LMFDB - Embedded newform 45.5.k.a.7.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(7,45)] 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("45.7"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	45.7
Dual form			45.5.k.a.13.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.46311 - 1.46384i) q^{2} +(7.72308 - 4.62104i) q^{3} +(13.8464 - 7.99420i) q^{4} +(22.0807 + 11.7237i) q^{5} +(35.4276 - 36.5506i) q^{6} +(-85.6591 + 22.9523i) q^{7} +(-0.0464312 + 0.0464312i) q^{8} +(38.2920 - 71.3773i) q^{9} +(137.791 + 31.7253i) q^{10} +(33.9524 - 58.8072i) q^{11} +(69.9951 - 125.724i) q^{12} +(-120.611 - 32.3175i) q^{13} +(-434.367 + 250.782i) q^{14} +(224.706 - 11.4926i) q^{15} +(-128.093 + 221.863i) q^{16} +(233.925 + 233.925i) q^{17} +(104.709 - 445.995i) q^{18} -347.290i q^{19} +(399.458 - 14.1869i) q^{20} +(-555.489 + 573.096i) q^{21} +(99.4014 - 370.971i) q^{22} +(-14.1222 - 3.78404i) q^{23} +(-0.144032 + 0.573153i) q^{24} +(350.111 + 517.733i) q^{25} -706.217 q^{26} +(-34.1045 - 728.202i) q^{27} +(-1002.58 + 1002.58i) q^{28} +(-497.806 - 287.408i) q^{29} +(1210.77 - 391.718i) q^{30} +(283.023 + 490.210i) q^{31} +(-374.742 + 1398.56i) q^{32} +(-9.53338 - 611.068i) q^{33} +(1620.39 + 935.532i) q^{34} +(-2160.49 - 497.438i) q^{35} +(-40.3991 - 1294.43i) q^{36} +(1486.90 + 1486.90i) q^{37} +(-508.376 - 1897.28i) q^{38} +(-1080.83 + 307.755i) q^{39} +(-1.56958 + 0.480887i) q^{40} +(-868.102 - 1503.60i) q^{41} +(-2195.78 + 3944.03i) q^{42} +(-435.208 - 1624.22i) q^{43} -1085.69i q^{44} +(1682.32 - 1127.13i) q^{45} -82.6905 q^{46} +(1842.30 - 493.642i) q^{47} +(35.9668 + 2305.39i) q^{48} +(4731.34 - 2731.64i) q^{49} +(2670.57 + 2315.93i) q^{50} +(2887.60 + 725.648i) q^{51} +(-1928.37 + 516.705i) q^{52} +(402.755 - 402.755i) q^{53} +(-1252.28 - 3928.32i) q^{54} +(1439.13 - 900.455i) q^{55} +(2.91155 - 5.04296i) q^{56} +(-1604.84 - 2682.15i) q^{57} +(-3140.29 - 841.438i) q^{58} +(-498.977 + 288.085i) q^{59} +(3019.49 - 1955.48i) q^{60} +(1325.12 - 2295.17i) q^{61} +(2263.77 + 2263.77i) q^{62} +(-1641.79 + 6993.00i) q^{63} +4090.05i q^{64} +(-2284.28 - 2127.59i) q^{65} +(-946.585 - 3324.38i) q^{66} +(-369.394 + 1378.60i) q^{67} +(5109.06 + 1368.97i) q^{68} +(-126.553 + 36.0349i) q^{69} +(-12531.2 + 445.049i) q^{70} -2934.32 q^{71} +(1.53619 + 5.09208i) q^{72} +(-996.318 + 996.318i) q^{73} +(10299.7 + 5946.53i) q^{74} +(5096.40 + 2380.62i) q^{75} +(-2776.31 - 4808.70i) q^{76} +(-1558.57 + 5816.65i) q^{77} +(-5454.17 + 3263.45i) q^{78} +(-8580.07 - 4953.70i) q^{79} +(-5429.43 + 3397.17i) q^{80} +(-3628.44 - 5466.37i) q^{81} +(-6943.56 - 6943.56i) q^{82} +(227.549 + 849.223i) q^{83} +(-3110.05 + 12376.0i) q^{84} +(2422.76 + 7907.69i) q^{85} +(-4755.17 - 8236.20i) q^{86} +(-5172.72 + 80.7005i) q^{87} +(1.15404 + 4.30694i) q^{88} +776.997i q^{89} +(7540.75 - 8620.30i) q^{90} +11073.2 q^{91} +(-225.792 + 60.5007i) q^{92} +(4451.09 + 2478.07i) q^{93} +(9342.07 - 5393.64i) q^{94} +(4071.52 - 7668.40i) q^{95} +(3568.61 + 12532.9i) q^{96} +(3678.34 - 985.608i) q^{97} +(21849.2 - 21849.2i) q^{98} +(-2897.40 - 4675.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) $ 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	5.46311	−	1.46384i	1.36578	−	0.365959i	0.499843	−	0.866116i	$-0.333391\pi$
$2$	5.46311	−	1.46384i	1.36578	−	0.365959i	0.865935	+	0.500157i	$0.166724\pi$
$3$	7.72308	−	4.62104i	0.858120	−	0.513449i
$3$	7.72308	−	4.62104i	0.858120	−	0.513449i
$4$	13.8464	−	7.99420i	0.865397	−	0.499637i
$5$	22.0807	+	11.7237i	0.883226	+	0.468947i
$5$	22.0807	+	11.7237i	0.883226	+	0.468947i
$6$	35.4276	−	36.5506i	0.984100	−	1.01529i
$7$	−85.6591	+	22.9523i	−1.74814	+	0.468414i	−0.984228	−	0.176902i	$-0.943392\pi$
$7$	−85.6591	+	22.9523i	−1.74814	+	0.468414i	−0.763916	+	0.645316i	$0.776726\pi$
$8$	−0.0464312	+	0.0464312i	−0.000725488	+	0.000725488i
$9$	38.2920	−	71.3773i	0.472741	−	0.881201i
$10$	137.791	+	31.7253i	1.37791	+	0.317253i
$11$	33.9524	−	58.8072i	0.280598	−	0.486010i	−0.690934	−	0.722918i	$-0.742801\pi$
$11$	33.9524	−	58.8072i	0.280598	−	0.486010i	0.971532	+	0.236908i	$0.0761339\pi$
$12$	69.9951	−	125.724i	0.486077	−	0.873086i
$13$	−120.611	−	32.3175i	−0.713672	−	0.191228i	−0.116326	−	0.993211i	$-0.537112\pi$
$13$	−120.611	−	32.3175i	−0.713672	−	0.191228i	−0.597347	+	0.801983i	$0.703778\pi$
$14$	−434.367	+	250.782i	−2.21616	+	1.27950i
$15$	224.706	−	11.4926i	0.998695	−	0.0510781i
$16$	−128.093	+	221.863i	−0.500363	+	0.866653i
$17$	233.925	+	233.925i	0.809430	+	0.809430i	0.984548	−	0.175117i	$-0.0560304\pi$
$17$	233.925	+	233.925i	0.809430	+	0.809430i	−0.175117	+	0.984548i	$0.556030\pi$
$18$	104.709	−	445.995i	0.323176	−	1.37653i
$19$		−	347.290i		−	0.962023i	−0.876714	−	0.481011i	$-0.840270\pi$
$19$		−	347.290i		−	0.962023i	0.876714	−	0.481011i	$-0.159730\pi$
$20$	399.458	−	14.1869i	0.998645	−	0.0354672i
$21$	−555.489	+	573.096i	−1.25961	+	1.29954i
$22$	99.4014	−	370.971i	0.205375	−	0.766469i
$23$	−14.1222	−	3.78404i	−0.0266961	−	0.00715319i	0.245446	−	0.969410i	$-0.421066\pi$
$23$	−14.1222	−	3.78404i	−0.0266961	−	0.00715319i	−0.272142	+	0.962257i	$0.587732\pi$
$24$	−0.144032	+	0.573153i	−0.000250055	+	0.000995057i
$25$	350.111	+	517.733i	0.560177	+	0.828373i
$26$	−706.217			−1.04470
$27$	−34.1045	−	728.202i	−0.0467826	−	0.998905i
$28$	−1002.58	+	1002.58i	−1.27880	+	1.27880i
$29$	−497.806	−	287.408i	−0.591922	−	0.341746i	0.173935	−	0.984757i	$-0.444352\pi$
$29$	−497.806	−	287.408i	−0.591922	−	0.341746i	−0.765857	+	0.643011i	$0.777685\pi$
$30$	1210.77	−	391.718i	1.34530	−	0.435243i
$31$	283.023	+	490.210i	0.294509	+	0.510104i	0.974870	−	0.222772i	$-0.0715107\pi$
$31$	283.023	+	490.210i	0.294509	+	0.510104i	−0.680362	+	0.732876i	$0.738177\pi$
$32$	−374.742	+	1398.56i	−0.365959	+	1.36578i
$33$	−9.53338	−	611.068i	−0.00875425	−	0.561128i
$34$	1620.39	+	935.532i	1.40172	+	0.809284i
$35$	−2160.49	−	497.438i	−1.76367	−	0.406072i
$36$	−40.3991	−	1294.43i	−0.0311721	−	0.998788i
$37$	1486.90	+	1486.90i	1.08612	+	1.08612i	0.995924	+	0.0901982i	$0.0287501\pi$
$37$	1486.90	+	1486.90i	1.08612	+	1.08612i	0.0901982	+	0.995924i	$0.471250\pi$
$38$	−508.376	−	1897.28i	−0.352061	−	1.31391i
$39$	−1080.83	+	307.755i	−0.710602	+	0.202337i
$40$	−1.56958	+	0.480887i	−0.000980986	+	0.000300554i
$41$	−868.102	−	1503.60i	−0.516420	−	0.894466i	−0.999818	−	0.0190651i	$-0.993931\pi$
$41$	−868.102	−	1503.60i	−0.516420	−	0.894466i	0.483398	−	0.875401i	$-0.339402\pi$
$42$	−2195.78	+	3944.03i	−1.24477	+	2.23585i
$43$	−435.208	−	1624.22i	−0.235375	−	0.878430i	−0.977980	−	0.208700i	$-0.933077\pi$
$43$	−435.208	−	1624.22i	−0.235375	−	0.878430i	0.742605	−	0.669730i	$-0.233590\pi$
$44$		−	1085.69i		−	0.560789i
$45$	1682.32	−	1127.13i	0.830774	−	0.556609i
$46$	−82.6905			−0.0390787
$47$	1842.30	−	493.642i	0.833996	−	0.223469i	0.183540	−	0.983012i	$-0.441244\pi$
$47$	1842.30	−	493.642i	0.833996	−	0.223469i	0.650456	+	0.759544i	$0.274578\pi$
$48$	35.9668	+	2305.39i	0.0156106	+	1.00060i
$49$	4731.34	−	2731.64i	1.97057	−	1.13771i
$50$	2670.57	+	2315.93i	1.06823	+	0.926371i
$51$	2887.60	+	725.648i	1.11019	+	0.278988i
$52$	−1928.37	+	516.705i	−0.713154	+	0.191089i
$53$	402.755	−	402.755i	0.143380	−	0.143380i	−0.631773	−	0.775153i	$-0.717673\pi$
$53$	402.755	−	402.755i	0.143380	−	0.143380i	0.775153	+	0.631773i	$0.217673\pi$
$54$	−1252.28	−	3928.32i	−0.429453	−	1.34716i
$55$	1439.13	−	900.455i	0.475745	−	0.297671i
$56$	2.91155	−	5.04296i	0.000928429	−	0.00160809i
$57$	−1604.84	−	2682.15i	−0.493949	−	0.825531i
$58$	−3140.29	−	841.438i	−0.933498	−	0.250130i
$59$	−498.977	+	288.085i	−0.143343	+	0.0827592i	−0.569956	−	0.821675i	$-0.693040\pi$
$59$	−498.977	+	288.085i	−0.143343	+	0.0827592i	0.426613	+	0.904434i	$0.359707\pi$
$60$	3019.49	−	1955.48i	0.838747	−	0.543188i
$61$	1325.12	−	2295.17i	0.356118	−	0.616815i	−0.631190	−	0.775628i	$-0.717433\pi$
$61$	1325.12	−	2295.17i	0.356118	−	0.616815i	0.987309	+	0.158813i	$0.0507667\pi$
$62$	2263.77	+	2263.77i	0.588910	+	0.588910i
$63$	−1641.79	+	6993.00i	−0.413653	+	1.76191i
$64$			4090.05i			0.998548i
$65$	−2284.28	−	2127.59i	−0.540658	−	0.503572i
$66$	−946.585	−	3324.38i	−0.217306	−	0.763172i
$67$	−369.394	+	1378.60i	−0.0822887	+	0.307105i	−0.994787	−	0.101975i	$-0.967484\pi$
$67$	−369.394	+	1378.60i	−0.0822887	+	0.307105i	0.912498	+	0.409081i	$0.134150\pi$
$68$	5109.06	+	1368.97i	1.10490	+	0.296057i
$69$	−126.553	+	36.0349i	−0.0265812	+	0.00756876i
$70$	−12531.2	+	445.049i	−2.55738	+	0.0908263i
$71$	−2934.32			−0.582091			−0.291045	−	0.956709i	$-0.594003\pi$
$71$	−2934.32			−0.582091			−0.291045	+	0.956709i	$0.594003\pi$
$72$	1.53619	+	5.09208i	0.000296333	+	0.000982269i
$73$	−996.318	+	996.318i	−0.186962	+	0.186962i	−0.794381	−	0.607420i	$-0.792205\pi$
$73$	−996.318	+	996.318i	−0.186962	+	0.186962i	0.607420	+	0.794381i	$0.292205\pi$
$74$	10299.7	+	5946.53i	1.88088	+	1.08593i
$75$	5096.40	+	2380.62i	0.906026	+	0.423222i
$76$	−2776.31	−	4808.70i	−0.480662	−	0.832532i
$77$	−1558.57	+	5816.65i	−0.262872	+	0.981052i
$78$	−5454.17	+	3263.45i	−0.896478	+	0.536399i
$79$	−8580.07	−	4953.70i	−1.37479	−	0.793736i	−0.383264	−	0.923639i	$-0.625200\pi$
$79$	−8580.07	−	4953.70i	−1.37479	−	0.793736i	−0.991527	+	0.129903i	$0.958533\pi$
$80$	−5429.43	+	3397.17i	−0.848348	+	0.530807i
$81$	−3628.44	−	5466.37i	−0.553031	−	0.833160i
$82$	−6943.56	−	6943.56i	−1.03265	−	1.03265i
$83$	227.549	+	849.223i	0.0330307	+	0.123272i	0.980473	−	0.196655i	$-0.0630080\pi$
$83$	227.549	+	849.223i	0.0330307	+	0.123272i	−0.947442	+	0.319928i	$0.896341\pi$
$84$	−3110.05	+	12376.0i	−0.440767	+	1.75396i
$85$	2422.76	+	7907.69i	0.335330	+	1.09449i
$86$	−4755.17	−	8236.20i	−0.642939	−	1.11360i
$87$	−5172.72	+	80.7005i	−0.683409	+	0.0106620i
$88$	1.15404	+	4.30694i	0.000149024	+	0.000556165i
$89$			776.997i			0.0980933i	0.998796	+	0.0490467i	$0.0156183\pi$
$89$			776.997i			0.0980933i	−0.998796	+	0.0490467i	$0.984382\pi$
$90$	7540.75	−	8620.30i	0.930957	−	1.06423i
$91$	11073.2			1.33718
$92$	−225.792	+	60.5007i	−0.0266767	+	0.00714800i
$93$	4451.09	+	2478.07i	0.514636	+	0.286516i
$94$	9342.07	−	5393.64i	1.05727	−	0.610417i
$95$	4071.52	−	7668.40i	0.451138	−	0.849684i
$96$	3568.61	+	12532.9i	0.387219	+	1.35990i
$97$	3678.34	−	985.608i	0.390938	−	0.104752i	−0.0579949	−	0.998317i	$-0.518471\pi$
$97$	3678.34	−	985.608i	0.390938	−	0.104752i	0.448933	+	0.893565i	$0.351804\pi$
$98$	21849.2	−	21849.2i	2.27501	−	2.27501i
$99$	−2897.40	−	4675.28i	−0.295622	−	0.477020i
$100$	8986.61	+	4369.86i	0.898661	+	0.436986i
$101$	−10121.0	+	17530.1i	−0.992157	+	1.71847i	−0.387829	+	0.921731i	$0.626775\pi$
$101$	−10121.0	+	17530.1i	−0.992157	+	1.71847i	−0.604328	+	0.796736i	$0.706558\pi$
$102$	16837.5	−	262.685i	1.61837	−	0.0252485i
$103$	−9382.18	−	2513.95i	−0.884360	−	0.236964i	−0.212073	−	0.977254i	$-0.568021\pi$
$103$	−9382.18	−	2513.95i	−0.884360	−	0.236964i	−0.672287	+	0.740290i	$0.734688\pi$
$104$	7.10064	−	4.09956i	0.000656494	−	0.000379027i
$105$	−18984.4	+	6141.96i	−1.72194	+	0.557094i
$106$	1610.73	−	2789.86i	0.143354	−	0.248297i
$107$	4553.52	+	4553.52i	0.397722	+	0.397722i	0.877429	−	0.479707i	$-0.159257\pi$
$107$	4553.52	+	4553.52i	0.397722	+	0.397722i	−0.479707	+	0.877429i	$0.659257\pi$
$108$	−6293.61	−	9810.30i	−0.539576	−	0.841075i
$109$			11613.5i			0.977489i	0.872427	+	0.488744i	$0.162545\pi$
$109$			11613.5i			0.977489i	−0.872427	+	0.488744i	$0.837455\pi$
$110$	6543.99	−	7025.93i	0.540826	−	0.580656i
$111$	18354.5	+	4612.44i	1.48969	+	0.374356i
$112$	5880.04	−	21944.6i	0.468753	−	1.74941i
$113$	6352.91	+	1702.26i	0.497526	+	0.133312i	0.498852	−	0.866687i	$-0.333755\pi$
$113$	6352.91	+	1702.26i	0.497526	+	0.133312i	−0.00132558	+	0.999999i	$0.500422\pi$
$114$	−12693.7	−	12303.7i	−0.976735	−	0.946727i
$115$	−267.465	−	249.119i	−0.0202242	−	0.0188369i
$116$	−9190.40			−0.682996
$117$	−6925.16	+	7371.36i	−0.505893	+	0.538488i
$118$	−2304.26	+	2304.26i	−0.165488	+	0.165488i
$119$	−25407.0	−	14668.7i	−1.79415	−	1.03585i
$120$	−9.89978	+	10.9670i	−0.000687485	+	0.000761598i
$121$	5014.97	+	8686.19i	0.342530	+	0.593279i
$122$	3879.51	−	14478.5i	0.260649	−	0.972757i
$123$	−13652.6	−	7600.87i	−0.902413	−	0.502404i
$124$	7837.67	+	4525.08i	0.509734	+	0.294295i
$125$	1660.94	+	15536.5i	0.106300	+	0.994334i
$126$	1267.34	+	40606.9i	0.0798272	+	2.55775i
$127$	7717.85	+	7717.85i	0.478508	+	0.478508i	0.904654	−	0.426147i	$-0.140129\pi$
$127$	7717.85	+	7717.85i	0.478508	+	0.478508i	−0.426147	+	0.904654i	$0.640129\pi$
$128$	−8.70144	−	32.4742i	−0.000531094	−	0.00198207i
$129$	−10866.7	−	10532.9i	−0.653008	−	0.632946i
$130$	−15593.7	−	8279.46i	−0.922706	−	0.489909i
$131$	−3525.83	−	6106.92i	−0.205456	−	0.355860i	0.744822	−	0.667263i	$-0.232534\pi$
$131$	−3525.83	−	6106.92i	−0.205456	−	0.355860i	−0.950278	+	0.311403i	$0.899201\pi$
$132$	−5017.00	−	8384.85i	−0.287936	−	0.481224i
$133$	7971.10	+	29748.6i	0.450625	+	1.68175i
$134$			8072.16i			0.449552i
$135$	7784.15	−	16479.0i	0.427114	−	0.904198i
$136$	−21.7229			−0.00117446
$137$	−3789.94	+	1015.51i	−0.201925	+	0.0541057i	−0.358364	−	0.933582i	$-0.616665\pi$
$137$	−3789.94	+	1015.51i	−0.201925	+	0.0541057i	0.156439	+	0.987688i	$0.449999\pi$
$138$	−638.626	+	382.116i	−0.0335342	+	0.0200649i
$139$	8913.02	−	5145.94i	0.461313	−	0.266339i	−0.251283	−	0.967914i	$-0.580853\pi$
$139$	8913.02	−	5145.94i	0.461313	−	0.266339i	0.712596	+	0.701575i	$0.247519\pi$
$140$	−33891.6	+	10383.7i	−1.72916	+	0.529781i
$141$	11947.1	−	12325.8i	0.600930	−	0.619977i
$142$	−16030.5	+	4295.36i	−0.795007	+	0.213021i
$143$	−5995.52	+	5995.52i	−0.293194	+	0.293194i
$144$	10931.1	+	17638.5i	0.527154	+	0.850623i
$145$	−7622.40	−	12182.3i	−0.362540	−	0.579419i
$146$	−3984.55	+	6901.44i	−0.186928	+	0.323768i
$147$	23917.5	−	42960.4i	1.10683	−	1.98808i
$148$	32474.7	+	8701.58i	1.48259	+	0.397260i
$149$	26483.3	−	15290.1i	1.19289	−	0.688713i	0.233926	−	0.972254i	$-0.424843\pi$
$149$	26483.3	−	15290.1i	1.19289	−	0.688713i	0.958960	+	0.283541i	$0.0915093\pi$
$150$	31327.0	+	5545.31i	1.39231	+	0.246458i
$151$	12922.2	−	22381.9i	0.566737	−	0.981617i	−0.430149	−	0.902758i	$-0.641539\pi$
$151$	12922.2	−	22381.9i	0.566737	−	0.981617i	0.996886	−	0.0788593i	$-0.0251278\pi$
$152$	16.1251	+	16.1251i	0.000697936	+	0.000697936i
$153$	25654.4	−	7739.48i	1.09592	−	0.330620i
$154$			34058.5i			1.43610i
$155$	502.265	+	14142.2i	0.0209060	+	0.588646i
$156$	−12505.2	+	12901.6i	−0.513858	+	0.530146i
$157$	−6270.36	+	23401.3i	−0.254386	+	0.949381i	0.714045	+	0.700100i	$0.246861\pi$
$157$	−6270.36	+	23401.3i	−0.254386	+	0.949381i	−0.968431	+	0.249282i	$0.919806\pi$
$158$	−54125.3	−	14502.8i	−2.16813	−	0.580949i
$159$	1249.37	−	4971.66i	0.0494191	−	0.196656i
$160$	−24670.8	+	26487.7i	−0.963702	+	1.03467i
$161$	1296.55			0.0500193
$162$	−27824.4	−	24551.9i	−1.06022	−	0.935525i
$163$	−1758.19	+	1758.19i	−0.0661745	+	0.0661745i	−0.739419	−	0.673245i	$-0.764900\pi$
$163$	−1758.19	+	1758.19i	−0.0661745	+	0.0661745i	0.673245	+	0.739419i	$0.264900\pi$
$164$	−24040.1	−	13879.6i	−0.893817	−	0.516045i
$165$	6953.46	−	13604.6i	0.255407	−	0.499708i
$166$	2486.25	+	4306.31i	0.0902252	+	0.156275i
$167$	−7643.90	+	28527.4i	−0.274083	+	1.02289i	0.682371	+	0.731006i	$0.260949\pi$
$167$	−7643.90	+	28527.4i	−0.274083	+	1.02289i	−0.956454	+	0.291885i	$0.905718\pi$
$168$	−0.817526	−	52.4016i	−2.89656e−5	−	0.00185663i
$169$	−11232.1	−	6484.83i	−0.393266	−	0.227052i
$170$	24811.4	+	39654.1i	0.858525	+	1.37211i
$171$	−24788.6	−	13298.4i	−0.847736	−	0.454788i
$172$	−19010.3	−	19010.3i	−0.642589	−	0.642589i
$173$	5052.46	+	18856.0i	0.168815	+	0.630025i	0.997523	+	0.0703440i	$0.0224097\pi$
$173$	5052.46	+	18856.0i	0.168815	+	0.630025i	−0.828708	+	0.559681i	$0.810924\pi$
$174$	−28141.0	+	8012.89i	−0.929483	+	0.264662i
$175$	−41873.3	−	36312.7i	−1.36729	−	1.18572i
$176$	8698.11	+	15065.6i	0.280801	+	0.486362i
$177$	−2522.39	+	4530.70i	−0.0805131	+	0.144617i
$178$	1137.40	+	4244.82i	0.0358981	+	0.133974i
$179$			6318.29i			0.197194i	0.995127	+	0.0985969i	$0.0314354\pi$
$179$			6318.29i			0.197194i	−0.995127	+	0.0985969i	$0.968565\pi$
$180$	14283.4	−	29055.5i	0.440847	−	0.896774i
$181$	−35255.5			−1.07614			−0.538071	−	0.842900i	$-0.680847\pi$
$181$	−35255.5			−1.07614			−0.538071	+	0.842900i	$0.680847\pi$
$182$	60493.8	−	16209.3i	1.82628	−	0.489351i
$183$	−372.075	−	23849.2i	−0.0111104	−	0.712150i
$184$	0.831410	−	0.480015i	2.45572e−5	−	1.41781e-5i
$185$	15399.8	+	50263.7i	0.449958	+	1.46863i
$186$	27944.3	+	7022.33i	0.807731	+	0.202981i
$187$	21698.8	−	5814.18i	0.620516	−	0.166267i
$188$	21562.8	−	21562.8i	0.610085	−	0.610085i
$189$	19635.3	+	61594.3i	0.549684	+	1.72432i
$190$	11017.9	−	47853.3i	0.305205	−	1.32558i
$191$	32543.7	−	56367.3i	0.892072	−	1.54511i	0.0546857	−	0.998504i	$-0.482584\pi$
$191$	32543.7	−	56367.3i	0.892072	−	1.54511i	0.837387	−	0.546611i	$-0.184082\pi$
$192$	18900.3	+	31587.8i	0.512703	+	0.856875i
$193$	48353.7	+	12956.3i	1.29812	+	0.347831i	0.840740	−	0.541440i	$-0.182121\pi$
$193$	48353.7	+	12956.3i	1.29812	+	0.347831i	0.457382	+	0.889270i	$0.348787\pi$
$194$	18652.4	−	10769.0i	0.495600	−	0.286135i
$195$	−27473.4	−	5875.82i	−0.722508	−	0.154525i
$196$	43674.5	−	75646.5i	1.13688	−	1.96914i
$197$	−42539.4	−	42539.4i	−1.09612	−	1.09612i	−0.994860	−	0.101261i	$-0.967712\pi$
$197$	−42539.4	−	42539.4i	−1.09612	−	1.09612i	−0.101261	−	0.994860i	$-0.532288\pi$
$198$	−22672.6	−	21300.2i	−0.578324	−	0.543318i
$199$			20545.3i			0.518806i	0.965769	+	0.259403i	$0.0835259\pi$
$199$			20545.3i			0.518806i	−0.965769	+	0.259403i	$0.916474\pi$
$200$	−40.2951	−	7.78291i	−0.00100738	−	0.000194573i
$201$	3517.69	+	12354.0i	0.0870693	+	0.305784i
$202$	−29631.0	+	110584.i	−0.726178	+	2.71013i
$203$	49238.3	+	13193.4i	1.19484	+	0.320157i
$204$	45783.7	−	13036.5i	1.10015	−	0.313257i
$205$	−1540.57	−	43377.7i	−0.0366585	−	1.03219i
$206$	−54935.9			−1.29456
$207$	−810.863	+	863.108i	−0.0189237	+	0.0201430i
$208$	22619.4	−	22619.4i	0.522823	−	0.522823i
$209$	−20423.2	−	11791.3i	−0.467553	−	0.269942i
$210$	−94722.8	+	61344.2i	−2.14791	+	1.39102i
$211$	−568.544	−	984.747i	−0.0127702	−	0.0221187i	0.859570	−	0.511019i	$-0.170732\pi$
$211$	−568.544	−	984.747i	−0.0127702	−	0.0221187i	−0.872340	+	0.488900i	$0.837398\pi$
$212$	2356.99	−	8796.39i	0.0524427	−	0.195719i
$213$	−22662.0	+	13559.6i	−0.499504	+	0.298874i
$214$	31542.0	+	18210.8i	0.688750	+	0.397650i
$215$	9432.13	−	40966.0i	0.204048	−	0.886231i
$216$	35.3948	+	32.2278i	0.000758634	+	0.000690753i
$217$	−35494.9	−	35494.9i	−0.753783	−	0.753783i
$218$	17000.3	+	63446.1i	0.357721	+	1.33503i
$219$	−3090.62	+	12298.7i	−0.0644404	+	0.256431i
$220$	12728.2	−	23972.7i	0.262980	−	0.495303i
$221$	−20654.0	−	35773.8i	−0.422882	−	0.732454i
$222$	107024.	−	1669.71i	2.17159	−	0.0338793i
$223$	19854.4	+	74097.7i	0.399252	+	1.49003i	0.814415	+	0.580283i	$0.197058\pi$
$223$	19854.4	+	74097.7i	0.399252	+	1.49003i	−0.415162	+	0.909747i	$0.636275\pi$
$224$		−	128400.i		−	2.55899i
$225$	50360.8	−	5164.90i	0.994782	−	0.102023i
$226$	37198.5			0.728296
$227$	−68087.2	+	18243.9i	−1.32134	+	0.354051i	−0.849478	−	0.527623i	$-0.823083\pi$
$227$	−68087.2	+	18243.9i	−1.32134	+	0.354051i	−0.471858	+	0.881674i	$0.656417\pi$
$228$	−43662.8	−	24308.6i	−0.839928	−	0.467617i
$229$	23542.3	−	13592.1i	0.448929	−	0.259189i	−0.258449	−	0.966025i	$-0.583211\pi$
$229$	23542.3	−	13592.1i	0.448929	−	0.259189i	0.707378	+	0.706836i	$0.249878\pi$
$230$	−1825.86	−	969.437i	−0.0345153	−	0.0183258i
$231$	14842.0	+	52124.7i	0.278144	+	0.976832i
$232$	36.4585	−	9.76902i	0.000677365	−	0.000181499i
$233$	−57865.2	+	57865.2i	−1.06587	+	1.06587i	−0.0682027	+	0.997671i	$0.521726\pi$
$233$	−57865.2	+	57865.2i	−1.06587	+	1.06587i	−0.997671	+	0.0682027i	$0.978274\pi$
$234$	−27042.5	+	50407.8i	−0.493872	+	0.920590i
$235$	46466.5	+	10698.6i	0.841402	+	0.193727i
$236$	−4606.01	+	7977.85i	−0.0826991	+	0.143239i
$237$	−89155.8	+	1390.94i	−1.58728	+	0.0247634i
$238$	−160274.	−	42945.2i	−2.82949	−	0.758159i
$239$	50927.7	−	29403.1i	0.891575	−	0.514751i	0.0171179	−	0.999853i	$-0.494551\pi$
$239$	50927.7	−	29403.1i	0.891575	−	0.514751i	0.874457	+	0.485102i	$0.161218\pi$
$240$	−26233.5	+	51326.2i	−0.455442	+	0.891080i
$241$	284.721	−	493.152i	0.00490214	−	0.00849075i	−0.863564	−	0.504239i	$-0.831773\pi$
$241$	284.721	−	493.152i	0.00490214	−	0.00849075i	0.868466	+	0.495749i	$0.165106\pi$
$242$	40112.5	+	40112.5i	0.684935	+	0.684935i
$243$	−53283.0	−	25450.0i	−0.902353	−	0.430999i
$244$		−	42373.0i		−	0.711720i
$245$	136496.	−	4847.70i	2.27399	−	0.0807613i
$246$	−85712.1	−	21539.2i	−1.41635	−	0.355926i
$247$	−11223.6	+	41886.9i	−0.183966	+	0.686569i
$248$	−35.9021	−	9.61995i	−0.000583737	−	0.000156412i
$249$	5681.67	+	5507.11i	0.0916383	+	0.0888229i
$250$	31816.7	+	82446.1i	0.509068	+	1.31914i
$251$	−30858.8			−0.489814			−0.244907	−	0.969547i	$-0.578757\pi$
$251$	−30858.8			−0.489814			−0.244907	+	0.969547i	$0.578757\pi$
$252$	33170.6	+	109952.i	0.522339	+	1.73142i
$253$	−702.012	+	702.012i	−0.0109674	+	0.0109674i
$254$	53461.1	+	30865.8i	0.828649	+	0.478421i
$255$	55252.9	+	49876.1i	0.849718	+	0.767030i
$256$	−32815.5	−	56838.1i	−0.500725	−	0.867281i
$257$	−2345.46	+	8753.36i	−0.0355109	+	0.132528i	−0.981406	−	0.191945i	$-0.938520\pi$
$257$	−2345.46	+	8753.36i	−0.0355109	+	0.132528i	0.945895	+	0.324473i	$0.105187\pi$
$258$	−74784.4	−	41635.1i	−1.12350	−	0.625489i
$259$	−161494.	−	93238.8i	−2.40745	−	1.38994i
$260$	−48637.3	−	11198.4i	−0.719487	−	0.165657i
$261$	−39576.5	+	24526.6i	−0.580973	+	0.360045i
$262$	−28201.5	−	28201.5i	−0.410837	−	0.410837i
$263$	−31432.4	−	117307.i	−0.454429	−	1.69595i	−0.689762	−	0.724036i	$-0.742285\pi$
$263$	−31432.4	−	117307.i	−0.454429	−	1.69595i	0.235334	−	0.971915i	$-0.424382\pi$
$264$	28.8153	+	27.9300i	0.000413443	+	0.000400740i
$265$	13614.9	−	4171.33i	0.193875	−	0.0593994i
$266$	87094.0	+	150851.i	1.23091	+	2.13199i
$267$	3590.53	+	6000.81i	0.0503659	+	0.0841759i
$268$	5906.01	+	22041.5i	0.0822290	+	0.306883i
$269$			94241.6i			1.30238i	0.758914	+	0.651191i	$0.225730\pi$
$269$			94241.6i			1.30238i	−0.758914	+	0.651191i	$0.774270\pi$
$270$	18403.1	−	101421.i	0.252444	−	1.39124i
$271$	−59781.2			−0.814003			−0.407002	−	0.913427i	$-0.633426\pi$
$271$	−59781.2			−0.814003			−0.407002	+	0.913427i	$0.633426\pi$
$272$	−81863.6	+	21935.3i	−1.10650	+	0.296487i
$273$	85518.9	−	51169.4i	1.14746	−	0.686571i
$274$	−19218.3	+	11095.7i	−0.255985	+	0.147793i
$275$	42333.5	−	3010.77i	0.559782	−	0.0398119i
$276$	−1464.23	+	1510.64i	−0.0192217	+	0.0198310i
$277$	123252.	−	33025.3i	1.60633	−	0.430414i	0.659382	−	0.751808i	$-0.270818\pi$
$277$	123252.	−	33025.3i	1.60633	−	0.430414i	0.946946	+	0.321393i	$0.104151\pi$
$278$	41160.0	−	41160.0i	0.532581	−	0.532581i
$279$	45827.4	−	1430.27i	0.588731	−	0.0183742i
$280$	123.411	−	77.2177i	0.00157412	−	0.000984920i
$281$	8153.16	−	14121.7i	0.103256	−	0.178844i	−0.809769	−	0.586749i	$-0.800407\pi$
$281$	8153.16	−	14121.7i	0.103256	−	0.178844i	0.913024	+	0.407905i	$0.133741\pi$
$282$	47225.3	−	84825.6i	0.593850	−	1.06667i
$283$	62811.4	+	16830.3i	0.784270	+	0.210145i	0.628666	−	0.777675i	$-0.283601\pi$
$283$	62811.4	+	16830.3i	0.784270	+	0.210145i	0.155604	+	0.987820i	$0.450268\pi$
$284$	−40629.6	+	23457.5i	−0.503740	+	0.290834i
$285$	−3991.25	−	78038.3i	−0.0491383	−	0.960767i
$286$	−23977.7	+	41530.6i	−0.293140	+	0.507734i
$287$	108872.	+	108872.i	1.32176	+	1.32176i
$288$	85475.5	+	80301.6i	1.03052	+	0.968142i
$289$			25921.2i			0.310355i
$290$	−59474.9	−	55395.2i	−0.707192	−	0.658683i
$291$	23853.6	−	24609.7i	0.281688	−	0.290616i
$292$	−5830.61	+	21760.1i	−0.0683830	+	0.255209i
$293$	−139071.	−	37263.9i	−1.61995	−	0.434063i	−0.668960	−	0.743299i	$-0.733260\pi$
$293$	−139071.	−	37263.9i	−1.61995	−	0.434063i	−0.950985	+	0.309236i	$0.899927\pi$
$294$	67777.1	−	269709.i	0.784131	−	3.12033i
$295$	−14395.2	+	511.249i	−0.165414	+	0.00587473i
$296$	−138.077			−0.00157594
$297$	−43981.4	−	22718.6i	−0.498605	−	0.257554i
$298$	122299.	−	122299.i	1.37718	−	1.37718i
$299$	1581.00	+	912.790i	0.0176844	+	0.0102101i
$300$	89597.7	−	7778.67i	0.995530	−	0.0864297i
$301$	74558.9	+	129140.i	0.822937	+	1.42537i
$302$	37831.9	−	141190.i	0.414805	−	1.54807i
$303$	2841.84	+	182156.i	0.0309539	+	1.98407i
$304$	77050.9	+	44485.4i	0.833740	+	0.481360i
$305$	56167.3	−	35143.6i	0.603787	−	0.377787i
$306$	128824.	−	79835.6i	1.37579	−	0.852616i
$307$	−17181.4	−	17181.4i	−0.182298	−	0.182298i	0.610058	−	0.792357i	$-0.291146\pi$
$307$	−17181.4	−	17181.4i	−0.182298	−	0.182298i	−0.792357	+	0.610058i	$0.791146\pi$
$308$	24919.0	+	92998.9i	0.262681	+	0.980340i
$309$	−84076.4	+	23940.0i	−0.880556	+	0.250730i
$310$	23445.8	+	76525.3i	0.243973	+	0.796309i
$311$	−62654.4	−	108521.i	−0.647785	−	1.12200i	−0.983651	−	0.180086i	$-0.942362\pi$
$311$	−62654.4	−	108521.i	−0.647785	−	1.12200i	0.335866	−	0.941910i	$-0.390971\pi$
$312$	35.8946	−	64.4735i	0.000368740	−	0.000662327i
$313$	−39946.6	−	149083.i	−0.407748	−	1.52173i	−0.798932	−	0.601422i	$-0.794601\pi$
$313$	−39946.6	−	149083.i	−0.407748	−	1.52173i	0.391184	−	0.920312i	$-0.372066\pi$
$314$			137023.i			1.38974i
$315$	−118235.	+	135162.i	−1.19159	+	1.36218i
$316$	−158404.			−1.58632
$317$	−45779.1	+	12266.5i	−0.455564	+	0.122068i	−0.479301	−	0.877650i	$-0.659110\pi$
$317$	−45779.1	+	12266.5i	−0.455564	+	0.122068i	0.0237379	+	0.999718i	$0.492443\pi$
$318$	−452.271	−	28989.6i	−0.00447244	−	0.286674i
$319$	−33803.4	+	19516.4i	−0.332184	+	0.191787i
$320$	−47950.5	+	90311.1i	−0.468266	+	0.881944i
$321$	56209.2	+	14125.2i	0.545503	+	0.137084i
$322$	7083.19	−	1897.94i	0.0683152	−	0.0183050i
$323$	81240.0	−	81240.0i	0.778691	−	0.778691i
$324$	−93939.8	−	46682.8i	−0.894870	−	0.444699i
$325$	−25495.2	−	73758.8i	−0.241375	−	0.698308i
$326$	−7031.49	+	12178.9i	−0.0661625	+	0.114597i
$327$	53666.6	+	89692.4i	0.501890	+	0.838803i
$328$	110.121	+	29.5068i	0.00102358	+	0.000274268i
$329$	−146479.	+	84569.9i	−1.35327	+	0.781311i
$330$	18072.7	−	84501.9i	0.165957	−	0.775959i
$331$	−8527.54	+	14770.1i	−0.0778337	+	0.134812i	−0.902315	−	0.431077i	$-0.858134\pi$
$331$	−8527.54	+	14770.1i	−0.0778337	+	0.134812i	0.824481	+	0.565889i	$0.191467\pi$
$332$	9939.57	+	9939.57i	0.0901761	+	0.0901761i
$333$	163067.	−	49194.5i	1.47055	−	0.443638i
$334$			167038.i			1.49734i
$335$	−24318.7	+	26109.7i	−0.216696	+	0.232655i
$336$	−55994.8	−	196652.i	−0.495986	−	1.74189i
$337$	34597.9	−	129121.i	0.304642	−	1.13694i	−0.628612	−	0.777719i	$-0.716376\pi$
$337$	34597.9	−	129121.i	0.304642	−	1.13694i	0.933253	−	0.359219i	$-0.116957\pi$
$338$	−70854.7	−	18985.5i	−0.620205	−	0.166183i
$339$	56930.2	−	16210.4i	0.495386	−	0.141057i
$340$	96762.0	+	90124.7i	0.837042	+	0.779625i
$341$	38437.2			0.330554
$342$	−154890.	−	36364.4i	−1.32425	−	0.310902i
$343$	−192026.	+	192026.i	−1.63219	+	1.63219i
$344$	95.6216	+	55.2072i	0.000808052	+	0.000466529i
$345$	−3216.84	−	687.997i	−0.0270266	−	0.00578027i
$346$	55204.2	+	95616.6i	0.461127	+	0.798695i
$347$	38939.9	−	145326.i	0.323397	−	1.20694i	−0.592516	−	0.805559i	$-0.701865\pi$
$347$	38939.9	−	145326.i	0.323397	−	1.20694i	0.915913	−	0.401376i	$-0.131468\pi$
$348$	−70978.2	+	42469.2i	−0.586093	+	0.350683i
$349$	156387.	+	90289.9i	1.28395	+	0.741291i	0.977569	−	0.210617i	$-0.0675474\pi$
$349$	156387.	+	90289.9i	1.28395	+	0.741291i	0.306384	+	0.951908i	$0.400881\pi$
$350$	−281914.	−	137085.i	−2.30134	−	1.11906i
$351$	−19420.3	+	88931.0i	−0.157631	+	0.721837i
$352$	69521.8	+	69521.8i	0.561094	+	0.561094i
$353$	6116.90	+	22828.6i	0.0490888	+	0.183202i	0.986117	−	0.166052i	$-0.0531019\pi$
$353$	6116.90	+	22828.6i	0.0490888	+	0.183202i	−0.937028	+	0.349254i	$0.886435\pi$
$354$	−7147.92	+	28444.1i	−0.0570392	+	0.226979i
$355$	−64791.7	−	34401.0i	−0.514118	−	0.272970i
$356$	6211.47	+	10758.6i	0.0490111	+	0.0848896i
$357$	−264005.	+	4118.78i	−2.07145	+	0.0323171i
$358$	9248.94	+	34517.5i	0.0721648	+	0.269323i
$359$		−	23851.8i		−	0.185068i	−0.995710	−	0.0925341i	$-0.970503\pi$
$359$		−	23851.8i		−	0.185068i	0.995710	−	0.0925341i	$-0.0294967\pi$
$360$	−25.7779	+	130.446i	−0.000198903	+	0.00100653i
$361$	9710.52			0.0745123
$362$	−192604.	+	51608.2i	−1.46977	+	0.393824i
$363$	78870.3	+	43909.8i	0.598550	+	0.333233i
$364$	153323.	−	88520.9i	1.15719	−	0.668103i
$365$	−33679.9	+	10318.8i	−0.252804	+	0.0774542i
$366$	−36944.0	−	129746.i	−0.275792	−	0.968573i
$367$	60890.5	−	16315.6i	0.452082	−	0.121135i	−0.0255914	−	0.999672i	$-0.508147\pi$
$367$	60890.5	−	16315.6i	0.452082	−	0.121135i	0.477673	+	0.878537i	$0.341480\pi$
$368$	2648.49	−	2648.49i	0.0195571	−	0.0195571i
$369$	−140564.	+	4387.00i	−1.03234	+	0.0322192i
$370$	157709.	+	252053.i	1.15200	+	1.84115i
$371$	−25255.5	+	43743.8i	−0.183488	+	0.317811i
$372$	81441.5	−	1270.58i	0.588518	−	0.00918157i
$373$	−83538.0	−	22383.9i	−0.600436	−	0.160886i	−0.0542174	−	0.998529i	$-0.517266\pi$
$373$	−83538.0	−	22383.9i	−0.600436	−	0.160886i	−0.546218	+	0.837643i	$0.683933\pi$
$374$	110032.	−	63527.0i	0.786640	−	0.454167i
$375$	84622.2	+	112314.i	0.601758	+	0.798679i
$376$	−62.6198	+	108.461i	−0.000442931	+	0.000767178i
$377$	50752.4	+	50752.4i	0.357087	+	0.357087i
$378$	197434.	+	307754.i	1.38177	+	2.15387i
$379$		−	227379.i		−	1.58297i	−0.611189	−	0.791485i	$-0.709308\pi$
$379$		−	227379.i		−	1.58297i	0.611189	−	0.791485i	$-0.290692\pi$
$380$	−4926.96	−	138728.i	−0.0341202	−	0.960719i
$381$	95270.0	+	23941.1i	0.656306	+	0.164928i
$382$	95277.3	−	355580.i	0.652924	−	2.43674i
$383$	139200.	+	37298.5i	0.948946	+	0.254269i	0.699915	−	0.714226i	$-0.253221\pi$
$383$	139200.	+	37298.5i	0.948946	+	0.254269i	0.249031	+	0.968496i	$0.419888\pi$
$384$	−217.267	−	210.591i	−0.00147343	−	0.00142816i
$385$	−102607.	+	110163.i	−0.692237	+	0.743217i
$386$	283128.			1.90024
$387$	−132597.	−	31130.6i	−0.885345	−	0.207858i
$388$	43052.4	−	43052.4i	0.285979	−	0.285979i
$389$	27350.7	+	15790.9i	0.180746	+	0.104354i	0.587643	−	0.809120i	$-0.300056\pi$
$389$	27350.7	+	15790.9i	0.180746	+	0.104354i	−0.406897	+	0.913474i	$0.633389\pi$
$390$	−158691.	+	8116.24i	−1.04334	+	0.0533612i
$391$	−2418.36	−	4188.73i	−0.0158186	−	0.0273986i
$392$	−92.8485	+	346.515i	−0.000604231	+	0.00225502i
$393$	−55450.6	−	30871.2i	−0.359022	−	0.199880i
$394$	−294668.	−	170127.i	−1.89819	−	1.09592i
$395$	−131378.	−	209971.i	−0.842031	−	1.34575i
$396$	−77493.4	−	41573.2i	−0.494168	−	0.265108i
$397$	71600.9	+	71600.9i	0.454294	+	0.454294i	0.896777	−	0.442483i	$-0.145902\pi$
$397$	71600.9	+	71600.9i	0.454294	+	0.454294i	−0.442483	+	0.896777i	$0.645902\pi$
$398$	30074.9	+	112241.i	0.189862	+	0.708574i
$399$	199031.	+	192916.i	1.25018	+	1.21178i
$400$	−159713.	+	11358.8i	−0.998204	+	0.0709926i
$401$	−13931.6	−	24130.3i	−0.0866388	−	0.150063i	0.819450	−	0.573151i	$-0.194279\pi$
$401$	−13931.6	−	24130.3i	−0.0866388	−	0.150063i	−0.906088	+	0.423088i	$0.860946\pi$
$402$	37301.7	+	62341.9i	0.230822	+	0.385770i
$403$	−18293.2	−	68271.1i	−0.112637	−	0.420365i
$404$			323637.i			1.98287i
$405$	−16032.4	−	163240.i	−0.0977437	−	0.995212i
$406$	288307.			1.74905
$407$	137924.	−	36956.7i	0.832630	−	0.223103i
$408$	−167.768	+	100.382i	−0.00100783	+	0.000603027i
$409$	259567.	−	149861.i	1.55168	−	0.895863i	0.553675	−	0.832733i	$-0.313225\pi$
$409$	259567.	−	149861.i	1.55168	−	0.895863i	0.998005	−	0.0631308i	$-0.0201085\pi$
$410$	−71914.2	−	234722.i	−0.427806	−	1.39633i
$411$	−24577.3	+	25356.3i	−0.145496	+	0.150107i
$412$	−150006.	+	40194.0i	−0.883719	+	0.236792i
$413$	36129.7	−	36129.7i	0.211819	−	0.211819i
$414$	−3166.39	+	5902.22i	−0.0184741	+	0.0344362i
$415$	−4931.60	+	21419.1i	−0.0286346	+	0.124367i
$416$	90395.7	−	156570.i	0.522349	−	0.904735i
$417$	45056.5	−	80929.9i	0.259110	−	0.465411i
$418$	−128835.	−	34521.1i	−0.737361	−	0.197575i
$419$	−78258.0	+	45182.3i	−0.445760	+	0.257360i	−0.706038	−	0.708174i	$-0.749519\pi$
$419$	−78258.0	+	45182.3i	−0.445760	+	0.257360i	0.260278	+	0.965534i	$0.416186\pi$
$420$	−213764.	+	236808.i	−1.21181	+	1.34245i
$421$	−128707.	+	222927.i	−0.726171	+	1.25776i	0.232320	+	0.972639i	$0.425368\pi$
$421$	−128707.	+	222927.i	−0.726171	+	1.25776i	−0.958490	+	0.285125i	$0.907965\pi$
$422$	−4547.53	−	4547.53i	−0.0255359	−	0.0255359i
$423$	35310.5	−	150401.i	0.197344	−	0.840562i
$424$			37.4008i			0.000208041i
$425$	−39211.1	+	203011.i	−0.217086	+	1.12393i
$426$	−103956.	+	107251.i	−0.572836	+	0.590993i
$427$	−60828.9	+	227016.i	−0.333622	+	1.24509i
$428$	99451.4	+	26647.9i	0.542904	+	0.145471i
$429$	−18598.4	+	74009.4i	−0.101056	+	0.402135i
$430$	−8438.75	−	237609.i	−0.0456396	−	1.28507i
$431$	20822.6			0.112093			0.0560466	−	0.998428i	$-0.482150\pi$
$431$	20822.6			0.112093			0.0560466	+	0.998428i	$0.482150\pi$
$432$	165930.	+	85710.9i	0.889113	+	0.459270i
$433$	33376.0	−	33376.0i	0.178016	−	0.178016i	−0.612475	−	0.790490i	$-0.709826\pi$
$433$	33376.0	−	33376.0i	0.178016	−	0.178016i	0.790490	+	0.612475i	$0.209826\pi$
$434$	−245871.	−	141954.i	−1.30535	−	0.753646i
$435$	−115163.	−	58861.4i	−0.608605	−	0.311066i
$436$	92840.9	+	160805.i	0.488390	+	0.845916i
$437$	−1314.16	+	4904.51i	−0.00688153	+	0.0256822i
$438$	1118.81	+	71713.1i	0.00583187	+	0.373810i
$439$	−142448.	−	82242.2i	−0.739139	−	0.426742i	0.0826171	−	0.996581i	$-0.473672\pi$
$439$	−142448.	−	82242.2i	−0.739139	−	0.426742i	−0.821756	+	0.569839i	$0.807005\pi$
$440$	−25.0112	+	108.630i	−0.000129190	+	0.000561104i
$441$	−13804.5	−	442310.i	−0.0709811	−	2.27431i
$442$	−165202.	−	165202.i	−0.845611	−	0.845611i
$443$	60267.2	+	224920.i	0.307096	+	1.14610i	0.931126	+	0.364697i	$0.118827\pi$
$443$	60267.2	+	224920.i	0.307096	+	1.14610i	−0.624031	+	0.781400i	$0.714506\pi$
$444$	291015.	−	82863.9i	1.47622	−	0.420339i
$445$	−9109.26	+	17156.6i	−0.0460006	+	0.0866386i
$446$	216934.	+	375740.i	1.09058	+	1.88894i
$447$	133876.	−	240467.i	0.670021	−	1.20348i
$448$	−93876.0	−	350350.i	−0.467734	−	1.74561i
$449$			33041.1i			0.163894i	0.996637	+	0.0819469i	$0.0261138\pi$
$449$			33041.1i			0.163894i	−0.996637	+	0.0819469i	$0.973886\pi$
$450$	267566.	−	101936.i	1.32131	−	0.503390i
$451$	−117896.			−0.579626
$452$	101573.	−	27216.3i	0.497165	−	0.133215i
$453$	−3628.38	−	232571.i	−0.0176814	−	1.13334i
$454$	−345262.	+	199337.i	−1.67508	+	0.967110i
$455$	244502.	+	129818.i	1.18103	+	0.627065i
$456$	199.050	+	50.0209i	0.000957267	+	0.000240559i
$457$	17801.9	−	4770.00i	0.0852381	−	0.0228395i	−0.215948	−	0.976405i	$-0.569284\pi$
$457$	17801.9	−	4770.00i	0.0852381	−	0.0228395i	0.301186	+	0.953565i	$0.402617\pi$
$458$	108717.	−	108717.i	0.518285	−	0.518285i
$459$	162367.	−	178323.i	0.770677	−	0.846412i
$460$	−5694.92	−	1311.21i	−0.0269136	−	0.00619666i
$461$	135469.	−	234640.i	0.637440	−	1.10408i	−0.348553	−	0.937289i	$-0.613327\pi$
$461$	135469.	−	234640.i	0.637440	−	1.10408i	0.985993	−	0.166789i	$-0.0533399\pi$
$462$	157386.	+	263037.i	0.737363	+	1.23235i
$463$	−113298.	−	30358.0i	−0.528517	−	0.141616i	−0.0153137	−	0.999883i	$-0.504875\pi$
$463$	−113298.	−	30358.0i	−0.528517	−	0.141616i	−0.513203	+	0.858267i	$0.671541\pi$
$464$	127531.	−	73629.9i	0.592351	−	0.341994i
$465$	69230.8	+	106901.i	0.320179	+	0.494395i
$466$	−231419.	+	400829.i	−1.06568	+	1.84581i
$467$	−20059.0	−	20059.0i	−0.0919760	−	0.0919760i	0.659622	−	0.751598i	$-0.270716\pi$
$467$	−20059.0	−	20059.0i	−0.0919760	−	0.0919760i	−0.751598	+	0.659622i	$0.770716\pi$
$468$	−36960.2	+	157427.i	−0.168749	+	0.718768i
$469$		−	126568.i		−	0.575410i
$470$	269512.	−	9571.81i	1.22006	−	0.0433310i
$471$	59711.7	+	209706.i	0.269165	+	0.945297i
$472$	9.79201	−	36.5443i	4.39529e−5	−	0.000164035i
$473$	−110292.	−	29552.6i	−0.492971	−	0.132091i
$474$	−485032.	+	138108.i	−2.15881	+	0.614700i
$475$	179804.	−	121590.i	0.796914	−	0.538903i
$476$	−469058.			−2.07020
$477$	−13325.3	−	44169.9i	−0.0585651	−	0.194129i
$478$	235182.	−	235182.i	1.02932	−	1.02932i
$479$	42700.6	+	24653.2i	0.186107	+	0.107449i	0.590159	−	0.807287i	$-0.299065\pi$
$479$	42700.6	+	24653.2i	0.186107	+	0.107449i	−0.404052	+	0.914736i	$0.632398\pi$
$480$	−68133.9	+	318571.i	−0.295720	+	1.38269i
$481$	−131283.	−	227389.i	−0.567438	−	0.982832i
$482$	833.570	−	3110.93i	0.00358796	−	0.0133905i
$483$	10013.4	−	5991.40i	0.0429225	−	0.0256823i
$484$	138878.	+	80181.4i	0.592848	+	0.342281i
$485$	92775.1	+	21360.8i	0.394410	+	0.0908101i
$486$	−328346.	−	61038.8i	−1.39014	−	0.258424i
$487$	142866.	+	142866.i	0.602381	+	0.602381i	0.940944	−	0.338563i	$-0.109941\pi$
$487$	142866.	+	142866.i	0.602381	+	0.602381i	−0.338563	+	0.940944i	$0.609941\pi$
$488$	45.0407	+	168.094i	0.000189132	+	0.000705852i
$489$	−5453.99	+	21703.3i	−0.0228085	+	0.0907629i
$490$	738596.	−	226291.i	3.07620	−	0.942488i
$491$	103744.	+	179690.i	0.430329	+	0.745352i	0.996902	−	0.0786598i	$-0.0250641\pi$
$491$	103744.	+	179690.i	0.430329	+	0.745352i	−0.566572	+	0.824012i	$0.691731\pi$
$492$	−249802.	+	3897.20i	−1.03196	+	0.0160999i
$493$	−49217.3	−	183682.i	−0.202500	−	0.755739i
$494$			245262.i			1.00502i
$495$	−9164.95	−	137201.i	−0.0374041	−	0.559948i
$496$	−145013.			−0.589444
$497$	251351.	−	67349.3i	1.01758	−	0.272659i
$498$	39101.1	+	21768.9i	0.157663	+	0.0877765i
$499$	−82957.7	+	47895.6i	−0.333162	+	0.192351i	−0.657244	−	0.753678i	$-0.728278\pi$
$499$	−82957.7	+	47895.6i	−0.333162	+	0.192351i	0.324082	+	0.946029i	$0.394945\pi$
$500$	147199.	+	201846.i	0.588798	+	0.807382i
$501$	72791.8	+	255642.i	0.290006	+	1.01849i
$502$	−168585.	+	45172.2i	−0.668978	+	0.179252i
$503$	−22513.7	+	22513.7i	−0.0889837	+	0.0889837i	−0.750198	−	0.661214i	$-0.770042\pi$
$503$	−22513.7	+	22513.7i	−0.0889837	+	0.0889837i	0.661214	+	0.750198i	$0.270042\pi$
$504$	−248.463	−	400.924i	−0.000978141	−	0.00157834i
$505$	−428995.	+	268420.i	−1.68217	+	1.05253i
$506$	−2807.54	+	4862.80i	−0.0109654	+	0.0189926i
$507$	−116713.	+	1820.86i	−0.454049	+	0.00708369i
$508$	168562.	+	45166.1i	0.653179	+	0.175019i
$509$	190461.	−	109963.i	0.735140	−	0.424433i	−0.0851594	−	0.996367i	$-0.527140\pi$
$509$	190461.	−	109963.i	0.735140	−	0.424433i	0.820300	+	0.571934i	$0.193807\pi$
$510$	374863.	+	191597.i	1.44123	+	0.736630i
$511$	62475.9	−	108211.i	0.239260	−	0.414411i
$512$	−262096.	−	262096.i	−0.999817	−	0.999817i
$513$	−252897.	+	11844.2i	−0.960969	+	0.0450060i
$514$			51253.9i			0.194000i
$515$	−177692.	−	165503.i	−0.669967	−	0.624011i
$516$	−234666.	−	58971.0i	−0.881355	−	0.221482i
$517$	33520.6	−	125101.i	0.125410	−	0.468035i
$518$	−1.01875e6	−	272973.i	−3.79671	−	1.01732i
$519$	126155.	+	122279.i	0.468349	+	0.453960i
$520$	204.849	−	7.27527i	0.000757577	−	2.69056e-5i
$521$	−79512.2			−0.292926			−0.146463	−	0.989216i	$-0.546789\pi$
$521$	−79512.2			−0.292926			−0.146463	+	0.989216i	$0.546789\pi$
$522$	−180308.	+	191925.i	−0.661718	+	0.704353i
$523$	−321864.	+	321864.i	−1.17671	+	1.17671i	−0.196129	+	0.980578i	$0.562837\pi$
$523$	−321864.	+	321864.i	−1.17671	+	1.17671i	−0.980578	+	0.196129i	$0.937163\pi$
$524$	−97639.8	−	56372.3i	−0.355602	−	0.205307i
$525$	−491193.	−	86947.9i	−1.78211	−	0.315457i
$526$	−343437.	−	594850.i	−1.24130	−	2.14999i
$527$	−48466.3	+	180879.i	−0.174509	+	0.651278i
$528$	136795.	+	76158.3i	0.490684	+	0.273180i
$529$	−242164.	−	139814.i	−0.865364	−	0.499618i
$530$	68273.4	−	42718.3i	0.243052	−	0.152077i
$531$	1455.85	+	46647.0i	0.00516330	+	0.165438i
$532$	348186.	+	348186.i	1.23024	+	1.23024i
$533$	56109.8	+	209405.i	0.197508	+	0.737109i
$534$	28399.7	+	27527.2i	0.0995935	+	0.0965337i
$535$	47160.7	+	153929.i	0.164768	+	0.537789i
$536$	−46.8585	−	81.1614i	−0.000163102	−	0.000282501i
$537$	29197.0	+	48796.7i	0.101249	+	0.169216i
$538$	137954.	+	514852.i	0.476618	+	1.77876i
$539$		−	370983.i		−	1.27696i
$540$	−23954.2	−	290402.i	−0.0821476	−	0.995892i
$541$	498098.			1.70185			0.850923	−	0.525291i	$-0.176043\pi$
$541$	498098.			1.70185			0.850923	+	0.525291i	$0.176043\pi$
$542$	−326591.	+	87509.9i	−1.11175	+	0.297892i
$543$	−272281.	+	162917.i	−0.923459	+	0.552543i
$544$	−414819.	+	239496.i	−1.40172	+	0.809283i
$545$	−136153.	+	256435.i	−0.458391	+	0.863344i
$546$	392295.	−	404730.i	1.31592	−	1.35763i
$547$	279107.	−	74786.4i	0.932816	−	0.249947i	0.239761	−	0.970832i	$-0.422931\pi$
$547$	279107.	−	74786.4i	0.932816	−	0.249947i	0.693055	+	0.720885i	$0.256264\pi$
$548$	−44358.6	+	44358.6i	−0.147712	+	0.147712i
$549$	−113082.	−	182470.i	−0.375186	−	0.605406i
$550$	226865.	−	78417.5i	0.749968	−	0.259231i
$551$	−99814.1	+	172883.i	−0.328768	+	0.569442i
$552$	4.20288	−	7.54917i	1.37933e−5	−	2.47754e-5i
$553$	848659.	+	227398.i	2.77513	+	0.743594i
$554$	624995.	−	360841.i	2.03637	−	1.17570i
$555$	351204.	+	317028.i	1.14018	+	1.02923i
$556$	82275.2	−	142505.i	0.266146	−	0.460978i
$557$	−381821.	−	381821.i	−1.23069	−	1.23069i	−0.963698	−	0.266996i	$-0.913969\pi$
$557$	−381821.	−	381821.i	−1.23069	−	1.23069i	−0.266996	−	0.963698i	$-0.586031\pi$
$558$	248266.	−	74897.5i	0.797351	−	0.240546i
$559$			209963.i			0.671921i
$560$	387107.	−	415616.i	1.23440	−	1.32531i
$561$	140714.	−	145174.i	0.447108	−	0.461280i
$562$	23869.8	−	89083.3i	0.0755746	−	0.282048i
$563$	−292395.	−	78347.0i	−0.922472	−	0.247176i	−0.233830	−	0.972277i	$-0.575126\pi$
$563$	−292395.	−	78347.0i	−0.922472	−	0.247176i	−0.688642	+	0.725102i	$0.741793\pi$
$564$	66888.9	−	266174.i	0.210279	−	0.836773i
$565$	120320.	+	112066.i	0.376912	+	0.351058i
$566$	367782.			1.14804
$567$	436274.	+	384963.i	1.35704	+	1.19744i
$568$	136.244	−	136.244i	0.000422300	−	0.000422300i
$569$	−189188.	−	109228.i	−0.584346	−	0.337372i	0.178513	−	0.983938i	$-0.442871\pi$
$569$	−189188.	−	109228.i	−0.584346	−	0.337372i	−0.762859	+	0.646565i	$0.776205\pi$
$570$	−136040.	−	420489.i	−0.418713	−	1.29421i
$571$	113644.	+	196837.i	0.348558	+	0.603720i	0.985993	−	0.166784i	$-0.0533382\pi$
$571$	113644.	+	196837.i	0.348558	+	0.603720i	−0.637436	+	0.770503i	$0.720005\pi$
$572$	−35086.7	+	130945.i	−0.107238	+	0.400219i
$573$	−9137.84	−	585715.i	−0.0278314	−	1.78393i
$574$	754149.	+	435408.i	2.28893	+	1.32152i
$575$	−2985.22	−	8636.38i	−0.00902902	−	0.0261214i
$576$	291937.	+	156616.i	0.879922	+	0.472055i
$577$	302536.	+	302536.i	0.908711	+	0.908711i	0.996168	−	0.0874570i	$-0.0278740\pi$
$577$	302536.	+	302536.i	0.908711	+	0.908711i	−0.0874570	+	0.996168i	$0.527874\pi$
$578$	37944.4	+	141610.i	0.113577	+	0.423876i
$579$	433312.	−	123381.i	1.29254	−	0.368038i
$580$	−202930.	−	107745.i	−0.603240	−	0.320289i
$581$	−38983.2	−	67520.9i	−0.115485	−	0.200026i
$582$	94290.3	−	169363.i	0.278369	−	0.500003i
$583$	−10010.4	−	37359.4i	−0.0294520	−	0.109916i
$584$		−	92.5205i		−	0.000271277i
$585$	−239332.	+	81576.0i	−0.699340	+	0.238369i
$586$	−814307.			−2.37133
$587$	−327964.	+	87877.6i	−0.951808	+	0.255036i	−0.701129	−	0.713034i	$-0.747320\pi$
$587$	−327964.	+	87877.6i	−0.951808	+	0.255036i	−0.250679	+	0.968070i	$0.580654\pi$
$588$	−12263.2	−	786046.i	−0.0354691	−	2.27349i
$589$	170245.	−	98291.0i	0.490732	−	0.283324i
$590$	−77894.0	+	23865.2i	−0.223769	+	0.0685584i
$591$	−525111.	−	131959.i	−1.50341	−	0.377802i
$592$	−520350.	+	139427.i	−1.48475	+	0.397837i
$593$	−3099.72	+	3099.72i	−0.00881482	+	0.00881482i	−0.711500	−	0.702686i	$-0.751984\pi$
$593$	−3099.72	+	3099.72i	−0.00881482	+	0.00881482i	0.702686	+	0.711500i	$0.251984\pi$
$594$	−273532.	−	59732.5i	−0.775238	−	0.169292i
$595$	−389031.	−	621758.i	−1.09888	−	1.75625i
$596$	244464.	−	423425.i	0.688213	−	1.19202i
$597$	94940.4	+	158673.i	0.266380	+	0.445198i
$598$	9973.35	+	2672.35i	0.0278894	+	0.00747293i
$599$	−378935.	+	218778.i	−1.05611	+	0.609748i	−0.924355	−	0.381534i	$-0.875396\pi$
$599$	−378935.	+	218778.i	−1.05611	+	0.609748i	−0.131760	+	0.991282i	$0.542063\pi$
$600$	−347.167	+	126.097i	−0.000964353	+	0.000350269i
$601$	157731.	−	273198.i	0.436685	−	0.756360i	−0.560747	−	0.827987i	$-0.689486\pi$
$601$	157731.	−	273198.i	0.436685	−	0.756360i	0.997431	+	0.0716274i	$0.0228193\pi$
$602$	596363.	+	596363.i	1.64558	+	1.64558i
$603$	84255.7	+	79155.6i	0.231721	+	0.217694i
$604$		−	413209.i		−	1.13265i
$605$	8899.81	+	250591.i	0.0243148	+	0.684627i
$606$	282171.	+	990977.i	0.768366	+	2.69847i
$607$	−108662.	+	405531.i	−0.294916	+	1.10064i	0.646367	+	0.763026i	$0.276287\pi$
$607$	−108662.	+	405531.i	−0.294916	+	1.10064i	−0.941284	+	0.337617i	$0.890379\pi$
$608$	485705.	+	130144.i	1.31391	+	0.352061i
$609$	441238.	−	125639.i	1.18970	−	0.338757i
$610$	255403.	−	274213.i	0.686384	−	0.736934i
$611$	−238154.			−0.637933
$612$	293350.	−	312250.i	0.783218	−	0.833681i
$613$	150459.	−	150459.i	0.400404	−	0.400404i	−0.477972	−	0.878375i	$-0.658628\pi$
$613$	150459.	−	150459.i	0.400404	−	0.400404i	0.878375	+	0.477972i	$0.158628\pi$
$614$	−119015.	−	68713.2i	−0.315693	−	0.182265i
$615$	−212348.	−	327891.i	−0.561433	−	0.866920i
$616$	−197.708	−	342.441i	−0.000521031	−	0.000902452i
$617$	−22948.8	+	85646.2i	−0.0602824	+	0.224977i	−0.989495	−	0.144570i	$-0.953820\pi$
$617$	−22948.8	+	85646.2i	−0.0602824	+	0.224977i	0.929212	+	0.369546i	$0.120487\pi$
$618$	−424274.	+	253861.i	−1.11089	+	0.664689i
$619$	144897.	+	83656.2i	0.378162	+	0.218332i	0.677018	−	0.735966i	$-0.263272\pi$
$619$	144897.	+	83656.2i	0.378162	+	0.218332i	−0.298856	+	0.954298i	$0.596605\pi$
$620$	120010.	+	191803.i	0.312201	+	0.498967i
$621$	−2273.91	+	10412.9i	−0.00589645	+	0.0270015i
$622$	−501144.	−	501144.i	−1.29533	−	1.29533i
$623$	−17833.9	−	66556.8i	−0.0459483	−	0.171481i
$624$	70166.5	−	279217.i	0.180202	−	0.717088i
$625$	−145470.	+	362528.i	−0.372403	+	0.928071i
$626$	−436466.	−	755981.i	−1.11378	−	1.92913i
$627$	−212218.	+	3310.85i	−0.539818	+	0.00842179i
$628$	100253.	+	374149.i	0.254201	+	0.948692i
$629$			695648.i			1.75828i
$630$	−448078.	+	911484.i	−1.12894	+	2.29651i
$631$	646284.			1.62317			0.811586	−	0.584233i	$-0.198605\pi$
$631$	646284.			1.62317			0.811586	+	0.584233i	$0.198605\pi$
$632$	628.390	−	168.377i	0.00157324	−	0.000421548i
$633$	−8941.47	−	4978.02i	−0.0223152	−	0.0124237i
$634$	−232140.	+	134026.i	−0.577527	+	0.333435i
$635$	79933.6	+	260897.i	0.198236	+	0.647025i
$636$	−22445.3	−	78827.0i	−0.0554894	−	0.194877i
$637$	−658930.	+	176560.i	−1.62390	+	0.435124i
$638$	−156103.	+	156103.i	−0.383504	+	0.383504i
$639$	−112361.	+	209444.i	−0.275178	+	0.512939i
$640$	188.584	−	819.065i	0.000460410	−	0.00199967i
$641$	−59143.7	+	102440.i	−0.143944	+	0.249318i	−0.928978	−	0.370134i	$-0.879312\pi$
$641$	−59143.7	+	102440.i	−0.143944	+	0.249318i	0.785035	+	0.619452i	$0.212645\pi$
$642$	327754.	−	5113.35i	0.795203	−	0.0124061i
$643$	−458700.	−	122908.i	−1.10945	−	0.297276i	−0.342841	−	0.939393i	$-0.611389\pi$
$643$	−458700.	−	122908.i	−1.10945	−	0.297276i	−0.766606	+	0.642118i	$0.778056\pi$
$644$	17952.5	−	10364.9i	0.0432865	−	0.0249915i
$645$	−116460.	−	359970.i	−0.279936	−	0.865261i
$646$	324901.	−	562745.i	0.778549	−	1.34849i
$647$	170106.	+	170106.i	0.406359	+	0.406359i	0.880467	−	0.474108i	$-0.157229\pi$
$647$	170106.	+	170106.i	0.406359	+	0.406359i	−0.474108	+	0.880467i	$0.657229\pi$
$648$	422.283	+	85.3372i	0.00100567	+	0.000203230i
$649$			39124.6i			0.0928883i
$650$	−247254.	−	365632.i	−0.585216	−	0.865400i
$651$	−438153.	−	110107.i	−1.03387	−	0.259808i
$652$	−10289.2	+	38399.8i	−0.0242040	+	0.0903305i
$653$	−363055.	−	97280.4i	−0.851425	−	0.228139i	−0.193386	−	0.981123i	$-0.561947\pi$
$653$	−363055.	−	97280.4i	−0.851425	−	0.228139i	−0.658039	+	0.752984i	$0.728614\pi$
$654$	424481.	+	411440.i	0.992438	+	0.961947i
$655$	−6257.10	−	176180.i	−0.0145845	−	0.410653i
$656$	444790.			1.03359
$657$	32963.4	+	109266.i	0.0763663	+	0.253135i
$658$	−676436.	+	676436.i	−1.56234	+	1.56234i
$659$	−29215.0	−	16867.3i	−0.0672722	−	0.0388396i	0.465987	−	0.884792i	$-0.345699\pi$
$659$	−29215.0	−	16867.3i	−0.0672722	−	0.0388396i	−0.533259	+	0.845952i	$0.679033\pi$
$660$	−12477.3	−	243961.i	−0.0286440	−	0.560057i
$661$	−60726.6	−	105182.i	−0.138988	−	0.240733i	0.788126	−	0.615514i	$-0.211051\pi$
$661$	−60726.6	−	105182.i	−0.138988	−	0.240733i	−0.927114	+	0.374780i	$0.877718\pi$
$662$	−24965.8	+	93173.8i	−0.0569679	+	0.212607i
$663$	−324824.	−	180841.i	−0.738961	−	0.411405i
$664$	−49.9958	−	28.8651i	−0.000113396	−	6.54692e-5i
$665$	−172755.	+	750318.i	−0.390650	+	1.69669i
$666$	818843.	−	507459.i	1.84609	−	1.14407i
$667$	5942.57	+	5942.57i	0.0133574	+	0.0133574i
$668$	122214.	+	456107.i	0.273884	+	1.02215i
$669$	495746.	+	480515.i	1.10766	+	1.07363i
$670$	−94635.4	+	178239.i	−0.210816	+	0.397056i
$671$	−89981.7	−	155853.i	−0.199852	−	0.346154i
$672$	−593342.	−	991645.i	−1.31391	−	2.19593i
$673$	72484.2	+	270515.i	0.160034	+	0.597256i	0.998622	+	0.0524887i	$0.0167154\pi$
$673$	72484.2	+	270515.i	0.160034	+	0.597256i	−0.838587	+	0.544767i	$0.816618\pi$
$674$		−	756048.i		−	1.66429i
$675$	365074.	−	272608.i	0.801259	−	0.598317i
$676$	−207364.			−0.453774
$677$	−85497.0	+	22908.8i	−0.186541	+	0.0499834i	−0.350880	−	0.936420i	$-0.614117\pi$
$677$	−85497.0	+	22908.8i	−0.186541	+	0.0499834i	0.164339	+	0.986404i	$0.447451\pi$
$678$	287287.	−	171895.i	0.624966	−	0.373943i
$679$	−292461.	+	168853.i	−0.634350	+	0.366242i
$680$	−479.656	−	254.672i	−0.00103732	−	0.000550762i
$681$	−441537.	+	455532.i	−0.952079	+	0.982257i
$682$	209986.	−	56265.7i	0.451463	−	0.120969i
$683$	622174.	−	622174.i	1.33374	−	1.33374i	0.431740	−	0.901998i	$-0.357900\pi$
$683$	622174.	−	622174.i	1.33374	−	1.33374i	0.901998	−	0.431740i	$-0.142100\pi$
$684$	−449543.	+	14030.2i	−0.960857	+	0.0299883i
$685$	−95589.8	−	22008.9i	−0.203718	−	0.0469047i
$686$	−767964.	+	1.33015e6i	−1.63190	+	2.82653i
$687$	119009.	−	213763.i	0.252155	−	0.452918i
$688$	416101.	+	111494.i	0.879067	+	0.235545i
$689$	−61592.6	+	35560.5i	−0.129745	+	0.0749082i
$690$	−18581.1	+	950.326i	−0.0390277	+	0.00199606i
$691$	−270995.	+	469377.i	−0.567551	+	0.983028i	0.429256	+	0.903183i	$0.358776\pi$
$691$	−270995.	+	469377.i	−0.567551	+	0.983028i	−0.996807	+	0.0798447i	$0.974558\pi$
$692$	220697.	+	220697.i	0.460876	+	0.460876i
$693$	355496.	+	333978.i	0.740233	+	0.695427i
$694$		−	850933.i		−	1.76675i
$695$	257135.	−	9132.22i	0.532342	−	0.0189063i
$696$	236.429	−	243.923i	0.000488070	−	0.000503540i
$697$	148658.	−	554801.i	0.306002	−	1.14201i
$698$	986528.	+	264339.i	2.02488	+	0.542564i
$699$	−179501.	+	714296.i	−0.367377	+	1.46192i
$700$	−870083.	−	168055.i	−1.77568	−	0.342969i
$701$	−141221.			−0.287384			−0.143692	−	0.989622i	$-0.545898\pi$
$701$	−141221.			−0.287384			−0.143692	+	0.989622i	$0.545898\pi$
$702$	24085.2	+	514268.i	0.0488738	+	1.04356i
$703$	516386.	−	516386.i	1.04487	−	1.04487i
$704$	240525.	+	138867.i	0.485304	+	0.280191i
$705$	408303.	−	132097.i	0.821493	−	0.265776i
$706$	66834.6	+	115761.i	0.134089	+	0.232248i
$707$	464600.	−	1.73391e6i	0.929480	−	3.46887i
$708$	1293.31	+	82898.1i	0.00258009	+	0.165378i
$709$	341588.	+	197216.i	0.679533	+	0.392328i	0.799679	−	0.600428i	$-0.205003\pi$
$709$	341588.	+	197216.i	0.679533	+	0.392328i	−0.120146	+	0.992756i	$0.538336\pi$
$710$	−404322.	−	93092.2i	−0.802067	−	0.184670i
$711$	−682130.	+	422735.i	−1.34936	+	0.836236i
$712$	−36.0769	−	36.0769i	−7.11655e−5	−	7.11655e-5i
$713$	−2141.94	−	7993.82i	−0.00421335	−	0.0157245i
$714$	−1.43626e6	+	408961.i	−2.81732	+	0.802205i
$715$	−202674.	+	62095.4i	−0.396449	+	0.121464i
$716$	50509.6	+	87485.2i	0.0985254	+	0.170651i
$717$	257446.	−	462421.i	0.500781	−	0.899497i
$718$	−34915.1	−	130305.i	−0.0677274	−	0.252762i
$719$		−	517774.i		−	1.00157i	−0.865571	−	0.500786i	$-0.833044\pi$
$719$		−	517774.i		−	1.00157i	0.865571	−	0.500786i	$-0.166956\pi$
$720$	34576.8	+	517622.i	0.0666991	+	0.998500i
$721$	861369.			1.65699
$722$	53049.7	−	14214.6i	0.101767	−	0.0272685i
$723$	−79.9460	−	5124.36i	−0.000152940	−	0.00980309i
$724$	−488160.	+	281839.i	−0.931289	+	0.537680i
$725$	−25486.4	−	358355.i	−0.0484877	−	0.681770i
$726$	495154.	+	124431.i	0.939435	+	0.236078i
$727$	435737.	−	116755.i	0.824434	−	0.220906i	0.178150	−	0.984003i	$-0.442989\pi$
$727$	435737.	−	116755.i	0.824434	−	0.220906i	0.646284	+	0.763097i	$0.276322\pi$
$728$	−514.140	+	514.140i	−0.000970105	+	0.000970105i
$729$	−529115.	+	49670.0i	−0.995623	+	0.0934628i
$730$	−168892.	+	105675.i	−0.316929	+	0.198301i
$731$	278139.	−	481752.i	0.520509	−	0.901547i
$732$	−195807.	−	327250.i	−0.365432	−	0.610741i
$733$	−456274.	−	122258.i	−0.849216	−	0.227547i	−0.192137	−	0.981368i	$-0.561542\pi$
$733$	−456274.	−	122258.i	−0.849216	−	0.227547i	−0.657079	+	0.753821i	$0.728208\pi$
$734$	308768.	−	178267.i	0.573113	−	0.330887i
$735$	1.03177e6	−	668192.i	1.90989	−	1.23688i
$736$	10584.4	−	18332.7i	0.0195393	−	0.0338431i
$737$	68529.6	+	68529.6i	0.126166	+	0.126166i
$738$	−761495.	+	229729.i	−1.39815	+	0.421797i
$739$		−	432935.i		−	0.792745i	−0.918090	−	0.396372i	$-0.870269\pi$
$739$		−	432935.i		−	0.792745i	0.918090	−	0.396372i	$-0.129731\pi$
$740$	615049.	+	572860.i	1.12317	+	1.04613i
$741$	106880.	+	375360.i	0.194653	+	0.683616i
$742$	−73939.8	+	275947.i	−0.134298	+	0.501208i
$743$	610684.	+	163632.i	1.10621	+	0.296409i	0.765293	−	0.643683i	$-0.222594\pi$
$743$	610684.	+	163632.i	1.10621	+	0.296409i	0.340921	+	0.940092i	$0.389261\pi$
$744$	−321.729	+	91.6095i	−0.000581226	+	0.000165499i
$745$	764024.	−	27134.6i	1.37656	−	0.0488889i
$746$	−489144.			−0.878939
$747$	69328.6	+	16276.7i	0.124243	+	0.0291692i
$748$	253970.	−	253970.i	0.453920	−	0.453920i
$749$	−494564.	−	285537.i	−0.881574	−	0.508977i
$750$	626710.	+	489712.i	1.11415	+	0.870599i
$751$	−84344.5	−	146089.i	−0.149547	−	0.259023i	0.781513	−	0.623889i	$-0.214448\pi$
$751$	−84344.5	−	146089.i	−0.149547	−	0.259023i	−0.931060	+	0.364866i	$0.881115\pi$
$752$	−126464.	+	471970.i	−0.223631	+	0.834601i
$753$	−238325.	+	142600.i	−0.420320	+	0.251494i
$754$	351559.	+	202973.i	0.618380	+	0.357022i
$755$	547728.	−	342711.i	0.960884	−	0.601220i
$756$	764274.	+	695888.i	1.33723	+	1.21758i
$757$	−344491.	−	344491.i	−0.601154	−	0.601154i	0.339465	−	0.940619i	$-0.389754\pi$
$757$	−344491.	−	344491.i	−0.601154	−	0.601154i	−0.940619	+	0.339465i	$0.889754\pi$
$758$	−332846.	−	1.24220e6i	−0.579302	−	2.16198i
$759$	−2177.67	+	8665.72i	−0.00378015	+	0.0150425i
$760$	167.007	+	545.099i	0.000289140	+	0.000943730i
$761$	336633.	+	583065.i	0.581282	+	1.00681i	0.995328	+	0.0965540i	$0.0307821\pi$
$761$	336633.	+	583065.i	0.581282	+	1.00681i	−0.414046	+	0.910256i	$0.635885\pi$
$762$	555517.	−	8666.71i	0.956725	−	0.0149260i
$763$	−266557.	−	994805.i	−0.457869	−	1.70879i
$764$		−	1.04064e6i		−	1.78285i
$765$	657202.	+	129872.i	1.12299	+	0.221917i
$766$	815063.			1.38910
$767$	69492.2	−	18620.4i	0.118126	−	0.0316517i
$768$	−516088.	−	287324.i	−0.874986	−	0.487135i
$769$	358173.	−	206791.i	0.605676	−	0.349687i	−0.165595	−	0.986194i	$-0.552955\pi$
$769$	358173.	−	206791.i	0.605676	−	0.349687i	0.771271	+	0.636507i	$0.219621\pi$
$770$	−399291.	+	752034.i	−0.673454	+	1.26840i
$771$	22335.5	+	78441.4i	0.0375739	+	0.131958i
$772$	773098.	−	207151.i	1.29718	−	0.347578i
$773$	140161.	−	140161.i	0.234568	−	0.234568i	−0.580028	−	0.814596i	$-0.696959\pi$
$773$	140161.	−	140161.i	0.234568	−	0.234568i	0.814596	+	0.580028i	$0.196959\pi$
$774$	−769963.	+	24030.5i	−1.28525	+	0.0401126i
$775$	−154709.	+	318158.i	−0.257579	+	0.529711i
$776$	−125.027	+	216.553i	−0.000207625	+	0.000359617i
$777$	−1.67809e6	+	26180.2i	−2.77955	+	0.0433642i
$778$	172535.	+	46230.7i	0.285048	+	0.0763785i
$779$	−522184.	+	301483.i	−0.860496	+	0.496808i
$780$	−427378.	+	138269.i	−0.702463	+	0.227266i
$781$	−99627.1	+	172559.i	−0.163334	+	0.282902i
$782$	−19343.4	−	19343.4i	−0.0316315	−	0.0316315i
$783$	−192314.	+	372305.i	−0.313680	+	0.607261i
$784$			1.39961e6i			2.27707i
$785$	−412803.	+	443204.i	−0.669890	+	0.719225i
$786$	−348123.	−	87482.4i	−0.563492	−	0.141604i
$787$	−80367.8	+	299937.i	−0.129757	+	0.484262i	−0.999965	−	0.00842471i	$-0.997318\pi$
$787$	−80367.8	+	299937.i	−0.129757	+	0.484262i	0.870207	+	0.492686i	$0.163985\pi$
$788$	−929083.	−	248947.i	−1.49624	−	0.400917i
$789$	−784836.	−	760723.i	−1.26074	−	1.22200i
$790$	−1.02509e6	−	954779.i	−1.64252	−	1.52985i
$791$	−583255.			−0.932192
$792$	351.608	+	82.5492i	0.000560543	+	0.000131602i
$793$	−233997.	+	233997.i	−0.372104	+	0.372104i
$794$	495975.	+	286351.i	0.786718	+	0.454212i
$795$	85872.9	−	95130.3i	0.135870	−	0.150517i
$796$	164243.	+	284477.i	0.259215	+	0.448974i
$797$	170172.	−	635092.i	0.267900	−	0.999815i	−0.692552	−	0.721368i	$-0.743514\pi$
$797$	170172.	−	635092.i	0.267900	−	0.999815i	0.960452	−	0.278447i	$-0.0898197\pi$
$798$	1.36972e6	+	762572.i	2.15093	+	1.19750i
$799$	546436.	+	315485.i	0.855944	+	0.494180i
$800$	−855280.	+	295633.i	−1.33637	+	0.461927i
$801$	55460.0	+	29752.8i	0.0864399	+	0.0463727i
$802$	−111433.	−	111433.i	−0.173246	−	0.173246i
$803$	24763.3	+	92418.0i	0.0384041	+	0.143326i
$804$	147467.	+	142937.i	0.228131	+	0.221122i
$805$	28628.7	+	15200.3i	0.0441783	+	0.0234564i
$806$	−199875.	−	346194.i	−0.307673	−	0.532905i
$807$	435494.	+	727836.i	0.668706	+	1.11760i
$808$	−344.013	−	1283.87i	−0.000526929	−	0.00196653i
$809$			877608.i			1.34092i	0.741945	+	0.670461i	$0.233904\pi$
$809$			877608.i			1.34092i	−0.741945	+	0.670461i	$0.766096\pi$
$810$	−326543.	−	868327.i	−0.497703	−	1.32347i
$811$	−834885.			−1.26936			−0.634680	−	0.772775i	$-0.718868\pi$
$811$	−834885.			−1.26936			−0.634680	+	0.772775i	$0.718868\pi$
$812$	787241.	−	210941.i	1.19398	−	0.319925i
$813$	−461695.	+	276251.i	−0.698513	+	0.417949i
$814$	699397.	−	403797.i	1.05554	−	0.609417i
$815$	−59434.5	+	18209.5i	−0.0894794	+	0.0274147i
$816$	−530876.	+	547703.i	−0.797283	+	0.822555i
$817$	−564075.	+	151143.i	−0.845069	+	0.226436i
$818$	1.19867e6	−	1.19867e6i	1.79140	−	1.79140i
$819$	424014.	−	790372.i	0.632138	−	1.17832i
$820$	−368102.	−	588308.i	−0.547444	−	0.874937i
$821$	−35525.8	+	61532.5i	−0.0527057	+	0.0912890i	−0.891175	−	0.453661i	$-0.850118\pi$
$821$	−35525.8	+	61532.5i	−0.0527057	+	0.0912890i	0.838469	+	0.544950i	$0.183451\pi$
$822$	−97150.9	+	174501.i	−0.143782	+	0.258259i
$823$	−58672.5	−	15721.3i	−0.0866234	−	0.0232107i	0.215247	−	0.976560i	$-0.430944\pi$
$823$	−58672.5	−	15721.3i	−0.0866234	−	0.0232107i	−0.301870	+	0.953349i	$0.597611\pi$
$824$	552.352	−	318.900i	0.000813507	−	0.000469679i
$825$	313032.	−	218877.i	0.459919	−	0.321583i
$826$	144493.	−	250269.i	0.211780	−	0.366815i
$827$	383281.	+	383281.i	0.560411	+	0.560411i	0.929424	−	0.369013i	$-0.120304\pi$
$827$	383281.	+	383281.i	0.560411	+	0.560411i	−0.369013	+	0.929424i	$0.620304\pi$
$828$	−4327.65	+	18433.1i	−0.00631235	+	0.0268867i
$829$		−	513439.i		−	0.747101i	−0.927610	−	0.373551i	$-0.878140\pi$
$829$		−	513439.i		−	0.747101i	0.927610	−	0.373551i	$-0.121860\pi$
$830$	4412.21	+	124234.i	0.00640472	+	0.180337i
$831$	799274.	−	824609.i	1.15743	−	1.19411i
$832$	132180.	−	493304.i	0.190950	−	0.712636i
$833$	1.74578e6	+	467781.i	2.51594	+	0.674143i
$834$	127680.	−	508084.i	0.183566	−	0.730472i
$835$	−503228.	+	540289.i	−0.721759	+	0.774914i
$836$	−377048.			−0.539492
$837$	347319.	−	222816.i	0.495767	−	0.318050i
$838$	−361393.	+	361393.i	−0.514626	+	0.514626i
$839$	798813.	+	461195.i	1.13480	+	0.655180i	0.945139	−	0.326669i	$-0.105926\pi$
$839$	798813.	+	461195.i	1.13480	+	0.655180i	0.189666	+	0.981849i	$0.439259\pi$
$840$	596.288	−	1166.65i	0.000845079	−	0.00165341i
$841$	−188433.	−	326376.i	−0.266419	−	0.461452i
$842$	−376812.	+	1.40628e6i	−0.531497	+	1.98358i
$843$	−2289.30	−	146739.i	−0.00322142	−	0.206486i
$844$	−15744.5	−	9090.10i	−0.0221027	−	0.0127610i
$845$	−171985.	−	274870.i	−0.240867	−	0.384959i
$846$	−27257.0	−	873345.i	−0.0380836	−	1.22024i
$847$	−628946.	−	628946.i	−0.876691	−	0.876691i
$848$	37766.5	+	140947.i	0.0525189	+	0.196003i
$849$	562871.	−	160272.i	0.780897	−	0.222353i
$850$	82959.6	+	1.16647e6i	0.114823	+	1.61449i
$851$	−15371.9	−	26624.8i	−0.0212260	−	0.0367644i
$852$	−205388.	+	368915.i	−0.282941	+	0.508215i
$853$	271956.	+	1.01495e6i	0.373766	+	1.39491i	0.855139	+	0.518398i	$0.173472\pi$
$853$	271956.	+	1.01495e6i	0.373766	+	1.39491i	−0.481373	+	0.876516i	$0.659862\pi$
$854$			1.32926e6i			1.82261i
$855$	−391443.	−	584253.i	−0.535471	−	0.799224i
$856$	−422.851			−0.000577085
$857$	57525.6	−	15413.9i	0.0783248	−	0.0209871i	−0.219444	−	0.975625i	$-0.570424\pi$
$857$	57525.6	−	15413.9i	0.0783248	−	0.0209871i	0.297769	+	0.954638i	$0.403758\pi$
$858$	6732.63	+	431546.i	0.00914556	+	0.586210i
$859$	544185.	−	314185.i	0.737497	−	0.425794i	−0.0836614	−	0.996494i	$-0.526661\pi$
$859$	544185.	−	314185.i	0.737497	−	0.425794i	0.821159	+	0.570700i	$0.193328\pi$
$860$	−196890.	−	642632.i	−0.266211	−	0.868891i
$861$	1.34393e6	+	337725.i	1.81288	+	0.455572i
$862$	113756.	−	30480.8i	0.153094	−	0.0410215i
$863$	−975081.	+	975081.i	−1.30924	+	1.30924i	−0.387276	+	0.921964i	$0.626584\pi$
$863$	−975081.	+	975081.i	−1.30924	+	1.30924i	−0.921964	+	0.387276i	$0.873416\pi$
$864$	1.03121e6	+	225191.i	1.38140	+	0.301663i
$865$	−109500.	+	475587.i	−0.146347	+	0.635620i
$866$	133480.	−	231194.i	0.177983	−	0.308276i
$867$	119783.	+	200192.i	0.159352	+	0.266322i
$868$	−775228.	−	207722.i	−1.02894	−	0.275704i
$869$	−582627.	+	336380.i	−0.771527	+	0.445441i
$870$	−715313.	−	152986.i	−0.945056	−	0.202122i
$871$	89105.6	−	154335.i	0.117454	−	0.203437i
$872$	−539.231	−	539.231i	−0.000709156	−	0.000709156i
$873$	70501.1	−	300291.i	0.0925054	−	0.394016i
$874$			28717.6i			0.0375946i
$875$	−498872.	−	1.29272e6i	−0.651587	−	1.68845i
$876$	55524.1	+	194999.i	0.0723558	+	0.254111i
$877$	−174529.	+	651350.i	−0.226917	+	0.846868i	0.754710	+	0.656059i	$0.227778\pi$
$877$	−174529.	+	651350.i	−0.226917	+	0.846868i	−0.981627	+	0.190809i	$0.938889\pi$
$878$	−898596.	−	240778.i	−1.16567	−	0.312340i
$879$	−1.24625e6	+	354859.i	−1.61298	+	0.459280i
$880$	15436.1	+	434631.i	0.0199329	+	0.561249i
$881$	−808689.			−1.04191			−0.520954	−	0.853585i	$-0.674424\pi$
$881$	−808689.			−1.04191			−0.520954	+	0.853585i	$0.674424\pi$
$882$	−722885.	−	2.39618e6i	−0.929249	−	3.08023i
$883$	−810584.	+	810584.i	−1.03962	+	1.03962i	−0.0404423	+	0.999182i	$0.512877\pi$
$883$	−810584.	+	810584.i	−1.03962	+	1.03962i	−0.999182	+	0.0404423i	$0.987123\pi$
$884$	−571965.	−	330224.i	−0.731922	−	0.422575i
$885$	−108813.	+	70469.0i	−0.138929	+	0.0899729i
$886$	658493.	+	1.14054e6i	0.838849	+	1.45293i
$887$	−314429.	+	1.17346e6i	−0.399646	+	1.49150i	0.414076	+	0.910242i	$0.364105\pi$
$887$	−314429.	+	1.17346e6i	−0.399646	+	1.49150i	−0.813721	+	0.581255i	$0.802562\pi$
$888$	−1066.38	+	638.060i	−0.00135234	+	0.000809163i
$889$	−838246.	−	483961.i	−1.06064	−	0.612361i
$890$	−24650.5	+	107063.i	−0.0311204	+	0.135163i
$891$	−444656.	+	27782.4i	−0.560104	+	0.0349957i
$892$	867263.	+	867263.i	1.08999	+	1.08999i
$893$	−171437.	−	639812.i	−0.214982	−	0.802323i
$894$	379376.	−	1.50967e6i	0.474674	−	1.88889i
$895$	−74073.6	+	139512.i	−0.0924735	+	0.174167i
$896$	1490.72	+	2581.99i	0.00185686	+	0.00321617i
$897$	16428.2	−	256.300i	0.0204177	−	0.000318539i
$898$	48366.8	+	180507.i	0.0599784	+	0.223842i
$899$		−	325373.i		−	0.402589i
$900$	656025.	−	474109.i	0.809907	−	0.585320i
$901$	188429.			0.232113
$902$	−644081.	+	172581.i	−0.791640	+	0.212119i
$903$	1.17259e6	+	652818.i	1.43803	+	0.800603i
$904$	−374.011	+	215.936i	−0.000457665	+	0.000264233i
$905$	−778464.	−	413324.i	−0.950476	−	0.504653i
$906$	−360268.	−	1.26525e6i	−0.438903	−	1.54141i
$907$	−274478.	+	73546.2i	−0.333651	+	0.0894016i	−0.421755	−	0.906710i	$-0.638586\pi$
$907$	−274478.	+	73546.2i	−0.333651	+	0.0894016i	0.0881039	+	0.996111i	$0.471919\pi$
$908$	−796913.	+	796913.i	−0.966584	+	0.966584i
$909$	863696.	+	1.39367e6i	1.04528	+	1.68668i
$910$	1.52578e6	+	351299.i	1.84250	+	0.424223i
$911$	407578.	−	705945.i	0.491104	−	0.850618i	−0.508843	−	0.860859i	$-0.669927\pi$
$911$	407578.	−	705945.i	0.491104	−	0.850618i	0.999948	+	0.0102416i	$0.00326005\pi$
$912$	800639.	−	12490.9i	0.962603	−	0.0150177i
$913$	57666.3	+	15451.6i	0.0691799	+	0.0185367i
$914$	90271.2	−	52118.1i	0.108058	−	0.0623873i
$915$	271385.	−	530968.i	0.324148	−	0.634200i
$916$	217317.	−	376403.i	0.259001	−	0.448603i
$917$	442187.	+	442187.i	0.525856	+	0.525856i
$918$	625993.	−	1.21188e6i	0.742821	−	1.43805i
$919$			549888.i			0.651094i	0.945526	+	0.325547i	$0.105548\pi$
$919$			549888.i			0.651094i	−0.945526	+	0.325547i	$0.894452\pi$
$920$	23.9856	−	0.851857i	2.83384e−5	−	1.00645e-6i
$921$	−212090.	−	53297.6i	−0.250035	−	0.0628331i
$922$	396610.	−	1.48017e6i	0.466554	−	1.74120i
$923$	353910.	+	94829.9i	0.415422	+	0.111312i
$924$	622203.	+	603087.i	0.728766	+	0.706376i
$925$	−249238.	+	1.29040e6i	−0.291293	+	1.50813i
$926$	−663397.			−0.773662
$927$	−538702.	+	573410.i	−0.626886	+	0.667277i
$928$	588505.	−	588505.i	0.683368	−	0.683368i
$929$	−150619.	−	86960.2i	−0.174522	−	0.100760i	0.410194	−	0.911998i	$-0.365461\pi$
$929$	−150619.	−	86960.2i	−0.174522	−	0.100760i	−0.584716	+	0.811238i	$0.698794\pi$
$930$	534700.	+	482667.i	0.618222	+	0.558061i
$931$	−948672.	−	1.64315e6i	−1.09450	−	1.89573i
$932$	−338636.	+	1.26381e6i	−0.389854	+	1.45495i
$933$	−985363.	−	548585.i	−1.13196	−	0.630204i
$934$	−138947.	−	80221.3i	−0.159278	−	0.0919593i
$935$	547288.	+	126009.i	0.626026	+	0.144138i
$936$	−20.7173	−	663.805i	−2.36473e−5	−	0.000757685i
$937$	−341751.	−	341751.i	−0.389252	−	0.389252i	0.485169	−	0.874421i	$-0.338758\pi$
$937$	−341751.	−	341751.i	−0.389252	−	0.389252i	−0.874421	+	0.485169i	$0.838758\pi$
$938$	−185274.	−	691453.i	−0.210576	−	0.785882i
$939$	−997428.	−	966784.i	−1.13123	−	1.09647i
$940$	728917.	−	223326.i	0.824940	−	0.252745i
$941$	450670.	+	780583.i	0.508955	+	0.881535i	0.999946	+	0.0103708i	$0.00330120\pi$
$941$	450670.	+	780583.i	0.508955	+	0.881535i	−0.490992	+	0.871164i	$0.663365\pi$
$942$	633187.	+	1.05824e6i	0.713559	+	1.19256i
$943$	6569.86	+	24519.1i	0.00738810	+	0.0275728i
$944$		−	147606.i		−	0.165638i
$945$	−288553.	+	1.59024e6i	−0.323118	+	1.78073i
$946$	−645798.			−0.721629
$947$	−222376.	+	59585.6i	−0.247964	+	0.0664418i	−0.380660	−	0.924715i	$-0.624303\pi$
$947$	−222376.	+	59585.6i	−0.247964	+	0.0664418i	0.132696	+	0.991157i	$0.457637\pi$
$948$	−1.22336e6	+	731988.i	−1.36125	+	0.814493i
$949$	152365.	−	87968.0i	0.169181	−	0.0976770i
$950$	804299.	−	927463.i	0.891190	−	1.02766i
$951$	−296872.	+	306282.i	−0.328253	+	0.338657i
$952$	1860.76	−	498.590i	0.00205313	−	0.000550135i
$953$	952787.	−	952787.i	1.04908	−	1.04908i	0.0503521	−	0.998732i	$-0.483966\pi$
$953$	952787.	−	952787.i	1.04908	−	1.04908i	0.998732	−	0.0503521i	$-0.0160344\pi$
$954$	−137455.	−	221799.i	−0.151030	−	0.243704i
$955$	1.37942e6	−	863096.i	1.51248	−	0.946351i
$956$	470108.	−	814252.i	0.514378	−	0.890928i
$957$	−170880.	+	306933.i	−0.186581	+	0.335135i
$958$	269366.	+	72176.4i	0.293503	+	0.0786438i
$959$	301334.	−	173975.i	0.327651	−	0.189169i
$960$	47005.2	+	919061.i	0.0510039	+	0.997245i
$961$	301557.	−	522312.i	0.326529	−	0.565565i
$962$	−1.05007e6	−	1.05007e6i	−1.13467	−	1.13467i
$963$	499382.	−	150654.i	0.538493	−	0.162454i
$964$		−	9104.47i		−	0.00979716i
$965$	915786.	+	852968.i	0.983421	+	0.915964i
$966$	45933.6	−	47389.6i	0.0492240	−	0.0507842i
$967$	121222.	−	452408.i	0.129637	−	0.483812i	−0.870325	−	0.492477i	$-0.836091\pi$
$967$	121222.	−	452408.i	0.129637	−	0.483812i	0.999962	+	0.00866485i	$0.00275814\pi$
$968$	−636.162	−	170.459i	−0.000678918	−	0.000181915i
$969$	252010.	−	1.00284e6i	0.268393	−	1.06803i
$970$	538109.	−	19111.1i	0.571909	−	0.0203115i
$971$	767944.			0.814500			0.407250	−	0.913317i	$-0.366488\pi$
$971$	767944.			0.814500			0.407250	+	0.913317i	$0.366488\pi$
$972$	−941228.	+	73564.6i	−0.996236	+	0.0778639i
$973$	−645370.	+	645370.i	−0.681684	+	0.681684i
$974$	989626.	+	571361.i	1.04317	+	0.602272i
$975$	−537744.	−	451831.i	−0.565674	−	0.475299i
$976$	339476.	+	587989.i	0.356377	+	0.617262i
$977$	330695.	−	1.23417e6i	0.346448	−	1.29296i	−0.544463	−	0.838785i	$-0.683267\pi$
$977$	330695.	−	1.23417e6i	0.346448	−	1.29296i	0.890911	−	0.454177i	$-0.150067\pi$
$978$	1974.35	+	126551.i	0.00206417	+	0.132309i
$979$	45693.0	+	26380.9i	0.0476743	+	0.0275248i
$980$	1.85122e6	−	1.15830e6i	1.92755	−	1.20606i
$981$	828943.	+	444706.i	0.861364	+	0.462099i
$982$	829803.	+	829803.i	0.860503	+	0.860503i
$983$	152864.	+	570497.i	0.158197	+	0.590400i	0.998810	+	0.0487638i	$0.0155282\pi$
$983$	152864.	+	570497.i	0.158197	+	0.590400i	−0.840613	+	0.541636i	$0.817805\pi$
$984$	986.825	−	280.989i	0.00101918	−	0.000290201i
$985$	−440579.	−	1.43801e6i	−0.454100	−	1.48215i
$986$	−537760.	−	931427.i	−0.553139	−	0.958065i
$987$	−740471.	+	1.33003e6i	−0.760106	+	1.36529i
$988$	179447.	+	669704.i	0.183832	+	0.686071i
$989$			24584.4i			0.0251343i
$990$	−250909.	−	736130.i	−0.256004	−	0.751076i
$991$	1.09114e6			1.11105			0.555523	−	0.831501i	$-0.312518\pi$
$991$	1.09114e6			1.11105			0.555523	+	0.831501i	$0.312518\pi$
$992$	−791646.	+	212121.i	−0.804466	+	0.215556i
$993$	2394.42	+	153477.i	0.00242830	+	0.155649i
$994$	1.27457e6	−	735874.i	1.29000	−	0.744784i
$995$	−240866.	+	453653.i	−0.243293	+	0.458223i
$996$	122695.	+	30833.0i	0.123683	+	0.0310812i
$997$	−573470.	+	153661.i	−0.576927	+	0.154587i	−0.535471	−	0.844553i	$-0.679866\pi$
$997$	−573470.	+	153661.i	−0.576927	+	0.154587i	−0.0414551	+	0.999140i	$0.513199\pi$
$998$	−383096.	+	383096.i	−0.384633	+	0.384633i
$999$	1.03205e6	−	1.13347e6i	1.03412	−	1.13574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.k.a.7.18	✓	88
3.2	odd	2		135.5.l.a.127.5		88
5.3	odd	4	inner	45.5.k.a.43.5	yes	88
9.4	even	3	inner	45.5.k.a.22.5	yes	88
9.5	odd	6		135.5.l.a.37.18		88
15.8	even	4		135.5.l.a.73.18		88
45.13	odd	12	inner	45.5.k.a.13.18	yes	88
45.23	even	12		135.5.l.a.118.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.k.a.7.18	✓	88	1.1	even	1	trivial
45.5.k.a.13.18	yes	88	45.13	odd	12	inner
45.5.k.a.22.5	yes	88	9.4	even	3	inner
45.5.k.a.43.5	yes	88	5.3	odd	4	inner
135.5.l.a.37.18		88	9.5	odd	6
135.5.l.a.73.18		88	15.8	even	4
135.5.l.a.118.5		88	45.23	even	12
135.5.l.a.127.5		88	3.2	odd	2

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.46311 - 1.46384i) q^{2} +(7.72308 - 4.62104i) q^{3} +(13.8464 - 7.99420i) q^{4} +(22.0807 + 11.7237i) q^{5} +(35.4276 - 36.5506i) q^{6} +(-85.6591 + 22.9523i) q^{7} +(-0.0464312 + 0.0464312i) q^{8} +(38.2920 - 71.3773i) q^{9} +(137.791 + 31.7253i) q^{10} +(33.9524 - 58.8072i) q^{11} +(69.9951 - 125.724i) q^{12} +(-120.611 - 32.3175i) q^{13} +(-434.367 + 250.782i) q^{14} +(224.706 - 11.4926i) q^{15} +(-128.093 + 221.863i) q^{16} +(233.925 + 233.925i) q^{17} +(104.709 - 445.995i) q^{18} -347.290i q^{19} +(399.458 - 14.1869i) q^{20} +(-555.489 + 573.096i) q^{21} +(99.4014 - 370.971i) q^{22} +(-14.1222 - 3.78404i) q^{23} +(-0.144032 + 0.573153i) q^{24} +(350.111 + 517.733i) q^{25} -706.217 q^{26} +(-34.1045 - 728.202i) q^{27} +(-1002.58 + 1002.58i) q^{28} +(-497.806 - 287.408i) q^{29} +(1210.77 - 391.718i) q^{30} +(283.023 + 490.210i) q^{31} +(-374.742 + 1398.56i) q^{32} +(-9.53338 - 611.068i) q^{33} +(1620.39 + 935.532i) q^{34} +(-2160.49 - 497.438i) q^{35} +(-40.3991 - 1294.43i) q^{36} +(1486.90 + 1486.90i) q^{37} +(-508.376 - 1897.28i) q^{38} +(-1080.83 + 307.755i) q^{39} +(-1.56958 + 0.480887i) q^{40} +(-868.102 - 1503.60i) q^{41} +(-2195.78 + 3944.03i) q^{42} +(-435.208 - 1624.22i) q^{43} -1085.69i q^{44} +(1682.32 - 1127.13i) q^{45} -82.6905 q^{46} +(1842.30 - 493.642i) q^{47} +(35.9668 + 2305.39i) q^{48} +(4731.34 - 2731.64i) q^{49} +(2670.57 + 2315.93i) q^{50} +(2887.60 + 725.648i) q^{51} +(-1928.37 + 516.705i) q^{52} +(402.755 - 402.755i) q^{53} +(-1252.28 - 3928.32i) q^{54} +(1439.13 - 900.455i) q^{55} +(2.91155 - 5.04296i) q^{56} +(-1604.84 - 2682.15i) q^{57} +(-3140.29 - 841.438i) q^{58} +(-498.977 + 288.085i) q^{59} +(3019.49 - 1955.48i) q^{60} +(1325.12 - 2295.17i) q^{61} +(2263.77 + 2263.77i) q^{62} +(-1641.79 + 6993.00i) q^{63} +4090.05i q^{64} +(-2284.28 - 2127.59i) q^{65} +(-946.585 - 3324.38i) q^{66} +(-369.394 + 1378.60i) q^{67} +(5109.06 + 1368.97i) q^{68} +(-126.553 + 36.0349i) q^{69} +(-12531.2 + 445.049i) q^{70} -2934.32 q^{71} +(1.53619 + 5.09208i) q^{72} +(-996.318 + 996.318i) q^{73} +(10299.7 + 5946.53i) q^{74} +(5096.40 + 2380.62i) q^{75} +(-2776.31 - 4808.70i) q^{76} +(-1558.57 + 5816.65i) q^{77} +(-5454.17 + 3263.45i) q^{78} +(-8580.07 - 4953.70i) q^{79} +(-5429.43 + 3397.17i) q^{80} +(-3628.44 - 5466.37i) q^{81} +(-6943.56 - 6943.56i) q^{82} +(227.549 + 849.223i) q^{83} +(-3110.05 + 12376.0i) q^{84} +(2422.76 + 7907.69i) q^{85} +(-4755.17 - 8236.20i) q^{86} +(-5172.72 + 80.7005i) q^{87} +(1.15404 + 4.30694i) q^{88} +776.997i q^{89} +(7540.75 - 8620.30i) q^{90} +11073.2 q^{91} +(-225.792 + 60.5007i) q^{92} +(4451.09 + 2478.07i) q^{93} +(9342.07 - 5393.64i) q^{94} +(4071.52 - 7668.40i) q^{95} +(3568.61 + 12532.9i) q^{96} +(3678.34 - 985.608i) q^{97} +(21849.2 - 21849.2i) q^{98} +(-2897.40 - 4675.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) \) 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

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