LMFDB - Embedded newform 294.6.e.d.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not 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:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-38.0000 + 65.8179i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-38.0000 + 65.8179i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-152.000 - 263.272i) q^{10} +(-325.000 - 562.917i) q^{11} +(72.0000 - 124.708i) q^{12} +762.000 q^{13} -684.000 q^{15} +(-128.000 + 221.703i) q^{16} +(278.000 + 481.510i) q^{17} +(-162.000 - 280.592i) q^{18} +(1226.00 - 2123.49i) q^{19} +1216.00 q^{20} +2600.00 q^{22} +(1475.00 - 2554.77i) q^{23} +(288.000 + 498.831i) q^{24} +(-1325.50 - 2295.83i) q^{25} +(-1524.00 + 2639.65i) q^{26} -729.000 q^{27} -674.000 q^{29} +(1368.00 - 2369.45i) q^{30} +(1512.00 + 2618.86i) q^{31} +(-512.000 - 886.810i) q^{32} +(2925.00 - 5066.25i) q^{33} -2224.00 q^{34} +1296.00 q^{36} +(-3865.00 + 6694.38i) q^{37} +(4904.00 + 8493.98i) q^{38} +(3429.00 + 5939.20i) q^{39} +(-2432.00 + 4212.35i) q^{40} -17016.0 q^{41} +21836.0 q^{43} +(-5200.00 + 9006.66i) q^{44} +(-3078.00 - 5331.25i) q^{45} +(5900.00 + 10219.1i) q^{46} +(11970.0 - 20732.6i) q^{47} -2304.00 q^{48} +10604.0 q^{50} +(-2502.00 + 4333.59i) q^{51} +(-6096.00 - 10558.6i) q^{52} +(-7797.00 - 13504.8i) q^{53} +(1458.00 - 2525.33i) q^{54} +49400.0 q^{55} +22068.0 q^{57} +(1348.00 - 2334.80i) q^{58} +(-2804.00 - 4856.67i) q^{59} +(5472.00 + 9477.78i) q^{60} +(-75.0000 + 129.904i) q^{61} -12096.0 q^{62} +4096.00 q^{64} +(-28956.0 + 50153.3i) q^{65} +(11700.0 + 20265.0i) q^{66} +(21892.0 + 37918.1i) q^{67} +(4448.00 - 7704.16i) q^{68} +26550.0 q^{69} -39178.0 q^{71} +(-2592.00 + 4489.48i) q^{72} +(11785.0 + 20412.2i) q^{73} +(-15460.0 - 26777.5i) q^{74} +(11929.5 - 20662.5i) q^{75} -39232.0 q^{76} -27432.0 q^{78} +(8946.00 - 15494.9i) q^{79} +(-9728.00 - 16849.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(34032.0 - 58945.2i) q^{82} +38972.0 q^{83} -42256.0 q^{85} +(-43672.0 + 75642.1i) q^{86} +(-3033.00 - 5253.31i) q^{87} +(-20800.0 - 36026.7i) q^{88} +(-3012.00 + 5216.94i) q^{89} +24624.0 q^{90} -47200.0 q^{92} +(-13608.0 + 23569.7i) q^{93} +(47880.0 + 82930.6i) q^{94} +(93176.0 + 161386. i) q^{95} +(4608.00 - 7981.29i) q^{96} +108430. q^{97} +52650.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} - 76 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 - 76 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} - 76 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9} - 304 q^{10} - 650 q^{11} + 144 q^{12} + 1524 q^{13} - 1368 q^{15} - 256 q^{16} + 556 q^{17} - 324 q^{18} + 2452 q^{19} + 2432 q^{20} + 5200 q^{22} + 2950 q^{23} + 576 q^{24} - 2651 q^{25} - 3048 q^{26} - 1458 q^{27} - 1348 q^{29} + 2736 q^{30} + 3024 q^{31} - 1024 q^{32} + 5850 q^{33} - 4448 q^{34} + 2592 q^{36} - 7730 q^{37} + 9808 q^{38} + 6858 q^{39} - 4864 q^{40} - 34032 q^{41} + 43672 q^{43} - 10400 q^{44} - 6156 q^{45} + 11800 q^{46} + 23940 q^{47} - 4608 q^{48} + 21208 q^{50} - 5004 q^{51} - 12192 q^{52} - 15594 q^{53} + 2916 q^{54} + 98800 q^{55} + 44136 q^{57} + 2696 q^{58} - 5608 q^{59} + 10944 q^{60} - 150 q^{61} - 24192 q^{62} + 8192 q^{64} - 57912 q^{65} + 23400 q^{66} + 43784 q^{67} + 8896 q^{68} + 53100 q^{69} - 78356 q^{71} - 5184 q^{72} + 23570 q^{73} - 30920 q^{74} + 23859 q^{75} - 78464 q^{76} - 54864 q^{78} + 17892 q^{79} - 19456 q^{80} - 6561 q^{81} + 68064 q^{82} + 77944 q^{83} - 84512 q^{85} - 87344 q^{86} - 6066 q^{87} - 41600 q^{88} - 6024 q^{89} + 49248 q^{90} - 94400 q^{92} - 27216 q^{93} + 95760 q^{94} + 186352 q^{95} + 9216 q^{96} + 216860 q^{97} + 105300 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 - 76 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9 - 304 * q^10 - 650 * q^11 + 144 * q^12 + 1524 * q^13 - 1368 * q^15 - 256 * q^16 + 556 * q^17 - 324 * q^18 + 2452 * q^19 + 2432 * q^20 + 5200 * q^22 + 2950 * q^23 + 576 * q^24 - 2651 * q^25 - 3048 * q^26 - 1458 * q^27 - 1348 * q^29 + 2736 * q^30 + 3024 * q^31 - 1024 * q^32 + 5850 * q^33 - 4448 * q^34 + 2592 * q^36 - 7730 * q^37 + 9808 * q^38 + 6858 * q^39 - 4864 * q^40 - 34032 * q^41 + 43672 * q^43 - 10400 * q^44 - 6156 * q^45 + 11800 * q^46 + 23940 * q^47 - 4608 * q^48 + 21208 * q^50 - 5004 * q^51 - 12192 * q^52 - 15594 * q^53 + 2916 * q^54 + 98800 * q^55 + 44136 * q^57 + 2696 * q^58 - 5608 * q^59 + 10944 * q^60 - 150 * q^61 - 24192 * q^62 + 8192 * q^64 - 57912 * q^65 + 23400 * q^66 + 43784 * q^67 + 8896 * q^68 + 53100 * q^69 - 78356 * q^71 - 5184 * q^72 + 23570 * q^73 - 30920 * q^74 + 23859 * q^75 - 78464 * q^76 - 54864 * q^78 + 17892 * q^79 - 19456 * q^80 - 6561 * q^81 + 68064 * q^82 + 77944 * q^83 - 84512 * q^85 - 87344 * q^86 - 6066 * q^87 - 41600 * q^88 - 6024 * q^89 + 49248 * q^90 - 94400 * q^92 - 27216 * q^93 + 95760 * q^94 + 186352 * q^95 + 9216 * q^96 + 216860 * q^97 + 105300 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−38.0000	+	65.8179i	−0.679765	+	1.17739i	0.295287	+	0.955409i	$0.404585\pi$
$5$	−38.0000	+	65.8179i	−0.679765	+	1.17739i	−0.975052	+	0.221978i	$0.928749\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−152.000	−	263.272i	−0.480666	−	0.832538i
$11$	−325.000	−	562.917i	−0.809845	−	1.40269i	−0.912971	−	0.408024i	$-0.866218\pi$
$11$	−325.000	−	562.917i	−0.809845	−	1.40269i	0.103127	−	0.994668i	$-0.467115\pi$
$12$	72.0000	−	124.708i	0.144338	−	0.250000i
$13$	762.000			1.25054			0.625269	−	0.780410i	$-0.284989\pi$
$13$	762.000			1.25054			0.625269	+	0.780410i	$0.284989\pi$
$14$		0			0
$15$	−684.000			−0.784925
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	278.000	+	481.510i	0.233304	+	0.404095i	0.958778	−	0.284155i	$-0.0917129\pi$
$17$	278.000	+	481.510i	0.233304	+	0.404095i	−0.725474	+	0.688249i	$0.758380\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	1226.00	−	2123.49i	0.779124	−	1.34948i	−0.153324	−	0.988176i	$-0.548998\pi$
$19$	1226.00	−	2123.49i	0.779124	−	1.34948i	0.932447	−	0.361306i	$-0.117669\pi$
$20$	1216.00			0.679765
$21$		0			0
$22$	2600.00			1.14529
$23$	1475.00	−	2554.77i	0.581397	−	1.00701i	−0.413918	−	0.910314i	$-0.635840\pi$
$23$	1475.00	−	2554.77i	0.581397	−	1.00701i	0.995314	−	0.0966940i	$-0.0308268\pi$
$24$	288.000	+	498.831i	0.102062	+	0.176777i
$25$	−1325.50	−	2295.83i	−0.424160	−	0.734667i
$26$	−1524.00	+	2639.65i	−0.442132	+	0.765794i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−674.000			−0.148821			−0.0744106	−	0.997228i	$-0.523708\pi$
$29$	−674.000			−0.148821			−0.0744106	+	0.997228i	$0.523708\pi$
$30$	1368.00	−	2369.45i	0.277513	−	0.480666i
$31$	1512.00	+	2618.86i	0.282584	+	0.489450i	0.972020	−	0.234896i	$-0.0754751\pi$
$31$	1512.00	+	2618.86i	0.282584	+	0.489450i	−0.689436	+	0.724346i	$0.742142\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	2925.00	−	5066.25i	0.467564	−	0.809845i
$34$	−2224.00			−0.329942
$35$		0			0
$36$	1296.00			0.166667
$37$	−3865.00	+	6694.38i	−0.464136	+	0.803907i	−0.999162	−	0.0409285i	$-0.986968\pi$
$37$	−3865.00	+	6694.38i	−0.464136	+	0.803907i	0.535026	+	0.844835i	$0.320302\pi$
$38$	4904.00	+	8493.98i	0.550924	+	0.954228i
$39$	3429.00	+	5939.20i	0.360999	+	0.625269i
$40$	−2432.00	+	4212.35i	−0.240333	+	0.416269i
$41$	−17016.0			−1.58088			−0.790438	−	0.612542i	$-0.790147\pi$
$41$	−17016.0			−1.58088			−0.790438	+	0.612542i	$0.790147\pi$
$42$		0			0
$43$	21836.0			1.80095			0.900476	−	0.434907i	$-0.143219\pi$
$43$	21836.0			1.80095			0.900476	+	0.434907i	$0.143219\pi$
$44$	−5200.00	+	9006.66i	−0.404922	+	0.701346i
$45$	−3078.00	−	5331.25i	−0.226588	−	0.392462i
$46$	5900.00	+	10219.1i	0.411109	+	0.712062i
$47$	11970.0	−	20732.6i	0.790405	−	1.36902i	−0.135312	−	0.990803i	$-0.543204\pi$
$47$	11970.0	−	20732.6i	0.790405	−	1.36902i	0.925717	−	0.378218i	$-0.123463\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	10604.0			0.599853
$51$	−2502.00	+	4333.59i	−0.134698	+	0.233304i
$52$	−6096.00	−	10558.6i	−0.312634	−	0.541498i
$53$	−7797.00	−	13504.8i	−0.381275	−	0.660387i	0.609970	−	0.792424i	$-0.291181\pi$
$53$	−7797.00	−	13504.8i	−0.381275	−	0.660387i	−0.991245	+	0.132037i	$0.957848\pi$
$54$	1458.00	−	2525.33i	0.0680414	−	0.117851i
$55$	49400.0			2.20201
$56$		0			0
$57$	22068.0			0.899655
$58$	1348.00	−	2334.80i	0.0526163	−	0.0911340i
$59$	−2804.00	−	4856.67i	−0.104869	−	0.181639i	0.808816	−	0.588062i	$-0.200109\pi$
$59$	−2804.00	−	4856.67i	−0.104869	−	0.181639i	−0.913685	+	0.406424i	$0.866776\pi$
$60$	5472.00	+	9477.78i	0.196231	+	0.339882i
$61$	−75.0000	+	129.904i	−0.00258069	+	0.00446989i	−0.867313	−	0.497763i	$-0.834155\pi$
$61$	−75.0000	+	129.904i	−0.00258069	+	0.00446989i	0.864732	+	0.502233i	$0.167488\pi$
$62$	−12096.0			−0.399634
$63$		0			0
$64$	4096.00			0.125000
$65$	−28956.0	+	50153.3i	−0.850071	+	1.47237i
$66$	11700.0	+	20265.0i	0.330618	+	0.572647i
$67$	21892.0	+	37918.1i	0.595797	+	1.03195i	0.993434	+	0.114408i	$0.0364971\pi$
$67$	21892.0	+	37918.1i	0.595797	+	1.03195i	−0.397637	+	0.917543i	$0.630170\pi$
$68$	4448.00	−	7704.16i	0.116652	−	0.202047i
$69$	26550.0			0.671339
$70$		0			0
$71$	−39178.0			−0.922351			−0.461176	−	0.887309i	$-0.652572\pi$
$71$	−39178.0			−0.922351			−0.461176	+	0.887309i	$0.652572\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	11785.0	+	20412.2i	0.258835	+	0.448315i	0.965930	−	0.258803i	$-0.0833282\pi$
$73$	11785.0	+	20412.2i	0.258835	+	0.448315i	−0.707095	+	0.707118i	$0.749995\pi$
$74$	−15460.0	−	26777.5i	−0.328194	−	0.568448i
$75$	11929.5	−	20662.5i	0.244889	−	0.424160i
$76$	−39232.0			−0.779124
$77$		0			0
$78$	−27432.0			−0.510530
$79$	8946.00	−	15494.9i	0.161273	−	0.279333i	−0.774053	−	0.633121i	$-0.781773\pi$
$79$	8946.00	−	15494.9i	0.161273	−	0.279333i	0.935325	+	0.353789i	$0.115107\pi$
$80$	−9728.00	−	16849.4i	−0.169941	−	0.294347i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	34032.0	−	58945.2i	0.558924	−	0.968085i
$83$	38972.0			0.620951			0.310476	−	0.950581i	$-0.399512\pi$
$83$	38972.0			0.620951			0.310476	+	0.950581i	$0.399512\pi$
$84$		0			0
$85$	−42256.0			−0.634368
$86$	−43672.0	+	75642.1i	−0.636732	+	1.10285i
$87$	−3033.00	−	5253.31i	−0.0429610	−	0.0744106i
$88$	−20800.0	−	36026.7i	−0.286323	−	0.495926i
$89$	−3012.00	+	5216.94i	−0.0403070	+	0.0698137i	−0.885475	−	0.464687i	$-0.846167\pi$
$89$	−3012.00	+	5216.94i	−0.0403070	+	0.0698137i	0.845168	+	0.534501i	$0.179500\pi$
$90$	24624.0			0.320444
$91$		0			0
$92$	−47200.0			−0.581397
$93$	−13608.0	+	23569.7i	−0.163150	+	0.282584i
$94$	47880.0	+	82930.6i	0.558901	+	0.968044i
$95$	93176.0	+	161386.i	1.05924	+	1.83466i
$96$	4608.00	−	7981.29i	0.0510310	−	0.0883883i
$97$	108430.			1.17009			0.585046	−	0.811000i	$-0.301076\pi$
$97$	108430.			1.17009			0.585046	+	0.811000i	$0.301076\pi$
$98$		0			0
$99$	52650.0			0.539896
$100$	−21208.0	+	36733.3i	−0.212080	+	0.367333i
$101$	35212.0	+	60989.0i	0.343469	+	0.594905i	0.985074	−	0.172129i	$-0.0550647\pi$
$101$	35212.0	+	60989.0i	0.343469	+	0.594905i	−0.641606	+	0.767035i	$0.721731\pi$
$102$	−10008.0	−	17334.4i	−0.0952460	−	0.164971i
$103$	15776.0	−	27324.8i	0.146522	−	0.253784i	−0.783418	−	0.621496i	$-0.786525\pi$
$103$	15776.0	−	27324.8i	0.146522	−	0.253784i	0.929940	+	0.367712i	$0.119859\pi$
$104$	48768.0			0.442132
$105$		0			0
$106$	62376.0			0.539204
$107$	−54141.0	+	93775.0i	−0.457159	+	0.791822i	−0.998809	−	0.0487817i	$-0.984466\pi$
$107$	−54141.0	+	93775.0i	−0.457159	+	0.791822i	0.541651	+	0.840604i	$0.317799\pi$
$108$	5832.00	+	10101.3i	0.0481125	+	0.0833333i
$109$	36073.0	+	62480.3i	0.290814	+	0.503705i	0.974003	−	0.226537i	$-0.0727404\pi$
$109$	36073.0	+	62480.3i	0.290814	+	0.503705i	−0.683188	+	0.730242i	$0.739407\pi$
$110$	−98800.0	+	171127.i	−0.778530	+	1.34845i
$111$	−69570.0			−0.535938
$112$		0			0
$113$	220906.			1.62746			0.813732	−	0.581240i	$-0.197432\pi$
$113$	220906.			1.62746			0.813732	+	0.581240i	$0.197432\pi$
$114$	−44136.0	+	76445.8i	−0.318076	+	0.550924i
$115$	112100.	+	194163.i	0.790426	+	1.36906i
$116$	5392.00	+	9339.22i	0.0372053	+	0.0644415i
$117$	−30861.0	+	53452.8i	−0.208423	+	0.360999i
$118$	22432.0			0.148307
$119$		0			0
$120$	−43776.0			−0.277513
$121$	−130724.	+	226421.i	−0.811696	+	1.40590i
$122$	−300.000	−	519.615i	−0.00182483	−	0.00316069i
$123$	−76572.0	−	132627.i	−0.456360	−	0.790438i
$124$	24192.0	−	41901.8i	0.141292	−	0.244725i
$125$	−36024.0			−0.206213
$126$		0			0
$127$	−239652.			−1.31847			−0.659237	−	0.751935i	$-0.729121\pi$
$127$	−239652.			−1.31847			−0.659237	+	0.751935i	$0.729121\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	98262.0	+	170195.i	0.519890	+	0.900476i
$130$	−115824.	−	200613.i	−0.601091	−	1.04112i
$131$	137086.	−	237440.i	0.697935	−	1.20886i	−0.271246	−	0.962510i	$-0.587436\pi$
$131$	137086.	−	237440.i	0.697935	−	1.20886i	0.969181	−	0.246349i	$-0.0792308\pi$
$132$	−93600.0			−0.467564
$133$		0			0
$134$	−175136.			−0.842584
$135$	27702.0	−	47981.3i	0.130821	−	0.226588i
$136$	17792.0	+	30816.6i	0.0824855	+	0.142869i
$137$	195577.	+	338749.i	0.890259	+	1.54197i	0.839565	+	0.543260i	$0.182810\pi$
$137$	195577.	+	338749.i	0.890259	+	1.54197i	0.0506942	+	0.998714i	$0.483857\pi$
$138$	−53100.0	+	91971.9i	−0.237354	+	0.411109i
$139$	339364.			1.48980			0.744901	−	0.667175i	$-0.232497\pi$
$139$	339364.			1.48980			0.744901	+	0.667175i	$0.232497\pi$
$140$		0			0
$141$	215460.			0.912681
$142$	78356.0	−	135717.i	0.326100	−	0.564823i
$143$	−247650.	−	428942.i	−1.01274	−	1.75412i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	25612.0	−	44361.3i	0.101163	−	0.175220i
$146$	−94280.0			−0.366047
$147$		0			0
$148$	123680.			0.464136
$149$	14667.0	−	25404.0i	0.0541222	−	0.0937424i	−0.837695	−	0.546138i	$-0.816097\pi$
$149$	14667.0	−	25404.0i	0.0541222	−	0.0937424i	0.891817	+	0.452396i	$0.149431\pi$
$150$	47718.0	+	82650.0i	0.173163	+	0.299926i
$151$	−35804.0	−	62014.3i	−0.127788	−	0.221335i	0.795031	−	0.606568i	$-0.207454\pi$
$151$	−35804.0	−	62014.3i	−0.127788	−	0.221335i	−0.922819	+	0.385233i	$0.874121\pi$
$152$	78464.0	−	135904.i	0.275462	−	0.477114i
$153$	−45036.0			−0.155536
$154$		0			0
$155$	−229824.			−0.768362
$156$	54864.0	−	95027.2i	0.180499	−	0.312634i
$157$	−148159.	−	256619.i	−0.479710	−	0.830882i	0.520019	−	0.854155i	$-0.325925\pi$
$157$	−148159.	−	256619.i	−0.479710	−	0.830882i	−0.999729	+	0.0232723i	$0.992592\pi$
$158$	35784.0	+	61979.7i	0.114037	+	0.197518i
$159$	70173.0	−	121543.i	0.220129	−	0.381275i
$160$	77824.0			0.240333
$161$		0			0
$162$	26244.0			0.0785674
$163$	240200.	−	416039.i	0.708115	−	1.22649i	−0.257440	−	0.966294i	$-0.582879\pi$
$163$	240200.	−	416039.i	0.708115	−	1.22649i	0.965555	−	0.260197i	$-0.0837877\pi$
$164$	136128.	+	235781.i	0.395219	+	0.684539i
$165$	222300.	+	385035.i	0.635667	+	1.10101i
$166$	−77944.0	+	135003.i	−0.219539	+	0.380253i
$167$	160180.			0.444444			0.222222	−	0.974996i	$-0.428669\pi$
$167$	160180.			0.444444			0.222222	+	0.974996i	$0.428669\pi$
$168$		0			0
$169$	209351.			0.563843
$170$	84512.0	−	146379.i	0.224283	−	0.388469i
$171$	99306.0	+	172003.i	0.259708	+	0.449827i
$172$	−174688.	−	302568.i	−0.450238	−	0.779835i
$173$	4492.00	−	7780.37i	0.0114110	−	0.0197645i	−0.860264	−	0.509850i	$-0.829701\pi$
$173$	4492.00	−	7780.37i	0.0114110	−	0.0197645i	0.871675	+	0.490085i	$0.163034\pi$
$174$	24264.0			0.0607560
$175$		0			0
$176$	166400.			0.404922
$177$	25236.0	−	43710.0i	0.0605463	−	0.104869i
$178$	−12048.0	−	20867.7i	−0.0285013	−	0.0493657i
$179$	−91443.0	−	158384.i	−0.213313	−	0.369469i	0.739436	−	0.673227i	$-0.235092\pi$
$179$	−91443.0	−	158384.i	−0.213313	−	0.369469i	−0.952749	+	0.303757i	$0.901759\pi$
$180$	−49248.0	+	85300.0i	−0.113294	+	0.196231i
$181$	138330.			0.313848			0.156924	−	0.987611i	$-0.449842\pi$
$181$	138330.			0.313848			0.156924	+	0.987611i	$0.449842\pi$
$182$		0			0
$183$	−1350.00			−0.00297993
$184$	94400.0	−	163506.i	0.205555	−	0.356031i
$185$	−293740.	−	508773.i	−0.631006	−	1.09294i
$186$	−54432.0	−	94279.0i	−0.115364	−	0.199817i
$187$	180700.	−	312982.i	0.377880	−	0.654508i
$188$	−383040.			−0.790405
$189$		0			0
$190$	−745408.			−1.49799
$191$	−163611.	+	283383.i	−0.324511	+	0.562069i	−0.981413	−	0.191906i	$-0.938533\pi$
$191$	−163611.	+	283383.i	−0.324511	+	0.562069i	0.656902	+	0.753976i	$0.271866\pi$
$192$	18432.0	+	31925.2i	0.0360844	+	0.0625000i
$193$	−393451.	−	681477.i	−0.760322	−	1.31692i	−0.942685	−	0.333685i	$-0.891708\pi$
$193$	−393451.	−	681477.i	−0.760322	−	1.31692i	0.182363	−	0.983231i	$-0.441625\pi$
$194$	−216860.	+	375613.i	−0.413690	+	0.716532i
$195$	−521208.			−0.981577
$196$		0			0
$197$	423098.			0.776740			0.388370	−	0.921504i	$-0.373038\pi$
$197$	423098.			0.776740			0.388370	+	0.921504i	$0.373038\pi$
$198$	−105300.	+	182385.i	−0.190882	+	0.330618i
$199$	−511960.	−	886741.i	−0.916439	−	1.58732i	−0.804781	−	0.593571i	$-0.797717\pi$
$199$	−511960.	−	886741.i	−0.916439	−	1.58732i	−0.111657	−	0.993747i	$-0.535616\pi$
$200$	−84832.0	−	146933.i	−0.149963	−	0.259744i
$201$	−197028.	+	341263.i	−0.343984	+	0.595797i
$202$	−281696.			−0.485738
$203$		0			0
$204$	80064.0			0.134698
$205$	646608.	−	1.11996e6i	1.07462	−	1.86130i
$206$	63104.0	+	109299.i	0.103607	+	0.179452i
$207$	119475.	+	206937.i	0.193799	+	0.335669i
$208$	−97536.0	+	168937.i	−0.156317	+	0.270749i
$209$	−1.59380e6			−2.52388
$210$		0			0
$211$	461516.			0.713642			0.356821	−	0.934173i	$-0.383861\pi$
$211$	461516.			0.713642			0.356821	+	0.934173i	$0.383861\pi$
$212$	−124752.	+	216077.i	−0.190637	+	0.330193i
$213$	−176301.	−	305362.i	−0.266260	−	0.461176i
$214$	−216564.	−	375100.i	−0.323260	−	0.559903i
$215$	−829768.	+	1.43720e6i	−1.22422	+	2.12042i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−288584.			−0.411274
$219$	−106065.	+	183710.i	−0.149438	+	0.258835i
$220$	−395200.	−	684506.i	−0.550504	−	0.953500i
$221$	211836.	+	366911.i	0.291756	+	0.505335i
$222$	139140.	−	240998.i	0.189483	−	0.328194i
$223$	995048.			1.33993			0.669965	−	0.742393i	$-0.266309\pi$
$223$	995048.			1.33993			0.669965	+	0.742393i	$0.266309\pi$
$224$		0			0
$225$	214731.			0.282773
$226$	−441812.	+	765241.i	−0.575395	+	0.996614i
$227$	47784.0	+	82764.3i	0.0615486	+	0.106605i	0.895158	−	0.445749i	$-0.147063\pi$
$227$	47784.0	+	82764.3i	0.0615486	+	0.106605i	−0.833609	+	0.552355i	$0.813729\pi$
$228$	−176544.	−	305783.i	−0.224914	−	0.389562i
$229$	522043.	−	904205.i	0.657836	−	1.13941i	−0.323339	−	0.946283i	$-0.604805\pi$
$229$	522043.	−	904205.i	0.657836	−	1.13941i	0.981175	−	0.193122i	$-0.0618613\pi$
$230$	−896800.			−1.11783
$231$		0			0
$232$	−43136.0			−0.0526163
$233$	584705.	−	1.01274e6i	0.705581	−	1.22210i	−0.260900	−	0.965366i	$-0.584019\pi$
$233$	584705.	−	1.01274e6i	0.705581	−	1.22210i	0.966481	−	0.256737i	$-0.0826473\pi$
$234$	−123444.	−	213811.i	−0.147377	−	0.255265i
$235$	909720.	+	1.57568e6i	1.07458	+	1.86122i
$236$	−44864.0	+	77706.7i	−0.0524346	+	0.0908194i
$237$	161028.			0.186222
$238$		0			0
$239$	−27342.0			−0.0309625			−0.0154812	−	0.999880i	$-0.504928\pi$
$239$	−27342.0			−0.0309625			−0.0154812	+	0.999880i	$0.504928\pi$
$240$	87552.0	−	151645.i	0.0981156	−	0.169941i
$241$	453857.	+	786103.i	0.503357	+	0.871841i	0.999992	+	0.00388111i	$0.00123540\pi$
$241$	453857.	+	786103.i	0.503357	+	0.871841i	−0.496635	+	0.867959i	$0.665431\pi$
$242$	−522898.	−	905686.i	−0.573956	−	0.994121i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	2400.00			0.00258069
$245$		0			0
$246$	612576.			0.645390
$247$	934212.	−	1.61810e6i	0.974323	−	1.68758i
$248$	96768.0	+	167607.i	0.0999085	+	0.173047i
$249$	175374.	+	303757.i	0.179253	+	0.310476i
$250$	72048.0	−	124791.i	0.0729074	−	0.126279i
$251$	44088.0			0.0441709			0.0220854	−	0.999756i	$-0.492969\pi$
$251$	44088.0			0.0441709			0.0220854	+	0.999756i	$0.492969\pi$
$252$		0			0
$253$	−1.91750e6			−1.88336
$254$	479304.	−	830179.i	0.466151	−	0.807397i
$255$	−190152.	−	329353.i	−0.183126	−	0.317184i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	414600.	−	718108.i	0.391558	−	0.678199i	−0.601097	−	0.799176i	$-0.705269\pi$
$257$	414600.	−	718108.i	0.391558	−	0.678199i	0.992655	+	0.120977i	$0.0386028\pi$
$258$	−786096.			−0.735235
$259$		0			0
$260$	926592.			0.850071
$261$	27297.0	−	47279.8i	0.0248035	−	0.0429610i
$262$	548344.	+	949760.i	0.493514	+	0.854792i
$263$	−659733.	−	1.14269e6i	−0.588137	−	1.01868i	−0.994476	−	0.104961i	$-0.966528\pi$
$263$	−659733.	−	1.14269e6i	−0.588137	−	1.01868i	0.406339	−	0.913722i	$-0.366805\pi$
$264$	187200.	−	324240.i	0.165309	−	0.286323i
$265$	1.18514e6			1.03671
$266$		0			0
$267$	−54216.0			−0.0465425
$268$	350272.	−	606689.i	0.297899	−	0.515975i
$269$	391894.	+	678780.i	0.330208	+	0.571937i	0.982553	−	0.185985i	$-0.0595477\pi$
$269$	391894.	+	678780.i	0.330208	+	0.571937i	−0.652344	+	0.757923i	$0.726214\pi$
$270$	110808.	+	191925.i	0.0925043	+	0.160222i
$271$	−477540.	+	827124.i	−0.394990	+	0.684143i	−0.993100	−	0.117271i	$-0.962585\pi$
$271$	−477540.	+	827124.i	−0.394990	+	0.684143i	0.598110	+	0.801414i	$0.295919\pi$
$272$	−142336.			−0.116652
$273$		0			0
$274$	−1.56462e6			−1.25902
$275$	−861575.	+	1.49229e6i	−0.687007	+	1.18993i
$276$	−212400.	−	367888.i	−0.167835	−	0.290698i
$277$	−956365.	−	1.65647e6i	−0.748901	−	1.29713i	−0.948350	−	0.317226i	$-0.897249\pi$
$277$	−956365.	−	1.65647e6i	−0.748901	−	1.29713i	0.199449	−	0.979908i	$-0.436085\pi$
$278$	−678728.	+	1.17559e6i	−0.526725	+	0.912314i
$279$	−244944.			−0.188389
$280$		0			0
$281$	−1.02620e6			−0.775295			−0.387648	−	0.921808i	$-0.626712\pi$
$281$	−1.02620e6			−0.775295			−0.387648	+	0.921808i	$0.626712\pi$
$282$	−430920.	+	746375.i	−0.322681	+	0.558901i
$283$	−873338.	−	1.51267e6i	−0.648211	−	1.12273i	−0.983550	−	0.180637i	$-0.942184\pi$
$283$	−873338.	−	1.51267e6i	−0.648211	−	1.12273i	0.335339	−	0.942097i	$-0.391149\pi$
$284$	313424.	+	542866.i	0.230588	+	0.399390i
$285$	−838584.	+	1.45247e6i	−0.611553	+	1.05924i
$286$	1.98120e6			1.43223
$287$		0			0
$288$	82944.0			0.0589256
$289$	555360.	−	961913.i	0.391138	−	0.677471i
$290$	102448.	+	177445.i	0.0715333	+	0.123899i
$291$	487935.	+	845128.i	0.337777	+	0.585046i
$292$	188560.	−	326596.i	0.129417	−	0.224157i
$293$	2.23212e6			1.51897			0.759484	−	0.650526i	$-0.225452\pi$
$293$	2.23212e6			1.51897			0.759484	+	0.650526i	$0.225452\pi$
$294$		0			0
$295$	426208.			0.285146
$296$	−247360.	+	428440.i	−0.164097	+	0.284224i
$297$	236925.	+	410366.i	0.155855	+	0.269948i
$298$	58668.0	+	101616.i	0.0382702	+	0.0662859i
$299$	1.12395e6	−	1.94674e6i	0.727058	−	1.25930i
$300$	−381744.			−0.244889
$301$		0			0
$302$	286432.			0.180719
$303$	−316908.	+	548901.i	−0.198302	+	0.343469i
$304$	313856.	+	543615.i	0.194781	+	0.337370i
$305$	−5700.00	−	9872.69i	−0.00350853	−	0.00607695i
$306$	90072.0	−	156009.i	0.0549903	−	0.0952460i
$307$	1.85324e6			1.12224			0.561119	−	0.827735i	$-0.310371\pi$
$307$	1.85324e6			1.12224			0.561119	+	0.827735i	$0.310371\pi$
$308$		0			0
$309$	283968.			0.169189
$310$	459648.	−	796134.i	0.271657	−	0.470524i
$311$	225478.	+	390539.i	0.132191	+	0.228962i	0.924521	−	0.381131i	$-0.124465\pi$
$311$	225478.	+	390539.i	0.132191	+	0.228962i	−0.792330	+	0.610093i	$0.791132\pi$
$312$	219456.	+	380109.i	0.127632	+	0.221066i
$313$	−801317.	+	1.38792e6i	−0.462321	+	0.800763i	−0.999076	−	0.0429747i	$-0.986317\pi$
$313$	−801317.	+	1.38792e6i	−0.462321	+	0.800763i	0.536755	+	0.843738i	$0.319650\pi$
$314$	1.18527e6			0.678413
$315$		0			0
$316$	−286272.			−0.161273
$317$	10431.0	−	18067.0i	0.00583012	−	0.0100981i	−0.863096	−	0.505041i	$-0.831478\pi$
$317$	10431.0	−	18067.0i	0.00583012	−	0.0100981i	0.868926	+	0.494942i	$0.164811\pi$
$318$	280692.	+	486173.i	0.155655	+	0.269602i
$319$	219050.	+	379406.i	0.120522	+	0.208750i
$320$	−155648.	+	269590.i	−0.0849706	+	0.147173i
$321$	−974538.			−0.527881
$322$		0			0
$323$	1.36331e6			0.727091
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	−1.01003e6	−	1.74943e6i	−0.530428	−	0.918728i
$326$	960800.	+	1.66415e6i	0.500713	+	0.867261i
$327$	−324657.	+	562322.i	−0.167902	+	0.290814i
$328$	−1.08902e6			−0.558924
$329$		0			0
$330$	−1.77840e6			−0.898969
$331$	−1.03811e6	+	1.79805e6i	−0.520801	+	0.902054i	0.478907	+	0.877866i	$0.341033\pi$
$331$	−1.03811e6	+	1.79805e6i	−0.520801	+	0.902054i	−0.999707	+	0.0241877i	$0.992300\pi$
$332$	−311776.	−	540012.i	−0.155238	−	0.268880i
$333$	−313065.	−	542244.i	−0.154712	−	0.267969i
$334$	−320360.	+	554880.i	−0.157135	+	0.272165i
$335$	−3.32758e6			−1.62001
$336$		0			0
$337$	1.20508e6			0.578019			0.289009	−	0.957326i	$-0.406674\pi$
$337$	1.20508e6			0.578019			0.289009	+	0.957326i	$0.406674\pi$
$338$	−418702.	+	725213.i	−0.199349	+	0.345282i
$339$	994077.	+	1.72179e6i	0.469808	+	0.813732i
$340$	338048.	+	585516.i	0.158592	+	0.274689i
$341$	982800.	−	1.70226e6i	0.457698	−	0.792757i
$342$	−794448.			−0.367282
$343$		0			0
$344$	1.39750e6			0.636732
$345$	−1.00890e6	+	1.74747e6i	−0.456352	+	0.790426i
$346$	17968.0	+	31121.5i	0.00806881	+	0.0139756i
$347$	438321.	+	759194.i	0.195420	+	0.338477i	0.947038	−	0.321121i	$-0.104060\pi$
$347$	438321.	+	759194.i	0.195420	+	0.338477i	−0.751618	+	0.659598i	$0.770726\pi$
$348$	−48528.0	+	84053.0i	−0.0214805	+	0.0372053i
$349$	−1.29593e6			−0.569532			−0.284766	−	0.958597i	$-0.591916\pi$
$349$	−1.29593e6			−0.569532			−0.284766	+	0.958597i	$0.591916\pi$
$350$		0			0
$351$	−555498.			−0.240666
$352$	−332800.	+	576427.i	−0.143162	+	0.247963i
$353$	1.99520e6	+	3.45578e6i	0.852215	+	1.47608i	0.879205	+	0.476444i	$0.158075\pi$
$353$	1.99520e6	+	3.45578e6i	0.852215	+	1.47608i	−0.0269896	+	0.999636i	$0.508592\pi$
$354$	100944.	+	174840.i	0.0428127	+	0.0741537i
$355$	1.48876e6	−	2.57861e6i	0.626982	−	1.08596i
$356$	96384.0			0.0403070
$357$		0			0
$358$	731544.			0.301671
$359$	−2.03226e6	+	3.51998e6i	−0.832229	+	1.44146i	0.0640374	+	0.997947i	$0.479602\pi$
$359$	−2.03226e6	+	3.51998e6i	−0.832229	+	1.44146i	−0.896267	+	0.443516i	$0.853731\pi$
$360$	−196992.	−	341200.i	−0.0801110	−	0.138756i
$361$	−1.76810e6	−	3.06244e6i	−0.714068	−	1.23680i
$362$	−276660.	+	479189.i	−0.110962	+	0.192192i
$363$	−2.35304e6			−0.937266
$364$		0			0
$365$	−1.79132e6			−0.703787
$366$	2700.00	−	4676.54i	0.00105356	−	0.00182483i
$367$	836216.	+	1.44837e6i	0.324081	+	0.561324i	0.981326	−	0.192352i	$-0.0616117\pi$
$367$	836216.	+	1.44837e6i	0.324081	+	0.561324i	−0.657245	+	0.753677i	$0.728278\pi$
$368$	377600.	+	654022.i	0.145349	+	0.251752i
$369$	689148.	−	1.19364e6i	0.263479	−	0.456360i
$370$	2.34992e6			0.892378
$371$		0			0
$372$	435456.			0.163150
$373$	−1.58384e6	+	2.74330e6i	−0.589441	+	1.02094i	0.404865	+	0.914376i	$0.367318\pi$
$373$	−1.58384e6	+	2.74330e6i	−0.589441	+	1.02094i	−0.994306	+	0.106565i	$0.966015\pi$
$374$	722800.	+	1.25193e6i	0.267202	+	0.462807i
$375$	−162108.	−	280779.i	−0.0595287	−	0.103107i
$376$	766080.	−	1.32689e6i	0.279450	−	0.484022i
$377$	−513588.			−0.186106
$378$		0			0
$379$	−4.20388e6			−1.50332			−0.751662	−	0.659548i	$-0.770748\pi$
$379$	−4.20388e6			−1.50332			−0.751662	+	0.659548i	$0.770748\pi$
$380$	1.49082e6	−	2.58217e6i	0.529621	−	0.917330i
$381$	−1.07843e6	−	1.86790e6i	−0.380611	−	0.659237i
$382$	−654444.	−	1.13353e6i	−0.229464	−	0.397443i
$383$	171308.	−	296714.i	0.0596734	−	0.103357i	−0.834645	−	0.550788i	$-0.814327\pi$
$383$	171308.	−	296714.i	0.0596734	−	0.103357i	0.894319	+	0.447430i	$0.147661\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	3.14761e6			1.07526
$387$	−884358.	+	1.53175e6i	−0.300159	+	0.519890i
$388$	−867440.	−	1.50245e6i	−0.292523	−	0.506665i
$389$	1.91980e6	+	3.32519e6i	0.643252	+	1.11415i	0.984702	+	0.174246i	$0.0557487\pi$
$389$	1.91980e6	+	3.32519e6i	0.643252	+	1.11415i	−0.341450	+	0.939900i	$0.610918\pi$
$390$	1.04242e6	−	1.80552e6i	0.347040	−	0.601091i
$391$	1.64020e6			0.542569
$392$		0			0
$393$	2.46755e6			0.805906
$394$	−846196.	+	1.46565e6i	−0.274619	+	0.475654i
$395$	679896.	+	1.17761e6i	0.219255	+	0.379761i
$396$	−421200.	−	729540.i	−0.134974	−	0.233782i
$397$	−1.71947e6	+	2.97821e6i	−0.547543	+	0.948373i	0.450899	+	0.892575i	$0.351104\pi$
$397$	−1.71947e6	+	2.97821e6i	−0.547543	+	0.948373i	−0.998442	+	0.0557979i	$0.982230\pi$
$398$	4.09568e6			1.29604
$399$		0			0
$400$	678656.			0.212080
$401$	1.94710e6	−	3.37248e6i	0.604684	−	1.04734i	−0.387417	−	0.921904i	$-0.626633\pi$
$401$	1.94710e6	−	3.37248e6i	0.604684	−	1.04734i	0.992101	−	0.125439i	$-0.0400339\pi$
$402$	−788112.	−	1.36505e6i	−0.243233	−	0.421292i
$403$	1.15214e6	+	1.99557e6i	0.353382	+	0.612075i
$404$	563392.	−	975824.i	0.171734	−	0.297453i
$405$	498636.			0.151059
$406$		0			0
$407$	5.02450e6			1.50351
$408$	−160128.	+	277350.i	−0.0476230	+	0.0824855i
$409$	823397.	+	1.42617e6i	0.243389	+	0.421562i	0.961677	−	0.274183i	$-0.0884075\pi$
$409$	823397.	+	1.42617e6i	0.243389	+	0.421562i	−0.718288	+	0.695745i	$0.755074\pi$
$410$	2.58643e6	+	4.47983e6i	0.759874	+	1.31614i
$411$	−1.76019e6	+	3.04874e6i	−0.513991	+	0.890259i
$412$	−504832.			−0.146522
$413$		0			0
$414$	−955800.			−0.274073
$415$	−1.48094e6	+	2.56506e6i	−0.422101	+	0.731100i
$416$	−390144.	−	675749.i	−0.110533	−	0.191449i
$417$	1.52714e6	+	2.64508e6i	0.430069	+	0.744901i
$418$	3.18760e6	−	5.52109e6i	0.892325	−	1.54555i
$419$	−1.67659e6			−0.466544			−0.233272	−	0.972412i	$-0.574943\pi$
$419$	−1.67659e6			−0.466544			−0.233272	+	0.972412i	$0.574943\pi$
$420$		0			0
$421$	−566742.			−0.155840			−0.0779202	−	0.996960i	$-0.524828\pi$
$421$	−566742.			−0.155840			−0.0779202	+	0.996960i	$0.524828\pi$
$422$	−923032.	+	1.59874e6i	−0.252311	+	0.437015i
$423$	969570.	+	1.67934e6i	0.263468	+	0.456340i
$424$	−499008.	−	864307.i	−0.134801	−	0.233482i
$425$	736978.	−	1.27648e6i	0.197917	−	0.342802i
$426$	1.41041e6			0.376548
$427$		0			0
$428$	1.73251e6			0.457159
$429$	2.22885e6	−	3.86048e6i	0.584706	−	1.01274i
$430$	−3.31907e6	−	5.74880e6i	−0.865656	−	1.49936i
$431$	−3.34234e6	−	5.78910e6i	−0.866677	−	1.50113i	−0.865372	−	0.501130i	$-0.832918\pi$
$431$	−3.34234e6	−	5.78910e6i	−0.866677	−	1.50113i	−0.00130487	−	0.999999i	$-0.500415\pi$
$432$	93312.0	−	161621.i	0.0240563	−	0.0416667i
$433$	6.91337e6			1.77203			0.886013	−	0.463661i	$-0.153464\pi$
$433$	6.91337e6			1.77203			0.886013	+	0.463661i	$0.153464\pi$
$434$		0			0
$435$	461016.			0.116813
$436$	577168.	−	999684.i	0.145407	−	0.251853i
$437$	−3.61670e6	−	6.26431e6i	−0.905960	−	1.56917i
$438$	−424260.	−	734840.i	−0.105669	−	0.183024i
$439$	2.28140e6	−	3.95151e6i	0.564990	−	0.978592i	−0.432060	−	0.901845i	$-0.642213\pi$
$439$	2.28140e6	−	3.95151e6i	0.564990	−	0.978592i	0.997051	−	0.0767470i	$-0.0244534\pi$
$440$	3.16160e6			0.778530
$441$		0			0
$442$	−1.69469e6			−0.412605
$443$	−2.29880e6	+	3.98164e6i	−0.556534	+	0.963945i	0.441248	+	0.897385i	$0.354536\pi$
$443$	−2.29880e6	+	3.98164e6i	−0.556534	+	0.963945i	−0.997782	+	0.0665601i	$0.978798\pi$
$444$	556560.	+	963990.i	0.133985	+	0.232068i
$445$	−228912.	−	396487.i	−0.0547985	−	0.0949138i
$446$	−1.99010e6	+	3.44695e6i	−0.473737	+	0.820536i
$447$	264006.			0.0624950
$448$		0			0
$449$	1.70658e6			0.399494			0.199747	−	0.979848i	$-0.435988\pi$
$449$	1.70658e6			0.399494			0.199747	+	0.979848i	$0.435988\pi$
$450$	−429462.	+	743850.i	−0.0999755	+	0.173163i
$451$	5.53020e6	+	9.57859e6i	1.28026	+	2.21748i
$452$	−1.76725e6	−	3.06096e6i	−0.406866	−	0.704713i
$453$	322236.	−	558129.i	0.0737783	−	0.127788i
$454$	−382272.			−0.0870428
$455$		0			0
$456$	1.41235e6			0.318076
$457$	3.46958e6	−	6.00949e6i	0.777117	−	1.34601i	−0.156480	−	0.987681i	$-0.550015\pi$
$457$	3.46958e6	−	6.00949e6i	0.777117	−	1.34601i	0.933597	−	0.358325i	$-0.116652\pi$
$458$	2.08817e6	+	3.61682e6i	0.465160	+	0.805681i
$459$	−202662.	−	351021.i	−0.0448994	−	0.0777681i
$460$	1.79360e6	−	3.10661e6i	0.395213	−	0.684529i
$461$	−2.61805e6			−0.573753			−0.286877	−	0.957968i	$-0.592617\pi$
$461$	−2.61805e6			−0.573753			−0.286877	+	0.957968i	$0.592617\pi$
$462$		0			0
$463$	7.13602e6			1.54705			0.773524	−	0.633767i	$-0.218492\pi$
$463$	7.13602e6			1.54705			0.773524	+	0.633767i	$0.218492\pi$
$464$	86272.0	−	149427.i	0.0186027	−	0.0322207i
$465$	−1.03421e6	−	1.79130e6i	−0.221807	−	0.384181i
$466$	2.33882e6	+	4.05096e6i	0.498921	+	0.864157i
$467$	1.08699e6	−	1.88272e6i	0.230639	−	0.399478i	−0.727357	−	0.686259i	$-0.759252\pi$
$467$	1.08699e6	−	1.88272e6i	0.230639	−	0.399478i	0.957996	+	0.286781i	$0.0925851\pi$
$468$	987552.			0.208423
$469$		0			0
$470$	−7.27776e6			−1.51968
$471$	1.33343e6	−	2.30957e6i	0.276961	−	0.479710i
$472$	−179456.	−	310827.i	−0.0370769	−	0.0642190i
$473$	−7.09670e6	−	1.22918e7i	−1.45849	−	2.52618i
$474$	−322056.	+	557817.i	−0.0658394	+	0.114037i
$475$	−6.50025e6			−1.32189
$476$		0			0
$477$	1.26311e6			0.254183
$478$	54684.0	−	94715.5i	0.0109469	−	0.0189606i
$479$	2.31647e6	+	4.01224e6i	0.461305	+	0.799003i	0.999026	−	0.0441193i	$-0.0140482\pi$
$479$	2.31647e6	+	4.01224e6i	0.461305	+	0.799003i	−0.537722	+	0.843122i	$0.680715\pi$
$480$	350208.	+	606578.i	0.0693782	+	0.120167i
$481$	−2.94513e6	+	5.10111e6i	−0.580419	+	1.00532i
$482$	−3.63086e6			−0.711855
$483$		0			0
$484$	4.18318e6			0.811696
$485$	−4.12034e6	+	7.13664e6i	−0.795387	+	1.37765i
$486$	118098.	+	204552.i	0.0226805	+	0.0392837i
$487$	2.28322e6	+	3.95466e6i	0.436241	+	0.755591i	0.997396	−	0.0721195i	$-0.0229763\pi$
$487$	2.28322e6	+	3.95466e6i	0.436241	+	0.755591i	−0.561155	+	0.827710i	$0.689643\pi$
$488$	−4800.00	+	8313.84i	−0.000912413	+	0.00158035i
$489$	4.32360e6			0.817661
$490$		0			0
$491$	−5.31429e6			−0.994813			−0.497407	−	0.867518i	$-0.665714\pi$
$491$	−5.31429e6			−0.994813			−0.497407	+	0.867518i	$0.665714\pi$
$492$	−1.22515e6	+	2.12203e6i	−0.228180	+	0.395219i
$493$	−187372.	−	324538.i	−0.0347206	−	0.0601379i
$494$	3.73685e6	+	6.47241e6i	0.688951	+	1.19330i
$495$	−2.00070e6	+	3.46531e6i	−0.367002	+	0.635667i
$496$	−774144.			−0.141292
$497$		0			0
$498$	−1.40299e6			−0.253502
$499$	1.23157e6	−	2.13314e6i	0.221415	−	0.383503i	−0.733823	−	0.679341i	$-0.762266\pi$
$499$	1.23157e6	−	2.13314e6i	0.221415	−	0.383503i	0.955238	+	0.295838i	$0.0955990\pi$
$500$	288192.	+	499163.i	0.0515534	+	0.0892930i
$501$	720810.	+	1.24848e6i	0.128300	+	0.222222i
$502$	−88176.0	+	152725.i	−0.0156168	+	0.0270490i
$503$	2.79924e6			0.493310			0.246655	−	0.969103i	$-0.420669\pi$
$503$	2.79924e6			0.493310			0.246655	+	0.969103i	$0.420669\pi$
$504$		0			0
$505$	−5.35222e6			−0.933912
$506$	3.83500e6	−	6.64241e6i	0.665869	−	1.15332i
$507$	942079.	+	1.63173e6i	0.162767	+	0.281922i
$508$	1.91722e6	+	3.32072e6i	0.329619	+	0.570916i
$509$	−999570.	+	1.73131e6i	−0.171009	+	0.296196i	−0.938773	−	0.344537i	$-0.888036\pi$
$509$	−999570.	+	1.73131e6i	−0.171009	+	0.296196i	0.767764	+	0.640733i	$0.221369\pi$
$510$	1.52122e6			0.258980
$511$		0			0
$512$	262144.			0.0441942
$513$	−893754.	+	1.54803e6i	−0.149942	+	0.259708i
$514$	1.65840e6	+	2.87243e6i	0.276874	+	0.479559i
$515$	1.19898e6	+	2.07669e6i	0.199201	+	0.345027i
$516$	1.57219e6	−	2.72312e6i	0.259945	−	0.450238i
$517$	−1.55610e7			−2.56042
$518$		0			0
$519$	80856.0			0.0131763
$520$	−1.85318e6	+	3.20981e6i	−0.300545	+	0.520560i
$521$	−1.76080e6	−	3.04980e6i	−0.284195	−	0.492240i	0.688219	−	0.725503i	$-0.258393\pi$
$521$	−1.76080e6	−	3.04980e6i	−0.284195	−	0.492240i	−0.972414	+	0.233263i	$0.925060\pi$
$522$	109188.	+	189119.i	0.0175388	+	0.0303780i
$523$	−1.30343e6	+	2.25760e6i	−0.208369	+	0.360905i	−0.951201	−	0.308573i	$-0.900149\pi$
$523$	−1.30343e6	+	2.25760e6i	−0.208369	+	0.360905i	0.742832	+	0.669478i	$0.233482\pi$
$524$	−4.38675e6			−0.697935
$525$		0			0
$526$	5.27786e6			0.831752
$527$	−840672.	+	1.45609e6i	−0.131856	+	0.228381i
$528$	748800.	+	1.29696e6i	0.116891	+	0.202461i
$529$	−1.13308e6	−	1.96255e6i	−0.176044	−	0.304917i
$530$	−2.37029e6	+	4.10546e6i	−0.366532	+	0.634851i
$531$	454248.			0.0699128
$532$		0			0
$533$	−1.29662e7			−1.97694
$534$	108432.	−	187810.i	0.0164552	−	0.0285013i
$535$	−4.11472e6	−	7.12690e6i	−0.621520	−	1.07650i
$536$	1.40109e6	+	2.42676e6i	0.210646	+	0.364850i
$537$	822987.	−	1.42546e6i	0.123156	−	0.213313i
$538$	−3.13515e6			−0.466985
$539$		0			0
$540$	−886464.			−0.130821
$541$	687207.	−	1.19028e6i	0.100947	−	0.174846i	−0.811128	−	0.584869i	$-0.801146\pi$
$541$	687207.	−	1.19028e6i	0.100947	−	0.174846i	0.912075	+	0.410023i	$0.134479\pi$
$542$	−1.91016e6	−	3.30849e6i	−0.279300	−	0.483762i
$543$	622485.	+	1.07818e6i	0.0906002	+	0.156924i
$544$	284672.	−	493066.i	0.0412427	−	0.0714345i
$545$	−5.48310e6			−0.790742
$546$		0			0
$547$	−8.78398e6			−1.25523			−0.627614	−	0.778524i	$-0.715968\pi$
$547$	−8.78398e6			−1.25523			−0.627614	+	0.778524i	$0.715968\pi$
$548$	3.12923e6	−	5.41999e6i	0.445129	−	0.770987i
$549$	−6075.00	−	10522.2i	−0.000860232	−	0.00148996i
$550$	−3.44630e6	−	5.96917e6i	−0.485788	−	0.841409i
$551$	−826324.	+	1.43124e6i	−0.115950	+	0.200832i
$552$	1.69920e6			0.237354
$553$		0			0
$554$	7.65092e6			1.05911
$555$	2.64366e6	−	4.57895e6i	0.364312	−	0.631006i
$556$	−2.71491e6	−	4.70237e6i	−0.372451	−	0.645104i
$557$	−3.14631e6	−	5.44957e6i	−0.429698	−	0.744259i	0.567148	−	0.823616i	$-0.308047\pi$
$557$	−3.14631e6	−	5.44957e6i	−0.429698	−	0.744259i	−0.996846	+	0.0793569i	$0.974713\pi$
$558$	489888.	−	848511.i	0.0666057	−	0.115364i
$559$	1.66390e7			2.25216
$560$		0			0
$561$	3.25260e6			0.436338
$562$	2.05240e6	−	3.55487e6i	0.274108	−	0.474769i
$563$	−2.43291e6	−	4.21392e6i	−0.323485	−	0.560293i	0.657719	−	0.753263i	$-0.271521\pi$
$563$	−2.43291e6	−	4.21392e6i	−0.323485	−	0.560293i	−0.981205	+	0.192970i	$0.938188\pi$
$564$	−1.72368e6	−	2.98550e6i	−0.228170	−	0.395202i
$565$	−8.39443e6	+	1.45396e7i	−1.10629	+	1.91615i
$566$	6.98670e6			0.916709
$567$		0			0
$568$	−2.50739e6			−0.326100
$569$	2.23191e6	−	3.86579e6i	0.288999	−	0.500561i	−0.684572	−	0.728945i	$-0.740011\pi$
$569$	2.23191e6	−	3.86579e6i	0.288999	−	0.500561i	0.973571	+	0.228384i	$0.0733442\pi$
$570$	−3.35434e6	−	5.80988e6i	−0.432434	−	0.748997i
$571$	−4.08527e6	−	7.07589e6i	−0.524361	−	0.908220i	−0.999598	−	0.0283618i	$-0.990971\pi$
$571$	−4.08527e6	−	7.07589e6i	−0.524361	−	0.908220i	0.475237	−	0.879858i	$-0.342362\pi$
$572$	−3.96240e6	+	6.86308e6i	−0.506370	+	0.877059i
$573$	−2.94500e6			−0.374713
$574$		0			0
$575$	−7.82045e6			−0.986421
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	2.75172e6	+	4.76611e6i	0.344084	+	0.595970i	0.985187	−	0.171484i	$-0.0548563\pi$
$577$	2.75172e6	+	4.76611e6i	0.344084	+	0.595970i	−0.641103	+	0.767455i	$0.721523\pi$
$578$	2.22144e6	+	3.84765e6i	0.276577	+	0.479045i
$579$	3.54106e6	−	6.13329e6i	0.438972	−	0.760322i
$580$	−819584.			−0.101163
$581$		0			0
$582$	−3.90348e6			−0.477688
$583$	−5.06805e6	+	8.77812e6i	−0.617546	+	1.06962i
$584$	754240.	+	1.30638e6i	0.0915119	+	0.158503i
$585$	−2.34544e6	−	4.06241e6i	−0.283357	−	0.490789i
$586$	−4.46424e6	+	7.73229e6i	−0.537036	+	0.930174i
$587$	8.14251e6			0.975356			0.487678	−	0.873024i	$-0.337844\pi$
$587$	8.14251e6			0.975356			0.487678	+	0.873024i	$0.337844\pi$
$588$		0			0
$589$	7.41485e6			0.880672
$590$	−852416.	+	1.47643e6i	−0.100814	+	0.174615i
$591$	1.90394e6	+	3.29772e6i	0.224225	+	0.388370i
$592$	−989440.	−	1.71376e6i	−0.116034	−	0.200977i
$593$	1.36568e6	−	2.36542e6i	0.159482	−	0.276231i	−0.775200	−	0.631716i	$-0.782351\pi$
$593$	1.36568e6	−	2.36542e6i	0.159482	−	0.276231i	0.934682	+	0.355485i	$0.115684\pi$
$594$	−1.89540e6			−0.220412
$595$		0			0
$596$	−469344.			−0.0541222
$597$	4.60764e6	−	7.98067e6i	0.529106	−	0.916439i
$598$	4.49580e6	+	7.78695e6i	0.514108	+	0.890460i
$599$	−618663.	−	1.07156e6i	−0.0704510	−	0.122025i	0.828648	−	0.559770i	$-0.189111\pi$
$599$	−618663.	−	1.07156e6i	−0.0704510	−	0.122025i	−0.899099	+	0.437745i	$0.855777\pi$
$600$	763488.	−	1.32240e6i	0.0865813	−	0.149963i
$601$	−1.59756e7			−1.80414			−0.902071	−	0.431587i	$-0.857954\pi$
$601$	−1.59756e7			−1.80414			−0.902071	+	0.431587i	$0.857954\pi$
$602$		0			0
$603$	−3.54650e6			−0.397198
$604$	−572864.	+	992230.i	−0.0638939	+	0.110667i
$605$	−9.93506e6	−	1.72080e7i	−1.10352	−	1.91136i
$606$	−1.26763e6	−	2.19560e6i	−0.140221	−	0.242869i
$607$	941376.	−	1.63051e6i	0.103703	−	0.179619i	−0.809505	−	0.587114i	$-0.800264\pi$
$607$	941376.	−	1.63051e6i	0.103703	−	0.179619i	0.913208	+	0.407495i	$0.133598\pi$
$608$	−2.51085e6			−0.275462
$609$		0			0
$610$	45600.0			0.00496181
$611$	9.12114e6	−	1.57983e7i	0.988430	−	1.71201i
$612$	360288.	+	624037.i	0.0388840	+	0.0673491i
$613$	4.91402e6	+	8.51133e6i	0.528185	+	0.914843i	0.999460	+	0.0328566i	$0.0104605\pi$
$613$	4.91402e6	+	8.51133e6i	0.528185	+	0.914843i	−0.471275	+	0.881986i	$0.656206\pi$
$614$	−3.70647e6	+	6.41980e6i	−0.396771	+	0.687227i
$615$	1.16389e7			1.24087
$616$		0			0
$617$	−8.21262e6			−0.868498			−0.434249	−	0.900793i	$-0.642986\pi$
$617$	−8.21262e6			−0.868498			−0.434249	+	0.900793i	$0.642986\pi$
$618$	−567936.	+	983694.i	−0.0598175	+	0.103607i
$619$	−3.49233e6	−	6.04889e6i	−0.366343	−	0.634525i	0.622648	−	0.782502i	$-0.286057\pi$
$619$	−3.49233e6	−	6.04889e6i	−0.366343	−	0.634525i	−0.988991	+	0.147977i	$0.952724\pi$
$620$	1.83859e6	+	3.18453e6i	0.192091	+	0.332711i
$621$	−1.07528e6	+	1.86243e6i	−0.111890	+	0.193799i
$622$	−1.80382e6			−0.186947
$623$		0			0
$624$	−1.75565e6			−0.180499
$625$	5.51110e6	−	9.54550e6i	0.564337	−	0.977460i
$626$	−3.20527e6	−	5.55169e6i	−0.326910	−	0.566225i
$627$	−7.17210e6	−	1.24224e7i	−0.728580	−	1.26194i
$628$	−2.37054e6	+	4.10590e6i	−0.239855	+	0.415441i
$629$	−4.29788e6			−0.433139
$630$		0			0
$631$	1.26789e7			1.26767			0.633837	−	0.773467i	$-0.281479\pi$
$631$	1.26789e7			1.26767			0.633837	+	0.773467i	$0.281479\pi$
$632$	572544.	−	991675.i	0.0570186	−	0.0987590i
$633$	2.07682e6	+	3.59716e6i	0.206011	+	0.356821i
$634$	41724.0	+	72268.1i	0.00412252	+	0.00714041i
$635$	9.10678e6	−	1.57734e7i	0.896252	−	1.55235i
$636$	−2.24554e6			−0.220129
$637$		0			0
$638$	−1.75240e6			−0.170444
$639$	1.58671e6	−	2.74826e6i	0.153725	−	0.266260i
$640$	−622592.	−	1.07836e6i	−0.0600833	−	0.104067i
$641$	7.01619e6	+	1.21524e7i	0.674460	+	1.16820i	0.976626	+	0.214944i	$0.0689568\pi$
$641$	7.01619e6	+	1.21524e7i	0.674460	+	1.16820i	−0.302166	+	0.953255i	$0.597710\pi$
$642$	1.94908e6	−	3.37590e6i	0.186634	−	0.323260i
$643$	1.30368e6			0.124349			0.0621745	−	0.998065i	$-0.480196\pi$
$643$	1.30368e6			0.124349			0.0621745	+	0.998065i	$0.480196\pi$
$644$		0			0
$645$	−1.49358e7			−1.41361
$646$	−2.72662e6	+	4.72265e6i	−0.257066	+	0.445251i
$647$	−785550.	−	1.36061e6i	−0.0737757	−	0.127783i	0.826778	−	0.562529i	$-0.190172\pi$
$647$	−785550.	−	1.36061e6i	−0.0737757	−	0.127783i	−0.900553	+	0.434746i	$0.856838\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	−1.82260e6	+	3.15684e6i	−0.169856	+	0.294198i
$650$	8.08025e6			0.750138
$651$		0			0
$652$	−7.68640e6			−0.708115
$653$	4.17057e6	−	7.22364e6i	0.382748	−	0.662939i	−0.608706	−	0.793396i	$-0.708311\pi$
$653$	4.17057e6	−	7.22364e6i	0.382748	−	0.662939i	0.991454	+	0.130457i	$0.0416445\pi$
$654$	−1.29863e6	−	2.24929e6i	−0.118725	−	0.205637i
$655$	1.04185e7	+	1.80454e7i	0.948863	+	1.64348i
$656$	2.17805e6	−	3.77249e6i	0.197610	−	0.342270i
$657$	−1.90917e6			−0.172556
$658$		0			0
$659$	6.18334e6			0.554638			0.277319	−	0.960778i	$-0.410554\pi$
$659$	6.18334e6			0.554638			0.277319	+	0.960778i	$0.410554\pi$
$660$	3.55680e6	−	6.16056e6i	0.317833	−	0.550504i
$661$	−464483.	−	804508.i	−0.0413491	−	0.0716188i	0.844610	−	0.535382i	$-0.179832\pi$
$661$	−464483.	−	804508.i	−0.0413491	−	0.0716188i	−0.885959	+	0.463763i	$0.846499\pi$
$662$	−4.15242e6	−	7.19221e6i	−0.368262	−	0.637848i
$663$	−1.90652e6	+	3.30220e6i	−0.168445	+	0.291756i
$664$	2.49421e6			0.219539
$665$		0			0
$666$	2.50452e6			0.218796
$667$	−994150.	+	1.72192e6i	−0.0865241	+	0.149864i
$668$	−1.28144e6	−	2.21952e6i	−0.111111	−	0.192450i
$669$	4.47772e6	+	7.75563e6i	0.386804	+	0.669965i
$670$	6.65517e6	−	1.15271e7i	0.572759	−	0.992048i
$671$	97500.0			0.00835985
$672$		0			0
$673$	1.79131e7			1.52452			0.762259	−	0.647272i	$-0.224090\pi$
$673$	1.79131e7			1.52452			0.762259	+	0.647272i	$0.224090\pi$
$674$	−2.41016e6	+	4.17453e6i	−0.204360	+	0.353963i
$675$	966290.	+	1.67366e6i	0.0816296	+	0.141387i
$676$	−1.67481e6	−	2.90085e6i	−0.140961	−	0.244151i
$677$	2.48198e6	−	4.29892e6i	0.208126	−	0.360486i	−0.742998	−	0.669294i	$-0.766597\pi$
$677$	2.48198e6	−	4.29892e6i	0.208126	−	0.360486i	0.951124	+	0.308808i	$0.0999301\pi$
$678$	−7.95262e6			−0.664409
$679$		0			0
$680$	−2.70438e6			−0.224283
$681$	−430056.	+	744879.i	−0.0355351	+	0.0615486i
$682$	3.93120e6	+	6.80904e6i	0.323641	+	0.560564i
$683$	−44763.0	−	77531.8i	−0.00367170	−	0.00635957i	0.864184	−	0.503176i	$-0.167835\pi$
$683$	−44763.0	−	77531.8i	−0.00367170	−	0.00635957i	−0.867855	+	0.496817i	$0.834502\pi$
$684$	1.58890e6	−	2.75205e6i	0.129854	−	0.224914i
$685$	−2.97277e7			−2.42067
$686$		0			0
$687$	9.39677e6			0.759603
$688$	−2.79501e6	+	4.84110e6i	−0.225119	+	0.389917i
$689$	−5.94131e6	−	1.02907e7i	−0.476798	−	0.825838i
$690$	−4.03560e6	−	6.98986e6i	−0.322690	−	0.558915i
$691$	71198.0	−	123319.i	0.00567248	−	0.00982502i	−0.863175	−	0.504904i	$-0.831528\pi$
$691$	71198.0	−	123319.i	0.00567248	−	0.00982502i	0.868848	+	0.495079i	$0.164861\pi$
$692$	−143744.			−0.0114110
$693$		0			0
$694$	−3.50657e6			−0.276365
$695$	−1.28958e7	+	2.23362e7i	−1.01272	+	1.75407i
$696$	−194112.	−	336212.i	−0.0151890	−	0.0263081i
$697$	−4.73045e6	−	8.19338e6i	−0.368825	−	0.638824i
$698$	2.59186e6	−	4.48923e6i	0.201360	−	0.348766i
$699$	1.05247e7			0.814735
$700$		0			0
$701$	1.03935e7			0.798852			0.399426	−	0.916765i	$-0.369209\pi$
$701$	1.03935e7			0.798852			0.399426	+	0.916765i	$0.369209\pi$
$702$	1.11100e6	−	1.92430e6i	0.0850883	−	0.147377i
$703$	9.47698e6	+	1.64146e7i	0.723239	+	1.25269i
$704$	−1.33120e6	−	2.30571e6i	−0.101231	−	0.175336i
$705$	−8.18748e6	+	1.41811e7i	−0.620408	+	1.07458i
$706$	−1.59616e7			−1.20521
$707$		0			0
$708$	−807552.			−0.0605463
$709$	−2.32752e6	+	4.03137e6i	−0.173891	+	0.301188i	−0.939777	−	0.341789i	$-0.888967\pi$
$709$	−2.32752e6	+	4.03137e6i	−0.173891	+	0.301188i	0.765886	+	0.642976i	$0.222301\pi$
$710$	5.95506e6	+	1.03145e7i	0.443343	+	0.767893i
$711$	724626.	+	1.25509e6i	0.0537576	+	0.0931109i
$712$	−192768.	+	333884.i	−0.0142507	+	0.0246829i
$713$	8.92080e6			0.657173
$714$		0			0
$715$	3.76428e7			2.75370
$716$	−1.46309e6	+	2.53414e6i	−0.106657	+	0.184735i
$717$	−123039.	−	213110.i	−0.00893809	−	0.0154812i
$718$	−8.12904e6	−	1.40799e7i	−0.588475	−	1.01927i
$719$	3.36067e6	−	5.82085e6i	0.242440	−	0.419918i	−0.718969	−	0.695042i	$-0.755386\pi$
$719$	3.36067e6	−	5.82085e6i	0.242440	−	0.419918i	0.961409	+	0.275124i	$0.0887190\pi$
$720$	1.57594e6			0.113294
$721$		0			0
$722$	1.41448e7			1.00984
$723$	−4.08471e6	+	7.07493e6i	−0.290614	+	0.503357i
$724$	−1.10664e6	−	1.91676e6i	−0.0784621	−	0.135900i
$725$	893387.	+	1.54739e6i	0.0631240	+	0.109334i
$726$	4.70608e6	−	8.15117e6i	0.331374	−	0.573956i
$727$	−1.24076e7			−0.870670			−0.435335	−	0.900269i	$-0.643370\pi$
$727$	−1.24076e7			−0.870670			−0.435335	+	0.900269i	$0.643370\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	3.58264e6	−	6.20531e6i	0.248826	−	0.430980i
$731$	6.07041e6	+	1.05143e7i	0.420169	+	0.727755i
$732$	10800.0	+	18706.1i	0.000744982	+	0.00129035i
$733$	−6.79790e6	+	1.17743e7i	−0.467321	+	0.809423i	−0.999303	−	0.0373325i	$-0.988114\pi$
$733$	−6.79790e6	+	1.17743e7i	−0.467321	+	0.809423i	0.531982	+	0.846755i	$0.321447\pi$
$734$	−6.68973e6			−0.458319
$735$		0			0
$736$	−3.02080e6			−0.205555
$737$	1.42298e7	−	2.46467e7i	0.965006	−	1.67144i
$738$	2.75659e6	+	4.77456e6i	0.186308	+	0.322695i
$739$	−1.28410e6	−	2.22412e6i	−0.0864941	−	0.149812i	0.819533	−	0.573032i	$-0.194233\pi$
$739$	−1.28410e6	−	2.22412e6i	−0.0864941	−	0.149812i	−0.906027	+	0.423220i	$0.860900\pi$
$740$	−4.69984e6	+	8.14036e6i	−0.315503	+	0.546468i
$741$	1.68158e7			1.12505
$742$		0			0
$743$	−2.02133e7			−1.34327			−0.671637	−	0.740880i	$-0.734409\pi$
$743$	−2.02133e7			−1.34327			−0.671637	+	0.740880i	$0.734409\pi$
$744$	−870912.	+	1.50846e6i	−0.0576822	+	0.0999085i
$745$	1.11469e6	+	1.93070e6i	0.0735807	+	0.127446i
$746$	−6.33537e6	−	1.09732e7i	−0.416797	−	0.721914i
$747$	−1.57837e6	+	2.73381e6i	−0.103492	+	0.179253i
$748$	−5.78240e6			−0.377880
$749$		0			0
$750$	1.29686e6			0.0841863
$751$	−3.52406e6	+	6.10386e6i	−0.228005	+	0.394916i	−0.957217	−	0.289372i	$-0.906554\pi$
$751$	−3.52406e6	+	6.10386e6i	−0.228005	+	0.394916i	0.729212	+	0.684288i	$0.239887\pi$
$752$	3.06432e6	+	5.30756e6i	0.197601	+	0.342255i
$753$	198396.	+	343632.i	0.0127510	+	0.0220854i
$754$	1.02718e6	−	1.77912e6i	0.0657986	−	0.113966i
$755$	5.44221e6			0.347462
$756$		0			0
$757$	−2.04120e7			−1.29463			−0.647315	−	0.762223i	$-0.724108\pi$
$757$	−2.04120e7			−1.29463			−0.647315	+	0.762223i	$0.724108\pi$
$758$	8.40777e6	−	1.45627e7i	0.531505	−	0.920594i
$759$	−8.62875e6	−	1.49454e7i	−0.543680	−	0.941682i
$760$	5.96326e6	+	1.03287e7i	0.374498	+	0.648650i
$761$	2.53987e6	−	4.39918e6i	0.158983	−	0.275366i	−0.775519	−	0.631324i	$-0.782512\pi$
$761$	2.53987e6	−	4.39918e6i	0.158983	−	0.275366i	0.934502	+	0.355958i	$0.115845\pi$
$762$	8.62747e6			0.538265
$763$		0			0
$764$	5.23555e6			0.324511
$765$	1.71137e6	−	2.96418e6i	0.105728	−	0.183126i
$766$	685232.	+	1.18686e6i	0.0421955	+	0.0730847i
$767$	−2.13665e6	−	3.70078e6i	−0.131143	−	0.227146i
$768$	294912.	−	510803.i	0.0180422	−	0.0312500i
$769$	2.33898e7			1.42630			0.713149	−	0.701012i	$-0.247268\pi$
$769$	2.33898e7			1.42630			0.713149

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-38.0000 + 65.8179i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-38.0000 + 65.8179i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-152.000 - 263.272i) q^{10} +(-325.000 - 562.917i) q^{11} +(72.0000 - 124.708i) q^{12} +762.000 q^{13} -684.000 q^{15} +(-128.000 + 221.703i) q^{16} +(278.000 + 481.510i) q^{17} +(-162.000 - 280.592i) q^{18} +(1226.00 - 2123.49i) q^{19} +1216.00 q^{20} +2600.00 q^{22} +(1475.00 - 2554.77i) q^{23} +(288.000 + 498.831i) q^{24} +(-1325.50 - 2295.83i) q^{25} +(-1524.00 + 2639.65i) q^{26} -729.000 q^{27} -674.000 q^{29} +(1368.00 - 2369.45i) q^{30} +(1512.00 + 2618.86i) q^{31} +(-512.000 - 886.810i) q^{32} +(2925.00 - 5066.25i) q^{33} -2224.00 q^{34} +1296.00 q^{36} +(-3865.00 + 6694.38i) q^{37} +(4904.00 + 8493.98i) q^{38} +(3429.00 + 5939.20i) q^{39} +(-2432.00 + 4212.35i) q^{40} -17016.0 q^{41} +21836.0 q^{43} +(-5200.00 + 9006.66i) q^{44} +(-3078.00 - 5331.25i) q^{45} +(5900.00 + 10219.1i) q^{46} +(11970.0 - 20732.6i) q^{47} -2304.00 q^{48} +10604.0 q^{50} +(-2502.00 + 4333.59i) q^{51} +(-6096.00 - 10558.6i) q^{52} +(-7797.00 - 13504.8i) q^{53} +(1458.00 - 2525.33i) q^{54} +49400.0 q^{55} +22068.0 q^{57} +(1348.00 - 2334.80i) q^{58} +(-2804.00 - 4856.67i) q^{59} +(5472.00 + 9477.78i) q^{60} +(-75.0000 + 129.904i) q^{61} -12096.0 q^{62} +4096.00 q^{64} +(-28956.0 + 50153.3i) q^{65} +(11700.0 + 20265.0i) q^{66} +(21892.0 + 37918.1i) q^{67} +(4448.00 - 7704.16i) q^{68} +26550.0 q^{69} -39178.0 q^{71} +(-2592.00 + 4489.48i) q^{72} +(11785.0 + 20412.2i) q^{73} +(-15460.0 - 26777.5i) q^{74} +(11929.5 - 20662.5i) q^{75} -39232.0 q^{76} -27432.0 q^{78} +(8946.00 - 15494.9i) q^{79} +(-9728.00 - 16849.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(34032.0 - 58945.2i) q^{82} +38972.0 q^{83} -42256.0 q^{85} +(-43672.0 + 75642.1i) q^{86} +(-3033.00 - 5253.31i) q^{87} +(-20800.0 - 36026.7i) q^{88} +(-3012.00 + 5216.94i) q^{89} +24624.0 q^{90} -47200.0 q^{92} +(-13608.0 + 23569.7i) q^{93} +(47880.0 + 82930.6i) q^{94} +(93176.0 + 161386. i) q^{95} +(4608.00 - 7981.29i) q^{96} +108430. q^{97} +52650.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} - 76 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 - 76 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} - 76 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9} - 304 q^{10} - 650 q^{11} + 144 q^{12} + 1524 q^{13} - 1368 q^{15} - 256 q^{16} + 556 q^{17} - 324 q^{18} + 2452 q^{19} + 2432 q^{20} + 5200 q^{22} + 2950 q^{23} + 576 q^{24} - 2651 q^{25} - 3048 q^{26} - 1458 q^{27} - 1348 q^{29} + 2736 q^{30} + 3024 q^{31} - 1024 q^{32} + 5850 q^{33} - 4448 q^{34} + 2592 q^{36} - 7730 q^{37} + 9808 q^{38} + 6858 q^{39} - 4864 q^{40} - 34032 q^{41} + 43672 q^{43} - 10400 q^{44} - 6156 q^{45} + 11800 q^{46} + 23940 q^{47} - 4608 q^{48} + 21208 q^{50} - 5004 q^{51} - 12192 q^{52} - 15594 q^{53} + 2916 q^{54} + 98800 q^{55} + 44136 q^{57} + 2696 q^{58} - 5608 q^{59} + 10944 q^{60} - 150 q^{61} - 24192 q^{62} + 8192 q^{64} - 57912 q^{65} + 23400 q^{66} + 43784 q^{67} + 8896 q^{68} + 53100 q^{69} - 78356 q^{71} - 5184 q^{72} + 23570 q^{73} - 30920 q^{74} + 23859 q^{75} - 78464 q^{76} - 54864 q^{78} + 17892 q^{79} - 19456 q^{80} - 6561 q^{81} + 68064 q^{82} + 77944 q^{83} - 84512 q^{85} - 87344 q^{86} - 6066 q^{87} - 41600 q^{88} - 6024 q^{89} + 49248 q^{90} - 94400 q^{92} - 27216 q^{93} + 95760 q^{94} + 186352 q^{95} + 9216 q^{96} + 216860 q^{97} + 105300 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 - 76 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9 - 304 * q^10 - 650 * q^11 + 144 * q^12 + 1524 * q^13 - 1368 * q^15 - 256 * q^16 + 556 * q^17 - 324 * q^18 + 2452 * q^19 + 2432 * q^20 + 5200 * q^22 + 2950 * q^23 + 576 * q^24 - 2651 * q^25 - 3048 * q^26 - 1458 * q^27 - 1348 * q^29 + 2736 * q^30 + 3024 * q^31 - 1024 * q^32 + 5850 * q^33 - 4448 * q^34 + 2592 * q^36 - 7730 * q^37 + 9808 * q^38 + 6858 * q^39 - 4864 * q^40 - 34032 * q^41 + 43672 * q^43 - 10400 * q^44 - 6156 * q^45 + 11800 * q^46 + 23940 * q^47 - 4608 * q^48 + 21208 * q^50 - 5004 * q^51 - 12192 * q^52 - 15594 * q^53 + 2916 * q^54 + 98800 * q^55 + 44136 * q^57 + 2696 * q^58 - 5608 * q^59 + 10944 * q^60 - 150 * q^61 - 24192 * q^62 + 8192 * q^64 - 57912 * q^65 + 23400 * q^66 + 43784 * q^67 + 8896 * q^68 + 53100 * q^69 - 78356 * q^71 - 5184 * q^72 + 23570 * q^73 - 30920 * q^74 + 23859 * q^75 - 78464 * q^76 - 54864 * q^78 + 17892 * q^79 - 19456 * q^80 - 6561 * q^81 + 68064 * q^82 + 77944 * q^83 - 84512 * q^85 - 87344 * q^86 - 6066 * q^87 - 41600 * q^88 - 6024 * q^89 + 49248 * q^90 - 94400 * q^92 - 27216 * q^93 + 95760 * q^94 + 186352 * q^95 + 9216 * q^96 + 216860 * q^97 + 105300 * q^99

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