LMFDB - Embedded newform 138.5.g.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,5,Mod(29,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 18]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("138.29");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	138.g (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.2650549056$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.12
Character	$\chi$	$=$	138.29
Dual form			138.5.g.a.119.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57283 - 1.17497i) q^{2} +(6.96735 + 5.69702i) q^{3} +(5.23889 + 6.04600i) q^{4} +(-16.5641 - 25.7742i) q^{5} +(-11.2320 - 22.8439i) q^{6} +(-5.23680 + 36.4227i) q^{7} +(-6.37488 - 21.7108i) q^{8} +(16.0880 + 79.3863i) q^{9} +O(q^{10})$	\(q+(-2.57283 - 1.17497i) q^{2} +(6.96735 + 5.69702i) q^{3} +(5.23889 + 6.04600i) q^{4} +(-16.5641 - 25.7742i) q^{5} +(-11.2320 - 22.8439i) q^{6} +(-5.23680 + 36.4227i) q^{7} +(-6.37488 - 21.7108i) q^{8} +(16.0880 + 79.3863i) q^{9} +(12.3326 + 85.7749i) q^{10} +(128.570 - 58.7160i) q^{11} +(2.05700 + 71.9706i) q^{12} +(-13.6536 - 94.9631i) q^{13} +(56.2690 - 87.5563i) q^{14} +(31.4284 - 273.944i) q^{15} +(-9.10815 + 63.3486i) q^{16} +(285.127 + 247.064i) q^{17} +(51.8850 - 223.150i) q^{18} +(214.499 + 247.545i) q^{19} +(69.0535 - 235.174i) q^{20} +(-243.987 + 223.936i) q^{21} -399.778 q^{22} +(-404.409 + 341.020i) q^{23} +(79.2711 - 187.585i) q^{24} +(-130.307 + 285.332i) q^{25} +(-76.4505 + 260.366i) q^{26} +(-340.174 + 644.765i) q^{27} +(-247.647 + 159.153i) q^{28} +(235.460 + 204.027i) q^{29} +(-402.736 + 667.883i) q^{30} +(1575.39 - 462.576i) q^{31} +(97.8664 - 152.283i) q^{32} +(1230.30 + 323.371i) q^{33} +(-443.290 - 970.670i) q^{34} +(1025.51 - 468.334i) q^{35} +(-395.686 + 513.163i) q^{36} +(1956.33 + 1257.26i) q^{37} +(-261.010 - 888.920i) q^{38} +(445.877 - 739.426i) q^{39} +(-453.986 + 523.928i) q^{40} +(886.270 + 1379.06i) q^{41} +(890.856 - 289.470i) q^{42} +(-1602.66 - 470.584i) q^{43} +(1028.56 + 469.728i) q^{44} +(1779.64 - 1729.61i) q^{45} +(1441.16 - 402.217i) q^{46} -871.035i q^{47} +(-424.358 + 389.482i) q^{48} +(1004.55 + 294.963i) q^{49} +(670.514 - 581.003i) q^{50} +(579.053 + 3345.76i) q^{51} +(502.617 - 580.051i) q^{52} +(2497.05 + 359.022i) q^{53} +(1632.79 - 1259.18i) q^{54} +(-3643.00 - 2341.21i) q^{55} +(824.152 - 118.495i) q^{56} +(84.2211 + 2946.73i) q^{57} +(-366.071 - 801.584i) q^{58} +(-4258.41 + 612.267i) q^{59} +(1820.91 - 1245.14i) q^{60} +(-178.900 + 52.5298i) q^{61} +(-4596.72 - 660.909i) q^{62} +(-2975.71 + 170.238i) q^{63} +(-430.722 + 276.808i) q^{64} +(-2221.44 + 1924.89i) q^{65} +(-2785.39 - 2277.54i) q^{66} +(-456.186 + 998.908i) q^{67} +3018.22i q^{68} +(-4760.45 + 72.0824i) q^{69} -3188.74 q^{70} +(2980.92 + 1361.34i) q^{71} +(1620.98 - 855.361i) q^{72} +(-2708.36 - 3125.61i) q^{73} +(-3556.06 - 5533.34i) q^{74} +(-2533.43 + 1245.65i) q^{75} +(-372.920 + 2593.72i) q^{76} +(1465.30 + 4990.35i) q^{77} +(-2015.97 + 1378.52i) q^{78} +(-1636.78 - 11384.0i) q^{79} +(1783.63 - 814.555i) q^{80} +(-6043.35 + 2554.33i) q^{81} +(-659.861 - 4589.44i) q^{82} +(-2403.41 + 3739.78i) q^{83} +(-2632.14 - 301.974i) q^{84} +(1645.01 - 11441.3i) q^{85} +(3570.45 + 3093.81i) q^{86} +(478.185 + 2762.94i) q^{87} +(-2094.39 - 2417.06i) q^{88} +(154.148 - 524.979i) q^{89} +(-6610.94 + 2358.98i) q^{90} +3530.32 q^{91} +(-4180.46 - 658.489i) q^{92} +(13611.6 + 5752.10i) q^{93} +(-1023.44 + 2241.02i) q^{94} +(2827.30 - 9628.89i) q^{95} +(1549.43 - 503.463i) q^{96} +(-8307.60 + 5338.97i) q^{97} +(-2237.97 - 1939.21i) q^{98} +(6729.67 + 9262.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 20 q^{3} + 256 q^{4} - 64 q^{6} + 172 q^{9}+O(q^{10}) $ 320 * q + 20 * q^3 + 256 * q^4 - 64 * q^6 + 172 * q^9	$ 320 q + 20 q^{3} + 256 q^{4} - 64 q^{6} + 172 q^{9} - 160 q^{12} - 200 q^{13} + 2202 q^{15} - 2048 q^{16} - 3392 q^{18} + 520 q^{19} - 982 q^{21} + 640 q^{22} + 512 q^{24} + 1680 q^{25} + 8786 q^{27} - 2752 q^{30} + 5368 q^{31} - 12050 q^{33} - 640 q^{34} - 1376 q^{36} - 8936 q^{37} + 132 q^{39} + 1984 q^{42} - 11704 q^{43} - 10396 q^{45} + 2112 q^{46} + 1280 q^{48} + 36752 q^{49} + 10060 q^{51} + 1600 q^{52} - 28896 q^{54} - 36788 q^{55} - 6074 q^{57} + 10880 q^{58} + 15648 q^{60} + 44536 q^{61} + 61826 q^{63} + 16384 q^{64} + 25600 q^{66} + 21628 q^{67} - 21406 q^{69} - 45568 q^{70} - 23552 q^{72} - 14212 q^{73} - 65058 q^{75} - 4160 q^{76} - 31840 q^{78} - 29024 q^{79} - 43964 q^{81} + 23808 q^{82} + 17184 q^{84} + 75252 q^{85} - 34892 q^{87} - 5120 q^{88} - 1088 q^{90} + 12840 q^{91} + 14988 q^{93} - 23040 q^{94} - 4096 q^{96} + 158244 q^{97} + 86652 q^{99}+O(q^{100}) $ 320 * q + 20 * q^3 + 256 * q^4 - 64 * q^6 + 172 * q^9 - 160 * q^12 - 200 * q^13 + 2202 * q^15 - 2048 * q^16 - 3392 * q^18 + 520 * q^19 - 982 * q^21 + 640 * q^22 + 512 * q^24 + 1680 * q^25 + 8786 * q^27 - 2752 * q^30 + 5368 * q^31 - 12050 * q^33 - 640 * q^34 - 1376 * q^36 - 8936 * q^37 + 132 * q^39 + 1984 * q^42 - 11704 * q^43 - 10396 * q^45 + 2112 * q^46 + 1280 * q^48 + 36752 * q^49 + 10060 * q^51 + 1600 * q^52 - 28896 * q^54 - 36788 * q^55 - 6074 * q^57 + 10880 * q^58 + 15648 * q^60 + 44536 * q^61 + 61826 * q^63 + 16384 * q^64 + 25600 * q^66 + 21628 * q^67 - 21406 * q^69 - 45568 * q^70 - 23552 * q^72 - 14212 * q^73 - 65058 * q^75 - 4160 * q^76 - 31840 * q^78 - 29024 * q^79 - 43964 * q^81 + 23808 * q^82 + 17184 * q^84 + 75252 * q^85 - 34892 * q^87 - 5120 * q^88 - 1088 * q^90 + 12840 * q^91 + 14988 * q^93 - 23040 * q^94 - 4096 * q^96 + 158244 * q^97 + 86652 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−2.57283	−	1.17497i	−0.643207	−	0.293743i
$2$	−2.57283	−	1.17497i	−0.643207	−	0.293743i
$3$	6.96735	+	5.69702i	0.774150	+	0.633002i
$3$	6.96735	+	5.69702i	0.774150	+	0.633002i
$4$	5.23889	+	6.04600i	0.327430	+	0.377875i
$5$	−16.5641	−	25.7742i	−0.662563	−	1.03097i	−0.996100	−	0.0882313i	$-0.971879\pi$
$5$	−16.5641	−	25.7742i	−0.662563	−	1.03097i	0.333537	−	0.942737i	$-0.391758\pi$
$6$	−11.2320	−	22.8439i	−0.311999	−	0.634552i
$7$	−5.23680	+	36.4227i	−0.106873	+	0.743321i	0.863959	+	0.503562i	$0.167977\pi$
$7$	−5.23680	+	36.4227i	−0.106873	+	0.743321i	−0.970833	+	0.239759i	$0.922932\pi$
$8$	−6.37488	−	21.7108i	−0.0996075	−	0.339232i
$9$	16.0880	+	79.3863i	0.198617	+	0.980077i
$10$	12.3326	+	85.7749i	0.123326	+	0.857749i
$11$	128.570	−	58.7160i	1.06256	−	0.485256i	0.194085	−	0.980985i	$-0.437826\pi$
$11$	128.570	−	58.7160i	1.06256	−	0.485256i	0.868477	+	0.495729i	$0.165099\pi$
$12$	2.05700	+	71.9706i	0.0142848	+	0.499796i
$13$	−13.6536	−	94.9631i	−0.0807907	−	0.561912i	−0.989506	−	0.144495i	$-0.953844\pi$
$13$	−13.6536	−	94.9631i	−0.0807907	−	0.561912i	0.908715	−	0.417417i	$-0.137065\pi$
$14$	56.2690	−	87.5563i	0.287087	−	0.446716i
$15$	31.4284	−	273.944i	0.139682	−	1.21753i
$16$	−9.10815	+	63.3486i	−0.0355787	+	0.247455i
$17$	285.127	+	247.064i	0.986600	+	0.854894i	0.989417	−	0.145102i	$-0.0463512\pi$
$17$	285.127	+	247.064i	0.986600	+	0.854894i	−0.00281688	+	0.999996i	$0.500897\pi$
$18$	51.8850	−	223.150i	0.160139	−	0.688735i
$19$	214.499	+	247.545i	0.594179	+	0.685720i	0.970591	−	0.240733i	$-0.0773877\pi$
$19$	214.499	+	247.545i	0.594179	+	0.685720i	−0.376412	+	0.926452i	$0.622842\pi$
$20$	69.0535	−	235.174i	0.172634	−	0.587936i
$21$	−243.987	+	223.936i	−0.553260	+	0.507791i
$22$	−399.778			−0.825988
$23$	−404.409	+	341.020i	−0.764478	+	0.644650i
$23$	−404.409	+	341.020i	−0.764478	+	0.644650i
$24$	79.2711	−	187.585i	0.137623	−	0.325668i
$25$	−130.307	+	285.332i	−0.208491	+	0.456531i
$26$	−76.4505	+	260.366i	−0.113092	+	0.385157i
$27$	−340.174	+	644.765i	−0.466632	+	0.884452i
$28$	−247.647	+	159.153i	−0.315876	+	0.203001i
$29$	235.460	+	204.027i	0.279976	+	0.242600i	0.783516	−	0.621371i	$-0.213424\pi$
$29$	235.460	+	204.027i	0.279976	+	0.242600i	−0.503541	+	0.863972i	$0.667970\pi$
$30$	−402.736	+	667.883i	−0.447484	+	0.742092i
$31$	1575.39	−	462.576i	1.63932	−	0.481349i	0.673207	−	0.739454i	$-0.264916\pi$
$31$	1575.39	−	462.576i	1.63932	−	0.481349i	0.966117	+	0.258105i	$0.0830979\pi$
$32$	97.8664	−	152.283i	0.0955727	−	0.148714i
$33$	1230.30	+	323.371i	1.12975	+	0.296943i
$34$	−443.290	−	970.670i	−0.383469	−	0.839680i
$35$	1025.51	−	468.334i	0.837150	−	0.382314i
$36$	−395.686	+	513.163i	−0.305313	+	0.395959i
$37$	1956.33	+	1257.26i	1.42902	+	0.918377i	0.999885	+	0.0151370i	$0.00481845\pi$
$37$	1956.33	+	1257.26i	1.42902	+	0.918377i	0.429137	+	0.903240i	$0.358818\pi$
$38$	−261.010	−	888.920i	−0.180755	−	0.615596i
$39$	445.877	−	739.426i	0.293147	−	0.486145i
$40$	−453.986	+	523.928i	−0.283741	+	0.327455i
$41$	886.270	+	1379.06i	0.527228	+	0.820383i	0.998087	−	0.0618256i	$-0.0196923\pi$
$41$	886.270	+	1379.06i	0.527228	+	0.820383i	−0.470859	+	0.882209i	$0.656056\pi$
$42$	890.856	−	289.470i	0.505020	−	0.164099i
$43$	−1602.66	−	470.584i	−0.866772	−	0.254507i	−0.182030	−	0.983293i	$-0.558267\pi$
$43$	−1602.66	−	470.584i	−0.866772	−	0.254507i	−0.684742	+	0.728786i	$0.740085\pi$
$44$	1028.56	+	469.728i	0.531281	+	0.242628i
$45$	1779.64	−	1729.61i	0.878832	−	0.854131i
$46$	1441.16	−	402.217i	0.681079	−	0.190084i
$47$		−	871.035i		−	0.394312i	−0.980372	−	0.197156i	$-0.936829\pi$
$47$		−	871.035i		−	0.394312i	0.980372	−	0.197156i	$-0.0631705\pi$
$48$	−424.358	+	389.482i	−0.184183	+	0.169046i
$49$	1004.55	+	294.963i	0.418389	+	0.122850i
$50$	670.514	−	581.003i	0.268205	−	0.232401i
$51$	579.053	+	3345.76i	0.222627	+	1.28634i
$52$	502.617	−	580.051i	0.185879	−	0.214516i
$53$	2497.05	+	359.022i	0.888947	+	0.127811i	0.571633	−	0.820509i	$-0.306310\pi$
$53$	2497.05	+	359.022i	0.888947	+	0.127811i	0.317314	+	0.948321i	$0.397219\pi$
$54$	1632.79	−	1259.18i	0.559942	−	0.431816i
$55$	−3643.00	−	2341.21i	−1.20430	−	0.773955i
$56$	824.152	−	118.495i	0.262804	−	0.0377854i
$57$	84.2211	+	2946.73i	0.0259222	+	0.906967i
$58$	−366.071	−	801.584i	−0.108820	−	0.238283i
$59$	−4258.41	+	612.267i	−1.22333	+	0.175888i	−0.723555	−	0.690267i	$-0.757493\pi$
$59$	−4258.41	+	612.267i	−1.22333	+	0.175888i	−0.499775	+	0.866155i	$0.666584\pi$
$60$	1820.91	−	1245.14i	0.505809	−	0.345873i
$61$	−178.900	+	52.5298i	−0.0480785	+	0.0141171i	−0.305683	−	0.952133i	$-0.598885\pi$
$61$	−178.900	+	52.5298i	−0.0480785	+	0.0141171i	0.257605	+	0.966250i	$0.417067\pi$
$62$	−4596.72	−	660.909i	−1.19582	−	0.171933i
$63$	−2975.71	+	170.238i	−0.749739	+	0.0428919i
$64$	−430.722	+	276.808i	−0.105157	+	0.0675801i
$65$	−2221.44	+	1924.89i	−0.525784	+	0.455595i
$66$	−2785.39	−	2277.54i	−0.639438	−	0.522852i
$67$	−456.186	+	998.908i	−0.101623	+	0.222524i	−0.953613	−	0.301034i	$-0.902668\pi$
$67$	−456.186	+	998.908i	−0.101623	+	0.222524i	0.851990	+	0.523558i	$0.175395\pi$
$68$			3018.22i			0.652729i
$69$	−4760.45	+	72.0824i	−0.999885	+	0.0151402i
$70$	−3188.74			−0.650763
$71$	2980.92	+	1361.34i	0.591335	+	0.270054i	0.688525	−	0.725212i	$-0.258258\pi$
$71$	2980.92	+	1361.34i	0.591335	+	0.270054i	−0.0971905	+	0.995266i	$0.530986\pi$
$72$	1620.98	−	855.361i	0.312690	−	0.165000i
$73$	−2708.36	−	3125.61i	−0.508230	−	0.586528i	0.442415	−	0.896810i	$-0.354122\pi$
$73$	−2708.36	−	3125.61i	−0.508230	−	0.586528i	−0.950644	+	0.310282i	$0.899576\pi$
$74$	−3556.06	−	5533.34i	−0.649390	−	1.01047i
$75$	−2533.43	+	1245.65i	−0.450388	+	0.221449i
$76$	−372.920	+	2593.72i	−0.0645638	+	0.449051i
$77$	1465.30	+	4990.35i	0.247141	+	0.841685i
$78$	−2015.97	+	1378.52i	−0.331356	+	0.226582i
$79$	−1636.78	−	11384.0i	−0.262262	−	1.82407i	−0.515756	−	0.856736i	$-0.672489\pi$
$79$	−1636.78	−	11384.0i	−0.262262	−	1.82407i	0.253494	−	0.967337i	$-0.418420\pi$
$80$	1783.63	−	814.555i	0.278692	−	0.127274i
$81$	−6043.35	+	2554.33i	−0.921103	+	0.389320i
$82$	−659.861	−	4589.44i	−0.0981352	−	0.682545i
$83$	−2403.41	+	3739.78i	−0.348877	+	0.542862i	−0.970700	−	0.240295i	$-0.922756\pi$
$83$	−2403.41	+	3739.78i	−0.348877	+	0.542862i	0.621823	+	0.783158i	$0.286392\pi$
$84$	−2632.14	−	301.974i	−0.373035	−	0.0427967i
$85$	1645.01	−	11441.3i	0.227684	−	1.58357i
$86$	3570.45	+	3093.81i	0.482754	+	0.418309i
$87$	478.185	+	2762.94i	0.0631767	+	0.365034i
$88$	−2094.39	−	2417.06i	−0.270453	−	0.312120i
$89$	154.148	−	524.979i	0.0194606	−	0.0662768i	−0.949190	−	0.314703i	$-0.898095\pi$
$89$	154.148	−	524.979i	0.0194606	−	0.0662768i	0.968651	+	0.248426i	$0.0799133\pi$
$90$	−6610.94	+	2358.98i	−0.816166	+	0.291232i
$91$	3530.32			0.426315
$92$	−4180.46	−	658.489i	−0.493910	−	0.0777988i
$93$	13611.6	+	5752.10i	1.57378	+	0.665059i
$94$	−1023.44	+	2241.02i	−0.115826	+	0.253624i
$95$	2827.30	−	9628.89i	0.313274	−	1.06691i
$96$	1549.43	−	503.463i	0.168124	−	0.0546293i
$97$	−8307.60	+	5338.97i	−0.882942	+	0.567432i	−0.901686	−	0.432392i	$-0.857670\pi$
$97$	−8307.60	+	5338.97i	−0.882942	+	0.567432i	0.0187440	+	0.999824i	$0.494033\pi$
$98$	−2237.97	−	1939.21i	−0.233025	−	0.201917i
$99$	6729.67	+	9262.07i	0.686631	+	0.945013i
$100$	−2407.78	+	706.987i	−0.240778	+	0.0706987i
$101$	5672.19	−	8826.09i	0.556042	−	0.865218i	−0.443475	−	0.896287i	$-0.646255\pi$
$101$	5672.19	−	8826.09i	0.556042	−	0.865218i	0.999517	+	0.0310683i	$0.00989093\pi$
$102$	2441.37	−	9288.43i	0.234657	−	0.892775i
$103$	−8383.80	−	18358.0i	−0.790254	−	1.73041i	−0.675924	−	0.736971i	$-0.736255\pi$
$103$	−8383.80	−	18358.0i	−0.790254	−	1.73041i	−0.114329	−	0.993443i	$-0.536472\pi$
$104$	−1974.69	+	901.810i	−0.182571	+	0.0833774i
$105$	9813.19	+	2579.29i	0.890086	+	0.233950i
$106$	−6002.64	−	3857.66i	−0.534233	−	0.343331i
$107$	−800.537	−	2726.38i	−0.0699220	−	0.238132i	0.917116	−	0.398621i	$-0.130511\pi$
$107$	−800.537	−	2726.38i	−0.0699220	−	0.238132i	−0.987038	+	0.160489i	$0.948693\pi$
$108$	−5680.38	+	1321.16i	−0.487001	+	0.113268i
$109$	−7855.93	+	9066.22i	−0.661218	+	0.763086i	−0.982976	−	0.183736i	$-0.941181\pi$
$109$	−7855.93	+	9066.22i	−0.661218	+	0.763086i	0.321758	+	0.946822i	$0.395726\pi$
$110$	6621.95	+	10304.0i	0.547269	+	0.851567i
$111$	6467.83	+	19905.0i	0.524943	+	1.61554i
$112$	−2259.63	−	663.487i	−0.180136	−	0.0528928i
$113$	−1950.94	−	890.964i	−0.152787	−	0.0697756i	0.337554	−	0.941306i	$-0.390400\pi$
$113$	−1950.94	−	890.964i	−0.152787	−	0.0697756i	−0.490341	+	0.871531i	$0.663128\pi$
$114$	3245.64	−	7680.40i	0.249742	−	0.590982i
$115$	15488.2	+	4774.63i	1.17113	+	0.361031i
$116$			2492.46i			0.185230i
$117$	7319.11	−	2611.67i	0.534671	−	0.190786i
$118$	11675.6	+	3428.25i	0.838520	+	0.246212i
$119$	−10491.9	+	9091.29i	−0.740901	+	0.641995i
$120$	−6147.90	+	1064.02i	−0.426938	+	0.0738904i
$121$	3494.87	−	4033.29i	0.238704	−	0.275479i
$122$	522.000	+	75.0523i	0.0350712	+	0.00504248i
$123$	−1681.59	+	14657.5i	−0.111150	+	0.968836i
$124$	11050.0	+	7101.42i	0.718654	+	0.461851i
$125$	−9441.14	+	1357.43i	−0.604233	+	0.0868756i
$126$	7856.02	+	3058.38i	0.494836	+	0.192642i
$127$	−6835.51	−	14967.7i	−0.423803	−	0.927999i	−0.994292	−	0.106693i	$-0.965974\pi$
$127$	−6835.51	−	14967.7i	−0.423803	−	0.927999i	0.570489	−	0.821305i	$-0.306754\pi$
$128$	1433.41	−	206.094i	0.0874887	−	0.0125790i
$129$	−8485.38	−	12409.1i	−0.509908	−	0.745695i
$130$	7977.07	−	2342.28i	0.472016	−	0.138596i
$131$	16159.9	+	2323.44i	0.941664	+	0.135391i	0.596015	−	0.802973i	$-0.296750\pi$
$131$	16159.9	+	2323.44i	0.941664	+	0.135391i	0.345649	+	0.938364i	$0.387659\pi$
$132$	4490.29	+	9132.48i	0.257707	+	0.524132i
$133$	−10139.5	+	6516.29i	−0.573212	+	0.368381i
$134$	2347.38	−	2034.01i	0.130729	−	0.113278i
$135$	22253.0	−	1912.22i	1.22101	−	0.104923i
$136$	3546.32	−	7765.36i	0.191735	−	0.419840i
$137$		−	33526.2i		−	1.78625i	−0.449806	−	0.893126i	$-0.648507\pi$
$137$		−	33526.2i		−	1.78625i	0.449806	−	0.893126i	$-0.351493\pi$
$138$	12332.5	+	5407.94i	0.647581	+	0.283971i
$139$	−896.878			−0.0464199			−0.0232099	−	0.999731i	$-0.507389\pi$
$139$	−896.878			−0.0464199			−0.0232099	+	0.999731i	$0.507389\pi$
$140$	8204.07	+	3746.68i	0.418575	+	0.191157i
$141$	4962.30	−	6068.81i	0.249600	−	0.305257i
$142$	−6069.86	−	7004.99i	−0.301024	−	0.347401i
$143$	−7331.30	−	11407.7i	−0.358516	−	0.557862i
$144$	−5175.54	+	296.088i	−0.249592	+	0.0142789i
$145$	1358.46	−	9448.30i	0.0646117	−	0.449384i
$146$	3295.63	+	11223.9i	0.154608	+	0.526548i
$147$	5318.66	+	7778.07i	0.246132	+	0.359946i
$148$	2647.62	+	18414.6i	0.120874	+	0.840696i
$149$	−581.125	+	265.391i	−0.0261756	+	0.0119540i	−0.428460	−	0.903561i	$-0.640944\pi$
$149$	−581.125	+	265.391i	−0.0261756	+	0.0119540i	0.402284	+	0.915515i	$0.368216\pi$
$150$	7981.69	−	228.126i	0.354742	−	0.0101389i
$151$	4904.27	+	34109.9i	0.215090	+	1.49598i	0.755815	+	0.654785i	$0.227241\pi$
$151$	4904.27	+	34109.9i	0.215090	+	1.49598i	−0.540725	+	0.841199i	$0.681850\pi$
$152$	4007.00	−	6235.02i	0.173433	−	0.269867i
$153$	−15026.4	+	26610.0i	−0.641906	+	1.13674i
$154$	2093.56	−	14561.0i	0.0882761	−	0.613974i
$155$	−38017.4	−	32942.3i	−1.58241	−	1.37117i
$156$	6806.47	−	1178.00i	0.279687	−	0.0484057i
$157$	15045.7	+	17363.7i	0.610400	+	0.704439i	0.973854	−	0.227173i	$-0.0729483\pi$
$157$	15045.7	+	17363.7i	0.610400	+	0.704439i	−0.363455	+	0.931612i	$0.618403\pi$
$158$	−9164.77	+	31212.3i	−0.367119	+	1.25029i
$159$	15352.5	+	16727.2i	0.607274	+	0.661650i
$160$	−5546.05			−0.216642
$161$	−10303.1	−	16515.5i	−0.397480	−	0.637148i
$162$	18549.8	+	528.925i	0.706820	+	0.0201541i
$163$	−19952.0	+	43688.8i	−0.750950	+	1.64435i	0.0137003	+	0.999906i	$0.495639\pi$
$163$	−19952.0	+	43688.8i	−0.750950	+	1.64435i	−0.764650	+	0.644445i	$0.777088\pi$
$164$	−3694.74	+	12583.1i	−0.137372	+	0.467844i
$165$	−12044.1	−	37066.3i	−0.442392	−	1.36148i
$166$	10577.7	−	6797.87i	0.383862	−	0.246693i
$167$	−2683.45	−	2325.22i	−0.0962188	−	0.0833740i	0.605423	−	0.795904i	$-0.293004\pi$
$167$	−2683.45	−	2325.22i	−0.0962188	−	0.0833740i	−0.701642	+	0.712530i	$0.747549\pi$
$168$	6417.23	+	3869.61i	0.227368	+	0.137104i
$169$	18572.5	−	5453.38i	0.650275	−	0.190938i
$170$	−17675.6	+	27503.7i	−0.611611	+	0.951685i
$171$	−16200.8	+	21010.7i	−0.554044	+	0.718537i
$172$	−5551.01	−	12155.0i	−0.187636	−	0.410865i
$173$	21070.5	−	9622.57i	0.704016	−	0.321513i	−0.0310416	−	0.999518i	$-0.509882\pi$
$173$	21070.5	−	9622.57i	0.704016	−	0.321513i	0.735057	+	0.678005i	$0.237155\pi$
$174$	2016.09	−	7670.43i	0.0665905	−	0.253350i
$175$	−9710.17	−	6240.35i	−0.317067	−	0.203767i
$176$	2548.54	+	8679.52i	0.0822746	+	0.280201i
$177$	−33157.9	−	19994.4i	−1.05838	−	0.638206i
$178$	−1013.43	+	1169.56i	−0.0319856	+	0.0369133i
$179$	19682.2	+	30626.1i	0.614283	+	0.955842i	0.999455	+	0.0329978i	$0.0105054\pi$
$179$	19682.2	+	30626.1i	0.614283	+	0.955842i	−0.385173	+	0.922844i	$0.625858\pi$
$180$	19780.6	+	1698.42i	0.610511	+	0.0524203i
$181$	−22754.5	−	6681.31i	−0.694560	−	0.203941i	−0.0846484	−	0.996411i	$-0.526977\pi$
$181$	−22754.5	−	6681.31i	−0.694560	−	0.203941i	−0.609911	+	0.792470i	$0.708795\pi$
$182$	−9082.89	−	4148.02i	−0.274209	−	0.125227i
$183$	−1545.72	−	653.203i	−0.0461561	−	0.0195050i
$184$	9981.89	+	6606.09i	0.294834	+	0.195123i
$185$		−	71248.2i		−	2.08176i
$186$	−28261.8	−	30792.4i	−0.816909	−	0.890057i
$187$	51165.4	+	15023.5i	1.46317	+	0.429624i
$188$	5266.28	−	4563.25i	0.149001	−	0.129110i
$189$	−21702.7	−	15766.6i	−0.607561	−	0.441381i
$190$	−18587.8	+	21451.5i	−0.514898	+	0.594224i
$191$	−29888.0	−	4297.25i	−0.819277	−	0.117794i	−0.280083	−	0.959976i	$-0.590362\pi$
$191$	−29888.0	−	4297.25i	−0.819277	−	0.117794i	−0.539194	+	0.842182i	$0.681271\pi$
$192$	−4577.97	−	525.211i	−0.124185	−	0.0142473i
$193$	24818.2	+	15949.7i	0.666279	+	0.428191i	0.829582	−	0.558384i	$-0.188579\pi$
$193$	24818.2	+	15949.7i	0.666279	+	0.428191i	−0.163303	+	0.986576i	$0.552215\pi$
$194$	27647.2	−	3975.06i	0.734593	−	0.105619i
$195$	−26443.7	+	755.791i	−0.695429	+	0.0198762i
$196$	3479.39	+	7618.80i	0.0905714	+	0.198324i
$197$	60185.6	−	8653.38i	1.55082	−	0.222974i	0.686953	−	0.726702i	$-0.258948\pi$
$197$	60185.6	−	8653.38i	1.55082	−	0.222974i	0.863862	+	0.503728i	$0.168039\pi$
$198$	−6431.61	−	31736.9i	−0.164055	−	0.809532i
$199$	20827.8	−	6115.60i	0.525942	−	0.154431i	−0.00797370	−	0.999968i	$-0.502538\pi$
$199$	20827.8	−	6115.60i	0.525942	−	0.154431i	0.533916	+	0.845538i	$0.320720\pi$
$200$	7025.49	+	1010.11i	0.175637	+	0.0252528i
$201$	−8869.21	+	4360.84i	−0.219529	+	0.107939i
$202$	−24964.0	+	16043.4i	−0.611802	+	0.393181i
$203$	−8664.26	+	7507.63i	−0.210252	+	0.182184i
$204$	−17194.9	+	21029.0i	−0.413179	+	0.505310i
$205$	20864.0	−	45685.8i	0.496467	−	1.08711i
$206$			57082.6i			1.34515i
$207$	−33578.4	−	26618.2i	−0.783645	−	0.621209i
$208$	6140.14			0.141923
$209$	42112.9	+	19232.3i	0.964102	+	0.440291i
$210$	−22217.1	−	18166.3i	−0.503788	−	0.411934i
$211$	−16647.7	−	19212.5i	−0.373929	−	0.431537i	0.537329	−	0.843373i	$-0.319433\pi$
$211$	−16647.7	−	19212.5i	−0.373929	−	0.431537i	−0.911258	+	0.411835i	$0.864888\pi$
$212$	10911.1	+	16978.0i	0.242772	+	0.377760i
$213$	13013.5	+	26467.3i	0.286838	+	0.583378i
$214$	−1143.77	+	7955.11i	−0.0249754	+	0.173707i
$215$	14417.7	+	49102.1i	0.311902	+	1.06224i
$216$	16167.0	+	3275.17i	0.346514	+	0.0701983i
$217$	8598.29	+	59802.4i	0.182597	+	1.26999i
$218$	30864.5	−	14095.3i	0.649451	−	0.296594i
$219$	−1063.41	−	37206.8i	−0.0221725	−	0.775771i
$220$	−4930.29	−	34290.9i	−0.101866	−	0.708490i
$221$	19569.0	−	30449.9i	0.400667	−	0.623450i
$222$	6747.21	−	58811.7i	0.136905	−	1.19332i
$223$	8805.86	−	61246.1i	0.177077	−	1.23160i	−0.686406	−	0.727219i	$-0.740813\pi$
$223$	8805.86	−	61246.1i	0.177077	−	1.23160i	0.863483	−	0.504378i	$-0.168278\pi$
$224$	5034.06	+	4362.04i	0.100328	+	0.0869347i
$225$	−24747.8	−	5754.15i	−0.488846	−	0.113662i
$226$	3972.57	+	4584.60i	0.0777777	+	0.0897603i
$227$	−12793.5	+	43570.7i	−0.248278	+	0.845556i	0.737189	+	0.675687i	$0.236153\pi$
$227$	−12793.5	+	43570.7i	−0.248278	+	0.845556i	−0.985467	+	0.169869i	$0.945665\pi$
$228$	−17374.7	+	15946.8i	−0.334232	+	0.306764i
$229$	−80368.8			−1.53256			−0.766279	−	0.642508i	$-0.777894\pi$
$229$	−80368.8			−1.53256			−0.766279	+	0.642508i	$0.777894\pi$
$230$	−34238.4	−	30482.5i	−0.647228	−	0.576228i
$231$	−18220.9	+	43117.4i	−0.341464	+	0.808032i
$232$	2928.57	−	6412.67i	0.0544101	−	0.119142i
$233$	−12837.4	+	43720.0i	−0.236463	+	0.805320i	0.752683	+	0.658384i	$0.228759\pi$
$233$	−12837.4	+	43720.0i	−0.236463	+	0.805320i	−0.989146	+	0.146937i	$0.953059\pi$
$234$	−21899.4	−	1880.35i	−0.399946	−	0.0343405i
$235$	−22450.2	+	14427.9i	−0.406523	+	0.261257i
$236$	−26011.1	−	22538.7i	−0.467019	−	0.404674i
$237$	53451.1	−	88641.3i	0.951611	−	1.57812i
$238$	37675.9	−	11062.6i	0.665134	−	0.195301i
$239$	−15328.6	+	23851.8i	−0.268354	+	0.417567i	−0.949111	−	0.314943i	$-0.898015\pi$
$239$	−15328.6	+	23851.8i	−0.268354	+	0.417567i	0.680757	+	0.732509i	$0.261651\pi$
$240$	17067.7	+	4486.06i	0.296314	+	0.0778831i
$241$	−2863.95	−	6271.17i	−0.0493096	−	0.107973i	0.883374	−	0.468669i	$-0.155266\pi$
$241$	−2863.95	−	6271.17i	−0.0493096	−	0.107973i	−0.932683	+	0.360696i	$0.882539\pi$
$242$	−13730.7	+	6270.59i	−0.234456	+	0.107073i
$243$	−56658.2	−	16632.2i	−0.959512	−	0.281668i
$244$	−1254.83	−	806.431i	−0.0210769	−	0.0135453i
$245$	−9037.04	−	30777.3i	−0.150555	−	0.512742i
$246$	21548.6	−	35735.5i	0.356081	−	0.590512i
$247$	20578.9	−	23749.4i	0.337310	−	0.389276i
$248$	−20085.9	−	31254.2i	−0.326578	−	0.508165i
$249$	−38051.0	+	12364.1i	−0.613716	+	0.199418i
$250$	25885.4	+	7600.63i	0.414166	+	0.121610i
$251$	46909.3	+	21422.7i	0.744580	+	0.340038i	0.751319	−	0.659939i	$-0.229418\pi$
$251$	46909.3	+	21422.7i	0.744580	+	0.340038i	−0.00673931	+	0.999977i	$0.502145\pi$
$252$	−16618.7	−	17099.3i	−0.261695	−	0.269263i
$253$	−31971.5	+	67590.2i	−0.499485	+	1.05595i
$254$			46540.8i			0.721384i
$255$	76642.8	−	70344.0i	1.17867	−	1.08180i
$256$	−3930.08	−	1153.98i	−0.0599683	−	0.0176083i
$257$	33611.5	−	29124.6i	0.508888	−	0.440954i	−0.362186	−	0.932106i	$-0.617969\pi$
$257$	33611.5	−	29124.6i	0.508888	−	0.440954i	0.871074	+	0.491152i	$0.163424\pi$
$258$	7251.07	+	41896.6i	0.108934	+	0.629418i
$259$	−56037.6	+	64670.9i	−0.835373	+	0.964072i
$260$	−23275.7	−	3346.55i	−0.344316	−	0.0495051i
$261$	−12408.9	+	21974.6i	−0.182159	+	0.322582i
$262$	−38846.7	−	24965.2i	−0.565915	−	0.363692i
$263$	−109095.	+	15685.5i	−1.57722	+	0.226770i	−0.874618	−	0.484812i	$-0.838888\pi$
$263$	−109095.	+	15685.5i	−1.57722	+	0.226770i	−0.702603	+	0.711582i	$0.747979\pi$
$264$	−822.345	−	28772.3i	−0.0117990	−	0.412825i
$265$	−32107.9	−	70306.4i	−0.457214	−	1.00116i
$266$	33743.7	−	4851.62i	0.476903	−	0.0685683i
$267$	4064.81	−	2779.53i	0.0570188	−	0.0389896i
$268$	−8429.30	+	2475.07i	−0.117361	+	0.0344602i
$269$	15848.8	+	2278.72i	0.219025	+	0.0314910i	0.250953	−	0.967999i	$-0.419256\pi$
$269$	15848.8	+	2278.72i	0.219025	+	0.0314910i	−0.0319289	+	0.999490i	$0.510165\pi$
$270$	−59499.9	−	21226.8i	−0.816185	−	0.291177i
$271$	64794.7	−	41641.0i	0.882269	−	0.567000i	−0.0192138	−	0.999815i	$-0.506116\pi$
$271$	64794.7	−	41641.0i	0.882269	−	0.567000i	0.901482	+	0.432816i	$0.142480\pi$
$272$	−18248.1	+	15812.1i	−0.246650	+	0.213723i
$273$	24597.0	+	20112.3i	0.330032	+	0.269858i
$274$	−39392.3	+	86257.1i	−0.524699	+	1.14893i
$275$			44336.2i			0.586264i
$276$	−25375.3	−	28404.1i	−0.333114	−	0.372874i
$277$	−76512.1			−0.997173			−0.498586	−	0.866840i	$-0.666147\pi$
$277$	−76512.1			−0.997173			−0.498586	+	0.866840i	$0.666147\pi$
$278$	2307.51	+	1053.81i	0.0298576	+	0.0136355i
$279$	62067.0	+	117622.i	0.797357	+	1.51106i
$280$	−16705.4	−	19279.1i	−0.213080	−	0.245907i
$281$	−54038.9	−	84086.1i	−0.684374	−	1.06491i	−0.993494	−	0.113884i	$-0.963671\pi$
$281$	−54038.9	−	84086.1i	−0.684374	−	1.06491i	0.309120	−	0.951023i	$-0.399966\pi$
$282$	−19897.8	+	9783.44i	−0.250212	+	0.123025i
$283$	−6071.80	+	42230.3i	−0.0758132	+	0.527292i	0.916157	+	0.400820i	$0.131275\pi$
$283$	−6071.80	+	42230.3i	−0.0758132	+	0.527292i	−0.991970	+	0.126472i	$0.959634\pi$
$284$	7386.04	+	25154.5i	0.0915746	+	0.311874i
$285$	74554.7	−	50980.7i	0.917879	−	0.627648i
$286$	5458.42	+	37964.2i	0.0667322	+	0.464132i
$287$	−54870.5	+	25058.5i	−0.666154	+	0.304222i
$288$	13663.7	+	5319.32i	0.164734	+	0.0641315i
$289$	8370.58	+	58218.7i	0.100221	+	0.697054i
$290$	−14596.6	+	22712.7i	−0.173562	+	0.270068i
$291$	−88298.2	−	10130.1i	−1.04272	−	0.119626i
$292$	4708.65	−	32749.4i	0.0552244	−	0.384094i
$293$	−68137.2	−	59041.2i	−0.793687	−	0.687734i	0.160470	−	0.987041i	$-0.448699\pi$
$293$	−68137.2	−	59041.2i	−0.793687	−	0.687734i	−0.954157	+	0.299307i	$0.903245\pi$
$294$	−4544.99	−	26260.9i	−0.0525822	−	0.303819i
$295$	86317.4	+	99615.5i	0.991869	+	1.14468i
$296$	14824.8	−	50488.5i	0.169201	−	0.576247i
$297$	−5878.22	+	102871.i	−0.0666396	+	1.16622i
$298$	1806.96			0.0203477
$299$	37906.0	+	33747.7i	0.423999	+	0.377487i
$300$	−20803.6	−	8791.33i	−0.231151	−	0.0976814i
$301$	25532.8	−	55908.9i	0.281815	−	0.617090i
$302$	27460.3	−	93521.4i	0.301087	−	1.02541i
$303$	89802.5	−	29179.9i	0.978145	−	0.317833i
$304$	−17635.3	+	11333.5i	−0.190825	+	0.122636i
$305$	4317.23	+	3740.90i	0.0464093	+	0.0402139i
$306$	69926.2	−	50807.3i	0.746788	−	0.542604i
$307$	104741.	−	30754.6i	1.11132	−	0.326312i	0.325978	−	0.945377i	$-0.394306\pi$
$307$	104741.	−	30754.6i	1.11132	−	0.326312i	0.785340	+	0.619065i	$0.212488\pi$
$308$	−22495.1	+	35003.1i	−0.237130	+	0.368982i
$309$	46172.8	−	175669.i	0.483581	−	1.83983i
$310$	59106.1	+	129424.i	0.615048	+	1.34677i
$311$	66688.5	−	30455.6i	0.689493	−	0.314881i	−0.0396778	−	0.999213i	$-0.512633\pi$
$311$	66688.5	−	30455.6i	0.689493	−	0.314881i	0.729171	+	0.684332i	$0.239906\pi$
$312$	−18896.0	−	4966.61i	−0.194116	−	0.0510212i
$313$	97744.3	+	62816.5i	0.997707	+	0.641187i	0.934183	−	0.356793i	$-0.116130\pi$
$313$	97744.3	+	62816.5i	0.997707	+	0.641187i	0.0635233	+	0.997980i	$0.479766\pi$
$314$	−18308.2	−	62352.1i	−0.185689	−	0.632400i
$315$	53677.7	+	73876.8i	0.540969	+	0.744538i
$316$	60253.0	−	69535.6i	0.603398	−	0.696359i
$317$	−32320.0	−	50290.8i	−0.321627	−	0.500461i	0.642363	−	0.766401i	$-0.277954\pi$
$317$	−32320.0	−	50290.8i	−0.321627	−	0.500461i	−0.963990	+	0.265939i	$0.914318\pi$
$318$	−19845.3	−	61074.9i	−0.196248	−	0.603960i
$319$	42252.7	+	12406.5i	0.415215	+	0.121918i
$320$	14269.0	+	6516.44i	0.139346	+	0.0636371i
$321$	9954.60	−	23556.3i	0.0966082	−	0.228611i
$322$	7102.77	+	54597.4i	0.0685040	+	0.526575i
$323$			123577.i			1.18449i
$324$	−47103.9	−	23156.3i	−0.448711	−	0.220586i
$325$	28875.2	+	8478.52i	0.273374	+	0.0802700i
$326$	102666.	−	88960.7i	0.966033	−	0.837072i
$327$	−106385.	+	18412.2i	−0.994917	+	0.172191i
$328$	24290.8	−	28033.0i	0.225784	−	0.260569i
$329$	31725.5	+	4561.43i	0.293100	+	0.0421415i
$330$	−12564.4	+	109517.i	−0.115375	+	1.00566i
$331$	66632.9	+	42822.4i	0.608181	+	0.390854i	0.808175	−	0.588943i	$-0.200456\pi$
$331$	66632.9	+	42822.4i	0.608181	+	0.390854i	−0.199994	+	0.979797i	$0.564092\pi$
$332$	−35201.9	+	5061.27i	−0.319367	+	0.0459180i
$333$	−68335.6	+	175533.i	−0.616252	+	1.58296i
$334$	4171.98	+	9135.36i	0.0373981	+	0.0818903i
$335$	33302.4	−	4788.16i	0.296746	−	0.0426657i
$336$	−11963.7	−	17495.9i	−0.105971	−	0.154974i
$337$	24451.3	−	7179.56i	0.215299	−	0.0632176i	−0.172304	−	0.985044i	$-0.555121\pi$
$337$	24451.3	−	7179.56i	0.215299	−	0.0632176i	0.387603	+	0.921826i	$0.373303\pi$
$338$	−54191.4	−	7791.55i	−0.474348	−	0.0682010i
$339$	−8517.04	−	17322.2i	−0.0741121	−	0.150731i
$340$	77792.2	−	49994.0i	0.672943	−	0.432474i
$341$	175387.	−	151974.i	1.50831	−	1.30695i
$342$	66368.9	−	35021.6i	0.567430	−	0.299422i
$343$	−52706.0	+	115410.i	−0.447994	+	0.980969i
$344$			37795.1i			0.319388i
$345$	80710.4	+	121503.i	0.678096	+	1.02082i
$346$	−65517.0			−0.547270
$347$	−154479.	−	70548.2i	−1.28295	−	0.585905i	−0.346945	−	0.937885i	$-0.612781\pi$
$347$	−154479.	−	70548.2i	−1.28295	−	0.585905i	−0.936007	+	0.351981i	$0.885508\pi$
$348$	−14199.6	+	17365.8i	−0.117251	+	0.143396i
$349$	−68582.4	−	79148.4i	−0.563070	−	0.649817i	0.400808	−	0.916162i	$-0.368729\pi$
$349$	−68582.4	−	79148.4i	−0.563070	−	0.649817i	−0.963878	+	0.266345i	$0.914184\pi$
$350$	17650.4	+	27464.5i	0.144085	+	0.224200i
$351$	65873.5	+	23500.6i	0.534684	+	0.190750i
$352$	3641.24	−	25325.4i	0.0293876	−	0.204395i
$353$	46532.3	+	158474.i	0.373426	+	1.27177i	0.905236	+	0.424909i	$0.139694\pi$
$353$	46532.3	+	158474.i	0.373426	+	1.27177i	−0.531809	+	0.846864i	$0.678488\pi$
$354$	61816.9	+	90401.7i	0.493288	+	0.721390i
$355$	−14288.7	−	99380.2i	−0.113380	−	0.788575i
$356$	3981.58	−	1818.33i	0.0314163	−	0.0143474i
$357$	−124894.	+	3569.62i	−0.979953	+	0.0280082i
$358$	−14654.1	−	101922.i	−0.114339	−	0.795245i
$359$	77093.8	−	119960.i	0.598178	−	0.930784i	−0.401709	−	0.915767i	$-0.631584\pi$
$359$	77093.8	−	119960.i	0.598178	−	0.930784i	0.999887	−	0.0150163i	$-0.00478001\pi$
$360$	−48896.4	−	27611.3i	−0.377287	−	0.213050i
$361$	3277.92	−	22798.4i	0.0251527	−	0.174941i
$362$	50693.0	+	43925.7i	0.386839	+	0.335198i
$363$	47327.7	−	8191.03i	0.359172	−	0.0621621i
$364$	18494.9	+	21344.3i	0.139589	+	0.161094i
$365$	−35698.7	+	121579.i	−0.267958	+	0.912581i
$366$	3209.38	+	3496.76i	0.0239585	+	0.0261038i
$367$	−104295.			−0.774340			−0.387170	−	0.922008i	$-0.626547\pi$
$367$	−104295.			−0.774340			−0.387170	+	0.922008i	$0.626547\pi$
$368$	−17919.7	−	28724.8i	−0.132323	−	0.212110i
$369$	−95220.4	+	92544.0i	−0.699322	+	0.679666i
$370$	−83714.6	+	183309.i	−0.611502	+	1.33900i
$371$	−26153.1	+	89069.3i	−0.190010	+	0.647113i
$372$	36532.5	+	112430.i	0.263994	+	0.812452i
$373$	25023.7	−	16081.8i	0.179860	−	0.115589i	−0.447613	−	0.894227i	$-0.647726\pi$
$373$	25023.7	−	16081.8i	0.179860	−	0.115589i	0.627473	+	0.778638i	$0.284089\pi$
$374$	−113988.	−	98770.8i	−0.814919	−	0.706131i
$375$	−73513.1	−	44328.7i	−0.522759	−	0.315226i
$376$	−18910.9	+	5552.74i	−0.133763	+	0.0392764i
$377$	16160.1	−	25145.7i	0.113701	−	0.176922i
$378$	37312.0	+	66064.7i	0.261135	+	0.462366i
$379$	60025.2	+	131437.i	0.417884	+	0.915038i	0.995140	+	0.0984744i	$0.0313963\pi$
$379$	60025.2	+	131437.i	0.417884	+	0.915038i	−0.577256	+	0.816563i	$0.695876\pi$
$380$	73028.1	−	33350.8i	0.505735	−	0.230961i
$381$	37645.8	−	143227.i	0.259338	−	0.986678i
$382$	71847.6	+	46173.7i	0.492363	+	0.316423i
$383$	8915.75	+	30364.3i	0.0607800	+	0.206998i	0.984285	−	0.176590i	$-0.0565066\pi$
$383$	8915.75	+	30364.3i	0.0607800	+	0.206998i	−0.923505	+	0.383588i	$0.874688\pi$
$384$	11161.2	+	6730.26i	0.0756919	+	0.0456425i
$385$	104351.	−	120428.i	0.704004	−	0.812464i
$386$	−45112.6	−	70196.5i	−0.302777	−	0.471130i
$387$	11574.3	−	134800.i	0.0772812	−	0.900053i
$388$	−75801.9	−	22257.5i	−0.503520	−	0.147847i
$389$	175845.	+	80305.6i	1.16206	+	0.530697i	0.900657	−	0.434532i	$-0.143086\pi$
$389$	175845.	+	80305.6i	1.16206	+	0.530697i	0.261408	+	0.965229i	$0.415813\pi$
$390$	68923.0	+	29126.0i	0.453143	+	0.191493i
$391$	−199562.	−	2680.80i	−1.30534	−	0.0175352i
$392$		−	23690.0i		−	0.154168i
$393$	99355.0	+	108252.i	0.643287	+	0.700888i
$394$	−165015.	−	48452.7i	−1.06299	−	0.312123i
$395$	−266303.	+	230753.i	−1.70680	+	1.47895i
$396$	−20742.5	+	89210.5i	−0.132273	+	0.568886i
$397$	−55827.6	+	64428.5i	−0.354216	+	0.408787i	−0.904693	−	0.426063i	$-0.859900\pi$
$397$	−55827.6	+	64428.5i	−0.354216	+	0.408787i	0.550478	+	0.834850i	$0.314446\pi$
$398$	−60772.1	−	8737.71i	−0.383652	−	0.0551609i
$399$	−107769.	−	12363.9i	−0.676937	−	0.0776621i
$400$	−16888.5	−	10853.6i	−0.105553	−	0.0678350i
$401$	110166.	−	15839.5i	0.685107	−	0.0985035i	0.209033	−	0.977909i	$-0.432968\pi$
$401$	110166.	−	15839.5i	0.685107	−	0.0985035i	0.476074	+	0.879405i	$0.342059\pi$
$402$	27942.8	−	798.638i	0.172909	−	0.00494195i
$403$	−65437.5	−	143288.i	−0.402918	−	0.882267i
$404$	83078.5	−	11944.9i	0.509009	−	0.0731845i
$405$	165938.	+	113453.i	1.01166	+	0.691679i
$406$	31112.9	−	9135.57i	0.188751	−	0.0554222i
$407$	325347.	+	46777.8i	1.96407	+	0.282391i
$408$	68947.9	−	33900.5i	0.414191	−	0.203651i
$409$	−13058.4	+	8392.11i	−0.0780626	+	0.0501678i	−0.579090	−	0.815264i	$-0.696592\pi$
$409$	−13058.4	+	8392.11i	−0.0780626	+	0.0501678i	0.501027	+	0.865431i	$0.332956\pi$
$410$	−107359.	+	93027.2i	−0.638662	+	0.553404i
$411$	190999.	−	233589.i	1.13070	−	1.38283i
$412$	67070.4	−	146864.i	0.395127	−	0.865207i
$413$		−	158309.i		−	0.928124i
$414$	55115.9	+	107938.i	0.321570	+	0.629756i
$415$	136200.			0.790827
$416$	−15797.5	−	7214.48i	−0.0912856	−	0.0416887i
$417$	−6248.86	−	5109.53i	−0.0359359	−	0.0293839i
$418$	−85751.9	−	98963.0i	−0.490785	−	0.566396i
$419$	−149574.	−	232741.i	−0.851975	−	1.32570i	−0.944001	−	0.329942i	$-0.892971\pi$
$419$	−149574.	−	232741.i	−0.851975	−	1.32570i	0.0920260	−	0.995757i	$-0.470666\pi$
$420$	35815.8	+	72843.2i	0.203037	+	0.412943i
$421$	45093.4	−	313632.i	0.254419	−	1.76952i	−0.316577	−	0.948567i	$-0.602533\pi$
$421$	45093.4	−	313632.i	0.254419	−	1.76952i	0.570995	−	0.820953i	$-0.306557\pi$
$422$	20257.6	+	68990.9i	0.113753	+	0.387407i
$423$	69148.2	−	14013.2i	0.386456	−	0.0783170i
$424$	−8123.74	−	56501.8i	−0.0451881	−	0.314290i
$425$	−107649.	+	49161.8i	−0.595982	+	0.272176i
$426$	−2383.28	−	83386.3i	−0.0131327	−	0.459489i
$427$	−976.414	−	6791.11i	−0.00535523	−	0.0372465i
$428$	12289.7	−	19123.2i	0.0670896	−	0.104394i
$429$	13910.3	−	121248.i	0.0755825	−	0.658810i
$430$	20599.4	−	143272.i	0.111408	−	0.774860i
$431$	−150279.	−	130218.i	−0.808992	−	0.700995i	0.148671	−	0.988887i	$-0.452500\pi$
$431$	−150279.	−	130218.i	−0.808992	−	0.700995i	−0.957663	+	0.287891i	$0.907046\pi$
$432$	−37746.6	−	27422.2i	−0.202260	−	0.146938i
$433$	10757.0	+	12414.2i	0.0573740	+	0.0662132i	0.783711	−	0.621126i	$-0.213324\pi$
$433$	10757.0	+	12414.2i	0.0573740	+	0.0662132i	−0.726337	+	0.687339i	$0.758779\pi$
$434$	48144.2	−	163964.i	0.255602	−	0.870501i
$435$	63292.0	−	58090.4i	0.334480	−	0.306991i
$436$	−95970.7			−0.504854
$437$	−171163.	−	26960.9i	−0.896286	−	0.141179i
$438$	−40980.9	+	96976.1i	−0.213616	+	0.505494i
$439$	−31290.0	+	68515.5i	−0.162359	+	0.355517i	−0.973274	−	0.229648i	$-0.926243\pi$
$439$	−31290.0	+	68515.5i	−0.162359	+	0.355517i	0.810915	+	0.585164i	$0.198970\pi$
$440$	−27606.1	+	94017.6i	−0.142593	+	0.485628i
$441$	−7254.82	+	84493.0i	−0.0373035	+	0.434454i
$442$	−86125.3	+	55349.4i	−0.440845	+	0.283314i
$443$	64875.7	+	56215.1i	0.330578	+	0.286448i	0.804296	−	0.594229i	$-0.202543\pi$
$443$	64875.7	+	56215.1i	0.330578	+	0.286448i	−0.473717	+	0.880677i	$0.657088\pi$
$444$	−86461.4	+	143385.i	−0.438588	+	0.727338i
$445$	−16084.2	+	4722.76i	−0.0812232	+	0.0238493i
$446$	−94618.3	+	147229.i	−0.475670	+	0.740157i
$447$	−5560.84	−	1461.61i	−0.0278308	−	0.00731502i
$448$	−7826.50	−	17137.6i	−0.0389952	−	0.0853877i
$449$	−230401.	+	105221.i	−1.14286	+	0.521926i	−0.894644	−	0.446779i	$-0.852571\pi$
$449$	−230401.	+	105221.i	−1.14286	+	0.521926i	−0.248214	+	0.968705i	$0.579844\pi$
$450$	56910.9	+	43882.4i	0.281041	+	0.216703i
$451$	194921.	+	125268.i	0.958308	+	0.615867i
$452$	−4833.98	−	16463.0i	−0.0236607	−	0.0805811i
$453$	−160155.	+	265596.i	−0.780449	+	1.29427i
$454$	84109.7	−	97067.8i	0.408070	−	0.470938i
$455$	−58476.4	−	90991.1i	−0.282461	−	0.439517i
$456$	63439.2	−	20613.6i	0.305090	−	0.0991343i
$457$	−296081.	−	86937.2i	−1.41768	−	0.416268i	−0.518963	−	0.854797i	$-0.673682\pi$
$457$	−296081.	−	86937.2i	−1.41768	−	0.416268i	−0.898717	+	0.438529i	$0.855500\pi$
$458$	206775.	+	94431.1i	0.985752	+	0.450178i
$459$	−256291.	+	99795.3i	−1.21649	+	0.473680i
$460$	52273.4	+	118655.i	0.247039	+	0.560752i
$461$			167199.i			0.786742i	0.919380	+	0.393371i	$0.128691\pi$
$461$			167199.i			0.786742i	−0.919380	+	0.393371i	$0.871309\pi$
$462$	97540.8	−	89524.6i	0.456986	−	0.419429i
$463$	−395601.	−	116159.i	−1.84542	−	0.541865i	−0.999969	−	0.00781292i	$-0.997513\pi$
$463$	−395601.	−	116159.i	−1.84542	−	0.541865i	−0.845452	−	0.534052i	$-0.820669\pi$
$464$	−15069.4	+	13057.7i	−0.0699939	+	0.0606501i
$465$	−77208.0	−	446107.i	−0.357072	−	2.06316i
$466$	84398.1	−	97400.6i	0.388652	−	0.448528i
$467$	−15711.0	−	2258.90i	−0.0720394	−	0.0103577i	0.106201	−	0.994345i	$-0.466131\pi$
$467$	−15711.0	−	2258.90i	−0.0720394	−	0.0103577i	−0.178240	+	0.983987i	$0.557040\pi$
$468$	54134.1	+	30569.0i	0.247161	+	0.139569i
$469$	−33994.0	−	21846.6i	−0.154546	−	0.0993204i
$470$	74713.0	−	10742.1i	0.338221	−	0.0486288i
$471$	5907.58	+	206695.i	0.0266298	+	0.931726i
$472$	40439.7	+	88550.6i	0.181520	+	0.397473i
$473$	−233685.	+	33598.8i	−1.04450	+	0.150176i
$474$	−241671.	+	165255.i	−1.07564	+	0.735528i
$475$	−98583.1	+	28946.6i	−0.436933	+	0.128295i
$476$	−109932.	−	15805.8i	−0.485187	−	0.0697594i
$477$	11671.1	+	204008.i	0.0512949	+	0.896622i
$478$	67463.1	−	43355.9i	0.295264	−	0.189755i
$479$	101130.	−	87629.3i	0.440765	−	0.381925i	−0.406016	−	0.913866i	$-0.633082\pi$
$479$	101130.	−	87629.3i	0.440765	−	0.381925i	0.846782	+	0.531940i	$0.178537\pi$
$480$	−38641.2	−	31595.9i	−0.167714	−	0.137135i
$481$	92682.1	−	202945.i	0.400595	−	0.877181i
$482$			19499.7i			0.0839332i
$483$	22304.1	−	173766.i	0.0956071	−	0.744854i
$484$	42694.5			0.182256
$485$	275215.	+	125687.i	1.17001	+	0.534325i
$486$	126229.	+	109364.i	0.534427	+	0.463020i
$487$	−193243.	−	223015.i	−0.814792	−	0.940320i	0.184302	−	0.982870i	$-0.440997\pi$
$487$	−193243.	−	223015.i	−0.814792	−	0.940320i	−0.999094	+	0.0425494i	$0.986452\pi$
$488$	2280.93	+	3549.20i	0.00957795	+	0.0149036i
$489$	−387908.	+	190728.i	−1.62223	+	0.797622i
$490$	−12911.7	+	89803.1i	−0.0537765	+	0.374024i
$491$	−130235.	−	443541.i	−0.540214	−	1.83980i	−0.542892	−	0.839803i	$-0.682671\pi$
$491$	−130235.	−	443541.i	−0.540214	−	1.83980i	0.00267783	−	0.999996i	$-0.499148\pi$
$492$	−97429.0	+	66622.2i	−0.402493	+	0.275225i
$493$	16728.2	+	116347.i	0.0688265	+	0.478699i
$494$	−80850.9	+	36923.4i	−0.331307	+	0.151303i
$495$	127252.	−	326870.i	0.519342	−	1.33403i
$496$	14954.7	+	104012.i	0.0607874	+	0.422785i
$497$	−65194.2	+	101444.i	−0.263934	+	0.410690i
$498$	112426.	+	12898.2i	0.453324	+	0.0520079i
$499$	55971.6	−	389291.i	0.224784	−	1.56341i	−0.494801	−	0.869006i	$-0.664759\pi$
$499$	55971.6	−	389291.i	0.224784	−	1.56341i	0.719585	−	0.694404i	$-0.244332\pi$
$500$	−57668.1	−	49969.7i	−0.230672	−	0.199879i
$501$	−5449.69	−	31488.3i	−0.0217118	−	0.125451i
$502$	−95518.4	−	110234.i	−0.379035	−	0.437430i
$503$	−82705.9	+	281671.i	−0.326889	+	1.11328i	0.618078	+	0.786117i	$0.287912\pi$
$503$	−82705.9	+	281671.i	−0.326889	+	1.11328i	−0.944967	+	0.327166i	$0.893906\pi$
$504$	22665.8	+	63520.0i	0.0892299	+	0.250063i
$505$	−321440.			−1.26043
$506$	161674.	−	136332.i	0.631449	−	0.532473i
$507$	160469.	+	67812.3i	0.624275	+	0.263811i
$508$	54684.1	−	119742.i	0.211901	−	0.463999i
$509$	137333.	−	467714.i	0.530078	−	1.80528i	−0.0603329	−	0.998178i	$-0.519216\pi$
$509$	137333.	−	467714.i	0.530078	−	1.80528i	0.590411	−	0.807103i	$-0.298966\pi$
$510$	−279841.	+	90930.0i	−1.07590	+	0.349596i
$511$	128026.	−	82277.5i	0.490295	−	0.315093i
$512$	8755.54	+	7586.72i	0.0333997	+	0.0289410i
$513$	−232575.	+	54093.0i	−0.883749	+	0.205545i
$514$	−120697.	+	35439.9i	−0.456847	+	0.134142i
$515$	−334292.	+	520168.i	−1.26041	+	1.96123i
$516$	30571.5	−	116313.i	0.114820	−	0.436845i
$517$	−51143.7	−	111989.i	−0.191342	−	0.418981i
$518$	220162.	−	100544.i	0.820507	−	0.374713i
$519$	201625.	+	52995.1i	0.748533	+	0.196744i
$520$	55952.4	+	35958.4i	0.206924	+	0.132982i
$521$	24359.8	+	82961.8i	0.0897424	+	0.305635i	0.992117	−	0.125319i	$-0.0399954\pi$
$521$	24359.8	+	82961.8i	0.0897424	+	0.305635i	−0.902374	+	0.430954i	$0.858177\pi$
$522$	57745.4	−	41956.9i	0.211922	−	0.153979i
$523$	−32150.7	+	37103.9i	−0.117541	+	0.135649i	−0.811470	−	0.584394i	$-0.801332\pi$
$523$	−32150.7	+	37103.9i	−0.117541	+	0.135649i	0.693930	+	0.720043i	$0.255878\pi$
$524$	70612.4	+	109875.i	0.257169	+	0.400162i
$525$	−32102.8	−	98797.8i	−0.116473	−	0.358450i
$526$	299112.	+	87827.2i	1.08109	+	0.317437i
$527$	563473.	+	257330.i	2.02886	+	0.926549i
$528$	−31690.8	+	74992.3i	−0.113675	+	0.268998i
$529$	47251.7	−	275823.i	0.168852	−	0.985641i
$530$			218612.i			0.778256i
$531$	−117115.	−	328209.i	−0.415358	−	1.16402i
$532$	−92517.3	−	27165.5i	−0.326889	−	0.0959832i
$533$	118859.	−	102992.i	0.418388	−	0.362535i
$534$	−13723.9	+	2375.21i	−0.0481278	+	0.00832951i
$535$	−57010.1	+	65793.1i	−0.199179	+	0.229865i
$536$	24595.3	+	3536.27i	0.0856095	+	0.0123088i
$537$	−37344.7	+	325513.i	−0.129503	+	1.12881i
$538$	−38098.9	−	24484.7i	−0.131628	−	0.0845921i
$539$	146474.	−	21059.8i	0.504178	−	0.0724899i
$540$	128142.	+	124524.i	0.439445	+	0.427036i
$541$	188381.	+	412496.i	0.643638	+	1.40937i	0.897014	+	0.442002i	$0.145732\pi$
$541$	188381.	+	412496.i	0.643638	+	1.40937i	−0.253376	+	0.967368i	$0.581541\pi$
$542$	−215633.	+	31003.3i	−0.734033	+	0.105538i
$543$	−120475.	−	176184.i	−0.408598	−	0.597539i
$544$	65528.1	−	19240.8i	0.221427	−	0.0650167i
$545$	363801.	+	52306.7i	1.22482	+	0.176102i
$546$	−39652.4	−	80646.1i	−0.133010	−	0.270519i
$547$	−483086.	+	310461.i	−1.61454	+	1.03761i	−0.655166	+	0.755485i	$0.727401\pi$
$547$	−483086.	+	310461.i	−1.61454	+	1.03761i	−0.959379	+	0.282120i	$0.908962\pi$
$548$	202699.	−	175640.i	0.674980	−	0.584873i
$549$	−7048.28	−	13357.1i	−0.0233851	−	0.0443167i
$550$	52093.8	−	114069.i	0.172211	−	0.377089i
$551$			102050.i			0.336133i
$552$	31912.3	+	102894.i	0.104732	+	0.337685i
$553$	423209.			1.38390
$554$	196852.	+	89899.5i	0.641389	+	0.292912i
$555$	405902.	−	496411.i	1.31776	−	1.61159i
$556$	−4698.64	−	5422.52i	−0.0151993	−	0.0175409i
$557$	95558.3	+	148692.i	0.308005	+	0.479266i	0.960404	−	0.278610i	$-0.0898737\pi$
$557$	95558.3	+	148692.i	0.308005	+	0.479266i	−0.652399	+	0.757876i	$0.726237\pi$
$558$	−21484.8	−	375549.i	−0.0690023	−	1.20614i
$559$	−22806.0	+	158619.i	−0.0729835	+	0.507611i
$560$	20327.8	+	69230.2i	0.0648209	+	0.220760i
$561$	270898.	+	396165.i	0.860757	+	1.25878i
$562$	40233.9	+	279833.i	0.127385	+	0.885986i
$563$	−427654.	+	195303.i	−1.34920	+	0.616158i	−0.953269	−	0.302123i	$-0.902305\pi$
$563$	−427654.	+	195303.i	−1.34920	+	0.616158i	−0.395929	+	0.918281i	$0.629577\pi$
$564$	62688.9	−	1791.72i	0.197076	−	0.00563265i
$565$	9351.62	+	65041.9i	0.0292948	+	0.203749i
$566$	65241.1	−	101517.i	0.203652	−	0.316888i
$567$	−61387.7	−	233492.i	−0.190948	−	0.726283i
$568$	10552.8	−	73396.7i	0.0327094	−	0.227499i
$569$	274874.	+	238180.i	0.849004	+	0.735666i	0.966297	−	0.257431i	$-0.0828761\pi$
$569$	274874.	+	238180.i	0.849004	+	0.735666i	−0.117293	+	0.993097i	$0.537422\pi$
$570$	−251717.	+	43564.9i	−0.774753	+	0.134087i
$571$	−176564.	−	203765.i	−0.541539	−	0.624969i	0.417352	−	0.908745i	$-0.362958\pi$
$571$	−176564.	−	203765.i	−0.541539	−	0.624969i	−0.958891	+	0.283776i	$0.908413\pi$
$572$	30563.2	−	104089.i	0.0934129	−	0.318135i
$573$	−183759.	−	200213.i	−0.559679	−	0.609794i
$574$	170615.			0.517838
$575$	−44606.7	−	159828.i	−0.134916	−	0.483411i
$576$	−28904.2	−	29740.1i	−0.0871196	−	0.0896391i
$577$	−141233.	+	309258.i	−0.424215	+	0.928901i	0.570015	+	0.821634i	$0.306937\pi$
$577$	−141233.	+	309258.i	−0.424215	+	0.928901i	−0.994230	+	0.107267i	$0.965790\pi$
$578$	46869.2	−	159622.i	0.140292	−	0.477789i
$579$	82051.5	+	252517.i	0.244754	+	0.753240i
$580$	64241.2	−	41285.3i	0.190967	−	0.122727i
$581$	−123627.	−	107123.i	−0.366235	−	0.317345i
$582$	215273.	+	129811.i	0.635542	+	0.383234i
$583$	342126.	−	100457.i	1.00658	−	0.295559i
$584$	−50594.2	+	78726.1i	−0.148346	+	0.230830i
$585$	−188548.	−	145384.i	−0.550948	−	0.424821i
$586$	105934.	+	231962.i	0.308488	+	0.675495i
$587$	247812.	−	113172.i	0.719194	−	0.328445i	−0.0219796	−	0.999758i	$-0.506997\pi$
$587$	247812.	−	113172.i	0.719194	−	0.328445i	0.741173	+	0.671314i	$0.234270\pi$
$588$	−19162.3	+	72905.0i	−0.0554234	+	0.210864i
$589$	452428.	+	290758.i	1.30412	+	0.838109i
$590$	−105034.	−	357714.i	−0.301736	−	1.02762i
$591$	468633.	+	282587.i	1.34171	+	0.809054i
$592$	−97464.0	+	112479.i	−0.278100	+	0.320944i
$593$	−211019.	−	328353.i	−0.600085	−	0.933751i	−0.999853	−	0.0171347i	$-0.994546\pi$
$593$	−211019.	−	328353.i	−0.600085	−	0.933751i	0.399768	−	0.916616i	$-0.369091\pi$
$594$	135994.	−	257763.i	0.385432	−	0.730546i
$595$	408109.	+	119832.i	1.15277	+	0.338484i
$596$	−4649.00	−	2123.13i	−0.0130878	−	0.00597700i
$597$	179956.	+	76047.0i	0.504913	+	0.213370i
$598$	−57872.9	−	131366.i	−0.161835	−	0.367349i
$599$		−	103566.i		−	0.288644i	−0.989531	−	0.144322i	$-0.953900\pi$
$599$		−	103566.i		−	0.288644i	0.989531	−	0.144322i	$-0.0461001\pi$
$600$	43194.4	+	47062.1i	0.119984	+	0.130728i
$601$	321271.	+	94333.6i	0.889452	+	0.261167i	0.694368	−	0.719620i	$-0.255684\pi$
$601$	321271.	+	94333.6i	0.889452	+	0.261167i	0.195084	+	0.980787i	$0.437502\pi$
$602$	−131383.	+	113844.i	−0.362531	+	0.314135i
$603$	−86638.7	−	20144.5i	−0.238274	−	0.0554015i
$604$	−180536.	+	208349.i	−0.494868	+	0.571108i
$605$	−161844.	−	23269.7i	−0.442167	−	0.0635740i
$606$	−265332.	−	30440.4i	−0.722511	−	0.0828905i
$607$	418919.	+	269223.i	1.13698	+	0.730693i	0.967006	−	0.254755i	$-0.0819949\pi$
$607$	418919.	+	269223.i	1.13698	+	0.730693i	0.169975	+	0.985448i	$0.445631\pi$
$608$	58689.1	−	8438.22i	0.158763	−	0.0228267i
$609$	−103138.	+	2947.81i	−0.278089	+	0.00794812i
$610$	−6712.03	−	14697.3i	−0.0180383	−	0.0394983i
$611$	−82716.2	+	11892.8i	−0.221569	+	0.0318568i
$612$	−239605.	+	48557.0i	−0.639725	+	0.129643i
$613$	−239940.	+	70452.7i	−0.638530	+	0.187489i	−0.584944	−	0.811074i	$-0.698883\pi$
$613$	−239940.	+	70452.7i	−0.638530	+	0.187489i	−0.0535862	+	0.998563i	$0.517065\pi$
$614$	−305615.	−	43940.8i	−0.810659	−	0.116555i
$615$	405640.	−	199447.i	1.07248	−	0.527322i
$616$	99003.7	−	63625.8i	0.260909	−	0.167676i
$617$	463723.	−	401818.i	1.21811	−	1.05550i	0.221344	−	0.975196i	$-0.428956\pi$
$617$	463723.	−	401818.i	1.21811	−	1.05550i	0.996770	−	0.0803059i	$-0.0255897\pi$
$618$	−325201.	+	397714.i	−0.851480	+	1.04134i
$619$	62634.3	−	137150.i	0.163467	−	0.357943i	−0.810118	−	0.586267i	$-0.800597\pi$
$619$	62634.3	−	137150.i	0.163467	−	0.357943i	0.973585	+	0.228323i	$0.0733243\pi$
$620$		−	402434.i		−	1.04692i
$621$	−82308.4	−	376755.i	−0.213433	−	0.976958i
$622$	−207362.			−0.535981
$623$	18313.9	+	8363.68i	0.0471851	+	0.0215487i
$624$	42780.5	+	34980.5i	0.109869	+	0.0898373i
$625$	319755.	+	369017.i	0.818574	+	0.944684i
$626$	−177672.	−	276463.i	−0.453388	−	0.705485i
$627$	183849.	+	373917.i	0.467655	+	0.951129i
$628$	−26158.0	+	181933.i	−0.0663263	+	0.461309i
$629$	247180.	+	841818.i	0.624758	+	2.12773i
$630$	−51300.3	−	253142.i	−0.129252	−	0.637798i
$631$	−8978.49	−	62446.8i	−0.0225499	−	0.156838i	0.975435	−	0.220287i	$-0.0706992\pi$
$631$	−8978.49	−	62446.8i	−0.0225499	−	0.156838i	−0.997985	+	0.0634485i	$0.979790\pi$
$632$	−236723.	+	108108.i	−0.592661	+	0.270659i
$633$	−6536.58	−	228702.i	−0.0163133	−	0.570773i
$634$	24063.4	+	167365.i	0.0598658	+	0.416376i
$635$	−272556.	+	424106.i	−0.675941	+	1.05178i
$636$	−20702.6	+	180453.i	−0.0511812	+	0.446118i
$637$	14294.8	−	99422.8i	0.0352290	−	0.245023i
$638$	−94131.5	−	81565.4i	−0.231256	−	0.200385i
$639$	−60114.8	+	258545.i	−0.147224	+	0.633191i
$640$	−29055.1	−	33531.4i	−0.0709353	−	0.0818637i
$641$	132460.	−	451117.i	0.322380	−	1.09793i	−0.625744	−	0.780028i	$-0.715205\pi$
$641$	132460.	−	451117.i	0.322380	−	1.09793i	0.948125	−	0.317899i	$-0.102977\pi$
$642$	−53289.5	+	48909.9i	−0.129292	+	0.118666i
$643$	206509.			0.499479			0.249740	−	0.968313i	$-0.419655\pi$
$643$	206509.			0.499479			0.249740	+	0.968313i	$0.419655\pi$
$644$	45876.1	−	148815.i	0.110615	−	0.358819i
$645$	−179283.	+	424250.i	−0.430942	+	1.01977i
$646$	145199.	−	317942.i	0.347936	−	0.761873i
$647$	74227.9	−	252797.i	0.177320	−	0.603898i	−0.822083	−	0.569367i	$-0.807188\pi$
$647$	74227.9	−	252797.i	0.177320	−	0.603898i	0.999404	−	0.0345306i	$-0.0109936\pi$
$648$	93982.3	+	114923.i	0.223818	+	0.273688i
$649$	−511554.	+	328756.i	−1.21451	+	0.780520i
$650$	−64328.8	−	55741.3i	−0.152258	−	0.131932i
$651$	−280788.	+	465649.i	−0.662547	+	1.09874i
$652$	−368668.	+	108251.i	−0.867243	+	0.254645i
$653$	−116287.	+	180946.i	−0.272712	+	0.424348i	−0.950413	−	0.310989i	$-0.899340\pi$
$653$	−116287.	+	180946.i	−0.272712	+	0.424348i	0.677702	+	0.735337i	$0.262976\pi$
$654$	295345.	+	77628.4i	0.690517	+	0.181495i
$655$	−207789.	−	454994.i	−0.484328	−	1.06053i
$656$	−95434.0	+	43583.2i	−0.221766	+	0.101277i
$657$	204558.	−	265291.i	0.473900	−	0.614599i
$658$	−76264.6	−	49012.3i	−0.176145	−	0.113202i
$659$	−32177.8	−	109587.i	−0.0740944	−	0.252342i	0.914114	−	0.405457i	$-0.132888\pi$
$659$	−32177.8	−	109587.i	−0.0740944	−	0.252342i	−0.988208	+	0.153115i	$0.951069\pi$
$660$	161005.	−	267005.i	0.369617	−	0.612959i
$661$	18247.0	−	21058.2i	0.0417628	−	0.0481969i	−0.734484	−	0.678626i	$-0.762576\pi$
$661$	18247.0	−	21058.2i	0.0417628	−	0.0481969i	0.776247	+	0.630429i	$0.217121\pi$
$662$	−121120.	−	188466.i	−0.276376	−	0.430049i
$663$	309818.	−	100670.i	0.704821	−	0.229021i
$664$	96515.2	+	28339.4i	0.218907	+	0.0642769i
$665$	335904.	+	153402.i	0.759578	+	0.346887i
$666$	382061.	−	371323.i	0.861360	−	0.837149i
$667$	−164799.	−	2213.82i	−0.370427	−	0.00497612i
$668$		−	28405.7i		−	0.0636578i
$669$	410274.	−	376556.i	0.916688	−	0.841351i
$670$	−91307.2	−	26810.2i	−0.203402	−	0.0597242i
$671$	−19916.8	+	17258.0i	−0.0442359	+	0.0383307i
$672$	10223.5	+	59071.0i	0.0226391	+	0.130808i
$673$	524669.	−	605500.i	1.15839	−	1.33685i	0.226545	−	0.974001i	$-0.427257\pi$
$673$	524669.	−	605500.i	1.15839	−	1.33685i	0.931846	−	0.362854i	$-0.118198\pi$
$674$	−71344.8	−	10257.8i	−0.157052	−	0.0225806i
$675$	−139645.	−	181080.i	−0.306491	−	0.397432i
$676$	130270.	+	83719.7i	0.285070	+	0.183204i
$677$	−717988.	+	103231.i	−1.56654	+	0.225234i	−0.870279	−	0.492559i	$-0.836061\pi$
$677$	−717988.	+	103231.i	−1.56654	+	0.225234i	−0.696256	+	0.717793i	$0.745152\pi$
$678$	1559.80	+	54574.3i	0.00339320	+	0.118721i
$679$	−150955.	−	330544.i	−0.327421	−	0.716952i
$680$	−258888.	+	37222.4i	−0.559878	+	0.0804983i
$681$	−337360.	+	230687.i	−0.727443	+	0.497427i
$682$	−629807.	+	184928.i	−1.35406	+	0.397588i
$683$	−368188.	−	52937.4i	−0.789274	−	0.113481i	−0.264123	−	0.964489i	$-0.585082\pi$
$683$	−368188.	−	52937.4i	−0.789274	−	0.113481i	−0.525152	+	0.851009i	$0.675991\pi$
$684$	−211905.	+	12122.9i	−0.452928	+	0.0259116i
$685$	−864111.	+	555330.i	−1.84157	+	1.18351i
$686$	271207.	−	235002.i	0.576305	−	0.499371i
$687$	−559958.	−	457863.i	−1.18643	−	0.970112i
$688$	44408.1	−	97240.2i	0.0938178	−	0.205432i
$689$		−	242030.i		−	0.509836i
$690$	−64891.5	−	407439.i	−0.136298	−	0.855784i
$691$	634240.			1.32830			0.664152	−	0.747598i	$-0.268793\pi$
$691$	634240.			1.32830			0.664152	+	0.747598i	$0.268793\pi$
$692$	168564.	+	76980.6i	0.352008	+	0.160757i
$693$	−372592.	+	196609.i	−0.775830	+	0.409390i
$694$	314556.	+	363017.i	0.653099	+	0.753716i
$695$	14856.0	+	23116.3i	0.0307561	+	0.0478574i
$696$	56937.5	−	27995.2i	0.117538	−	0.0577917i
$697$	−88017.4	+	612174.i	−0.181177	+	1.26011i
$698$	83453.8	+	284218.i	0.171291	+	0.583364i
$699$	−338516.	+	231478.i	−0.692827	+	0.473757i
$700$	−13141.4	−	91400.2i	−0.0268191	−	0.186531i
$701$	−688773.	+	314552.i	−1.40165	+	0.640113i	−0.965653	−	0.259834i	$-0.916332\pi$
$701$	−688773.	+	314552.i	−1.40165	+	0.640113i	−0.435999	+	0.899947i	$0.643605\pi$
$702$	−141869.	−	137863.i	−0.287881	−	0.279751i
$703$	108403.	+	753960.i	0.219347	+	1.52559i
$704$	−39124.9	+	60879.5i	−0.0789419	+	0.122836i
$705$	−238615.	−	27375.2i	−0.480086	−	0.0550782i
$706$	66483.3	−	462402.i	0.133384	−	0.927705i
$707$	291766.	+	252817.i	0.583709	+	0.505786i
$708$	−52824.8	−	305221.i	−0.105383	−	0.608903i
$709$	−343838.	−	396810.i	−0.684009	−	0.789388i	0.302491	−	0.953152i	$-0.402182\pi$
$709$	−343838.	−	396810.i	−0.684009	−	0.789388i	−0.986500	+	0.163764i	$0.947636\pi$
$710$	−80006.4	+	272477.i	−0.158711	+	0.540522i
$711$	877404.	−	313084.i	1.73564	−	0.619329i
$712$	−12380.4			−0.0244216
$713$	−479354.	+	724310.i	−0.942925	+	1.42477i
$714$	325525.	+	137563.i	0.638540	+	0.269839i
$715$	−172589.	+	377917.i	−0.337599	+	0.739238i
$716$	−82052.6	+	279446.i	−0.160054	+	0.545094i
$717$	−242684.	+	78856.5i	−0.472067	+	0.153391i
$718$	−339299.	+	218054.i	−0.658163	+	0.422976i
$719$	−336315.	−	291419.i	−0.650562	−	0.563716i	0.265818	−	0.964023i	$-0.414358\pi$
$719$	−336315.	−	291419.i	−0.650562	−	0.563716i	−0.916381	+	0.400308i	$0.868903\pi$
$720$	93359.4	+	128491.i	0.180091	+	0.247861i
$721$	712551.	−	209224.i	1.37071	−	0.402477i
$722$	−35221.0	+	54805.0i	−0.0675659	+	0.105135i
$723$	15772.8	−	60009.4i	0.0301740	−	0.114800i
$724$	−78812.8	−	172576.i	−0.150356	−	0.329233i
$725$	−88897.3	+	40598.1i	−0.169127	+	0.0772377i
$726$	−131390.	−	34534.5i	−0.249281	−	0.0655210i
$727$	−510925.	−	328352.i	−0.966693	−	0.621256i	−0.0408504	−	0.999165i	$-0.513007\pi$
$727$	−510925.	−	328352.i	−0.966693	−	0.621256i	−0.925843	+	0.377909i	$0.876643\pi$
$728$	−22505.3	−	76646.2i	−0.0424642	−	0.144620i
$729$	−300004.	−	438665.i	−0.564510	−	0.825426i
$730$	234698.	−	270856.i	0.440416	−	0.508267i
$731$	−340698.	−	530137.i	−0.637581	−	0.992095i
$732$	−4148.60	−	12767.5i	−0.00774246	−	0.0238278i
$733$	−174072.	−	51112.2i	−0.323982	−	0.0951298i	0.115697	−	0.993285i	$-0.463090\pi$
$733$	−174072.	−	51112.2i	−0.323982	−	0.0951298i	−0.439680	+	0.898155i	$0.644908\pi$
$734$	268333.	+	122544.i	0.498061	+	0.227457i
$735$	112375.	−	265921.i	0.208015	−	0.492241i
$736$	12353.6	+	94959.0i	0.0228053	+	0.175300i
$737$			155215.i			0.285758i
$738$	353722.	−	126219.i	0.649456	−	0.231745i
$739$	−75618.2	−	22203.5i	−0.138464	−	0.0406568i	0.211766	−	0.977320i	$-0.432079\pi$
$739$	−75618.2	−	22203.5i	−0.138464	−	0.0406568i	−0.350230	+	0.936664i	$0.613897\pi$
$740$	430766.	−	373261.i	0.786644	−	0.681631i
$741$	278681.	−	48231.5i	0.507541	−	0.0878405i
$742$	171941.	−	198431.i	0.312300	−	0.360414i
$743$	167962.	+	24149.3i	0.304252	+	0.0437448i	0.292750	−	0.956189i	$-0.405430\pi$
$743$	167962.	+	24149.3i	0.304252	+	0.0437448i	0.0115018	+	0.999934i	$0.496339\pi$
$744$	38110.5	−	332188.i	0.0688493	−	0.600121i
$745$	16466.0	+	10582.1i	0.0296672	+	0.0190659i
$746$	−83277.4	+	11973.5i	−0.149641	+	0.0215151i
$747$	−335553.	−	130632.i	−0.601340	−	0.234104i
$748$	177218.	+	388053.i	0.316741	+	0.693565i
$749$	103494.	−	14880.2i	0.184482	−	0.0265244i
$750$	137052.	+	200426.i	0.243647	+	0.356312i
$751$	733866.	−	215482.i	1.30118	−	0.382060i	0.443512	−	0.896268i	$-0.353732\pi$
$751$	733866.	−	215482.i	1.30118	−	0.382060i	0.857666	+	0.514208i	$0.171914\pi$
$752$	55178.8	+	7933.52i	0.0975746	+	0.0140291i
$753$	204788.	+	416503.i	0.361172	+	0.734561i
$754$	−71122.7	+	45707.8i	−0.125102	+	0.0803984i
$755$	797922.	−	691403.i	1.39980	−	1.21293i
$756$	−18373.2	−	213814.i	−0.0321470	−	0.374104i
$757$	−201077.	+	440296.i	−0.350889	+	0.768340i	0.649082	+	0.760718i	$0.275153\pi$
$757$	−201077.	+	440296.i	−0.350889	+	0.768340i	−0.999971	+	0.00762127i	$0.997574\pi$
$758$		−	408693.i		−	0.711309i
$759$	−607819.	+	288782.i	−1.05509	+	0.501288i
$760$	−227075.			−0.393135
$761$	120678.	+	55111.6i	0.208381	+	0.0951642i	0.516871	−	0.856063i	$-0.327097\pi$
$761$	120678.	+	55111.6i	0.208381	+	0.0951642i	−0.308491	+	0.951227i	$0.599824\pi$
$762$	−265144.	+	324266.i	−0.456638	+	0.558460i
$763$	−289077.	−	333612.i	−0.496551	−	0.573050i
$764$	−130599.	−	203216.i	−0.223745	−	0.348153i
$765$	934749.	−	53476.1i	1.59725	−	0.0913770i
$766$	12738.4	−	88597.8i	0.0217099	−	0.150996i
$767$	116286.	+	396032.i	0.197667	+	0.673194i
$768$	−20808.0	−	30429.9i	−0.0352784	−	0.0515915i
$769$	−80262.1	−	558235.i	−0.135724	−	0.943984i	−0.937902	−	0.346899i	$-0.887235\pi$
$769$	−80262.1	−	558235.i	−0.135724	−	0.943984i	0.802178	−	0.597085i	$-0.203674\pi$
$770$	−409976.	+	187230.i	−0.691476	+	0.315786i
$771$	400107.	−	11435.5i	0.673080	−	0.0192374i
$772$	33588.0	+	233610.i	0.0563572	+	0.391973i
$773$	477135.	−	742436.i	0.798513	−	1.24251i	−0.167973	−	0.985792i	$-0.553722\pi$
$773$	477135.	−	742436.i	0.798513	−	1.24251i	0.966486	−	0.256719i	$-0.0826416\pi$
$774$	−188165.	+	333218.i	−0.314092	+	0.556220i
$775$	−73296.2	+	509786.i	−0.122033	+	0.848760i
$776$	168873.	+	146330.i	0.280439	+	0.243002i
$777$	−758865.	+	131337.i	−1.25696	+	0.217543i
$778$	−358061.	−	413225.i	−0.591559	−	0.682696i
$779$	−151276.	+	515199.i	−0.249285	+	0.848985i
$780$	−143105.	−	155919.i	−0.235215	−	0.256277i
$781$	463189.			0.759375
$782$	510288.	+	241377.i	0.834453	+	0.394713i
$783$	−211647.	+	82411.4i	−0.345214	+	0.134420i
$784$	−27835.1	+	60950.4i	−0.0452857	+	0.0991618i
$785$	198317.	−	675406.i	0.321826	−	1.09604i
$786$	−128431.	−	395252.i	−0.207886	−	0.639777i
$787$	−34139.5	+	21940.2i	−0.0551199	+	0.0354234i	−0.567911	−	0.823090i	$-0.692248\pi$
$787$	−34139.5	+	21940.2i	−0.0551199	+	0.0354234i	0.512791	+	0.858514i	$0.328612\pi$
$788$	367624.	+	318548.i	0.592040	+	0.513006i
$789$	−849462.	−	512229.i	−1.36455	−	0.822830i
$790$	956279.	−	280789.i	1.53225	−	0.449910i
$791$	42668.0	−	66392.7i	0.0681945	−	0.106113i
$792$	158187.	−	205151.i	0.252185	−	0.327058i
$793$	7431.03	+	16271.7i	0.0118169	+	0.0258753i
$794$	219336.	−	100168.i	0.347912	−	0.158886i
$795$	176830.	−	672768.i	0.279783	−	1.06446i
$796$	146090.	+	93886.0i	0.230565	+	0.148175i
$797$	86096.9	+	293219.i	0.135541	+	0.461610i	0.999090	−	0.0426549i	$-0.0135816\pi$
$797$	86096.9	+	293219.i	0.135541	+	0.461610i	−0.863549	+	0.504265i	$0.831763\pi$
$798$	262744.	+	158436.i	0.412598	+	0.248798i
$799$	215202.	−	248356.i	0.337095	−	0.389028i
$800$	30698.6	+	47767.9i	0.0479666	+	0.0746374i
$801$	44156.0	+	3791.37i	0.0688216	+	0.00590923i
$802$	−302049.	−	88689.5i	−0.469600	−	0.137887i
$803$	−531736.	−	242836.i	−0.824642	−	0.376601i
$804$	−72830.4	−	30777.2i	−0.112668	−	0.0476121i
$805$	−255013.	+	539118.i	−0.393524	+	0.831940i
$806$			445543.i			0.685835i
$807$	97442.5	+	106168.i	0.149624	+	0.163022i
$808$	−227781.	−	66882.7i	−0.348896	−	0.102445i
$809$	394365.	−	341719.i	0.602561	−	0.522122i	−0.299294	−	0.954161i	$-0.596751\pi$
$809$	394365.	−	341719.i	0.602561	−	0.522122i	0.901855	+	0.432039i	$0.142206\pi$
$810$	−293627.	−	486867.i	−0.447534	−	0.742062i
$811$	−302462.	+	349059.i	−0.459863	+	0.530710i	−0.937564	−	0.347812i	$-0.886925\pi$
$811$	−302462.	+	349059.i	−0.459863	+	0.530710i	0.477701	+	0.878522i	$0.341470\pi$
$812$	−90782.2	−	13052.5i	−0.137686	−	0.0197962i
$813$	688677.	+	79008.9i	1.04192	+	0.119535i
$814$	−782098.	−	502624.i	−1.18035	−	0.758568i
$815$	1.45653e6	−	209417.i	2.19283	−	0.315281i
$816$	−217223.	+	6208.49i	−0.326231	+	0.00932408i
$817$	−227278.	−	497670.i	−0.340498	−	0.745586i
$818$	43457.5	−	6248.24i	0.0649468	−	0.00933794i
$819$	56795.6	+	280259.i	0.0846734	+	0.417822i
$820$	385521.	−	113199.i	0.573350	−	0.168351i
$821$	877891.	+	126222.i	1.30243	+	0.187261i	0.758392	−	0.651799i	$-0.225985\pi$
$821$	877891.	+	126222.i	1.30243	+	0.187261i	0.544039	+	0.839060i	$0.316895\pi$
$822$	−765868.	+	376565.i	−1.13347	+	0.557309i
$823$	131461.	−	84484.7i	0.194087	−	0.124732i	−0.439988	−	0.898004i	$-0.645017\pi$
$823$	131461.	−	84484.7i	0.194087	−	0.124732i	0.634075	+	0.773271i	$0.281381\pi$
$824$	−345121.	+	299049.i	−0.508297	+	0.440441i
$825$	−252584.	+	308906.i	−0.371106	+	0.453856i
$826$	−186009.	+	407302.i	−0.272630	+	0.596976i
$827$			894746.i			1.30824i	0.756389	+	0.654122i	$0.226962\pi$
$827$			894746.i			1.30824i	−0.756389	+	0.654122i	$0.773038\pi$
$828$	−14980.1	−	342465.i	−0.0218501	−	0.499522i
$829$	1.13915e6			1.65757			0.828784	−	0.559569i	$-0.189033\pi$
$829$	1.13915e6			1.65757			0.828784	+	0.559569i	$0.189033\pi$
$830$	−350419.	−	160031.i	−0.508665	−	0.232300i
$831$	−533087.	−	435891.i	−0.771962	−	0.631213i
$832$	32167.5	+	37123.3i	0.0464698	+	0.0536290i
$833$	213551.	+	332291.i	0.307759	+	0.478882i
$834$	10073.7	+	20488.2i	0.0144829	+	0.0294558i
$835$	−15481.9	+	107679.i	−0.0222050	+	0.154439i
$836$	104346.	+	355371.i	0.149302	+	0.508474i
$837$	−237654.	+	1.17311e6i	−0.339231	+	1.67452i
$838$	111363.	+	774547.i	0.158582	+	1.10296i
$839$	−876879.	+	400457.i	−1.24571	+	0.568895i	−0.925606	−	0.378489i	$-0.876444\pi$
$839$	−876879.	+	400457.i	−1.24571	+	0.568895i	−0.320100	+	0.947384i	$0.603717\pi$
$840$	−6559.25	−	229495.i	−0.00929599	−	0.325249i
$841$	−86842.3	−	604002.i	−0.122783	−	0.853977i
$842$	−484526.	+	753936.i	−0.683428	+	1.06343i
$843$	102532.	−	893718.i	0.144280	−	1.25761i
$844$	28943.1	−	201304.i	0.0406313	−	0.282597i
$845$	−448193.	−	388361.i	−0.627699	−	0.543905i
$846$	−194372.	−	45193.7i	−0.271576	−	0.0631447i
$847$	128601.	+	148414.i	0.179258	+	0.206875i
$848$	−45487.0	+	154915.i	−0.0632552	+	0.215427i
$849$	−282891.	+	259642.i	−0.392468	+	0.360213i
$850$	334727.			0.463290
$851$	−1.21991e6	+	158702.i	−1.68449	+	0.219141i
$852$	−91844.7	+	217339.i	−0.126525	+	0.299404i
$853$	−376476.	+	824368.i	−0.517415	+	1.13298i	0.452993	+	0.891514i	$0.350356\pi$
$853$	−376476.	+	824368.i	−0.517415	+	1.13298i	−0.970409	+	0.241468i	$0.922371\pi$
$854$	−5467.21	+	18619.6i	−0.00749636	+	0.0255302i
$855$	809887.	+	69539.3i	1.10788	+	0.0951257i
$856$	−54088.6	+	34760.7i	−0.0738174	+	0.0474395i
$857$	−633242.	−	548708.i	−0.862201	−	0.747101i	0.106768	−	0.994284i	$-0.465950\pi$
$857$	−633242.	−	548708.i	−0.862201	−	0.747101i	−0.968969	+	0.247183i	$0.920495\pi$
$858$	−178252.	+	295606.i	−0.242136	+	0.401550i
$859$	−762544.	+	223903.i	−1.03342	+	0.303441i	−0.754102	−	0.656757i	$-0.771928\pi$
$859$	−762544.	+	223903.i	−1.03342	+	0.303441i	−0.279322	+	0.960198i	$0.590110\pi$
$860$	−221339.	+	344410.i	−0.299268	+	0.465670i
$861$	−525060.	−	138007.i	−0.708277	−	0.186163i
$862$	233640.	+	511601.i	0.314437	+	0.688521i
$863$	630352.	−	287872.i	0.846372	−	0.386525i	0.0554643	−	0.998461i	$-0.482336\pi$
$863$	630352.	−	287872.i	0.846372	−	0.386525i	0.790908	+	0.611936i	$0.209609\pi$
$864$	64895.2	+	114904.i	0.0869331	+	0.153924i
$865$	−597027.	−	383686.i	−0.797925	−	0.512795i
$866$	−13089.5	−	44578.9i	−0.0174537	−	0.0594420i
$867$	−273352.	+	453317.i	−0.363650	+	0.603065i
$868$	−316520.	+	365283.i	−0.420108	+	0.484831i
$869$	−878865.	−	1.36754e6i	−1.16381	−	1.81093i
$870$	−231094.	+	75090.4i	−0.305316	+	0.0992079i
$871$	101088.	+	29682.1i	0.133249	+	0.0391254i
$872$	246916.	+	112763.i	0.324725	+	0.148297i
$873$	−557493.	−	573616.i	−0.731494	−	0.752649i
$874$	408694.	+	270477.i	0.535027	+	0.354085i
$875$		−	350981.i		−	0.458424i
$876$	219381.	−	201351.i	0.285884	−	0.262389i
$877$	408653.	+	119991.i	0.531319	+	0.156009i	0.536378	−	0.843978i	$-0.319792\pi$
$877$	408653.	+	119991.i	0.531319	+	0.156009i	−0.00505889	+	0.999987i	$0.501610\pi$
$878$	161008.	−	139514.i	0.208861	−	0.180979i
$879$	−138377.	−	799540.i	−0.179096	−	1.03481i
$880$	181494.	−	209455.i	0.234367	−	0.270474i
$881$	−424242.	−	60996.8i	−0.546590	−	0.0785878i	−0.136512	−	0.990638i	$-0.543589\pi$
$881$	−424242.	−	60996.8i	−0.546590	−	0.0785878i	−0.410078	+	0.912051i	$0.634498\pi$
$882$	117942.	−	208862.i	0.151612	−	0.268486i
$883$	−187087.	−	120234.i	−0.239951	−	0.154207i	0.415139	−	0.909758i	$-0.363733\pi$
$883$	−187087.	−	120234.i	−0.239951	−	0.154207i	−0.655090	+	0.755551i	$0.727369\pi$
$884$	286620.	−	41209.7i	0.366776	−	0.0527345i
$885$	33891.8	+	1.18581e6i	0.0432721	+	1.51401i
$886$	−100863.	−	220859.i	−0.128488	−	0.281350i
$887$	460300.	−	66181.2i	0.585051	−	0.0841177i	0.156568	−	0.987667i	$-0.449957\pi$
$887$	460300.	−	66181.2i	0.585051	−	0.0841177i	0.428484	+	0.903550i	$0.359048\pi$
$888$	390923.	−	267314.i	0.495753	−	0.338997i
$889$	580960.	−	170585.i	0.735094	−	0.215843i
$890$	46931.0	+	6747.67i	0.0592489	+	0.00851870i
$891$	−627014.	+	683251.i	−0.789809	+	0.860647i
$892$	416427.	−	267621.i	0.523370	−	0.336349i
$893$	215620.	−	186836.i	0.270387	−	0.234292i
$894$	12589.7	+	10294.3i	0.0157522	+	0.0128802i
$895$	463347.	−	1.01459e6i	0.578442	−	1.26661i
$896$			53288.1i			0.0663765i
$897$	71842.7	+	451083.i	0.0892889	+	0.560624i
$898$	716415.			0.888407
$899$	465319.	+	212504.i	0.575746	+	0.262935i
$900$	−94861.3	−	179771.i	−0.117113	−	0.221939i
$901$	623276.	+	719299.i	0.767770	+	0.886053i
$902$	−354311.	−	551319.i	−0.435484	−	0.677626i
$903$	496410.	−	244077.i	0.608786	−	0.299330i
$904$	−6906.58	+	48036.3i	−0.00845136	+	0.0587805i
$905$	204701.	+	697148.i	0.249933	+	0.851193i
$906$	724119.	−	495154.i	0.882172	−	0.603231i
$907$	−123953.	−	862111.i	−0.150675	−	1.04797i	−0.915092	−	0.403246i	$-0.867882\pi$
$907$	−123953.	−	862111.i	−0.150675	−	1.04797i	0.764416	−	0.644723i	$-0.223027\pi$
$908$	−330452.	+	150912.i	−0.400808	+	0.183043i
$909$	791924.	+	308300.i	0.958420	+	0.373117i
$910$	43537.9	+	302813.i	0.0525756	+	0.365671i
$911$	−437800.	+	681230.i	−0.527520	+	0.820838i	−0.998106	−	0.0615166i	$-0.980406\pi$
$911$	−437800.	+	681230.i	−0.527520	+	0.820838i	0.470586	+	0.882354i	$0.344043\pi$
$912$	−187439.	−	21504.0i	−0.225356	−	0.0258541i
$913$	−89421.8	+	621942.i	−0.107276	+	0.746119i
$914$	659617.	+	571561.i	0.789586	+	0.684180i
$915$	8767.67	+	50659.5i	0.0104723	+	0.0605088i
$916$	−421043.	−	485910.i	−0.501806	−	0.579115i
$917$	−169252.	+	576420.i	−0.201278	+	0.685489i
$918$	776650.	+	44379.0i	0.921595	+	0.0526614i
$919$	−706262.			−0.836248			−0.418124	−	0.908390i	$-0.637312\pi$
$919$	−706262.			−0.836248			−0.418124	+	0.908390i	$0.637312\pi$
$920$	4926.04	−	366699.i	0.00581999	−	0.433246i
$921$	904974.	+	382431.i	1.06688	+	0.450852i
$922$	196454.	−	430175.i	0.231100	−	0.506038i
$923$	88576.7	−	301665.i	0.103972	−	0.354096i
$924$	−356145.	+	115724.i	−0.417140	+	0.135543i
$925$	−613659.	+	394375.i	−0.717205	+	0.460920i
$926$	881330.	+	763677.i	1.02782	+	0.890610i
$927$	1.32249e6	−	960901.i	1.53898	−	1.11820i
$928$	54113.4	−	15889.1i	0.0628361	−	0.0184503i
$929$	292719.	−	455479.i	0.339171	−	0.527761i	−0.629210	−	0.777235i	$-0.716621\pi$
$929$	292719.	−	455479.i	0.339171	−	0.527761i	0.968381	+	0.249474i	$0.0802578\pi$
$930$	−325520.	+	1.23847e6i	−0.376367	+	1.43193i
$931$	142459.	+	311941.i	0.164357	+	0.359893i
$932$	−331585.	+	151430.i	−0.381735	+	0.174333i
$933$	638148.	+	167731.i	0.733092	+	0.192685i
$934$	37767.6	+	24271.8i	0.0432938	+	0.0278232i
$935$	−460289.	−	1.56760e6i	−0.526511	−	1.79313i
$936$	−103360.	−	142255.i	−0.117978	−	0.162374i
$937$	−615507.	+	710333.i	−0.701057	+	0.809063i	−0.988895	−	0.148616i	$-0.952518\pi$
$937$	−615507.	+	710333.i	−0.701057	+	0.809063i	0.287838	+	0.957679i	$0.407064\pi$
$938$	61791.5	+	96149.5i	0.0702301	+	0.109280i
$939$	323153.	+	994516.i	0.366502	+	1.12793i
$940$	−204845.	−	60148.0i	−0.231830	−	0.0680715i
$941$	−253398.	−	115723.i	−0.286170	−	0.130690i	0.267158	−	0.963653i	$-0.413915\pi$
$941$	−253398.	−	115723.i	−0.286170	−	0.130690i	−0.553329	+	0.832963i	$0.686643\pi$
$942$	227661.	−	538732.i	0.256559	−	0.607115i
$943$	−828704.	−	255469.i	−0.931914	−	0.287287i
$944$		−	275341.i		−	0.308977i
$945$	−46886.3	+	820528.i	−0.0525027	+	0.918819i
$946$	640709.	+	188129.i	0.715943	+	0.210220i
$947$	−181844.	+	157569.i	−0.202768	+	0.175699i	−0.750325	−	0.661069i	$-0.770103\pi$
$947$	−181844.	+	157569.i	−0.202768	+	0.175699i	0.547558	+	0.836768i	$0.315558\pi$
$948$	815949.	−	141217.i	0.907918	−	0.157134i
$949$	−259839.	+	299870.i	−0.288517	+	0.332966i
$950$	287649.	+	41357.6i	0.318724	+	0.0458256i
$951$	61323.3	−	534521.i	0.0678055	−	0.591023i
$952$	264264.	+	169832.i	0.291584	+	0.187390i
$953$	827055.	−	118913.i	0.910644	−	0.130931i	0.328958	−	0.944344i	$-0.393302\pi$
$953$	827055.	−	118913.i	0.910644	−	0.130931i	0.581686	+	0.813414i	$0.302393\pi$
$954$	209675.	−	538589.i	0.230383	−	0.591781i
$955$	384310.	+	841520.i	0.421380	+	0.922694i
$956$	−224513.	+	32280.1i	−0.245655	+	0.0353199i
$957$	223709.	+	327155.i	0.244264	+	0.357215i
$958$	−363151.	+	106631.i	−0.395691	+	0.116185i
$959$	1.22111e6	+	175570.i	1.32776	+	0.190903i
$960$	62293.0	+	126693.i	0.0675922	+	0.137471i
$961$	1.49096e6	−	958184.i	1.61443	−	1.03753i
$962$	−476910.	+	413245.i	−0.515331	+	0.446537i
$963$	203558.	−	107413.i	0.219500	−	0.115826i
$964$	22911.6	−	50169.4i	0.0246548	−	0.0539864i
$965$		−	903862.i		−	0.970616i
$966$	−261555.	+	420864.i	−0.280291	+	0.451011i
$967$	−73865.6			−0.0789931			−0.0394965	−	0.999220i	$-0.512575\pi$
$967$	−73865.6			−0.0789931			−0.0394965	+	0.999220i	$0.512575\pi$
$968$	−109845.	−	50164.8i	−0.117228	−	0.0535363i
$969$	−704019.	+	861003.i	−0.749785	+	0.916974i
$970$	−560404.	−	646740.i	−0.595604	−	0.687363i
$971$	−692060.	−	1.07687e6i	−0.734016	−	1.14215i	−0.984730	−	0.174089i	$-0.944302\pi$
$971$	−692060.	−	1.07687e6i	−0.734016	−	1.14215i	0.250714	−	0.968061i	$-0.419335\pi$
$972$	−196268.	−	429690.i	−0.207738	−	0.454802i
$973$	4696.77	−	32666.7i	0.00496105	−	0.0345048i
$974$	235146.	+	800834.i	0.247868	+	0.844160i
$975$	152881.	+	223575.i	0.160822	+	0.235188i
$976$	−1698.24	−	11811.5i	−0.00178279	−	0.0123995i
$977$	1.21738e6	−	555958.i	1.27537	−	0.582442i	0.341443	−	0.939903i	$-0.389084\pi$
$977$	1.21738e6	−	555958.i	1.27537	−	0.582442i	0.933928	+	0.357460i	$0.116357\pi$
$978$	1.22212e6	−	34929.7i	1.27772	−	0.0365188i
$979$	−11005.9	−	76547.5i	−0.0114831	−	0.0798666i
$980$	138736.	−	215877.i	0.144456	−	0.224778i
$981$	−846119.	−	477796.i	−0.879212	−	0.496483i
$982$	−186074.	+	1.29418e6i	−0.192958	+	1.34206i
$983$	−464791.	−	402744.i	−0.481006	−	0.416794i	0.380314	−	0.924858i	$-0.375816\pi$
$983$	−464791.	−	402744.i	−0.481006	−	0.416794i	−0.861320	+	0.508064i	$0.830362\pi$
$984$	328947.	−	56931.1i	0.339732	−	0.0587976i
$985$	−1.21995e6	−	1.40790e6i	−1.25739	−	1.45111i
$986$	93665.9	−	318997.i	0.0963446	−	0.328120i
$987$	195056.	+	212522.i	0.200228	+	0.218157i
$988$	251399.			0.257543
$989$	808609.	−	356231.i	0.826696	−	0.364200i
$990$	−711459.	+	691462.i	−0.725905	+	0.705501i
$991$	592465.	−	1.29732e6i	0.603275	−	1.32099i	−0.323805	−	0.946124i	$-0.604962\pi$
$991$	592465.	−	1.29732e6i	0.603275	−	1.32099i	0.927080	−	0.374864i	$-0.122311\pi$
$992$	83735.3	−	285176.i	0.0850913	−	0.289794i
$993$	220295.	+	677968.i	0.223412	+	0.687560i
$994$	286927.	−	184397.i	0.290402	−	0.186630i
$995$	−502619.	−	435522.i	−0.507683	−	0.439910i
$996$	−274098.	−	165282.i	−0.276304	−	0.166612i
$997$	−117347.	+	34456.1i	−0.118054	+	0.0346637i	−0.340226	−	0.940344i	$-0.610504\pi$
$997$	−117347.	+	34456.1i	−0.118054	+	0.0346637i	0.222172	+	0.975007i	$0.428685\pi$
$998$	−601411.	+	935813.i	−0.603823	+	0.939568i
$999$	−1.47613e6	+	833688.i	−1.47909	+	0.835357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.5.g.a.29.12	✓	320
3.2	odd	2	inner	138.5.g.a.29.32	yes	320
23.4	even	11	inner	138.5.g.a.119.32	yes	320
69.50	odd	22	inner	138.5.g.a.119.12	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.5.g.a.29.12	✓	320	1.1	even	1	trivial
138.5.g.a.29.32	yes	320	3.2	odd	2	inner
138.5.g.a.119.12	yes	320	69.50	odd	22	inner
138.5.g.a.119.32	yes	320	23.4	even	11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	138.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57283 - 1.17497i) q^{2} +(6.96735 + 5.69702i) q^{3} +(5.23889 + 6.04600i) q^{4} +(-16.5641 - 25.7742i) q^{5} +(-11.2320 - 22.8439i) q^{6} +(-5.23680 + 36.4227i) q^{7} +(-6.37488 - 21.7108i) q^{8} +(16.0880 + 79.3863i) q^{9} +O(q^{10})\)	\(q+(-2.57283 - 1.17497i) q^{2} +(6.96735 + 5.69702i) q^{3} +(5.23889 + 6.04600i) q^{4} +(-16.5641 - 25.7742i) q^{5} +(-11.2320 - 22.8439i) q^{6} +(-5.23680 + 36.4227i) q^{7} +(-6.37488 - 21.7108i) q^{8} +(16.0880 + 79.3863i) q^{9} +(12.3326 + 85.7749i) q^{10} +(128.570 - 58.7160i) q^{11} +(2.05700 + 71.9706i) q^{12} +(-13.6536 - 94.9631i) q^{13} +(56.2690 - 87.5563i) q^{14} +(31.4284 - 273.944i) q^{15} +(-9.10815 + 63.3486i) q^{16} +(285.127 + 247.064i) q^{17} +(51.8850 - 223.150i) q^{18} +(214.499 + 247.545i) q^{19} +(69.0535 - 235.174i) q^{20} +(-243.987 + 223.936i) q^{21} -399.778 q^{22} +(-404.409 + 341.020i) q^{23} +(79.2711 - 187.585i) q^{24} +(-130.307 + 285.332i) q^{25} +(-76.4505 + 260.366i) q^{26} +(-340.174 + 644.765i) q^{27} +(-247.647 + 159.153i) q^{28} +(235.460 + 204.027i) q^{29} +(-402.736 + 667.883i) q^{30} +(1575.39 - 462.576i) q^{31} +(97.8664 - 152.283i) q^{32} +(1230.30 + 323.371i) q^{33} +(-443.290 - 970.670i) q^{34} +(1025.51 - 468.334i) q^{35} +(-395.686 + 513.163i) q^{36} +(1956.33 + 1257.26i) q^{37} +(-261.010 - 888.920i) q^{38} +(445.877 - 739.426i) q^{39} +(-453.986 + 523.928i) q^{40} +(886.270 + 1379.06i) q^{41} +(890.856 - 289.470i) q^{42} +(-1602.66 - 470.584i) q^{43} +(1028.56 + 469.728i) q^{44} +(1779.64 - 1729.61i) q^{45} +(1441.16 - 402.217i) q^{46} -871.035i q^{47} +(-424.358 + 389.482i) q^{48} +(1004.55 + 294.963i) q^{49} +(670.514 - 581.003i) q^{50} +(579.053 + 3345.76i) q^{51} +(502.617 - 580.051i) q^{52} +(2497.05 + 359.022i) q^{53} +(1632.79 - 1259.18i) q^{54} +(-3643.00 - 2341.21i) q^{55} +(824.152 - 118.495i) q^{56} +(84.2211 + 2946.73i) q^{57} +(-366.071 - 801.584i) q^{58} +(-4258.41 + 612.267i) q^{59} +(1820.91 - 1245.14i) q^{60} +(-178.900 + 52.5298i) q^{61} +(-4596.72 - 660.909i) q^{62} +(-2975.71 + 170.238i) q^{63} +(-430.722 + 276.808i) q^{64} +(-2221.44 + 1924.89i) q^{65} +(-2785.39 - 2277.54i) q^{66} +(-456.186 + 998.908i) q^{67} +3018.22i q^{68} +(-4760.45 + 72.0824i) q^{69} -3188.74 q^{70} +(2980.92 + 1361.34i) q^{71} +(1620.98 - 855.361i) q^{72} +(-2708.36 - 3125.61i) q^{73} +(-3556.06 - 5533.34i) q^{74} +(-2533.43 + 1245.65i) q^{75} +(-372.920 + 2593.72i) q^{76} +(1465.30 + 4990.35i) q^{77} +(-2015.97 + 1378.52i) q^{78} +(-1636.78 - 11384.0i) q^{79} +(1783.63 - 814.555i) q^{80} +(-6043.35 + 2554.33i) q^{81} +(-659.861 - 4589.44i) q^{82} +(-2403.41 + 3739.78i) q^{83} +(-2632.14 - 301.974i) q^{84} +(1645.01 - 11441.3i) q^{85} +(3570.45 + 3093.81i) q^{86} +(478.185 + 2762.94i) q^{87} +(-2094.39 - 2417.06i) q^{88} +(154.148 - 524.979i) q^{89} +(-6610.94 + 2358.98i) q^{90} +3530.32 q^{91} +(-4180.46 - 658.489i) q^{92} +(13611.6 + 5752.10i) q^{93} +(-1023.44 + 2241.02i) q^{94} +(2827.30 - 9628.89i) q^{95} +(1549.43 - 503.463i) q^{96} +(-8307.60 + 5338.97i) q^{97} +(-2237.97 - 1939.21i) q^{98} +(6729.67 + 9262.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 20 q^{3} + 256 q^{4} - 64 q^{6} + 172 q^{9}+O(q^{10}) \) 320 * q + 20 * q^3 + 256 * q^4 - 64 * q^6 + 172 * q^9	\( 320 q + 20 q^{3} + 256 q^{4} - 64 q^{6} + 172 q^{9} - 160 q^{12} - 200 q^{13} + 2202 q^{15} - 2048 q^{16} - 3392 q^{18} + 520 q^{19} - 982 q^{21} + 640 q^{22} + 512 q^{24} + 1680 q^{25} + 8786 q^{27} - 2752 q^{30} + 5368 q^{31} - 12050 q^{33} - 640 q^{34} - 1376 q^{36} - 8936 q^{37} + 132 q^{39} + 1984 q^{42} - 11704 q^{43} - 10396 q^{45} + 2112 q^{46} + 1280 q^{48} + 36752 q^{49} + 10060 q^{51} + 1600 q^{52} - 28896 q^{54} - 36788 q^{55} - 6074 q^{57} + 10880 q^{58} + 15648 q^{60} + 44536 q^{61} + 61826 q^{63} + 16384 q^{64} + 25600 q^{66} + 21628 q^{67} - 21406 q^{69} - 45568 q^{70} - 23552 q^{72} - 14212 q^{73} - 65058 q^{75} - 4160 q^{76} - 31840 q^{78} - 29024 q^{79} - 43964 q^{81} + 23808 q^{82} + 17184 q^{84} + 75252 q^{85} - 34892 q^{87} - 5120 q^{88} - 1088 q^{90} + 12840 q^{91} + 14988 q^{93} - 23040 q^{94} - 4096 q^{96} + 158244 q^{97} + 86652 q^{99}+O(q^{100}) \) 320 * q + 20 * q^3 + 256 * q^4 - 64 * q^6 + 172 * q^9 - 160 * q^12 - 200 * q^13 + 2202 * q^15 - 2048 * q^16 - 3392 * q^18 + 520 * q^19 - 982 * q^21 + 640 * q^22 + 512 * q^24 + 1680 * q^25 + 8786 * q^27 - 2752 * q^30 + 5368 * q^31 - 12050 * q^33 - 640 * q^34 - 1376 * q^36 - 8936 * q^37 + 132 * q^39 + 1984 * q^42 - 11704 * q^43 - 10396 * q^45 + 2112 * q^46 + 1280 * q^48 + 36752 * q^49 + 10060 * q^51 + 1600 * q^52 - 28896 * q^54 - 36788 * q^55 - 6074 * q^57 + 10880 * q^58 + 15648 * q^60 + 44536 * q^61 + 61826 * q^63 + 16384 * q^64 + 25600 * q^66 + 21628 * q^67 - 21406 * q^69 - 45568 * q^70 - 23552 * q^72 - 14212 * q^73 - 65058 * q^75 - 4160 * q^76 - 31840 * q^78 - 29024 * q^79 - 43964 * q^81 + 23808 * q^82 + 17184 * q^84 + 75252 * q^85 - 34892 * q^87 - 5120 * q^88 - 1088 * q^90 + 12840 * q^91 + 14988 * q^93 - 23040 * q^94 - 4096 * q^96 + 158244 * q^97 + 86652 * q^99

Introduction

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