LMFDB - Embedded newform 690.3.k.b.277.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.15
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.06746 + 3.63124i) q^{10} +6.14155 q^{11} +(2.44949 + 2.44949i) q^{12} +(1.79785 - 1.79785i) q^{13} +0.234854i q^{14} +(-4.44734 + 7.43109i) q^{15} -4.00000 q^{16} +(5.21460 + 5.21460i) q^{17} +(-3.00000 + 3.00000i) q^{18} -28.4319i q^{19} +(-2.43622 - 9.69870i) q^{20} -0.287636 q^{21} +(-6.14155 - 6.14155i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.0324 - 11.8141i) q^{25} -3.59570 q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.234854 - 0.234854i) q^{28} +34.1603i q^{29} +(11.8784 - 2.98375i) q^{30} -24.7380 q^{31} +(4.00000 + 4.00000i) q^{32} +(7.52183 - 7.52183i) q^{33} -10.4292i q^{34} +(0.712483 + 0.426406i) q^{35} +6.00000 q^{36} +(-48.0222 - 48.0222i) q^{37} +(-28.4319 + 28.4319i) q^{38} -4.40382i q^{39} +(-7.26248 + 12.1349i) q^{40} -62.5499 q^{41} +(0.287636 + 0.287636i) q^{42} +(-26.2996 + 26.2996i) q^{43} +12.2831i q^{44} +(3.65433 + 14.5481i) q^{45} +6.78233 q^{46} +(-46.4294 - 46.4294i) q^{47} +(-4.89898 + 4.89898i) q^{48} -48.9724i q^{49} +(-33.8465 - 10.2183i) q^{50} +12.7731 q^{51} +(3.59570 + 3.59570i) q^{52} +(-4.24683 + 4.24683i) q^{53} +7.34847i q^{54} +(-29.7825 + 7.48108i) q^{55} -0.469708 q^{56} +(-34.8218 - 34.8218i) q^{57} +(34.1603 - 34.1603i) q^{58} -11.1749i q^{59} +(-14.8622 - 8.89469i) q^{60} +80.2086 q^{61} +(24.7380 + 24.7380i) q^{62} +(-0.352281 + 0.352281i) q^{63} -8.00000i q^{64} +(-6.52843 + 10.9084i) q^{65} -15.0437 q^{66} +(-74.7155 - 74.7155i) q^{67} +(-10.4292 + 10.4292i) q^{68} +8.30662i q^{69} +(-0.286078 - 1.13889i) q^{70} +5.49076 q^{71} +(-6.00000 - 6.00000i) q^{72} +(14.2498 - 14.2498i) q^{73} +96.0445i q^{74} +(12.5148 - 41.4533i) q^{75} +56.8637 q^{76} +(-0.721183 - 0.721183i) q^{77} +(-4.40382 + 4.40382i) q^{78} +66.3129i q^{79} +(19.3974 - 4.87244i) q^{80} -9.00000 q^{81} +(62.5499 + 62.5499i) q^{82} +(-113.788 + 113.788i) q^{83} -0.575272i q^{84} +(-31.6394 - 18.9355i) q^{85} +52.5993 q^{86} +(41.8376 + 41.8376i) q^{87} +(12.2831 - 12.2831i) q^{88} -35.8168i q^{89} +(10.8937 - 18.2024i) q^{90} -0.422232 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-30.2978 + 30.2978i) q^{93} +92.8588i q^{94} +(34.6331 + 137.876i) q^{95} +9.79796 q^{96} +(-93.7132 - 93.7132i) q^{97} +(-48.9724 + 48.9724i) q^{98} -18.4246i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	−4.84935	+	1.21811i	−0.969870	+	0.243622i
$5$	−4.84935	+	1.21811i	−0.969870	+	0.243622i
$6$	−2.44949			−0.408248
$7$	−0.117427	−	0.117427i	−0.0167753	−	0.0167753i	0.698669	−	0.715445i	$-0.253776\pi$
$7$	−0.117427	−	0.117427i	−0.0167753	−	0.0167753i	−0.715445	+	0.698669i	$0.753776\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	6.06746	+	3.63124i	0.606746	+	0.363124i
$11$	6.14155			0.558322			0.279161	−	0.960244i	$-0.409944\pi$
$11$	6.14155			0.558322			0.279161	+	0.960244i	$0.409944\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	1.79785	−	1.79785i	0.138296	−	0.138296i	−0.634570	−	0.772866i	$-0.718823\pi$
$13$	1.79785	−	1.79785i	0.138296	−	0.138296i	0.772866	+	0.634570i	$0.218823\pi$
$14$			0.234854i			0.0167753i
$15$	−4.44734	+	7.43109i	−0.296490	+	0.495406i
$16$	−4.00000			−0.250000
$17$	5.21460	+	5.21460i	0.306741	+	0.306741i	0.843644	−	0.536903i	$-0.180406\pi$
$17$	5.21460	+	5.21460i	0.306741	+	0.306741i	−0.536903	+	0.843644i	$0.680406\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	28.4319i		−	1.49641i	−0.663466	−	0.748207i	$-0.730915\pi$
$19$		−	28.4319i		−	1.49641i	0.663466	−	0.748207i	$-0.269085\pi$
$20$	−2.43622	−	9.69870i	−0.121811	−	0.484935i
$21$	−0.287636			−0.0136970
$22$	−6.14155	−	6.14155i	−0.279161	−	0.279161i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	22.0324	−	11.8141i	0.881297	−	0.472563i
$26$	−3.59570			−0.138296
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	0.234854	−	0.234854i	0.00838764	−	0.00838764i
$29$			34.1603i			1.17794i	0.808154	+	0.588971i	$0.200467\pi$
$29$			34.1603i			1.17794i	−0.808154	+	0.588971i	$0.799533\pi$
$30$	11.8784	−	2.98375i	0.395948	−	0.0994583i
$31$	−24.7380			−0.798001			−0.399000	−	0.916951i	$-0.630643\pi$
$31$	−24.7380			−0.798001			−0.399000	+	0.916951i	$0.630643\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	7.52183	−	7.52183i	0.227934	−	0.227934i
$34$		−	10.4292i		−	0.306741i
$35$	0.712483	+	0.426406i	0.0203567	+	0.0121830i
$36$	6.00000			0.166667
$37$	−48.0222	−	48.0222i	−1.29790	−	1.29790i	−0.929778	−	0.368121i	$-0.880001\pi$
$37$	−48.0222	−	48.0222i	−1.29790	−	1.29790i	−0.368121	−	0.929778i	$-0.619999\pi$
$38$	−28.4319	+	28.4319i	−0.748207	+	0.748207i
$39$		−	4.40382i		−	0.112918i
$40$	−7.26248	+	12.1349i	−0.181562	+	0.303373i
$41$	−62.5499			−1.52561			−0.762804	−	0.646630i	$-0.776178\pi$
$41$	−62.5499			−1.52561			−0.762804	+	0.646630i	$0.776178\pi$
$42$	0.287636	+	0.287636i	0.00684848	+	0.00684848i
$43$	−26.2996	+	26.2996i	−0.611619	+	0.611619i	−0.943368	−	0.331748i	$-0.892361\pi$
$43$	−26.2996	+	26.2996i	−0.611619	+	0.611619i	0.331748	+	0.943368i	$0.392361\pi$
$44$			12.2831i			0.279161i
$45$	3.65433	+	14.5481i	0.0812073	+	0.323290i
$46$	6.78233			0.147442
$47$	−46.4294	−	46.4294i	−0.987859	−	0.987859i	0.0120681	−	0.999927i	$-0.496159\pi$
$47$	−46.4294	−	46.4294i	−0.987859	−	0.987859i	−0.999927	+	0.0120681i	$0.996159\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	48.9724i		−	0.999437i
$50$	−33.8465	−	10.2183i	−0.676930	−	0.204367i
$51$	12.7731			0.250453
$52$	3.59570	+	3.59570i	0.0691481	+	0.0691481i
$53$	−4.24683	+	4.24683i	−0.0801289	+	0.0801289i	−0.746035	−	0.665906i	$-0.768045\pi$
$53$	−4.24683	+	4.24683i	−0.0801289	+	0.0801289i	0.665906	+	0.746035i	$0.268045\pi$
$54$			7.34847i			0.136083i
$55$	−29.7825	+	7.48108i	−0.541500	+	0.136020i
$56$	−0.469708			−0.00838764
$57$	−34.8218	−	34.8218i	−0.610908	−	0.610908i
$58$	34.1603	−	34.1603i	0.588971	−	0.588971i
$59$		−	11.1749i		−	0.189405i	−0.995506	−	0.0947023i	$-0.969810\pi$
$59$		−	11.1749i		−	0.189405i	0.995506	−	0.0947023i	$-0.0301899\pi$
$60$	−14.8622	−	8.89469i	−0.247703	−	0.148245i
$61$	80.2086			1.31489			0.657447	−	0.753501i	$-0.271636\pi$
$61$	80.2086			1.31489			0.657447	+	0.753501i	$0.271636\pi$
$62$	24.7380	+	24.7380i	0.399000	+	0.399000i
$63$	−0.352281	+	0.352281i	−0.00559176	+	0.00559176i
$64$		−	8.00000i		−	0.125000i
$65$	−6.52843	+	10.9084i	−0.100437	+	0.167821i
$66$	−15.0437			−0.227934
$67$	−74.7155	−	74.7155i	−1.11516	−	1.11516i	−0.992442	−	0.122714i	$-0.960840\pi$
$67$	−74.7155	−	74.7155i	−1.11516	−	1.11516i	−0.122714	−	0.992442i	$-0.539160\pi$
$68$	−10.4292	+	10.4292i	−0.153371	+	0.153371i
$69$			8.30662i			0.120386i
$70$	−0.286078	−	1.13889i	−0.00408683	−	0.0162698i
$71$	5.49076			0.0773346			0.0386673	−	0.999252i	$-0.487689\pi$
$71$	5.49076			0.0773346			0.0386673	+	0.999252i	$0.487689\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	14.2498	−	14.2498i	0.195203	−	0.195203i	−0.602737	−	0.797940i	$-0.705923\pi$
$73$	14.2498	−	14.2498i	0.195203	−	0.195203i	0.797940	+	0.602737i	$0.205923\pi$
$74$			96.0445i			1.29790i
$75$	12.5148	−	41.4533i	0.166865	−	0.552711i
$76$	56.8637			0.748207
$77$	−0.721183	−	0.721183i	−0.00936601	−	0.00936601i
$78$	−4.40382	+	4.40382i	−0.0564592	+	0.0564592i
$79$			66.3129i			0.839404i	0.907662	+	0.419702i	$0.137865\pi$
$79$			66.3129i			0.839404i	−0.907662	+	0.419702i	$0.862135\pi$
$80$	19.3974	−	4.87244i	0.242468	−	0.0609055i
$81$	−9.00000			−0.111111
$82$	62.5499	+	62.5499i	0.762804	+	0.762804i
$83$	−113.788	+	113.788i	−1.37094	+	1.37094i	−0.511886	+	0.859053i	$0.671053\pi$
$83$	−113.788	+	113.788i	−1.37094	+	1.37094i	−0.859053	+	0.511886i	$0.828947\pi$
$84$		−	0.575272i		−	0.00684848i
$85$	−31.6394	−	18.9355i	−0.372228	−	0.222770i
$86$	52.5993			0.611619
$87$	41.8376	+	41.8376i	0.480892	+	0.480892i
$88$	12.2831	−	12.2831i	0.139581	−	0.139581i
$89$		−	35.8168i		−	0.402436i	−0.979547	−	0.201218i	$-0.935510\pi$
$89$		−	35.8168i		−	0.402436i	0.979547	−	0.201218i	$-0.0644899\pi$
$90$	10.8937	−	18.2024i	0.121041	−	0.202249i
$91$	−0.422232			−0.00463991
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−30.2978	+	30.2978i	−0.325783	+	0.325783i
$94$			92.8588i			0.987859i
$95$	34.6331	+	137.876i	0.364559	+	1.45133i
$96$	9.79796			0.102062
$97$	−93.7132	−	93.7132i	−0.966115	−	0.966115i	0.0333292	−	0.999444i	$-0.489389\pi$
$97$	−93.7132	−	93.7132i	−0.966115	−	0.966115i	−0.999444	+	0.0333292i	$0.989389\pi$
$98$	−48.9724	+	48.9724i	−0.499719	+	0.499719i
$99$		−	18.4246i		−	0.186107i
$100$	23.6282	+	44.0648i	0.236282	+	0.440648i
$101$	46.9695			0.465044			0.232522	−	0.972591i	$-0.425302\pi$
$101$	46.9695			0.465044			0.232522	+	0.972591i	$0.425302\pi$
$102$	−12.7731	−	12.7731i	−0.125227	−	0.125227i
$103$	16.5301	−	16.5301i	0.160487	−	0.160487i	−0.622296	−	0.782782i	$-0.713800\pi$
$103$	16.5301	−	16.5301i	0.160487	−	0.160487i	0.782782	+	0.622296i	$0.213800\pi$
$104$		−	7.19140i		−	0.0691481i
$105$	1.39485	−	0.350372i	0.0132843	−	0.00333688i
$106$	8.49366			0.0801289
$107$	−89.6601	−	89.6601i	−0.837945	−	0.837945i	0.150643	−	0.988588i	$-0.451866\pi$
$107$	−89.6601	−	89.6601i	−0.837945	−	0.837945i	−0.988588	+	0.150643i	$0.951866\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			20.9512i			0.192213i	0.995371	+	0.0961064i	$0.0306389\pi$
$109$			20.9512i			0.192213i	−0.995371	+	0.0961064i	$0.969361\pi$
$110$	37.2636	+	22.3014i	0.338760	+	0.202740i
$111$	−117.630			−1.05973
$112$	0.469708	+	0.469708i	0.00419382	+	0.00419382i
$113$	134.864	−	134.864i	1.19349	−	1.19349i	0.217404	−	0.976082i	$-0.430241\pi$
$113$	134.864	−	134.864i	1.19349	−	1.19349i	0.976082	−	0.217404i	$-0.0697590\pi$
$114$			69.6435i			0.610908i
$115$	12.3141	−	20.5758i	0.107079	−	0.178920i
$116$	−68.3206			−0.588971
$117$	−5.39355	−	5.39355i	−0.0460987	−	0.0460987i
$118$	−11.1749	+	11.1749i	−0.0947023	+	0.0947023i
$119$		−	1.22467i		−	0.0102913i
$120$	5.96750	+	23.7569i	0.0497291	+	0.197974i
$121$	−83.2814			−0.688276
$122$	−80.2086	−	80.2086i	−0.657447	−	0.657447i
$123$	−76.6077	+	76.6077i	−0.622826	+	0.622826i
$124$		−	49.4761i		−	0.399000i
$125$	−92.4521	+	84.1286i	−0.739617	+	0.673028i
$126$	0.704562			0.00559176
$127$	14.6980	+	14.6980i	0.115733	+	0.115733i	0.762601	−	0.646869i	$-0.223922\pi$
$127$	14.6980	+	14.6980i	0.115733	+	0.115733i	−0.646869	+	0.762601i	$0.723922\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			64.4207i			0.499385i
$130$	17.4368	−	4.37996i	0.134129	−	0.0336920i
$131$	−68.9070			−0.526007			−0.263004	−	0.964795i	$-0.584713\pi$
$131$	−68.9070			−0.526007			−0.263004	+	0.964795i	$0.584713\pi$
$132$	15.0437	+	15.0437i	0.113967	+	0.113967i
$133$	−3.33867	+	3.33867i	−0.0251028	+	0.0251028i
$134$			149.431i			1.11516i
$135$	22.2933	+	13.3420i	0.165135	+	0.0988299i
$136$	20.8584			0.153371
$137$	148.355	+	148.355i	1.08288	+	1.08288i	0.996239	+	0.0866447i	$0.0276145\pi$
$137$	148.355	+	148.355i	1.08288	+	1.08288i	0.0866447	+	0.996239i	$0.472386\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	170.164i		−	1.22420i	−0.790781	−	0.612099i	$-0.790325\pi$
$139$		−	170.164i		−	1.22420i	0.790781	−	0.612099i	$-0.209675\pi$
$140$	−0.852811	+	1.42497i	−0.00609151	+	0.0101783i
$141$	−113.728			−0.806584
$142$	−5.49076	−	5.49076i	−0.0386673	−	0.0386673i
$143$	11.0416	−	11.0416i	0.0772138	−	0.0772138i
$144$			12.0000i			0.0833333i
$145$	−41.6110	−	165.655i	−0.286972	−	1.14245i
$146$	−28.4997			−0.195203
$147$	−59.9787	−	59.9787i	−0.408019	−	0.408019i
$148$	96.0445	−	96.0445i	0.648949	−	0.648949i
$149$			209.754i			1.40774i	0.710328	+	0.703871i	$0.248547\pi$
$149$			209.754i			1.40774i	−0.710328	+	0.703871i	$0.751453\pi$
$150$	−53.9682	+	28.9385i	−0.359788	+	0.192923i
$151$	5.19070			0.0343755			0.0171878	−	0.999852i	$-0.494529\pi$
$151$	5.19070			0.0343755			0.0171878	+	0.999852i	$0.494529\pi$
$152$	−56.8637	−	56.8637i	−0.374103	−	0.374103i
$153$	15.6438	−	15.6438i	0.102247	−	0.102247i
$154$			1.44237i			0.00936601i
$155$	119.963	−	30.1336i	0.773957	−	0.194411i
$156$	8.80763			0.0564592
$157$	−2.34153	−	2.34153i	−0.0149142	−	0.0149142i	0.699610	−	0.714525i	$-0.253357\pi$
$157$	−2.34153	−	2.34153i	−0.0149142	−	0.0149142i	−0.714525	+	0.699610i	$0.753357\pi$
$158$	66.3129	−	66.3129i	0.419702	−	0.419702i
$159$			10.4026i			0.0654249i
$160$	−24.2698	−	14.5250i	−0.151687	−	0.0907810i
$161$	0.796428			0.00494676
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	80.0854	−	80.0854i	0.491321	−	0.491321i	−0.417401	−	0.908722i	$-0.637059\pi$
$163$	80.0854	−	80.0854i	0.491321	−	0.491321i	0.908722	+	0.417401i	$0.137059\pi$
$164$		−	125.100i		−	0.762804i
$165$	−27.3136	+	45.6384i	−0.165537	+	0.276596i
$166$	227.576			1.37094
$167$	−212.730	−	212.730i	−1.27383	−	1.27383i	−0.944060	−	0.329773i	$-0.893028\pi$
$167$	−212.730	−	212.730i	−1.27383	−	1.27383i	−0.329773	−	0.944060i	$-0.606972\pi$
$168$	−0.575272	+	0.575272i	−0.00342424	+	0.00342424i
$169$			162.535i			0.961748i
$170$	12.7039	+	50.5749i	0.0747289	+	0.297499i
$171$	−85.2956			−0.498805
$172$	−52.5993	−	52.5993i	−0.305810	−	0.305810i
$173$	−153.930	+	153.930i	−0.889769	+	0.889769i	−0.994501	−	0.104731i	$-0.966602\pi$
$173$	−153.930	+	153.930i	−0.889769	+	0.889769i	0.104731	+	0.994501i	$0.466602\pi$
$174$		−	83.6753i		−	0.480892i
$175$	−3.97449	−	1.19991i	−0.0227114	−	0.00685661i
$176$	−24.5662			−0.139581
$177$	−13.6864	−	13.6864i	−0.0773241	−	0.0773241i
$178$	−35.8168	+	35.8168i	−0.201218	+	0.201218i
$179$		−	119.472i		−	0.667440i	−0.942672	−	0.333720i	$-0.891696\pi$
$179$		−	119.472i		−	0.667440i	0.942672	−	0.333720i	$-0.108304\pi$
$180$	−29.0961	+	7.30866i	−0.161645	+	0.0406037i
$181$	104.780			0.578895			0.289447	−	0.957194i	$-0.406528\pi$
$181$	104.780			0.578895			0.289447	+	0.957194i	$0.406528\pi$
$182$	0.422232	+	0.422232i	0.00231996	+	0.00231996i
$183$	98.2350	−	98.2350i	0.536803	−	0.536803i
$184$			13.5647i			0.0737210i
$185$	291.373	+	174.380i	1.57499	+	0.942597i
$186$	60.5955			0.325783
$187$	32.0257	+	32.0257i	0.171261	+	0.171261i
$188$	92.8588	−	92.8588i	0.493930	−	0.493930i
$189$			0.862908i			0.00456565i
$190$	103.243	−	172.509i	0.543384	−	0.907943i
$191$	243.162			1.27310			0.636549	−	0.771237i	$-0.280361\pi$
$191$	243.162			1.27310			0.636549	+	0.771237i	$0.280361\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	127.755	−	127.755i	0.661940	−	0.661940i	−0.293897	−	0.955837i	$-0.594952\pi$
$193$	127.755	−	127.755i	0.661940	−	0.661940i	0.955837	+	0.293897i	$0.0949522\pi$
$194$			187.426i			0.966115i
$195$	5.36433	+	21.3556i	0.0275094	+	0.109516i
$196$	97.9448			0.499719
$197$	−158.665	−	158.665i	−0.805407	−	0.805407i	0.178528	−	0.983935i	$-0.442866\pi$
$197$	−158.665	−	158.665i	−0.805407	−	0.805407i	−0.983935	+	0.178528i	$0.942866\pi$
$198$	−18.4246	+	18.4246i	−0.0930537	+	0.0930537i
$199$			185.886i			0.934098i	0.884231	+	0.467049i	$0.154683\pi$
$199$			185.886i			0.934098i	−0.884231	+	0.467049i	$0.845317\pi$
$200$	20.4367	−	67.6930i	0.102183	−	0.338465i
$201$	−183.015			−0.910521
$202$	−46.9695	−	46.9695i	−0.232522	−	0.232522i
$203$	4.01134	−	4.01134i	0.0197603	−	0.0197603i
$204$			25.5462i			0.125227i
$205$	303.326	−	76.1926i	1.47964	−	0.371671i
$206$	−33.0602			−0.160487
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−7.19140	+	7.19140i	−0.0345740	+	0.0345740i
$209$		−	174.616i		−	0.835481i
$210$	−1.74522	−	1.04448i	−0.00831058	−	0.00497370i
$211$	−19.0575			−0.0903197			−0.0451599	−	0.998980i	$-0.514380\pi$
$211$	−19.0575			−0.0903197			−0.0451599	+	0.998980i	$0.514380\pi$
$212$	−8.49366	−	8.49366i	−0.0400644	−	0.0400644i
$213$	6.72477	−	6.72477i	0.0315717	−	0.0315717i
$214$			179.320i			0.837945i
$215$	95.5003	−	159.572i	0.444188	−	0.742195i
$216$	−14.6969			−0.0680414
$217$	2.90491	+	2.90491i	0.0133867	+	0.0133867i
$218$	20.9512	−	20.9512i	0.0961064	−	0.0961064i
$219$		−	34.9049i		−	0.159383i
$220$	−14.9622	−	59.5650i	−0.0680098	−	0.270750i
$221$	18.7501			0.0848423
$222$	117.630	+	117.630i	0.529865	+	0.529865i
$223$	159.166	−	159.166i	0.713748	−	0.713748i	−0.253569	−	0.967317i	$-0.581605\pi$
$223$	159.166	−	159.166i	0.713748	−	0.713748i	0.967317	+	0.253569i	$0.0816046\pi$
$224$		−	0.939416i		−	0.00419382i
$225$	−35.4423	−	66.0972i	−0.157521	−	0.293766i
$226$	−269.728			−1.19349
$227$	2.50235	+	2.50235i	0.0110235	+	0.0110235i	0.712597	−	0.701574i	$-0.247519\pi$
$227$	2.50235	+	2.50235i	0.0110235	+	0.0110235i	−0.701574	+	0.712597i	$0.747519\pi$
$228$	69.6435	−	69.6435i	0.305454	−	0.305454i
$229$		−	108.398i		−	0.473354i	−0.971588	−	0.236677i	$-0.923942\pi$
$229$		−	108.398i		−	0.473354i	0.971588	−	0.236677i	$-0.0760583\pi$
$230$	−32.8899	+	8.26162i	−0.143000	+	0.0359201i
$231$	−1.76653			−0.00764732
$232$	68.3206	+	68.3206i	0.294485	+	0.294485i
$233$	24.7659	−	24.7659i	0.106292	−	0.106292i	−0.651961	−	0.758253i	$-0.726053\pi$
$233$	24.7659	−	24.7659i	0.106292	−	0.106292i	0.758253	+	0.651961i	$0.226053\pi$
$234$			10.7871i			0.0460987i
$235$	281.708	+	168.596i	1.19876	+	0.717431i
$236$	22.3497			0.0947023
$237$	81.2164	+	81.2164i	0.342685	+	0.342685i
$238$	−1.22467	+	1.22467i	−0.00514567	+	0.00514567i
$239$			264.476i			1.10659i	0.832985	+	0.553296i	$0.186630\pi$
$239$			264.476i			1.10659i	−0.832985	+	0.553296i	$0.813370\pi$
$240$	17.7894	−	29.7244i	0.0741224	−	0.123852i
$241$	467.027			1.93787			0.968936	−	0.247311i	$-0.0795469\pi$
$241$	467.027			1.93787			0.968936	+	0.247311i	$0.0795469\pi$
$242$	83.2814	+	83.2814i	0.344138	+	0.344138i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			160.417i			0.657447i
$245$	59.6538	+	237.484i	0.243485	+	0.969324i
$246$	153.215			0.622826
$247$	−51.1162	−	51.1162i	−0.206948	−	0.206948i
$248$	−49.4761	+	49.4761i	−0.199500	+	0.199500i
$249$			278.722i			1.11937i
$250$	176.581	+	8.32351i	0.706323	+	0.0332940i
$251$	204.851			0.816141			0.408070	−	0.912950i	$-0.366202\pi$
$251$	204.851			0.816141			0.408070	+	0.912950i	$0.366202\pi$
$252$	−0.704562	−	0.704562i	−0.00279588	−	0.00279588i
$253$	−20.8270	+	20.8270i	−0.0823201	+	0.0823201i
$254$		−	29.3961i		−	0.115733i
$255$	−61.9413	+	15.5591i	−0.242907	+	0.0610159i
$256$	16.0000			0.0625000
$257$	−142.969	−	142.969i	−0.556301	−	0.556301i	0.371952	−	0.928252i	$-0.378689\pi$
$257$	−142.969	−	142.969i	−0.556301	−	0.556301i	−0.928252	+	0.371952i	$0.878689\pi$
$258$	64.4207	−	64.4207i	0.249693	−	0.249693i
$259$			11.2782i			0.0435452i
$260$	−21.8168	−	13.0569i	−0.0839107	−	0.0502187i
$261$	102.481			0.392647
$262$	68.9070	+	68.9070i	0.263004	+	0.263004i
$263$	337.181	−	337.181i	1.28206	−	1.28206i	0.342559	−	0.939496i	$-0.388706\pi$
$263$	337.181	−	337.181i	1.28206	−	1.28206i	0.939496	−	0.342559i	$-0.111294\pi$
$264$		−	30.0873i		−	0.113967i
$265$	15.4213	−	25.7675i	0.0581934	−	0.0972357i
$266$	6.67733			0.0251028
$267$	−43.8664	−	43.8664i	−0.164294	−	0.164294i
$268$	149.431	−	149.431i	0.557578	−	0.557578i
$269$			284.631i			1.05811i	0.848588	+	0.529054i	$0.177453\pi$
$269$			284.631i			1.05811i	−0.848588	+	0.529054i	$0.822547\pi$
$270$	−8.95124	−	35.6353i	−0.0331528	−	0.131983i
$271$	19.1966			0.0708361			0.0354180	−	0.999373i	$-0.488724\pi$
$271$	19.1966			0.0708361			0.0354180	+	0.999373i	$0.488724\pi$
$272$	−20.8584	−	20.8584i	−0.0766853	−	0.0766853i
$273$	−0.517127	+	0.517127i	−0.00189424	+	0.00189424i
$274$		−	296.710i		−	1.08288i
$275$	135.313	−	72.5568i	0.492048	−	0.263843i
$276$	−16.6132			−0.0601929
$277$	−38.3293	−	38.3293i	−0.138373	−	0.138373i	0.634527	−	0.772900i	$-0.281195\pi$
$277$	−38.3293	−	38.3293i	−0.138373	−	0.138373i	−0.772900	+	0.634527i	$0.781195\pi$
$278$	−170.164	+	170.164i	−0.612099	+	0.612099i
$279$			74.2141i			0.266000i
$280$	2.27778	−	0.572156i	0.00813492	−	0.00204341i
$281$	−222.591			−0.792138			−0.396069	−	0.918221i	$-0.629626\pi$
$281$	−222.591			−0.792138			−0.396069	+	0.918221i	$0.629626\pi$
$282$	113.728	+	113.728i	0.403292	+	0.403292i
$283$	339.400	−	339.400i	1.19929	−	1.19929i	0.224916	−	0.974378i	$-0.427789\pi$
$283$	339.400	−	339.400i	1.19929	−	1.19929i	0.974378	−	0.224916i	$-0.0722107\pi$
$284$			10.9815i			0.0386673i
$285$	211.280	+	126.446i	0.741332	+	0.443671i
$286$	−22.0832			−0.0772138
$287$	7.34504	+	7.34504i	0.0255925	+	0.0255925i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	234.616i		−	0.811819i
$290$	−124.044	+	207.266i	−0.427739	+	0.714711i
$291$	−229.549			−0.788830
$292$	28.4997	+	28.4997i	0.0976017	+	0.0976017i
$293$	320.705	−	320.705i	1.09456	−	1.09456i	0.0995214	−	0.995035i	$-0.468269\pi$
$293$	320.705	−	320.705i	1.09456	−	1.09456i	0.995035	−	0.0995214i	$-0.0317312\pi$
$294$			119.957i			0.408019i
$295$	13.6122	+	54.1909i	0.0461431	+	0.183698i
$296$	−192.089			−0.648949
$297$	−22.5655	−	22.5655i	−0.0759780	−	0.0759780i
$298$	209.754	−	209.754i	0.703871	−	0.703871i
$299$			12.1936i			0.0407813i
$300$	82.9067	+	25.0297i	0.276356	+	0.0834323i
$301$	6.17657			0.0205202
$302$	−5.19070	−	5.19070i	−0.0171878	−	0.0171878i
$303$	57.5256	−	57.5256i	0.189854	−	0.189854i
$304$			113.727i			0.374103i
$305$	−388.959	+	97.7028i	−1.27528	+	0.320337i
$306$	−31.2876			−0.102247
$307$	45.3708	+	45.3708i	0.147788	+	0.147788i	0.777129	−	0.629341i	$-0.216675\pi$
$307$	45.3708	+	45.3708i	0.147788	+	0.147788i	−0.629341	+	0.777129i	$0.716675\pi$
$308$	1.44237	−	1.44237i	0.00468301	−	0.00468301i
$309$		−	40.4904i		−	0.131037i
$310$	−150.097	−	89.8298i	−0.484184	−	0.289773i
$311$	−197.722			−0.635761			−0.317881	−	0.948131i	$-0.602971\pi$
$311$	−197.722			−0.635761			−0.317881	+	0.948131i	$0.602971\pi$
$312$	−8.80763	−	8.80763i	−0.0282296	−	0.0282296i
$313$	−330.259	+	330.259i	−1.05514	+	1.05514i	−0.0567518	+	0.998388i	$0.518074\pi$
$313$	−330.259	+	330.259i	−1.05514	+	1.05514i	−0.998388	+	0.0567518i	$0.981926\pi$
$314$			4.68306i			0.0149142i
$315$	1.27922	−	2.13745i	0.00406101	−	0.00678556i
$316$	−132.626			−0.419702
$317$	−106.236	−	106.236i	−0.335128	−	0.335128i	0.519402	−	0.854530i	$-0.326155\pi$
$317$	−106.236	−	106.236i	−0.335128	−	0.335128i	−0.854530	+	0.519402i	$0.826155\pi$
$318$	10.4026	−	10.4026i	0.0327125	−	0.0327125i
$319$			209.797i			0.657671i
$320$	9.74488	+	38.7948i	0.0304527	+	0.121234i
$321$	−219.622			−0.684179
$322$	−0.796428	−	0.796428i	−0.00247338	−	0.00247338i
$323$	148.261	−	148.261i	0.459012	−	0.459012i
$324$		−	18.0000i		−	0.0555556i
$325$	18.3710	−	60.8509i	0.0565262	−	0.187234i
$326$	−160.171			−0.491321
$327$	25.6599	+	25.6599i	0.0784705	+	0.0784705i
$328$	−125.100	+	125.100i	−0.381402	+	0.381402i
$329$			10.9041i			0.0331432i
$330$	72.9520	−	18.3248i	0.221067	−	0.0555298i
$331$	−273.823			−0.827259			−0.413630	−	0.910445i	$-0.635739\pi$
$331$	−273.823			−0.827259			−0.413630	+	0.910445i	$0.635739\pi$
$332$	−227.576	−	227.576i	−0.685470	−	0.685470i
$333$	−144.067	+	144.067i	−0.432633	+	0.432633i
$334$			425.460i			1.27383i
$335$	453.333	+	271.310i	1.35323	+	0.809880i
$336$	1.15054			0.00342424
$337$	136.789	+	136.789i	0.405901	+	0.405901i	0.880306	−	0.474406i	$-0.157337\pi$
$337$	136.789	+	136.789i	0.405901	+	0.405901i	−0.474406	+	0.880306i	$0.657337\pi$
$338$	162.535	−	162.535i	0.480874	−	0.480874i
$339$		−	330.348i		−	0.974477i
$340$	37.8710	−	63.2788i	0.111385	−	0.186114i
$341$	−151.930			−0.445542
$342$	85.2956	+	85.2956i	0.249402	+	0.249402i
$343$	−11.5046	+	11.5046i	−0.0335411	+	0.0335411i
$344$			105.199i			0.305810i
$345$	−10.1184	−	40.2817i	−0.0293286	−	0.116759i
$346$	307.860			0.889769
$347$	234.167	+	234.167i	0.674832	+	0.674832i	0.958826	−	0.283994i	$-0.0916597\pi$
$347$	234.167	+	234.167i	0.674832	+	0.674832i	−0.283994	+	0.958826i	$0.591660\pi$
$348$	−83.6753	+	83.6753i	−0.240446	+	0.240446i
$349$		−	99.7358i		−	0.285776i	−0.989739	−	0.142888i	$-0.954361\pi$
$349$		−	99.7358i		−	0.285776i	0.989739	−	0.142888i	$-0.0456389\pi$
$350$	2.77458	+	5.17440i	0.00792738	+	0.0147840i
$351$	−13.2114			−0.0376395
$352$	24.5662	+	24.5662i	0.0697903	+	0.0697903i
$353$	−380.797	+	380.797i	−1.07874	+	1.07874i	−0.0821221	+	0.996622i	$0.526170\pi$
$353$	−380.797	+	380.797i	−1.07874	+	1.07874i	−0.996622	+	0.0821221i	$0.973830\pi$
$354$			27.3727i			0.0773241i
$355$	−26.6266	+	6.68834i	−0.0750045	+	0.0188404i
$356$	71.6336			0.201218
$357$	−1.49991	−	1.49991i	−0.00420142	−	0.00420142i
$358$	−119.472	+	119.472i	−0.333720	+	0.333720i
$359$		−	219.427i		−	0.611218i	−0.952157	−	0.305609i	$-0.901140\pi$
$359$		−	219.427i		−	0.611218i	0.952157	−	0.305609i	$-0.0988600\pi$
$360$	36.4048	+	21.7874i	0.101124	+	0.0605207i
$361$	−447.371			−1.23925
$362$	−104.780	−	104.780i	−0.289447	−	0.289447i
$363$	−101.998	+	101.998i	−0.280988	+	0.280988i
$364$		−	0.844464i		−	0.00231996i
$365$	−51.7446	+	86.4604i	−0.141766	+	0.236878i
$366$	−196.470			−0.536803
$367$	68.5769	+	68.5769i	0.186858	+	0.186858i	0.794336	−	0.607478i	$-0.207819\pi$
$367$	68.5769	+	68.5769i	0.186858	+	0.186858i	−0.607478	+	0.794336i	$0.707819\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			187.650i			0.508536i
$370$	−116.993	−	465.754i	−0.316197	−	1.25879i
$371$	0.997384			0.00268837
$372$	−60.5955	−	60.5955i	−0.162891	−	0.162891i
$373$	−273.348	+	273.348i	−0.732835	+	0.732835i	−0.971180	−	0.238345i	$-0.923395\pi$
$373$	−273.348	+	273.348i	−0.732835	+	0.732835i	0.238345	+	0.971180i	$0.423395\pi$
$374$		−	64.0514i		−	0.171261i
$375$	−10.1942	+	216.266i	−0.0271845	+	0.576710i
$376$	−185.718			−0.493930
$377$	61.4151	+	61.4151i	0.162905	+	0.162905i
$378$	0.862908	−	0.862908i	0.00228283	−	0.00228283i
$379$			63.4309i			0.167364i	0.996493	+	0.0836819i	$0.0266680\pi$
$379$			63.4309i			0.167364i	−0.996493	+	0.0836819i	$0.973332\pi$
$380$	−275.752	+	69.2663i	−0.725664	+	0.182280i
$381$	36.0027			0.0944952
$382$	−243.162	−	243.162i	−0.636549	−	0.636549i
$383$	205.490	−	205.490i	0.536528	−	0.536528i	−0.385979	−	0.922507i	$-0.626136\pi$
$383$	205.490	−	205.490i	0.536528	−	0.536528i	0.922507	+	0.385979i	$0.126136\pi$
$384$			19.5959i			0.0510310i
$385$	4.37575	+	2.61879i	0.0113656	+	0.00680205i
$386$	−255.509			−0.661940
$387$	78.8989	+	78.8989i	0.203873	+	0.203873i
$388$	187.426	−	187.426i	0.483058	−	0.483058i
$389$			223.663i			0.574968i	0.957785	+	0.287484i	$0.0928188\pi$
$389$			223.663i			0.574968i	−0.957785	+	0.287484i	$0.907181\pi$
$390$	15.9913	−	26.7200i	0.0410034	−	0.0685128i
$391$	−35.3672			−0.0904531
$392$	−97.9448	−	97.9448i	−0.249859	−	0.249859i
$393$	−84.3935	+	84.3935i	−0.214742	+	0.214742i
$394$			317.330i			0.805407i
$395$	−80.7764	−	321.575i	−0.204497	−	0.814113i
$396$	36.8493			0.0930537
$397$	−364.562	−	364.562i	−0.918293	−	0.918293i	0.0786121	−	0.996905i	$-0.474951\pi$
$397$	−364.562	−	364.562i	−0.918293	−	0.918293i	−0.996905	+	0.0786121i	$0.974951\pi$
$398$	185.886	−	185.886i	0.467049	−	0.467049i
$399$			8.17803i			0.0204963i
$400$	−88.1297	+	47.2563i	−0.220324	+	0.118141i
$401$	−66.6545			−0.166221			−0.0831103	−	0.996540i	$-0.526485\pi$
$401$	−66.6545			−0.166221			−0.0831103	+	0.996540i	$0.526485\pi$
$402$	183.015	+	183.015i	0.455261	+	0.455261i
$403$	−44.4753	+	44.4753i	−0.110360	+	0.110360i
$404$			93.9389i			0.232522i
$405$	43.6442	−	10.9630i	0.107763	−	0.0270691i
$406$	−8.02268			−0.0197603
$407$	−294.931	−	294.931i	−0.724646	−	0.724646i
$408$	25.5462	−	25.5462i	0.0626133	−	0.0626133i
$409$		−	383.884i		−	0.938592i	−0.883041	−	0.469296i	$-0.844508\pi$
$409$		−	383.884i		−	0.938592i	0.883041	−	0.469296i	$-0.155492\pi$
$410$	−379.519	−	227.134i	−0.925656	−	0.553985i
$411$	363.394			0.884171
$412$	33.0602	+	33.0602i	0.0802433	+	0.0802433i
$413$	−1.31223	+	1.31223i	−0.00317731	+	0.00317731i
$414$		−	20.3470i		−	0.0491473i
$415$	413.192	−	690.404i	0.995642	−	1.66362i
$416$	14.3828			0.0345740
$417$	−208.407	−	208.407i	−0.499777	−	0.499777i
$418$	−174.616	+	174.616i	−0.417741	+	0.417741i
$419$		−	557.095i		−	1.32958i	−0.747030	−	0.664791i	$-0.768521\pi$
$419$		−	557.095i		−	1.32958i	0.747030	−	0.664791i	$-0.231479\pi$
$420$	0.700745	+	2.78970i	0.00166844	+	0.00664214i
$421$	−104.927			−0.249233			−0.124617	−	0.992205i	$-0.539770\pi$
$421$	−104.927			−0.249233			−0.124617	+	0.992205i	$0.539770\pi$
$422$	19.0575	+	19.0575i	0.0451599	+	0.0451599i
$423$	−139.288	+	139.288i	−0.329286	+	0.329286i
$424$			16.9873i			0.0400644i
$425$	176.496	+	53.2845i	0.415285	+	0.125375i
$426$	−13.4495			−0.0315717
$427$	−9.41865	−	9.41865i	−0.0220577	−	0.0220577i
$428$	179.320	−	179.320i	0.418972	−	0.418972i
$429$		−	27.0462i		−	0.0630448i
$430$	−255.072	+	64.0717i	−0.593192	+	0.149004i
$431$	238.158			0.552571			0.276286	−	0.961076i	$-0.410896\pi$
$431$	238.158			0.552571			0.276286	+	0.961076i	$0.410896\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−495.395	+	495.395i	−1.14410	+	1.14410i	−0.156407	+	0.987693i	$0.549991\pi$
$433$	−495.395	+	495.395i	−1.14410	+	1.14410i	−0.987693	+	0.156407i	$0.950009\pi$
$434$		−	5.80982i		−	0.0133867i
$435$	−253.848	−	151.923i	−0.583559	−	0.349247i
$436$	−41.9024			−0.0961064
$437$	96.4171	+	96.4171i	0.220634	+	0.220634i
$438$	−34.9049	+	34.9049i	−0.0796915	+	0.0796915i
$439$			689.182i			1.56989i	0.619564	+	0.784946i	$0.287309\pi$
$439$			689.182i			1.56989i	−0.619564	+	0.784946i	$0.712691\pi$
$440$	−44.6029	+	74.5272i	−0.101370	+	0.169380i
$441$	−146.917			−0.333146
$442$	−18.7501	−	18.7501i	−0.0424212	−	0.0424212i
$443$	87.5468	−	87.5468i	0.197623	−	0.197623i	−0.601357	−	0.798980i	$-0.705373\pi$
$443$	87.5468	−	87.5468i	0.197623	−	0.197623i	0.798980	+	0.601357i	$0.205373\pi$
$444$		−	235.260i		−	0.529865i
$445$	43.6288	+	173.688i	0.0980422	+	0.390310i
$446$	−318.332			−0.713748
$447$	256.895	+	256.895i	0.574708	+	0.574708i
$448$	−0.939416	+	0.939416i	−0.00209691	+	0.00209691i
$449$			387.507i			0.863045i	0.902102	+	0.431523i	$0.142023\pi$
$449$			387.507i			0.863045i	−0.902102	+	0.431523i	$0.857977\pi$
$450$	−30.6550	+	101.540i	−0.0681222	+	0.225643i
$451$	−384.153			−0.851781
$452$	269.728	+	269.728i	0.596743	+	0.596743i
$453$	6.35729	−	6.35729i	0.0140337	−	0.0140337i
$454$		−	5.00469i		−	0.0110235i
$455$	2.04755	−	0.514325i	0.00450011	−	0.00113038i
$456$	−139.287			−0.305454
$457$	277.891	+	277.891i	0.608077	+	0.608077i	0.942443	−	0.334366i	$-0.108522\pi$
$457$	277.891	+	277.891i	0.608077	+	0.608077i	−0.334366	+	0.942443i	$0.608522\pi$
$458$	−108.398	+	108.398i	−0.236677	+	0.236677i
$459$		−	38.3193i		−	0.0834844i
$460$	41.1515	+	24.6283i	0.0894598	+	0.0535397i
$461$	15.1488			0.0328607			0.0164304	−	0.999865i	$-0.494770\pi$
$461$	15.1488			0.0328607			0.0164304	+	0.999865i	$0.494770\pi$
$462$	1.76653	+	1.76653i	0.00382366	+	0.00382366i
$463$	−384.007	+	384.007i	−0.829390	+	0.829390i	−0.987432	−	0.158043i	$-0.949482\pi$
$463$	−384.007	+	384.007i	−0.829390	+	0.829390i	0.158043	+	0.987432i	$0.449482\pi$
$464$		−	136.641i		−	0.294485i
$465$	110.019	−	183.831i	0.236599	−	0.395335i
$466$	−49.5319			−0.106292
$467$	−296.796	−	296.796i	−0.635538	−	0.635538i	0.313914	−	0.949452i	$-0.398360\pi$
$467$	−296.796	−	296.796i	−0.635538	−	0.635538i	−0.949452	+	0.313914i	$0.898360\pi$
$468$	10.7871	−	10.7871i	0.0230494	−	0.0230494i
$469$			17.5472i			0.0374141i
$470$	−113.112	−	450.305i	−0.240664	−	0.958095i
$471$	−5.73555			−0.0121774
$472$	−22.3497	−	22.3497i	−0.0473511	−	0.0473511i
$473$	−161.520	+	161.520i	−0.341481	+	0.341481i
$474$		−	162.433i		−	0.342685i
$475$	−335.896	−	626.423i	−0.707150	−	1.31878i
$476$	2.44934			0.00514567
$477$	12.7405	+	12.7405i	0.0267096	+	0.0267096i
$478$	264.476	−	264.476i	0.553296	−	0.553296i
$479$			769.722i			1.60694i	0.595348	+	0.803468i	$0.297014\pi$
$479$			769.722i			1.60694i	−0.595348	+	0.803468i	$0.702986\pi$
$480$	−47.5137	+	11.9350i	−0.0989870	+	0.0248646i
$481$	−172.674			−0.358989
$482$	−467.027	−	467.027i	−0.968936	−	0.968936i
$483$	0.975421	−	0.975421i	0.00201951	−	0.00201951i
$484$		−	166.563i		−	0.344138i
$485$	568.601	+	340.295i	1.17237	+	0.701640i
$486$	22.0454			0.0453609
$487$	302.447	+	302.447i	0.621041	+	0.621041i	0.945798	−	0.324757i	$-0.105282\pi$
$487$	302.447	+	302.447i	0.621041	+	0.621041i	−0.324757	+	0.945798i	$0.605282\pi$
$488$	160.417	−	160.417i	0.328724	−	0.328724i
$489$		−	196.168i		−	0.401162i
$490$	177.831	−	297.138i	0.362920	−	0.606405i
$491$	317.270			0.646171			0.323086	−	0.946370i	$-0.395280\pi$
$491$	317.270			0.646171			0.323086	+	0.946370i	$0.395280\pi$
$492$	−153.215	−	153.215i	−0.311413	−	0.311413i
$493$	−178.132	+	178.132i	−0.361323	+	0.361323i
$494$			102.232i			0.206948i
$495$	22.4432	+	89.3475i	0.0453399	+	0.180500i
$496$	98.9521			0.199500
$497$	−0.644763	−	0.644763i	−0.00129731	−	0.00129731i
$498$	278.722	−	278.722i	0.559684	−	0.559684i
$499$			524.718i			1.05154i	0.850627	+	0.525769i	$0.176223\pi$
$499$			524.718i			1.05154i	−0.850627	+	0.525769i	$0.823777\pi$
$500$	−168.257	−	184.904i	−0.336514	−	0.369808i
$501$	−521.080			−1.04008
$502$	−204.851	−	204.851i	−0.408070	−	0.408070i
$503$	325.215	−	325.215i	0.646551	−	0.646551i	−0.305607	−	0.952158i	$-0.598859\pi$
$503$	325.215	−	325.215i	0.646551	−	0.646551i	0.952158	+	0.305607i	$0.0988594\pi$
$504$			1.40912i			0.00279588i
$505$	−227.771	+	57.2140i	−0.451033	+	0.113295i
$506$	41.6540			0.0823201
$507$	199.064	+	199.064i	0.392632	+	0.392632i
$508$	−29.3961	+	29.3961i	−0.0578663	+	0.0578663i
$509$			104.801i			0.205897i	0.994687	+	0.102948i	$0.0328276\pi$
$509$			104.801i			0.205897i	−0.994687	+	0.102948i	$0.967172\pi$
$510$	77.5004	+	46.3823i	0.151962	+	0.0909456i
$511$	−3.34663			−0.00654918
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−104.465	+	104.465i	−0.203636	+	0.203636i
$514$			285.938i			0.556301i
$515$	−60.0248	+	100.296i	−0.116553	+	0.194749i
$516$	−128.841			−0.249693
$517$	−285.148	−	285.148i	−0.551544	−	0.551544i
$518$	11.2782	−	11.2782i	0.0217726	−	0.0217726i
$519$			377.050i			0.726493i
$520$	8.75992	+	34.8736i	0.0168460	+	0.0670647i
$521$	678.468			1.30224			0.651121	−	0.758974i	$-0.274299\pi$
$521$	678.468			1.30224			0.651121	+	0.758974i	$0.274299\pi$
$522$	−102.481	−	102.481i	−0.196324	−	0.196324i
$523$	−494.733	+	494.733i	−0.945952	+	0.945952i	−0.998612	−	0.0526604i	$-0.983230\pi$
$523$	−494.733	+	494.733i	−0.945952	+	0.945952i	0.0526604	+	0.998612i	$0.483230\pi$
$524$		−	137.814i		−	0.263004i
$525$	−6.33732	+	3.39816i	−0.0120711	+	0.00647268i
$526$	−674.361			−1.28206
$527$	−128.999	−	128.999i	−0.244780	−	0.244780i
$528$	−30.0873	+	30.0873i	−0.0569835	+	0.0569835i
$529$		−	23.0000i		−	0.0434783i
$530$	−41.1887	+	10.3462i	−0.0777146	+	0.0195212i
$531$	−33.5246			−0.0631348
$532$	−6.67733	−	6.67733i	−0.0125514	−	0.0125514i
$533$	−112.455	+	112.455i	−0.210986	+	0.210986i
$534$			87.7328i			0.164294i
$535$	544.009	+	325.578i	1.01684	+	0.608556i
$536$	−298.862			−0.557578
$537$	−146.322	−	146.322i	−0.272481	−	0.272481i
$538$	284.631	−	284.631i	0.529054	−	0.529054i
$539$		−	300.766i		−	0.558008i
$540$	−26.6841	+	44.5866i	−0.0494149	+	0.0825677i
$541$	−981.574			−1.81437			−0.907185	−	0.420732i	$-0.861773\pi$
$541$	−981.574			−1.81437			−0.907185	+	0.420732i	$0.861773\pi$
$542$	−19.1966	−	19.1966i	−0.0354180	−	0.0354180i
$543$	128.329	−	128.329i	0.236333	−	0.236333i
$544$			41.7168i			0.0766853i
$545$	−25.5209	−	101.600i	−0.0468273	−	0.186421i
$546$	1.03425			0.00189424
$547$	−420.807	−	420.807i	−0.769300	−	0.769300i	0.208683	−	0.977983i	$-0.433082\pi$
$547$	−420.807	−	420.807i	−0.769300	−	0.769300i	−0.977983	+	0.208683i	$0.933082\pi$
$548$	−296.710	+	296.710i	−0.541442	+	0.541442i
$549$		−	240.626i		−	0.438298i
$550$	−207.870	−	62.7563i	−0.377945	−	0.114102i
$551$	971.241			1.76269
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	7.78692	−	7.78692i	0.0140812	−	0.0140812i
$554$			76.6586i			0.138373i
$555$	570.429	−	143.286i	1.02780	−	0.258173i
$556$	340.327			0.612099
$557$	113.406	+	113.406i	0.203602	+	0.203602i	0.801541	−	0.597940i	$-0.204014\pi$
$557$	113.406	+	113.406i	0.203602	+	0.203602i	−0.597940	+	0.801541i	$0.704014\pi$
$558$	74.2141	−	74.2141i	0.133000	−	0.133000i
$559$			94.5656i			0.169169i
$560$	−2.84993	−	1.70562i	−0.00508917	−	0.00304575i
$561$	78.4467			0.139834
$562$	222.591	+	222.591i	0.396069	+	0.396069i
$563$	265.151	−	265.151i	0.470962	−	0.470962i	−0.431264	−	0.902226i	$-0.641932\pi$
$563$	265.151	−	265.151i	0.470962	−	0.470962i	0.902226	+	0.431264i	$0.141932\pi$
$564$		−	227.457i		−	0.403292i
$565$	−489.723	+	818.282i	−0.866767	+	1.44829i
$566$	−678.800			−1.19929
$567$	1.05684	+	1.05684i	0.00186392	+	0.00186392i
$568$	10.9815	−	10.9815i	0.0193336	−	0.0193336i
$569$			262.710i			0.461705i	0.972989	+	0.230852i	$0.0741515\pi$
$569$			262.710i			0.461705i	−0.972989	+	0.230852i	$0.925849\pi$
$570$	−84.8335	−	337.726i	−0.148831	−	0.592502i
$571$	311.028			0.544707			0.272354	−	0.962197i	$-0.412198\pi$
$571$	311.028			0.544707			0.272354	+	0.962197i	$0.412198\pi$
$572$	22.0832	+	22.0832i	0.0386069	+	0.0386069i
$573$	297.811	−	297.811i	0.519740	−	0.519740i
$574$		−	14.6901i		−	0.0255925i
$575$	−34.6520	+	114.779i	−0.0602644	+	0.199616i
$576$	−24.0000			−0.0416667
$577$	639.863	+	639.863i	1.10895	+	1.10895i	0.993289	+	0.115658i	$0.0368978\pi$
$577$	639.863	+	639.863i	1.10895	+	1.10895i	0.115658	+	0.993289i	$0.463102\pi$
$578$	−234.616	+	234.616i	−0.405910	+	0.405910i
$579$		−	312.933i		−	0.540472i
$580$	331.311	−	83.2220i	0.571225	−	0.143486i
$581$	26.7235			0.0459958
$582$	229.549	+	229.549i	0.394415	+	0.394415i
$583$	−26.0821	+	26.0821i	−0.0447377	+	0.0447377i
$584$		−	56.9994i		−	0.0976017i
$585$	32.7252	+	19.5853i	0.0559404	+	0.0334791i
$586$	−641.410			−1.09456
$587$	−210.805	−	210.805i	−0.359124	−	0.359124i	0.504366	−	0.863490i	$-0.331726\pi$
$587$	−210.805	−	210.805i	−0.359124	−	0.359124i	−0.863490	+	0.504366i	$0.831726\pi$
$588$	119.957	−	119.957i	0.204009	−	0.204009i
$589$			703.348i			1.19414i
$590$	40.5786	−	67.8031i	0.0687774	−	0.114920i
$591$	−388.649			−0.657612
$592$	192.089	+	192.089i	0.324475	+	0.324475i
$593$	−20.9100	+	20.9100i	−0.0352615	+	0.0352615i	−0.724518	−	0.689256i	$-0.757937\pi$
$593$	−20.9100	+	20.9100i	−0.0352615	+	0.0352615i	0.689256	+	0.724518i	$0.257937\pi$
$594$			45.1310i			0.0759780i
$595$	1.49178	+	5.93885i	0.00250720	+	0.00998127i
$596$	−419.507			−0.703871
$597$	227.662	+	227.662i	0.381344	+	0.381344i
$598$	12.1936	−	12.1936i	0.0203907	−	0.0203907i
$599$		−	290.370i		−	0.484759i	−0.970182	−	0.242379i	$-0.922072\pi$
$599$		−	290.370i		−	0.484759i	0.970182	−	0.242379i	$-0.0779278\pi$
$600$	−57.8770	−	107.936i	−0.0964616	−	0.179894i
$601$	240.612			0.400353			0.200177	−	0.979760i	$-0.435848\pi$
$601$	240.612			0.400353			0.200177	+	0.979760i	$0.435848\pi$
$602$	−6.17657	−	6.17657i	−0.0102601	−	0.0102601i
$603$	−224.146	+	224.146i	−0.371719	+	0.371719i
$604$			10.3814i			0.0171878i
$605$	403.861	−	101.446i	0.667539	−	0.167679i
$606$	−115.051			−0.189854
$607$	−311.886	−	311.886i	−0.513816	−	0.513816i	0.401877	−	0.915693i	$-0.368358\pi$
$607$	−311.886	−	311.886i	−0.513816	−	0.513816i	−0.915693	+	0.401877i	$0.868358\pi$
$608$	113.727	−	113.727i	0.187052	−	0.187052i
$609$		−	9.82573i		−	0.0161342i
$610$	486.662	+	291.257i	0.797807	+	0.477470i
$611$	−166.946			−0.273234
$612$	31.2876	+	31.2876i	0.0511236	+	0.0511236i
$613$	−815.318	+	815.318i	−1.33005	+	1.33005i	−0.424722	+	0.905324i	$0.639628\pi$
$613$	−815.318	+	815.318i	−1.33005	+	1.33005i	−0.905324	+	0.424722i	$0.860372\pi$
$614$		−	90.7416i		−	0.147788i
$615$	278.181	−	464.814i	0.452327	−	0.755795i
$616$	−2.88473			−0.00468301
$617$	169.873	+	169.873i	0.275321	+	0.275321i	0.831238	−	0.555917i	$-0.187633\pi$
$617$	169.873	+	169.873i	0.275321	+	0.275321i	−0.555917	+	0.831238i	$0.687633\pi$
$618$	−40.4904	+	40.4904i	−0.0655184	+	0.0655184i
$619$		−	541.211i		−	0.874331i	−0.899381	−	0.437166i	$-0.855982\pi$
$619$		−	541.211i		−	0.874331i	0.899381	−	0.437166i	$-0.144018\pi$
$620$	60.2673	+	239.927i	0.0972053	+	0.386979i
$621$	24.9199			0.0401286
$622$	197.722	+	197.722i	0.317881	+	0.317881i
$623$	−4.20586	+	4.20586i	−0.00675097	+	0.00675097i
$624$			17.6153i			0.0282296i
$625$	345.855	−	520.586i	0.553368	−	0.832937i
$626$	660.518			1.05514
$627$	−213.860	−	213.860i	−0.341084	−	0.341084i
$628$	4.68306	−	4.68306i	0.00745709	−	0.00745709i
$629$		−	500.834i		−	0.796238i
$630$	−3.41667	+	0.858234i	−0.00542328	+	0.00136228i
$631$	488.542			0.774235			0.387118	−	0.922030i	$-0.373471\pi$
$631$	488.542			0.774235			0.387118	+	0.922030i	$0.373471\pi$
$632$	132.626	+	132.626i	0.209851	+	0.209851i
$633$	−23.3405	+	23.3405i	−0.0368729	+	0.0368729i
$634$			212.471i			0.335128i
$635$	−89.1798	−	53.3721i	−0.140441	−	0.0840506i
$636$	−20.8051			−0.0327125
$637$	−88.0451	−	88.0451i	−0.138218	−	0.138218i
$638$	209.797	−	209.797i	0.328835	−	0.328835i
$639$		−	16.4723i		−	0.0257782i
$640$	29.0499	−	48.5397i	0.0453905	−	0.0758433i
$641$	−914.915			−1.42732			−0.713662	−	0.700490i	$-0.752965\pi$
$641$	−914.915			−1.42732			−0.713662	+	0.700490i	$0.752965\pi$
$642$	219.622	+	219.622i	0.342090	+	0.342090i
$643$	762.346	−	762.346i	1.18561	−	1.18561i	0.207339	−	0.978269i	$-0.433520\pi$
$643$	762.346	−	762.346i	1.18561	−	1.18561i	0.978269	−	0.207339i	$-0.0664804\pi$
$644$			1.59286i			0.00247338i
$645$	−78.4715	−	312.399i	−0.121661	−	0.484339i
$646$	−296.522			−0.459012
$647$	−54.6116	−	54.6116i	−0.0844074	−	0.0844074i	0.663643	−	0.748050i	$-0.269010\pi$
$647$	−54.6116	−	54.6116i	−0.0844074	−	0.0844074i	−0.748050	+	0.663643i	$0.769010\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	68.6310i		−	0.105749i
$650$	−79.2220	+	42.4799i	−0.121880	+	0.0653537i
$651$	7.11555			0.0109302
$652$	160.171	+	160.171i	0.245661	+	0.245661i
$653$	−455.974	+	455.974i	−0.698276	+	0.698276i	−0.964039	−	0.265763i	$-0.914376\pi$
$653$	−455.974	+	455.974i	−0.698276	+	0.698276i	0.265763	+	0.964039i	$0.414376\pi$
$654$		−	51.3197i		−	0.0784705i
$655$	334.154	−	83.9363i	0.510159	−	0.128147i
$656$	250.200			0.381402
$657$	−42.7495	−	42.7495i	−0.0650678	−	0.0650678i
$658$	10.9041	−	10.9041i	0.0165716	−	0.0165716i
$659$			89.6678i			0.136066i	0.997683	+	0.0680332i	$0.0216724\pi$
$659$			89.6678i			0.136066i	−0.997683	+	0.0680332i	$0.978328\pi$
$660$	−91.2768	−	54.6271i	−0.138298	−	0.0827684i
$661$	1014.42			1.53468			0.767338	−	0.641243i	$-0.221581\pi$
$661$	1014.42			1.53468			0.767338	+	0.641243i	$0.221581\pi$
$662$	273.823	+	273.823i	0.413630	+	0.413630i
$663$	22.9641	−	22.9641i	0.0346367	−	0.0346367i
$664$			455.152i			0.685470i
$665$	12.1235	−	20.2572i	0.0182308	−	0.0304620i
$666$	288.133			0.432633
$667$	−115.843	−	115.843i	−0.173678	−	0.173678i
$668$	425.460	−	425.460i	0.636917	−	0.636917i
$669$		−	389.875i		−	0.582773i
$670$	−182.023	−	724.643i	−0.271677	−	1.08156i
$671$	492.604			0.734135
$672$	−1.15054	−	1.15054i	−0.00171212	−	0.00171212i
$673$	150.044	−	150.044i	0.222949	−	0.222949i	−0.586790	−	0.809739i	$-0.699609\pi$
$673$	150.044	−	150.044i	0.222949	−	0.222949i	0.809739	+	0.586790i	$0.199609\pi$
$674$		−	273.577i		−	0.405901i
$675$	−124.360	−	37.5445i	−0.184237	−	0.0556215i
$676$	−325.071			−0.480874
$677$	405.045	+	405.045i	0.598294	+	0.598294i	0.939859	−	0.341564i	$-0.110957\pi$
$677$	405.045	+	405.045i	0.598294	+	0.598294i	−0.341564	+	0.939859i	$0.610957\pi$
$678$	−330.348	+	330.348i	−0.487239	+	0.487239i
$679$			22.0089i			0.0324137i
$680$	−101.150	+	25.4078i	−0.148750	+	0.0373645i
$681$	6.12947			0.00900069
$682$	151.930	+	151.930i	0.222771	+	0.222771i
$683$	285.685	−	285.685i	0.418279	−	0.418279i	−0.466331	−	0.884610i	$-0.654424\pi$
$683$	285.685	−	285.685i	0.418279	−	0.418279i	0.884610	+	0.466331i	$0.154424\pi$
$684$		−	170.591i		−	0.249402i
$685$	−900.139	−	538.713i	−1.31407	−	0.786443i
$686$	23.0092			0.0335411
$687$	−132.760	−	132.760i	−0.193246	−	0.193246i
$688$	105.199	−	105.199i	0.152905	−	0.152905i
$689$			15.2703i			0.0221630i
$690$	−30.1634	+	50.4001i	−0.0437150	+	0.0730437i
$691$	586.921			0.849380			0.424690	−	0.905339i	$-0.360383\pi$
$691$	586.921			0.849380			0.424690	+	0.905339i	$0.360383\pi$
$692$	−307.860	−	307.860i	−0.444885	−	0.444885i
$693$	−2.16355	+	2.16355i	−0.00312200	+	0.00312200i
$694$		−	468.333i		−	0.674832i
$695$	207.278	+	825.183i	0.298242	+	1.18731i
$696$	167.351			0.240446
$697$	−326.173	−	326.173i	−0.467967	−	0.467967i
$698$	−99.7358	+	99.7358i	−0.142888	+	0.142888i
$699$		−	60.6639i		−	0.0867867i
$700$	2.39981	−	7.94898i	0.00342831	−	0.0113557i
$701$	−188.831			−0.269373			−0.134687	−	0.990888i	$-0.543003\pi$
$701$	−188.831			−0.269373			−0.134687	+	0.990888i	$0.543003\pi$
$702$	13.2114	+	13.2114i	0.0188197	+	0.0188197i
$703$	−1365.36	+	1365.36i	−1.94219	+	1.94219i
$704$		−	49.1324i		−	0.0697903i
$705$	551.508	−	138.534i	0.782281	−	0.196501i
$706$	761.594			1.07874
$707$	−5.51548	−	5.51548i	−0.00780125	−	0.00780125i
$708$	27.3727	−	27.3727i	0.0386620	−	0.0386620i
$709$			166.680i			0.235092i	0.993067	+	0.117546i	$0.0375027\pi$
$709$			166.680i			0.235092i	−0.993067	+	0.117546i	$0.962497\pi$
$710$	33.3149	+	19.9383i	0.0469225	+	0.0280821i
$711$	198.939			0.279801
$712$	−71.6336	−	71.6336i	−0.100609	−	0.100609i
$713$	83.8907	−	83.8907i	0.117659	−	0.117659i
$714$			2.99982i			0.00420142i
$715$	−40.0946	+	66.9944i	−0.0560764	+	0.0936984i
$716$	238.944			0.333720
$717$	323.915	+	323.915i	0.451764	+	0.451764i
$718$	−219.427	+	219.427i	−0.305609	+	0.305609i
$719$		−	891.573i		−	1.24002i	−0.784594	−	0.620009i	$-0.787129\pi$
$719$		−	891.573i		−	1.24002i	0.784594	−	0.620009i	$-0.212871\pi$
$720$	−14.6173	−	58.1922i	−0.0203018	−	0.0808225i
$721$	−3.88216			−0.00538441
$722$	447.371	+	447.371i	0.619627	+	0.619627i
$723$	571.989	−	571.989i	0.791133	−	0.791133i
$724$			209.560i			0.289447i
$725$	403.573	+	752.634i	0.556652	+	1.03812i
$726$	203.997			0.280988
$727$	−277.079	−	277.079i	−0.381127	−	0.381127i	0.490381	−	0.871508i	$-0.336858\pi$
$727$	−277.079	−	277.079i	−0.381127	−	0.381127i	−0.871508	+	0.490381i	$0.836858\pi$
$728$	−0.844464	+	0.844464i	−0.00115998	+	0.00115998i
$729$			27.0000i			0.0370370i
$730$	138.205	−	34.7158i	0.189322	−	0.0475558i
$731$	−274.284			−0.375218
$732$	196.470	+	196.470i	0.268402	+	0.268402i
$733$	−746.187	+	746.187i	−1.01799	+	1.01799i	−0.0181547	+	0.999835i	$0.505779\pi$
$733$	−746.187	+	746.187i	−1.01799	+	1.01799i	−0.999835	+	0.0181547i	$0.994221\pi$
$734$		−	137.154i		−	0.186858i
$735$	363.919	+	217.797i	0.495127	+	0.296323i
$736$	−27.1293			−0.0368605
$737$	−458.868	−	458.868i	−0.622617	−	0.622617i
$738$	187.650	−	187.650i	0.254268	−	0.254268i
$739$		−	948.207i		−	1.28309i	−0.767083	−	0.641547i	$-0.778293\pi$
$739$		−	948.207i		−	1.28309i	0.767083	−	0.641547i	$-0.221707\pi$
$740$	−348.761	+	582.746i	−0.471298	+	0.787495i
$741$	−125.209			−0.168973
$742$	−0.997384	−	0.997384i	−0.00134418	−	0.00134418i
$743$	442.342	−	442.342i	0.595346	−	0.595346i	−0.343724	−	0.939071i	$-0.611689\pi$
$743$	442.342	−	442.342i	0.595346	−	0.595346i	0.939071	+	0.343724i	$0.111689\pi$
$744$			121.191i			0.162891i
$745$	−255.503	−	1017.17i	−0.342957	−	1.36533i
$746$	546.695			0.732835
$747$	341.364	+	341.364i	0.456980	+	0.456980i
$748$	−64.0514	+	64.0514i	−0.0856303	+	0.0856303i
$749$			21.0570i			0.0281135i
$750$	226.460	−	206.072i	0.301947	−	0.274763i
$751$	1168.45			1.55586			0.777930	−	0.628351i	$-0.216270\pi$
$751$	1168.45			1.55586			0.777930	+	0.628351i	$0.216270\pi$
$752$	185.718	+	185.718i	0.246965	+	0.246965i
$753$	250.891	−	250.891i	0.333188	−	0.333188i
$754$		−	122.830i		−	0.162905i
$755$	−25.1715	+	6.32285i	−0.0333398	+	0.00837463i
$756$	−1.72582			−0.00228283
$757$	121.372	+	121.372i	0.160332	+	0.160332i	0.782714	−	0.622382i	$-0.213835\pi$
$757$	121.372	+	121.372i	0.160332	+	0.160332i	−0.622382	+	0.782714i	$0.713835\pi$
$758$	63.4309	−	63.4309i	0.0836819	−	0.0836819i
$759$			51.0155i			0.0672141i
$760$	345.018	+	206.486i	0.453972	+	0.271692i
$761$	−503.571			−0.661723			−0.330862	−	0.943679i	$-0.607339\pi$
$761$	−503.571			−0.661723			−0.330862	+	0.943679i	$0.607339\pi$
$762$	−36.0027	−	36.0027i	−0.0472476	−	0.0472476i
$763$	2.46023	−	2.46023i	0.00322442	−	0.00322442i
$764$			486.323i			0.636549i
$765$	−56.8064	+	94.9182i	−0.0742568	+	0.124076i
$766$	−410.980			−0.536528
$767$	−20.0907	−	20.0907i	−0.0261939	−	0.0261939i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	612.600i		−	0.796619i	−0.917251	−	0.398310i	$-0.869597\pi$
$769$		−	612.600i		−	0.796619i	0.917251	−	0.398310i	$-0.130403\pi$
$770$	−1.75696	−	6.99454i	−0.00228177	−	0.00908382i
$771$	−350.202			−0.454217
$772$	255.509	+	255.509i	0.330970	+	0.330970i
$773$	205.059	−	205.059i	0.265276	−	0.265276i	−0.561917	−	0.827194i	$-0.689936\pi$
$773$	205.059	−	205.059i	0.265276	−	0.265276i	0.827194	+	0.561917i	$0.189936\pi$
$774$		−	157.798i		−	0.203873i
$775$	−545.039	+	292.257i	−0.703276	+	0.377106i
$776$	−374.853			−0.483058
$777$	13.8129	+	13.8129i	0.0177773	+	0.0177773i
$778$	223.663	−	223.663i	0.287484	−	0.287484i
$779$			1778.41i			2.28294i
$780$	−42.7113	+	10.7287i	−0.0547581	+	0.0137547i
$781$	33.7217			0.0431776
$782$	35.3672	+	35.3672i	0.0452265	+	0.0452265i
$783$	125.513	−	125.513i	0.160297	−	0.160297i
$784$			195.890i			0.249859i
$785$	14.2071	+	8.50265i	0.0180983	+	0.0108314i
$786$	168.787			0.214742
$787$	−167.255	−	167.255i	−0.212523	−	0.212523i	0.592816	−	0.805338i	$-0.298016\pi$
$787$	−167.255	−	167.255i	−0.212523	−	0.212523i	−0.805338	+	0.592816i	$0.798016\pi$
$788$	317.330	−	317.330i	0.402703	−	0.402703i
$789$		−	825.920i		−	1.04679i
$790$	−240.798	+	402.351i	−0.304808	+	0.509305i
$791$	−31.6733			−0.0400421
$792$	−36.8493	−	36.8493i	−0.0465269	−	0.0465269i
$793$	144.203	−	144.203i	0.181845	−	0.181845i
$794$			729.125i			0.918293i
$795$	−12.6715	−	50.4457i	−0.0159390	−	0.0634537i
$796$	−371.771			−0.467049
$797$	−637.573	−	637.573i	−0.799967	−	0.799967i	0.183123	−	0.983090i	$-0.441379\pi$
$797$	−637.573	−	637.573i	−0.799967	−	0.799967i	−0.983090	+	0.183123i	$0.941379\pi$
$798$	8.17803	−	8.17803i	0.0102482	−	0.0102482i
$799$		−	484.222i		−	0.606034i
$800$	135.386	+	40.8733i	0.169233	+	0.0510916i
$801$	−107.450			−0.134145
$802$	66.6545	+	66.6545i	0.0831103	+	0.0831103i
$803$	87.5161	−	87.5161i	0.108986	−	0.108986i
$804$		−	366.030i		−	0.455261i
$805$	−3.86216	+	0.970137i	−0.00479771	+	0.00120514i
$806$	88.9505			0.110360
$807$	348.601	+	348.601i	0.431971	+	0.431971i
$808$	93.9389	−	93.9389i	0.116261	−	0.116261i
$809$		−	474.971i		−	0.587109i	−0.955942	−	0.293554i	$-0.905162\pi$
$809$		−	474.971i		−	0.587109i	0.955942	−	0.293554i	$-0.0948382\pi$
$810$	−54.6072	−	32.6812i	−0.0674162	−	0.0403471i
$811$	457.901			0.564612			0.282306	−	0.959324i	$-0.408901\pi$
$811$	457.901			0.564612			0.282306	+	0.959324i	$0.408901\pi$
$812$	8.02268	+	8.02268i	0.00988014	+	0.00988014i
$813$	23.5109	−	23.5109i	0.0289187	−	0.0289187i
$814$			589.862i			0.724646i
$815$	−290.809	+	485.915i	−0.356821	+	0.596215i
$816$	−51.0925			−0.0626133
$817$	747.748	+	747.748i	0.915236	+	0.915236i
$818$	−383.884	+	383.884i	−0.469296	+	0.469296i
$819$			1.26670i			0.00154664i
$820$	152.385	+	606.653i	0.185836	+	0.739820i
$821$	1381.89			1.68318			0.841589	−	0.540118i	$-0.181620\pi$
$821$	1381.89			1.68318			0.841589	+	0.540118i	$0.181620\pi$
$822$	−363.394	−	363.394i	−0.442086	−	0.442086i
$823$	−456.704	+	456.704i	−0.554925	+	0.554925i	−0.927858	−	0.372933i	$-0.878352\pi$
$823$	−456.704	+	456.704i	−0.554925	+	0.554925i	0.372933	+	0.927858i	$0.378352\pi$
$824$		−	66.1205i		−	0.0802433i
$825$	76.8605	−	254.588i	0.0931642	−	0.308591i
$826$	2.62446			0.00317731
$827$	−944.758	−	944.758i	−1.14239	−	1.14239i	−0.988012	−	0.154380i	$-0.950662\pi$
$827$	−944.758	−	944.758i	−1.14239	−	1.14239i	−0.154380	−	0.988012i	$-0.549338\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	1642.59i		−	1.98141i	−0.136025	−	0.990705i	$-0.543433\pi$
$829$		−	1642.59i		−	1.98141i	0.136025	−	0.990705i	$-0.456567\pi$
$830$	−1103.60	+	277.213i	−1.32963	+	0.333991i
$831$	−93.8872			−0.112981
$832$	−14.3828	−	14.3828i	−0.0172870	−	0.0172870i
$833$	255.372	−	255.372i	0.306569	−	0.306569i
$834$			416.814i			0.499777i
$835$	1290.73	+	772.475i	1.54579	+	0.925119i
$836$	349.231			0.417741
$837$	90.8933	+	90.8933i	0.108594	+	0.108594i
$838$	−557.095	+	557.095i	−0.664791	+	0.664791i
$839$			336.880i			0.401526i	0.979640	+	0.200763i	$0.0643420\pi$
$839$			336.880i			0.401526i	−0.979640	+	0.200763i	$0.935658\pi$
$840$	2.08895	−	3.49044i	0.00248685	−	0.00415529i
$841$	−325.926			−0.387545
$842$	104.927	+	104.927i	0.124617	+	0.124617i
$843$	−272.617	+	272.617i	−0.323389	+	0.323389i
$844$		−	38.1149i		−	0.0451599i
$845$	−197.986	−	788.192i	−0.234303	−	0.932771i
$846$	278.576			0.329286
$847$	9.77948	+	9.77948i	0.0115460	+	0.0115460i
$848$	16.9873	−	16.9873i	0.0200322	−	0.0200322i
$849$		−	831.357i		−	0.979219i
$850$	−123.212	−	229.781i	−0.144955	−	0.270330i
$851$	325.703			0.382729
$852$	13.4495	+	13.4495i	0.0157859	+	0.0157859i
$853$	305.350	−	305.350i	0.357972	−	0.357972i	−0.505093	−	0.863065i	$-0.668542\pi$
$853$	305.350	−	305.350i	0.357972	−	0.357972i	0.863065	+	0.505093i	$0.168542\pi$
$854$			18.8373i			0.0220577i
$855$	413.628	−	103.899i	0.483776	−	0.121520i
$856$	−358.640			−0.418972
$857$	334.054	+	334.054i	0.389795	+	0.389795i	0.874614	−	0.484819i	$-0.161115\pi$
$857$	334.054	+	334.054i	0.389795	+	0.389795i	−0.484819	+	0.874614i	$0.661115\pi$
$858$	−27.0462	+	27.0462i	−0.0315224	+	0.0315224i
$859$			748.434i			0.871286i	0.900120	+	0.435643i	$0.143479\pi$
$859$			748.434i			0.871286i	−0.900120	+	0.435643i	$0.856521\pi$
$860$	319.144	+	191.001i	0.371098	+	0.222094i
$861$	17.9916			0.0208962
$862$	−238.158	−	238.158i	−0.276286	−	0.276286i
$863$	−354.851	+	354.851i	−0.411183	+	0.411183i	−0.882151	−	0.470968i	$-0.843905\pi$
$863$	−354.851	+	354.851i	−0.411183	+	0.411183i	0.470968	+	0.882151i	$0.343905\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	558.957	−	933.965i	0.646193	−	1.07973i
$866$	990.791			1.14410
$867$	−287.345	−	287.345i	−0.331424	−	0.331424i
$868$	−5.80982	+	5.80982i	−0.00669334	+	0.00669334i
$869$			407.264i			0.468658i
$870$	101.926	+	405.771i	0.117156	+	0.466403i
$871$	−268.654			−0.308444
$872$	41.9024	+	41.9024i	0.0480532	+	0.0480532i
$873$	−281.140	+	281.140i	−0.322038	+	0.322038i
$874$		−	192.834i		−	0.220634i
$875$	20.7353	+	0.977404i	0.0236975	+	0.00111703i
$876$	69.8097			0.0796915
$877$	978.439	+	978.439i	1.11567	+	1.11567i	0.992370	+	0.123296i	$0.0393465\pi$
$877$	978.439	+	978.439i	1.11567	+	1.11567i	0.123296	+	0.992370i	$0.460653\pi$
$878$	689.182	−	689.182i	0.784946	−	0.784946i
$879$		−	785.564i		−	0.893702i
$880$	119.130	−	29.9243i	0.135375	−	0.0340049i
$881$	1376.09			1.56196			0.780981	−	0.624555i	$-0.214720\pi$
$881$	1376.09			1.56196			0.780981	+	0.624555i	$0.214720\pi$
$882$	146.917	+	146.917i	0.166573	+	0.166573i
$883$	−568.323	+	568.323i	−0.643628	+	0.643628i	−0.951445	−	0.307818i	$-0.900401\pi$
$883$	−568.323	+	568.323i	−0.643628	+	0.643628i	0.307818	+	0.951445i	$0.400401\pi$
$884$			37.5003i			0.0424212i
$885$	83.0415	+	49.6985i	0.0938322	+	0.0561565i
$886$	−175.094			−0.197623
$887$	−263.629	−	263.629i	−0.297214	−	0.297214i	0.542708	−	0.839922i	$-0.317399\pi$
$887$	−263.629	−	263.629i	−0.297214	−	0.297214i	−0.839922	+	0.542708i	$0.817399\pi$
$888$	−235.260	+	235.260i	−0.264932	+	0.264932i
$889$		−	3.45189i		−	0.00388289i
$890$	130.059	−	217.317i	0.146134	−	0.244176i
$891$	−55.2739			−0.0620358
$892$	318.332	+	318.332i	0.356874	+	0.356874i
$893$	−1320.07	+	1320.07i	−1.47825	+	1.47825i
$894$		−	513.789i		−	0.574708i
$895$	145.530	+	579.360i	0.162603	+	0.647330i
$896$	1.87883			0.00209691
$897$	14.9341	+	14.9341i	0.0166489	+	0.0166489i
$898$	387.507	−	387.507i	0.431523	−	0.431523i
$899$		−	845.058i		−	0.939998i
$900$	132.194	−	70.8845i	0.146883	−	0.0787606i
$901$	−44.2911			−0.0491577
$902$	384.153	+	384.153i	0.425890	+	0.425890i
$903$	7.56472	−	7.56472i	0.00837733	−	0.00837733i
$904$		−	539.456i		−	0.596743i
$905$	−508.115	+	127.634i	−0.561453	+	0.141032i
$906$	−12.7146			−0.0140337
$907$	−215.247	−	215.247i	−0.237317	−	0.237317i	0.578421	−	0.815738i	$-0.303669\pi$
$907$	−215.247	−	215.247i	−0.237317	−	0.237317i	−0.815738	+	0.578421i	$0.803669\pi$
$908$	−5.00469	+	5.00469i	−0.00551177	+	0.00551177i
$909$		−	140.908i		−	0.155015i
$910$	−2.56188	−	1.53323i	−0.00281525	−	0.00168486i
$911$	1604.01			1.76071			0.880354	−	0.474316i	$-0.157305\pi$
$911$	1604.01			1.76071			0.880354	+	0.474316i	$0.157305\pi$
$912$	139.287	+	139.287i	0.152727	+	0.152727i
$913$	−698.834	+	698.834i	−0.765426	+	0.765426i
$914$		−	555.782i		−	0.608077i
$915$	−356.715	+	596.037i	−0.389853	+	0.651407i
$916$	216.796			0.236677
$917$	8.09154	+	8.09154i	0.00882392	+	0.00882392i
$918$	−38.3193	+	38.3193i	−0.0417422	+	0.0417422i
$919$		−	1253.92i		−	1.36444i	−0.731146	−	0.682221i	$-0.761014\pi$
$919$		−	1253.92i		−	1.36444i	0.731146	−	0.682221i	$-0.238986\pi$
$920$	−16.5232	−	65.7798i	−0.0179601	−	0.0714998i
$921$	111.135			0.120668
$922$	−15.1488	−	15.1488i	−0.0164304	−	0.0164304i
$923$	9.87156	−	9.87156i	0.0106951	−	0.0106951i
$924$		−	3.53306i		−	0.00382366i
$925$	−1625.39	−	490.707i	−1.75717	−	0.530494i
$926$	768.015			0.829390
$927$	−49.5904	−	49.5904i	−0.0534955	−	0.0534955i
$928$	−136.641	+	136.641i	−0.147243	+	0.147243i
$929$			1164.33i			1.25332i	0.779294	+	0.626659i	$0.215578\pi$
$929$			1164.33i			1.25332i	−0.779294	+	0.626659i	$0.784422\pi$
$930$	−293.849	+	73.8120i	−0.315967	+	0.0793678i
$931$	−1392.38			−1.49557
$932$	49.5319	+	49.5319i	0.0531458	+	0.0531458i
$933$	−242.159	+	242.159i	−0.259548	+	0.259548i
$934$			593.592i			0.635538i
$935$	−194.315	−	116.293i	−0.207823	−	0.124378i
$936$	−21.5742			−0.0230494
$937$	859.432	+	859.432i	0.917217	+	0.917217i	0.996826	−	0.0796094i	$-0.0253673\pi$
$937$	859.432	+	859.432i	0.917217	+	0.917217i	−0.0796094	+	0.996826i	$0.525367\pi$
$938$	17.5472	−	17.5472i	0.0187071	−	0.0187071i
$939$			808.966i			0.861518i
$940$	−337.193	+	563.417i	−0.358715	+	0.599380i
$941$	−317.148			−0.337033			−0.168516	−	0.985699i	$-0.553898\pi$
$941$	−317.148			−0.337033			−0.168516	+	0.985699i	$0.553898\pi$
$942$	5.73555	+	5.73555i	0.00608869	+	0.00608869i
$943$	212.117	−	212.117i	0.224938	−	0.224938i
$944$			44.6995i			0.0473511i
$945$	−1.05112	−	4.18455i	−0.00111229	−	0.00442809i
$946$	323.041			0.341481
$947$	−1135.72	−	1135.72i	−1.19929	−	1.19929i	−0.974381	−	0.224906i	$-0.927793\pi$
$947$	−1135.72	−	1135.72i	−1.19929	−	1.19929i	−0.224906	−	0.974381i	$-0.572207\pi$
$948$	−162.433	+	162.433i	−0.171343	+	0.171343i
$949$		−	51.2382i		−	0.0539918i
$950$	−290.526	+	962.319i	−0.305817	+	1.01297i
$951$	−260.223			−0.273631
$952$	−2.44934	−	2.44934i	−0.00257284	−	0.00257284i
$953$	−373.614	+	373.614i	−0.392040	+	0.392040i	−0.875414	−	0.483374i	$-0.839411\pi$
$953$	−373.614	+	373.614i	−0.392040	+	0.392040i	0.483374	+	0.875414i	$0.339411\pi$
$954$		−	25.4810i		−	0.0267096i
$955$	−1179.18	+	296.198i	−1.23474	+	0.310154i
$956$	−528.951			−0.553296
$957$	256.948	+	256.948i	0.268493	+	0.268493i
$958$	769.722	−	769.722i	0.803468	−	0.803468i
$959$		−	34.8418i		−	0.0363314i
$960$	59.4487	+	35.5788i	0.0619258	+	0.0370612i
$961$	−349.030			−0.363194
$962$	172.674	+	172.674i	0.179494	+	0.179494i
$963$	−268.980	+	268.980i	−0.279315	+	0.279315i
$964$			934.055i			0.968936i
$965$	−463.907	+	775.146i	−0.480733	+	0.803260i
$966$	−1.95084			−0.00201951
$967$	717.234	+	717.234i	0.741711	+	0.741711i	0.972907	−	0.231196i	$-0.0742640\pi$
$967$	717.234	+	717.234i	0.741711	+	0.741711i	−0.231196	+	0.972907i	$0.574264\pi$
$968$	−166.563	+	166.563i	−0.172069	+	0.172069i
$969$		−	363.163i		−	0.374782i
$970$	−228.306	−	908.896i	−0.235367	−	0.937006i
$971$	−853.079			−0.878557			−0.439279	−	0.898351i	$-0.644766\pi$
$971$	−853.079			−0.878557			−0.439279	+	0.898351i	$0.644766\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	−19.9818	+	19.9818i	−0.0205363	+	0.0205363i
$974$		−	604.894i		−	0.621041i
$975$	−52.0271	−	97.0267i	−0.0533611	−	0.0995146i
$976$	−320.834			−0.328724
$977$	663.800	+	663.800i	0.679427	+	0.679427i	0.959871	−	0.280443i	$-0.0904815\pi$
$977$	663.800	+	663.800i	0.679427	+	0.679427i	−0.280443	+	0.959871i	$0.590482\pi$
$978$	−196.168	+	196.168i	−0.200581	+	0.200581i
$979$		−	219.970i		−	0.224689i
$980$	−474.969	+	119.308i	−0.484662	+	0.121742i
$981$	62.8536			0.0640709
$982$	−317.270	−	317.270i	−0.323086	−	0.323086i
$983$	1209.46	−	1209.46i	1.23038	−	1.23038i	0.266557	−	0.963819i	$-0.414114\pi$
$983$	1209.46	−	1209.46i	1.23038	−	1.23038i	0.963819	−	0.266557i	$-0.0858860\pi$
$984$			306.431i			0.311413i
$985$	962.694	+	576.151i	0.977355	+	0.584925i
$986$	356.265			0.361323
$987$	13.3548	+	13.3548i	0.0135307	+	0.0135307i
$988$	102.232	−	102.232i	0.103474	−	0.103474i
$989$		−	178.373i		−	0.180357i
$990$	66.9043	−	111.791i	0.0675801	−	0.112920i
$991$	260.145			0.262508			0.131254	−	0.991349i	$-0.458100\pi$
$991$	260.145			0.262508			0.131254	+	0.991349i	$0.458100\pi$
$992$	−98.9521	−	98.9521i	−0.0997501	−	0.0997501i
$993$	−335.363	+	335.363i	−0.337727	+	0.337727i
$994$			1.28953i			0.00129731i
$995$	−226.429	−	901.424i	−0.227567	−	0.905954i
$996$	−557.445			−0.559684
$997$	152.329	+	152.329i	0.152787	+	0.152787i	0.779362	−	0.626574i	$-0.215543\pi$
$997$	152.329	+	152.329i	0.152787	+	0.152787i	−0.626574	+	0.779362i	$0.715543\pi$
$998$	524.718	−	524.718i	0.525769	−	0.525769i
$999$			352.890i			0.353243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.15	✓	48
5.3	odd	4	inner	690.3.k.b.553.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.15	✓	48	1.1	even	1	trivial
690.3.k.b.553.15	yes	48	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.06746 + 3.63124i) q^{10} +6.14155 q^{11} +(2.44949 + 2.44949i) q^{12} +(1.79785 - 1.79785i) q^{13} +0.234854i q^{14} +(-4.44734 + 7.43109i) q^{15} -4.00000 q^{16} +(5.21460 + 5.21460i) q^{17} +(-3.00000 + 3.00000i) q^{18} -28.4319i q^{19} +(-2.43622 - 9.69870i) q^{20} -0.287636 q^{21} +(-6.14155 - 6.14155i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.0324 - 11.8141i) q^{25} -3.59570 q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.234854 - 0.234854i) q^{28} +34.1603i q^{29} +(11.8784 - 2.98375i) q^{30} -24.7380 q^{31} +(4.00000 + 4.00000i) q^{32} +(7.52183 - 7.52183i) q^{33} -10.4292i q^{34} +(0.712483 + 0.426406i) q^{35} +6.00000 q^{36} +(-48.0222 - 48.0222i) q^{37} +(-28.4319 + 28.4319i) q^{38} -4.40382i q^{39} +(-7.26248 + 12.1349i) q^{40} -62.5499 q^{41} +(0.287636 + 0.287636i) q^{42} +(-26.2996 + 26.2996i) q^{43} +12.2831i q^{44} +(3.65433 + 14.5481i) q^{45} +6.78233 q^{46} +(-46.4294 - 46.4294i) q^{47} +(-4.89898 + 4.89898i) q^{48} -48.9724i q^{49} +(-33.8465 - 10.2183i) q^{50} +12.7731 q^{51} +(3.59570 + 3.59570i) q^{52} +(-4.24683 + 4.24683i) q^{53} +7.34847i q^{54} +(-29.7825 + 7.48108i) q^{55} -0.469708 q^{56} +(-34.8218 - 34.8218i) q^{57} +(34.1603 - 34.1603i) q^{58} -11.1749i q^{59} +(-14.8622 - 8.89469i) q^{60} +80.2086 q^{61} +(24.7380 + 24.7380i) q^{62} +(-0.352281 + 0.352281i) q^{63} -8.00000i q^{64} +(-6.52843 + 10.9084i) q^{65} -15.0437 q^{66} +(-74.7155 - 74.7155i) q^{67} +(-10.4292 + 10.4292i) q^{68} +8.30662i q^{69} +(-0.286078 - 1.13889i) q^{70} +5.49076 q^{71} +(-6.00000 - 6.00000i) q^{72} +(14.2498 - 14.2498i) q^{73} +96.0445i q^{74} +(12.5148 - 41.4533i) q^{75} +56.8637 q^{76} +(-0.721183 - 0.721183i) q^{77} +(-4.40382 + 4.40382i) q^{78} +66.3129i q^{79} +(19.3974 - 4.87244i) q^{80} -9.00000 q^{81} +(62.5499 + 62.5499i) q^{82} +(-113.788 + 113.788i) q^{83} -0.575272i q^{84} +(-31.6394 - 18.9355i) q^{85} +52.5993 q^{86} +(41.8376 + 41.8376i) q^{87} +(12.2831 - 12.2831i) q^{88} -35.8168i q^{89} +(10.8937 - 18.2024i) q^{90} -0.422232 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-30.2978 + 30.2978i) q^{93} +92.8588i q^{94} +(34.6331 + 137.876i) q^{95} +9.79796 q^{96} +(-93.7132 - 93.7132i) q^{97} +(-48.9724 + 48.9724i) q^{98} -18.4246i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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