LMFDB - Embedded newform 69.6.e.b.58.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.4
Character	$\chi$	$=$	69.58
Dual form			69.6.e.b.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76019 + 1.77387i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-8.82123 + 19.3158i) q^{4} +(-80.1801 + 23.5430i) q^{5} +(-12.2670 - 26.8609i) q^{6} +(-77.8978 - 89.8988i) q^{7} +(-24.8575 - 172.888i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(-2.76019 + 1.77387i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-8.82123 + 19.3158i) q^{4} +(-80.1801 + 23.5430i) q^{5} +(-12.2670 - 26.8609i) q^{6} +(-77.8978 - 89.8988i) q^{7} +(-24.8575 - 172.888i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(179.550 - 207.212i) q^{10} +(635.239 + 408.243i) q^{11} +(-160.774 - 103.323i) q^{12} +(-201.266 + 232.273i) q^{13} +(374.481 + 109.958i) q^{14} +(-107.033 - 744.430i) q^{15} +(-69.6944 - 80.4316i) q^{16} +(74.3195 + 162.737i) q^{17} +(254.999 - 74.8745i) q^{18} +(533.941 - 1169.17i) q^{19} +(252.535 - 1756.42i) q^{20} +(900.628 - 578.799i) q^{21} -2477.55 q^{22} +(836.003 + 2395.30i) q^{23} +1571.99 q^{24} +(3245.65 - 2085.85i) q^{25} +(143.510 - 998.136i) q^{26} +(302.838 - 663.122i) q^{27} +(2423.62 - 711.640i) q^{28} +(-3346.17 - 7327.10i) q^{29} +(1615.95 + 1864.91i) q^{30} +(-868.301 - 6039.17i) q^{31} +(5697.94 + 1673.07i) q^{32} +(-4450.43 + 5136.07i) q^{33} +(-493.810 - 317.352i) q^{34} +(8362.34 + 5374.15i) q^{35} +(1126.37 - 1299.90i) q^{36} +(-14598.6 - 4286.55i) q^{37} +(600.168 + 4174.26i) q^{38} +(-1811.39 - 2090.46i) q^{39} +(6063.37 + 13276.9i) q^{40} +(-16162.3 + 4745.69i) q^{41} +(-1459.19 + 3195.19i) q^{42} +(467.616 - 3252.34i) q^{43} +(-13489.1 + 8668.94i) q^{44} +6768.77 q^{45} +(-6556.46 - 5128.52i) q^{46} +23003.2 q^{47} +(805.783 - 517.845i) q^{48} +(378.149 - 2630.09i) q^{49} +(-5258.59 + 11514.7i) q^{50} +(-1544.92 + 453.628i) q^{51} +(-2711.13 - 5936.54i) q^{52} +(13641.2 + 15742.8i) q^{53} +(340.400 + 2367.54i) q^{54} +(-60544.8 - 17777.6i) q^{55} +(-13606.1 + 15702.2i) q^{56} +(9731.51 + 6254.06i) q^{57} +(22233.4 + 14288.5i) q^{58} +(-5271.22 + 6083.32i) q^{59} +(15323.4 + 4499.36i) q^{60} +(-3072.39 - 21369.0i) q^{61} +(13109.4 + 15129.0i) q^{62} +(4002.61 + 8764.50i) q^{63} +(-15427.5 + 4529.92i) q^{64} +(10669.1 - 23362.0i) q^{65} +(3173.33 - 22071.0i) q^{66} +(-3366.04 + 2163.22i) q^{67} -3798.99 q^{68} +(-22409.0 + 4379.47i) q^{69} -32614.7 q^{70} +(34442.8 - 22135.1i) q^{71} +(-2013.46 + 14003.9i) q^{72} +(-20769.5 + 45478.8i) q^{73} +(47898.8 - 14064.4i) q^{74} +(14424.5 + 31585.2i) q^{75} +(17873.4 + 20627.0i) q^{76} +(-12783.1 - 88908.5i) q^{77} +(8707.97 + 2556.89i) q^{78} +(22292.4 - 25726.7i) q^{79} +(7481.70 + 4808.20i) q^{80} +(5519.46 + 3547.14i) q^{81} +(36192.9 - 41768.8i) q^{82} +(-64971.0 - 19077.2i) q^{83} +(3235.31 + 22502.1i) q^{84} +(-9790.26 - 11298.6i) q^{85} +(4478.51 + 9806.57i) q^{86} +(69558.5 - 20424.2i) q^{87} +(54789.8 - 119973. i) q^{88} +(9640.60 - 67051.9i) q^{89} +(-18683.1 + 12006.9i) q^{90} +36559.2 q^{91} +(-53641.6 - 4981.39i) q^{92} +54911.4 q^{93} +(-63493.2 + 40804.6i) q^{94} +(-15285.7 + 106314. i) q^{95} +(-22202.4 + 48616.5i) q^{96} +(47819.6 - 14041.1i) q^{97} +(3621.66 + 7930.33i) q^{98} +(-40053.8 - 46224.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.76019	+	1.77387i	−0.487937	+	0.313578i	−0.761375	−	0.648311i	$-0.775476\pi$
$2$	−2.76019	+	1.77387i	−0.487937	+	0.313578i	0.273438	+	0.961890i	$0.411839\pi$
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$4$	−8.82123	+	19.3158i	−0.275663	+	0.603619i
$5$	−80.1801	+	23.5430i	−1.43430	+	0.421150i	−0.904319	−	0.426857i	$-0.859621\pi$
$5$	−80.1801	+	23.5430i	−1.43430	+	0.421150i	−0.529985	+	0.848007i	$0.677803\pi$
$6$	−12.2670	−	26.8609i	−0.139110	−	0.304609i
$7$	−77.8978	−	89.8988i	−0.600869	−	0.693440i	0.371088	−	0.928598i	$-0.378985\pi$
$7$	−77.8978	−	89.8988i	−0.600869	−	0.693440i	−0.971957	+	0.235158i	$0.924439\pi$
$8$	−24.8575	−	172.888i	−0.137320	−	0.955079i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	179.550	−	207.212i	0.567787	−	0.655262i
$11$	635.239	+	408.243i	1.58291	+	1.01727i	0.974706	+	0.223490i	$0.0717449\pi$
$11$	635.239	+	408.243i	1.58291	+	1.01727i	0.608201	+	0.793783i	$0.291891\pi$
$12$	−160.774	−	103.323i	−0.322302	−	0.207131i
$13$	−201.266	+	232.273i	−0.330302	+	0.381189i	−0.896473	−	0.443099i	$-0.853879\pi$
$13$	−201.266	+	232.273i	−0.330302	+	0.381189i	0.566171	+	0.824288i	$0.308424\pi$
$14$	374.481	+	109.958i	0.510634	+	0.149936i
$15$	−107.033	−	744.430i	−0.122826	−	0.854271i
$16$	−69.6944	−	80.4316i	−0.0680609	−	0.0785465i
$17$	74.3195	+	162.737i	0.0623707	+	0.136573i	0.938251	−	0.345956i	$-0.112446\pi$
$17$	74.3195	+	162.737i	0.0623707	+	0.136573i	−0.875880	+	0.482529i	$0.839718\pi$
$18$	254.999	−	74.8745i	0.185506	−	0.0544694i
$19$	533.941	−	1169.17i	0.339320	−	0.743006i	−0.660651	−	0.750693i	$-0.729720\pi$
$19$	533.941	−	1169.17i	0.339320	−	0.743006i	0.999970	+	0.00768696i	$0.00244686\pi$
$20$	252.535	−	1756.42i	0.141171	−	0.981869i
$21$	900.628	−	578.799i	0.445654	−	0.286404i
$22$	−2477.55			−1.09135
$23$	836.003	+	2395.30i	0.329525	+	0.944147i
$23$	836.003	+	2395.30i	0.329525	+	0.944147i
$24$	1571.99			0.557085
$25$	3245.65	−	2085.85i	1.03861	−	0.667473i
$26$	143.510	−	998.136i	0.0416341	−	0.289572i
$27$	302.838	−	663.122i	0.0799467	−	0.175059i
$28$	2423.62	−	711.640i	0.584211	−	0.171540i
$29$	−3346.17	−	7327.10i	−0.738845	−	1.61784i	−0.785445	−	0.618931i	$-0.787566\pi$
$29$	−3346.17	−	7327.10i	−0.738845	−	1.61784i	0.0466001	−	0.998914i	$-0.485161\pi$
$30$	1615.95	+	1864.91i	0.327812	+	0.378315i
$31$	−868.301	−	6039.17i	−0.162280	−	1.12869i	−0.894321	−	0.447425i	$-0.852341\pi$
$31$	−868.301	−	6039.17i	−0.162280	−	1.12869i	0.732041	−	0.681261i	$-0.238568\pi$
$32$	5697.94	+	1673.07i	0.983655	+	0.288827i
$33$	−4450.43	+	5136.07i	−0.711405	+	0.821005i
$34$	−493.810	−	317.352i	−0.0732592	−	0.0470809i
$35$	8362.34	+	5374.15i	1.15387	+	0.741548i
$36$	1126.37	−	1299.90i	0.144852	−	0.167168i
$37$	−14598.6	−	4286.55i	−1.75311	−	0.514758i	−0.761970	−	0.647612i	$-0.775768\pi$
$37$	−14598.6	−	4286.55i	−1.75311	−	0.514758i	−0.991136	+	0.132854i	$0.957586\pi$
$38$	600.168	+	4174.26i	0.0674239	+	0.468944i
$39$	−1811.39	−	2090.46i	−0.190700	−	0.220079i
$40$	6063.37	+	13276.9i	0.599189	+	1.31204i
$41$	−16162.3	+	4745.69i	−1.50157	+	0.440899i	−0.926211	−	0.377005i	$-0.876954\pi$
$41$	−16162.3	+	4745.69i	−1.50157	+	0.440899i	−0.575354	+	0.817904i	$0.695136\pi$
$42$	−1459.19	+	3195.19i	−0.127641	+	0.279495i
$43$	467.616	−	3252.34i	0.0385672	−	0.268241i	−0.961409	−	0.275123i	$-0.911281\pi$
$43$	467.616	−	3252.34i	0.0385672	−	0.268241i	0.999976	+	0.00688184i	$0.00219058\pi$
$44$	−13489.1	+	8668.94i	−1.05039	+	0.675048i
$45$	6768.77			0.498286
$46$	−6556.46	−	5128.52i	−0.456851	−	0.357353i
$47$	23003.2			1.51895			0.759475	−	0.650536i	$-0.225456\pi$
$47$	23003.2			1.51895			0.759475	+	0.650536i	$0.225456\pi$
$48$	805.783	−	517.845i	0.0504795	−	0.0324412i
$49$	378.149	−	2630.09i	0.0224995	−	0.156488i
$50$	−5258.59	+	11514.7i	−0.297471	+	0.651370i
$51$	−1544.92	+	453.628i	−0.0831724	+	0.0244216i
$52$	−2711.13	−	5936.54i	−0.139041	−	0.304456i
$53$	13641.2	+	15742.8i	0.667057	+	0.769824i	0.983913	−	0.178649i	$-0.0571727\pi$
$53$	13641.2	+	15742.8i	0.667057	+	0.769824i	−0.316856	+	0.948474i	$0.602627\pi$
$54$	340.400	+	2367.54i	0.0158857	+	0.110487i
$55$	−60544.8	−	17777.6i	−2.69880	−	0.792438i
$56$	−13606.1	+	15702.2i	−0.579779	+	0.669101i
$57$	9731.51	+	6254.06i	0.396728	+	0.254962i
$58$	22233.4	+	14288.5i	0.867831	+	0.557721i
$59$	−5271.22	+	6083.32i	−0.197143	+	0.227515i	−0.845710	−	0.533642i	$-0.820823\pi$
$59$	−5271.22	+	6083.32i	−0.197143	+	0.227515i	0.648567	+	0.761157i	$0.275368\pi$
$60$	15323.4	+	4499.36i	0.549513	+	0.161352i
$61$	−3072.39	−	21369.0i	−0.105719	−	0.735291i	−0.971872	−	0.235511i	$-0.924324\pi$
$61$	−3072.39	−	21369.0i	−0.105719	−	0.735291i	0.866153	−	0.499779i	$-0.166586\pi$
$62$	13109.4	+	15129.0i	0.433114	+	0.499840i
$63$	4002.61	+	8764.50i	0.127055	+	0.278212i
$64$	−15427.5	+	4529.92i	−0.470810	+	0.138242i
$65$	10669.1	−	23362.0i	0.313216	−	0.685847i
$66$	3173.33	−	22071.0i	0.0896717	−	0.623680i
$67$	−3366.04	+	2163.22i	−0.0916078	+	0.0588727i	−0.585643	−	0.810569i	$-0.699158\pi$
$67$	−3366.04	+	2163.22i	−0.0916078	+	0.0588727i	0.494035	+	0.869442i	$0.335521\pi$
$68$	−3798.99			−0.0996312
$69$	−22409.0	+	4379.47i	−0.566631	+	0.110738i
$70$	−32614.7			−0.795551
$71$	34442.8	−	22135.1i	0.810874	−	0.521117i	−0.0682739	−	0.997667i	$-0.521749\pi$
$71$	34442.8	−	22135.1i	0.810874	−	0.521117i	0.879147	+	0.476550i	$0.158113\pi$
$72$	−2013.46	+	14003.9i	−0.0457732	+	0.318360i
$73$	−20769.5	+	45478.8i	−0.456161	+	0.998853i	0.532185	+	0.846628i	$0.321371\pi$
$73$	−20769.5	+	45478.8i	−0.456161	+	0.998853i	−0.988346	+	0.152225i	$0.951356\pi$
$74$	47898.8	−	14064.4i	1.01682	−	0.298566i
$75$	14424.5	+	31585.2i	0.296106	+	0.648381i
$76$	17873.4	+	20627.0i	0.354955	+	0.409639i
$77$	−12783.1	−	88908.5i	−0.245703	−	1.70890i
$78$	8707.97	+	2556.89i	0.162062	+	0.0475856i
$79$	22292.4	−	25726.7i	0.401872	−	0.463785i	−0.518357	−	0.855164i	$-0.673456\pi$
$79$	22292.4	−	25726.7i	0.401872	−	0.463785i	0.920230	+	0.391379i	$0.128002\pi$
$80$	7481.70	+	4808.20i	0.130700	+	0.0839957i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	36192.9	−	41768.8i	0.594413	−	0.685990i
$83$	−64971.0	−	19077.2i	−1.03520	−	0.303962i	−0.280377	−	0.959890i	$-0.590459\pi$
$83$	−64971.0	−	19077.2i	−1.03520	−	0.303962i	−0.754824	+	0.655928i	$0.772278\pi$
$84$	3235.31	+	22502.1i	0.0500285	+	0.347956i
$85$	−9790.26	−	11298.6i	−0.146976	−	0.169620i
$86$	4478.51	+	9806.57i	0.0652962	+	0.142979i
$87$	69558.5	−	20424.2i	0.985263	−	0.289299i
$88$	54789.8	−	119973.i	0.754211	−	1.65149i
$89$	9640.60	−	67051.9i	0.129012	−	0.897296i	−0.817799	−	0.575504i	$-0.804806\pi$
$89$	9640.60	−	67051.9i	0.129012	−	0.897296i	0.946810	−	0.321792i	$-0.104285\pi$
$90$	−18683.1	+	12006.9i	−0.243132	+	0.156252i
$91$	36559.2			0.462800
$92$	−53641.6	−	4981.39i	−0.660743	−	0.0613594i
$93$	54911.4			0.658348
$94$	−63493.2	+	40804.6i	−0.741153	+	0.476310i
$95$	−15285.7	+	106314.i	−0.173771	+	1.20860i
$96$	−22202.4	+	48616.5i	−0.245880	+	0.538401i
$97$	47819.6	−	14041.1i	0.516032	−	0.151521i	−0.0133392	−	0.999911i	$-0.504246\pi$
$97$	47819.6	−	14041.1i	0.516032	−	0.151521i	0.529371	+	0.848390i	$0.322428\pi$
$98$	3621.66	+	7930.33i	0.0380927	+	0.0834115i
$99$	−40053.8	−	46224.6i	−0.410730	−	0.474008i
$100$	11659.3	+	81092.2i	0.116593	+	0.810922i
$101$	−40742.2	−	11963.0i	−0.397412	−	0.116691i	0.0769189	−	0.997037i	$-0.475492\pi$
$101$	−40742.2	−	11963.0i	−0.397412	−	0.116691i	−0.474331	+	0.880347i	$0.657310\pi$
$102$	3459.59	−	3992.58i	0.0329248	−	0.0379973i
$103$	−52635.1	−	33826.5i	−0.488857	−	0.314170i	0.272888	−	0.962046i	$-0.412021\pi$
$103$	−52635.1	−	33826.5i	−0.488857	−	0.314170i	−0.761746	+	0.647876i	$0.775657\pi$
$104$	45160.1	+	29022.6i	0.409422	+	0.263120i
$105$	−58585.8	+	67611.6i	−0.518584	+	0.598478i
$106$	−65577.9	−	19255.4i	−0.566882	−	0.166452i
$107$	5736.86	+	39900.7i	0.0484412	+	0.336916i	0.999602	+	0.0282194i	$0.00898369\pi$
$107$	5736.86	+	39900.7i	0.0484412	+	0.336916i	−0.951161	+	0.308697i	$0.900107\pi$
$108$	10137.3	+	11699.1i	0.0836304	+	0.0965146i
$109$	−79103.7	−	173213.i	−0.637721	−	1.39641i	−0.901902	−	0.431941i	$-0.857829\pi$
$109$	−79103.7	−	173213.i	−0.637721	−	1.39641i	0.264181	−	0.964473i	$-0.414898\pi$
$110$	198650.	−	58328.9i	1.56533	−	0.459624i
$111$	56884.7	−	124560.i	0.438216	−	0.959559i
$112$	−1801.67	+	12530.9i	−0.0135716	+	0.0943923i
$113$	−113675.	+	73054.5i	−0.837469	+	0.538209i	−0.887643	−	0.460532i	$-0.847659\pi$
$113$	−113675.	+	73054.5i	−0.837469	+	0.538209i	0.0501743	+	0.998740i	$0.484022\pi$
$114$	−37954.7			−0.273529
$115$	−123423.	−	172373.i	−0.870266	−	1.21541i
$116$	171046.			1.18023
$117$	20942.7	−	13459.1i	0.141439	−	0.0908971i
$118$	3758.59	−	26141.6i	0.0248496	−	0.172833i
$119$	8840.54	−	19358.1i	0.0572284	−	0.125313i
$120$	−126042.	+	37009.4i	−0.799030	+	0.234616i
$121$	169963.	+	372167.i	1.05534	+	2.31086i
$122$	46386.1	+	53532.4i	0.282155	+	0.325625i
$123$	−21575.2	−	150059.i	−0.128585	−	0.894332i
$124$	124311.	+	36501.0i	0.726031	+	0.213182i
$125$	−40118.6	+	46299.3i	−0.229652	+	0.265033i
$126$	−26595.0	−	17091.6i	−0.149236	−	0.0959082i
$127$	111800.	+	71849.8i	0.615084	+	0.395290i	0.810760	−	0.585378i	$-0.199054\pi$
$127$	111800.	+	71849.8i	0.615084	+	0.395290i	−0.195677	+	0.980668i	$0.562690\pi$
$128$	−89896.9	+	103747.i	−0.484975	+	0.559691i
$129$	28374.2	+	8331.42i	0.150124	+	0.0440803i
$130$	11992.4	+	83409.3i	0.0622371	+	0.432868i
$131$	−68922.7	−	79541.1i	−0.350901	−	0.404961i	0.552670	−	0.833400i	$-0.313609\pi$
$131$	−68922.7	−	79541.1i	−0.350901	−	0.404961i	−0.903571	+	0.428439i	$0.859064\pi$
$132$	−59949.0	−	131270.i	−0.299466	−	0.655739i
$133$	−146700.	+	43074.9i	−0.719117	+	0.211152i
$134$	5453.64	−	11941.8i	0.0262376	−	0.0574524i
$135$	−8669.67	+	60298.8i	−0.0409419	+	0.284757i
$136$	26287.8	−	16894.2i	0.121873	−	0.0783230i
$137$	−38839.6			−0.176796			−0.0883982	−	0.996085i	$-0.528175\pi$
$137$	−38839.6			−0.176796			−0.0883982	+	0.996085i	$0.528175\pi$
$138$	54084.6	−	51838.8i	0.241755	−	0.231717i
$139$	−198995.			−0.873583			−0.436792	−	0.899563i	$-0.643885\pi$
$139$	−198995.			−0.873583			−0.436792	+	0.899563i	$0.643885\pi$
$140$	−177572.	+	114119.i	−0.765693	+	0.492081i
$141$	−29463.3	+	204922.i	−0.124805	+	0.868040i
$142$	−55804.1	+	122194.i	−0.232245	+	0.508545i
$143$	−222676.	+	65383.5i	−0.910610	+	0.267379i
$144$	3581.10	+	7841.50i	0.0143916	+	0.0315132i
$145$	440798.	+	508708.i	1.74108	+	2.00932i
$146$	−23345.6	−	162372.i	−0.0906407	−	0.630420i
$147$	22945.5	+	6737.41i	0.0875798	+	0.0257158i
$148$	211576.	−	244172.i	0.793985	−	0.916308i
$149$	−82022.5	−	52712.6i	−0.302668	−	0.194513i	0.380487	−	0.924786i	$-0.375756\pi$
$149$	−82022.5	−	52712.6i	−0.302668	−	0.194513i	−0.683155	+	0.730273i	$0.739393\pi$
$150$	−95842.2	−	61594.0i	−0.347799	−	0.223517i
$151$	188799.	−	217885.i	0.673840	−	0.777653i	−0.311132	−	0.950367i	$-0.600708\pi$
$151$	188799.	−	217885.i	0.673840	−	0.777653i	0.984972	+	0.172714i	$0.0552536\pi$
$152$	−215407.	−	63249.2i	−0.756225	−	0.222048i
$153$	−2062.32	−	14343.7i	−0.00712241	−	0.0495375i
$154$	192996.	+	222729.i	0.655761	+	0.756789i
$155$	211801.	+	463779.i	0.708105	+	1.55053i
$156$	56357.5	−	16548.1i	0.185413	−	0.0544422i
$157$	−63912.6	+	139949.i	−0.206937	+	0.453128i	−0.984433	−	0.175759i	$-0.943762\pi$
$157$	−63912.6	+	139949.i	−0.206937	+	0.453128i	0.777497	+	0.628887i	$0.216489\pi$
$158$	−15895.3	+	110554.i	−0.0506555	+	0.352317i
$159$	−157715.	+	101357.i	−0.494743	+	0.317952i
$160$	−496250.			−1.53250
$161$	150212.	−	261744.i	0.456708	−	0.795815i
$162$	−21526.9			−0.0644458
$163$	−52685.2	+	33858.7i	−0.155317	+	0.0998162i	−0.615991	−	0.787753i	$-0.711244\pi$
$163$	−52685.2	+	33858.7i	−0.155317	+	0.0998162i	0.460674	+	0.887570i	$0.347608\pi$
$164$	50904.9	−	354051.i	0.147792	−	1.02791i
$165$	235917.	−	516587.i	0.674605	−	1.47718i
$166$	213173.	−	62593.2i	0.600429	−	0.176302i
$167$	−168795.	−	369610.i	−0.468348	−	1.02554i	−0.985505	−	0.169648i	$-0.945737\pi$
$167$	−168795.	−	369610.i	−0.468348	−	1.02554i	0.517157	−	0.855891i	$-0.326990\pi$
$168$	−122455.	−	141320.i	−0.334736	−	0.386305i
$169$	39397.7	+	274017.i	0.106109	+	0.738007i
$170$	47065.1	+	13819.6i	0.124904	+	0.0366752i
$171$	−68178.1	+	78681.7i	−0.178301	+	0.205771i
$172$	58696.7	+	37722.0i	0.151284	+	0.0972241i
$173$	−337816.	−	217101.i	−0.858153	−	0.551502i	0.0359545	−	0.999353i	$-0.488553\pi$
$173$	−337816.	−	217101.i	−0.858153	−	0.551502i	−0.894108	+	0.447852i	$0.852189\pi$
$174$	−155765.	+	179762.i	−0.390029	+	0.450117i
$175$	−440345.	−	129297.i	−1.08692	−	0.319149i
$176$	−11436.9	−	79545.5i	−0.0278309	−	0.193568i
$177$	−47441.0	−	54749.9i	−0.113821	−	0.131356i
$178$	92331.2	+	202177.i	0.218423	+	0.478280i
$179$	−163856.	+	48112.4i	−0.382234	+	0.112234i	−0.467204	−	0.884149i	$-0.654739\pi$
$179$	−163856.	+	48112.4i	−0.382234	+	0.112234i	0.0849701	+	0.996384i	$0.472921\pi$
$180$	−59708.9	+	130744.i	−0.137359	+	0.300775i
$181$	28552.3	−	198585.i	0.0647805	−	0.450558i	−0.931454	−	0.363859i	$-0.881459\pi$
$181$	28552.3	−	198585.i	0.0647805	−	0.450558i	0.996235	−	0.0866993i	$-0.0276319\pi$
$182$	−100910.	+	64851.2i	−0.225817	+	0.145124i
$183$	194298.			0.428886
$184$	393336.	−	204076.i	0.856485	−	0.444372i
$185$	1.27144e6			2.73128
$186$	−151566.	+	97405.6i	−0.321233	+	0.206444i
$187$	−19225.7	+	133717.i	−0.0402047	+	0.279630i
$188$	−202917.	+	444325.i	−0.418719	+	0.916867i
$189$	−83204.3	+	24431.0i	−0.169430	+	0.0497492i
$190$	−146396.	−	320563.i	−0.294202	−	0.644213i
$191$	−190909.	−	220320.i	−0.378653	−	0.436989i	0.534149	−	0.845390i	$-0.320632\pi$
$191$	−190909.	−	220320.i	−0.378653	−	0.436989i	−0.912803	+	0.408401i	$0.866087\pi$
$192$	−20594.3	−	143236.i	−0.0403175	−	0.280414i
$193$	354205.	+	104004.i	0.684481	+	0.200982i	0.605441	−	0.795890i	$-0.292997\pi$
$193$	354205.	+	104004.i	0.684481	+	0.200982i	0.0790391	+	0.996872i	$0.474815\pi$
$194$	−107084.	+	123582.i	−0.204278	+	0.235749i
$195$	194453.	+	124967.i	0.366208	+	0.235348i
$196$	47466.5	+	30504.9i	0.0882565	+	0.0567190i
$197$	592913.	−	684259.i	1.08849	−	1.25619i	0.123943	−	0.992289i	$-0.460446\pi$
$197$	592913.	−	684259.i	1.08849	−	1.25619i	0.964550	−	0.263899i	$-0.0850085\pi$
$198$	192553.	+	56538.5i	0.349049	+	0.102490i
$199$	−50899.6	−	354015.i	−0.0911133	−	0.633707i	−0.983293	−	0.182027i	$-0.941734\pi$
$199$	−50899.6	−	354015.i	−0.0911133	−	0.633707i	0.892180	−	0.451680i	$-0.149175\pi$
$200$	−441298.	−	509284.i	−0.780111	−	0.900296i
$201$	−14959.5	−	32756.7i	−0.0261172	−	0.0571887i
$202$	133677.	−	39251.1i	0.230504	−	0.0676820i
$203$	−398038.	+	871582.i	−0.677929	+	1.48446i
$204$	4865.87	−	33842.9i	0.00818625	−	0.0569366i
$205$	1.18417e6	−	761019.i	1.96802	−	1.26477i
$206$	205287.			0.337049
$207$	−10311.8	−	205238.i	−0.0167266	−	0.332913i
$208$	32709.1			0.0524217
$209$	816485.	−	524723.i	1.29295	−	0.830930i
$210$	41774.0	−	290544.i	0.0653668	−	0.454636i
$211$	−129909.	+	284462.i	−0.200879	+	0.439863i	−0.983083	−	0.183158i	$-0.941368\pi$
$211$	−129909.	+	284462.i	−0.200879	+	0.439863i	0.782205	+	0.623022i	$0.214095\pi$
$212$	−424416.	+	124620.i	−0.648564	+	0.190435i
$213$	153072.	+	335182.i	0.231179	+	0.506211i
$214$	−86613.4	−	99957.2i	−0.129286	−	0.149204i
$215$	39076.4	+	271782.i	0.0576525	+	0.400982i
$216$	−122173.	−	35873.3i	−0.178173	−	0.0523164i
$217$	−475276.	+	548497.i	−0.685167	+	0.790724i
$218$	525598.	+	337781.i	0.749053	+	0.481387i
$219$	−378540.	−	243273.i	−0.533337	−	0.342755i
$220$	877467.	−	1.01265e6i	1.22229	−	1.41060i
$221$	−52757.4	−	15491.0i	−0.0726612	−	0.0213352i
$222$	63940.4	+	444715.i	0.0870749	+	0.605619i
$223$	411730.	+	475162.i	0.554435	+	0.639852i	0.961911	−	0.273364i	$-0.0881364\pi$
$223$	411730.	+	475162.i	0.554435	+	0.639852i	−0.407476	+	0.913216i	$0.633591\pi$
$224$	−293450.	−	642566.i	−0.390764	−	0.855653i
$225$	−299849.	+	88043.5i	−0.394862	+	0.115942i
$226$	184176.	−	403288.i	0.239862	−	0.525224i
$227$	59503.3	−	413855.i	0.0766438	−	0.533069i	−0.914939	−	0.403593i	$-0.867761\pi$
$227$	59503.3	−	413855.i	0.0766438	−	0.533069i	0.991583	−	0.129476i	$-0.0413296\pi$
$228$	−206646.	+	132803.i	−0.263263	+	0.169189i
$229$	−663838.			−0.836514			−0.418257	−	0.908329i	$-0.637359\pi$
$229$	−663838.			−0.836514			−0.418257	+	0.908329i	$0.637359\pi$
$230$	646438.	+	256846.i	0.805763	+	0.320150i
$231$	808405.			0.996779
$232$	−1.18359e6	+	760646.i	−1.44371	+	0.927817i
$233$	−105616.	+	734576.i	−0.127450	+	0.886435i	0.821320	+	0.570468i	$0.193238\pi$
$233$	−105616.	+	734576.i	−0.127450	+	0.886435i	−0.948770	+	0.315967i	$0.897671\pi$
$234$	−33931.3	+	74299.1i	−0.0405098	+	0.0887041i
$235$	−1.84440e6	+	541564.i	−2.17864	+	0.639706i
$236$	−71005.5	−	155480.i	−0.0829873	−	0.181717i
$237$	200631.	+	231541.i	0.232021	+	0.267767i
$238$	9937.09	+	69114.0i	0.0113715	+	0.0790903i
$239$	−255103.	−	74905.0i	−0.288882	−	0.0848234i	0.134081	−	0.990970i	$-0.457192\pi$
$239$	−255103.	−	74905.0i	−0.288882	−	0.0848234i	−0.422963	+	0.906147i	$0.639010\pi$
$240$	−52416.1	+	60491.4i	−0.0587404	+	0.0677900i
$241$	−1.12325e6	−	721872.i	−1.24576	−	0.800603i	−0.259493	−	0.965745i	$-0.583555\pi$
$241$	−1.12325e6	−	721872.i	−1.24576	−	0.800603i	−0.986270	+	0.165142i	$0.947192\pi$
$242$	−1.12931e6	−	725760.i	−1.23958	−	0.796627i
$243$	−38668.9	+	44626.3i	−0.0420093	+	0.0484814i
$244$	439861.	+	129155.i	0.472978	+	0.138879i
$245$	31600.1	+	219783.i	0.0336335	+	0.233926i
$246$	325736.	+	375919.i	0.343185	+	0.396056i
$247$	164102.	+	359333.i	0.171148	+	0.374761i
$248$	−1.02251e6	+	300237.i	−1.05570	+	0.309981i
$249$	253164.	−	554353.i	0.258764	−	0.566615i
$250$	28606.1	−	198960.i	0.0289474	−	0.201333i
$251$	−1.33282e6	+	856551.i	−1.33533	+	0.858161i	−0.996573	−	0.0827143i	$-0.973641\pi$
$251$	−1.33282e6	+	856551.i	−1.33533	+	0.858161i	−0.338752	+	0.940876i	$0.610005\pi$
$252$	−204601.			−0.202958
$253$	−446802.	+	1.86288e6i	−0.438848	+	1.82971i
$254$	−436043.			−0.424077
$255$	113192.	−	72743.9i	0.109009	−	0.0700561i
$256$	137324.	−	955110.i	0.130962	−	0.910864i
$257$	320092.	−	700903.i	0.302302	−	0.661950i	−0.696130	−	0.717915i	$-0.745096\pi$
$257$	320092.	−	700903.i	0.302302	−	0.661950i	0.998433	+	0.0559656i	$0.0178237\pi$
$258$	−93097.0	+	27335.8i	−0.0870736	+	0.0255671i
$259$	751846.	+	1.64631e6i	0.696434	+	1.52498i
$260$	357142.	+	412164.i	0.327648	+	0.378126i
$261$	92854.2	+	645815.i	0.0843723	+	0.586823i
$262$	331335.	+	97288.8i	0.298205	+	0.0875608i
$263$	−23956.8	+	27647.7i	−0.0213570	+	0.0246473i	−0.766328	−	0.642450i	$-0.777918\pi$
$263$	−23956.8	+	27647.7i	−0.0213570	+	0.0246473i	0.744971	+	0.667097i	$0.232463\pi$
$264$	998590.	+	641755.i	0.881814	+	0.566708i
$265$	−1.46438e6	−	941102.i	−1.28097	−	0.823232i
$266$	328510.	−	379120.i	0.284672	−	0.328528i
$267$	584976.	+	171765.i	0.502181	+	0.147454i
$268$	−12091.8	−	84100.1i	−0.0102838	−	0.0715252i
$269$	1.52595e6	+	1.76104e6i	1.28576	+	1.48384i	0.786791	+	0.617220i	$0.211741\pi$
$269$	1.52595e6	+	1.76104e6i	1.28576	+	1.48384i	0.498965	+	0.866622i	$0.333713\pi$
$270$	−83032.2	−	181815.i	−0.0693166	−	0.151782i
$271$	−1.32139e6	+	387995.i	−1.09297	+	0.320924i	−0.778055	−	0.628196i	$-0.783794\pi$
$271$	−1.32139e6	+	387995.i	−1.09297	+	0.320924i	−0.314913	+	0.949121i	$0.601975\pi$
$272$	7909.54	−	17319.5i	0.00648230	−	0.0141943i
$273$	−46826.3	+	325684.i	−0.0380262	+	0.264478i
$274$	107205.	−	68896.3i	0.0862656	−	0.0554395i
$275$	2.91330e6			2.32302
$276$	113082.	−	471480.i	0.0893556	−	0.372556i
$277$	−175720.			−0.137601			−0.0688004	−	0.997630i	$-0.521917\pi$
$277$	−175720.			−0.137601			−0.0688004	+	0.997630i	$0.521917\pi$
$278$	549263.	−	352990.i	0.426254	−	0.273937i
$279$	−70332.4	+	489173.i	−0.0540935	+	0.376229i
$280$	721257.	−	1.57933e6i	0.549788	−	1.20387i
$281$	−65029.8	+	19094.5i	−0.0491300	+	0.0144259i	−0.306205	−	0.951966i	$-0.599059\pi$
$281$	−65029.8	+	19094.5i	−0.0491300	+	0.0144259i	0.257075	+	0.966391i	$0.417241\pi$
$282$	−282179.	−	617887.i	−0.211301	−	0.462686i
$283$	−1.13823e6	−	1.31358e6i	−0.844817	−	0.974971i	0.155099	−	0.987899i	$-0.450430\pi$
$283$	−1.13823e6	−	1.31358e6i	−0.844817	−	0.974971i	−0.999916	+	0.0129278i	$0.995885\pi$
$284$	123728.	+	860550.i	0.0910277	+	0.633111i
$285$	−927512.	−	272342.i	−0.676406	−	0.198611i
$286$	498646.	−	575468.i	0.360476	−	0.416012i
$287$	1.68564e6	+	1.08330e6i	1.20798	+	0.776323i
$288$	−404658.	−	260058.i	−0.287479	−	0.184752i
$289$	908849.	−	1.04887e6i	0.640099	−	0.738713i
$290$	−2.11907e6	−	622214.i	−1.47962	−	0.434455i
$291$	63834.7	+	443980.i	0.0441900	+	0.307348i
$292$	−695247.	−	802357.i	−0.477180	−	0.550695i
$293$	−304935.	−	667715.i	−0.207510	−	0.454383i	0.777048	−	0.629441i	$-0.216716\pi$
$293$	−304935.	−	667715.i	−0.207510	−	0.454383i	−0.984558	+	0.175058i	$0.943989\pi$
$294$	−75285.2	+	22105.7i	−0.0507974	+	0.0149155i
$295$	279428.	−	611861.i	0.186945	−	0.409353i
$296$	−378206.	+	2.63048e6i	−0.250899	+	1.74504i
$297$	463089.	−	297609.i	0.304631	−	0.195774i
$298$	319903.			0.208678
$299$	−724621.	−	287910.i	−0.468741	−	0.186242i
$300$	−737335.			−0.473001
$301$	−328808.	+	211312.i	−0.209183	+	0.134434i
$302$	−134621.	+	936309.i	−0.0849366	+	0.590747i
$303$	158755.	−	347625.i	0.0993392	−	0.217523i
$304$	−131251.	+	38538.7i	−0.0814549	+	0.0239173i
$305$	749434.	+	1.64103e6i	0.461300	+	1.01011i
$306$	31136.3	+	35933.2i	0.0190092	+	0.0219378i
$307$	−19415.1	−	135035.i	−0.0117569	−	0.0817713i	0.983098	−	0.183079i	$-0.0586064\pi$
$307$	−19415.1	−	135035.i	−0.0117569	−	0.0817713i	−0.994855	+	0.101308i	$0.967697\pi$
$308$	1.83010e6	+	537366.i	1.09926	+	0.322770i
$309$	368757.	−	425568.i	0.219707	−	0.253555i
$310$	−1.40729e6	−	904411.i	−0.831725	−	0.534517i
$311$	−871800.	−	560272.i	−0.511112	−	0.328472i	0.259536	−	0.965734i	$-0.416431\pi$
$311$	−871800.	−	560272.i	−0.511112	−	0.328472i	−0.770647	+	0.637262i	$0.780067\pi$
$312$	−316388.	+	365131.i	−0.184006	+	0.212355i
$313$	−13313.7	−	3909.25i	−0.00768136	−	0.00225545i	0.277890	−	0.960613i	$-0.410365\pi$
$313$	−13313.7	−	3909.25i	−0.00768136	−	0.00225545i	−0.285571	+	0.958358i	$0.592183\pi$
$314$	−71840.0	−	499658.i	−0.0411190	−	0.285989i
$315$	−527272.	−	608504.i	−0.299405	−	0.345531i
$316$	300287.	+	657536.i	0.169168	+	0.370426i
$317$	−871656.	+	255941.i	−0.487188	+	0.143051i	−0.516096	−	0.856531i	$-0.672615\pi$
$317$	−871656.	+	255941.i	−0.487188	+	0.143051i	0.0289079	+	0.999582i	$0.490797\pi$
$318$	255529.	−	559531.i	0.141701	−	0.310282i
$319$	865619.	−	6.02051e6i	0.476266	−	3.31251i
$320$	1.13033e6	−	726419.i	0.617064	−	0.396563i
$321$	−362800.			−0.196519
$322$	49686.4	+	988918.i	0.0267053	+	0.531521i
$323$	229949.			0.122638
$324$	−117204.	+	75322.7i	−0.0620271	+	0.0398624i
$325$	−168751.	+	1.17369e6i	−0.0886212	+	0.616374i
$326$	85360.3	−	186913.i	0.0444848	−	0.0974081i
$327$	1.64437e6	−	482830.i	0.850412	−	0.249704i
$328$	1.22223e6	+	2.67630e6i	0.627288	+	1.37357i
$329$	−1.79190e6	−	2.06796e6i	−0.912691	−	1.05330i
$330$	265179.	+	1.84436e6i	0.134046	+	0.932313i
$331$	857146.	+	251681.i	0.430016	+	0.126264i	0.489576	−	0.871961i	$-0.337152\pi$
$331$	857146.	+	251681.i	0.430016	+	0.126264i	−0.0595598	+	0.998225i	$0.518970\pi$
$332$	941616.	−	1.08668e6i	0.468844	−	0.541075i
$333$	1.03677e6	+	666292.i	0.512356	+	0.329271i
$334$	1.12154e6	+	720773.i	0.550111	+	0.353535i
$335$	218961.	−	252694.i	0.106599	−	0.123022i
$336$	−109322.	−	32100.0i	−0.0528276	−	0.0155116i
$337$	−405205.	−	2.81826e6i	−0.194357	−	1.35178i	−0.820309	−	0.571920i	$-0.806199\pi$
$337$	−405205.	−	2.81826e6i	−0.194357	−	1.35178i	0.625952	−	0.779861i	$-0.284710\pi$
$338$	−594814.	−	686452.i	−0.283198	−	0.326827i
$339$	−505199.	−	1.10623e6i	−0.238761	−	0.522814i
$340$	304603.	−	89439.5i	0.142901	−	0.0419597i
$341$	1.91387e6	−	4.19079e6i	0.891306	−	1.95169i
$342$	48613.6	−	338115.i	0.0224746	−	0.156315i
$343$	−1.94777e6	+	1.25176e6i	−0.893929	+	0.574493i
$344$	−573914.			−0.261487
$345$	1.69365e6	−	878721.i	0.766084	−	0.397469i
$346$	1.31754e6			0.591664
$347$	−2.72234e6	+	1.74954e6i	−1.21372	+	0.780012i	−0.981278	−	0.192598i	$-0.938309\pi$
$347$	−2.72234e6	+	1.74954e6i	−1.21372	+	0.780012i	−0.232444	+	0.972610i	$0.574672\pi$
$348$	−219082.	+	1.52375e6i	−0.0969746	+	0.674473i
$349$	974974.	−	2.13490e6i	0.428479	−	0.938238i	−0.565092	−	0.825028i	$-0.691159\pi$
$349$	974974.	−	2.13490e6i	0.428479	−	0.938238i	0.993571	−	0.113210i	$-0.0361134\pi$
$350$	1.44479e6	−	424229.i	0.630428	−	0.185110i
$351$	93074.4	+	203805.i	0.0403239	+	0.0882970i
$352$	2.93653e6	+	3.38894e6i	1.26322	+	1.45783i
$353$	63363.9	+	440706.i	0.0270648	+	0.188240i	0.998869	−	0.0475500i	$-0.0151414\pi$
$353$	63363.9	+	440706.i	0.0270648	+	0.188240i	−0.971804	+	0.235790i	$0.924232\pi$
$354$	228065.	+	66966.0i	0.0967277	+	0.0284018i
$355$	−2.24050e6	+	2.58568e6i	−0.943571	+	1.08894i
$356$	1.21012e6	+	777696.i	0.506061	+	0.325226i
$357$	161126.	+	103550.i	0.0669107	+	0.0430009i
$358$	366928.	−	423458.i	0.151312	−	0.174624i
$359$	−2.06126e6	−	605241.i	−0.844107	−	0.247852i	−0.169040	−	0.985609i	$-0.554067\pi$
$359$	−2.06126e6	−	605241.i	−0.844107	−	0.247852i	−0.675066	+	0.737757i	$0.735885\pi$
$360$	−168255.	−	1.17024e6i	−0.0684244	−	0.475902i
$361$	539641.	+	622779.i	0.217940	+	0.251516i
$362$	273454.	+	598782.i	0.109676	+	0.240158i
$363$	−3.53311e6	+	1.03741e6i	−1.40731	+	0.413224i
$364$	−322497.	+	706171.i	−0.127577	+	0.279355i
$365$	594590.	−	4.13547e6i	0.233607	−	1.62477i
$366$	−536301.	+	344659.i	−0.209269	+	0.134489i
$367$	−1.73165e6			−0.671111			−0.335556	−	0.942020i	$-0.608924\pi$
$367$	−1.73165e6			−0.671111			−0.335556	+	0.942020i	$0.608924\pi$
$368$	134393.	−	234180.i	0.0517316	−	0.0901425i
$369$	1.36442e6			0.521652
$370$	−3.50941e6	+	2.25536e6i	−1.33269	+	0.856470i
$371$	352639.	−	2.45265e6i	0.133013	−	0.925128i
$372$	−484387.	+	1.06066e6i	−0.181482	+	0.397391i
$373$	−794959.	+	233421.i	−0.295851	+	0.0868696i	−0.426290	−	0.904587i	$-0.640180\pi$
$373$	−794959.	+	233421.i	−0.295851	+	0.0868696i	0.130439	+	0.991456i	$0.458361\pi$
$374$	−184130.	−	403189.i	−0.0680685	−	0.149049i
$375$	−361067.	−	416694.i	−0.132590	−	0.153017i
$376$	−571802.	−	3.97697e6i	−0.208582	−	1.45072i
$377$	2.37536e6	+	697467.i	0.860746	+	0.252738i
$378$	186322.	−	215027.i	0.0670711	−	0.0774042i
$379$	1.81733e6	+	1.16793e6i	0.649884	+	0.417655i	0.823624	−	0.567137i	$-0.191949\pi$
$379$	1.81733e6	+	1.16793e6i	0.649884	+	0.417655i	−0.173740	+	0.984792i	$0.555585\pi$
$380$	−1.91871e6	−	1.23308e6i	−0.681633	−	0.438059i
$381$	−783264.	+	903935.i	−0.276437	+	0.319025i
$382$	917763.	+	269479.i	0.321790	+	0.0944859i
$383$	495295.	+	3.44485e6i	0.172531	+	1.19998i	0.873513	+	0.486801i	$0.161836\pi$
$383$	495295.	+	3.44485e6i	0.172531	+	1.19998i	−0.700982	+	0.713179i	$0.747255\pi$
$384$	−809072.	−	933719.i	−0.280001	−	0.323138i
$385$	3.11812e6	+	6.82774e6i	1.07212	+	2.34760i
$386$	−1.16216e6	+	341241.i	−0.397007	+	0.116572i
$387$	−110562.	+	242097.i	−0.0375257	+	0.0821699i
$388$	−150613.	+	1.04753e6i	−0.0507904	+	0.353255i
$389$	−4.67841e6	+	3.00663e6i	−1.56756	+	1.00741i	−0.587377	+	0.809313i	$0.699840\pi$
$389$	−4.67841e6	+	3.00663e6i	−1.56756	+	1.00741i	−0.980183	+	0.198096i	$0.936524\pi$
$390$	−758403.			−0.252487
$391$	−327672.	+	314066.i	−0.108392	+	0.103891i
$392$	−464109.			−0.152548
$393$	796862.	−	512112.i	0.260257	−	0.167257i
$394$	−422771.	+	2.94043e6i	−0.137203	+	0.954269i
$395$	−1.18172e6	+	2.58760e6i	−0.381084	+	0.834458i
$396$	1.24619e6	−	365914.i	0.399343	−	0.117258i
$397$	−74445.0	−	163012.i	−0.0237060	−	0.0519090i	0.897409	−	0.441200i	$-0.145447\pi$
$397$	−74445.0	−	163012.i	−0.0237060	−	0.0519090i	−0.921115	+	0.389291i	$0.872720\pi$
$398$	768468.	+	886859.i	0.243174	+	0.280638i
$399$	−195830.	−	1.36203e6i	−0.0615811	−	0.428306i
$400$	−393972.	−	115681.i	−0.123116	−	0.0361502i
$401$	1.87882e6	−	2.16827e6i	0.583477	−	0.673368i	−0.384872	−	0.922970i	$-0.625754\pi$
$401$	1.87882e6	−	2.16827e6i	0.583477	−	0.673368i	0.968349	+	0.249602i	$0.0802998\pi$
$402$	99397.2	+	63878.7i	0.0306767	+	0.0197147i
$403$	1.57749e6	+	1.01379e6i	0.483844	+	0.310948i
$404$	590471.	−	681440.i	0.179989	−	0.207718i
$405$	−526061.	−	154466.i	−0.159367	−	0.0467944i
$406$	−447409.	−	3.11180e6i	−0.134707	−	0.936907i
$407$	−7.52367e6	−	8.68278e6i	−2.25135	−	2.59820i
$408$	116830.	+	255821.i	0.0347458	+	0.0760827i
$409$	4.48337e6	−	1.31644e6i	1.32524	−	0.389127i	0.458862	−	0.888508i	$-0.348257\pi$
$409$	4.48337e6	−	1.31644e6i	1.32524	−	0.389127i	0.866383	+	0.499381i	$0.166439\pi$
$410$	−1.91858e6	+	4.20112e6i	−0.563665	+	1.23426i
$411$	49747.1	−	345999.i	0.0145266	−	0.101034i
$412$	1.11769e6	−	718297.i	0.324399	−	0.208478i
$413$	957500.			0.276225
$414$	392527.	+	548203.i	0.112556	+	0.157196i
$415$	5.65851e6			1.61281
$416$	−1.53541e6	+	986746.i	−0.435001	+	0.279558i
$417$	254879.	−	1.77272e6i	0.0717784	−	0.499230i
$418$	−1.32286e6	+	2.89667e6i	−0.370318	+	0.810883i
$419$	3.23845e6	−	950895.i	0.901160	−	0.264605i	0.201845	−	0.979418i	$-0.435306\pi$
$419$	3.23845e6	−	950895.i	0.901160	−	0.264605i	0.699316	+	0.714813i	$0.253488\pi$
$420$	−789174.	−	1.72805e6i	−0.218298	−	0.478005i
$421$	−977862.	−	1.12851e6i	−0.268888	−	0.310314i	0.605207	−	0.796068i	$-0.293090\pi$
$421$	−977862.	−	1.12851e6i	−0.268888	−	0.310314i	−0.874095	+	0.485754i	$0.838545\pi$
$422$	−146023.	−	1.01561e6i	−0.0399153	−	0.277617i
$423$	−1.78778e6	−	524941.i	−0.485808	−	0.142646i
$424$	2.38265e6	−	2.74972e6i	0.643643	−	0.742804i
$425$	580661.	+	373168.i	0.155937	+	0.100215i
$426$	−1.01708e6	−	653636.i	−0.271537	−	0.174507i
$427$	−1.68171e6	+	1.94080e6i	−0.446357	+	0.515123i
$428$	−821321.	−	241162.i	−0.216722	−	0.0636354i
$429$	−297251.	−	2.06743e6i	−0.0779795	−	0.542359i
$430$	−589963.	−	680854.i	−0.153870	−	0.177575i
$431$	1.19362e6	+	2.61367e6i	0.309510	+	0.677732i	0.998911	−	0.0466474i	$-0.0148537\pi$
$431$	1.19362e6	+	2.61367e6i	0.309510	+	0.677732i	−0.689402	+	0.724379i	$0.742126\pi$
$432$	−74442.0	+	21858.1i	−0.0191915	+	0.00563513i
$433$	−430472.	+	942602.i	−0.110338	+	0.241606i	−0.956744	−	0.290932i	$-0.906035\pi$
$433$	−430472.	+	942602.i	−0.110338	+	0.241606i	0.846406	+	0.532539i	$0.178762\pi$
$434$	338890.	−	2.35703e6i	0.0863644	−	0.600677i
$435$	−5.09636e6	+	3.27523e6i	−1.29133	+	0.829887i
$436$	4.04354e6			1.01870
$437$	3.24688e6	+	301519.i	0.813321	+	0.0755285i
$438$	1.47638e6			0.367716
$439$	−4.62323e6	+	2.97117e6i	−1.14494	+	0.735811i	−0.968626	−	0.248522i	$-0.920055\pi$
$439$	−4.62323e6	+	2.97117e6i	−1.14494	+	0.735811i	−0.176319	+	0.984333i	$0.556419\pi$
$440$	−1.56853e6	+	1.09094e7i	−0.386243	+	2.68638i
$441$	−89408.8	+	195778.i	−0.0218919	+	0.0479366i
$442$	173099.	−	50826.5i	0.0421444	−	0.0123747i
$443$	1.70680e6	+	3.73737e6i	0.413212	+	0.904808i	0.995758	+	0.0920104i	$0.0293293\pi$
$443$	1.70680e6	+	3.73737e6i	0.413212	+	0.904808i	−0.582546	+	0.812798i	$0.697943\pi$
$444$	1.90419e6	+	2.19755e6i	0.458408	+	0.529031i
$445$	805617.	+	5.60319e6i	0.192854	+	1.34133i
$446$	−1.97933e6	−	581183.i	−0.471173	−	0.138349i
$447$	574642.	−	663172.i	0.136028	−	0.156985i
$448$	1.60900e6	+	1.03404e6i	0.378758	+	0.243413i
$449$	3.53643e6	+	2.27272e6i	0.827845	+	0.532024i	0.884592	−	0.466365i	$-0.154437\pi$
$449$	3.53643e6	+	2.27272e6i	0.827845	+	0.532024i	−0.0567474	+	0.998389i	$0.518073\pi$
$450$	671462.	−	774908.i	0.156311	−	0.180393i
$451$	−1.22043e7	−	3.58352e6i	−2.82535	−	0.829599i
$452$	−408352.	−	2.84015e6i	−0.0940132	−	0.653876i
$453$	1.69919e6	+	1.96097e6i	0.389042	+	0.448978i
$454$	569883.	+	1.24787e6i	0.129762	+	0.284138i
$455$	−2.93132e6	+	860713.i	−0.663796	+	0.194908i
$456$	839350.	−	1.83792e6i	0.189030	−	0.413918i
$457$	545855.	−	3.79650e6i	0.122261	−	0.850342i	−0.832724	−	0.553688i	$-0.813220\pi$
$457$	545855.	−	3.79650e6i	0.122261	−	0.850342i	0.954985	−	0.296654i	$-0.0958708\pi$
$458$	1.83232e6	−	1.17756e6i	0.408167	−	0.262313i
$459$	130421.			0.0288946
$460$	4.41827e6	−	863476.i	0.973548	−	0.190264i
$461$	−511487.			−0.112094			−0.0560470	−	0.998428i	$-0.517850\pi$
$461$	−511487.			−0.112094			−0.0560470	+	0.998428i	$0.517850\pi$
$462$	−2.23135e6	+	1.43400e6i	−0.486366	+	0.312568i
$463$	−444236.	+	3.08973e6i	−0.0963077	+	0.669835i	0.883284	+	0.468838i	$0.155327\pi$
$463$	−444236.	+	3.08973e6i	−0.0963077	+	0.669835i	−0.979592	+	0.200997i	$0.935582\pi$
$464$	−356121.	+	779795.i	−0.0767895	+	0.168146i
$465$	−4.40280e6	+	1.29278e6i	−0.944271	+	0.277263i
$466$	−1.01152e6	−	2.21492e6i	−0.215779	−	0.472490i
$467$	−2.21729e6	−	2.55889e6i	−0.470468	−	0.542949i	0.470074	−	0.882627i	$-0.344227\pi$
$467$	−2.21729e6	−	2.55889e6i	−0.470468	−	0.542949i	−0.940542	+	0.339678i	$0.889682\pi$
$468$	75232.0	+	523250.i	0.0158777	+	0.110432i
$469$	456678.	+	134093.i	0.0958690	+	0.0281497i
$470$	4.13023e6	−	4.76654e6i	0.862441	−	0.995310i
$471$	−1.16486e6	−	748610.i	−0.241948	−	0.155490i
$472$	1.18276e6	+	760114.i	0.244367	+	0.157045i
$473$	1.62480e6	−	1.87511e6i	0.333923	−	0.385367i
$474$	−964503.	−	283204.i	−0.197178	−	0.0578966i
$475$	−705726.	−	4.90843e6i	−0.143517	−	0.998180i
$476$	295933.	+	341524.i	0.0598653	+	0.0690883i
$477$	−700923.	−	1.53481e6i	−0.141051	−	0.308858i
$478$	837004.	−	245767.i	0.167555	−	0.0491986i
$479$	3.44152e6	−	7.53587e6i	0.685348	−	1.50070i	−0.171528	−	0.985179i	$-0.554870\pi$
$479$	3.44152e6	−	7.53587e6i	0.685348	−	1.50070i	0.856876	−	0.515523i	$-0.172402\pi$
$480$	635614.	−	4.42079e6i	0.125919	−	0.875783i
$481$	3.93385e6	−	2.52813e6i	0.775275	−	0.498239i
$482$	4.38090e6			0.858906
$483$	2.13932e6	+	1.67339e6i	0.417262	+	0.326385i
$484$	−8.68799e6			−1.68580
$485$	−3.50361e6	+	2.25163e6i	−0.676334	+	0.434653i
$486$	27572.4	−	191770.i	0.00529522	−	0.0368291i
$487$	2.00638e6	−	4.39336e6i	0.383346	−	0.839411i	−0.615345	−	0.788258i	$-0.710983\pi$
$487$	2.00638e6	−	4.39336e6i	0.383346	−	0.839411i	0.998691	−	0.0511530i	$-0.0162896\pi$
$488$	−3.61806e6	+	1.06236e6i	−0.687743	+	0.201940i
$489$	−234146.	−	512707.i	−0.0442806	−	0.0969611i
$490$	−477088.	−	550589.i	−0.0897653	−	0.103595i
$491$	−686514.	−	4.77481e6i	−0.128513	−	0.893825i	−0.947441	−	0.319930i	$-0.896341\pi$
$491$	−686514.	−	4.77481e6i	−0.128513	−	0.893825i	0.818929	−	0.573895i	$-0.194568\pi$
$492$	3.08883e6	+	906961.i	0.575282	+	0.168918i
$493$	943704.	−	1.08909e6i	0.174871	−	0.201812i
$494$	−1.09036e6	−	700733.i	−0.201026	−	0.129192i
$495$	4.29979e6	+	2.76330e6i	0.788740	+	0.506892i
$496$	−425224.	+	490735.i	−0.0776093	+	0.0895659i
$497$	−4.67294e6	−	1.37210e6i	−0.848592	−	0.249169i
$498$	284566.	+	1.97920e6i	0.0514173	+	0.357615i
$499$	2.44443e6	+	2.82102e6i	0.439467	+	0.507172i	0.931668	−	0.363310i	$-0.118353\pi$
$499$	2.44443e6	+	2.82102e6i	0.439467	+	0.507172i	−0.492202	+	0.870481i	$0.663808\pi$
$500$	−540413.	−	1.18334e6i	−0.0966721	−	0.211682i
$501$	3.50883e6	−	1.03028e6i	0.624550	−	0.183385i
$502$	2.15943e6	−	4.72849e6i	0.382454	−	0.837458i
$503$	−764129.	+	5.31463e6i	−0.134662	+	0.936598i	0.804702	+	0.593678i	$0.202325\pi$
$503$	−764129.	+	5.31463e6i	−0.134662	+	0.936598i	−0.939365	+	0.342919i	$0.888584\pi$
$504$	1.41578e6	−	909866.i	0.248267	−	0.159552i
$505$	3.54836e6			0.619154
$506$	−2.07124e6	−	5.93447e6i	−0.359628	−	1.03040i
$507$	−2.49151e6			−0.430470
$508$	−2.37405e6	+	1.52571e6i	−0.408161	+	0.262309i
$509$	−1.33047e6	+	9.25365e6i	−0.227621	+	1.58314i	0.480467	+	0.877013i	$0.340467\pi$
$509$	−1.33047e6	+	9.25365e6i	−0.227621	+	1.58314i	−0.708088	+	0.706125i	$0.750442\pi$
$510$	−183393.	+	401574.i	−0.0312217	+	0.0683660i
$511$	5.70638e6	−	1.67555e6i	0.966738	−	0.283860i
$512$	−509656.	−	1.11599e6i	−0.0859215	−	0.188142i
$513$	−613603.	−	708135.i	−0.102942	−	0.118802i
$514$	359794.	+	2.50243e6i	0.0600685	+	0.417785i
$515$	5.01666e6	+	1.47302e6i	0.833483	+	0.244733i
$516$	−411223.	+	474577.i	−0.0679913	+	0.0784662i
$517$	1.46125e7	+	9.39091e6i	2.40436	+	1.54519i
$518$	−4.99558e6	−	3.21046e6i	−0.818016	−	0.525707i
$519$	2.36671e6	−	2.73133e6i	0.385679	−	0.445098i
$520$	−4.30422e6	−	1.26383e6i	−0.698049	−	0.204966i
$521$	516519.	+	3.59247e6i	0.0833665	+	0.579827i	0.988096	+	0.153840i	$0.0491640\pi$
$521$	516519.	+	3.59247e6i	0.0833665	+	0.579827i	−0.904729	+	0.425987i	$0.859927\pi$
$522$	−1.40188e6	−	1.61786e6i	−0.225183	−	0.259875i
$523$	−1.43274e6	−	3.13725e6i	−0.229040	−	0.501528i	0.759864	−	0.650082i	$-0.225265\pi$
$523$	−1.43274e6	−	3.13725e6i	−0.229040	−	0.501528i	−0.988904	+	0.148554i	$0.952538\pi$
$524$	2.14438e6	−	629648.i	0.341173	−	0.100177i
$525$	1.71584e6	−	3.75716e6i	0.271693	−	0.594924i
$526$	17082.2	−	118809.i	0.00269202	−	0.0187234i
$527$	918265.	−	590133.i	0.144026	−	0.0925600i
$528$	723272.			0.112906
$529$	−5.03854e6	+	4.00495e6i	−0.782827	+	0.622240i
$530$	5.71137e6			0.883183
$531$	548497.	−	352498.i	0.0844186	−	0.0542525i
$532$	462045.	−	3.21359e6i	0.0707791	−	0.492280i
$533$	2.15063e6	−	4.70921e6i	0.327904	−	0.718010i
$534$	−1.91933e6	+	563567.i	−0.291271	+	0.0855249i
$535$	−1.39936e6	−	3.06418e6i	−0.211372	−	0.462839i
$536$	457666.	+	528175.i	0.0688077	+	0.0794083i
$537$	−218732.	−	1.52132e6i	−0.0327324	−	0.227659i
$538$	−7.33575e6	−	2.15397e6i	−1.09267	−	0.320837i
$539$	1.31393e6	−	1.51636e6i	0.194805	−	0.224817i
$540$	−1.08824e6	−	699372.i	−0.160599	−	0.103210i
$541$	−1.11524e7	−	7.16720e6i	−1.63823	−	1.05283i	−0.942330	−	0.334684i	$-0.891370\pi$
$541$	−1.11524e7	−	7.16720e6i	−1.63823	−	1.05283i	−0.695897	−	0.718141i	$-0.744993\pi$
$542$	2.95903e6	−	3.41491e6i	0.432665	−	0.499322i
$543$	1.73251e6	+	508710.i	0.252160	+	0.0740407i
$544$	151198.	+	1.05161e6i	0.0219053	+	0.152355i
$545$	1.04205e7	+	1.20259e7i	1.50279	+	1.73431i
$546$	−448470.	−	982013.i	−0.0643802	−	0.140973i
$547$	3.40304e6	−	999223.i	0.486294	−	0.142789i	−0.0293894	−	0.999568i	$-0.509356\pi$
$547$	3.40304e6	−	999223.i	0.486294	−	0.142789i	0.515683	+	0.856779i	$0.327538\pi$
$548$	342613.	−	750218.i	0.0487363	−	0.106718i
$549$	−248864.	+	1.73089e6i	−0.0352396	+	0.245097i
$550$	−8.04127e6	+	5.16781e6i	−1.13349	+	0.728450i
$551$	−1.03533e7			−1.45277
$552$	1.31419e6	+	3.76538e6i	0.183573	+	0.525970i
$553$	−4.04933e6			−0.563080
$554$	485020.	−	311703.i	0.0671406	−	0.0431487i
$555$	−1.62850e6	+	1.13265e7i	−0.224417	+	1.56085i
$556$	1.75538e6	−	3.84374e6i	0.240815	−	0.527311i
$557$	−5.84736e6	+	1.71694e6i	−0.798586	+	0.234486i	−0.655471	−	0.755220i	$-0.727530\pi$
$557$	−5.84736e6	+	1.71694e6i	−0.798586	+	0.234486i	−0.143115	+	0.989706i	$0.545712\pi$
$558$	−673596.	−	1.47497e6i	−0.0915829	−	0.200538i
$559$	661316.	+	763199.i	0.0895116	+	0.103302i
$560$	−150557.	−	1.04714e6i	−0.0202875	−	0.141103i
$561$	−1.16658e6	−	342539.i	−0.156498	−	0.0459519i
$562$	145624.	−	168059.i	0.0194487	−	0.0224450i
$563$	3.55111e6	+	2.28216e6i	0.472164	+	0.303441i	0.754998	−	0.655728i	$-0.227638\pi$
$563$	3.55111e6	+	2.28216e6i	0.472164	+	0.303441i	−0.282833	+	0.959169i	$0.591274\pi$
$564$	−3.69832e6	−	2.37677e6i	−0.489561	−	0.314622i
$565$	7.39454e6	−	8.53376e6i	0.974519	−	1.12465i
$566$	5.47185e6	+	1.60668e6i	0.717948	+	0.210808i
$567$	−111070.	−	772508.i	−0.0145090	−	0.100913i
$568$	−4.68305e6	−	5.40452e6i	−0.609057	−	0.702889i
$569$	2.31115e6	+	5.06071e6i	0.299259	+	0.655285i	0.998205	−	0.0598888i	$-0.0190746\pi$
$569$	2.31115e6	+	5.06071e6i	0.299259	+	0.655285i	−0.698946	+	0.715174i	$0.746347\pi$
$570$	3.04321e6	−	893567.i	0.392324	−	0.115197i
$571$	4.93746e6	−	1.08115e7i	0.633743	−	1.38770i	−0.271347	−	0.962482i	$-0.587469\pi$
$571$	4.93746e6	−	1.08115e7i	0.633743	−	1.38770i	0.905089	−	0.425221i	$-0.139804\pi$
$572$	701339.	−	4.87792e6i	0.0896268	−	0.623368i
$573$	2.20722e6	−	1.41849e6i	0.280840	−	0.180485i
$574$	−6.57431e6			−0.832858
$575$	7.70961e6	+	6.03052e6i	0.972440	+	0.760650i
$576$	1.30238e6			0.163562
$577$	1.79551e6	−	1.15391e6i	0.224517	−	0.144288i	−0.423547	−	0.905874i	$-0.639215\pi$
$577$	1.79551e6	−	1.15391e6i	0.224517	−	0.144288i	0.648064	+	0.761586i	$0.275579\pi$
$578$	−648045.	+	4.50725e6i	−0.0806836	+	0.561167i
$579$	−1.38018e6	+	3.02218e6i	−0.171096	+	0.374649i
$580$	−1.37145e7	+	4.02694e6i	−1.69282	+	0.497055i
$581$	3.34608e6	+	7.32689e6i	0.411241	+	0.900491i
$582$	−963757.	−	1.11224e6i	−0.117940	−	0.136110i
$583$	2.23853e6	+	1.55694e7i	0.272767	+	1.89714i
$584$	8.37900e6	+	2.46030e6i	1.01662	+	0.298507i
$585$	−1.36232e6	+	1.57220e6i	−0.164585	+	0.189941i
$586$	2.02612e6	+	1.30211e6i	0.243737	+	0.156640i
$587$	6.71356e6	+	4.31455e6i	0.804188	+	0.516821i	0.876980	−	0.480527i	$-0.159554\pi$
$587$	6.71356e6	+	4.31455e6i	0.804188	+	0.516821i	−0.0727917	+	0.997347i	$0.523191\pi$
$588$	−332546.	+	383778.i	−0.0396651	+	0.0457759i
$589$	−7.52442e6	−	2.20937e6i	−0.893686	−	0.262410i
$590$	314087.	+	2.18452e6i	0.0371466	+	0.258361i
$591$	5.33622e6	+	6.15833e6i	0.628442	+	0.725261i
$592$	672669.	+	1.47294e6i	0.0788855	+	0.172735i
$593$	−5.13627e6	+	1.50815e6i	−0.599807	+	0.176119i	−0.567520	−	0.823360i	$-0.692097\pi$
$593$	−5.13627e6	+	1.50815e6i	−0.599807	+	0.176119i	−0.0322865	+	0.999479i	$0.510279\pi$
$594$	−750295.	+	1.64292e6i	−0.0872501	+	0.191051i
$595$	−253088.	+	1.76027e6i	−0.0293075	+	0.203838i
$596$	1.74173e6	−	1.11934e6i	0.200846	−	0.129076i
$597$	3.21890e6			0.369633
$598$	2.51081e6	−	490695.i	0.287118	−	0.0561124i
$599$	−5.98212e6			−0.681221			−0.340611	−	0.940204i	$-0.610634\pi$
$599$	−5.98212e6			−0.681221			−0.340611	+	0.940204i	$0.610634\pi$
$600$	5.10214e6	−	3.27894e6i	0.578594	−	0.371840i
$601$	−489854.	+	3.40701e6i	−0.0553197	+	0.384757i	0.943287	+	0.331980i	$0.107717\pi$
$601$	−489854.	+	3.40701e6i	−0.0553197	+	0.384757i	−0.998606	+	0.0527776i	$0.983193\pi$
$602$	532733.	−	1.16652e6i	0.0599127	−	0.131190i
$603$	310971.	−	91309.2i	0.0348278	−	0.0102264i
$604$	2.54319e6	+	5.56882e6i	0.283653	+	0.621113i
$605$	−2.23896e7	−	2.58389e7i	−2.48689	−	2.87003i
$606$	178446.	+	1.24112e6i	0.0197390	+	0.137288i
$607$	−1.61996e7	−	4.75663e6i	−1.78457	−	0.523996i	−0.788695	−	0.614784i	$-0.789243\pi$
$607$	−1.61996e7	−	4.75663e6i	−1.78457	−	0.523996i	−0.995870	+	0.0907887i	$0.971061\pi$
$608$	4.99845e6	−	5.76852e6i	0.548374	−	0.632857i
$609$	−7.25457e6	−	4.66223e6i	−0.792626	−	0.509390i
$610$	−4.97955e6	−	3.20016e6i	−0.541833	−	0.348215i
$611$	−4.62975e6	+	5.34302e6i	−0.501712	+	0.579007i
$612$	295253.	+	86694.1i	0.0318651	+	0.00935645i
$613$	1.97140e6	+	1.37114e7i	0.211896	+	1.47377i	0.766816	+	0.641866i	$0.221840\pi$
$613$	1.97140e6	+	1.37114e7i	0.211896	+	1.47377i	−0.554920	+	0.831904i	$0.687251\pi$
$614$	293124.	+	338283.i	0.0313783	+	0.0362125i
$615$	5.26273e6	+	1.15238e7i	0.561078	+	1.22859i
$616$	−1.50534e7	+	4.42009e6i	−1.59839	+	0.469331i
$617$	−6.32095e6	+	1.38410e7i	−0.668451	+	1.46370i	0.205981	+	0.978556i	$0.433962\pi$
$617$	−6.32095e6	+	1.38410e7i	−0.668451	+	1.46370i	−0.874432	+	0.485148i	$0.838766\pi$
$618$	−262938.	+	1.82877e6i	−0.0276938	+	0.192614i
$619$	1.08622e7	−	6.98072e6i	1.13944	−	0.732274i	0.171932	−	0.985109i	$-0.444999\pi$
$619$	1.08622e7	−	6.98072e6i	1.13944	−	0.732274i	0.967510	+	0.252835i	$0.0813628\pi$
$620$	−1.08266e7			−1.13113
$621$	1.84155e6	+	171014.i	0.191626	+	0.0177952i
$622$	3.40018e6			0.352392
$623$	−6.77887e6	+	4.35651e6i	−0.699740	+	0.449696i
$624$	−41895.0	+	291386.i	−0.00430725	+	0.0299576i
$625$	−2.88181e6	+	6.31028e6i	−0.295097	+	0.646173i
$626$	43682.8	−	12826.4i	0.00445528	−	0.00130819i
$627$	3.62866e6	+	7.94565e6i	0.368618	+	0.807162i
$628$	−2.13944e6	−	2.46905e6i	−0.216472	−	0.249822i
$629$	−387384.	−	2.69431e6i	−0.0390405	−	0.271532i
$630$	2.53478e6	+	744278.i	0.254442	+	0.0747108i
$631$	5.21795e6	−	6.02184e6i	0.521707	−	0.602082i	−0.432351	−	0.901706i	$-0.642316\pi$
$631$	5.21795e6	−	6.02184e6i	0.521707	−	0.602082i	0.954057	+	0.299624i	$0.0968612\pi$
$632$	−5.00197e6	−	3.21457e6i	−0.498137	−	0.320133i
$633$	−2.36771e6	−	1.52163e6i	−0.234865	−	0.150939i
$634$	1.95193e6	−	2.25265e6i	0.192860	−	0.222572i
$635$	−1.06557e7	−	3.12880e6i	−1.04869	−	0.307924i
$636$	−566556.	−	3.94049e6i	−0.0555393	−	0.386284i
$637$	534789.	+	617180.i	0.0522197	+	0.0602647i
$638$	8.29031e6	+	1.81532e7i	0.806342	+	1.76564i
$639$	−3.18199e6	+	934317.i	−0.308281	+	0.0905195i
$640$	4.76543e6	−	1.04348e7i	0.459888	−	1.00702i
$641$	1.36222e6	−	9.47443e6i	0.130949	−	0.910769i	−0.813372	−	0.581743i	$-0.802371\pi$
$641$	1.36222e6	−	9.47443e6i	0.130949	−	0.910769i	0.944321	−	0.329025i	$-0.106720\pi$
$642$	1.00140e6	−	643558.i	0.0958889	−	0.0616240i
$643$	7.72512e6			0.736848			0.368424	−	0.929658i	$-0.379898\pi$
$643$	7.72512e6			0.736848			0.368424	+	0.929658i	$0.379898\pi$
$644$	3.73074e6	+	5.21036e6i	0.354471	+	0.495055i
$645$	−2.47119e6			−0.233888
$646$	−634703.	+	407899.i	−0.0598397	+	0.0384566i
$647$	1.19406e6	−	8.30490e6i	0.112142	−	0.779962i	−0.853688	−	0.520785i	$-0.825639\pi$
$647$	1.19406e6	−	8.30490e6i	0.112142	−	0.779962i	0.965830	−	0.259178i	$-0.0834515\pi$
$648$	476058.	−	1.04242e6i	0.0445371	−	0.0975227i
$649$	−5.83196e6	+	1.71242e6i	−0.543504	+	0.159587i
$650$	−1.61618e6	−	3.53894e6i	−0.150040	−	0.328542i
$651$	−4.27748e6	−	4.93648e6i	−0.395581	−	0.456525i
$652$	−189260.	−	1.31633e6i	−0.0174357	−	0.121268i
$653$	759850.	+	223112.i	0.0697341	+	0.0204758i	0.316414	−	0.948621i	$-0.397521\pi$
$653$	759850.	+	223112.i	0.0697341	+	0.0204758i	−0.246679	+	0.969097i	$0.579339\pi$
$654$	−3.68229e6	+	4.24959e6i	−0.336646	+	0.388511i
$655$	7.39886e6	+	4.75496e6i	0.673848	+	0.433056i
$656$	1.50813e6	+	969214.i	0.136829	+	0.0879346i
$657$	2.65202e6	−	3.06060e6i	0.239697	−	0.276626i
$658$	8.61427e6	+	2.52938e6i	0.775629	+	0.227745i
$659$	−2.03680e6	−	1.41663e7i	−0.182699	−	1.27070i	−0.850348	−	0.526222i	$-0.823608\pi$
$659$	−2.03680e6	−	1.41663e7i	−0.182699	−	1.27070i	0.667649	−	0.744476i	$-0.267301\pi$
$660$	7.89720e6	+	9.11386e6i	0.705689	+	0.814409i
$661$	−236187.	−	517177.i	−0.0210258	−	0.0460400i	0.898828	−	0.438302i	$-0.144420\pi$
$661$	−236187.	−	517177.i	−0.0210258	−	0.0460400i	−0.919854	+	0.392262i	$0.871693\pi$
$662$	−2.81234e6	+	825776.i	−0.249415	+	0.0732348i
$663$	205573.	−	450142.i	0.0181628	−	0.0397709i
$664$	−1.68320e6	+	1.17069e7i	−0.148155	+	1.03044i
$665$	1.07483e7	−	6.90749e6i	0.942507	−	0.605712i
$666$	−4.04360e6			−0.353250
$667$	1.47532e7	−	1.41405e7i	1.28402	−	1.23070i
$668$	8.62829e6			0.748141
$669$	−4.76029e6	+	3.05925e6i	−0.411214	+	0.264271i
$670$	−156128.	+	1.08589e6i	−0.0134367	+	0.0934543i
$671$	6.77203e6	−	1.48287e7i	0.580648	−	1.27144i
$672$	6.10009e6	−	1.79115e6i	0.521091	−	0.153006i
$673$	−6.47895e6	−	1.41869e7i	−0.551400	−	1.20740i	−0.956125	−	0.292959i	$-0.905360\pi$
$673$	−6.47895e6	−	1.41869e7i	−0.551400	−	1.20740i	0.404725	−	0.914438i	$-0.367367\pi$
$674$	6.11766e6	+	7.06016e6i	0.518723	+	0.598639i
$675$	−400270.	−	2.78394e6i	−0.0338138	−	0.235180i
$676$	−5.64039e6	−	1.65617e6i	−0.474725	−	0.139392i
$677$	−5.72905e6	+	6.61167e6i	−0.480408	+	0.554421i	−0.943277	−	0.332006i	$-0.892275\pi$
$677$	−5.72905e6	+	6.61167e6i	−0.480408	+	0.554421i	0.462869	+	0.886427i	$0.346820\pi$
$678$	3.35675e6	+	2.15725e6i	0.280443	+	0.180230i
$679$	−4.98732e6	−	3.20515e6i	−0.415138	−	0.266793i
$680$	−1.71002e6	+	1.97347e6i	−0.141817	+	0.163666i
$681$	3.61057e6	+	1.06016e6i	0.298337	+	0.0875998i
$682$	2.15126e6	+	1.49623e7i	0.177105	+	1.23180i
$683$	1.59405e6	+	1.83963e6i	0.130752	+	0.150896i	0.817350	−	0.576141i	$-0.195442\pi$
$683$	1.59405e6	+	1.83963e6i	0.130752	+	0.150896i	−0.686598	+	0.727037i	$0.740897\pi$
$684$	−918386.	−	2.01098e6i	−0.0750559	−	0.164349i
$685$	3.11416e6	−	914401.i	0.253580	−	0.0744578i
$686$	3.15577e6	−	6.91018e6i	0.256033	−	0.560633i
$687$	850266.	−	5.91373e6i	0.0687326	−	0.478046i
$688$	−294181.	+	189059.i	−0.0236943	+	0.0152274i
$689$	−6.40212e6			−0.513779
$690$	−3.11606e6	+	5.42975e6i	−0.249163	+	0.434167i
$691$	2.01819e7			1.60793			0.803964	−	0.594679i	$-0.202721\pi$
$691$	2.01819e7			1.60793			0.803964	+	0.594679i	$0.202721\pi$
$692$	7.17344e6	−	4.61009e6i	0.569458	−	0.365969i
$693$	−1.03543e6	+	7.20159e6i	−0.0819009	+	0.569633i
$694$	4.41073e6	−	9.65815e6i	0.347626	−	0.761194i
$695$	1.59554e7	−	4.68493e6i	1.25298	−	0.367909i
$696$	−5.26015e6	−	1.15181e7i	−0.411600	−	0.901278i
$697$	−1.97347e6	−	2.27751e6i	−0.153868	−	0.177574i
$698$	1.09591e6	+	7.62219e6i	0.0851402	+	0.592163i
$699$	−6.40861e6	−	1.88174e6i	−0.496102	−	0.145669i
$700$	6.38186e6	−	7.36506e6i	0.492269	−	0.568108i
$701$	5.44726e6	+	3.50074e6i	0.418681	+	0.269070i	0.732975	−	0.680256i	$-0.238131\pi$
$701$	5.44726e6	+	3.50074e6i	0.418681	+	0.269070i	−0.314294	+	0.949326i	$0.601768\pi$
$702$	−618425.	−	397438.i	−0.0473636	−	0.0304387i
$703$	−1.28065e7	+	1.47795e7i	−0.977332	+	1.12790i
$704$	−1.16495e7	−	3.42059e6i	−0.885879	−	0.260117i
$705$	−2.46210e6	−	1.71243e7i	−0.186566	−	1.29760i
$706$	−956649.	−	1.10403e6i	−0.0722339	−	0.0833624i
$707$	2.09827e6	+	4.59457e6i	0.157875	+	0.345697i
$708$	1.47603e6	−	433400.i	0.110665	−	0.0324942i
$709$	−4.84331e6	+	1.06054e7i	−0.361848	+	0.792337i	0.637905	+	0.770115i	$0.279801\pi$
$709$	−4.84331e6	+	1.06054e7i	−0.361848	+	0.792337i	−0.999753	+	0.0222218i	$0.992926\pi$
$710$	1.59757e6	−	1.11113e7i	0.118936	−	0.827218i
$711$	−2.31963e6	+	1.49074e6i	−0.172086	+	0.110593i
$712$	−1.18321e7			−0.874704
$713$	1.37397e7	−	7.12860e6i	1.01217	−	0.525147i
$714$	−628422.			−0.0461324
$715$	1.63148e7	−	1.04849e7i	1.19349	−	0.767007i
$716$	516081.	−	3.58942e6i	0.0376214	−	0.261663i
$717$	994027.	−	2.17662e6i	0.0722105	−	0.158119i
$718$	6.76310e6	−	1.98582e6i	0.489592	−	0.143757i
$719$	6.57445e6	+	1.43960e7i	0.474282	+	1.03853i	0.983996	+	0.178189i	$0.0570240\pi$
$719$	6.57445e6	+	1.43960e7i	0.474282	+	1.03853i	−0.509714	+	0.860344i	$0.670249\pi$
$720$	−471745.	−	544423.i	−0.0339138	−	0.0391386i
$721$	1.05919e6	+	7.36684e6i	0.0758816	+	0.527768i
$722$	−2.59424e6	−	761737.i	−0.185211	−	0.0543829i
$723$	7.86942e6	−	9.08179e6i	0.559882	−	0.646139i
$724$	3.58397e6	+	2.30328e6i	0.254108	+	0.163305i
$725$	−2.61438e7	−	1.68016e7i	−1.84724	−	1.18715i
$726$	7.91181e6	−	9.13072e6i	0.557101	−	0.642929i
$727$	−1.81138e7	−	5.31870e6i	−1.27108	−	0.373224i	−0.424476	−	0.905439i	$-0.639542\pi$
$727$	−1.81138e7	−	5.31870e6i	−1.27108	−	0.373224i	−0.846609	+	0.532215i	$0.821360\pi$
$728$	−908771.	−	6.32064e6i	−0.0635515	−	0.442010i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	5.69458e6	+	1.24694e7i	0.395508	+	0.866041i
$731$	564029.	−	165614.i	0.0390399	−	0.0114631i
$732$	−1.71395e6	+	3.75303e6i	−0.118228	+	0.258883i
$733$	−309642.	+	2.15361e6i	−0.0212863	+	0.148049i	−0.997693	−	0.0678917i	$-0.978373\pi$
$733$	−309642.	+	2.15361e6i	−0.0212863	+	0.148049i	0.976406	+	0.215941i	$0.0692819\pi$
$734$	4.77968e6	−	3.07171e6i	0.327460	−	0.210446i
$735$	−1.99839e6			−0.136446
$736$	756005.	+	1.50469e7i	0.0514435	+	1.02389i
$737$	−3.02136e6			−0.204896
$738$	−3.76605e6	+	2.42029e6i	−0.254534	+	0.163579i
$739$	1.56138e6	−	1.08596e7i	0.105171	−	0.731481i	−0.867186	−	0.497984i	$-0.834074\pi$
$739$	1.56138e6	−	1.08596e7i	0.105171	−	0.731481i	0.972357	−	0.233497i	$-0.0750169\pi$
$740$	−1.12157e7	+	2.45589e7i	−0.752914	+	1.64865i
$741$	−3.41127e6	+	1.00164e6i	−0.228229	+	0.0670140i
$742$	3.37733e6	+	7.39533e6i	0.225198	+	0.493114i
$743$	1.86730e7	+	2.15498e7i	1.24092	+	1.43209i	0.862190	+	0.506585i	$0.169092\pi$
$743$	1.86730e7	+	2.15498e7i	1.24092	+	1.43209i	0.378726	+	0.925509i	$0.376362\pi$
$744$	−1.36496e6	−	9.49351e6i	−0.0904041	−	0.628774i
$745$	7.81758e6	+	2.29545e6i	0.516038	+	0.151522i
$746$	1.78018e6	−	2.05444e6i	0.117116	−	0.135159i
$747$	4.61413e6	+	2.96532e6i	0.302544	+	0.194433i
$748$	−2.41326e6	−	1.55091e6i	−0.157707	−	0.101352i
$749$	3.14014e6	−	3.62392e6i	0.204524	−	0.236034i
$750$	1.73577e6	+	509669.i	0.112678	+	0.0330853i
$751$	−1.83366e6	−	1.27534e7i	−0.118636	−	0.825134i	−0.959060	−	0.283204i	$-0.908603\pi$
$751$	−1.83366e6	−	1.27534e7i	−0.118636	−	0.825134i	0.840423	−	0.541930i	$-0.182306\pi$
$752$	−1.60319e6	−	1.85018e6i	−0.103381	−	0.119308i
$753$	−5.92337e6	−	1.29704e7i	−0.380699	−	0.833615i
$754$	−7.79365e6	+	2.28842e6i	−0.499243	+	0.146591i
$755$	−1.00082e7	+	2.19149e7i	−0.638983	+	1.39918i
$756$	262060.	−	1.82267e6i	0.0166762	−	0.115985i
$757$	6.71975e6	−	4.31852e6i	0.426200	−	0.273902i	−0.309908	−	0.950767i	$-0.600298\pi$
$757$	6.71975e6	−	4.31852e6i	0.426200	−	0.273902i	0.736107	+	0.676865i	$0.236662\pi$
$758$	−7.08792e6			−0.448070
$759$	−1.60230e7	−	6.36632e6i	−1.00958	−	0.401129i
$760$	1.87604e7			1.17817
$761$	119150.	−	76572.8i	0.00745814	−	0.00479306i	−0.536906	−	0.843642i	$-0.680407\pi$
$761$	119150.	−	76572.8i	0.00745814	−	0.00479306i	0.544365	+	0.838849i	$0.316771\pi$
$762$	558498.	−	3.88444e6i	0.0348445	−	0.242349i
$763$	−9.40964e6	+	2.06042e7i	−0.585143	+	1.28128i
$764$	5.93971e6	−	1.74406e6i	0.368156	−	0.108100i
$765$	503051.	+	1.10153e6i	0.0310784	+	0.0680522i
$766$	−7.47782e6	−	8.62986e6i	−0.460472	−	0.531413i
$767$	−352074.	−	2.44873e6i	−0.0216095	−	0.150297i
$768$	8.33261e6	+	2.44667e6i	0.509774	+	0.149683i
$769$	895175.	−	1.03309e6i	0.0545873	−	0.0629971i	−0.727799	−	0.685790i	$-0.759457\pi$
$769$	895175.	−	1.03309e6i	0.0545873	−	0.0629971i	0.782387	+	0.622793i	$0.214002\pi$
$770$	−2.07181e7	−	1.33147e7i	−1.25928	−	0.809292i
$771$	5.83393e6	+	3.74924e6i	0.353448	+	0.227147i
$772$	−5.13344e6	+	5.92431e6i	−0.310003	+	0.357762i
$773$	−1.62627e7	−	4.77516e6i	−0.978913	−	0.287435i	−0.247137	−	0.968980i	$-0.579490\pi$
$773$	−1.62627e7	−	4.77516e6i	−0.978913	−	0.287435i	−0.731776	+	0.681546i	$0.761308\pi$
$774$	−124276.	−	864358.i	−0.00745649	−	0.0518610i
$775$	−1.54150e7	−	1.77899e7i	−0.921914	−	1.06395i
$776$	−3.61621e6	−	7.91839e6i	−0.215575	−	0.472044i
$777$	−1.56290e7	+	4.58909e6i	−0.928707	+	0.272693i
$778$	7.57994e6	−	1.65977e7i	0.448969	−	0.983106i
$779$	−3.08122e6	+	2.14304e7i	−0.181920	+	1.26528i
$780$	−4.12916e6	+	2.65365e6i	−0.243011	+	0.156173i
$781$	3.09159e7			1.81366
$782$	347326.	−	1.44813e6i	0.0203105	−	0.0846818i
$783$	−5.87210e6			−0.342286
$784$	−237897.	+	152887.i	−0.0138229	+	0.00888342i
$785$	1.82970e6	−	1.27258e7i	0.105975	−	0.737075i
$786$	−1.29107e6	+	2.82705e6i	−0.0745408	+	0.163222i
$787$	−1.67627e7	+	4.92196e6i	−0.964730	+	0.283270i	−0.725907	−	0.687793i	$-0.758580\pi$
$787$	−1.67627e7	+	4.92196e6i	−0.964730	+	0.283270i	−0.238823	+	0.971063i	$0.576762\pi$
$788$	7.98678e6	+	1.74886e7i	0.458201	+	1.00332i
$789$	−215611.	−	248829.i	−0.0123305	−	0.0142301i
$790$	−1.32829e6	−	9.23848e6i	−0.0757227	−	0.526663i
$791$	1.54225e7	+	4.52847e6i	0.876425	+	0.257342i
$792$	−6.99603e6	+	8.07385e6i	−0.396313	+	0.457370i
$793$	5.58180e6	+	3.58720e6i	0.315204	+	0.202569i
$794$	494643.	+	317888.i	0.0278446	+	0.0178946i
$795$	1.02593e7	−	1.18399e7i	0.575707	−	0.664402i
$796$	7.28708e6	+	2.13968e6i	0.407634	+	0.119692i
$797$	−2.85860e6	−	1.98820e7i	−0.159407	−	1.10870i	−0.899729	−	0.436449i	$-0.856236\pi$
$797$	−2.85860e6	−	1.98820e7i	−0.159407	−	1.10870i	0.740322	−	0.672252i	$-0.234673\pi$
$798$	2.95659e6	+	3.41208e6i	0.164355	+	0.189676i
$799$	1.70959e6	+	3.74347e6i	0.0947380	+	0.207447i
$800$	2.19833e7	−	6.45488e6i	1.21442	−	0.356585i
$801$	−2.27940e6	+	4.99120e6i	−0.125528	+	0.274867i
$802$	−1.33967e6	+	9.31761e6i	−0.0735465	+	0.511527i
$803$	−3.17600e7	+	2.04109e7i	−1.73817	+	1.11705i
$804$	764684.			0.0417198
$805$	−5.88174e6	+	2.45231e7i	−0.319901	+	1.33378i
$806$	−6.15252e6			−0.333592
$807$	−1.76425e7	+	1.13381e7i	−0.953621	+	0.612855i
$808$	−1.05550e6	+	7.34119e6i	−0.0568763	+	0.395584i
$809$	−616688.	+	1.35036e6i	−0.0331279	+	0.0725401i	−0.925473	−	0.378815i	$-0.876332\pi$
$809$	−616688.	+	1.35036e6i	−0.0331279	+	0.0725401i	0.892345	+	0.451355i	$0.149059\pi$
$810$	1.72603e6	−	506808.i	0.0924349	−	0.0271413i
$811$	−2.71474e6	−	5.94446e6i	−0.144936	−	0.317366i	0.823216	−	0.567728i	$-0.192178\pi$
$811$	−2.71474e6	−	5.94446e6i	−0.144936	−	0.317366i	−0.968152	+	0.250362i	$0.919450\pi$
$812$	−1.33241e7	−	1.53768e7i	−0.709167	−	0.818422i
$813$	−1.76393e6	−	1.22684e7i	−0.0935956	−	0.650971i
$814$	3.61689e7	+	1.06201e7i	1.91326	+	0.561784i
$815$	3.42716e6	−	3.95516e6i	0.180734	−	0.208579i
$816$	144158.	+	92644.7i	0.00757902	+	0.00487074i
$817$	−3.55285e6	−	2.28328e6i	−0.186218	−	0.119675i
$818$	−1.00398e7	+	1.15865e7i	−0.524614	+	0.605437i
$819$	−2.84134e6	−	834293.i	−0.148018	−	0.0434619i
$820$	4.25387e6	+	2.95863e7i	0.220927	+	1.53658i
$821$	5.66351e6	+	6.53604e6i	0.293243	+	0.338421i	0.883185	−	0.469025i	$-0.155395\pi$
$821$	5.66351e6	+	6.53604e6i	0.293243	+	0.338421i	−0.589942	+	0.807446i	$0.700849\pi$
$822$	476444.	+	1.04327e6i	0.0245942	+	0.0538537i
$823$	1.73405e7	−	5.09164e6i	0.892407	−	0.262034i	0.196789	−	0.980446i	$-0.436949\pi$
$823$	1.73405e7	−	5.09164e6i	0.892407	−	0.262034i	0.695618	+	0.718412i	$0.255131\pi$
$824$	−4.53981e6	+	9.94080e6i	−0.232927	+	0.510039i
$825$	−3.73145e6	+	2.59528e7i	−0.190872	+	1.32755i
$826$	−2.64288e6	+	1.69848e6i	−0.134781	+	0.0866183i
$827$	1.46090e7			0.742775			0.371387	−	0.928478i	$-0.378882\pi$
$827$	1.46090e7			0.742775			0.371387	+	0.928478i	$0.378882\pi$
$828$	4.05529e6	+	1.61127e6i	0.205564	+	0.0816756i
$829$	−2.08776e7			−1.05510			−0.527550	−	0.849524i	$-0.676889\pi$
$829$	−2.08776e7			−1.05510			−0.527550	+	0.849524i	$0.676889\pi$
$830$	−1.56186e7	+	1.00375e7i	−0.786948	+	0.505741i
$831$	225068.	−	1.56538e6i	0.0113060	−	0.0786353i
$832$	2.05285e6	−	4.49511e6i	0.102813	−	0.225129i
$833$	456116.	−	133928.i	0.0227752	−	0.00668741i
$834$	2.44106e6	+	5.34517e6i	0.121524	+	0.266101i
$835$	2.22357e7	+	2.56614e7i	1.10366	+	1.27369i
$836$	2.93304e6	+	2.03998e7i	0.145145	+	1.00951i
$837$	−4.26766e6	−	1.25310e6i	−0.210560	−	0.0618260i
$838$	−7.25198e6	+	8.36923e6i	−0.356736	+	0.411695i
$839$	−1.88265e7	−	1.20990e7i	−0.923345	−	0.593398i	−0.00971840	−	0.999953i	$-0.503094\pi$
$839$	−1.88265e7	−	1.20990e7i	−0.923345	−	0.593398i	−0.913626	+	0.406555i	$0.866730\pi$
$840$	1.31455e7	+	8.44811e6i	0.642805	+	0.413106i
$841$	−2.90575e7	+	3.35342e7i	−1.41667	+	1.63492i
$842$	4.70092e6	+	1.38031e6i	0.228508	+	0.0670961i
$843$	−86808.8	−	603768.i	−0.00420721	−	0.0292618i
$844$	−4.34865e6	−	5.01861e6i	−0.210135	−	0.242509i
$845$	−9.61008e6	−	2.10431e7i	−0.463004	−	1.01384i
$846$	5.86580e6	−	1.72235e6i	0.281774	−	0.0827364i
$847$	2.02176e7	−	4.42705e7i	0.968327	−	2.12034i
$848$	315502.	−	2.19437e6i	0.0150665	−	0.104790i
$849$	1.31598e7	−	8.45729e6i	0.626585	−	0.402682i
$850$	−2.26469e6			−0.107513
$851$	−1.93696e6	−	3.85516e7i	−0.0916845	−	1.82482i
$852$	−7.82459e6			−0.369286
$853$	6.78170e6	−	4.35833e6i	0.319129	−	0.205092i	−0.371262	−	0.928528i	$-0.621075\pi$
$853$	6.78170e6	−	4.35833e6i	0.319129	−	0.205092i	0.690391	+	0.723436i	$0.257439\pi$
$854$	1.19913e6	−	8.34011e6i	0.0562627	−	0.391316i
$855$	3.61412e6	−	7.91382e6i	0.169078	−	0.370229i
$856$	6.75575e6	−	1.98367e6i	0.315129	−	0.0925303i
$857$	−2.40444e6	−	5.26498e6i	−0.111831	−	0.244875i	0.845439	−	0.534072i	$-0.179339\pi$
$857$	−2.40444e6	−	5.26498e6i	−0.111831	−	0.244875i	−0.957270	+	0.289197i	$0.906612\pi$
$858$	4.48781e6	+	5.17921e6i	0.208121	+	0.240185i
$859$	−2.22468e6	−	1.54730e7i	−0.102869	−	0.715469i	−0.974350	−	0.225039i	$-0.927749\pi$
$859$	−2.22468e6	−	1.54730e7i	−0.102869	−	0.715469i	0.871481	−	0.490430i	$-0.163160\pi$
$860$	−5.59439e6	−	1.64266e6i	−0.257933	−	0.0757359i
$861$	−1.18095e7	+	1.36288e7i	−0.542903	+	0.626543i
$862$	−7.93094e6	−	5.09690e6i	−0.363543	−	0.233635i
$863$	2.92875e7	+	1.88219e7i	1.33861	+	0.860275i	0.996834	−	0.0795053i	$-0.0253341\pi$
$863$	2.92875e7	+	1.88219e7i	1.33861	+	0.860275i	0.341779	+	0.939780i	$0.388970\pi$
$864$	2.83500e6	−	3.27176e6i	0.129202	−	0.149107i
$865$	3.21973e7	+	9.45398e6i	1.46312	+	0.429610i
$866$	−483866.	−	3.36536e6i	−0.0219245	−	0.152488i
$867$	8.17964e6	+	9.43981e6i	0.369561	+	0.426496i
$868$	−6.40215e6	−	1.40188e7i	−0.288421	−	0.631553i
$869$	2.46637e7	−	7.24193e6i	1.10792	−	0.325316i
$870$	8.25710e6	−	1.80805e7i	0.369853	−	0.809866i
$871$	175010.	−	1.21722e6i	0.00781660	−	0.0543656i
$872$	−2.79801e7	+	1.79817e7i	−1.24611	+	0.800829i
$873$	−4.03691e6			−0.179272
$874$	−9.49685e6	+	4.92728e6i	−0.420534	+	0.218187i
$875$	7.28741e6			0.321775
$876$	8.03821e6	−	5.16584e6i	0.353915	−	0.227447i
$877$	−5.81512e6	+	4.04451e7i	−0.255305	+	1.77569i	0.309931	+	0.950759i	$0.399694\pi$
$877$	−5.81512e6	+	4.04451e7i	−0.255305	+	1.77569i	−0.565237	+	0.824929i	$0.691215\pi$
$878$	7.49054e6	−	1.64020e7i	0.327927	−	0.718060i
$879$	6.33884e6	−	1.86125e6i	0.276718	−	0.0812518i
$880$	2.78975e6	+	6.10871e6i	0.121439	+	0.265915i
$881$	−8.32027e6	−	9.60210e6i	−0.361158	−	0.416799i	0.545869	−	0.837870i	$-0.316200\pi$
$881$	−8.32027e6	−	9.60210e6i	−0.361158	−	0.416799i	−0.907027	+	0.421072i	$0.861654\pi$
$882$	−100499.	−	698984.i	−0.00435000	−	0.0302549i
$883$	−3.27056e7	−	9.60324e6i	−1.41163	−	0.414492i	−0.514969	−	0.857209i	$-0.672196\pi$
$883$	−3.27056e7	−	9.60324e6i	−1.41163	−	0.414492i	−0.896661	+	0.442717i	$0.854015\pi$
$884$	764605.	−	882401.i	0.0329084	−	0.0379783i
$885$	5.09280e6	+	3.27294e6i	0.218574	+	0.140469i
$886$	−1.13407e7	−	7.28821e6i	−0.485350	−	0.311915i
$887$	7.90138e6	−	9.11867e6i	0.337205	−	0.389155i	−0.561670	−	0.827362i	$-0.689841\pi$
$887$	7.90138e6	−	9.11867e6i	0.337205	−	0.389155i	0.898874	+	0.438207i	$0.144386\pi$
$888$	−2.29489e7	−	6.73841e6i	−0.976630	−	0.286764i
$889$	−2.24980e6	−	1.56477e7i	−0.0954748	−	0.664042i
$890$	−1.21630e7	−	1.40368e7i	−0.514712	−	0.594010i
$891$	2.05808e6	+	4.50657e6i	0.0868497	+	0.190174i
$892$	−1.28101e7	+	3.76139e6i	−0.539064	+	0.158284i
$893$	1.22823e7	−	2.68946e7i	0.515410	−	1.12859i
$894$	−409742.	+	2.84982e6i	−0.0171462	+	0.119254i
$895$	1.20053e7	−	7.71532e6i	0.500973	−	0.321956i
$896$	1.63295e7			0.679519
$897$	3.49293e6	−	6.08644e6i	0.144947	−	0.252570i
$898$	−1.37927e7			−0.570768
$899$	−4.13441e7	+	2.65702e7i	−1.70614	+	1.09647i
$900$	944403.	−	6.56847e6i	0.0388643	−	0.270307i
$901$	−1.54813e6	+	3.38992e6i	−0.0635322	+	0.139116i
$902$	4.00430e7	−	1.17577e7i	1.63874	−	0.481177i
$903$	−1.46130e6	−	3.19981e6i	−0.0596377	−	0.130588i
$904$	1.54559e7	+	1.78371e7i	0.629032	+	0.725942i
$905$	2.38597e6	+	1.65948e7i	0.0968376	+	0.673520i
$906$	−8.16858e6	−	2.39851e6i	−0.330618	−	0.0970781i
$907$	−2.06653e7	+	2.38490e7i	−0.834109	+	0.962613i	−0.999722	−	0.0235780i	$-0.992494\pi$
$907$	−2.06653e7	+	2.38490e7i	−0.834109	+	0.962613i	0.165613	+	0.986191i	$0.447040\pi$
$908$	7.46905e6	+	4.80006e6i	0.300643	+	0.193211i
$909$	2.89344e6	+	1.85950e6i	0.116146	+	0.0746426i
$910$	6.56421e6	−	7.57550e6i	0.262772	−	0.303255i
$911$	3.09204e7	+	9.07905e6i	1.23438	+	0.362447i	0.832902	−	0.553421i	$-0.186678\pi$
$911$	3.09204e7	+	9.07905e6i	1.23438	+	0.362447i	0.401480	+	0.915868i	$0.368496\pi$
$912$	−175207.	−	1.21859e6i	−0.00697533	−	0.0485145i
$913$	−3.34840e7	−	3.86426e7i	−1.32941	−	1.53423i
$914$	5.22783e6	+	1.14473e7i	0.206993	+	0.453252i
$915$	−1.55789e7	+	4.57437e6i	−0.615153	+	0.180625i
$916$	5.85587e6	−	1.28226e7i	0.230596	−	0.504936i
$917$	−1.78172e6	+	1.23921e7i	−0.0699708	+	0.486657i
$918$	−359987.	+	231350.i	−0.0140987	+	0.00906071i
$919$	4.42810e7			1.72953			0.864765	−	0.502176i	$-0.167467\pi$
$919$	4.42810e7			1.72953			0.864765	+	0.502176i	$0.167467\pi$
$920$	−2.67332e7	+	2.56231e7i	−1.04131	+	0.998073i
$921$	1.22781e6			0.0476961
$922$	1.41180e6	−	907309.i	0.0546948	−	0.0351502i
$923$	−1.79078e6	+	1.24552e7i	−0.0691893	+	0.481222i
$924$	−7.13113e6	+	1.56150e7i	−0.274776	+	0.601675i
$925$	−5.63232e7	+	1.65380e7i	−2.16438	+	0.635519i
$926$	−4.25459e6	−	9.31625e6i	−0.163054	−	0.357038i
$927$	3.31881e6	+	3.83011e6i	0.126848	+	0.146390i
$928$	−6.80757e6	−	4.73477e7i	−0.259491	−	1.80480i
$929$	2.41358e7	+	7.08690e6i	0.917534	+	0.269412i	0.706209	−	0.708004i	$-0.250404\pi$
$929$	2.41358e7	+	7.08690e6i	0.917534	+	0.269412i	0.211325	+	0.977416i	$0.432222\pi$
$930$	9.85936e6	−	1.13783e7i	0.373802	−	0.431390i
$931$	−2.87310e6	−	1.84643e6i	−0.108637	−	0.0698166i
$932$	−1.32573e7	−	8.51992e6i	−0.499935	−	0.321289i
$933$	6.10775e6	−	7.04872e6i	0.229709	−	0.265098i
$934$	1.06593e7	+	3.12984e6i	0.399816	+	0.117397i
$935$	−1.60659e6	−	1.11741e7i	−0.0601003	−	0.418007i
$936$	−2.84749e6	−	3.28618e6i	−0.106236	−	0.122603i
$937$	72448.3	+	158640.i	0.00269575	+	0.00590286i	0.910975	−	0.412461i	$-0.135331\pi$
$937$	72448.3	+	158640.i	0.00269575	+	0.00590286i	−0.908279	+	0.418364i	$0.862604\pi$
$938$	−1.49838e6	+	439965.i	−0.0556052	+	0.0163272i
$939$	51877.8	−	113597.i	0.00192007	−	0.00420437i
$940$	5.80912e6	−	4.04033e7i	0.214432	−	1.49141i
$941$	−6.52962e6	+	4.19633e6i	−0.240389	+	0.154488i	−0.655289	−	0.755379i	$-0.727453\pi$
$941$	−6.52962e6	+	4.19633e6i	−0.240389	+	0.154488i	0.414900	+	0.909867i	$0.363817\pi$
$942$	4.54317e6			0.166814
$943$	−2.48791e7	−	3.47461e7i	−0.911077	−	1.27241i
$944$	856665.			0.0312882
$945$	6.09614e6	−	3.91775e6i	0.222063	−	0.142711i
$946$	−1.15854e6	+	8.05784e6i	−0.0420905	+	0.292746i
$947$	−1.44716e7	+	3.16884e7i	−0.524375	+	1.14822i	0.443381	+	0.896333i	$0.353779\pi$
$947$	−1.44716e7	+	3.16884e7i	−0.524375	+	1.14822i	−0.967756	+	0.251889i	$0.918948\pi$
$948$	−6.24221e6	+	1.83288e6i	−0.225589	+	0.0662388i
$949$	−6.38331e6	−	1.39775e7i	−0.230081	−	0.503806i
$950$	1.06548e7	+	1.22963e7i	0.383035	+	0.442046i
$951$	−1.16358e6	−	8.09287e6i	−0.0417200	−	0.290169i
$952$	−3.56653e6	−	1.04723e6i	−0.127542	−	0.0374497i
$953$	1.75130e7	−	2.02111e7i	0.624637	−	0.720870i	−0.351944	−	0.936021i	$-0.614479\pi$
$953$	1.75130e7	−	2.02111e7i	0.624637	−	0.720870i	0.976581	+	0.215152i	$0.0690246\pi$
$954$	4.65723e6	+	2.99302e6i	0.165675	+	0.106473i
$955$	2.04941e7	+	1.31707e7i	0.727142	+	0.467306i
$956$	3.69717e6	−	4.26676e6i	0.130835	−	0.150992i
$957$	5.25244e7	+	1.54225e7i	1.85388	+	0.544347i
$958$	3.86839e6	+	2.69052e7i	0.136181	+	0.947159i
$959$	3.02552e6	+	3.49164e6i	0.106232	+	0.122598i
$960$	5.02346e6	+	1.09998e7i	0.175924	+	0.385220i
$961$	−8.24815e6	+	2.42187e6i	−0.288103	+	0.0845947i
$962$	−6.37361e6	+	1.39563e7i	−0.222049	+	0.486219i
$963$	464686.	−	3.23196e6i	0.0161471	−	0.112305i
$964$	2.38520e7	−	1.53288e7i	0.826671	−	0.531269i
$965$	−3.08487e7			−1.06640
$966$	−8.87331e6	−	824014.i	−0.305945	−	0.0284113i
$967$	2.96628e7			1.02011			0.510053	−	0.860143i	$-0.329626\pi$
$967$	2.96628e7			1.02011			0.510053	+	0.860143i	$0.329626\pi$
$968$	6.01183e7	−	3.86357e7i	2.06214	−	1.32526i
$969$	−294526.	+	2.04848e6i	−0.0100766	+	0.0700844i
$970$	5.67653e6	−	1.24299e7i	0.193711	−	0.424167i
$971$	3.39683e7	−	9.97400e6i	1.15618	−	0.339485i	0.353234	−	0.935535i	$-0.385082\pi$
$971$	3.39683e7	−	9.97400e6i	1.15618	−	0.339485i	0.802948	+	0.596050i	$0.203264\pi$
$972$	−520885.	−	1.14058e6i	−0.0176838	−	0.0387222i
$973$	1.55012e7	+	1.78894e7i	0.524909	+	0.605778i
$974$	2.25525e6	+	1.56856e7i	0.0761722	+	0.529789i
$975$	−1.02395e7	−	3.00660e6i	−0.344960	−	0.101289i
$976$	−1.50461e6	+	1.73641e6i	−0.0505591	+	0.0583484i
$977$	−3.46785e7	−	2.22865e7i	−1.16232	−	0.746975i	−0.190262	−	0.981733i	$-0.560934\pi$
$977$	−3.46785e7	−	2.22865e7i	−1.16232	−	0.746975i	−0.972054	+	0.234759i	$0.924570\pi$
$978$	1.55576e6	+	999827.i	0.0520111	+	0.0334255i
$979$	3.34976e7	−	3.86582e7i	1.11701	−	1.28910i
$980$	−4.52404e6	−	1.32838e6i	−0.150474	−	0.0441831i
$981$	2.19508e6	+	1.52671e7i	0.0728245	+	0.506505i
$982$	1.03648e7	+	1.19616e7i	0.342990	+	0.395832i
$983$	−2.40471e7	−	5.26557e7i	−0.793740	−	1.73805i	−0.665622	−	0.746289i	$-0.731834\pi$
$983$	−2.40471e7	−	5.26557e7i	−0.793740	−	1.73805i	−0.128118	−	0.991759i	$-0.540894\pi$
$984$	−2.54070e7	+	7.46017e6i	−0.836500	+	0.245619i
$985$	−3.14303e7	+	6.88229e7i	−1.03219	+	2.26018i
$986$	−672898.	+	4.68011e6i	−0.0220423	+	0.153308i
$987$	2.07173e7	−	1.33142e7i	0.676926	−	0.435034i
$988$	−8.38839e6			−0.273392
$989$	8.18125e6	−	1.59889e6i	0.265968	−	0.0519789i
$990$	−1.67700e7			−0.543806
$991$	−2.46734e7	+	1.58566e7i	−0.798077	+	0.512893i	−0.874988	−	0.484145i	$-0.839131\pi$
$991$	−2.46734e7	+	1.58566e7i	−0.798077	+	0.512893i	0.0769111	+	0.997038i	$0.475494\pi$
$992$	5.15640e6	−	3.58635e7i	0.166367	−	1.15711i
$993$	−3.33993e6	+	7.31344e6i	−0.107489	+	0.235369i
$994$	1.53321e7	−	4.50192e6i	0.492194	−	0.144521i
$995$	1.24157e7	+	2.71866e7i	0.397570	+	0.870557i
$996$	8.47454e6	+	9.78015e6i	0.270687	+	0.312390i
$997$	−348956.	−	2.42704e6i	−0.0111181	−	0.0773284i	0.983507	−	0.180870i	$-0.0578915\pi$
$997$	−348956.	−	2.42704e6i	−0.0111181	−	0.0773284i	−0.994625	+	0.103542i	$0.966982\pi$
$998$	−1.17512e7	−	3.45046e6i	−0.373470	−	0.109661i
$999$	−7.26352e6	+	8.38255e6i	−0.230268	+	0.265743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.58.4	yes	100
23.2	even	11	inner	69.6.e.b.25.4	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.25.4	✓	100	23.2	even	11	inner
69.6.e.b.58.4	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76019 + 1.77387i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-8.82123 + 19.3158i) q^{4} +(-80.1801 + 23.5430i) q^{5} +(-12.2670 - 26.8609i) q^{6} +(-77.8978 - 89.8988i) q^{7} +(-24.8575 - 172.888i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(-2.76019 + 1.77387i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-8.82123 + 19.3158i) q^{4} +(-80.1801 + 23.5430i) q^{5} +(-12.2670 - 26.8609i) q^{6} +(-77.8978 - 89.8988i) q^{7} +(-24.8575 - 172.888i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(179.550 - 207.212i) q^{10} +(635.239 + 408.243i) q^{11} +(-160.774 - 103.323i) q^{12} +(-201.266 + 232.273i) q^{13} +(374.481 + 109.958i) q^{14} +(-107.033 - 744.430i) q^{15} +(-69.6944 - 80.4316i) q^{16} +(74.3195 + 162.737i) q^{17} +(254.999 - 74.8745i) q^{18} +(533.941 - 1169.17i) q^{19} +(252.535 - 1756.42i) q^{20} +(900.628 - 578.799i) q^{21} -2477.55 q^{22} +(836.003 + 2395.30i) q^{23} +1571.99 q^{24} +(3245.65 - 2085.85i) q^{25} +(143.510 - 998.136i) q^{26} +(302.838 - 663.122i) q^{27} +(2423.62 - 711.640i) q^{28} +(-3346.17 - 7327.10i) q^{29} +(1615.95 + 1864.91i) q^{30} +(-868.301 - 6039.17i) q^{31} +(5697.94 + 1673.07i) q^{32} +(-4450.43 + 5136.07i) q^{33} +(-493.810 - 317.352i) q^{34} +(8362.34 + 5374.15i) q^{35} +(1126.37 - 1299.90i) q^{36} +(-14598.6 - 4286.55i) q^{37} +(600.168 + 4174.26i) q^{38} +(-1811.39 - 2090.46i) q^{39} +(6063.37 + 13276.9i) q^{40} +(-16162.3 + 4745.69i) q^{41} +(-1459.19 + 3195.19i) q^{42} +(467.616 - 3252.34i) q^{43} +(-13489.1 + 8668.94i) q^{44} +6768.77 q^{45} +(-6556.46 - 5128.52i) q^{46} +23003.2 q^{47} +(805.783 - 517.845i) q^{48} +(378.149 - 2630.09i) q^{49} +(-5258.59 + 11514.7i) q^{50} +(-1544.92 + 453.628i) q^{51} +(-2711.13 - 5936.54i) q^{52} +(13641.2 + 15742.8i) q^{53} +(340.400 + 2367.54i) q^{54} +(-60544.8 - 17777.6i) q^{55} +(-13606.1 + 15702.2i) q^{56} +(9731.51 + 6254.06i) q^{57} +(22233.4 + 14288.5i) q^{58} +(-5271.22 + 6083.32i) q^{59} +(15323.4 + 4499.36i) q^{60} +(-3072.39 - 21369.0i) q^{61} +(13109.4 + 15129.0i) q^{62} +(4002.61 + 8764.50i) q^{63} +(-15427.5 + 4529.92i) q^{64} +(10669.1 - 23362.0i) q^{65} +(3173.33 - 22071.0i) q^{66} +(-3366.04 + 2163.22i) q^{67} -3798.99 q^{68} +(-22409.0 + 4379.47i) q^{69} -32614.7 q^{70} +(34442.8 - 22135.1i) q^{71} +(-2013.46 + 14003.9i) q^{72} +(-20769.5 + 45478.8i) q^{73} +(47898.8 - 14064.4i) q^{74} +(14424.5 + 31585.2i) q^{75} +(17873.4 + 20627.0i) q^{76} +(-12783.1 - 88908.5i) q^{77} +(8707.97 + 2556.89i) q^{78} +(22292.4 - 25726.7i) q^{79} +(7481.70 + 4808.20i) q^{80} +(5519.46 + 3547.14i) q^{81} +(36192.9 - 41768.8i) q^{82} +(-64971.0 - 19077.2i) q^{83} +(3235.31 + 22502.1i) q^{84} +(-9790.26 - 11298.6i) q^{85} +(4478.51 + 9806.57i) q^{86} +(69558.5 - 20424.2i) q^{87} +(54789.8 - 119973. i) q^{88} +(9640.60 - 67051.9i) q^{89} +(-18683.1 + 12006.9i) q^{90} +36559.2 q^{91} +(-53641.6 - 4981.39i) q^{92} +54911.4 q^{93} +(-63493.2 + 40804.6i) q^{94} +(-15285.7 + 106314. i) q^{95} +(-22202.4 + 48616.5i) q^{96} +(47819.6 - 14041.1i) q^{97} +(3621.66 + 7930.33i) q^{98} +(-40053.8 - 46224.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Introduction

L-functions

Modular forms

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Database

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