LMFDB - Embedded newform 62.6.g.a.41.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	62.41
Dual form			62.6.g.a.59.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(0.180031 + 1.71288i) q^{3} +(4.94427 + 15.2169i) q^{4} +(16.3913 + 28.3905i) q^{5} +(3.44463 - 5.96628i) q^{6} +(-166.864 - 35.4680i) q^{7} +(19.7771 - 60.8676i) q^{8} +(234.788 - 49.9058i) q^{9} +(13.7068 - 130.412i) q^{10} +(112.522 - 124.968i) q^{11} +(-25.1746 + 11.2085i) q^{12} +(-572.280 - 254.795i) q^{13} +(456.592 + 507.097i) q^{14} +(-45.6787 + 33.1875i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1254.54 - 1393.31i) q^{17} +(-877.127 - 390.522i) q^{18} +(-2664.22 + 1186.19i) q^{19} +(-350.973 + 389.795i) q^{20} +(30.7118 - 292.203i) q^{21} +(-657.947 + 139.851i) q^{22} +(-104.991 + 323.128i) q^{23} +(107.820 + 22.9177i) q^{24} +(1025.15 - 1775.62i) q^{25} +(1252.88 + 2170.05i) q^{26} +(257.083 + 791.219i) q^{27} +(-285.307 - 2714.51i) q^{28} +(-4905.09 - 3563.76i) q^{29} +225.848 q^{30} +(-4081.97 + 3459.29i) q^{31} +1024.00 q^{32} +(234.314 + 170.239i) q^{33} +(783.912 + 7458.42i) q^{34} +(-1728.15 - 5318.71i) q^{35} +(1920.27 + 3326.00i) q^{36} +(7607.12 - 13175.9i) q^{37} +(11410.5 + 2425.38i) q^{38} +(333.406 - 1026.12i) q^{39} +(2052.23 - 436.216i) q^{40} +(-1653.34 + 15730.5i) q^{41} +(-786.396 + 873.381i) q^{42} +(10723.1 - 4774.24i) q^{43} +(2457.97 + 1094.36i) q^{44} +(5265.33 + 5847.74i) q^{45} +(1099.48 - 798.817i) q^{46} +(14672.1 - 10659.9i) q^{47} +(-295.028 - 327.662i) q^{48} +(11231.5 + 5000.61i) q^{49} +(-7492.19 + 3335.74i) q^{50} +(2160.71 - 2399.71i) q^{51} +(1047.69 - 9968.11i) q^{52} +(-28813.3 + 6124.45i) q^{53} +(1028.33 - 3164.88i) q^{54} +(5392.30 + 1146.17i) q^{55} +(-5458.93 + 9455.14i) q^{56} +(-2511.44 - 4349.95i) q^{57} +(7494.31 + 23065.1i) q^{58} +(35.6740 + 339.415i) q^{59} +(-730.858 - 531.000i) q^{60} +13059.6 q^{61} +(21342.8 - 1597.20i) q^{62} -40947.7 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2146.62 - 20423.7i) q^{65} +(-357.999 - 1101.81i) q^{66} +(15730.2 + 27245.6i) q^{67} +(14999.0 - 25979.1i) q^{68} +(-572.382 - 121.664i) q^{69} +(-6912.61 + 21274.8i) q^{70} +(-68098.3 + 14474.7i) q^{71} +(1605.78 - 15278.0i) q^{72} +(20563.8 - 22838.4i) q^{73} +(-55595.6 + 24752.7i) q^{74} +(3225.98 + 1436.30i) q^{75} +(-31222.8 - 34676.4i) q^{76} +(-23208.2 + 16861.8i) q^{77} +(-3491.48 + 2536.71i) q^{78} +(-30649.1 - 34039.3i) q^{79} +(-7666.78 - 3413.47i) q^{80} +(51976.5 - 23141.4i) q^{81} +(42334.9 - 47017.7i) q^{82} +(-7157.42 + 68098.3i) q^{83} +(4598.27 - 977.393i) q^{84} +(18993.2 - 58455.0i) q^{85} +(-45925.6 - 9761.79i) q^{86} +(5221.23 - 9043.43i) q^{87} +(-5381.17 - 9320.46i) q^{88} +(34733.3 + 106898. i) q^{89} +(-3290.10 - 31303.2i) q^{90} +(86455.6 + 62813.7i) q^{91} -5436.11 q^{92} +(-6660.23 - 6369.15i) q^{93} -72542.7 q^{94} +(-77346.5 - 56195.5i) q^{95} +(184.352 + 1753.99i) q^{96} +(-15490.3 - 47674.2i) q^{97} +(-24588.9 - 42589.3i) q^{98} +(20182.2 - 34956.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) $ 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	0.180031	+	1.71288i	0.0115490	+	0.109881i	0.998778	−	0.0494281i	$-0.0157399\pi$
$3$	0.180031	+	1.71288i	0.0115490	+	0.109881i	−0.987229	+	0.159310i	$0.949073\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	16.3913	+	28.3905i	0.293216	+	0.507865i	0.974568	−	0.224091i	$-0.0719412\pi$
$5$	16.3913	+	28.3905i	0.293216	+	0.507865i	−0.681352	+	0.731956i	$0.738608\pi$
$6$	3.44463	−	5.96628i	0.0390629	−	0.0676590i
$7$	−166.864	−	35.4680i	−1.28711	−	0.273584i	−0.486983	−	0.873411i	$-0.661903\pi$
$7$	−166.864	−	35.4680i	−1.28711	−	0.273584i	−0.800130	+	0.599827i	$0.795236\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	234.788	−	49.9058i	0.966207	−	0.205374i
$10$	13.7068	−	130.412i	0.0433448	−	0.412398i
$11$	112.522	−	124.968i	0.280386	−	0.311400i	−0.586458	−	0.809980i	$-0.699478\pi$
$11$	112.522	−	124.968i	0.280386	−	0.311400i	0.866844	+	0.498580i	$0.166145\pi$
$12$	−25.1746	+	11.2085i	−0.0504673	+	0.0224695i
$13$	−572.280	−	254.795i	−0.939183	−	0.418151i	−0.120704	−	0.992688i	$-0.538515\pi$
$13$	−572.280	−	254.795i	−0.939183	−	0.418151i	−0.818478	+	0.574537i	$0.805182\pi$
$14$	456.592	+	507.097i	0.622599	+	0.691466i
$15$	−45.6787	+	33.1875i	−0.0524186	+	0.0380843i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−1254.54	−	1393.31i	−1.05284	−	1.16929i	−0.985169	−	0.171587i	$-0.945111\pi$
$17$	−1254.54	−	1393.31i	−1.05284	−	1.16929i	−0.0676684	−	0.997708i	$-0.521556\pi$
$18$	−877.127	−	390.522i	−0.638089	−	0.284095i
$19$	−2664.22	+	1186.19i	−1.69312	+	0.753824i	−0.693679	+	0.720285i	$0.744011\pi$
$19$	−2664.22	+	1186.19i	−1.69312	+	0.753824i	−0.999437	+	0.0335391i	$0.989322\pi$
$20$	−350.973	+	389.795i	−0.196200	+	0.217902i
$21$	30.7118	−	292.203i	0.0151970	−	0.144589i
$22$	−657.947	+	139.851i	−0.289824	+	0.0616040i
$23$	−104.991	+	323.128i	−0.0413839	+	0.127366i	−0.969614	−	0.244640i	$-0.921330\pi$
$23$	−104.991	+	323.128i	−0.0413839	+	0.127366i	0.928230	+	0.372007i	$0.121330\pi$
$24$	107.820	+	22.9177i	0.0382093	+	0.00812164i
$25$	1025.15	−	1775.62i	0.328049	−	0.568197i
$26$	1252.88	+	2170.05i	0.363475	+	0.629558i
$27$	257.083	+	791.219i	0.0678677	+	0.208875i
$28$	−285.307	−	2714.51i	−0.0687728	−	0.654330i
$29$	−4905.09	−	3563.76i	−1.08306	−	0.786888i	−0.104845	−	0.994489i	$-0.533435\pi$
$29$	−4905.09	−	3563.76i	−1.08306	−	0.786888i	−0.978214	+	0.207600i	$0.933435\pi$
$30$	225.848			0.0458155
$31$	−4081.97	+	3459.29i	−0.762896	+	0.646521i
$31$	−4081.97	+	3459.29i	−0.762896	+	0.646521i
$32$	1024.00			0.176777
$33$	234.314	+	170.239i	0.0374552	+	0.0272128i
$34$	783.912	+	7458.42i	0.116297	+	1.10650i
$35$	−1728.15	−	5318.71i	−0.238458	−	0.733899i
$36$	1920.27	+	3326.00i	0.246948	+	0.427727i
$37$	7607.12	−	13175.9i	0.913515	−	1.58225i	0.104454	−	0.994530i	$-0.466690\pi$
$37$	7607.12	−	13175.9i	0.913515	−	1.58225i	0.809061	−	0.587725i	$-0.199976\pi$
$38$	11410.5	+	2425.38i	1.28188	+	0.272471i
$39$	333.406	−	1026.12i	0.0351004	−	0.108028i
$40$	2052.23	−	436.216i	0.202804	−	0.0431074i
$41$	−1653.34	+	15730.5i	−0.153604	+	1.46145i	0.597822	+	0.801629i	$0.296033\pi$
$41$	−1653.34	+	15730.5i	−0.153604	+	1.46145i	−0.751426	+	0.659817i	$0.770634\pi$
$42$	−786.396	+	873.381i	−0.0687889	+	0.0763978i
$43$	10723.1	−	4774.24i	0.884402	−	0.393761i	0.0862900	−	0.996270i	$-0.472499\pi$
$43$	10723.1	−	4774.24i	0.884402	−	0.393761i	0.798112	+	0.602509i	$0.205832\pi$
$44$	2457.97	+	1094.36i	0.191401	+	0.0852174i
$45$	5265.33	+	5847.74i	0.387609	+	0.430484i
$46$	1099.48	−	798.817i	0.0766111	−	0.0556612i
$47$	14672.1	−	10659.9i	0.968828	−	0.703895i	0.0136437	−	0.999907i	$-0.495657\pi$
$47$	14672.1	−	10659.9i	0.968828	−	0.703895i	0.955184	+	0.296012i	$0.0956569\pi$
$48$	−295.028	−	327.662i	−0.0184825	−	0.0205269i
$49$	11231.5	+	5000.61i	0.668266	+	0.297531i
$50$	−7492.19	+	3335.74i	−0.423822	+	0.188698i
$51$	2160.71	−	2399.71i	0.116325	−	0.129191i
$52$	1047.69	−	9968.11i	0.0537309	−	0.511216i
$53$	−28813.3	+	6124.45i	−1.40897	+	0.299486i	−0.848723	−	0.528837i	$-0.822628\pi$
$53$	−28813.3	+	6124.45i	−1.40897	+	0.299486i	−0.560250	+	0.828324i	$0.689295\pi$
$54$	1028.33	−	3164.88i	0.0479897	−	0.147697i
$55$	5392.30	+	1146.17i	0.240363	+	0.0510907i
$56$	−5458.93	+	9455.14i	−0.232615	+	0.402901i
$57$	−2511.44	−	4349.95i	−0.102385	−	0.177336i
$58$	7494.31	+	23065.1i	0.292524	+	0.900297i
$59$	35.6740	+	339.415i	0.00133420	+	0.0126941i	0.995169	−	0.0981793i	$-0.0313019\pi$
$59$	35.6740	+	339.415i	0.00133420	+	0.0126941i	−0.993835	+	0.110873i	$0.964635\pi$
$60$	−730.858	−	531.000i	−0.0262093	−	0.0190422i
$61$	13059.6			0.449371			0.224686	−	0.974431i	$-0.427864\pi$
$61$	13059.6			0.449371			0.224686	+	0.974431i	$0.427864\pi$
$62$	21342.8	−	1597.20i	0.705135	−	0.0527692i
$63$	−40947.7			−1.29980
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−2146.62	−	20423.7i	−0.0630191	−	0.599587i
$66$	−357.999	−	1101.81i	−0.0101163	−	0.0311348i
$67$	15730.2	+	27245.6i	0.428103	+	0.741496i	0.996705	−	0.0811169i	$-0.0258487\pi$
$67$	15730.2	+	27245.6i	0.428103	+	0.741496i	−0.568602	+	0.822613i	$0.692515\pi$
$68$	14999.0	−	25979.1i	0.393360	−	0.681320i
$69$	−572.382	−	121.664i	−0.0144732	−	0.00307636i
$70$	−6912.61	+	21274.8i	−0.168615	+	0.518945i
$71$	−68098.3	+	14474.7i	−1.60321	+	0.340773i	−0.920751	−	0.390151i	$-0.872423\pi$
$71$	−68098.3	+	14474.7i	−1.60321	+	0.340773i	−0.682459	+	0.730924i	$0.739090\pi$
$72$	1605.78	−	15278.0i	0.0365053	−	0.347324i
$73$	20563.8	−	22838.4i	0.451643	−	0.501600i	−0.473724	−	0.880674i	$-0.657090\pi$
$73$	20563.8	−	22838.4i	0.451643	−	0.501600i	0.925367	+	0.379073i	$0.123757\pi$
$74$	−55595.6	+	24752.7i	−1.18021	+	0.525465i
$75$	3225.98	+	1436.30i	0.0662229	+	0.0294844i
$76$	−31222.8	−	34676.4i	−0.620065	−	0.688652i
$77$	−23208.2	+	16861.8i	−0.446082	+	0.324098i
$78$	−3491.48	+	2536.71i	−0.0649789	+	0.0472099i
$79$	−30649.1	−	34039.3i	−0.552522	−	0.613638i	0.400589	−	0.916258i	$-0.368805\pi$
$79$	−30649.1	−	34039.3i	−0.552522	−	0.613638i	−0.953111	+	0.302620i	$0.902139\pi$
$80$	−7666.78	−	3413.47i	−0.133933	−	0.0596308i
$81$	51976.5	−	23141.4i	0.880226	−	0.391902i
$82$	42334.9	−	47017.7i	0.695287	−	0.772195i
$83$	−7157.42	+	68098.3i	−0.114041	+	1.08503i	0.776497	+	0.630121i	$0.216995\pi$
$83$	−7157.42	+	68098.3i	−0.114041	+	1.08503i	−0.890538	+	0.454908i	$0.849672\pi$
$84$	4598.27	−	977.393i	0.0711044	−	0.0151137i
$85$	18993.2	−	58455.0i	0.285135	−	0.877555i
$86$	−45925.6	−	9761.79i	−0.669590	−	0.142326i
$87$	5221.23	−	9043.43i	0.0739562	−	0.128096i
$88$	−5381.17	−	9320.46i	−0.0740747	−	0.128301i
$89$	34733.3	+	106898.i	0.464805	+	1.43052i	0.859228	+	0.511593i	$0.170944\pi$
$89$	34733.3	+	106898.i	0.464805	+	1.43052i	−0.394423	+	0.918929i	$0.629056\pi$
$90$	−3290.10	−	31303.2i	−0.0428157	−	0.407364i
$91$	86455.6	+	62813.7i	1.09443	+	0.795153i
$92$	−5436.11			−0.0669605
$93$	−6660.23	−	6369.15i	−0.0798513	−	0.0763615i
$94$	−72542.7			−0.846787
$95$	−77346.5	−	56195.5i	−0.879289	−	0.638841i
$96$	184.352	+	1753.99i	0.00204159	+	0.0194245i
$97$	−15490.3	−	47674.2i	−0.167159	−	0.514463i	0.832030	−	0.554731i	$-0.187179\pi$
$97$	−15490.3	−	47674.2i	−0.167159	−	0.514463i	−0.999189	+	0.0402679i	$0.987179\pi$
$98$	−24588.9	−	42589.3i	−0.258627	−	0.447955i
$99$	20182.2	−	34956.6i	0.206957	−	0.358461i
$100$	32088.0	+	6820.52i	0.320880	+	0.0682052i
$101$	25669.0	−	79001.1i	0.250384	−	0.770601i	−0.744321	−	0.667822i	$-0.767227\pi$
$101$	25669.0	−	79001.1i	0.250384	−	0.770601i	0.994704	−	0.102779i	$-0.0327734\pi$
$102$	−12634.3	+	2685.50i	−0.120240	+	0.0255578i
$103$	−21241.4	+	202098.i	−0.197283	+	1.87702i	0.230404	+	0.973095i	$0.425995\pi$
$103$	−21241.4	+	202098.i	−0.197283	+	1.87702i	−0.427687	+	0.903927i	$0.640671\pi$
$104$	−26826.8	+	29794.2i	−0.243212	+	0.270115i
$105$	8799.20	−	3917.66i	0.0778879	−	0.0346779i
$106$	107641.	+	47924.9i	0.930494	+	0.414282i
$107$	−18422.1	−	20459.8i	−0.155553	−	0.172759i	0.660331	−	0.750975i	$-0.270416\pi$
$107$	−18422.1	−	20459.8i	−0.155553	−	0.172759i	−0.815884	+	0.578215i	$0.803749\pi$
$108$	−10768.8	+	7824.00i	−0.0888400	+	0.0645461i
$109$	22324.7	−	16219.9i	0.179978	−	0.130762i	−0.494149	−	0.869377i	$-0.664520\pi$
$109$	22324.7	−	16219.9i	0.179978	−	0.130762i	0.674127	+	0.738616i	$0.264520\pi$
$110$	−14755.0	−	16387.1i	−0.116268	−	0.129128i
$111$	23938.3	+	10658.0i	0.184411	+	0.0821049i
$112$	39895.8	−	17762.8i	0.300526	−	0.133803i
$113$	11059.8	−	12283.2i	0.0814803	−	0.0904930i	−0.701026	−	0.713136i	$-0.747274\pi$
$113$	11059.8	−	12283.2i	0.0814803	−	0.0904930i	0.782506	+	0.622643i	$0.213941\pi$
$114$	−2100.14	+	19981.5i	−0.0151351	+	0.144001i
$115$	−10894.7	+	2315.74i	−0.0768194	+	0.0163285i
$116$	29977.3	−	92260.5i	0.206846	−	0.636606i
$117$	−147080.	−	31262.9i	−0.993322	−	0.211137i
$118$	682.570	−	1182.25i	0.00451276	−	0.00781633i
$119$	159919.	+	276988.i	1.03522	+	1.79305i
$120$	1116.65	+	3436.70i	0.00707888	+	0.0217866i
$121$	13878.5	+	132045.i	0.0861747	+	0.819898i
$122$	−42261.8	−	30705.0i	−0.257068	−	0.186771i
$123$	−27242.1			−0.162360
$124$	−72822.0	−	45011.3i	−0.425313	−	0.262886i
$125$	169660.			0.971188
$126$	132510.	+	96273.8i	0.743568	+	0.540234i
$127$	−15388.7	−	146414.i	−0.0846628	−	0.805512i	−0.951651	−	0.307183i	$-0.900614\pi$
$127$	−15388.7	−	146414.i	−0.0846628	−	0.805512i	0.866988	−	0.498329i	$-0.166053\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	10108.2	+	17507.9i	0.0534810	+	0.0926318i
$130$	−41072.5	+	71139.6i	−0.213154	+	0.369193i
$131$	22602.1	+	4804.22i	0.115072	+	0.0244593i	0.265088	−	0.964224i	$-0.414599\pi$
$131$	22602.1	+	4804.22i	0.115072	+	0.0244593i	−0.150016	+	0.988684i	$0.547932\pi$
$132$	−1432.00	+	4407.23i	−0.00715331	+	0.0220156i
$133$	486634.	−	103437.i	2.38547	−	0.507046i
$134$	13154.1	−	125153.i	0.0632846	−	0.602112i
$135$	−18249.2	+	20267.8i	−0.0861806	+	0.0957132i
$136$	−109618.	+	48805.2i	−0.508201	+	0.226266i
$137$	−288832.	−	128596.i	−1.31475	−	0.585364i	−0.374936	−	0.927051i	$-0.622335\pi$
$137$	−288832.	−	128596.i	−1.31475	−	0.585364i	−0.939814	+	0.341686i	$0.889002\pi$
$138$	1566.22	+	1739.46i	0.00700091	+	0.00777530i
$139$	−30139.7	+	21897.8i	−0.132313	+	0.0961309i	−0.651973	−	0.758242i	$-0.726059\pi$
$139$	−30139.7	+	21897.8i	−0.132313	+	0.0961309i	0.519660	+	0.854373i	$0.326059\pi$
$140$	72389.8	−	52594.3i	0.312146	−	0.226787i
$141$	20900.5	+	23212.4i	0.0885339	+	0.0983269i
$142$	254403.	+	113267.i	1.05877	+	0.471394i
$143$	−96235.5	+	42846.8i	−0.393546	+	0.175218i
$144$	−41117.1	+	45665.2i	−0.165241	+	0.183518i
$145$	20776.2	−	197673.i	0.0820629	−	0.780776i
$146$	−120242.	+	25558.2i	−0.466846	+	0.0992312i
$147$	−6543.42	+	20138.6i	−0.0249753	+	0.0768662i
$148$	238108.	+	50611.5i	0.893553	+	0.189930i
$149$	100386.	−	173874.i	0.370431	−	0.641606i	−0.619201	−	0.785233i	$-0.712543\pi$
$149$	100386.	−	173874.i	0.370431	−	0.641606i	0.989632	+	0.143627i	$0.0458765\pi$
$150$	−7062.55	−	12232.7i	−0.0256291	−	0.0443909i
$151$	27003.8	+	83109.3i	0.0963792	+	0.296625i	0.987611	−	0.156924i	$-0.0501578\pi$
$151$	27003.8	+	83109.3i	0.0963792	+	0.296625i	−0.891231	+	0.453549i	$0.850158\pi$
$152$	19509.9	+	185624.i	0.0684930	+	0.651667i
$153$	−364085.	−	264523.i	−1.25740	−	0.913555i
$154$	114748.			0.389890
$155$	−165120.	−	59187.1i	−0.552039	−	0.197878i
$156$	17262.8			0.0567937
$157$	185499.	+	134773.i	0.600610	+	0.436369i	0.846095	−	0.533032i	$-0.178947\pi$
$157$	185499.	+	134773.i	0.600610	+	0.436369i	−0.245485	+	0.969400i	$0.578947\pi$
$158$	19151.4	+	182214.i	0.0610321	+	0.580682i
$159$	−15677.7	−	48251.1i	−0.0491802	−	0.151361i
$160$	16784.7	+	29071.9i	0.0518337	+	0.0897787i
$161$	28979.8	−	50194.5i	0.0881112	−	0.152613i
$162$	−222608.	−	47316.8i	−0.666428	−	0.141654i
$163$	66658.7	−	205154.i	0.196511	−	0.604800i	−0.803444	−	0.595380i	$-0.797002\pi$
$163$	66658.7	−	205154.i	0.196511	−	0.604800i	0.999956	−	0.00941978i	$-0.00299845\pi$
$164$	−247544.	+	52617.1i	−0.718692	+	0.152763i
$165$	−992.469	+	9442.71i	−0.00283797	+	0.0270014i
$166$	183271.	−	203543.i	0.516206	−	0.573305i
$167$	−14065.0	+	6262.16i	−0.0390256	+	0.0173753i	−0.426157	−	0.904649i	$-0.640133\pi$
$167$	−14065.0	+	6262.16i	−0.0390256	+	0.0173753i	0.387131	+	0.922025i	$0.373466\pi$
$168$	−17178.3	−	7648.28i	−0.0469578	−	0.0209069i
$169$	14140.0	+	15704.1i	0.0380832	+	0.0422957i
$170$	−198899.	+	144509.i	−0.527850	+	0.383506i
$171$	−566331.	+	411464.i	−1.48109	+	1.07607i
$172$	125667.	+	139567.i	0.323892	+	0.359719i
$173$	−531508.	−	236643.i	−1.35019	−	0.601143i	−0.401066	−	0.916049i	$-0.631360\pi$
$173$	−531508.	−	236643.i	−1.35019	−	0.601143i	−0.949123	+	0.314906i	$0.898027\pi$
$174$	−38158.6	+	16989.3i	−0.0955476	+	0.0425405i
$175$	−234038.	+	259926.i	−0.577686	+	0.641585i
$176$	−4499.88	+	42813.5i	−0.0109501	+	0.104184i
$177$	−574.956	+	122.211i	−0.00137944	+	0.000293208i
$178$	138933.	−	427592.i	0.328667	−	1.01153i
$179$	−442320.	−	94018.0i	−1.03182	−	0.219320i	−0.339269	−	0.940689i	$-0.610180\pi$
$179$	−442320.	−	94018.0i	−1.03182	−	0.219320i	−0.692551	+	0.721369i	$0.743513\pi$
$180$	−62951.3	+	109035.i	−0.144818	+	0.250833i
$181$	−222214.	−	384885.i	−0.504167	−	0.873242i	−0.999988	−	0.00481781i	$-0.998466\pi$
$181$	−222214.	−	384885.i	−0.504167	−	0.873242i	0.495822	−	0.868424i	$-0.334867\pi$
$182$	−132092.	−	406539.i	−0.295597	−	0.909753i
$183$	2351.13	+	22369.6i	0.00518979	+	0.0493776i
$184$	17591.6	+	12781.1i	0.0383055	+	0.0278306i
$185$	498761.			1.07143
$186$	6578.19	+	36270.2i	0.0139420	+	0.0768718i
$187$	−315282.			−0.659319
$188$	234753.	+	170558.i	0.484414	+	0.351947i
$189$	−14834.8	−	141144.i	−0.0302084	−	0.287414i
$190$	118175.	+	363705.i	0.237488	+	0.730913i
$191$	−247294.	−	428326.i	−0.490490	−	0.849554i	0.509450	−	0.860500i	$-0.329849\pi$
$191$	−247294.	−	428326.i	−0.490490	−	0.849554i	−0.999940	+	0.0109466i	$0.996516\pi$
$192$	3527.30	−	6109.47i	0.00690542	−	0.0119605i
$193$	344266.	+	73175.9i	0.665274	+	0.141408i	0.528157	−	0.849147i	$-0.322883\pi$
$193$	344266.	+	73175.9i	0.665274	+	0.141408i	0.137117	+	0.990555i	$0.456216\pi$
$194$	−61961.2	+	190697.i	−0.118199	+	0.363780i
$195$	34597.0	−	7353.82i	0.0651556	−	0.0138493i
$196$	−20561.9	+	195634.i	−0.0382317	+	0.363750i
$197$	295473.	−	328156.i	0.542441	−	0.602442i	−0.408139	−	0.912920i	$-0.633822\pi$
$197$	295473.	−	328156.i	0.542441	−	0.602442i	0.950581	+	0.310477i	$0.100489\pi$
$198$	−147499.	+	65670.8i	−0.267378	+	0.119044i
$199$	−26300.7	−	11709.8i	−0.0470798	−	0.0209613i	0.383062	−	0.923723i	$-0.374870\pi$
$199$	−26300.7	−	11709.8i	−0.0470798	−	0.0209613i	−0.430142	+	0.902761i	$0.641536\pi$
$200$	−87803.0	−	97515.1i	−0.155215	−	0.172384i
$201$	−43836.5	+	31849.1i	−0.0765325	+	0.0556041i
$202$	−268809.	+	195301.i	−0.463517	+	0.336765i
$203$	692082.	+	768635.i	1.17874	+	1.30912i
$204$	47199.3	+	21014.5i	0.0794073	+	0.0353544i
$205$	−473697.	+	210904.i	−0.787256	+	0.350509i
$206$	543900.	−	604062.i	0.892999	−	0.991776i
$207$	−8524.62	+	81106.3i	−0.0138277	+	0.131562i
$208$	156864.	−	33342.4i	0.251399	−	0.0534366i
$209$	−151548.	+	466416.i	−0.239985	+	0.738598i
$210$	−37685.8	−	8010.36i	−0.0589697	−	0.0125344i
$211$	222317.	−	385064.i	0.343769	−	0.595425i	−0.641361	−	0.767240i	$-0.721630\pi$
$211$	222317.	−	385064.i	0.343769	−	0.595425i	0.985129	+	0.171815i	$0.0549631\pi$
$212$	−235656.	−	408168.i	−0.360113	−	0.623733i
$213$	−37053.3	−	114038.i	−0.0559601	−	0.172227i
$214$	11511.2	+	109522.i	0.0171825	+	0.163481i
$215$	311309.	+	226179.i	0.459298	+	0.333700i
$216$	53244.0			0.0776490
$217$	803826.	−	432450.i	1.15881	−	0.623429i
$218$	−110380.			−0.157307
$219$	42821.5	+	31111.7i	0.0603326	+	0.0438342i
$220$	9219.85	+	87721.0i	0.0128430	+	0.122193i
$221$	362939.	+	1.11701e6i	0.499865	+	1.53843i
$222$	−52407.5	−	90772.4i	−0.0713692	−	0.123615i
$223$	−189052.	+	327447.i	−0.254577	+	0.440940i	−0.964780	−	0.263056i	$-0.915269\pi$
$223$	−189052.	+	327447.i	−0.254577	+	0.440940i	0.710204	+	0.703996i	$0.248603\pi$
$224$	−170868.	−	36319.2i	−0.227532	−	0.0483633i
$225$	152080.	−	468055.i	0.200270	−	0.616369i
$226$	−64669.9	+	13746.0i	−0.0842230	+	0.0179022i
$227$	3076.43	−	29270.3i	0.00396262	−	0.0377018i	−0.992362	−	0.123361i	$-0.960633\pi$
$227$	3076.43	−	29270.3i	0.00396262	−	0.0377018i	0.996325	+	0.0856588i	$0.0272995\pi$
$228$	53775.5	−	59723.7i	0.0685090	−	0.0760869i
$229$	−24219.1	+	10783.1i	−0.0305190	+	0.0135879i	−0.421939	−	0.906624i	$-0.638650\pi$
$229$	−24219.1	+	10783.1i	−0.0305190	+	0.0135879i	0.391420	+	0.920212i	$0.371984\pi$
$230$	40700.6	+	18121.1i	0.0507320	+	0.0225873i
$231$	−33060.4	−	36717.3i	−0.0407641	−	0.0452731i
$232$	−313926.	+	228081.i	−0.382919	+	0.278207i
$233$	206093.	−	149735.i	0.248698	−	0.180690i	−0.456452	−	0.889748i	$-0.650880\pi$
$233$	206093.	−	149735.i	0.248698	−	0.180690i	0.705150	+	0.709059i	$0.250880\pi$
$234$	402459.	+	446976.i	0.480487	+	0.533635i
$235$	543133.	+	241819.i	0.641559	+	0.285641i
$236$	−4988.47	+	2221.01i	−0.00583025	+	0.00259580i
$237$	52787.4	−	58626.4i	0.0610463	−	0.0677988i
$238$	133729.	−	1.27234e6i	0.153032	−	1.45600i
$239$	662365.	−	140790.i	0.750071	−	0.159433i	0.183013	−	0.983110i	$-0.441415\pi$
$239$	662365.	−	140790.i	0.750071	−	0.159433i	0.567058	+	0.823678i	$0.308082\pi$
$240$	4466.61	−	13746.8i	0.00500553	−	0.0154054i
$241$	1.58207e6	+	336280.i	1.75462	+	0.372957i	0.969252	−	0.246070i	$-0.0791392\pi$
$241$	1.58207e6	+	336280.i	1.75462	+	0.372957i	0.785370	+	0.619026i	$0.212473\pi$
$242$	265545.	−	459938.i	0.291474	−	0.504848i
$243$	150076.	+	259940.i	0.163041	+	0.282395i
$244$	64570.2	+	198727.i	0.0694317	+	0.213689i
$245$	42129.5	+	400836.i	0.0448406	+	0.426630i
$246$	88157.4	+	64050.1i	0.0928797	+	0.0674811i
$247$	1.82692e6			1.90536
$248$	129829.	+	316874.i	0.134043	+	0.327158i
$249$	−117933.			−0.120542
$250$	−549030.	−	398894.i	−0.555579	−	0.403652i
$251$	−126959.	−	1.20793e6i	−0.127197	−	1.21020i	−0.852856	−	0.522147i	$-0.825131\pi$
$251$	−126959.	−	1.20793e6i	−0.127197	−	1.21020i	0.725658	−	0.688055i	$-0.241535\pi$
$252$	−202457.	−	623097.i	−0.200831	−	0.618094i
$253$	28567.0	+	49479.6i	0.0280585	+	0.0485987i
$254$	−294440.	+	509985.i	−0.286360	+	0.495991i
$255$	103546.	+	22009.4i	0.0997200	+	0.0211961i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−301047.	+	63989.4i	−0.284316	+	0.0604332i	−0.347862	−	0.937546i	$-0.613092\pi$
$257$	−301047.	+	63989.4i	−0.284316	+	0.0604332i	0.0635464	+	0.997979i	$0.479759\pi$
$258$	8452.76	−	80422.6i	0.00790586	−	0.0752192i
$259$	−1.73667e6	+	1.92877e6i	−1.60868	+	1.78662i
$260$	300173.	−	133645.i	0.275383	−	0.122609i
$261$	−1.32951e6	−	591936.i	−1.20807	−	0.537865i
$262$	−61846.5	−	68687.4i	−0.0556624	−	0.0618193i
$263$	−1.20042e6	+	872157.i	−1.07015	+	0.777509i	−0.975939	−	0.218044i	$-0.930033\pi$
$263$	−1.20042e6	+	872157.i	−1.07015	+	0.777509i	−0.0942100	+	0.995552i	$0.530033\pi$
$264$	14996.1	−	10895.3i	0.0132424	−	0.00962119i
$265$	−646162.	−	717636.i	−0.565232	−	0.627754i
$266$	−1.81798e6	−	809415.i	−1.57538	−	0.701402i
$267$	−176851.	+	78738.9i	−0.151820	+	0.0675945i
$268$	−336819.	+	374075.i	−0.286457	+	0.318143i
$269$	−75830.2	+	721476.i	−0.0638942	+	0.607913i	0.914987	+	0.403483i	$0.132201\pi$
$269$	−75830.2	+	721476.i	−0.0638942	+	0.607913i	−0.978881	+	0.204430i	$0.934466\pi$
$270$	106708.	−	22681.5i	0.0890816	−	0.0189349i
$271$	55063.0	−	169467.i	0.0455446	−	0.140172i	−0.925698	−	0.378263i	$-0.876522\pi$
$271$	55063.0	−	169467.i	0.0455446	−	0.140172i	0.971243	+	0.238091i	$0.0765216\pi$
$272$	469480.	+	99791.1i	0.384764	+	0.0817842i
$273$	−92027.7	+	159397.i	−0.0747329	+	0.129441i
$274$	632331.	+	1.09523e6i	0.508825	+	0.881310i
$275$	−106544.	−	327908.i	−0.0849563	−	0.261469i
$276$	−978.669	−	9311.42i	−0.000773327	−	0.00735772i
$277$	−239447.	−	173968.i	−0.187503	−	0.136229i	0.490074	−	0.871681i	$-0.336970\pi$
$277$	−239447.	−	173968.i	−0.187503	−	0.136229i	−0.677577	+	0.735452i	$0.736970\pi$
$278$	149019.			0.115646
$279$	−785760.	+	1.01591e6i	−0.604338	+	0.781352i
$280$	−357915.			−0.272825
$281$	928670.	+	674719.i	0.701610	+	0.509750i	0.880456	−	0.474128i	$-0.157236\pi$
$281$	928670.	+	674719.i	0.701610	+	0.509750i	−0.178846	+	0.983877i	$0.557236\pi$
$282$	−13059.9	−	124257.i	−0.00977954	−	0.0930461i
$283$	−290255.	−	893313.i	−0.215434	−	0.663037i	−0.999123	−	0.0418833i	$-0.986664\pi$
$283$	−290255.	−	893313.i	−0.215434	−	0.663037i	0.783689	−	0.621154i	$-0.213336\pi$
$284$	−556957.	−	964678.i	−0.409757	−	0.709720i
$285$	82331.5	−	142602.i	0.0600418	−	0.103996i
$286$	412163.	+	87608.0i	0.297958	+	0.0633328i
$287$	833811.	−	2.56621e6i	0.597535	−	1.83902i
$288$	240423.	−	51103.5i	0.170803	−	0.0363053i
$289$	−219019.	+	2.08383e6i	−0.154254	+	1.46763i
$290$	−531989.	+	590834.i	−0.371457	+	0.412544i
$291$	78871.6	−	35115.9i	0.0545994	−	0.0243092i
$292$	449202.	+	199998.i	0.308308	+	0.137268i
$293$	−672440.	−	746820.i	−0.457598	−	0.508214i	0.469552	−	0.882905i	$-0.344416\pi$
$293$	−672440.	−	746820.i	−0.457598	−	0.508214i	−0.927150	+	0.374691i	$0.877749\pi$
$294$	68523.6	−	49785.3i	0.0462351	−	0.0335918i
$295$	−9051.43	+	6576.25i	−0.00605567	+	0.00439970i
$296$	−651540.	−	723608.i	−0.432227	−	0.480036i
$297$	127805.	+	56902.4i	0.0840729	+	0.0374317i
$298$	−733658.	+	326646.i	−0.478578	+	0.213077i
$299$	142416.	−	158169.i	0.0921255	−	0.102316i
$300$	−5905.90	+	56190.9i	−0.00378864	+	0.0360465i
$301$	−1.95863e6	+	416320.i	−1.24605	+	0.264857i
$302$	108015.	−	332437.i	0.0681504	−	0.209745i
$303$	139941.	+	29745.3i	0.0875664	+	0.0186128i
$304$	373294.	−	646563.i	0.231668	−	0.401261i
$305$	214063.	+	370769.i	0.131763	+	0.228220i
$306$	556272.	+	1.71203e6i	0.339612	+	1.04522i
$307$	−300572.	−	2.85975e6i	−0.182013	−	1.73174i	−0.580235	−	0.814449i	$-0.697039\pi$
$307$	−300572.	−	2.85975e6i	−0.182013	−	1.73174i	0.398222	−	0.917289i	$-0.369627\pi$
$308$	−371331.	−	269788.i	−0.223041	−	0.162049i
$309$	−349994.			−0.208528
$310$	395181.	+	579753.i	0.233556	+	0.342641i
$311$	903981.			0.529979			0.264989	−	0.964251i	$-0.414632\pi$
$311$	903981.			0.529979			0.264989	+	0.964251i	$0.414632\pi$
$312$	−55863.6	−	40587.3i	−0.0324895	−	0.0236050i
$313$	−224253.	−	2.13362e6i	−0.129383	−	1.23100i	−0.845868	−	0.533393i	$-0.820917\pi$
$313$	−224253.	−	2.13362e6i	−0.129383	−	1.23100i	0.716485	−	0.697602i	$-0.245750\pi$
$314$	−283417.	−	872269.i	−0.162219	−	0.499259i
$315$	−671185.	−	1.16253e6i	−0.381123	−	0.660125i
$316$	366435.	−	634683.i	0.206433	−	0.357552i
$317$	−28937.4	−	6150.83i	−0.0161738	−	0.00343784i	0.199818	−	0.979833i	$-0.435965\pi$
$317$	−28937.4	−	6150.83i	−0.0161738	−	0.00343784i	−0.215991	+	0.976395i	$0.569298\pi$
$318$	−62710.9	+	193004.i	−0.0347757	+	0.107029i
$319$	−997288.	+	211980.i	−0.548711	+	0.116632i
$320$	14035.8	−	133542.i	0.00766235	−	0.0729024i
$321$	31728.6	−	35238.2i	0.0171865	−	0.0190876i
$322$	−211795.	+	94297.3i	−0.113835	+	0.0506827i
$323$	4.99509e6	+	2.22396e6i	2.66402	+	1.18610i
$324$	609126.	+	676503.i	0.322363	+	0.358020i
$325$	−1.03909e6	+	754945.i	−0.545690	+	0.396467i
$326$	−698059.	+	507169.i	−0.363788	+	0.264307i
$327$	31801.9	+	35319.5i	0.0164469	+	0.0182661i
$328$	924780.	+	411738.i	0.474628	+	0.211318i
$329$	−2.82632e6	+	1.25836e6i	−1.43957	+	0.640936i
$330$	25412.8	−	28223.8i	0.0128460	−	0.0142669i
$331$	99921.4	−	950689.i	0.0501290	−	0.476945i	−0.940443	−	0.339952i	$-0.889589\pi$
$331$	99921.4	−	950689.i	0.0501290	−	0.476945i	0.990572	−	0.136994i	$-0.0437440\pi$
$332$	−1.07163e6	+	227783.i	−0.533582	+	0.113416i
$333$	1.12851e6	−	3.47319e6i	0.557691	−	1.71640i
$334$	60238.7	+	12804.1i	0.0295467	+	0.00628035i
$335$	−515677.	+	893179.i	−0.251053	+	0.434837i
$336$	37608.0	+	65139.0i	0.0181732	+	0.0314770i
$337$	320178.	+	985408.i	0.153574	+	0.472652i	0.998014	−	0.0629988i	$-0.0200664\pi$
$337$	320178.	+	985408.i	0.153574	+	0.472652i	−0.844440	+	0.535651i	$0.820066\pi$
$338$	−8835.56	−	84064.7i	−0.00420671	−	0.0400241i
$339$	23030.8	+	16732.8i	0.0108845	+	0.00790806i
$340$	983412.			0.461358
$341$	−27010.1	+	899363.i	−0.0125788	+	0.418841i
$342$	2.80009e6			1.29452
$343$	622782.	+	452478.i	0.285825	+	0.207664i
$344$	−78524.5	−	747111.i	−0.0357774	−	0.340400i
$345$	−5927.98	−	18244.4i	−0.00268138	−	0.00825245i
$346$	1.16362e6	+	2.01544e6i	0.522540	+	0.905066i
$347$	−1.37086e6	+	2.37440e6i	−0.611180	+	1.05860i	0.379862	+	0.925043i	$0.375972\pi$
$347$	−1.37086e6	+	2.37440e6i	−0.611180	+	1.05860i	−0.991042	+	0.133552i	$0.957362\pi$
$348$	163428.	+	34737.7i	0.0723400	+	0.0153764i
$349$	−87469.4	+	269203.i	−0.0384408	+	0.118309i	−0.968435	−	0.249264i	$-0.919811\pi$
$349$	−87469.4	+	269203.i	−0.0384408	+	0.118309i	0.929995	+	0.367573i	$0.119811\pi$
$350$	1.36849e6	−	290881.i	0.597132	−	0.126924i
$351$	54475.8	−	518302.i	0.0236013	−	0.224551i
$352$	115223.	−	127968.i	0.0495657	−	0.0550482i
$353$	551148.	−	245387.i	0.235414	−	0.104813i	−0.285640	−	0.958337i	$-0.592206\pi$
$353$	551148.	−	245387.i	0.235414	−	0.104813i	0.521053	+	0.853524i	$0.325539\pi$
$354$	2147.93	+	956.321i	0.000910987	+	0.000405598i
$355$	−1.52716e6	−	1.69609e6i	−0.643153	−	0.714294i
$356$	−1.45493e6	+	1.05707e6i	−0.608437	+	0.442056i
$357$	−445657.	+	323789.i	−0.185068	+	0.134459i
$358$	1.21033e6	+	1.34421e6i	0.499109	+	0.554317i
$359$	−3.84792e6	−	1.71320e6i	−1.57576	−	0.701573i	−0.582006	−	0.813184i	$-0.697732\pi$
$359$	−3.84792e6	−	1.71320e6i	−1.57576	−	0.701573i	−0.993752	+	0.111612i	$0.964399\pi$
$360$	460071.	−	204837.i	0.187098	−	0.0833013i
$361$	4.03421e6	−	4.48045e6i	1.62926	−	1.80948i
$362$	−185821.	+	1.76797e6i	−0.0745287	+	0.709093i
$363$	−223679.	+	47544.5i	−0.0890963	+	0.0189380i
$364$	−528370.	+	1.62616e6i	−0.209018	+	0.643293i
$365$	985459.	+	209466.i	0.387174	+	0.0822964i
$366$	44985.5	−	77917.2i	0.0175538	−	0.0304040i
$367$	−732194.	−	1.26820e6i	−0.283766	−	0.491498i	0.688543	−	0.725196i	$-0.258251\pi$
$367$	−732194.	−	1.26820e6i	−0.283766	−	0.491498i	−0.972309	+	0.233698i	$0.924917\pi$
$368$	−26877.6	−	82720.8i	−0.0103460	−	0.0318416i
$369$	396858.	+	3.77585e6i	0.151729	+	1.44361i
$370$	−1.61403e6	−	1.17266e6i	−0.612923	−	0.445315i
$371$	5.02511e6			1.89544
$372$	63988.8	−	132839.i	0.0239743	−	0.0497700i
$373$	−4.78240e6			−1.77981			−0.889906	−	0.456144i	$-0.849230\pi$
$373$	−4.78240e6			−1.77981			−0.889906	+	0.456144i	$0.849230\pi$
$374$	1.02027e6	+	741273.i	0.377171	+	0.274031i
$375$	30544.0	+	290607.i	0.0112163	+	0.106716i
$376$	−358671.	−	1.10388e6i	−0.130836	−	0.402671i
$377$	1.89906e6	+	3.28926e6i	0.688152	+	1.19191i
$378$	−283843.	+	491630.i	−0.102176	+	0.176974i
$379$	−267180.	−	56790.9i	−0.0955445	−	0.0203086i	0.159891	−	0.987135i	$-0.448886\pi$
$379$	−267180.	−	56790.9i	−0.0955445	−	0.0203086i	−0.255436	+	0.966826i	$0.582219\pi$
$380$	472700.	−	1.45482e6i	0.167929	−	0.516833i
$381$	248019.	−	52718.0i	0.0875331	−	0.0186057i
$382$	−206794.	+	1.96751e6i	−0.0725070	+	0.689858i
$383$	2.06742e6	−	2.29611e6i	0.720166	−	0.799825i	−0.266283	−	0.963895i	$-0.585795\pi$
$383$	2.06742e6	−	2.29611e6i	0.720166	−	0.799825i	0.986449	+	0.164070i	$0.0524622\pi$
$384$	−25778.8	+	11477.5i	−0.00892144	+	0.00397208i
$385$	−859126.	−	382508.i	−0.295396	−	0.131519i
$386$	−942020.	−	1.04622e6i	−0.321804	−	0.357400i
$387$	2.27940e6	−	1.65608e6i	0.773647	−	0.562088i
$388$	648866.	−	471429.i	0.218814	−	0.158978i
$389$	1.22213e6	+	1.35732e6i	0.409492	+	0.454786i	0.912246	−	0.409643i	$-0.134347\pi$
$389$	1.22213e6	+	1.35732e6i	0.409492	+	0.454786i	−0.502754	+	0.864429i	$0.667680\pi$
$390$	−129248.	−	57545.0i	−0.0430291	−	0.0191578i
$391$	581931.	−	259092.i	0.192499	−	0.0857063i
$392$	526502.	−	584740.i	0.173055	−	0.192197i
$393$	−4159.98	+	39579.6i	−0.00135866	+	0.0129268i
$394$	−1.72771e6	+	367237.i	−0.560701	+	0.119181i
$395$	464014.	−	1.42809e6i	0.149637	−	0.460535i
$396$	631718.	+	134276.i	0.202435	+	0.0430288i
$397$	−3.01025e6	+	5.21390e6i	−0.958575	+	1.66030i	−0.232609	+	0.972570i	$0.574726\pi$
$397$	−3.01025e6	+	5.21390e6i	−0.958575	+	1.66030i	−0.725966	+	0.687731i	$0.758607\pi$
$398$	57579.4	+	99730.5i	0.0182205	+	0.0315588i
$399$	264785.	+	814924.i	0.0832647	+	0.256262i
$400$	54864.7	+	522003.i	0.0171452	+	0.163126i
$401$	1.14374e6	+	830974.i	0.355194	+	0.258063i	0.751045	−	0.660251i	$-0.229550\pi$
$401$	1.14374e6	+	830974.i	0.355194	+	0.258063i	−0.395851	+	0.918315i	$0.629550\pi$
$402$	216740.			0.0668918
$403$	3.21744e6	−	939613.i	0.986842	−	0.288195i
$404$	1.32907e6			0.405129
$405$	1.50896e6	+	1.09632e6i	0.457129	+	0.332124i
$406$	−432456.	−	4.11454e6i	−0.130205	−	1.23881i
$407$	−790604.	−	2.43323e6i	−0.236577	−	0.728110i
$408$	−103332.	−	178977.i	−0.0307316	−	0.0532287i
$409$	−405634.	+	702578.i	−0.119902	+	0.207676i	−0.919729	−	0.392555i	$-0.871591\pi$
$409$	−405634.	+	702578.i	−0.119902	+	0.207676i	0.799827	+	0.600231i	$0.204925\pi$
$410$	2.02878e6	+	431231.i	0.596040	+	0.126692i
$411$	168271.	−	517886.i	0.0491366	−	0.151227i
$412$	−3.18033e6	+	676000.i	−0.923059	+	0.196202i
$413$	6085.68	−	57901.4i	0.00175563	−	0.0167037i
$414$	218279.	−	242423.i	0.0625908	−	0.0695141i
$415$	−2.05067e6	+	913015.i	−0.584487	+	0.260230i
$416$	−586015.	−	260911.i	−0.166026	−	0.0739194i
$417$	−42934.4	−	47683.5i	−0.0120911	−	0.0134285i
$418$	1.58703e6	−	1.15304e6i	0.444267	−	0.322779i
$419$	−2.38446e6	+	1.73241e6i	−0.663522	+	0.482077i	−0.867850	−	0.496825i	$-0.834499\pi$
$419$	−2.38446e6	+	1.73241e6i	−0.663522	+	0.482077i	0.204329	+	0.978902i	$0.434499\pi$
$420$	103120.	+	114527.i	0.0285247	+	0.0316799i
$421$	−3.84299e6	−	1.71101e6i	−1.05673	−	0.470486i	−0.196558	−	0.980492i	$-0.562976\pi$
$421$	−3.84299e6	−	1.71101e6i	−1.05673	−	0.470486i	−0.860171	+	0.510006i	$0.829643\pi$
$422$	−1.62477e6	+	723395.i	−0.444131	+	0.197740i
$423$	2.91284e6	−	3.23504e6i	0.791527	−	0.879080i
$424$	−197062.	+	1.87492e6i	−0.0532338	+	0.506486i
$425$	−3.76007e6	+	799227.i	−1.00977	+	0.214634i
$426$	−148213.	+	456154.i	−0.0395698	+	0.121783i
$427$	−2.17917e6	−	463198.i	−0.578392	−	0.122941i
$428$	220251.	−	381485.i	0.0581176	−	0.100663i
$429$	−90716.9	−	157126.i	−0.0237982	−	0.0412198i
$430$	−475637.	−	1.46386e6i	−0.124052	−	0.381794i
$431$	197336.	+	1.87753e6i	0.0511698	+	0.486848i	0.989856	+	0.142075i	$0.0453775\pi$
$431$	197336.	+	1.87753e6i	0.0511698	+	0.486848i	−0.938686	+	0.344773i	$0.887956\pi$
$432$	−172301.	−	125184.i	−0.0444200	−	0.0322730i
$433$	4.48185e6			1.14878			0.574391	−	0.818581i	$-0.305239\pi$
$433$	4.48185e6			1.14878			0.574391	+	0.818581i	$0.305239\pi$
$434$	−3.61799e6	−	490471.i	−0.922025	−	0.124994i
$435$	342330.			0.0867405
$436$	357196.	+	259518.i	0.0899891	+	0.0653809i
$437$	−103572.	−	985424.i	−0.0259442	−	0.246842i
$438$	−65425.5	−	201359.i	−0.0162953	−	0.0501517i
$439$	−1.30620e6	−	2.26241e6i	−0.323481	−	0.560285i	0.657723	−	0.753260i	$-0.271520\pi$
$439$	−1.30620e6	−	2.26241e6i	−0.323481	−	0.560285i	−0.981204	+	0.192975i	$0.938186\pi$
$440$	176408.	−	305548.i	0.0434398	−	0.0752399i
$441$	2.88660e6	+	613565.i	0.706788	+	0.150233i
$442$	1.45176e6	−	4.46804e6i	0.353458	−	1.08783i
$443$	−1.10797e6	+	235507.i	−0.268237	+	0.0570156i	−0.340067	−	0.940401i	$-0.610450\pi$
$443$	−1.10797e6	+	235507.i	−0.268237	+	0.0570156i	0.0718293	+	0.997417i	$0.477116\pi$
$444$	−43824.6	+	416963.i	−0.0105502	+	0.100378i
$445$	−2.46557e6	+	2.73829e6i	−0.590224	+	0.655510i
$446$	1.38166e6	−	615154.i	0.328900	−	0.146436i
$447$	315898.	+	140647.i	0.0747787	+	0.0332936i
$448$	467550.	+	519267.i	0.110061	+	0.122235i
$449$	−1.06586e6	+	774391.i	−0.249507	+	0.181278i	−0.705508	−	0.708702i	$-0.749281\pi$
$449$	−1.06586e6	+	774391.i	−0.249507	+	0.181278i	0.456001	+	0.889979i	$0.349281\pi$
$450$	−1.59261e6	+	1.15710e6i	−0.370746	+	0.269363i
$451$	1.77978e6	+	1.97664e6i	0.412026	+	0.457601i
$452$	241595.	+	107565.i	0.0556214	+	0.0247642i
$453$	−137495.	+	61216.7i	−0.0314805	+	0.0140160i
$454$	−78774.1	+	87487.5i	−0.0179367	+	0.0199208i
$455$	−366195.	+	3.48412e6i	−0.0829248	+	0.788977i
$456$	−314440.	+	66836.3i	−0.0708151	+	0.0150522i
$457$	554869.	−	1.70771e6i	0.124280	−	0.382493i	−0.869490	−	0.493951i	$-0.835552\pi$
$457$	554869.	−	1.70771e6i	0.124280	−	0.382493i	0.993769	+	0.111458i	$0.0355521\pi$
$458$	103727.	+	22047.9i	0.0231062	+	0.00491138i
$459$	779890.	−	1.35081e6i	0.172783	−	0.299269i
$460$	−89104.8	−	154334.i	−0.0196339	−	0.0340069i
$461$	−1.65990e6	−	5.10865e6i	−0.363773	−	1.11958i	−0.950746	−	0.309971i	$-0.899681\pi$
$461$	−1.65990e6	−	5.10865e6i	−0.363773	−	1.11958i	0.586973	−	0.809606i	$-0.300319\pi$
$462$	20658.2	+	196549.i	0.00450284	+	0.0428417i
$463$	−4.08364e6	−	2.96694e6i	−0.885310	−	0.643215i	0.0493413	−	0.998782i	$-0.484288\pi$
$463$	−4.08364e6	−	2.96694e6i	−0.885310	−	0.643215i	−0.934651	+	0.355567i	$0.884288\pi$
$464$	1.55213e6			0.334684
$465$	71653.9	−	293486.i	0.0153676	−	0.0629441i
$466$	−1.01898e6			−0.217370
$467$	−892499.	−	648439.i	−0.189372	−	0.137587i	0.489060	−	0.872250i	$-0.337340\pi$
$467$	−892499.	−	648439.i	−0.189372	−	0.137587i	−0.678432	+	0.734664i	$0.737340\pi$
$468$	−251481.	−	2.39268e6i	−0.0530750	−	0.504975i
$469$	−1.65846e6	−	5.10422e6i	−0.348155	−	1.07151i
$470$	−1.18907e6	−	2.05952e6i	−0.248291	−	0.430053i
$471$	−197454.	+	342001.i	−0.0410123	+	0.0710355i
$472$	21364.9	+	4541.26i	0.00441414	+	0.000938255i
$473$	609958.	−	1.87726e6i	0.125357	−	0.385808i
$474$	−308663.	+	65608.3i	−0.0631013	+	0.0134126i
$475$	−625020.	+	5.94666e6i	−0.127104	+	1.20931i
$476$	−3.42421e6	+	3.80298e6i	−0.692697	+	0.769318i
$477$	−6.45937e6	+	2.87590e6i	−1.29985	+	0.578732i
$478$	−2.47447e6	−	1.10171e6i	−0.495351	−	0.220545i
$479$	5.71960e6	+	6.35226e6i	1.13901	+	1.26500i	0.959645	+	0.281213i	$0.0907368\pi$
$479$	5.71960e6	+	6.35226e6i	1.13901	+	1.26500i	0.179362	+	0.983783i	$0.442597\pi$
$480$	−46774.9	+	33984.0i	−0.00926638	+	0.00673242i
$481$	−7.71056e6	+	5.60205e6i	−1.51958	+	1.10404i
$482$	−4.32905e6	−	4.80790e6i	−0.848741	−	0.942622i
$483$	91194.6	+	40602.4i	0.0177869	+	0.00791925i
$484$	−1.94070e6	+	864056.i	−0.376570	+	0.167660i
$485$	1.09959e6	−	1.22122e6i	0.212264	−	0.235743i
$486$	125498.	−	1.19403e6i	0.0241016	−	0.229311i
$487$	7.07243e6	−	1.50329e6i	1.35128	−	0.287224i	0.525299	−	0.850918i	$-0.323953\pi$
$487$	7.07243e6	−	1.50329e6i	1.35128	−	0.287224i	0.825984	+	0.563694i	$0.190620\pi$
$488$	258281.	−	794907.i	0.0490956	−	0.151101i
$489$	363406.	+	77244.3i	0.0687258	+	0.0146081i
$490$	806087.	−	1.39618e6i	0.151667	−	0.262695i
$491$	2.66915e6	+	4.62310e6i	0.499654	+	0.865426i	1.00000		0.000399751i	$-0.000127245\pi$
$491$	2.66915e6	+	4.62310e6i	0.499654	+	0.865426i	−0.500346	+	0.865825i	$0.666794\pi$
$492$	−134693.	−	414541.i	−0.0250860	−	0.0772066i
$493$	1.18822e6	+	1.13052e7i	0.220181	+	2.09488i
$494$	−5.91203e6	−	4.29534e6i	−1.08998	−	0.791918i
$495$	1.32325e6			0.242733
$496$	324881.	−	1.33067e6i	0.0592952	−	0.242866i
$497$	1.18765e7			2.15674
$498$	381639.	+	277277.i	0.0689572	+	0.0501003i
$499$	−829140.	−	7.88874e6i	−0.149065	−	1.41826i	−0.771818	−	0.635843i	$-0.780652\pi$
$499$	−829140.	−	7.88874e6i	−0.149065	−	1.41826i	0.622753	−	0.782419i	$-0.286014\pi$
$500$	838843.	+	2.58169e6i	0.150057	+	0.461828i
$501$	−13258.5	−	22964.4i	−0.00235993	−	0.00408752i
$502$	−2.42917e6	+	4.20745e6i	−0.430228	+	0.745177i
$503$	−5.47771e6	−	1.16432e6i	−0.965337	−	0.205189i	−0.301832	−	0.953361i	$-0.597598\pi$
$503$	−5.47771e6	−	1.16432e6i	−0.965337	−	0.205189i	−0.663504	+	0.748172i	$0.730932\pi$
$504$	−809826.	+	2.49239e6i	−0.142009	+	0.437058i
$505$	2.66363e6	−	566172.i	0.464778	−	0.0987916i
$506$	23888.5	−	227284.i	0.00414776	−	0.0394633i
$507$	−24353.6	+	27047.4i	−0.00420769	+	0.00467311i
$508$	2.15188e6	−	958077.i	0.369963	−	0.164718i
$509$	1.09679e6	+	488321.i	0.187641	+	0.0835431i	0.498406	−	0.866943i	$-0.333919\pi$
$509$	1.09679e6	+	488321.i	0.187641	+	0.0835431i	−0.310766	+	0.950487i	$0.600585\pi$
$510$	−283334.	−	314675.i	−0.0482363	−	0.0535718i
$511$	−4.24137e6	+	3.08154e6i	−0.718546	+	0.522054i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−1.62346e6	−	1.80304e6i	−0.272363	−	0.302490i
$514$	1.12466e6	+	500729.i	0.187764	+	0.0835978i
$515$	−6.08584e6	+	2.70959e6i	−1.01112	+	0.450180i
$516$	−216439.	+	240379.i	−0.0357858	+	0.0397441i
$517$	318783.	−	3.03302e6i	0.0524528	−	0.499055i
$518$	1.01548e7	−	2.15847e6i	1.66283	−	0.353445i
$519$	309653.	−	953014.i	0.0504611	−	0.155303i
$520$	−1.28560e6	−	273262.i	−0.208496	−	0.0443171i
$521$	2.08154e6	−	3.60534e6i	0.335963	−	0.581905i	−0.647706	−	0.761890i	$-0.724272\pi$
$521$	2.08154e6	−	3.60534e6i	0.335963	−	0.581905i	0.983669	+	0.179985i	$0.0576050\pi$
$522$	2.91066e6	+	5.04141e6i	0.467536	+	0.809797i
$523$	−2.37198e6	−	7.30021e6i	−0.379190	−	1.16703i	−0.940608	−	0.339495i	$-0.889744\pi$
$523$	−2.37198e6	−	7.30021e6i	−0.379190	−	1.16703i	0.561418	−	0.827533i	$-0.310256\pi$
$524$	38645.5	+	367687.i	0.00614851	+	0.0584992i
$525$	−487356.	−	354085.i	−0.0771700	−	0.0560673i
$526$	5.93521e6			0.935345
$527$	9.94083e6	+	1.34762e6i	1.55918	+	0.211369i
$528$	−74144.6			−0.0115743
$529$	5.11372e6	+	3.71534e6i	0.794507	+	0.577243i
$530$	403762.	+	3.84154e6i	0.0624361	+	0.594039i
$531$	25314.6	+	77910.4i	0.00389615	+	0.0119911i
$532$	3.98004e6	+	6.89364e6i	0.609690	+	1.05601i
$533$	4.95423e6	−	8.58098e6i	0.755368	−	1.30834i
$534$	757427.	+	160996.i	0.114944	+	0.0244322i
$535$	278902.	−	858373.i	0.0421277	−	0.129656i
$536$	1.96947e6	−	418624.i	0.296100	−	0.0629379i
$537$	81410.4	−	774568.i	0.0121827	−	0.115911i
$538$	1.94168e6	−	2.15646e6i	0.289216	−	0.321207i
$539$	1.88871e6	−	840910.i	0.280023	−	0.124674i
$540$	−398642.	−	177487.i	−0.0588300	−	0.0261928i
$541$	−5.38540e6	−	5.98110e6i	−0.791089	−	0.878593i	0.203858	−	0.979001i	$-0.434652\pi$
$541$	−5.38540e6	−	5.98110e6i	−0.791089	−	0.878593i	−0.994946	+	0.100407i	$0.967985\pi$
$542$	−576627.	+	418944.i	−0.0843135	+	0.0612573i
$543$	619257.	−	449917.i	0.0901305	−	0.0654836i
$544$	−1.28465e6	−	1.42674e6i	−0.186117	−	0.206704i
$545$	826421.	+	367946.i	0.119182	+	0.0530632i
$546$	672572.	−	299448.i	0.0965511	−	0.0429873i
$547$	−7.57275e6	+	8.41039e6i	−1.08214	+	1.20184i	−0.103856	+	0.994592i	$0.533118\pi$
$547$	−7.57275e6	+	8.41039e6i	−1.08214	+	1.20184i	−0.978288	+	0.207250i	$0.933549\pi$
$548$	528773.	−	5.03094e6i	0.0752173	−	0.715645i
$549$	3.06624e6	−	651750.i	0.434186	−	0.0922890i
$550$	−426175.	+	1.31163e6i	−0.0600732	+	0.184886i
$551$	1.72956e7	+	3.67628e6i	2.42692	+	0.515858i
$552$	−18725.4	+	32433.4i	−0.00261567	+	0.00453048i
$553$	3.90691e6	+	6.76697e6i	0.543277	+	0.940983i
$554$	365842.	+	1.12595e6i	0.0506429	+	0.155863i
$555$	89792.5	+	854319.i	0.0123739	+	0.117730i
$556$	−482235.	−	350365.i	−0.0661564	−	0.0480655i
$557$	2.81076e6			0.383872			0.191936	−	0.981407i	$-0.438523\pi$
$557$	2.81076e6			0.383872			0.191936	+	0.981407i	$0.438523\pi$
$558$	4.93133e6	−	1.44013e6i	0.670469	−	0.195802i
$559$	−7.35308e6			−0.995267
$560$	1.15824e6	+	841509.i	0.156073	+	0.113394i
$561$	−56760.6	−	540041.i	−0.00761447	−	0.0724469i
$562$	−1.41888e6	−	4.36687e6i	−0.189498	−	0.583216i
$563$	−2.96313e6	−	5.13229e6i	−0.393985	−	0.682402i	0.598986	−	0.800759i	$-0.295570\pi$
$563$	−2.96313e6	−	5.13229e6i	−0.393985	−	0.682402i	−0.992971	+	0.118357i	$0.962237\pi$
$564$	−249883.	+	432810.i	−0.0330780	+	0.0572927i
$565$	530011.	+	112657.i	0.0698495	+	0.0148470i
$566$	−1.16102e6	+	3.57325e6i	−0.152335	+	0.468838i
$567$	−9.49376e6	+	2.01796e6i	−1.24017	+	0.263606i
$568$	−465743.	+	4.43125e6i	−0.0605725	+	0.576309i
$569$	−7.50663e6	+	8.33695e6i	−0.971995	+	1.07951i	0.0248144	+	0.999692i	$0.492101\pi$
$569$	−7.50663e6	+	8.33695e6i	−0.971995	+	1.07951i	−0.996809	+	0.0798178i	$0.974566\pi$
$570$	−601709.	+	267898.i	−0.0775710	+	0.0345368i
$571$	7.78136e6	+	3.46449e6i	0.998770	+	0.444681i	0.839972	−	0.542630i	$-0.182572\pi$
$571$	7.78136e6	+	3.46449e6i	0.998770	+	0.444681i	0.158798	+	0.987311i	$0.449238\pi$
$572$	−1.12781e6	−	1.25256e6i	−0.144127	−	0.160069i
$573$	689151.	−	500697.i	0.0876855	−	0.0637072i
$574$	−8.73179e6	+	6.34401e6i	−1.10617	+	0.803682i
$575$	466120.	+	517679.i	0.0587933	+	0.0652966i
$576$	−898178.	−	399894.i	−0.112799	−	0.0502214i
$577$	2.42951e6	−	1.08169e6i	0.303794	−	0.135258i	−0.249178	−	0.968458i	$-0.580160\pi$
$577$	2.42951e6	−	1.08169e6i	0.303794	−	0.135258i	0.552972	+	0.833200i	$0.313494\pi$
$578$	5.60813e6	−	6.22846e6i	0.698230	−	0.775463i
$579$	−63363.2	+	602860.i	−0.00785490	+	0.0747344i
$580$	3.11069e6	−	661197.i	0.383960	−	0.0816133i
$581$	3.60962e6	−	1.11093e7i	0.443631	−	1.36535i
$582$	−337796.	−	71800.8i	−0.0413378	−	0.00878662i
$583$	−2.47676e6	+	4.28988e6i	−0.301796	+	0.522726i
$584$	−983426.	−	1.70334e6i	−0.119319	−	0.206666i
$585$	−1.52326e6	−	4.68813e6i	−0.184029	−	0.566382i
$586$	420181.	+	3.99776e6i	0.0505467	+	0.480920i
$587$	−1.19782e7	−	8.70266e6i	−1.43481	−	1.04245i	−0.989095	−	0.147281i	$-0.952948\pi$
$587$	−1.19782e7	−	8.70266e6i	−1.43481	−	1.04245i	−0.445719	−	0.895173i	$-0.647052\pi$
$588$	−338799.			−0.0404110
$589$	6.77191e6	−	1.40583e7i	0.804310	−	1.66972i
$590$	44752.8			0.00529285
$591$	615288.	+	447033.i	0.0724619	+	0.0526466i
$592$	407122.	+	3.87351e6i	0.0477442	+	0.454255i
$593$	−1.57799e6	−	4.85656e6i	−0.184276	−	0.567142i	0.815660	−	0.578532i	$-0.196374\pi$
$593$	−1.57799e6	−	4.85656e6i	−0.184276	−	0.567142i	−0.999935	+	0.0113903i	$0.996374\pi$
$594$	−279800.	−	484627.i	−0.0325373	−	0.0563562i
$595$	−5.24255e6	+	9.08037e6i	−0.607086	+	1.05150i
$596$	3.14216e6	+	667886.i	0.362337	+	0.0770170i
$597$	15322.6	−	47158.1i	0.00175953	−	0.00541528i
$598$	−832743.	+	177005.i	−0.0952266	+	0.0202410i
$599$	−163003.	+	1.55087e6i	−0.0185622	+	0.176607i	−0.999875	−	0.0158119i	$-0.994967\pi$
$599$	−163003.	+	1.55087e6i	−0.0185622	+	0.176607i	0.981313	+	0.192419i	$0.0616334\pi$
$600$	151225.	−	167952.i	0.0171492	−	0.0190461i
$601$	5.55839e6	−	2.47475e6i	0.627715	−	0.279477i	−0.0681214	−	0.997677i	$-0.521701\pi$
$601$	5.55839e6	−	2.47475e6i	0.627715	−	0.279477i	0.695836	+	0.718200i	$0.255034\pi$
$602$	7.31709e6	+	3.25778e6i	0.822900	+	0.366379i
$603$	5.05299e6	+	5.61191e6i	0.565920	+	0.628518i
$604$	−1.13115e6	+	821830.i	−0.126162	+	0.0916621i
$605$	−3.52135e6	+	2.55841e6i	−0.391129	+	0.284172i
$606$	−382922.	−	425278.i	−0.0423574	−	0.0470427i
$607$	−7.11325e6	−	3.16702e6i	−0.783603	−	0.348883i	−0.0243716	−	0.999703i	$-0.507758\pi$
$607$	−7.11325e6	−	3.16702e6i	−0.783603	−	0.348883i	−0.759232	+	0.650820i	$0.774425\pi$
$608$	−2.72817e6	+	1.21466e6i	−0.299303	+	0.133258i
$609$	−1.19199e6	+	1.32383e6i	−0.130235	+	0.144641i
$610$	179006.	−	1.70313e6i	0.0194779	−	0.185320i
$611$	−1.11126e7	+	2.36206e6i	−1.20424	+	0.255969i
$612$	2.22509e6	−	6.84812e6i	0.240142	−	0.739082i
$613$	−8.03298e6	−	1.70746e6i	−0.863427	−	0.183527i	−0.245148	−	0.969486i	$-0.578837\pi$
$613$	−8.03298e6	−	1.70746e6i	−0.863427	−	0.183527i	−0.618279	+	0.785959i	$0.712170\pi$
$614$	−5.75100e6	+	9.96103e6i	−0.615634	+	1.06631i
$615$	−446533.	−	773418.i	−0.0476065	−	0.0824568i
$616$	567344.	+	1.74611e6i	0.0602413	+	0.185404i
$617$	1.51524e6	+	1.44166e7i	0.160240	+	1.52458i	0.718860	+	0.695155i	$0.244664\pi$
$617$	1.51524e6	+	1.44166e7i	0.160240	+	1.52458i	−0.558621	+	0.829423i	$0.688669\pi$
$618$	1.13261e6	+	822886.i	0.119291	+	0.0866700i
$619$	3.05889e6			0.320876			0.160438	−	0.987046i	$-0.448709\pi$
$619$	3.05889e6			0.320876			0.160438	+	0.987046i	$0.448709\pi$
$620$	84248.3	−	2.80525e6i	0.00880201	−	0.293084i
$621$	−282656.			−0.0294124
$622$	−2.92534e6	−	2.12539e6i	−0.303180	−	0.220273i
$623$	−2.00426e6	−	1.90693e7i	−0.206888	−	1.96841i
$624$	85352.0	+	262686.i	0.00877510	+	0.0270070i
$625$	−422665.	−	732076.i	−0.0432808	−	0.0749646i
$626$	−4.29075e6	+	7.43179e6i	−0.437620	+	0.757980i
$627$	−826199.	−	175614.i	−0.0839297	−	0.0178398i
$628$	−1.13367e6	+	3.48907e6i	−0.114706	+	0.353030i
$629$	−2.79015e7	+	5.93064e6i	−2.81190	+	0.597689i
$630$	−561263.	+	5.34006e6i	−0.0563398	+	0.536037i
$631$	9.74099e6	−	1.08185e7i	0.973934	−	1.08166i	−0.0227046	−	0.999742i	$-0.507228\pi$
$631$	9.74099e6	−	1.08185e7i	0.973934	−	1.08166i	0.996639	−	0.0819213i	$-0.0261056\pi$
$632$	−2.67804e6	+	1.19234e6i	−0.266701	+	0.118743i
$633$	699593.	+	311479.i	0.0693963	+	0.0308972i
$634$	79181.8	+	87940.3i	0.00782352	+	0.00868890i
$635$	3.90452e6	−	2.83680e6i	0.384267	−	0.279186i
$636$	656718.	−	477133.i	0.0643778	−	0.0467732i
$637$	−5.15346e6	−	5.72349e6i	−0.503211	−	0.558872i
$638$	3.72569e6	+	1.65878e6i	0.362372	+	0.161338i
$639$	−1.52663e7	+	6.79700e6i	−1.47905	+	0.658514i
$640$	−359396.	+	399150.i	−0.0346835	+	0.0385200i
$641$	628312.	−	5.97799e6i	0.0603991	−	0.574659i	−0.921912	−	0.387400i	$-0.873373\pi$
$641$	628312.	−	5.97799e6i	0.0603991	−	0.574659i	0.982311	−	0.187259i	$-0.0599602\pi$
$642$	−185526.	+	39434.7i	−0.0177651	+	0.00377608i
$643$	991650.	−	3.05198e6i	0.0945869	−	0.291108i	−0.892559	−	0.450931i	$-0.851092\pi$
$643$	991650.	−	3.05198e6i	0.0945869	−	0.291108i	0.987146	+	0.159822i	$0.0510921\pi$
$644$	907090.	+	192808.i	0.0861858	+	0.0183193i
$645$	−331372.	+	573954.i	−0.0313630	+	0.0543223i
$646$	−1.09356e7	−	1.89410e7i	−1.03101	−	1.78576i
$647$	−562816.	−	1.73217e6i	−0.0528574	−	0.162678i	0.921143	−	0.389224i	$-0.127257\pi$
$647$	−562816.	−	1.73217e6i	−0.0528574	−	0.162678i	−0.974001	+	0.226546i	$0.927257\pi$
$648$	−380619.	−	3.62135e6i	−0.0356085	−	0.338792i
$649$	46430.3	+	33733.6i	0.00432703	+	0.00314377i
$650$	5.13756e6			0.476951
$651$	885450.	+	1.29901e6i	0.0818863	+	0.120132i
$652$	3.45139e6			0.317962
$653$	−1.04407e7	−	7.58563e6i	−0.958181	−	0.696159i	−0.00545347	−	0.999985i	$-0.501736\pi$
$653$	−1.04407e7	−	7.58563e6i	−0.958181	−	0.696159i	−0.952728	+	0.303826i	$0.901736\pi$
$654$	−19871.8	−	189067.i	−0.00181674	−	0.0172851i
$655$	234082.	+	720432.i	0.0213189	+	0.0656130i
$656$	−2.02459e6	−	3.50670e6i	−0.183687	−	0.318155i
$657$	3.68836e6	−	6.38843e6i	0.333365	−	0.577405i
$658$	1.21047e7	+	2.57294e6i	1.08991	+	0.231668i
$659$	−1.53844e6	+	4.73484e6i	−0.137996	+	0.424709i	−0.996044	−	0.0888610i	$-0.971677\pi$
$659$	−1.53844e6	+	4.73484e6i	−0.137996	+	0.424709i	0.858048	+	0.513570i	$0.171677\pi$
$660$	−148596.	+	31585.0i	−0.0132784	+	0.00282242i
$661$	−1.11665e6	+	1.06242e7i	−0.0994059	+	0.945784i	0.825195	+	0.564848i	$0.191065\pi$
$661$	−1.11665e6	+	1.06242e7i	−0.0994059	+	0.945784i	−0.924601	+	0.380937i	$0.875602\pi$
$662$	−2.55856e6	+	2.84157e6i	−0.226908	+	0.252007i
$663$	−1.84797e6	+	822768.i	−0.163272	+	0.0726932i
$664$	4.00343e6	+	1.78244e6i	0.352381	+	0.156890i
$665$	1.09132e7	+	1.21203e7i	0.956968	+	1.06282i
$666$	−1.18179e7	+	8.58620e6i	−1.03241	+	0.750093i
$667$	1.66654e6	−	1.21081e6i	0.145044	−	0.105381i
$668$	−164832.	−	183065.i	−0.0142923	−	0.0158732i
$669$	−594914.	−	264873.i	−0.0513912	−	0.0228808i
$670$	3.76876e6	−	1.67796e6i	0.324348	−	0.144409i
$671$	1.46949e6	−	1.63204e6i	0.125997	−	0.139934i
$672$	31448.9	−	299216.i	0.00268647	−	0.0255600i
$673$	1.41839e7	−	3.01487e6i	1.20714	−	0.256585i	0.439958	−	0.898018i	$-0.354993\pi$
$673$	1.41839e7	−	3.01487e6i	1.20714	−	0.256585i	0.767179	+	0.641433i	$0.221660\pi$
$674$	1.28071e6	−	3.94163e6i	0.108593	−	0.334215i
$675$	1.66845e6	+	354640.i	0.140946	+	0.0299591i
$676$	−169056.	+	292813.i	−0.0142286	+	0.0246447i
$677$	4.45938e6	+	7.72388e6i	0.373941	+	0.647685i	0.990168	−	0.139884i	$-0.0446729\pi$
$677$	4.45938e6	+	7.72388e6i	0.373941	+	0.647685i	−0.616227	+	0.787569i	$0.711340\pi$
$678$	−35187.9	−	108297.i	−0.00293981	−	0.00904780i
$679$	893860.	+	8.50451e6i	0.0744038	+	0.707904i
$680$	−3.18239e6	−	2.31214e6i	−0.263925	−	0.191753i
$681$	50690.4			0.00418849
$682$	2.20194e6	−	2.84690e6i	0.181277	−	0.234375i
$683$	−2.26396e6			−0.185702			−0.0928512	−	0.995680i	$-0.529598\pi$
$683$	−2.26396e6			−0.185702			−0.0928512	+	0.995680i	$0.529598\pi$
$684$	−9.06129e6	−	6.58342e6i	−0.740543	−	0.538036i
$685$	−1.08341e6	−	1.03079e7i	−0.0882196	−	0.839354i
$686$	−951527.	−	2.92850e6i	−0.0771988	−	0.237594i
$687$	−22830.3	−	39543.2i	−0.00184552	−	0.00319654i
$688$	−1.50245e6	+	2.60232e6i	−0.121012	+	0.209600i
$689$	1.80497e7	+	3.83659e6i	1.44851	+	0.307891i
$690$	−23711.9	+	72977.7i	−0.00189602	+	0.00583536i
$691$	2.13506e7	−	4.53821e6i	1.70104	−	0.361567i	0.747834	−	0.663886i	$-0.231094\pi$
$691$	2.13506e7	−	4.53821e6i	1.70104	−	0.361567i	0.953207	+	0.302319i	$0.0977607\pi$
$692$	973048.	−	9.25793e6i	0.0772448	−	0.734935i
$693$	−4.60752e6	+	5.11717e6i	−0.364447	+	0.404759i
$694$	1.00187e7	−	4.46063e6i	0.789613	−	0.351559i
$695$	−1.11572e6	−	496749.i	−0.0876178	−	0.0390100i
$696$	−447191.	−	496656.i	−0.0349921	−	0.0388627i
$697$	2.39916e7	−	1.74309e7i	1.87058	−	1.35906i
$698$	915991.	−	665506.i	0.0711627	−	0.0517028i
$699$	293581.	+	326055.i	0.0227267	+	0.0252405i
$700$	−5.11241e6	−	2.27619e6i	−0.394349	−	0.175576i
$701$	−8.33836e6	+	3.71248e6i	−0.640893	+	0.285344i	−0.701340	−	0.712827i	$-0.747414\pi$
$701$	−8.33836e6	+	3.71248e6i	−0.640893	+	0.285344i	0.0604462	+	0.998171i	$0.480748\pi$
$702$	−1.39489e6	+	1.54918e6i	−0.106831	+	0.118648i
$703$	−4.63794e6	+	4.41271e7i	−0.353946	+	3.36757i
$704$	−673738.	+	143207.i	−0.0512341	+	0.0108902i
$705$	−316426.	+	973858.i	−0.0239772	+	0.0737943i
$706$	−2.36049e6	−	501738.i	−0.178234	−	0.0378848i
$707$	−7.08524e6	+	1.22720e7i	−0.533096	+	0.923350i
$708$	−4702.41	−	8144.81i	−0.000352563	−	0.000610657i
$709$	−3.56233e6	−	1.09637e7i	−0.266145	−	0.819111i	−0.991427	−	0.130659i	$-0.958291\pi$
$709$	−3.56233e6	−	1.09637e7i	−0.266145	−	0.819111i	0.725282	−	0.688452i	$-0.241709\pi$
$710$	954265.	+	9.07923e6i	0.0710433	+	0.675932i
$711$	−8.89480e6	−	6.46245e6i	−0.659876	−	0.479428i
$712$	7.19355e6			0.531794
$713$	−689224.	−	1.68219e6i	−0.0507734	−	0.123923i
$714$	2.20345e6			0.161755
$715$	−2.79386e6	−	2.02986e6i	−0.204381	−	0.148491i
$716$	−756287.	−	7.19559e6i	−0.0551320	−	0.524546i
$717$	360403.	+	1.10921e6i	0.0261812	+	0.0805776i
$718$	8.42414e6	+	1.45910e7i	0.609838	+	1.05627i
$719$	−418919.	+	725590.i	−0.0302210	+	0.0523442i	−0.880740	−	0.473599i	$-0.842954\pi$
$719$	−418919.	+	725590.i	−0.0302210	+	0.0523442i	0.850519	+	0.525944i	$0.176288\pi$
$720$	−1.97042e6	−	418826.i	−0.141654	−	0.0301094i
$721$	1.07124e7	−	3.29695e7i	0.767449	−	2.36197i
$722$	−2.35891e7	+	5.01403e6i	−1.68410	+	0.357968i
$723$	−291185.	+	2.77044e6i	−0.0207169	+	0.197108i
$724$	4.75808e6	−	5.28438e6i	0.337353	−	0.374669i
$725$	−1.13563e7	+	5.05617e6i	−0.802404	+	0.357253i
$726$	835626.	+	372045.i	0.0588397	+	0.0261971i
$727$	1.36083e7	+	1.51135e7i	0.954921	+	1.06055i	0.998108	+	0.0614800i	$0.0195820\pi$
$727$	1.36083e7	+	1.51135e7i	0.954921	+	1.06055i	−0.0431876	+	0.999067i	$0.513751\pi$
$728$	5.53316e6	−	4.02008e6i	0.386941	−	0.281129i
$729$	1.07669e7	−	7.82260e6i	0.750363	−	0.545170i
$730$	−2.69653e6	−	2.99480e6i	−0.187283	−	0.207999i
$731$	−2.01045e7	−	8.95111e6i	−1.39155	−	0.619560i
$732$	−328771.	+	146378.i	−0.0226786	+	0.0100971i
$733$	5.12895e6	−	5.69627e6i	0.352589	−	0.391589i	−0.540594	−	0.841284i	$-0.681800\pi$
$733$	5.12895e6	−	5.69627e6i	0.352589	−	0.391589i	0.893183	+	0.449694i	$0.148467\pi$
$734$	−612281.	+	5.82546e6i	−0.0419479	+	0.399108i
$735$	−678999.	+	144326.i	−0.0463608	+	0.00985430i
$736$	−107510.	+	330883.i	−0.00731571	+	0.0225154i
$737$	5.17483e6	+	1.09994e6i	0.350936	+	0.0745937i
$738$	7.59329e6	−	1.31520e7i	0.513203	−	0.888894i
$739$	1.43715e7	+	2.48921e7i	0.968033	+	1.67668i	0.701236	+	0.712930i	$0.252632\pi$
$739$	1.43715e7	+	2.48921e7i	0.968033	+	1.67668i	0.266797	+	0.963753i	$0.414035\pi$
$740$	2.46601e6	+	7.58960e6i	0.165545	+	0.509495i
$741$	328902.	+	3.12929e6i	0.0220050	+	0.209363i
$742$	−1.62616e7	−	1.18147e7i	−1.08431	−	0.787797i
$743$	4.24723e6			0.282250			0.141125	−	0.989992i	$-0.454928\pi$
$743$	4.24723e6			0.282250			0.141125	+	0.989992i	$0.454928\pi$
$744$	−519395.	+	279429.i	−0.0344006	+	0.0185071i
$745$	6.58182e6			0.434466
$746$	1.54762e7	+	1.12441e7i	1.01816	+	0.739738i
$747$	1.71802e6	+	1.63459e7i	0.112649	+	1.07178i
$748$	−1.55884e6	−	4.79762e6i	−0.101870	−	0.313525i
$749$	2.34830e6	+	4.06738e6i	0.152950	+	0.264917i
$750$	584415.	−	1.01224e6i	0.0379375	−	0.0657096i
$751$	1.76654e7	+	3.75489e6i	1.14294	+	0.242939i	0.740207	−	0.672379i	$-0.234727\pi$
$751$	1.76654e7	+	3.75489e6i	1.14294	+	0.242939i	0.402732	+	0.915318i	$0.368061\pi$
$752$	−1.43468e6	+	4.41550e6i	−0.0925148	+	0.284731i
$753$	2.04619e6	−	434930.i	0.131510	−	0.0279533i
$754$	1.58804e6	−	1.51092e7i	0.101726	−	0.967863i
$755$	−1.91689e6	+	2.12892e6i	−0.122385	+	0.135923i
$756$	2.07443e6	−	923594.i	0.132006	−	0.0587728i
$757$	2.20389e7	+	9.81236e6i	1.39782	+	0.622349i	0.960835	−	0.277121i	$-0.0893803\pi$
$757$	2.20389e7	+	9.81236e6i	1.39782	+	0.622349i	0.436983	+	0.899470i	$0.356047\pi$
$758$	731089.	+	811957.i	0.0462165	+	0.0513287i
$759$	−79609.7	+	57839.8i	−0.00501604	+	0.00364437i
$760$	−4.95018e6	+	3.59651e6i	−0.310876	+	0.225864i
$761$	−1.03456e6	−	1.14899e6i	−0.0647579	−	0.0719209i	0.709895	−	0.704307i	$-0.248742\pi$
$761$	−1.03456e6	−	1.14899e6i	−0.0647579	−	0.0719209i	−0.774653	+	0.632386i	$0.782076\pi$
$762$	−926553.	−	412528.i	−0.0578073	−	0.0257375i
$763$	−4.30047e6	+	1.91469e6i	−0.267427	+	0.119066i
$764$	5.29510e6	−	5.88081e6i	0.328202	−	0.364505i
$765$	1.54213e6	−	1.46724e7i	0.0952727	−	0.906459i
$766$	−1.20888e7	+	2.56955e6i	−0.744408	+	0.158229i
$767$	66066.0	−	203330.i	0.00405499	−	0.0124800i
$768$	110407.	+	23467.8i	0.00675452	+	0.00143572i
$769$	−1.26791e7	+	2.19609e7i	−0.773167	+	1.33916i	0.162652	+	0.986683i	$0.447995\pi$
$769$	−1.26791e7	+	2.19609e7i	−0.773167	+	1.33916i	−0.935819	+	0.352481i	$0.885338\pi$
$770$	1.88086e6	+	3.25775e6i	0.114322	+	0.198012i
$771$	−163804.	−	504137.i	−0.00992404	−	0.0305431i
$772$	588632.	+	5.60046e6i	0.0355468	+	0.338205i
$773$	5454.08	+	3962.62i	0.000328302	+	0.000238525i	0.587949	−	0.808898i	$-0.299935\pi$
$773$	5454.08	+	3962.62i	0.000328302	+	0.000238525i	−0.587621	+	0.809136i	$0.699935\pi$
$774$	−1.12700e7			−0.676193
$775$	1.95772e6	+	1.07943e7i	0.117084	+	0.645566i
$776$	−3.20817e6			−0.191251
$777$	−3.61641e6	−	2.62748e6i	−0.214895	−	0.156130i
$778$	−763664.	−	7.26578e6i	−0.0452328	−	0.430361i
$779$	−1.42545e7	−	4.38707e7i	−0.841603	−	2.59019i
$780$	282959.	+	490100.i	0.0166528	+	0.0288435i
$781$	−5.85368e6	+	1.01389e7i	−0.343401	+	0.594787i
$782$	−2.49233e6	−	529761.i	−0.145743	−	0.0309787i
$783$	1.55870e6	−	4.79718e6i	0.0908569	−	0.279629i
$784$	−3.07860e6	+	654377.i	−0.178881	+	0.0380223i
$785$	−785708.	+	7.47551e6i	−0.0455079	+	0.432979i
$786$	106519.	−	118302.i	0.00614995	−	0.00683021i
$787$	1.90590e7	−	8.48561e6i	1.09689	−	0.488367i	0.223162	−	0.974781i	$-0.428362\pi$
$787$	1.90590e7	−	8.48561e6i	1.09689	−	0.488367i	0.873728	+	0.486415i	$0.161696\pi$
$788$	6.45443e6	+	2.87370e6i	0.370290	+	0.164864i
$789$	−1.71002e6	−	1.89916e6i	−0.0977929	−	0.108610i
$790$	−4.85922e6	+	3.53043e6i	−0.277012	+	0.201261i
$791$	−2.28114e6	+	1.65735e6i	−0.129632	+	0.0941830i
$792$	−1.72858e6	−	1.91978e6i	−0.0979212	−	0.108753i
$793$	−7.47375e6	−	3.32753e6i	−0.422042	−	0.187905i
$794$	2.20000e7	−	9.79503e6i	1.23843	−	0.551384i
$795$	1.11290e6	−	1.23600e6i	0.0624506	−	0.0693584i
$796$	48149.5	−	458112.i	0.00269345	−	0.0256265i
$797$	−1.67416e7	+	3.55853e6i	−0.933577	+	0.198438i	−0.649498	−	0.760363i	$-0.725021\pi$
$797$	−1.67416e7	+	3.55853e6i	−0.933577	+	0.198438i	−0.284079	+	0.958801i	$0.591688\pi$
$798$	1.05914e6	−	3.25970e6i	0.0588771	−	0.181205i
$799$	−3.32591e7	−	7.06944e6i	−1.84308	−	0.391758i
$800$	1.04976e6	−	1.81823e6i	0.0579914	−	0.100444i
$801$	1.34898e7	+	2.33650e7i	0.742889	+	1.28672i
$802$	−1.74747e6	−	5.37817e6i	−0.0959345	−	0.295256i
$803$	−540198.	−	5.13964e6i	−0.0295641	−	0.281283i
$804$	−701384.	−	509585.i	−0.0382662	−	0.0278021i
$805$	1.90006e6			0.103342
$806$	−1.26210e7	−	4.52400e6i	−0.684316	−	0.245293i
$807$	−1.24946e6			−0.0675363
$808$	−4.30095e6	−	3.12482e6i	−0.231759	−	0.168383i
$809$	615088.	+	5.85217e6i	0.0330420	+	0.314373i	0.998542	+	0.0539720i	$0.0171882\pi$
$809$	615088.	+	5.85217e6i	0.0330420	+	0.314373i	−0.965500	+	0.260401i	$0.916145\pi$
$810$	−2.30548e6	−	7.09554e6i	−0.123466	−	0.379991i
$811$	4.94351e6	+	8.56241e6i	0.263927	+	0.457134i	0.967282	−	0.253704i	$-0.0816490\pi$
$811$	4.94351e6	+	8.56241e6i	0.263927	+	0.457134i	−0.703355	+	0.710839i	$0.748316\pi$
$812$	−8.27441e6	+	1.43317e7i	−0.440399	+	0.762794i
$813$	300189.	+	63807.2i	0.0159283	+	0.00338566i
$814$	−3.16242e6	+	9.73292e6i	−0.167285	+	0.514852i
$815$	6.91706e6	−	1.47027e6i	0.364777	−	0.0775357i
$816$	−86409.3	+	822129.i	−0.00454292	+	0.0432230i
$817$	−2.29056e7	+	2.54393e7i	−1.20057	+	1.33337i
$818$	2.96452e6	−	1.31989e6i	0.154907	−	0.0689690i
$819$	2.34335e7	+	1.04333e7i	1.22075	+	0.543515i
$820$	−5.55139e6	−	6.16544e6i	−0.288315	−	0.320206i
$821$	−2.48368e6	+	1.80450e6i	−0.128599	+	0.0934326i	−0.650225	−	0.759741i	$-0.725325\pi$
$821$	−2.48368e6	+	1.80450e6i	−0.128599	+	0.0934326i	0.521626	+	0.853174i	$0.325325\pi$
$822$	−1.76216e6	+	1.28028e6i	−0.0909632	+	0.0660886i
$823$	−8.62825e6	−	9.58264e6i	−0.444041	−	0.493157i	0.479024	−	0.877802i	$-0.340991\pi$
$823$	−8.62825e6	−	9.58264e6i	−0.444041	−	0.493157i	−0.923065	+	0.384645i	$0.874324\pi$
$824$	1.18811e7	+	5.28983e6i	0.609593	+	0.271408i
$825$	542486.	−	241530.i	0.0277494	−	0.0123548i
$826$	−155828.	+	173065.i	−0.00794686	+	0.00882588i
$827$	1.09050e6	−	1.03755e7i	0.0554452	−	0.527526i	−0.931185	−	0.364548i	$-0.881223\pi$
$827$	1.09050e6	−	1.03755e7i	0.0554452	−	0.527526i	0.986630	−	0.162978i	$-0.0521098\pi$
$828$	−1.27634e6	+	271294.i	−0.0646977	+	0.0137519i
$829$	1.07984e7	−	3.32339e7i	0.545722	−	1.67956i	−0.173545	−	0.984826i	$-0.555522\pi$
$829$	1.07984e7	−	3.32339e7i	0.545722	−	1.67956i	0.719267	−	0.694734i	$-0.244478\pi$
$830$	8.78272e6	+	1.86683e6i	0.442521	+	0.0940607i
$831$	254879.	−	441463.i	0.0128036	−	0.0221764i
$832$	1.28295e6	+	2.22213e6i	0.0642540	+	0.111291i
$833$	−7.12303e6	−	2.19224e7i	−0.355674	−	1.09465i
$834$	26828.0	+	255252.i	0.00133559	+	0.0127073i
$835$	−408330.	−	296669.i	−0.0202673	−	0.0147250i
$836$	−7.84670e6			−0.388304
$837$	−3.78646e6	−	2.34041e6i	−0.186818	−	0.115472i
$838$	1.17894e7			0.579939
$839$	−9.59477e6	−	6.97101e6i	−0.470576	−	0.341893i	0.327090	−	0.944993i	$-0.393932\pi$
$839$	−9.59477e6	−	6.97101e6i	−0.470576	−	0.341893i	−0.797666	+	0.603100i	$0.793932\pi$
$840$	−64435.8	−	613066.i	−0.00315086	−	0.0299784i
$841$	5.02126e6	+	1.54539e7i	0.244807	+	0.753437i
$842$	8.41335e6	+	1.45723e7i	0.408967	+	0.708352i
$843$	−988523.	+	1.71217e6i	−0.0479091	+	0.0829810i
$844$	6.95868e6	+	1.47911e6i	0.336257	+	0.0714735i
$845$	−214074.	+	658853.i	−0.0103139	+	0.0317429i
$846$	−1.70322e7	+	3.62030e6i	−0.818171	+	0.173908i
$847$	2.36756e6	−	2.25258e7i	0.113395	−	1.07888i
$848$	5.04590e6	−	5.60404e6i	0.240962	−	0.267616i
$849$	1.47789e6	−	657997.i	0.0703674	−	0.0313296i
$850$	1.40469e7	+	6.25410e6i	0.666859	+	0.296905i
$851$	3.45883e6	+	3.84142e6i	0.163721	+	0.181831i
$852$	1.55211e6	−	1.12767e6i	0.0732527	−	0.0532212i
$853$	−1.36296e7	+	9.90246e6i	−0.641371	+	0.465983i	−0.860321	−	0.509753i	$-0.829737\pi$
$853$	−1.36296e7	+	9.90246e6i	−0.641371	+	0.465983i	0.218950	+	0.975736i	$0.429737\pi$
$854$	5.96291e6	+	6.62248e6i	0.279778	+	0.310725i
$855$	−2.09645e7	−	9.33402e6i	−0.980777	−	0.436670i
$856$	−1.60967e6	+	716672.i	−0.0750849	+	0.0334300i
$857$	−5.94409e6	+	6.60158e6i	−0.276461	+	0.307041i	−0.865345	−	0.501177i	$-0.832901\pi$
$857$	−5.94409e6	+	6.60158e6i	−0.276461	+	0.307041i	0.588884	+	0.808217i	$0.299567\pi$
$858$	−75860.0	+	721759.i	−0.00351799	+	0.0334714i
$859$	2.29768e7	−	4.88387e6i	1.06244	−	0.225830i	0.356644	−	0.934240i	$-0.383921\pi$
$859$	2.29768e7	−	4.88387e6i	1.06244	−	0.225830i	0.705801	+	0.708411i	$0.250587\pi$
$860$	−1.90255e6	+	5.85544e6i	−0.0877182	+	0.269969i
$861$	4.54572e6	+	966223.i	0.208975	+	0.0444191i
$862$	3.77574e6	−	6.53978e6i	0.173075	−	0.299775i
$863$	−1.27157e7	−	2.20242e7i	−0.581181	−	1.00664i	−0.995340	−	0.0964307i	$-0.969257\pi$
$863$	−1.27157e7	−	2.20242e7i	−0.581181	−	1.00664i	0.414158	−	0.910205i	$-0.364076\pi$
$864$	263253.	+	810208.i	0.0119974	+	0.0369243i
$865$	−1.99369e6	−	1.89687e7i	−0.0905976	−	0.861979i
$866$	−1.45036e7	−	1.05375e7i	−0.657174	−	0.477465i
$867$	−3.60878e6			−0.163047
$868$	1.05549e7	+	1.00936e7i	0.475504	+	0.454723i
$869$	−7.70253e6			−0.346006
$870$	−1.10780e6	−	804866.i	−0.0496209	−	0.0360517i
$871$	−2.06005e6	−	1.96001e7i	−0.0920095	−	0.875412i
$872$	−545746.	−	1.67963e6i	−0.0243052	−	0.0748038i
$873$	−6.01616e6	−	1.04203e7i	−0.267168	−	0.462748i
$874$	−1.98170e6	+	3.43241e6i	−0.0877527	+	0.151992i
$875$	−2.83100e7	−	6.01748e6i	−1.25003	−	0.265702i
$876$	−261702.	+	805436.i	−0.0115225	+	0.0354626i
$877$	−1.16232e7	+	2.47059e6i	−0.510301	+	0.108468i	−0.455864	−	0.890049i	$-0.650670\pi$
$877$	−1.16232e7	+	2.47059e6i	−0.510301	+	0.108468i	−0.0544369	+	0.998517i	$0.517336\pi$
$878$	−1.09228e6	+	1.03924e7i	−0.0478187	+	0.454965i
$879$	1.15815e6	−	1.28626e6i	0.0505585	−	0.0561509i
$880$	−1.28926e6	+	574014.i	−0.0561220	+	0.0249871i
$881$	−2.80638e7	−	1.24948e7i	−1.21817	−	0.542364i	−0.305942	−	0.952050i	$-0.598971\pi$
$881$	−2.80638e7	−	1.24948e7i	−1.21817	−	0.542364i	−0.912226	+	0.409687i	$0.865638\pi$
$882$	−7.89864e6	−	8.77233e6i	−0.341886	−	0.379703i
$883$	−1.29954e7	+	9.44172e6i	−0.560904	+	0.407520i	−0.831790	−	0.555091i	$-0.812683\pi$
$883$	−1.29954e7	+	9.44172e6i	−0.560904	+	0.407520i	0.270886	+	0.962611i	$0.412683\pi$
$884$	−1.52030e7	+	1.10456e7i	−0.654332	+	0.475400i
$885$	−12893.9	−	14320.1i	−0.000553383	−	0.000614594i
$886$	4.13918e6	+	1.84288e6i	0.177146	+	0.0788703i
$887$	2.87646e7	−	1.28068e7i	1.22758	−	0.546554i	0.312535	−	0.949906i	$-0.398822\pi$
$887$	2.87646e7	−	1.28068e7i	1.22758	−	0.546554i	0.915045	+	0.403352i	$0.132155\pi$
$888$	1.12216e6	−	1.24628e6i	0.0477553	−	0.0530376i
$889$	−2.62518e6	+	2.49769e7i	−0.111405	+	1.05995i
$890$	1.44168e7	−	3.06439e6i	0.610092	−	0.129679i
$891$	2.95655e6	−	9.09933e6i	0.124765	−	0.383986i
$892$	−5.91746e6	−	1.25779e6i	−0.249014	−	0.0529295i
$893$	−2.64450e7	+	4.58041e7i	−1.10973	+	1.92210i
$894$	−691586.	−	1.19786e6i	−0.0289403	−	0.0501260i
$895$	−4.58097e6	−	1.40988e7i	−0.191161	−	0.588333i
$896$	−292154.	−	2.77966e6i	−0.0121574	−	0.115670i
$897$	296563.	+	215466.i	0.0123065	+	0.00894123i
$898$	5.26989e6			0.218077
$899$	3.23505e7	−	2.42097e6i	1.33500	−	0.0999056i
$900$	7.87427e6			0.324044
$901$	4.46805e7	+	3.24623e7i	1.83361	+	1.33219i
$902$	−1.11211e6	−	1.05811e7i	−0.0455127	−	0.433025i
$903$	−1.06572e6	−	3.27995e6i	−0.0434935	−	0.133859i
$904$	−528917.	−	916111.i	−0.0215262	−	0.0372844i
$905$	7.28472e6	−	1.26175e7i	0.295659	−	0.512097i
$906$	588872.	+	125169.i	0.0238342	+	0.00506611i
$907$	1.10267e6	−	3.39367e6i	0.0445069	−	0.136978i	−0.926334	−	0.376704i	$-0.877057\pi$
$907$	1.10267e6	−	3.39367e6i	0.0445069	−	0.136978i	0.970841	+	0.239726i	$0.0770575\pi$
$908$	460614.	−	97906.5i	0.0185405	−	0.00394091i
$909$	2.08417e6	−	1.98296e7i	0.0836612	−	0.795983i
$910$	9.37668e6	−	1.04139e7i	0.375358	−	0.416877i
$911$	−1.98269e7	+	8.82750e6i	−0.791514	+	0.352405i	−0.762346	−	0.647170i	$-0.775953\pi$
$911$	−1.98269e7	+	8.82750e6i	−0.791514	+	0.352405i	−0.0291682	+	0.999575i	$0.509286\pi$
$912$	1.17469e6	+	523006.i	0.0467667	+	0.0208219i
$913$	7.70477e6	+	8.55702e6i	0.305902	+	0.339739i
$914$	−5.81066e6	+	4.22169e6i	−0.230070	+	0.167156i
$915$	−596545.	+	433415.i	−0.0235554	+	0.0171140i
$916$	−283831.	−	315226.i	−0.0111769	−	0.0124132i
$917$	−3.60107e6	−	1.60330e6i	−0.141419	−	0.0629638i
$918$	−5.69972e6	+	2.53768e6i	−0.223227	+	0.0993870i
$919$	−3.96894e6	+	4.40795e6i	−0.155019	+	0.172166i	−0.815652	−	0.578543i	$-0.803621\pi$
$919$	−3.96894e6	+	4.40795e6i	−0.155019	+	0.172166i	0.660633	+	0.750709i	$0.270288\pi$
$920$	−74511.9	+	708933.i	−0.00290239	+	0.0276144i
$921$	4.84430e6	−	1.02969e6i	0.188184	−	0.0399997i
$922$	−6.63961e6	+	2.04346e7i	−0.257226	+	0.791661i
$923$	4.26594e7	+	9.06753e6i	1.64820	+	0.350336i
$924$	395264.	−	684617.i	0.0152303	−	0.0263796i
$925$	−1.55969e7	−	2.70146e7i	−0.599355	−	1.03811i
$926$	6.23925e6	+	1.92024e7i	0.239114	+	0.735917i
$927$	5.09864e6	+	4.85104e7i	0.194875	+	1.85411i
$928$	−5.02281e6	−	3.64929e6i	−0.191460	−	0.139104i
$929$	4.93678e6			0.187674			0.0938371	−	0.995588i	$-0.470087\pi$
$929$	4.93678e6			0.187674			0.0938371	+	0.995588i	$0.470087\pi$
$930$	−921903.	+	781272.i	−0.0349525	+	0.0296207i
$931$	−3.58550e7			−1.35574
$932$	3.29748e6	+	2.39576e6i	0.124349	+	0.0903449i
$933$	162745.	+	1.54841e6i	0.00612072	+	0.0582348i
$934$	1.36362e6	+	4.19678e6i	0.0511476	+	0.157416i
$935$	−5.16788e6	−	8.95102e6i	−0.193323	−	0.334845i
$936$	−4.81172e6	+	8.33414e6i	−0.179519	+	0.310936i
$937$	−2.51849e7	−	5.35321e6i	−0.937110	−	0.199189i	−0.286050	−	0.958215i	$-0.592342\pi$
$937$	−2.51849e7	−	5.35321e6i	−0.937110	−	0.199189i	−0.651061	+	0.759026i	$0.725676\pi$
$938$	−6.63384e6	+	2.04169e7i	−0.246183	+	0.757673i
$939$	3.61427e6	−	768236.i	0.133769	−	0.0284335i
$940$	−994331.	+	9.46042e6i	−0.0367038	+	0.349213i
$941$	5.55658e6	−	6.17120e6i	0.204566	−	0.227193i	−0.632128	−	0.774864i	$-0.717818\pi$
$941$	5.55658e6	−	6.17120e6i	0.204566	−	0.227193i	0.836694	+	0.547670i	$0.184485\pi$
$942$	1.44307e6	−	642496.i	0.0529858	−	0.0235908i
$943$	−4.90938e6	−	2.18580e6i	−0.179782	−	0.0800443i
$944$	−58461.2	−	64927.8i	−0.00213520	−	0.00237138i
$945$	3.76399e6	−	2.73470e6i	0.137110	−	0.0996161i
$946$	−6.38756e6	+	4.64084e6i	−0.232064	+	0.168604i
$947$	−2.54846e7	−	2.83035e7i	−0.923427	−	1.02557i	−0.999595	−	0.0284748i	$-0.990935\pi$
$947$	−2.54846e7	−	2.83035e7i	−0.923427	−	1.02557i	0.0761673	−	0.997095i	$-0.475732\pi$
$948$	1.15311e6	+	513396.i	0.0416724	+	0.0185538i
$949$	−1.75873e7	+	7.83039e6i	−0.633920	+	0.282239i
$950$	1.60041e7	−	1.77743e7i	0.575335	−	0.638974i
$951$	5326.01	−	50673.6i	0.000190964	−	0.00181690i
$952$	2.00223e7	−	4.25588e6i	0.716015	−	0.152194i
$953$	−1.07357e7	+	3.30411e7i	−0.382911	+	1.17848i	0.555073	+	0.831801i	$0.312690\pi$
$953$	−1.07357e7	+	3.30411e7i	−0.382911	+	1.17848i	−0.937984	+	0.346677i	$0.887310\pi$
$954$	2.76646e7	+	5.88029e6i	0.984132	+	0.209184i
$955$	8.10693e6	−	1.40416e7i	0.287639	−	0.498205i
$956$	5.41730e6	+	9.38304e6i	0.191707	+	0.332046i
$957$	−542640.	−	1.67007e6i	−0.0191528	−	0.0589462i
$958$	−3.57396e6	−	3.40039e7i	−0.125816	−	1.19706i
$959$	4.36344e7	+	3.17023e7i	1.53209	+	1.11313i
$960$	231268.			0.00809911
$961$	4.69581e6	−	2.82414e7i	0.164022	−	0.986457i
$962$	3.81231e7			1.32816
$963$	−5.34634e6	−	3.88435e6i	−0.185777	−	0.134975i
$964$	2.70506e6	+	2.57369e7i	0.0937527	+	0.891997i
$965$	3.56545e6	+	1.09733e7i	0.123253	+	0.379332i
$966$	−199650.	−	345804.i	−0.00688376	−	0.0119230i
$967$	9.42008e6	−	1.63161e7i	0.323958	−	0.561111i	−0.657343	−	0.753591i	$-0.728320\pi$
$967$	9.42008e6	−	1.63161e7i	0.323958	−	0.561111i	0.981301	+	0.192480i	$0.0616531\pi$
$968$	8.31176e6	+	1.76672e6i	0.285105	+	0.0606009i
$969$	−2.91011e6	+	8.95638e6i	−0.0995633	+	0.306424i
$970$	−6.42961e6	+	1.36665e6i	−0.219409	+	0.0466369i
$971$	−3.38117e6	+	3.21697e7i	−0.115085	+	1.09496i	0.772721	+	0.634745i	$0.218895\pi$
$971$	−3.38117e6	+	3.21697e7i	−0.115085	+	1.09496i	−0.887806	+	0.460217i	$0.847772\pi$
$972$	−3.21346e6	+	3.56891e6i	−0.109096	+	0.121163i
$973$	5.80589e6	−	2.58495e6i	0.196602	−	0.0875327i
$974$	−2.64213e7	−	1.17635e7i	−0.892395	−	0.397320i
$975$	−1.48020e6	−	1.64393e6i	−0.0498665	−	0.0553824i
$976$	−2.70475e6	+	1.96512e6i	−0.0908873	+	0.0660335i
$977$	2.93759e7	−	2.13428e7i	0.984587	−	0.715344i	0.0258580	−	0.999666i	$-0.491768\pi$
$977$	2.93759e7	−	2.13428e7i	0.984587	−	0.715344i	0.958729	+	0.284321i	$0.0917682\pi$
$978$	−994393.	−	1.10439e6i	−0.0332438	−	0.0369210i
$979$	1.72671e7	+	7.68782e6i	0.575789	+	0.256358i
$980$	−5.89118e6	+	2.62292e6i	−0.195946	+	0.0872409i
$981$	4.43212e6	−	4.92237e6i	0.147041	−	0.163306i
$982$	2.23202e6	−	2.12362e7i	0.0738616	−	0.702746i
$983$	−2.19402e7	+	4.66353e6i	−0.724196	+	0.153933i	−0.555239	−	0.831691i	$-0.687373\pi$
$983$	−2.19402e7	+	4.66353e6i	−0.724196	+	0.153933i	−0.168957	+	0.985623i	$0.554040\pi$
$984$	−538770.	+	1.65816e6i	−0.0177385	+	0.0545933i
$985$	1.41597e7	+	3.00974e6i	0.465012	+	0.0988413i
$986$	2.27349e7	−	3.93779e7i	0.744732	−	1.28991i
$987$	−2.66424e6	−	4.61461e6i	−0.0870525	−	0.150779i
$988$	9.03278e6	+	2.78000e7i	0.294394	+	0.906051i
$989$	416863.	+	3.96619e6i	0.0135520	+	0.128939i
$990$	−4.28212e6	−	3.11114e6i	−0.138858	−	0.100886i
$991$	4.21503e7			1.36338			0.681689	−	0.731642i	$-0.261246\pi$
$991$	4.21503e7			1.36338			0.681689	+	0.731642i	$0.261246\pi$
$992$	−4.17994e6	+	3.54231e6i	−0.134862	+	0.114290i
$993$	1.64641e6			0.0529864
$994$	−3.84332e7	−	2.79234e7i	−1.23379	−	0.896400i
$995$	−98654.0	−	938630.i	−0.00315905	−	0.0300564i
$996$	−583093.	−	1.79457e6i	−0.0186247	−	0.0573209i
$997$	−7.21292e6	−	1.24931e7i	−0.229812	−	0.398047i	0.727940	−	0.685641i	$-0.240478\pi$
$997$	−7.21292e6	−	1.24931e7i	−0.229812	−	0.398047i	−0.957752	+	0.287594i	$0.907145\pi$
$998$	−1.58644e7	+	2.74779e7i	−0.504193	+	0.873289i
$999$	1.23807e7	+	2.63160e6i	0.392492	+	0.0834268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.a.41.4	✓	56
31.28	even	15	inner	62.6.g.a.59.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.a.41.4	✓	56	1.1	even	1	trivial
62.6.g.a.59.4	yes	56	31.28	even	15	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(0.180031 + 1.71288i) q^{3} +(4.94427 + 15.2169i) q^{4} +(16.3913 + 28.3905i) q^{5} +(3.44463 - 5.96628i) q^{6} +(-166.864 - 35.4680i) q^{7} +(19.7771 - 60.8676i) q^{8} +(234.788 - 49.9058i) q^{9} +(13.7068 - 130.412i) q^{10} +(112.522 - 124.968i) q^{11} +(-25.1746 + 11.2085i) q^{12} +(-572.280 - 254.795i) q^{13} +(456.592 + 507.097i) q^{14} +(-45.6787 + 33.1875i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1254.54 - 1393.31i) q^{17} +(-877.127 - 390.522i) q^{18} +(-2664.22 + 1186.19i) q^{19} +(-350.973 + 389.795i) q^{20} +(30.7118 - 292.203i) q^{21} +(-657.947 + 139.851i) q^{22} +(-104.991 + 323.128i) q^{23} +(107.820 + 22.9177i) q^{24} +(1025.15 - 1775.62i) q^{25} +(1252.88 + 2170.05i) q^{26} +(257.083 + 791.219i) q^{27} +(-285.307 - 2714.51i) q^{28} +(-4905.09 - 3563.76i) q^{29} +225.848 q^{30} +(-4081.97 + 3459.29i) q^{31} +1024.00 q^{32} +(234.314 + 170.239i) q^{33} +(783.912 + 7458.42i) q^{34} +(-1728.15 - 5318.71i) q^{35} +(1920.27 + 3326.00i) q^{36} +(7607.12 - 13175.9i) q^{37} +(11410.5 + 2425.38i) q^{38} +(333.406 - 1026.12i) q^{39} +(2052.23 - 436.216i) q^{40} +(-1653.34 + 15730.5i) q^{41} +(-786.396 + 873.381i) q^{42} +(10723.1 - 4774.24i) q^{43} +(2457.97 + 1094.36i) q^{44} +(5265.33 + 5847.74i) q^{45} +(1099.48 - 798.817i) q^{46} +(14672.1 - 10659.9i) q^{47} +(-295.028 - 327.662i) q^{48} +(11231.5 + 5000.61i) q^{49} +(-7492.19 + 3335.74i) q^{50} +(2160.71 - 2399.71i) q^{51} +(1047.69 - 9968.11i) q^{52} +(-28813.3 + 6124.45i) q^{53} +(1028.33 - 3164.88i) q^{54} +(5392.30 + 1146.17i) q^{55} +(-5458.93 + 9455.14i) q^{56} +(-2511.44 - 4349.95i) q^{57} +(7494.31 + 23065.1i) q^{58} +(35.6740 + 339.415i) q^{59} +(-730.858 - 531.000i) q^{60} +13059.6 q^{61} +(21342.8 - 1597.20i) q^{62} -40947.7 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2146.62 - 20423.7i) q^{65} +(-357.999 - 1101.81i) q^{66} +(15730.2 + 27245.6i) q^{67} +(14999.0 - 25979.1i) q^{68} +(-572.382 - 121.664i) q^{69} +(-6912.61 + 21274.8i) q^{70} +(-68098.3 + 14474.7i) q^{71} +(1605.78 - 15278.0i) q^{72} +(20563.8 - 22838.4i) q^{73} +(-55595.6 + 24752.7i) q^{74} +(3225.98 + 1436.30i) q^{75} +(-31222.8 - 34676.4i) q^{76} +(-23208.2 + 16861.8i) q^{77} +(-3491.48 + 2536.71i) q^{78} +(-30649.1 - 34039.3i) q^{79} +(-7666.78 - 3413.47i) q^{80} +(51976.5 - 23141.4i) q^{81} +(42334.9 - 47017.7i) q^{82} +(-7157.42 + 68098.3i) q^{83} +(4598.27 - 977.393i) q^{84} +(18993.2 - 58455.0i) q^{85} +(-45925.6 - 9761.79i) q^{86} +(5221.23 - 9043.43i) q^{87} +(-5381.17 - 9320.46i) q^{88} +(34733.3 + 106898. i) q^{89} +(-3290.10 - 31303.2i) q^{90} +(86455.6 + 62813.7i) q^{91} -5436.11 q^{92} +(-6660.23 - 6369.15i) q^{93} -72542.7 q^{94} +(-77346.5 - 56195.5i) q^{95} +(184.352 + 1753.99i) q^{96} +(-15490.3 - 47674.2i) q^{97} +(-24588.9 - 42589.3i) q^{98} +(20182.2 - 34956.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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