LMFDB - Embedded newform 138.6.d.a.137.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,6,Mod(137,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("138.137");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	138.d (of order $2$, degree $1$, 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:	$22.1329671342$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	138.137
Dual form			138.6.d.a.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} +(-1.79544 + 15.4847i) q^{3} -16.0000 q^{4} +69.6024 q^{5} +(61.9389 + 7.18174i) q^{6} -161.717i q^{7} +64.0000i q^{8} +(-236.553 - 55.6036i) q^{9} +O(q^{10})$	\(q-4.00000i q^{2} +(-1.79544 + 15.4847i) q^{3} -16.0000 q^{4} +69.6024 q^{5} +(61.9389 + 7.18174i) q^{6} -161.717i q^{7} +64.0000i q^{8} +(-236.553 - 55.6036i) q^{9} -278.410i q^{10} -206.485 q^{11} +(28.7270 - 247.755i) q^{12} +54.3582 q^{13} -646.867 q^{14} +(-124.967 + 1077.77i) q^{15} +256.000 q^{16} +1079.76 q^{17} +(-222.414 + 946.211i) q^{18} -503.925i q^{19} -1113.64 q^{20} +(2504.14 + 290.352i) q^{21} +825.941i q^{22} +(-563.118 - 2473.71i) q^{23} +(-991.022 - 114.908i) q^{24} +1719.50 q^{25} -217.433i q^{26} +(1285.72 - 3563.12i) q^{27} +2587.47i q^{28} -7254.99i q^{29} +(4311.10 + 499.867i) q^{30} +4839.06 q^{31} -1024.00i q^{32} +(370.731 - 3197.37i) q^{33} -4319.02i q^{34} -11255.9i q^{35} +(3784.85 + 889.658i) q^{36} -2909.35i q^{37} -2015.70 q^{38} +(-97.5967 + 841.722i) q^{39} +4454.56i q^{40} -86.4971i q^{41} +(1161.41 - 10016.6i) q^{42} +7002.50i q^{43} +3303.77 q^{44} +(-16464.7 - 3870.15i) q^{45} +(-9894.84 + 2252.47i) q^{46} -6595.86i q^{47} +(-459.631 + 3964.09i) q^{48} -9345.33 q^{49} -6877.99i q^{50} +(-1938.63 + 16719.7i) q^{51} -869.731 q^{52} +32188.0 q^{53} +(-14252.5 - 5142.89i) q^{54} -14371.9 q^{55} +10349.9 q^{56} +(7803.13 + 904.764i) q^{57} -29020.0 q^{58} -25468.2i q^{59} +(1999.47 - 17244.4i) q^{60} -24154.2i q^{61} -19356.2i q^{62} +(-8992.04 + 38254.6i) q^{63} -4096.00 q^{64} +3783.46 q^{65} +(-12789.5 - 1482.92i) q^{66} -5063.06i q^{67} -17276.1 q^{68} +(39315.7 - 4278.33i) q^{69} -45023.5 q^{70} -4030.70i q^{71} +(3558.63 - 15139.4i) q^{72} +10897.3 q^{73} -11637.4 q^{74} +(-3087.25 + 26625.9i) q^{75} +8062.79i q^{76} +33392.1i q^{77} +(3366.89 + 390.387i) q^{78} -67758.5i q^{79} +17818.2 q^{80} +(52865.5 + 26306.4i) q^{81} -345.988 q^{82} -72499.7 q^{83} +(-40066.2 - 4645.63i) q^{84} +75153.6 q^{85} +28010.0 q^{86} +(112341. + 13025.9i) q^{87} -13215.1i q^{88} +67033.0 q^{89} +(-15480.6 + 65858.6i) q^{90} -8790.64i q^{91} +(9009.89 + 39579.4i) q^{92} +(-8688.22 + 74931.5i) q^{93} -26383.4 q^{94} -35074.4i q^{95} +(15856.3 + 1838.53i) q^{96} +165763. i q^{97} +37381.3i q^{98} +(48844.7 + 11481.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9}+O(q^{10}) $ 40 * q - 4 * q^3 - 640 * q^4 + 80 * q^6 + 504 * q^9	$ 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96}+O(q^{100}) $ 40 * q - 4 * q^3 - 640 * q^4 + 80 * q^6 + 504 * q^9 + 64 * q^12 - 1048 * q^13 + 10240 * q^16 + 1280 * q^18 - 1280 * q^24 + 30480 * q^25 + 1700 * q^27 - 22576 * q^31 - 8064 * q^36 + 55608 * q^39 + 1088 * q^46 - 1024 * q^48 - 23224 * q^49 + 16768 * q^52 + 25456 * q^54 + 210400 * q^55 - 83168 * q^58 - 163840 * q^64 + 99076 * q^69 + 167520 * q^70 - 20480 * q^72 + 241160 * q^73 - 255604 * q^75 - 233440 * q^78 + 78512 * q^81 - 8832 * q^82 - 460296 * q^85 - 4136 * q^87 + 500704 * q^93 - 138272 * q^94 + 20480 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$97$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$	−1.79544	+	15.4847i	−0.115177	+	0.993345i
$3$	−1.79544	+	15.4847i	−0.115177	+	0.993345i
$4$	−16.0000			−0.500000
$5$	69.6024			1.24509			0.622543	−	0.782586i	$-0.286100\pi$
$5$	69.6024			1.24509			0.622543	+	0.782586i	$0.286100\pi$
$6$	61.9389	+	7.18174i	0.702401	+	0.0814426i
$7$		−	161.717i		−	1.24741i	−0.781659	−	0.623706i	$-0.785626\pi$
$7$		−	161.717i		−	1.24741i	0.781659	−	0.623706i	$-0.214374\pi$
$8$			64.0000i			0.353553i
$9$	−236.553	−	55.6036i	−0.973468	−	0.228821i
$10$		−	278.410i		−	0.880409i
$11$	−206.485			−0.514526			−0.257263	−	0.966341i	$-0.582821\pi$
$11$	−206.485			−0.514526			−0.257263	+	0.966341i	$0.582821\pi$
$12$	28.7270	−	247.755i	0.0575886	−	0.496672i
$13$	54.3582			0.0892086			0.0446043	−	0.999005i	$-0.485797\pi$
$13$	54.3582			0.0892086			0.0446043	+	0.999005i	$0.485797\pi$
$14$	−646.867			−0.882054
$15$	−124.967	+	1077.77i	−0.143406	+	1.23680i
$16$	256.000			0.250000
$17$	1079.76			0.906156			0.453078	−	0.891471i	$-0.350326\pi$
$17$	1079.76			0.906156			0.453078	+	0.891471i	$0.350326\pi$
$18$	−222.414	+	946.211i	−0.161801	+	0.688346i
$19$		−	503.925i		−	0.320244i	−0.987097	−	0.160122i	$-0.948811\pi$
$19$		−	503.925i		−	0.320244i	0.987097	−	0.160122i	$-0.0511888\pi$
$20$	−1113.64			−0.622543
$21$	2504.14	+	290.352i	1.23911	+	0.143674i
$22$			825.941i			0.363825i
$23$	−563.118	−	2473.71i	−0.221963	−	0.975055i
$23$	−563.118	−	2473.71i	−0.221963	−	0.975055i
$24$	−991.022	−	114.908i	−0.351200	−	0.0407213i
$25$	1719.50			0.550240
$26$		−	217.433i		−	0.0630800i
$27$	1285.72	−	3563.12i	0.339420	−	0.940635i
$28$			2587.47i			0.623706i
$29$		−	7254.99i		−	1.60192i	−0.598715	−	0.800962i	$-0.704322\pi$
$29$		−	7254.99i		−	1.60192i	0.598715	−	0.800962i	$-0.295678\pi$
$30$	4311.10	+	499.867i	0.874550	+	0.101403i
$31$	4839.06			0.904392			0.452196	−	0.891919i	$-0.350641\pi$
$31$	4839.06			0.904392			0.452196	+	0.891919i	$0.350641\pi$
$32$		−	1024.00i		−	0.176777i
$33$	370.731	−	3197.37i	0.0592617	−	0.511102i
$34$		−	4319.02i		−	0.640749i
$35$		−	11255.9i		−	1.55314i
$36$	3784.85	+	889.658i	0.486734	+	0.114411i
$37$		−	2909.35i		−	0.349375i	−0.984624	−	0.174688i	$-0.944108\pi$
$37$		−	2909.35i		−	0.349375i	0.984624	−	0.174688i	$-0.0558916\pi$
$38$	−2015.70			−0.226447
$39$	−97.5967	+	841.722i	−0.0102748	+	0.0886149i
$40$			4454.56i			0.440204i
$41$		−	86.4971i		−	0.00803604i	−0.999992	−	0.00401802i	$-0.998721\pi$
$41$		−	86.4971i		−	0.00803604i	0.999992	−	0.00401802i	$-0.00127898\pi$
$42$	1161.41	−	10016.6i	0.101593	−	0.876184i
$43$			7002.50i			0.577540i	0.957398	+	0.288770i	$0.0932463\pi$
$43$			7002.50i			0.577540i	−0.957398	+	0.288770i	$0.906754\pi$
$44$	3303.77			0.257263
$45$	−16464.7	−	3870.15i	−1.21205	−	0.284902i
$46$	−9894.84	+	2252.47i	−0.689468	+	0.156951i
$47$		−	6595.86i		−	0.435539i	−0.976000	−	0.217769i	$-0.930122\pi$
$47$		−	6595.86i		−	0.435539i	0.976000	−	0.217769i	$-0.0698780\pi$
$48$	−459.631	+	3964.09i	−0.0287943	+	0.248336i
$49$	−9345.33			−0.556038
$50$		−	6877.99i		−	0.389078i
$51$	−1938.63	+	16719.7i	−0.104369	+	0.900125i
$52$	−869.731			−0.0446043
$53$	32188.0			1.57400			0.786998	−	0.616955i	$-0.211634\pi$
$53$	32188.0			1.57400			0.786998	+	0.616955i	$0.211634\pi$
$54$	−14252.5	−	5142.89i	−0.665129	−	0.240006i
$55$	−14371.9			−0.640629
$56$	10349.9			0.441027
$57$	7803.13	+	904.764i	0.318113	+	0.0368849i
$58$	−29020.0			−1.13273
$59$		−	25468.2i		−	0.952507i	−0.879308	−	0.476253i	$-0.841995\pi$
$59$		−	25468.2i		−	0.952507i	0.879308	−	0.476253i	$-0.158005\pi$
$60$	1999.47	−	17244.4i	0.0717028	−	0.618400i
$61$		−	24154.2i		−	0.831127i	−0.909564	−	0.415563i	$-0.863584\pi$
$61$		−	24154.2i		−	0.831127i	0.909564	−	0.415563i	$-0.136416\pi$
$62$		−	19356.2i		−	0.639502i
$63$	−8992.04	+	38254.6i	−0.285435	+	1.21432i
$64$	−4096.00			−0.125000
$65$	3783.46			0.111072
$66$	−12789.5	−	1482.92i	−0.361404	−	0.0419044i
$67$		−	5063.06i		−	0.137793i	−0.997624	−	0.0688963i	$-0.978052\pi$
$67$		−	5063.06i		−	0.137793i	0.997624	−	0.0688963i	$-0.0219478\pi$
$68$	−17276.1			−0.453078
$69$	39315.7	−	4278.33i	0.994131	−	0.108181i
$70$	−45023.5			−1.09823
$71$		−	4030.70i		−	0.0948931i	−0.998874	−	0.0474466i	$-0.984892\pi$
$71$		−	4030.70i		−	0.0948931i	0.998874	−	0.0474466i	$-0.0151084\pi$
$72$	3558.63	−	15139.4i	0.0809006	−	0.344173i
$73$	10897.3			0.239338			0.119669	−	0.992814i	$-0.461817\pi$
$73$	10897.3			0.239338			0.119669	+	0.992814i	$0.461817\pi$
$74$	−11637.4			−0.247046
$75$	−3087.25	+	26625.9i	−0.0633751	+	0.546578i
$76$			8062.79i			0.160122i
$77$			33392.1i			0.641826i
$78$	3366.89	+	390.387i	0.0626602	+	0.00726538i
$79$		−	67758.5i		−	1.22151i	−0.791820	−	0.610754i	$-0.790866\pi$
$79$		−	67758.5i		−	1.22151i	0.791820	−	0.610754i	$-0.209134\pi$
$80$	17818.2			0.311272
$81$	52865.5	+	26306.4i	0.895281	+	0.445501i
$82$	−345.988			−0.00568234
$83$	−72499.7			−1.15516			−0.577578	−	0.816335i	$-0.696002\pi$
$83$	−72499.7			−1.15516			−0.577578	+	0.816335i	$0.696002\pi$
$84$	−40066.2	−	4645.63i	−0.619555	−	0.0718368i
$85$	75153.6			1.12824
$86$	28010.0			0.408383
$87$	112341.	+	13025.9i	1.59126	+	0.184505i
$88$		−	13215.1i		−	0.181912i
$89$	67033.0			0.897043			0.448522	−	0.893772i	$-0.351951\pi$
$89$	67033.0			0.897043			0.448522	+	0.893772i	$0.351951\pi$
$90$	−15480.6	+	65858.6i	−0.201456	+	0.857050i
$91$		−	8790.64i		−	0.111280i
$92$	9009.89	+	39579.4i	0.110981	+	0.487528i
$93$	−8688.22	+	74931.5i	−0.104165	+	0.898373i
$94$	−26383.4			−0.307972
$95$		−	35074.4i		−	0.398732i
$96$	15856.3	+	1838.53i	0.175600	+	0.0203607i
$97$			165763.i			1.78878i	0.447286	+	0.894391i	$0.352391\pi$
$97$			165763.i			1.78878i	−0.447286	+	0.894391i	$0.647609\pi$
$98$			37381.3i			0.393178i
$99$	48844.7	+	11481.3i	0.500875	+	0.117735i
$100$	−27512.0			−0.275120
$101$			109083.i			1.06403i	0.846736	+	0.532014i	$0.178565\pi$
$101$			109083.i			1.06403i	−0.846736	+	0.532014i	$0.821435\pi$
$102$	66878.8	+	7754.52i	0.636485	+	0.0737997i
$103$			70362.0i			0.653499i	0.945111	+	0.326750i	$0.105953\pi$
$103$			70362.0i			0.653499i	−0.945111	+	0.326750i	$0.894047\pi$
$104$			3478.93i			0.0315400i
$105$	174294.	+	20209.2i	1.54280	+	0.178886i
$106$		−	128752.i		−	1.11298i
$107$	−75744.3			−0.639574			−0.319787	−	0.947489i	$-0.603611\pi$
$107$	−75744.3			−0.639574			−0.319787	+	0.947489i	$0.603611\pi$
$108$	−20571.5	+	57009.9i	−0.169710	+	0.470317i
$109$			128302.i			1.03435i	0.855880	+	0.517175i	$0.173016\pi$
$109$			128302.i			1.03435i	−0.855880	+	0.517175i	$0.826984\pi$
$110$			57487.5i			0.452993i
$111$	45050.5	+	5223.56i	0.347050	+	0.0402401i
$112$		−	41399.5i		−	0.311853i
$113$	−211958.			−1.56154			−0.780771	−	0.624817i	$-0.785174\pi$
$113$	−211958.			−1.56154			−0.780771	+	0.624817i	$0.785174\pi$
$114$	3619.06	−	31212.5i	0.0260815	−	0.224940i
$115$	−39194.4	−	172176.i	−0.276363	−	1.21403i
$116$			116080.i			0.800962i
$117$	−12858.6	−	3022.51i	−0.0868418	−	0.0204128i
$118$	−101873.			−0.673524
$119$		−	174615.i		−	1.13035i
$120$	−68977.5	−	7997.87i	−0.437275	−	0.0507015i
$121$	−118415.			−0.735263
$122$	−96616.6			−0.587695
$123$	1339.38	+	155.300i	0.00798256	+	0.000925569i
$124$	−77425.0			−0.452196
$125$	−97826.3			−0.559990
$126$	153018.	+	35968.2i	0.858652	+	0.201833i
$127$	−81298.6			−0.447274			−0.223637	−	0.974672i	$-0.571793\pi$
$127$	−81298.6			−0.447274			−0.223637	+	0.974672i	$0.571793\pi$
$128$			16384.0i			0.0883883i
$129$	−108432.	−	12572.5i	−0.573697	−	0.0665195i
$130$		−	15133.9i		−	0.0785401i
$131$			201311.i			1.02492i	0.858712	+	0.512458i	$0.171265\pi$
$131$			201311.i			1.02492i	−0.858712	+	0.512458i	$0.828735\pi$
$132$	−5931.70	+	51157.9i	−0.0296309	+	0.255551i
$133$	−81493.1			−0.399477
$134$	−20252.2			−0.0974341
$135$	89489.3	−	248002.i	0.422607	−	1.17117i
$136$			69104.3i			0.320375i
$137$	378364.			1.72230			0.861149	−	0.508353i	$-0.169746\pi$
$137$	378364.			1.72230			0.861149	+	0.508353i	$0.169746\pi$
$138$	−17113.3	−	157263.i	−0.0764957	−	0.702957i
$139$	−444405.			−1.95093			−0.975466	−	0.220149i	$-0.929346\pi$
$139$	−444405.			−1.95093			−0.975466	+	0.220149i	$0.929346\pi$
$140$			180094.i			0.776568i
$141$	102135.	+	11842.4i	0.432640	+	0.0501641i
$142$	−16122.8			−0.0670996
$143$	−11224.2			−0.0459002
$144$	−60557.5	−	14234.5i	−0.243367	−	0.0572054i
$145$		−	504965.i		−	1.99453i
$146$		−	43589.2i		−	0.169238i
$147$	16778.9	−	144710.i	0.0640429	−	0.552337i
$148$			46549.7i			0.174688i
$149$	327377.			1.20804			0.604021	−	0.796969i	$-0.293564\pi$
$149$	327377.			1.20804			0.604021	+	0.796969i	$0.293564\pi$
$150$	106504.	+	12349.0i	0.386489	+	0.0448129i
$151$	208726.			0.744961			0.372481	−	0.928040i	$-0.378507\pi$
$151$	208726.			0.744961			0.372481	+	0.928040i	$0.378507\pi$
$152$	32251.2			0.113224
$153$	−255419.	−	60038.3i	−0.882114	−	0.207348i
$154$	133569.			0.453840
$155$	336810.			1.12605
$156$	1561.55	−	13467.5i	0.00513740	−	0.0443075i
$157$			503658.i			1.63075i	0.578935	+	0.815374i	$0.303468\pi$
$157$			503658.i			1.63075i	−0.578935	+	0.815374i	$0.696532\pi$
$158$	−271034.			−0.863737
$159$	−57791.4	+	498421.i	−0.181289	+	1.56352i
$160$		−	71272.9i		−	0.220102i
$161$	−400041.	+	91065.6i	−1.21630	+	0.276879i
$162$	105226.	−	211462.i	0.315017	−	0.633060i
$163$	102012.			0.300734			0.150367	−	0.988630i	$-0.451954\pi$
$163$	102012.			0.300734			0.150367	+	0.988630i	$0.451954\pi$
$164$			1383.95i			0.00401802i
$165$	25803.8	−	222544.i	0.0737859	−	0.636366i
$166$			289999.i			0.816819i
$167$		−	227618.i		−	0.631560i	−0.948832	−	0.315780i	$-0.897734\pi$
$167$		−	227618.i		−	0.631560i	0.948832	−	0.315780i	$-0.102266\pi$
$168$	−18582.5	+	160265.i	−0.0507963	+	0.438092i
$169$	−368338.			−0.992042
$170$		−	300614.i		−	0.797788i
$171$	−28020.0	+	119205.i	−0.0732788	+	0.311748i
$172$		−	112040.i		−	0.288770i
$173$			236191.i			0.599996i	0.953940	+	0.299998i	$0.0969861\pi$
$173$			236191.i			0.599996i	−0.953940	+	0.299998i	$0.903014\pi$
$174$	52103.5	−	449366.i	0.130465	−	1.12519i
$175$		−	278072.i		−	0.686376i
$176$	−52860.2			−0.128632
$177$	394368.	+	45726.5i	0.946168	+	0.109707i
$178$		−	268132.i		−	0.634305i
$179$		−	631541.i		−	1.47323i	−0.676315	−	0.736613i	$-0.736424\pi$
$179$		−	631541.i		−	1.47323i	0.676315	−	0.736613i	$-0.263576\pi$
$180$	263434.	+	61922.3i	0.606026	+	0.142451i
$181$			89158.9i			0.202287i	0.994872	+	0.101144i	$0.0322501\pi$
$181$			89158.9i			0.202287i	−0.994872	+	0.101144i	$0.967750\pi$
$182$	−35162.6			−0.0786868
$183$	374020.	+	43367.2i	0.825595	+	0.0957269i
$184$	158317.	−	36039.5i	0.344734	−	0.0784756i
$185$		−	202498.i		−	0.435003i
$186$	299726.	+	34752.9i	0.635246	+	0.0736561i
$187$	−222954.			−0.466241
$188$			105534.i			0.217769i
$189$	−576216.	−	207923.i	−1.17336	−	0.423397i
$190$	−140298.			−0.281946
$191$	868473.			1.72255			0.861277	−	0.508136i	$-0.169665\pi$
$191$	868473.			1.72255			0.861277	+	0.508136i	$0.169665\pi$
$192$	7354.10	−	63425.4i	0.0143972	−	0.124168i
$193$	492149.			0.951050			0.475525	−	0.879702i	$-0.342258\pi$
$193$	492149.			0.951050			0.475525	+	0.879702i	$0.342258\pi$
$194$	663051.			1.26486
$195$	−6792.97	+	58585.9i	−0.0127930	+	0.110333i
$196$	149525.			0.278019
$197$		−	660203.i		−	1.21203i	−0.795455	−	0.606013i	$-0.792768\pi$
$197$		−	660203.i		−	1.21203i	0.795455	−	0.606013i	$-0.207232\pi$
$198$	45925.3	−	195379.i	0.0832510	−	0.354172i
$199$		−	321030.i		−	0.574662i	−0.957831	−	0.287331i	$-0.907232\pi$
$199$		−	321030.i		−	0.574662i	0.957831	−	0.287331i	$-0.0927679\pi$
$200$			110048.i			0.194539i
$201$	78400.0	+	9090.40i	0.136876	+	0.0158706i
$202$	436331.			0.752381
$203$	−1.17325e6			−1.99826
$204$	31018.1	−	267515.i	0.0521843	−	0.450063i
$205$		−	6020.41i		−	0.0100056i
$206$	281448.			0.462094
$207$	−4340.09	+	616474.i	−0.00704000	+	0.999975i
$208$	13915.7			0.0223022
$209$			104053.i			0.164774i
$210$	80836.9	−	697177.i	0.126491	−	1.09092i
$211$	−908998.			−1.40558			−0.702792	−	0.711395i	$-0.748064\pi$
$211$	−908998.			−1.40558			−0.702792	+	0.711395i	$0.748064\pi$
$212$	−515007.			−0.786998
$213$	62414.3	+	7236.86i	0.0942616	+	0.0109295i
$214$			302977.i			0.452247i
$215$			487391.i			0.719087i
$216$	228040.	+	82286.2i	0.332565	+	0.120003i
$217$		−	782557.i		−	1.12815i
$218$	513208.			0.731396
$219$	−19565.4	+	168742.i	−0.0275663	+	0.237745i
$220$	229950.			0.320315
$221$	58693.6			0.0808369
$222$	20894.2	−	180202.i	0.0284540	−	0.245402i
$223$	−1.18620e6			−1.59734			−0.798668	−	0.601771i	$-0.794462\pi$
$223$	−1.18620e6			−1.59734			−0.798668	+	0.601771i	$0.794462\pi$
$224$	−165598.			−0.220513
$225$	−406752.	−	95610.3i	−0.535641	−	0.125907i
$226$			847832.i			1.10418i
$227$	−68032.8			−0.0876302			−0.0438151	−	0.999040i	$-0.513951\pi$
$227$	−68032.8			−0.0876302			−0.0438151	+	0.999040i	$0.513951\pi$
$228$	−124850.	−	14476.2i	−0.159057	−	0.0184424i
$229$			1.46238e6i			1.84277i	0.388654	+	0.921384i	$0.372940\pi$
$229$			1.46238e6i			1.84277i	−0.388654	+	0.921384i	$0.627060\pi$
$230$	−688705.	+	156778.i	−0.858447	+	0.195418i
$231$	−517068.	−	59953.4i	−0.637555	−	0.0739238i
$232$	464320.			0.566366
$233$		−	1.41277e6i		−	1.70483i	−0.522865	−	0.852415i	$-0.675137\pi$
$233$		−	1.41277e6i		−	1.70483i	0.522865	−	0.852415i	$-0.324863\pi$
$234$	−12090.1	+	51434.4i	−0.0144341	+	0.0614064i
$235$		−	459088.i		−	0.542283i
$236$			407491.i			0.476253i
$237$	1.04922e6	+	121656.i	1.21338	+	0.140690i
$238$	−698458.			−0.799278
$239$			61779.6i			0.0699600i	0.999388	+	0.0349800i	$0.0111368\pi$
$239$			61779.6i			0.0699600i	−0.999388	+	0.0349800i	$0.988863\pi$
$240$	−31991.5	+	275910.i	−0.0358514	+	0.309200i
$241$		−	719864.i		−	0.798376i	−0.916869	−	0.399188i	$-0.869292\pi$
$241$		−	719864.i		−	0.798376i	0.916869	−	0.399188i	$-0.130708\pi$
$242$			473659.i			0.519909i
$243$	−502263.	+	771375.i	−0.545652	+	0.838012i
$244$			386466.i			0.415563i
$245$	−650458.			−0.692315
$246$	621.200	−	5357.53i	0.000654476	−	0.00564452i
$247$		−	27392.4i		−	0.0285686i
$248$			309700.i			0.319751i
$249$	130168.	−	1.12264e6i	0.133048	−	1.14747i
$250$			391305.i			0.395973i
$251$	−1.22069e6			−1.22299			−0.611493	−	0.791250i	$-0.709431\pi$
$251$	−1.22069e6			−1.22299			−0.611493	+	0.791250i	$0.709431\pi$
$252$	143873.	−	612073.i	0.142717	−	0.607158i
$253$	116276.	+	510785.i	0.114206	+	0.501691i
$254$			325195.i			0.316271i
$255$	−134933.	+	1.16373e6i	−0.129948	+	1.12073i
$256$	65536.0			0.0625000
$257$		−	834833.i		−	0.788437i	−0.919017	−	0.394218i	$-0.871015\pi$
$257$		−	834833.i		−	0.788437i	0.919017	−	0.394218i	$-0.128985\pi$
$258$	−50290.2	+	433727.i	−0.0470364	+	0.405665i
$259$	−470492.			−0.435815
$260$	−60535.4			−0.0555362
$261$	−403404.	+	1.71619e6i	−0.366555	+	1.55942i
$262$	805243.			0.724726
$263$	1.12349e6			1.00157			0.500784	−	0.865572i	$-0.333045\pi$
$263$	1.12349e6			1.00157			0.500784	+	0.865572i	$0.333045\pi$
$264$	204631.	+	23726.8i	0.180702	+	0.0209522i
$265$	2.24036e6			1.95976
$266$			325972.i			0.282473i
$267$	−120353.	+	1.03799e6i	−0.103319	+	0.891073i
$268$			81008.9i			0.0688963i
$269$			1.79005e6i			1.50829i	0.656708	+	0.754145i	$0.271948\pi$
$269$			1.79005e6i			1.50829i	−0.656708	+	0.754145i	$0.728052\pi$
$270$	−992007.	−	357957.i	−0.828143	−	0.298828i
$271$	1.00599e6			0.832093			0.416047	−	0.909343i	$-0.363415\pi$
$271$	1.00599e6			0.832093			0.416047	+	0.909343i	$0.363415\pi$
$272$	276417.			0.226539
$273$	136121.	+	15783.0i	0.110539	+	0.0128169i
$274$		−	1.51345e6i		−	1.21785i
$275$	−355051.			−0.283113
$276$	−629052.	+	68453.3i	−0.497066	+	0.0540906i
$277$	810020.			0.634303			0.317151	−	0.948375i	$-0.397274\pi$
$277$	810020.			0.634303			0.317151	+	0.948375i	$0.397274\pi$
$278$			1.77762e6i			1.37952i
$279$	−1.14469e6	−	269069.i	−0.880397	−	0.206944i
$280$	720377.			0.549117
$281$	2.59916e6			1.96367			0.981833	−	0.189749i	$-0.0607674\pi$
$281$	2.59916e6			1.96367			0.981833	+	0.189749i	$0.0607674\pi$
$282$	47369.7	−	408540.i	0.0354714	−	0.305923i
$283$			231605.i			0.171902i	0.996299	+	0.0859512i	$0.0273929\pi$
$283$			231605.i			0.171902i	−0.996299	+	0.0859512i	$0.972607\pi$
$284$			64491.2i			0.0474466i
$285$	543117.	+	62973.8i	0.396078	+	0.0459248i
$286$			44896.7i			0.0324563i
$287$	−13988.0			−0.0100243
$288$	−56938.1	+	242230.i	−0.0404503	+	0.172087i
$289$	−253986.			−0.178881
$290$	−2.01986e6			−1.41035
$291$	−2.56679e6	−	297616.i	−1.77688	−	0.206027i
$292$	−174357.			−0.119669
$293$	842053.			0.573021			0.286510	−	0.958077i	$-0.407505\pi$
$293$	842053.			0.573021			0.286510	+	0.958077i	$0.407505\pi$
$294$	−578839.	−	67115.7i	−0.390562	−	0.0452852i
$295$		−	1.77265e6i		−	1.18595i
$296$	186199.			0.123523
$297$	−265483.	+	735732.i	−0.174640	+	0.483981i
$298$		−	1.30951e6i		−	0.854214i
$299$	−30610.1	−	134466.i	−0.0198010	−	0.0869833i
$300$	49396.0	−	426015.i	0.0316875	−	0.273289i
$301$	1.13242e6			0.720431
$302$		−	834903.i		−	0.526767i
$303$	−1.68912e6	−	195851.i	−1.05695	−	0.122552i
$304$		−	129005.i		−	0.0800611i
$305$		−	1.68119e6i		−	1.03482i
$306$	−240153.	+	1.02168e6i	−0.146617	+	0.623749i
$307$	1.84521e6			1.11737			0.558687	−	0.829378i	$-0.311305\pi$
$307$	1.84521e6			1.11737			0.558687	+	0.829378i	$0.311305\pi$
$308$		−	534274.i		−	0.320913i
$309$	−1.08954e6	−	126330.i	−0.649150	−	0.0752682i
$310$		−	1.34724e6i		−	0.796235i
$311$			1.14413e6i			0.670773i	0.942081	+	0.335386i	$0.108867\pi$
$311$			1.14413e6i			0.670773i	−0.942081	+	0.335386i	$0.891133\pi$
$312$	−53870.2	−	6246.19i	−0.0313301	−	0.00363269i
$313$			2.18693e6i			1.26175i	0.775883	+	0.630876i	$0.217305\pi$
$313$			2.18693e6i			1.26175i	−0.775883	+	0.630876i	$0.782695\pi$
$314$	2.01463e6			1.15311
$315$	−625868.	+	2.66261e6i	−0.355391	+	1.51193i
$316$			1.08414e6i			0.610754i
$317$		−	1.68556e6i		−	0.942099i	−0.882107	−	0.471050i	$-0.843875\pi$
$317$		−	1.68556e6i		−	0.942099i	0.882107	−	0.471050i	$-0.156125\pi$
$318$	1.99369e6	+	231166.i	1.10558	+	0.128190i
$319$			1.49805e6i			0.824232i
$320$	−285092.			−0.155636
$321$	135994.	−	1.17288e6i	0.0736643	−	0.635317i
$322$	364263.	+	1.60016e6i	0.195783	+	0.860051i
$323$		−	544115.i		−	0.290191i
$324$	−845848.	−	420902.i	−0.447641	−	0.222750i
$325$	93468.9			0.0490861
$326$		−	408049.i		−	0.212651i
$327$	−1.98672e6	−	230358.i	−1.02747	−	0.119134i
$328$	5535.81			0.00284117
$329$	−1.06666e6			−0.543296
$330$	−890178.	−	103215.i	−0.449979	−	0.0521745i
$331$	1.06005e6			0.531807			0.265904	−	0.964000i	$-0.414330\pi$
$331$	1.06005e6			0.531807			0.265904	+	0.964000i	$0.414330\pi$
$332$	1.15999e6			0.577578
$333$	−161771.	+	688216.i	−0.0799446	+	0.340106i
$334$	−910471.			−0.446580
$335$		−	352401.i		−	0.171564i
$336$	641060.	+	74330.1i	0.309778	+	0.0359184i
$337$			3.38924e6i			1.62565i	0.582505	+	0.812827i	$0.302073\pi$
$337$			3.38924e6i			1.62565i	−0.582505	+	0.812827i	$0.697927\pi$
$338$			1.47335e6i			0.701479i
$339$	380557.	−	3.28211e6i	0.179854	−	1.55115i
$340$	−1.20246e6			−0.564121
$341$	−999195.			−0.465333
$342$	476819.	+	112080.i	0.220439	+	0.0518159i
$343$		−	1.20668e6i		−	0.553804i
$344$	−448160.			−0.204191
$345$	2.73647e6	−	297782.i	1.23778	−	0.134695i
$346$	944765.			0.424261
$347$			3.01418e6i			1.34383i	0.740626	+	0.671917i	$0.234529\pi$
$347$			3.01418e6i			1.34383i	−0.740626	+	0.671917i	$0.765471\pi$
$348$	−1.79746e6	−	208414.i	−0.795632	−	0.0922526i
$349$	1.13383e6			0.498294			0.249147	−	0.968466i	$-0.419850\pi$
$349$	1.13383e6			0.498294			0.249147	+	0.968466i	$0.419850\pi$
$350$	−1.11229e6			−0.485341
$351$	69889.5	−	193685.i	0.0302792	−	0.0839127i
$352$			211441.i			0.0909562i
$353$			1.33122e6i			0.568607i	0.958734	+	0.284303i	$0.0917623\pi$
$353$			1.33122e6i			0.568607i	−0.958734	+	0.284303i	$0.908238\pi$
$354$	182906.	−	1.57747e6i	0.0775746	−	0.669042i
$355$		−	280547.i		−	0.118150i
$356$	−1.07253e6			−0.448522
$357$	2.70386e6	+	313509.i	1.12283	+	0.130191i
$358$	−2.52617e6			−1.04173
$359$	505912.			0.207176			0.103588	−	0.994620i	$-0.466968\pi$
$359$	505912.			0.207176			0.103588	+	0.994620i	$0.466968\pi$
$360$	247689.	−	1.05374e6i	0.100728	−	0.428525i
$361$	2.22216e6			0.897444
$362$	356635.			0.143039
$363$	212606.	−	1.83362e6i	0.0846855	−	0.730370i
$364$			140650.i			0.0556400i
$365$	758479.			0.297997
$366$	173469.	−	1.49608e6i	0.0676891	−	0.583784i
$367$			1.67768e6i			0.650195i	0.945681	+	0.325097i	$0.105397\pi$
$367$			1.67768e6i			0.650195i	−0.945681	+	0.325097i	$0.894603\pi$
$368$	−144158.	−	633270.i	−0.0554906	−	0.243764i
$369$	−4809.55	+	20461.1i	−0.00183882	+	0.00782283i
$370$	−809993.			−0.307593
$371$		−	5.20533e6i		−	1.96342i
$372$	139012.	−	1.19890e6i	0.0520827	−	0.449187i
$373$		−	4.15921e6i		−	1.54789i	−0.633255	−	0.773943i	$-0.718282\pi$
$373$		−	4.15921e6i		−	1.54789i	0.633255	−	0.773943i	$-0.281718\pi$
$374$			891814.i			0.329682i
$375$	175641.	−	1.51481e6i	0.0644982	−	0.556264i
$376$	422135.			0.153986
$377$		−	394368.i		−	0.142905i
$378$	−831691.	+	2.30487e6i	−0.299387	+	0.829691i
$379$			3.49912e6i			1.25130i	0.780105	+	0.625649i	$0.215166\pi$
$379$			3.49912e6i			1.25130i	−0.780105	+	0.625649i	$0.784834\pi$
$380$			561190.i			0.199366i
$381$	145966.	−	1.25889e6i	0.0515158	−	0.444298i
$382$		−	3.47389e6i		−	1.21803i
$383$	4.14879e6			1.44519			0.722594	−	0.691273i	$-0.242950\pi$
$383$	4.14879e6			1.44519			0.722594	+	0.691273i	$0.242950\pi$
$384$	−253702.	−	29416.4i	−0.0878001	−	0.0101803i
$385$			2.32417e6i			0.799129i
$386$		−	1.96860e6i		−	0.672494i
$387$	389364.	−	1.65646e6i	0.132154	−	0.562217i
$388$		−	2.65220e6i		−	0.894391i
$389$	−852861.			−0.285762			−0.142881	−	0.989740i	$-0.545637\pi$
$389$	−852861.			−0.285762			−0.142881	+	0.989740i	$0.545637\pi$
$390$	234343.	+	27171.9i	0.0780174	+	0.00904603i
$391$	−608029.	−	2.67100e6i	−0.201133	−	0.883552i
$392$		−	598101.i		−	0.196589i
$393$	−3.11724e6	−	361440.i	−1.01810	−	0.118047i
$394$	−2.64081e6			−0.857031
$395$		−	4.71616e6i		−	1.52088i
$396$	−781515.	−	183701.i	−0.250437	−	0.0588673i
$397$	3.60362e6			1.14753			0.573764	−	0.819021i	$-0.305483\pi$
$397$	3.60362e6			1.14753			0.573764	+	0.819021i	$0.305483\pi$
$398$	−1.28412e6			−0.406347
$399$	146316.	−	1.26190e6i	0.0460106	−	0.396818i
$400$	440192.			0.137560
$401$	−4.44430e6			−1.38020			−0.690101	−	0.723713i	$-0.742434\pi$
$401$	−4.44430e6			−1.38020			−0.690101	+	0.723713i	$0.742434\pi$
$402$	36361.6	−	313600.i	0.0112222	−	0.0967857i
$403$	263043.			0.0806796
$404$		−	1.74532e6i		−	0.532014i
$405$	3.67957e6	+	1.83099e6i	1.11470	+	0.554687i
$406$			4.69302e6i			1.41298i
$407$			600739.i			0.179763i
$408$	−1.07006e6	−	124072.i	−0.318242	−	0.0368999i
$409$	2.76985e6			0.818743			0.409372	−	0.912368i	$-0.365748\pi$
$409$	2.76985e6			0.818743			0.409372	+	0.912368i	$0.365748\pi$
$410$	−24081.6			−0.00707500
$411$	−679328.	+	5.85885e6i	−0.198369	+	1.71084i
$412$		−	1.12579e6i		−	0.326750i
$413$	−4.11863e6			−1.18817
$414$	2.46590e6	+	17360.3i	0.707089	+	0.00497803i
$415$	−5.04615e6			−1.43827
$416$		−	55662.8i		−	0.0157700i
$417$	797901.	−	6.88149e6i	0.224703	−	1.93795i
$418$	416212.			0.116513
$419$	2.23595e6			0.622197			0.311098	−	0.950378i	$-0.399303\pi$
$419$	2.23595e6			0.622197			0.311098	+	0.950378i	$0.399303\pi$
$420$	−2.78871e6	−	323347.i	−0.771400	−	0.0894430i
$421$		−	2.95228e6i		−	0.811806i	−0.913916	−	0.405903i	$-0.866957\pi$
$421$		−	2.95228e6i		−	0.811806i	0.913916	−	0.405903i	$-0.133043\pi$
$422$			3.63599e6i			0.993898i
$423$	−366754.	+	1.56027e6i	−0.0996606	+	0.423983i
$424$			2.06003e6i			0.556492i
$425$	1.85664e6			0.498603
$426$	28947.5	−	249657.i	0.00772834	−	0.0666530i
$427$	−3.90613e6			−1.03676
$428$	1.21191e6			0.319787
$429$	20152.3	−	173803.i	0.00528665	−	0.0455947i
$430$	1.94956e6			0.508471
$431$	2.95362e6			0.765882			0.382941	−	0.923773i	$-0.374911\pi$
$431$	2.95362e6			0.765882			0.382941	+	0.923773i	$0.374911\pi$
$432$	329145.	−	912159.i	0.0848550	−	0.235159i
$433$		−	1.50584e6i		−	0.385975i	−0.981201	−	0.192988i	$-0.938182\pi$
$433$		−	1.50584e6i		−	0.385975i	0.981201	−	0.192988i	$-0.0618177\pi$
$434$	−3.13023e6			−0.797723
$435$	7.81924e6	+	906632.i	1.98126	+	0.229725i
$436$		−	2.05283e6i		−	0.517175i
$437$	−1.24656e6	+	283769.i	−0.312256	+	0.0710823i
$438$	674966.	+	78261.6i	0.168111	+	0.0194923i
$439$	−4.71087e6			−1.16665			−0.583324	−	0.812239i	$-0.698248\pi$
$439$	−4.71087e6			−1.16665			−0.583324	+	0.812239i	$0.698248\pi$
$440$		−	919800.i		−	0.226497i
$441$	2.21066e6	+	519634.i	0.541285	+	0.127233i
$442$		−	234774.i		−	0.0571603i
$443$			3.28592e6i			0.795514i	0.917491	+	0.397757i	$0.130211\pi$
$443$			3.28592e6i			0.795514i	−0.917491	+	0.397757i	$0.869789\pi$
$444$	−720808.	−	83576.9i	−0.173525	−	0.0201200i
$445$	4.66566e6			1.11690
$446$			4.74481e6i			1.12949i
$447$	−587783.	+	5.06933e6i	−0.139139	+	1.20000i
$448$			662392.i			0.155927i
$449$		−	1.93965e6i		−	0.454053i	−0.973889	−	0.227027i	$-0.927100\pi$
$449$		−	1.93965e6i		−	0.454053i	0.973889	−	0.227027i	$-0.0729004\pi$
$450$	−382441.	+	1.62701e6i	−0.0890294	+	0.378755i
$451$			17860.4i			0.00413475i
$452$	3.39133e6			0.780771
$453$	−374754.	+	3.23206e6i	−0.0858026	+	0.740003i
$454$			272131.i			0.0619639i
$455$		−	611850.i		−	0.138553i
$456$	−57904.9	+	499400.i	−0.0130408	+	0.112470i
$457$		−	3.75357e6i		−	0.840724i	−0.907356	−	0.420362i	$-0.861903\pi$
$457$		−	3.75357e6i		−	0.840724i	0.907356	−	0.420362i	$-0.138097\pi$
$458$	5.84951e6			1.30303
$459$	1.38826e6	−	3.84730e6i	0.307567	−	0.852362i
$460$	627110.	+	2.75482e6i	0.138181	+	0.607014i
$461$			1.84989e6i			0.405409i	0.979240	+	0.202705i	$0.0649732\pi$
$461$			1.84989e6i			0.405409i	−0.979240	+	0.202705i	$0.935027\pi$
$462$	−239814.	+	2.06827e6i	−0.0522720	+	0.450819i
$463$	−7.13479e6			−1.54678			−0.773391	−	0.633930i	$-0.781441\pi$
$463$	−7.13479e6			−1.54678			−0.773391	+	0.633930i	$0.781441\pi$
$464$		−	1.85728e6i		−	0.400481i
$465$	−604721.	+	5.21541e6i	−0.129695	+	1.11855i
$466$	−5.65107e6			−1.20550
$467$	−5.91650e6			−1.25537			−0.627687	−	0.778466i	$-0.715998\pi$
$467$	−5.91650e6			−1.25537			−0.627687	+	0.778466i	$0.715998\pi$
$468$	205737.	+	48360.2i	0.0434209	+	0.0102064i
$469$	−818782.			−0.171884
$470$	−1.83635e6			−0.383452
$471$	−7.79900e6	−	904286.i	−1.61989	−	0.187825i
$472$	1.62996e6			0.336762
$473$		−	1.44591e6i		−	0.297160i
$474$	486624.	−	4.19689e6i	0.0994828	−	0.857988i
$475$		−	866498.i		−	0.176211i
$476$			2.79383e6i			0.565175i
$477$	−7.61415e6	−	1.78977e6i	−1.53224	−	0.360164i
$478$	247118.			0.0494692
$479$	−3.08280e6			−0.613912			−0.306956	−	0.951724i	$-0.599310\pi$
$479$	−3.08280e6			−0.613912			−0.306956	+	0.951724i	$0.599310\pi$
$480$	1.10364e6	+	127966.i	0.218637	+	0.0253508i
$481$		−	158147.i		−	0.0311673i
$482$	−2.87945e6			−0.564537
$483$	−691879.	−	6.35802e6i	−0.134947	−	1.24009i
$484$	1.89464e6			0.367631
$485$			1.15375e7i			2.22719i
$486$	3.08550e6	+	2.00905e6i	0.592564	+	0.385834i
$487$	5.26182e6			1.00534			0.502670	−	0.864478i	$-0.332351\pi$
$487$	5.26182e6			1.00534			0.502670	+	0.864478i	$0.332351\pi$
$488$	1.54587e6			0.293848
$489$	−183156.	+	1.57963e6i	−0.0346377	+	0.298733i
$490$			2.60183e6i			0.489541i
$491$		−	675547.i		−	0.126460i	−0.997999	−	0.0632298i	$-0.979860\pi$
$491$		−	675547.i		−	0.126460i	0.997999	−	0.0632298i	$-0.0201401\pi$
$492$	−21430.1	−	2484.80i	−0.00399128	−	0.000462784i
$493$		−	7.83361e6i		−	1.45159i
$494$	−109570.			−0.0202010
$495$	3.39971e6	+	799129.i	0.623633	+	0.146590i
$496$	1.23880e6			0.226098
$497$	−651832.			−0.118371
$498$	−4.49055e6	−	520674.i	−0.811383	−	0.0940789i
$499$	328864.			0.0591242			0.0295621	−	0.999563i	$-0.490589\pi$
$499$	328864.			0.0591242			0.0295621	+	0.999563i	$0.490589\pi$
$500$	1.56522e6			0.279995
$501$	3.52459e6	+	408673.i	0.627357	+	0.0727414i
$502$			4.88276e6i			0.864782i
$503$	3.33152e6			0.587114			0.293557	−	0.955942i	$-0.405161\pi$
$503$	3.33152e6			0.587114			0.293557	+	0.955942i	$0.405161\pi$
$504$	−2.44829e6	−	575491.i	−0.429326	−	0.100916i
$505$			7.59243e6i			1.32481i
$506$	2.04314e6	−	465102.i	0.354749	−	0.0807555i
$507$	661327.	−	5.70361e6i	0.114261	−	0.985440i
$508$	1.30078e6			0.223637
$509$			5.58496e6i			0.955488i	0.878499	+	0.477744i	$0.158545\pi$
$509$			5.58496e6i			0.955488i	−0.878499	+	0.477744i	$0.841455\pi$
$510$	4.65493e6	+	539734.i	0.792478	+	0.0918870i
$511$		−	1.76228e6i		−	0.298553i
$512$		−	262144.i		−	0.0441942i
$513$	−1.79554e6	−	647907.i	−0.301233	−	0.108697i
$514$	−3.33933e6			−0.557509
$515$			4.89737e6i			0.813663i
$516$	1.73491e6	+	201161.i	0.286848	+	0.0332597i
$517$			1.36195e6i			0.224096i
$518$			1.88197e6i			0.308168i
$519$	−3.65735e6	−	424066.i	−0.596003	−	0.0691059i
$520$			242142.i			0.0392700i
$521$	4.71551e6			0.761087			0.380544	−	0.924763i	$-0.375737\pi$
$521$	4.71551e6			0.761087			0.380544	+	0.924763i	$0.375737\pi$
$522$	6.86476e6	+	1.61362e6i	1.10268	+	0.259193i
$523$			6.29748e6i			1.00673i	0.864074	+	0.503365i	$0.167905\pi$
$523$			6.29748e6i			1.00673i	−0.864074	+	0.503365i	$0.832095\pi$
$524$		−	3.22097e6i		−	0.512458i
$525$	4.30586e6	+	499260.i	0.681808	+	0.0790549i
$526$		−	4.49397e6i		−	0.708216i
$527$	5.22500e6			0.819520
$528$	94907.2	−	818526.i	0.0148154	−	0.127775i
$529$	−5.80214e6	+	2.78598e6i	−0.901465	+	0.432852i
$530$		−	8.96144e6i		−	1.38576i
$531$	−1.41612e6	+	6.02457e6i	−0.217954	+	0.927235i
$532$	1.30389e6			0.199738
$533$		−	4701.83i		−	0.000716884i
$534$	4.15195e6	+	481413.i	0.630084	+	0.0730575i
$535$	−5.27199e6			−0.796324
$536$	324036.			0.0487171
$537$	9.77924e6	+	1.13389e6i	1.46342	+	0.169682i
$538$	7.16021e6			1.06652
$539$	1.92967e6			0.286096
$540$	−1.43183e6	+	3.96803e6i	−0.211304	+	0.585586i
$541$	3.80956e6			0.559605			0.279802	−	0.960058i	$-0.409731\pi$
$541$	3.80956e6			0.559605			0.279802	+	0.960058i	$0.409731\pi$
$542$		−	4.02398e6i		−	0.588379i
$543$	−1.38060e6	−	160079.i	−0.200941	−	0.0232989i
$544$		−	1.10567e6i		−	0.160187i
$545$			8.93014e6i			1.28785i
$546$	63132.1	−	544482.i	0.00906293	−	0.0781631i
$547$	5.13990e6			0.734490			0.367245	−	0.930124i	$-0.380301\pi$
$547$	5.13990e6			0.734490			0.367245	+	0.930124i	$0.380301\pi$
$548$	−6.05382e6			−0.861149
$549$	−1.34306e6	+	5.71373e6i	−0.190180	+	0.809076i
$550$			1.42020e6i			0.200191i
$551$	−3.65597e6			−0.513007
$552$	273813.	+	2.51621e6i	0.0382478	+	0.351478i
$553$	−1.09577e7			−1.52372
$554$		−	3.24008e6i		−	0.448520i
$555$	3.13563e6	+	363572.i	0.432108	+	0.0501024i
$556$	7.11048e6			0.975466
$557$	9.73106e6			1.32899			0.664496	−	0.747292i	$-0.268646\pi$
$557$	9.73106e6			1.32899			0.664496	+	0.747292i	$0.268646\pi$
$558$	−1.07628e6	+	4.57877e6i	−0.146332	+	0.622535i
$559$			380644.i			0.0515216i
$560$		−	2.88151e6i		−	0.388284i
$561$	400299.	−	3.45237e6i	0.0537003	−	0.463138i
$562$		−	1.03966e7i		−	1.38852i
$563$	−9.00766e6			−1.19768			−0.598840	−	0.800869i	$-0.704371\pi$
$563$	−9.00766e6			−1.19768			−0.598840	+	0.800869i	$0.704371\pi$
$564$	−1.63416e6	−	189479.i	−0.216320	−	0.0250821i
$565$	−1.47528e7			−1.94426
$566$	926420.			0.121553
$567$	4.25418e6	−	8.54924e6i	0.555723	−	1.11679i
$568$	257965.			0.0335498
$569$	−6.85439e6			−0.887541			−0.443770	−	0.896141i	$-0.646359\pi$
$569$	−6.85439e6			−0.887541			−0.443770	+	0.896141i	$0.646359\pi$
$570$	251895.	−	2.17247e6i	0.0324738	−	0.280070i
$571$			2.23685e6i			0.287109i	0.989642	+	0.143554i	$0.0458532\pi$
$571$			2.23685e6i			0.287109i	−0.989642	+	0.143554i	$0.954147\pi$
$572$	179587.			0.0229501
$573$	−1.55929e6	+	1.34481e7i	−0.198399	+	1.71109i
$574$			55952.1i			0.00708822i
$575$	−968281.	−	4.25354e6i	−0.122133	−	0.536514i
$576$	968920.	+	227752.i	0.121684	+	0.0286027i
$577$	−2.74296e6			−0.342989			−0.171495	−	0.985185i	$-0.554860\pi$
$577$	−2.74296e6			−0.342989			−0.171495	+	0.985185i	$0.554860\pi$
$578$			1.01594e6i			0.126488i
$579$	−883622.	+	7.62079e6i	−0.109539	+	0.944721i
$580$			8.07944e6i			0.997267i
$581$			1.17244e7i			1.44096i
$582$	−1.19046e6	+	1.02672e7i	−0.145683	+	1.25644i
$583$	−6.64634e6			−0.809862
$584$			697427.i			0.0846188i
$585$	−894989.	−	210374.i	−0.108125	−	0.0254158i
$586$		−	3.36821e6i		−	0.405187i
$587$		−	6.30841e6i		−	0.755656i	−0.925876	−	0.377828i	$-0.876671\pi$
$587$		−	6.30841e6i		−	0.755656i	0.925876	−	0.377828i	$-0.123329\pi$
$588$	−268463.	+	2.31536e6i	−0.0320215	+	0.276169i
$589$		−	2.43852e6i		−	0.289627i
$590$	−7.09059e6			−0.838595
$591$	1.02230e7	+	1.18535e6i	1.20396	+	0.139598i
$592$		−	744795.i		−	0.0873439i
$593$		−	1.00776e7i		−	1.17685i	−0.808551	−	0.588426i	$-0.799748\pi$
$593$		−	1.00776e7i		−	1.17685i	0.808551	−	0.588426i	$-0.200252\pi$
$594$	2.94293e6	+	1.06193e6i	0.342226	+	0.123489i
$595$		−	1.21536e7i		−	1.40738i
$596$	−5.23802e6			−0.604021
$597$	4.97105e6	+	576388.i	0.570837	+	0.0661880i
$598$	−537866.	+	122440.i	−0.0615065	+	0.0140014i
$599$			5.42459e6i			0.617732i	0.951106	+	0.308866i	$0.0999495\pi$
$599$			5.42459e6i			0.617732i	−0.951106	+	0.308866i	$0.900051\pi$
$600$	−1.70406e6	−	197584.i	−0.193244	−	0.0224065i
$601$	4.80737e6			0.542902			0.271451	−	0.962452i	$-0.412497\pi$
$601$	4.80737e6			0.542902			0.271451	+	0.962452i	$0.412497\pi$
$602$		−	4.52969e6i		−	0.509421i
$603$	−281524.	+	1.19768e6i	−0.0315299	+	0.134137i
$604$	−3.33961e6			−0.372481
$605$	−8.24196e6			−0.915466
$606$	−783405.	+	6.75646e6i	−0.0866572	+	0.747374i
$607$	−5.07839e6			−0.559441			−0.279720	−	0.960082i	$-0.590242\pi$
$607$	−5.07839e6			−0.559441			−0.279720	+	0.960082i	$0.590242\pi$
$608$	−516019.			−0.0566118
$609$	2.10650e6	−	1.81675e7i	0.230154	−	1.98496i
$610$	−6.72475e6			−0.731731
$611$		−	358539.i		−	0.0388538i
$612$	4.08671e6	+	960613.i	0.441057	+	0.103674i
$613$		−	1.67900e7i		−	1.80467i	−0.431030	−	0.902337i	$-0.641850\pi$
$613$		−	1.67900e7i		−	1.80467i	0.431030	−	0.902337i	$-0.358150\pi$
$614$		−	7.38082e6i		−	0.790103i
$615$	93224.3	+	10809.3i	0.00993897	+	0.00115241i
$616$	−2.13710e6			−0.226920
$617$	1.01227e7			1.07049			0.535244	−	0.844698i	$-0.320220\pi$
$617$	1.01227e7			1.07049			0.535244	+	0.844698i	$0.320220\pi$
$618$	−505322.	+	4.35814e6i	−0.0532227	+	0.459018i
$619$		−	3.83644e6i		−	0.402441i	−0.979546	−	0.201220i	$-0.935509\pi$
$619$		−	3.83644e6i		−	0.402441i	0.979546	−	0.201220i	$-0.0644907\pi$
$620$	−5.38897e6			−0.563023
$621$	−9.53814e6	−	1.17405e6i	−0.992509	−	0.122168i
$622$	4.57653e6			0.474308
$623$		−	1.08404e7i		−	1.11898i
$624$	−24984.7	+	215481.i	−0.00256870	+	0.0221537i
$625$	−1.21824e7			−1.24748
$626$	8.74773e6			0.892194
$627$	−1.61123e6	−	186821.i	−0.163678	−	0.0189782i
$628$		−	8.05853e6i		−	0.815374i
$629$		−	3.14139e6i		−	0.316589i
$630$	1.06504e7	+	2.50347e6i	1.06910	+	0.251299i
$631$		−	5.03058e6i		−	0.502973i	−0.967861	−	0.251486i	$-0.919081\pi$
$631$		−	5.03058e6i		−	0.502973i	0.967861	−	0.251486i	$-0.0809194\pi$
$632$	4.33655e6			0.431868
$633$	1.63205e6	−	1.40756e7i	0.161891	−	1.39623i
$634$	−6.74225e6			−0.666165
$635$	−5.65858e6			−0.556895
$636$	924663.	−	7.97474e6i	0.0906443	−	0.781761i
$637$	−507995.			−0.0496034
$638$	5.99220e6			0.582820
$639$	−224122.	+	953474.i	−0.0217136	+	0.0923754i
$640$			1.14037e6i			0.110051i
$641$	5.60080e6			0.538400			0.269200	−	0.963084i	$-0.413241\pi$
$641$	5.60080e6			0.538400			0.269200	+	0.963084i	$0.413241\pi$
$642$	−4.69152e6	−	543976.i	−0.449237	−	0.0520886i
$643$			1.11278e7i			1.06141i	0.847557	+	0.530704i	$0.178072\pi$
$643$			1.11278e7i			1.06141i	−0.847557	+	0.530704i	$0.821928\pi$
$644$	6.40065e6	−	1.45705e6i	0.608148	−	0.138439i
$645$	−7.54711e6	−	875080.i	−0.714302	−	0.0828225i
$646$	−2.17646e6			−0.205196
$647$		−	2.00274e7i		−	1.88089i	−0.339941	−	0.940447i	$-0.610407\pi$
$647$		−	2.00274e7i		−	1.88089i	0.339941	−	0.940447i	$-0.389593\pi$
$648$	−1.68361e6	+	3.38339e6i	−0.157508	+	0.316530i
$649$			5.25881e6i			0.490090i
$650$		−	373876.i		−	0.0347091i
$651$	1.21177e7	+	1.40503e6i	1.12064	+	0.129937i
$652$	−1.63219e6			−0.150367
$653$			6.93311e6i			0.636276i	0.948044	+	0.318138i	$0.103058\pi$
$653$			6.93311e6i			0.636276i	−0.948044	+	0.318138i	$0.896942\pi$
$654$	−921433.	+	7.94689e6i	−0.0842402	+	0.726528i
$655$			1.40117e7i			1.27611i
$656$		−	22143.3i		−	0.00200901i
$657$	−2.57779e6	−	605929.i	−0.232988	−	0.0547657i
$658$			4.26664e6i			0.384168i
$659$	1.26648e6			0.113601			0.0568007	−	0.998386i	$-0.481910\pi$
$659$	1.26648e6			0.113601			0.0568007	+	0.998386i	$0.481910\pi$
$660$	−412861.	+	3.56071e6i	−0.0368930	+	0.318183i
$661$			9.43907e6i			0.840283i	0.907459	+	0.420141i	$0.138020\pi$
$661$			9.43907e6i			0.840283i	−0.907459	+	0.420141i	$0.861980\pi$
$662$		−	4.24018e6i		−	0.376045i
$663$	−105380.	+	908853.i	−0.00931057	+	0.0802989i
$664$		−	4.63998e6i		−	0.408409i
$665$	−5.67212e6			−0.497383
$666$	2.75286e6	+	647083.i	0.240491	+	0.0565294i
$667$	−1.79467e7	+	4.08542e6i	−1.56196	+	0.355567i
$668$			3.64188e6i			0.315780i
$669$	2.12975e6	−	1.83680e7i	0.183977	−	1.58671i
$670$	−1.40960e6			−0.121314
$671$			4.98748e6i			0.427636i
$672$	297321.	−	2.56424e6i	0.0253981	−	0.219046i
$673$	−1.43890e7			−1.22459			−0.612297	−	0.790628i	$-0.709754\pi$
$673$	−1.43890e7			−1.22459			−0.612297	+	0.790628i	$0.709754\pi$
$674$	1.35570e7			1.14951
$675$	2.21080e6	−	6.12678e6i	0.186762	−	0.517575i
$676$	5.89341e6			0.496021
$677$	5.07004e6			0.425148			0.212574	−	0.977145i	$-0.431815\pi$
$677$	5.07004e6			0.425148			0.212574	+	0.977145i	$0.431815\pi$
$678$	−1.31284e7	−	1.52223e6i	−1.09683	−	0.127176i
$679$	2.68066e7			2.23135
$680$			4.80983e6i			0.398894i
$681$	122148.	−	1.05347e6i	0.0100930	−	0.0870470i
$682$			3.99678e6i			0.329040i
$683$		−	6.49326e6i		−	0.532612i	−0.963889	−	0.266306i	$-0.914197\pi$
$683$		−	6.49326e6i		−	0.532612i	0.963889	−	0.266306i	$-0.0858032\pi$
$684$	448321.	−	1.90728e6i	0.0366394	−	0.155874i
$685$	2.63350e7			2.14441
$686$	−4.82671e6			−0.391598
$687$	−2.26445e7	−	2.62560e6i	−1.83050	−	0.212245i
$688$			1.79264e6i			0.144385i
$689$	1.74968e6			0.140414
$690$	−1.19113e6	−	1.09459e7i	−0.0952437	−	0.875242i
$691$	2.89533e6			0.230676			0.115338	−	0.993326i	$-0.463205\pi$
$691$	2.89533e6			0.230676			0.115338	+	0.993326i	$0.463205\pi$
$692$		−	3.77906e6i		−	0.299998i
$693$	1.85672e6	−	7.89901e6i	0.146864	−	0.624798i
$694$	1.20567e7			0.950234
$695$	−3.09317e7			−2.42908
$696$	−833656.	+	7.18986e6i	−0.0652324	+	0.562597i
$697$		−	93395.7i		−	0.00728190i
$698$		−	4.53533e6i		−	0.352347i
$699$	2.18763e7	+	2.53654e6i	1.69349	+	0.196358i
$700$			4.44915e6i			0.343188i
$701$	1.34326e7			1.03244			0.516219	−	0.856456i	$-0.327339\pi$
$701$	1.34326e7			1.03244			0.516219	+	0.856456i	$0.327339\pi$
$702$	−774739.	−	279558.i	−0.0593353	−	0.0214106i
$703$	−1.46610e6			−0.111886
$704$	845764.			0.0643158
$705$	7.10884e6	+	824262.i	0.538674	+	0.0624587i
$706$	5.32487e6			0.402066
$707$	1.76405e7			1.32728
$708$	−6.30988e6	−	731624.i	−0.473084	−	0.0548535i
$709$			5.16169e6i			0.385635i	0.981235	+	0.192818i	$0.0617626\pi$
$709$			5.16169e6i			0.385635i	−0.981235	+	0.192818i	$0.938237\pi$
$710$	−1.12219e6			−0.0835447
$711$	−3.76762e6	+	1.60285e7i	−0.279507	+	1.18910i
$712$			4.29011e6i			0.317153i
$713$	−2.72496e6	−	1.19704e7i	−0.200741	−	0.881832i
$714$	1.25404e6	−	1.08154e7i	0.0920587	−	0.793959i
$715$	−781230.			−0.0571497
$716$			1.01047e7i			0.736613i
$717$	−956639.	−	110921.i	−0.0694945	−	0.00805781i
$718$		−	2.02365e6i		−	0.146495i
$719$			1.92320e7i			1.38740i	0.720265	+	0.693699i	$0.244020\pi$
$719$			1.92320e7i			1.38740i	−0.720265	+	0.693699i	$0.755980\pi$
$720$	−4.21495e6	−	990758.i	−0.303013	−	0.0712256i
$721$	1.13787e7			0.815183
$722$		−	8.88864e6i		−	0.634588i
$723$	1.11469e7	+	1.29247e6i	0.793063	+	0.0919548i
$724$		−	1.42654e6i		−	0.101144i
$725$		−	1.24749e7i		−	0.881442i
$726$	−7.33448e6	−	850425.i	−0.516449	−	0.0598817i
$727$		−	1.13754e7i		−	0.798238i	−0.916899	−	0.399119i	$-0.869316\pi$
$727$		−	1.13754e7i		−	0.798238i	0.916899	−	0.399119i	$-0.130684\pi$
$728$	562601.			0.0393434
$729$	−1.10427e7	−	9.16236e6i	−0.769588	−	0.638541i
$730$		−	3.03391e6i		−	0.210715i
$731$			7.56099e6i			0.523341i
$732$	−5.98432e6	−	693876.i	−0.412798	−	0.0478634i
$733$			926603.i			0.0636991i	0.999493	+	0.0318496i	$0.0101397\pi$
$733$			926603.i			0.0636991i	−0.999493	+	0.0318496i	$0.989860\pi$
$734$	6.71071e6			0.459757
$735$	1.16785e6	−	1.00722e7i	0.0797389	−	0.687708i
$736$	−2.53308e6	+	576633.i	−0.172367	+	0.0392378i
$737$			1.04545e6i			0.0708979i
$738$	81844.5	+	19238.2i	0.00553157	+	0.00130024i
$739$	2.74568e7			1.84943			0.924716	−	0.380658i	$-0.124303\pi$
$739$	2.74568e7			1.84943			0.924716	+	0.380658i	$0.124303\pi$
$740$			3.23997e6i			0.217501i
$741$	424164.	+	49181.4i	0.0283784	+	0.00329045i
$742$	−2.08213e7			−1.38835
$743$	3.74066e6			0.248586			0.124293	−	0.992246i	$-0.460334\pi$
$743$	3.74066e6			0.248586			0.124293	+	0.992246i	$0.460334\pi$
$744$	−4.79561e6	−	556046.i	−0.317623	−	0.0368280i
$745$	2.27862e7			1.50412
$746$	−1.66369e7			−1.09452
$747$	1.71500e7	+	4.03124e6i	1.12451	+	0.264325i
$748$	3.56726e6			0.233120
$749$			1.22491e7i			0.797812i
$750$	−6.05925e6	−	702563.i	−0.393338	−	0.0456071i
$751$			2.33816e7i			1.51277i	0.654124	+	0.756387i	$0.273037\pi$
$751$			2.33816e7i			1.51277i	−0.654124	+	0.756387i	$0.726963\pi$
$752$		−	1.68854e6i		−	0.108885i
$753$	2.19167e6	−	1.89021e7i	0.140860	−	1.21485i
$754$	−1.57747e6			−0.101049
$755$	1.45278e7			0.927541
$756$	9.21946e6	+	3.32676e6i	0.586680	+	0.211698i
$757$		−	2.48284e7i		−	1.57474i	−0.616478	−	0.787372i	$-0.711441\pi$
$757$		−	2.48284e7i		−	1.57474i	0.616478	−	0.787372i	$-0.288559\pi$
$758$	1.39965e7			0.884801
$759$	−8.11812e6	+	883413.i	−0.511507	+	0.0556621i
$760$	2.24476e6			0.140973
$761$			9.69843e6i			0.607071i	0.952820	+	0.303536i	$0.0981672\pi$
$761$			9.69843e6i			0.607071i	−0.952820	+	0.303536i	$0.901833\pi$
$762$	−5.03554e6	−	583866.i	−0.314166	−	0.0364272i
$763$	2.07486e7			1.29026
$764$	−1.38956e7			−0.861277
$765$	−1.77778e7	−	4.17881e6i	−1.09831	−	0.258166i
$766$		−	1.65952e7i		−	1.02190i
$767$		−	1.38441e6i		−	0.0849718i
$768$	−117666.	+	1.01481e6i	−0.00719858	+	0.0620841i
$769$			4.77111e6i			0.290940i	0.989363	+	0.145470i	$0.0464694\pi$
$769$			4.77111e6i			0.290940i	−0.989363	+	0.145470i	$0.953531\pi$
$770$	9.29670e6			0.565070
$771$	1.29272e7	+	1.49889e6i	0.783190	+	0.0908100i
$772$	−7.87438e6			−0.475525
$773$	−5.35197e6			−0.322155			−0.161077	−	0.986942i	$-0.551497\pi$
$773$	−5.35197e6			−0.322155			−0.161077	+	0.986942i	$0.551497\pi$
$774$	−6.62585e6	−	1.55746e6i	−0.397548	−	0.0934467i
$775$	8.32076e6			0.497632
$776$	−1.06088e7			−0.632430
$777$	844737.	−	7.28543e6i	0.0501960	−	0.432915i
$778$			3.41144e6i			0.202064i
$779$	−43588.0			−0.00257350
$780$	108687.	−	937374.i	0.00639651	−	0.0551666i
$781$			832281.i			0.0488250i
$782$	−1.06840e7	+	2.43212e6i	−0.624766	+	0.142222i
$783$	−2.58504e7	−	9.32790e6i	−1.50683	−	0.543725i
$784$	−2.39240e6			−0.139009
$785$			3.50558e7i			2.03042i
$786$	−1.44576e6	+	1.24690e7i	−0.0834719	+	0.719903i
$787$		−	1.04516e7i		−	0.601516i	−0.953700	−	0.300758i	$-0.902760\pi$
$787$		−	1.04516e7i		−	0.601516i	0.953700	−	0.300758i	$-0.0972397\pi$
$788$			1.05632e7i			0.606013i
$789$	−2.01716e6	+	1.73970e7i	−0.115358	+	0.994903i
$790$	−1.88646e7			−1.07543
$791$			3.42772e7i			1.94789i
$792$	−734805.	+	3.12606e6i	−0.0416255	+	0.177086i
$793$		−	1.31298e6i		−	0.0741437i
$794$		−	1.44145e7i		−	0.811425i
$795$	−4.02242e6	+	3.46913e7i	−0.225720	+	1.94672i
$796$			5.13647e6i			0.287331i
$797$	−3.22171e7			−1.79656			−0.898279	−	0.439426i	$-0.855182\pi$
$797$	−3.22171e7			−1.79656			−0.898279	+	0.439426i	$0.855182\pi$
$798$	−5.04759e6	−	585262.i	−0.280593	−	0.0325344i
$799$		−	7.12191e6i		−	0.394666i
$800$		−	1.76077e6i		−	0.0972695i
$801$	−1.58568e7	−	3.72727e6i	−0.873243	−	0.205263i
$802$			1.77772e7i			0.975950i
$803$	−2.25013e6			−0.123146
$804$	−1.25440e6	−	145446.i	−0.0684378	−	0.00793529i
$805$	−2.78438e7	+	6.33839e6i	−1.51439	+	0.344738i
$806$		−	1.05217e6i		−	0.0570491i
$807$	−2.77184e7	−	3.21392e6i	−1.49825	−	0.173721i
$808$	−6.98130e6			−0.376191
$809$			1.83714e7i			0.986896i	0.869775	+	0.493448i	$0.164264\pi$
$809$			1.83714e7i			0.986896i	−0.869775	+	0.493448i	$0.835736\pi$
$810$	7.32395e6	−	1.47183e7i	0.392223	−	0.788214i
$811$	1.43500e7			0.766126			0.383063	−	0.923722i	$-0.374869\pi$
$811$	1.43500e7			0.766126			0.383063	+	0.923722i	$0.374869\pi$
$812$	1.87721e7			0.999130
$813$	−1.80620e6	+	1.55775e7i	−0.0958382	+	0.826556i
$814$	2.40296e6			0.127111
$815$	7.10029e6			0.374440
$816$	−496289.	+	4.28024e6i	−0.0260921	+	0.225031i
$817$	3.52873e6			0.184954
$818$		−	1.10794e7i		−	0.578939i
$819$	−488791.	+	2.07945e6i	−0.0254632	+	0.108328i
$820$			96326.5i			0.00500278i
$821$			1.06499e6i			0.0551425i	0.999620	+	0.0275713i	$0.00877732\pi$
$821$			1.06499e6i			0.0551425i	−0.999620	+	0.0275713i	$0.991223\pi$
$822$	2.34354e7	+	2.71731e6i	1.20974	+	0.140268i
$823$	2.94140e7			1.51375			0.756874	−	0.653560i	$-0.226725\pi$
$823$	2.94140e7			1.51375			0.756874	+	0.653560i	$0.226725\pi$
$824$	−4.50317e6			−0.231047
$825$	637472.	−	5.49787e6i	0.0326081	−	0.281229i
$826$			1.64745e7i			0.840162i
$827$	4.46470e6			0.227002			0.113501	−	0.993538i	$-0.463794\pi$
$827$	4.46470e6			0.227002			0.113501	+	0.993538i	$0.463794\pi$
$828$	69441.4	−	9.86359e6i	0.00352000	−	0.499988i
$829$	−5.93754e6			−0.300068			−0.150034	−	0.988681i	$-0.547938\pi$
$829$	−5.93754e6			−0.300068			−0.150034	+	0.988681i	$0.547938\pi$
$830$			2.01846e7i			1.01701i
$831$	−1.45434e6	+	1.25429e7i	−0.0730572	+	0.630081i
$832$	−222651.			−0.0111511
$833$	−1.00907e7			−0.503857
$834$	−2.75260e7	−	3.19160e6i	−1.37034	−	0.158889i
$835$		−	1.58427e7i		−	0.786347i
$836$		−	1.66485e6i		−	0.0823871i
$837$	6.22168e6	−	1.72422e7i	0.306969	−	0.850703i
$838$		−	8.94381e6i		−	0.439959i
$839$	1.80873e7			0.887091			0.443546	−	0.896252i	$-0.353720\pi$
$839$	1.80873e7			0.887091			0.443546	+	0.896252i	$0.353720\pi$
$840$	−1.29339e6	+	1.11548e7i	−0.0632457	+	0.545462i
$841$	−3.21238e7			−1.56616
$842$	−1.18091e7			−0.574034
$843$	−4.66663e6	+	4.02473e7i	−0.226170	+	1.95060i
$844$	1.45440e7			0.702792
$845$	−2.56372e7			−1.23518
$846$	6.24108e6	+	1.46701e6i	0.299801	+	0.0704707i
$847$			1.91497e7i			0.917176i
$848$	8.24012e6			0.393499
$849$	−3.58634e6	−	415832.i	−0.170758	−	0.0197992i
$850$		−	7.42655e6i		−	0.352565i
$851$	−7.19690e6	+	1.63831e6i	−0.340660	+	0.0775483i
$852$	−998628.	−	115790.i	−0.0471308	−	0.00546476i
$853$	−1.50380e7			−0.707648			−0.353824	−	0.935312i	$-0.615119\pi$
$853$	−1.50380e7			−0.707648			−0.353824	+	0.935312i	$0.615119\pi$
$854$			1.56245e7i			0.733098i
$855$	−1.95026e6	+	8.29694e6i	−0.0912384	+	0.388153i
$856$		−	4.84764e6i		−	0.226123i
$857$		−	1.70855e7i		−	0.794648i	−0.917678	−	0.397324i	$-0.869939\pi$
$857$		−	1.70855e7i		−	0.794648i	0.917678	−	0.397324i	$-0.130061\pi$
$858$	−695213.	−	80609.1i	−0.0322403	−	0.00373823i
$859$	1.55553e7			0.719275			0.359638	−	0.933092i	$-0.382900\pi$
$859$	1.55553e7			0.719275			0.359638	+	0.933092i	$0.382900\pi$
$860$		−	7.79826e6i		−	0.359544i
$861$	25114.6	−	216601.i	0.00115457	−	0.00995754i
$862$		−	1.18145e7i		−	0.541561i
$863$		−	3.06109e7i		−	1.39910i	−0.714582	−	0.699551i	$-0.753383\pi$
$863$		−	3.06109e7i		−	1.39910i	0.714582	−	0.699551i	$-0.246617\pi$
$864$	−3.64864e6	−	1.31658e6i	−0.166282	−	0.0600016i
$865$			1.64395e7i			0.747047i
$866$	−6.02337e6			−0.272926
$867$	456015.	−	3.93290e6i	0.0206031	−	0.177691i
$868$			1.25209e7i			0.564075i
$869$			1.39911e7i			0.628498i
$870$	3.62653e6	−	3.12770e7i	0.162440	−	1.40096i
$871$		−	275219.i		−	0.0122923i
$872$	−8.21133e6			−0.365698
$873$	9.21701e6	−	3.92116e7i	0.409312	−	1.74132i
$874$	1.13508e6	+	4.98625e6i	0.0502628	+	0.220798i
$875$			1.58202e7i			0.698539i
$876$	313046.	−	2.69987e6i	0.0137831	−	0.118873i
$877$	−3.07416e7			−1.34967			−0.674835	−	0.737968i	$-0.735785\pi$
$877$	−3.07416e7			−1.34967			−0.674835	+	0.737968i	$0.735785\pi$
$878$			1.88435e7i			0.824945i
$879$	−1.51185e6	+	1.30389e7i	−0.0659989	+	0.569207i
$880$	−3.67920e6			−0.160157
$881$	−9.68909e6			−0.420575			−0.210287	−	0.977640i	$-0.567440\pi$
$881$	−9.68909e6			−0.420575			−0.210287	+	0.977640i	$0.567440\pi$
$882$	2.07854e6	−	8.84266e6i	0.0899676	−	0.382747i
$883$	4.03019e7			1.73950			0.869748	−	0.493497i	$-0.164282\pi$
$883$	4.03019e7			1.73950			0.869748	+	0.493497i	$0.164282\pi$
$884$	−939097.			−0.0404185
$885$	2.74489e7	+	3.18268e6i	1.17806	+	0.136595i
$886$	1.31437e7			0.562513
$887$		−	7.22829e6i		−	0.308480i	−0.988033	−	0.154240i	$-0.950707\pi$
$887$		−	7.22829e6i		−	0.308480i	0.988033	−	0.154240i	$-0.0492929\pi$
$888$	−334308.	+	2.88323e6i	−0.0142270	+	0.122701i
$889$			1.31474e7i			0.557936i
$890$		−	1.86626e7i		−	0.789765i
$891$	−1.09159e7	−	5.43188e6i	−0.460646	−	0.229222i
$892$	1.89792e7			0.798668
$893$	−3.32382e6			−0.139479
$894$	2.02773e7	+	2.35113e6i	0.848530	+	0.0983861i
$895$		−	4.39568e7i		−	1.83429i
$896$	2.64957e6			0.110257
$897$	2.13713e6	−	232563.i	0.0886851	−	0.00965070i
$898$	−7.75858e6			−0.321064
$899$		−	3.51073e7i		−	1.44877i
$900$	6.50804e6	+	1.52977e6i	0.267820	+	0.0629533i
$901$	3.47551e7			1.42629
$902$	71441.5			0.00292371
$903$	−2.03319e6	+	1.75352e7i	−0.0829772	+	0.715636i
$904$		−	1.35653e7i		−	0.552089i
$905$			6.20567e6i			0.251865i
$906$	1.29282e7	+	1.49901e6i	0.523261	+	0.0606716i
$907$			2.10333e7i			0.848965i	0.905436	+	0.424483i	$0.139544\pi$
$907$			2.10333e7i			0.848965i	−0.905436	+	0.424483i	$0.860456\pi$
$908$	1.08852e6			0.0438151
$909$	6.06540e6	−	2.58038e7i	0.243472	−	1.03580i
$910$	−2.44740e6			−0.0979719
$911$	2.89727e7			1.15662			0.578312	−	0.815815i	$-0.303711\pi$
$911$	2.89727e7			1.15662			0.578312	+	0.815815i	$0.303711\pi$
$912$	1.99760e6	+	231620.i	0.0795283	+	0.00922122i
$913$	1.49701e7			0.594358
$914$	−1.50143e7			−0.594482
$915$	2.60327e7	+	3.01846e6i	1.02794	+	0.119188i
$916$		−	2.33980e7i		−	0.921384i
$917$	3.25553e7			1.27849
$918$	−1.53892e7	−	5.55306e6i	−0.602711	−	0.217483i
$919$		−	8.34384e6i		−	0.325895i	−0.986635	−	0.162947i	$-0.947900\pi$
$919$		−	8.34384e6i		−	0.325895i	0.986635	−	0.162947i	$-0.0521001\pi$
$920$	1.10193e7	−	2.50844e6i	0.429224	−	0.0977089i
$921$	−3.31295e6	+	2.85725e7i	−0.128696	+	1.10994i
$922$	7.39957e6			0.286668
$923$		−	219102.i		−	0.00846528i
$924$	8.27309e6	+	959255.i	0.318777	+	0.0369619i
$925$		−	5.00263e6i		−	0.192240i
$926$			2.85392e7i			1.09374i
$927$	3.91238e6	−	1.66443e7i	0.149535	−	0.636161i
$928$	−7.42911e6			−0.283183
$929$			1.62448e6i			0.0617553i	0.999523	+	0.0308777i	$0.00983023\pi$
$929$			1.62448e6i			0.0617553i	−0.999523	+	0.0308777i	$0.990170\pi$
$930$	2.08617e7	+	2.41889e6i	0.790936	+	0.0917081i
$931$			4.70934e6i			0.178068i
$932$			2.26043e7i			0.852415i
$933$	−1.77166e7	−	2.05422e6i	−0.666309	−	0.0772578i
$934$			2.36660e7i			0.887683i
$935$	−1.55181e7			−0.580510
$936$	193441.	−	822950.i	0.00721703	−	0.0307032i
$937$			2.06686e7i			0.769065i	0.923111	+	0.384532i	$0.125637\pi$
$937$			2.06686e7i			0.769065i	−0.923111	+	0.384532i	$0.874363\pi$
$938$			3.27513e6i			0.121541i
$939$	−3.38640e7	−	3.92649e6i	−1.25336	−	0.145325i
$940$			7.34540e6i			0.271142i
$941$	−3.43634e7			−1.26509			−0.632546	−	0.774523i	$-0.717990\pi$
$941$	−3.43634e7			−1.26509			−0.632546	+	0.774523i	$0.717990\pi$
$942$	−3.61714e6	+	3.11960e7i	−0.132812	+	1.14544i
$943$	−213969.	+	48708.1i	−0.00783558	+	0.00178370i
$944$		−	6.51986e6i		−	0.238127i
$945$	−4.01061e7	−	1.44719e7i	−1.46093	−	0.527166i
$946$	−5.78366e6			−0.210124
$947$		−	4.54948e7i		−	1.64849i	−0.566233	−	0.824245i	$-0.691600\pi$
$947$		−	4.54948e7i		−	1.64849i	0.566233	−	0.824245i	$-0.308400\pi$
$948$	−1.67875e7	−	1.94650e6i	−0.606689	−	0.0703450i
$949$	592358.			0.0213510
$950$	−3.46599e6			−0.124600
$951$	2.61004e7	+	3.02632e6i	0.935829	+	0.108508i
$952$	1.11753e7			0.399639
$953$	3.96228e7			1.41323			0.706615	−	0.707598i	$-0.250221\pi$
$953$	3.96228e7			1.41323			0.706615	+	0.707598i	$0.250221\pi$
$954$	−7.15907e6	+	3.04566e7i	−0.254675	+	1.08345i
$955$	6.04478e7			2.14473
$956$		−	988473.i		−	0.0349800i
$957$	−2.31969e7	−	2.68965e6i	−0.818747	−	0.0949328i
$958$			1.23312e7i			0.434101i
$959$		−	6.11878e7i		−	2.14841i
$960$	511864.	−	4.41456e6i	0.0179257	−	0.154600i
$961$	−5.21265e6			−0.182075
$962$	−632589.			−0.0220386
$963$	1.79175e7	+	4.21166e6i	0.622605	+	0.146348i
$964$			1.15178e7i			0.399188i
$965$	3.42548e7			1.18414
$966$	−2.54321e7	+	2.76751e6i	−0.876877	+	0.0954217i
$967$	−4.93693e7			−1.69782			−0.848908	−	0.528541i	$-0.822739\pi$
$967$	−4.93693e7			−1.69782			−0.848908	+	0.528541i	$0.822739\pi$
$968$		−	7.57855e6i		−	0.259955i
$969$	8.42547e6	+	976924.i	0.288260	+	0.0334234i
$970$	4.61500e7			1.57486
$971$	−1.31154e7			−0.446408			−0.223204	−	0.974772i	$-0.571652\pi$
$971$	−1.31154e7			−0.446408			−0.223204	+	0.974772i	$0.571652\pi$
$972$	8.03621e6	−	1.23420e7i	0.272826	−	0.419006i
$973$			7.18678e7i			2.43362i
$974$		−	2.10473e7i		−	0.710883i
$975$	−167817.	+	1.44734e6i	−0.00565360	+	0.0487594i
$976$		−	6.18346e6i		−	0.207782i
$977$	−3.95989e7			−1.32723			−0.663615	−	0.748074i	$-0.730979\pi$
$977$	−3.95989e7			−1.32723			−0.663615	+	0.748074i	$0.730979\pi$
$978$	6.31852e6	+	732625.i	0.211236	+	0.0244926i
$979$	−1.38413e7			−0.461552
$980$	1.04073e7			0.346158
$981$	7.13406e6	−	3.03502e7i	0.236681	−	1.00691i
$982$	−2.70219e6			−0.0894204
$983$	4.19732e7			1.38544			0.692721	−	0.721206i	$-0.256412\pi$
$983$	4.19732e7			1.38544			0.692721	+	0.721206i	$0.256412\pi$
$984$	−9939.20	+	85720.5i	−0.000327238	+	0.00282226i
$985$		−	4.59517e7i		−	1.50908i
$986$	−3.13345e7			−1.02643
$987$	1.91512e6	−	1.65169e7i	0.0625754	−	0.539681i
$988$			438279.i			0.0142843i
$989$	1.73222e7	−	3.94323e6i	0.563134	−	0.128192i
$990$	3.19651e6	−	1.35988e7i	0.103655	−	0.440975i
$991$	−3.71123e7			−1.20042			−0.600210	−	0.799842i	$-0.704916\pi$
$991$	−3.71123e7			−1.20042			−0.600210	+	0.799842i	$0.704916\pi$
$992$		−	4.95520e6i		−	0.159875i
$993$	−1.90324e6	+	1.64145e7i	−0.0612521	+	0.528268i
$994$			2.60733e6i			0.0837008i
$995$		−	2.23444e7i		−	0.715504i
$996$	−2.08270e6	+	1.79622e7i	−0.0665238	+	0.573734i
$997$	−5.59859e7			−1.78378			−0.891889	−	0.452254i	$-0.850620\pi$
$997$	−5.59859e7			−1.78378			−0.891889	+	0.452254i	$0.850620\pi$
$998$		−	1.31546e6i		−	0.0418071i
$999$	−1.03664e7	−	3.74062e6i	−0.328635	−	0.118585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.6.d.a.137.6	yes	40
3.2	odd	2	inner	138.6.d.a.137.7	yes	40
23.22	odd	2	inner	138.6.d.a.137.5	✓	40
69.68	even	2	inner	138.6.d.a.137.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.6.d.a.137.5	✓	40	23.22	odd	2	inner
138.6.d.a.137.6	yes	40	1.1	even	1	trivial
138.6.d.a.137.7	yes	40	3.2	odd	2	inner
138.6.d.a.137.8	yes	40	69.68	even	2	inner

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	138.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} +(-1.79544 + 15.4847i) q^{3} -16.0000 q^{4} +69.6024 q^{5} +(61.9389 + 7.18174i) q^{6} -161.717i q^{7} +64.0000i q^{8} +(-236.553 - 55.6036i) q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} +(-1.79544 + 15.4847i) q^{3} -16.0000 q^{4} +69.6024 q^{5} +(61.9389 + 7.18174i) q^{6} -161.717i q^{7} +64.0000i q^{8} +(-236.553 - 55.6036i) q^{9} -278.410i q^{10} -206.485 q^{11} +(28.7270 - 247.755i) q^{12} +54.3582 q^{13} -646.867 q^{14} +(-124.967 + 1077.77i) q^{15} +256.000 q^{16} +1079.76 q^{17} +(-222.414 + 946.211i) q^{18} -503.925i q^{19} -1113.64 q^{20} +(2504.14 + 290.352i) q^{21} +825.941i q^{22} +(-563.118 - 2473.71i) q^{23} +(-991.022 - 114.908i) q^{24} +1719.50 q^{25} -217.433i q^{26} +(1285.72 - 3563.12i) q^{27} +2587.47i q^{28} -7254.99i q^{29} +(4311.10 + 499.867i) q^{30} +4839.06 q^{31} -1024.00i q^{32} +(370.731 - 3197.37i) q^{33} -4319.02i q^{34} -11255.9i q^{35} +(3784.85 + 889.658i) q^{36} -2909.35i q^{37} -2015.70 q^{38} +(-97.5967 + 841.722i) q^{39} +4454.56i q^{40} -86.4971i q^{41} +(1161.41 - 10016.6i) q^{42} +7002.50i q^{43} +3303.77 q^{44} +(-16464.7 - 3870.15i) q^{45} +(-9894.84 + 2252.47i) q^{46} -6595.86i q^{47} +(-459.631 + 3964.09i) q^{48} -9345.33 q^{49} -6877.99i q^{50} +(-1938.63 + 16719.7i) q^{51} -869.731 q^{52} +32188.0 q^{53} +(-14252.5 - 5142.89i) q^{54} -14371.9 q^{55} +10349.9 q^{56} +(7803.13 + 904.764i) q^{57} -29020.0 q^{58} -25468.2i q^{59} +(1999.47 - 17244.4i) q^{60} -24154.2i q^{61} -19356.2i q^{62} +(-8992.04 + 38254.6i) q^{63} -4096.00 q^{64} +3783.46 q^{65} +(-12789.5 - 1482.92i) q^{66} -5063.06i q^{67} -17276.1 q^{68} +(39315.7 - 4278.33i) q^{69} -45023.5 q^{70} -4030.70i q^{71} +(3558.63 - 15139.4i) q^{72} +10897.3 q^{73} -11637.4 q^{74} +(-3087.25 + 26625.9i) q^{75} +8062.79i q^{76} +33392.1i q^{77} +(3366.89 + 390.387i) q^{78} -67758.5i q^{79} +17818.2 q^{80} +(52865.5 + 26306.4i) q^{81} -345.988 q^{82} -72499.7 q^{83} +(-40066.2 - 4645.63i) q^{84} +75153.6 q^{85} +28010.0 q^{86} +(112341. + 13025.9i) q^{87} -13215.1i q^{88} +67033.0 q^{89} +(-15480.6 + 65858.6i) q^{90} -8790.64i q^{91} +(9009.89 + 39579.4i) q^{92} +(-8688.22 + 74931.5i) q^{93} -26383.4 q^{94} -35074.4i q^{95} +(15856.3 + 1838.53i) q^{96} +165763. i q^{97} +37381.3i q^{98} +(48844.7 + 11481.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9}+O(q^{10}) \) 40 * q - 4 * q^3 - 640 * q^4 + 80 * q^6 + 504 * q^9	\( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96}+O(q^{100}) \) 40 * q - 4 * q^3 - 640 * q^4 + 80 * q^6 + 504 * q^9 + 64 * q^12 - 1048 * q^13 + 10240 * q^16 + 1280 * q^18 - 1280 * q^24 + 30480 * q^25 + 1700 * q^27 - 22576 * q^31 - 8064 * q^36 + 55608 * q^39 + 1088 * q^46 - 1024 * q^48 - 23224 * q^49 + 16768 * q^52 + 25456 * q^54 + 210400 * q^55 - 83168 * q^58 - 163840 * q^64 + 99076 * q^69 + 167520 * q^70 - 20480 * q^72 + 241160 * q^73 - 255604 * q^75 - 233440 * q^78 + 78512 * q^81 - 8832 * q^82 - 460296 * q^85 - 4136 * q^87 + 500704 * q^93 - 138272 * q^94 + 20480 * q^96

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