LMFDB - Embedded newform 82.6.d.b.37.9

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			37.9
Character	$\chi$	$=$	82.37
Dual form			82.6.d.b.51.9

$q$-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} +27.6062 q^{3} +(4.94427 - 15.2169i) q^{4} +(-30.5964 + 94.1661i) q^{5} +(89.3355 - 64.9061i) q^{6} +(-19.4012 - 14.0958i) q^{7} +(-19.7771 - 60.8676i) q^{8} +519.102 q^{9} +(122.386 + 376.664i) q^{10} +(182.007 + 560.160i) q^{11} +(136.493 - 420.081i) q^{12} +(904.165 - 656.914i) q^{13} -95.9250 q^{14} +(-844.651 + 2599.57i) q^{15} +(-207.108 - 150.473i) q^{16} +(-45.7320 - 140.749i) q^{17} +(1679.85 - 1220.48i) q^{18} +(-1968.15 - 1429.94i) q^{19} +(1281.64 + 931.166i) q^{20} +(-535.594 - 389.132i) q^{21} +(1906.00 + 1384.79i) q^{22} +(417.434 - 303.284i) q^{23} +(-545.970 - 1680.32i) q^{24} +(-5402.93 - 3925.46i) q^{25} +(1381.44 - 4251.64i) q^{26} +7622.12 q^{27} +(-310.420 + 225.533i) q^{28} +(-1883.35 + 5796.36i) q^{29} +(3378.60 + 10398.3i) q^{30} +(-890.979 - 2742.15i) q^{31} -1024.00 q^{32} +(5024.52 + 15463.9i) q^{33} +(-478.912 - 347.950i) q^{34} +(1920.96 - 1395.66i) q^{35} +(2566.58 - 7899.12i) q^{36} +(1899.35 - 5845.59i) q^{37} -9731.07 q^{38} +(24960.5 - 18134.9i) q^{39} +6336.77 q^{40} +(-5319.33 - 9357.40i) q^{41} -2648.12 q^{42} +(2199.88 - 1598.31i) q^{43} +9423.79 q^{44} +(-15882.7 + 48881.8i) q^{45} +(637.783 - 1962.89i) q^{46} +(-180.841 + 131.388i) q^{47} +(-5717.47 - 4153.99i) q^{48} +(-5015.93 - 15437.5i) q^{49} -26713.6 q^{50} +(-1262.49 - 3885.54i) q^{51} +(-5525.76 - 17006.5i) q^{52} +(-3386.04 + 10421.2i) q^{53} +(24665.7 - 17920.7i) q^{54} -58316.8 q^{55} +(-474.279 + 1459.68i) q^{56} +(-54333.1 - 39475.3i) q^{57} +(7533.41 + 23185.5i) q^{58} +(-19434.0 + 14119.6i) q^{59} +(35381.2 + 25705.9i) q^{60} +(18499.4 + 13440.6i) q^{61} +(-9330.45 - 6778.97i) q^{62} +(-10071.2 - 7317.17i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(34194.8 + 105241. i) q^{65} +(52617.5 + 38228.8i) q^{66} +(10256.1 - 31565.0i) q^{67} -2367.87 q^{68} +(11523.8 - 8372.51i) q^{69} +(2934.96 - 9032.88i) q^{70} +(-787.754 - 2424.46i) q^{71} +(-10266.3 - 31596.5i) q^{72} -32562.7 q^{73} +(-7597.39 - 23382.4i) q^{74} +(-149154. - 108367. i) q^{75} +(-31490.4 + 22879.1i) q^{76} +(4364.76 - 13433.3i) q^{77} +(38136.3 - 117372. i) q^{78} +60715.5 q^{79} +(20506.2 - 14898.6i) q^{80} +84276.0 q^{81} +(-39214.3 - 17774.7i) q^{82} +1703.74 q^{83} +(-8569.51 + 6226.11i) q^{84} +14653.0 q^{85} +(3361.12 - 10344.5i) q^{86} +(-51992.2 + 160016. i) q^{87} +(30496.0 - 22156.7i) q^{88} +(-51362.0 - 37316.7i) q^{89} +(63530.6 + 195527. i) q^{90} -26801.7 q^{91} +(-2551.13 - 7851.58i) q^{92} +(-24596.5 - 75700.3i) q^{93} +(-276.300 + 850.364i) q^{94} +(194871. - 141582. i) q^{95} -28268.7 q^{96} +(-13473.7 + 41467.8i) q^{97} +(-52527.5 - 38163.5i) q^{98} +(94480.2 + 290780. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) $ 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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
$3$	27.6062			1.77094			0.885469	−	0.464698i	$-0.153837\pi$
$3$	27.6062			1.77094			0.885469	+	0.464698i	$0.153837\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−30.5964	+	94.1661i	−0.547325	+	1.68449i	0.168071	+	0.985775i	$0.446246\pi$
$5$	−30.5964	+	94.1661i	−0.547325	+	1.68449i	−0.715396	+	0.698719i	$0.753754\pi$
$6$	89.3355	−	64.9061i	1.01309	−	0.736050i
$7$	−19.4012	−	14.0958i	−0.149653	−	0.108729i	0.510439	−	0.859914i	$-0.329483\pi$
$7$	−19.4012	−	14.0958i	−0.149653	−	0.108729i	−0.660092	+	0.751185i	$0.729483\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	519.102			2.13622
$10$	122.386	+	376.664i	0.387017	+	1.19112i
$11$	182.007	+	560.160i	0.453530	+	1.39582i	0.872852	+	0.487985i	$0.162268\pi$
$11$	182.007	+	560.160i	0.453530	+	1.39582i	−0.419321	+	0.907838i	$0.637732\pi$
$12$	136.493	−	420.081i	0.273625	−	0.842131i
$13$	904.165	−	656.914i	1.48385	−	1.07808i	0.507555	−	0.861619i	$-0.330549\pi$
$13$	904.165	−	656.914i	1.48385	−	1.07808i	0.976292	−	0.216459i	$-0.0694507\pi$
$14$	−95.9250			−0.130801
$15$	−844.651	+	2599.57i	−0.969279	+	2.98313i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−45.7320	−	140.749i	−0.0383794	−	0.118120i	0.930031	−	0.367480i	$-0.119780\pi$
$17$	−45.7320	−	140.749i	−0.0383794	−	0.118120i	−0.968411	+	0.249361i	$0.919780\pi$
$18$	1679.85	−	1220.48i	1.22205	−	0.887871i
$19$	−1968.15	−	1429.94i	−1.25076	−	0.908730i	−0.252494	−	0.967598i	$-0.581251\pi$
$19$	−1968.15	−	1429.94i	−1.25076	−	0.908730i	−0.998266	+	0.0588679i	$0.981251\pi$
$20$	1281.64	+	931.166i	0.716458	+	0.520537i
$21$	−535.594	−	389.132i	−0.265026	−	0.192552i
$22$	1906.00	+	1384.79i	0.839589	+	0.609997i
$23$	417.434	−	303.284i	0.164539	−	0.119545i	−0.502469	−	0.864595i	$-0.667575\pi$
$23$	417.434	−	303.284i	0.164539	−	0.119545i	0.667008	+	0.745051i	$0.267575\pi$
$24$	−545.970	−	1680.32i	−0.193482	−	0.595477i
$25$	−5402.93	−	3925.46i	−1.72894	−	1.25615i
$26$	1381.44	−	4251.64i	0.400773	−	1.23345i
$27$	7622.12			2.01218
$28$	−310.420	+	225.533i	−0.0748263	+	0.0543645i
$29$	−1883.35	+	5796.36i	−0.415850	+	1.27985i	0.495638	+	0.868529i	$0.334934\pi$
$29$	−1883.35	+	5796.36i	−0.415850	+	1.27985i	−0.911488	+	0.411326i	$0.865066\pi$
$30$	3378.60	+	10398.3i	0.685384	+	2.10939i
$31$	−890.979	−	2742.15i	−0.166519	−	0.512492i	0.832626	−	0.553835i	$-0.186836\pi$
$31$	−890.979	−	2742.15i	−0.166519	−	0.512492i	−0.999145	+	0.0413434i	$0.986836\pi$
$32$	−1024.00			−0.176777
$33$	5024.52	+	15463.9i	0.803174	+	2.47192i
$34$	−478.912	−	347.950i	−0.0710491	−	0.0516202i
$35$	1920.96	−	1395.66i	0.265062	−	0.192579i
$36$	2566.58	−	7899.12i	0.330064	−	1.01583i
$37$	1899.35	−	5845.59i	0.228087	−	0.701979i	−0.769877	−	0.638193i	$-0.779682\pi$
$37$	1899.35	−	5845.59i	0.228087	−	0.701979i	0.997964	−	0.0637864i	$-0.0203176\pi$
$38$	−9731.07			−1.09320
$39$	24960.5	−	18134.9i	2.62780	−	1.90921i
$40$	6336.77			0.626207
$41$	−5319.33	−	9357.40i	−0.494194	−	0.869352i
$41$	−5319.33	−	9357.40i	−0.494194	−	0.869352i
$42$	−2648.12			−0.231641
$43$	2199.88	−	1598.31i	0.181438	−	0.131822i	−0.493359	−	0.869826i	$-0.664231\pi$
$43$	2199.88	−	1598.31i	0.181438	−	0.131822i	0.674797	+	0.738003i	$0.264231\pi$
$44$	9423.79			0.733828
$45$	−15882.7	+	48881.8i	−1.16921	+	3.59845i
$46$	637.783	−	1962.89i	0.0444404	−	0.136774i
$47$	−180.841	+	131.388i	−0.0119413	+	0.00867586i	−0.593740	−	0.804657i	$-0.702349\pi$
$47$	−180.841	+	131.388i	−0.0119413	+	0.00867586i	0.581799	+	0.813333i	$0.302349\pi$
$48$	−5717.47	−	4153.99i	−0.358180	−	0.260233i
$49$	−5015.93	−	15437.5i	−0.298443	−	0.918513i
$50$	−26713.6			−1.51115
$51$	−1262.49	−	3885.54i	−0.0679675	−	0.209183i
$52$	−5525.76	−	17006.5i	−0.283390	−	0.872183i
$53$	−3386.04	+	10421.2i	−0.165578	+	0.509597i	−0.999078	−	0.0429221i	$-0.986333\pi$
$53$	−3386.04	+	10421.2i	−0.165578	+	0.509597i	0.833500	+	0.552519i	$0.186333\pi$
$54$	24665.7	−	17920.7i	1.15109	−	0.836315i
$55$	−58316.8			−2.59948
$56$	−474.279	+	1459.68i	−0.0202099	+	0.0621997i
$57$	−54333.1	−	39475.3i	−2.21502	−	1.60931i
$58$	7533.41	+	23185.5i	0.294050	+	0.904994i
$59$	−19434.0	+	14119.6i	−0.726829	+	0.528072i	−0.888559	−	0.458763i	$-0.848293\pi$
$59$	−19434.0	+	14119.6i	−0.726829	+	0.528072i	0.161730	+	0.986835i	$0.448293\pi$
$60$	35381.2	+	25705.9i	1.26880	+	0.921839i
$61$	18499.4	+	13440.6i	0.636550	+	0.462481i	0.858663	−	0.512540i	$-0.171295\pi$
$61$	18499.4	+	13440.6i	0.636550	+	0.462481i	−0.222113	+	0.975021i	$0.571295\pi$
$62$	−9330.45	−	6778.97i	−0.308264	−	0.223967i
$63$	−10071.2	−	7317.17i	−0.319691	−	0.232269i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	34194.8	+	105241.i	1.00387	+	3.08959i
$66$	52617.5	+	38228.8i	1.48686	+	1.08027i
$67$	10256.1	−	31565.0i	0.279123	−	0.859051i	−0.708976	−	0.705232i	$-0.750843\pi$
$67$	10256.1	−	31565.0i	0.279123	−	0.859051i	0.988099	−	0.153819i	$-0.0491573\pi$
$68$	−2367.87			−0.0620992
$69$	11523.8	−	8372.51i	0.291388	−	0.211706i
$70$	2934.96	−	9032.88i	0.0715908	−	0.220334i
$71$	−787.754	−	2424.46i	−0.0185458	−	0.0570780i	0.941355	−	0.337417i	$-0.109553\pi$
$71$	−787.754	−	2424.46i	−0.0185458	−	0.0570780i	−0.959901	+	0.280339i	$0.909553\pi$
$72$	−10266.3	−	31596.5i	−0.233391	−	0.718303i
$73$	−32562.7			−0.715178			−0.357589	−	0.933879i	$-0.616401\pi$
$73$	−32562.7			−0.715178			−0.357589	+	0.933879i	$0.616401\pi$
$74$	−7597.39	−	23382.4i	−0.161282	−	0.496374i
$75$	−149154.	−	108367.i	−3.06184	−	2.22456i
$76$	−31490.4	+	22879.1i	−0.625380	+	0.454365i
$77$	4364.76	−	13433.3i	0.0838945	−	0.258201i
$78$	38136.3	−	117372.i	0.709745	−	2.18437i
$79$	60715.5			1.09454			0.547270	−	0.836956i	$-0.315667\pi$
$79$	60715.5			1.09454			0.547270	+	0.836956i	$0.315667\pi$
$80$	20506.2	−	14898.6i	0.358229	−	0.260269i
$81$	84276.0			1.42722
$82$	−39214.3	−	17774.7i	−0.644035	−	0.291922i
$83$	1703.74			0.0271461			0.0135730	−	0.999908i	$-0.495679\pi$
$83$	1703.74			0.0271461			0.0135730	+	0.999908i	$0.495679\pi$
$84$	−8569.51	+	6226.11i	−0.132513	+	0.0962762i
$85$	14653.0			0.219978
$86$	3361.12	−	10344.5i	0.0490047	−	0.150821i
$87$	−51992.2	+	160016.i	−0.736445	+	2.26654i
$88$	30496.0	−	22156.7i	0.419794	−	0.304999i
$89$	−51362.0	−	37316.7i	−0.687333	−	0.499377i	0.188449	−	0.982083i	$-0.439654\pi$
$89$	−51362.0	−	37316.7i	−0.687333	−	0.499377i	−0.875782	+	0.482706i	$0.839654\pi$
$90$	63530.6	+	195527.i	0.826755	+	2.54449i
$91$	−26801.7			−0.339280
$92$	−2551.13	−	7851.58i	−0.0314241	−	0.0967136i
$93$	−24596.5	−	75700.3i	−0.294894	−	0.907591i
$94$	−276.300	+	850.364i	−0.00322523	+	0.00992625i
$95$	194871.	−	141582.i	2.21532	−	1.60953i
$96$	−28268.7			−0.313061
$97$	−13473.7	+	41467.8i	−0.145398	+	0.447489i	−0.997062	−	0.0765994i	$-0.975594\pi$
$97$	−13473.7	+	41467.8i	−0.145398	+	0.447489i	0.851664	+	0.524088i	$0.175594\pi$
$98$	−52527.5	−	38163.5i	−0.552487	−	0.401405i
$99$	94480.2	+	290780.i	0.968841	+	2.98179i
$100$	−86446.9	+	62807.4i	−0.864469	+	0.628074i
$101$	−37311.2	−	27108.1i	−0.363945	−	0.264421i	0.390751	−	0.920496i	$-0.372215\pi$
$101$	−37311.2	−	27108.1i	−0.363945	−	0.264421i	−0.754695	+	0.656075i	$0.772215\pi$
$102$	−13220.9	−	9605.57i	−0.125824	−	0.0914161i
$103$	142451.	+	103497.i	1.32304	+	0.961242i	0.999889	+	0.0148938i	$0.00474103\pi$
$103$	142451.	+	103497.i	1.32304	+	0.961242i	0.323148	+	0.946349i	$0.395259\pi$
$104$	−57866.5	−	42042.5i	−0.524619	−	0.381158i
$105$	53030.3	−	38528.8i	0.469409	−	0.341045i
$106$	13544.2	+	41684.7i	0.117081	+	0.360339i
$107$	−65011.9	−	47233.9i	−0.548951	−	0.398836i	0.278448	−	0.960451i	$-0.410180\pi$
$107$	−65011.9	−	47233.9i	−0.548951	−	0.398836i	−0.827398	+	0.561615i	$0.810180\pi$
$108$	37685.8	−	115985.i	0.310899	−	0.956848i
$109$	87029.4			0.701616			0.350808	−	0.936447i	$-0.385907\pi$
$109$	87029.4			0.701616			0.350808	+	0.936447i	$0.385907\pi$
$110$	−188717.	+	137111.i	−1.48706	+	1.08042i
$111$	52433.8	−	161374.i	0.403928	−	1.24316i
$112$	1897.12	+	5838.73i	0.0142906	+	0.0439818i
$113$	22880.3	+	70418.4i	0.168564	+	0.518788i	0.999281	−	0.0379073i	$-0.0120692\pi$
$113$	22880.3	+	70418.4i	0.168564	+	0.518788i	−0.830717	+	0.556695i	$0.812069\pi$
$114$	−268638.			−1.93600
$115$	15787.1	+	48587.6i	0.111316	+	0.342595i
$116$	78890.9	+	57317.6i	0.544355	+	0.395497i
$117$	469354.	−	341005.i	3.16983	−	2.30301i
$118$	−29692.5	+	91384.1i	−0.196310	+	0.604179i
$119$	−1096.71	+	3375.33i	−0.00709945	+	0.0218499i
$120$	174934.			1.10897
$121$	−150360.	+	109243.i	−0.933615	+	0.678311i
$122$	91466.0			0.556365
$123$	−146846.	−	258322.i	−0.875186	−	1.53957i
$124$	−46132.3			−0.269433
$125$	284636.	−	206800.i	1.62935	−	1.18379i
$126$	−49794.9			−0.279420
$127$	−48668.2	+	149785.i	−0.267754	+	0.824063i	0.723292	+	0.690542i	$0.242628\pi$
$127$	−48668.2	+	149785.i	−0.267754	+	0.824063i	−0.991046	+	0.133520i	$0.957372\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	60730.3	−	44123.2i	0.321315	−	0.233449i
$130$	358093.	+	260170.i	1.85839	+	1.35020i
$131$	−94478.4	−	290775.i	−0.481010	−	1.48040i	−0.837677	−	0.546166i	$-0.816087\pi$
$131$	−94478.4	−	290775.i	−0.481010	−	1.48040i	0.356667	−	0.934232i	$-0.383913\pi$
$132$	260155.			1.29956
$133$	18028.3	+	55485.4i	0.0883742	+	0.271988i
$134$	−41024.4	−	126260.i	−0.197370	−	0.607441i
$135$	−233210.	+	717745.i	−1.10132	+	3.38950i
$136$	−7662.59	+	5567.20i	−0.0355245	+	0.0258101i
$137$	−186661.			−0.849673			−0.424837	−	0.905270i	$-0.639668\pi$
$137$	−186661.			−0.849673			−0.424837	+	0.905270i	$0.639668\pi$
$138$	17606.8	−	54188.0i	0.0787013	−	0.242218i
$139$	274419.	+	199377.i	1.20470	+	0.875263i	0.994738	−	0.102448i	$-0.0326674\pi$
$139$	274419.	+	199377.i	1.20470	+	0.875263i	0.209958	+	0.977711i	$0.432667\pi$
$140$	−11739.8	−	36131.5i	−0.0506224	−	0.155800i
$141$	−4992.32	+	3627.13i	−0.0211473	+	0.0153644i
$142$	−8249.47	−	5993.59i	−0.0343325	−	0.0249440i
$143$	532541.	+	386914.i	2.17778	+	1.58225i
$144$	−107510.	−	78110.8i	−0.432060	−	0.313910i
$145$	−488197.	−	354696.i	−1.92830	−	1.40099i
$146$	−105375.	+	76559.6i	−0.409126	+	0.297247i
$147$	−138471.	−	426169.i	−0.528524	−	1.62663i
$148$	−79560.9	−	57804.4i	−0.298569	−	0.216923i
$149$	−58096.9	+	178804.i	−0.214382	+	0.659799i	0.784815	+	0.619730i	$0.212758\pi$
$149$	−58096.9	+	178804.i	−0.214382	+	0.659799i	−0.999197	+	0.0400690i	$0.987242\pi$
$150$	−737460.			−2.67615
$151$	−235375.	+	171010.i	−0.840076	+	0.610351i	−0.922392	−	0.386255i	$-0.873768\pi$
$151$	−235375.	+	171010.i	−0.840076	+	0.610351i	0.0823158	+	0.996606i	$0.473768\pi$
$152$	−48113.0	+	148077.i	−0.168909	+	0.519850i
$153$	−23739.6	−	73062.9i	−0.0819869	−	0.252330i
$154$	−17459.0	−	53733.4i	−0.0593223	−	0.182575i
$155$	285478.			0.954430
$156$	−152545.	−	469486.i	−0.501865	−	1.54458i
$157$	−124248.	−	90271.3i	−0.402290	−	0.292281i	0.368183	−	0.929753i	$-0.379980\pi$
$157$	−124248.	−	90271.3i	−0.402290	−	0.292281i	−0.770473	+	0.637472i	$0.779980\pi$
$158$	196480.	−	142751.i	0.626145	−	0.454921i
$159$	−93475.7	+	287689.i	−0.293228	+	0.902464i
$160$	31330.7	−	96426.1i	0.0967544	−	0.297779i
$161$	−12373.8			−0.0376217
$162$	272723.	−	198145.i	0.816458	−	0.593192i
$163$	189235.			0.557869			0.278935	−	0.960310i	$-0.410019\pi$
$163$	189235.			0.557869			0.278935	+	0.960310i	$0.410019\pi$
$164$	−168691.	+	34678.2i	−0.489758	+	0.100681i
$165$	−1.60991e6			−4.60353
$166$	5513.41	−	4005.72i	0.0155292	−	0.0112826i
$167$	−28105.6			−0.0779834			−0.0389917	−	0.999240i	$-0.512415\pi$
$167$	−28105.6			−0.0779834			−0.0389917	+	0.999240i	$0.512415\pi$
$168$	−13093.0	+	40296.3i	−0.0357905	+	0.110152i
$169$	271242.	−	834796.i	0.730533	−	2.24835i
$170$	47418.1	−	34451.2i	0.125841	−	0.0914287i
$171$	−1.02167e6	−	742287.i	−2.67190	−	1.94125i
$172$	−13444.5	−	41377.8i	−0.0346515	−	0.106647i
$173$	505041.			1.28295			0.641477	−	0.767142i	$-0.278322\pi$
$173$	505041.			1.28295			0.641477	+	0.767142i	$0.278322\pi$
$174$	207969.	+	640062.i	0.520745	+	1.60269i
$175$	49491.0	+	152318.i	0.122161	+	0.375972i
$176$	46593.8	−	143401.i	0.113383	−	0.348956i
$177$	−536499.	+	389789.i	−1.28717	+	0.935183i
$178$	−253948.			−0.600751
$179$	107392.	−	330517.i	0.250517	−	0.771013i	−0.744162	−	0.667999i	$-0.767151\pi$
$179$	107392.	−	330517.i	0.250517	−	0.771013i	0.994680	−	0.103015i	$-0.0328488\pi$
$180$	665301.	+	483370.i	1.53051	+	1.11198i
$181$	−145785.	−	448680.i	−0.330762	−	1.01798i	−0.968772	−	0.247954i	$-0.920242\pi$
$181$	−145785.	−	448680.i	−0.330762	−	1.01798i	0.638009	−	0.770029i	$-0.279758\pi$
$182$	−86732.0	+	63014.5i	−0.194089	+	0.141014i
$183$	510698.	+	371043.i	1.12729	+	0.819025i
$184$	−26715.8	−	19410.2i	−0.0581733	−	0.0422654i
$185$	492343.	+	357708.i	1.05764	+	0.768422i
$186$	−257578.	−	187141.i	−0.545917	−	0.396632i
$187$	70518.2	−	51234.5i	0.147468	−	0.107142i
$188$	1105.20	+	3401.46i	0.00228058	+	0.00701892i
$189$	−147879.	−	107440.i	−0.301128	−	0.218782i
$190$	297736.	−	916336.i	0.598339	−	1.84150i
$191$	−395620.			−0.784684			−0.392342	−	0.919819i	$-0.628335\pi$
$191$	−395620.			−0.784684			−0.392342	+	0.919819i	$0.628335\pi$
$192$	−91479.6	+	66463.8i	−0.179090	+	0.130116i
$193$	−34328.1	+	105651.i	−0.0663371	+	0.204165i	−0.978731	−	0.205150i	$-0.934232\pi$
$193$	−34328.1	+	105651.i	−0.0663371	+	0.204165i	0.912394	+	0.409314i	$0.134232\pi$
$194$	53894.9	+	165871.i	0.102812	+	0.316422i
$195$	943989.	+	2.90530e6i	1.77779	+	5.47147i
$196$	−259710.			−0.482891
$197$	237815.	+	731919.i	0.436590	+	1.34368i	0.891449	+	0.453121i	$0.149690\pi$
$197$	237815.	+	731919.i	0.436590	+	1.34368i	−0.454859	+	0.890563i	$0.650310\pi$
$198$	989409.	+	718848.i	1.79355	+	1.30309i
$199$	302783.	−	219985.i	0.542000	−	0.393786i	−0.282828	−	0.959171i	$-0.591272\pi$
$199$	302783.	−	219985.i	0.542000	−	0.393786i	0.824827	+	0.565385i	$0.191272\pi$
$200$	−132079.	+	406498.i	−0.233485	+	0.718594i
$201$	283132.	−	871390.i	0.494309	−	1.52133i
$202$	−184476.			−0.318099
$203$	118244.	−	85909.3i	0.201390	−	0.146319i
$204$	−65367.9			−0.109974
$205$	1.04390e6	−	214597.i	1.73490	−	0.356648i
$206$	704316.			1.15638
$207$	216691.	−	157435.i	0.351492	−	0.255374i
$208$	−286108.			−0.458534
$209$	442781.	−	1.36274e6i	0.701169	−	2.15798i
$210$	81023.1	−	249364.i	0.126783	−	0.390198i
$211$	158581.	−	115216.i	0.245214	−	0.178159i	−0.458389	−	0.888752i	$-0.651573\pi$
$211$	158581.	−	115216.i	0.245214	−	0.178159i	0.703603	+	0.710593i	$0.251573\pi$
$212$	141836.	+	103050.i	0.216744	+	0.157474i
$213$	−21746.9	−	66930.1i	−0.0328434	−	0.101082i
$214$	−321436.			−0.479801
$215$	83197.8	+	256057.i	0.122748	+	0.377781i
$216$	−150743.	−	463940.i	−0.219839	−	0.676593i
$217$	−21366.8	+	65760.2i	−0.0308028	+	0.0948012i
$218$	281633.	−	204618.i	0.401368	−	0.291611i
$219$	−898934.			−1.26654
$220$	−288334.	+	887402.i	−0.401642	+	1.23613i
$221$	−133809.	−	97218.0i	−0.184291	−	0.133895i
$222$	−209735.	−	645498.i	−0.285620	−	0.879048i
$223$	−776959.	+	564494.i	−1.04625	+	0.760146i	−0.971496	−	0.237056i	$-0.923817\pi$
$223$	−776959.	+	564494.i	−1.04625	+	0.760146i	−0.0747550	+	0.997202i	$0.523817\pi$
$224$	19866.9	+	14434.1i	0.0264551	+	0.0192208i
$225$	−2.80467e6	−	2.03771e6i	−3.69340	−	2.68341i
$226$	239606.	+	174084.i	0.312051	+	0.226719i
$227$	985546.	+	716041.i	1.26944	+	0.922302i	0.999180	−	0.0404853i	$-0.0128904\pi$
$227$	985546.	+	716041.i	1.26944	+	0.922302i	0.270260	+	0.962787i	$0.412890\pi$
$228$	−869330.	+	631605.i	−1.10751	+	0.804653i
$229$	195796.	+	602598.i	0.246726	+	0.759344i	0.995348	+	0.0963471i	$0.0307159\pi$
$229$	195796.	+	602598.i	0.246726	+	0.759344i	−0.748622	+	0.662997i	$0.769284\pi$
$230$	165324.	+	120115.i	0.206071	+	0.149719i
$231$	120494.	−	370843.i	0.148572	−	0.457257i
$232$	390058.			0.475783
$233$	−126157.	+	91658.4i	−0.152237	+	0.110607i	−0.661296	−	0.750125i	$-0.729993\pi$
$233$	−126157.	+	91658.4i	−0.152237	+	0.110607i	0.509059	+	0.860732i	$0.329993\pi$
$234$	717108.	−	2.20703e6i	0.856141	−	2.63493i
$235$	−6839.26	−	21049.1i	−0.00807866	−	0.0248636i
$236$	118770.	+	365536.i	0.138812	+	0.427219i
$237$	1.67612e6			1.93836
$238$	4386.85	+	13501.3i	0.00502007	+	0.0154502i
$239$	221873.	+	161201.i	0.251253	+	0.182546i	0.706282	−	0.707931i	$-0.250371\pi$
$239$	221873.	+	161201.i	0.251253	+	0.182546i	−0.455029	+	0.890477i	$0.650371\pi$
$240$	566099.	−	411295.i	0.634402	−	0.460920i
$241$	−349622.	+	1.07602e6i	−0.387753	+	1.19338i	0.546710	+	0.837322i	$0.315880\pi$
$241$	−349622.	+	1.07602e6i	−0.387753	+	1.19338i	−0.934463	+	0.356060i	$0.884120\pi$
$242$	−229729.	+	707034.i	−0.252161	+	0.776071i
$243$	474364.			0.515342
$244$	295990.	−	215049.i	0.318275	−	0.231240i
$245$	1.60715e6			1.71058
$246$	−1.08256e6	−	490692.i	−1.14055	−	0.516977i
$247$	−2.71888e6			−2.83562
$248$	−149287.	+	108463.i	−0.154132	+	0.111984i
$249$	47033.7			0.0480740
$250$	434884.	−	1.33844e6i	0.440072	−	1.35440i
$251$	38393.4	−	118163.i	0.0384656	−	0.118385i	−0.929980	−	0.367610i	$-0.880176\pi$
$251$	38393.4	−	118163.i	0.0384656	−	0.118385i	0.968445	+	0.249225i	$0.0801760\pi$
$252$	−161140.	+	117075.i	−0.159846	+	0.116135i
$253$	245863.	+	178630.i	0.241486	+	0.175450i
$254$	194673.	+	599142.i	0.189331	+	0.582700i
$255$	404513.			0.389567
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−164388.	−	505935.i	−0.155252	−	0.477817i	0.842934	−	0.538017i	$-0.180826\pi$
$257$	−164388.	−	505935.i	−0.155252	−	0.477817i	−0.998186	+	0.0601994i	$0.980826\pi$
$258$	92787.7	−	285571.i	0.0867843	−	0.267095i
$259$	−119248.	+	86638.9i	−0.110459	+	0.0802534i
$260$	1.77051e6			1.62429
$261$	−977652.	+	3.00890e6i	−0.888348	+	2.73405i
$262$	−989391.	−	718834.i	−0.890460	−	0.646957i
$263$	641594.	+	1.97462e6i	0.571967	+	1.76033i	0.646282	+	0.763099i	$0.276323\pi$
$263$	641594.	+	1.97462e6i	0.571967	+	1.76033i	−0.0743150	+	0.997235i	$0.523677\pi$
$264$	841879.	−	611661.i	0.743430	−	0.540133i
$265$	−877720.	−	637701.i	−0.767788	−	0.557830i
$266$	188795.	+	137167.i	0.163601	+	0.118863i
$267$	−1.41791e6	−	1.03017e6i	−1.21722	−	0.884365i
$268$	−429613.	−	312132.i	−0.365376	−	0.265462i
$269$	−951856.	+	691564.i	−0.802030	+	0.582709i	−0.911509	−	0.411280i	$-0.865082\pi$
$269$	−951856.	+	691564.i	−0.802030	+	0.582709i	0.109479	+	0.993989i	$0.465082\pi$
$270$	932838.	+	2.87098e6i	0.778748	+	2.39674i
$271$	−46180.5	−	33552.1i	−0.0381976	−	0.0277521i	0.568523	−	0.822668i	$-0.307515\pi$
$271$	−46180.5	−	33552.1i	−0.0381976	−	0.0277521i	−0.606720	+	0.794915i	$0.707515\pi$
$272$	−11707.4	+	36031.7i	−0.00959485	+	0.0295299i
$273$	−739892.			−0.600844
$274$	−604047.	+	438866.i	−0.486065	+	0.353147i
$275$	1.21551e6	−	3.74097e6i	0.969233	−	2.98299i
$276$	−70427.0	−	216752.i	−0.0556502	−	0.171274i
$277$	−7449.96	−	22928.6i	−0.00583384	−	0.0179547i	0.948097	−	0.317981i	$-0.103005\pi$
$277$	−7449.96	−	22928.6i	−0.00583384	−	0.0179547i	−0.953931	+	0.300026i	$0.903005\pi$
$278$	1.35680e6			1.05294
$279$	−462509.	−	1.42346e6i	−0.355721	−	1.09480i
$280$	−122941.	−	89322.1i	−0.0937136	−	0.0680869i
$281$	−1.92824e6	+	1.40095e6i	−1.45678	+	1.05841i	−0.472595	+	0.881280i	$0.656683\pi$
$281$	−1.92824e6	+	1.40095e6i	−1.45678	+	1.05841i	−0.984187	+	0.177134i	$0.943317\pi$
$282$	−7627.59	+	23475.3i	−0.00571169	+	0.0175788i
$283$	−421505.	+	1.29726e6i	−0.312850	+	0.962854i	0.663780	+	0.747928i	$0.268951\pi$
$283$	−421505.	+	1.29726e6i	−0.312850	+	0.962854i	−0.976630	+	0.214926i	$0.931049\pi$
$284$	−40787.6			−0.0300077
$285$	5.37963e6	−	3.90853e6i	3.92320	−	2.85037i
$286$	2.63303e6			1.90345
$287$	−28698.7	+	256526.i	−0.0205664	+	0.183834i
$288$	−531560.			−0.377634
$289$	1.13097e6	−	821698.i	0.796538	−	0.578719i
$290$	−2.41378e6			−1.68540
$291$	−371958.	+	1.14477e6i	−0.257491	+	0.792475i
$292$	−160999.	+	495504.i	−0.110501	+	0.340087i
$293$	869728.	−	631894.i	0.591854	−	0.430007i	−0.251124	−	0.967955i	$-0.580800\pi$
$293$	869728.	−	631894.i	0.591854	−	0.430007i	0.842978	+	0.537948i	$0.180800\pi$
$294$	−1.45009e6	−	1.05355e6i	−0.978420	−	0.710863i
$295$	−734979.	−	2.26203e6i	−0.491722	−	1.51337i
$296$	−393371.			−0.260959
$297$	1.38728e6	+	4.26961e6i	0.912584	+	2.80864i
$298$	232388.	+	715216.i	0.151591	+	0.466548i
$299$	178198.	−	548437.i	0.115272	−	0.354772i
$300$	−2.38647e6	+	1.73387e6i	−1.53092	+	1.11228i
$301$	−65209.9			−0.0414856
$302$	−359622.	+	1.10680e6i	−0.226897	+	0.698317i
$303$	−1.03002e6	−	748353.i	−0.644523	−	0.468274i
$304$	192452.	+	592307.i	0.119437	+	0.367589i
$305$	−1.83166e6	+	1.33078e6i	−1.12745	+	0.819138i
$306$	−248604.	−	180621.i	−0.151777	−	0.110272i
$307$	1.00380e6	+	729305.i	0.607858	+	0.441635i	0.848659	−	0.528940i	$-0.177410\pi$
$307$	1.00380e6	+	729305.i	0.607858	+	0.441635i	−0.240801	+	0.970574i	$0.577410\pi$
$308$	−182833.	−	132836.i	−0.109819	−	0.0797884i
$309$	3.93252e6	+	2.85715e6i	2.34302	+	1.70230i
$310$	923827.	−	671200.i	0.545992	−	0.396687i
$311$	−348312.	−	1.07199e6i	−0.204205	−	0.628480i	−0.999745	−	0.0225781i	$-0.992813\pi$
$311$	−348312.	−	1.07199e6i	−0.204205	−	0.628480i	0.795540	−	0.605901i	$-0.207187\pi$
$312$	−1.59747e6	−	1.16063e6i	−0.929068	−	0.675007i
$313$	−42148.8	+	129721.i	−0.0243178	+	0.0748425i	−0.962479	−	0.271356i	$-0.912528\pi$
$313$	−42148.8	+	129721.i	−0.0243178	+	0.0748425i	0.938161	+	0.346199i	$0.112528\pi$
$314$	−614315.			−0.351615
$315$	997173.	−	724488.i	0.566231	−	0.411391i
$316$	300194.	−	923902.i	0.169116	−	0.520485i
$317$	−899451.	−	2.76822e6i	−0.502723	−	1.54722i	−0.804564	−	0.593865i	$-0.797601\pi$
$317$	−899451.	−	2.76822e6i	−0.502723	−	1.54722i	0.301841	−	0.953358i	$-0.402399\pi$
$318$	373903.	+	1.15075e6i	0.207344	+	0.638139i
$319$	−3.58967e6			−1.97505
$320$	−125323.	−	385704.i	−0.0684157	−	0.210562i
$321$	−1.79473e6	−	1.30395e6i	−0.972158	−	0.706314i
$322$	−40042.4	+	29092.5i	−0.0215219	+	0.0156366i
$323$	−111255.	+	342409.i	−0.0593355	+	0.182616i
$324$	416683.	−	1.28242e6i	0.220518	−	0.678684i
$325$	−7.46383e6			−3.91971
$326$	612377.	−	444918.i	0.319135	−	0.231865i
$327$	2.40255e6			1.24252
$328$	−464362.	+	508837.i	−0.238326	+	0.261152i
$329$	5360.56			0.00273036
$330$	−5.20976e6	+	3.78512e6i	−2.63350	+	1.91335i
$331$	−2.68386e6			−1.34645			−0.673224	−	0.739439i	$-0.735091\pi$
$331$	−2.68386e6			−1.34645			−0.673224	+	0.739439i	$0.735091\pi$
$332$	8423.74	−	25925.6i	0.00419430	−	0.0129087i
$333$	985955.	−	3.03446e6i	0.487244	−	1.49958i
$334$	−90951.8	+	66080.3i	−0.0446113	+	0.0324120i
$335$	2.65856e6	+	1.93155e6i	1.29430	+	0.940361i
$336$	52372.2	+	161185.i	0.0253077	+	0.0778891i
$337$	2.19677e6			1.05368			0.526842	−	0.849963i	$-0.323376\pi$
$337$	2.19677e6			1.05368			0.526842	+	0.849963i	$0.323376\pi$
$338$	−1.08497e6	−	3.33919e6i	−0.516565	−	1.58982i
$339$	631638.	+	1.94398e6i	0.298517	+	0.918741i
$340$	72448.4	−	222973.i	0.0339884	−	0.104606i
$341$	1.37388e6	−	998181.i	0.639827	−	0.464861i
$342$	−5.05141e6			−2.33533
$343$	−244839.	+	753536.i	−0.112368	+	0.345835i
$344$	−140792.	−	102292.i	−0.0641480	−	0.0466062i
$345$	435821.	+	1.34132e6i	0.197133	+	0.606714i
$346$	1.63435e6	−	1.18742e6i	0.733929	−	0.533230i
$347$	529248.	+	384521.i	0.235959	+	0.171434i	0.699481	−	0.714651i	$-0.253415\pi$
$347$	529248.	+	384521.i	0.235959	+	0.171434i	−0.463522	+	0.886085i	$0.653415\pi$
$348$	2.17788e6	+	1.58232e6i	0.964019	+	0.700400i
$349$	−135171.	−	98207.7i	−0.0594047	−	0.0431600i	0.557687	−	0.830052i	$-0.311689\pi$
$349$	−135171.	−	98207.7i	−0.0594047	−	0.0431600i	−0.617091	+	0.786892i	$0.711689\pi$
$350$	518277.	+	376550.i	0.226147	+	0.164306i
$351$	6.89165e6	−	5.00708e6i	2.98576	−	2.16928i
$352$	−186375.	−	573604.i	−0.0801736	−	0.246749i
$353$	−920330.	−	668659.i	−0.393104	−	0.285606i	0.373623	−	0.927581i	$-0.378116\pi$
$353$	−920330.	−	668659.i	−0.393104	−	0.285606i	−0.766726	+	0.641974i	$0.778116\pi$
$354$	−819697.	+	2.52277e6i	−0.347652	+	1.06996i
$355$	252404.			0.106298
$356$	−821792.	+	597067.i	−0.343666	+	0.249688i
$357$	−30276.0	+	93180.0i	−0.0125727	+	0.0386948i
$358$	−429567.	−	1.32207e6i	−0.177143	−	0.545189i
$359$	549278.	+	1.69050e6i	0.224934	+	0.692277i	0.998298	+	0.0583145i	$0.0185726\pi$
$359$	549278.	+	1.69050e6i	0.224934	+	0.692277i	−0.773364	+	0.633962i	$0.781427\pi$
$360$	3.28943e6			1.33772
$361$	1.06371e6	+	3.27378e6i	0.429593	+	1.32215i
$362$	−1.52668e6	−	1.10920e6i	−0.612317	−	0.444875i
$363$	−4.15086e6	+	3.01577e6i	−1.65337	+	1.20125i
$364$	−132515.	+	407838.i	−0.0524217	+	0.161337i
$365$	996303.	−	3.06631e6i	0.391435	−	1.20471i
$366$	2.52503e6			0.985288
$367$	891222.	−	647510.i	0.345399	−	0.250947i	−0.401538	−	0.915843i	$-0.631524\pi$
$367$	891222.	−	647510.i	0.345399	−	0.250947i	0.746936	+	0.664896i	$0.231524\pi$
$368$	−132090.			−0.0508453
$369$	−2.76127e6	−	4.85744e6i	−1.05571	−	1.85713i
$370$	2.43428e6			0.924413
$371$	212588.	−	154455.i	0.0801871	−	0.0582594i
$372$	−1.27354e6			−0.477149
$373$	971638.	−	2.99039e6i	0.361603	−	1.11290i	−0.590477	−	0.807054i	$-0.701061\pi$
$373$	971638.	−	2.99039e6i	0.361603	−	1.11290i	0.952081	−	0.305847i	$-0.0989395\pi$
$374$	107742.	−	331597.i	0.0398297	−	0.122583i
$375$	7.85770e6	−	5.70896e6i	2.88548	−	2.09642i
$376$	11573.8	+	8408.86i	0.00422189	+	0.00306738i
$377$	2.10485e6	+	6.47807e6i	0.762725	+	2.34743i
$378$	−731152.			−0.263195
$379$	586044.	+	1.80366e6i	0.209571	+	0.644995i	0.999495	+	0.0317888i	$0.0101204\pi$
$379$	586044.	+	1.80366e6i	0.209571	+	0.644995i	−0.789923	+	0.613206i	$0.789880\pi$
$380$	−1.19094e6	−	3.66535e6i	−0.423089	−	1.30213i
$381$	−1.34354e6	+	4.13501e6i	−0.474176	+	1.45936i
$382$	−1.28025e6	+	930159.i	−0.448888	+	0.326136i
$383$	1.40402e6			0.489075			0.244537	−	0.969640i	$-0.421364\pi$
$383$	1.40402e6			0.489075			0.244537	+	0.969640i	$0.421364\pi$
$384$	−139768.	+	430163.i	−0.0483705	+	0.148869i
$385$	1.13142e6	+	822024.i	0.389020	+	0.282639i
$386$	137312.	+	422604.i	0.0469074	+	0.144366i
$387$	1.14196e6	−	829684.i	0.387591	−	0.281602i
$388$	564394.	+	410057.i	0.190328	+	0.138282i
$389$	−590840.	−	429270.i	−0.197968	−	0.143832i	0.484385	−	0.874855i	$-0.339043\pi$
$389$	−590840.	−	429270.i	−0.197968	−	0.143832i	−0.682353	+	0.731023i	$0.739043\pi$
$390$	9.88558e6	+	7.18230e6i	3.29110	+	2.39112i
$391$	−61776.9	−	44883.6i	−0.0204355	−	0.0148472i
$392$	−840440.	+	610616.i	−0.276243	+	0.200703i
$393$	−2.60819e6	−	8.02718e6i	−0.851839	−	2.62169i
$394$	2.49043e6	+	1.80940e6i	0.808228	+	0.587212i
$395$	−1.85768e6	+	5.71734e6i	−0.599070	+	1.84375i
$396$	4.89191e6			1.56762
$397$	−2.49106e6	+	1.80986e6i	−0.793245	+	0.576326i	−0.908925	−	0.416960i	$-0.863095\pi$
$397$	−2.49106e6	+	1.80986e6i	−0.793245	+	0.576326i	0.115680	+	0.993287i	$0.463095\pi$
$398$	462611.	−	1.42377e6i	0.146389	−	0.450539i
$399$	497693.	+	1.53174e6i	0.156505	+	0.481674i
$400$	528317.	+	1.62599e6i	0.165099	+	0.508122i
$401$	−4.98528e6			−1.54821			−0.774103	−	0.633060i	$-0.781799\pi$
$401$	−4.98528e6			−1.54821			−0.774103	+	0.633060i	$0.781799\pi$
$402$	−1.13253e6	−	3.48556e6i	−0.349529	−	1.07574i
$403$	−2.60695e6	−	1.89406e6i	−0.799594	−	0.580939i
$404$	−596978.	+	433730.i	−0.181972	+	0.132211i
$405$	−2.57854e6	+	7.93594e6i	−0.781154	+	2.40415i
$406$	180661.	−	556016.i	0.0543937	−	0.167407i
$407$	3.62016e6			1.08328
$408$	−211535.	+	153689.i	−0.0629118	+	0.0457081i
$409$	−3.59529e6			−1.06274			−0.531368	−	0.847141i	$-0.678322\pi$
$409$	−3.59529e6			−1.06274			−0.531368	+	0.847141i	$0.678322\pi$
$410$	2.87359e6	−	3.14881e6i	0.844238	−	0.925097i
$411$	−5.15300e6			−1.50472
$412$	2.27921e6	−	1.65595e6i	0.661518	−	0.480621i
$413$	576071.			0.166189
$414$	331074.	−	1.01894e6i	0.0949346	−	0.292179i
$415$	−52128.2	+	160434.i	−0.0148577	+	0.0457274i
$416$	−925865.	+	672680.i	−0.262310	+	0.190579i
$417$	7.57567e6	+	5.50405e6i	2.13344	+	1.55004i
$418$	−1.77112e6	−	5.45095e6i	−0.495801	−	1.52592i
$419$	−1.62560e6			−0.452354			−0.226177	−	0.974086i	$-0.572623\pi$
$419$	−1.62560e6			−0.452354			−0.226177	+	0.974086i	$0.572623\pi$
$420$	−324093.	−	997454.i	−0.0896491	−	0.275911i
$421$	−1.52968e6	−	4.70786e6i	−0.420624	−	1.29455i	−0.907123	−	0.420866i	$-0.861726\pi$
$421$	−1.52968e6	−	4.70786e6i	−0.420624	−	1.29455i	0.486499	−	0.873681i	$-0.338274\pi$
$422$	242291.	−	745694.i	0.0662301	−	0.203835i
$423$	−93874.7	+	68204.0i	−0.0255093	+	0.0185336i
$424$	701278.			0.189442
$425$	−305416.	+	939975.i	−0.0820201	+	0.252432i
$426$	−227736.	−	165460.i	−0.0608007	−	0.0441743i
$427$	−169455.	−	521528.i	−0.0449764	−	0.138423i
$428$	−1.04019e6	+	755742.i	−0.274475	+	0.199418i
$429$	1.47014e7	+	1.06812e7i	3.85671	+	2.80206i
$430$	871259.	+	633007.i	0.227235	+	0.165096i
$431$	919525.	+	668074.i	0.238435	+	0.173233i	0.700586	−	0.713568i	$-0.252922\pi$
$431$	919525.	+	668074.i	0.238435	+	0.173233i	−0.462151	+	0.886801i	$0.652922\pi$
$432$	−1.57860e6	−	1.14692e6i	−0.406972	−	0.295682i
$433$	3.19565e6	−	2.32177e6i	0.819104	−	0.595114i	−0.0973520	−	0.995250i	$-0.531037\pi$
$433$	3.19565e6	−	2.32177e6i	0.819104	−	0.595114i	0.916456	+	0.400136i	$0.131037\pi$
$434$	85467.1	+	263041.i	0.0217809	+	0.0670346i
$435$	−1.34773e7	−	9.79180e6i	−3.41490	−	2.48107i
$436$	430297.	−	1.32432e6i	0.108406	−	0.333638i
$437$	−1.25525e6			−0.314433
$438$	−2.90901e6	+	2.11352e6i	−0.724536	+	0.526406i
$439$	−1.66712e6	+	5.13085e6i	−0.412861	+	1.27066i	0.501288	+	0.865280i	$0.332860\pi$
$439$	−1.66712e6	+	5.13085e6i	−0.412861	+	1.27066i	−0.914150	+	0.405377i	$0.867140\pi$
$440$	1.15334e6	+	3.54961e6i	0.284004	+	0.874075i
$441$	−2.60378e6	−	8.01361e6i	−0.637541	−	1.96215i
$442$	−661588.			−0.161077
$443$	−1.58334e6	−	4.87302e6i	−0.383323	−	1.17975i	−0.937690	−	0.347474i	$-0.887040\pi$
$443$	−1.58334e6	−	4.87302e6i	−0.383323	−	1.17975i	0.554367	−	0.832272i	$-0.312960\pi$
$444$	−2.19637e6	−	1.59576e6i	−0.528748	−	0.384158i
$445$	5.08546e6	−	3.69480e6i	1.21739	−	0.884487i
$446$	−1.18709e6	+	3.65348e6i	−0.282583	+	0.869700i
$447$	−1.60384e6	+	4.93610e6i	−0.379657	+	1.16846i
$448$	98227.2			0.0231226
$449$	−2.27230e6	+	1.65093e6i	−0.531925	+	0.386466i	−0.821077	−	0.570817i	$-0.806627\pi$
$449$	−2.27230e6	+	1.65093e6i	−0.531925	+	0.386466i	0.289152	+	0.957283i	$0.406627\pi$
$450$	−1.38671e7			−3.22815
$451$	4.27349e6	−	4.68279e6i	0.989330	−	1.08408i
$452$	1.18468e6			0.272743
$453$	−6.49782e6	+	4.72094e6i	−1.48772	+	1.08089i
$454$	4.87281e6			1.10953
$455$	820035.	−	2.52381e6i	0.185697	−	0.571515i
$456$	−1.32822e6	+	4.08783e6i	−0.299128	+	0.920621i
$457$	−2.73669e6	+	1.98832e6i	−0.612964	+	0.445345i	−0.850457	−	0.526045i	$-0.823674\pi$
$457$	−2.73669e6	+	1.98832e6i	−0.612964	+	0.445345i	0.237493	+	0.971389i	$0.423674\pi$
$458$	2.05040e6	+	1.48970e6i	0.456746	+	0.331846i
$459$	−348575.	−	1.07280e6i	−0.0772262	−	0.237678i
$460$	817408.			0.180113
$461$	−1.52917e6	−	4.70629e6i	−0.335122	−	1.03140i	−0.966662	−	0.256056i	$-0.917577\pi$
$461$	−1.52917e6	−	4.70629e6i	−0.335122	−	1.03140i	0.631540	−	0.775343i	$-0.282423\pi$
$462$	−481977.	−	1.48337e6i	−0.105056	−	0.323330i
$463$	−706123.	+	2.17322e6i	−0.153083	+	0.471142i	−0.997962	−	0.0638164i	$-0.979673\pi$
$463$	−706123.	+	2.17322e6i	−0.153083	+	0.471142i	0.844878	+	0.534959i	$0.179673\pi$
$464$	1.26225e6	−	917082.i	0.272177	−	0.197748i
$465$	7.88097e6			1.69024
$466$	−192751.	+	593226.i	−0.0411179	+	0.126548i
$467$	4.30564e6	+	3.12823e6i	0.913577	+	0.663753i	0.941917	−	0.335846i	$-0.109022\pi$
$467$	4.30564e6	+	3.12823e6i	0.913577	+	0.663753i	−0.0283398	+	0.999598i	$0.509022\pi$
$468$	−2.86843e6	−	8.82813e6i	−0.605383	−	1.86318i
$469$	−643916.	+	467833.i	−0.135175	+	0.0982106i
$470$	−71621.7	−	52036.2i	−0.0149555	−	0.0108658i
$471$	−3.43001e6	−	2.49205e6i	−0.712431	−	0.517612i
$472$	1.24378e6	+	903656.i	0.256973	+	0.186702i
$473$	1.29570e6	+	941382.i	0.266288	+	0.193470i
$474$	5.42405e6	−	3.94080e6i	1.10886	−	0.805636i
$475$	5.02059e6	+	1.54518e7i	1.02099	+	3.14228i
$476$	45939.6	+	33377.1i	0.00929331	+	0.00675198i
$477$	−1.75770e6	+	5.40965e6i	−0.353711	+	1.08861i
$478$	1.09700e6			0.219603
$479$	4.50370e6	−	3.27213e6i	0.896873	−	0.651616i	−0.0407878	−	0.999168i	$-0.512987\pi$
$479$	4.50370e6	−	3.27213e6i	0.896873	−	0.651616i	0.937661	+	0.347551i	$0.112987\pi$
$480$	864922.	−	2.66196e6i	0.171346	−	0.527349i
$481$	−2.12273e6	−	6.53308e6i	−0.418342	−	1.28752i
$482$	1.39849e6	+	4.30410e6i	0.274183	+	0.843849i
$483$	−341593.			−0.0666256
$484$	918916.	+	2.82813e6i	0.178305	+	0.548765i
$485$	−3.49262e6	−	2.53753e6i	−0.674212	−	0.489844i
$486$	1.53507e6	−	1.11530e6i	0.294807	−	0.214190i
$487$	−1.55703e6	+	4.79206e6i	−0.297492	+	0.915587i	0.684880	+	0.728655i	$0.259854\pi$
$487$	−1.55703e6	+	4.79206e6i	−0.297492	+	0.915587i	−0.982373	+	0.186932i	$0.940146\pi$
$488$	452233.	−	1.39183e6i	0.0859632	−	0.264567i
$489$	5.22406e6			0.987952
$490$	5.20086e6	−	3.77865e6i	0.978554	−	0.710961i
$491$	670574.			0.125529			0.0627643	−	0.998028i	$-0.480008\pi$
$491$	670574.			0.125529			0.0627643	+	0.998028i	$0.480008\pi$
$492$	−4.65691e6	+	957332.i	−0.867332	+	0.178299i
$493$	901960.			0.167136
$494$	−8.79849e6	+	6.39247e6i	−1.62215	+	1.17856i
$495$	−3.02724e7			−5.55308
$496$	−228091.	+	701990.i	−0.0416297	+	0.128123i
$497$	−18891.3	+	58141.6i	−0.00343061	+	0.0105583i
$498$	152204.	−	110583.i	0.0275013	−	0.0199809i
$499$	7.58860e6	+	5.51344e6i	1.36430	+	0.991223i	0.998158	+	0.0606652i	$0.0193222\pi$
$499$	7.58860e6	+	5.51344e6i	1.36430	+	0.991223i	0.366144	+	0.930558i	$0.380678\pi$
$500$	−1.73954e6	−	5.35375e6i	−0.311178	−	0.957707i
$501$	−775890.			−0.138104
$502$	−153574.	−	472651.i	−0.0271993	−	0.0837108i
$503$	−1.88564e6	−	5.80342e6i	−0.332307	−	1.02274i	−0.968033	−	0.250822i	$-0.919299\pi$
$503$	−1.88564e6	−	5.80342e6i	−0.332307	−	1.02274i	0.635726	−	0.771915i	$-0.280701\pi$
$504$	−246199.	+	757724.i	−0.0431728	+	0.132872i
$505$	3.69426e6	−	2.68403e6i	0.644612	−	0.468338i
$506$	1.21562e6			0.211067
$507$	7.48795e6	−	2.30455e7i	1.29373	−	3.98169i
$508$	2.03864e6	+	1.48116e6i	0.350495	+	0.254649i
$509$	−1.64047e6	−	5.04886e6i	−0.280656	−	0.863771i	−0.987667	−	0.156569i	$-0.949957\pi$
$509$	−1.64047e6	−	5.04886e6i	−0.280656	−	0.863771i	0.707011	−	0.707203i	$-0.250043\pi$
$510$	1.30903e6	−	951068.i	0.222856	−	0.161915i
$511$	631758.	+	458999.i	0.107028	+	0.0777606i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	−1.50015e7	−	1.08992e7i	−2.51675	−	1.82853i
$514$	−1.72150e6	−	1.25074e6i	−0.287408	−	0.208814i
$515$	−1.41044e7	+	1.02474e7i	−2.34334	+	1.70254i
$516$	−371151.	−	1.14228e6i	−0.0613657	−	0.188864i
$517$	−106513.	−	77386.1i	−0.0175257	−	0.0127332i
$518$	−182195.	+	560738.i	−0.0298340	+	0.0918197i
$519$	1.39423e7			2.27203
$520$	5.72949e6	−	4.16272e6i	0.929196	−	0.675100i
$521$	−1.25547e6	+	3.86392e6i	−0.202633	+	0.623641i	0.797169	+	0.603756i	$0.206330\pi$
$521$	−1.25547e6	+	3.86392e6i	−0.202633	+	0.623641i	−0.999802	+	0.0198845i	$0.993670\pi$
$522$	3.91061e6	+	1.20356e7i	0.628157	+	1.93327i
$523$	2.37895e6	+	7.32167e6i	0.380305	+	1.17046i	0.939829	+	0.341644i	$0.110984\pi$
$523$	2.37895e6	+	7.32167e6i	0.380305	+	1.17046i	−0.559525	+	0.828814i	$0.689016\pi$
$524$	−4.89182e6			−0.778291
$525$	1.36626e6	+	4.20491e6i	0.216339	+	0.665823i
$526$	6.71886e6	+	4.88154e6i	1.05884	+	0.769294i
$527$	−345208.	+	250808.i	−0.0541445	+	0.0393383i
$528$	1.28628e6	−	3.95875e6i	0.200794	−	0.617979i
$529$	−1.90667e6	+	5.86812e6i	−0.296235	+	0.911717i
$530$	−4.33968e6			−0.671071
$531$	−1.00882e7	+	7.32952e6i	−1.55267	+	1.12808i
$532$	933453.			0.142992
$533$	−1.09566e7	−	4.96629e6i	−1.67054	−	0.757206i
$534$	−7.01053e6			−1.06389
$535$	6.43696e6	−	4.67673e6i	0.972292	−	0.706411i
$536$	−2.12412e6			−0.319351
$537$	2.96467e6	−	9.12433e6i	0.443651	−	1.36542i
$538$	−1.45431e6	+	4.47590e6i	−0.216621	+	0.666691i
$539$	7.73451e6	−	5.61945e6i	1.14673	−	0.833147i
$540$	9.76881e6	+	7.09746e6i	1.44164	+	1.04741i
$541$	3.45029e6	+	1.06189e7i	0.506830	+	1.55986i	0.797671	+	0.603092i	$0.206065\pi$
$541$	3.45029e6	+	1.06189e7i	0.506830	+	1.55986i	−0.290841	+	0.956771i	$0.593935\pi$
$542$	−228329.			−0.0333859
$543$	−4.02457e6	−	1.23863e7i	−0.585760	−	1.80278i
$544$	46829.6	+	144127.i	0.00678458	+	0.0208808i
$545$	−2.66279e6	+	8.19522e6i	−0.384012	+	1.18187i
$546$	−2.39434e6	+	1.73959e6i	−0.343720	+	0.249727i
$547$	−1.31488e7			−1.87896			−0.939480	−	0.342604i	$-0.888691\pi$
$547$	−1.31488e7			−1.87896			−0.939480	+	0.342604i	$0.888691\pi$
$548$	−922902.	+	2.84040e6i	−0.131282	+	0.404044i
$549$	9.60306e6	+	6.97703e6i	1.35981	+	0.987961i
$550$	−4.86206e6	−	1.49639e7i	−0.685352	−	2.10930i
$551$	1.19952e7	−	8.71502e6i	1.68317	−	1.22290i
$552$	−737522.	−	535841.i	−0.103021	−	0.0748494i
$553$	−1.17796e6	−	855836.i	−0.163801	−	0.119008i
$554$	−78017.0	−	56682.7i	−0.0107998	−	0.00784650i
$555$	1.35917e7	+	9.87496e6i	1.87302	+	1.36083i
$556$	4.39071e6	−	3.19004e6i	0.602348	−	0.437631i
$557$	3.47214e6	+	1.06861e7i	0.474197	+	1.45943i	0.847037	+	0.531533i	$0.178384\pi$
$557$	3.47214e6	+	1.06861e7i	0.474197	+	1.45943i	−0.372840	+	0.927895i	$0.621616\pi$
$558$	−4.84345e6	−	3.51897e6i	−0.658521	−	0.478443i
$559$	939104.	−	2.89026e6i	0.127111	−	0.391208i
$560$	−607855.			−0.0819087
$561$	1.94674e6	−	1.41439e6i	0.261156	−	0.189741i
$562$	−2.94608e6	+	9.06711e6i	−0.393463	+	1.21096i
$563$	−2.86313e6	−	8.81181e6i	−0.380689	−	1.17164i	−0.939560	−	0.342385i	$-0.888765\pi$
$563$	−2.86313e6	−	8.81181e6i	−0.380689	−	1.17164i	0.558871	−	0.829255i	$-0.311235\pi$
$564$	30510.4	+	93901.2i	0.00403877	+	0.0124301i
$565$	−7.33108e6			−0.966155
$566$	1.68602e6	+	5.18903e6i	0.221219	+	0.680841i
$567$	−1.63506e6	−	1.18794e6i	−0.213587	−	0.155180i
$568$	−131992.	+	95897.4i	−0.0171662	+	0.0124720i
$569$	3.46968e6	−	1.06786e7i	0.449271	−	1.38271i	−0.428461	−	0.903560i	$-0.640944\pi$
$569$	3.46968e6	−	1.06786e7i	0.449271	−	1.38271i	0.877731	−	0.479153i	$-0.159056\pi$
$570$	8.21935e6	−	2.52966e7i	1.05962	−	3.26118i
$571$	−3.25523e6			−0.417822			−0.208911	−	0.977935i	$-0.566992\pi$
$571$	−3.25523e6			−0.417822			−0.208911	+	0.977935i	$0.566992\pi$
$572$	8.52066e6	−	6.19062e6i	1.08889	−	0.791123i
$573$	−1.09216e7			−1.38963
$574$	510257.	+	897609.i	0.0646411	+	0.113712i
$575$	−3.44590e6			−0.434643
$576$	−1.72017e6	+	1.24977e6i	−0.216030	+	0.156955i
$577$	1.37951e7			1.72498			0.862492	−	0.506071i	$-0.168903\pi$
$577$	1.37951e7			1.72498			0.862492	+	0.506071i	$0.168903\pi$
$578$	1.72797e6	−	5.31814e6i	0.215137	−	0.662125i
$579$	−947668.	+	2.91662e6i	−0.117479	+	0.361563i
$580$	−7.81115e6	+	5.67514e6i	−0.964151	+	0.700497i
$581$	−33054.6	−	24015.6i	−0.00406248	−	0.00295157i
$582$	1.48783e6	+	4.57908e6i	0.182073	+	0.560364i
$583$	−6.45380e6			−0.786401
$584$	643996.	+	1.98202e6i	0.0781360	+	0.240478i
$585$	1.77506e7	+	5.46307e7i	2.14449	+	6.60005i
$586$	1.32883e6	−	4.08971e6i	0.159854	−	0.491981i
$587$	1.44092e6	−	1.04689e6i	0.172601	−	0.125402i	−0.498131	−	0.867102i	$-0.665980\pi$
$587$	1.44092e6	−	1.04689e6i	0.172601	−	0.125402i	0.670732	+	0.741700i	$0.265980\pi$
$588$	−7.16961e6			−0.855170
$589$	−2.16754e6	+	6.67101e6i	−0.257442	+	0.792325i
$590$	−7.69680e6	−	5.59205e6i	−0.910291	−	0.661365i
$591$	6.56516e6	+	2.02055e7i	0.773173	+	2.37958i
$592$	−1.27297e6	+	924870.i	−0.149285	+	0.108462i
$593$	4.24117e6	+	3.08139e6i	0.495278	+	0.359841i	0.807211	−	0.590264i	$-0.200976\pi$
$593$	4.24117e6	+	3.08139e6i	0.495278	+	0.359841i	−0.311932	+	0.950104i	$0.600976\pi$
$594$	1.45278e7	+	1.05550e7i	1.68940	+	1.22742i
$595$	−284286.	−	206546.i	−0.0329203	−	0.0239180i
$596$	2.43360e6	+	1.76811e6i	0.280629	+	0.203889i
$597$	8.35869e6	−	6.07294e6i	0.959848	−	0.697370i
$598$	−712792.	−	2.19375e6i	−0.0815098	−	0.250861i
$599$	−725424.	−	527051.i	−0.0826085	−	0.0600186i	0.545714	−	0.837971i	$-0.316258\pi$
$599$	−725424.	−	527051.i	−0.0826085	−	0.0600186i	−0.628323	+	0.777953i	$0.716258\pi$
$600$	−3.64620e6	+	1.12219e7i	−0.413488	+	1.27258i
$601$	1.66844e7			1.88419			0.942093	−	0.335351i	$-0.108855\pi$
$601$	1.66844e7			1.88419			0.942093	+	0.335351i	$0.108855\pi$
$602$	−211024.	+	153318.i	−0.0237323	+	0.0172425i
$603$	5.32396e6	−	1.63855e7i	0.596268	−	1.83512i
$604$	1.43849e6	+	4.42721e6i	0.160440	+	0.493784i
$605$	−5.68649e6	−	1.75012e7i	−0.631620	−	1.94393i
$606$	−5.09269e6			−0.563334
$607$	−2.50854e6	−	7.72051e6i	−0.276344	−	0.850500i	−0.988861	−	0.148844i	$-0.952445\pi$
$607$	−2.50854e6	−	7.72051e6i	−0.276344	−	0.850500i	0.712517	−	0.701655i	$-0.247555\pi$
$608$	2.01538e6	+	1.46426e6i	0.221105	+	0.160642i
$609$	3.26427e6	−	2.37163e6i	0.356650	−	0.259121i
$610$	−2.79853e6	+	8.61299e6i	−0.304513	+	0.937194i
$611$	−77198.8	+	237594.i	−0.00836580	+	0.0257473i
$612$	−1.22917e6			−0.132658
$613$	8.62961e6	−	6.26978e6i	0.927555	−	0.673908i	−0.0178379	−	0.999841i	$-0.505678\pi$
$613$	8.62961e6	−	6.26978e6i	0.927555	−	0.673908i	0.945393	+	0.325933i	$0.105678\pi$
$614$	4.96307e6			0.531287
$615$	2.88182e7	−	5.92422e6i	3.07241	−	0.631602i
$616$	−903978.			−0.0959856
$617$	−2.35709e6	+	1.71253e6i	−0.249267	+	0.181103i	−0.705402	−	0.708808i	$-0.749233\pi$
$617$	−2.35709e6	+	1.71253e6i	−0.249267	+	0.181103i	0.456135	+	0.889911i	$0.349233\pi$
$618$	1.94435e7			2.04787
$619$	−1.11650e6	+	3.43622e6i	−0.117120	+	0.360458i	−0.992383	−	0.123189i	$-0.960688\pi$
$619$	−1.11650e6	+	3.43622e6i	−0.117120	+	0.360458i	0.875263	+	0.483647i	$0.160688\pi$
$620$	1.41148e6	−	4.34410e6i	0.147467	−	0.453858i
$621$	3.18174e6	−	2.31167e6i	0.331082	−	0.240545i
$622$	−3.64757e6	−	2.65011e6i	−0.378031	−	0.274656i
$623$	470477.	+	1.44798e6i	0.0485645	+	0.149466i
$624$	−7.89835e6			−0.812035
$625$	4.31553e6	+	1.32818e7i	0.441910	+	1.36006i
$626$	168595.	+	518883.i	0.0171953	+	0.0529216i
$627$	1.22235e7	−	3.76200e7i	1.24173	−	3.82164i
$628$	−1.98796e6	+	1.44434e6i	−0.201145	+	0.146140i
$629$	−909620.			−0.0916713
$630$	1.52354e6	−	4.68899e6i	0.152934	−	0.470682i
$631$	−1.26319e7	−	9.17762e6i	−1.26298	−	0.917606i	−0.264077	−	0.964502i	$-0.585067\pi$
$631$	−1.26319e7	−	9.17762e6i	−1.26298	−	0.917606i	−0.998900	+	0.0468951i	$0.985067\pi$
$632$	−1.20078e6	−	3.69561e6i	−0.119583	−	0.368039i
$633$	4.37783e6	−	3.18068e6i	0.434259	−	0.315508i
$634$	−9.41917e6	−	6.84343e6i	−0.930657	−	0.676162i
$635$	−1.26156e7	−	9.16579e6i	−1.24158	−	0.902061i
$636$	3.91556e6	+	2.84482e6i	0.383841	+	0.278877i
$637$	−1.46763e7	−	1.06630e7i	−1.43307	−	1.04119i
$638$	−1.16164e7	+	8.43983e6i	−1.12985	+	0.820885i
$639$	−408925.	−	1.25854e6i	−0.0396179	−	0.121931i
$640$	−1.31240e6	−	953513.i	−0.126653	−	0.0920189i
$641$	−2.84375e6	+	8.75215e6i	−0.273367	+	0.841336i	0.716280	+	0.697813i	$0.245843\pi$
$641$	−2.84375e6	+	8.75215e6i	−0.273367	+	0.841336i	−0.989647	+	0.143524i	$0.954157\pi$
$642$	−8.87364e6			−0.849697
$643$	9.88821e6	−	7.18420e6i	0.943170	−	0.685253i	−0.00601143	−	0.999982i	$-0.501914\pi$
$643$	9.88821e6	−	7.18420e6i	0.943170	−	0.685253i	0.949182	+	0.314729i	$0.101914\pi$
$644$	−61179.4	+	188291.i	−0.00581287	+	0.0178902i
$645$	2.29678e6	+	7.06875e6i	0.217380	+	0.669026i
$646$	445021.	+	1.36963e6i	0.0419565	+	0.129129i
$647$	−2.15262e6			−0.202165			−0.101083	−	0.994878i	$-0.532231\pi$
$647$	−2.15262e6			−0.202165			−0.101083	+	0.994878i	$0.532231\pi$
$648$	−1.66673e6	−	5.12968e6i	−0.155930	−	0.479902i
$649$	−1.14464e7	−	8.31627e6i	−1.06673	−	0.775027i
$650$	−2.41535e7	+	1.75485e7i	−2.24231	+	1.62914i
$651$	−589856.	+	1.81539e6i	−0.0545498	+	0.167887i
$652$	935629.	−	2.87957e6i	0.0861955	−	0.265283i
$653$	−1.07533e7			−0.986864			−0.493432	−	0.869784i	$-0.664258\pi$
$653$	−1.07533e7			−0.986864			−0.493432	+	0.869784i	$0.664258\pi$
$654$	7.77482e6	−	5.64873e6i	0.710797	−	0.516424i
$655$	3.02718e7			2.75699
$656$	−306359.	+	2.73841e6i	−0.0277953	+	0.248450i
$657$	−1.69034e7			−1.52778
$658$	17347.1	−	12603.4i	0.00156194	−	0.00113481i
$659$	1.79130e7			1.60677			0.803386	−	0.595459i	$-0.203030\pi$
$659$	1.79130e7			1.60677			0.803386	+	0.595459i	$0.203030\pi$
$660$	−7.95981e6	+	2.44978e7i	−0.711284	+	2.18911i
$661$	−5.29127e6	+	1.62849e7i	−0.471038	+	1.44971i	0.380189	+	0.924909i	$0.375859\pi$
$661$	−5.29127e6	+	1.62849e7i	−0.471038	+	1.44971i	−0.851227	+	0.524798i	$0.824141\pi$
$662$	−8.68514e6	+	6.31013e6i	−0.770251	+	0.559620i
$663$	−3.69396e6	−	2.68382e6i	−0.326369	−	0.237121i
$664$	−33694.9	−	103702.i	−0.00296582	−	0.00912785i
$665$	−5.77644e6			−0.506531
$666$	−3.94382e6	−	1.21378e7i	−0.344533	−	1.06036i
$667$	971767.	+	2.99079e6i	0.0845761	+	0.260299i
$668$	−138962.	+	427681.i	−0.0120491	+	0.0370833i
$669$	−2.14489e7	+	1.55835e7i	−1.85285	+	1.34617i
$670$	1.31446e7			1.13126
$671$	−4.16186e6	+	1.28089e7i	−0.356846	+	1.09826i
$672$	548449.	+	398471.i	0.0468504	+	0.0340388i
$673$	−2.72739e6	−	8.39404e6i	−0.232118	−	0.714387i	−0.997491	−	0.0707990i	$-0.977445\pi$
$673$	−2.72739e6	−	8.39404e6i	−0.232118	−	0.714387i	0.765372	−	0.643588i	$-0.222555\pi$
$674$	7.10891e6	−	5.16493e6i	0.602772	−	0.437940i
$675$	−4.11818e7	−	2.99203e7i	−3.47893	−	2.52759i
$676$	−1.13619e7	−	8.25492e6i	−0.956280	−	0.694778i
$677$	−1.26176e7	−	9.16720e6i	−1.05804	−	0.768714i	−0.0843187	−	0.996439i	$-0.526871\pi$
$677$	−1.26176e7	−	9.16720e6i	−1.05804	−	0.768714i	−0.973726	+	0.227725i	$0.926871\pi$
$678$	6.61460e6	+	4.80579e6i	0.552624	+	0.401505i
$679$	845931.	−	614605.i	0.0704142	−	0.0511589i
$680$	−289793.	−	891893.i	−0.0240335	−	0.0739674i
$681$	2.72072e7	+	1.97672e7i	2.24810	+	1.63334i
$682$	2.09910e6	−	6.46036e6i	0.172811	−	0.531858i
$683$	−5.29972e6			−0.434712			−0.217356	−	0.976092i	$-0.569743\pi$
$683$	−5.29972e6			−0.434712			−0.217356	+	0.976092i	$0.569743\pi$
$684$	−1.63467e7	+	1.18766e7i	−1.33595	+	0.970625i
$685$	5.71116e6	−	1.75771e7i	0.465048	−	1.43127i
$686$	979354.	+	3.01414e6i	0.0794565	+	0.244542i
$687$	5.40518e6	+	1.66354e7i	0.436936	+	1.34475i
$688$	−696116.			−0.0560674
$689$	3.78427e6	+	1.16468e7i	0.303693	+	0.934670i
$690$	4.56397e6	+	3.31592e6i	0.364939	+	0.265144i
$691$	1.56083e7	−	1.13401e7i	1.24354	−	0.903486i	0.245713	−	0.969343i	$-0.420978\pi$
$691$	1.56083e7	−	1.13401e7i	1.24354	−	0.903486i	0.997829	+	0.0658561i	$0.0209778\pi$
$692$	2.49706e6	−	7.68516e6i	0.198227	−	0.610081i
$693$	2.26575e6	−	6.97327e6i	0.179217	−	0.551574i
$694$	2.61675e6			0.206235
$695$	−2.71708e7	+	1.97408e7i	−2.13374	+	1.55025i
$696$	1.07680e7			0.842583
$697$	−1.07378e6	+	1.17662e6i	−0.0837207	+	0.0917392i
$698$	−668323.			−0.0519216
$699$	−3.48271e6	+	2.53034e6i	−0.269603	+	0.195878i
$700$	2.56250e6			0.197660
$701$	2.46472e6	−	7.58564e6i	0.189441	−	0.583038i	−0.810556	−	0.585661i	$-0.800835\pi$
$701$	2.46472e6	−	7.58564e6i	0.189441	−	0.583038i	0.999997	+	0.00262285i	$0.000834880\pi$
$702$	1.05295e7	−	3.24065e7i	0.806427	−	2.48193i
$703$	−1.20971e7	+	8.78903e6i	−0.923191	+	0.670738i
$704$	−1.95175e6	−	1.41803e6i	−0.148420	−	0.107833i
$705$	−188806.	−	581085.i	−0.0143068	−	0.0440318i
$706$	−4.55036e6			−0.343585
$707$	341771.	+	1.05186e6i	0.0257150	+	0.0791427i
$708$	3.27879e6	+	1.00911e7i	0.245827	+	0.756579i
$709$	6.25892e6	−	1.92630e7i	0.467610	−	1.43916i	−0.388060	−	0.921634i	$-0.626855\pi$
$709$	6.25892e6	−	1.92630e7i	0.467610	−	1.43916i	0.855670	−	0.517522i	$-0.173145\pi$
$710$	816797.	−	593438.i	0.0608091	−	0.0441804i
$711$	3.15175e7			2.33818
$712$	−1.25559e6	+	3.86430e6i	−0.0928211	+	0.285674i
$713$	−1.20358e6	−	874448.i	−0.0886644	−	0.0644185i
$714$	121104.	+	372720.i	0.00889024	+	0.0273613i
$715$	−5.27280e7	+	3.83092e7i	−3.85724	+	2.80245i
$716$	−4.49848e6	−	3.26834e6i	−0.327932	−	0.238256i
$717$	6.12508e6	+	4.45013e6i	0.444953	+	0.323277i
$718$	5.75211e6	+	4.17915e6i	0.416405	+	0.302536i
$719$	8.36580e6	+	6.07811e6i	0.603511	+	0.438477i	0.847123	−	0.531396i	$-0.178332\pi$
$719$	8.36580e6	+	6.07811e6i	0.603511	+	0.438477i	−0.243612	+	0.969873i	$0.578332\pi$
$720$	1.06448e7	−	7.73392e6i	0.765257	−	0.555992i
$721$	−1.30485e6	−	4.01592e6i	−0.0934810	−	0.287705i
$722$	1.11394e7	+	8.09322e6i	0.795275	+	0.577801i
$723$	−9.65172e6	+	2.97049e7i	−0.686687	+	2.11341i
$724$	−7.54832e6			−0.535185
$725$	3.29290e7	−	2.39243e7i	2.32667	−	1.69042i
$726$	−6.34195e6	+	1.95185e7i	−0.446561	+	1.37437i
$727$	−1.30534e6	−	4.01742e6i	−0.0915983	−	0.281911i	0.894754	−	0.446560i	$-0.147351\pi$
$727$	−1.30534e6	−	4.01742e6i	−0.0915983	−	0.281911i	−0.986352	+	0.164649i	$0.947351\pi$
$728$	530059.	+	1.63135e6i	0.0370677	+	0.114083i
$729$	−7.38369e6			−0.514582
$730$	−3.98521e6	−	1.22652e7i	−0.276786	−	0.851860i
$731$	−325565.	−	236536.i	−0.0225343	−	0.0163721i
$732$	8.17116e6	−	5.93670e6i	0.563645	−	0.409512i
$733$	−2.26214e6	+	6.96214e6i	−0.155510	+	0.478611i	−0.998212	−	0.0597692i	$-0.980964\pi$
$733$	−2.26214e6	+	6.96214e6i	−0.155510	+	0.478611i	0.842702	+	0.538380i	$0.180964\pi$
$734$	1.36167e6	−	4.19078e6i	0.0932890	−	0.287114i
$735$	4.43674e7			3.02932
$736$	−427453.	+	310563.i	−0.0290866	+	0.0211327i
$737$	1.95481e7			1.32567
$738$	−2.03562e7	−	9.22688e6i	−1.37580	−	0.623611i
$739$	7.62072e6			0.513316			0.256658	−	0.966502i	$-0.417379\pi$
$739$	7.62072e6			0.513316			0.256658	+	0.966502i	$0.417379\pi$
$740$	7.87749e6	−	5.72333e6i	0.528821	−	0.384211i
$741$	−7.50580e7			−5.02171
$742$	324806.	−	999651.i	0.0216578	−	0.0666559i
$743$	−6.24336e6	+	1.92151e7i	−0.414903	+	1.27694i	0.497435	+	0.867501i	$0.334275\pi$
$743$	−6.24336e6	+	1.92151e7i	−0.414903	+	1.27694i	−0.912338	+	0.409439i	$0.865725\pi$
$744$	−4.12125e6	+	2.99426e6i	−0.272959	+	0.198316i
$745$	−1.50597e7	−	1.09415e7i	−0.994091	−	0.722249i
$746$	−3.88655e6	−	1.19616e7i	−0.255692	−	0.786940i
$747$	884413.			0.0579901
$748$	−430969.	−	1.32639e6i	−0.0281639	−	0.0866794i
$749$	595511.	+	1.83279e6i	0.0387869	+	0.119374i
$750$	1.20055e7	−	3.69491e7i	0.779340	−	2.39856i
$751$	1.33773e7	−	9.71919e6i	0.865504	−	0.628826i	−0.0638726	−	0.997958i	$-0.520345\pi$
$751$	1.33773e7	−	9.71919e6i	0.865504	−	0.628826i	0.929377	+	0.369132i	$0.120345\pi$
$752$	57224.0			0.00369006
$753$	1.05990e6	−	3.26202e6i	0.0681202	−	0.209652i
$754$	2.20423e7	+	1.60147e7i	1.41198	+	1.02586i
$755$	−8.90172e6	−	2.73967e7i	−0.568338	−	1.74916i
$756$	−2.36606e6	+	1.71904e6i	−0.150564	+	0.109391i
$757$	−2.50164e7	−	1.81754e7i	−1.58666	−	1.15278i	−0.908517	−	0.417849i	$-0.862784\pi$
$757$	−2.50164e7	−	1.81754e7i	−1.58666	−	1.15278i	−0.678145	−	0.734928i	$-0.737216\pi$
$758$	6.13713e6	+	4.45889e6i	0.387965	+	0.281873i
$759$	6.78735e6	+	4.93130e6i	0.427658	+	0.310711i
$760$	−1.24717e7	−	9.06123e6i	−0.783235	−	0.569054i
$761$	1.65550e7	−	1.20279e7i	1.03626	−	0.752887i	0.0667076	−	0.997773i	$-0.478751\pi$
$761$	1.65550e7	−	1.20279e7i	1.03626	−	0.752887i	0.969552	+	0.244886i	$0.0787505\pi$
$762$	5.37418e6	+	1.65400e7i	0.335293	+	1.03193i
$763$	−1.68848e6	−	1.22675e6i	−0.104999	−	0.0762861i
$764$	−1.95605e6	+	6.02012e6i	−0.121240	+	0.373140i
$765$	7.60639e6			0.469921
$766$	4.54349e6	−	3.30104e6i	0.279781	−	0.203273i
$767$	−8.29615e6	+	2.55329e7i	−0.509200	+	1.56716i
$768$	559073.	+	1.72065e6i	0.0342031	+	0.105266i
$769$	−8.21394e6	−	2.52799e7i	−0.500882	−	1.54156i	−0.807585	−	0.589752i	$-0.799226\pi$
$769$	−8.21394e6	−	2.52799e7i	−0.500882	−	1.54156i	0.306702	−	0.951806i	$-0.400774\pi$
$770$	5.59404e6			0.340016
$771$	−4.53813e6	−	1.39669e7i	−0.274942	−	0.846185i
$772$	1.43795e6	+	1.04473e6i	0.0868364	+	0.0630903i
$773$	1.76845e7	−	1.28485e7i	1.06450	−	0.773402i	0.0895814	−	0.995980i	$-0.471447\pi$
$773$	1.76845e7	−	1.28485e7i	1.06450	−	0.773402i	0.974915	+	0.222578i	$0.0714471\pi$
$774$	1.74476e6	−	5.36983e6i	0.104685	−	0.322187i
$775$	−5.95031e6	+	1.83132e7i	−0.355865	+	1.09524i
$776$	2.79052e6			0.166353
$777$	−3.29199e6	+	2.39177e6i	−0.195617	+	0.142124i
$778$	−2.92127e6			−0.173031
$779$	−2.91133e6	+	2.60231e7i	−0.171889	+	1.53644i
$780$	4.88770e7			2.87652
$781$	1.21471e6	−	882537.i	0.0712597	−	0.0517732i
$782$	−305442.			−0.0178612
$783$	−1.43551e7	+	4.41806e7i	−0.836764	+	2.57530i
$784$	−1.28408e6	+	3.95199e6i	−0.0746108	+	0.229628i
$785$	1.23020e7	−	8.93795e6i	0.712529	−	0.517683i
$786$	−2.73133e7	−	1.98443e7i	−1.57695	−	1.14572i
$787$	6.70922e6	+	2.06488e7i	0.386131	+	1.18839i	0.935656	+	0.352913i	$0.114809\pi$
$787$	6.70922e6	+	2.06488e7i	0.386131	+	1.18839i	−0.549525	+	0.835477i	$0.685191\pi$
$788$	1.23134e7			0.706417
$789$	1.77120e7	+	5.45118e7i	1.01292	+	3.11744i
$790$	7.43071e6	+	2.28694e7i	0.423606	+	1.30373i
$791$	548699.	−	1.68872e6i	0.0311812	−	0.0959658i
$792$	1.58305e7	−	1.15016e7i	0.896774	−	0.651544i
$793$	2.55558e7			1.44313
$794$	−3.80600e6	+	1.17137e7i	−0.214248	+	0.659388i
$795$	−2.42305e7	−	1.76045e7i	−1.35970	−	0.987883i
$796$	−1.85045e6	−	5.69509e6i	−0.103513	−	0.318579i
$797$	4.65531e6	−	3.38228e6i	0.259599	−	0.188610i	−0.450371	−	0.892841i	$-0.648708\pi$
$797$	4.65531e6	−	3.38228e6i	0.259599	−	0.188610i	0.709970	+	0.704232i	$0.248708\pi$
$798$	5.21190e6	+	3.78667e6i	0.289727	+	0.210499i
$799$	26763.0	+	19444.4i	0.00148309	+	0.00107753i
$800$	5.53260e6	+	4.01967e6i	0.305636	+	0.222058i
$801$	−2.66621e7	−	1.93712e7i	−1.46830	−	1.06678i
$802$	−1.61327e7	+	1.17211e7i	−0.885668	+	0.643476i
$803$	−5.92665e6	−	1.82403e7i	−0.324355	−	0.998261i
$804$	−1.18600e7	−	8.61678e6i	−0.647059	−	0.470116i
$805$	378594.	−	1.16519e6i	0.0205913	−	0.0633735i
$806$	−1.28895e7			−0.698871
$807$	−2.62771e7	+	1.90914e7i	−1.42035	+	1.03194i
$808$	−912102.	+	2.80716e6i	−0.0491490	+	0.151265i
$809$	1.20484e6	+	3.70811e6i	0.0647227	+	0.199196i	0.978188	−	0.207720i	$-0.0666042\pi$
$809$	1.20484e6	+	3.70811e6i	0.0647227	+	0.199196i	−0.913466	+	0.406916i	$0.866604\pi$
$810$	1.03142e7	+	3.17438e7i	0.552359	+	1.69999i
$811$	−2.50067e7			−1.33507			−0.667534	−	0.744579i	$-0.732650\pi$
$811$	−2.50067e7			−1.33507			−0.667534	+	0.744579i	$0.732650\pi$
$812$	−722643.	−	2.22407e6i	−0.0384622	−	0.118374i
$813$	−1.27487e6	−	926246.i	−0.0676455	−	0.0491473i
$814$	1.17151e7	−	8.51151e6i	0.619704	−	0.450241i
$815$	−5.78991e6	+	1.78195e7i	−0.305336	+	0.939727i
$816$	−323197.	+	994697.i	−0.0169919	+	0.0522956i
$817$	−6.61518e6			−0.346726
$818$	−1.16346e7	+	8.45303e6i	−0.607950	+	0.441702i
$819$	−1.39128e7			−0.724777
$820$	1.89583e6	−	1.69460e7i	0.0984610	−	0.880101i
$821$	−2.43705e7			−1.26184			−0.630922	−	0.775846i	$-0.717323\pi$
$821$	−2.43705e7			−1.26184			−0.630922	+	0.775846i	$0.717323\pi$
$822$	−1.66755e7	+	1.21154e7i	−0.860792	+	0.625402i
$823$	1.90075e7			0.978195			0.489098	−	0.872229i	$-0.337326\pi$
$823$	1.90075e7			0.978195			0.489098	+	0.872229i	$0.337326\pi$
$824$	3.48233e6	−	1.07175e7i	0.178670	−	0.549890i
$825$	3.35557e7	−	1.03274e8i	1.71645	−	5.28270i
$826$	1.86421e6	−	1.35443e6i	0.0950701	−	0.0690725i
$827$	−1.42776e7	−	1.03733e7i	−0.725925	−	0.527415i	0.162347	−	0.986734i	$-0.448094\pi$
$827$	−1.42776e7	−	1.03733e7i	−0.725925	−	0.527415i	−0.888272	+	0.459319i	$0.848094\pi$
$828$	−1.32430e6	−	4.07577e6i	−0.0671289	−	0.206602i
$829$	9.05141e6			0.457436			0.228718	−	0.973493i	$-0.426547\pi$
$829$	9.05141e6			0.457436			0.228718	+	0.973493i	$0.426547\pi$
$830$	208513.	+	641737.i	0.0105060	+	0.0323342i
$831$	−205665.	−	632972.i	−0.0103314	−	0.0317967i
$832$	−1.41460e6	+	4.35368e6i	−0.0708474	+	0.218046i
$833$	−1.94341e6	+	1.41197e6i	−0.0970404	+	0.0705040i
$834$	3.74562e7			1.86470
$835$	859932.	−	2.64660e6i	0.0426823	−	0.131363i
$836$	−1.85474e7	−	1.34755e7i	−0.917842	−	0.666851i
$837$	−6.79115e6	−	2.09010e7i	−0.335065	−	1.03122i
$838$	−5.26055e6	+	3.82201e6i	−0.258774	+	0.188011i
$839$	1.45490e7	+	1.05705e7i	0.713557	+	0.518430i	0.884319	−	0.466883i	$-0.154623\pi$
$839$	1.45490e7	+	1.05705e7i	0.713557	+	0.518430i	−0.170762	+	0.985312i	$0.554623\pi$
$840$	−3.39394e6	−	2.46584e6i	−0.165961	−	0.120578i
$841$	−1.34570e7	−	9.77705e6i	−0.656080	−	0.476670i
$842$	−1.60190e7	−	1.16385e7i	−0.778672	−	0.565738i
$843$	−5.32313e7	+	3.86748e7i	−2.57987	+	1.87439i
$844$	−969163.	−	2.98278e6i	−0.0468318	−	0.144133i
$845$	7.03105e7	+	5.10835e7i	3.38749	+	2.46116i
$846$	−143428.	+	441425.i	−0.00688981	+	0.0212047i
$847$	4.45703e6			0.213470
$848$	2.26938e6	−	1.64880e6i	0.108372	−	0.0787370i
$849$	−1.16361e7	+	3.58124e7i	−0.554038	+	1.70515i
$850$	1.22167e6	+	3.75990e6i	0.0579969	+	0.178496i
$851$	−980020.	−	3.01619e6i	−0.0463886	−	0.142769i
$852$	−1.12599e6			−0.0531418
$853$	−7.72062e6	−	2.37616e7i	−0.363312	−	1.11816i	−0.951032	−	0.309094i	$-0.899974\pi$
$853$	−7.72062e6	−	2.37616e7i	−0.363312	−	1.11816i	0.587720	−	0.809065i	$-0.300026\pi$
$854$	−1.77455e6	−	1.28929e6i	−0.0832616	−	0.0604931i
$855$	1.01158e8	−	7.34954e7i	4.73242	−	3.43831i
$856$	−1.58927e6	+	4.89127e6i	−0.0741333	+	0.228159i
$857$	5.89045e6	−	1.81290e7i	0.273966	−	0.843181i	−0.715525	−	0.698587i	$-0.753812\pi$
$857$	5.89045e6	−	1.81290e7i	0.273966	−	0.843181i	0.989491	−	0.144594i	$-0.0461875\pi$
$858$	7.26879e7			3.37088
$859$	2.06441e7	−	1.49988e7i	0.954583	−	0.693545i	0.00269684	−	0.999996i	$-0.499142\pi$
$859$	2.06441e7	−	1.49988e7i	0.954583	−	0.693545i	0.951886	+	0.306451i	$0.0991416\pi$
$860$	4.30774e6			0.198611
$861$	−792263.	+	7.08169e6i	−0.0364218	+	0.325559i
$862$	4.54638e6			0.208400
$863$	6.25438e6	−	4.54407e6i	0.285863	−	0.207691i	−0.435608	−	0.900137i	$-0.643467\pi$
$863$	6.25438e6	−	4.54407e6i	0.285863	−	0.207691i	0.721470	+	0.692445i	$0.243467\pi$
$864$	−7.80505e6			−0.355706
$865$	−1.54524e7	+	4.75577e7i	−0.702193	+	2.16113i
$866$	4.88251e6	−	1.50268e7i	0.221232	−	0.680883i
$867$	3.12218e7	−	2.26839e7i	1.41062	−	1.02487i
$868$	895024.	+	650273.i	0.0403214	+	0.0292952i
$869$	1.10507e7	+	3.40104e7i	0.496408	+	1.52779i
$870$	−6.66353e7			−2.98474
$871$	−1.14623e7	−	3.52774e7i	−0.511949	−	1.57562i
$872$	−1.72119e6	−	5.29727e6i	−0.0766544	−	0.235918i
$873$	−6.99423e6	+	2.15260e7i	−0.310602	+	0.955935i
$874$	−4.06208e6	+	2.95128e6i	−0.179875	+	0.130687i
$875$	−8.43730e6			−0.372549
$876$	−4.44457e6	+	1.36790e7i	−0.195690	+	0.602273i
$877$	1.50274e7	+	1.09181e7i	0.659759	+	0.479343i	0.866582	−	0.499035i	$-0.166312\pi$
$877$	1.50274e7	+	1.09181e7i	0.659759	+	0.479343i	−0.206822	+	0.978379i	$0.566312\pi$
$878$	6.66846e6	+	2.05234e7i	0.291937	+	0.898490i
$879$	2.40099e7	−	1.74442e7i	1.04814	−	0.761515i
$880$	1.20779e7	+	8.77511e6i	0.525757	+	0.381985i
$881$	−2.02921e7	−	1.47430e7i	−0.880818	−	0.639952i	0.0526497	−	0.998613i	$-0.483233\pi$
$881$	−2.02921e7	−	1.47430e7i	−0.880818	−	0.639952i	−0.933468	+	0.358661i	$0.883233\pi$
$882$	−2.72671e7	−	1.98107e7i	−1.18023	−	0.857490i
$883$	3.34619e7	+	2.43115e7i	1.44427	+	1.04932i	0.987128	+	0.159930i	$0.0511268\pi$
$883$	3.34619e7	+	2.43115e7i	1.44427	+	1.04932i	0.457142	+	0.889394i	$0.348873\pi$
$884$	−2.14095e6	+	1.55549e6i	−0.0921457	+	0.0669477i
$885$	−2.02900e7	−	6.24461e7i	−0.870810	−	2.68008i
$886$	−1.65809e7	−	1.20468e7i	−0.709619	−	0.515568i
$887$	−5.65128e6	+	1.73929e7i	−0.241178	+	0.742270i	0.755063	+	0.655652i	$0.227606\pi$
$887$	−5.65128e6	+	1.73929e7i	−0.241178	+	0.742270i	−0.996242	+	0.0866182i	$0.972394\pi$
$888$	−1.08595e7			−0.462143
$889$	3.05557e6	−	2.22000e6i	0.129670	−	0.0942105i
$890$	7.76989e6	−	2.39133e7i	0.328806	−	1.01196i
$891$	1.53388e7	+	4.72080e7i	0.647288	+	1.99215i
$892$	4.74835e6	+	1.46139e7i	0.199816	+	0.614971i
$893$	543800.			0.0228197
$894$	6.41534e6	+	1.97444e7i	0.268458	+	0.826228i
$895$	2.78377e7	+	2.02253e7i	1.16165	+	0.843990i
$896$	317870.	−	230946.i	0.0132276	−	0.00961038i
$897$	4.91937e6	−	1.51403e7i	0.204140	−	0.628279i
$898$	−3.47177e6	+	1.06850e7i	−0.143668	+	0.442165i
$899$	1.75725e7			0.725162
$900$	−4.48748e7	+	3.26034e7i	−1.84670	+	1.34170i
$901$	1.62162e6			0.0665482
$902$	2.81940e6	−	2.52014e7i	0.115383	−	1.03135i
$903$	−1.80020e6			−0.0734684
$904$	3.83369e6	−	2.78534e6i	0.156026	−	0.113359i
$905$	4.67109e7			1.89582
$906$	−9.92778e6	+	3.05546e7i	−0.401820	+	1.23668i
$907$	−9.35606e6	+	2.87950e7i	−0.377637	+	1.16225i	0.564045	+	0.825744i	$0.309245\pi$
$907$	−9.35606e6	+	2.87950e7i	−0.377637	+	1.16225i	−0.941682	+	0.336504i	$0.890755\pi$
$908$	1.57687e7	−	1.14567e7i	0.634720	−	0.461151i
$909$	−1.93683e7	−	1.40719e7i	−0.777466	−	0.564862i
$910$	−3.28014e6	−	1.00952e7i	−0.131307	−	0.404122i
$911$	1.63408e7			0.652345			0.326173	−	0.945310i	$-0.394241\pi$
$911$	1.63408e7			0.652345			0.326173	+	0.945310i	$0.394241\pi$
$912$	5.31287e6	+	1.63513e7i	0.211515	+	0.650978i
$913$	310092.	+	954365.i	0.0123116	+	0.0378911i
$914$	−4.18129e6	+	1.28687e7i	−0.165556	+	0.509529i
$915$	−5.05652e7	+	3.67378e7i	−1.99664	+	1.45064i
$916$	1.01377e7			0.399211
$917$	−2.26571e6	+	6.97314e6i	−0.0889777	+	0.273845i
$918$	−3.65032e6	−	2.65212e6i	−0.142963	−	0.103869i
$919$	6.31659e6	+	1.94405e7i	0.246714	+	0.759308i	0.995350	+	0.0963264i	$0.0307093\pi$
$919$	6.31659e6	+	1.94405e7i	0.246714	+	0.759308i	−0.748636	+	0.662982i	$0.769291\pi$
$920$	2.64519e6	−	1.92184e6i	0.103036	−	0.0748597i
$921$	2.77111e7	+	2.01333e7i	1.07648	+	0.782108i
$922$	−1.60137e7	−	1.16346e7i	−0.620388	−	0.450738i
$923$	−2.30492e6	−	1.67462e6i	−0.0890536	−	0.0647012i
$924$	−5.04733e6	−	3.66710e6i	−0.194483	−	0.141300i
$925$	−3.32087e7	+	2.41275e7i	−1.27614	+	0.927168i
$926$	2.82449e6	+	8.69289e6i	0.108246	+	0.333148i
$927$	7.39465e7	+	5.37253e7i	2.82630	+	2.05343i
$928$	1.92855e6	−	5.93548e6i	0.0735126	−	0.226248i
$929$	−2.57581e7			−0.979207			−0.489604	−	0.871945i	$-0.662859\pi$
$929$	−2.57581e7			−0.979207			−0.489604	+	0.871945i	$0.662859\pi$
$930$	2.55034e7	−	1.85293e7i	0.966919	−	0.702507i
$931$	−1.22026e7	+	3.75557e7i	−0.461400	+	1.42004i
$932$	771003.	+	2.37290e6i	0.0290748	+	0.0894829i
$933$	−9.61556e6	−	2.95937e7i	−0.361635	−	1.11300i
$934$	2.12882e7			0.798496
$935$	2.66695e6	+	8.20802e6i	0.0997666	+	0.307050i
$936$	−3.00386e7	−	2.18243e7i	−1.12070	−	0.814238i
$937$	2.00381e7	−	1.45585e7i	0.745602	−	0.541712i	−0.148858	−	0.988859i	$-0.547560\pi$
$937$	2.00381e7	−	1.45585e7i	0.745602	−	0.541712i	0.894461	+	0.447147i	$0.147560\pi$
$938$	−983817.	+	3.02788e6i	−0.0365096	+	0.112365i
$939$	−1.16357e6	+	3.58109e6i	−0.0430653	+	0.132541i
$940$	−354117.			−0.0130715
$941$	6.41440e6	−	4.66033e6i	0.236147	−	0.171571i	−0.463418	−	0.886140i	$-0.653377\pi$
$941$	6.41440e6	−	4.66033e6i	0.236147	−	0.171571i	0.699565	+	0.714569i	$0.253377\pi$
$942$	−1.69589e7			−0.622688
$943$	−5.05842e6	−	2.29283e6i	−0.185240	−	0.0839641i
$944$	6.14956e6			0.224602
$945$	1.46418e7	−	1.06379e7i	0.533352	−	0.387503i
$946$	6.40630e6			0.232744
$947$	2.86114e6	−	8.80569e6i	0.103673	−	0.319072i	−0.885744	−	0.464174i	$-0.846351\pi$
$947$	2.86114e6	−	8.80569e6i	0.103673	−	0.319072i	0.989417	+	0.145102i	$0.0463512\pi$
$948$	8.28721e6	−	2.55054e7i	0.299494	−	0.921747i
$949$	−2.94421e7	+	2.13909e7i	−1.06121	+	0.771017i
$950$	5.25763e7	+	3.81989e7i	1.89008	+	1.37323i
$951$	−2.48304e7	−	7.64201e7i	−0.890292	−	2.74004i
$952$	227138.			0.00812265
$953$	−7.43385e6	−	2.28790e7i	−0.265144	−	0.816029i	−0.991660	−	0.128880i	$-0.958862\pi$
$953$	−7.43385e6	−	2.28790e7i	−0.265144	−	0.816029i	0.726516	−	0.687149i	$-0.241138\pi$
$954$	7.03080e6	+	2.16386e7i	0.250112	+	0.769765i
$955$	1.21046e7	−	3.72540e7i	0.429478	−	1.32180i
$956$	3.54998e6	−	2.57921e6i	0.125626	−	0.0912729i
$957$	−9.90973e7			−3.49769
$958$	6.88105e6	−	2.11777e7i	0.242237	−	0.745529i
$959$	3.62145e6	+	2.63114e6i	0.127156	+	0.0923842i
$960$	−3.45969e6	−	1.06478e7i	−0.121160	−	0.372892i
$961$	1.64359e7	−	1.19414e7i	0.574098	−	0.417106i
$962$	−2.22295e7	−	1.61507e7i	−0.774447	−	0.562669i
$963$	−3.37478e7	−	2.45192e7i	−1.17268	−	0.852002i
$964$	1.46451e7	+	1.06403e7i	0.507576	+	0.368775i
$965$	−8.89842e6	−	6.46508e6i	−0.307606	−	0.223489i
$966$	−1.10542e6	+	803134.i	−0.0381139	+	0.0276914i
$967$	−1.40223e7	−	4.31563e7i	−0.482230	−	1.48415i	−0.835954	−	0.548800i	$-0.815085\pi$
$967$	−1.40223e7	−	4.31563e7i	−0.482230	−	1.48415i	0.353724	−	0.935350i	$-0.384915\pi$
$968$	9.62302e6	+	6.99153e6i	0.330083	+	0.239819i
$969$	−3.07134e6	+	9.45260e6i	−0.105079	+	0.323401i
$970$	−1.72684e7			−0.589283
$971$	1.23362e7	−	8.96275e6i	0.419887	−	0.305065i	−0.357706	−	0.933834i	$-0.616441\pi$
$971$	1.23362e7	−	8.96275e6i	0.419887	−	0.305065i	0.777592	+	0.628769i	$0.216441\pi$
$972$	2.34538e6	−	7.21834e6i	0.0796247	−	0.245060i
$973$	−2.51369e6	−	7.73633e6i	−0.0851195	−	0.261971i
$974$	6.22814e6	+	1.91682e7i	0.210359	+	0.647418i
$975$	−2.06048e8			−6.94156
$976$	−1.80893e6	−	5.56732e6i	−0.0607851	−	0.187077i
$977$	−2.75041e7	−	1.99829e7i	−0.921853	−	0.669765i	0.0221318	−	0.999755i	$-0.492955\pi$
$977$	−2.75041e7	−	1.99829e7i	−0.921853	−	0.669765i	−0.943984	+	0.329990i	$0.892955\pi$
$978$	1.69054e7	−	1.22825e7i	0.565169	−	0.410619i
$979$	1.15551e7	−	3.55629e7i	0.385315	−	1.18588i
$980$	7.94621e6	−	2.44559e7i	0.264299	−	0.813427i
$981$	4.51771e7			1.49881
$982$	2.17002e6	−	1.57661e6i	0.0718101	−	0.0521731i
$983$	−3.10202e7			−1.02391			−0.511954	−	0.859013i	$-0.671078\pi$
$983$	−3.10202e7			−1.02391			−0.511954	+	0.859013i	$0.671078\pi$
$984$	−1.28193e7	+	1.40471e7i	−0.422061	+	0.462485i
$985$	−7.61982e7			−2.50239
$986$	2.91880e6	−	2.12064e6i	0.0956121	−	0.0694662i
$987$	147985.			0.00483531
$988$	−1.34429e7	+	4.13730e7i	−0.438127	+	1.34842i
$989$	433565.	−	1.33438e6i	0.0140950	−	0.0433798i
$990$	−9.79635e7	+	7.11746e7i	−3.17670	+	2.30801i
$991$	2.74161e7	+	1.99190e7i	0.886792	+	0.644292i	0.935040	−	0.354543i	$-0.115364\pi$
$991$	2.74161e7	+	1.99190e7i	0.886792	+	0.644292i	−0.0482475	+	0.998835i	$0.515364\pi$
$992$	912362.	+	2.80796e6i	0.0294366	+	0.0905966i
$993$	−7.40911e7			−2.38447
$994$	75565.3	+	232566.i	0.00242581	+	0.00746587i
$995$	1.14510e7	+	3.52426e7i	0.366680	+	1.12852i
$996$	232547.	−	715707.i	0.00742785	−	0.0228606i
$997$	1.19551e7	−	8.68592e6i	0.380905	−	0.276744i	−0.380813	−	0.924652i	$-0.624356\pi$
$997$	1.19551e7	−	8.68592e6i	0.380905	−	0.276744i	0.761719	+	0.647908i	$0.224356\pi$
$998$	3.75201e7			1.19244
$999$	1.44771e7	−	4.45558e7i	0.458951	−	1.41251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.37.9	✓	36
41.10	even	5	inner	82.6.d.b.51.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.37.9	✓	36	1.1	even	1	trivial
82.6.d.b.51.9	yes	36	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} +27.6062 q^{3} +(4.94427 - 15.2169i) q^{4} +(-30.5964 + 94.1661i) q^{5} +(89.3355 - 64.9061i) q^{6} +(-19.4012 - 14.0958i) q^{7} +(-19.7771 - 60.8676i) q^{8} +519.102 q^{9} +(122.386 + 376.664i) q^{10} +(182.007 + 560.160i) q^{11} +(136.493 - 420.081i) q^{12} +(904.165 - 656.914i) q^{13} -95.9250 q^{14} +(-844.651 + 2599.57i) q^{15} +(-207.108 - 150.473i) q^{16} +(-45.7320 - 140.749i) q^{17} +(1679.85 - 1220.48i) q^{18} +(-1968.15 - 1429.94i) q^{19} +(1281.64 + 931.166i) q^{20} +(-535.594 - 389.132i) q^{21} +(1906.00 + 1384.79i) q^{22} +(417.434 - 303.284i) q^{23} +(-545.970 - 1680.32i) q^{24} +(-5402.93 - 3925.46i) q^{25} +(1381.44 - 4251.64i) q^{26} +7622.12 q^{27} +(-310.420 + 225.533i) q^{28} +(-1883.35 + 5796.36i) q^{29} +(3378.60 + 10398.3i) q^{30} +(-890.979 - 2742.15i) q^{31} -1024.00 q^{32} +(5024.52 + 15463.9i) q^{33} +(-478.912 - 347.950i) q^{34} +(1920.96 - 1395.66i) q^{35} +(2566.58 - 7899.12i) q^{36} +(1899.35 - 5845.59i) q^{37} -9731.07 q^{38} +(24960.5 - 18134.9i) q^{39} +6336.77 q^{40} +(-5319.33 - 9357.40i) q^{41} -2648.12 q^{42} +(2199.88 - 1598.31i) q^{43} +9423.79 q^{44} +(-15882.7 + 48881.8i) q^{45} +(637.783 - 1962.89i) q^{46} +(-180.841 + 131.388i) q^{47} +(-5717.47 - 4153.99i) q^{48} +(-5015.93 - 15437.5i) q^{49} -26713.6 q^{50} +(-1262.49 - 3885.54i) q^{51} +(-5525.76 - 17006.5i) q^{52} +(-3386.04 + 10421.2i) q^{53} +(24665.7 - 17920.7i) q^{54} -58316.8 q^{55} +(-474.279 + 1459.68i) q^{56} +(-54333.1 - 39475.3i) q^{57} +(7533.41 + 23185.5i) q^{58} +(-19434.0 + 14119.6i) q^{59} +(35381.2 + 25705.9i) q^{60} +(18499.4 + 13440.6i) q^{61} +(-9330.45 - 6778.97i) q^{62} +(-10071.2 - 7317.17i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(34194.8 + 105241. i) q^{65} +(52617.5 + 38228.8i) q^{66} +(10256.1 - 31565.0i) q^{67} -2367.87 q^{68} +(11523.8 - 8372.51i) q^{69} +(2934.96 - 9032.88i) q^{70} +(-787.754 - 2424.46i) q^{71} +(-10266.3 - 31596.5i) q^{72} -32562.7 q^{73} +(-7597.39 - 23382.4i) q^{74} +(-149154. - 108367. i) q^{75} +(-31490.4 + 22879.1i) q^{76} +(4364.76 - 13433.3i) q^{77} +(38136.3 - 117372. i) q^{78} +60715.5 q^{79} +(20506.2 - 14898.6i) q^{80} +84276.0 q^{81} +(-39214.3 - 17774.7i) q^{82} +1703.74 q^{83} +(-8569.51 + 6226.11i) q^{84} +14653.0 q^{85} +(3361.12 - 10344.5i) q^{86} +(-51992.2 + 160016. i) q^{87} +(30496.0 - 22156.7i) q^{88} +(-51362.0 - 37316.7i) q^{89} +(63530.6 + 195527. i) q^{90} -26801.7 q^{91} +(-2551.13 - 7851.58i) q^{92} +(-24596.5 - 75700.3i) q^{93} +(-276.300 + 850.364i) q^{94} +(194871. - 141582. i) q^{95} -28268.7 q^{96} +(-13473.7 + 41467.8i) q^{97} +(-52527.5 - 38163.5i) q^{98} +(94480.2 + 290780. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) \) 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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