LMFDB - Embedded newform 198.6.e.b.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, degree $2$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Character	$\chi$	$=$	198.133
Dual form			198.6.e.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-15.1654 - 3.60721i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.5761 + 40.8350i) q^{5} +(-42.8265 + 45.3199i) q^{6} +(19.3963 - 33.5953i) q^{7} -64.0000 q^{8} +(216.976 + 109.409i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-15.1654 - 3.60721i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.5761 + 40.8350i) q^{5} +(-42.8265 + 45.3199i) q^{6} +(19.3963 - 33.5953i) q^{7} -64.0000 q^{8} +(216.976 + 109.409i) q^{9} +188.609 q^{10} +(-60.5000 + 104.789i) q^{11} +(71.3398 + 238.995i) q^{12} +(-285.414 - 494.352i) q^{13} +(-77.5851 - 134.381i) q^{14} +(-210.239 - 704.321i) q^{15} +(-128.000 + 221.703i) q^{16} +303.714 q^{17} +(812.957 - 532.808i) q^{18} +2037.81 q^{19} +(377.217 - 653.359i) q^{20} +(-415.337 + 439.519i) q^{21} +(242.000 + 419.156i) q^{22} +(-2185.73 - 3785.80i) q^{23} +(970.583 + 230.862i) q^{24} +(450.838 - 780.874i) q^{25} -2283.32 q^{26} +(-2895.86 - 2441.91i) q^{27} -620.681 q^{28} +(-3824.16 + 6623.63i) q^{29} +(-2860.32 - 680.352i) q^{30} +(-1517.63 - 2628.61i) q^{31} +(512.000 + 886.810i) q^{32} +(1295.50 - 1370.93i) q^{33} +(607.429 - 1052.10i) q^{34} +1829.15 q^{35} +(-219.787 - 3881.78i) q^{36} -6001.75 q^{37} +(4075.62 - 7059.19i) q^{38} +(2545.18 + 8526.58i) q^{39} +(-1508.87 - 2613.44i) q^{40} +(-9828.23 - 17023.0i) q^{41} +(691.864 + 2317.81i) q^{42} +(-5324.35 + 9222.04i) q^{43} +1936.00 q^{44} +(647.715 + 11439.6i) q^{45} -17485.9 q^{46} +(-10083.5 + 17465.1i) q^{47} +(2740.89 - 2900.47i) q^{48} +(7651.07 + 13252.0i) q^{49} +(-1803.35 - 3123.50i) q^{50} +(-4605.94 - 1095.56i) q^{51} +(-4566.63 + 7909.64i) q^{52} -35104.4 q^{53} +(-14250.7 + 5147.71i) q^{54} -5705.41 q^{55} +(-1241.36 + 2150.10i) q^{56} +(-30904.1 - 7350.82i) q^{57} +(15296.6 + 26494.5i) q^{58} +(-3320.08 - 5750.55i) q^{59} +(-8077.44 + 8547.72i) q^{60} +(381.943 - 661.545i) q^{61} -12141.0 q^{62} +(7884.17 - 5167.25i) q^{63} +4096.00 q^{64} +(13457.9 - 23309.8i) q^{65} +(-2158.03 - 7229.60i) q^{66} +(-34425.0 - 59625.9i) q^{67} +(-2429.71 - 4208.39i) q^{68} +(19491.2 + 65297.4i) q^{69} +(3658.30 - 6336.37i) q^{70} +81765.2 q^{71} +(-13886.5 - 7002.20i) q^{72} -49437.1 q^{73} +(-12003.5 + 20790.7i) q^{74} +(-9653.90 + 10216.0i) q^{75} +(-16302.5 - 28236.7i) q^{76} +(2346.95 + 4065.04i) q^{77} +(34627.3 + 8236.41i) q^{78} +(29221.5 - 50613.2i) q^{79} -12070.9 q^{80} +(35108.2 + 47478.4i) q^{81} -78625.8 q^{82} +(17362.9 - 30073.5i) q^{83} +(9412.85 + 2238.93i) q^{84} +(7160.39 + 12402.2i) q^{85} +(21297.4 + 36888.2i) q^{86} +(81887.5 - 86655.2i) q^{87} +(3872.00 - 6706.50i) q^{88} -73257.9 q^{89} +(40923.5 + 20635.5i) q^{90} -22143.9 q^{91} +(-34971.7 + 60572.8i) q^{92} +(13533.4 + 45338.2i) q^{93} +(40333.9 + 69860.4i) q^{94} +(48043.6 + 83213.9i) q^{95} +(-4565.75 - 15295.7i) q^{96} +(31282.5 - 54182.9i) q^{97} +61208.5 q^{98} +(-24592.0 + 16117.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) $ 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	−15.1654	−	3.60721i	−0.972858	−	0.231403i
$3$	−15.1654	−	3.60721i	−0.972858	−	0.231403i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	23.5761	+	40.8350i	0.421742	+	0.730478i	0.996110	−	0.0881191i	$-0.0280856\pi$
$5$	23.5761	+	40.8350i	0.421742	+	0.730478i	−0.574368	+	0.818597i	$0.694752\pi$
$6$	−42.8265	+	45.3199i	−0.485662	+	0.513938i
$7$	19.3963	−	33.5953i	0.149614	−	0.259140i	−0.781471	−	0.623942i	$-0.785530\pi$
$7$	19.3963	−	33.5953i	0.149614	−	0.259140i	0.931085	+	0.364802i	$0.118863\pi$
$8$	−64.0000			−0.353553
$9$	216.976	+	109.409i	0.892905	+	0.450244i
$10$	188.609			0.596433
$11$	−60.5000	+	104.789i	−0.150756	+	0.261116i
$11$	−60.5000	+	104.789i	−0.150756	+	0.261116i
$12$	71.3398	+	238.995i	0.143014	+	0.479111i
$13$	−285.414	−	494.352i	−0.468401	−	0.811294i	0.530947	−	0.847405i	$-0.321836\pi$
$13$	−285.414	−	494.352i	−0.468401	−	0.811294i	−0.999348	+	0.0361113i	$0.988503\pi$
$14$	−77.5851	−	134.381i	−0.105793	−	0.183239i
$15$	−210.239	−	704.321i	−0.241260	−	0.808243i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	303.714			0.254884			0.127442	−	0.991846i	$-0.459323\pi$
$17$	303.714			0.254884			0.127442	+	0.991846i	$0.459323\pi$
$18$	812.957	−	532.808i	0.591407	−	0.387605i
$19$	2037.81			1.29503			0.647515	−	0.762052i	$-0.275808\pi$
$19$	2037.81			1.29503			0.647515	+	0.762052i	$0.275808\pi$
$20$	377.217	−	653.359i	0.210871	−	0.365239i
$21$	−415.337	+	439.519i	−0.205519	+	0.217485i
$22$	242.000	+	419.156i	0.106600	+	0.184637i
$23$	−2185.73	−	3785.80i	−0.861544	−	1.49224i	−0.870438	−	0.492278i	$-0.836164\pi$
$23$	−2185.73	−	3785.80i	−0.861544	−	1.49224i	0.00889397	−	0.999960i	$-0.497169\pi$
$24$	970.583	+	230.862i	0.343957	+	0.0818133i
$25$	450.838	−	780.874i	0.144268	−	0.249880i
$26$	−2283.32			−0.662419
$27$	−2895.86	−	2441.91i	−0.764482	−	0.644645i
$28$	−620.681			−0.149614
$29$	−3824.16	+	6623.63i	−0.844385	+	1.46252i	0.0417689	+	0.999127i	$0.486701\pi$
$29$	−3824.16	+	6623.63i	−0.844385	+	1.46252i	−0.886154	+	0.463391i	$0.846633\pi$
$30$	−2860.32	−	680.352i	−0.580244	−	0.138016i
$31$	−1517.63	−	2628.61i	−0.283636	−	0.491272i	0.688641	−	0.725102i	$-0.258207\pi$
$31$	−1517.63	−	2628.61i	−0.283636	−	0.491272i	−0.972278	+	0.233830i	$0.924874\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	1295.50	−	1370.93i	0.207087	−	0.219144i
$34$	607.429	−	1052.10i	0.0901152	−	0.156084i
$35$	1829.15			0.252394
$36$	−219.787	−	3881.78i	−0.0282648	−	0.499200i
$37$	−6001.75			−0.720732			−0.360366	−	0.932811i	$-0.617348\pi$
$37$	−6001.75			−0.720732			−0.360366	+	0.932811i	$0.617348\pi$
$38$	4075.62	−	7059.19i	0.457862	−	0.793041i
$39$	2545.18	+	8526.58i	0.267952	+	0.897663i
$40$	−1508.87	−	2613.44i	−0.149108	−	0.258263i
$41$	−9828.23	−	17023.0i	−0.913094	−	1.58153i	−0.809668	−	0.586888i	$-0.800353\pi$
$41$	−9828.23	−	17023.0i	−0.913094	−	1.58153i	−0.103426	−	0.994637i	$-0.532981\pi$
$42$	691.864	+	2317.81i	0.0605198	+	0.202747i
$43$	−5324.35	+	9222.04i	−0.439132	+	0.760600i	−0.997623	−	0.0689114i	$-0.978047\pi$
$43$	−5324.35	+	9222.04i	−0.439132	+	0.760600i	0.558490	+	0.829511i	$0.311381\pi$
$44$	1936.00			0.150756
$45$	647.715	+	11439.6i	0.0476818	+	0.842134i
$46$	−17485.9			−1.21841
$47$	−10083.5	+	17465.1i	−0.665834	+	1.15326i	0.313225	+	0.949679i	$0.398591\pi$
$47$	−10083.5	+	17465.1i	−0.665834	+	1.15326i	−0.979059	+	0.203579i	$0.934743\pi$
$48$	2740.89	−	2900.47i	0.171707	−	0.181705i
$49$	7651.07	+	13252.0i	0.455231	+	0.788483i
$50$	−1803.35	−	3123.50i	−0.102013	−	0.176692i
$51$	−4605.94	−	1095.56i	−0.247966	−	0.0589810i
$52$	−4566.63	+	7909.64i	−0.234200	+	0.405647i
$53$	−35104.4			−1.71661			−0.858306	−	0.513138i	$-0.828483\pi$
$53$	−35104.4			−1.71661			−0.858306	+	0.513138i	$0.828483\pi$
$54$	−14250.7	+	5147.71i	−0.665048	+	0.240232i
$55$	−5705.41			−0.254320
$56$	−1241.36	+	2150.10i	−0.0528967	+	0.0916197i
$57$	−30904.1	−	7350.82i	−1.25988	−	0.299674i
$58$	15296.6	+	26494.5i	0.597070	+	1.03416i
$59$	−3320.08	−	5750.55i	−0.124171	−	0.215070i	0.797238	−	0.603665i	$-0.206294\pi$
$59$	−3320.08	−	5750.55i	−0.124171	−	0.215070i	−0.921408	+	0.388596i	$0.872960\pi$
$60$	−8077.44	+	8547.72i	−0.289665	+	0.306529i
$61$	381.943	−	661.545i	0.0131424	−	0.0227633i	−0.859379	−	0.511338i	$-0.829150\pi$
$61$	381.943	−	661.545i	0.0131424	−	0.0227633i	0.872522	+	0.488575i	$0.162483\pi$
$62$	−12141.0			−0.401122
$63$	7884.17	−	5167.25i	0.250268	−	0.164024i
$64$	4096.00			0.125000
$65$	13457.9	−	23309.8i	0.395088	−	0.684313i
$66$	−2158.03	−	7229.60i	−0.0609814	−	0.204293i
$67$	−34425.0	−	59625.9i	−0.936887	−	1.62274i	−0.771234	−	0.636552i	$-0.780360\pi$
$67$	−34425.0	−	59625.9i	−0.936887	−	1.62274i	−0.165653	−	0.986184i	$-0.552973\pi$
$68$	−2429.71	−	4208.39i	−0.0637211	−	0.110368i
$69$	19491.2	+	65297.4i	0.492852	+	1.65110i
$70$	3658.30	−	6336.37i	0.0892349	−	0.154559i
$71$	81765.2			1.92496			0.962482	−	0.271344i	$-0.0874682\pi$
$71$	81765.2			1.92496			0.962482	+	0.271344i	$0.0874682\pi$
$72$	−13886.5	−	7002.20i	−0.315690	−	0.159185i
$73$	−49437.1			−1.08579			−0.542895	−	0.839801i	$-0.682672\pi$
$73$	−49437.1			−1.08579			−0.542895	+	0.839801i	$0.682672\pi$
$74$	−12003.5	+	20790.7i	−0.254817	+	0.441356i
$75$	−9653.90	+	10216.0i	−0.198175	+	0.209713i
$76$	−16302.5	−	28236.7i	−0.323758	−	0.560765i
$77$	2346.95	+	4065.04i	0.0451104	+	0.0781336i
$78$	34627.3	+	8236.41i	0.644439	+	0.153286i
$79$	29221.5	−	50613.2i	0.526787	−	0.912422i	−0.472726	−	0.881210i	$-0.656730\pi$
$79$	29221.5	−	50613.2i	0.526787	−	0.912422i	0.999513	−	0.0312123i	$-0.00993679\pi$
$80$	−12070.9			−0.210871
$81$	35108.2	+	47478.4i	0.594560	+	0.804051i
$82$	−78625.8			−1.29131
$83$	17362.9	−	30073.5i	0.276648	−	0.479168i	−0.693902	−	0.720070i	$-0.744110\pi$
$83$	17362.9	−	30073.5i	0.276648	−	0.479168i	0.970550	+	0.240902i	$0.0774431\pi$
$84$	9412.85	+	2238.93i	0.145554	+	0.0346212i
$85$	7160.39	+	12402.2i	0.107495	+	0.186187i
$86$	21297.4	+	36888.2i	0.310513	+	0.537825i
$87$	81887.5	−	86655.2i	1.15990	−	1.22743i
$88$	3872.00	−	6706.50i	0.0533002	−	0.0923186i
$89$	−73257.9			−0.980346			−0.490173	−	0.871625i	$-0.663066\pi$
$89$	−73257.9			−0.980346			−0.490173	+	0.871625i	$0.663066\pi$
$90$	40923.5	+	20635.5i	0.532558	+	0.268540i
$91$	−22143.9			−0.280318
$92$	−34971.7	+	60572.8i	−0.430772	+	0.746119i
$93$	13533.4	+	45338.2i	0.162256	+	0.543572i
$94$	40333.9	+	69860.4i	0.470816	+	0.815477i
$95$	48043.6	+	83213.9i	0.546168	+	0.945991i
$96$	−4565.75	−	15295.7i	−0.0505631	−	0.169391i
$97$	31282.5	−	54182.9i	0.337577	−	0.584700i	−0.646400	−	0.762999i	$-0.723726\pi$
$97$	31282.5	−	54182.9i	0.337577	−	0.584700i	0.983976	+	0.178299i	$0.0570595\pi$
$98$	61208.5			0.643794
$99$	−24592.0	+	16117.4i	−0.252177	+	0.165275i
$100$	−14426.8			−0.144268
$101$	26612.5	−	46094.2i	0.259587	−	0.449617i	−0.706545	−	0.707669i	$-0.749747\pi$
$101$	26612.5	−	46094.2i	0.259587	−	0.449617i	0.966131	+	0.258051i	$0.0830804\pi$
$102$	−13007.0	+	13764.3i	−0.123788	+	0.130995i
$103$	−103803.	−	179791.i	−0.964085	−	1.66984i	−0.712055	−	0.702124i	$-0.752235\pi$
$103$	−103803.	−	179791.i	−0.964085	−	1.66984i	−0.252030	−	0.967719i	$-0.581098\pi$
$104$	18266.5	+	31638.5i	0.165605	+	0.286836i
$105$	−27739.7	−	6598.14i	−0.245544	−	0.0584048i
$106$	−70208.9	+	121605.i	−0.606914	+	1.05121i
$107$	−86468.6			−0.730128			−0.365064	−	0.930982i	$-0.618953\pi$
$107$	−86468.6			−0.730128			−0.365064	+	0.930982i	$0.618953\pi$
$108$	−10669.3	+	59661.4i	−0.0880188	+	0.492192i
$109$	−128712.			−1.03765			−0.518826	−	0.854880i	$-0.673631\pi$
$109$	−128712.			−1.03765			−0.518826	+	0.854880i	$0.673631\pi$
$110$	−11410.8	+	19764.1i	−0.0899156	+	0.155738i
$111$	91018.7	+	21649.6i	0.701170	+	0.166779i
$112$	4965.45	+	8600.41i	0.0374036	+	0.0647849i
$113$	−21697.6	−	37581.4i	−0.159851	−	0.276871i	0.774964	−	0.632006i	$-0.217768\pi$
$113$	−21697.6	−	37581.4i	−0.159851	−	0.276871i	−0.934815	+	0.355135i	$0.884435\pi$
$114$	−87272.3	+	92353.4i	−0.628947	+	0.665566i
$115$	103062.	−	178509.i	0.726698	−	1.25868i
$116$	122373.			0.844385
$117$	−7841.31	−	138490.i	−0.0529570	−	0.935303i
$118$	−26560.6			−0.175604
$119$	5890.93	−	10203.4i	0.0381343	−	0.0660506i
$120$	13455.3	+	45076.5i	0.0852983	+	0.285757i
$121$	−7320.50	−	12679.5i	−0.0454545	−	0.0787296i
$122$	−1527.77	−	2646.18i	−0.00929307	−	0.0160961i
$123$	87643.0	+	293612.i	0.522341	+	1.74989i
$124$	−24282.1	+	42057.8i	−0.141818	+	0.245636i
$125$	189866.			1.08686
$126$	−2131.53	−	37646.1i	−0.0119609	−	0.211248i
$127$	−6405.24			−0.0352392			−0.0176196	−	0.999845i	$-0.505609\pi$
$127$	−6405.24			−0.0352392			−0.0176196	+	0.999845i	$0.505609\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	114012.	−	120650.i	0.603218	−	0.638339i
$130$	−53831.6	−	93239.1i	−0.279369	−	0.483882i
$131$	−145910.	−	252724.i	−0.742861	−	1.28667i	−0.951188	−	0.308613i	$-0.900135\pi$
$131$	−145910.	−	252724.i	−0.742861	−	1.28667i	0.208327	−	0.978059i	$-0.433198\pi$
$132$	−29360.1	−	6983.57i	−0.146664	−	0.0348853i
$133$	39526.0	−	68461.0i	0.193755	−	0.335594i
$134$	−275400.			−1.32496
$135$	31442.4	−	175823.i	0.148485	−	0.830311i
$136$	−19437.7			−0.0901152
$137$	−120284.	+	208338.i	−0.547529	+	0.948347i	0.450914	+	0.892567i	$0.351098\pi$
$137$	−120284.	+	208338.i	−0.547529	+	0.948347i	−0.998443	+	0.0557802i	$0.982235\pi$
$138$	265179.	+	63075.3i	1.18534	+	0.281943i
$139$	33935.1	+	58777.2i	0.148974	+	0.258031i	0.930849	−	0.365405i	$-0.119069\pi$
$139$	33935.1	+	58777.2i	0.148974	+	0.258031i	−0.781874	+	0.623436i	$0.785736\pi$
$140$	−14633.2	−	25345.5i	−0.0630986	−	0.109290i
$141$	215920.	−	228491.i	0.914629	−	0.967881i
$142$	163530.	−	283243.i	0.680578	−	1.17880i
$143$	69070.3			0.282456
$144$	−52029.3	+	34099.7i	−0.209094	+	0.137039i
$145$	−360634.			−1.42445
$146$	−98874.2	+	171255.i	−0.383885	+	0.664908i
$147$	−68228.2	−	228571.i	−0.260418	−	0.872424i
$148$	48014.0	+	83162.7i	0.180183	+	0.312086i
$149$	81754.8	+	141603.i	0.301681	+	0.522526i	0.976517	−	0.215441i	$-0.0691190\pi$
$149$	81754.8	+	141603.i	0.301681	+	0.522526i	−0.674836	+	0.737968i	$0.735786\pi$
$150$	16081.3	+	53874.0i	0.0583572	+	0.195502i
$151$	147292.	−	255118.i	0.525700	−	0.910539i	−0.473852	−	0.880605i	$-0.657137\pi$
$151$	147292.	−	255118.i	0.525700	−	0.910539i	0.999552	−	0.0299346i	$-0.00952991\pi$
$152$	−130420.			−0.457862
$153$	65898.7	+	33229.2i	0.227588	+	0.114760i
$154$	18775.6			0.0637958
$155$	71559.5	−	123945.i	0.239242	−	0.414380i
$156$	97786.3	−	103480.i	0.321712	−	0.340442i
$157$	74524.4	+	129080.i	0.241295	+	0.417936i	0.961084	−	0.276258i	$-0.0890944\pi$
$157$	74524.4	+	129080.i	0.241295	+	0.417936i	−0.719788	+	0.694194i	$0.755761\pi$
$158$	−116886.	−	202453.i	−0.372495	−	0.645180i
$159$	532371.	+	126629.i	1.67002	+	0.397229i
$160$	−24141.9	+	41815.0i	−0.0745541	+	0.129131i
$161$	−169580.			−0.515598
$162$	234686.	−	26661.5i	0.702588	−	0.0798172i
$163$	258213.			0.761219			0.380610	−	0.924736i	$-0.375714\pi$
$163$	258213.			0.761219			0.380610	+	0.924736i	$0.375714\pi$
$164$	−157252.	+	272368.i	−0.456547	+	0.790763i
$165$	86524.6	+	20580.6i	0.247417	+	0.0588503i
$166$	−69451.7	−	120294.i	−0.195620	−	0.338823i
$167$	339386.	+	587835.i	0.941680	+	1.63104i	0.762266	+	0.647264i	$0.224087\pi$
$167$	339386.	+	587835.i	0.941680	+	1.63104i	0.179414	+	0.983774i	$0.442580\pi$
$168$	26581.6	−	28129.2i	0.0726620	−	0.0768925i
$169$	22723.8	−	39358.7i	0.0612017	−	0.106004i
$170$	57283.1			0.152021
$171$	442156.	+	222956.i	1.15634	+	0.583080i
$172$	170379.			0.439132
$173$	−188510.	+	326510.i	−0.478873	+	0.829432i	−0.999707	−	0.0242262i	$-0.992288\pi$
$173$	−188510.	+	326510.i	−0.478873	+	0.829432i	0.520834	+	0.853658i	$0.325621\pi$
$174$	−136407.	−	456977.i	−0.341558	−	1.14425i
$175$	−17489.2	−	30292.1i	−0.0431692	−	0.0747712i
$176$	−15488.0	−	26826.0i	−0.0376889	−	0.0652791i
$177$	29606.7	+	99185.3i	0.0710325	+	0.237966i
$178$	−146516.	+	253773.i	−0.346605	+	0.600337i
$179$	318546.			0.743088			0.371544	−	0.928415i	$-0.378829\pi$
$179$	318546.			0.743088			0.371544	+	0.928415i	$0.378829\pi$
$180$	153331.	−	100492.i	0.352734	−	0.231180i
$181$	52523.6			0.119168			0.0595838	−	0.998223i	$-0.481023\pi$
$181$	52523.6			0.119168			0.0595838	+	0.998223i	$0.481023\pi$
$182$	−44287.8	+	76708.8i	−0.0991073	+	0.171659i
$183$	−8178.64	+	8654.82i	−0.0180532	+	0.0191043i
$184$	139887.	+	242291.i	0.304602	+	0.527586i
$185$	−141498.	−	245081.i	−0.303963	−	0.526479i
$186$	184123.	+	43795.3i	0.390235	+	0.0928208i
$187$	−18374.7	+	31825.9i	−0.0384252	+	0.0665545i
$188$	322671.			0.665834
$189$	−138206.	+	49923.3i	−0.281431	+	0.101660i
$190$	384349.			0.772399
$191$	−161844.	+	280322.i	−0.321006	+	0.555999i	−0.980696	−	0.195539i	$-0.937354\pi$
$191$	−161844.	+	280322.i	−0.321006	+	0.555999i	0.659690	+	0.751538i	$0.270688\pi$
$192$	−62117.3	−	14775.2i	−0.121607	−	0.0289254i
$193$	−444091.	−	769189.i	−0.858182	−	1.48641i	−0.873662	−	0.486534i	$-0.838261\pi$
$193$	−444091.	−	769189.i	−0.858182	−	1.48641i	0.0154802	−	0.999880i	$-0.495072\pi$
$194$	−125130.	−	216732.i	−0.238703	−	0.413445i
$195$	−288177.	+	304955.i	−0.542716	+	0.574314i
$196$	122417.	−	212033.i	0.227616	−	0.394242i
$197$	442133.			0.811685			0.405843	−	0.913943i	$-0.366978\pi$
$197$	442133.			0.811685			0.405843	+	0.913943i	$0.366978\pi$
$198$	6648.56	+	117424.i	0.0120522	+	0.212860i
$199$	58151.9			0.104095			0.0520476	−	0.998645i	$-0.483425\pi$
$199$	58151.9			0.104095			0.0520476	+	0.998645i	$0.483425\pi$
$200$	−28853.6	+	49975.9i	−0.0510065	+	0.0883458i
$201$	306984.	+	1.02843e6i	0.535952	+	1.79549i
$202$	−106450.	−	184377.i	−0.183555	−	0.317927i
$203$	148349.	+	256948.i	0.252664	+	0.437627i
$204$	21666.9	+	72586.2i	0.0364520	+	0.122118i
$205$	463422.	−	802670.i	0.770180	−	1.33399i
$206$	−830421.			−1.36342
$207$	−60049.5	−	1.06057e6i	−0.0974056	−	1.72033i
$208$	146132.			0.234200
$209$	−123288.	+	213540.i	−0.195233	+	0.338154i
$210$	−78336.1	+	82897.0i	−0.122578	+	0.129715i
$211$	185746.	+	321722.i	0.287220	+	0.497479i	0.973145	−	0.230193i	$-0.0739357\pi$
$211$	185746.	+	321722.i	0.287220	+	0.497479i	−0.685925	+	0.727672i	$0.740602\pi$
$212$	280835.	+	486421.i	0.429153	+	0.743315i
$213$	−1.24000e6	−	294945.i	−1.87272	−	0.445442i
$214$	−172937.	+	299536.i	−0.258139	+	0.447110i
$215$	−502109.			−0.740801
$216$	185335.	+	156282.i	0.270285	+	0.227916i
$217$	−117745.			−0.169744
$218$	−257423.	+	445870.i	−0.366865	+	0.635429i
$219$	749731.	+	178330.i	1.05632	+	0.251255i
$220$	45643.3	+	79056.5i	0.0635799	+	0.110124i
$221$	−86684.4	−	150142.i	−0.119388	−	0.206786i
$222$	257034.	−	271999.i	0.350032	−	0.370412i
$223$	44811.4	−	77615.7i	0.0603430	−	0.104517i	−0.834276	−	0.551347i	$-0.814114\pi$
$223$	44811.4	−	77615.7i	0.0603430	−	0.104517i	0.894619	+	0.446830i	$0.147447\pi$
$224$	39723.6			0.0528967
$225$	183256.	−	120105.i	0.241325	−	0.158163i
$226$	−173581.			−0.226064
$227$	−290919.	+	503887.i	−0.374721	+	0.649035i	−0.990285	−	0.139051i	$-0.955595\pi$
$227$	−290919.	+	503887.i	−0.374721	+	0.649035i	0.615565	+	0.788086i	$0.288928\pi$
$228$	145377.	+	487027.i	0.185208	+	0.620463i
$229$	143065.	+	247795.i	0.180278	+	0.312251i	0.941975	−	0.335682i	$-0.108967\pi$
$229$	143065.	+	247795.i	0.180278	+	0.312251i	−0.761697	+	0.647933i	$0.775633\pi$
$230$	−412248.	−	714034.i	−0.513853	−	0.890020i
$231$	−20928.9	−	70113.7i	−0.0258057	−	0.0864516i
$232$	244746.	−	423912.i	0.298535	−	0.517078i
$233$	−1.07083e6			−1.29220			−0.646099	−	0.763253i	$-0.723601\pi$
$233$	−1.07083e6			−1.29220			−0.646099	+	0.763253i	$0.723601\pi$
$234$	−495425.	−	249816.i	−0.591477	−	0.298250i
$235$	−950916.			−1.12324
$236$	−53121.3	+	92008.7i	−0.0620853	+	0.107535i
$237$	−625727.	+	662158.i	−0.723626	+	0.765757i
$238$	−23563.7	−	40813.5i	−0.0269651	−	0.0467048i
$239$	−54316.6	−	94079.1i	−0.0615089	−	0.106536i	0.833631	−	0.552322i	$-0.186258\pi$
$239$	−54316.6	−	94079.1i	−0.0615089	−	0.106536i	−0.895140	+	0.445785i	$0.852925\pi$
$240$	183060.	+	43542.5i	0.205147	+	0.0487961i
$241$	260498.	−	451195.i	0.288909	−	0.500405i	−0.684640	−	0.728881i	$-0.740041\pi$
$241$	260498.	−	451195.i	0.288909	−	0.500405i	0.973550	+	0.228476i	$0.0733741\pi$
$242$	−58564.0			−0.0642824
$243$	−361163.	−	846670.i	−0.392363	−	0.919811i
$244$	−12222.2			−0.0131424
$245$	−360764.	+	624862.i	−0.383980	+	0.665072i
$246$	1.19239e6	+	283620.i	1.25626	+	0.298813i
$247$	−581621.	−	1.00740e6i	−0.606593	−	1.05065i
$248$	97128.3	+	168231.i	0.100280	+	0.173691i
$249$	−371796.	+	393443.i	−0.380020	+	0.402146i
$250$	379733.	−	657716.i	0.384263	−	0.665562i
$251$	1.73320e6			1.73646			0.868231	−	0.496161i	$-0.165257\pi$
$251$	1.73320e6			1.73646			0.868231	+	0.496161i	$0.165257\pi$
$252$	−134673.	−	67908.3i	−0.133591	−	0.0673630i
$253$	528947.			0.519531
$254$	−12810.5	+	22188.4i	−0.0124589	+	0.0215795i
$255$	−63852.6	−	213912.i	−0.0614934	−	0.206009i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	315851.	+	547070.i	0.298297	+	0.516666i	0.975747	−	0.218903i	$-0.0702480\pi$
$257$	315851.	+	547070.i	0.298297	+	0.516666i	−0.677449	+	0.735570i	$0.736915\pi$
$258$	−189919.	−	636247.i	−0.177631	−	0.595081i
$259$	−116412.	+	201631.i	−0.107832	+	0.186770i
$260$	−430653.			−0.395088
$261$	−1.55444e6	+	1.01877e6i	−1.41245	+	0.925711i
$262$	−1.16728e6			−1.05056
$263$	−643865.	+	1.11521e6i	−0.573991	+	0.994182i	0.422159	+	0.906522i	$0.361272\pi$
$263$	−643865.	+	1.11521e6i	−0.573991	+	0.994182i	−0.996150	+	0.0876602i	$0.972061\pi$
$264$	−82912.0	+	87739.3i	−0.0732163	+	0.0774791i
$265$	−827625.	−	1.43349e6i	−0.723967	−	1.25395i
$266$	−158104.	−	273844.i	−0.137006	−	0.237301i
$267$	1.11098e6	+	264257.i	0.953738	+	0.226855i
$268$	−550800.	+	954014.i	−0.468443	+	0.811368i
$269$	−1.60073e6			−1.34877			−0.674385	−	0.738380i	$-0.735591\pi$
$269$	−1.60073e6			−1.34877			−0.674385	+	0.738380i	$0.735591\pi$
$270$	−546183.	−	460565.i	−0.455962	−	0.384487i
$271$	−1.13989e6			−0.942840			−0.471420	−	0.881909i	$-0.656258\pi$
$271$	−1.13989e6			−0.942840			−0.471420	+	0.881909i	$0.656258\pi$
$272$	−38875.4	+	67334.2i	−0.0318605	+	0.0551841i
$273$	335820.	+	79877.8i	0.272710	+	0.0648664i
$274$	481136.	+	833353.i	0.387161	+	0.670583i
$275$	54551.4	+	94485.7i	0.0434985	+	0.0753416i
$276$	748858.	−	792458.i	0.591734	−	0.626186i
$277$	−274406.	+	475284.i	−0.214879	+	0.372181i	−0.953235	−	0.302230i	$-0.902269\pi$
$277$	−274406.	+	475284.i	−0.214879	+	0.372181i	0.738356	+	0.674411i	$0.235602\pi$
$278$	271480.			0.210682
$279$	−41694.4	−	736388.i	−0.0320677	−	0.566365i
$280$	−117066.			−0.0892349
$281$	564981.	−	978576.i	0.426843	−	0.739314i	−0.569748	−	0.821820i	$-0.692959\pi$
$281$	564981.	−	978576.i	0.426843	−	0.739314i	0.996591	+	0.0825061i	$0.0262924\pi$
$282$	−359677.	−	1.20495e6i	−0.269333	−	0.902291i
$283$	−41396.8	−	71701.4i	−0.0307256	−	0.0532184i	0.850254	−	0.526373i	$-0.176448\pi$
$283$	−41396.8	−	71701.4i	−0.0307256	−	0.0532184i	−0.880979	+	0.473155i	$0.843115\pi$
$284$	−654122.	−	1.13297e6i	−0.481241	−	0.833534i
$285$	−428428.	−	1.43527e6i	−0.312439	−	1.04670i
$286$	138141.	−	239266.i	0.0998633	−	0.172968i
$287$	−762524.			−0.546448
$288$	14066.4	+	248434.i	0.00999312	+	0.176494i
$289$	−1.32761e6			−0.935034
$290$	−721269.	+	1.24927e6i	−0.503619	+	0.872294i
$291$	−669860.	+	708860.i	−0.463715	+	0.490714i
$292$	395497.	+	685020.i	0.271447	+	0.470161i
$293$	304098.	+	526714.i	0.206940	+	0.358431i	0.950749	−	0.309961i	$-0.100316\pi$
$293$	304098.	+	526714.i	0.206940	+	0.358431i	−0.743809	+	0.668392i	$0.766983\pi$
$294$	−928249.	−	220792.i	−0.626320	−	0.148976i
$295$	156549.	−	271151.i	0.104736	−	0.181408i
$296$	384112.			0.254817
$297$	431085.	−	155718.i	0.283577	−	0.102435i
$298$	654038.			0.426641
$299$	−1.24768e6	+	2.16104e6i	−0.807096	+	1.39793i
$300$	218788.	+	52040.6i	0.140352	+	0.0333841i
$301$	206545.	+	357747.i	0.131401	+	0.227593i
$302$	−589170.	−	1.02047e6i	−0.371726	−	0.643848i
$303$	−569860.	+	603038.i	−0.356584	+	0.377345i
$304$	−260840.	+	451788.i	−0.161879	+	0.280382i
$305$	36018.9			0.0221708
$306$	246907.	−	161821.i	0.150740	−	0.0987945i
$307$	225284.			0.136422			0.0682109	−	0.997671i	$-0.478271\pi$
$307$	225284.			0.136422			0.0682109	+	0.997671i	$0.478271\pi$
$308$	37551.2	−	65040.6i	0.0225552	−	0.0390668i
$309$	925657.	+	3.10104e6i	0.551511	+	1.84761i
$310$	−286238.	−	495778.i	−0.169170	−	0.293011i
$311$	506958.	+	878078.i	0.297215	+	0.514792i	0.975498	−	0.220009i	$-0.0706087\pi$
$311$	506958.	+	878078.i	0.297215	+	0.514792i	−0.678282	+	0.734801i	$0.737275\pi$
$312$	−162891.	−	545701.i	−0.0947352	−	0.317372i
$313$	−408842.	+	708135.i	−0.235882	+	0.408559i	−0.959529	−	0.281611i	$-0.909131\pi$
$313$	−408842.	+	708135.i	−0.235882	+	0.408559i	0.723647	+	0.690170i	$0.242464\pi$
$314$	596195.			0.341243
$315$	396882.	+	200126.i	0.225364	+	0.113639i
$316$	−935089.			−0.526787
$317$	1.04044e6	−	1.80209e6i	0.581526	−	1.00723i	−0.413773	−	0.910380i	$-0.635789\pi$
$317$	1.04044e6	−	1.80209e6i	0.581526	−	1.00723i	0.995299	−	0.0968520i	$-0.0308773\pi$
$318$	1.50340e6	−	1.59093e6i	0.833693	−	0.882233i
$319$	−462723.	−	801460.i	−0.254592	−	0.440966i
$320$	96567.6	+	167260.i	0.0527177	+	0.0913097i
$321$	1.31133e6	+	311911.i	0.710311	+	0.168954i
$322$	−339161.	+	587444.i	−0.182291	+	0.315738i
$323$	618913.			0.330083
$324$	377015.	−	866301.i	0.199524	−	0.458465i
$325$	−514702.			−0.270301
$326$	516427.	−	894478.i	0.269132	−	0.466150i
$327$	1.95196e6	+	464291.i	1.00949	+	0.240116i
$328$	629007.	+	1.08947e6i	0.322828	+	0.559154i
$329$	391164.	+	677516.i	0.199237	+	0.345088i
$330$	244343.	−	258569.i	0.123513	−	0.130705i
$331$	1.79995e6	−	3.11761e6i	0.903006	−	1.56405i	0.0794349	−	0.996840i	$-0.474688\pi$
$331$	1.79995e6	−	3.11761e6i	0.903006	−	1.56405i	0.823571	−	0.567213i	$-0.191978\pi$
$332$	−555613.			−0.276648
$333$	−1.30224e6	−	656648.i	−0.643545	−	0.324505i
$334$	2.71509e6			1.33174
$335$	1.62321e6	−	2.81149e6i	0.790248	−	1.36875i
$336$	−44279.3	−	148340.i	−0.0213970	−	0.0716818i
$337$	148052.	+	256433.i	0.0710132	+	0.122999i	0.899346	−	0.437238i	$-0.144043\pi$
$337$	148052.	+	256433.i	0.0710132	+	0.122999i	−0.828332	+	0.560237i	$0.810710\pi$
$338$	−90895.1	−	157435.i	−0.0432761	−	0.0749565i
$339$	193488.	+	648203.i	0.0914439	+	0.306346i
$340$	114566.	−	198435.i	0.0537476	−	0.0930936i
$341$	367266.			0.171039
$342$	1.65665e6	−	1.08576e6i	0.765890	−	0.501961i
$343$	1.24560e6			0.571665
$344$	340758.	−	590211.i	0.155257	−	0.268913i
$345$	−2.20689e6	+	2.33538e6i	−0.998236	+	1.05635i
$346$	754042.	+	1.30604e6i	0.338614	+	0.586497i
$347$	−746253.	−	1.29255e6i	−0.332707	−	0.576266i	0.650335	−	0.759648i	$-0.274629\pi$
$347$	−746253.	−	1.29255e6i	−0.332707	−	0.576266i	−0.983042	+	0.183382i	$0.941295\pi$
$348$	−1.85583e6	−	441426.i	−0.821467	−	0.195393i
$349$	−477000.	+	826188.i	−0.209631	+	0.363091i	−0.951598	−	0.307345i	$-0.900560\pi$
$349$	−477000.	+	826188.i	−0.209631	+	0.363091i	0.741968	+	0.670436i	$0.233893\pi$
$350$	−139913.			−0.0610504
$351$	−380645.	+	2.12853e6i	−0.164912	+	0.922172i
$352$	−123904.			−0.0533002
$353$	760158.	−	1.31663e6i	0.324689	−	0.562377i	−0.656761	−	0.754099i	$-0.728074\pi$
$353$	760158.	−	1.31663e6i	0.324689	−	0.562377i	0.981449	+	0.191722i	$0.0614071\pi$
$354$	402801.	+	95809.9i	0.170837	+	0.0406352i
$355$	1.92770e6	+	3.33888e6i	0.811838	+	1.40614i
$356$	586063.	+	1.01509e6i	0.245087	+	0.424502i
$357$	−126144.	+	133488.i	−0.0523836	+	0.0554335i
$358$	637093.	−	1.10348e6i	0.262721	−	0.455047i
$359$	3.10922e6			1.27325			0.636626	−	0.771172i	$-0.280329\pi$
$359$	3.10922e6			1.27325			0.636626	+	0.771172i	$0.280329\pi$
$360$	−41453.8	−	732137.i	−0.0168581	−	0.297739i
$361$	1.67658e6			0.677105
$362$	105047.	−	181947.i	0.0421321	−	0.0729749i
$363$	65280.4	+	218695.i	0.0260026	+	0.0871110i
$364$	177151.	+	306835.i	0.0700795	+	0.121381i
$365$	−1.16553e6	−	2.01876e6i	−0.457923	−	0.793145i
$366$	13623.9	+	45641.3i	0.00531616	+	0.0178096i
$367$	−2.04660e6	+	3.54481e6i	−0.793172	+	1.37381i	0.130821	+	0.991406i	$0.458239\pi$
$367$	−2.04660e6	+	3.54481e6i	−0.793172	+	1.37381i	−0.923993	+	0.382409i	$0.875095\pi$
$368$	1.11910e6			0.430772
$369$	−270015.	−	4.76888e6i	−0.103234	−	1.82327i
$370$	−1.13198e6			−0.429868
$371$	−680895.	+	1.17935e6i	−0.256830	+	0.444842i
$372$	519958.	−	550230.i	0.194810	−	0.206152i
$373$	937411.	+	1.62364e6i	0.348866	+	0.604253i	0.986048	−	0.166460i	$-0.0532336\pi$
$373$	937411.	+	1.62364e6i	0.348866	+	0.604253i	−0.637183	+	0.770713i	$0.719900\pi$
$374$	73498.9	+	127304.i	0.0271708	+	0.0470611i
$375$	−2.87939e6	−	684889.i	−1.05736	−	0.251502i
$376$	645343.	−	1.11777e6i	0.235408	−	0.407738i
$377$	4.36588e6			1.58204
$378$	−103472.	+	578605.i	−0.0372472	+	0.208282i
$379$	−3.59456e6			−1.28543			−0.642715	−	0.766106i	$-0.722192\pi$
$379$	−3.59456e6			−1.28543			−0.642715	+	0.766106i	$0.722192\pi$
$380$	768698.	−	1.33142e6i	0.273084	−	0.472996i
$381$	97137.7	+	23105.1i	0.0342827	+	0.00815445i
$382$	647376.	+	1.12129e6i	0.226986	+	0.393150i
$383$	233621.	+	404643.i	0.0813794	+	0.140953i	0.903843	−	0.427865i	$-0.140734\pi$
$383$	233621.	+	404643.i	0.0813794	+	0.140953i	−0.822463	+	0.568818i	$0.807401\pi$
$384$	−175417.	+	185630.i	−0.0607078	+	0.0642423i
$385$	−110664.	+	191675.i	−0.0380499	+	0.0659043i
$386$	−3.55273e6			−1.21365
$387$	−2.16423e6	+	1.41843e6i	−0.734559	+	0.481427i
$388$	−1.00104e6			−0.337577
$389$	−147466.	+	255418.i	−0.0494103	+	0.0855811i	−0.889673	−	0.456599i	$-0.849068\pi$
$389$	−147466.	+	255418.i	−0.0494103	+	0.0855811i	0.840262	+	0.542180i	$0.182401\pi$
$390$	480042.	+	1.60819e6i	0.159815	+	0.535395i
$391$	−663838.	−	1.14980e6i	−0.219594	−	0.380348i
$392$	−489668.	−	848131.i	−0.160948	−	0.278771i
$393$	1.30115e6	+	4.35898e6i	0.424958	+	1.42365i
$394$	884267.	−	1.53160e6i	0.286974	−	0.497054i
$395$	2.75571e6			0.888672
$396$	420066.	+	211817.i	0.134611	+	0.0678769i
$397$	1.39898e6			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$397$	1.39898e6			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$398$	116304.	−	201444.i	0.0368032	−	0.0637451i
$399$	−846379.	+	895657.i	−0.266154	+	0.281650i
$400$	115414.	+	199904.i	0.0360670	+	0.0624699i
$401$	1.05150e6	+	1.82125e6i	0.326548	+	0.565598i	0.981824	−	0.189791i	$-0.0607811\pi$
$401$	1.05150e6	+	1.82125e6i	0.326548	+	0.565598i	−0.655276	+	0.755389i	$0.727448\pi$
$402$	4.17654e6	+	993427.i	1.28900	+	0.306599i
$403$	−866306.	+	1.50049e6i	−0.265711	+	0.460224i
$404$	−851600.			−0.259587
$405$	−1.11107e6	+	2.55300e6i	−0.336591	+	0.773415i
$406$	1.18679e6			0.357321
$407$	363106.	−	628918.i	0.108654	−	0.188195i
$408$	294780.	+	70116.0i	0.0876693	+	0.0208529i
$409$	−1.22377e6	−	2.11963e6i	−0.361736	−	0.626545i	0.626511	−	0.779413i	$-0.284482\pi$
$409$	−1.22377e6	−	2.11963e6i	−0.361736	−	0.626545i	−0.988247	+	0.152868i	$0.951149\pi$
$410$	−1.85369e6	−	3.21068e6i	−0.544599	−	0.943273i
$411$	2.57567e6	−	2.72563e6i	0.752118	−	0.795908i
$412$	−1.66084e6	+	2.87666e6i	−0.482042	+	0.834922i
$413$	−257589.			−0.0743108
$414$	−3.79401e6	−	1.91312e6i	−1.08792	−	0.548581i
$415$	1.63740e6			0.466696
$416$	292264.	−	506217.i	0.0828023	−	0.143418i
$417$	−302615.	−	1.01379e6i	−0.0852218	−	0.285501i
$418$	493150.	+	854162.i	0.138051	+	0.239111i
$419$	−343695.	−	595297.i	−0.0956396	−	0.165653i	0.814236	−	0.580534i	$-0.197156\pi$
$419$	−343695.	−	595297.i	−0.0956396	−	0.165653i	−0.909875	+	0.414882i	$0.863823\pi$
$420$	130491.	+	437158.i	0.0360960	+	0.120925i
$421$	−356446.	+	617383.i	−0.0980141	+	0.169765i	−0.910863	−	0.412710i	$-0.864582\pi$
$421$	−356446.	+	617383.i	−0.0980141	+	0.169765i	0.812848	+	0.582475i	$0.197916\pi$
$422$	1.48597e6			0.406190
$423$	−4.09872e6	+	2.68628e6i	−1.11377	+	0.729962i
$424$	2.24668e6			0.606914
$425$	136926.	−	237163.i	0.0367717	−	0.0636904i
$426$	−3.50172e6	+	3.70559e6i	−0.934882	+	0.989313i
$427$	−14816.6	−	25663.0i	−0.00393258	−	0.00681143i
$428$	691749.	+	1.19814e6i	0.182532	+	0.316155i
$429$	−1.04748e6	−	249151.i	−0.274790	−	0.0653612i
$430$	−1.00422e6	+	1.73936e6i	−0.261913	+	0.453646i
$431$	6.47534e6			1.67907			0.839537	−	0.543303i	$-0.182827\pi$
$431$	6.47534e6			1.67907			0.839537	+	0.543303i	$0.182827\pi$
$432$	912047.	−	329454.i	0.235130	−	0.0849347i
$433$	−71548.4			−0.0183392			−0.00916960	−	0.999958i	$-0.502919\pi$
$433$	−71548.4			−0.0183392			−0.00916960	+	0.999958i	$0.502919\pi$
$434$	−235491.	+	407882.i	−0.0600136	+	0.103947i
$435$	5.46915e6	+	1.30089e6i	1.38579	+	0.329622i
$436$	1.02969e6	+	1.78348e6i	0.259413	+	0.449316i
$437$	−4.45411e6	−	7.71475e6i	−1.11573	−	1.93249i
$438$	2.11722e6	−	2.24048e6i	0.527327	−	0.558029i
$439$	3.02583e6	−	5.24088e6i	0.749346	−	1.29791i	−0.198790	−	0.980042i	$-0.563701\pi$
$439$	3.02583e6	−	5.24088e6i	0.749346	−	1.29791i	0.948136	−	0.317864i	$-0.102965\pi$
$440$	365146.			0.0899156
$441$	210201.	+	3.71247e6i	0.0514681	+	0.909006i
$442$	−693475.			−0.168840
$443$	1.79467e6	−	3.10846e6i	0.434486	−	0.752552i	−0.562767	−	0.826615i	$-0.690263\pi$
$443$	1.79467e6	−	3.10846e6i	0.434486	−	0.752552i	0.997254	+	0.0740633i	$0.0235967\pi$
$444$	−428164.	−	1.43439e6i	−0.103075	−	0.345310i
$445$	−1.72713e6	−	2.99148e6i	−0.413453	−	0.716121i
$446$	−179246.	−	310463.i	−0.0426689	−	0.0739048i
$447$	−729047.	−	2.44237e6i	−0.172578	−	0.578154i
$448$	79447.2	−	137607.i	0.0187018	−	0.0323925i
$449$	6.34580e6			1.48549			0.742747	−	0.669573i	$-0.233523\pi$
$449$	6.34580e6			1.48549			0.742747	+	0.669573i	$0.233523\pi$
$450$	−49544.2	−	875027.i	−0.0115335	−	0.203700i
$451$	2.37843e6			0.550617
$452$	−347162.	+	601302.i	−0.0799256	+	0.138435i
$453$	−3.15401e6	+	3.33764e6i	−0.722133	+	0.764177i
$454$	1.16368e6	+	2.01555e6i	0.264967	+	0.458937i
$455$	−522066.	−	904245.i	−0.118222	−	0.204766i
$456$	1.97786e6	+	470453.i	0.445435	+	0.105951i
$457$	2.64329e6	−	4.57831e6i	0.592045	−	1.02545i	−0.401912	−	0.915678i	$-0.631654\pi$
$457$	2.64329e6	−	4.57831e6i	0.592045	−	1.02545i	0.993957	−	0.109773i	$-0.0350124\pi$
$458$	1.14452e6			0.254952
$459$	−879513.	−	741643.i	−0.194854	−	0.164310i
$460$	−3.29798e6			−0.726698
$461$	−2.63302e6	+	4.56053e6i	−0.577035	+	0.999455i	0.418782	+	0.908087i	$0.362457\pi$
$461$	−2.63302e6	+	4.56053e6i	−0.577035	+	0.999455i	−0.995817	+	0.0913677i	$0.970876\pi$
$462$	−284739.	−	67727.6i	−0.0620642	−	0.0147625i
$463$	1.65165e6	+	2.86074e6i	0.358067	+	0.620191i	0.987638	−	0.156753i	$-0.0501025\pi$
$463$	1.65165e6	+	2.86074e6i	0.358067	+	0.620191i	−0.629571	+	0.776943i	$0.716769\pi$
$464$	−978984.	−	1.69565e6i	−0.211096	−	0.365630i
$465$	−1.53232e6	+	1.62153e6i	−0.328637	+	0.347771i
$466$	−2.14165e6	+	3.70945e6i	−0.456861	+	0.791307i
$467$	8.58306e6			1.82117			0.910584	−	0.413324i	$-0.135632\pi$
$467$	8.58306e6			1.82117			0.910584	+	0.413324i	$0.135632\pi$
$468$	−1.85624e6	+	1.21657e6i	−0.391759	+	0.256757i
$469$	−2.67087e6			−0.560687
$470$	−1.90183e6	+	3.29407e6i	−0.397125	+	0.687841i
$471$	−664569.	−	2.22637e6i	−0.138035	−	0.462429i
$472$	212485.	+	368035.i	0.0439009	+	0.0760386i
$473$	−644246.	−	1.11587e6i	−0.132403	−	0.229329i
$474$	1.04233e6	+	3.49190e6i	0.213088	+	0.713865i
$475$	918723.	−	1.59127e6i	0.186832	−	0.323602i
$476$	−188510.			−0.0381343
$477$	−7.61682e6	−	3.84075e6i	−1.53277	−	0.772895i
$478$	−434533.			−0.0869867
$479$	4.14479e6	−	7.17900e6i	0.825400	−	1.42963i	−0.0762139	−	0.997091i	$-0.524283\pi$
$479$	4.14479e6	−	7.17900e6i	0.825400	−	1.42963i	0.901613	−	0.432543i	$-0.142383\pi$
$480$	516956.	−	547054.i	0.102412	−	0.108375i
$481$	1.71299e6	+	2.96698e6i	0.337591	+	0.584725i
$482$	−1.04199e6	−	1.80478e6i	−0.204290	−	0.353840i
$483$	2.57175e6	+	611713.i	0.501603	+	0.119311i
$484$	−117128.	+	202872.i	−0.0227273	+	0.0393648i
$485$	2.95007e6			0.569480
$486$	−3.65528e6	−	442234.i	−0.701988	−	0.0849300i
$487$	−1.28307e6			−0.245147			−0.122574	−	0.992459i	$-0.539115\pi$
$487$	−1.28307e6			−0.245147			−0.122574	+	0.992459i	$0.539115\pi$
$488$	−24444.4	+	42338.9i	−0.00464654	+	0.00804804i
$489$	−3.91590e6	−	931431.i	−0.740558	−	0.176148i
$490$	1.44306e6	+	2.49945e6i	0.271515	+	0.470277i
$491$	−4.35241e6	−	7.53859e6i	−0.814753	−	1.41119i	−0.909505	−	0.415692i	$-0.863539\pi$
$491$	−4.35241e6	−	7.53859e6i	−0.814753	−	1.41119i	0.0947525	−	0.995501i	$-0.469794\pi$
$492$	3.36727e6	−	3.56331e6i	0.627140	−	0.663654i
$493$	−1.16145e6	+	2.01169e6i	−0.215220	+	0.372773i
$494$	−4.65297e6			−0.857852
$495$	−1.23794e6	−	624225.i	−0.227083	−	0.114506i
$496$	777026.			0.141818
$497$	1.58594e6	−	2.74693e6i	0.288002	−	0.498835i
$498$	619334.	+	2.07483e6i	0.111905	+	0.374894i
$499$	1.15864e6	+	2.00683e6i	0.208304	+	0.360793i	0.951180	−	0.308635i	$-0.0998723\pi$
$499$	1.15864e6	+	2.00683e6i	0.208304	+	0.360793i	−0.742876	+	0.669429i	$0.766539\pi$
$500$	−1.51893e6	−	2.63087e6i	−0.271715	−	0.470624i
$501$	−3.02647e6	−	1.01390e7i	−0.538694	−	1.80468i
$502$	3.46641e6	−	6.00399e6i	0.613932	−	1.06336i
$503$	1.18946e6			0.209618			0.104809	−	0.994492i	$-0.466577\pi$
$503$	1.18946e6			0.209618			0.104809	+	0.994492i	$0.466577\pi$
$504$	−504587.	+	330704.i	−0.0884830	+	0.0579913i
$505$	2.50967e6			0.437914
$506$	1.05789e6	−	1.83233e6i	0.183682	−	0.318146i
$507$	−486589.	+	514919.i	−0.0840703	+	0.0889651i
$508$	51241.9	+	88753.6i	0.00880980	+	0.0152590i
$509$	3.59230e6	+	6.22204e6i	0.614579	+	1.06448i	0.990458	+	0.137813i	$0.0440074\pi$
$509$	3.59230e6	+	6.22204e6i	0.614579	+	1.06448i	−0.375879	+	0.926669i	$0.622659\pi$
$510$	−868719.	−	206633.i	−0.147895	−	0.0351782i
$511$	−958896.	+	1.66086e6i	−0.162450	+	0.281371i
$512$	−262144.			−0.0441942
$513$	−5.90121e6	−	4.97616e6i	−0.990028	−	0.834835i
$514$	2.52681e6			0.421856
$515$	4.89451e6	−	8.47755e6i	0.813189	−	1.40848i
$516$	−2.58386e6	−	614594.i	−0.427213	−	0.101617i
$517$	−1.22010e6	−	2.11328e6i	−0.200756	−	0.347720i
$518$	465647.	+	806524.i	0.0762486	+	0.132067i
$519$	4.03662e6	−	4.27164e6i	0.657808	−	0.696107i
$520$	−861306.	+	1.49182e6i	−0.139685	+	0.241941i
$521$	−4.86345e6			−0.784965			−0.392482	−	0.919760i	$-0.628384\pi$
$521$	−4.86345e6			−0.784965			−0.392482	+	0.919760i	$0.628384\pi$
$522$	420250.	+	7.42227e6i	0.0675044	+	1.19223i
$523$	−6.39186e6			−1.02182			−0.510908	−	0.859635i	$-0.670691\pi$
$523$	−6.39186e6			−1.02182			−0.510908	+	0.859635i	$0.670691\pi$
$524$	−2.33456e6	+	4.04358e6i	−0.371430	+	0.643336i
$525$	155959.	+	522478.i	0.0246952	+	0.0827312i
$526$	2.57546e6	+	4.46083e6i	0.405873	+	0.702993i
$527$	−460926.	−	798347.i	−0.0722944	−	0.125217i
$528$	138114.	+	462694.i	0.0215602	+	0.0722286i
$529$	−6.33669e6	+	1.09755e7i	−0.984517	+	1.70523i
$530$	−6.62100e6			−1.02384
$531$	−91213.9	−	1.61098e6i	−0.0140386	−	0.247944i
$532$	−1.26483e6			−0.193755
$533$	−5.61024e6	+	9.71721e6i	−0.855388	+	1.48158i
$534$	3.13738e6	−	3.32004e6i	0.476117	−	0.503837i
$535$	−2.03859e6	−	3.53094e6i	−0.307925	−	0.533343i
$536$	2.20320e6	+	3.81606e6i	0.331240	+	0.573724i
$537$	−4.83087e6	−	1.14907e6i	−0.722919	−	0.171953i
$538$	−3.20147e6	+	5.54510e6i	−0.476862	+	0.825950i
$539$	−1.85156e6			−0.274515
$540$	−2.68781e6	+	970903.i	−0.396656	+	0.143282i
$541$	1.49180e6			0.219138			0.109569	−	0.993979i	$-0.465053\pi$
$541$	1.49180e6			0.219138			0.109569	+	0.993979i	$0.465053\pi$
$542$	−2.27977e6	+	3.94868e6i	−0.333344	+	0.577369i
$543$	−796539.	−	189464.i	−0.115933	−	0.0275757i
$544$	155502.	+	269337.i	0.0225288	+	0.0390210i
$545$	−3.03452e6	−	5.25593e6i	−0.437621	−	0.757982i
$546$	948345.	−	1.00356e6i	0.136140	−	0.144066i
$547$	−1.29656e6	+	2.24572e6i	−0.185279	+	0.320912i	−0.943670	−	0.330887i	$-0.892652\pi$
$547$	−1.29656e6	+	2.24572e6i	−0.185279	+	0.320912i	0.758392	+	0.651799i	$0.225986\pi$
$548$	3.84909e6			0.547529
$549$	155252.	−	101751.i	0.0219840	−	0.0144082i
$550$	436411.			0.0615161
$551$	−7.79291e6	+	1.34977e7i	−1.09350	+	1.89401i
$552$	−1.24744e6	−	4.17904e6i	−0.174249	−	0.583752i
$553$	−1.13358e6	−	1.96341e6i	−0.157630	−	0.273023i
$554$	1.09762e6	+	1.90114e6i	0.151942	+	0.263172i
$555$	1.26180e6	+	4.22716e6i	0.173884	+	0.582527i
$556$	542961.	−	940436.i	0.0744872	−	0.129016i
$557$	7.54328e6			1.03020			0.515101	−	0.857130i	$-0.327755\pi$
$557$	7.54328e6			1.03020			0.515101	+	0.857130i	$0.327755\pi$
$558$	−2.63431e6	−	1.32834e6i	−0.358164	−	0.180603i
$559$	6.07858e6			0.822759
$560$	−234131.	+	405528.i	−0.0315493	+	0.0546450i
$561$	393462.	−	416370.i	0.0527832	−	0.0558563i
$562$	−2.25992e6	−	3.91430e6i	−0.301823	−	0.522774i
$563$	2.15140e6	+	3.72634e6i	0.286056	+	0.495463i	0.972865	−	0.231375i	$-0.0743224\pi$
$563$	2.15140e6	+	3.72634e6i	0.286056	+	0.495463i	−0.686809	+	0.726838i	$0.740989\pi$
$564$	−4.89343e6	−	1.16395e6i	−0.647762	−	0.154076i
$565$	1.02309e6	−	1.77204e6i	0.134832	−	0.233536i
$566$	−331175.			−0.0434526
$567$	2.27602e6	−	258566.i	0.297316	−	0.0337765i
$568$	−5.23297e6			−0.680578
$569$	−4.67036e6	+	8.08929e6i	−0.604741	+	1.04744i	0.387352	+	0.921932i	$0.373390\pi$
$569$	−4.67036e6	+	8.08929e6i	−0.604741	+	1.04744i	−0.992092	+	0.125510i	$0.959943\pi$
$570$	−5.82879e6	−	1.38643e6i	−0.751434	−	0.178735i
$571$	513431.	+	889288.i	0.0659009	+	0.114144i	0.897093	−	0.441841i	$-0.145675\pi$
$571$	513431.	+	889288.i	0.0659009	+	0.114144i	−0.831192	+	0.555985i	$0.812341\pi$
$572$	−552562.	−	957066.i	−0.0706141	−	0.122307i
$573$	3.46560e6	−	3.66738e6i	0.440953	−	0.466626i
$574$	−1.52505e6	+	2.64146e6i	−0.193199	+	0.334630i
$575$	−3.94164e6			−0.497173
$576$	888734.	+	448141.i	0.111613	+	0.0562805i
$577$	9.30871e6			1.16399			0.581996	−	0.813192i	$-0.302272\pi$
$577$	9.30871e6			1.16399			0.581996	+	0.813192i	$0.302272\pi$
$578$	−2.65523e6	+	4.59899e6i	−0.330584	+	0.572589i
$579$	3.96018e6	+	1.32670e7i	0.490928	+	1.64466i
$580$	2.88507e6	+	4.99710e6i	0.356112	+	0.616805i
$581$	−673552.	−	1.16663e6i	−0.0827810	−	0.143381i
$582$	1.11584e6	+	3.73818e6i	0.136551	+	0.457460i
$583$	2.12382e6	−	3.67856e6i	0.258789	−	0.448236i
$584$	3.16397e6			0.383885
$585$	5.47035e6	−	3.58524e6i	0.660884	−	0.433140i
$586$	2.43279e6			0.292658
$587$	−5.01225e6	+	8.68148e6i	−0.600396	+	1.03992i	0.392365	+	0.919810i	$0.371657\pi$
$587$	−5.01225e6	+	8.68148e6i	−0.600396	+	1.03992i	−0.992761	+	0.120107i	$0.961676\pi$
$588$	−2.62135e6	+	2.77397e6i	−0.312666	+	0.330870i
$589$	−3.09264e6	−	5.35661e6i	−0.367317	−	0.636212i
$590$	−626195.	−	1.08460e6i	−0.0740593	−	0.128275i
$591$	−6.70511e6	−	1.59487e6i	−0.789655	−	0.187826i
$592$	768224.	−	1.33060e6i	0.0900915	−	0.156043i
$593$	−7.01154e6			−0.818798			−0.409399	−	0.912355i	$-0.634262\pi$
$593$	−7.01154e6			−0.818798			−0.409399	+	0.912355i	$0.634262\pi$
$594$	322745.	−	1.80476e6i	0.0375313	−	0.209871i
$595$	555540.			0.0643314
$596$	1.30808e6	−	2.26566e6i	0.150840	−	0.261263i
$597$	−881894.	−	209766.i	−0.101270	−	0.0240879i
$598$	4.99072e6	+	8.64418e6i	0.570703	+	0.988486i
$599$	−5.52816e6	−	9.57505e6i	−0.629525	−	1.09037i	−0.987647	−	0.156695i	$-0.949916\pi$
$599$	−5.52816e6	−	9.57505e6i	−0.629525	−	1.09037i	0.358122	−	0.933675i	$-0.383417\pi$
$600$	617849.	−	653822.i	0.0700655	−	0.0741449i
$601$	−3.39488e6	+	5.88011e6i	−0.383388	+	0.664048i	−0.991544	−	0.129770i	$-0.958576\pi$
$601$	−3.39488e6	+	5.88011e6i	−0.383388	+	0.664048i	0.608156	+	0.793818i	$0.291910\pi$
$602$	1.65236e6			0.185829
$603$	−945773.	−	1.67038e7i	−0.105924	−	1.87078i
$604$	−4.71336e6			−0.525700
$605$	345177.	−	597865.i	0.0383401	−	0.0664071i
$606$	949266.	+	3.18013e6i	0.105004	+	0.351773i
$607$	−4.11936e6	−	7.13494e6i	−0.453793	−	0.785992i	0.544825	−	0.838550i	$-0.316596\pi$
$607$	−4.11936e6	−	7.13494e6i	−0.453793	−	0.785992i	−0.998618	+	0.0525574i	$0.983263\pi$
$608$	1.04336e6	+	1.80715e6i	0.114466	+	0.198260i
$609$	−1.32290e6	−	4.43183e6i	−0.144538	−	0.484217i
$610$	72037.8	−	124773.i	0.00783855	−	0.0135768i
$611$	1.15119e7			1.24751
$612$	−66752.5	−	1.17895e6i	−0.00720426	−	0.127238i
$613$	−4.42748e6			−0.475889			−0.237944	−	0.971279i	$-0.576474\pi$
$613$	−4.42748e6			−0.475889			−0.237944	+	0.971279i	$0.576474\pi$
$614$	450567.	−	780405.i	0.0482324	−	0.0835409i
$615$	−9.92336e6	+	1.05011e7i	−1.05796	+	1.11956i
$616$	−150205.	−	260162.i	−0.0159489	−	0.0276244i
$617$	−8.41757e6	−	1.45797e7i	−0.890172	−	1.54182i	−0.839669	−	0.543099i	$-0.817251\pi$
$617$	−8.41757e6	−	1.45797e7i	−0.890172	−	1.54182i	−0.0505026	−	0.998724i	$-0.516082\pi$
$618$	1.25936e7	+	2.99551e6i	1.32642	+	0.315500i
$619$	−7.76135e6	+	1.34431e7i	−0.814162	+	1.41017i	0.0957665	+	0.995404i	$0.469470\pi$
$619$	−7.76135e6	+	1.34431e7i	−0.814162	+	1.41017i	−0.909928	+	0.414766i	$0.863864\pi$
$620$	−2.28990e6			−0.239242
$621$	−2.91502e6	+	1.63005e7i	−0.303328	+	1.69618i
$622$	4.05567e6			0.420326
$623$	−1.42093e6	+	2.46112e6i	−0.146674	+	0.254047i
$624$	−2.21615e6	−	527130.i	−0.227844	−	0.0541946i
$625$	3.06743e6	+	5.31295e6i	0.314105	+	0.544046i
$626$	1.63537e6	+	2.83254e6i	0.166794	+	0.288895i
$627$	2.63999e6	−	2.79369e6i	0.268184	−	0.283798i
$628$	1.19239e6	−	2.06528e6i	0.120648	−	0.208968i
$629$	−1.82282e6			−0.183703
$630$	1.48702e6	−	974587.i	0.149268	−	0.0978294i
$631$	2.43074e6			0.243033			0.121517	−	0.992589i	$-0.461224\pi$
$631$	2.43074e6			0.243033			0.121517	+	0.992589i	$0.461224\pi$
$632$	−1.87018e6	+	3.23924e6i	−0.186247	+	0.322590i
$633$	−1.65639e6	−	5.54906e6i	−0.164306	−	0.550440i
$634$	−4.16176e6	−	7.20838e6i	−0.411201	−	0.712221i
$635$	−151010.	−	261558.i	−0.0148618	−	0.0257414i
$636$	−2.50434e6	−	8.38978e6i	−0.245500	−	0.822447i
$637$	4.36745e6	−	7.56465e6i	0.426461	−	0.738652i
$638$	−3.70178e6			−0.360047
$639$	1.77411e7	+	8.94588e6i	1.71881	+	0.866704i
$640$	772541.			0.0745541
$641$	−2.02717e6	+	3.51117e6i	−0.194870	+	0.337526i	−0.946858	−	0.321652i	$-0.895762\pi$
$641$	−2.02717e6	+	3.51117e6i	−0.194870	+	0.337526i	0.751988	+	0.659177i	$0.229095\pi$
$642$	3.70315e6	−	3.91875e6i	0.354596	−	0.375241i
$643$	7.35972e6	+	1.27474e7i	0.701994	+	1.21589i	0.967765	+	0.251854i	$0.0810402\pi$
$643$	7.35972e6	+	1.27474e7i	0.701994	+	1.21589i	−0.265771	+	0.964036i	$0.585626\pi$
$644$	1.35664e6	+	2.34977e6i	0.128899	+	0.223260i
$645$	7.61466e6	+	1.81121e6i	0.720695	+	0.171424i
$646$	1.23783e6	−	2.14398e6i	0.116702	−	0.202134i
$647$	−6.06351e6			−0.569460			−0.284730	−	0.958608i	$-0.591904\pi$
$647$	−6.06351e6			−0.569460			−0.284730	+	0.958608i	$0.591904\pi$
$648$	−2.24692e6	−	3.03862e6i	−0.210209	−	0.284275i
$649$	803459.			0.0748776
$650$	−1.02940e6	+	1.78298e6i	−0.0955659	+	0.165525i
$651$	1.78565e6	+	424733.i	0.165137	+	0.0392793i
$652$	−2.06571e6	−	3.57791e6i	−0.190305	−	0.329618i
$653$	2.01007e6	+	3.48155e6i	0.184471	+	0.319514i	0.943398	−	0.331662i	$-0.107609\pi$
$653$	2.01007e6	+	3.48155e6i	0.184471	+	0.319514i	−0.758927	+	0.651176i	$0.774276\pi$
$654$	5.51227e6	−	5.83320e6i	0.503948	−	0.533289i
$655$	6.87998e6	−	1.19165e7i	0.626591	−	1.08529i
$656$	5.03205e6			0.456547
$657$	−1.07267e7	−	5.40888e6i	−0.969507	−	0.488871i
$658$	3.12931e6			0.281763
$659$	−1.60311e6	+	2.77666e6i	−0.143797	+	0.249063i	−0.928923	−	0.370272i	$-0.879264\pi$
$659$	−1.60311e6	+	2.77666e6i	−0.143797	+	0.249063i	0.785127	+	0.619335i	$0.212598\pi$
$660$	−407023.	−	1.36356e6i	−0.0363713	−	0.121847i
$661$	−5.55009e6	−	9.61304e6i	−0.494079	−	0.855770i	0.505898	−	0.862593i	$-0.331161\pi$
$661$	−5.55009e6	−	9.61304e6i	−0.494079	−	0.855770i	−0.999977	+	0.00682356i	$0.997828\pi$
$662$	−7.19980e6	−	1.24704e7i	−0.638522	−	1.10595i
$663$	773006.	+	2.58964e6i	0.0682966	+	0.228800i
$664$	−1.11123e6	+	1.92470e6i	−0.0978098	+	0.169412i
$665$	3.72747e6			0.326859
$666$	−4.87917e6	+	3.19778e6i	−0.426246	+	0.279359i
$667$	3.34343e7			2.90990
$668$	5.43018e6	−	9.40535e6i	0.470840	−	0.815519i
$669$	−959558.	+	1.01543e6i	−0.0828907	+	0.0877168i
$670$	−6.49285e6	−	1.12460e7i	−0.558790	−	0.967853i
$671$	46215.1	+	80047.0i	0.00396258	+	0.00686339i
$672$	−602422.	−	143291.i	−0.0514610	−	0.0122404i
$673$	7.66199e6	−	1.32710e7i	0.652084	−	1.12944i	−0.330532	−	0.943795i	$-0.607228\pi$
$673$	7.66199e6	−	1.32710e7i	0.652084	−	1.12944i	0.982616	−	0.185649i	$-0.0594386\pi$
$674$	1.18442e6			0.100428
$675$	−3.21239e6	+	1.16039e6i	−0.271374	+	0.0980269i
$676$	−727161.			−0.0612017
$677$	1.16596e6	−	2.01950e6i	0.0977715	−	0.169345i	−0.812990	−	0.582277i	$-0.802162\pi$
$677$	1.16596e6	−	2.01950e6i	0.0977715	−	0.169345i	0.910762	+	0.412932i	$0.135495\pi$
$678$	2.63242e6	+	626144.i	0.219928	+	0.0523118i
$679$	−1.21353e6	−	2.10189e6i	−0.101013	−	0.174959i
$680$	−458265.	−	793738.i	−0.0380053	−	0.0658271i
$681$	6.22952e6	−	6.59221e6i	0.514739	−	0.544708i
$682$	734532.	−	1.27225e6i	0.0604714	−	0.104740i
$683$	1.07124e7			0.878688			0.439344	−	0.898319i	$-0.355211\pi$
$683$	1.07124e7			0.878688			0.439344	+	0.898319i	$0.355211\pi$
$684$	−447885.	−	7.91034e6i	−0.0366038	−	0.646480i
$685$	−1.13433e7			−0.923662
$686$	2.49119e6	−	4.31487e6i	0.202114	−	0.350072i
$687$	−1.27578e6	−	4.27397e6i	−0.103129	−	0.345493i
$688$	−1.36303e6	−	2.36084e6i	−0.109783	−	0.190150i
$689$	1.00193e7	+	1.73540e7i	0.804062	+	1.39268i
$690$	3.67621e6	+	1.23157e7i	0.293953	+	0.984770i
$691$	−2.28098e6	+	3.95078e6i	−0.181730	+	0.314766i	−0.942470	−	0.334291i	$-0.891503\pi$
$691$	−2.28098e6	+	3.95078e6i	−0.181730	+	0.314766i	0.760740	+	0.649057i	$0.224836\pi$
$692$	6.03233e6			0.478873
$693$	64478.7	+	1.13879e6i	0.00510015	+	0.0900766i
$694$	−5.97002e6			−0.470519
$695$	−1.60011e6	+	2.77147e6i	−0.125657	+	0.217645i
$696$	−5.24080e6	+	5.54593e6i	−0.410086	+	0.433962i
$697$	−2.98497e6	−	5.17013e6i	−0.232733	−	0.403106i
$698$	1.90800e6	+	3.30475e6i	0.148231	+	0.256744i
$699$	1.62395e7	+	3.86270e6i	1.25713	+	0.299019i
$700$	−279826.	+	484674.i	−0.0215846	+	0.0373856i
$701$	−5.55152e6			−0.426695			−0.213347	−	0.976976i	$-0.568437\pi$
$701$	−5.55152e6			−0.426695			−0.213347	+	0.976976i	$0.568437\pi$
$702$	6.61215e6	+	5.57565e6i	0.506407	+	0.427025i
$703$	−1.22304e7			−0.933370
$704$	−247808.	+	429216.i	−0.0188445	+	0.0326396i
$705$	1.44210e7	+	3.43016e6i	1.09275	+	0.259921i
$706$	−3.04063e6	−	5.26653e6i	−0.229590	−	0.397661i
$707$	−1.03237e6	−	1.78811e6i	−0.0776758	−	0.134538i
$708$	1.13750e6	−	1.20373e6i	0.0852840	−	0.0902494i
$709$	−8.81952e6	+	1.52759e7i	−0.658915	+	1.14127i	0.321982	+	0.946746i	$0.395651\pi$
$709$	−8.81952e6	+	1.52759e7i	−0.658915	+	1.14127i	−0.980897	+	0.194528i	$0.937682\pi$
$710$	1.54216e7			1.14811
$711$	1.18779e7	−	7.78473e6i	0.881184	−	0.577524i
$712$	4.68851e6			0.346605
$713$	−6.63426e6	+	1.14909e7i	−0.488730	+	0.846505i
$714$	210129.	+	703951.i	0.0154255	+	0.0516770i
$715$	1.62841e6	+	2.82048e6i	0.119124	+	0.206328i
$716$	−2.54837e6	−	4.41391e6i	−0.185772	−	0.321766i
$717$	484367.	+	1.62267e6i	0.0351865	+	0.117878i
$718$	6.21843e6	−	1.07706e7i	0.450163	−	0.779705i
$719$	−9.42694e6			−0.680062			−0.340031	−	0.940414i	$-0.610438\pi$
$719$	−9.42694e6			−0.680062			−0.340031	+	0.940414i	$0.610438\pi$
$720$	−2.61911e6	−	1.32067e6i	−0.188288	−	0.0949434i
$721$	−8.05354e6			−0.576964
$722$	3.35316e6	−	5.80784e6i	0.239393	−	0.414640i
$723$	−5.57810e6	+	5.90287e6i	−0.396863	+	0.419969i
$724$	−420189.	−	727788.i	−0.0297919	−	0.0516011i
$725$	3.44815e6	+	5.97237e6i	0.243636	+	0.421989i
$726$	888144.	+	211253.i	0.0625377	+	0.0148751i
$727$	5.37819e6	−	9.31530e6i	0.377398	−	0.653673i	−0.613284	−	0.789862i	$-0.710152\pi$
$727$	5.37819e6	−	9.31530e6i	0.377398	−	0.653673i	0.990683	+	0.136189i	$0.0434854\pi$
$728$	1.41721e6			0.0991073
$729$	2.42305e6	+	1.41428e7i	0.168866	+	0.985639i
$730$	−9.32426e6			−0.647600
$731$	−1.61708e6	+	2.80087e6i	−0.111928	+	0.193865i
$732$	185354.	+	44088.1i	0.0127857	+	0.00304119i
$733$	−1.06908e7	−	1.85171e7i	−0.734940	−	1.27295i	−0.954750	−	0.297411i	$-0.903877\pi$
$733$	−1.06908e7	−	1.85171e7i	−0.734940	−	1.27295i	0.219809	−	0.975543i	$-0.429456\pi$
$734$	8.18640e6	+	1.41793e7i	0.560858	+	0.971434i
$735$	7.72513e6	−	8.17490e6i	0.527457	−	0.558167i
$736$	2.23819e6	−	3.87666e6i	0.152301	−	0.263793i
$737$	8.33085e6			0.564964
$738$	−1.70599e7	−	8.60240e6i	−1.15302	−	0.581405i
$739$	1.74395e7			1.17469			0.587343	−	0.809338i	$-0.300174\pi$
$739$	1.74395e7			1.17469			0.587343	+	0.809338i	$0.300174\pi$
$740$	−2.26396e6	+	3.92130e6i	−0.151981	+	0.263239i
$741$	5.18659e6	+	1.73756e7i	0.347006	+	1.16250i
$742$	2.72358e6	+	4.71738e6i	0.181606	+	0.314551i
$743$	−1.00051e7	−	1.73294e7i	−0.664892	−	1.15163i	−0.979315	−	0.202343i	$-0.935144\pi$
$743$	−1.00051e7	−	1.73294e7i	−0.664892	−	1.15163i	0.314423	−	0.949283i	$-0.398189\pi$
$744$	−866139.	−	2.90165e6i	−0.0573661	−	0.192182i
$745$	−3.85491e6	+	6.67691e6i	−0.254463	+	0.440742i
$746$	7.49929e6			0.493370
$747$	7.05765e6	−	4.62555e6i	0.462763	−	0.303293i
$748$	587991.			0.0384252
$749$	−1.67717e6	+	2.90494e6i	−0.109238	+	0.189205i
$750$	−8.13131e6	+	8.60473e6i	−0.527846	+	0.558578i
$751$	3.23242e6	+	5.59871e6i	0.209135	+	0.362233i	0.951442	−	0.307827i	$-0.0996017\pi$
$751$	3.23242e6	+	5.59871e6i	0.209135	+	0.362233i	−0.742307	+	0.670060i	$0.766268\pi$
$752$	−2.58137e6	−	4.47107e6i	−0.166458	−	0.288315i
$753$	−2.62846e7	−	6.25203e6i	−1.68933	−	0.401822i
$754$	8.73175e6	−	1.51238e7i	0.559336	−	0.968799i
$755$	1.38903e7			0.886838
$756$	1.79740e6	+	1.51565e6i	0.114378	+	0.0964481i
$757$	1.80478e7			1.14468			0.572340	−	0.820017i	$-0.306036\pi$
$757$	1.80478e7			1.14468			0.572340	+	0.820017i	$0.306036\pi$
$758$	−7.18913e6	+	1.24519e7i	−0.454468	+	0.787162i
$759$	−8.02168e6	−	1.90803e6i	−0.505430	−	0.120221i
$760$	−3.07479e6	−	5.32569e6i	−0.193100	−	0.334458i
$761$	3.61509e6	+	6.26152e6i	0.226286	+	0.391939i	0.956704	−	0.291061i	$-0.0940083\pi$
$761$	3.61509e6	+	6.26152e6i	0.226286	+	0.391939i	−0.730419	+	0.683000i	$0.760675\pi$
$762$	274314.	−	290285.i	0.0171143	−	0.0181108i
$763$	−2.49653e6	+	4.32411e6i	−0.155248	+	0.268897i
$764$	5.17901e6			0.321006
$765$	196720.	+	3.47439e6i	0.0121533	+	0.214647i
$766$	1.86897e6			0.115088
$767$	−1.89520e6	+	3.28258e6i	−0.116323	+	0.201477i
$768$	292208.	+	978924.i	0.0178768	+	0.0598888i
$769$	−5.01219e6	−	8.68136e6i	−0.305641	−	0.529385i	0.671763	−	0.740766i	$-0.265537\pi$
$769$	−5.01219e6	−	8.68136e6i	−0.305641	−	0.529385i	−0.977404	+	0.211381i	$0.932204\pi$
$770$	442655.	+	766701.i	0.0269053	+	0.0466014i
$771$	−2.81659e6	−	9.43585e6i	−0.170643	−	0.571670i
$772$	−7.10546e6	+	1.23070e7i	−0.429091	+	0.743207i
$773$	−2.07426e7			−1.24857			−0.624287	−	0.781195i	$-0.714610\pi$
$773$	−2.07426e7			−1.24857			−0.624287	+	0.781195i	$0.714610\pi$
$774$	585112.	+	1.03340e7i	0.0351064	+	0.620034i
$775$	−2.73682e6			−0.163679
$776$	−2.00208e6	+	3.46771e6i	−0.119351	+	0.206723i
$777$	2.49275e6	−	2.63788e6i	0.148124	−	0.156748i
$778$	589863.	+	1.02167e6i	0.0349384	+	0.0605150i
$779$	−2.00281e7	−	3.46897e7i	−1.18249	−	2.04812i
$780$	6.53100e6	+	1.55346e6i	0.384365	+	0.0914245i
$781$	−4.94680e6	+	8.56810e6i	−0.290199	+	0.502640i
$782$	−5.31071e6			−0.310553
$783$	2.72485e7	−	9.84283e6i	1.58832	−	0.573741i
$784$	−3.91735e6			−0.227616
$785$	−3.51398e6	+	6.08640e6i	−0.203529	+	0.352522i
$786$	1.77022e7	+	4.21064e6i	1.02205	+	0.243104i
$787$	−1.32878e7	−	2.30152e7i	−0.764747	−	1.32458i	−0.940380	−	0.340125i	$-0.889531\pi$
$787$	−1.32878e7	−	2.30152e7i	−0.764747	−	1.32458i	0.175634	−	0.984456i	$-0.443803\pi$
$788$	−3.53707e6	−	6.12638e6i	−0.202921	−	0.351470i
$789$	1.37872e7	−	1.45899e7i	0.788469	−	0.834375i
$790$	5.51143e6	−	9.54607e6i	0.314193	−	0.544198i
$791$	−1.68341e6			−0.0956642
$792$	1.57389e6	−	1.03152e6i	0.0891580	−	0.0584337i
$793$	−436048.			−0.0246236
$794$	2.79795e6	−	4.84620e6i	0.157503	−	0.272803i
$795$	7.38032e6	+	2.47248e7i	0.414150	+	1.38744i
$796$	−465215.	−	805776.i	−0.0260238	−	0.0450746i
$797$	1.12149e7	+	1.94248e7i	0.625387	+	1.08320i	0.988466	+	0.151444i	$0.0483923\pi$
$797$	1.12149e7	+	1.94248e7i	0.625387	+	1.08320i	−0.363079	+	0.931759i	$0.618274\pi$
$798$	1.40989e6	+	4.72326e6i	0.0783749	+	0.262563i
$799$	−3.06250e6	+	5.30440e6i	−0.169711	+	0.293947i
$800$	923316.			0.0510065
$801$	−1.58952e7	−	8.01510e6i	−0.875356	−	0.441395i
$802$	8.41198e6			0.461809
$803$	2.99094e6	−	5.18047e6i	0.163689	−	0.283518i
$804$	1.17944e7	−	1.24811e7i	0.643482	−	0.680947i
$805$	−3.99804e6	−	6.92481e6i	−0.217449	−	0.376633i
$806$	3.46523e6	+	6.00195e6i	0.187886	+	0.325428i
$807$	2.42757e7	+	5.77419e6i	1.31216	+	0.312109i
$808$	−1.70320e6	+	2.95003e6i	−0.0917777	+	0.158964i
$809$	−1.47106e7			−0.790240			−0.395120	−	0.918630i	$-0.629297\pi$
$809$	−1.47106e7			−0.790240			−0.395120	+	0.918630i	$0.629297\pi$
$810$	6.62170e6	+	8.95484e6i	0.354615	+	0.479562i
$811$	5.70815e6			0.304749			0.152375	−	0.988323i	$-0.451308\pi$
$811$	5.70815e6			0.304749			0.152375	+	0.988323i	$0.451308\pi$
$812$	2.37358e6	−	4.11116e6i	0.126332	−	0.218814i
$813$	1.72868e7	+	4.11181e6i	0.917250	+	0.218176i
$814$	−1.45242e6	−	2.51567e6i	−0.0768303	−	0.133074i
$815$	6.08766e6	+	1.05441e7i	0.321038	+	0.556054i
$816$	832449.	−	880915.i	0.0437655	−	0.0463136i
$817$	−1.08500e7	+	1.87928e7i	−0.568690	+	0.985000i
$818$	−9.79016e6			−0.511572
$819$	−4.80470e6	−	2.42275e6i	−0.250297	−	0.126212i
$820$	−1.48295e7			−0.770180
$821$	1.81761e7	−	3.14819e7i	0.941113	−	1.63006i	0.177760	−	0.984074i	$-0.443115\pi$
$821$	1.81761e7	−	3.14819e7i	0.941113	−	1.63006i	0.763353	−	0.645982i	$-0.223552\pi$
$822$	−4.29052e6	−	1.43737e7i	−0.221478	−	0.741972i
$823$	−1.11028e7	−	1.92307e7i	−0.571393	−	0.989681i	−0.996423	−	0.0845023i	$-0.973070\pi$
$823$	−1.11028e7	−	1.92307e7i	−0.571393	−	0.989681i	0.425031	−	0.905179i	$-0.360263\pi$
$824$	6.64337e6	+	1.15066e7i	0.340855	+	0.590379i
$825$	−486461.	−	1.62969e6i	−0.0248836	−	0.0833623i
$826$	−515178.	+	892314.i	−0.0262728	+	0.0455059i
$827$	−2.64511e7			−1.34487			−0.672435	−	0.740156i	$-0.734752\pi$
$827$	−2.64511e7			−1.34487			−0.672435	+	0.740156i	$0.734752\pi$
$828$	−1.42153e7	+	9.31661e6i	−0.720575	+	0.472261i
$829$	2.05263e7			1.03735			0.518675	−	0.854971i	$-0.326425\pi$
$829$	2.05263e7			1.03735			0.518675	+	0.854971i	$0.326425\pi$
$830$	3.27479e6	−	5.67211e6i	0.165002	−	0.285792i
$831$	5.87591e6	−	6.21802e6i	0.295170	−	0.312356i
$832$	−1.16906e6	−	2.02487e6i	−0.0585501	−	0.101412i
$833$	2.32374e6	+	4.02483e6i	0.116031	+	0.200972i
$834$	−4.11710e6	−	979288.i	−0.204963	−	0.0487523i
$835$	−1.60028e7	+	2.77177e7i	−0.794291	+	1.37575i
$836$	3.94520e6			0.195233
$837$	−2.02400e6	+	1.13180e7i	−0.0998612	+	0.558413i
$838$	−2.74956e6			−0.135255
$839$	−9.79129e6	+	1.69590e7i	−0.480214	+	0.831756i	−0.999742	−	0.0226978i	$-0.992774\pi$
$839$	−9.79129e6	+	1.69590e7i	−0.480214	+	0.831756i	0.519528	+	0.854453i	$0.326108\pi$
$840$	1.77534e6	+	422281.i	0.0868129	+	0.0206492i
$841$	−1.89928e7	−	3.28964e7i	−0.925973	−	1.60383i
$842$	1.42578e6	+	2.46953e6i	0.0693065	+	0.120042i
$843$	−1.20981e7	+	1.28024e7i	−0.586337	+	0.620474i
$844$	2.97194e6	−	5.14755e6i	0.143610	−	0.248739i
$845$	2.14295e6			0.103245
$846$	1.10811e6	+	1.95709e7i	0.0532301	+	0.940126i
$847$	−567962.			−0.0272026
$848$	4.49337e6	−	7.78274e6i	0.214577	−	0.371657i
$849$	369155.	+	1.23670e6i	0.0175768	+	0.0588839i
$850$	−547704.	−	948650.i	−0.0260015	−	0.0450359i
$851$	1.31182e7	+	2.27214e7i	0.620942	+	1.07550i
$852$	5.83312e6	+	1.95415e7i	0.275297	+	0.922271i
$853$	1.03810e7	−	1.79804e7i	0.488501	−	0.846109i	−0.511411	−	0.859336i	$-0.670877\pi$
$853$	1.03810e7	−	1.79804e7i	0.488501	−	0.846109i	0.999913	+	0.0132268i	$0.00421035\pi$
$854$	−118532.			−0.00556151
$855$	1.31992e6	+	2.33118e7i	0.0617494	+	1.09059i
$856$	5.53399e6			0.258139
$857$	−2.01274e7	+	3.48616e7i	−0.936128	+	1.62142i	−0.163517	+	0.986541i	$0.552284\pi$
$857$	−2.01274e7	+	3.48616e7i	−0.936128	+	1.62142i	−0.772611	+	0.634880i	$0.781050\pi$
$858$	−2.95804e6	+	3.13026e6i	−0.137178	+	0.145165i
$859$	9.64711e6	+	1.67093e7i	0.446082	+	0.772636i	0.998127	−	0.0611781i	$-0.0194858\pi$
$859$	9.64711e6	+	1.67093e7i	0.446082	+	0.772636i	−0.552045	+	0.833814i	$0.686152\pi$
$860$	4.01687e6	+	6.95743e6i	0.185200	+	0.320776i
$861$	1.15640e7	+	2.75059e6i	0.531616	+	0.126450i
$862$	1.29507e7	−	2.24312e7i	0.593642	−	1.02822i
$863$	1.94264e6			0.0887905			0.0443952	−	0.999014i	$-0.485864\pi$
$863$	1.94264e6			0.0887905			0.0443952	+	0.999014i	$0.485864\pi$
$864$	682833.	−	3.81833e6i	0.0311193	−	0.174016i
$865$	−1.77773e7			−0.807842
$866$	−143097.	+	247851.i	−0.00648389	+	0.0112304i
$867$	2.01337e7	+	4.78899e6i	0.909655	+	0.216370i
$868$	941964.	+	1.63153e6i	0.0424360	+	0.0735014i
$869$	3.53580e6	+	6.12419e6i	0.158832	+	0.275106i
$870$	1.54447e7	−	1.63439e7i	0.691801	−	0.732079i
$871$	−1.96508e7	+	3.40362e7i	−0.877677	+	1.52018i
$872$	8.23755e6			0.366865
$873$	1.27157e7	−	8.33379e6i	0.564682	−	0.370090i
$874$	−3.56329e7			−1.57788
$875$	3.68270e6	−	6.37863e6i	0.162610	−	0.281648i
$876$	−3.52683e6	−	1.18152e7i	−0.155283	−	0.520213i
$877$	1.56206e7	+	2.70557e7i	0.685803	+	1.18785i	0.973184	+	0.230029i	$0.0738821\pi$
$877$	1.56206e7	+	2.70557e7i	0.685803	+	1.18785i	−0.287381	+	0.957816i	$0.592785\pi$
$878$	−1.21033e7	−	2.09635e7i	−0.529868	−	0.917758i
$879$	−2.71179e6	−	9.08475e6i	−0.118381	−	0.396589i
$880$	730292.	−	1.26490e6i	0.0317900	−	0.0550618i
$881$	−1.35618e7			−0.588678			−0.294339	−	0.955701i	$-0.595100\pi$
$881$	−1.35618e7			−0.588678			−0.294339	+	0.955701i	$0.595100\pi$
$882$	1.32808e7	+	6.69679e6i	0.574847	+	0.289865i
$883$	−2.35001e7			−1.01430			−0.507151	−	0.861857i	$-0.669302\pi$
$883$	−2.35001e7			−1.01430			−0.507151	+	0.861857i	$0.669302\pi$
$884$	−1.38695e6	+	2.40227e6i	−0.0596940	+	0.103393i
$885$	−3.35222e6	+	3.54739e6i	−0.143871	+	0.152248i
$886$	−7.17869e6	−	1.24339e7i	−0.307228	−	0.532135i
$887$	−7.81708e6	−	1.35396e7i	−0.333607	−	0.577825i	0.649609	−	0.760269i	$-0.274933\pi$
$887$	−7.81708e6	−	1.35396e7i	−0.333607	−	0.577825i	−0.983216	+	0.182444i	$0.941599\pi$
$888$	−5.82520e6	−	1.38557e6i	−0.247901	−	0.0589654i
$889$	−124238.	+	215186.i	−0.00527229	+	0.00913187i
$890$	−1.38171e7			−0.584710
$891$	−7.09926e6	+	806509.i	−0.299584	+	0.0340341i
$892$	−1.43397e6			−0.0603430
$893$	−2.05482e7	+	3.55906e7i	−0.862275	+	1.49350i
$894$	−9.91872e6	−	2.35926e6i	−0.415061	−	0.0987260i
$895$	7.51007e6	+	1.30078e7i	0.313391	+	0.542809i
$896$	−317789.	−	550426.i	−0.0132242	−	0.0229049i
$897$	2.67168e7	−	2.82724e7i	1.10867	−	1.17322i
$898$	1.26916e7	−	2.19825e7i	0.525201	−	0.909675i
$899$	2.32146e7			0.957992
$900$	−3.13027e6	−	1.57843e6i	−0.128818	−	0.0649559i
$901$	−1.06617e7			−0.437537
$902$	4.75686e6	−	8.23913e6i	0.194672	−	0.337182i
$903$	−1.84186e6	−	6.17041e6i	−0.0751688	−	0.251823i
$904$	1.38865e6	+	2.40521e6i	0.0565160	+	0.0978885i
$905$	1.23830e6	+	2.14480e6i	0.0502579	+	0.0870493i
$906$	5.25391e6	+	1.76011e7i	0.212648	+	0.712392i
$907$	2.13331e7	−	3.69500e7i	0.861065	−	1.49141i	−0.00983661	−	0.999952i	$-0.503131\pi$
$907$	2.13331e7	−	3.69500e7i	0.861065	−	1.49141i	0.870902	−	0.491457i	$-0.163536\pi$
$908$	9.30941e6			0.374721
$909$	1.08174e7	−	7.08968e6i	0.434224	−	0.284588i
$910$	−4.17653e6			−0.167191
$911$	4.27923e6	−	7.41184e6i	0.170832	−	0.295890i	−0.767879	−	0.640595i	$-0.778688\pi$
$911$	4.27923e6	−	7.41184e6i	0.170832	−	0.295890i	0.938711	+	0.344705i	$0.112021\pi$
$912$	5.58543e6	−	5.91062e6i	0.222366	−	0.235313i
$913$	2.10091e6	+	3.63889e6i	0.0834125	+	0.144475i
$914$	−1.05732e7	−	1.83133e7i	−0.418639	−	0.725104i
$915$	−546239.	−	129928.i	−0.0215690	−	0.00513038i
$916$	2.28903e6	−	3.96472e6i	0.0901392	−	0.156126i
$917$	−1.13205e7			−0.444571
$918$	−4.32815e6	+	1.56343e6i	−0.169510	+	0.0612312i
$919$	7.53250e6			0.294205			0.147103	−	0.989121i	$-0.453005\pi$
$919$	7.53250e6			0.294205			0.147103	+	0.989121i	$0.453005\pi$
$920$	−6.59597e6	+	1.14246e7i	−0.256927	+	0.445010i
$921$	−3.41651e6	−	812646.i	−0.132719	−	0.0315684i
$922$	1.05321e7	+	1.82421e7i	0.408026	+	0.706721i
$923$	−2.33370e7	−	4.04208e7i	−0.901655	−	1.56171i
$924$	−804093.	+	850908.i	−0.0309832	+	0.0327871i
$925$	−2.70582e6	+	4.68661e6i	−0.103979	+	0.180096i
$926$	1.32132e7			0.506384
$927$	−2.85181e6	−	5.03674e7i	−0.108999	−	1.92509i
$928$	−7.83187e6			−0.298535
$929$	8.30112e6	−	1.43780e7i	0.315571	−	0.546586i	−0.663987	−	0.747744i	$-0.731137\pi$
$929$	8.30112e6	−	1.43780e7i	0.315571	−	0.546586i	0.979559	+	0.201158i	$0.0644705\pi$
$930$	2.55252e6	+	8.55118e6i	0.0967747	+	0.324204i
$931$	1.55914e7	+	2.70052e7i	0.589538	+	1.02111i
$932$	8.56661e6	+	1.48378e7i	0.323050	+	0.559538i
$933$	−4.52079e6	−	1.51451e7i	−0.170024	−	0.569596i
$934$	1.71661e7	−	2.97326e7i	0.643880	−	1.11523i
$935$	−1.73281e6			−0.0648221
$936$	501844.	+	8.86333e6i	0.0187231	+	0.330680i
$937$	1.62303e6			0.0603919			0.0301959	−	0.999544i	$-0.490387\pi$
$937$	1.62303e6			0.0603919			0.0301959	+	0.999544i	$0.490387\pi$
$938$	−5.34174e6	+	9.25216e6i	−0.198233	+	0.343349i
$939$	8.75462e6	−	9.26433e6i	0.324021	−	0.342886i
$940$	7.60732e6	+	1.31763e7i	0.280810	+	0.486377i
$941$	2.10301e7	+	3.64252e7i	0.774225	+	1.34100i	0.935229	+	0.354043i	$0.115193\pi$
$941$	2.10301e7	+	3.64252e7i	0.774225	+	1.34100i	−0.161005	+	0.986954i	$0.551473\pi$
$942$	−9.04151e6	−	2.15060e6i	−0.331981	−	0.0789647i
$943$	−4.29638e7	+	7.44154e7i	−1.57334	+	2.72511i
$944$	1.69988e6			0.0620853
$945$	−5.29696e6	−	4.46663e6i	−0.192951	−	0.162705i
$946$	−5.15397e6			−0.187247
$947$	−7.66417e6	+	1.32747e7i	−0.277709	+	0.481006i	−0.970815	−	0.239830i	$-0.922908\pi$
$947$	−7.66417e6	+	1.32747e7i	−0.277709	+	0.481006i	0.693106	+	0.720836i	$0.256242\pi$
$948$	1.41810e7	+	3.37307e6i	0.512489	+	0.121900i
$949$	1.41101e7	+	2.44393e7i	0.508585	+	0.880894i
$950$	−3.67489e6	−	6.36510e6i	−0.132110	−	0.228821i
$951$	−2.22792e7	+	2.35763e7i	−0.798818	+	0.845327i
$952$	−377019.	+	653017.i	−0.0134825	+	0.0233524i
$953$	−1.44856e7			−0.516661			−0.258331	−	0.966057i	$-0.583172\pi$
$953$	−1.44856e7			−0.516661			−0.258331	+	0.966057i	$0.583172\pi$
$954$	−2.85384e7	+	1.87039e7i	−1.01522	+	0.665368i
$955$	−1.52626e7			−0.541526
$956$	−869065.	+	1.50527e6i	−0.0307544	+	0.0532682i
$957$	4.12632e6	+	1.38236e7i	0.145641	+	0.487910i
$958$	−1.65792e7	−	2.87160e7i	−0.583646	−	1.01090i
$959$	4.66613e6	+	8.08197e6i	0.163836	+	0.283773i
$960$	−861139.	−	2.88490e6i	−0.0301575	−	0.101030i
$961$	9.70818e6	−	1.68151e7i	0.339101	−	0.587340i
$962$	1.37039e7			0.477426
$963$	−1.87616e7	−	9.46048e6i	−0.651935	−	0.328736i
$964$	−8.33593e6			−0.288909
$965$	2.09399e7	−	3.62689e7i	0.723862	−	1.25377i
$966$	7.26253e6	−	7.68537e6i	0.250406	−	0.264985i
$967$	−2.70681e7	−	4.68834e7i	−0.930877	−	1.61233i	−0.781826	−	0.623497i	$-0.785711\pi$
$967$	−2.70681e7	−	4.68834e7i	−0.930877	−	1.61233i	−0.149051	−	0.988829i	$-0.547622\pi$
$968$	468512.	+	811487.i	0.0160706	+	0.0278351i
$969$	−9.38603e6	−	2.23255e6i	−0.321124	−	0.0763821i
$970$	5.90015e6	−	1.02194e7i	0.201342	−	0.348734i
$971$	−3.43903e7			−1.17054			−0.585272	−	0.810837i	$-0.699012\pi$
$971$	−3.43903e7			−1.17054			−0.585272	+	0.810837i	$0.699012\pi$
$972$	−8.84250e6	+	1.17778e7i	−0.300199	+	0.399851i
$973$	2.63286e6			0.0891548
$974$	−2.56614e6	+	4.44468e6i	−0.0866727	+	0.150122i
$975$	7.80564e6	+	1.85664e6i	0.262965	+	0.0625485i
$976$	97777.5	+	169356.i	0.00328560	+	0.00569082i
$977$	−1.90639e7	−	3.30197e7i	−0.638964	−	1.10672i	−0.985661	−	0.168740i	$-0.946030\pi$
$977$	−1.90639e7	−	3.30197e7i	−0.638964	−	1.10672i	0.346697	−	0.937977i	$-0.387303\pi$
$978$	−1.10584e7	+	1.17022e7i	−0.369695	+	0.391220i
$979$	4.43210e6	−	7.67663e6i	0.147793	−	0.255985i
$980$	1.15445e7			0.383980
$981$	−2.79273e7	−	1.40823e7i	−0.926525	−	0.467197i
$982$	−3.48193e7			−1.15223
$983$	5.49262e6	−	9.51350e6i	0.181299	−	0.314019i	−0.761024	−	0.648724i	$-0.775303\pi$
$983$	5.49262e6	−	9.51350e6i	0.181299	−	0.314019i	0.942323	+	0.334704i	$0.108636\pi$
$984$	−5.60915e6	−	1.87912e7i	−0.184676	−	0.618680i
$985$	1.04238e7	+	1.80545e7i	0.342321	+	0.592918i
$986$	4.64580e6	+	8.04677e6i	0.152184	+	0.263590i
$987$	−3.48820e6	−	1.16858e7i	−0.113975	−	0.381826i
$988$	−9.30593e6	+	1.61183e7i	−0.303297	+	0.525325i
$989$	4.65504e7			1.51333
$990$	−4.63825e6	+	3.03989e6i	−0.150406	+	0.0985757i
$991$	−1.01854e7			−0.329454			−0.164727	−	0.986339i	$-0.552674\pi$
$991$	−1.01854e7			−0.329454			−0.164727	+	0.986339i	$0.552674\pi$
$992$	1.55405e6	−	2.69170e6i	0.0501402	−	0.0868454i
$993$	−3.85428e7	+	4.07868e7i	−1.24042	+	1.31264i
$994$	−6.34376e6	−	1.09877e7i	−0.203648	−	0.352729i
$995$	1.37099e6	+	2.37463e6i	0.0439013	+	0.0760393i
$996$	8.42607e6	+	2.00422e6i	0.269139	+	0.0640171i
$997$	2.33475e7	−	4.04391e7i	0.743880	−	1.28844i	−0.206837	−	0.978375i	$-0.566317\pi$
$997$	2.33475e7	−	4.04391e7i	0.743880	−	1.28844i	0.950716	−	0.310062i	$-0.100350\pi$
$998$	9.26913e6			0.294586
$999$	1.73802e7	+	1.46557e7i	0.550987	+	0.464616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.e.b.133.1	yes	24
3.2	odd	2		594.6.e.a.397.5		24
9.4	even	3	inner	198.6.e.b.67.1	✓	24
9.5	odd	6		594.6.e.a.199.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.e.b.67.1	✓	24	9.4	even	3	inner
198.6.e.b.133.1	yes	24	1.1	even	1	trivial
594.6.e.a.199.5		24	9.5	odd	6
594.6.e.a.397.5		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-15.1654 - 3.60721i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.5761 + 40.8350i) q^{5} +(-42.8265 + 45.3199i) q^{6} +(19.3963 - 33.5953i) q^{7} -64.0000 q^{8} +(216.976 + 109.409i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-15.1654 - 3.60721i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.5761 + 40.8350i) q^{5} +(-42.8265 + 45.3199i) q^{6} +(19.3963 - 33.5953i) q^{7} -64.0000 q^{8} +(216.976 + 109.409i) q^{9} +188.609 q^{10} +(-60.5000 + 104.789i) q^{11} +(71.3398 + 238.995i) q^{12} +(-285.414 - 494.352i) q^{13} +(-77.5851 - 134.381i) q^{14} +(-210.239 - 704.321i) q^{15} +(-128.000 + 221.703i) q^{16} +303.714 q^{17} +(812.957 - 532.808i) q^{18} +2037.81 q^{19} +(377.217 - 653.359i) q^{20} +(-415.337 + 439.519i) q^{21} +(242.000 + 419.156i) q^{22} +(-2185.73 - 3785.80i) q^{23} +(970.583 + 230.862i) q^{24} +(450.838 - 780.874i) q^{25} -2283.32 q^{26} +(-2895.86 - 2441.91i) q^{27} -620.681 q^{28} +(-3824.16 + 6623.63i) q^{29} +(-2860.32 - 680.352i) q^{30} +(-1517.63 - 2628.61i) q^{31} +(512.000 + 886.810i) q^{32} +(1295.50 - 1370.93i) q^{33} +(607.429 - 1052.10i) q^{34} +1829.15 q^{35} +(-219.787 - 3881.78i) q^{36} -6001.75 q^{37} +(4075.62 - 7059.19i) q^{38} +(2545.18 + 8526.58i) q^{39} +(-1508.87 - 2613.44i) q^{40} +(-9828.23 - 17023.0i) q^{41} +(691.864 + 2317.81i) q^{42} +(-5324.35 + 9222.04i) q^{43} +1936.00 q^{44} +(647.715 + 11439.6i) q^{45} -17485.9 q^{46} +(-10083.5 + 17465.1i) q^{47} +(2740.89 - 2900.47i) q^{48} +(7651.07 + 13252.0i) q^{49} +(-1803.35 - 3123.50i) q^{50} +(-4605.94 - 1095.56i) q^{51} +(-4566.63 + 7909.64i) q^{52} -35104.4 q^{53} +(-14250.7 + 5147.71i) q^{54} -5705.41 q^{55} +(-1241.36 + 2150.10i) q^{56} +(-30904.1 - 7350.82i) q^{57} +(15296.6 + 26494.5i) q^{58} +(-3320.08 - 5750.55i) q^{59} +(-8077.44 + 8547.72i) q^{60} +(381.943 - 661.545i) q^{61} -12141.0 q^{62} +(7884.17 - 5167.25i) q^{63} +4096.00 q^{64} +(13457.9 - 23309.8i) q^{65} +(-2158.03 - 7229.60i) q^{66} +(-34425.0 - 59625.9i) q^{67} +(-2429.71 - 4208.39i) q^{68} +(19491.2 + 65297.4i) q^{69} +(3658.30 - 6336.37i) q^{70} +81765.2 q^{71} +(-13886.5 - 7002.20i) q^{72} -49437.1 q^{73} +(-12003.5 + 20790.7i) q^{74} +(-9653.90 + 10216.0i) q^{75} +(-16302.5 - 28236.7i) q^{76} +(2346.95 + 4065.04i) q^{77} +(34627.3 + 8236.41i) q^{78} +(29221.5 - 50613.2i) q^{79} -12070.9 q^{80} +(35108.2 + 47478.4i) q^{81} -78625.8 q^{82} +(17362.9 - 30073.5i) q^{83} +(9412.85 + 2238.93i) q^{84} +(7160.39 + 12402.2i) q^{85} +(21297.4 + 36888.2i) q^{86} +(81887.5 - 86655.2i) q^{87} +(3872.00 - 6706.50i) q^{88} -73257.9 q^{89} +(40923.5 + 20635.5i) q^{90} -22143.9 q^{91} +(-34971.7 + 60572.8i) q^{92} +(13533.4 + 45338.2i) q^{93} +(40333.9 + 69860.4i) q^{94} +(48043.6 + 83213.9i) q^{95} +(-4565.75 - 15295.7i) q^{96} +(31282.5 - 54182.9i) q^{97} +61208.5 q^{98} +(-24592.0 + 16117.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Introduction

L-functions

Modular forms

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