	35.9662i	−0.124883	+	0.124883i
$289$			377.249i			1.30536i
$290$	−135.646	+	104.019i	−0.467745	+	0.358687i
$291$	−0.349610			−0.00120141
$292$	67.1390	+	67.1390i	0.229928	+	0.229928i
$293$	270.813	−	270.813i	0.924277	−	0.924277i	−0.0730512	−	0.997328i	$-0.523274\pi$
$293$	270.813	−	270.813i	0.924277	−	0.924277i	0.997328	+	0.0730512i	$0.0232736\pi$
$294$		−	3.51935i		−	0.0119706i
$295$	60.5815	−	459.081i	0.205361	−	1.55621i
$296$	12.1008			0.0408811
$297$	−13.2050	−	13.2050i	−0.0444613	−	0.0444613i
$298$	224.861	−	224.861i	0.754567	−	0.754567i
$299$			41.2338i			0.137906i
$300$	−2.29481	−	3.98033i	−0.00764937	−	0.0132678i
$301$	−320.555			−1.06497
$302$	−248.329	−	248.329i	−0.822283	−	0.822283i
$303$	−2.08518	+	2.08518i	−0.00688180	+	0.00688180i
$304$		−	91.7086i		−	0.301673i
$305$	561.868	+	74.1455i	1.84219	+	0.243100i
$306$	328.222			1.07262
$307$	110.923	+	110.923i	0.361314	+	0.361314i	0.864297	−	0.502982i	$-0.167764\pi$
$307$	110.923	+	110.923i	0.361314	+	0.361314i	−0.502982	+	0.864297i	$0.667764\pi$
$308$	74.7885	−	74.7885i	0.242820	−	0.242820i
$309$			3.00077i			0.00971124i
$310$	6.26192	+	8.16584i	0.0201997	+	0.0263414i
$311$	460.089			1.47938			0.739692	−	0.672945i	$-0.234971\pi$
$311$	460.089			1.47938			0.739692	+	0.672945i	$0.234971\pi$
$312$	1.58010	+	1.58010i	0.00506443	+	0.00506443i
$313$	305.558	−	305.558i	0.976222	−	0.976222i	−0.0235016	−	0.999724i	$-0.507481\pi$
$313$	305.558	−	305.558i	0.976222	−	0.976222i	0.999724	+	0.0235016i	$0.00748149\pi$
$314$			308.044i			0.981033i
$315$	−167.022	+	128.080i	−0.530228	+	0.406602i
$316$	−111.980			−0.354367
$317$	308.414	+	308.414i	0.972915	+	0.972915i	0.999643	−	0.0267276i	$-0.00850866\pi$
$317$	308.414	+	308.414i	0.972915	+	0.972915i	−0.0267276	+	0.999643i	$0.508509\pi$
$318$	−9.00724	+	9.00724i	−0.0283246	+	0.0283246i
$319$			273.070i			0.856018i
$320$	−5.23313	+	39.6562i	−0.0163535	+	0.123926i
$321$	0.100351			0.000312621
$322$	−22.4525	−	22.4525i	−0.0697282	−	0.0697282i
$323$	−418.459	+	418.459i	−1.29554	+	1.29554i
$324$		−	161.544i		−	0.498593i
$325$	186.214	−	107.360i	0.572966	−	0.330337i
$326$	1.48485			0.00455476
$327$	−1.15673	−	1.15673i	−0.00353741	−	0.00353741i
$328$	93.7689	−	93.7689i	0.285881	−	0.285881i
$329$		−	62.3709i		−	0.189577i
$330$	−7.27648	−	0.960222i	−0.0220499	−	0.00290976i
$331$	−12.4523			−0.0376203			−0.0188101	−	0.999823i	$-0.505988\pi$
$331$	−12.4523			−0.0376203			−0.0188101	+	0.999823i	$0.505988\pi$
$332$	155.831	+	155.831i	0.469371	+	0.469371i
$333$	−27.2013	+	27.2013i	−0.0816855	+	0.0816855i
$334$		−	231.292i		−	0.692492i
$335$	29.0308	+	37.8576i	0.0866591	+	0.113008i
$336$	−1.72078			−0.00512137
$337$	−147.444	−	147.444i	−0.437520	−	0.437520i	0.453657	−	0.891177i	$-0.350119\pi$
$337$	−147.444	−	147.444i	−0.437520	−	0.437520i	−0.891177	+	0.453657i	$0.850119\pi$
$338$	95.0772	−	95.0772i	0.281293	−	0.281293i
$339$		−	6.53057i		−	0.0192642i
$340$	204.827	−	157.070i	0.602431	−	0.461970i
$341$	16.4387			0.0482073
$342$	206.151	+	206.151i	0.602780	+	0.602780i
$343$	−251.865	+	251.865i	−0.734299	+	0.734299i
$344$		−	193.663i		−	0.562974i
$345$	−0.288271	+	2.18449i	−0.000835568	+	0.00633186i
$346$	−271.341			−0.784224
$347$	−476.493	−	476.493i	−1.37318	−	1.37318i	−0.855690	−	0.517488i	$-0.826867\pi$
$347$	−476.493	−	476.493i	−1.37318	−	1.37318i	−0.517488	−	0.855690i	$-0.673133\pi$
$348$	3.14148	−	3.14148i	0.00902725	−	0.00902725i
$349$			193.545i			0.554571i	0.960788	+	0.277286i	$0.0894348\pi$
$349$			193.545i			0.554571i	−0.960788	+	0.277286i	$0.910565\pi$
$350$	−42.9376	+	159.856i	−0.122679	+	0.456730i
$351$	−14.2142			−0.0404964
$352$	45.1835	+	45.1835i	0.128362	+	0.128362i
$353$	−155.526	+	155.526i	−0.440584	+	0.440584i	−0.892208	−	0.451624i	$-0.850845\pi$
$353$	−155.526	+	155.526i	−0.440584	+	0.440584i	0.451624	+	0.892208i	$0.350845\pi$
$354$			12.0351i			0.0339974i
$355$	132.590	+	17.4969i	0.373492	+	0.0492869i
$356$	−163.008			−0.457889
$357$	7.85180	+	7.85180i	0.0219938	+	0.0219938i
$358$	−317.529	+	317.529i	−0.886952	+	0.886952i
$359$		−	264.514i		−	0.736808i	−0.929666	−	0.368404i	$-0.879904\pi$
$359$		−	264.514i		−	0.736808i	0.929666	−	0.368404i	$-0.120096\pi$
$360$	−77.3792	−	100.906i	−0.214942	−	0.280295i
$361$	−164.654			−0.456106
$362$	−39.6540	−	39.6540i	−0.109541	−	0.109541i
$363$	−0.428617	+	0.428617i	−0.00118076	+	0.00118076i
$364$		−	80.5044i		−	0.221166i
$365$	−188.364	+	144.446i	−0.516066	+	0.395742i
$366$	−14.7297			−0.0402451
$367$	13.5911	+	13.5911i	0.0370329	+	0.0370329i	0.725381	−	0.688348i	$-0.241664\pi$
$367$	13.5911	+	13.5911i	0.0370329	+	0.0370329i	−0.688348	+	0.725381i	$0.741664\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			421.564i			1.14245i
$370$	−3.95782	+	29.9920i	−0.0106968	+	0.0810594i
$371$	458.909			1.23695
$372$	−0.189116	−	0.189116i	−0.000508377	−	0.000508377i
$373$	−491.491	+	491.491i	−1.31767	+	1.31767i	−0.402054	+	0.915616i	$0.631704\pi$
$373$	−491.491	+	491.491i	−1.31767	+	1.31767i	−0.915616	+	0.402054i	$0.868296\pi$
$374$		−	412.337i		−	1.10251i
$375$	10.6159	−	4.38587i	0.0283090	−	0.0116957i
$376$	37.6814			0.100216
$377$	146.970	+	146.970i	0.389841	+	0.389841i
$378$	7.73988	−	7.73988i	0.0204759	−	0.0204759i
$379$		−	617.809i		−	1.63010i	−0.579389	−	0.815051i	$-0.696709\pi$
$379$		−	617.809i		−	1.63010i	0.579389	−	0.815051i	$-0.303291\pi$
$380$	227.301	+	29.9952i	0.598160	+	0.0789347i
$381$	−3.24839			−0.00852596
$382$	−106.653	−	106.653i	−0.279197	−	0.279197i
$383$	235.834	−	235.834i	0.615755	−	0.615755i	−0.328685	−	0.944440i	$-0.606605\pi$
$383$	235.834	−	235.834i	0.615755	−	0.615755i	0.944440	+	0.328685i	$0.106605\pi$
$384$		−	1.03961i		−	0.00270732i
$385$	160.903	+	209.825i	0.417930	+	0.545001i
$386$	282.160			0.730985
$387$	435.333	+	435.333i	1.12489	+	1.12489i
$388$	−5.38063	+	5.38063i	−0.0138676	+	0.0138676i
$389$			226.762i			0.582935i	0.956581	+	0.291467i	$0.0941435\pi$
$389$			226.762i			0.582935i	−0.956581	+	0.291467i	$0.905856\pi$
$390$	−4.43310	+	3.39950i	−0.0113669	+	0.00871665i
$391$	−123.789			−0.316596
$392$	−54.1641	−	54.1641i	−0.138174	−	0.138174i
$393$	−12.5869	+	12.5869i	−0.0320277	+	0.0320277i
$394$			253.453i			0.643281i
$395$	36.6253	−	277.543i	0.0927223	−	0.702642i
$396$	−203.135			−0.512967
$397$	67.6041	+	67.6041i	0.170287	+	0.170287i	0.787106	−	0.616818i	$-0.211579\pi$
$397$	67.6041	+	67.6041i	0.170287	+	0.170287i	−0.616818	+	0.787106i	$0.711579\pi$
$398$	−96.1858	+	96.1858i	−0.241673	+	0.241673i
$399$			9.86315i			0.0247197i
$400$	−96.5768	−	25.9408i	−0.241442	−	0.0648519i
$401$	−424.222			−1.05791			−0.528955	−	0.848650i	$-0.677416\pi$
$401$	−424.222			−1.05791			−0.528955	+	0.848650i	$0.677416\pi$
$402$	−0.876759	−	0.876759i	−0.00218099	−	0.00218099i
$403$	8.84753	−	8.84753i	0.0219542	−	0.0219542i
$404$			64.1836i			0.158870i
$405$	400.389	+	52.8364i	0.988616	+	0.130460i
$406$	−160.055			−0.394224
$407$	34.1723	+	34.1723i	0.0839613	+	0.0839613i
$408$	−4.74366	+	4.74366i	−0.0116266	+	0.0116266i
$409$		−	10.9416i		−	0.0267521i	−0.999911	−	0.0133761i	$-0.995742\pi$
$409$		−	10.9416i		−	0.0267521i	0.999911	−	0.0133761i	$-0.00425786\pi$
$410$	201.738	+	263.076i	0.492045	+	0.641650i
$411$	−10.8155			−0.0263151
$412$	46.1830	+	46.1830i	0.112095	+	0.112095i
$413$	306.587	−	306.587i	0.742341	−	0.742341i
$414$			60.9837i			0.147304i
$415$	−437.198	+	335.262i	−1.05349	+	0.807860i
$416$	48.6367			0.116915
$417$	9.36433	+	9.36433i	0.0224564	+	0.0224564i
$418$	258.982	−	258.982i	0.619574	−	0.619574i
$419$			47.1621i			0.112559i	0.998415	+	0.0562794i	$0.0179238\pi$
$419$			47.1621i			0.112559i	−0.998415	+	0.0562794i	$0.982076\pi$
$420$	0.562817	−	4.26498i	0.00134004	−	0.0101547i
$421$	317.805			0.754882			0.377441	−	0.926034i	$-0.376804\pi$
$421$	317.805			0.754882			0.377441	+	0.926034i	$0.376804\pi$
$422$	−380.514	−	380.514i	−0.901692	−	0.901692i
$423$	−84.7036	+	84.7036i	−0.200245	+	0.200245i
$424$			277.250i			0.653891i
$425$	322.307	+	559.038i	0.758369	+	1.31538i
$426$	−3.47592			−0.00815943
$427$	375.231	+	375.231i	0.878760	+	0.878760i
$428$	1.54444	−	1.54444i	0.00360851	−	0.00360851i
$429$			8.92430i			0.0208026i
$430$	479.996	+	63.3415i	1.11627	+	0.147306i
$431$	526.966			1.22266			0.611330	−	0.791376i	$-0.290635\pi$
$431$	526.966			1.22266			0.611330	+	0.791376i	$0.290635\pi$
$432$	4.67605	+	4.67605i	0.0108242	+	0.0108242i
$433$	−156.271	+	156.271i	−0.360904	+	0.360904i	−0.864146	−	0.503242i	$-0.832140\pi$
$433$	−156.271	+	156.271i	−0.360904	+	0.360904i	0.503242	+	0.864146i	$0.332140\pi$
$434$			9.63525i			0.0222010i
$435$	6.75872	+	8.81369i	0.0155373	+	0.0202614i
$436$	−35.6052			−0.0816632
$437$	−77.7498	−	77.7498i	−0.177917	−	0.177917i
$438$	4.36240	−	4.36240i	0.00995982	−	0.00995982i
$439$			217.027i			0.494366i	0.968969	+	0.247183i	$0.0795048\pi$
$439$			217.027i			0.494366i	−0.968969	+	0.247183i	$0.920495\pi$
$440$	−126.766	+	97.2096i	−0.288104	+	0.220931i
$441$	243.510			0.552176
$442$	−221.926	−	221.926i	−0.502094	−	0.502094i
$443$	−54.4175	+	54.4175i	−0.122839	+	0.122839i	−0.765854	−	0.643015i	$-0.777683\pi$
$443$	−54.4175	+	54.4175i	−0.122839	+	0.122839i	0.643015	+	0.765854i	$0.277683\pi$
$444$		−	0.786258i		−	0.00177085i
$445$	53.3153	−	404.019i	0.119810	−	0.907907i
$446$	121.262			0.271887
$447$	−14.6105	−	14.6105i	−0.0326856	−	0.0326856i
$448$	−26.4835	+	26.4835i	−0.0591149	+	0.0591149i
$449$		−	318.334i		−	0.708984i	−0.935059	−	0.354492i	$-0.884654\pi$
$449$		−	318.334i		−	0.708984i	0.935059	−	0.354492i	$-0.115346\pi$
$450$	275.406	−	158.782i	0.612013	−	0.352849i
$451$	529.600			1.17428
$452$	−100.508	−	100.508i	−0.222363	−	0.222363i
$453$	−16.1354	+	16.1354i	−0.0356189	+	0.0356189i
$454$			469.893i			1.03501i
$455$	199.531	+	26.3306i	0.438530	+	0.0578695i
$456$	−5.95883			−0.0130676
$457$	−402.986	−	402.986i	−0.881807	−	0.881807i	0.111911	−	0.993718i	$-0.464303\pi$
$457$	−402.986	−	402.986i	−0.881807	−	0.881807i	−0.993718	+	0.111911i	$0.964303\pi$
$458$	−338.701	+	338.701i	−0.739523	+	0.739523i
$459$		−	42.6729i		−	0.0929694i
$460$	29.1836	+	38.0568i	0.0634426	+	0.0827321i
$461$	446.523			0.968597			0.484299	−	0.874903i	$-0.339075\pi$
$461$	446.523			0.968597			0.484299	+	0.874903i	$0.339075\pi$
$462$	−4.85943	−	4.85943i	−0.0105182	−	0.0105182i
$463$	288.951	−	288.951i	0.624085	−	0.624085i	−0.322488	−	0.946573i	$-0.604519\pi$
$463$	288.951	−	288.951i	0.624085	−	0.624085i	0.946573	+	0.322488i	$0.104519\pi$
$464$		−	96.6973i		−	0.208399i
$465$	0.530581	−	0.406872i	0.00114103	−	0.000874994i
$466$	389.990			0.836888
$467$	−408.528	−	408.528i	−0.874792	−	0.874792i	0.118198	−	0.992990i	$-0.462288\pi$
$467$	−408.528	−	408.528i	−0.874792	−	0.874792i	−0.992990	+	0.118198i	$0.962288\pi$
$468$	−109.330	+	109.330i	−0.233611	+	0.233611i
$469$			44.6699i			0.0952449i
$470$	−12.3245	+	93.3938i	−0.0262223	+	0.198710i
$471$	20.0154			0.0424955
$472$	185.225	+	185.225i	0.392425	+	0.392425i
$473$	546.898	−	546.898i	1.15623	−	1.15623i
$474$			7.27596i			0.0153501i
$475$	−148.687	+	553.558i	−0.313025	+	1.16538i
$476$	241.684			0.507740
$477$	−623.226	−	623.226i	−1.30655	−	1.30655i
$478$	197.284	−	197.284i	0.412728	−	0.412728i
$479$		−	315.169i		−	0.657973i	−0.944335	−	0.328986i	$-0.893293\pi$
$479$		−	315.169i		−	0.657973i	0.944335	−	0.328986i	$-0.106707\pi$
$480$	2.57669	+	0.340026i	0.00536810	+	0.000708388i
$481$	36.7840			0.0764739
$482$	95.2497	+	95.2497i	0.197613	+	0.197613i
$483$	−1.45886	+	1.45886i	−0.00302042	+	0.00302042i
$484$			13.1932i			0.0272586i
$485$	−11.5761	−	15.0958i	−0.0238683	−	0.0311254i
$486$	−31.5387			−0.0648944
$487$	−222.544	−	222.544i	−0.456969	−	0.456969i	0.440690	−	0.897659i	$-0.354734\pi$
$487$	−222.544	−	222.544i	−0.456969	−	0.456969i	−0.897659	+	0.440690i	$0.854734\pi$
$488$	−226.696	+	226.696i	−0.464540	+	0.464540i
$489$		−	0.0964792i		−	0.000197299i
$490$	151.962	−	116.531i	0.310126	−	0.237818i
$491$	−515.585			−1.05007			−0.525035	−	0.851080i	$-0.675948\pi$
$491$	−515.585			−1.05007			−0.525035	+	0.851080i	$0.675948\pi$
$492$	−6.09269	−	6.09269i	−0.0123835	−	0.0123835i
$493$	−441.222	+	441.222i	−0.894974	+	0.894974i
$494$		−	278.775i		−	0.564323i
$495$	66.4394	−	503.472i	0.134221	−	1.01712i
$496$	−5.82114			−0.0117362
$497$	88.5470	+	88.5470i	0.178163	+	0.178163i
$498$	10.1252	−	10.1252i	0.0203318	−	0.0203318i
$499$			327.060i			0.655430i	0.944777	+	0.327715i	$0.106279\pi$
$499$			327.060i			0.655430i	−0.944777	+	0.327715i	$0.893721\pi$
$500$	95.8819	−	230.882i	0.191764	−	0.461765i
$501$	−15.0284			−0.0299967
$502$	287.374	+	287.374i	0.572459	+	0.572459i
$503$	126.415	−	126.415i	0.251322	−	0.251322i	−0.570190	−	0.821513i	$-0.693131\pi$
$503$	126.415	−	126.415i	0.251322	−	0.251322i	0.821513	+	0.570190i	$0.193131\pi$
$504$		−	119.064i		−	0.236238i
$505$	−159.080	−	20.9926i	−0.315009	−	0.0415694i
$506$	76.6123			0.151408
$507$	−6.17770	−	6.17770i	−0.0121848	−	0.0121848i
$508$	−49.9940	+	49.9940i	−0.0984134	+	0.0984134i
$509$		−	270.227i		−	0.530898i	−0.964125	−	0.265449i	$-0.914480\pi$
$509$		−	270.227i		−	0.530898i	0.964125	−	0.265449i	$-0.0855202\pi$
$510$	−10.2057	−	13.3087i	−0.0200112	−	0.0260956i
$511$	−222.259			−0.434950
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	26.8021	−	26.8021i	0.0522459	−	0.0522459i
$514$			255.183i			0.496465i
$515$	−129.570	+	99.3601i	−0.251593	+	0.192932i
$516$	−12.5834			−0.0243864
$517$	106.411	+	106.411i	0.205824	+	0.205824i
$518$	−20.0295	+	20.0295i	−0.0386669	+	0.0386669i
$519$			17.6306i			0.0339703i
$520$	−15.9076	+	120.547i	−0.0305916	+	0.231821i
$521$	−371.214			−0.712502			−0.356251	−	0.934390i	$-0.615945\pi$
$521$	−371.214			−0.712502			−0.356251	+	0.934390i	$0.615945\pi$
$522$	217.365	+	217.365i	0.416408	+	0.416408i
$523$	−417.334	+	417.334i	−0.797962	+	0.797962i	−0.982774	−	0.184812i	$-0.940832\pi$
$523$	−417.334	+	417.334i	−0.797962	+	0.797962i	0.184812	+	0.982774i	$0.440832\pi$
$524$			387.434i			0.739378i
$525$	10.3867	+	2.78990i	0.0197842	+	0.00531409i
$526$	578.902			1.10057
$527$	26.5614	+	26.5614i	0.0504012	+	0.0504012i
$528$	2.93582	−	2.93582i	0.00556027	−	0.00556027i
$529$		−	23.0000i		−	0.0434783i
$530$	−687.167	−	90.6802i	−1.29654	−	0.171095i
$531$	−832.729			−1.56823
$532$	151.798	+	151.798i	0.285334	+	0.285334i
$533$	285.038	−	285.038i	0.534781	−	0.534781i
$534$			10.5916i			0.0198344i
$535$	3.32278	+	4.33307i	0.00621081	+	0.00809919i
$536$	−26.9873			−0.0503494
$537$	20.6316	+	20.6316i	0.0384202	+	0.0384202i
$538$	−336.736	+	336.736i	−0.625903	+	0.625903i
$539$		−	305.915i		−	0.567560i
$540$	−13.1191	+	10.0603i	−0.0242945	+	0.0186301i
$541$	560.715			1.03644			0.518221	−	0.855247i	$-0.326594\pi$
$541$	560.715			1.03644			0.518221	+	0.855247i	$0.326594\pi$
$542$	−201.995	−	201.995i	−0.372685	−	0.372685i
$543$	−2.57654	+	2.57654i	−0.00474502	+	0.00474502i
$544$			146.014i			0.268407i
$545$	11.6454	−	88.2478i	0.0213677	−	0.161923i
$546$	−5.23082			−0.00958026
$547$	−76.6064	−	76.6064i	−0.140048	−	0.140048i	0.633607	−	0.773655i	$-0.281574\pi$
$547$	−76.6064	−	76.6064i	−0.140048	−	0.140048i	−0.773655	+	0.633607i	$0.781574\pi$
$548$	−166.455	+	166.455i	−0.303750	+	0.303750i
$549$		−	1019.17i		−	1.85642i
$550$	−199.474	−	345.985i	−0.362680	−	0.629064i
$551$	−554.248			−1.00590
$552$	−0.881373	−	0.881373i	−0.00159669	−	0.00159669i
$553$	185.351	−	185.351i	0.335174	−	0.335174i
$554$			463.245i			0.836182i
$555$	1.94875	+	0.257162i	0.00351126	+	0.000463354i
$556$	288.241			0.518420
$557$	−262.627	−	262.627i	−0.471502	−	0.471502i	0.430898	−	0.902401i	$-0.358197\pi$
$557$	−262.627	−	262.627i	−0.471502	−	0.471502i	−0.902401	+	0.430898i	$0.858197\pi$
$558$	13.0853	−	13.0853i	0.0234503	−	0.0234503i
$559$		−	588.696i		−	1.05312i
$560$	−56.9777	−	74.3016i	−0.101746	−	0.132681i
$561$	−26.7919			−0.0477574
$562$	14.7060	+	14.7060i	0.0261673	+	0.0261673i
$563$	516.006	−	516.006i	0.916529	−	0.916529i	−0.0802456	−	0.996775i	$-0.525570\pi$
$563$	516.006	−	516.006i	0.916529	−	0.916529i	0.996775	+	0.0802456i	$0.0255705\pi$
$564$		−	2.44837i		−	0.00434109i
$565$	281.984	−	216.237i	0.499086	−	0.382721i
$566$	407.143			0.719334
$567$	267.391	+	267.391i	0.471589	+	0.471589i
$568$	−53.4957	+	53.4957i	−0.0941825	+	0.0941825i
$569$			231.361i			0.406609i	0.979116	+	0.203305i	$0.0651682\pi$
$569$			231.361i			0.406609i	−0.979116	+	0.203305i	$0.934832\pi$
$570$	1.94896	−	14.7690i	0.00341922	−	0.0259106i
$571$	−1110.09			−1.94411			−0.972056	−	0.234751i	$-0.924573\pi$
$571$	−1110.09			−1.94411			−0.972056	+	0.234751i	$0.924573\pi$
$572$	137.348	+	137.348i	0.240120	+	0.240120i
$573$	−6.92988	+	6.92988i	−0.0120940	+	0.0120940i
$574$			310.416i			0.540794i
$575$	−103.869	+	59.8846i	−0.180642	+	0.104147i
$576$	71.9325			0.124883
$577$	−78.6205	−	78.6205i	−0.136257	−	0.136257i	0.635688	−	0.771946i	$-0.280716\pi$
$577$	−78.6205	−	78.6205i	−0.136257	−	0.136257i	−0.771946	+	0.635688i	$0.780716\pi$
$578$	377.249	−	377.249i	0.652680	−	0.652680i
$579$		−	18.3335i		−	0.0316642i
$580$	239.665	+	31.6268i	0.413216	+	0.0545290i
$581$	−515.870			−0.887899
$582$	0.349610	+	0.349610i	0.000600705	+	0.000600705i
$583$	−782.944	+	782.944i	−1.34296	+	1.34296i
$584$		−	134.278i		−	0.229928i
$585$	−235.217	−	306.734i	−0.402080	−	0.524332i
$586$	−541.626			−0.924277
$587$	417.321	+	417.321i	0.710939	+	0.710939i	0.966732	−	0.255793i	$-0.0823365\pi$
$587$	417.321	+	417.321i	0.710939	+	0.710939i	−0.255793	+	0.966732i	$0.582336\pi$
$588$	−3.51935	+	3.51935i	−0.00598528	+	0.00598528i
$589$			33.3655i			0.0566478i
$590$	−519.663	+	398.500i	−0.880785	+	0.675424i
$591$	16.4683			0.0278651
$592$	−12.1008	−	12.1008i	−0.0204405	−	0.0204405i
$593$	667.040	−	667.040i	1.12486	−	1.12486i	0.133855	−	0.991001i	$-0.457264\pi$
$593$	667.040	−	667.040i	1.12486	−	1.12486i	0.991001	−	0.133855i	$-0.0427358\pi$
$594$			26.4100i			0.0444613i
$595$	−79.0478	+	599.018i	−0.132854	+	1.00675i
$596$	−449.722			−0.754567
$597$	6.24973	+	6.24973i	0.0104686	+	0.0104686i
$598$	41.2338	−	41.2338i	0.0689528	−	0.0689528i
$599$			226.878i			0.378761i	0.981904	+	0.189381i	$0.0606480\pi$
$599$			226.878i			0.378761i	−0.981904	+	0.189381i	$0.939352\pi$
$600$	−1.68552	+	6.27514i	−0.00280920	+	0.0104586i
$601$	278.390			0.463212			0.231606	−	0.972810i	$-0.425602\pi$
$601$	278.390			0.463212			0.231606	+	0.972810i	$0.425602\pi$
$602$	320.555	+	320.555i	0.532483	+	0.532483i
$603$	60.6645	−	60.6645i	0.100604	−	0.100604i
$604$			496.659i			0.822283i
$605$	−32.6994	−	4.31510i	−0.0540487	−	0.00713239i
$606$	4.17037			0.00688180
$607$	−213.989	−	213.989i	−0.352536	−	0.352536i	0.508516	−	0.861052i	$-0.330194\pi$
$607$	−213.989	−	213.989i	−0.352536	−	0.352536i	−0.861052	+	0.508516i	$0.830194\pi$
$608$	−91.7086	+	91.7086i	−0.150837	+	0.150837i
$609$			10.3997i			0.0170766i
$610$	−487.723	−	636.013i	−0.799545	−	1.04265i
$611$	114.544			0.187469
$612$	−328.222	−	328.222i	−0.536311	−	0.536311i
$613$	−598.265	+	598.265i	−0.975962	+	0.975962i	−0.999718	−	0.0237560i	$-0.992438\pi$
$613$	−598.265	+	598.265i	−0.975962	+	0.975962i	0.0237560	+	0.999718i	$0.492438\pi$
$614$		−	221.847i		−	0.361314i
$615$	17.0936	−	13.1081i	0.0277944	−	0.0213139i
$616$	−149.577			−0.242820
$617$	279.954	+	279.954i	0.453734	+	0.453734i	0.896592	−	0.442858i	$-0.146035\pi$
$617$	279.954	+	279.954i	0.453734	+	0.453734i	−0.442858	+	0.896592i	$0.646035\pi$
$618$	3.00077	−	3.00077i	0.00485562	−	0.00485562i
$619$		−	492.991i		−	0.796431i	−0.917292	−	0.398216i	$-0.869630\pi$
$619$		−	492.991i		−	0.796431i	0.917292	−	0.398216i	$-0.130370\pi$
$620$	1.90392	−	14.4278i	0.00307084	−	0.0232706i
$621$	7.92863			0.0127675
$622$	−460.089	−	460.089i	−0.739692	−	0.739692i
$623$	269.814	−	269.814i	0.433089	−	0.433089i
$624$		−	3.16020i		−	0.00506443i
$625$	540.885	+	313.159i	0.865415	+	0.501055i
$626$	−611.115			−0.976222
$627$	−16.8275	−	16.8275i	−0.0268382	−	0.0268382i
$628$	308.044	−	308.044i	0.490516	−	0.490516i
$629$			110.430i			0.175565i
$630$	295.101	+	38.9423i	0.468415	+	0.0618132i
$631$	−1160.95			−1.83986			−0.919932	−	0.392078i	$-0.871756\pi$
$631$	−1160.95			−1.83986			−0.919932	+	0.392078i	$0.871756\pi$
$632$	111.980	+	111.980i	0.177183	+	0.177183i
$633$	−24.7241	+	24.7241i	−0.0390587	+	0.0390587i
$634$		−	616.828i		−	0.972915i
$635$	−107.559	−	140.262i	−0.169385	−	0.220886i
$636$	18.0145			0.0283246
$637$	−164.648	−	164.648i	−0.258474	−	0.258474i
$638$	273.070	−	273.070i	0.428009	−	0.428009i
$639$		−	240.505i		−	0.376377i
$640$	44.8893	−	34.4231i	0.0701396	−	0.0537860i
$641$	589.604			0.919818			0.459909	−	0.887966i	$-0.347882\pi$
$641$	589.604			0.919818			0.459909	+	0.887966i	$0.347882\pi$
$642$	−0.100351	−	0.100351i	−0.000156310	−	0.000156310i
$643$	−529.425	+	529.425i	−0.823368	+	0.823368i	−0.986589	−	0.163222i	$-0.947811\pi$
$643$	−529.425	+	529.425i	−0.823368	+	0.823368i	0.163222	+	0.986589i	$0.447811\pi$
$644$			44.9049i			0.0697282i
$645$	4.11565	−	31.1881i	0.00638086	−	0.0483536i
$646$	836.919			1.29554
$647$	97.4272	+	97.4272i	0.150583	+	0.150583i	0.778378	−	0.627795i	$-0.216043\pi$
$647$	97.4272	+	97.4272i	0.150583	+	0.150583i	−0.627795	+	0.778378i	$0.716043\pi$
$648$	−161.544	+	161.544i	−0.249297	+	0.249297i
$649$			1046.14i			1.61192i
$650$	−293.574	−	78.8546i	−0.451652	−	0.121315i
$651$	0.626057			0.000961684
$652$	−1.48485	−	1.48485i	−0.00227738	−	0.00227738i
$653$	290.130	−	290.130i	0.444303	−	0.444303i	−0.449152	−	0.893455i	$-0.648274\pi$
$653$	290.130	−	290.130i	0.444303	−	0.444303i	0.893455	+	0.449152i	$0.148274\pi$
$654$			2.31347i			0.00353741i
$655$	−960.260	−	126.718i	−1.46605	−	0.193463i
$656$	−187.538			−0.285881
$657$	301.842	+	301.842i	0.459425	+	0.459425i
$658$	−62.3709	+	62.3709i	−0.0947886	+	0.0947886i
$659$		−	821.428i		−	1.24648i	−0.782032	−	0.623238i	$-0.785817\pi$
$659$		−	821.428i		−	1.24648i	0.782032	−	0.623238i	$-0.214183\pi$
$660$	6.31626	+	8.23670i	0.00957009	+	0.0124798i
$661$	226.046			0.341976			0.170988	−	0.985273i	$-0.445304\pi$
$661$	226.046			0.341976			0.170988	+	0.985273i	$0.445304\pi$
$662$	12.4523	+	12.4523i	0.0188101	+	0.0188101i
$663$	−14.4198	+	14.4198i	−0.0217493	+	0.0217493i
$664$		−	311.663i		−	0.469371i
$665$	−425.881	+	326.584i	−0.640423	+	0.491104i
$666$	54.4025			0.0816855
$667$	−81.9791	−	81.9791i	−0.122907	−	0.122907i
$668$	−231.292	+	231.292i	−0.346246	+	0.346246i
$669$		−	7.87905i		−	0.0117774i
$670$	8.82676	−	66.8884i	0.0131743	−	0.0998334i
$671$	−1280.36			−1.90814
$672$	1.72078	+	1.72078i	0.00256069	+	0.00256069i
$673$	744.480	−	744.480i	1.10621	−	1.10621i	0.112566	−	0.993644i	$-0.464093\pi$
$673$	744.480	−	744.480i	1.10621	−	1.10621i	0.993644	−	0.112566i	$-0.0359070\pi$
$674$			294.888i			0.437520i
$675$	−20.6436	−	35.8062i	−0.0305831	−	0.0530462i
$676$	−190.154			−0.281293
$677$	−777.563	−	777.563i	−1.14854	−	1.14854i	−0.986840	−	0.161702i	$-0.948302\pi$
$677$	−777.563	−	777.563i	−1.14854	−	1.14854i	−0.161702	−	0.986840i	$-0.551698\pi$
$678$	−6.53057	+	6.53057i	−0.00963211	+	0.00963211i
$679$		−	17.8122i		−	0.0262330i
$680$	−361.897	−	47.7568i	−0.532201	−	0.0702305i
$681$	30.5316			0.0448334
$682$	−16.4387	−	16.4387i	−0.0241037	−	0.0241037i
$683$	−224.810	+	224.810i	−0.329151	+	0.329151i	−0.852264	−	0.523112i	$-0.824771\pi$
$683$	−224.810	+	224.810i	−0.329151	+	0.329151i	0.523112	+	0.852264i	$0.324771\pi$
$684$		−	412.302i		−	0.602780i
$685$	−358.118	−	467.003i	−0.522800	−	0.681756i
$686$	503.729			0.734299
$687$	22.0073	+	22.0073i	0.0320340	+	0.0320340i
$688$	−193.663	+	193.663i	−0.281487	+	0.281487i
$689$			842.782i			1.22320i
$690$	2.47276	−	1.89622i	0.00358372	−	0.00274815i
$691$	957.450			1.38560			0.692800	−	0.721130i	$-0.256377\pi$
$691$	957.450			1.38560			0.692800	+	0.721130i	$0.256377\pi$
$692$	271.341	+	271.341i	0.392112	+	0.392112i
$693$	336.232	−	336.232i	0.485184	−	0.485184i
$694$			952.986i			1.37318i
$695$	−94.2753	+	714.410i	−0.135648	+	1.02793i
$696$	−6.28297			−0.00902725
$697$	855.721	+	855.721i	1.22772	+	1.22772i
$698$	193.545	−	193.545i	0.277286	−	0.277286i
$699$		−	25.3398i		−	0.0362516i
$700$	202.793	−	116.918i	0.289705	−	0.167026i
$701$	551.764			0.787110			0.393555	−	0.919301i	$-0.371245\pi$
$701$	551.764			0.787110			0.393555	+	0.919301i	$0.371245\pi$
$702$	14.2142	+	14.2142i	0.0202482	+	0.0202482i
$703$	−69.3592	+	69.3592i	−0.0986618	+	0.0986618i
$704$		−	90.3669i		−	0.128362i
$705$	6.06832	+	0.800791i	0.00860755	+	0.00113587i
$706$	311.052			0.440584
$707$	−106.238	−	106.238i	−0.150266	−	0.150266i
$708$	12.0351	−	12.0351i	0.0169987	−	0.0169987i
$709$		−	283.238i		−	0.399489i	−0.979848	−	0.199744i	$-0.935989\pi$
$709$		−	283.238i		−	0.399489i	0.979848	−	0.199744i	$-0.0640112\pi$
$710$	−115.093	−	150.087i	−0.162103	−	0.211390i
$711$	−503.437			−0.708068
$712$	163.008	+	163.008i	0.228944	+	0.228944i
$713$	−4.93511	+	4.93511i	−0.00692161	+	0.00692161i
$714$		−	15.7036i		−	0.0219938i
$715$	−385.343	+	295.497i	−0.538941	+	0.413283i
$716$	635.058			0.886952
$717$	−12.8187	−	12.8187i	−0.0178782	−	0.0178782i
$718$	−264.514	+	264.514i	−0.368404	+	0.368404i
$719$			278.263i			0.387014i	0.981099	+	0.193507i	$0.0619862\pi$
$719$			278.263i			0.387014i	−0.981099	+	0.193507i	$0.938014\pi$
$720$	−23.5270	+	178.285i	−0.0326764	+	0.247619i
$721$	−152.886			−0.212047
$722$	164.654	+	164.654i	0.228053	+	0.228053i
$723$	6.18891	−	6.18891i	0.00856004	−	0.00856004i
$724$			79.3080i			0.109541i
$725$	−156.775	+	583.670i	−0.216241	+	0.805061i
$726$	0.857235			0.00118076
$727$	912.951	+	912.951i	1.25578	+	1.25578i	0.953089	+	0.302689i	$0.0978844\pi$
$727$	912.951	+	912.951i	1.25578	+	1.25578i	0.302689	+	0.953089i	$0.402116\pi$
$728$	−80.5044	+	80.5044i	−0.110583	+	0.110583i
$729$		−	724.900i		−	0.994375i
$730$	332.810	+	43.9184i	0.455904	+	0.0601622i
$731$	1767.34			2.41770
$732$	14.7297	+	14.7297i	0.0201225	+	0.0201225i
$733$	457.180	−	457.180i	0.623711	−	0.623711i	−0.322767	−	0.946478i	$-0.604613\pi$
$733$	457.180	−	457.180i	0.623711	−	0.623711i	0.946478	+	0.322767i	$0.104613\pi$
$734$		−	27.1822i		−	0.0370329i
$735$	−7.57167	−	9.87382i	−0.0103016	−	0.0134338i
$736$	−27.1293			−0.0368605
$737$	−76.2112	−	76.2112i	−0.103407	−	0.103407i
$738$	421.564	−	421.564i	0.571225	−	0.571225i
$739$		−	480.868i		−	0.650701i	−0.945593	−	0.325351i	$-0.894518\pi$
$739$		−	480.868i		−	0.650701i	0.945593	−	0.325351i	$-0.105482\pi$
$740$	33.9498	−	26.0342i	0.0458781	−	0.0351813i
$741$	−18.1136			−0.0244448
$742$	−458.909	−	458.909i	−0.618475	−	0.618475i
$743$	280.766	−	280.766i	0.377882	−	0.377882i	−0.492456	−	0.870338i	$-0.663901\pi$
$743$	280.766	−	280.766i	0.377882	−	0.377882i	0.870338	+	0.492456i	$0.163901\pi$
$744$			0.378232i			0.000508377i
$745$	147.091	−	1114.64i	0.197437	−	1.49616i
$746$	982.982			1.31767
$747$	700.583	+	700.583i	0.937862	+	0.937862i
$748$	−412.337	+	412.337i	−0.551253	+	0.551253i
$749$			5.11278i			0.00682615i
$750$	−15.0017	−	6.22999i	−0.0200023	−	0.00830665i
$751$	109.950			0.146405			0.0732025	−	0.997317i	$-0.476678\pi$
$751$	109.950			0.146405			0.0732025	+	0.997317i	$0.476678\pi$
$752$	−37.6814	−	37.6814i	−0.0501082	−	0.0501082i
$753$	18.6723	−	18.6723i	0.0247972	−	0.0247972i
$754$		−	293.940i		−	0.389841i
$755$	−1230.98	−	162.443i	−1.63043	−	0.215156i
$756$	−15.4798			−0.0204759
$757$	288.009	+	288.009i	0.380461	+	0.380461i	0.871268	−	0.490807i	$-0.163298\pi$
$757$	288.009	+	288.009i	0.380461	+	0.380461i	−0.490807	+	0.871268i	$0.663298\pi$
$758$	−617.809	+	617.809i	−0.815051	+	0.815051i
$759$		−	4.97793i		−	0.00655854i
$760$	−197.306	−	257.296i	−0.259613	−	0.338548i
$761$	−61.1841			−0.0803996			−0.0401998	−	0.999192i	$-0.512799\pi$
$761$	−61.1841			−0.0803996			−0.0401998	+	0.999192i	$0.512799\pi$
$762$	3.24839	+	3.24839i	0.00426298	+	0.00426298i
$763$	58.9343	−	58.9343i	0.0772402	−	0.0772402i
$764$			213.307i			0.279197i
$765$	920.855	−	706.151i	1.20373	−	0.923074i
$766$	−471.668			−0.615755
$767$	563.045	+	563.045i	0.734087	+	0.734087i
$768$	−1.03961	+	1.03961i	−0.00135366	+	0.00135366i
$769$			759.640i			0.987828i	0.869511	+	0.493914i	$0.164434\pi$
$769$			759.640i			0.987828i	−0.869511	+	0.493914i	$0.835566\pi$
$770$	48.9222	−	370.728i	0.0635354	−	0.481465i
$771$	16.5807			0.0215054
$772$	−282.160	−	282.160i	−0.365493	−	0.365493i
$773$	698.836	−	698.836i	0.904058	−	0.904058i	−0.0917267	−	0.995784i	$-0.529239\pi$
$773$	698.836	−	698.836i	0.904058	−	0.904058i	0.995784	+	0.0917267i	$0.0292386\pi$
$774$		−	870.666i		−	1.12489i
$775$	35.1367	+	9.43780i	0.0453376	+	0.0121778i
$776$	10.7613			0.0138676
$777$	1.30143	+	1.30143i	0.00167494	+	0.00167494i
$778$	226.762	−	226.762i	0.291467	−	0.291467i
$779$			1074.93i			1.37988i
$780$	7.83260	+	1.03361i	0.0100418	+	0.00132514i
$781$	−302.140			−0.386863
$782$	123.789	+	123.789i	0.158298	+	0.158298i
$783$	28.2601	−	28.2601i	0.0360921	−	0.0360921i
$784$			108.328i			0.138174i
$785$	662.739	+	864.244i	0.844254	+	1.10095i
$786$	25.1738			0.0320277
$787$	357.294	+	357.294i	0.453995	+	0.453995i	0.896678	−	0.442683i	$-0.145973\pi$
$787$	357.294	+	357.294i	0.453995	+	0.453995i	−0.442683	+	0.896678i	$0.645973\pi$
$788$	253.453	−	253.453i	0.321641	−	0.321641i
$789$		−	37.6145i		−	0.0476737i
$790$	−314.169	+	240.918i	−0.397682	+	0.304960i
$791$	332.725			0.420639
$792$	203.135	+	203.135i	0.256483	+	0.256483i
$793$	−689.108	+	689.108i	−0.868989	+	0.868989i
$794$		−	135.208i		−	0.170287i
$795$	−5.89201	+	44.6491i	−0.00741133	+	0.0561624i
$796$	192.372			0.241673
$797$	609.058	+	609.058i	0.764188	+	0.764188i	0.977076	−	0.212889i	$-0.0682871\pi$
$797$	609.058	+	609.058i	0.764188	+	0.764188i	−0.212889	+	0.977076i	$0.568287\pi$
$798$	9.86315	−	9.86315i	0.0123598	−	0.0123598i
$799$			343.875i			0.430381i
$800$	70.6360	+	122.518i	0.0882950	+	0.153147i
$801$	−732.850			−0.914919
$802$	424.222	+	424.222i	0.528955	+	0.528955i
$803$	379.197	−	379.197i	0.472225	−	0.472225i
$804$			1.75352i			0.00218099i
$805$	−111.297	−	14.6871i	−0.138258	−	0.0182448i
$806$	−17.6951			−0.0219542
$807$	21.8796	+	21.8796i	0.0271123	+	0.0271123i
$808$	64.1836	−	64.1836i	0.0794351	−	0.0794351i
$809$			974.708i			1.20483i	0.798183	+	0.602415i	$0.205795\pi$
$809$			974.708i			1.20483i	−0.798183	+	0.602415i	$0.794205\pi$
$810$	−347.553	−	453.226i	−0.429078	−	0.559538i
$811$	347.990			0.429087			0.214543	−	0.976714i	$-0.431174\pi$
$811$	347.990			0.429087			0.214543	+	0.976714i	$0.431174\pi$
$812$	160.055	+	160.055i	0.197112	+	0.197112i
$813$	−13.1248	+	13.1248i	−0.0161436	+	0.0161436i
$814$		−	68.3445i		−	0.0839613i
$815$	4.16588	−	3.19457i	0.00511151	−	0.00391972i
$816$	9.48733			0.0116266
$817$	1110.04	+	1110.04i	1.35867	+	1.35867i
$818$	−10.9416	+	10.9416i	−0.0133761	+	0.0133761i
$819$		−	361.930i		−	0.441917i
$820$	61.3381	−	464.815i	0.0748026	−	0.566847i
$821$	−1001.46			−1.21980			−0.609902	−	0.792477i	$-0.708791\pi$
$821$	−1001.46			−1.21980			−0.609902	+	0.792477i	$0.708791\pi$
$822$	10.8155	+	10.8155i	0.0131576	+	0.0131576i
$823$	953.159	−	953.159i	1.15815	−	1.15815i	0.173280	−	0.984873i	$-0.444564\pi$
$823$	953.159	−	953.159i	1.15815	−	1.15815i	0.984873	−	0.173280i	$-0.0554365\pi$
$824$		−	92.3660i		−	0.112095i
$825$	−22.4806	+	12.9609i	−0.0272492	+	0.0157102i
$826$	−613.174			−0.742341
$827$	633.756	+	633.756i	0.766332	+	0.766332i	0.977459	−	0.211127i	$-0.0677134\pi$
$827$	633.756	+	633.756i	0.766332	+	0.766332i	−0.211127	+	0.977459i	$0.567713\pi$
$828$	60.9837	−	60.9837i	0.0736518	−	0.0736518i
$829$			187.497i			0.226172i	0.993585	+	0.113086i	$0.0360736\pi$
$829$			187.497i			0.226172i	−0.993585	+	0.113086i	$0.963926\pi$
$830$	772.460	+	101.936i	0.930674	+	0.122814i
$831$	30.0996			0.0362210
$832$	−48.6367	−	48.6367i	−0.0584576	−	0.0584576i
$833$	494.293	−	494.293i	0.593389	−	0.593389i
$834$		−	18.7287i		−	0.0224564i
$835$	−497.612	−	648.909i	−0.595942	−	0.777137i
$836$	−517.964			−0.619574
$837$	−1.70125	−	1.70125i	−0.00203255	−	0.00203255i
$838$	47.1621	−	47.1621i	0.0562794	−	0.0562794i
$839$			415.818i			0.495611i	0.968810	+	0.247806i	$0.0797094\pi$
$839$			415.818i			0.495611i	−0.968810	+	0.247806i	$0.920291\pi$
$840$	−4.82780	+	3.70216i	−0.00574738	+	0.00440733i
$841$	256.602			0.305116
$842$	−317.805	−	317.805i	−0.377441	−	0.377441i
$843$	0.955535	−	0.955535i	0.00113349	−	0.00113349i
$844$			761.028i			0.901692i
$845$	62.1939	−	471.300i	0.0736023	−	0.557752i
$846$	169.407			0.200245
$847$	−21.8376	−	21.8376i	−0.0257823	−	0.0257823i
$848$	277.250	−	277.250i	0.326945	−	0.326945i
$849$		−	26.4544i		−	0.0311594i
$850$	236.731	−	881.345i	0.278508	−	1.03688i
$851$	−20.5179			−0.0241104
$852$	3.47592	+	3.47592i	0.00407971	+	0.00407971i
$853$	482.084	−	482.084i	0.565163	−	0.565163i	−0.365607	−	0.930769i	$-0.619138\pi$
$853$	482.084	−	482.084i	0.565163	−	0.565163i	0.930769	+	0.365607i	$0.119138\pi$
$854$		−	750.461i		−	0.878760i
$855$	1021.89	+	134.852i	1.19520	+	0.157721i
$856$	−3.08889			−0.00360851
$857$	115.279	+	115.279i	0.134515	+	0.134515i	0.771158	−	0.636644i	$-0.219678\pi$
$857$	115.279	+	115.279i	0.134515	+	0.134515i	−0.636644	+	0.771158i	$0.719678\pi$
$858$	8.92430	−	8.92430i	0.0104013	−	0.0104013i
$859$		−	761.975i		−	0.887048i	−0.896262	−	0.443524i	$-0.853728\pi$
$859$		−	761.975i		−	0.887048i	0.896262	−	0.443524i	$-0.146272\pi$
$860$	−416.655	−	543.338i	−0.484482	−	0.631788i
$861$	20.1695			0.0234256
$862$	−526.966	−	526.966i	−0.611330	−	0.611330i
$863$	−622.781	+	622.781i	−0.721647	+	0.721647i	−0.968941	−	0.247294i	$-0.920459\pi$
$863$	−622.781	+	622.781i	−0.721647	+	0.721647i	0.247294	+	0.968941i	$0.420459\pi$
$864$		−	9.35210i		−	0.0108242i
$865$	−761.271	+	583.775i	−0.880082	+	0.674885i
$866$	312.543			0.360904
$867$	−24.5120	−	24.5120i	−0.0282722	−	0.0282722i
$868$	9.63525	−	9.63525i	0.0111005	−	0.0111005i
$869$			632.455i			0.727796i
$870$	2.05497	−	15.5724i	0.00236204	−	0.0178993i
$871$	−82.0359			−0.0941858
$872$	35.6052	+	35.6052i	0.0408316	+	0.0408316i
$873$	−24.1901	+	24.1901i	−0.0277092	+	0.0277092i
$874$			155.500i			0.177917i
$875$	223.455	+	540.866i	0.255377	+	0.618133i
$876$	−8.72480			−0.00995982
$877$	−416.753	−	416.753i	−0.475203	−	0.475203i	0.428390	−	0.903594i	$-0.359081\pi$
$877$	−416.753	−	416.753i	−0.475203	−	0.475203i	−0.903594	+	0.428390i	$0.859081\pi$
$878$	217.027	−	217.027i	0.247183	−	0.247183i
$879$			35.1925i			0.0400370i
$880$	223.976	+	29.5564i	0.254518	+	0.0335868i
$881$	−964.219			−1.09446			−0.547230	−	0.836982i	$-0.684318\pi$
$881$	−964.219			−1.09446			−0.547230	+	0.836982i	$0.684318\pi$
$882$	−243.510	−	243.510i	−0.276088	−	0.276088i
$883$	507.321	−	507.321i	0.574542	−	0.574542i	−0.358852	−	0.933394i	$-0.616832\pi$
$883$	507.321	−	507.321i	0.574542	−	0.574542i	0.933394	+	0.358852i	$0.116832\pi$
$884$			443.851i			0.502094i
$885$	25.8928	+	33.7654i	0.0292574	+	0.0381530i
$886$	108.835			0.122839
$887$	−892.012	−	892.012i	−1.00565	−	1.00565i	−0.999984	−	0.00566696i	$-0.998196\pi$
$887$	−892.012	−	892.012i	−1.00565	−	1.00565i	−0.00566696	−	0.999984i	$-0.501804\pi$
$888$	−0.786258	+	0.786258i	−0.000885425	+	0.000885425i
$889$		−	165.502i		−	0.186166i
$890$	−457.334	+	350.703i	−0.513858	+	0.394049i
$891$	−912.391			−1.02401
$892$	−121.262	−	121.262i	−0.135943	−	0.135943i
$893$	−215.982	+	215.982i	−0.241861	+	0.241861i
$894$			29.2210i			0.0326856i
$895$	−207.709	+	1574.00i	−0.232077	+	1.75866i
$896$	52.9670			0.0591149
$897$	−2.67919	−	2.67919i	−0.00298684	−	0.00298684i
$898$	−318.334	+	318.334i	−0.354492	+	0.354492i
$899$			35.1805i			0.0391329i
$900$	−434.188	−	116.624i	−0.482431	−	0.129582i
$901$	−2530.14			−2.80814
$902$	−529.600	−	529.600i	−0.587140	−	0.587140i
$903$	20.8282	−	20.8282i	0.0230656	−	0.0230656i
$904$			201.016i			0.222363i
$905$	−196.566	−	25.9393i	−0.217200	−	0.0286622i
$906$	32.2707			0.0356189
$907$	−632.605	−	632.605i	−0.697470	−	0.697470i	0.266394	−	0.963864i	$-0.414168\pi$
$907$	−632.605	−	632.605i	−0.697470	−	0.697470i	−0.963864	+	0.266394i	$0.914168\pi$
$908$	469.893	−	469.893i	0.517503	−	0.517503i
$909$			288.555i			0.317442i
$910$	−173.200	−	225.862i	−0.190330	−	0.248200i
$911$	1670.00			1.83315			0.916573	−	0.399867i	$-0.130944\pi$
$911$	1670.00			1.83315			0.916573	+	0.399867i	$0.130944\pi$
$912$	5.95883	+	5.95883i	0.00653380	+	0.00653380i
$913$	880.125	−	880.125i	0.963992	−	0.963992i
$914$			805.972i			0.881807i
$915$	−41.3254	+	31.6901i	−0.0451644	+	0.0346340i
$916$	677.403			0.739523
$917$	−641.288	−	641.288i	−0.699332	−	0.699332i
$918$	−42.6729	+	42.6729i	−0.0464847	+	0.0464847i
$919$		−	259.027i		−	0.281857i	−0.990020	−	0.140929i	$-0.954991\pi$
$919$		−	259.027i		−	0.281857i	0.990020	−	0.140929i	$-0.0450088\pi$
$920$	8.87320	−	67.2404i	0.00964479	−	0.0730873i
$921$	−14.4146			−0.0156511
$922$	−446.523	−	446.523i	−0.484299	−	0.484299i
$923$	−162.616	+	162.616i	−0.176182	+	0.176182i
$924$			9.71886i			0.0105182i
$925$	53.4220	+	92.6601i	0.0577536	+	0.100173i
$926$	−577.903			−0.624085
$927$	207.629	+	207.629i	0.223979	+	0.223979i
$928$	−96.6973	+	96.6973i	−0.104200	+	0.104200i
$929$			1646.83i			1.77269i	0.463023	+	0.886346i	$0.346765\pi$
$929$			1646.83i			1.77269i	−0.463023	+	0.886346i	$0.653235\pi$
$930$	−0.937453	−	0.123709i	−0.00100801	−	0.000133020i
$931$	620.914			0.666932
$932$	−389.990	−	389.990i	−0.418444	−	0.418444i
$933$	−29.8946	+	29.8946i	−0.0320413	+	0.0320413i
$934$			817.056i			0.874792i
$935$	−887.120	−	1156.85i	−0.948792	−	1.23727i
$936$	218.660			0.233611
$937$	960.988	+	960.988i	1.02560	+	1.02560i	0.999664	+	0.0259367i	$0.00825685\pi$
$937$	960.988	+	960.988i	1.02560	+	1.02560i	0.0259367	+	0.999664i	$0.491743\pi$
$938$	44.6699	−	44.6699i	0.0476225	−	0.0476225i
$939$			39.7076i			0.0422871i
$940$	105.718	−	81.0693i	0.112466	−	0.0862440i
$941$	546.195			0.580441			0.290221	−	0.956960i	$-0.406271\pi$
$941$	546.195			0.580441			0.290221	+	0.956960i	$0.406271\pi$
$942$	−20.0154	−	20.0154i	−0.0212477	−	0.0212477i
$943$	−158.993	+	158.993i	−0.168603	+	0.168603i
$944$		−	370.449i		−	0.392425i
$945$	5.06298	−	38.3668i	0.00535765	−	0.0405998i
$946$	−1093.80			−1.15623
$947$	−432.367	−	432.367i	−0.456565	−	0.456565i	0.440961	−	0.897526i	$-0.354638\pi$
$947$	−432.367	−	432.367i	−0.456565	−	0.456565i	−0.897526	+	0.440961i	$0.854638\pi$
$948$	7.27596	−	7.27596i	0.00767507	−	0.00767507i
$949$		−	408.178i		−	0.430114i
$950$	702.245	−	404.871i	0.739205	−	0.426180i
$951$	−40.0788			−0.0421439
$952$	−241.684	−	241.684i	−0.253870	−	0.253870i
$953$	−817.027	+	817.027i	−0.857321	+	0.857321i	−0.991022	−	0.133701i	$-0.957314\pi$
$953$	−817.027	+	817.027i	−0.857321	+	0.857321i	0.133701	+	0.991022i	$0.457314\pi$
$954$			1246.45i			1.30655i
$955$	−528.684	−	69.7664i	−0.553596	−	0.0730538i
$956$	−394.568			−0.412728
$957$	−17.7429	−	17.7429i	−0.0185401	−	0.0185401i
$958$	−315.169	+	315.169i	−0.328986	+	0.328986i
$959$		−	551.038i		−	0.574597i
$960$	−2.23666	−	2.91671i	−0.00232986	−	0.00303824i
$961$	−958.882			−0.997796
$962$	−36.7840	−	36.7840i	−0.0382370	−	0.0382370i
$963$	6.94348	−	6.94348i	0.00721026	−	0.00721026i
$964$		−	190.499i		−	0.197613i
$965$	791.624	−	607.052i	0.820336	−	0.629069i
$966$	2.91773			0.00302042
$967$	840.345	+	840.345i	0.869023	+	0.869023i	0.992364	−	0.123341i	$-0.0393610\pi$
$967$	840.345	+	840.345i	0.869023	+	0.869023i	−0.123341	+	0.992364i	$0.539361\pi$
$968$	13.1932	−	13.1932i	0.0136293	−	0.0136293i
$969$		−	54.3793i		−	0.0561190i
$970$	−3.51969	+	26.6719i	−0.00362855	+	0.0274968i
$971$	−967.764			−0.996668			−0.498334	−	0.866985i	$-0.666055\pi$
$971$	−967.764			−0.996668			−0.498334	+	0.866985i	$0.666055\pi$
$972$	31.5387	+	31.5387i	0.0324472	+	0.0324472i
$973$	−477.102	+	477.102i	−0.490341	+	0.490341i
$974$			445.088i			0.456969i
$975$	−5.12363	+	19.0751i	−0.00525500	+	0.0195642i
$976$	453.391			0.464540
$977$	22.2028	+	22.2028i	0.0227255	+	0.0227255i	0.718378	−	0.695653i	$-0.244885\pi$
$977$	22.2028	+	22.2028i	0.0227255	+	0.0227255i	−0.695653	+	0.718378i	$0.744885\pi$
$978$	−0.0964792	+	0.0964792i	−9.86495e−5	+	9.86495e-5i
$979$			920.661i			0.940409i
$980$	−268.493	−	35.4310i	−0.273972	−	0.0361540i
$981$	−160.073			−0.163173
$982$	515.585	+	515.585i	0.525035	+	0.525035i
$983$	1032.01	−	1032.01i	1.04986	−	1.04986i	0.0511687	−	0.998690i	$-0.483705\pi$
$983$	1032.01	−	1032.01i	1.04986	−	1.04986i	0.998690	−	0.0511687i	$-0.0162946\pi$
$984$			12.1854i			0.0123835i
$985$	545.289	+	711.083i	0.553593	+	0.721911i
$986$	882.445			0.894974
$987$	4.05259	+	4.05259i	0.00410597	+	0.00410597i
$988$	−278.775	+	278.775i	−0.282161	+	0.282161i
$989$			328.372i			0.332024i
$990$	−569.912	+	437.033i	−0.575668	+	0.441447i
$991$	326.492			0.329457			0.164729	−	0.986339i	$-0.447325\pi$
$991$	326.492			0.329457			0.164729	+	0.986339i	$0.447325\pi$
$992$	5.82114	+	5.82114i	0.00586808	+	0.00586808i
$993$	0.809097	−	0.809097i	0.000814800	−	0.000814800i
$994$		−	177.094i		−	0.178163i
$995$	−62.9191	+	476.795i	−0.0632353	+	0.479191i
$996$	−20.2505			−0.0203318
$997$	19.2512	+	19.2512i	0.0193092	+	0.0193092i	0.716695	−	0.697386i	$-0.245654\pi$
$997$	19.2512	+	19.2512i	0.0193092	+	0.0193092i	−0.697386	+	0.716695i	$0.745654\pi$
$998$	327.060	−	327.060i	0.327715	−	0.327715i
$999$		−	7.07300i		−	0.00708008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.47.5	✓	20
5.3	odd	4	inner	230.3.f.a.93.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.5	✓	20	1.1	even	1	trivial
230.3.f.a.93.5	yes	20	5.3	odd	4	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.0649756 + 0.0649756i) q^{3} +2.00000i q^{4} +(-4.95703 - 0.654141i) q^{5} +0.129951 q^{6} +(-3.31044 - 3.31044i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.99156i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.0649756 + 0.0649756i) q^{3} +2.00000i q^{4} +(-4.95703 - 0.654141i) q^{5} +0.129951 q^{6} +(-3.31044 - 3.31044i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.99156i q^{9} +(4.30288 + 5.61117i) q^{10} +11.2959 q^{11} +(-0.129951 - 0.129951i) q^{12} +(6.07959 - 6.07959i) q^{13} +6.62087i q^{14} +(0.364589 - 0.279583i) q^{15} -4.00000 q^{16} +(18.2517 + 18.2517i) q^{17} +(8.99156 - 8.99156i) q^{18} +22.9272i q^{19} +(1.30828 - 9.91405i) q^{20} +0.430195 q^{21} +(-11.2959 - 11.2959i) q^{22} +(-3.39116 + 3.39116i) q^{23} +0.259903i q^{24} +(24.1442 + 6.48519i) q^{25} -12.1592 q^{26} +(-1.16901 - 1.16901i) q^{27} +(6.62087 - 6.62087i) q^{28} +24.1743i q^{29} +(-0.644172 - 0.0850065i) q^{30} +1.45528 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.733956 + 0.733956i) q^{33} -36.5034i q^{34} +(14.2444 + 18.5754i) q^{35} -17.9831 q^{36} +(3.02520 + 3.02520i) q^{37} +(22.9272 - 22.9272i) q^{38} +0.790050i q^{39} +(-11.2223 + 8.60577i) q^{40} +46.8844 q^{41} +(-0.430195 - 0.430195i) q^{42} +(48.4158 - 48.4158i) q^{43} +22.5917i q^{44} +(5.88175 - 44.5714i) q^{45} +6.78233 q^{46} +(9.42035 + 9.42035i) q^{47} +(0.259903 - 0.259903i) q^{48} -27.0820i q^{49} +(-17.6590 - 30.6294i) q^{50} -2.37183 q^{51} +(12.1592 + 12.1592i) q^{52} +(-69.3124 + 69.3124i) q^{53} +2.33803i q^{54} +(-55.9939 - 7.38909i) q^{55} -13.2417 q^{56} +(-1.48971 - 1.48971i) q^{57} +(24.1743 - 24.1743i) q^{58} +92.6123i q^{59} +(0.559165 + 0.729178i) q^{60} -113.348 q^{61} +(-1.45528 - 1.45528i) q^{62} +(29.7660 - 29.7660i) q^{63} -8.00000i q^{64} +(-34.1136 + 26.1598i) q^{65} +1.46791 q^{66} +(-6.74683 - 6.74683i) q^{67} +(-36.5034 + 36.5034i) q^{68} -0.440686i q^{69} +(4.33099 - 32.8198i) q^{70} -26.7478 q^{71} +(17.9831 + 17.9831i) q^{72} +(33.5695 - 33.5695i) q^{73} -6.05040i q^{74} +(-1.99016 + 1.14741i) q^{75} -45.8543 q^{76} +(-37.3942 - 37.3942i) q^{77} +(0.790050 - 0.790050i) q^{78} +55.9899i q^{79} +(19.8281 + 2.61657i) q^{80} -80.7721 q^{81} +(-46.8844 - 46.8844i) q^{82} +(77.9157 - 77.9157i) q^{83} +0.860391i q^{84} +(-78.5349 - 102.413i) q^{85} -96.8315 q^{86} +(-1.57074 - 1.57074i) q^{87} +(22.5917 - 22.5917i) q^{88} +81.5042i q^{89} +(-50.4531 + 38.6896i) q^{90} -40.2522 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-0.0945580 + 0.0945580i) q^{93} -18.8407i q^{94} +(14.9976 - 113.650i) q^{95} -0.519805 q^{96} +(2.69032 + 2.69032i) q^{97} +(-27.0820 + 27.0820i) q^{98} +101.567i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more