LMFDB - Embedded newform 82.6.d.a.51.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(37,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.37"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-36] 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:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.5
Character	$\chi$	$=$	82.51
Dual form			82.6.d.a.37.5

$q$-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} +3.92057 q^{3} +(4.94427 + 15.2169i) q^{4} +(18.6494 + 57.3970i) q^{5} +(-12.6872 - 9.21782i) q^{6} +(152.716 - 110.955i) q^{7} +(19.7771 - 60.8676i) q^{8} -227.629 q^{9} +(74.5976 - 229.588i) q^{10} +(-192.701 + 593.074i) q^{11} +(19.3844 + 59.6590i) q^{12} +(-159.963 - 116.220i) q^{13} -755.072 q^{14} +(73.1163 + 225.029i) q^{15} +(-207.108 + 150.473i) q^{16} +(-471.810 + 1452.08i) q^{17} +(736.623 + 535.188i) q^{18} +(1324.67 - 962.431i) q^{19} +(-781.196 + 567.572i) q^{20} +(598.736 - 435.007i) q^{21} +(2017.99 - 1466.16i) q^{22} +(2829.00 + 2055.39i) q^{23} +(77.5375 - 238.636i) q^{24} +(-418.434 + 304.010i) q^{25} +(244.402 + 752.192i) q^{26} -1845.14 q^{27} +(2443.46 + 1775.28i) q^{28} +(935.967 + 2880.61i) q^{29} +(292.465 - 900.116i) q^{30} +(-3235.33 + 9957.32i) q^{31} +1024.00 q^{32} +(-755.499 + 2325.19i) q^{33} +(4940.86 - 3589.75i) q^{34} +(9216.55 + 6696.22i) q^{35} +(-1125.46 - 3463.81i) q^{36} +(1341.56 + 4128.89i) q^{37} -6549.54 q^{38} +(-627.147 - 455.649i) q^{39} +3862.45 q^{40} +(-7384.06 - 7831.47i) q^{41} -2960.31 q^{42} +(1628.41 + 1183.11i) q^{43} -9977.51 q^{44} +(-4245.15 - 13065.2i) q^{45} +(-4322.33 - 13302.8i) q^{46} +(18358.6 + 13338.3i) q^{47} +(-811.983 + 589.940i) q^{48} +(5817.66 - 17904.9i) q^{49} +2068.85 q^{50} +(-1849.77 + 5692.99i) q^{51} +(977.608 - 3008.77i) q^{52} +(1158.12 + 3564.32i) q^{53} +(5970.98 + 4338.17i) q^{54} -37634.4 q^{55} +(-3733.28 - 11489.9i) q^{56} +(5193.48 - 3773.28i) q^{57} +(3743.87 - 11522.4i) q^{58} +(-30077.6 - 21852.7i) q^{59} +(-3062.74 + 2225.21i) q^{60} +(-24701.3 + 17946.5i) q^{61} +(33880.8 - 24615.8i) q^{62} +(-34762.7 + 25256.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(3687.46 - 11348.8i) q^{65} +(7911.69 - 5748.18i) q^{66} +(-7297.82 - 22460.4i) q^{67} -24429.0 q^{68} +(11091.3 + 8058.31i) q^{69} +(-14081.6 - 43338.8i) q^{70} +(21538.4 - 66288.4i) q^{71} +(-4501.84 + 13855.2i) q^{72} +28933.4 q^{73} +(5366.23 - 16515.6i) q^{74} +(-1640.50 + 1191.89i) q^{75} +(21194.8 + 15398.9i) q^{76} +(36375.8 + 111953. i) q^{77} +(958.196 + 2949.02i) q^{78} +10922.1 q^{79} +(-12499.1 - 9081.16i) q^{80} +48079.9 q^{81} +(5482.43 + 42704.1i) q^{82} -1312.85 q^{83} +(9579.77 + 6960.11i) q^{84} -92144.1 q^{85} +(-2487.99 - 7657.25i) q^{86} +(3669.53 + 11293.6i) q^{87} +(32287.9 + 23458.5i) q^{88} +(68282.0 - 49609.8i) q^{89} +(-16980.6 + 52260.9i) q^{90} -37324.2 q^{91} +(-17289.3 + 53211.1i) q^{92} +(-12684.3 + 39038.4i) q^{93} +(-28049.4 - 86327.2i) q^{94} +(79945.0 + 58083.4i) q^{95} +4014.67 q^{96} +(9083.46 + 27956.0i) q^{97} +(-60923.3 + 44263.4i) q^{98} +(43864.4 - 135001. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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
$3$	3.92057			0.251505			0.125752	−	0.992062i	$-0.459866\pi$
$3$	3.92057			0.251505			0.125752	+	0.992062i	$0.459866\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	18.6494	+	57.3970i	0.333611	+	1.02675i	0.967402	+	0.253244i	$0.0814977\pi$
$5$	18.6494	+	57.3970i	0.333611	+	1.02675i	−0.633792	+	0.773504i	$0.718502\pi$
$6$	−12.6872	−	9.21782i	−0.143876	−	0.104532i
$7$	152.716	−	110.955i	1.17799	−	0.855858i	0.186045	−	0.982541i	$-0.440433\pi$
$7$	152.716	−	110.955i	1.17799	−	0.855858i	0.991943	+	0.126683i	$0.0404331\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−227.629			−0.936745
$10$	74.5976	−	229.588i	0.235898	−	0.726021i
$11$	−192.701	+	593.074i	−0.480179	+	1.47784i	0.358665	+	0.933466i	$0.383232\pi$
$11$	−192.701	+	593.074i	−0.480179	+	1.47784i	−0.838844	+	0.544372i	$0.816768\pi$
$12$	19.3844	+	59.6590i	0.0388596	+	0.119598i
$13$	−159.963	−	116.220i	−0.262520	−	0.190732i	0.448737	−	0.893664i	$-0.351874\pi$
$13$	−159.963	−	116.220i	−0.262520	−	0.190732i	−0.711257	+	0.702932i	$0.751874\pi$
$14$	−755.072			−1.02960
$15$	73.1163	+	225.029i	0.0839047	+	0.258232i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−471.810	+	1452.08i	−0.395954	+	1.21862i	0.532261	+	0.846580i	$0.321342\pi$
$17$	−471.810	+	1452.08i	−0.395954	+	1.21862i	−0.928216	+	0.372042i	$0.878658\pi$
$18$	736.623	+	535.188i	0.535876	+	0.389337i
$19$	1324.67	−	962.431i	0.841831	−	0.611626i	−0.0810508	−	0.996710i	$-0.525828\pi$
$19$	1324.67	−	962.431i	0.841831	−	0.611626i	0.922881	+	0.385084i	$0.125828\pi$
$20$	−781.196	+	567.572i	−0.436702	+	0.317283i
$21$	598.736	−	435.007i	0.296270	−	0.215252i
$22$	2017.99	−	1466.16i	0.888921	−	0.645839i
$23$	2829.00	+	2055.39i	1.11510	+	0.810168i	0.983459	−	0.181129i	$-0.0579752\pi$
$23$	2829.00	+	2055.39i	1.11510	+	0.810168i	0.131641	+	0.991297i	$0.457975\pi$
$24$	77.5375	−	238.636i	0.0274779	−	0.0845683i
$25$	−418.434	+	304.010i	−0.133899	+	0.0972831i
$26$	244.402	+	752.192i	0.0709041	+	0.218220i
$27$	−1845.14			−0.487101
$28$	2443.46	+	1775.28i	0.588994	+	0.427929i
$29$	935.967	+	2880.61i	0.206664	+	0.636048i	0.999641	+	0.0267955i	$0.00853029\pi$
$29$	935.967	+	2880.61i	0.206664	+	0.636048i	−0.792977	+	0.609252i	$0.791470\pi$
$30$	292.465	−	900.116i	0.0593296	−	0.182598i
$31$	−3235.33	+	9957.32i	−0.604664	+	1.86096i	−0.105581	+	0.994411i	$0.533670\pi$
$31$	−3235.33	+	9957.32i	−0.604664	+	1.86096i	−0.499083	+	0.866554i	$0.666330\pi$
$32$	1024.00			0.176777
$33$	−755.499	+	2325.19i	−0.120767	+	0.371683i
$34$	4940.86	−	3589.75i	0.733002	−	0.532557i
$35$	9216.55	+	6696.22i	1.27174	+	0.923973i
$36$	−1125.46	−	3463.81i	−0.144735	−	0.445449i
$37$	1341.56	+	4128.89i	0.161103	+	0.495825i	0.998728	−	0.0504209i	$-0.0160563\pi$
$37$	1341.56	+	4128.89i	0.161103	+	0.495825i	−0.837625	+	0.546246i	$0.816056\pi$
$38$	−6549.54			−0.735787
$39$	−627.147	−	455.649i	−0.0660250	−	0.0479699i
$40$	3862.45			0.381692
$41$	−7384.06	−	7831.47i	−0.686018	−	0.727585i
$41$	−7384.06	−	7831.47i	−0.686018	−	0.727585i
$42$	−2960.31			−0.258949
$43$	1628.41	+	1183.11i	0.134305	+	0.0975784i	0.652909	−	0.757436i	$-0.273548\pi$
$43$	1628.41	+	1183.11i	0.134305	+	0.0975784i	−0.518604	+	0.855014i	$0.673548\pi$
$44$	−9977.51			−0.776945
$45$	−4245.15	−	13065.2i	−0.312508	−	0.961802i
$46$	−4322.33	−	13302.8i	−0.301178	−	0.926932i
$47$	18358.6	+	13338.3i	1.21226	+	0.880755i	0.995434	−	0.0954560i	$-0.0304309\pi$
$47$	18358.6	+	13338.3i	1.21226	+	0.880755i	0.216822	+	0.976211i	$0.430431\pi$
$48$	−811.983	+	589.940i	−0.0508679	+	0.0369577i
$49$	5817.66	−	17904.9i	0.346145	−	1.06532i
$50$	2068.85			0.117032
$51$	−1849.77	+	5692.99i	−0.0995844	+	0.306489i
$52$	977.608	−	3008.77i	0.0501368	−	0.154305i
$53$	1158.12	+	3564.32i	0.0566322	+	0.174296i	0.975371	−	0.220569i	$-0.0707914\pi$
$53$	1158.12	+	3564.32i	0.0566322	+	0.174296i	−0.918739	+	0.394865i	$0.870791\pi$
$54$	5970.98	+	4338.17i	0.278652	+	0.202452i
$55$	−37634.4			−1.67756
$56$	−3733.28	−	11489.9i	−0.159082	−	0.489603i
$57$	5193.48	−	3773.28i	0.211724	−	0.153827i
$58$	3743.87	−	11522.4i	0.146134	−	0.449754i
$59$	−30077.6	−	21852.7i	−1.12490	−	0.817287i	−0.139954	−	0.990158i	$-0.544696\pi$
$59$	−30077.6	−	21852.7i	−1.12490	−	0.817287i	−0.984944	+	0.172871i	$0.944696\pi$
$60$	−3062.74	+	2225.21i	−0.109833	+	0.0797981i
$61$	−24701.3	+	17946.5i	−0.849953	+	0.617527i	−0.925133	−	0.379643i	$-0.876047\pi$
$61$	−24701.3	+	17946.5i	−0.849953	+	0.617527i	0.0751799	+	0.997170i	$0.476047\pi$
$62$	33880.8	−	24615.8i	1.11937	−	0.813271i
$63$	−34762.7	+	25256.6i	−1.10347	+	0.801721i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	3687.46	−	11348.8i	0.108254	−	0.333172i
$66$	7911.69	−	5748.18i	0.223568	−	0.162432i
$67$	−7297.82	−	22460.4i	−0.198612	−	0.611266i	−0.999915	−	0.0130074i	$-0.995859\pi$
$67$	−7297.82	−	22460.4i	−0.198612	−	0.611266i	0.801303	−	0.598259i	$-0.204141\pi$
$68$	−24429.0			−0.640668
$69$	11091.3	+	8058.31i	0.280453	+	0.203761i
$70$	−14081.6	−	43338.8i	−0.343485	−	1.05714i
$71$	21538.4	−	66288.4i	0.507070	−	1.56060i	−0.290192	−	0.956968i	$-0.593719\pi$
$71$	21538.4	−	66288.4i	0.507070	−	1.56060i	0.797262	−	0.603633i	$-0.206281\pi$
$72$	−4501.84	+	13855.2i	−0.102343	+	0.314980i
$73$	28933.4			0.635465			0.317733	−	0.948180i	$-0.397079\pi$
$73$	28933.4			0.635465			0.317733	+	0.948180i	$0.397079\pi$
$74$	5366.23	−	16515.6i	0.113917	−	0.350602i
$75$	−1640.50	+	1191.89i	−0.0336762	+	0.0244672i
$76$	21194.8	+	15398.9i	0.420915	+	0.305813i
$77$	36375.8	+	111953.i	0.699175	+	2.15184i
$78$	958.196	+	2949.02i	0.0178327	+	0.0548835i
$79$	10922.1			0.196897			0.0984486	−	0.995142i	$-0.468612\pi$
$79$	10922.1			0.196897			0.0984486	+	0.995142i	$0.468612\pi$
$80$	−12499.1	−	9081.16i	−0.218351	−	0.158641i
$81$	48079.9			0.814237
$82$	5482.43	+	42704.1i	0.0900407	+	0.701351i
$83$	−1312.85			−0.0209179			−0.0104590	−	0.999945i	$-0.503329\pi$
$83$	−1312.85			−0.0209179			−0.0104590	+	0.999945i	$0.503329\pi$
$84$	9579.77	+	6960.11i	0.148135	+	0.107626i
$85$	−92144.1			−1.38331
$86$	−2487.99	−	7657.25i	−0.0362746	−	0.111642i
$87$	3669.53	+	11293.6i	0.0519771	+	0.159969i
$88$	32287.9	+	23458.5i	0.444461	+	0.322919i
$89$	68282.0	−	49609.8i	0.913758	−	0.663884i	−0.0282042	−	0.999602i	$-0.508979\pi$
$89$	68282.0	−	49609.8i	0.913758	−	0.663884i	0.941963	+	0.335718i	$0.108979\pi$
$90$	−16980.6	+	52260.9i	−0.220977	+	0.680096i
$91$	−37324.2			−0.472484
$92$	−17289.3	+	53211.1i	−0.212965	+	0.655440i
$93$	−12684.3	+	39038.4i	−0.152076	+	0.468041i
$94$	−28049.4	−	86327.2i	−0.327419	−	1.00769i
$95$	79945.0	+	58083.4i	0.908829	+	0.660303i
$96$	4014.67			0.0444602
$97$	9083.46	+	27956.0i	0.0980216	+	0.301679i	0.988029	−	0.154266i	$-0.0493012\pi$
$97$	9083.46	+	27956.0i	0.0980216	+	0.301679i	−0.890008	+	0.455945i	$0.849301\pi$
$98$	−60923.3	+	44263.4i	−0.640794	+	0.465564i
$99$	43864.4	−	135001.i	0.449805	−	1.38436i
$100$	−6694.94	−	4864.16i	−0.0669494	−	0.0486416i
$101$	−832.157	+	604.597i	−0.00811712	+	0.00589743i	−0.591836	−	0.806058i	$-0.701597\pi$
$101$	−832.157	+	604.597i	−0.00811712	+	0.00589743i	0.583719	+	0.811956i	$0.301597\pi$
$102$	19371.0	−	14073.9i	0.184354	−	0.133941i
$103$	116184.	−	84412.8i	1.07908	−	0.783998i	0.101558	−	0.994830i	$-0.467617\pi$
$103$	116184.	−	84412.8i	1.07908	−	0.783998i	0.977522	+	0.210832i	$0.0676171\pi$
$104$	−10237.6	+	7438.09i	−0.0928147	+	0.0674338i
$105$	36134.2	+	26253.0i	0.319849	+	0.232384i
$106$	4632.48	−	14257.3i	0.0400450	−	0.123246i
$107$	−164106.	+	119230.i	−1.38568	+	1.00676i	−0.389361	+	0.921085i	$0.627304\pi$
$107$	−164106.	+	119230.i	−1.38568	+	1.00676i	−0.996323	+	0.0856735i	$0.972696\pi$
$108$	−9122.85	−	28077.2i	−0.0752612	−	0.231630i
$109$	−109983.			−0.886662			−0.443331	−	0.896358i	$-0.646203\pi$
$109$	−109983.			−0.886662			−0.443331	+	0.896358i	$0.646203\pi$
$110$	121787.	+	88483.8i	0.959668	+	0.697239i
$111$	5259.67	+	16187.6i	0.0405183	+	0.124702i
$112$	−14933.1	+	45959.4i	−0.112488	+	0.346202i
$113$	57985.0	−	178460.i	0.427189	−	1.31475i	−0.473694	−	0.880689i	$-0.657080\pi$
$113$	57985.0	−	178460.i	0.427189	−	1.31475i	0.900883	−	0.434062i	$-0.142920\pi$
$114$	−25678.0			−0.185054
$115$	−65214.0	+	200708.i	−0.459829	+	1.41521i
$116$	−39206.3	+	28485.1i	−0.270527	+	0.196550i
$117$	36412.3	+	26455.1i	0.245914	+	0.178667i
$118$	45954.5	+	141433.i	0.303825	+	0.935076i
$119$	89062.7	+	274107.i	0.576538	+	1.77440i
$120$	15143.0			0.0959973
$121$	−184309.	−	133909.i	−1.14442	−	0.831467i
$122$	122130.			0.742886
$123$	−28949.7	−	30703.8i	−0.172537	−	0.182991i
$124$	−167516.			−0.978367
$125$	127325.	+	92506.8i	0.728849	+	0.529540i
$126$	171876.			0.964472
$127$	−91272.1	−	280907.i	−0.502145	−	1.54544i	−0.805518	−	0.592571i	$-0.798113\pi$
$127$	−91272.1	−	280907.i	−0.502145	−	1.54544i	0.303374	−	0.952872i	$-0.401887\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	6384.30	+	4638.47i	0.0337784	+	0.0245414i
$130$	−38615.6	+	28055.9i	−0.200403	+	0.145601i
$131$	74067.5	−	227956.i	0.377094	−	1.16058i	−0.564961	−	0.825117i	$-0.691109\pi$
$131$	74067.5	−	227956.i	0.377094	−	1.16058i	0.942055	−	0.335458i	$-0.108891\pi$
$132$	−39117.5			−0.195405
$133$	95512.8	−	293958.i	0.468201	−	1.44098i
$134$	−29191.3	+	89841.6i	−0.140440	+	0.432230i
$135$	−34410.7	−	105905.i	−0.162502	−	0.500130i
$136$	79053.8	+	57435.9i	0.366501	+	0.266279i
$137$	22866.8			0.104089			0.0520443	−	0.998645i	$-0.483426\pi$
$137$	22866.8			0.104089			0.0520443	+	0.998645i	$0.483426\pi$
$138$	−16946.0	−	52154.5i	−0.0757478	−	0.233128i
$139$	−142396.	+	103457.i	−0.625116	+	0.454174i	−0.854705	−	0.519114i	$-0.826262\pi$
$139$	−142396.	+	103457.i	−0.625116	+	0.454174i	0.229589	+	0.973288i	$0.426262\pi$
$140$	−56326.6	+	173355.i	−0.242881	+	0.747510i
$141$	71976.1	+	52293.7i	0.304888	+	0.221514i
$142$	−225553.	+	163874.i	−0.938703	+	0.682008i
$143$	99752.2	−	72474.2i	0.407927	−	0.296376i
$144$	47143.9	−	34252.0i	0.189461	−	0.137651i
$145$	−147883.	+	107443.i	−0.584115	+	0.424385i
$146$	−93630.4	−	68026.4i	−0.363525	−	0.264117i
$147$	22808.5	−	70197.5i	0.0870571	−	0.267934i
$148$	−56195.9	+	40828.7i	−0.210887	+	0.153218i
$149$	152494.	+	469328.i	0.562713	+	1.73185i	0.674649	+	0.738138i	$0.264295\pi$
$149$	152494.	+	469328.i	0.562713	+	1.73185i	−0.111936	+	0.993715i	$0.535705\pi$
$150$	8111.07			0.0294341
$151$	77734.2	+	56477.2i	0.277440	+	0.201572i	0.717800	−	0.696249i	$-0.245149\pi$
$151$	77734.2	+	56477.2i	0.277440	+	0.201572i	−0.440360	+	0.897821i	$0.645149\pi$
$152$	−32382.7	−	99663.8i	−0.113685	−	0.349887i
$153$	107398.	−	330536.i	0.370908	−	1.14154i
$154$	145503.	−	447813.i	0.494392	−	1.52158i
$155$	−631857.			−2.11246
$156$	3832.78	−	11796.1i	0.0126096	−	0.0388085i
$157$	448820.	−	326087.i	1.45319	−	1.05581i	0.468121	−	0.883665i	$-0.344931\pi$
$157$	448820.	−	326087.i	1.45319	−	1.05581i	0.985072	−	0.172142i	$-0.0550687\pi$
$158$	−35344.8	−	25679.5i	−0.112637	−	0.0818358i
$159$	4540.49	+	13974.2i	0.0142433	+	0.0438363i
$160$	19097.0	+	58774.5i	0.0589746	+	0.181505i
$161$	660092.			2.00696
$162$	−155590.	−	113043.i	−0.465794	−	0.338419i
$163$	99039.6			0.291971			0.145986	−	0.989287i	$-0.453365\pi$
$163$	99039.6			0.291971			0.145986	+	0.989287i	$0.453365\pi$
$164$	82661.9	−	151083.i	0.239991	−	0.438639i
$165$	−147548.			−0.421914
$166$	4248.46	+	3086.69i	0.0119663	+	0.00869406i
$167$	−465588.			−1.29185			−0.645923	−	0.763403i	$-0.723527\pi$
$167$	−465588.			−1.29185			−0.645923	+	0.763403i	$0.723527\pi$
$168$	−14636.6	−	45046.8i	−0.0400098	−	0.123138i
$169$	−102655.	−	315939.i	−0.276479	−	0.850915i
$170$	298185.	+	216644.i	0.791340	+	0.574942i
$171$	−301534.	+	219077.i	−0.788581	+	0.572938i
$172$	−9951.96	+	30629.0i	−0.0256500	+	0.0789426i
$173$	105494.			0.267987			0.133993	−	0.990982i	$-0.457220\pi$
$173$	105494.			0.267987			0.133993	+	0.990982i	$0.457220\pi$
$174$	14678.1	−	45174.6i	0.0367534	−	0.113115i
$175$	−30170.3	+	92854.6i	−0.0744705	+	0.229197i
$176$	−49331.5	−	151827.i	−0.120045	−	0.369460i
$177$	−117921.	−	85674.9i	−0.282917	−	0.205551i
$178$	−337605.			−0.798654
$179$	70627.6	+	217369.i	0.164756	+	0.507068i	0.999018	−	0.0443007i	$-0.0141060\pi$
$179$	70627.6	+	217369.i	0.164756	+	0.507068i	−0.834262	+	0.551368i	$0.814106\pi$
$180$	177823.	−	129196.i	0.409079	−	0.297213i
$181$	133109.	−	409668.i	0.302003	−	0.929471i	−0.678775	−	0.734346i	$-0.737489\pi$
$181$	133109.	−	409668.i	0.302003	−	0.929471i	0.980778	−	0.195125i	$-0.0625112\pi$
$182$	120784.	+	87754.5i	0.270290	+	0.196377i
$183$	−96843.2	+	70360.7i	−0.213767	+	0.155311i
$184$	181056.	−	131545.i	0.394248	−	0.286438i
$185$	−211966.	+	154003.i	−0.455342	+	0.330825i
$186$	132832.	−	96508.2i	0.281527	−	0.204542i
$187$	−770273.	−	559636.i	−1.61080	−	1.17031i
$188$	−112198.	+	345309.i	−0.231520	+	0.712546i
$189$	−281783.	+	204727.i	−0.573799	+	0.416889i
$190$	−122145.	−	375924.i	−0.245466	−	0.755468i
$191$	−529805.			−1.05083			−0.525415	−	0.850846i	$-0.676090\pi$
$191$	−529805.			−1.05083			−0.525415	+	0.850846i	$0.676090\pi$
$192$	−12991.7	−	9439.04i	−0.0254340	−	0.0184788i
$193$	128060.	+	394127.i	0.247468	+	0.761628i	0.995221	+	0.0976510i	$0.0311329\pi$
$193$	128060.	+	394127.i	0.247468	+	0.761628i	−0.747753	+	0.663977i	$0.768867\pi$
$194$	36333.8	−	111824.i	0.0693117	−	0.213320i
$195$	14457.0	−	44493.9i	0.0272264	−	0.0837943i
$196$	301221.			0.560074
$197$	120001.	−	369325.i	0.220302	−	0.678021i	−0.778432	−	0.627729i	$-0.783985\pi$
$197$	120001.	−	369325.i	0.220302	−	0.678021i	0.998735	−	0.0502922i	$-0.0160153\pi$
$198$	−459354.	+	333740.i	−0.832693	+	0.604987i
$199$	543900.	+	395166.i	0.973613	+	0.707371i	0.956272	−	0.292479i	$-0.0944800\pi$
$199$	543900.	+	395166.i	0.973613	+	0.707371i	0.0173406	+	0.999850i	$0.494480\pi$
$200$	10229.0	+	31481.5i	0.0180824	+	0.0556519i
$201$	−28611.6	−	88057.6i	−0.0499520	−	0.153736i
$202$	4114.41			0.00709462
$203$	462556.	+	336067.i	0.787815	+	0.572381i
$204$	−95775.5			−0.161131
$205$	311794.	−	569875.i	0.518183	−	0.947098i
$206$	−574446.			−0.943151
$207$	−643964.	−	467867.i	−1.04457	−	0.758921i
$208$	50617.7			0.0811230
$209$	315526.	+	971090.i	0.499655	+	1.53778i
$210$	−55208.1	−	169913.i	−0.0863882	−	0.265875i
$211$	467094.	+	339364.i	0.722267	+	0.524758i	0.887108	−	0.461562i	$-0.152711\pi$
$211$	467094.	+	339364.i	0.722267	+	0.524758i	−0.164840	+	0.986320i	$0.552711\pi$
$212$	−48511.9	+	35246.0i	−0.0741325	+	0.0538604i
$213$	84442.9	−	259889.i	0.127531	−	0.392499i
$214$	811383.			1.21113
$215$	−37538.0	+	115530.i	−0.0553828	+	0.170451i
$216$	−36491.4	+	112309.i	−0.0532177	+	0.163787i
$217$	610726.	+	1.87962e6i	0.880435	+	2.70970i
$218$	355911.	+	258585.i	0.507225	+	0.368521i
$219$	113435.			0.159823
$220$	−186075.	−	572679.i	−0.259197	−	0.797727i
$221$	244234.	−	177446.i	0.336376	−	0.244391i
$222$	21038.7	−	64750.4i	0.0286508	−	0.0881780i
$223$	−96088.0	−	69812.0i	−0.129392	−	0.0940087i	0.521207	−	0.853430i	$-0.325482\pi$
$223$	−96088.0	−	69812.0i	−0.129392	−	0.0940087i	−0.650599	+	0.759422i	$0.725482\pi$
$224$	156382.	−	113618.i	0.208241	−	0.151296i
$225$	95247.7	−	69201.5i	0.125429	−	0.0911295i
$226$	−607227.	+	441176.i	−0.790824	+	0.574568i
$227$	−905716.	+	658041.i	−1.16661	+	0.847595i	−0.990600	−	0.136792i	$-0.956321\pi$
$227$	−905716.	+	658041.i	−1.16661	+	0.847595i	−0.176015	+	0.984387i	$0.556321\pi$
$228$	83095.6	+	60372.5i	0.105862	+	0.0769134i
$229$	−31246.7	+	96167.6i	−0.0393746	+	0.121183i	−0.968812	−	0.247798i	$-0.920293\pi$
$229$	−31246.7	+	96167.6i	−0.0393746	+	0.121183i	0.929437	+	0.368980i	$0.120293\pi$
$230$	682930.	−	496178.i	0.851249	−	0.618469i
$231$	142614.	+	438921.i	0.175846	+	0.541198i
$232$	193847.			0.236449
$233$	17691.6	+	12853.7i	0.0213489	+	0.0155109i	0.598409	−	0.801191i	$-0.295800\pi$
$233$	17691.6	+	12853.7i	0.0213489	+	0.0155109i	−0.577060	+	0.816702i	$0.695800\pi$
$234$	−55633.0	−	171221.i	−0.0664191	−	0.204417i
$235$	−423201.	+	1.30248e6i	−0.499892	+	1.53851i
$236$	183818.	−	565734.i	0.214837	−	0.661199i
$237$	42821.0			0.0495206
$238$	356251.	−	1.09643e6i	0.407674	−	1.25469i
$239$	1.00056e6	−	726950.i	1.13305	−	0.823208i	0.146913	−	0.989149i	$-0.453066\pi$
$239$	1.00056e6	−	726950.i	1.13305	−	0.823208i	0.986136	+	0.165941i	$0.0530662\pi$
$240$	−49003.8	−	35603.3i	−0.0549163	−	0.0398990i
$241$	−102361.	−	315034.i	−0.113525	−	0.349394i	0.878112	−	0.478456i	$-0.158803\pi$
$241$	−102361.	−	315034.i	−0.113525	−	0.349394i	−0.991637	+	0.129062i	$0.958803\pi$
$242$	281600.	+	866675.i	0.309096	+	0.951301i
$243$	636868.			0.691885
$244$	−395221.	−	287145.i	−0.424977	−	0.308764i
$245$	1.13618e6			1.20930
$246$	21494.3	+	167425.i	0.0226457	+	0.176393i
$247$	−323753.			−0.337654
$248$	542093.	+	393854.i	0.559686	+	0.406636i
$249$	−5147.11			−0.00526096
$250$	−194535.	−	598716.i	−0.196855	−	0.605858i
$251$	−28617.4	−	88075.4i	−0.0286712	−	0.0882410i	0.935697	−	0.352805i	$-0.114772\pi$
$251$	−28617.4	−	88075.4i	−0.0286712	−	0.0882410i	−0.964368	+	0.264564i	$0.914772\pi$
$252$	−556203.	−	404105.i	−0.551737	−	0.400861i
$253$	−1.76415e6	+	1.28173e6i	−1.73274	+	1.25891i
$254$	−365089.	+	1.12363e6i	−0.355070	+	1.09279i
$255$	−361258.			−0.347910
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	157642.	−	485172.i	0.148881	−	0.458208i	−0.848609	−	0.529021i	$-0.822559\pi$
$257$	157642.	−	485172.i	0.148881	−	0.458208i	0.997490	+	0.0708127i	$0.0225593\pi$
$258$	−9754.34	−	30020.8i	−0.00912323	−	0.0280784i
$259$	662999.	+	481697.i	0.614134	+	0.446195i
$260$	190926.			0.175159
$261$	−213053.	−	655711.i	−0.193592	−	0.595815i
$262$	−775645.	+	563539.i	−0.698087	+	0.507190i
$263$	−376605.	+	1.15907e6i	−0.335735	+	1.03329i	0.630624	+	0.776088i	$0.282799\pi$
$263$	−376605.	+	1.15907e6i	−0.335735	+	1.03329i	−0.966359	+	0.257197i	$0.917201\pi$
$264$	126587.	+	91970.9i	0.111784	+	0.0812158i
$265$	−182983.	+	132945.i	−0.160065	+	0.116294i
$266$	−1.00022e6	+	726705.i	−0.866748	+	0.629729i
$267$	267705.	−	194499.i	0.229815	−	0.166970i
$268$	305695.	−	222101.i	0.259987	−	0.188892i
$269$	1.13118e6	+	821848.i	0.953124	+	0.692485i	0.951544	−	0.307513i	$-0.0994969\pi$
$269$	1.13118e6	+	821848.i	0.953124	+	0.692485i	0.00158051	+	0.999999i	$0.499497\pi$
$270$	−137643.	+	423621.i	−0.114906	+	0.353645i
$271$	−277657.	+	201729.i	−0.229660	+	0.166858i	−0.696664	−	0.717397i	$-0.745333\pi$
$271$	−277657.	+	201729.i	−0.229660	+	0.166858i	0.467004	+	0.884255i	$0.345333\pi$
$272$	−120783.	−	371733.i	−0.0989886	−	0.304656i
$273$	−146332.			−0.118832
$274$	−73998.4	−	53763.0i	−0.0595451	−	0.0432620i
$275$	−99667.5	−	306745.i	−0.0794734	−	0.244594i
$276$	−67784.1	+	208618.i	−0.0535618	+	0.164846i
$277$	342382.	−	1.05374e6i	0.268109	−	0.825155i	−0.722852	−	0.691003i	$-0.757169\pi$
$277$	342382.	−	1.05374e6i	0.268109	−	0.825155i	0.990961	−	0.134152i	$-0.0428309\pi$
$278$	704045.			0.546372
$279$	736455.	−	2.26658e6i	0.566416	−	1.74325i
$280$	589859.	−	428558.i	0.449628	−	0.326674i
$281$	616680.	+	448044.i	0.465902	+	0.338497i	0.795842	−	0.605504i	$-0.207029\pi$
$281$	616680.	+	448044.i	0.465902	+	0.338497i	−0.329940	+	0.944002i	$0.607029\pi$
$282$	−109970.	−	338452.i	−0.0823474	−	0.253439i
$283$	−481888.	−	1.48310e6i	−0.357668	−	1.10079i	−0.954446	−	0.298382i	$-0.903553\pi$
$283$	−481888.	−	1.48310e6i	−0.357668	−	1.10079i	0.596779	−	0.802406i	$-0.296447\pi$
$284$	1.11520e6			0.820457
$285$	313430.	+	227720.i	0.228575	+	0.166069i
$286$	−493202.			−0.356541
$287$	−1.99661e6	−	376696.i	−1.43083	−	0.269952i
$288$	−233092.			−0.165595
$289$	−737251.	−	535644.i	−0.519243	−	0.377252i
$290$	731174.			0.510536
$291$	35612.3	+	109604.i	0.0246529	+	0.0758738i
$292$	143054.	+	440276.i	0.0981848	+	0.302182i
$293$	−920123.	−	668509.i	−0.626148	−	0.454923i	0.228916	−	0.973446i	$-0.426482\pi$
$293$	−920123.	−	668509.i	−0.626148	−	0.454923i	−0.855064	+	0.518523i	$0.826482\pi$
$294$	−238854.	+	173538.i	−0.161163	+	0.117092i
$295$	693347.	−	2.13390e6i	0.463869	−	1.42764i
$296$	277848.			0.184322
$297$	355560.	−	1.09430e6i	0.233895	−	0.719856i
$298$	609976.	−	1.87731e6i	0.397898	−	1.22461i
$299$	−213659.	−	657575.i	−0.138211	−	0.425370i
$300$	−26248.0	−	19070.3i	−0.0168381	−	0.0122336i
$301$	379957.			0.241723
$302$	−118767.	−	365528.i	−0.0749341	−	0.230623i
$303$	−3262.53	+	2370.37i	−0.00204149	+	0.00148323i
$304$	−129531.	+	398655.i	−0.0803877	+	0.247408i
$305$	−1.49074e6	−	1.08309e6i	−0.917598	−	0.666674i
$306$	−1.12468e6	+	817131.i	−0.686637	+	0.498871i
$307$	−1.02012e6	+	741162.i	−0.617741	+	0.448815i	−0.852132	−	0.523327i	$-0.824690\pi$
$307$	−1.02012e6	+	741162.i	−0.617741	+	0.448815i	0.234391	+	0.972142i	$0.424690\pi$
$308$	−1.52373e6	+	1.10705e6i	−0.915232	+	0.664955i
$309$	455508.	−	330946.i	0.271394	−	0.197179i
$310$	2.04473e6	+	1.48558e6i	1.20846	+	0.877997i
$311$	70400.4	−	216670.i	0.0412738	−	0.127028i	−0.928296	−	0.371841i	$-0.878727\pi$
$311$	70400.4	−	216670.i	0.0412738	−	0.127028i	0.969570	+	0.244813i	$0.0787267\pi$
$312$	−40137.4	+	29161.6i	−0.0233433	+	0.0169599i
$313$	−107540.	−	330974.i	−0.0620453	−	0.190956i	0.915229	−	0.402934i	$-0.132010\pi$
$313$	−107540.	−	330974.i	−0.0620453	−	0.190956i	−0.977274	+	0.211978i	$0.932010\pi$
$314$	−2.21909e6			−1.27014
$315$	−2.09796e6	−	1.52425e6i	−1.19130	−	0.865528i
$316$	54002.0	+	166201.i	0.0304223	+	0.0936302i
$317$	−495741.	+	1.52573e6i	−0.277081	+	0.852767i	0.711581	+	0.702605i	$0.247980\pi$
$317$	−495741.	+	1.52573e6i	−0.277081	+	0.852767i	−0.988661	+	0.150162i	$0.952020\pi$
$318$	18162.0	−	55896.7i	0.0100715	−	0.0309969i
$319$	−1.88878e6			−1.03921
$320$	76388.0	−	235098.i	0.0417013	−	0.128344i
$321$	−643388.	+	467449.i	−0.348506	+	0.253205i
$322$	−2.13610e6	−	1.55197e6i	−1.14811	−	0.834148i
$323$	772536.	+	2.37762e6i	0.412014	+	1.26805i
$324$	237720.	+	731627.i	0.125807	+	0.387193i
$325$	102266.			0.0537060
$326$	−320499.	−	232856.i	−0.167025	−	0.121351i
$327$	−431195.			−0.223000
$328$	−622718.	+	294566.i	−0.319600	+	0.151182i
$329$	4.28360e6			2.18182
$330$	477476.	+	346907.i	0.241361	+	0.175359i
$331$	1.25100e6			0.627605			0.313803	−	0.949488i	$-0.398397\pi$
$331$	1.25100e6			0.627605			0.313803	+	0.949488i	$0.398397\pi$
$332$	−6491.07	−	19977.5i	−0.00323200	−	0.00994707i
$333$	−305377.	−	939855.i	−0.150913	−	0.464462i
$334$	1.50667e6	+	1.09466e6i	0.739015	+	0.536926i
$335$	1.15306e6	−	837746.i	0.561357	−	0.407850i
$336$	−58546.4	+	180187.i	−0.0282912	+	0.0870714i
$337$	1.00780e6			0.483390			0.241695	−	0.970352i	$-0.422297\pi$
$337$	1.00780e6			0.483390			0.241695	+	0.970352i	$0.422297\pi$
$338$	−410619.	+	1.26375e6i	−0.195500	+	0.601688i
$339$	227334.	−	699664.i	0.107440	−	0.330666i
$340$	−455586.	−	1.40215e6i	−0.213734	−	0.657804i
$341$	−5.28197e6	−	3.83758e6i	−2.45986	−	1.78719i
$342$	1.49087e6			0.689245
$343$	−117793.	−	362529.i	−0.0540609	−	0.166382i
$344$	104218.	−	75719.0i	0.0474841	−	0.0344992i
$345$	−255676.	+	786891.i	−0.115649	+	0.355932i
$346$	−341386.	−	248032.i	−0.153305	−	0.111382i
$347$	853721.	−	620265.i	0.380621	−	0.276537i	−0.380981	−	0.924583i	$-0.624414\pi$
$347$	853721.	−	620265.i	0.380621	−	0.276537i	0.761601	+	0.648046i	$0.224414\pi$
$348$	−153711.	+	111678.i	−0.0680389	+	0.0494331i
$349$	1.57929e6	−	1.14742e6i	0.694063	−	0.504266i	−0.183930	−	0.982939i	$-0.558882\pi$
$349$	1.57929e6	−	1.14742e6i	0.694063	−	0.504266i	0.877993	+	0.478673i	$0.158882\pi$
$350$	315947.	−	229549.i	0.137862	−	0.100163i
$351$	295154.	+	214442.i	0.127874	+	0.0929055i
$352$	−197326.	+	607307.i	−0.0848844	+	0.261247i
$353$	1.65202e6	−	1.20027e6i	0.705634	−	0.512673i	−0.176128	−	0.984367i	$-0.556357\pi$
$353$	1.65202e6	−	1.20027e6i	0.705634	−	0.512673i	0.881762	+	0.471694i	$0.156357\pi$
$354$	180168.	+	554500.i	0.0764134	+	0.235176i
$355$	4.20643e6			1.77151
$356$	1.09251e6	+	793757.i	0.456879	+	0.331942i
$357$	349177.	+	1.07465e6i	0.145002	+	0.446271i
$358$	282510.	−	869478.i	0.116500	−	0.358551i
$359$	−914597.	+	2.81484e6i	−0.374536	+	1.15270i	0.569255	+	0.822161i	$0.307232\pi$
$359$	−914597.	+	2.81484e6i	−0.374536	+	1.15270i	−0.943791	+	0.330542i	$0.892768\pi$
$360$	−879206.			−0.357548
$361$	63328.0	−	194904.i	0.0255757	−	0.0787140i
$362$	−1.39394e6	+	1.01276e6i	−0.559078	+	0.406194i
$363$	−722598.	−	524998.i	−0.287826	−	0.209118i
$364$	−184541.	−	567959.i	−0.0730028	−	0.224680i
$365$	539590.	+	1.66069e6i	0.211998	+	0.652463i
$366$	478819.			0.186839
$367$	2.42036e6	+	1.75849e6i	0.938024	+	0.681515i	0.947944	−	0.318436i	$-0.103158\pi$
$367$	2.42036e6	+	1.75849e6i	0.938024	+	0.681515i	−0.00991989	+	0.999951i	$0.503158\pi$
$368$	−895192.			−0.344585
$369$	1.68083e6	+	1.78267e6i	0.642624	+	0.681561i
$370$	1.04802e6			0.397984
$371$	572343.	+	415832.i	0.215885	+	0.156849i
$372$	−656758.			−0.246064
$373$	241919.	+	744551.i	0.0900323	+	0.277091i	0.985927	−	0.167175i	$-0.0534645\pi$
$373$	241919.	+	744551.i	0.0900323	+	0.277091i	−0.895895	+	0.444266i	$0.853464\pi$
$374$	1.17687e6	+	3.62204e6i	0.435062	+	1.33898i
$375$	499185.	+	362679.i	0.183309	+	0.133182i
$376$	1.17495e6	−	853650.i	0.428597	−	0.311394i
$377$	185065.	−	569570.i	0.0670610	−	0.206392i
$378$	1.39321e6			0.501518
$379$	−725052.	+	2.23148e6i	−0.259281	+	0.797986i	0.733675	+	0.679501i	$0.237804\pi$
$379$	−725052.	+	2.23148e6i	−0.259281	+	0.797986i	−0.992956	+	0.118485i	$0.962196\pi$
$380$	−488580.	+	1.50370e6i	−0.173571	+	0.534196i
$381$	−357839.	−	1.10131e6i	−0.126292	−	0.388686i
$382$	1.71448e6	+	1.24565e6i	0.601139	+	0.436753i
$383$	1.94711e6			0.678256			0.339128	−	0.940740i	$-0.389868\pi$
$383$	1.94711e6			0.678256			0.339128	+	0.940740i	$0.389868\pi$
$384$	19849.6	+	61090.8i	0.00686948	+	0.0211421i
$385$	−5.74739e6	+	4.17572e6i	−1.97615	+	1.43575i
$386$	512239.	−	1.57651e6i	0.174986	−	0.538553i
$387$	−370674.	−	269310.i	−0.125810	−	0.0914061i
$388$	−380493.	+	276444.i	−0.128312	+	0.0932241i
$389$	3.20855e6	−	2.33115e6i	1.07507	−	0.781081i	0.0982498	−	0.995162i	$-0.468676\pi$
$389$	3.20855e6	−	2.33115e6i	1.07507	−	0.781081i	0.976816	+	0.214081i	$0.0686756\pi$
$390$	−151395.	+	109995.i	−0.0504023	+	0.0366194i
$391$	−4.31935e6	+	3.13819e6i	−1.42882	+	1.03810i
$392$	−974773.	−	708214.i	−0.320397	−	0.232782i
$393$	290387.	−	893719.i	0.0948409	−	0.291890i
$394$	−1.25667e6	+	913021.i	−0.407830	+	0.296306i
$395$	203691.	+	626897.i	0.0656870	+	0.202164i
$396$	2.27117e6			0.727800
$397$	−647426.	−	470382.i	−0.206164	−	0.149787i	0.479912	−	0.877317i	$-0.340669\pi$
$397$	−647426.	−	470382.i	−0.206164	−	0.149787i	−0.686077	+	0.727529i	$0.740669\pi$
$398$	−831005.	−	2.55757e6i	−0.262964	−	0.809319i
$399$	374465.	−	1.15248e6i	0.117755	−	0.362412i
$400$	40915.8	−	125926.i	0.0127862	−	0.0393519i
$401$	588087.			0.182633			0.0913167	−	0.995822i	$-0.470892\pi$
$401$	588087.			0.182633			0.0913167	+	0.995822i	$0.470892\pi$
$402$	−114447.	+	352230.i	−0.0353214	+	0.108708i
$403$	1.67477e6	−	1.21679e6i	0.513681	−	0.373211i
$404$	−13314.5	−	9673.56i	−0.00405856	−	0.00294872i
$405$	896661.	+	2.75964e6i	0.271638	+	0.836017i
$406$	−706723.	−	2.17507e6i	−0.212781	−	0.654874i
$407$	−2.70725e6			−0.810108
$408$	309936.	+	225182.i	0.0921768	+	0.0669704i
$409$	−2.60497e6			−0.770006			−0.385003	−	0.922915i	$-0.625800\pi$
$409$	−2.60497e6			−0.770006			−0.385003	+	0.922915i	$0.625800\pi$
$410$	−2.34884e6	+	1.11108e6i	−0.690072	+	0.326427i
$411$	89650.8			0.0261788
$412$	1.85895e6	+	1.35060e6i	0.539540	+	0.391999i
$413$	−7.01801e6			−2.02460
$414$	983889.	+	3.02810e6i	0.282127	+	0.868299i
$415$	−24483.8	−	75353.5i	−0.00697845	−	0.0214775i
$416$	−163802.	−	119009.i	−0.0464074	−	0.0337169i
$417$	−558274.	+	405610.i	−0.157220	+	0.114227i
$418$	1.26211e6	−	3.88436e6i	0.353309	−	1.08737i
$419$	6.25415e6			1.74034			0.870169	−	0.492754i	$-0.164010\pi$
$419$	6.25415e6			1.74034			0.870169	+	0.492754i	$0.164010\pi$
$420$	−220832.	+	679652.i	−0.0610857	+	0.188002i
$421$	154742.	−	476246.i	0.0425503	−	0.130956i	−0.927525	−	0.373762i	$-0.878068\pi$
$421$	154742.	−	476246.i	0.0425503	−	0.130956i	0.970075	+	0.242806i	$0.0780677\pi$
$422$	−713656.	−	2.19641e6i	−0.195078	−	0.600388i
$423$	−4.17894e6	−	3.03618e6i	−1.13557	−	0.825043i
$424$	239856.			0.0647942
$425$	−244026.	−	751035.i	−0.0655336	−	0.201692i
$426$	−884298.	+	642480.i	−0.236088	+	0.171528i
$427$	−1.78104e6	+	5.48146e6i	−0.472719	+	1.45488i
$428$	−2.62569e6	−	1.90768e6i	−0.692842	−	0.503379i
$429$	391086.	−	284140.i	0.102596	−	0.0745400i
$430$	393103.	−	285606.i	0.102526	−	0.0744897i
$431$	−76108.5	+	55296.0i	−0.0197351	+	0.0143384i	−0.597609	−	0.801788i	$-0.703883\pi$
$431$	−76108.5	+	55296.0i	−0.0197351	+	0.0143384i	0.577874	+	0.816126i	$0.303883\pi$
$432$	382143.	−	277643.i	0.0985182	−	0.0715777i
$433$	1.83933e6	+	1.33635e6i	0.471454	+	0.342532i	0.798008	−	0.602647i	$-0.205887\pi$
$433$	1.83933e6	+	1.33635e6i	0.471454	+	0.342532i	−0.326553	+	0.945179i	$0.605887\pi$
$434$	2.44291e6	−	7.51849e6i	0.622562	−	1.91605i
$435$	−579786.	+	421239.i	−0.146908	+	0.106735i
$436$	−543784.	−	1.67360e6i	−0.136997	−	0.421633i
$437$	5.72568e6			1.43425
$438$	−367085.	−	266703.i	−0.0914283	−	0.0664266i
$439$	308382.	+	949103.i	0.0763709	+	0.235045i	0.981953	−	0.189126i	$-0.0605654\pi$
$439$	308382.	+	949103.i	0.0763709	+	0.235045i	−0.905582	+	0.424171i	$0.860565\pi$
$440$	−744299.	+	2.29072e6i	−0.183280	+	0.564078i
$441$	−1.32427e6	+	4.07568e6i	−0.324250	+	0.997938i
$442$	−1.20756e6			−0.294003
$443$	390159.	−	1.20079e6i	0.0944565	−	0.290707i	−0.892655	−	0.450740i	$-0.851160\pi$
$443$	390159.	−	1.20079e6i	0.0944565	−	0.290707i	0.987112	+	0.160033i	$0.0511601\pi$
$444$	−220320.	+	160072.i	−0.0530391	+	0.0385352i
$445$	4.12087e6	+	2.99399e6i	0.986482	+	0.716721i
$446$	146809.	+	451833.i	0.0349475	+	0.107557i
$447$	597864.	+	1.84004e6i	0.141525	+	0.435569i
$448$	−773193.			−0.182009
$449$	−6.57959e6	−	4.78035e6i	−1.54022	−	1.11904i	−0.950198	−	0.311648i	$-0.899119\pi$
$449$	−6.57959e6	−	4.78035e6i	−1.54022	−	1.11904i	−0.590022	−	0.807387i	$-0.700881\pi$
$450$	−470930.			−0.109629
$451$	6.06755e6	−	2.87016e6i	1.40466	−	0.664453i
$452$	3.00230e6			0.691206
$453$	304762.	+	221423.i	0.0697776	+	0.0506964i
$454$	4.47811e6			1.01966
$455$	−696075.	−	2.14230e6i	−0.157626	−	0.485122i
$456$	−126959.	−	390739.i	−0.0285924	−	0.0879984i
$457$	3.35661e6	+	2.43872e6i	0.751814	+	0.546225i	0.896389	−	0.443269i	$-0.146181\pi$
$457$	3.35661e6	+	2.43872e6i	0.751814	+	0.546225i	−0.144575	+	0.989494i	$0.546181\pi$
$458$	327220.	−	237739.i	0.0728914	−	0.0529587i
$459$	870554.	−	2.67929e6i	0.192870	−	0.593592i
$460$	−3.37659e6			−0.744019
$461$	−2.03911e6	+	6.27575e6i	−0.446878	+	1.37535i	0.433533	+	0.901138i	$0.357267\pi$
$461$	−2.03911e6	+	6.27575e6i	−0.446878	+	1.37535i	−0.880411	+	0.474212i	$0.842733\pi$
$462$	570456.	−	1.75568e6i	0.124342	−	0.382685i
$463$	−1.16094e6	−	3.57302e6i	−0.251686	−	0.774610i	−0.994465	−	0.105073i	$-0.966493\pi$
$463$	−1.16094e6	−	3.57302e6i	−0.251686	−	0.774610i	0.742779	−	0.669537i	$-0.233507\pi$
$464$	−627301.	−	455761.i	−0.135264	−	0.0982748i
$465$	−2.47724e6			−0.531295
$466$	−27030.3	−	83190.7i	−0.00576615	−	0.0177464i
$467$	−969773.	+	704581.i	−0.205768	+	0.149499i	−0.685897	−	0.727699i	$-0.740590\pi$
$467$	−969773.	+	704581.i	−0.205768	+	0.149499i	0.480129	+	0.877198i	$0.340590\pi$
$468$	−222532.	+	684884.i	−0.0469654	+	0.144545i
$469$	−3.60659e6	−	2.62034e6i	−0.757120	−	0.550080i
$470$	4.43181e6	−	3.21990e6i	0.925416	−	0.672354i
$471$	1.75963e6	−	1.27845e6i	0.365485	−	0.265540i
$472$	−1.92497e6	+	1.39857e6i	−0.397712	+	0.288954i
$473$	−1.01547e6	+	737781.i	−0.208696	+	0.151626i
$474$	−138572.	−	100678.i	−0.0283288	−	0.0205821i
$475$	−261699.	+	805427.i	−0.0532192	+	0.163792i
$476$	−3.73071e6	+	2.71052e6i	−0.754699	+	0.548321i
$477$	−263622.	−	811344.i	−0.0530500	−	0.163271i
$478$	−4.94704e6			−0.990321
$479$	5.21919e6	+	3.79196e6i	1.03936	+	0.755137i	0.970160	−	0.242467i	$-0.0779565\pi$
$479$	5.21919e6	+	3.79196e6i	1.03936	+	0.755137i	0.0691965	+	0.997603i	$0.477956\pi$
$480$	74871.1	+	230430.i	0.0148324	+	0.0456494i
$481$	265260.	−	816386.i	0.0522768	−	0.160891i
$482$	−409443.	+	1.26014e6i	−0.0802742	+	0.247059i
$483$	2.58794e6			0.504761
$484$	1.12640e6	−	3.46670e6i	0.218564	−	0.672671i
$485$	−1.43519e6	+	1.04273e6i	−0.277048	+	0.201287i
$486$	−2.06095e6	−	1.49737e6i	−0.395801	−	0.287566i
$487$	−1.49854e6	−	4.61204e6i	−0.286317	−	0.881192i	−0.986001	−	0.166740i	$-0.946676\pi$
$487$	−1.49854e6	−	4.61204e6i	−0.286317	−	0.881192i	0.699684	−	0.714452i	$-0.253324\pi$
$488$	603843.	+	1.85844e6i	0.114782	+	0.353263i
$489$	388292.			0.0734321
$490$	−3.67677e6	−	2.67133e6i	−0.691792	−	0.502617i
$491$	−6.55084e6			−1.22629			−0.613145	−	0.789971i	$-0.710096\pi$
$491$	−6.55084e6			−1.22629			−0.613145	+	0.789971i	$0.710096\pi$
$492$	324082.	−	592333.i	0.0603590	−	0.110320i
$493$	−4.62449e6			−0.856932
$494$	1.04769e6	+	761189.i	0.193159	+	0.140338i
$495$	8.56668e6			1.57145
$496$	−828244.	−	2.54907e6i	−0.151166	−	0.465241i
$497$	−4.06576e6	−	1.25131e7i	−0.738331	−	2.27235i
$498$	16656.4	+	12101.6i	0.00300959	+	0.00218660i
$499$	3.88228e6	−	2.82064e6i	0.697967	−	0.507103i	−0.181302	−	0.983427i	$-0.558031\pi$
$499$	3.88228e6	−	2.82064e6i	0.697967	−	0.507103i	0.879270	+	0.476325i	$0.158031\pi$
$500$	−778139.	+	2.39487e6i	−0.139198	+	0.428407i
$501$	−1.82537e6			−0.324905
$502$	−114470.	+	352302.i	−0.0202736	+	0.0623958i
$503$	−556814.	+	1.71370e6i	−0.0981273	+	0.302005i	−0.988056	−	0.154095i	$-0.950754\pi$
$503$	−556814.	+	1.71370e6i	−0.0981273	+	0.302005i	0.889929	+	0.456100i	$0.150754\pi$
$504$	849803.	+	2.61543e6i	0.149019	+	0.458634i
$505$	−50221.3	−	36487.9i	−0.00876313	−	0.00636679i
$506$	8.72245e6			1.51447
$507$	−402465.	−	1.23866e6i	−0.0695358	−	0.214009i
$508$	3.82326e6	−	2.77776e6i	0.657316	−	0.477568i
$509$	−87038.2	+	267876.i	−0.0148907	+	0.0458289i	−0.958226	−	0.286013i	$-0.907670\pi$
$509$	−87038.2	+	267876.i	−0.0148907	+	0.0458289i	0.943335	+	0.331842i	$0.107670\pi$
$510$	1.16905e6	+	849368.i	0.199026	+	0.144601i
$511$	4.41860e6	−	3.21030e6i	0.748571	−	0.543868i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−2.44420e6	+	1.77582e6i	−0.410056	+	0.297923i
$514$	−1.65085e6	+	1.19941e6i	−0.275613	+	0.200244i
$515$	7.01180e6	+	5.09437e6i	1.16496	+	0.846394i
$516$	−39017.4	+	120083.i	−0.00645110	+	0.0198544i
$517$	−1.14483e7	+	8.31768e6i	−1.88371	+	1.36860i
$518$	−1.01297e6	−	3.11761e6i	−0.165872	−	0.510501i
$519$	413597.			0.0673999
$520$	−617850.	−	448894.i	−0.100202	−	0.0728007i
$521$	−1.42590e6	−	4.38848e6i	−0.230142	−	0.708304i	−0.997729	−	0.0673591i	$-0.978543\pi$
$521$	−1.42590e6	−	4.38848e6i	−0.230142	−	0.708304i	0.767587	−	0.640945i	$-0.221457\pi$
$522$	−852214.	+	2.62284e6i	−0.136890	+	0.421305i
$523$	−2.10292e6	+	6.47214e6i	−0.336178	+	1.03465i	0.629961	+	0.776627i	$0.283071\pi$
$523$	−2.10292e6	+	6.47214e6i	−0.336178	+	1.03465i	−0.966139	+	0.258023i	$0.916929\pi$
$524$	3.83500e6			0.610150
$525$	−118285.	+	364043.i	−0.0187297	+	0.0576441i
$526$	3.94385e6	−	2.86538e6i	0.621522	−	0.451562i
$527$	−1.29324e7	−	9.39593e6i	−2.02839	−	1.47371i
$528$	−193408.	−	595248.i	−0.0301918	−	0.0929208i
$529$	1.78969e6	+	5.50810e6i	0.278060	+	0.855782i
$530$	904718.			0.139902
$531$	6.84654e6	+	4.97430e6i	1.05374	+	0.765589i
$532$	4.94538e6			0.757566
$533$	271004.	+	2.11092e6i	0.0413198	+	0.321851i
$534$	−1.32360e6			−0.200865
$535$	−9.90390e6	−	7.19561e6i	−1.49597	−	1.08688i
$536$	−1.51144e6			−0.227237
$537$	276901.	+	852212.i	0.0414370	+	0.127530i
$538$	−1.72828e6	−	5.31911e6i	−0.257430	−	0.792288i
$539$	9.49786e6	+	6.90060e6i	1.40817	+	1.02309i
$540$	1.44141e6	−	1.04725e6i	0.212718	−	0.154549i
$541$	−2.89341e6	+	8.90500e6i	−0.425027	+	1.30810i	0.477941	+	0.878392i	$0.341383\pi$
$541$	−2.89341e6	+	8.90500e6i	−0.425027	+	1.30810i	−0.902968	+	0.429707i	$0.858617\pi$
$542$	1.37281e6			0.200730
$543$	521864.	−	1.60613e6i	0.0759553	−	0.233766i
$544$	−483134.	+	1.48693e6i	−0.0699955	+	0.215424i
$545$	−2.05111e6	−	6.31267e6i	−0.295800	−	0.910379i
$546$	473541.	+	344048.i	0.0679792	+	0.0493898i
$547$	−1.00054e7			−1.42977			−0.714887	−	0.699240i	$-0.753522\pi$
$547$	−1.00054e7			−1.42977			−0.714887	+	0.699240i	$0.753522\pi$
$548$	113059.	+	347961.i	0.0160826	+	0.0494971i
$549$	5.62273e6	−	4.08515e6i	0.796190	−	0.578466i
$550$	−398670.	+	1.22698e6i	−0.0561962	+	0.172954i
$551$	4.01224e6	+	2.91506e6i	0.563000	+	0.409043i
$552$	709844.	−	515732.i	0.0991552	−	0.0720404i
$553$	1.66799e6	−	1.21187e6i	0.231943	−	0.168516i
$554$	−3.58547e6	+	2.60500e6i	−0.496331	+	0.360606i
$555$	−831029.	+	603778.i	−0.114521	+	0.0832042i
$556$	−2.27834e6	−	1.65531e6i	−0.312558	−	0.227087i
$557$	3.19928e6	−	9.84638e6i	0.436933	−	1.34474i	−0.454160	−	0.890920i	$-0.650061\pi$
$557$	3.19928e6	−	9.84638e6i	0.436933	−	1.34474i	0.891093	−	0.453821i	$-0.149939\pi$
$558$	−7.71226e6	+	5.60328e6i	−1.04857	+	0.761828i
$559$	−122985.	−	378508.i	−0.0166465	−	0.0512325i
$560$	−2.91643e6			−0.392989
$561$	−3.01991e6	−	2.19409e6i	−0.405123	−	0.294339i
$562$	−942204.	−	2.89980e6i	−0.125836	−	0.387283i
$563$	1.95992e6	−	6.03203e6i	0.260596	−	0.802033i	−0.732079	−	0.681220i	$-0.761450\pi$
$563$	1.95992e6	−	6.03203e6i	0.260596	−	0.802033i	0.992675	−	0.120813i	$-0.0385502\pi$
$564$	−439879.	+	1.35381e6i	−0.0582284	+	0.179209i
$565$	1.13244e7			1.49243
$566$	−1.92755e6	+	5.93239e6i	−0.252909	+	0.778375i
$567$	7.34259e6	−	5.33470e6i	0.959161	−	0.696872i
$568$	−3.60885e6	−	2.62198e6i	−0.469352	−	0.341004i
$569$	−338150.	−	1.04072e6i	−0.0437853	−	0.134757i	0.926774	−	0.375619i	$-0.122570\pi$
$569$	−338150.	−	1.04072e6i	−0.0437853	−	0.134757i	−0.970559	+	0.240862i	$0.922570\pi$
$570$	−478879.	−	1.47384e6i	−0.0617360	−	0.190004i
$571$	6.94891e6			0.891922			0.445961	−	0.895053i	$-0.352862\pi$
$571$	6.94891e6			0.891922			0.445961	+	0.895053i	$0.352862\pi$
$572$	1.59604e6	+	1.15959e6i	0.203963	+	0.148188i
$573$	−2.07714e6			−0.264289
$574$	5.57549e6	+	5.91332e6i	0.706323	+	0.749120i
$575$	−1.80861e6			−0.228126
$576$	754302.	+	548033.i	0.0947304	+	0.0688256i
$577$	1.15168e7			1.44010			0.720048	−	0.693924i	$-0.244120\pi$
$577$	1.15168e7			1.44010			0.720048	+	0.693924i	$0.244120\pi$
$578$	1.12642e6	+	3.46676e6i	0.140243	+	0.431623i
$579$	502067.	+	1.54520e6i	0.0622394	+	0.191553i
$580$	−2.36613e6	−	1.71909e6i	−0.292058	−	0.212192i
$581$	−200493.	+	145667.i	−0.0246411	+	0.0179028i
$582$	142449.	−	438414.i	0.0174322	−	0.0536509i
$583$	−2.33708e6			−0.284775
$584$	572218.	−	1.76111e6i	0.0694271	−	0.213675i
$585$	−839374.	+	2.58333e6i	−0.101406	+	0.312097i
$586$	1.40582e6	+	4.32668e6i	0.169117	+	0.520488i
$587$	−313596.	−	227841.i	−0.0375643	−	0.0272920i	0.568845	−	0.822445i	$-0.307391\pi$
$587$	−313596.	−	227841.i	−0.0375643	−	0.0272920i	−0.606409	+	0.795153i	$0.707391\pi$
$588$	1.18096e6			0.140861
$589$	5.29748e6	+	1.63040e7i	0.629189	+	1.93645i
$590$	−7.26083e6	+	5.27530e6i	−0.858729	+	0.623903i
$591$	470472.	−	1.44796e6i	0.0554071	−	0.170525i
$592$	−899134.	−	653259.i	−0.105444	−	0.0766092i
$593$	−9.20948e6	+	6.69108e6i	−1.07547	+	0.781375i	−0.976888	−	0.213754i	$-0.931431\pi$
$593$	−9.20948e6	+	6.69108e6i	−1.07547	+	0.781375i	−0.0985829	+	0.995129i	$0.531431\pi$
$594$	−3.72347e6	+	2.70526e6i	−0.432994	+	0.314589i
$595$	−1.40719e7	+	1.02239e7i	−1.62953	+	1.18392i
$596$	−6.38775e6	+	4.64097e6i	−0.736601	+	0.535172i
$597$	2.13240e6	+	1.54928e6i	0.244868	+	0.177907i
$598$	−854636.	+	2.63030e6i	−0.0977300	+	0.300782i
$599$	2.46187e6	−	1.78865e6i	0.280348	−	0.203685i	−0.438721	−	0.898623i	$-0.644568\pi$
$599$	2.46187e6	−	1.78865e6i	0.280348	−	0.203685i	0.719069	+	0.694939i	$0.244568\pi$
$600$	40103.3	+	123425.i	0.00454781	+	0.0139967i
$601$	−1.21969e7			−1.37741			−0.688705	−	0.725042i	$-0.741821\pi$
$601$	−1.21969e7			−1.37741			−0.688705	+	0.725042i	$0.741821\pi$
$602$	−1.22957e6	−	893333.i	−0.138281	−	0.100467i
$603$	1.66120e6	+	5.11264e6i	0.186049	+	0.572601i
$604$	−475069.	+	1.46211e6i	−0.0529864	+	0.163075i
$605$	4.24869e6	−	1.30761e7i	0.471918	−	1.45241i
$606$	16130.8			0.00178433
$607$	2.71400e6	−	8.35282e6i	0.298977	−	0.920156i	−0.682880	−	0.730531i	$-0.739273\pi$
$607$	2.71400e6	−	8.35282e6i	0.298977	−	0.920156i	0.981857	−	0.189625i	$-0.0607273\pi$
$608$	1.35647e6	−	985530.i	0.148816	−	0.108121i
$609$	1.81348e6	+	1.31757e6i	0.198139	+	0.143957i
$610$	2.27765e6	+	7.00989e6i	0.247835	+	0.762757i
$611$	−1.38652e6	−	4.26727e6i	−0.150253	−	0.462431i
$612$	5.56074e6			0.600142
$613$	3.14777e6	+	2.28699e6i	0.338339	+	0.245818i	0.743961	−	0.668223i	$-0.232945\pi$
$613$	3.14777e6	+	2.28699e6i	0.338339	+	0.245818i	−0.405622	+	0.914041i	$0.632945\pi$
$614$	5.04376e6			0.539925
$615$	1.22241e6	−	2.23423e6i	0.130326	−	0.238200i
$616$	7.53374e6			0.799942
$617$	8.45744e6	+	6.14469e6i	0.894388	+	0.649811i	0.937018	−	0.349280i	$-0.113574\pi$
$617$	8.45744e6	+	6.14469e6i	0.894388	+	0.649811i	−0.0426305	+	0.999091i	$0.513574\pi$
$618$	−2.25216e6			−0.237207
$619$	4.47697e6	+	1.37787e7i	0.469632	+	1.44538i	0.853062	+	0.521809i	$0.174743\pi$
$619$	4.47697e6	+	1.37787e7i	0.469632	+	1.44538i	−0.383430	+	0.923570i	$0.625257\pi$
$620$	−3.12407e6	−	9.61490e6i	−0.326394	−	1.00454i
$621$	−5.21990e6	−	3.79248e6i	−0.543166	−	0.394633i
$622$	−737242.	+	535638.i	−0.0764072	+	0.0555131i
$623$	4.92333e6	−	1.51525e7i	0.508205	−	1.56410i
$624$	198450.			0.0204028
$625$	−3.43454e6	+	1.05704e7i	−0.351697	+	1.08241i
$626$	−430160.	+	1.32390e6i	−0.0438727	+	0.135026i
$627$	1.23704e6	+	3.80723e6i	0.125666	+	0.386759i
$628$	7.18112e6	+	5.21739e6i	0.726596	+	0.527903i
$629$	−6.62845e6			−0.668014
$630$	3.20539e6	+	9.86518e6i	0.321758	+	0.990270i
$631$	−7.20971e6	+	5.23816e6i	−0.720849	+	0.523728i	−0.886655	−	0.462431i	$-0.846977\pi$
$631$	−7.20971e6	+	5.23816e6i	−0.720849	+	0.523728i	0.165806	+	0.986158i	$0.446977\pi$
$632$	216008.	−	664804.i	0.0215118	−	0.0662066i
$633$	1.83127e6	+	1.33050e6i	0.181654	+	0.131979i
$634$	5.19146e6	−	3.77182e6i	0.512940	−	0.372673i
$635$	1.44210e7	−	1.04775e7i	1.41926	−	1.03115i
$636$	−190194.	+	138184.i	−0.0186447	+	0.0135462i
$637$	−3.01152e6	+	2.18800e6i	−0.294061	+	0.213648i
$638$	6.11221e6	+	4.44078e6i	0.594493	+	0.431924i
$639$	−4.90277e6	+	1.50892e7i	−0.474996	+	1.46189i
$640$	−799945.	+	581194.i	−0.0771988	+	0.0560882i
$641$	−6.28420e6	−	1.93408e7i	−0.604094	−	1.85921i	−0.502900	−	0.864345i	$-0.667734\pi$
$641$	−6.28420e6	−	1.93408e7i	−0.604094	−	1.85921i	−0.101194	−	0.994867i	$-0.532266\pi$
$642$	3.18109e6			0.304606
$643$	1.87893e6	+	1.36512e6i	0.179219	+	0.130210i	0.673778	−	0.738934i	$-0.264670\pi$
$643$	1.87893e6	+	1.36512e6i	0.179219	+	0.130210i	−0.494559	+	0.869144i	$0.664670\pi$
$644$	3.26367e6	+	1.00446e7i	0.310093	+	0.954368i
$645$	−147170.	+	452944.i	−0.0139290	+	0.0428692i
$646$	3.09014e6	−	9.51048e6i	0.291338	−	0.896646i
$647$	−364554.			−0.0342374			−0.0171187	−	0.999853i	$-0.505449\pi$
$647$	−364554.			−0.0342374			−0.0171187	+	0.999853i	$0.505449\pi$
$648$	950880.	−	2.92651e6i	0.0889587	−	0.273787i
$649$	1.87562e7	−	1.36272e7i	1.74797	−	1.26997i
$650$	−330940.	−	240442.i	−0.0307232	−	0.0223217i
$651$	2.39440e6	+	7.36919e6i	0.221434	+	0.681503i
$652$	489679.	+	1.50708e6i	0.0451120	+	0.138840i
$653$	−1.81323e6			−0.166407			−0.0832033	−	0.996533i	$-0.526515\pi$
$653$	−1.81323e6			−0.166407			−0.0832033	+	0.996533i	$0.526515\pi$
$654$	1.39538e6	+	1.01380e6i	0.127570	+	0.0926847i
$655$	1.44653e7			1.31742
$656$	2.70772e6	+	510860.i	0.245666	+	0.0463492i
$657$	−6.58608e6			−0.595269
$658$	−1.38620e7	−	1.00714e7i	−1.24814	−	0.906825i
$659$	−3.47420e6			−0.311632			−0.155816	−	0.987786i	$-0.549801\pi$
$659$	−3.47420e6			−0.311632			−0.155816	+	0.987786i	$0.549801\pi$
$660$	−729519.	−	2.24523e6i	−0.0651894	−	0.200632i
$661$	−6.40372e6	−	1.97086e7i	−0.570070	−	1.75450i	−0.652383	−	0.757889i	$-0.726231\pi$
$661$	−6.40372e6	−	1.97086e7i	−0.570070	−	1.75450i	0.0823126	−	0.996607i	$-0.473769\pi$
$662$	−4.04831e6	−	2.94127e6i	−0.359029	−	0.260850i
$663$	957535.	−	695690.i	0.0846001	−	0.0614656i
$664$	−25964.3	+	79909.9i	−0.00228537	+	0.00703364i
$665$	1.86536e7			1.63572
$666$	−1.22151e6	+	3.75942e6i	−0.106712	+	0.328424i
$667$	−3.27293e6	+	1.00730e7i	−0.284854	+	0.876690i
$668$	−2.30199e6	−	7.08481e6i	−0.199601	−	0.614309i
$669$	−376720.	−	273703.i	−0.0325427	−	0.0236436i
$670$	−5.70103e6			−0.490644
$671$	−5.88365e6	−	1.81080e7i	−0.504476	−	1.55262i
$672$	613105.	−	445447.i	0.0523735	−	0.0380516i
$673$	463818.	−	1.42748e6i	0.0394739	−	0.121488i	−0.929378	−	0.369130i	$-0.879656\pi$
$673$	463818.	−	1.42748e6i	0.0394739	−	0.121488i	0.968852	+	0.247642i	$0.0796557\pi$
$674$	−3.26130e6	−	2.36947e6i	−0.276529	−	0.200910i
$675$	772067.	−	560939.i	0.0652222	−	0.0473867i
$676$	4.30006e6	−	3.12417e6i	0.361916	−	0.262947i
$677$	−1.14798e7	+	8.34053e6i	−0.962633	+	0.699394i	−0.953761	−	0.300567i	$-0.902824\pi$
$677$	−1.14798e7	+	8.34053e6i	−0.962633	+	0.699394i	−0.00887255	+	0.999961i	$0.502824\pi$
$678$	−2.38068e6	+	1.72966e6i	−0.198896	+	0.144506i
$679$	4.48905e6	+	3.26149e6i	0.373663	+	0.271482i
$680$	−1.82234e6	+	5.60859e6i	−0.151132	+	0.465138i
$681$	−3.55092e6	+	2.57990e6i	−0.293409	+	0.213174i
$682$	8.07013e6	+	2.48373e7i	0.664385	+	2.04477i
$683$	−2.40146e7			−1.96981			−0.984904	−	0.173102i	$-0.944621\pi$
$683$	−2.40146e7			−1.96981			−0.984904	+	0.173102i	$0.944621\pi$
$684$	−4.82455e6	−	3.50524e6i	−0.394290	−	0.286469i
$685$	426452.	+	1.31248e6i	0.0347251	+	0.106873i
$686$	−471171.	+	1.45012e6i	−0.0382268	+	0.117650i
$687$	−122505.	+	377032.i	−0.00990290	+	0.0304780i
$688$	−515284.			−0.0415026
$689$	228990.	−	704757.i	0.0183767	−	0.0565577i
$690$	2.67748e6	−	1.94530e6i	0.214093	−	0.155548i
$691$	−4.77212e6	−	3.46715e6i	−0.380203	−	0.276234i	0.381226	−	0.924482i	$-0.375502\pi$
$691$	−4.77212e6	−	3.46715e6i	−0.380203	−	0.276234i	−0.761429	+	0.648248i	$0.775502\pi$
$692$	521592.	+	1.60529e6i	0.0414062	+	0.127435i
$693$	−8.28020e6	−	2.54838e7i	−0.654949	−	2.01573i
$694$	−4.22103e6			−0.332675
$695$	−8.59371e6	−	6.24369e6i	−0.674867	−	0.490320i
$696$	759990.			0.0594682
$697$	1.48558e7	−	7.02730e6i	1.15828	−	0.547907i
$698$	−7.80845e6			−0.606633
$699$	69361.0	+	50393.7i	0.00536936	+	0.00390107i
$700$	−1.56213e6			−0.120496
$701$	2.48583e6	+	7.65059e6i	0.191063	+	0.588030i	1.00000		0.000135392i	$4.30966e-5\pi$
$701$	2.48583e6	+	7.65059e6i	0.191063	+	0.588030i	−0.808937	+	0.587895i	$0.799957\pi$
$702$	−450955.	−	1.38790e6i	−0.0345375	−	0.106295i
$703$	5.75090e6	+	4.17827e6i	0.438881	+	0.318866i
$704$	2.06643e6	−	1.50135e6i	0.157141	−	0.114169i
$705$	−1.65919e6	+	5.10645e6i	−0.125725	+	0.386943i
$706$	−8.16806e6			−0.616747
$707$	−60001.0	+	184664.i	−0.00451450	+	0.0138942i
$708$	720672.	−	2.21800e6i	0.0540324	−	0.166295i
$709$	−1.66997e6	−	5.13964e6i	−0.124765	−	0.383987i	0.869093	−	0.494649i	$-0.164703\pi$
$709$	−1.66997e6	−	5.13964e6i	−0.124765	−	0.383987i	−0.993858	+	0.110661i	$0.964703\pi$
$710$	−1.36123e7	−	9.88992e6i	−1.01341	−	0.736287i
$711$	−2.48620e6			−0.184443
$712$	−1.66921e6	−	5.13730e6i	−0.123399	−	0.379783i
$713$	−2.96190e7	+	2.15194e7i	−2.18196	+	1.58528i
$714$	1.39671e6	−	4.29862e6i	0.102532	−	0.315561i
$715$	6.02012e6	+	4.37387e6i	0.440393	+	0.319964i
$716$	−2.95849e6	+	2.14947e6i	−0.215669	+	0.156692i
$717$	3.92277e6	−	2.85006e6i	0.284967	−	0.207041i
$718$	9.57778e6	−	6.95866e6i	0.693352	−	0.503750i
$719$	5.07630e6	−	3.68815e6i	0.366206	−	0.266064i	−0.389430	−	0.921056i	$-0.627328\pi$
$719$	5.07630e6	−	3.68815e6i	0.366206	−	0.266064i	0.755636	+	0.654992i	$0.227328\pi$
$720$	2.84517e6	+	2.06714e6i	0.204539	+	0.148607i
$721$	8.37722e6	−	2.57824e7i	0.600153	−	1.84708i
$722$	−663180.	+	481828.i	−0.0473465	+	0.0343993i
$723$	−401313.	−	1.23511e6i	−0.0285521	−	0.0878742i
$724$	6.89201e6			0.488652
$725$	−1.26737e6	−	920801.i	−0.0895488	−	0.0650610i
$726$	1.10403e6	+	3.39786e6i	0.0777392	+	0.239257i
$727$	2.17987e6	−	6.70895e6i	0.152966	−	0.470780i	−0.844983	−	0.534793i	$-0.820390\pi$
$727$	2.17987e6	−	6.70895e6i	0.152966	−	0.470780i	0.997949	+	0.0640123i	$0.0203897\pi$
$728$	−738165.	+	2.27184e6i	−0.0516208	+	0.158872i
$729$	−9.18653e6			−0.640225
$730$	2.15836e6	−	6.64275e6i	0.149905	−	0.461361i
$731$	−2.48627e6	+	1.80638e6i	−0.172090	+	0.125031i
$732$	−1.54949e6	−	1.12577e6i	−0.106884	−	0.0776555i
$733$	−4.71995e6	−	1.45265e7i	−0.324472	−	0.998622i	−0.971678	−	0.236307i	$-0.924063\pi$
$733$	−4.71995e6	−	1.45265e7i	−0.324472	−	0.998622i	0.647207	−	0.762315i	$-0.275937\pi$
$734$	−3.69798e6	−	1.13812e7i	−0.253352	−	0.779736i
$735$	4.45449e6			0.304144
$736$	2.89690e6	+	2.10472e6i	0.197124	+	0.143219i
$737$	1.47270e7			0.998722
$738$	−1.24796e6	−	9.72070e6i	−0.0843452	−	0.656987i
$739$	2.11003e7			1.42127			0.710636	−	0.703560i	$-0.248407\pi$
$739$	2.11003e7			1.42127			0.710636	+	0.703560i	$0.248407\pi$
$740$	−3.39146e6	−	2.46404e6i	−0.227671	−	0.165413i
$741$	−1.26930e6			−0.0849215
$742$	−874463.	−	2.69132e6i	−0.0583085	−	0.179455i
$743$	1.37981e6	+	4.24662e6i	0.0916953	+	0.282209i	0.986378	−	0.164492i	$-0.0525986\pi$
$743$	1.37981e6	+	4.24662e6i	0.0916953	+	0.282209i	−0.894683	+	0.446702i	$0.852599\pi$
$744$	2.12531e6	+	1.54413e6i	0.140764	+	0.102271i
$745$	−2.40941e7	+	1.75054e7i	−1.59045	+	1.15553i
$746$	967677.	−	2.97821e6i	0.0636625	−	0.195933i
$747$	298842.			0.0195948
$748$	4.70749e6	−	1.44882e7i	0.307635	−	0.946803i
$749$	−1.18325e7	+	3.64167e7i	−0.770677	+	2.37190i
$750$	−762687.	−	2.34731e6i	−0.0495101	−	0.152376i
$751$	−1.18944e7	−	8.64181e6i	−0.769562	−	0.559120i	0.132266	−	0.991214i	$-0.457775\pi$
$751$	−1.18944e7	−	8.64181e6i	−0.769562	−	0.559120i	−0.901828	+	0.432095i	$0.857775\pi$
$752$	−5.80926e6			−0.374608
$753$	−112197.	−	345306.i	−0.00721095	−	0.0221930i
$754$	−1.93802e6	+	1.40805e6i	−0.124145	+	0.0901968i
$755$	−1.79192e6	+	5.51497e6i	−0.114407	+	0.352108i
$756$	−4.50852e6	−	3.27563e6i	−0.286899	−	0.208445i
$757$	6.07398e6	−	4.41300e6i	0.385242	−	0.279895i	−0.378261	−	0.925699i	$-0.623478\pi$
$757$	6.07398e6	−	4.41300e6i	0.385242	−	0.279895i	0.763503	+	0.645804i	$0.223478\pi$
$758$	7.59284e6	−	5.51652e6i	0.479989	−	0.348733i
$759$	−6.91648e6	+	5.02512e6i	−0.435794	+	0.316623i
$760$	5.11648e6	−	3.71734e6i	0.321320	−	0.233452i
$761$	6.06135e6	+	4.40383e6i	0.379409	+	0.275657i	0.761102	−	0.648633i	$-0.224659\pi$
$761$	6.06135e6	+	4.40383e6i	0.379409	+	0.275657i	−0.381693	+	0.924289i	$0.624659\pi$
$762$	−1.43136e6	+	4.40526e6i	−0.0893018	+	0.274843i
$763$	−1.67962e7	+	1.22031e7i	−1.04448	+	0.758857i
$764$	−2.61950e6	−	8.06199e6i	−0.162362	−	0.499699i
$765$	2.09747e7			1.29581
$766$	−6.30099e6	−	4.57793e6i	−0.388004	−	0.281902i
$767$	2.27159e6	+	6.99125e6i	0.139426	+	0.429108i
$768$	79398.4	−	244363.i	0.00485745	−	0.0149497i
$769$	4.10939e6	−	1.26474e7i	0.250589	−	0.771233i	−0.744078	−	0.668093i	$-0.767111\pi$
$769$	4.10939e6	−	1.26474e7i	0.250589	−	0.771233i	0.994667	−	0.103140i	$-0.0328890\pi$
$770$	2.84167e7			1.72721
$771$	618046.	−	1.90215e6i	0.0374443	−	0.115242i
$772$	−5.36423e6	+	3.89734e6i	−0.323940	+	0.235356i
$773$	−1.01666e7	−	7.38647e6i	−0.611966	−	0.444619i	0.238140	−	0.971231i	$-0.423462\pi$
$773$	−1.01666e7	−	7.38647e6i	−0.611966	−	0.444619i	−0.850106	+	0.526612i	$0.823462\pi$
$774$	566339.	+	1.74301e6i	0.0339801	+	0.104580i
$775$	−1.67335e6	−	5.15005e6i	−0.100077	−	0.308005i
$776$	1.88126e6			0.112149
$777$	2.59933e6	+	1.88853e6i	0.154458	+	0.112220i
$778$	−1.58640e7			−0.939642
$779$	−1.73187e7	−	3.26748e6i	−1.02252	−	0.192917i
$780$	748539.			0.0440533
$781$	3.51634e7	+	2.55477e7i	2.06283	+	1.49873i
$782$	2.13561e7			1.24883
$783$	−1.72699e6	−	5.31512e6i	−0.100666	−	0.309819i
$784$	1.48932e6	+	4.58366e6i	0.0865362	+	0.266331i
$785$	2.70866e7	+	1.96796e7i	1.56885	+	1.13983i
$786$	−3.04097e6	+	2.20939e6i	−0.175572	+	0.127561i
$787$	1.66152e6	−	5.11364e6i	0.0956245	−	0.294302i	−0.891791	−	0.452447i	$-0.850551\pi$
$787$	1.66152e6	−	5.11364e6i	0.0956245	−	0.294302i	0.987416	+	0.158145i	$0.0505513\pi$
$788$	6.21330e6			0.356457
$789$	−1.47651e6	+	4.54422e6i	−0.0844389	+	0.259876i
$790$	814765.	−	2.50759e6i	0.0464478	−	0.142951i
$791$	−1.09457e7	−	3.36874e7i	−0.622018	−	1.91437i
$792$	−7.34967e6	−	5.33985e6i	−0.416346	−	0.302493i
$793$	6.03705e6			0.340911
$794$	989179.	+	3.04438e6i	0.0556831	+	0.171375i
$795$	−717398.	+	521220.i	−0.0402571	+	0.0292485i
$796$	−3.32402e6	+	1.02303e7i	−0.185943	+	0.572275i
$797$	−1.51179e7	−	1.09838e7i	−0.843033	−	0.612499i	0.0801835	−	0.996780i	$-0.474449\pi$
$797$	−1.51179e7	−	1.09838e7i	−0.843033	−	0.612499i	−0.923216	+	0.384281i	$0.874449\pi$
$798$	−3.92145e6	+	2.84910e6i	−0.217991	+	0.158380i
$799$	−2.80301e7	+	2.03650e7i	−1.55331	+	1.12854i
$800$	−428476.	+	311306.i	−0.0236702	+	0.0171974i
$801$	−1.55430e7	+	1.12926e7i	−0.855959	+	0.621891i
$802$	−1.90309e6	−	1.38267e6i	−0.104478	−	0.0759074i
$803$	−5.57550e6	+	1.71596e7i	−0.305137	+	0.939115i
$804$	1.19850e6	−	870761.i	0.0653880	−	0.0475071i
$805$	1.23103e7	+	3.78873e7i	0.669545	+	2.06065i
$806$	−8.28054e6			−0.448974
$807$	4.43486e6	+	3.22211e6i	0.239715	+	0.174163i
$808$	20342.8	+	62608.6i	0.00109618	+	0.00337369i
$809$	−3.88710e6	+	1.19633e7i	−0.208812	+	0.642656i	0.790724	+	0.612173i	$0.209705\pi$
$809$	−3.88710e6	+	1.19633e7i	−0.208812	+	0.642656i	−0.999535	+	0.0304830i	$0.990295\pi$
$810$	3.58665e6	−	1.10386e7i	0.192077	−	0.591153i
$811$	1.22865e7			0.655958			0.327979	−	0.944685i	$-0.393632\pi$
$811$	1.22865e7			0.655958			0.327979	+	0.944685i	$0.393632\pi$
$812$	−2.82689e6	+	8.70027e6i	−0.150459	+	0.463066i
$813$	−1.08857e6	+	790894.i	−0.0577605	+	0.0419655i
$814$	8.76086e6	+	6.36514e6i	0.463432	+	0.336703i
$815$	1.84703e6	+	5.68457e6i	0.0974047	+	0.299781i
$816$	−473540.	−	1.45741e6i	−0.0248961	−	0.0766223i
$817$	3.29577e6			0.172744
$818$	8.42985e6	+	6.12465e6i	0.440491	+	0.320035i
$819$	8.49608e6			0.442597
$820$	1.02133e7	+	1.92693e6i	0.530435	+	0.100076i
$821$	1.20570e7			0.624280			0.312140	−	0.950036i	$-0.398954\pi$
$821$	1.20570e7			0.624280			0.312140	+	0.950036i	$0.398954\pi$
$822$	−290116.	−	210782.i	−0.0149759	−	0.0108806i
$823$	−1.87589e7			−0.965402			−0.482701	−	0.875785i	$-0.660344\pi$
$823$	−1.87589e7			−0.965402			−0.482701	+	0.875785i	$0.660344\pi$
$824$	−2.84022e6	−	8.74129e6i	−0.145725	−	0.448495i
$825$	−390754.	−	1.20262e6i	−0.0199879	−	0.0615166i
$826$	2.27108e7	+	1.65003e7i	1.15819	+	0.841478i
$827$	2.93113e6	−	2.12959e6i	0.149029	−	0.108276i	−0.510772	−	0.859716i	$-0.670640\pi$
$827$	2.93113e6	−	2.12959e6i	0.149029	−	0.108276i	0.659801	+	0.751440i	$0.270640\pi$
$828$	3.93556e6	−	1.21124e7i	0.199494	−	0.613980i
$829$	3.67025e7			1.85485			0.927426	−	0.374007i	$-0.122017\pi$
$829$	3.67025e7			1.85485			0.927426	+	0.374007i	$0.122017\pi$
$830$	−97935.3	+	301414.i	−0.00493451	+	0.0151869i
$831$	1.34233e6	−	4.13128e6i	0.0674307	−	0.207530i
$832$	250268.	+	770245.i	0.0125342	+	0.0385763i
$833$	2.32546e7	+	1.68954e7i	1.16117	+	0.843640i
$834$	2.76026e6			0.137415
$835$	−8.68294e6	−	2.67233e7i	−0.430974	−	1.32640i
$836$	−1.32169e7	+	9.60267e6i	−0.654056	+	0.475200i
$837$	5.96962e6	−	1.83726e7i	0.294532	−	0.906477i
$838$	−2.02389e7	−	1.47044e7i	−0.995580	−	0.723331i
$839$	9.34789e6	−	6.79164e6i	0.458467	−	0.333096i	−0.334462	−	0.942409i	$-0.608555\pi$
$839$	9.34789e6	−	6.79164e6i	0.458467	−	0.333096i	0.792930	+	0.609313i	$0.208555\pi$
$840$	2.31259e6	−	1.68019e6i	0.113084	−	0.0821600i
$841$	9.17198e6	−	6.66383e6i	0.447171	−	0.324888i
$842$	−1.62048e6	+	1.17735e6i	−0.0787703	+	0.0572300i
$843$	2.41774e6	+	1.75659e6i	0.117176	+	0.0851337i
$844$	−2.85462e6	+	8.78563e6i	−0.137941	+	0.424538i
$845$	1.62195e7	−	1.17841e7i	0.781439	−	0.567749i
$846$	6.38486e6	+	1.96506e7i	0.306708	+	0.943951i
$847$	−4.30049e7			−2.05973
$848$	−776191.	−	563935.i	−0.0370663	−	0.0269302i
$849$	−1.88928e6	−	5.81459e6i	−0.0899551	−	0.276853i
$850$	−976105.	+	3.00414e6i	−0.0463393	+	0.142618i
$851$	−4.69121e6	+	1.44381e7i	−0.222055	+	0.683416i
$852$	4.37221e6			0.206349
$853$	4.01578e6	−	1.23593e7i	0.188972	−	0.581595i	−0.811022	−	0.585015i	$-0.801089\pi$
$853$	4.01578e6	−	1.23593e7i	0.188972	−	0.581595i	0.999994	+	0.00341976i	$0.00108854\pi$
$854$	1.86512e7	−	1.35509e7i	0.875111	−	0.635805i
$855$	−1.81978e7	−	1.32215e7i	−0.851342	−	0.618536i
$856$	4.01170e6	+	1.23467e7i	0.187130	+	0.575928i
$857$	1.04528e7	+	3.21705e7i	0.486164	+	1.49626i	0.830289	+	0.557334i	$0.188176\pi$
$857$	1.04528e7	+	3.21705e7i	0.486164	+	1.49626i	−0.344125	+	0.938924i	$0.611824\pi$
$858$	−1.93363e6			−0.0896718
$859$	5.24662e6	+	3.81189e6i	0.242603	+	0.176262i	0.702442	−	0.711741i	$-0.252093\pi$
$859$	5.24662e6	+	3.81189e6i	0.242603	+	0.176262i	−0.459839	+	0.888002i	$0.652093\pi$
$860$	−1.94361e6			−0.0896113
$861$	−7.82784e6	−	1.47686e6i	−0.359861	−	0.0678941i
$862$	376301.			0.0172491
$863$	3.19926e7	+	2.32440e7i	1.46225	+	1.06239i	0.982769	+	0.184838i	$0.0591760\pi$
$863$	3.19926e7	+	2.32440e7i	1.46225	+	1.06239i	0.479484	+	0.877551i	$0.340824\pi$
$864$	−1.88942e6			−0.0861080
$865$	1.96740e6	+	6.05504e6i	0.0894032	+	0.275155i
$866$	−2.81025e6	−	8.64905e6i	−0.127335	−	0.391898i
$867$	−2.89045e6	−	2.10003e6i	−0.130592	−	0.0948808i
$868$	−2.55824e7	+	1.85867e7i	−1.15250	+	0.837343i
$869$	−2.10471e6	+	6.47763e6i	−0.0945459	+	0.290982i
$870$	2.86662e6			0.128402
$871$	−1.44297e6	+	4.44099e6i	−0.0644482	+	0.198351i
$872$	−2.17514e6	+	6.69438e6i	−0.0968714	+	0.298139i
$873$	−2.06766e6	−	6.36360e6i	−0.0918213	−	0.282597i
$874$	−1.85287e7	−	1.34619e7i	−0.820477	−	0.596111i
$875$	2.97087e7			1.31179
$876$	560855.	+	1.72614e6i	0.0246939	+	0.0760002i
$877$	1.98688e7	−	1.44355e7i	0.872314	−	0.633773i	−0.0588931	−	0.998264i	$-0.518757\pi$
$877$	1.98688e7	−	1.44355e7i	0.872314	−	0.633773i	0.931207	+	0.364491i	$0.118757\pi$
$878$	1.23353e6	−	3.79641e6i	0.0540024	−	0.166202i
$879$	−3.60741e6	−	2.62094e6i	−0.157479	−	0.114415i
$880$	7.79440e6	−	5.66296e6i	0.339294	−	0.246511i
$881$	−2.31267e7	+	1.68025e7i	−1.00386	+	0.729347i	−0.962912	−	0.269814i	$-0.913038\pi$
$881$	−2.31267e7	+	1.68025e7i	−1.00386	+	0.729347i	−0.0409474	+	0.999161i	$0.513038\pi$
$882$	1.38679e7	−	1.00756e7i	0.600260	−	0.436115i
$883$	−3.43311e7	+	2.49430e7i	−1.48179	+	1.07658i	−0.504813	+	0.863229i	$0.668439\pi$
$883$	−3.43311e7	+	2.49430e7i	−1.48179	+	1.07658i	−0.976975	+	0.213354i	$0.931561\pi$
$884$	3.90774e6	+	2.83914e6i	0.168188	+	0.122196i
$885$	2.71832e6	−	8.36612e6i	0.116665	−	0.359059i
$886$	−4.08580e6	+	2.96850e6i	−0.174861	+	0.127044i
$887$	8.12549e6	+	2.50077e7i	0.346769	+	1.06725i	0.960630	+	0.277831i	$0.0896156\pi$
$887$	8.12549e6	+	2.50077e7i	0.346769	+	1.06725i	−0.613861	+	0.789414i	$0.710384\pi$
$888$	1.08932e6			0.0463579
$889$	−4.51068e7	−	3.27720e7i	−1.91420	−	1.39075i
$890$	−6.29613e6	−	1.93775e7i	−0.266440	−	0.820017i
$891$	−9.26506e6	+	2.85149e7i	−0.390979	+	1.20331i
$892$	587238.	−	1.80733e6i	0.0247116	−	0.0760546i
$893$	3.71563e7			1.55921
$894$	2.39146e6	−	7.36014e6i	0.100073	−	0.307994i
$895$	−1.11592e7	+	8.10762e6i	−0.465666	+	0.338326i
$896$	2.50211e6	+	1.81789e6i	0.104120	+	0.0756479i
$897$	−837665.	−	2.57807e6i	−0.0347608	−	0.106983i
$898$	1.00527e7	+	3.09391e7i	0.415999	+	1.28031i
$899$	−3.17113e7			−1.30862
$900$	1.52396e6	+	1.10722e6i	0.0627145	+	0.0455648i
$901$	−5.72211e6			−0.234825
$902$	−2.63832e7	−	4.97765e6i	−1.07972	−	0.203708i
$903$	1.48965e6			0.0607945
$904$	−9.71564e6	−	7.05882e6i	−0.395412	−	0.287284i
$905$	2.59961e7			1.05508
$906$	−465636.	−	1.43308e6i	−0.0188463	−	0.0580029i
$907$	1.36432e7	+	4.19894e7i	0.550678	+	1.69481i	0.707093	+	0.707121i	$0.250006\pi$
$907$	1.36432e7	+	4.19894e7i	0.550678	+	1.69481i	−0.156415	+	0.987691i	$0.549994\pi$
$908$	−1.44915e7	−	1.05287e7i	−0.583307	−	0.423798i
$909$	189423.	−	137624.i	0.00760367	−	0.00552439i
$910$	−2.78430e6	+	8.56919e6i	−0.111458	+	0.343033i
$911$	2.50016e7			0.998094			0.499047	−	0.866575i	$-0.333683\pi$
$911$	2.50016e7			0.998094			0.499047	+	0.866575i	$0.333683\pi$
$912$	−507835.	+	1.56296e6i	−0.0202179	+	0.0622242i
$913$	252987.	−	778615.i	0.0100444	−	0.0309133i
$914$	−5.12844e6	−	1.57837e7i	−0.203058	−	0.624948i
$915$	−5.84456e6	−	4.24632e6i	−0.230780	−	0.167672i
$916$	−1.61787e6			−0.0637094
$917$	−1.39816e7	−	4.30308e7i	−0.549076	−	1.68988i
$918$	−9.11656e6	+	6.62357e6i	−0.357046	+	0.259409i
$919$	1.24636e7	−	3.83589e7i	0.486803	−	1.49823i	−0.342549	−	0.939500i	$-0.611290\pi$
$919$	1.24636e7	−	3.83589e7i	0.486803	−	1.49823i	0.829352	−	0.558726i	$-0.188710\pi$
$920$	1.09269e7	+	7.93885e6i	0.425625	+	0.309234i
$921$	−3.99946e6	+	2.90578e6i	−0.155365	+	0.112879i
$922$	2.13539e7	−	1.55145e7i	0.827274	−	0.601050i
$923$	−1.11494e7	+	8.10052e6i	−0.430772	+	0.312974i
$924$	−5.97389e6	+	4.34029e6i	−0.230185	+	0.167239i
$925$	−1.81658e6	−	1.31982e6i	−0.0698070	−	0.0507178i
$926$	−4.64378e6	+	1.42921e7i	−0.177969	+	0.547732i
$927$	−2.64469e7	+	1.92148e7i	−1.01082	+	0.734407i
$928$	958431.	+	2.94975e6i	0.0365335	+	0.112438i
$929$	2.31906e7			0.881604			0.440802	−	0.897604i	$-0.354694\pi$
$929$	2.31906e7			0.881604			0.440802	+	0.897604i	$0.354694\pi$
$930$	8.01652e6	+	5.82434e6i	0.303933	+	0.220820i
$931$	−9.52575e6	−	2.93172e7i	−0.360184	−	1.10853i
$932$	−108121.	+	332763.i	−0.00407729	+	0.0125486i
$933$	276010.	−	849471.i	0.0103805	−	0.0319480i
$934$	4.79482e6			0.179848
$935$	1.77563e7	−	5.46483e7i	0.664237	−	2.04431i
$936$	2.33039e6	−	1.69313e6i	0.0869438	−	0.0631683i
$937$	−9.68752e6	−	7.03840e6i	−0.360465	−	0.261893i	0.392781	−	0.919632i	$-0.371513\pi$
$937$	−9.68752e6	−	7.03840e6i	−0.360465	−	0.261893i	−0.753246	+	0.657739i	$0.771513\pi$
$938$	5.51038e6	+	1.69592e7i	0.204491	+	0.629359i
$939$	−421618.	−	1.29761e6i	−0.0156047	−	0.0480263i
$940$	−2.19121e7			−0.808843
$941$	−3.42683e7	−	2.48974e7i	−1.26159	−	0.916600i	−0.262757	−	0.964862i	$-0.584632\pi$
$941$	−3.42683e7	−	2.48974e7i	−1.26159	−	0.916600i	−0.998835	+	0.0482623i	$0.984632\pi$
$942$	−8.70010e6			−0.319446
$943$	−4.79280e6	−	3.73324e7i	−0.175513	−	1.36712i
$944$	9.51756e6			0.347613
$945$	−1.70058e7	−	1.23554e7i	−0.619466	−	0.450068i
$946$	5.02075e6			0.182407
$947$	1.17908e7	+	3.62882e7i	0.427235	+	1.31489i	0.900838	+	0.434156i	$0.142953\pi$
$947$	1.17908e7	+	3.62882e7i	0.427235	+	1.31489i	−0.473603	+	0.880739i	$0.657047\pi$
$948$	211719.	+	651603.i	0.00765135	+	0.0235484i
$949$	−4.62828e6	−	3.36264e6i	−0.166822	−	0.121203i
$950$	2.74055e6	−	1.99113e6i	0.0985210	−	0.0715797i
$951$	−1.94359e6	+	5.98175e6i	−0.0696871	+	0.214475i
$952$	1.84456e7			0.659631
$953$	7.54081e6	−	2.32082e7i	0.268959	−	0.827771i	−0.721796	−	0.692106i	$-0.756683\pi$
$953$	7.54081e6	−	2.32082e7i	0.268959	−	0.827771i	0.990755	−	0.135665i	$-0.0433169\pi$
$954$	−1.05449e6	+	3.24538e6i	−0.0375120	+	0.115450i
$955$	−9.88054e6	−	3.04092e7i	−0.350568	−	1.07894i
$956$	1.60090e7	+	1.16312e7i	0.566525	+	0.411604i
$957$	−7.40508e6			−0.261367
$958$	−7.97421e6	−	2.45421e7i	−0.280721	−	0.863969i
$959$	3.49213e6	−	2.53718e6i	0.122615	−	0.0890851i
$960$	299484.	−	921718.i	0.0104881	−	0.0322790i
$961$	−6.55194e7	−	4.76026e7i	−2.28855	−	1.66273i
$962$	−2.77784e6	+	2.01822e6i	−0.0967764	+	0.0703122i
$963$	3.73552e7	−	2.71402e7i	1.29803	−	0.943076i
$964$	4.28775e6	−	3.11523e6i	0.148606	−	0.107969i
$965$	−2.02335e7	+	1.47005e7i	−0.699443	+	0.508175i
$966$	−8.37474e6	−	6.08460e6i	−0.288754	−	0.209792i
$967$	1.62091e7	−	4.98863e7i	0.557431	−	1.71560i	−0.132003	−	0.991249i	$-0.542141\pi$
$967$	1.62091e7	−	4.98863e7i	0.557431	−	1.71560i	0.689434	−	0.724348i	$-0.257859\pi$
$968$	−1.17958e7	+	8.57015e6i	−0.404612	+	0.293968i
$969$	3.02878e6	+	9.32163e6i	0.103624	+	0.318920i
$970$	7.09596e6			0.242149
$971$	1.55139e7	+	1.12715e7i	0.528047	+	0.383649i	0.819627	−	0.572898i	$-0.194181\pi$
$971$	1.55139e7	+	1.12715e7i	0.528047	+	0.383649i	−0.291580	+	0.956547i	$0.594181\pi$
$972$	3.14885e6	+	9.69117e6i	0.106902	+	0.329011i
$973$	−1.02672e7	+	3.15991e7i	−0.347671	+	1.07002i
$974$	−5.99417e6	+	1.84482e7i	−0.202456	+	0.623097i
$975$	400941.			0.0135073
$976$	2.41537e6	−	7.43376e6i	0.0811633	−	0.249795i
$977$	3.92551e7	−	2.85205e7i	1.31571	−	0.955917i	0.315733	−	0.948848i	$-0.397750\pi$
$977$	3.92551e7	−	2.85205e7i	1.31571	−	0.955917i	0.999975	−	0.00706925i	$-0.00225023\pi$
$978$	−1.25654e6	−	912929.i	−0.0420077	−	0.0305204i
$979$	1.62642e7	+	5.00561e7i	0.542346	+	1.66917i
$980$	5.61760e6	+	1.72892e7i	0.186847	+	0.575055i
$981$	2.50353e7			0.830577
$982$	2.11989e7	+	1.54019e7i	0.701513	+	0.509679i
$983$	−5.96438e7			−1.96871			−0.984354	−	0.176204i	$-0.943618\pi$
$983$	−5.96438e7			−1.96871			−0.984354	+	0.176204i	$0.943618\pi$
$984$	−2.44141e6	+	1.15487e6i	−0.0803809	+	0.0380229i
$985$	2.34361e7			0.769652
$986$	1.49651e7	+	1.08728e7i	0.490217	+	0.356164i
$987$	1.67942e7			0.548739
$988$	−1.60072e6	−	4.92652e6i	−0.0521703	−	0.160564i
$989$	2.17503e6	+	6.69405e6i	0.0707089	+	0.217620i
$990$	−2.77224e7	−	2.01415e7i	−0.898964	−	0.653136i
$991$	−1.87870e7	+	1.36496e7i	−0.607678	+	0.441504i	−0.848596	−	0.529042i	$-0.822552\pi$
$991$	−1.87870e7	+	1.36496e7i	−0.607678	+	0.441504i	0.240918	+	0.970545i	$0.422552\pi$
$992$	−3.31298e6	+	1.01963e7i	−0.106891	+	0.328975i
$993$	4.90462e6			0.157846
$994$	−1.62631e7	+	5.00525e7i	−0.522079	+	1.60679i
$995$	−1.25379e7	+	3.85878e7i	−0.401484	+	1.23564i
$996$	−25448.7	−	78323.1i	−0.000812863	−	0.00250174i
$997$	−3.26593e6	−	2.37284e6i	−0.104056	−	0.0756014i	0.534540	−	0.845143i	$-0.320485\pi$
$997$	−3.26593e6	−	2.37284e6i	−0.104056	−	0.0756014i	−0.638597	+	0.769542i	$0.720485\pi$
$998$	−1.91950e7			−0.610046
$999$	−2.47535e6	−	7.61836e6i	−0.0784736	−	0.241517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.a.51.5	yes	36
41.37	even	5	inner	82.6.d.a.37.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.a.37.5	✓	36	41.37	even	5	inner
82.6.d.a.51.5	yes	36	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +3.92057 q^{3} +(4.94427 + 15.2169i) q^{4} +(18.6494 + 57.3970i) q^{5} +(-12.6872 - 9.21782i) q^{6} +(152.716 - 110.955i) q^{7} +(19.7771 - 60.8676i) q^{8} -227.629 q^{9} +(74.5976 - 229.588i) q^{10} +(-192.701 + 593.074i) q^{11} +(19.3844 + 59.6590i) q^{12} +(-159.963 - 116.220i) q^{13} -755.072 q^{14} +(73.1163 + 225.029i) q^{15} +(-207.108 + 150.473i) q^{16} +(-471.810 + 1452.08i) q^{17} +(736.623 + 535.188i) q^{18} +(1324.67 - 962.431i) q^{19} +(-781.196 + 567.572i) q^{20} +(598.736 - 435.007i) q^{21} +(2017.99 - 1466.16i) q^{22} +(2829.00 + 2055.39i) q^{23} +(77.5375 - 238.636i) q^{24} +(-418.434 + 304.010i) q^{25} +(244.402 + 752.192i) q^{26} -1845.14 q^{27} +(2443.46 + 1775.28i) q^{28} +(935.967 + 2880.61i) q^{29} +(292.465 - 900.116i) q^{30} +(-3235.33 + 9957.32i) q^{31} +1024.00 q^{32} +(-755.499 + 2325.19i) q^{33} +(4940.86 - 3589.75i) q^{34} +(9216.55 + 6696.22i) q^{35} +(-1125.46 - 3463.81i) q^{36} +(1341.56 + 4128.89i) q^{37} -6549.54 q^{38} +(-627.147 - 455.649i) q^{39} +3862.45 q^{40} +(-7384.06 - 7831.47i) q^{41} -2960.31 q^{42} +(1628.41 + 1183.11i) q^{43} -9977.51 q^{44} +(-4245.15 - 13065.2i) q^{45} +(-4322.33 - 13302.8i) q^{46} +(18358.6 + 13338.3i) q^{47} +(-811.983 + 589.940i) q^{48} +(5817.66 - 17904.9i) q^{49} +2068.85 q^{50} +(-1849.77 + 5692.99i) q^{51} +(977.608 - 3008.77i) q^{52} +(1158.12 + 3564.32i) q^{53} +(5970.98 + 4338.17i) q^{54} -37634.4 q^{55} +(-3733.28 - 11489.9i) q^{56} +(5193.48 - 3773.28i) q^{57} +(3743.87 - 11522.4i) q^{58} +(-30077.6 - 21852.7i) q^{59} +(-3062.74 + 2225.21i) q^{60} +(-24701.3 + 17946.5i) q^{61} +(33880.8 - 24615.8i) q^{62} +(-34762.7 + 25256.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(3687.46 - 11348.8i) q^{65} +(7911.69 - 5748.18i) q^{66} +(-7297.82 - 22460.4i) q^{67} -24429.0 q^{68} +(11091.3 + 8058.31i) q^{69} +(-14081.6 - 43338.8i) q^{70} +(21538.4 - 66288.4i) q^{71} +(-4501.84 + 13855.2i) q^{72} +28933.4 q^{73} +(5366.23 - 16515.6i) q^{74} +(-1640.50 + 1191.89i) q^{75} +(21194.8 + 15398.9i) q^{76} +(36375.8 + 111953. i) q^{77} +(958.196 + 2949.02i) q^{78} +10922.1 q^{79} +(-12499.1 - 9081.16i) q^{80} +48079.9 q^{81} +(5482.43 + 42704.1i) q^{82} -1312.85 q^{83} +(9579.77 + 6960.11i) q^{84} -92144.1 q^{85} +(-2487.99 - 7657.25i) q^{86} +(3669.53 + 11293.6i) q^{87} +(32287.9 + 23458.5i) q^{88} +(68282.0 - 49609.8i) q^{89} +(-16980.6 + 52260.9i) q^{90} -37324.2 q^{91} +(-17289.3 + 53211.1i) q^{92} +(-12684.3 + 39038.4i) q^{93} +(-28049.4 - 86327.2i) q^{94} +(79945.0 + 58083.4i) q^{95} +4014.67 q^{96} +(9083.46 + 27956.0i) q^{97} +(-60923.3 + 44263.4i) q^{98} +(43864.4 - 135001. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Introduction

L-functions

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