LMFDB - Embedded newform 645.2.i.g.436.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [645,2,Mod(436,645)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("645.436"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(645, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 645 = 3 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	645.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,2,7,26,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.15035093037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 14 x^{12} - 7 x^{11} + 131 x^{10} - 59 x^{9} + 627 x^{8} - 130 x^{7} + 2078 x^{6} + \cdots + 16 $ x^14 - x^13 + 14x^12 - 7x^11 + 131x^10 - 59x^9 + 627x^8 - 130x^7 + 2078x^6 - 532x^5 + 2313x^4 + 516x^3 + 1396x^2 - 144x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{43}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			436.7
Root			$1.38158 + 2.39297i$ of defining polynomial
Character	$\chi$	$=$	645.436
Dual form			645.2.i.g.466.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.76317 q^{2} +(0.500000 - 0.866025i) q^{3} +5.63508 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.38158 - 2.39297i) q^{6} +(-2.31958 - 4.01763i) q^{7} +10.0443 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.38158 + 2.39297i) q^{10} -3.31850 q^{11} +(2.81754 - 4.88013i) q^{12} +(2.76988 + 4.79757i) q^{13} +(-6.40939 - 11.1014i) q^{14} +(0.500000 + 0.866025i) q^{15} +16.4840 q^{16} +(-0.104426 - 0.180871i) q^{17} +(-1.38158 - 2.39297i) q^{18} +(-2.78387 + 4.82181i) q^{19} +(-2.81754 + 4.88013i) q^{20} -4.63916 q^{21} -9.16957 q^{22} +(1.32568 - 2.29614i) q^{23} +(5.02217 - 8.69865i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.65364 + 13.2565i) q^{26} -1.00000 q^{27} +(-13.0710 - 22.6397i) q^{28} +(2.23071 + 3.86370i) q^{29} +(1.38158 + 2.39297i) q^{30} +(-1.37691 + 2.38487i) q^{31} +25.4593 q^{32} +(-1.65925 + 2.87391i) q^{33} +(-0.288546 - 0.499776i) q^{34} +4.63916 q^{35} +(-2.81754 - 4.88013i) q^{36} +(-3.48096 + 6.02919i) q^{37} +(-7.69230 + 13.3234i) q^{38} +5.53976 q^{39} +(-5.02217 + 8.69865i) q^{40} -5.32258 q^{41} -12.8188 q^{42} +(-4.26733 - 4.97895i) q^{43} -18.7000 q^{44} +1.00000 q^{45} +(3.66307 - 6.34462i) q^{46} +3.76509 q^{47} +(8.24200 - 14.2756i) q^{48} +(-7.26092 + 12.5763i) q^{49} +(-1.38158 - 2.39297i) q^{50} -0.208852 q^{51} +(15.6085 + 27.0347i) q^{52} +(4.30151 - 7.45043i) q^{53} -2.76317 q^{54} +(1.65925 - 2.87391i) q^{55} +(-23.2987 - 40.3545i) q^{56} +(2.78387 + 4.82181i) q^{57} +(6.16381 + 10.6760i) q^{58} +9.40323 q^{59} +(2.81754 + 4.88013i) q^{60} +(-0.465502 - 0.806273i) q^{61} +(-3.80462 + 6.58980i) q^{62} +(-2.31958 + 4.01763i) q^{63} +37.3804 q^{64} -5.53976 q^{65} +(-4.58479 + 7.94108i) q^{66} +(-1.05174 + 1.82167i) q^{67} +(-0.588448 - 1.01922i) q^{68} +(-1.32568 - 2.29614i) q^{69} +12.8188 q^{70} +(-7.09501 - 12.2889i) q^{71} +(-5.02217 - 8.69865i) q^{72} +(-0.919020 - 1.59179i) q^{73} +(-9.61846 + 16.6597i) q^{74} -1.00000 q^{75} +(-15.6873 + 27.1713i) q^{76} +(7.69754 + 13.3325i) q^{77} +15.3073 q^{78} +(-7.44443 - 12.8941i) q^{79} +(-8.24200 + 14.2756i) q^{80} +(-0.500000 + 0.866025i) q^{81} -14.7072 q^{82} +(0.283171 - 0.490467i) q^{83} -26.1421 q^{84} +0.208852 q^{85} +(-11.7913 - 13.7577i) q^{86} +4.46141 q^{87} -33.3322 q^{88} +(5.78172 - 10.0142i) q^{89} +2.76317 q^{90} +(12.8499 - 22.2567i) q^{91} +(7.47031 - 12.9390i) q^{92} +(1.37691 + 2.38487i) q^{93} +10.4036 q^{94} +(-2.78387 - 4.82181i) q^{95} +(12.7297 - 22.0484i) q^{96} +7.14019 q^{97} +(-20.0631 + 34.7503i) q^{98} +(1.65925 + 2.87391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 7 q^{3} + 26 q^{4} - 7 q^{5} + q^{6} + q^{7} + 12 q^{8} - 7 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 2 q^{13} + 4 q^{14} + 7 q^{15} + 50 q^{16} + 3 q^{17} - q^{18} - 21 q^{19} - 13 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) $ 14 * q + 2 * q^2 + 7 * q^3 + 26 * q^4 - 7 * q^5 + q^6 + q^7 + 12 * q^8 - 7 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 2 * q^13 + 4 * q^14 + 7 * q^15 + 50 * q^16 + 3 * q^17 - q^18 - 21 * q^19 - 13 * q^20 + 2 * q^21 + 26 * q^22 + 9 * q^23 + 6 * q^24 - 7 * q^25 + 23 * q^26 - 14 * q^27 - 25 * q^28 - 8 * q^29 + q^30 + 2 * q^31 + 56 * q^32 - 3 * q^33 + 11 * q^34 - 2 * q^35 - 13 * q^36 + 7 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^40 - 20 * q^41 + 8 * q^42 - 14 * q^43 - 64 * q^44 + 14 * q^45 + 8 * q^46 - 12 * q^47 + 25 * q^48 - 40 * q^49 - q^50 + 6 * q^51 - 17 * q^52 + 18 * q^53 - 2 * q^54 + 3 * q^55 - 40 * q^56 + 21 * q^57 + 12 * q^58 - 24 * q^59 + 13 * q^60 - 11 * q^61 - 47 * q^62 + q^63 + 20 * q^64 + 4 * q^65 + 13 * q^66 - 15 * q^67 + 9 * q^68 - 9 * q^69 - 8 * q^70 - 25 * q^71 - 6 * q^72 - 6 * q^73 - 49 * q^74 - 14 * q^75 - 23 * q^76 + 8 * q^77 + 46 * q^78 - 30 * q^79 - 25 * q^80 - 7 * q^81 + 44 * q^82 + 9 * q^83 - 50 * q^84 - 6 * q^85 - 113 * q^86 - 16 * q^87 - 26 * q^88 + 13 * q^89 + 2 * q^90 + 31 * q^91 + 19 * q^92 - 2 * q^93 - 14 * q^94 - 21 * q^95 + 28 * q^96 - 54 * q^97 + 3 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/645\mathbb{Z}\right)^\times$.

$n$	$46$	$431$	$517$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	2.76317			1.95385			0.976927	−	0.213576i	$-0.0685110\pi$
$2$	2.76317			1.95385			0.976927	+	0.213576i	$0.0685110\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	5.63508			2.81754
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.38158	−	2.39297i	0.564029	−	0.976927i
$7$	−2.31958	−	4.01763i	−0.876719	−	1.51852i	−0.854920	−	0.518760i	$-0.826394\pi$
$7$	−2.31958	−	4.01763i	−0.876719	−	1.51852i	−0.0217995	−	0.999762i	$-0.506940\pi$
$8$	10.0443			3.55121
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.38158	+	2.39297i	−0.436895	+	0.756724i
$11$	−3.31850			−1.00057			−0.500283	−	0.865862i	$-0.666771\pi$
$11$	−3.31850			−1.00057			−0.500283	+	0.865862i	$0.666771\pi$
$12$	2.81754	−	4.88013i	0.813354	−	1.40877i
$13$	2.76988	+	4.79757i	0.768226	+	1.33061i	0.938524	+	0.345214i	$0.112194\pi$
$13$	2.76988	+	4.79757i	0.768226	+	1.33061i	−0.170297	+	0.985393i	$0.554473\pi$
$14$	−6.40939	−	11.1014i	−1.71298	−	2.96697i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	16.4840			4.12100
$17$	−0.104426	−	0.180871i	−0.0253270	−	0.0438676i	0.853084	−	0.521773i	$-0.174729\pi$
$17$	−0.104426	−	0.180871i	−0.0253270	−	0.0438676i	−0.878411	+	0.477906i	$0.841396\pi$
$18$	−1.38158	−	2.39297i	−0.325642	−	0.564029i
$19$	−2.78387	+	4.82181i	−0.638664	+	1.10620i	0.347062	+	0.937842i	$0.387179\pi$
$19$	−2.78387	+	4.82181i	−0.638664	+	1.10620i	−0.985726	+	0.168356i	$0.946154\pi$
$20$	−2.81754	+	4.88013i	−0.630021	+	1.09123i
$21$	−4.63916			−1.01235
$22$	−9.16957			−1.95496
$23$	1.32568	−	2.29614i	0.276423	−	0.478779i	−0.694070	−	0.719907i	$-0.744184\pi$
$23$	1.32568	−	2.29614i	0.276423	−	0.478779i	0.970493	+	0.241129i	$0.0775175\pi$
$24$	5.02217	−	8.69865i	1.02515	−	1.77560i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	7.65364	+	13.2565i	1.50100	+	2.59981i
$27$	−1.00000			−0.192450
$28$	−13.0710	−	22.6397i	−2.47019	−	4.27850i
$29$	2.23071	+	3.86370i	0.414232	+	0.717471i	0.995347	−	0.0963503i	$-0.0307169\pi$
$29$	2.23071	+	3.86370i	0.414232	+	0.717471i	−0.581116	+	0.813821i	$0.697384\pi$
$30$	1.38158	+	2.39297i	0.252241	+	0.436895i
$31$	−1.37691	+	2.38487i	−0.247300	+	0.428336i	−0.962776	−	0.270301i	$-0.912877\pi$
$31$	−1.37691	+	2.38487i	−0.247300	+	0.428336i	0.715476	+	0.698638i	$0.246210\pi$
$32$	25.4593			4.50062
$33$	−1.65925	+	2.87391i	−0.288839	+	0.500283i
$34$	−0.288546	−	0.499776i	−0.0494852	−	0.0857109i
$35$	4.63916			0.784162
$36$	−2.81754	−	4.88013i	−0.469590	−	0.813354i
$37$	−3.48096	+	6.02919i	−0.572266	+	0.991193i	0.424067	+	0.905631i	$0.360602\pi$
$37$	−3.48096	+	6.02919i	−0.572266	+	0.991193i	−0.996333	+	0.0855624i	$0.972731\pi$
$38$	−7.69230	+	13.3234i	−1.24786	+	2.16135i
$39$	5.53976			0.887071
$40$	−5.02217	+	8.69865i	−0.794075	+	1.37538i
$41$	−5.32258			−0.831248			−0.415624	−	0.909537i	$-0.636437\pi$
$41$	−5.32258			−0.831248			−0.415624	+	0.909537i	$0.636437\pi$
$42$	−12.8188			−1.97798
$43$	−4.26733	−	4.97895i	−0.650761	−	0.759282i
$43$	−4.26733	−	4.97895i	−0.650761	−	0.759282i
$44$	−18.7000			−2.81914
$45$	1.00000			0.149071
$46$	3.66307	−	6.34462i	0.540090	−	0.935464i
$47$	3.76509			0.549195			0.274597	−	0.961559i	$-0.411455\pi$
$47$	3.76509			0.549195			0.274597	+	0.961559i	$0.411455\pi$
$48$	8.24200	−	14.2756i	1.18963	−	2.06050i
$49$	−7.26092	+	12.5763i	−1.03727	+	1.79661i
$50$	−1.38158	−	2.39297i	−0.195385	−	0.338417i
$51$	−0.208852			−0.0292451
$52$	15.6085	+	27.0347i	2.16451	+	3.74904i
$53$	4.30151	−	7.45043i	0.590858	−	1.02340i	−0.403259	−	0.915086i	$-0.632123\pi$
$53$	4.30151	−	7.45043i	0.590858	−	1.02340i	0.994117	−	0.108310i	$-0.0345440\pi$
$54$	−2.76317			−0.376019
$55$	1.65925	−	2.87391i	0.223733	−	0.387518i
$56$	−23.2987	−	40.3545i	−3.11341	−	5.39259i
$57$	2.78387	+	4.82181i	0.368733	+	0.638664i
$58$	6.16381	+	10.6760i	0.809348	+	1.40183i
$59$	9.40323			1.22420			0.612098	−	0.790782i	$-0.290326\pi$
$59$	9.40323			1.22420			0.612098	+	0.790782i	$0.290326\pi$
$60$	2.81754	+	4.88013i	0.363743	+	0.630021i
$61$	−0.465502	−	0.806273i	−0.0596014	−	0.103233i	0.834685	−	0.550727i	$-0.185650\pi$
$61$	−0.465502	−	0.806273i	−0.0596014	−	0.103233i	−0.894287	+	0.447495i	$0.852316\pi$
$62$	−3.80462	+	6.58980i	−0.483188	+	0.836906i
$63$	−2.31958	+	4.01763i	−0.292240	+	0.506174i
$64$	37.3804			4.67255
$65$	−5.53976			−0.687123
$66$	−4.58479	+	7.94108i	−0.564348	+	0.977480i
$67$	−1.05174	+	1.82167i	−0.128491	+	0.222552i	−0.923092	−	0.384579i	$-0.874347\pi$
$67$	−1.05174	+	1.82167i	−0.128491	+	0.222552i	0.794601	+	0.607132i	$0.207680\pi$
$68$	−0.588448	−	1.01922i	−0.0713598	−	0.123599i
$69$	−1.32568	−	2.29614i	−0.159593	−	0.276423i
$70$	12.8188			1.53214
$71$	−7.09501	−	12.2889i	−0.842023	−	1.45843i	−0.888182	−	0.459492i	$-0.848031\pi$
$71$	−7.09501	−	12.2889i	−0.842023	−	1.45843i	0.0461588	−	0.998934i	$-0.485302\pi$
$72$	−5.02217	−	8.69865i	−0.591868	−	1.02515i
$73$	−0.919020	−	1.59179i	−0.107563	−	0.186305i	0.807219	−	0.590252i	$-0.200971\pi$
$73$	−0.919020	−	1.59179i	−0.107563	−	0.186305i	−0.914783	+	0.403947i	$0.867638\pi$
$74$	−9.61846	+	16.6597i	−1.11812	+	1.93665i
$75$	−1.00000			−0.115470
$76$	−15.6873	+	27.1713i	−1.79946	+	3.11676i
$77$	7.69754	+	13.3325i	0.877216	+	1.51938i
$78$	15.3073			1.73321
$79$	−7.44443	−	12.8941i	−0.837564	−	1.45070i	−0.891926	−	0.452182i	$-0.850646\pi$
$79$	−7.44443	−	12.8941i	−0.837564	−	1.45070i	0.0543615	−	0.998521i	$-0.482688\pi$
$80$	−8.24200	+	14.2756i	−0.921483	+	1.59606i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−14.7072			−1.62414
$83$	0.283171	−	0.490467i	0.0310821	−	0.0538357i	−0.850066	−	0.526676i	$-0.823438\pi$
$83$	0.283171	−	0.490467i	0.0310821	−	0.0538357i	0.881148	+	0.472841i	$0.156771\pi$
$84$	−26.1421			−2.85233
$85$	0.208852			0.0226531
$86$	−11.7913	−	13.7577i	−1.27149	−	1.48353i
$87$	4.46141			0.478314
$88$	−33.3322			−3.55322
$89$	5.78172	−	10.0142i	0.612861	−	1.06151i	−0.377895	−	0.925849i	$-0.623352\pi$
$89$	5.78172	−	10.0142i	0.612861	−	1.06151i	0.990756	−	0.135658i	$-0.0433147\pi$
$90$	2.76317			0.291263
$91$	12.8499	−	22.2567i	1.34704	−	2.33314i
$92$	7.47031	−	12.9390i	0.778834	−	1.34898i
$93$	1.37691	+	2.38487i	0.142779	+	0.247300i
$94$	10.4036			1.07305
$95$	−2.78387	−	4.82181i	−0.285619	−	0.494707i
$96$	12.7297	−	22.0484i	1.29922	−	2.25031i
$97$	7.14019			0.724976			0.362488	−	0.931988i	$-0.381927\pi$
$97$	7.14019			0.724976			0.362488	+	0.931988i	$0.381927\pi$
$98$	−20.0631	+	34.7503i	−2.02668	+	3.51031i
$99$	1.65925	+	2.87391i	0.166761	+	0.288839i
$100$	−2.81754	−	4.88013i	−0.281754	−	0.488013i
$101$	−3.73591	−	6.47079i	−0.371737	−	0.643868i	0.618096	−	0.786103i	$-0.287904\pi$
$101$	−3.73591	−	6.47079i	−0.371737	−	0.643868i	−0.989833	+	0.142235i	$0.954571\pi$
$102$	−0.577092			−0.0571406
$103$	−1.63274	−	2.82800i	−0.160879	−	0.278651i	0.774305	−	0.632812i	$-0.218100\pi$
$103$	−1.63274	−	2.82800i	−0.160879	−	0.278651i	−0.935184	+	0.354162i	$0.884766\pi$
$104$	27.8216	+	48.1884i	2.72813	+	4.72526i
$105$	2.31958	−	4.01763i	0.226368	−	0.392081i
$106$	11.8858	−	20.5868i	1.15445	−	1.99957i
$107$	−9.21460			−0.890809			−0.445404	−	0.895329i	$-0.646940\pi$
$107$	−9.21460			−0.890809			−0.445404	+	0.895329i	$0.646940\pi$
$108$	−5.63508			−0.542236
$109$	−2.61769	+	4.53397i	−0.250729	+	0.434275i	−0.963727	−	0.266891i	$-0.914004\pi$
$109$	−2.61769	+	4.53397i	−0.250729	+	0.434275i	0.712998	+	0.701166i	$0.247337\pi$
$110$	4.58479	−	7.94108i	0.437142	−	0.757153i
$111$	3.48096	+	6.02919i	0.330398	+	0.572266i
$112$	−38.2360	−	66.2266i	−3.61296	−	6.25783i
$113$	−7.23323			−0.680445			−0.340223	−	0.940345i	$-0.610502\pi$
$113$	−7.23323			−0.680445			−0.340223	+	0.940345i	$0.610502\pi$
$114$	7.69230	+	13.3234i	0.720450	+	1.24786i
$115$	1.32568	+	2.29614i	0.123620	+	0.214116i
$116$	12.5702	+	21.7723i	1.16712	+	2.02150i
$117$	2.76988	−	4.79757i	0.256075	−	0.443536i
$118$	25.9827			2.39190
$119$	−0.484448	+	0.839089i	−0.0444093	+	0.0769192i
$120$	5.02217	+	8.69865i	0.458459	+	0.794075i
$121$	0.0124625			0.00113295
$122$	−1.28626	−	2.22787i	−0.116452	−	0.201702i
$123$	−2.66129	+	4.60949i	−0.239961	+	0.415624i
$124$	−7.75899	+	13.4390i	−0.696778	+	1.20685i
$125$	1.00000			0.0894427
$126$	−6.40939	+	11.1014i	−0.570994	+	0.988990i
$127$	2.73664			0.242838			0.121419	−	0.992601i	$-0.461256\pi$
$127$	2.73664			0.242838			0.121419	+	0.992601i	$0.461256\pi$
$128$	52.3695			4.62885
$129$	−6.44556	+	1.20614i	−0.567500	+	0.106195i
$130$	−15.3073			−1.34254
$131$	10.4394			0.912094			0.456047	−	0.889956i	$-0.349265\pi$
$131$	10.4394			0.912094			0.456047	+	0.889956i	$0.349265\pi$
$132$	−9.35002	+	16.1947i	−0.813815	+	1.40957i
$133$	25.8297			2.23972
$134$	−2.90614	+	5.03357i	−0.251052	+	0.434835i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−1.04889	−	1.81673i	−0.0899414	−	0.155783i
$137$	17.4328			1.48938			0.744691	−	0.667409i	$-0.232597\pi$
$137$	17.4328			1.48938			0.744691	+	0.667409i	$0.232597\pi$
$138$	−3.66307	−	6.34462i	−0.311821	−	0.540090i
$139$	−7.37645	+	12.7764i	−0.625662	+	1.08368i	0.362750	+	0.931886i	$0.381838\pi$
$139$	−7.37645	+	12.7764i	−0.625662	+	1.08368i	−0.988412	+	0.151792i	$0.951496\pi$
$140$	26.1421			2.20941
$141$	1.88254	−	3.26066i	0.158539	−	0.274597i
$142$	−19.6047	−	33.9563i	−1.64519	−	2.84955i
$143$	−9.19185	−	15.9208i	−0.768661	−	1.33136i
$144$	−8.24200	−	14.2756i	−0.686833	−	1.18963i
$145$	−4.46141			−0.370500
$146$	−2.53940	−	4.39838i	−0.210163	−	0.364012i
$147$	7.26092	+	12.5763i	0.598870	+	1.03727i
$148$	−19.6155	+	33.9750i	−1.61238	+	2.79273i
$149$	−3.26852	+	5.66124i	−0.267768	+	0.463787i	−0.968285	−	0.249848i	$-0.919619\pi$
$149$	−3.26852	+	5.66124i	−0.267768	+	0.463787i	0.700517	+	0.713635i	$0.252953\pi$
$150$	−2.76317			−0.225612
$151$	−6.55686			−0.533590			−0.266795	−	0.963753i	$-0.585965\pi$
$151$	−6.55686			−0.533590			−0.266795	+	0.963753i	$0.585965\pi$
$152$	−27.9621	+	48.4318i	−2.26803	+	3.92834i
$153$	−0.104426	+	0.180871i	−0.00844233	+	0.0146225i
$154$	21.2696	+	36.8400i	1.71395	+	2.96865i
$155$	−1.37691	−	2.38487i	−0.110596	−	0.191558i
$156$	31.2170			2.49936
$157$	10.8797	+	18.8442i	0.868297	+	1.50393i	0.863736	+	0.503945i	$0.168119\pi$
$157$	10.8797	+	18.8442i	0.868297	+	1.50393i	0.00456126	+	0.999990i	$0.498548\pi$
$158$	−20.5702	−	35.6286i	−1.63648	−	2.83446i
$159$	−4.30151	−	7.45043i	−0.341132	−	0.590858i
$160$	−12.7297	+	22.0484i	−1.00637	+	1.74308i
$161$	−12.3001			−0.969382
$162$	−1.38158	+	2.39297i	−0.108547	+	0.188010i
$163$	5.31322	+	9.20276i	0.416163	+	0.720816i	0.995550	−	0.0942371i	$-0.0300412\pi$
$163$	5.31322	+	9.20276i	0.416163	+	0.720816i	−0.579387	+	0.815053i	$0.696708\pi$
$164$	−29.9932			−2.34208
$165$	−1.65925	−	2.87391i	−0.129173	−	0.223733i
$166$	0.782448	−	1.35524i	0.0607298	−	0.105187i
$167$	−6.19420	+	10.7287i	−0.479321	+	0.830209i	−0.999719	−	0.0237153i	$-0.992450\pi$
$167$	−6.19420	+	10.7287i	−0.479321	+	0.830209i	0.520397	+	0.853924i	$0.325784\pi$
$168$	−46.5973			−3.59506
$169$	−8.84447	+	15.3191i	−0.680344	+	1.17839i
$170$	0.577092			0.0442609
$171$	5.56774			0.425776
$172$	−24.0467	−	28.0568i	−1.83355	−	2.13931i
$173$	−2.14222			−0.162870			−0.0814348	−	0.996679i	$-0.525950\pi$
$173$	−2.14222			−0.162870			−0.0814348	+	0.996679i	$0.525950\pi$
$174$	12.3276			0.934555
$175$	−2.31958	+	4.01763i	−0.175344	+	0.303704i
$176$	−54.7022			−4.12333
$177$	4.70161	−	8.14343i	0.353395	−	0.612098i
$178$	15.9758	−	27.6710i	1.19744	−	2.07403i
$179$	−0.246715	−	0.427323i	−0.0184403	−	0.0319396i	0.856658	−	0.515885i	$-0.172537\pi$
$179$	−0.246715	−	0.427323i	−0.0184403	−	0.0319396i	−0.875098	+	0.483945i	$0.839203\pi$
$180$	5.63508			0.420014
$181$	7.93779	+	13.7487i	0.590011	+	1.02193i	0.994230	+	0.107267i	$0.0342100\pi$
$181$	7.93779	+	13.7487i	0.590011	+	1.02193i	−0.404219	+	0.914662i	$0.632457\pi$
$182$	35.5065	−	61.4990i	2.63191	−	4.55861i
$183$	−0.931004			−0.0688218
$184$	13.3156	−	23.0632i	0.981636	−	1.70024i
$185$	−3.48096	−	6.02919i	−0.255925	−	0.443275i
$186$	3.80462	+	6.58980i	0.278969	+	0.483188i
$187$	0.346537	+	0.600220i	0.0253413	+	0.0438925i
$188$	21.2166			1.54738
$189$	2.31958	+	4.01763i	0.168725	+	0.292240i
$190$	−7.69230	−	13.3234i	−0.558058	−	0.966585i
$191$	5.28258	−	9.14970i	0.382234	−	0.662049i	−0.609147	−	0.793057i	$-0.708488\pi$
$191$	5.28258	−	9.14970i	0.382234	−	0.662049i	0.991381	+	0.131008i	$0.0418214\pi$
$192$	18.6902	−	32.3723i	1.34885	−	2.33627i
$193$	10.4128			0.749533			0.374767	−	0.927119i	$-0.377723\pi$
$193$	10.4128			0.749533			0.374767	+	0.927119i	$0.377723\pi$
$194$	19.7295			1.41650
$195$	−2.76988	+	4.79757i	−0.198355	+	0.343561i
$196$	−40.9159	+	70.8683i	−2.92256	+	5.06202i
$197$	1.79741	+	3.11321i	0.128060	+	0.221807i	0.922925	−	0.384980i	$-0.125792\pi$
$197$	1.79741	+	3.11321i	0.128060	+	0.221807i	−0.794865	+	0.606787i	$0.792458\pi$
$198$	4.58479	+	7.94108i	0.325827	+	0.564348i
$199$	7.54089			0.534559			0.267280	−	0.963619i	$-0.413875\pi$
$199$	7.54089			0.534559			0.267280	+	0.963619i	$0.413875\pi$
$200$	−5.02217	−	8.69865i	−0.355121	−	0.615087i
$201$	1.05174	+	1.82167i	0.0741841	+	0.128491i
$202$	−10.3229	−	17.8799i	−0.726320	−	1.25802i
$203$	10.3486	−	17.9243i	0.726330	−	1.25804i
$204$	−1.17690			−0.0823992
$205$	2.66129	−	4.60949i	0.185873	−	0.321941i
$206$	−4.51154	−	7.81422i	−0.314334	−	0.544443i
$207$	−2.65136			−0.184282
$208$	45.6587	+	79.0832i	3.16586	+	5.48343i
$209$	9.23829	−	16.0012i	0.639026	−	1.10682i
$210$	6.40939	−	11.1014i	0.442290	−	0.766068i
$211$	19.6601			1.35346			0.676728	−	0.736233i	$-0.263397\pi$
$211$	19.6601			1.35346			0.676728	+	0.736233i	$0.263397\pi$
$212$	24.2394	−	41.9838i	1.66477	−	2.88346i
$213$	−14.1900			−0.972284
$214$	−25.4615			−1.74051
$215$	6.44556	−	1.20614i	0.439583	−	0.0822581i
$216$	−10.0443			−0.683431
$217$	12.7754			0.867251
$218$	−7.23310	+	12.5281i	−0.489888	+	0.848510i
$219$	−1.83804			−0.124203
$220$	9.35002	−	16.1947i	0.630378	−	1.09185i
$221$	0.578494	−	1.00198i	0.0389137	−	0.0674005i
$222$	9.61846	+	16.6597i	0.645549	+	1.11812i
$223$	−9.42891			−0.631407			−0.315703	−	0.948858i	$-0.602240\pi$
$223$	−9.42891			−0.631407			−0.315703	+	0.948858i	$0.602240\pi$
$224$	−59.0550	−	102.286i	−3.94578	−	6.83429i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−19.9866			−1.32949
$227$	2.47181	−	4.28131i	0.164060	−	0.284160i	−0.772261	−	0.635305i	$-0.780874\pi$
$227$	2.47181	−	4.28131i	0.164060	−	0.284160i	0.936321	+	0.351145i	$0.114208\pi$
$228$	15.6873	+	27.1713i	1.03892	+	1.79946i
$229$	−12.5974	−	21.8193i	−0.832457	−	1.44186i	−0.896084	−	0.443884i	$-0.853600\pi$
$229$	−12.5974	−	21.8193i	−0.832457	−	1.44186i	0.0636271	−	0.997974i	$-0.479733\pi$
$230$	3.66307	+	6.34462i	0.241536	+	0.418352i
$231$	15.3951			1.01292
$232$	22.4060	+	38.8083i	1.47102	+	2.54789i
$233$	−10.2607	−	17.7720i	−0.672199	−	1.16428i	−0.977279	−	0.211956i	$-0.932017\pi$
$233$	−10.2607	−	17.7720i	−0.672199	−	1.16428i	0.305081	−	0.952327i	$-0.401317\pi$
$234$	7.65364	−	13.2565i	0.500334	−	0.866604i
$235$	−1.88254	+	3.26066i	−0.122804	+	0.212702i
$236$	52.9880			3.44922
$237$	−14.8889			−0.967136
$238$	−1.33861	+	2.31854i	−0.0867693	+	0.150289i
$239$	1.82749	−	3.16530i	0.118210	−	0.204746i	−0.800848	−	0.598868i	$-0.795618\pi$
$239$	1.82749	−	3.16530i	0.118210	−	0.204746i	0.919059	+	0.394121i	$0.128951\pi$
$240$	8.24200	+	14.2756i	0.532019	+	0.921483i
$241$	−2.56217	−	4.43781i	−0.165044	−	0.285864i	0.771627	−	0.636075i	$-0.219443\pi$
$241$	−2.56217	−	4.43781i	−0.165044	−	0.285864i	−0.936671	+	0.350211i	$0.886110\pi$
$242$	0.0344359			0.00221362
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.62314	−	4.54342i	−0.167929	−	0.290862i
$245$	−7.26092	−	12.5763i	−0.463883	−	0.803469i
$246$	−7.35359	+	12.7368i	−0.468848	+	0.812068i
$247$	−30.8440			−1.96255
$248$	−13.8301	+	23.9545i	−0.878214	+	1.52111i
$249$	−0.283171	−	0.490467i	−0.0179452	−	0.0310821i
$250$	2.76317			0.174758
$251$	1.41123	+	2.44432i	0.0890761	+	0.154284i	0.907121	−	0.420870i	$-0.138275\pi$
$251$	1.41123	+	2.44432i	0.0890761	+	0.154284i	−0.818045	+	0.575155i	$0.804942\pi$
$252$	−13.0710	+	22.6397i	−0.823398	+	1.42617i
$253$	−4.39927	+	7.61976i	−0.276580	+	0.479050i
$254$	7.56180			0.474469
$255$	0.104426	−	0.180871i	0.00653940	−	0.0113266i
$256$	69.9448			4.37155
$257$	−11.1304			−0.694297			−0.347148	−	0.937810i	$-0.612850\pi$
$257$	−11.1304			−0.694297			−0.347148	+	0.937810i	$0.612850\pi$
$258$	−17.8101	+	3.33277i	−1.10881	+	0.207489i
$259$	32.2974			2.00687
$260$	−31.2170			−1.93600
$261$	2.23071	−	3.86370i	0.138077	−	0.239157i
$262$	28.8458			1.78210
$263$	1.67244	−	2.89675i	0.103127	−	0.178621i	−0.809844	−	0.586645i	$-0.800448\pi$
$263$	1.67244	−	2.89675i	0.103127	−	0.178621i	0.912971	+	0.408023i	$0.133782\pi$
$264$	−16.6661	+	28.8665i	−1.02573	+	1.77661i
$265$	4.30151	+	7.45043i	0.264240	+	0.457677i
$266$	71.3716			4.37608
$267$	−5.78172	−	10.0142i	−0.353835	−	0.612861i
$268$	−5.92665	+	10.2653i	−0.362028	+	0.627050i
$269$	−5.36854			−0.327326			−0.163663	−	0.986516i	$-0.552331\pi$
$269$	−5.36854			−0.327326			−0.163663	+	0.986516i	$0.552331\pi$
$270$	1.38158	−	2.39297i	0.0840804	−	0.145632i
$271$	−7.06271	−	12.2330i	−0.429029	−	0.743100i	0.567758	−	0.823195i	$-0.307811\pi$
$271$	−7.06271	−	12.2330i	−0.429029	−	0.743100i	−0.996787	+	0.0800955i	$0.974477\pi$
$272$	−1.72135	−	2.98147i	−0.104372	−	0.180778i
$273$	−12.8499	−	22.2567i	−0.777713	−	1.34704i
$274$	48.1696			2.91003
$275$	1.65925	+	2.87391i	0.100057	+	0.173303i
$276$	−7.47031	−	12.9390i	−0.449660	−	0.778834i
$277$	10.6428	−	18.4339i	0.639467	−	1.10759i	−0.346083	−	0.938204i	$-0.612489\pi$
$277$	10.6428	−	18.4339i	0.639467	−	1.10759i	0.985550	−	0.169385i	$-0.0541781\pi$
$278$	−20.3823	+	35.3033i	−1.22245	+	2.11735i
$279$	2.75382			0.164867
$280$	46.5973			2.78472
$281$	14.0844	−	24.3949i	0.840204	−	1.45528i	−0.0495171	−	0.998773i	$-0.515768\pi$
$281$	14.0844	−	24.3949i	0.840204	−	1.45528i	0.889722	−	0.456504i	$-0.150898\pi$
$282$	5.20178	−	9.00975i	0.309762	−	0.536523i
$283$	5.05848	+	8.76154i	0.300695	+	0.520819i	0.976294	−	0.216450i	$-0.0694480\pi$
$283$	5.05848	+	8.76154i	0.300695	+	0.520819i	−0.675598	+	0.737270i	$0.736115\pi$
$284$	−39.9810	−	69.2491i	−2.37243	−	4.10918i
$285$	−5.56774			−0.329805
$286$	−25.3986	−	43.9917i	−1.50185	−	2.60128i
$287$	12.3462	+	21.3842i	0.728771	+	1.26227i
$288$	−12.7297	−	22.0484i	−0.750103	−	1.29922i
$289$	8.47819	−	14.6847i	0.498717	−	0.863803i
$290$	−12.3276			−0.723903
$291$	3.57009	−	6.18359i	0.209283	−	0.362488i
$292$	−5.17875	−	8.96986i	−0.303064	−	0.524922i
$293$	10.7551			0.628320			0.314160	−	0.949370i	$-0.398277\pi$
$293$	10.7551			0.628320			0.314160	+	0.949370i	$0.398277\pi$
$294$	20.0631	+	34.7503i	1.17010	+	2.02668i
$295$	−4.70161	+	8.14343i	−0.273739	+	0.474129i
$296$	−34.9639	+	60.5592i	−2.03223	+	3.51993i
$297$	3.31850			0.192559
$298$	−9.03146	+	15.6429i	−0.523178	+	0.906171i
$299$	14.6879			0.849422
$300$	−5.63508			−0.325342
$301$	−10.1052	+	28.6936i	−0.582452	+	1.65387i
$302$	−18.1177			−1.04256
$303$	−7.47183			−0.429245
$304$	−45.8893	+	79.4826i	−2.63193	+	4.55864i
$305$	0.931004			0.0533091
$306$	−0.288546	+	0.499776i	−0.0164951	+	0.0285703i
$307$	−10.6164	+	18.3882i	−0.605912	+	1.04947i	0.385994	+	0.922501i	$0.373858\pi$
$307$	−10.6164	+	18.3882i	−0.605912	+	1.04947i	−0.991907	+	0.126970i	$0.959475\pi$
$308$	43.3763	+	75.1299i	2.47159	+	4.28092i
$309$	−3.26549			−0.185767
$310$	−3.80462	−	6.58980i	−0.216088	−	0.374276i
$311$	1.62611	−	2.81650i	0.0922082	−	0.159709i	−0.816232	−	0.577724i	$-0.803941\pi$
$311$	1.62611	−	2.81650i	0.0922082	−	0.159709i	0.908440	+	0.418015i	$0.137274\pi$
$312$	55.6432			3.15018
$313$	−1.11131	+	1.92484i	−0.0628148	+	0.108798i	−0.895723	−	0.444613i	$-0.853341\pi$
$313$	−1.11131	+	1.92484i	−0.0628148	+	0.108798i	0.832908	+	0.553412i	$0.186674\pi$
$314$	30.0625	+	52.0698i	1.69652	+	2.93847i
$315$	−2.31958	−	4.01763i	−0.130694	−	0.226368i
$316$	−41.9500	−	72.6595i	−2.35987	−	4.08742i
$317$	−16.5682			−0.930565			−0.465283	−	0.885162i	$-0.654047\pi$
$317$	−16.5682			−0.930565			−0.465283	+	0.885162i	$0.654047\pi$
$318$	−11.8858	−	20.5868i	−0.666522	−	1.15445i
$319$	−7.40261	−	12.8217i	−0.414467	−	0.717877i
$320$	−18.6902	+	32.3723i	−1.04481	+	1.80967i
$321$	−4.60730	+	7.98008i	−0.257154	+	0.445404i
$322$	−33.9872			−1.89403
$323$	1.16283			0.0647017
$324$	−2.81754	+	4.88013i	−0.156530	+	0.271118i
$325$	2.76988	−	4.79757i	0.153645	−	0.266121i
$326$	14.6813	+	25.4287i	0.813122	+	1.40837i
$327$	2.61769	+	4.53397i	0.144758	+	0.250729i
$328$	−53.4618			−2.95193
$329$	−8.73343	−	15.1267i	−0.481489	−	0.833964i
$330$	−4.58479	−	7.94108i	−0.252384	−	0.437142i
$331$	−15.6633	−	27.1297i	−0.860934	−	1.49118i	−0.871029	−	0.491232i	$-0.836547\pi$
$331$	−15.6633	−	27.1297i	−0.860934	−	1.49118i	0.0100950	−	0.999949i	$-0.496787\pi$
$332$	1.59569	−	2.76382i	0.0875750	−	0.151684i
$333$	6.96191			0.381510
$334$	−17.1156	+	29.6451i	−0.936523	+	1.62211i
$335$	−1.05174	−	1.82167i	−0.0574628	−	0.0995284i
$336$	−76.4719			−4.17189
$337$	12.9633	+	22.4531i	0.706157	+	1.22310i	0.966272	+	0.257522i	$0.0829061\pi$
$337$	12.9633	+	22.4531i	0.706157	+	1.22310i	−0.260115	+	0.965578i	$0.583761\pi$
$338$	−24.4387	+	42.3291i	−1.32929	+	2.30240i
$339$	−3.61662	+	6.26416i	−0.196428	+	0.340223i
$340$	1.17690			0.0638262
$341$	4.56927	−	7.91421i	0.247440	−	0.428579i
$342$	15.3846			0.831904
$343$	34.8950			1.88415
$344$	−42.8625	−	50.0102i	−2.31099	−	2.69637i
$345$	2.65136			0.142744
$346$	−5.91929			−0.318223
$347$	8.05021	−	13.9434i	0.432158	−	0.748520i	−0.564901	−	0.825159i	$-0.691086\pi$
$347$	8.05021	−	13.9434i	0.432158	−	0.748520i	0.997059	+	0.0766392i	$0.0244189\pi$
$348$	25.1404			1.34767
$349$	−8.71474	+	15.0944i	−0.466489	+	0.807983i	−0.999267	−	0.0382717i	$-0.987815\pi$
$349$	−8.71474	+	15.0944i	−0.466489	+	0.807983i	0.532778	+	0.846255i	$0.321148\pi$
$350$	−6.40939	+	11.1014i	−0.342596	+	0.593394i
$351$	−2.76988	−	4.79757i	−0.147845	−	0.256075i
$352$	−84.4869			−4.50317
$353$	9.30912	+	16.1239i	0.495474	+	0.858187i	0.999986	−	0.00521803i	$-0.00166096\pi$
$353$	9.30912	+	16.1239i	0.495474	+	0.858187i	−0.504512	+	0.863405i	$0.668328\pi$
$354$	12.9913	−	22.5017i	0.690482	−	1.19595i
$355$	14.1900			0.753128
$356$	32.5805	−	56.4310i	1.72676	−	2.99084i
$357$	0.484448	+	0.839089i	0.0256397	+	0.0444093i
$358$	−0.681714	−	1.18076i	−0.0360297	−	0.0624053i
$359$	14.5804	+	25.2540i	0.769523	+	1.33285i	0.937822	+	0.347117i	$0.112839\pi$
$359$	14.5804	+	25.2540i	0.769523	+	1.33285i	−0.168299	+	0.985736i	$0.553827\pi$
$360$	10.0443			0.529383
$361$	−5.99988	−	10.3921i	−0.315783	−	0.546952i
$362$	21.9334	+	37.9898i	1.15279	+	1.99670i
$363$	0.00623124	−	0.0107928i	0.000327055	−	0.000566477i
$364$	72.4104	−	125.418i	3.79534	−	6.57371i
$365$	1.83804			0.0962074
$366$	−2.57252			−0.134468
$367$	−11.9502	+	20.6984i	−0.623796	+	1.08045i	0.364976	+	0.931017i	$0.381077\pi$
$367$	−11.9502	+	20.6984i	−0.623796	+	1.08045i	−0.988772	+	0.149429i	$0.952256\pi$
$368$	21.8525	−	37.8496i	1.13914	−	1.97305i
$369$	2.66129	+	4.60949i	0.138541	+	0.239961i
$370$	−9.61846	−	16.6597i	−0.500040	−	0.866094i
$371$	−39.9108			−2.07207
$372$	7.75899	+	13.4390i	0.402285	+	0.696778i
$373$	10.6984	+	18.5302i	0.553944	+	0.959459i	0.997985	+	0.0634525i	$0.0202111\pi$
$373$	10.6984	+	18.5302i	0.553944	+	0.959459i	−0.444041	+	0.896006i	$0.646456\pi$
$374$	0.957540	+	1.65851i	0.0495132	+	0.0857594i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	37.8178			1.95030
$377$	−12.3576	+	21.4040i	−0.636448	+	1.10236i
$378$	6.40939	+	11.1014i	0.329663	+	0.570994i
$379$	12.7098			0.652856			0.326428	−	0.945222i	$-0.394155\pi$
$379$	12.7098			0.652856			0.326428	+	0.945222i	$0.394155\pi$
$380$	−15.6873	−	27.1713i	−0.804744	−	1.39386i
$381$	1.36832	−	2.37000i	0.0701012	−	0.121419i
$382$	14.5967	−	25.2821i	0.746830	−	1.29355i
$383$	21.6615			1.10685			0.553426	−	0.832898i	$-0.313320\pi$
$383$	21.6615			1.10685			0.553426	+	0.832898i	$0.313320\pi$
$384$	26.1847	−	45.3533i	1.33623	−	2.31443i
$385$	−15.3951			−0.784606
$386$	28.7724			1.46448
$387$	−2.17823	+	6.18509i	−0.110726	+	0.314406i
$388$	40.2356			2.04265
$389$	−28.0782			−1.42362			−0.711811	−	0.702371i	$-0.752125\pi$
$389$	−28.0782			−1.42362			−0.711811	+	0.702371i	$0.752125\pi$
$390$	−7.65364	+	13.2565i	−0.387557	+	0.671268i
$391$	−0.553740			−0.0280039
$392$	−72.9311	+	126.320i	−3.68358	+	6.38014i
$393$	5.21970	−	9.04078i	0.263299	−	0.456047i
$394$	4.96655	+	8.60232i	0.250211	+	0.433378i
$395$	14.8889			0.749140
$396$	9.35002	+	16.1947i	0.469856	+	0.813815i
$397$	−13.2339	+	22.9218i	−0.664191	+	1.15041i	0.315313	+	0.948988i	$0.397890\pi$
$397$	−13.2339	+	22.9218i	−0.664191	+	1.15041i	−0.979504	+	0.201424i	$0.935443\pi$
$398$	20.8367			1.04445
$399$	12.9148	−	22.3691i	0.646550	−	1.11986i
$400$	−8.24200	−	14.2756i	−0.412100	−	0.713778i
$401$	6.26581	+	10.8527i	0.312900	+	0.541958i	0.978989	−	0.203914i	$-0.0653662\pi$
$401$	6.26581	+	10.8527i	0.312900	+	0.541958i	−0.666089	+	0.745872i	$0.732033\pi$
$402$	2.90614	+	5.03357i	0.144945	+	0.251052i
$403$	−15.2555			−0.759930
$404$	−21.0522	−	36.4634i	−1.04739	−	1.81412i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	28.5949	−	49.5279i	1.41914	−	2.45803i
$407$	11.5516	−	20.0079i	0.572590	−	0.991754i
$408$	−2.09778			−0.103855
$409$	−11.9224			−0.589524			−0.294762	−	0.955571i	$-0.595240\pi$
$409$	−11.9224			−0.589524			−0.294762	+	0.955571i	$0.595240\pi$
$410$	7.35359	−	12.7368i	0.363168	−	0.629025i
$411$	8.71639	−	15.0972i	0.429948	−	0.744691i
$412$	−9.20065	−	15.9360i	−0.453284	−	0.785110i
$413$	−21.8116	−	37.7787i	−1.07328	−	1.85897i
$414$	−7.32614			−0.360060
$415$	0.283171	+	0.490467i	0.0139003	+	0.0240761i
$416$	70.5193	+	122.143i	3.45749	+	5.98855i
$417$	7.37645	+	12.7764i	0.361226	+	0.625662i
$418$	25.5269	−	44.2139i	1.24856	−	2.16257i
$419$	−27.0791			−1.32290			−0.661451	−	0.749988i	$-0.730059\pi$
$419$	−27.0791			−1.32290			−0.661451	+	0.749988i	$0.730059\pi$
$420$	13.0710	−	22.6397i	0.637801	−	1.10470i
$421$	16.1708	+	28.0087i	0.788117	+	1.36506i	0.927119	+	0.374766i	$0.122277\pi$
$421$	16.1708	+	28.0087i	0.788117	+	1.36506i	−0.139002	+	0.990292i	$0.544390\pi$
$422$	54.3241			2.64445
$423$	−1.88254	−	3.26066i	−0.0915324	−	0.158539i
$424$	43.2058	−	74.8347i	2.09826	−	3.63429i
$425$	−0.104426	+	0.180871i	−0.00506540	+	0.00877352i
$426$	−39.2094			−1.89970
$427$	−2.15954	+	3.74043i	−0.104507	+	0.181012i
$428$	−51.9250			−2.50989
$429$	−18.3837			−0.887574
$430$	17.8101	−	3.33277i	0.858881	−	0.160720i
$431$	10.0881			0.485929			0.242964	−	0.970035i	$-0.421880\pi$
$431$	10.0881			0.485929			0.242964	+	0.970035i	$0.421880\pi$
$432$	−16.4840			−0.793087
$433$	12.9054	−	22.3528i	0.620195	−	1.07421i	−0.369254	−	0.929328i	$-0.620387\pi$
$433$	12.9054	−	22.3528i	0.620195	−	1.07421i	0.989449	−	0.144881i	$-0.0462798\pi$
$434$	35.3005			1.69448
$435$	−2.23071	+	3.86370i	−0.106954	+	0.185250i
$436$	−14.7509	+	25.5493i	−0.706439	+	1.22359i
$437$	7.38104	+	12.7843i	0.353083	+	0.611558i
$438$	−5.07881			−0.242675
$439$	−3.26761	−	5.65966i	−0.155954	−	0.270121i	0.777452	−	0.628943i	$-0.216512\pi$
$439$	−3.26761	−	5.65966i	−0.155954	−	0.270121i	−0.933406	+	0.358822i	$0.883179\pi$
$440$	16.6661	−	28.8665i	0.794524	−	1.37616i
$441$	14.5218			0.691516
$442$	1.59847	−	2.76864i	0.0760317	−	0.131691i
$443$	8.43011	+	14.6014i	0.400527	+	0.693732i	0.993789	−	0.111276i	$-0.0354939\pi$
$443$	8.43011	+	14.6014i	0.400527	+	0.693732i	−0.593263	+	0.805009i	$0.702161\pi$
$444$	19.6155	+	33.9750i	0.930909	+	1.61238i
$445$	5.78172	+	10.0142i	0.274080	+	0.474720i
$446$	−26.0536			−1.23368
$447$	3.26852	+	5.66124i	0.154596	+	0.267768i
$448$	−86.7068	−	150.181i	−4.09651	−	7.09537i
$449$	14.1731	−	24.5485i	0.668870	−	1.15852i	−0.309351	−	0.950948i	$-0.600112\pi$
$449$	14.1731	−	24.5485i	0.668870	−	1.15852i	0.978221	−	0.207568i	$-0.0665549\pi$
$450$	−1.38158	+	2.39297i	−0.0651284	+	0.112806i
$451$	17.6630			0.831718
$452$	−40.7599			−1.91718
$453$	−3.27843	+	5.67841i	−0.154034	+	0.266795i
$454$	6.83003	−	11.8300i	0.320549	−	0.555208i
$455$	12.8499	+	22.2567i	0.602414	+	1.04341i
$456$	27.9621	+	48.4318i	1.30945	+	2.26803i
$457$	−22.9260			−1.07243			−0.536216	−	0.844081i	$-0.680147\pi$
$457$	−22.9260			−1.07243			−0.536216	+	0.844081i	$0.680147\pi$
$458$	−34.8086	−	60.2903i	−1.62650	−	2.81718i
$459$	0.104426	+	0.180871i	0.00487418	+	0.00844233i
$460$	7.47031	+	12.9390i	0.348305	+	0.603282i
$461$	−6.08009	+	10.5310i	−0.283178	+	0.490478i	−0.972166	−	0.234294i	$-0.924722\pi$
$461$	−6.08009	+	10.5310i	−0.283178	+	0.490478i	0.688988	+	0.724773i	$0.258055\pi$
$462$	42.5391			1.97910
$463$	−7.17779	+	12.4323i	−0.333580	+	0.577778i	−0.983211	−	0.182472i	$-0.941590\pi$
$463$	−7.17779	+	12.4323i	−0.333580	+	0.577778i	0.649631	+	0.760250i	$0.274924\pi$
$464$	36.7710	+	63.6892i	1.70705	+	2.95670i
$465$	−2.75382			−0.127705
$466$	−28.3519	−	49.1070i	−1.31338	−	2.27484i
$467$	12.8094	−	22.1865i	0.592749	−	1.02667i	−0.401112	−	0.916029i	$-0.631376\pi$
$467$	12.8094	−	22.1865i	0.592749	−	1.02667i	0.993860	−	0.110641i	$-0.0352905\pi$
$468$	15.6085	−	27.0347i	0.721503	−	1.24968i
$469$	9.75840			0.450601
$470$	−5.20178	+	9.00975i	−0.239940	+	0.415589i
$471$	21.7595			1.00262
$472$	94.4492			4.34738
$473$	14.1611	+	16.5226i	0.651130	+	0.759712i
$474$	−41.1404			−1.88964
$475$	5.56774			0.255466
$476$	−2.72991	+	4.72834i	−0.125125	+	0.216723i
$477$	−8.60302			−0.393905
$478$	5.04965	−	8.74626i	0.230966	−	0.400045i
$479$	−14.5444	+	25.1917i	−0.664552	+	1.15104i	0.314854	+	0.949140i	$0.398044\pi$
$479$	−14.5444	+	25.1917i	−0.664552	+	1.15104i	−0.979407	+	0.201898i	$0.935289\pi$
$480$	12.7297	+	22.0484i	0.581027	+	1.00637i
$481$	−38.5673			−1.75852
$482$	−7.07970	−	12.2624i	−0.322471	−	0.558537i
$483$	−6.15004	+	10.6522i	−0.279836	+	0.484691i
$484$	0.0702271			0.00319214
$485$	−3.57009	+	6.18359i	−0.162110	+	0.280782i
$486$	1.38158	+	2.39297i	0.0626699	+	0.108547i
$487$	5.50653	+	9.53759i	0.249525	+	0.432190i	0.963394	−	0.268089i	$-0.0863923\pi$
$487$	5.50653	+	9.53759i	0.249525	+	0.432190i	−0.713869	+	0.700279i	$0.753059\pi$
$488$	−4.67566	−	8.09848i	−0.211657	−	0.366601i
$489$	10.6264			0.480544
$490$	−20.0631	−	34.7503i	−0.906359	−	1.56986i
$491$	−8.34502	−	14.4540i	−0.376606	−	0.652300i	0.613960	−	0.789337i	$-0.289575\pi$
$491$	−8.34502	−	14.4540i	−0.376606	−	0.652300i	−0.990566	+	0.137037i	$0.956242\pi$
$492$	−14.9966	+	25.9749i	−0.676099	+	1.17104i
$493$	0.465887	−	0.806940i	0.0209825	−	0.0363427i
$494$	−85.2269			−3.83454
$495$	−3.31850			−0.149156
$496$	−22.6969	+	39.3123i	−1.01912	+	1.76517i
$497$	−32.9149	+	57.0103i	−1.47644	+	2.55726i
$498$	−0.782448	−	1.35524i	−0.0350624	−	0.0607298i
$499$	6.96018	+	12.0554i	0.311580	+	0.539673i	0.978705	−	0.205273i	$-0.0658084\pi$
$499$	6.96018	+	12.0554i	0.311580	+	0.539673i	−0.667124	+	0.744946i	$0.732475\pi$
$500$	5.63508			0.252009
$501$	6.19420	+	10.7287i	0.276736	+	0.479321i
$502$	3.89946	+	6.75407i	0.174042	+	0.301449i
$503$	9.77787	+	16.9358i	0.435974	+	0.755129i	0.997375	−	0.0724154i	$-0.0230707\pi$
$503$	9.77787	+	16.9358i	0.435974	+	0.755129i	−0.561401	+	0.827544i	$0.689737\pi$
$504$	−23.2987	+	40.3545i	−1.03780	+	1.79753i
$505$	7.47183			0.332492
$506$	−12.1559	+	21.0547i	−0.540396	+	0.935993i
$507$	8.84447	+	15.3191i	0.392797	+	0.680344i
$508$	15.4212			0.684206
$509$	−5.12739	−	8.88090i	−0.227268	−	0.393639i	0.729730	−	0.683736i	$-0.239646\pi$
$509$	−5.12739	−	8.88090i	−0.227268	−	0.393639i	−0.956997	+	0.290097i	$0.906313\pi$
$510$	0.288546	−	0.499776i	0.0127770	−	0.0221305i
$511$	−4.26348	+	7.38457i	−0.188605	+	0.326674i
$512$	88.5300			3.91251
$513$	2.78387	−	4.82181i	0.122911	−	0.212888i
$514$	−30.7552			−1.35655
$515$	3.26549			0.143895
$516$	−36.3213	+	6.79671i	−1.59895	+	0.299208i
$517$	−12.4945			−0.549506
$518$	89.2432			3.92112
$519$	−1.07111	+	1.85521i	−0.0470164	+	0.0814348i
$520$	−55.6432			−2.44012
$521$	17.4153	−	30.1642i	0.762978	−	1.32152i	−0.178331	−	0.983971i	$-0.557070\pi$
$521$	17.4153	−	30.1642i	0.762978	−	1.32152i	0.941309	−	0.337546i	$-0.109597\pi$
$522$	6.16381	−	10.6760i	0.269783	−	0.467277i
$523$	−1.76882	−	3.06369i	−0.0773452	−	0.133966i	0.824758	−	0.565485i	$-0.191311\pi$
$523$	−1.76882	−	3.06369i	−0.0773452	−	0.133966i	−0.902104	+	0.431519i	$0.857978\pi$
$524$	58.8268			2.56986
$525$	2.31958	+	4.01763i	0.101235	+	0.175344i
$526$	4.62123	−	8.00421i	0.201495	−	0.349000i
$527$	0.575139			0.0250535
$528$	−27.3511	+	47.3735i	−1.19030	+	2.06167i
$529$	7.98515	+	13.8307i	0.347181	+	0.601334i
$530$	11.8858	+	20.5868i	0.516286	+	0.894233i
$531$	−4.70161	−	8.14343i	−0.204033	−	0.353395i
$532$	145.552			6.31049
$533$	−14.7429	−	25.5355i	−0.638586	−	1.10606i
$534$	−15.9758	−	27.6710i	−0.691342	−	1.19744i
$535$	4.60730	−	7.98008i	0.199191	−	0.345009i
$536$	−10.5640	+	18.2975i	−0.456297	+	0.790330i
$537$	−0.493430			−0.0212931
$538$	−14.8342			−0.639546
$539$	24.0954	−	41.7344i	1.03786	−	1.79763i
$540$	2.81754	−	4.88013i	0.121248	−	0.210007i
$541$	−15.3864	−	26.6500i	−0.661512	−	1.14577i	−0.980218	−	0.197919i	$-0.936582\pi$
$541$	−15.3864	−	26.6500i	−0.661512	−	1.14577i	0.318706	−	0.947854i	$-0.396752\pi$
$542$	−19.5154	−	33.8017i	−0.838259	−	1.45191i
$543$	15.8756			0.681286
$544$	−2.65861	−	4.60485i	−0.113987	−	0.197431i
$545$	−2.61769	−	4.53397i	−0.112129	−	0.194214i
$546$	−35.5065	−	61.4990i	−1.51954	−	2.63191i
$547$	16.8790	−	29.2353i	0.721695	−	1.25001i	−0.238625	−	0.971112i	$-0.576697\pi$
$547$	16.8790	−	29.2353i	0.721695	−	1.25001i	0.960320	−	0.278901i	$-0.0899701\pi$
$548$	98.2351			4.19640
$549$	−0.465502	+	0.806273i	−0.0198671	+	0.0344109i
$550$	4.58479	+	7.94108i	0.195496	+	0.338609i
$551$	−24.8400			−1.05822
$552$	−13.3156	−	23.0632i	−0.566748	−	0.981636i
$553$	−34.5359	+	59.8180i	−1.46862	+	2.54372i
$554$	29.4079	−	50.9360i	1.24942	−	2.16407i
$555$	−6.96191			−0.295517
$556$	−41.5669	+	71.9960i	−1.76283	+	3.05331i
$557$	−20.6870			−0.876534			−0.438267	−	0.898845i	$-0.644408\pi$
$557$	−20.6870			−0.876534			−0.438267	+	0.898845i	$0.644408\pi$
$558$	7.60925			0.322125
$559$	12.0669	−	34.2639i	0.510374	−	1.44921i
$560$	76.4719			3.23153
$561$	0.693075			0.0292616
$562$	38.9175	−	67.4071i	1.64164	−	2.84340i
$563$	−28.8886			−1.21751			−0.608755	−	0.793358i	$-0.708331\pi$
$563$	−28.8886			−1.21751			−0.608755	+	0.793358i	$0.708331\pi$
$564$	10.6083	−	18.3741i	0.446690	−	0.773689i
$565$	3.61662	−	6.26416i	0.152152	−	0.263535i
$566$	13.9774	+	24.2096i	0.587514	+	1.01760i
$567$	4.63916			0.194827
$568$	−71.2647	−	123.434i	−2.99020	−	5.17918i
$569$	−8.03629	+	13.9193i	−0.336899	+	0.583526i	−0.983848	−	0.179007i	$-0.942711\pi$
$569$	−8.03629	+	13.9193i	−0.336899	+	0.583526i	0.646949	+	0.762533i	$0.276045\pi$
$570$	−15.3846			−0.644390
$571$	17.5817	−	30.4523i	0.735769	−	1.27439i	−0.218616	−	0.975811i	$-0.570154\pi$
$571$	17.5817	−	30.4523i	0.735769	−	1.27439i	0.954385	−	0.298579i	$-0.0965126\pi$
$572$	−51.7969	−	89.7148i	−2.16574	−	3.75116i
$573$	−5.28258	−	9.14970i	−0.220683	−	0.382234i
$574$	34.1145	+	59.0880i	1.42391	+	2.46629i
$575$	−2.65136			−0.110569
$576$	−18.6902	−	32.3723i	−0.778758	−	1.34885i
$577$	4.97441	+	8.61592i	0.207087	+	0.358686i	0.950796	−	0.309818i	$-0.100268\pi$
$577$	4.97441	+	8.61592i	0.207087	+	0.358686i	−0.743709	+	0.668504i	$0.766935\pi$
$578$	23.4266	−	40.5761i	0.974420	−	1.68774i
$579$	5.20642	−	9.01779i	0.216372	−	0.374767i
$580$	−25.1404			−1.04390
$581$	−2.62735			−0.109001
$582$	9.86476	−	17.0863i	0.408908	−	0.708249i
$583$	−14.2746	+	24.7243i	−0.591193	+	1.02398i
$584$	−9.23094	−	15.9885i	−0.381979	−	0.661607i
$585$	2.76988	+	4.79757i	0.114520	+	0.198355i
$586$	29.7182			1.22765
$587$	−11.1648	−	19.3381i	−0.460822	−	0.798168i	0.538180	−	0.842830i	$-0.319112\pi$
$587$	−11.1648	−	19.3381i	−0.460822	−	0.798168i	−0.999002	+	0.0446623i	$0.985779\pi$
$588$	40.9159	+	70.8683i	1.68734	+	2.92256i
$589$	−7.66627	−	13.2784i	−0.315883	−	0.547126i
$590$	−12.9913	+	22.5017i	−0.534845	+	0.926378i
$591$	3.59483			0.147871
$592$	−57.3801	+	99.3852i	−2.35831	+	4.08471i
$593$	4.63209	+	8.02301i	0.190217	+	0.329466i	0.945322	−	0.326138i	$-0.105747\pi$
$593$	4.63209	+	8.02301i	0.190217	+	0.329466i	−0.755105	+	0.655604i	$0.772414\pi$
$594$	9.16957			0.376232
$595$	−0.484448	−	0.839089i	−0.0198604	−	0.0343993i
$596$	−18.4184	+	31.9016i	−0.754446	+	1.30674i
$597$	3.77044	−	6.53060i	0.154314	−	0.267280i
$598$	40.5851			1.65965
$599$	−15.4316	+	26.7283i	−0.630519	+	1.09209i	0.356927	+	0.934132i	$0.383824\pi$
$599$	−15.4316	+	26.7283i	−0.630519	+	1.09209i	−0.987446	+	0.157958i	$0.949509\pi$
$600$	−10.0443			−0.410058
$601$	−9.10987			−0.371599			−0.185800	−	0.982588i	$-0.559488\pi$
$601$	−9.10987			−0.371599			−0.185800	+	0.982588i	$0.559488\pi$
$602$	−27.9222	+	79.2852i	−1.13803	+	3.23143i
$603$	2.10348			0.0856604
$604$	−36.9485			−1.50341
$605$	−0.00623124	+	0.0107928i	−0.000253336	+	0.000438791i
$606$	−20.6459			−0.838682
$607$	4.14030	−	7.17121i	0.168050	−	0.291071i	−0.769684	−	0.638425i	$-0.779586\pi$
$607$	4.14030	−	7.17121i	0.168050	−	0.291071i	0.937734	+	0.347354i	$0.112920\pi$
$608$	−70.8755	+	122.760i	−2.87438	+	4.97858i
$609$	−10.3486	−	17.9243i	−0.419347	−	0.726330i
$610$	2.57252			0.104158
$611$	10.4288	+	18.0633i	0.421906	+	0.730762i
$612$	−0.588448	+	1.01922i	−0.0237866	+	0.0411996i
$613$	5.42292			0.219030			0.109515	−	0.993985i	$-0.465070\pi$
$613$	5.42292			0.219030			0.109515	+	0.993985i	$0.465070\pi$
$614$	−29.3350	+	50.8097i	−1.18386	+	2.05051i
$615$	−2.66129	−	4.60949i	−0.107314	−	0.185873i
$616$	77.3167	+	133.916i	3.11518	+	5.39564i
$617$	22.3628	+	38.7336i	0.900294	+	1.55935i	0.827113	+	0.562035i	$0.189982\pi$
$617$	22.3628	+	38.7336i	0.900294	+	1.55935i	0.0731804	+	0.997319i	$0.476685\pi$
$618$	−9.02309			−0.362962
$619$	19.9469	+	34.5490i	0.801732	+	1.38864i	0.918475	+	0.395479i	$0.129421\pi$
$619$	19.9469	+	34.5490i	0.801732	+	1.38864i	−0.116743	+	0.993162i	$0.537245\pi$
$620$	−7.75899	−	13.4390i	−0.311609	−	0.539722i
$621$	−1.32568	+	2.29614i	−0.0531977	+	0.0921410i
$622$	4.49321	−	7.78246i	0.180161	−	0.312048i
$623$	−53.6447			−2.14923
$624$	91.3174			3.65562
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.07073	+	5.31866i	−0.122731	+	0.212576i
$627$	−9.23829	−	16.0012i	−0.368942	−	0.639026i
$628$	61.3082	+	106.189i	2.44646	+	4.23740i
$629$	1.45401			0.0579750
$630$	−6.40939	−	11.1014i	−0.255356	−	0.442290i
$631$	−14.8578	−	25.7344i	−0.591479	−	1.02447i	−0.994033	−	0.109075i	$-0.965211\pi$
$631$	−14.8578	−	25.7344i	−0.591479	−	1.02447i	0.402555	−	0.915396i	$-0.368122\pi$
$632$	−74.7744	−	129.513i	−2.97437	−	5.15175i
$633$	9.83004	−	17.0261i	0.390709	−	0.676728i
$634$	−45.7808			−1.81819
$635$	−1.36832	+	2.37000i	−0.0543002	+	0.0940507i
$636$	−24.2394	−	41.9838i	−0.961154	−	1.66477i
$637$	−80.4474			−3.18744
$638$	−20.4546	−	35.4285i	−0.809807	−	1.40263i
$639$	−7.09501	+	12.2889i	−0.280674	+	0.486142i
$640$	−26.1847	+	45.3533i	−1.03504	+	1.79275i
$641$	−18.2684			−0.721557			−0.360778	−	0.932652i	$-0.617489\pi$
$641$	−18.2684			−0.721557			−0.360778	+	0.932652i	$0.617489\pi$
$642$	−12.7307	+	22.0503i	−0.502442	+	0.870255i
$643$	25.1791			0.992968			0.496484	−	0.868046i	$-0.334624\pi$
$643$	25.1791			0.992968			0.496484	+	0.868046i	$0.334624\pi$
$644$	−69.3120			−2.73127
$645$	2.17823	−	6.18509i	0.0857677	−	0.243538i
$646$	3.21310			0.126418
$647$	−1.84756			−0.0726352			−0.0363176	−	0.999340i	$-0.511563\pi$
$647$	−1.84756			−0.0726352			−0.0363176	+	0.999340i	$0.511563\pi$
$648$	−5.02217	+	8.69865i	−0.197289	+	0.341715i
$649$	−31.2046			−1.22489
$650$	7.65364	−	13.2565i	0.300200	−	0.519962i
$651$	6.38770	−	11.0638i	0.250354	−	0.433625i
$652$	29.9404	+	51.8583i	1.17256	+	2.03093i
$653$	20.4691			0.801017			0.400509	−	0.916293i	$-0.368833\pi$
$653$	20.4691			0.801017			0.400509	+	0.916293i	$0.368833\pi$
$654$	7.23310	+	12.5281i	0.282837	+	0.489888i
$655$	−5.21970	+	9.04078i	−0.203950	+	0.353252i
$656$	−87.7374			−3.42557
$657$	−0.919020	+	1.59179i	−0.0358544	+	0.0621016i
$658$	−24.1319	−	41.7977i	−0.940760	−	1.62944i
$659$	13.1974	+	22.8585i	0.514097	+	0.890441i	0.999866	+	0.0163545i	$0.00520604\pi$
$659$	13.1974	+	22.8585i	0.514097	+	0.890441i	−0.485770	+	0.874087i	$0.661461\pi$
$660$	−9.35002	−	16.1947i	−0.363949	−	0.630378i
$661$	−47.6467			−1.85324			−0.926620	−	0.375999i	$-0.877300\pi$
$661$	−47.6467			−1.85324			−0.926620	+	0.375999i	$0.877300\pi$
$662$	−43.2803	−	74.9637i	−1.68214	−	2.91355i
$663$	−0.578494	−	1.00198i	−0.0224668	−	0.0389137i
$664$	2.84427	−	4.92641i	0.110379	−	0.191182i
$665$	−12.9148	+	22.3691i	−0.500816	+	0.867438i
$666$	19.2369			0.745415
$667$	11.8288			0.458013
$668$	−34.9048	+	60.4569i	−1.35051	+	2.33915i
$669$	−4.71446	+	8.16568i	−0.182271	+	0.315703i
$670$	−2.90614	−	5.03357i	−0.112274	−	0.194464i
$671$	1.54477	+	2.67562i	0.0596352	+	0.103291i
$672$	−118.110			−4.55619
$673$	3.51530	+	6.08868i	0.135505	+	0.234701i	0.925790	−	0.378038i	$-0.123401\pi$
$673$	3.51530	+	6.08868i	0.135505	+	0.234701i	−0.790285	+	0.612739i	$0.790068\pi$
$674$	35.8198	+	62.0417i	1.37973	+	2.38976i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−49.8393	+	86.3242i	−1.91690	+	3.32016i
$677$	5.13066			0.197187			0.0985936	−	0.995128i	$-0.468566\pi$
$677$	5.13066			0.197187			0.0985936	+	0.995128i	$0.468566\pi$
$678$	−9.99331	+	17.3089i	−0.383791	+	0.664745i
$679$	−16.5623	−	28.6867i	−0.635601	−	1.10089i
$680$	2.09778			0.0804460
$681$	−2.47181	−	4.28131i	−0.0947201	−	0.164060i
$682$	12.6257	−	21.8683i	0.483461	−	0.837380i
$683$	−13.1490	+	22.7748i	−0.503134	+	0.871454i	0.496859	+	0.867831i	$0.334487\pi$
$683$	−13.1490	+	22.7748i	−0.503134	+	0.871454i	−0.999993	+	0.00362283i	$0.998847\pi$
$684$	31.3747			1.19964
$685$	−8.71639	+	15.0972i	−0.333036	+	0.576835i
$686$	96.4206			3.68136
$687$	−25.1947			−0.961239
$688$	−70.3426	−	82.0729i	−2.68179	−	3.12900i
$689$	47.6587			1.81565
$690$	7.32614			0.278901
$691$	0.715519	−	1.23932i	0.0272196	−	0.0471458i	−0.852095	−	0.523388i	$-0.824668\pi$
$691$	0.715519	−	1.23932i	0.0272196	−	0.0471458i	0.879314	+	0.476242i	$0.158001\pi$
$692$	−12.0716			−0.458892
$693$	7.69754	−	13.3325i	0.292405	−	0.506461i
$694$	22.2441	−	38.5279i	0.844373	−	1.46250i
$695$	−7.37645	−	12.7764i	−0.279805	−	0.484636i
$696$	44.8119			1.69859
$697$	0.555815	+	0.962700i	0.0210530	+	0.0364649i
$698$	−24.0803	+	41.7083i	−0.911452	+	1.57868i
$699$	−20.5213			−0.776188
$700$	−13.0710	+	22.6397i	−0.494039	+	0.855700i
$701$	21.6684	+	37.5308i	0.818405	+	1.41752i	0.906857	+	0.421438i	$0.138475\pi$
$701$	21.6684	+	37.5308i	0.818405	+	1.41752i	−0.0884522	+	0.996080i	$0.528192\pi$
$702$	−7.65364	−	13.2565i	−0.288868	−	0.500334i
$703$	−19.3811	−	33.5690i	−0.730971	−	1.26608i
$704$	−124.047			−4.67519
$705$	1.88254	+	3.26066i	0.0709007	+	0.122804i
$706$	25.7226	+	44.5529i	0.968084	+	1.67677i
$707$	−17.3315	+	30.0191i	−0.651818	+	1.12898i
$708$	26.4940	−	45.8889i	0.995705	−	1.72461i
$709$	−27.5623			−1.03512			−0.517562	−	0.855646i	$-0.673160\pi$
$709$	−27.5623			−1.03512			−0.517562	+	0.855646i	$0.673160\pi$
$710$	39.2094			1.47150
$711$	−7.44443	+	12.8941i	−0.279188	+	0.483568i
$712$	58.0735	−	100.586i	2.17640	−	3.76963i
$713$	3.65068	+	6.32316i	0.136719	+	0.236804i
$714$	1.33861	+	2.31854i	0.0500963	+	0.0867693i
$715$	18.3837			0.687512
$716$	−1.39026	−	2.40800i	−0.0519564	−	0.0899911i
$717$	−1.82749	−	3.16530i	−0.0682488	−	0.118210i
$718$	40.2880	+	69.7809i	1.50353	+	2.60420i
$719$	−6.18499	+	10.7127i	−0.230661	+	0.399517i	−0.958003	−	0.286759i	$-0.907422\pi$
$719$	−6.18499	+	10.7127i	−0.230661	+	0.399517i	0.727342	+	0.686275i	$0.240756\pi$
$720$	16.4840			0.614322
$721$	−7.57457	+	13.1195i	−0.282092	+	0.488597i
$722$	−16.5787	−	28.7151i	−0.616994	−	1.06866i
$723$	−5.12434			−0.190576
$724$	44.7301	+	77.4748i	1.66238	+	2.87933i
$725$	2.23071	−	3.86370i	0.0828464	−	0.143494i
$726$	0.0172180	−	0.0298224i	0.000639018	−	0.00110681i
$727$	−20.7346			−0.769005			−0.384503	−	0.923124i	$-0.625627\pi$
$727$	−20.7346			−0.769005			−0.384503	+	0.923124i	$0.625627\pi$
$728$	129.069	−	223.554i	4.78361	−	8.28546i
$729$	1.00000			0.0370370
$730$	5.07881			0.187975
$731$	−0.454927	+	1.29177i	−0.0168261	+	0.0477777i
$732$	−5.24628			−0.193908
$733$	−33.4470			−1.23539			−0.617697	−	0.786416i	$-0.711934\pi$
$733$	−33.4470			−1.23539			−0.617697	+	0.786416i	$0.711934\pi$
$734$	−33.0204	+	57.1930i	−1.21881	+	2.11103i
$735$	−14.5218			−0.535646
$736$	33.7509	−	58.4583i	1.24407	−	2.15480i
$737$	3.49021	−	6.04522i	0.128563	−	0.222678i
$738$	7.35359	+	12.7368i	0.270689	+	0.468848i
$739$	21.3809			0.786509			0.393255	−	0.919430i	$-0.371349\pi$
$739$	21.3809			0.786509			0.393255	+	0.919430i	$0.371349\pi$
$740$	−19.6155	−	33.9750i	−0.721079	−	1.24895i
$741$	−15.4220	+	26.7116i	−0.566540	+	0.981277i
$742$	−110.280			−4.04851
$743$	−14.5351	+	25.1754i	−0.533239	+	0.923598i	0.466007	+	0.884781i	$0.345692\pi$
$743$	−14.5351	+	25.1754i	−0.533239	+	0.923598i	−0.999246	+	0.0388166i	$0.987641\pi$
$744$	13.8301	+	23.9545i	0.507037	+	0.878214i
$745$	−3.26852	−	5.66124i	−0.119749	−	0.207412i
$746$	29.5615	+	51.2021i	1.08232	+	1.87464i
$747$	−0.566342			−0.0207214
$748$	1.95277	+	3.38229i	0.0714002	+	0.123669i
$749$	21.3740	+	37.0209i	0.780989	+	1.35271i
$750$	1.38158	−	2.39297i	0.0504483	−	0.0873790i
$751$	12.3934	−	21.4660i	0.452242	−	0.783306i	−0.546283	−	0.837601i	$-0.683958\pi$
$751$	12.3934	−	21.4660i	0.452242	−	0.783306i	0.998525	+	0.0542949i	$0.0172911\pi$
$752$	62.0637			2.26323
$753$	2.82246			0.102856
$754$	−34.1460	+	59.1427i	−1.24353	+	2.15385i
$755$	3.27843	−	5.67841i	0.119314	−	0.206658i
$756$	13.0710	+	22.6397i	0.475389	+	0.823398i
$757$	−9.28162	−	16.0762i	−0.337346	−	0.584301i	0.646586	−	0.762841i	$-0.276196\pi$
$757$	−9.28162	−	16.0762i	−0.337346	−	0.584301i	−0.983933	+	0.178540i	$0.942863\pi$
$758$	35.1192			1.27559
$759$	4.39927	+	7.61976i	0.159683	+	0.276580i
$760$	−27.9621	−	48.4318i	−1.01429	−	1.75681i
$761$	−18.9175	−	32.7661i	−0.685760	−	1.18777i	−0.973197	−	0.229971i	$-0.926137\pi$
$761$	−18.9175	−	32.7661i	−0.685760	−	1.18777i	0.287438	−	0.957799i	$-0.407197\pi$
$762$	3.78090	−	6.54871i	0.136968	−	0.237235i
$763$	24.2878			0.879276
$764$	29.7678	−	51.5593i	1.07696	−	1.86535i
$765$	−0.104426	−	0.180871i	−0.00377552	−	0.00653940i
$766$	59.8544			2.16263
$767$	26.0458	+	45.1127i	0.940460	+	1.62892i
$768$	34.9724	−	60.5739i	1.26196	−	2.18577i
$769$	5.22370	−	9.04772i	0.188372	−	0.326269i	−0.756336	−	0.654183i	$-0.773012\pi$
$769$	5.22370	−	9.04772i	0.188372	−	0.326269i	0.944707	+	0.327914i	$0.106346\pi$
$770$	−42.5391			−1.53300
$771$	−5.56521	+	9.63923i	−0.200426	+	0.347148i
$772$	58.6773			2.11184
$773$	−41.4286			−1.49008			−0.745042	−	0.667017i	$-0.767571\pi$
$773$	−41.4286			−1.49008			−0.745042	+	0.667017i	$0.767571\pi$
$774$	−6.01881	+	17.0904i	−0.216342	+	0.614303i
$775$	2.75382			0.0989200
$776$	71.7185			2.57454
$777$	16.1487	−	27.9704i	0.579332	−	1.00343i
$778$	−77.5847			−2.78155
$779$	14.8174	−	25.6645i	0.530888	−	0.919525i
$780$	−15.6085	+	27.0347i	−0.558874	+	0.967998i
$781$	23.5448	+	40.7808i	0.842500	+	1.45925i
$782$	−1.53008			−0.0547154
$783$	−2.23071	−	3.86370i	−0.0797190	−	0.138077i
$784$	−119.689	+	207.307i	−4.27460	+	7.40383i
$785$	−21.7595			−0.776628
$786$	14.4229	−	24.9812i	0.514447	−	0.891049i
$787$	16.6117	+	28.7723i	0.592143	+	1.02562i	0.993943	+	0.109894i	$0.0350513\pi$
$787$	16.6117	+	28.7723i	0.592143	+	1.02562i	−0.401800	+	0.915727i	$0.631615\pi$
$788$	10.1286	+	17.5432i	0.360815	+	0.624951i
$789$	−1.67244	−	2.89675i	−0.0595405	−	0.103127i
$790$	41.1404			1.46371
$791$	16.7781	+	29.0605i	0.596560	+	1.03327i
$792$	16.6661	+	28.8665i	0.592203	+	1.02573i
$793$	2.57877	−	4.46656i	0.0915748	−	0.158612i
$794$	−36.5675	+	63.3367i	−1.29773	+	2.24774i
$795$	8.60302			0.305118
$796$	42.4935			1.50614
$797$	10.7393	−	18.6010i	0.380405	−	0.658880i	−0.610716	−	0.791850i	$-0.709118\pi$
$797$	10.7393	−	18.6010i	0.380405	−	0.658880i	0.991120	+	0.132970i	$0.0424514\pi$
$798$	35.6858	−	61.8096i	1.26326	−	2.18804i
$799$	−0.393172	−	0.680995i	−0.0139094	−	0.0240919i
$800$	−12.7297	−	22.0484i	−0.450062	−	0.779530i
$801$	−11.5634			−0.408574
$802$	17.3135	+	29.9878i	0.611360	+	1.05891i
$803$	3.04977	+	5.28236i	0.107624	+	0.186410i
$804$	5.92665	+	10.2653i	0.209017	+	0.362028i
$805$	6.15004	−	10.6522i	0.216760	−	0.375440i
$806$	−42.1534			−1.48479
$807$	−2.68427	+	4.64929i	−0.0944907	+	0.163663i
$808$	−37.5248	−	64.9948i	−1.32012	−	2.28651i
$809$	−18.0124			−0.633281			−0.316640	−	0.948546i	$-0.602555\pi$
$809$	−18.0124			−0.633281			−0.316640	+	0.948546i	$0.602555\pi$
$810$	−1.38158	−	2.39297i	−0.0485439	−	0.0840804i
$811$	−15.6321	+	27.0755i	−0.548916	+	0.950751i	0.449433	+	0.893314i	$0.351626\pi$
$811$	−15.6321	+	27.0755i	−0.548916	+	0.950751i	−0.998349	+	0.0574368i	$0.981707\pi$
$812$	58.3153	−	101.005i	2.04647	−	3.54458i
$813$	−14.1254			−0.495400
$814$	31.9189	−	55.2851i	1.11876	−	1.93774i
$815$	−10.6264			−0.372228
$816$	−3.44271			−0.120519
$817$	35.8872	−	6.71548i	1.25553	−	0.234945i
$818$	−32.9435			−1.15184
$819$	−25.6998			−0.898025
$820$	14.9966	−	25.9749i	0.523704	−	0.907082i
$821$	2.43935			0.0851341			0.0425670	−	0.999094i	$-0.486446\pi$
$821$	2.43935			0.0851341			0.0425670	+	0.999094i	$0.486446\pi$
$822$	24.0848	−	41.7161i	0.840054	−	1.45502i
$823$	10.0202	−	17.3555i	0.349282	−	0.604975i	−0.636840	−	0.770996i	$-0.719759\pi$
$823$	10.0202	−	17.3555i	0.349282	−	0.604975i	0.986122	+	0.166021i	$0.0530920\pi$
$824$	−16.3998	−	28.4054i	−0.571315	−	0.989547i
$825$	3.31850			0.115535
$826$	−60.2689	−	104.389i	−2.09702	−	3.63215i
$827$	9.37878	−	16.2445i	0.326132	−	0.564878i	−0.655609	−	0.755101i	$-0.727588\pi$
$827$	9.37878	−	16.2445i	0.326132	−	0.564878i	0.981741	+	0.190223i	$0.0609212\pi$
$828$	−14.9406			−0.519222
$829$	20.4329	−	35.3908i	0.709663	−	1.22917i	−0.255320	−	0.966857i	$-0.582181\pi$
$829$	20.4329	−	35.3908i	0.709663	−	1.22917i	0.964982	−	0.262315i	$-0.0844860\pi$
$830$	0.782448	+	1.35524i	0.0271592	+	0.0470411i
$831$	−10.6428	−	18.4339i	−0.369196	−	0.639467i
$832$	103.539	+	179.335i	3.58957	+	6.21732i
$833$	3.03291			0.105084
$834$	20.3823	+	35.3033i	0.705783	+	1.22245i
$835$	−6.19420	−	10.7287i	−0.214359	−	0.371281i
$836$	52.0585	−	90.1680i	1.80048	−	3.11852i
$837$	1.37691	−	2.38487i	0.0475929	−	0.0824333i
$838$	−74.8241			−2.58476
$839$	−23.1150			−0.798017			−0.399008	−	0.916947i	$-0.630646\pi$
$839$	−23.1150			−0.798017			−0.399008	+	0.916947i	$0.630646\pi$
$840$	23.2987	−	40.3545i	0.803880	−	1.39236i
$841$	4.54789	−	7.87718i	0.156824	−	0.271627i
$842$	44.6826	+	77.3926i	1.53986	+	2.66712i
$843$	−14.0844	−	24.3949i	−0.485092	−	0.840204i
$844$	110.786			3.81342
$845$	−8.84447	−	15.3191i	−0.304259	−	0.526992i
$846$	−5.20178	−	9.00975i	−0.178841	−	0.309762i
$847$	−0.0289078	−	0.0500697i	−0.000993282	−	0.00172041i
$848$	70.9061	−	122.813i	2.43492	−	4.21741i
$849$	10.1170			0.347213
$850$	−0.288546	+	0.499776i	−0.00989704	+	0.0171422i
$851$	9.22926	+	15.9855i	0.316375	+	0.547977i
$852$	−79.9620			−2.73945
$853$	−1.32434	−	2.29382i	−0.0453444	−	0.0785388i	0.842462	−	0.538755i	$-0.181105\pi$
$853$	−1.32434	−	2.29382i	−0.0453444	−	0.0785388i	−0.887807	+	0.460216i	$0.847772\pi$
$854$	−5.96716	+	10.3354i	−0.204192	+	0.353671i
$855$	−2.78387	+	4.82181i	−0.0952064	+	0.164902i
$856$	−92.5545			−3.16345
$857$	27.8123	−	48.1722i	0.950048	−	1.64553i	0.204736	−	0.978817i	$-0.434367\pi$
$857$	27.8123	−	48.1722i	0.950048	−	1.64553i	0.745313	−	0.666715i	$-0.232300\pi$
$858$	−50.7972			−1.73419
$859$	41.4033			1.41266			0.706332	−	0.707881i	$-0.250349\pi$
$859$	41.4033			1.41266			0.706332	+	0.707881i	$0.250349\pi$
$860$	36.3213	−	6.79671i	1.23854	−	0.231766i
$861$	24.6923			0.841512
$862$	27.8752			0.949433
$863$	−17.2859	+	29.9401i	−0.588420	+	1.01917i	0.406019	+	0.913864i	$0.366917\pi$
$863$	−17.2859	+	29.9401i	−0.588420	+	1.01917i	−0.994440	+	0.105309i	$0.966417\pi$
$864$	−25.4593			−0.866144
$865$	1.07111	−	1.85521i	0.0364187	−	0.0630791i
$866$	35.6598	−	61.7646i	1.21177	−	2.09885i
$867$	−8.47819	−	14.6847i	−0.287934	−	0.498717i
$868$	71.9904			2.44352
$869$	24.7044	+	42.7892i	0.838038	+	1.45153i
$870$	−6.16381	+	10.6760i	−0.208973	+	0.361952i
$871$	−11.6528			−0.394840
$872$	−26.2929	+	45.5407i	−0.890391	+	1.54220i
$873$	−3.57009	−	6.18359i	−0.120829	−	0.209283i
$874$	20.3950	+	35.3252i	0.689872	+	1.19489i
$875$	−2.31958	−	4.01763i	−0.0784162	−	0.135821i
$876$	−10.3575			−0.349948
$877$	1.66679	+	2.88697i	0.0562835	+	0.0974859i	0.892794	−	0.450464i	$-0.148742\pi$
$877$	1.66679	+	2.88697i	0.0562835	+	0.0974859i	−0.836511	+	0.547950i	$0.815408\pi$
$878$	−9.02893	−	15.6386i	−0.304712	−	0.527776i
$879$	5.37756	−	9.31420i	0.181380	−	0.314160i
$880$	27.3511	−	47.3735i	0.922005	−	1.59696i
$881$	43.1690			1.45440			0.727200	−	0.686425i	$-0.240821\pi$
$881$	43.1690			1.45440			0.727200	+	0.686425i	$0.240821\pi$
$882$	40.1262			1.35112
$883$	−3.61662	+	6.26417i	−0.121709	+	0.210806i	−0.920442	−	0.390880i	$-0.872171\pi$
$883$	−3.61662	+	6.26417i	−0.121709	+	0.210806i	0.798733	+	0.601686i	$0.205504\pi$
$884$	3.25986	−	5.64625i	0.109641	−	0.189904i
$885$	4.70161	+	8.14343i	0.158043	+	0.273739i
$886$	23.2938	+	40.3460i	0.782570	+	1.35545i
$887$	35.4015			1.18867			0.594333	−	0.804219i	$-0.297416\pi$
$887$	35.4015			1.18867			0.594333	+	0.804219i	$0.297416\pi$
$888$	34.9639	+	60.5592i	1.17331	+	2.03223i
$889$	−6.34787	−	10.9948i	−0.212901	−	0.368755i
$890$	15.9758	+	27.6710i	0.535512	+	0.927533i
$891$	1.65925	−	2.87391i	0.0555870	−	0.0962795i
$892$	−53.1327			−1.77901
$893$	−10.4815	+	18.1545i	−0.350751	+	0.607518i
$894$	9.03146	+	15.6429i	0.302057	+	0.523178i
$895$	0.493430			0.0164935
$896$	−121.475	−	210.401i	−4.05820	−	7.02901i
$897$	7.34394	−	12.7201i	0.245207	−	0.424711i
$898$	39.1626	−	67.8316i	1.30687	−	2.26357i
$899$	−12.2859			−0.409758
$900$	−2.81754	+	4.88013i	−0.0939181	+	0.162671i
$901$	−1.79676			−0.0598586
$902$	48.8058			1.62506
$903$	19.7968	+	23.0981i	0.658797	+	0.768658i
$904$	−72.6530			−2.41640
$905$	−15.8756			−0.527722
$906$	−9.05885	+	15.6904i	−0.300960	+	0.521278i
$907$	−12.9840			−0.431125			−0.215563	−	0.976490i	$-0.569159\pi$
$907$	−12.9840			−0.431125			−0.215563	+	0.976490i	$0.569159\pi$
$908$	13.9289	−	24.1255i	0.462246	−	0.800634i
$909$	−3.73591	+	6.47079i	−0.123912	+	0.214623i
$910$	35.5065	+	61.4990i	1.17703	+	2.03867i
$911$	27.2421			0.902570			0.451285	−	0.892380i	$-0.350966\pi$
$911$	27.2421			0.902570			0.451285	+	0.892380i	$0.350966\pi$
$912$	45.8893	+	79.4826i	1.51955	+	2.63193i
$913$	−0.939704	+	1.62761i	−0.0310997	+	0.0538662i
$914$	−63.3483			−2.09538
$915$	0.465502	−	0.806273i	0.0153890	−	0.0266546i
$916$	−70.9872	−	122.953i	−2.34548	−	4.06249i
$917$	−24.2150	−	41.9416i	−0.799650	−	1.38504i
$918$	0.288546	+	0.499776i	0.00952343	+	0.0164951i
$919$	−29.0403			−0.957951			−0.478976	−	0.877828i	$-0.658992\pi$
$919$	−29.0403			−0.957951			−0.478976	+	0.877828i	$0.658992\pi$
$920$	13.3156	+	23.0632i	0.439001	+	0.760372i
$921$	10.6164	+	18.3882i	0.349824	+	0.605912i
$922$	−16.8003	+	29.0990i	−0.553288	+	0.958323i
$923$	39.3047	−	68.0777i	1.29373	−	2.24080i
$924$	86.7525			2.85395
$925$	6.96191			0.228906
$926$	−19.8334	+	34.3525i	−0.651767	+	1.12889i
$927$	−1.63274	+	2.82800i	−0.0536264	+	0.0928836i
$928$	56.7923	+	98.3672i	1.86430	+	3.22906i
$929$	−19.6954	−	34.1134i	−0.646184	−	1.11922i	−0.984027	−	0.178021i	$-0.943030\pi$
$929$	−19.6954	−	34.1134i	−0.646184	−	1.11922i	0.337843	−	0.941203i	$-0.390303\pi$
$930$	−7.60925			−0.249517
$931$	−40.4269	−	70.0215i	−1.32494	−	2.29486i
$932$	−57.8197	−	100.147i	−1.89395	−	3.28041i
$933$	−1.62611	−	2.81650i	−0.0532364	−	0.0922082i
$934$	35.3945	−	61.3051i	1.15814	−	2.00596i
$935$	−0.693075			−0.0226660
$936$	27.8216	−	48.1884i	0.909378	−	1.57509i
$937$	6.30165	+	10.9148i	0.205866	+	0.356570i	0.950408	−	0.311005i	$-0.100666\pi$
$937$	6.30165	+	10.9148i	0.205866	+	0.356570i	−0.744542	+	0.667575i	$0.767332\pi$
$938$	26.9641			0.880408
$939$	1.11131	+	1.92484i	0.0362662	+	0.0628148i
$940$	−10.6083	+	18.3741i	−0.346004	+	0.599297i
$941$	−5.95419	+	10.3130i	−0.194101	+	0.336193i	−0.946605	−	0.322394i	$-0.895512\pi$
$941$	−5.95419	+	10.3130i	−0.194101	+	0.336193i	0.752504	+	0.658587i	$0.228846\pi$
$942$	60.1250			1.95898
$943$	−7.05603	+	12.2214i	−0.229776	+	0.397984i
$944$	155.003			5.04491
$945$	−4.63916			−0.150912
$946$	39.1296	+	45.6548i	1.27221	+	1.48437i
$947$	50.3857			1.63732			0.818658	−	0.574282i	$-0.194719\pi$
$947$	50.3857			1.63732			0.818658	+	0.574282i	$0.194719\pi$
$948$	−83.9000			−2.72495
$949$	5.09115	−	8.81813i	0.165266	−	0.286249i
$950$	15.3846			0.499142
$951$	−8.28412	+	14.3485i	−0.268631	+	0.465283i
$952$	−4.86596	+	8.42809i	−0.157707	+	0.273156i
$953$	−23.1851	−	40.1578i	−0.751040	−	1.30084i	−0.947319	−	0.320292i	$-0.896219\pi$
$953$	−23.1851	−	40.1578i	−0.751040	−	1.30084i	0.196279	−	0.980548i	$-0.437114\pi$
$954$	−23.7716			−0.769633
$955$	5.28258	+	9.14970i	0.170940	+	0.296077i
$956$	10.2981	−	17.8368i	0.333063	−	0.576882i
$957$	−14.8052			−0.478585
$958$	−40.1887	+	69.6088i	−1.29844	+	2.24896i
$959$	−40.4367	−	70.0385i	−1.30577	−	2.26166i
$960$	18.6902	+	32.3723i	0.603223	+	1.04481i
$961$	11.7082	+	20.2793i	0.377685	+	0.654170i
$962$	−106.568			−3.43589
$963$	4.60730	+	7.98008i	0.148468	+	0.257154i
$964$	−14.4380	−	25.0074i	−0.465018	−	0.805434i
$965$	−5.20642	+	9.01779i	−0.167601	+	0.290293i
$966$	−16.9936	+	29.4337i	−0.546759	+	0.947015i
$967$	−18.7056			−0.601532			−0.300766	−	0.953698i	$-0.597242\pi$
$967$	−18.7056			−0.601532			−0.300766	+	0.953698i	$0.597242\pi$
$968$	0.125177			0.00402335
$969$	0.581416	−	1.00704i	0.0186778	−	0.0323509i
$970$	−9.86476	+	17.0863i	−0.316738	+	0.548607i
$971$	−21.5850	−	37.3863i	−0.692696	−	1.19978i	−0.970951	−	0.239277i	$-0.923089\pi$
$971$	−21.5850	−	37.3863i	−0.692696	−	1.19978i	0.278255	−	0.960507i	$-0.410244\pi$
$972$	2.81754	+	4.88013i	0.0903727	+	0.156530i
$973$	68.4411			2.19412
$974$	15.2155	+	26.3539i	0.487535	+	0.844435i
$975$	−2.76988	−	4.79757i	−0.0887071	−	0.153645i
$976$	−7.67333	−	13.2906i	−0.245617	−	0.425422i
$977$	−15.4498	+	26.7598i	−0.494281	+	0.856121i	−0.999978	−	0.00659063i	$-0.997902\pi$
$977$	−15.4498	+	26.7598i	−0.494281	+	0.856121i	0.505697	+	0.862711i	$0.331235\pi$
$978$	29.3626			0.938912
$979$	−19.1866	+	33.2323i	−0.613208	+	1.06211i
$980$	−40.9159	−	70.8683i	−1.30701	−	2.26381i
$981$	5.23537			0.167153
$982$	−23.0587	−	39.9388i	−0.735832	−	1.27450i
$983$	−4.80947	+	8.33025i	−0.153398	+	0.265694i	−0.932475	−	0.361235i	$-0.882355\pi$
$983$	−4.80947	+	8.33025i	−0.153398	+	0.265694i	0.779076	+	0.626929i	$0.215688\pi$
$984$	−26.7309	+	46.2993i	−0.852150	+	1.47597i
$985$	−3.59483			−0.114541
$986$	1.28732	−	2.22971i	0.0409967	−	0.0710084i
$987$	−17.4669			−0.555976
$988$	−173.808			−5.52958
$989$	−17.0895	+	3.19791i	−0.543414	+	0.101688i
$990$	−9.16957			−0.291428
$991$	30.2145			0.959796			0.479898	−	0.877324i	$-0.340674\pi$
$991$	30.2145			0.959796			0.479898	+	0.877324i	$0.340674\pi$
$992$	−35.0552	+	60.7173i	−1.11300	+	1.92778i
$993$	−31.3266			−0.994121
$994$	−90.9493	+	157.529i	−2.88474	+	4.99651i
$995$	−3.77044	+	6.53060i	−0.119531	+	0.207034i
$996$	−1.59569	−	2.76382i	−0.0505614	−	0.0875750i
$997$	−18.4041			−0.582864			−0.291432	−	0.956592i	$-0.594132\pi$
$997$	−18.4041			−0.582864			−0.291432	+	0.956592i	$0.594132\pi$
$998$	19.2321	+	33.3110i	0.608782	+	1.05444i
$999$	3.48096	−	6.02919i	0.110133	−	0.190755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	645.2.i.g.436.7	✓	14
43.36	even	3	inner	645.2.i.g.466.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
645.2.i.g.436.7	✓	14	1.1	even	1	trivial
645.2.i.g.466.7	yes	14	43.36	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 645 = 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	645.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.76317 q^{2} +(0.500000 - 0.866025i) q^{3} +5.63508 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.38158 - 2.39297i) q^{6} +(-2.31958 - 4.01763i) q^{7} +10.0443 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.38158 + 2.39297i) q^{10} -3.31850 q^{11} +(2.81754 - 4.88013i) q^{12} +(2.76988 + 4.79757i) q^{13} +(-6.40939 - 11.1014i) q^{14} +(0.500000 + 0.866025i) q^{15} +16.4840 q^{16} +(-0.104426 - 0.180871i) q^{17} +(-1.38158 - 2.39297i) q^{18} +(-2.78387 + 4.82181i) q^{19} +(-2.81754 + 4.88013i) q^{20} -4.63916 q^{21} -9.16957 q^{22} +(1.32568 - 2.29614i) q^{23} +(5.02217 - 8.69865i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.65364 + 13.2565i) q^{26} -1.00000 q^{27} +(-13.0710 - 22.6397i) q^{28} +(2.23071 + 3.86370i) q^{29} +(1.38158 + 2.39297i) q^{30} +(-1.37691 + 2.38487i) q^{31} +25.4593 q^{32} +(-1.65925 + 2.87391i) q^{33} +(-0.288546 - 0.499776i) q^{34} +4.63916 q^{35} +(-2.81754 - 4.88013i) q^{36} +(-3.48096 + 6.02919i) q^{37} +(-7.69230 + 13.3234i) q^{38} +5.53976 q^{39} +(-5.02217 + 8.69865i) q^{40} -5.32258 q^{41} -12.8188 q^{42} +(-4.26733 - 4.97895i) q^{43} -18.7000 q^{44} +1.00000 q^{45} +(3.66307 - 6.34462i) q^{46} +3.76509 q^{47} +(8.24200 - 14.2756i) q^{48} +(-7.26092 + 12.5763i) q^{49} +(-1.38158 - 2.39297i) q^{50} -0.208852 q^{51} +(15.6085 + 27.0347i) q^{52} +(4.30151 - 7.45043i) q^{53} -2.76317 q^{54} +(1.65925 - 2.87391i) q^{55} +(-23.2987 - 40.3545i) q^{56} +(2.78387 + 4.82181i) q^{57} +(6.16381 + 10.6760i) q^{58} +9.40323 q^{59} +(2.81754 + 4.88013i) q^{60} +(-0.465502 - 0.806273i) q^{61} +(-3.80462 + 6.58980i) q^{62} +(-2.31958 + 4.01763i) q^{63} +37.3804 q^{64} -5.53976 q^{65} +(-4.58479 + 7.94108i) q^{66} +(-1.05174 + 1.82167i) q^{67} +(-0.588448 - 1.01922i) q^{68} +(-1.32568 - 2.29614i) q^{69} +12.8188 q^{70} +(-7.09501 - 12.2889i) q^{71} +(-5.02217 - 8.69865i) q^{72} +(-0.919020 - 1.59179i) q^{73} +(-9.61846 + 16.6597i) q^{74} -1.00000 q^{75} +(-15.6873 + 27.1713i) q^{76} +(7.69754 + 13.3325i) q^{77} +15.3073 q^{78} +(-7.44443 - 12.8941i) q^{79} +(-8.24200 + 14.2756i) q^{80} +(-0.500000 + 0.866025i) q^{81} -14.7072 q^{82} +(0.283171 - 0.490467i) q^{83} -26.1421 q^{84} +0.208852 q^{85} +(-11.7913 - 13.7577i) q^{86} +4.46141 q^{87} -33.3322 q^{88} +(5.78172 - 10.0142i) q^{89} +2.76317 q^{90} +(12.8499 - 22.2567i) q^{91} +(7.47031 - 12.9390i) q^{92} +(1.37691 + 2.38487i) q^{93} +10.4036 q^{94} +(-2.78387 - 4.82181i) q^{95} +(12.7297 - 22.0484i) q^{96} +7.14019 q^{97} +(-20.0631 + 34.7503i) q^{98} +(1.65925 + 2.87391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 7 q^{3} + 26 q^{4} - 7 q^{5} + q^{6} + q^{7} + 12 q^{8} - 7 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 2 q^{13} + 4 q^{14} + 7 q^{15} + 50 q^{16} + 3 q^{17} - q^{18} - 21 q^{19} - 13 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 + 7 * q^3 + 26 * q^4 - 7 * q^5 + q^6 + q^7 + 12 * q^8 - 7 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 2 * q^13 + 4 * q^14 + 7 * q^15 + 50 * q^16 + 3 * q^17 - q^18 - 21 * q^19 - 13 * q^20 + 2 * q^21 + 26 * q^22 + 9 * q^23 + 6 * q^24 - 7 * q^25 + 23 * q^26 - 14 * q^27 - 25 * q^28 - 8 * q^29 + q^30 + 2 * q^31 + 56 * q^32 - 3 * q^33 + 11 * q^34 - 2 * q^35 - 13 * q^36 + 7 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^40 - 20 * q^41 + 8 * q^42 - 14 * q^43 - 64 * q^44 + 14 * q^45 + 8 * q^46 - 12 * q^47 + 25 * q^48 - 40 * q^49 - q^50 + 6 * q^51 - 17 * q^52 + 18 * q^53 - 2 * q^54 + 3 * q^55 - 40 * q^56 + 21 * q^57 + 12 * q^58 - 24 * q^59 + 13 * q^60 - 11 * q^61 - 47 * q^62 + q^63 + 20 * q^64 + 4 * q^65 + 13 * q^66 - 15 * q^67 + 9 * q^68 - 9 * q^69 - 8 * q^70 - 25 * q^71 - 6 * q^72 - 6 * q^73 - 49 * q^74 - 14 * q^75 - 23 * q^76 + 8 * q^77 + 46 * q^78 - 30 * q^79 - 25 * q^80 - 7 * q^81 + 44 * q^82 + 9 * q^83 - 50 * q^84 - 6 * q^85 - 113 * q^86 - 16 * q^87 - 26 * q^88 + 13 * q^89 + 2 * q^90 + 31 * q^91 + 19 * q^92 - 2 * q^93 - 14 * q^94 - 21 * q^95 + 28 * q^96 - 54 * q^97 + 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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