LMFDB - Embedded newform 38.6.e.b.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	38.17
Dual form			38.6.e.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694593 - 3.93923i) q^{2} +(-21.8341 - 18.3210i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.2104 - 12.0876i) q^{5} +(-87.3364 + 73.2839i) q^{6} +(-42.9494 - 74.3905i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(98.8729 + 560.736i) q^{9} +O(q^{10})$	\(q+(0.694593 - 3.93923i) q^{2} +(-21.8341 - 18.3210i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.2104 - 12.0876i) q^{5} +(-87.3364 + 73.2839i) q^{6} +(-42.9494 - 74.3905i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(98.8729 + 560.736i) q^{9} +(-24.5482 - 139.220i) q^{10} +(-299.827 + 519.315i) q^{11} +(228.019 + 394.941i) q^{12} +(417.425 - 350.261i) q^{13} +(-322.874 + 117.516i) q^{14} +(-946.577 - 344.526i) q^{15} +(196.107 + 164.554i) q^{16} +(252.825 - 1433.84i) q^{17} +2277.54 q^{18} +(-1570.74 - 94.1673i) q^{19} -565.469 q^{20} +(-425.146 + 2411.12i) q^{21} +(1837.44 + 1541.80i) q^{22} +(-3449.31 - 1255.45i) q^{23} +(1714.14 - 623.897i) q^{24} +(-1437.07 + 1205.84i) q^{25} +(-1089.82 - 1887.62i) q^{26} +(4651.39 - 8056.45i) q^{27} +(238.658 + 1353.50i) q^{28} +(17.7663 + 100.758i) q^{29} +(-2014.65 + 3489.48i) q^{30} +(440.821 + 763.524i) q^{31} +(784.430 - 658.215i) q^{32} +(16060.8 - 5845.65i) q^{33} +(-5472.63 - 1991.87i) q^{34} +(-2325.57 - 1951.38i) q^{35} +(1581.97 - 8971.77i) q^{36} -8650.33 q^{37} +(-1461.97 + 6122.11i) q^{38} -15531.2 q^{39} +(-392.771 + 2227.51i) q^{40} +(8167.44 + 6853.30i) q^{41} +(9202.67 + 3349.50i) q^{42} +(4719.08 - 1717.61i) q^{43} +(7349.78 - 6167.19i) q^{44} +(10061.6 + 17427.1i) q^{45} +(-7341.35 + 12715.6i) q^{46} +(1410.47 + 7999.19i) q^{47} +(-1267.04 - 7185.76i) q^{48} +(4714.21 - 8165.24i) q^{49} +(3751.91 + 6498.50i) q^{50} +(-31789.6 + 26674.7i) q^{51} +(-8192.76 + 2981.92i) q^{52} +(-24330.5 - 8855.56i) q^{53} +(-28505.4 - 23918.9i) q^{54} +(-3680.10 + 20870.9i) q^{55} +5497.52 q^{56} +(32570.5 + 30833.6i) q^{57} +409.248 q^{58} +(6278.09 - 35604.8i) q^{59} +(12346.5 + 10359.9i) q^{60} +(-36990.5 - 13463.4i) q^{61} +(3313.89 - 1206.16i) q^{62} +(37466.9 - 31438.4i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(9629.04 - 16678.0i) q^{65} +(-11871.7 - 67327.6i) q^{66} +(-2378.27 - 13487.8i) q^{67} +(-11647.7 + 20174.4i) q^{68} +(52311.5 + 90606.2i) q^{69} +(-9302.28 + 7805.54i) q^{70} +(70242.5 - 25566.2i) q^{71} +(-34243.1 - 12463.5i) q^{72} +(-45239.4 - 37960.3i) q^{73} +(-6008.46 + 34075.6i) q^{74} +53469.2 q^{75} +(23100.9 + 10011.4i) q^{76} +51509.4 q^{77} +(-10787.9 + 61181.1i) q^{78} +(4603.46 + 3862.77i) q^{79} +(8501.87 + 3094.43i) q^{80} +(-119144. + 43365.0i) q^{81} +(32669.8 - 27413.2i) q^{82} +(-36582.4 - 63362.6i) q^{83} +(19586.5 - 33924.9i) q^{84} +(-8935.30 - 50674.6i) q^{85} +(-3488.20 - 19782.6i) q^{86} +(1458.07 - 2525.45i) q^{87} +(-19188.9 - 33236.2i) q^{88} +(11723.9 - 9837.52i) q^{89} +(75638.2 - 27530.1i) q^{90} +(-43984.2 - 16008.9i) q^{91} +(44990.4 + 37751.5i) q^{92} +(4363.59 - 24747.1i) q^{93} +32490.4 q^{94} +(-53303.3 + 15859.2i) q^{95} -29186.4 q^{96} +(-18606.8 + 105524. i) q^{97} +(-28890.3 - 24241.9i) q^{98} +(-320843. - 116777. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) $ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$3$	−21.8341	−	18.3210i	−1.40066	−	1.17529i	−0.960806	−	0.277221i	$-0.910587\pi$
$3$	−21.8341	−	18.3210i	−1.40066	−	1.17529i	−0.439852	−	0.898070i	$-0.644969\pi$
$4$	−15.0351	−	5.47232i	−0.469846	−	0.171010i
$5$	33.2104	−	12.0876i	0.594086	−	0.216230i	−0.0274394	−	0.999623i	$-0.508735\pi$
$5$	33.2104	−	12.0876i	0.594086	−	0.216230i	0.621526	+	0.783394i	$0.286513\pi$
$6$	−87.3364	+	73.2839i	−0.990415	+	0.831057i
$7$	−42.9494	−	74.3905i	−0.331292	−	0.573815i	0.651473	−	0.758672i	$-0.274151\pi$
$7$	−42.9494	−	74.3905i	−0.331292	−	0.573815i	−0.982766	+	0.184856i	$0.940818\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	98.8729	+	560.736i	0.406884	+	2.30755i
$10$	−24.5482	−	139.220i	−0.0776281	−	0.440251i
$11$	−299.827	+	519.315i	−0.747117	+	1.29404i	0.202083	+	0.979368i	$0.435229\pi$
$11$	−299.827	+	519.315i	−0.747117	+	1.29404i	−0.949199	+	0.314676i	$0.898104\pi$
$12$	228.019	+	394.941i	0.457107	+	0.791733i
$13$	417.425	−	350.261i	0.685046	−	0.574822i	−0.232430	−	0.972613i	$-0.574668\pi$
$13$	417.425	−	350.261i	0.685046	−	0.574822i	0.917476	+	0.397791i	$0.130223\pi$
$14$	−322.874	+	117.516i	−0.440263	+	0.160243i
$15$	−946.577	−	344.526i	−1.08624	−	0.395361i
$16$	196.107	+	164.554i	0.191511	+	0.160697i
$17$	252.825	−	1433.84i	0.212177	−	1.20331i	−0.673562	−	0.739131i	$-0.735237\pi$
$17$	252.825	−	1433.84i	0.212177	−	1.20331i	0.885739	−	0.464184i	$-0.153652\pi$
$18$	2277.54			1.65686
$19$	−1570.74	−	94.1673i	−0.998208	−	0.0598434i
$19$	−1570.74	−	94.1673i	−0.998208	−	0.0598434i
$20$	−565.469			−0.316107
$21$	−425.146	+	2411.12i	−0.210373	+	1.19308i
$22$	1837.44	+	1541.80i	0.809389	+	0.679158i
$23$	−3449.31	−	1255.45i	−1.35960	−	0.494855i	−0.443672	−	0.896189i	$-0.646324\pi$
$23$	−3449.31	−	1255.45i	−1.35960	−	0.494855i	−0.915932	+	0.401334i	$0.868547\pi$
$24$	1714.14	−	623.897i	0.607462	−	0.221098i
$25$	−1437.07	+	1205.84i	−0.459861	+	0.385869i
$26$	−1089.82	−	1887.62i	−0.316170	−	0.547623i
$27$	4651.39	−	8056.45i	1.22793	−	2.12684i
$28$	238.658	+	1353.50i	0.0575283	+	0.326259i
$29$	17.7663	+	100.758i	0.00392285	+	0.0222476i	0.986706	−	0.162513i	$-0.0519600\pi$
$29$	17.7663	+	100.758i	0.00392285	+	0.0222476i	−0.982783	+	0.184761i	$0.940849\pi$
$30$	−2014.65	+	3489.48i	−0.408693	+	0.707876i
$31$	440.821	+	763.524i	0.0823869	+	0.142698i	0.904275	−	0.426951i	$-0.140412\pi$
$31$	440.821	+	763.524i	0.0823869	+	0.142698i	−0.821888	+	0.569649i	$0.807079\pi$
$32$	784.430	−	658.215i	0.135419	−	0.113630i
$33$	16060.8	−	5845.65i	2.56733	−	0.934433i
$34$	−5472.63	−	1991.87i	−0.811893	−	0.295505i
$35$	−2325.57	−	1951.38i	−0.320892	−	0.269261i
$36$	1581.97	−	8971.77i	0.203442	−	1.15378i
$37$	−8650.33			−1.03879			−0.519396	−	0.854534i	$-0.673843\pi$
$37$	−8650.33			−1.03879			−0.519396	+	0.854534i	$0.673843\pi$
$38$	−1461.97	+	6122.11i	−0.164241	+	0.687768i
$39$	−15531.2			−1.63510
$40$	−392.771	+	2227.51i	−0.0388140	+	0.220125i
$41$	8167.44	+	6853.30i	0.758799	+	0.636708i	0.937814	−	0.347139i	$-0.112847\pi$
$41$	8167.44	+	6853.30i	0.758799	+	0.636708i	−0.179015	+	0.983846i	$0.557291\pi$
$42$	9202.67	+	3349.50i	0.804990	+	0.292992i
$43$	4719.08	−	1717.61i	0.389212	−	0.141662i	−0.139999	−	0.990152i	$-0.544710\pi$
$43$	4719.08	−	1717.61i	0.389212	−	0.141662i	0.529211	+	0.848490i	$0.322488\pi$
$44$	7349.78	−	6167.19i	0.572325	−	0.480237i
$45$	10061.6	+	17427.1i	0.740686	+	1.28291i
$46$	−7341.35	+	12715.6i	−0.511542	+	0.886017i
$47$	1410.47	+	7999.19i	0.0931366	+	0.528204i	0.995302	+	0.0968145i	$0.0308654\pi$
$47$	1410.47	+	7999.19i	0.0931366	+	0.528204i	−0.902166	+	0.431389i	$0.858024\pi$
$48$	−1267.04	−	7185.76i	−0.0793758	−	0.450163i
$49$	4714.21	−	8165.24i	0.280491	−	0.485824i
$50$	3751.91	+	6498.50i	0.212240	+	0.367611i
$51$	−31789.6	+	26674.7i	−1.71143	+	1.43606i
$52$	−8192.76	+	2981.92i	−0.420167	+	0.152928i
$53$	−24330.5	−	8855.56i	−1.18976	−	0.433039i	−0.330123	−	0.943938i	$-0.607090\pi$
$53$	−24330.5	−	8855.56i	−1.18976	−	0.433039i	−0.859641	+	0.510899i	$0.829312\pi$
$54$	−28505.4	−	23918.9i	−1.33028	−	1.11624i
$55$	−3680.10	+	20870.9i	−0.164041	+	0.930323i
$56$	5497.52			0.234259
$57$	32570.5	+	30833.6i	1.32781	+	1.25701i
$58$	409.248			0.0159741
$59$	6278.09	−	35604.8i	0.234800	−	1.33161i	−0.608236	−	0.793756i	$-0.708122\pi$
$59$	6278.09	−	35604.8i	0.234800	−	1.33161i	0.843035	−	0.537858i	$-0.180766\pi$
$60$	12346.5	+	10359.9i	0.442757	+	0.371518i
$61$	−36990.5	−	13463.4i	−1.27281	−	0.463267i	−0.384765	−	0.923015i	$-0.625718\pi$
$61$	−36990.5	−	13463.4i	−1.27281	−	0.463267i	−0.888049	+	0.459748i	$0.847940\pi$
$62$	3313.89	−	1206.16i	0.109486	−	0.0398497i
$63$	37466.9	−	31438.4i	1.18931	−	0.997952i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	9629.04	−	16678.0i	0.282683	−	0.489621i
$66$	−11871.7	−	67327.6i	−0.335468	−	1.90254i
$67$	−2378.27	−	13487.8i	−0.0647253	−	0.367075i	−0.999916	−	0.0129318i	$-0.995884\pi$
$67$	−2378.27	−	13487.8i	−0.0647253	−	0.367075i	0.935191	−	0.354143i	$-0.115228\pi$
$68$	−11647.7	+	20174.4i	−0.305469	+	0.529089i
$69$	52311.5	+	90606.2i	1.32274	+	2.29105i
$70$	−9302.28	+	7805.54i	−0.226905	+	0.190396i
$71$	70242.5	−	25566.2i	1.65369	−	0.601894i	0.664337	−	0.747433i	$-0.268714\pi$
$71$	70242.5	−	25566.2i	1.65369	−	0.601894i	0.989353	+	0.145539i	$0.0464916\pi$
$72$	−34243.1	−	12463.5i	−0.778469	−	0.283340i
$73$	−45239.4	−	37960.3i	−0.993595	−	0.833725i	−0.00751058	−	0.999972i	$-0.502391\pi$
$73$	−45239.4	−	37960.3i	−0.993595	−	0.833725i	−0.986084	+	0.166247i	$0.946835\pi$
$74$	−6008.46	+	34075.6i	−0.127551	+	0.723377i
$75$	53469.2			1.09762
$76$	23100.9	+	10011.4i	0.458770	+	0.198821i
$77$	51509.4			0.990056
$78$	−10787.9	+	61181.1i	−0.200770	+	1.13862i
$79$	4603.46	+	3862.77i	0.0829883	+	0.0696355i	0.683338	−	0.730102i	$-0.260528\pi$
$79$	4603.46	+	3862.77i	0.0829883	+	0.0696355i	−0.600350	+	0.799738i	$0.704972\pi$
$80$	8501.87	+	3094.43i	0.148522	+	0.0540574i
$81$	−119144.	+	43365.0i	−2.01772	+	0.734390i
$82$	32669.8	−	27413.2i	0.536552	−	0.450220i
$83$	−36582.4	−	63362.6i	−0.582877	−	1.00957i	−0.995136	−	0.0985065i	$-0.968593\pi$
$83$	−36582.4	−	63362.6i	−0.582877	−	1.00957i	0.412259	−	0.911067i	$-0.364740\pi$
$84$	19586.5	−	33924.9i	0.302872	−	0.524590i
$85$	−8935.30	−	50674.6i	−0.134141	−	0.760752i
$86$	−3488.20	−	19782.6i	−0.0508576	−	0.288428i
$87$	1458.07	−	2525.45i	0.0206529	−	0.0357718i
$88$	−19188.9	−	33236.2i	−0.264146	−	0.457514i
$89$	11723.9	−	9837.52i	0.156891	−	0.131647i	−0.560963	−	0.827841i	$-0.689569\pi$
$89$	11723.9	−	9837.52i	0.156891	−	0.131647i	0.717854	+	0.696194i	$0.245125\pi$
$90$	75638.2	−	27530.1i	0.984317	−	0.358262i
$91$	−43984.2	−	16008.9i	−0.556793	−	0.202656i
$92$	44990.4	+	37751.5i	0.554180	+	0.465012i
$93$	4363.59	−	24747.1i	0.0523162	−	0.296700i
$94$	32490.4			0.379258
$95$	−53303.3	+	15859.2i	−0.605961	+	0.180290i
$96$	−29186.4			−0.323224
$97$	−18606.8	+	105524.i	−0.200790	+	1.13874i	0.703139	+	0.711052i	$0.251781\pi$
$97$	−18606.8	+	105524.i	−0.200790	+	1.13874i	−0.903929	+	0.427683i	$0.859330\pi$
$98$	−28890.3	−	24241.9i	−0.303870	−	0.254977i
$99$	−320843.	−	116777.i	−3.29007	−	1.19749i
$100$	28205.2	−	10265.8i	0.282052	−	0.102658i
$101$	59492.5	−	49920.1i	0.580308	−	0.486937i	−0.304740	−	0.952436i	$-0.598570\pi$
$101$	59492.5	−	49920.1i	0.580308	−	0.486937i	0.885048	+	0.465499i	$0.154125\pi$
$102$	82996.8	+	143755.i	0.789880	+	1.36811i
$103$	−3118.91	+	5402.12i	−0.0289675	+	0.0501731i	−0.880146	−	0.474704i	$-0.842555\pi$
$103$	−3118.91	+	5402.12i	−0.0289675	+	0.0501731i	0.851178	+	0.524877i	$0.175889\pi$
$104$	6055.84	+	34344.4i	0.0549024	+	0.311367i
$105$	15025.4	+	85213.4i	0.133001	+	0.754284i
$106$	−51783.9	+	89692.3i	−0.447641	+	0.775337i
$107$	74093.3	+	128333.i	0.625633	+	1.08363i	0.988418	+	0.151755i	$0.0484924\pi$
$107$	74093.3	+	128333.i	0.625633	+	1.08363i	−0.362786	+	0.931873i	$0.618174\pi$
$108$	−114022.	+	95675.4i	−0.940649	+	0.789298i
$109$	−12683.3	+	4616.34i	−0.102251	+	0.0372162i	−0.392639	−	0.919693i	$-0.628438\pi$
$109$	−12683.3	+	4616.34i	−0.102251	+	0.0372162i	0.290388	+	0.956909i	$0.406216\pi$
$110$	79659.0	+	28993.5i	0.627701	+	0.228465i
$111$	188872.	+	158483.i	1.45499	+	1.22088i
$112$	3818.54	−	21656.0i	0.0287642	−	0.163130i
$113$	113460.			0.835882			0.417941	−	0.908474i	$-0.362752\pi$
$113$	113460.			0.835882			0.417941	+	0.908474i	$0.362752\pi$
$114$	144084.	−	106886.i	1.03837	−	0.770297i
$115$	−129728.			−0.914724
$116$	284.261	−	1612.12i	0.00196143	−	0.0111238i
$117$	237676.	+	199434.i	1.60517	+	1.34690i
$118$	−135895.	−	49461.7i	−0.898458	−	0.327012i
$119$	−117523.	+	42774.8i	−0.760773	+	0.276899i
$120$	49386.0	−	41439.8i	0.313077	−	0.262703i
$121$	−99266.4	−	171935.i	−0.616367	−	1.06758i
$122$	−78728.8	+	136362.i	−0.478888	+	0.829459i
$123$	−52769.6	−	299271.i	−0.314500	−	1.78362i
$124$	−2449.53	−	13892.0i	−0.0143063	−	0.0811352i
$125$	−88371.4	+	153064.i	−0.505868	+	0.876188i
$126$	−97819.1	−	169428.i	−0.548905	−	0.950731i
$127$	209692.	−	175953.i	1.15365	−	0.968026i	0.153849	−	0.988094i	$-0.450833\pi$
$127$	209692.	−	175953.i	1.15365	−	0.968026i	0.999799	+	0.0200687i	$0.00638850\pi$
$128$	−15395.9	+	5603.66i	−0.0830579	+	0.0302306i
$129$	−134505.	−	48955.9i	−0.711647	−	0.259018i
$130$	−59010.2	−	49515.4i	−0.306245	−	0.256970i
$131$	47083.0	−	267021.i	0.239710	−	1.35946i	−0.592755	−	0.805383i	$-0.701960\pi$
$131$	47083.0	−	267021.i	0.239710	−	1.35946i	0.832464	−	0.554079i	$-0.186929\pi$
$132$	−273465.			−1.36605
$133$	60457.2	+	120893.i	0.296360	+	0.592613i
$134$	−54783.6			−0.263565
$135$	57091.6	−	323782.i	0.269611	−	1.52904i
$136$	71381.2	+	59896.0i	0.330931	+	0.277684i
$137$	347741.	+	126567.i	1.58290	+	0.576130i	0.975833	−	0.218518i	$-0.0701222\pi$
$137$	347741.	+	126567.i	1.58290	+	0.576130i	0.607071	+	0.794648i	$0.292344\pi$
$138$	393254.	−	143133.i	1.75782	−	0.639796i
$139$	−210050.	+	176253.i	−0.922115	+	0.773746i	−0.974385	−	0.224887i	$-0.927799\pi$
$139$	−210050.	+	176253.i	−0.922115	+	0.773746i	0.0522701	+	0.998633i	$0.483354\pi$
$140$	24286.5	+	42065.5i	0.104724	+	0.181387i
$141$	115757.	−	200496.i	0.490341	−	0.849296i
$142$	−51921.2	−	294459.i	−0.216084	−	1.22548i
$143$	56740.7	+	321793.i	0.232036	+	1.31594i
$144$	−72881.4	+	126234.i	−0.292894	+	0.507307i
$145$	1807.95	+	3131.46i	0.00714111	+	0.0123688i
$146$	−180957.	+	151841.i	−0.702578	+	0.589533i
$147$	−252526.	+	91911.8i	−0.963856	+	0.350815i
$148$	130058.	+	47337.4i	0.488072	+	0.177644i
$149$	−239526.	−	200986.i	−0.883865	−	0.741651i	0.0831047	−	0.996541i	$-0.473516\pi$
$149$	−239526.	−	200986.i	−0.883865	−	0.741651i	−0.966970	+	0.254890i	$0.917961\pi$
$150$	37139.3	−	210628.i	0.134774	−	0.764341i
$151$	−444816.			−1.58759			−0.793794	−	0.608187i	$-0.791897\pi$
$151$	−444816.			−1.58759			−0.793794	+	0.608187i	$0.791897\pi$
$152$	55483.0	−	84046.0i	0.194783	−	0.295059i
$153$	829005.			2.86305
$154$	35778.1	−	202908.i	0.121567	−	0.689440i
$155$	23869.0	+	20028.5i	0.0798005	+	0.0669606i
$156$	233513.	+	84991.9i	0.768245	+	0.279618i
$157$	−499309.	+	181734.i	−1.61667	+	0.588418i	−0.982743	−	0.184978i	$-0.940779\pi$
$157$	−499309.	+	181734.i	−1.61667	+	0.588418i	−0.633923	+	0.773396i	$0.718556\pi$
$158$	18413.9	−	15451.1i	0.0586816	−	0.0492397i
$159$	368991.	+	639111.i	1.15751	+	2.00486i
$160$	18095.0	−	31341.5i	0.0558803	−	0.0967875i
$161$	54752.4	+	310516.i	0.166471	+	0.944103i
$162$	88067.9	+	499458.i	0.263651	+	1.49524i
$163$	67437.4	−	116805.i	0.198807	−	0.344344i	−0.749335	−	0.662191i	$-0.769627\pi$
$163$	67437.4	−	116805.i	0.198807	−	0.344344i	0.948142	+	0.317847i	$0.102960\pi$
$164$	−85294.7	−	147735.i	−0.247635	−	0.428917i
$165$	462726.	−	388273.i	1.32317	−	1.11027i
$166$	−275010.	+	100095.i	−0.774601	+	0.281932i
$167$	−83232.3	−	30294.1i	−0.230941	−	0.0840556i	0.223958	−	0.974599i	$-0.428102\pi$
$167$	−83232.3	−	30294.1i	−0.230941	−	0.0840556i	−0.454899	+	0.890543i	$0.650324\pi$
$168$	−120033.	−	100720.i	−0.328117	−	0.275323i
$169$	−12913.6	+	73236.8i	−0.0347801	+	0.197248i
$170$	−205825.			−0.546231
$171$	−102501.	−	890082.i	−0.268063	−	2.32777i
$172$	−80351.1			−0.207095
$173$	76931.2	−	436299.i	0.195428	−	1.10833i	−0.716379	−	0.697711i	$-0.754202\pi$
$173$	76931.2	−	436299.i	0.195428	−	1.10833i	0.911808	−	0.410618i	$-0.134687\pi$
$174$	−8935.57	−	7497.83i	−0.0223743	−	0.0187742i
$175$	151424.	+	55113.9i	0.373766	+	0.136040i
$176$	−144253.	+	52503.9i	−0.351030	+	0.127764i
$177$	−789391.	+	662378.i	−1.89391	+	1.58918i
$178$	−30608.9	−	53016.2i	−0.0724099	−	0.125418i
$179$	95112.3	−	164739.i	0.221873	−	0.384295i	−0.733504	−	0.679685i	$-0.762116\pi$
$179$	95112.3	−	164739.i	0.221873	−	0.384295i	0.955377	+	0.295390i	$0.0954497\pi$
$180$	−55909.5	−	317079.i	−0.128619	−	0.729434i
$181$	−17063.9	−	96774.3i	−0.0387153	−	0.219565i	0.959312	−	0.282349i	$-0.0911135\pi$
$181$	−17063.9	−	96774.3i	−0.0387153	−	0.219565i	−0.998027	+	0.0627832i	$0.980002\pi$
$182$	−93614.1	+	162144.i	−0.209490	+	0.362847i
$183$	560990.	+	971663.i	1.23830	+	2.14481i
$184$	179962.	−	151006.i	0.391864	−	0.328813i
$185$	−287281.	+	104562.i	−0.617132	+	0.224618i
$186$	−94453.8	−	34378.4i	−0.200187	−	0.0728623i
$187$	668812.	+	561200.i	1.39862	+	1.17358i
$188$	22567.6	−	127987.i	0.0465683	−	0.264102i
$189$	−799097.			−1.62722
$190$	25448.9	+	220990.i	0.0511429	+	0.444107i
$191$	160536.			0.318411			0.159206	−	0.987245i	$-0.449107\pi$
$191$	160536.			0.318411			0.159206	+	0.987245i	$0.449107\pi$
$192$	−20272.7	+	114972.i	−0.0396879	+	0.225081i
$193$	−97771.2	−	82039.8i	−0.188937	−	0.158537i	0.543413	−	0.839466i	$-0.317132\pi$
$193$	−97771.2	−	82039.8i	−0.188937	−	0.158537i	−0.732350	+	0.680929i	$0.761576\pi$
$194$	402760.	+	146593.i	0.768320	+	0.279646i
$195$	−515799.	+	187735.i	−0.971390	+	0.353557i
$196$	−115561.	+	96967.5i	−0.214868	+	0.180296i
$197$	−208034.	−	360325.i	−0.381916	−	0.661498i	0.609420	−	0.792847i	$-0.291402\pi$
$197$	−208034.	−	360325.i	−0.381916	−	0.661498i	−0.991336	+	0.131350i	$0.958069\pi$
$198$	−682868.	+	1.18276e6i	−1.23787	+	2.14405i
$199$	93650.6	+	531119.i	0.167640	+	0.950734i	0.946301	+	0.323288i	$0.104788\pi$
$199$	93650.6	+	531119.i	0.167640	+	0.950734i	−0.778661	+	0.627445i	$0.784101\pi$
$200$	−20848.4	−	118237.i	−0.0368551	−	0.209016i
$201$	−195183.	+	338067.i	−0.340762	+	0.590218i
$202$	−155324.	−	269029.i	−0.267830	−	0.463896i
$203$	6732.36	−	5649.12i	0.0114664	−	0.00962146i
$204$	623932.	−	227093.i	1.04969	−	0.382057i
$205$	354084.	+	128876.i	0.588467	+	0.214184i
$206$	19113.8	+	16038.4i	0.0313819	+	0.0263325i
$207$	362930.	−	2.05828e6i	0.588705	−	3.33871i
$208$	139497.			0.223566
$209$	519853.	−	787476.i	0.823218	−	1.24701i
$210$	346112.			0.541587
$211$	−51782.0	+	293670.i	−0.0800705	+	0.454103i	0.918241	+	0.396021i	$0.129609\pi$
$211$	−51782.0	+	293670.i	−0.0800705	+	0.454103i	−0.998312	+	0.0580813i	$0.981502\pi$
$212$	317350.	+	266288.i	0.484952	+	0.406923i
$213$	−2.00208e6	−	728697.i	−3.02365	−	1.10052i
$214$	556999.	−	202731.i	0.831419	−	0.302612i
$215$	135961.	−	114085.i	0.200594	−	0.168318i
$216$	297689.	+	515613.i	0.434139	+	0.751950i
$217$	37865.9	−	65585.7i	0.0545883	−	0.0945497i
$218$	9375.11	+	53168.9i	0.0133609	+	0.0757733i
$219$	292290.	+	1.65766e6i	0.411816	+	2.33553i
$220$	169543.	−	293656.i	0.236169	−	0.409056i
$221$	−396684.	−	687077.i	−0.546341	−	0.946291i
$222$	755489.	−	633930.i	1.02883	−	0.863294i
$223$	490101.	−	178382.i	0.659968	−	0.240209i	0.00974564	−	0.999953i	$-0.496898\pi$
$223$	490101.	−	178382.i	0.659968	−	0.240209i	0.650223	+	0.759744i	$0.274676\pi$
$224$	−82655.6	−	30084.2i	−0.110066	−	0.0400607i
$225$	−818246.	−	686590.i	−1.07753	−	0.904151i
$226$	78808.2	−	446944.i	0.102636	−	0.582079i
$227$	15711.0			0.0202367			0.0101184	−	0.999949i	$-0.496779\pi$
$227$	15711.0			0.0202367			0.0101184	+	0.999949i	$0.496779\pi$
$228$	−320969.	−	641822.i	−0.408908	−	0.817669i
$229$	1.14920e6			1.44813			0.724065	−	0.689732i	$-0.242272\pi$
$229$	1.14920e6			1.44813			0.724065	+	0.689732i	$0.242272\pi$
$230$	−90108.4	+	511030.i	−0.112317	+	0.636981i
$231$	−1.12466e6	−	943703.i	−1.38673	−	1.16360i
$232$	−6153.08	−	2239.54i	−0.00750538	−	0.00273174i
$233$	263660.	−	95964.3i	0.318166	−	0.115803i	−0.178000	−	0.984030i	$-0.556963\pi$
$233$	263660.	−	95964.3i	0.318166	−	0.115803i	0.496166	+	0.868227i	$0.334741\pi$
$234$	950704.	−	797735.i	1.13503	−	0.952399i
$235$	143534.	+	248607.i	0.169545	+	0.293660i
$236$	−289232.	+	500965.i	−0.338039	+	0.585501i
$237$	−29742.8	−	168680.i	−0.0343963	−	0.195071i
$238$	86869.4	+	492661.i	0.0994087	+	0.563775i
$239$	−129647.	+	224555.i	−0.146814	+	0.254289i	−0.930048	−	0.367438i	$-0.880235\pi$
$239$	−129647.	+	224555.i	−0.146814	+	0.254289i	0.783234	+	0.621727i	$0.213568\pi$
$240$	−128938.	−	223327.i	−0.144495	−	0.250272i
$241$	617600.	−	518228.i	0.684960	−	0.574749i	−0.232491	−	0.972598i	$-0.574688\pi$
$241$	617600.	−	518228.i	0.684960	−	0.574749i	0.917451	+	0.397849i	$0.130243\pi$
$242$	−746240.	+	271609.i	−0.819106	+	0.298130i
$243$	1.27165e6	+	462843.i	1.38150	+	0.502826i
$244$	482478.	+	404847.i	0.518804	+	0.435328i
$245$	57862.5	−	328155.i	0.0615860	−	0.349272i
$246$	−1.21555e6			−1.28067
$247$	−688650.	+	510862.i	−0.718218	+	0.532797i
$248$	−56425.1			−0.0582563
$249$	−362121.	+	2.05369e6i	−0.370131	+	2.09912i
$250$	541571.	+	454432.i	0.548032	+	0.459853i
$251$	898704.	+	327102.i	0.900394	+	0.327716i	0.750410	−	0.660972i	$-0.229856\pi$
$251$	898704.	+	327102.i	0.900394	+	0.327716i	0.149983	+	0.988689i	$0.452078\pi$
$252$	−735359.	+	267649.i	−0.729454	+	0.265500i
$253$	1.68617e6	−	1.41486e6i	1.65615	−	1.38967i
$254$	−547468.	−	948242.i	−0.532445	−	0.922221i
$255$	−733314.	+	1.27014e6i	−0.706219	+	1.22321i
$256$	11380.2	+	64540.4i	0.0108530	+	0.0615505i
$257$	−106133.	−	601912.i	−0.100235	−	0.568461i	−0.993017	−	0.117972i	$-0.962361\pi$
$257$	−106133.	−	601912.i	−0.100235	−	0.568461i	0.892782	−	0.450489i	$-0.148750\pi$
$258$	−286275.	+	495842.i	−0.267753	+	0.463761i
$259$	371526.	+	643502.i	0.344144	+	0.596074i
$260$	−236041.	+	198062.i	−0.216548	+	0.181705i
$261$	−54741.9	+	19924.4i	−0.0497414	+	0.0181044i
$262$	−1.01915e6	−	370942.i	−0.917247	−	0.333851i
$263$	−518414.	−	435001.i	−0.462154	−	0.387794i	0.381769	−	0.924258i	$-0.375315\pi$
$263$	−518414.	−	435001.i	−0.462154	−	0.387794i	−0.843923	+	0.536464i	$0.819760\pi$
$264$	−189947.	+	1.07724e6i	−0.167734	+	0.951268i
$265$	−915068.			−0.800458
$266$	518217.	−	154184.i	0.449064	−	0.133609i
$267$	−436214.			−0.374474
$268$	−38052.3	+	215805.i	−0.0323626	+	0.183538i
$269$	327680.	+	274956.i	0.276102	+	0.231677i	0.770314	−	0.637664i	$-0.220099\pi$
$269$	327680.	+	274956.i	0.276102	+	0.231677i	−0.494213	+	0.869341i	$0.664544\pi$
$270$	−1.23580e6	−	449794.i	−1.03166	−	0.375495i
$271$	−338611.	+	123244.i	−0.280077	+	0.101940i	−0.478240	−	0.878229i	$-0.658725\pi$
$271$	−338611.	+	123244.i	−0.280077	+	0.101940i	0.198162	+	0.980169i	$0.436503\pi$
$272$	285525.	−	239584.i	0.234003	−	0.196352i
$273$	667056.	+	1.15537e6i	0.541696	+	0.938245i
$274$	740117.	−	1.28192e6i	0.595558	−	1.03154i
$275$	−195341.	−	1.10783e6i	−0.155762	−	0.883370i
$276$	−290682.	−	1.64854e6i	−0.229691	−	1.30265i
$277$	−902120.	+	1.56252e6i	−0.706423	+	1.22356i	0.259752	+	0.965675i	$0.416359\pi$
$277$	−902120.	+	1.56252e6i	−0.706423	+	1.22356i	−0.966175	+	0.257886i	$0.916974\pi$
$278$	548401.	+	949858.i	0.425585	+	0.737134i
$279$	−384550.	+	322676.i	−0.295762	+	0.248174i
$280$	182575.	−	66451.8i	0.139170	−	0.0506538i
$281$	−755867.	−	275113.i	−0.571057	−	0.207848i	0.0403203	−	0.999187i	$-0.487162\pi$
$281$	−755867.	−	275113.i	−0.571057	−	0.207848i	−0.611378	+	0.791339i	$0.709384\pi$
$282$	−709398.	−	595256.i	−0.531211	−	0.445739i
$283$	−155095.	+	879590.i	−0.115115	+	0.652851i	0.871578	+	0.490257i	$0.163097\pi$
$283$	−155095.	+	879590.i	−0.115115	+	0.652851i	−0.986693	+	0.162594i	$0.948014\pi$
$284$	−1.19601e6			−0.879910
$285$	1.45439e6	+	630298.i	1.06064	+	0.459657i
$286$	1.30703e6			0.944864
$287$	159034.	−	901925.i	0.113968	−	0.646347i
$288$	446643.	+	374778.i	0.317307	+	0.266252i
$289$	−657756.	−	239404.i	−0.463255	−	0.168611i
$290$	13591.3	−	4946.83i	0.00949001	−	0.00345408i
$291$	2.33957e6	−	1.96313e6i	1.61958	−	1.35899i
$292$	472446.	+	818301.i	0.324261	+	0.561637i
$293$	731039.	−	1.26620e6i	0.497476	−	0.861653i	−0.502520	−	0.864565i	$-0.667594\pi$
$293$	731039.	−	1.26620e6i	0.497476	−	0.861653i	0.999996	+	0.00291253i	$0.000927089\pi$
$294$	186659.	+	1.05860e6i	0.125945	+	0.714271i
$295$	−221879.	−	1.25834e6i	−0.148443	−	0.841865i
$296$	276811.	−	479450.i	0.183634	−	0.318064i
$297$	2.78922e6	+	4.83107e6i	1.83481	+	3.17799i
$298$	−958102.	+	803943.i	−0.624987	+	0.524427i
$299$	−1.87956e6	+	684104.i	−1.21585	+	0.442532i
$300$	−803915.	−	292601.i	−0.515711	−	0.187704i
$301$	−330455.	−	277285.i	−0.210231	−	0.176404i
$302$	−308966.	+	1.75223e6i	−0.194936	+	1.10554i
$303$	−2.21355e6			−1.38511
$304$	−292539.	−	276938.i	−0.181551	−	0.171870i
$305$	−1.39121e6			−0.856334
$306$	575821.	−	3.26564e6i	0.351547	−	1.99372i
$307$	809728.	+	679442.i	0.490335	+	0.411440i	0.854146	−	0.520033i	$-0.174080\pi$
$307$	809728.	+	679442.i	0.490335	+	0.411440i	−0.363811	+	0.931473i	$0.618525\pi$
$308$	−774448.	−	281876.i	−0.465174	−	0.169310i
$309$	167071.	−	60808.8i	0.0995415	−	0.0362301i
$310$	95476.2	−	80114.0i	0.0564275	−	0.0473483i
$311$	1.14038e6	+	1.97519e6i	0.668572	+	1.15800i	0.978304	+	0.207177i	$0.0664276\pi$
$311$	1.14038e6	+	1.97519e6i	0.668572	+	1.15800i	−0.309731	+	0.950824i	$0.600239\pi$
$312$	496999.	−	860828.i	0.289047	−	0.500645i
$313$	22446.3	+	127299.i	0.0129504	+	0.0734456i	0.990598	−	0.136805i	$-0.0436833\pi$
$313$	22446.3	+	127299.i	0.0129504	+	0.0734456i	−0.977648	+	0.210250i	$0.932572\pi$
$314$	369074.	+	2.09312e6i	0.211247	+	1.19804i
$315$	864276.	−	1.49697e6i	0.490768	−	0.850034i
$316$	−48075.2	−	83268.6i	−0.0270834	−	0.0469098i
$317$	−424551.	+	356241.i	−0.237291	+	0.199111i	−0.753677	−	0.657245i	$-0.771722\pi$
$317$	−424551.	+	356241.i	−0.237291	+	0.199111i	0.516386	+	0.856356i	$0.327277\pi$
$318$	2.77391e6	−	1.00962e6i	1.53824	−	0.559873i
$319$	−57651.8	−	20983.5i	−0.0317202	−	0.0115452i
$320$	−110893.	−	93050.0i	−0.0605379	−	0.0507974i
$321$	733433.	−	4.15950e6i	0.397281	−	2.25309i
$322$	1.26123e6			0.677880
$323$	−532144.	+	2.22839e6i	−0.283807	+	1.18846i
$324$	2.02865e6			1.07361
$325$	−177508.	+	1.00670e6i	−0.0932200	+	0.528677i
$326$	−413280.	−	346783.i	−0.215378	−	0.180723i
$327$	361504.	+	131577.i	0.186958	+	0.0680471i
$328$	−641207.	+	233380.i	−0.329089	+	0.119779i
$329$	534485.	−	448486.i	0.272236	−	0.228433i
$330$	−1.20809e6	−	2.09248e6i	−0.610682	−	1.05773i
$331$	746300.	−	1.29263e6i	0.374407	−	0.648491i	−0.615831	−	0.787878i	$-0.711180\pi$
$331$	746300.	−	1.29263e6i	0.374407	−	0.648491i	0.990238	+	0.139387i	$0.0445131\pi$
$332$	203279.	+	1.15285e6i	0.101216	+	0.574022i
$333$	−855283.	−	4.85055e6i	−0.422668	−	2.39707i
$334$	−177148.	+	306829.i	−0.0868901	+	0.150498i
$335$	−242019.	−	419189.i	−0.117825	−	0.204079i
$336$	−480133.	+	402880.i	−0.232014	+	0.194683i
$337$	−86013.8	+	31306.5i	−0.0412566	+	0.0150162i	−0.362566	−	0.931958i	$-0.618099\pi$
$337$	−86013.8	+	31306.5i	−0.0412566	+	0.0150162i	0.321309	+	0.946974i	$0.395877\pi$
$338$	279527.	+	101739.i	0.133086	+	0.0484393i
$339$	−2.47729e6	−	2.07869e6i	−1.17079	−	0.982406i
$340$	−142965.	+	810794.i	−0.0670705	+	0.380376i
$341$	−528679.			−0.246210
$342$	−3.57744e6	−	214470.i	−1.65389	−	0.0991520i
$343$	−2.25359e6			−1.03428
$344$	−55811.3	+	316521.i	−0.0254288	+	0.144214i
$345$	2.83250e6	+	2.37675e6i	1.28122	+	1.07507i
$346$	−1.66524e6	−	606100.i	−0.747804	−	0.272178i
$347$	499754.	−	181895.i	0.222809	−	0.0810958i	−0.228204	−	0.973613i	$-0.573285\pi$
$347$	499754.	−	181895.i	0.222809	−	0.0810958i	0.451012	+	0.892518i	$0.351063\pi$
$348$	−35742.3	+	29991.3i	−0.0158210	+	0.0132754i
$349$	−1.01888e6	−	1.76476e6i	−0.447777	−	0.775572i	0.550464	−	0.834859i	$-0.314451\pi$
$349$	−1.01888e6	−	1.76476e6i	−0.447777	−	0.775572i	−0.998241	+	0.0592869i	$0.981117\pi$
$350$	322285.	−	558213.i	0.140627	−	0.243573i
$351$	−880253.	−	4.99216e6i	−0.381364	−	2.16282i
$352$	106628.	+	604716.i	0.0458684	+	0.260133i
$353$	235828.	−	408466.i	0.100730	−	0.174469i	−0.811256	−	0.584692i	$-0.801216\pi$
$353$	235828.	−	408466.i	0.100730	−	0.174469i	0.911986	+	0.410222i	$0.134549\pi$
$354$	2.06095e6	+	3.56968e6i	0.874098	+	1.51398i
$355$	2.02375e6	−	1.69813e6i	0.852287	−	0.715154i
$356$	−230104.	+	83751.0i	−0.0962274	+	0.0350239i
$357$	3.34968e6	+	1.21919e6i	1.39102	+	0.506290i
$358$	−582882.	−	489096.i	−0.240366	−	0.201691i
$359$	54546.3	−	309348.i	0.0223372	−	0.126681i	−0.971600	−	0.236629i	$-0.923957\pi$
$359$	54546.3	−	309348.i	0.0223372	−	0.126681i	0.993937	+	0.109948i	$0.0350685\pi$
$360$	−1.28788e6			−0.523744
$361$	2.45836e6	+	295825.i	0.992838	+	0.119472i
$362$	−393069.			−0.157651
$363$	−982616.	+	5.57269e6i	−0.391397	+	2.21972i
$364$	573700.	+	481392.i	0.226951	+	0.190434i
$365$	−1.96127e6	−	713843.i	−0.770557	−	0.280460i
$366$	4.21727e6	−	1.53496e6i	1.64561	−	0.598955i
$367$	−1.31313e6	+	1.10185e6i	−0.508911	+	0.427027i	−0.860746	−	0.509035i	$-0.830002\pi$
$367$	−1.31313e6	+	1.10185e6i	−0.508911	+	0.427027i	0.351834	+	0.936062i	$0.385558\pi$
$368$	−469847.	−	813798.i	−0.180858	−	0.313254i
$369$	−3.03535e6	+	5.25738e6i	−1.16049	+	2.01004i
$370$	212350.	+	1.20429e6i	0.0806394	+	0.457329i
$371$	386208.	+	2.19029e6i	0.145676	+	0.826167i
$372$	−201031.	+	348196.i	−0.0753193	+	0.130457i
$373$	−1.28801e6	−	2.23090e6i	−0.479344	−	0.830247i	0.520376	−	0.853937i	$-0.325792\pi$
$373$	−1.28801e6	−	2.23090e6i	−0.479344	−	0.830247i	−0.999719	+	0.0236900i	$0.992459\pi$
$374$	2.67525e6	−	2.24480e6i	0.988975	−	0.829848i
$375$	4.73379e6	−	1.72296e6i	1.73832	−	0.632698i
$376$	−488495.	−	177798.i	−0.178193	−	0.0648570i
$377$	42707.6	+	35835.9i	0.0154758	+	0.0129857i
$378$	−555047.	+	3.14783e6i	−0.199802	+	1.13313i
$379$	2.53694e6			0.907218			0.453609	−	0.891201i	$-0.350136\pi$
$379$	2.53694e6			0.907218			0.453609	+	0.891201i	$0.350136\pi$
$380$	888206.	+	53248.7i	0.315540	+	0.0189169i
$381$	−7.80207e6			−2.75358
$382$	111507.	−	632388.i	0.0390970	−	0.221730i
$383$	−271462.	−	227783.i	−0.0945609	−	0.0793460i	0.594282	−	0.804257i	$-0.297436\pi$
$383$	−271462.	−	227783.i	−0.0945609	−	0.0793460i	−0.688843	+	0.724911i	$0.741881\pi$
$384$	438821.	+	159718.i	0.151865	+	0.0552745i
$385$	1.71065e6	−	622626.i	0.588179	−	0.214080i
$386$	−391085.	+	328159.i	−0.133599	+	0.112103i
$387$	1.42971e6	+	2.47633e6i	0.485256	+	0.840488i
$388$	857217.	−	1.48474e6i	0.289076	−	0.500694i
$389$	399414.	+	2.26519e6i	0.133829	+	0.758980i	0.975668	+	0.219252i	$0.0703617\pi$
$389$	399414.	+	2.26519e6i	0.133829	+	0.758980i	−0.841840	+	0.539728i	$0.818527\pi$
$390$	381263.	+	2.16225e6i	0.126930	+	0.719854i
$391$	−2.67218e6	+	4.62836e6i	−0.883943	+	1.53103i
$392$	301709.	+	522576.i	0.0991684	+	0.171765i
$393$	−5.92010e6	+	4.96755e6i	−1.93352	+	1.62241i
$394$	−1.56390e6	+	569213.i	−0.507538	+	0.184729i
$395$	199575.	+	72639.2i	0.0643595	+	0.0234249i
$396$	4.18486e6	+	3.51151e6i	1.34104	+	1.12527i
$397$	215206.	−	1.22050e6i	0.0685297	−	0.388651i	−0.931180	−	0.364560i	$-0.881220\pi$
$397$	215206.	−	1.22050e6i	0.0685297	−	0.388651i	0.999710	−	0.0240916i	$-0.00766934\pi$
$398$	2.15725e6			0.682641
$399$	894844.	−	3.74722e6i	0.281394	−	1.17836i
$400$	−480245.			−0.150077
$401$	−412287.	+	2.33819e6i	−0.128038	+	0.726139i	0.851419	+	0.524486i	$0.175742\pi$
$401$	−412287.	+	2.33819e6i	−0.128038	+	0.726139i	−0.979457	+	0.201653i	$0.935369\pi$
$402$	1.19615e6	+	1.00369e6i	0.369165	+	0.309766i
$403$	451443.	+	164312.i	0.138465	+	0.0503971i
$404$	−1.16765e6	+	424991.i	−0.355927	+	0.129547i
$405$	−3.43266e6	+	2.88034e6i	−1.03990	+	0.872582i
$406$	−17577.0	−	30444.2i	−0.00529211	−	0.00916620i
$407$	2.59360e6	−	4.49224e6i	0.776098	−	1.34424i
$408$	−461192.	−	2.61555e6i	−0.137161	−	0.777880i
$409$	−386681.	−	2.19298e6i	−0.114300	−	0.648225i	−0.987095	−	0.160138i	$-0.948806\pi$
$409$	−386681.	−	2.19298e6i	−0.114300	−	0.648225i	0.872795	−	0.488087i	$-0.162305\pi$
$410$	753617.	−	1.30530e6i	0.221407	−	0.383488i
$411$	−5.27377e6	−	9.13444e6i	−1.53999	−	2.66733i
$412$	76455.2	−	64153.6i	0.0221904	−	0.0186199i
$413$	−2.91830e6	+	1.06217e6i	−0.841888	+	0.306422i
$414$	−7.85595e6	−	2.85933e6i	−2.25267	−	0.819906i
$415$	−1.98082e6	−	1.66211e6i	−0.564579	−	0.473738i
$416$	96893.5	−	549510.i	0.0274512	−	0.155683i
$417$	7.81536e6			2.20094
$418$	−2.74096e6	−	2.59480e6i	−0.767295	−	0.726377i
$419$	3.64392e6			1.01399			0.506995	−	0.861949i	$-0.330756\pi$
$419$	3.64392e6			1.01399			0.506995	+	0.861949i	$0.330756\pi$
$420$	240407.	−	1.36341e6i	0.0665003	−	0.377142i
$421$	−2.28617e6	−	1.91833e6i	−0.628643	−	0.527494i	0.271864	−	0.962336i	$-0.412360\pi$
$421$	−2.28617e6	−	1.91833e6i	−0.628643	−	0.527494i	−0.900507	+	0.434842i	$0.856804\pi$
$422$	1.12087e6	+	407963.i	0.306389	+	0.111517i
$423$	−4.34598e6	+	1.58181e6i	−1.18096	+	0.429836i
$424$	1.26940e6	−	1.06515e6i	0.342913	−	0.287738i
$425$	1.36566e6	+	2.36539e6i	0.366750	+	0.635230i
$426$	−4.26114e6	+	7.38050e6i	−1.13763	+	1.97043i
$427$	587166.	+	3.32998e6i	0.155844	+	0.883837i
$428$	−411717.	−	2.33496e6i	−0.108640	−	0.616128i
$429$	4.65667e6	−	8.06560e6i	1.22161	−	2.11589i
$430$	−354969.	−	614824.i	−0.0925804	−	0.160354i
$431$	3.26496e6	−	2.73962e6i	0.846612	−	0.710392i	−0.112429	−	0.993660i	$-0.535863\pi$
$431$	3.26496e6	−	2.73962e6i	0.846612	−	0.710392i	0.959041	+	0.283268i	$0.0914186\pi$
$432$	2.23789e6	−	814525.i	0.576938	−	0.209988i
$433$	−191532.	−	69711.9i	−0.0490932	−	0.0178685i	0.317357	−	0.948306i	$-0.397205\pi$
$433$	−191532.	−	69711.9i	−0.0490932	−	0.0178685i	−0.366450	+	0.930438i	$0.619427\pi$
$434$	−232056.	−	194718.i	−0.0591383	−	0.0496229i
$435$	17896.5	−	101496.i	0.00453465	−	0.0257173i
$436$	215956.			0.0544064
$437$	5.29975e6	+	2.29679e6i	1.32755	+	0.575332i
$438$	6.73292e6			1.67694
$439$	139488.	−	791077.i	0.0345443	−	0.195910i	−0.962652	−	0.270742i	$-0.912731\pi$
$439$	139488.	−	791077.i	0.0345443	−	0.195910i	0.997196	+	0.0748318i	$0.0238420\pi$
$440$	−1.03902e6	−	871839.i	−0.255853	−	0.214686i
$441$	5.04465e6	+	1.83610e6i	1.23519	+	0.449573i
$442$	−2.98209e6	+	1.08539e6i	−0.726047	+	0.264259i
$443$	−1.73336e6	+	1.45446e6i	−0.419643	+	0.352122i	−0.828027	−	0.560688i	$-0.810537\pi$
$443$	−1.73336e6	+	1.45446e6i	−0.419643	+	0.352122i	0.408384	+	0.912810i	$0.366092\pi$
$444$	−1.97244e6	−	3.41637e6i	−0.474839	−	0.822445i
$445$	270444.	−	468422.i	0.0647406	−	0.112134i
$446$	−362268.	−	2.05452e6i	−0.0862368	−	0.489073i
$447$	1.54757e6	+	8.77669e6i	0.366337	+	2.07760i
$448$	−175921.	+	304703.i	−0.0414116	+	0.0717269i
$449$	388968.	+	673712.i	0.0910537	+	0.157710i	0.907955	−	0.419068i	$-0.137643\pi$
$449$	388968.	+	673712.i	0.0910537	+	0.157710i	−0.816901	+	0.576778i	$0.804310\pi$
$450$	−3.27298e6	+	2.74636e6i	−0.761925	+	0.639331i
$451$	−6.00784e6	+	2.18667e6i	−1.39084	+	0.506224i
$452$	−1.70587e6	−	620888.i	−0.392736	−	0.142944i
$453$	9.71214e6	+	8.14946e6i	2.22367	+	1.86588i
$454$	10912.8	−	61889.4i	0.00248482	−	0.0140921i
$455$	−1.65424e6			−0.374603
$456$	−2.75123e6	+	818565.i	−0.619604	+	0.184349i
$457$	6.92747e6			1.55162			0.775808	−	0.630969i	$-0.217343\pi$
$457$	6.92747e6			1.55162			0.775808	+	0.630969i	$0.217343\pi$
$458$	798227.	−	4.52697e6i	0.177813	−	1.00843i
$459$	−1.03757e7	−	8.70624e6i	−2.29872	−	1.92885i
$460$	1.95048e6	+	709915.i	0.429780	+	0.156427i
$461$	3.67015e6	−	1.33583e6i	0.804325	−	0.292750i	0.0930476	−	0.995662i	$-0.470339\pi$
$461$	3.67015e6	−	1.33583e6i	0.804325	−	0.292750i	0.711278	+	0.702911i	$0.248117\pi$
$462$	−4.49865e6	+	3.77481e6i	−0.980566	+	0.822793i
$463$	−3.26866e6	−	5.66148e6i	−0.708626	−	1.22738i	−0.965367	−	0.260896i	$-0.915982\pi$
$463$	−3.26866e6	−	5.66148e6i	−0.708626	−	1.22738i	0.256741	−	0.966480i	$-0.417351\pi$
$464$	−13095.9	+	22682.8i	−0.00282385	+	0.00489106i
$465$	−154217.	−	874608.i	−0.0330750	−	0.187578i
$466$	−194889.	−	1.10527e6i	−0.0415741	−	0.235779i
$467$	−1.37349e6	+	2.37895e6i	−0.291429	+	0.504769i	−0.974148	−	0.225912i	$-0.927464\pi$
$467$	−1.37349e6	+	2.37895e6i	−0.291429	+	0.504769i	0.682719	+	0.730681i	$0.260797\pi$
$468$	−2.48211e6	−	4.29914e6i	−0.523850	−	0.907334i
$469$	−901221.	+	756214.i	−0.189190	+	0.158750i
$470$	1.07902e6	−	392731.i	0.225312	−	0.0820069i
$471$	1.42315e7	+	5.17984e6i	2.95596	+	1.07588i
$472$	1.77252e6	+	1.48732e6i	0.366215	+	0.307291i
$473$	−522928.	+	2.96567e6i	−0.107470	+	0.609495i
$474$	−685129.			−0.140064
$475$	2.37081e6	−	1.75874e6i	0.482129	−	0.357658i
$476$	2.00104e6			0.404799
$477$	2.56001e6	−	1.45185e7i	0.515164	−	2.92164i
$478$	794521.	+	666682.i	0.159051	+	0.133459i
$479$	6.78968e6	+	2.47124e6i	1.35210	+	0.492126i	0.913604	−	0.406605i	$-0.133287\pi$
$479$	6.78968e6	+	2.47124e6i	1.35210	+	0.492126i	0.438501	+	0.898731i	$0.355510\pi$
$480$	−969295.	+	352794.i	−0.192023	+	0.0698906i
$481$	−3.61086e6	+	3.02987e6i	−0.711620	+	0.597120i
$482$	−1.61244e6	−	2.79283e6i	−0.316130	−	0.547554i
$483$	4.49349e6	−	7.78296e6i	0.876428	−	1.51802i
$484$	551598.	+	3.12827e6i	0.107031	+	0.607003i
$485$	657597.	+	3.72942e6i	0.126942	+	0.719924i
$486$	2.70652e6	−	4.68784e6i	0.519782	−	0.900289i
$487$	225859.	+	391200.i	0.0431535	+	0.0747440i	0.886795	−	0.462162i	$-0.152926\pi$
$487$	225859.	+	391200.i	0.0431535	+	0.0747440i	−0.843642	+	0.536906i	$0.819593\pi$
$488$	1.92991e6	−	1.61939e6i	0.366850	−	0.307824i
$489$	−3.61242e6	+	1.31481e6i	−0.683165	+	0.248652i
$490$	−1.25249e6	−	455868.i	−0.235658	−	0.0857726i
$491$	−6.39741e6	−	5.36806e6i	−1.19757	−	1.00488i	−0.999696	−	0.0246513i	$-0.992152\pi$
$491$	−6.39741e6	−	5.36806e6i	−1.19757	−	1.00488i	−0.197872	−	0.980228i	$-0.563403\pi$
$492$	−844313.	+	4.78834e6i	−0.157250	+	0.891810i
$493$	148963.			0.0276032
$494$	1.53407e6	+	3.06759e6i	0.282832	+	0.565562i
$495$	−1.20669e7			−2.21352
$496$	−39192.5	+	222271.i	−0.00715316	+	0.0405676i
$497$	−4.91875e6	−	4.12732e6i	−0.893231	−	0.749510i
$498$	7.83844e6	+	2.85296e6i	1.41630	+	0.515492i
$499$	−8.01413e6	+	2.91691e6i	−1.44080	+	0.524410i	−0.940007	−	0.341154i	$-0.889182\pi$
$499$	−8.01413e6	+	2.91691e6i	−1.44080	+	0.524410i	−0.500798	+	0.865564i	$0.666960\pi$
$500$	2.16629e6	−	1.81773e6i	0.387517	−	0.325165i
$501$	1.26229e6	+	2.18634e6i	0.224679	+	0.389156i
$502$	1.91276e6	−	3.31300e6i	0.338767	−	0.586762i
$503$	−132176.	−	749607.i	−0.0232934	−	0.132103i	0.970944	−	0.239309i	$-0.0769208\pi$
$503$	−132176.	−	749607.i	−0.0232934	−	0.132103i	−0.994237	+	0.107205i	$0.965810\pi$
$504$	543555.	+	3.08266e6i	0.0953163	+	0.540566i
$505$	1.37236e6	−	2.37699e6i	0.239463	−	0.414762i
$506$	−4.40227e6	−	7.62495e6i	−0.764364	−	1.32392i
$507$	1.62373e6	−	1.36247e6i	0.280539	−	0.235400i
$508$	−4.11561e6	+	1.49796e6i	−0.707579	+	0.257538i
$509$	−5.57731e6	−	2.02997e6i	−0.954179	−	0.347293i	−0.182429	−	0.983219i	$-0.558396\pi$
$509$	−5.57731e6	−	2.02997e6i	−0.954179	−	0.347293i	−0.771750	+	0.635926i	$0.780618\pi$
$510$	4.49401e6	+	3.77092e6i	0.765083	+	0.641981i
$511$	−880885.	+	4.99575e6i	−0.149234	+	0.846347i
$512$	262144.			0.0441942
$513$	−8.06479e6	+	1.22166e7i	−1.35301	+	2.04954i
$514$	−2.44479e6			−0.408163
$515$	−38281.8	+	217107.i	−0.00636025	+	0.0360708i
$516$	1.75439e6	+	1.47211e6i	0.290070	+	0.243398i
$517$	−4.57700e6	−	1.66589e6i	−0.753103	−	0.274107i
$518$	2.79296e6	−	1.01656e6i	0.457342	−	0.166459i
$519$	−9.67314e6	+	8.11673e6i	−1.57634	+	1.32270i
$520$	616259.	+	1.06739e6i	0.0999436	+	0.173107i
$521$	−4.51381e6	+	7.81814e6i	−0.728532	+	1.26185i	0.228972	+	0.973433i	$0.426464\pi$
$521$	−4.51381e6	+	7.81814e6i	−0.728532	+	1.26185i	−0.957504	+	0.288421i	$0.906870\pi$
$522$	40463.6	+	229480.i	0.00649962	+	0.0368612i
$523$	−21069.1	−	119489.i	−0.00336816	−	0.0191018i	0.983077	−	0.183191i	$-0.0586426\pi$
$523$	−21069.1	−	119489.i	−0.00336816	−	0.0191018i	−0.986446	+	0.164089i	$0.947532\pi$
$524$	−2.16912e6	+	3.75703e6i	−0.345108	+	0.597745i
$525$	−2.29647e6	−	3.97760e6i	−0.363632	−	0.629830i
$526$	−2.07365e6	+	1.74000e6i	−0.326792	+	0.274211i
$527$	1.20622e6	−	439030.i	0.189192	−	0.0688601i
$528$	4.11156e6	+	1.49649e6i	0.641833	+	0.233608i
$529$	5.39106e6	+	4.52363e6i	0.837596	+	0.702827i
$530$	−635599.	+	3.60466e6i	−0.0982865	+	0.557410i
$531$	2.05856e7			3.16831
$532$	−247416.	−	2.14847e6i	−0.0379008	−	0.329117i
$533$	5.80974e6			0.885806
$534$	−302991.	+	1.71835e6i	−0.0459808	+	0.260770i
$535$	4.01191e6	+	3.36639e6i	0.605992	+	0.508488i
$536$	823676.	+	299794.i	0.123835	+	0.0450724i
$537$	−5.09488e6	+	1.85438e6i	−0.762427	+	0.277501i
$538$	1.31072e6	−	1.09982e6i	0.195233	−	0.163820i
$539$	2.82689e6	+	4.89631e6i	0.419118	+	0.725934i
$540$	−2.63022e6	+	4.55567e6i	−0.388157	+	0.672307i
$541$	804583.	+	4.56302e6i	0.118189	+	0.670284i	0.985122	+	0.171859i	$0.0549772\pi$
$541$	804583.	+	4.56302e6i	0.118189	+	0.670284i	−0.866932	+	0.498426i	$0.833912\pi$
$542$	250291.	+	1.41947e6i	0.0365972	+	0.207553i
$543$	−1.40043e6	+	2.42561e6i	−0.203826	+	0.353038i
$544$	−745453.	−	1.29116e6i	−0.108000	−	0.187061i
$545$	−365417.	+	306621.i	−0.0526984	+	0.0442192i
$546$	5.01462e6	−	1.82517e6i	0.719874	−	0.262013i
$547$	−8.39540e6	−	3.05568e6i	−1.19970	−	0.436655i	−0.336581	−	0.941655i	$-0.609271\pi$
$547$	−8.39540e6	−	3.05568e6i	−1.19970	−	0.436655i	−0.863120	+	0.504999i	$0.831493\pi$
$548$	−4.53570e6	−	3.80590e6i	−0.645197	−	0.541385i
$549$	3.89207e6	−	2.20730e7i	0.551125	−	3.12559i
$550$	−4.49969e6			−0.634273
$551$	−18418.2	−	159937.i	−0.00258445	−	0.0224425i
$552$	−6.69588e6			−0.935319
$553$	89637.1	−	508357.i	0.0124645	−	0.0706897i
$554$	5.52851e6	+	4.63897e6i	0.765304	+	0.642166i
$555$	8.18820e6	+	2.98026e6i	1.12838	+	0.410697i
$556$	4.12262e6	−	1.50051e6i	0.565571	−	0.205851i
$557$	−5.69336e6	+	4.77730e6i	−0.777554	+	0.652446i	−0.942631	−	0.333835i	$-0.891657\pi$
$557$	−5.69336e6	+	4.77730e6i	−0.777554	+	0.652446i	0.165077	+	0.986281i	$0.447213\pi$
$558$	1.00399e6	+	1.73896e6i	0.136503	+	0.236431i
$559$	1.36825e6	−	2.36988e6i	0.185198	−	0.320773i
$560$	−134954.	−	765362.i	−0.0181851	−	0.103133i
$561$	−4.32117e6	−	2.45066e7i	−0.579688	−	3.28758i
$562$	−1.60875e6	+	2.78644e6i	−0.214857	+	0.372143i
$563$	−4.58247e6	−	7.93707e6i	−0.609297	−	1.05533i	−0.991357	−	0.131195i	$-0.958119\pi$
$563$	−4.58247e6	−	7.93707e6i	−0.609297	−	1.05533i	0.382060	−	0.924138i	$-0.375215\pi$
$564$	−2.83759e6	+	2.38102e6i	−0.375623	+	0.315185i
$565$	3.76804e6	−	1.37146e6i	0.496586	−	0.180743i
$566$	3.35718e6	+	1.22191e6i	0.440488	+	0.160324i
$567$	8.34311e6	+	7.00070e6i	1.08986	+	0.914501i
$568$	−830738.	+	4.71135e6i	−0.108042	+	0.612738i
$569$	660962.			0.0855846			0.0427923	−	0.999084i	$-0.486375\pi$
$569$	660962.			0.0855846			0.0427923	+	0.999084i	$0.486375\pi$
$570$	3.49309e6	−	5.29136e6i	0.450322	−	0.682150i
$571$	−1.00348e7			−1.28800			−0.644002	−	0.765024i	$-0.722727\pi$
$571$	−1.00348e7			−1.28800			−0.644002	+	0.765024i	$0.722727\pi$
$572$	907851.	−	5.14868e6i	0.116018	−	0.657970i
$573$	−3.50516e6	−	2.94117e6i	−0.445985	−	0.374226i
$574$	−3.44243e6	−	1.25294e6i	−0.436099	−	0.158727i
$575$	6.47075e6	−	2.35516e6i	0.816179	−	0.297065i
$576$	1.78657e6	−	1.49911e6i	0.224370	−	0.188269i
$577$	−4.45837e6	−	7.72213e6i	−0.557490	−	0.965600i	−0.997705	−	0.0677081i	$-0.978431\pi$
$577$	−4.45837e6	−	7.72213e6i	−0.557490	−	0.965600i	0.440216	−	0.897892i	$-0.354902\pi$
$578$	−1.39994e6	+	2.42476e6i	−0.174297	+	0.301891i
$579$	631696.	+	3.58253e6i	0.0783090	+	0.444113i
$580$	−10046.3	−	56975.4i	−0.00124004	−	0.00703262i
$581$	−3.14238e6	+	5.44277e6i	−0.386206	+	0.668928i
$582$	−6.10818e6	−	1.05797e7i	−0.747488	−	1.29469i
$583$	1.18937e7	−	9.98004e6i	1.44926	−	1.21608i
$584$	3.55163e6	−	1.29269e6i	0.430919	−	0.156842i
$585$	1.03040e7	+	3.75035e6i	1.24485	+	0.453087i
$586$	−4.48007e6	−	3.75922e6i	−0.538940	−	0.452225i
$587$	−2.52278e6	+	1.43074e7i	−0.302192	+	1.71382i	0.334243	+	0.942487i	$0.391520\pi$
$587$	−2.52278e6	+	1.43074e7i	−0.302192	+	1.71382i	−0.636435	+	0.771330i	$0.719592\pi$
$588$	4.29972e6			0.512857
$589$	−620517.	−	1.24081e6i	−0.0736997	−	0.147373i
$590$	−5.11100e6			−0.604471
$591$	−2.05928e6	+	1.16787e7i	−0.242519	+	1.37539i
$592$	−1.69639e6	−	1.42344e6i	−0.198940	−	0.166931i
$593$	−6.01170e6	−	2.18808e6i	−0.702038	−	0.255521i	−0.0337575	−	0.999430i	$-0.510747\pi$
$593$	−6.01170e6	−	2.18808e6i	−0.702038	−	0.255521i	−0.668281	+	0.743909i	$0.732970\pi$
$594$	2.09681e7	−	7.63176e6i	2.43833	−	0.887480i
$595$	−3.38594e6	+	2.84114e6i	−0.392091	+	0.329004i
$596$	2.50143e6	+	4.33260e6i	0.288451	+	0.499612i
$597$	7.68584e6	−	1.33123e7i	0.882583	−	1.52868i
$598$	1.38932e6	+	7.87920e6i	0.158872	+	0.901009i
$599$	−1.97109e6	−	1.11786e7i	−0.224460	−	1.27298i	−0.863715	−	0.503980i	$-0.831868\pi$
$599$	−1.97109e6	−	1.11786e7i	−0.224460	−	1.27298i	0.639255	−	0.768995i	$-0.279243\pi$
$600$	−1.71102e6	+	2.96357e6i	−0.194033	+	0.336075i
$601$	413398.	+	716027.i	0.0466856	+	0.0808618i	0.888424	−	0.459024i	$-0.151801\pi$
$601$	413398.	+	716027.i	0.0466856	+	0.0808618i	−0.841738	+	0.539886i	$0.818467\pi$
$602$	−1.32182e6	+	1.10914e6i	−0.148656	+	0.124737i
$603$	7.32796e6	−	2.66716e6i	0.820710	−	0.298714i
$604$	6.68784e6	+	2.43417e6i	0.745922	+	0.271493i
$605$	−5.37496e6	−	4.51013e6i	−0.597017	−	0.500957i
$606$	−1.53752e6	+	8.71969e6i	−0.170074	+	0.964538i
$607$	8.36168e6			0.921132			0.460566	−	0.887626i	$-0.347647\pi$
$607$	8.36168e6			0.921132			0.460566	+	0.887626i	$0.347647\pi$
$608$	−1.29412e6	+	960018.i	−0.141976	+	0.105322i
$609$	−250493.			−0.0273685
$610$	−966324.	+	5.48030e6i	−0.105147	+	0.596320i
$611$	3.39057e6	+	2.84503e6i	0.367426	+	0.308307i
$612$	−1.24642e7	−	4.53658e6i	−1.34519	−	0.489610i
$613$	470167.	−	171127.i	0.0505360	−	0.0183936i	−0.316628	−	0.948550i	$-0.602551\pi$
$613$	470167.	−	171127.i	0.0505360	−	0.0183936i	0.367164	+	0.930156i	$0.380329\pi$
$614$	3.23891e6	−	2.71777e6i	0.346719	−	0.290932i
$615$	−5.36997e6	−	9.30107e6i	−0.572512	−	0.991619i
$616$	−1.64830e6	+	2.85494e6i	−0.175019	+	0.303142i
$617$	207106.	+	1.17455e6i	0.0219017	+	0.124211i	0.993798	−	0.111197i	$-0.0354685\pi$
$617$	207106.	+	1.17455e6i	0.0219017	+	0.124211i	−0.971897	+	0.235408i	$0.924357\pi$
$618$	−123494.	−	700368.i	−0.0130069	−	0.0737658i
$619$	6.64643e6	−	1.15120e7i	0.697207	−	1.20760i	−0.272224	−	0.962234i	$-0.587759\pi$
$619$	6.64643e6	−	1.15120e7i	0.697207	−	1.20760i	0.969431	−	0.245364i	$-0.0789076\pi$
$620$	−249271.	−	431749.i	−0.0260430	−	0.0451079i
$621$	−2.61585e7	+	2.19496e7i	−2.72197	+	2.28401i
$622$	8.57285e6	−	3.12026e6i	0.888483	−	0.323381i
$623$	−1.23535e6	−	449631.i	−0.127518	−	0.0464126i
$624$	−3.04579e6	−	2.55572e6i	−0.313140	−	0.262755i
$625$	−66688.9	+	378212.i	−0.00682895	+	0.0387289i
$626$	517053.			0.0527350
$627$	−2.57778e7	+	7.66961e6i	−2.61865	+	0.779120i
$628$	8.50165e6			0.860210
$629$	−2.18702e6	+	1.24032e7i	−0.220408	+	1.24999i
$630$	−5.29659e6	−	4.44436e6i	−0.531673	−	0.446127i
$631$	1.21459e7	+	4.42074e6i	1.21438	+	0.442000i	0.868222	−	0.496175i	$-0.165263\pi$
$631$	1.21459e7	+	4.42074e6i	1.21438	+	0.442000i	0.346162	+	0.938175i	$0.387485\pi$
$632$	−361407.	+	131541.i	−0.0359918	+	0.0131000i
$633$	6.51094e6	−	5.46333e6i	0.645854	−	0.541936i
$634$	1.10842e6	+	1.91985e6i	0.109517	+	0.189690i
$635$	4.83713e6	−	8.37815e6i	0.476051	−	0.824544i
$636$	−2.05039e6	−	1.16283e7i	−0.200999	−	1.13992i
$637$	−892140.	−	5.05958e6i	−0.0871133	−	0.494044i
$638$	−122704.	+	212529.i	−0.0119345	+	0.0206712i
$639$	2.12809e7	+	3.68597e7i	2.06176	+	3.57108i
$640$	−443570.	+	372200.i	−0.0428068	+	0.0359192i
$641$	−1.27894e7	+	4.65497e6i	−1.22944	+	0.447478i	−0.873404	−	0.486996i	$-0.838093\pi$
$641$	−1.27894e7	+	4.65497e6i	−1.22944	+	0.447478i	−0.356032	+	0.934474i	$0.615871\pi$
$642$	−1.58758e7	−	5.77832e6i	−1.52019	−	0.553304i
$643$	−4.37967e6	−	3.67498e6i	−0.417747	−	0.350532i	0.409558	−	0.912284i	$-0.365683\pi$
$643$	−4.37967e6	−	3.67498e6i	−0.417747	−	0.350532i	−0.827305	+	0.561752i	$0.810127\pi$
$644$	876038.	−	4.96826e6i	0.0832354	−	0.472052i
$645$	−5.05873e6			−0.478787
$646$	8.40852e6	+	3.64406e6i	0.792754	+	0.343562i
$647$	−5.37466e6			−0.504766			−0.252383	−	0.967627i	$-0.581214\pi$
$647$	−5.37466e6			−0.504766			−0.252383	+	0.967627i	$0.581214\pi$
$648$	1.40909e6	−	7.99133e6i	0.131826	−	0.747621i
$649$	1.66078e7	+	1.39356e7i	1.54775	+	1.29871i
$650$	3.84232e6	+	1.39849e6i	0.356705	+	0.129830i
$651$	−2.02836e6	+	738264.i	−0.187583	+	0.0682746i
$652$	−1.65312e6	+	1.38713e6i	−0.152295	+	0.127791i
$653$	−6.43711e6	−	1.11494e7i	−0.590756	−	1.02322i	−0.994131	−	0.108184i	$-0.965496\pi$
$653$	−6.43711e6	−	1.11494e7i	−0.590756	−	1.02322i	0.403375	−	0.915035i	$-0.367837\pi$
$654$	769409.	−	1.33266e6i	0.0703417	−	0.121835i
$655$	−1.66400e6	−	9.43700e6i	−0.151548	−	0.859470i
$656$	473961.	+	2.68797e6i	0.0430014	+	0.243873i
$657$	1.68128e7	−	2.91206e7i	1.51959	−	2.63200i
$658$	−1.39544e6	−	2.41697e6i	−0.125645	−	0.217624i
$659$	4.07719e6	−	3.42117e6i	0.365719	−	0.306874i	−0.441346	−	0.897337i	$-0.645499\pi$
$659$	4.07719e6	−	3.42117e6i	0.365719	−	0.306874i	0.807065	+	0.590462i	$0.201055\pi$
$660$	−9.08188e6	+	3.30554e6i	−0.811551	+	0.295381i
$661$	−8.40410e6	−	3.05884e6i	−0.748148	−	0.272304i	−0.0603218	−	0.998179i	$-0.519213\pi$
$661$	−8.40410e6	−	3.05884e6i	−0.748148	−	0.272304i	−0.687826	+	0.725875i	$0.741435\pi$
$662$	−4.57359e6	−	3.83770e6i	−0.405614	−	0.340350i
$663$	−3.92668e6	+	2.22693e7i	−0.346930	+	1.96754i
$664$	4.68255e6			0.412157
$665$	3.46911e6	+	3.28411e6i	0.304204	+	0.287981i
$666$	−1.97015e7			−1.72113
$667$	65214.4	−	369849.i	0.00567582	−	0.0321892i
$668$	1.08563e6	+	910948.i	0.0941324	+	0.0789865i
$669$	−1.39690e7	−	5.08431e6i	−1.20671	−	0.439205i
$670$	−1.81939e6	+	662203.i	−0.156581	+	0.0569907i
$671$	1.80825e7	−	1.51730e7i	1.55043	−	1.30096i
$672$	1.25354e6	+	2.17119e6i	0.107082	+	0.185471i
$673$	255809.	−	443074.i	0.0217710	−	0.0377085i	−0.854935	−	0.518736i	$-0.826403\pi$
$673$	255809.	−	443074.i	0.0217710	−	0.0377085i	0.876706	+	0.481027i	$0.159736\pi$
$674$	63578.8	+	360573.i	0.00539092	+	0.0305734i
$675$	3.03044e6	+	1.71865e7i	0.256004	+	1.45187i
$676$	594932.	−	1.03045e6i	0.0500727	−	0.0867284i
$677$	9.59286e6	+	1.66153e7i	0.804408	+	1.39328i	0.916690	+	0.399600i	$0.130851\pi$
$677$	9.59286e6	+	1.66153e7i	0.804408	+	1.39328i	−0.112281	+	0.993676i	$0.535816\pi$
$678$	−9.90915e6	+	8.31477e6i	−0.827870	+	0.694666i
$679$	8.64914e6	−	3.14803e6i	0.719944	−	0.262038i
$680$	3.09460e6	+	1.12634e6i	0.256645	+	0.0934110i
$681$	−343036.	−	287842.i	−0.0283447	−	0.0237841i
$682$	−367217.	+	2.08259e6i	−0.0302316	+	0.171452i
$683$	1.69775e7			1.39259			0.696294	−	0.717757i	$-0.254831\pi$
$683$	1.69775e7			1.39259			0.696294	+	0.717757i	$0.254831\pi$
$684$	−3.32971e6	+	1.39434e7i	−0.272123	+	1.13954i
$685$	1.30785e7			1.06496
$686$	−1.56533e6	+	8.87740e6i	−0.126997	+	0.720237i
$687$	−2.50918e7	−	2.10545e7i	−2.02833	−	1.70197i
$688$	1.20808e6	+	439707.i	0.0973030	+	0.0354154i
$689$	−1.32579e7	+	4.82548e6i	−1.06396	+	0.387251i
$690$	1.13300e7	−	9.50700e6i	0.905957	−	0.760188i
$691$	1.13887e7	+	1.97257e7i	0.907355	+	1.57158i	0.817725	+	0.575610i	$0.195235\pi$
$691$	1.13887e7	+	1.97257e7i	0.907355	+	1.57158i	0.0896303	+	0.995975i	$0.471431\pi$
$692$	−3.54423e6	+	6.13879e6i	−0.281357	+	0.487324i
$693$	5.09288e6	+	2.88832e7i	0.402838	+	2.28461i
$694$	−369403.	−	2.09499e6i	−0.0291140	−	0.165114i
$695$	−4.84537e6	+	8.39242e6i	−0.380509	+	0.659061i
$696$	93316.4	+	161629.i	0.00730189	+	0.0126472i
$697$	1.18915e7	−	9.97815e6i	0.927159	−	0.777979i
$698$	−7.65951e6	+	2.78783e6i	−0.595062	+	0.216585i
$699$	−7.51493e6	−	2.73521e6i	−0.581744	−	0.211738i
$700$	−1.97507e6	−	1.65728e6i	−0.152349	−	0.127836i
$701$	−2.34987e6	+	1.33268e7i	−0.180613	+	1.02431i	0.750850	+	0.660472i	$0.229644\pi$
$701$	−2.34987e6	+	1.33268e7i	−0.180613	+	1.02431i	−0.931463	+	0.363835i	$0.881467\pi$
$702$	−2.02767e7			−1.55294
$703$	1.35874e7	+	814578.i	1.03693	+	0.0621648i
$704$	2.45618e6			0.186779
$705$	1.42081e6	−	8.05779e6i	0.107662	−	0.610581i
$706$	−1.44524e6	−	1.21270e6i	−0.109126	−	0.0915674i
$707$	−6.26875e6	−	2.28164e6i	−0.471663	−	0.171671i
$708$	1.54933e7	−	5.63910e6i	1.16161	−	0.422792i
$709$	−4.64256e6	+	3.89557e6i	−0.346850	+	0.291042i	−0.799524	−	0.600634i	$-0.794915\pi$
$709$	−4.64256e6	+	3.89557e6i	−0.346850	+	0.291042i	0.452674	+	0.891676i	$0.350470\pi$
$710$	−5.28364e6	−	9.15152e6i	−0.393357	−	0.681314i
$711$	−1.71083e6	+	2.96325e6i	−0.126921	+	0.219834i
$712$	170086.	+	964605.i	0.0125739	+	0.0713099i
$713$	−561964.	−	3.18706e6i	−0.0413985	−	0.234783i
$714$	7.12932e6	−	1.23483e7i	0.523362	−	0.906490i
$715$	5.77409e6	+	1.00010e7i	0.422394	+	0.731609i
$716$	−2.33153e6	+	1.95638e6i	−0.169964	+	0.142617i
$717$	6.94478e6	−	2.52769e6i	0.504499	−	0.183623i
$718$	−1.18070e6	−	429741.i	−0.0854732	−	0.0311097i
$719$	−1.21471e7	−	1.01927e7i	−0.876297	−	0.735301i	0.0891172	−	0.996021i	$-0.471595\pi$
$719$	−1.21471e7	−	1.01927e7i	−0.876297	−	0.735301i	−0.965414	+	0.260721i	$0.916040\pi$
$720$	−894552.	+	5.07326e6i	−0.0643094	+	0.364717i
$721$	535821.			0.0383868
$722$	2.87288e6	−	9.47859e6i	0.205105	−	0.676707i
$723$	−2.29792e7			−1.63489
$724$	−273023.	+	1.54839e6i	−0.0193576	+	0.109783i
$725$	−147029.	−	123372.i	−0.0103886	−	0.00871710i
$726$	2.12696e7	+	7.74150e6i	1.49768	+	0.545110i
$727$	−1.89949e7	+	6.91358e6i	−1.33291	+	0.485140i	−0.907573	−	0.419895i	$-0.862067\pi$
$727$	−1.89949e7	+	6.91358e6i	−1.33291	+	0.485140i	−0.425337	+	0.905035i	$0.639845\pi$
$728$	2.29480e6	−	1.92557e6i	0.160478	−	0.134657i
$729$	−3.88053e6	−	6.72127e6i	−0.270440	−	0.468417i
$730$	−4.17428e6	+	7.23006e6i	−0.289917	+	0.502151i
$731$	−1.26967e6	−	7.20068e6i	−0.0878817	−	0.498402i
$732$	−3.11728e6	−	1.76790e7i	−0.215029	−	1.21949i
$733$	7.09353e6	−	1.22863e7i	0.487643	−	0.844623i	−0.512256	−	0.858833i	$-0.671190\pi$
$733$	7.09353e6	−	1.22863e7i	0.487643	−	0.844623i	0.999899	+	0.0142099i	$0.00452332\pi$
$734$	3.42834e6	+	5.93805e6i	0.234879	+	0.406822i
$735$	−7.27549e6	+	6.10486e6i	−0.496757	+	0.416829i
$736$	−3.53209e6	+	1.28558e6i	−0.240346	+	0.0874789i
$737$	7.71750e6	+	2.80894e6i	0.523369	+	0.190491i
$738$	1.86017e7	+	1.56087e7i	1.25722	+	1.05493i
$739$	736938.	−	4.17938e6i	0.0496386	−	0.281515i	−0.949877	−	0.312623i	$-0.898792\pi$
$739$	736938.	−	4.17938e6i	0.0496386	−	0.281515i	0.999516	+	0.0311080i	$0.00990359\pi$
$740$	4.89149e6			0.328369
$741$	2.43956e7	+	1.46253e6i	1.63217	+	0.0978498i
$742$	8.89634e6			0.593200
$743$	2.17774e6	−	1.23506e7i	0.144722	−	0.820759i	−0.822868	−	0.568233i	$-0.807627\pi$
$743$	2.17774e6	−	1.23506e7i	0.144722	−	0.820759i	0.967590	−	0.252527i	$-0.0812615\pi$
$744$	1.23199e6	+	1.03376e6i	0.0815972	+	0.0684682i
$745$	−1.03842e7	−	3.77953e6i	−0.685459	−	0.249487i
$746$	−9.68266e6	+	3.52420e6i	−0.637012	+	0.231853i
$747$	3.19127e7	−	2.67779e7i	2.09248	−	1.75580i
$748$	−6.98458e6	−	1.20976e7i	−0.456443	−	0.790582i
$749$	6.36452e6	−	1.10237e7i	0.414535	−	0.717995i
$750$	−3.49908e6	−	1.98442e7i	−0.227143	−	1.28819i
$751$	−3.31893e6	−	1.88226e7i	−0.214733	−	1.21781i	−0.881369	−	0.472428i	$-0.843378\pi$
$751$	−3.31893e6	−	1.88226e7i	−0.214733	−	1.21781i	0.666636	−	0.745383i	$-0.267733\pi$
$752$	−1.03969e6	+	1.80080e6i	−0.0670440	+	0.116124i
$753$	−1.36296e7	−	2.36071e7i	−0.875981	−	1.51724i
$754$	170830.	−	143344.i	0.0109430	−	0.00918228i
$755$	−1.47725e7	+	5.37676e6i	−0.943164	+	0.343284i
$756$	1.20145e7	+	4.37292e6i	0.764541	+	0.278270i
$757$	−7.47001e6	−	6.26808e6i	−0.473785	−	0.397553i	0.374388	−	0.927272i	$-0.377853\pi$
$757$	−7.47001e6	−	6.26808e6i	−0.473785	−	0.397553i	−0.848173	+	0.529719i	$0.822297\pi$
$758$	1.76214e6	−	9.99358e6i	0.111395	−	0.631754i
$759$	−6.27375e7			−3.95297
$760$	826700.	−	3.46186e6i	0.0519175	−	0.217408i
$761$	7.08784e6			0.443662			0.221831	−	0.975085i	$-0.428797\pi$
$761$	7.08784e6			0.443662			0.221831	+	0.975085i	$0.428797\pi$
$762$	−5.41926e6	+	3.07342e7i	−0.338106	+	1.91749i
$763$	888151.	+	745247.i	0.0552300	+	0.0463435i
$764$	−2.41367e6	−	878504.i	−0.149604	−	0.0544516i
$765$	2.75316e7	−	1.00207e7i	1.70090	−	0.619076i
$766$	−1.08585e6	+	911133.i	−0.0668646	+	0.0561061i
$767$	−9.85035e6	−	1.70613e7i	−0.604593	−	1.04719i
$768$	933966.	−	1.61768e6i	0.0571384	−	0.0989666i
$769$	3.59173e6	+	2.03697e7i	0.219022	+	1.24214i	0.873789	+	0.486306i	$0.161656\pi$
$769$	3.59173e6	+	2.03697e7i	0.219022	+	1.24214i	−0.654766	+	0.755831i	$0.727233\pi$
$770$	−1.26446e6	−	7.17112e6i	−0.0768562	−	0.435873i
$771$	−8.71030e6	+	1.50867e7i	−0.527712	+	0.914024i
$772$	1.02105e6	+	1.76851e6i	0.0616600	+	0.106798i
$773$	1.37801e7	−	1.15628e7i	0.829473	−	0.696010i	−0.125697	−	0.992069i	$-0.540117\pi$
$773$	1.37801e7	−	1.15628e7i	0.829473	−	0.696010i	0.955170	+	0.296058i	$0.0956723\pi$
$774$	1.07479e7	−	3.91192e6i	0.644870	−	0.234713i
$775$	−1.55418e6	−	565675.i	−0.0929494	−	0.0338308i
$776$	−5.25333e6	−	4.40807e6i	−0.313170	−	0.262781i
$777$	3.67765e6	−	2.08570e7i	0.218534	−	1.23937i
$778$	9.20053e6			0.544959
$779$	−1.21836e7	−	1.15339e7i	−0.719336	−	0.680976i
$780$	8.78242e6			0.516866
$781$	−7.78367e6	+	4.41434e7i	−0.456622	+	2.58963i
$782$	1.63761e7	+	1.37412e7i	0.957620	+	0.803539i
$783$	894387.	+	325530.i	0.0521340	+	0.0189752i
$784$	2.26811e6	−	825525.i	0.131787	−	0.0479667i
$785$	−1.43855e7	+	1.20709e7i	−0.833205	+	0.699142i
$786$	1.54563e7	+	2.67711e7i	0.892378	+	1.54564i
$787$	3.58431e6	−	6.20820e6i	0.206285	−	0.357297i	−0.744256	−	0.667894i	$-0.767196\pi$
$787$	3.58431e6	−	6.20820e6i	0.206285	−	0.357297i	0.950541	+	0.310598i	$0.100529\pi$
$788$	1.15599e6	+	6.55594e6i	0.0663190	+	0.376114i
$789$	3.34945e6	+	1.89957e7i	0.191550	+	1.08633i
$790$	424766.	−	735716.i	0.0242149	−	0.0419414i
$791$	−4.87302e6	−	8.44031e6i	−0.276922	−	0.479642i
$792$	1.67394e7	−	1.40461e7i	0.948261	−	0.795686i
$793$	−2.01565e7	+	7.33635e6i	−1.13823	+	0.414283i
$794$	−4.65833e6	−	1.69550e6i	−0.262228	−	0.0954433i
$795$	1.99797e7	+	1.67649e7i	1.12117	+	0.940772i
$796$	1.49841e6	−	8.49790e6i	0.0838200	−	0.475367i
$797$	3.21068e7			1.79040			0.895202	−	0.445661i	$-0.147031\pi$
$797$	3.21068e7			1.79040			0.895202	+	0.445661i	$0.147031\pi$
$798$	−1.41396e7	−	6.12779e6i	−0.786014	−	0.340641i
$799$	1.18262e7			0.655357
$800$	−333575.	+	1.89180e6i	−0.0184276	+	0.104508i
$801$	6.67543e6	+	5.60135e6i	0.367619	+	0.308469i
$802$	8.92432e6	+	3.24819e6i	0.489936	+	0.178322i
$803$	3.32773e7	−	1.21120e7i	1.82121	−	0.662865i
$804$	4.78460e6	−	4.01476e6i	0.261039	−	0.219038i
$805$	5.57175e6	+	9.65055e6i	0.303041	+	0.524883i
$806$	960830.	−	1.66421e6i	0.0520966	−	0.0902339i
$807$	−2.11713e6	−	1.20068e7i	−0.114436	−	0.649000i
$808$	863095.	+	4.89485e6i	0.0465083	+	0.263761i
$809$	−1.31084e7	+	2.27044e7i	−0.704170	+	1.21966i	0.262821	+	0.964845i	$0.415347\pi$
$809$	−1.31084e7	+	2.27044e7i	−0.704170	+	1.21966i	−0.966990	+	0.254813i	$0.917986\pi$
$810$	8.96203e6	+	1.55227e7i	0.479947	+	0.831293i
$811$	−1.07787e7	+	9.04443e6i	−0.575460	+	0.482868i	−0.883453	−	0.468520i	$-0.844787\pi$
$811$	−1.07787e7	+	9.04443e6i	−0.575460	+	0.482868i	0.307992	+	0.951389i	$0.400343\pi$
$812$	−132135.	+	48093.4i	−0.00703282	+	0.00255974i
$813$	9.65123e6	+	3.51276e6i	0.512102	+	0.186390i
$814$	−1.58945e7	−	1.33371e7i	−0.840786	−	0.705504i
$815$	827732.	−	4.69430e6i	0.0436511	−	0.247558i
$816$	−1.06236e7			−0.558529
$817$	−7.57420e6	+	2.25353e6i	−0.396992	+	0.118116i
$818$	−8.90723e6			−0.465436
$819$	4.62794e6	−	2.62464e7i	0.241090	−	1.36729i
$820$	−4.61844e6	−	3.87533e6i	−0.239861	−	0.201268i
$821$	−2.61609e7	−	9.52179e6i	−1.35455	−	0.493016i	−0.440185	−	0.897907i	$-0.645087\pi$
$821$	−2.61609e7	−	9.52179e6i	−1.35455	−	0.493016i	−0.914365	+	0.404891i	$0.867309\pi$
$822$	−3.96458e7	+	1.44299e7i	−2.04653	+	0.744875i
$823$	−1.69239e7	+	1.42009e7i	−0.870966	+	0.730827i	−0.964301	−	0.264807i	$-0.914692\pi$
$823$	−1.69239e7	+	1.42009e7i	−0.870966	+	0.730827i	0.0933352	+	0.995635i	$0.470247\pi$
$824$	−199610.	−	345735.i	−0.0102415	−	0.0177389i
$825$	−1.60315e7	+	2.77674e7i	−0.820048	+	1.42036i
$826$	2.15712e6	+	1.22336e7i	0.110008	+	0.623886i
$827$	6.11809e6	+	3.46974e7i	0.311066	+	1.76414i	0.593479	+	0.804850i	$0.297754\pi$
$827$	6.11809e6	+	3.46974e7i	0.311066	+	1.76414i	−0.282413	+	0.959293i	$0.591135\pi$
$828$	−1.67203e7	+	2.89603e7i	−0.847554	+	1.46801i
$829$	−1.97359e7	−	3.41836e7i	−0.997404	−	1.72755i	−0.561068	−	0.827770i	$-0.689609\pi$
$829$	−1.97359e7	−	3.41836e7i	−0.997404	−	1.72755i	−0.436336	−	0.899784i	$-0.643724\pi$
$830$	−7.92328e6	+	6.64842e6i	−0.399218	+	0.334983i
$831$	4.83238e7	−	1.75884e7i	2.42750	−	0.883537i
$832$	−2.09735e6	−	763372.i	−0.105042	−	0.0382321i
$833$	−1.05158e7	−	8.82381e6i	−0.525086	−	0.440599i
$834$	5.42850e6	−	3.07865e7i	0.270249	−	1.53266i
$835$	−3.13037e6			−0.155374
$836$	−1.21254e7	+	8.99496e6i	−0.600038	+	0.445127i
$837$	8.20172e6			0.404661
$838$	2.53104e6	−	1.43542e7i	0.124506	−	0.706107i
$839$	−1.46657e7	−	1.23060e7i	−0.719278	−	0.603546i	0.207907	−	0.978149i	$-0.433335\pi$
$839$	−1.46657e7	−	1.23060e7i	−0.719278	−	0.603546i	−0.927186	+	0.374602i	$0.877779\pi$
$840$	−5.20382e6	−	1.89404e6i	−0.254463	−	0.0926169i
$841$	1.92643e7	−	7.01165e6i	0.939213	−	0.341846i
$842$	−9.14470e6	+	7.67331e6i	−0.444518	+	0.372995i
$843$	1.14633e7	+	1.98551e7i	0.555574	+	0.962283i
$844$	2.38561e6	−	4.13199e6i	0.115277	−	0.199666i
$845$	456391.	+	2.58832e6i	0.0219885	+	0.124703i
$846$	3.21242e6	+	1.82185e7i	0.154314	+	0.875159i
$847$	−8.52686e6	+	1.47690e7i	−0.408395	+	0.707361i
$848$	−3.31417e6	−	5.74031e6i	−0.158265	−	0.274123i
$849$	1.95013e7	−	1.63636e7i	0.928528	−	0.779127i
$850$	1.02664e7	−	3.73667e6i	0.487384	−	0.177393i
$851$	2.98377e7	+	1.08600e7i	1.41234	+	0.514051i
$852$	2.61138e7	+	2.19120e7i	1.23245	+	1.03415i
$853$	−3.70233e6	+	2.09970e7i	−0.174222	+	0.988062i	0.764816	+	0.644249i	$0.222830\pi$
$853$	−3.70233e6	+	2.09970e7i	−0.174222	+	0.988062i	−0.939038	+	0.343813i	$0.888281\pi$
$854$	1.35254e7			0.634608
$855$	−1.41631e7	−	2.83210e7i	−0.662585	−	1.32493i
$856$	−9.48394e6			−0.442389
$857$	2.36981e6	−	1.34398e7i	0.110220	−	0.625090i	−0.878786	−	0.477216i	$-0.841646\pi$
$857$	2.36981e6	−	1.34398e7i	0.110220	−	0.625090i	0.989006	−	0.147874i	$-0.0472429\pi$
$858$	−2.85378e7	−	2.39460e7i	−1.32343	−	1.11049i
$859$	−8.40692e6	−	3.05987e6i	−0.388735	−	0.141488i	0.140256	−	0.990115i	$-0.455207\pi$
$859$	−8.40692e6	−	3.05987e6i	−0.388735	−	0.141488i	−0.528991	+	0.848627i	$0.677430\pi$
$860$	−2.66849e6	+	971252.i	−0.123033	+	0.0447802i
$861$	−1.99965e7	+	1.67791e7i	−0.919277	+	0.771365i
$862$	−8.52420e6	−	1.47643e7i	−0.390738	−	0.676778i
$863$	−1.46585e7	+	2.53892e7i	−0.669979	+	1.16044i	0.307930	+	0.951409i	$0.400364\pi$
$863$	−1.46585e7	+	2.53892e7i	−0.669979	+	1.16044i	−0.977909	+	0.209029i	$0.932970\pi$
$864$	−1.65418e6	−	9.38133e6i	−0.0753874	−	0.427543i
$865$	−2.71889e6	−	1.54196e7i	−0.123552	−	0.700700i
$866$	−407648.	+	706067.i	−0.0184710	+	0.0319927i
$867$	9.97540e6	+	1.72779e7i	0.450695	+	0.780626i
$868$	−928224.	+	778872.i	−0.0418171	+	0.0350887i
$869$	−3.38623e6	+	1.23249e6i	−0.152113	+	0.0553647i
$870$	−387385.	−	140997.i	−0.0173518	−	0.00631554i
$871$	−5.71701e6	−	4.79714e6i	−0.255343	−	0.214258i
$872$	150002.	−	850702.i	0.00668044	−	0.0378867i
$873$	−6.10109e7			−2.70939
$874$	1.27288e7	−	1.92816e7i	0.563648	−	0.853817i
$875$	1.51820e7			0.670360
$876$	4.67664e6	−	2.65225e7i	0.205908	−	1.16776i
$877$	2.86079e7	+	2.40049e7i	1.25599	+	1.05390i	0.996097	+	0.0882682i	$0.0281333\pi$
$877$	2.86079e7	+	2.40049e7i	1.25599	+	1.05390i	0.259898	+	0.965636i	$0.416311\pi$
$878$	−3.01935e6	−	1.09895e6i	−0.132183	−	0.0481108i
$879$	−3.91596e7	+	1.42529e7i	−1.70949	+	0.622202i
$880$	−4.15607e6	+	3.48736e6i	−0.180916	+	0.151806i
$881$	2.61672e6	+	4.53229e6i	0.113584	+	0.196733i	0.917213	−	0.398398i	$-0.130434\pi$
$881$	2.61672e6	+	4.53229e6i	0.113584	+	0.196733i	−0.803629	+	0.595131i	$0.797100\pi$
$882$	1.07368e7	−	1.85967e7i	0.464733	−	0.804942i
$883$	−1.32777e6	−	7.53018e6i	−0.0573090	−	0.325015i	0.942653	−	0.333775i	$-0.108323\pi$
$883$	−1.32777e6	−	7.53018e6i	−0.0573090	−	0.325015i	−0.999962	+	0.00875998i	$0.997212\pi$
$884$	2.20427e6	+	1.25010e7i	0.0948711	+	0.538041i
$885$	−1.82095e7	+	3.15397e7i	−0.781518	+	1.35363i
$886$	4.52548e6	+	7.83837e6i	0.193678	+	0.335460i
$887$	2.26934e7	−	1.90420e7i	0.968480	−	0.812651i	−0.0138320	−	0.999904i	$-0.504403\pi$
$887$	2.26934e7	−	1.90420e7i	0.968480	−	0.812651i	0.982312	+	0.187253i	$0.0599586\pi$
$888$	−1.48279e7	+	5.39691e6i	−0.631026	+	0.229675i
$889$	−2.20954e7	−	8.04205e6i	−0.937663	−	0.341281i
$890$	−1.65738e6	−	1.39070e6i	−0.0701368	−	0.0588517i
$891$	1.32026e7	−	7.48754e7i	0.557139	−	3.15969i
$892$	−8.34487e6			−0.351162
$893$	−1.46223e6	−	1.26975e7i	−0.0613602	−	0.532831i
$894$	3.56483e7			1.49175
$895$	1.16742e6	−	6.62075e6i	0.0487156	−	0.276280i
$896$	1.07810e6	+	904636.i	0.0448632	+	0.0376447i
$897$	5.35720e7	+	1.94986e7i	2.22309	+	0.809138i
$898$	2.92408e6	−	1.06428e6i	0.121004	−	0.0440417i
$899$	−69099.2	+	57981.1i	−0.00285150	+	0.00239270i
$900$	8.54515e6	+	1.48006e7i	0.351652	+	0.609080i
$901$	−1.88488e7	+	3.26472e7i	−0.773522	+	1.33978i
$902$	4.44081e6	+	2.51851e7i	0.181738	+	1.03069i
$903$	2.13506e6	+	1.21085e7i	0.0871346	+	0.494165i
$904$	−3.63071e6	+	6.28857e6i	−0.147765	+	0.255936i
$905$	−1.73647e6	−	3.00766e6i	−0.0704768	−	0.122069i
$906$	3.88486e7	−	3.25978e7i	1.57237	−	1.31937i
$907$	−3.51561e7	+	1.27958e7i	−1.41900	+	0.516474i	−0.933758	−	0.357905i	$-0.883491\pi$
$907$	−3.51561e7	+	1.27958e7i	−1.41900	+	0.516474i	−0.485244	+	0.874379i	$0.661269\pi$
$908$	−236217.	−	85975.9i	−0.00950815	−	0.00346068i
$909$	3.38742e7	+	2.84238e7i	1.35975	+	1.14097i
$910$	−1.14903e6	+	6.51645e6i	−0.0459967	+	0.260860i
$911$	3.03078e6			0.120993			0.0604963	−	0.998168i	$-0.480732\pi$
$911$	3.03078e6			0.120993			0.0604963	+	0.998168i	$0.480732\pi$
$912$	1.31354e6	+	1.14063e7i	0.0522943	+	0.454106i
$913$	4.38735e7			1.74191
$914$	4.81177e6	−	2.72889e7i	0.190519	−	1.08049i
$915$	3.03758e7	+	2.54883e7i	1.19943	+	1.00644i
$916$	−1.72783e7	−	6.28880e6i	−0.680398	−	0.247645i
$917$	−2.18860e7	+	7.96585e6i	−0.859494	+	0.312830i
$918$	−4.15028e7	+	3.48250e7i	−1.62544	+	1.36390i
$919$	2.02436e7	+	3.50630e7i	0.790679	+	1.36950i	0.925547	+	0.378632i	$0.123605\pi$
$919$	2.02436e7	+	3.50630e7i	0.790679	+	1.36950i	−0.134869	+	0.990864i	$0.543061\pi$
$920$	4.15131e6	−	7.19028e6i	0.161702	−	0.280076i
$921$	−5.23162e6	−	2.96700e7i	−0.203230	−	1.15257i
$922$	−2.71287e6	−	1.53854e7i	−0.105100	−	0.596049i
$923$	2.03661e7	−	3.52752e7i	0.786872	−	1.36290i
$924$	1.17451e7	+	2.03432e7i	0.452562	+	0.783860i
$925$	1.24311e7	−	1.04309e7i	0.477700	−	0.400838i
$926$	−2.45723e7	+	8.94358e6i	−0.941712	+	0.342755i
$927$	−3.33754e6	−	1.21476e6i	−0.127564	−	0.0464293i
$928$	80256.6	+	67343.3i	0.00305922	+	0.00256699i
$929$	3.20690e6	−	1.81872e7i	0.121912	−	0.691397i	−0.861182	−	0.508296i	$-0.830275\pi$
$929$	3.20690e6	−	1.81872e7i	0.121912	−	0.691397i	0.983094	−	0.183101i	$-0.0586135\pi$
$930$	−3.55240e6			−0.134684
$931$	−8.17370e6	+	1.23816e7i	−0.309061	+	0.468168i
$932$	−4.48929e6			−0.169293
$933$	1.12884e7	−	6.40195e7i	0.424548	−	2.40773i
$934$	8.41721e6	+	7.06288e6i	0.315719	+	0.264920i
$935$	2.89951e7	+	1.05534e7i	1.08467	+	0.394786i
$936$	−1.86594e7	+	6.79146e6i	−0.696157	+	0.253381i
$937$	2.27703e7	−	1.91066e7i	0.847267	−	0.710941i	−0.111919	−	0.993717i	$-0.535700\pi$
$937$	2.27703e7	−	1.91066e7i	0.847267	−	0.710941i	0.959186	+	0.282776i	$0.0912554\pi$
$938$	2.35292e6	+	4.07538e6i	0.0873173	+	0.151238i
$939$	1.84216e6	−	3.19071e6i	0.0681808	−	0.118093i
$940$	−797579.	−	4.52330e6i	−0.0294411	−	0.166969i
$941$	3.88725e6	+	2.20457e7i	0.143109	+	0.811613i	0.968866	+	0.247587i	$0.0796374\pi$
$941$	3.88725e6	+	2.20457e7i	0.143109	+	0.811613i	−0.825756	+	0.564027i	$0.809251\pi$
$942$	3.02897e7	−	5.24633e7i	1.11216	−	1.92632i
$943$	−1.95681e7	−	3.38929e7i	−0.716587	−	1.24117i
$944$	7.09008e6	−	5.94928e6i	0.258953	−	0.217287i
$945$	−2.65384e7	+	9.65917e6i	−0.966706	+	0.351852i
$946$	1.13192e7	+	4.11987e6i	0.411235	+	0.149677i
$947$	−1.72545e7	−	1.44783e7i	−0.625214	−	0.524617i	0.274224	−	0.961666i	$-0.411579\pi$
$947$	−1.72545e7	−	1.44783e7i	−0.625214	−	0.524617i	−0.899438	+	0.437049i	$0.856024\pi$
$948$	−475885.	+	2.69888e6i	−0.0171981	+	0.0975355i
$949$	−3.21801e7			−1.15990
$950$	−5.28134e6	−	1.05608e7i	−0.189861	−	0.379653i
$951$	1.57964e7			0.566377
$952$	1.38991e6	−	7.88258e6i	0.0497044	−	0.281887i
$953$	1.99865e7	+	1.67707e7i	0.712860	+	0.598161i	0.925400	−	0.378991i	$-0.123729\pi$
$953$	1.99865e7	+	1.67707e7i	0.712860	+	0.598161i	−0.212540	+	0.977152i	$0.568173\pi$
$954$	−5.54137e7	−	2.01689e7i	−1.97127	−	0.717484i
$955$	5.33147e6	−	1.94049e6i	0.189164	−	0.0688500i
$956$	3.17808e6	−	2.66673e6i	0.112466	−	0.0943701i
$957$	874336.	+	1.51439e6i	0.0308602	+	0.0534514i
$958$	1.44508e7	−	2.50296e7i	0.508721	−	0.881130i
$959$	−5.51985e6	−	3.13046e7i	−0.193812	−	1.09916i
$960$	716474.	+	4.06332e6i	0.0250912	+	0.142299i
$961$	1.39259e7	−	2.41204e7i	0.486425	−	0.842512i
$962$	9.42729e6	+	1.63286e7i	0.328435	+	0.568866i
$963$	−6.46353e7	+	5.42354e7i	−2.24597	+	1.88459i
$964$	−1.21216e7	+	4.41190e6i	−0.420114	+	0.152909i
$965$	−4.23869e6	−	1.54276e6i	−0.146525	−	0.0533309i
$966$	−2.75377e7	−	2.31069e7i	−0.949479	−	0.796707i
$967$	34886.3	−	197850.i	0.00119974	−	0.00680408i	−0.984202	−	0.177049i	$-0.943345\pi$
$967$	34886.3	−	197850.i	0.00119974	−	0.00680408i	0.985402	+	0.170245i	$0.0544559\pi$
$968$	1.27061e7			0.435837
$969$	5.24452e7	−	3.89055e7i	1.79430	−	1.33107i
$970$	1.51478e7			0.516916
$971$	−6.10858e6	+	3.46435e7i	−0.207918	+	1.17916i	0.684863	+	0.728672i	$0.259862\pi$
$971$	−6.10858e6	+	3.46435e7i	−0.207918	+	1.17916i	−0.892781	+	0.450491i	$0.851249\pi$
$972$	−1.65865e7	−	1.39178e7i	−0.563106	−	0.472502i
$973$	2.21330e7	+	8.05576e6i	0.749477	+	0.272787i
$974$	1.69791e6	−	617988.i	0.0573478	−	0.0208729i
$975$	2.23194e7	−	1.87282e7i	0.751919	−	0.630935i
$976$	−5.03865e6	−	8.72719e6i	−0.169313	−	0.293258i
$977$	−1.11351e7	+	1.92866e7i	−0.373215	+	0.646427i	−0.990058	−	0.140659i	$-0.955078\pi$
$977$	−1.11351e7	+	1.92866e7i	−0.373215	+	0.646427i	0.616843	+	0.787086i	$0.288411\pi$
$978$	2.67019e6	+	1.51434e7i	0.0892678	+	0.506263i
$979$	1.59363e6	+	9.03794e6i	0.0531412	+	0.301379i
$980$	−2.66574e6	+	4.61719e6i	−0.0886650	+	0.153572i
$981$	−3.84258e6	−	6.65554e6i	−0.127482	−	0.220806i
$982$	−2.55896e7	+	2.14723e7i	−0.846809	+	0.710557i
$983$	5.61934e7	−	2.04527e7i	1.85482	−	0.675099i	0.872290	−	0.488988i	$-0.162634\pi$
$983$	5.61934e7	−	2.04527e7i	1.85482	−	0.675099i	0.982529	−	0.186110i	$-0.0595882\pi$
$984$	1.82759e7	+	6.65189e6i	0.601716	+	0.219007i
$985$	−1.12643e7	−	9.45191e6i	−0.369926	−	0.310405i
$986$	103468.	−	586798.i	0.00338934	−	0.0192219i
$987$	−1.98867e7			−0.649785
$988$	1.31495e7	−	3.91234e6i	0.428566	−	0.127510i
$989$	−1.84339e7			−0.599276
$990$	−8.38158e6	+	4.75343e7i	−0.271793	+	1.54141i
$991$	−3.47526e7	−	2.91609e7i	−1.12410	−	0.943228i	−0.125291	−	0.992120i	$-0.539986\pi$
$991$	−3.47526e7	−	2.91609e7i	−1.12410	−	0.943228i	−0.998804	+	0.0488922i	$0.984431\pi$
$992$	848356.	+	308776.i	0.0273715	+	0.00996242i
$993$	−3.99770e7	+	1.45505e7i	−1.28658	+	0.468278i
$994$	−1.96750e7	+	1.65093e7i	−0.631610	+	0.529983i
$995$	9.53013e6	+	1.65067e7i	0.305170	+	0.528569i
$996$	1.66830e7	−	2.88958e7i	0.532875	−	0.922966i
$997$	−7.24390e6	−	4.10822e7i	−0.230799	−	1.30893i	−0.851282	−	0.524708i	$-0.824175\pi$
$997$	−7.24390e6	−	4.10822e7i	−0.230799	−	1.30893i	0.620483	−	0.784220i	$-0.286936\pi$
$998$	5.92381e6	+	3.35956e7i	0.188267	+	1.06772i
$999$	−4.02361e7	+	6.96909e7i	−1.27556	+	2.20934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.17.1	yes	30
19.3	odd	18		722.6.a.q.1.14		15
19.9	even	9	inner	38.6.e.b.9.1	✓	30
19.16	even	9		722.6.a.r.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.1	✓	30	19.9	even	9	inner
38.6.e.b.17.1	yes	30	1.1	even	1	trivial
722.6.a.q.1.14		15	19.3	odd	18
722.6.a.r.1.2		15	19.16	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694593 - 3.93923i) q^{2} +(-21.8341 - 18.3210i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.2104 - 12.0876i) q^{5} +(-87.3364 + 73.2839i) q^{6} +(-42.9494 - 74.3905i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(98.8729 + 560.736i) q^{9} +O(q^{10})\)	\(q+(0.694593 - 3.93923i) q^{2} +(-21.8341 - 18.3210i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.2104 - 12.0876i) q^{5} +(-87.3364 + 73.2839i) q^{6} +(-42.9494 - 74.3905i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(98.8729 + 560.736i) q^{9} +(-24.5482 - 139.220i) q^{10} +(-299.827 + 519.315i) q^{11} +(228.019 + 394.941i) q^{12} +(417.425 - 350.261i) q^{13} +(-322.874 + 117.516i) q^{14} +(-946.577 - 344.526i) q^{15} +(196.107 + 164.554i) q^{16} +(252.825 - 1433.84i) q^{17} +2277.54 q^{18} +(-1570.74 - 94.1673i) q^{19} -565.469 q^{20} +(-425.146 + 2411.12i) q^{21} +(1837.44 + 1541.80i) q^{22} +(-3449.31 - 1255.45i) q^{23} +(1714.14 - 623.897i) q^{24} +(-1437.07 + 1205.84i) q^{25} +(-1089.82 - 1887.62i) q^{26} +(4651.39 - 8056.45i) q^{27} +(238.658 + 1353.50i) q^{28} +(17.7663 + 100.758i) q^{29} +(-2014.65 + 3489.48i) q^{30} +(440.821 + 763.524i) q^{31} +(784.430 - 658.215i) q^{32} +(16060.8 - 5845.65i) q^{33} +(-5472.63 - 1991.87i) q^{34} +(-2325.57 - 1951.38i) q^{35} +(1581.97 - 8971.77i) q^{36} -8650.33 q^{37} +(-1461.97 + 6122.11i) q^{38} -15531.2 q^{39} +(-392.771 + 2227.51i) q^{40} +(8167.44 + 6853.30i) q^{41} +(9202.67 + 3349.50i) q^{42} +(4719.08 - 1717.61i) q^{43} +(7349.78 - 6167.19i) q^{44} +(10061.6 + 17427.1i) q^{45} +(-7341.35 + 12715.6i) q^{46} +(1410.47 + 7999.19i) q^{47} +(-1267.04 - 7185.76i) q^{48} +(4714.21 - 8165.24i) q^{49} +(3751.91 + 6498.50i) q^{50} +(-31789.6 + 26674.7i) q^{51} +(-8192.76 + 2981.92i) q^{52} +(-24330.5 - 8855.56i) q^{53} +(-28505.4 - 23918.9i) q^{54} +(-3680.10 + 20870.9i) q^{55} +5497.52 q^{56} +(32570.5 + 30833.6i) q^{57} +409.248 q^{58} +(6278.09 - 35604.8i) q^{59} +(12346.5 + 10359.9i) q^{60} +(-36990.5 - 13463.4i) q^{61} +(3313.89 - 1206.16i) q^{62} +(37466.9 - 31438.4i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(9629.04 - 16678.0i) q^{65} +(-11871.7 - 67327.6i) q^{66} +(-2378.27 - 13487.8i) q^{67} +(-11647.7 + 20174.4i) q^{68} +(52311.5 + 90606.2i) q^{69} +(-9302.28 + 7805.54i) q^{70} +(70242.5 - 25566.2i) q^{71} +(-34243.1 - 12463.5i) q^{72} +(-45239.4 - 37960.3i) q^{73} +(-6008.46 + 34075.6i) q^{74} +53469.2 q^{75} +(23100.9 + 10011.4i) q^{76} +51509.4 q^{77} +(-10787.9 + 61181.1i) q^{78} +(4603.46 + 3862.77i) q^{79} +(8501.87 + 3094.43i) q^{80} +(-119144. + 43365.0i) q^{81} +(32669.8 - 27413.2i) q^{82} +(-36582.4 - 63362.6i) q^{83} +(19586.5 - 33924.9i) q^{84} +(-8935.30 - 50674.6i) q^{85} +(-3488.20 - 19782.6i) q^{86} +(1458.07 - 2525.45i) q^{87} +(-19188.9 - 33236.2i) q^{88} +(11723.9 - 9837.52i) q^{89} +(75638.2 - 27530.1i) q^{90} +(-43984.2 - 16008.9i) q^{91} +(44990.4 + 37751.5i) q^{92} +(4363.59 - 24747.1i) q^{93} +32490.4 q^{94} +(-53303.3 + 15859.2i) q^{95} -29186.4 q^{96} +(-18606.8 + 105524. i) q^{97} +(-28890.3 - 24241.9i) q^{98} +(-320843. - 116777. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Introduction

L-functions

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