LMFDB - Embedded newform 147.4.e.i.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.i.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(9.00000 - 15.5885i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(9.00000 - 15.5885i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-27.0000 - 46.7654i) q^{10} +(18.0000 + 31.1769i) q^{11} +(1.50000 - 2.59808i) q^{12} -34.0000 q^{13} +54.0000 q^{15} +(35.5000 - 61.4878i) q^{16} +(-21.0000 - 36.3731i) q^{17} +(13.5000 + 23.3827i) q^{18} +(62.0000 - 107.387i) q^{19} -18.0000 q^{20} +108.000 q^{22} +(31.5000 + 54.5596i) q^{24} +(-99.5000 - 172.339i) q^{25} +(-51.0000 + 88.3346i) q^{26} -27.0000 q^{27} +102.000 q^{29} +(81.0000 - 140.296i) q^{30} +(80.0000 + 138.564i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(-54.0000 + 93.5307i) q^{33} -126.000 q^{34} +9.00000 q^{36} +(-199.000 + 344.678i) q^{37} +(-186.000 - 322.161i) q^{38} +(-51.0000 - 88.3346i) q^{39} +(189.000 - 327.358i) q^{40} -318.000 q^{41} -268.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(81.0000 + 140.296i) q^{45} +(-120.000 + 207.846i) q^{47} +213.000 q^{48} -597.000 q^{50} +(63.0000 - 109.119i) q^{51} +(17.0000 + 29.4449i) q^{52} +(249.000 + 431.281i) q^{53} +(-40.5000 + 70.1481i) q^{54} +648.000 q^{55} +372.000 q^{57} +(153.000 - 265.004i) q^{58} +(66.0000 + 114.315i) q^{59} +(-27.0000 - 46.7654i) q^{60} +(-199.000 + 344.678i) q^{61} +480.000 q^{62} +433.000 q^{64} +(-306.000 + 530.008i) q^{65} +(162.000 + 280.592i) q^{66} +(-46.0000 - 79.6743i) q^{67} +(-21.0000 + 36.3731i) q^{68} -720.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(251.000 + 434.745i) q^{73} +(597.000 + 1034.03i) q^{74} +(298.500 - 517.017i) q^{75} -124.000 q^{76} -306.000 q^{78} +(512.000 - 886.810i) q^{79} +(-639.000 - 1106.78i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-477.000 + 826.188i) q^{82} -204.000 q^{83} -756.000 q^{85} +(-402.000 + 696.284i) q^{86} +(153.000 + 265.004i) q^{87} +(378.000 + 654.715i) q^{88} +(-177.000 + 306.573i) q^{89} +486.000 q^{90} +(-240.000 + 415.692i) q^{93} +(360.000 + 623.538i) q^{94} +(-1116.00 - 1932.97i) q^{95} +(67.5000 - 116.913i) q^{96} -286.000 q^{97} -324.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} - q^{4} + 18 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 - q^4 + 18 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} + 18 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9} - 54 q^{10} + 36 q^{11} + 3 q^{12} - 68 q^{13} + 108 q^{15} + 71 q^{16} - 42 q^{17} + 27 q^{18} + 124 q^{19} - 36 q^{20} + 216 q^{22} + 63 q^{24} - 199 q^{25} - 102 q^{26} - 54 q^{27} + 204 q^{29} + 162 q^{30} + 160 q^{31} - 45 q^{32} - 108 q^{33} - 252 q^{34} + 18 q^{36} - 398 q^{37} - 372 q^{38} - 102 q^{39} + 378 q^{40} - 636 q^{41} - 536 q^{43} + 36 q^{44} + 162 q^{45} - 240 q^{47} + 426 q^{48} - 1194 q^{50} + 126 q^{51} + 34 q^{52} + 498 q^{53} - 81 q^{54} + 1296 q^{55} + 744 q^{57} + 306 q^{58} + 132 q^{59} - 54 q^{60} - 398 q^{61} + 960 q^{62} + 866 q^{64} - 612 q^{65} + 324 q^{66} - 92 q^{67} - 42 q^{68} - 1440 q^{71} - 189 q^{72} + 502 q^{73} + 1194 q^{74} + 597 q^{75} - 248 q^{76} - 612 q^{78} + 1024 q^{79} - 1278 q^{80} - 81 q^{81} - 954 q^{82} - 408 q^{83} - 1512 q^{85} - 804 q^{86} + 306 q^{87} + 756 q^{88} - 354 q^{89} + 972 q^{90} - 480 q^{93} + 720 q^{94} - 2232 q^{95} + 135 q^{96} - 572 q^{97} - 648 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 + 18 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9 - 54 * q^10 + 36 * q^11 + 3 * q^12 - 68 * q^13 + 108 * q^15 + 71 * q^16 - 42 * q^17 + 27 * q^18 + 124 * q^19 - 36 * q^20 + 216 * q^22 + 63 * q^24 - 199 * q^25 - 102 * q^26 - 54 * q^27 + 204 * q^29 + 162 * q^30 + 160 * q^31 - 45 * q^32 - 108 * q^33 - 252 * q^34 + 18 * q^36 - 398 * q^37 - 372 * q^38 - 102 * q^39 + 378 * q^40 - 636 * q^41 - 536 * q^43 + 36 * q^44 + 162 * q^45 - 240 * q^47 + 426 * q^48 - 1194 * q^50 + 126 * q^51 + 34 * q^52 + 498 * q^53 - 81 * q^54 + 1296 * q^55 + 744 * q^57 + 306 * q^58 + 132 * q^59 - 54 * q^60 - 398 * q^61 + 960 * q^62 + 866 * q^64 - 612 * q^65 + 324 * q^66 - 92 * q^67 - 42 * q^68 - 1440 * q^71 - 189 * q^72 + 502 * q^73 + 1194 * q^74 + 597 * q^75 - 248 * q^76 - 612 * q^78 + 1024 * q^79 - 1278 * q^80 - 81 * q^81 - 954 * q^82 - 408 * q^83 - 1512 * q^85 - 804 * q^86 + 306 * q^87 + 756 * q^88 - 354 * q^89 + 972 * q^90 - 480 * q^93 + 720 * q^94 - 2232 * q^95 + 135 * q^96 - 572 * q^97 - 648 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$5$	9.00000	−	15.5885i	0.804984	−	1.39427i	−0.111317	−	0.993785i	$-0.535507\pi$
$5$	9.00000	−	15.5885i	0.804984	−	1.39427i	0.916302	−	0.400489i	$-0.131160\pi$
$6$	9.00000			0.612372
$7$		0			0
$7$		0			0
$8$	21.0000			0.928078
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−27.0000	−	46.7654i	−0.853815	−	1.47885i
$11$	18.0000	+	31.1769i	0.493382	+	0.854563i	0.999971	−	0.00762479i	$-0.00242707\pi$
$11$	18.0000	+	31.1769i	0.493382	+	0.854563i	−0.506589	+	0.862188i	$0.669094\pi$
$12$	1.50000	−	2.59808i	0.0360844	−	0.0625000i
$13$	−34.0000			−0.725377			−0.362689	−	0.931910i	$-0.618141\pi$
$13$	−34.0000			−0.725377			−0.362689	+	0.931910i	$0.618141\pi$
$14$		0			0
$15$	54.0000			0.929516
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	−21.0000	−	36.3731i	−0.299603	−	0.518927i	0.676442	−	0.736496i	$-0.263521\pi$
$17$	−21.0000	−	36.3731i	−0.299603	−	0.518927i	−0.976045	+	0.217568i	$0.930187\pi$
$18$	13.5000	+	23.3827i	0.176777	+	0.306186i
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	−0.199865	−	0.979824i	$-0.564050\pi$
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	0.948484	−	0.316824i	$-0.102616\pi$
$20$	−18.0000			−0.201246
$21$		0			0
$22$	108.000			1.04662
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	31.5000	+	54.5596i	0.267913	+	0.464039i
$25$	−99.5000	−	172.339i	−0.796000	−	1.37871i
$26$	−51.0000	+	88.3346i	−0.384689	+	0.666301i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	102.000			0.653135			0.326568	−	0.945174i	$-0.394108\pi$
$29$	102.000			0.653135			0.326568	+	0.945174i	$0.394108\pi$
$30$	81.0000	−	140.296i	0.492950	−	0.853815i
$31$	80.0000	+	138.564i	0.463498	+	0.802801i	0.999132	−	0.0416484i	$-0.0132609\pi$
$31$	80.0000	+	138.564i	0.463498	+	0.802801i	−0.535635	+	0.844450i	$0.679928\pi$
$32$	−22.5000	−	38.9711i	−0.124296	−	0.215287i
$33$	−54.0000	+	93.5307i	−0.284854	+	0.493382i
$34$	−126.000			−0.635554
$35$		0			0
$36$	9.00000			0.0416667
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.0375721	+	0.999294i	$0.511962\pi$
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.846628	+	0.532185i	$0.821371\pi$
$38$	−186.000	−	322.161i	−0.794031	−	1.37530i
$39$	−51.0000	−	88.3346i	−0.209398	−	0.362689i
$40$	189.000	−	327.358i	0.747088	−	1.29399i
$41$	−318.000			−1.21130			−0.605649	−	0.795732i	$-0.707087\pi$
$41$	−318.000			−1.21130			−0.605649	+	0.795732i	$0.707087\pi$
$42$		0			0
$43$	−268.000			−0.950456			−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000			−0.950456			−0.475228	+	0.879863i	$0.657634\pi$
$44$	18.0000	−	31.1769i	0.0616728	−	0.106820i
$45$	81.0000	+	140.296i	0.268328	+	0.464758i
$46$		0			0
$47$	−120.000	+	207.846i	−0.372421	+	0.645053i	−0.989937	−	0.141506i	$-0.954806\pi$
$47$	−120.000	+	207.846i	−0.372421	+	0.645053i	0.617516	+	0.786558i	$0.288139\pi$
$48$	213.000			0.640498
$49$		0			0
$50$	−597.000			−1.68857
$51$	63.0000	−	109.119i	0.172976	−	0.299603i
$52$	17.0000	+	29.4449i	0.0453361	+	0.0785244i
$53$	249.000	+	431.281i	0.645335	+	1.11775i	0.984224	+	0.176927i	$0.0566157\pi$
$53$	249.000	+	431.281i	0.645335	+	1.11775i	−0.338888	+	0.940827i	$0.610051\pi$
$54$	−40.5000	+	70.1481i	−0.102062	+	0.176777i
$55$	648.000			1.58866
$56$		0			0
$57$	372.000			0.864432
$58$	153.000	−	265.004i	0.346377	−	0.599943i
$59$	66.0000	+	114.315i	0.145635	+	0.252247i	0.929610	−	0.368546i	$-0.120144\pi$
$59$	66.0000	+	114.315i	0.145635	+	0.252247i	−0.783975	+	0.620793i	$0.786811\pi$
$60$	−27.0000	−	46.7654i	−0.0580948	−	0.100623i
$61$	−199.000	+	344.678i	−0.417694	+	0.723467i	−0.995707	−	0.0925602i	$-0.970495\pi$
$61$	−199.000	+	344.678i	−0.417694	+	0.723467i	0.578013	+	0.816028i	$0.303828\pi$
$62$	480.000			0.983227
$63$		0			0
$64$	433.000			0.845703
$65$	−306.000	+	530.008i	−0.583917	+	1.01137i
$66$	162.000	+	280.592i	0.302134	+	0.523311i
$67$	−46.0000	−	79.6743i	−0.0838775	−	0.145280i	0.821035	−	0.570878i	$-0.193397\pi$
$67$	−46.0000	−	79.6743i	−0.0838775	−	0.145280i	−0.904912	+	0.425598i	$0.860064\pi$
$68$	−21.0000	+	36.3731i	−0.0374504	+	0.0648659i
$69$		0			0
$70$		0			0
$71$	−720.000			−1.20350			−0.601748	−	0.798686i	$-0.705529\pi$
$71$	−720.000			−1.20350			−0.601748	+	0.798686i	$0.705529\pi$
$72$	−94.5000	+	163.679i	−0.154680	+	0.267913i
$73$	251.000	+	434.745i	0.402429	+	0.697028i	0.994019	−	0.109212i	$-0.0348326\pi$
$73$	251.000	+	434.745i	0.402429	+	0.697028i	−0.591589	+	0.806239i	$0.701499\pi$
$74$	597.000	+	1034.03i	0.937836	+	1.62438i
$75$	298.500	−	517.017i	0.459571	−	0.796000i
$76$	−124.000			−0.187155
$77$		0			0
$78$	−306.000			−0.444201
$79$	512.000	−	886.810i	0.729171	−	1.26296i	−0.228063	−	0.973646i	$-0.573239\pi$
$79$	512.000	−	886.810i	0.729171	−	1.26296i	0.957234	−	0.289315i	$-0.0934274\pi$
$80$	−639.000	−	1106.78i	−0.893030	−	1.54677i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−477.000	+	826.188i	−0.642388	+	1.11265i
$83$	−204.000			−0.269782			−0.134891	−	0.990860i	$-0.543068\pi$
$83$	−204.000			−0.269782			−0.134891	+	0.990860i	$0.543068\pi$
$84$		0			0
$85$	−756.000			−0.964703
$86$	−402.000	+	696.284i	−0.504056	+	0.873050i
$87$	153.000	+	265.004i	0.188544	+	0.326568i
$88$	378.000	+	654.715i	0.457897	+	0.793101i
$89$	−177.000	+	306.573i	−0.210809	+	0.365131i	−0.951968	−	0.306198i	$-0.900943\pi$
$89$	−177.000	+	306.573i	−0.210809	+	0.365131i	0.741159	+	0.671329i	$0.234276\pi$
$90$	486.000			0.569210
$91$		0			0
$92$		0			0
$93$	−240.000	+	415.692i	−0.267600	+	0.463498i
$94$	360.000	+	623.538i	0.395012	+	0.684182i
$95$	−1116.00	−	1932.97i	−1.20525	−	2.08756i
$96$	67.5000	−	116.913i	0.0717624	−	0.124296i
$97$	−286.000			−0.299370			−0.149685	−	0.988734i	$-0.547826\pi$
$97$	−286.000			−0.299370			−0.149685	+	0.988734i	$0.547826\pi$
$98$		0			0
$99$	−324.000			−0.328921
$100$	−99.5000	+	172.339i	−0.0995000	+	0.172339i
$101$	−207.000	−	358.535i	−0.203933	−	0.353223i	0.745859	−	0.666104i	$-0.232039\pi$
$101$	−207.000	−	358.535i	−0.203933	−	0.353223i	−0.949792	+	0.312881i	$0.898706\pi$
$102$	−189.000	−	327.358i	−0.183469	−	0.317777i
$103$	−28.0000	+	48.4974i	−0.0267857	+	0.0463941i	−0.879107	−	0.476624i	$-0.841860\pi$
$103$	−28.0000	+	48.4974i	−0.0267857	+	0.0463941i	0.852322	+	0.523018i	$0.175194\pi$
$104$	−714.000			−0.673206
$105$		0			0
$106$	1494.00			1.36896
$107$	−6.00000	+	10.3923i	−0.00542095	+	0.00938936i	−0.868723	−	0.495298i	$-0.835059\pi$
$107$	−6.00000	+	10.3923i	−0.00542095	+	0.00938936i	0.863302	+	0.504687i	$0.168392\pi$
$108$	13.5000	+	23.3827i	0.0120281	+	0.0208333i
$109$	−739.000	−	1279.99i	−0.649389	−	1.12477i	−0.983269	−	0.182159i	$-0.941692\pi$
$109$	−739.000	−	1279.99i	−0.649389	−	1.12477i	0.333880	−	0.942615i	$-0.391642\pi$
$110$	972.000	−	1683.55i	0.842514	−	1.45928i
$111$	−1194.00			−1.02099
$112$		0			0
$113$	402.000			0.334664			0.167332	−	0.985901i	$-0.446485\pi$
$113$	402.000			0.334664			0.167332	+	0.985901i	$0.446485\pi$
$114$	558.000	−	966.484i	0.458434	−	0.794031i
$115$		0			0
$116$	−51.0000	−	88.3346i	−0.0408210	−	0.0707040i
$117$	153.000	−	265.004i	0.120896	−	0.209398i
$118$	396.000			0.308939
$119$		0			0
$120$	1134.00			0.862663
$121$	17.5000	−	30.3109i	0.0131480	−	0.0227730i
$122$	597.000	+	1034.03i	0.443031	+	0.767353i
$123$	−477.000	−	826.188i	−0.349672	−	0.605649i
$124$	80.0000	−	138.564i	0.0579372	−	0.100350i
$125$	−1332.00			−0.953102
$126$		0			0
$127$	1280.00			0.894344			0.447172	−	0.894448i	$-0.352431\pi$
$127$	1280.00			0.894344			0.447172	+	0.894448i	$0.352431\pi$
$128$	829.500	−	1436.74i	0.572798	−	0.992115i
$129$	−402.000	−	696.284i	−0.274373	−	0.475228i
$130$	918.000	+	1590.02i	0.619338	+	1.07272i
$131$	−882.000	+	1527.67i	−0.588250	+	1.01888i	0.406212	+	0.913779i	$0.366849\pi$
$131$	−882.000	+	1527.67i	−0.588250	+	1.01888i	−0.994462	+	0.105099i	$0.966484\pi$
$132$	108.000			0.0712136
$133$		0			0
$134$	−276.000			−0.177931
$135$	−243.000	+	420.888i	−0.154919	+	0.268328i
$136$	−441.000	−	763.834i	−0.278055	−	0.481605i
$137$	1179.00	+	2042.09i	0.735246	+	1.27348i	0.954615	+	0.297842i	$0.0962669\pi$
$137$	1179.00	+	2042.09i	0.735246	+	1.27348i	−0.219369	+	0.975642i	$0.570400\pi$
$138$		0			0
$139$	−52.0000			−0.0317308			−0.0158654	−	0.999874i	$-0.505050\pi$
$139$	−52.0000			−0.0317308			−0.0158654	+	0.999874i	$0.505050\pi$
$140$		0			0
$141$	−720.000			−0.430035
$142$	−1080.00	+	1870.61i	−0.638251	+	1.10548i
$143$	−612.000	−	1060.02i	−0.357888	−	0.619881i
$144$	319.500	+	553.390i	0.184896	+	0.320249i
$145$	918.000	−	1590.02i	0.525764	−	0.910650i
$146$	1506.00			0.853681
$147$		0			0
$148$	398.000			0.221050
$149$	873.000	−	1512.08i	0.479993	−	0.831372i	−0.519744	−	0.854322i	$-0.673973\pi$
$149$	873.000	−	1512.08i	0.479993	−	0.831372i	0.999737	+	0.0229501i	$0.00730589\pi$
$150$	−895.500	−	1551.05i	−0.487448	−	0.844285i
$151$	116.000	+	200.918i	0.0625162	+	0.108281i	0.895590	−	0.444881i	$-0.146754\pi$
$151$	116.000	+	200.918i	0.0625162	+	0.108281i	−0.833073	+	0.553163i	$0.813421\pi$
$152$	1302.00	−	2255.13i	0.694777	−	1.20339i
$153$	378.000			0.199735
$154$		0			0
$155$	2880.00			1.49243
$156$	−51.0000	+	88.3346i	−0.0261748	+	0.0453361i
$157$	−847.000	−	1467.05i	−0.430560	−	0.745752i	0.566361	−	0.824157i	$-0.308351\pi$
$157$	−847.000	−	1467.05i	−0.430560	−	0.745752i	−0.996922	+	0.0784048i	$0.975017\pi$
$158$	−1536.00	−	2660.43i	−0.773403	−	1.33957i
$159$	−747.000	+	1293.84i	−0.372585	+	0.645335i
$160$	−810.000			−0.400226
$161$		0			0
$162$	−243.000			−0.117851
$163$	1466.00	−	2539.19i	0.704454	−	1.22015i	−0.262434	−	0.964950i	$-0.584525\pi$
$163$	1466.00	−	2539.19i	0.704454	−	1.22015i	0.966888	−	0.255200i	$-0.0821413\pi$
$164$	159.000	+	275.396i	0.0757062	+	0.131127i
$165$	972.000	+	1683.55i	0.458607	+	0.794330i
$166$	−306.000	+	530.008i	−0.143074	+	0.247811i
$167$	1176.00			0.544920			0.272460	−	0.962167i	$-0.412163\pi$
$167$	1176.00			0.544920			0.272460	+	0.962167i	$0.412163\pi$
$168$		0			0
$169$	−1041.00			−0.473828
$170$	−1134.00	+	1964.15i	−0.511611	+	0.886136i
$171$	558.000	+	966.484i	0.249540	+	0.432216i
$172$	134.000	+	232.095i	0.0594035	+	0.102890i
$173$	−435.000	+	753.442i	−0.191170	+	0.331116i	−0.945638	−	0.325220i	$-0.894562\pi$
$173$	−435.000	+	753.442i	−0.191170	+	0.331116i	0.754468	+	0.656337i	$0.227895\pi$
$174$	918.000			0.399962
$175$		0			0
$176$	2556.00			1.09469
$177$	−198.000	+	342.946i	−0.0840824	+	0.145635i
$178$	531.000	+	919.719i	0.223596	+	0.387280i
$179$	1158.00	+	2005.71i	0.483536	+	0.837509i	0.999821	−	0.0189075i	$-0.00601881\pi$
$179$	1158.00	+	2005.71i	0.483536	+	0.837509i	−0.516285	+	0.856417i	$0.672685\pi$
$180$	81.0000	−	140.296i	0.0335410	−	0.0580948i
$181$	−106.000			−0.0435299			−0.0217650	−	0.999763i	$-0.506929\pi$
$181$	−106.000			−0.0435299			−0.0217650	+	0.999763i	$0.506929\pi$
$182$		0			0
$183$	−1194.00			−0.482312
$184$		0			0
$185$	3582.00	+	6204.21i	1.42353	+	2.46563i
$186$	720.000	+	1247.08i	0.283833	+	0.491613i
$187$	756.000	−	1309.43i	0.295637	−	0.512059i
$188$	240.000			0.0931053
$189$		0			0
$190$	−6696.00			−2.55673
$191$	564.000	−	976.877i	0.213663	−	0.370075i	−0.739195	−	0.673491i	$-0.764794\pi$
$191$	564.000	−	976.877i	0.213663	−	0.370075i	0.952858	+	0.303416i	$0.0981273\pi$
$192$	649.500	+	1124.97i	0.244133	+	0.422852i
$193$	−2017.00	−	3493.55i	−0.752263	−	1.30296i	−0.946723	−	0.322048i	$-0.895629\pi$
$193$	−2017.00	−	3493.55i	−0.752263	−	1.30296i	0.194460	−	0.980910i	$-0.437705\pi$
$194$	−429.000	+	743.050i	−0.158765	+	0.274989i
$195$	−1836.00			−0.674250
$196$		0			0
$197$	−1314.00			−0.475221			−0.237611	−	0.971360i	$-0.576364\pi$
$197$	−1314.00			−0.475221			−0.237611	+	0.971360i	$0.576364\pi$
$198$	−486.000	+	841.777i	−0.174437	+	0.302134i
$199$	−2548.00	−	4413.27i	−0.907653	−	1.57210i	−0.817316	−	0.576190i	$-0.804539\pi$
$199$	−2548.00	−	4413.27i	−0.907653	−	1.57210i	−0.0903369	−	0.995911i	$-0.528794\pi$
$200$	−2089.50	−	3619.12i	−0.738750	−	1.27955i
$201$	138.000	−	239.023i	0.0484267	−	0.0838775i
$202$	−1242.00			−0.432608
$203$		0			0
$204$	−126.000			−0.0432439
$205$	−2862.00	+	4957.13i	−0.975077	+	1.68888i
$206$	84.0000	+	145.492i	0.0284105	+	0.0492084i
$207$		0			0
$208$	−1207.00	+	2090.59i	−0.402358	+	0.696904i
$209$	4464.00			1.47742
$210$		0			0
$211$	−3076.00			−1.00360			−0.501802	−	0.864982i	$-0.667330\pi$
$211$	−3076.00			−1.00360			−0.501802	+	0.864982i	$0.667330\pi$
$212$	249.000	−	431.281i	0.0806669	−	0.139719i
$213$	−1080.00	−	1870.61i	−0.347420	−	0.601748i
$214$	18.0000	+	31.1769i	0.00574979	+	0.00995893i
$215$	−2412.00	+	4177.71i	−0.765102	+	1.32520i
$216$	−567.000			−0.178609
$217$		0			0
$218$	−4434.00			−1.37756
$219$	−753.000	+	1304.23i	−0.232343	+	0.402429i
$220$	−324.000	−	561.184i	−0.0992913	−	0.171977i
$221$	714.000	+	1236.68i	0.217325	+	0.376418i
$222$	−1791.00	+	3102.10i	−0.541460	+	0.937836i
$223$	−1888.00			−0.566950			−0.283475	−	0.958980i	$-0.591487\pi$
$223$	−1888.00			−0.566950			−0.283475	+	0.958980i	$0.591487\pi$
$224$		0			0
$225$	1791.00			0.530667
$226$	603.000	−	1044.43i	0.177482	−	0.307408i
$227$	2358.00	+	4084.18i	0.689454	+	1.19417i	0.972015	+	0.234919i	$0.0754826\pi$
$227$	2358.00	+	4084.18i	0.689454	+	1.19417i	−0.282561	+	0.959249i	$0.591184\pi$
$228$	−186.000	−	322.161i	−0.0540270	−	0.0935775i
$229$	845.000	−	1463.58i	0.243839	−	0.422342i	−0.717965	−	0.696079i	$-0.754926\pi$
$229$	845.000	−	1463.58i	0.243839	−	0.422342i	0.961805	+	0.273737i	$0.0882598\pi$
$230$		0			0
$231$		0			0
$232$	2142.00			0.606160
$233$	−69.0000	+	119.512i	−0.0194006	+	0.0336028i	−0.875563	−	0.483104i	$-0.839509\pi$
$233$	−69.0000	+	119.512i	−0.0194006	+	0.0336028i	0.856162	+	0.516707i	$0.172842\pi$
$234$	−459.000	−	795.011i	−0.128230	−	0.222100i
$235$	2160.00	+	3741.23i	0.599587	+	1.03851i
$236$	66.0000	−	114.315i	0.0182044	−	0.0315309i
$237$	3072.00			0.841974
$238$		0			0
$239$	1896.00			0.513147			0.256573	−	0.966525i	$-0.417406\pi$
$239$	1896.00			0.513147			0.256573	+	0.966525i	$0.417406\pi$
$240$	1917.00	−	3320.34i	0.515591	−	0.893030i
$241$	1799.00	+	3115.96i	0.480846	+	0.832849i	0.999758	−	0.0219782i	$-0.00699644\pi$
$241$	1799.00	+	3115.96i	0.480846	+	0.832849i	−0.518913	+	0.854827i	$0.673663\pi$
$242$	−52.5000	−	90.9327i	−0.0139456	−	0.0241544i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	398.000			0.104424
$245$		0			0
$246$	−2862.00			−0.741766
$247$	−2108.00	+	3651.16i	−0.543032	+	0.940558i
$248$	1680.00	+	2909.85i	0.430162	+	0.745062i
$249$	−306.000	−	530.008i	−0.0778794	−	0.134891i
$250$	−1998.00	+	3460.64i	−0.505458	+	0.875480i
$251$	−3060.00			−0.769504			−0.384752	−	0.923020i	$-0.625713\pi$
$251$	−3060.00			−0.769504			−0.384752	+	0.923020i	$0.625713\pi$
$252$		0			0
$253$		0			0
$254$	1920.00	−	3325.54i	0.474297	−	0.821507i
$255$	−1134.00	−	1964.15i	−0.278486	−	0.482351i
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	3411.00	−	5908.03i	0.827908	−	1.43398i	−0.0717686	−	0.997421i	$-0.522864\pi$
$257$	3411.00	−	5908.03i	0.827908	−	1.43398i	0.899676	−	0.436557i	$-0.143802\pi$
$258$	−2412.00			−0.582033
$259$		0			0
$260$	612.000			0.145979
$261$	−459.000	+	795.011i	−0.108856	+	0.188544i
$262$	2646.00	+	4583.01i	0.623933	+	1.08068i
$263$	−1296.00	−	2244.74i	−0.303858	−	0.526298i	0.673148	−	0.739508i	$-0.264942\pi$
$263$	−1296.00	−	2244.74i	−0.303858	−	0.526298i	−0.977007	+	0.213209i	$0.931608\pi$
$264$	−1134.00	+	1964.15i	−0.264367	+	0.457897i
$265$	8964.00			2.07794
$266$		0			0
$267$	−1062.00			−0.243421
$268$	−46.0000	+	79.6743i	−0.0104847	+	0.0181600i
$269$	−4107.00	−	7113.53i	−0.930886	−	1.61234i	−0.781811	−	0.623515i	$-0.785704\pi$
$269$	−4107.00	−	7113.53i	−0.930886	−	1.61234i	−0.149074	−	0.988826i	$-0.547629\pi$
$270$	729.000	+	1262.67i	0.164317	+	0.284605i
$271$	2672.00	−	4628.04i	0.598939	−	1.03739i	−0.394039	−	0.919094i	$-0.628923\pi$
$271$	2672.00	−	4628.04i	0.598939	−	1.03739i	0.992978	−	0.118299i	$-0.0377441\pi$
$272$	−2982.00			−0.664744
$273$		0			0
$274$	7074.00			1.55969
$275$	3582.00	−	6204.21i	0.785464	−	1.36046i
$276$		0			0
$277$	3257.00	+	5641.29i	0.706477	+	1.22365i	0.966156	+	0.257959i	$0.0830500\pi$
$277$	3257.00	+	5641.29i	0.706477	+	1.22365i	−0.259679	+	0.965695i	$0.583617\pi$
$278$	−78.0000	+	135.100i	−0.0168278	+	0.0291466i
$279$	−1440.00			−0.308998
$280$		0			0
$281$	6618.00			1.40497			0.702485	−	0.711698i	$-0.252074\pi$
$281$	6618.00			1.40497			0.702485	+	0.711698i	$0.252074\pi$
$282$	−1080.00	+	1870.61i	−0.228061	+	0.395012i
$283$	−1630.00	−	2823.24i	−0.342380	−	0.593019i	0.642494	−	0.766290i	$-0.277900\pi$
$283$	−1630.00	−	2823.24i	−0.342380	−	0.593019i	−0.984874	+	0.173271i	$0.944566\pi$
$284$	360.000	+	623.538i	0.0752186	+	0.130282i
$285$	3348.00	−	5798.91i	0.695854	−	1.20525i
$286$	−3672.00			−0.759195
$287$		0			0
$288$	405.000			0.0828641
$289$	1574.50	−	2727.11i	0.320476	−	0.555081i
$290$	−2754.00	−	4770.07i	−0.557657	−	0.965890i
$291$	−429.000	−	743.050i	−0.0864207	−	0.149685i
$292$	251.000	−	434.745i	0.0503036	−	0.0871285i
$293$	5118.00			1.02047			0.510233	−	0.860036i	$-0.329559\pi$
$293$	5118.00			1.02047			0.510233	+	0.860036i	$0.329559\pi$
$294$		0			0
$295$	2376.00			0.468936
$296$	−4179.00	+	7238.24i	−0.820606	+	1.42133i
$297$	−486.000	−	841.777i	−0.0949514	−	0.164461i
$298$	−2619.00	−	4536.24i	−0.509109	−	0.881803i
$299$		0			0
$300$	−597.000			−0.114893
$301$		0			0
$302$	696.000			0.132617
$303$	621.000	−	1075.60i	0.117741	−	0.203933i
$304$	−4402.00	−	7624.49i	−0.830500	−	1.43847i
$305$	3582.00	+	6204.21i	0.672475	+	1.16476i
$306$	567.000	−	982.073i	0.105926	−	0.183469i
$307$	452.000			0.0840293			0.0420147	−	0.999117i	$-0.486622\pi$
$307$	452.000			0.0840293			0.0420147	+	0.999117i	$0.486622\pi$
$308$		0			0
$309$	−168.000			−0.0309294
$310$	4320.00	−	7482.46i	0.791482	−	1.37089i
$311$	−2508.00	−	4343.98i	−0.457285	−	0.792041i	0.541531	−	0.840681i	$-0.317845\pi$
$311$	−2508.00	−	4343.98i	−0.457285	−	0.792041i	−0.998816	+	0.0486397i	$0.984511\pi$
$312$	−1071.00	−	1855.03i	−0.194338	−	0.336603i
$313$	−2701.00	+	4678.27i	−0.487762	+	0.844829i	−0.999901	−	0.0140739i	$-0.995520\pi$
$313$	−2701.00	+	4678.27i	−0.487762	+	0.844829i	0.512139	+	0.858903i	$0.328853\pi$
$314$	−5082.00			−0.913356
$315$		0			0
$316$	−1024.00			−0.182293
$317$	−5043.00	+	8734.73i	−0.893511	+	1.54761i	−0.0578751	+	0.998324i	$0.518433\pi$
$317$	−5043.00	+	8734.73i	−0.893511	+	1.54761i	−0.835636	+	0.549283i	$0.814901\pi$
$318$	2241.00	+	3881.53i	0.395186	+	0.684482i
$319$	1836.00	+	3180.05i	0.322245	+	0.558145i
$320$	3897.00	−	6749.80i	0.680778	−	1.17914i
$321$	−36.0000			−0.00625958
$322$		0			0
$323$	−5208.00			−0.897154
$324$	−40.5000	+	70.1481i	−0.00694444	+	0.0120281i
$325$	3383.00	+	5859.53i	0.577400	+	1.00009i
$326$	−4398.00	−	7617.56i	−0.747186	−	1.29416i
$327$	2217.00	−	3839.96i	0.374925	−	0.649389i
$328$	−6678.00			−1.12418
$329$		0			0
$330$	5832.00			0.972852
$331$	4022.00	−	6966.31i	0.667883	−	1.15681i	−0.310613	−	0.950537i	$-0.600534\pi$
$331$	4022.00	−	6966.31i	0.667883	−	1.15681i	0.978495	−	0.206270i	$-0.0661325\pi$
$332$	102.000	+	176.669i	0.0168614	+	0.0292048i
$333$	−1791.00	−	3102.10i	−0.294733	−	0.510493i
$334$	1764.00	−	3055.34i	0.288987	−	0.500541i
$335$	−1656.00			−0.270080
$336$		0			0
$337$	4178.00			0.675342			0.337671	−	0.941264i	$-0.390361\pi$
$337$	4178.00			0.675342			0.337671	+	0.941264i	$0.390361\pi$
$338$	−1561.50	+	2704.60i	−0.251285	+	0.435239i
$339$	603.000	+	1044.43i	0.0966090	+	0.167332i
$340$	378.000	+	654.715i	0.0602939	+	0.104432i
$341$	−2880.00	+	4988.31i	−0.457363	+	0.792176i
$342$	3348.00			0.529354
$343$		0			0
$344$	−5628.00			−0.882097
$345$		0			0
$346$	1305.00	+	2260.33i	0.202767	+	0.351202i
$347$	−78.0000	−	135.100i	−0.0120670	−	0.0209007i	0.859929	−	0.510414i	$-0.170508\pi$
$347$	−78.0000	−	135.100i	−0.0120670	−	0.0209007i	−0.871996	+	0.489513i	$0.837174\pi$
$348$	153.000	−	265.004i	0.0235680	−	0.0408210i
$349$	−12418.0			−1.90464			−0.952321	−	0.305097i	$-0.901311\pi$
$349$	−12418.0			−1.90464			−0.952321	+	0.305097i	$0.901311\pi$
$350$		0			0
$351$	918.000			0.139599
$352$	810.000	−	1402.96i	0.122651	−	0.212438i
$353$	3915.00	+	6780.98i	0.590296	+	1.02242i	0.994192	+	0.107618i	$0.0343222\pi$
$353$	3915.00	+	6780.98i	0.590296	+	1.02242i	−0.403897	+	0.914805i	$0.632344\pi$
$354$	594.000	+	1028.84i	0.0891829	+	0.154469i
$355$	−6480.00	+	11223.7i	−0.968796	+	1.67800i
$356$	354.000			0.0527021
$357$		0			0
$358$	6948.00			1.02574
$359$	4656.00	−	8064.43i	0.684497	−	1.18558i	−0.289098	−	0.957299i	$-0.593355\pi$
$359$	4656.00	−	8064.43i	0.684497	−	1.18558i	0.973595	−	0.228283i	$-0.0733113\pi$
$360$	1701.00	+	2946.22i	0.249029	+	0.431332i
$361$	−4258.50	−	7375.94i	−0.620863	−	1.07537i
$362$	−159.000	+	275.396i	−0.0230852	+	0.0399848i
$363$	105.000			0.0151820
$364$		0			0
$365$	9036.00			1.29580
$366$	−1791.00	+	3102.10i	−0.255784	+	0.443031i
$367$	1880.00	+	3256.26i	0.267398	+	0.463148i	0.968189	−	0.250219i	$-0.0805027\pi$
$367$	1880.00	+	3256.26i	0.267398	+	0.463148i	−0.700791	+	0.713367i	$0.747169\pi$
$368$		0			0
$369$	1431.00	−	2478.56i	0.201883	−	0.349672i
$370$	21492.0			3.01977
$371$		0			0
$372$	480.000			0.0669001
$373$	−2935.00	+	5083.57i	−0.407422	+	0.705676i	−0.994600	−	0.103782i	$-0.966906\pi$
$373$	−2935.00	+	5083.57i	−0.407422	+	0.705676i	0.587178	+	0.809458i	$0.300239\pi$
$374$	−2268.00	−	3928.29i	−0.313571	−	0.543121i
$375$	−1998.00	−	3460.64i	−0.275137	−	0.476551i
$376$	−2520.00	+	4364.77i	−0.345636	+	0.598659i
$377$	−3468.00			−0.473769
$378$		0			0
$379$	−1852.00			−0.251005			−0.125502	−	0.992093i	$-0.540054\pi$
$379$	−1852.00			−0.251005			−0.125502	+	0.992093i	$0.540054\pi$
$380$	−1116.00	+	1932.97i	−0.150657	+	0.260945i
$381$	1920.00	+	3325.54i	0.258175	+	0.447172i
$382$	−1692.00	−	2930.63i	−0.226624	−	0.392524i
$383$	−1080.00	+	1870.61i	−0.144087	+	0.249566i	−0.929032	−	0.369999i	$-0.879358\pi$
$383$	−1080.00	+	1870.61i	−0.144087	+	0.249566i	0.784945	+	0.619566i	$0.212691\pi$
$384$	4977.00			0.661410
$385$		0			0
$386$	−12102.0			−1.59579
$387$	1206.00	−	2088.85i	0.158409	−	0.274373i
$388$	143.000	+	247.683i	0.0187106	+	0.0324078i
$389$	3393.00	+	5876.85i	0.442241	+	0.765985i	0.997855	−	0.0654557i	$-0.0208501\pi$
$389$	3393.00	+	5876.85i	0.442241	+	0.765985i	−0.555614	+	0.831440i	$0.687517\pi$
$390$	−2754.00	+	4770.07i	−0.357575	+	0.619338i
$391$		0			0
$392$		0			0
$393$	−5292.00			−0.679252
$394$	−1971.00	+	3413.87i	−0.252024	+	0.436519i
$395$	−9216.00	−	15962.6i	−1.17394	−	2.03333i
$396$	162.000	+	280.592i	0.0205576	+	0.0356068i
$397$	3257.00	−	5641.29i	0.411748	−	0.713169i	−0.583333	−	0.812233i	$-0.698252\pi$
$397$	3257.00	−	5641.29i	0.411748	−	0.713169i	0.995081	+	0.0990641i	$0.0315849\pi$
$398$	−15288.0			−1.92542
$399$		0			0
$400$	−14129.0			−1.76612
$401$	−1665.00	+	2883.86i	−0.207347	+	0.359135i	−0.950878	−	0.309566i	$-0.899816\pi$
$401$	−1665.00	+	2883.86i	−0.207347	+	0.359135i	0.743531	+	0.668701i	$0.233150\pi$
$402$	−414.000	−	717.069i	−0.0513643	−	0.0889656i
$403$	−2720.00	−	4711.18i	−0.336211	−	0.582334i
$404$	−207.000	+	358.535i	−0.0254917	+	0.0441529i
$405$	−1458.00			−0.178885
$406$		0			0
$407$	−14328.0			−1.74499
$408$	1323.00	−	2291.50i	0.160535	−	0.278055i
$409$	2699.00	+	4674.81i	0.326301	+	0.565169i	0.981775	−	0.190048i	$-0.0608645\pi$
$409$	2699.00	+	4674.81i	0.326301	+	0.565169i	−0.655474	+	0.755218i	$0.727531\pi$
$410$	8586.00	+	14871.4i	1.03423	+	1.79133i
$411$	−3537.00	+	6126.26i	−0.424495	+	0.735246i
$412$	56.0000			0.00669641
$413$		0			0
$414$		0			0
$415$	−1836.00	+	3180.05i	−0.217170	+	0.376150i
$416$	765.000	+	1325.02i	0.0901616	+	0.156164i
$417$	−78.0000	−	135.100i	−0.00915990	−	0.0158654i
$418$	6696.00	−	11597.8i	0.783522	−	1.35710i
$419$	13092.0			1.52646			0.763229	−	0.646128i	$-0.223613\pi$
$419$	13092.0			1.52646			0.763229	+	0.646128i	$0.223613\pi$
$420$		0			0
$421$	−322.000			−0.0372763			−0.0186381	−	0.999826i	$-0.505933\pi$
$421$	−322.000			−0.0372763			−0.0186381	+	0.999826i	$0.505933\pi$
$422$	−4614.00	+	7991.68i	−0.532242	+	0.921870i
$423$	−1080.00	−	1870.61i	−0.124140	−	0.215018i
$424$	5229.00	+	9056.89i	0.598921	+	1.03736i
$425$	−4179.00	+	7238.24i	−0.476968	+	0.826132i
$426$	−6480.00			−0.736988
$427$		0			0
$428$	12.0000			0.00135524
$429$	1836.00	−	3180.05i	0.206627	−	0.357888i
$430$	7236.00	+	12533.1i	0.811514	+	1.40558i
$431$	−1308.00	−	2265.52i	−0.146181	−	0.253193i	0.783632	−	0.621226i	$-0.213365\pi$
$431$	−1308.00	−	2265.52i	−0.146181	−	0.253193i	−0.929813	+	0.368032i	$0.880032\pi$
$432$	−958.500	+	1660.17i	−0.106750	+	0.184896i
$433$	4322.00			0.479681			0.239841	−	0.970812i	$-0.422905\pi$
$433$	4322.00			0.479681			0.239841	+	0.970812i	$0.422905\pi$
$434$		0			0
$435$	5508.00			0.607100
$436$	−739.000	+	1279.99i	−0.0811736	+	0.140597i
$437$		0			0
$438$	2259.00	+	3912.70i	0.246437	+	0.426841i
$439$	4508.00	−	7808.09i	0.490103	−	0.848883i	−0.509832	−	0.860274i	$-0.670293\pi$
$439$	4508.00	−	7808.09i	0.490103	−	0.848883i	0.999935	+	0.0113909i	$0.00362592\pi$
$440$	13608.0			1.47440
$441$		0			0
$442$	4284.00			0.461016
$443$	2634.00	−	4562.22i	0.282495	−	0.489295i	−0.689504	−	0.724282i	$-0.742171\pi$
$443$	2634.00	−	4562.22i	0.282495	−	0.489295i	0.971999	+	0.234987i	$0.0755047\pi$
$444$	597.000	+	1034.03i	0.0638116	+	0.110525i
$445$	3186.00	+	5518.31i	0.339395	+	0.587850i
$446$	−2832.00	+	4905.17i	−0.300671	+	0.520777i
$447$	5238.00			0.554248
$448$		0			0
$449$	−5310.00			−0.558117			−0.279058	−	0.960274i	$-0.590022\pi$
$449$	−5310.00			−0.558117			−0.279058	+	0.960274i	$0.590022\pi$
$450$	2686.50	−	4653.15i	0.281428	−	0.487448i
$451$	−5724.00	−	9914.26i	−0.597633	−	1.03513i
$452$	−201.000	−	348.142i	−0.0209165	−	0.0362284i
$453$	−348.000	+	602.754i	−0.0360937	+	0.0625162i
$454$	14148.0			1.46255
$455$		0			0
$456$	7812.00			0.802260
$457$	−7885.00	+	13657.2i	−0.807100	+	1.39794i	0.107764	+	0.994177i	$0.465631\pi$
$457$	−7885.00	+	13657.2i	−0.807100	+	1.39794i	−0.914864	+	0.403762i	$0.867702\pi$
$458$	−2535.00	−	4390.75i	−0.258631	−	0.447961i
$459$	567.000	+	982.073i	0.0576586	+	0.0998676i
$460$		0			0
$461$	−5370.00			−0.542529			−0.271264	−	0.962505i	$-0.587442\pi$
$461$	−5370.00			−0.542529			−0.271264	+	0.962505i	$0.587442\pi$
$462$		0			0
$463$	−3328.00			−0.334050			−0.167025	−	0.985953i	$-0.553416\pi$
$463$	−3328.00			−0.334050			−0.167025	+	0.985953i	$0.553416\pi$
$464$	3621.00	−	6271.76i	0.362286	−	0.627498i
$465$	4320.00	+	7482.46i	0.430828	+	0.746217i
$466$	207.000	+	358.535i	0.0205774	+	0.0356412i
$467$	−2274.00	+	3938.68i	−0.225328	+	0.390280i	−0.956418	−	0.292002i	$-0.905679\pi$
$467$	−2274.00	+	3938.68i	−0.225328	+	0.390280i	0.731090	+	0.682281i	$0.239012\pi$
$468$	−306.000			−0.0302240
$469$		0			0
$470$	12960.0			1.27192
$471$	2541.00	−	4401.14i	0.248584	−	0.430560i
$472$	1386.00	+	2400.62i	0.135161	+	0.234105i
$473$	−4824.00	−	8355.41i	−0.468938	−	0.812225i
$474$	4608.00	−	7981.29i	0.446524	−	0.773403i
$475$	−24676.0			−2.38361
$476$		0			0
$477$	−4482.00			−0.430224
$478$	2844.00	−	4925.95i	0.272137	−	0.471355i
$479$	4032.00	+	6983.63i	0.384607	+	0.666159i	0.991715	−	0.128461i	$-0.0410036\pi$
$479$	4032.00	+	6983.63i	0.384607	+	0.666159i	−0.607108	+	0.794620i	$0.707670\pi$
$480$	−1215.00	−	2104.44i	−0.115535	−	0.200113i
$481$	6766.00	−	11719.1i	0.641378	−	1.11090i
$482$	10794.0			1.02003
$483$		0			0
$484$	−35.0000			−0.00328700
$485$	−2574.00	+	4458.30i	−0.240988	+	0.417404i
$486$	−364.500	−	631.333i	−0.0340207	−	0.0589256i
$487$	−8308.00	−	14389.9i	−0.773042	−	1.33895i	−0.935888	−	0.352296i	$-0.885401\pi$
$487$	−8308.00	−	14389.9i	−0.773042	−	1.33895i	0.162847	−	0.986651i	$-0.447932\pi$
$488$	−4179.00	+	7238.24i	−0.387653	+	0.671434i
$489$	8796.00			0.813433
$490$		0			0
$491$	−7140.00			−0.656260			−0.328130	−	0.944633i	$-0.606418\pi$
$491$	−7140.00			−0.656260			−0.328130	+	0.944633i	$0.606418\pi$
$492$	−477.000	+	826.188i	−0.0437090	+	0.0757062i
$493$	−2142.00	−	3710.05i	−0.195681	−	0.338930i
$494$	6324.00	+	10953.5i	0.575972	+	0.997613i
$495$	−2916.00	+	5050.66i	−0.264777	+	0.458607i
$496$	11360.0			1.02839
$497$		0			0
$498$	−1836.00			−0.165207
$499$	4562.00	−	7901.62i	0.409265	−	0.708868i	−0.585543	−	0.810642i	$-0.699119\pi$
$499$	4562.00	−	7901.62i	0.409265	−	0.708868i	0.994808	+	0.101774i	$0.0324519\pi$
$500$	666.000	+	1153.55i	0.0595689	+	0.103176i
$501$	1764.00	+	3055.34i	0.157305	+	0.272460i
$502$	−4590.00	+	7950.11i	−0.408091	+	0.706834i
$503$	−6552.00			−0.580794			−0.290397	−	0.956906i	$-0.593787\pi$
$503$	−6552.00			−0.580794			−0.290397	+	0.956906i	$0.593787\pi$
$504$		0			0
$505$	−7452.00			−0.656653
$506$		0			0
$507$	−1561.50	−	2704.60i	−0.136782	−	0.236914i
$508$	−640.000	−	1108.51i	−0.0558965	−	0.0968155i
$509$	−1395.00	+	2416.21i	−0.121478	+	0.210406i	−0.920351	−	0.391094i	$-0.872097\pi$
$509$	−1395.00	+	2416.21i	−0.121478	+	0.210406i	0.798873	+	0.601500i	$0.205430\pi$
$510$	−6804.00			−0.590757
$511$		0			0
$512$	8733.00			0.753804
$513$	−1674.00	+	2899.45i	−0.144072	+	0.249540i
$514$	−10233.0	−	17724.1i	−0.878129	−	1.52096i
$515$	504.000	+	872.954i	0.0431241	+	0.0746931i
$516$	−402.000	+	696.284i	−0.0342966	+	0.0594035i
$517$	−8640.00			−0.734984
$518$		0			0
$519$	−2610.00			−0.220744
$520$	−6426.00	+	11130.2i	−0.541921	+	0.938634i
$521$	7431.00	+	12870.9i	0.624871	+	1.08231i	0.988566	+	0.150791i	$0.0481820\pi$
$521$	7431.00	+	12870.9i	0.624871	+	1.08231i	−0.363694	+	0.931518i	$0.618485\pi$
$522$	1377.00	+	2385.03i	0.115459	+	0.199981i
$523$	−8830.00	+	15294.0i	−0.738258	+	1.27870i	0.215021	+	0.976609i	$0.431018\pi$
$523$	−8830.00	+	15294.0i	−0.738258	+	1.27870i	−0.953279	+	0.302091i	$0.902315\pi$
$524$	1764.00			0.147062
$525$		0			0
$526$	−7776.00			−0.644581
$527$	3360.00	−	5819.69i	0.277730	−	0.481043i
$528$	3834.00	+	6640.68i	0.316010	+	0.547346i
$529$	6083.50	+	10536.9i	0.500000	+	0.866025i
$530$	13446.0	−	23289.2i	1.10199	−	1.90871i
$531$	−1188.00			−0.0970900
$532$		0			0
$533$	10812.0			0.878649
$534$	−1593.00	+	2759.16i	−0.129093	+	0.223596i
$535$	108.000	+	187.061i	0.00872756	+	0.0151166i
$536$	−966.000	−	1673.16i	−0.0778449	−	0.134831i
$537$	−3474.00	+	6017.14i	−0.279170	+	0.483536i
$538$	−24642.0			−1.97471
$539$		0			0
$540$	486.000			0.0387298
$541$	9917.00	−	17176.7i	0.788106	−	1.36504i	−0.139021	−	0.990290i	$-0.544395\pi$
$541$	9917.00	−	17176.7i	0.788106	−	1.36504i	0.927126	−	0.374749i	$-0.122271\pi$
$542$	−8016.00	−	13884.1i	−0.635271	−	1.10032i
$543$	−159.000	−	275.396i	−0.0125660	−	0.0217650i
$544$	−945.000	+	1636.79i	−0.0744789	+	0.129001i
$545$	−26604.0			−2.09099
$546$		0			0
$547$	20972.0			1.63930			0.819651	−	0.572863i	$-0.194167\pi$
$547$	20972.0			1.63930			0.819651	+	0.572863i	$0.194167\pi$
$548$	1179.00	−	2042.09i	0.0919058	−	0.159186i
$549$	−1791.00	−	3102.10i	−0.139231	−	0.241156i
$550$	−10746.0	−	18612.6i	−0.833111	−	1.44299i
$551$	6324.00	−	10953.5i	0.488950	−	0.846886i
$552$		0			0
$553$		0			0
$554$	19542.0			1.49866
$555$	−10746.0	+	18612.6i	−0.821878	+	1.42353i
$556$	26.0000	+	45.0333i	0.00198318	+	0.00343496i
$557$	−10587.0	−	18337.2i	−0.805360	−	1.39492i	−0.916048	−	0.401069i	$-0.868639\pi$
$557$	−10587.0	−	18337.2i	−0.805360	−	1.39492i	0.110688	−	0.993855i	$-0.464695\pi$
$558$	−2160.00	+	3741.23i	−0.163871	+	0.283833i
$559$	9112.00			0.689439
$560$		0			0
$561$	4536.00			0.341373
$562$	9927.00	−	17194.1i	0.745098	−	1.29055i
$563$	8886.00	+	15391.0i	0.665187	+	1.15214i	0.979235	+	0.202730i	$0.0649815\pi$
$563$	8886.00	+	15391.0i	0.665187	+	1.15214i	−0.314048	+	0.949407i	$0.601685\pi$
$564$	360.000	+	623.538i	0.0268772	+	0.0465527i
$565$	3618.00	−	6266.56i	0.269399	−	0.466613i
$566$	−9780.00			−0.726297
$567$		0			0
$568$	−15120.0			−1.11694
$569$	−4125.00	+	7144.71i	−0.303917	+	0.526400i	−0.977020	−	0.213149i	$-0.931628\pi$
$569$	−4125.00	+	7144.71i	−0.303917	+	0.526400i	0.673102	+	0.739549i	$0.264961\pi$
$570$	−10044.0	−	17396.7i	−0.738065	−	1.27837i
$571$	−10378.0	−	17975.2i	−0.760606	−	1.31741i	−0.942539	−	0.334097i	$-0.891569\pi$
$571$	−10378.0	−	17975.2i	−0.760606	−	1.31741i	0.181933	−	0.983311i	$-0.441765\pi$
$572$	−612.000	+	1060.02i	−0.0447360	+	0.0774851i
$573$	3384.00			0.246717
$574$		0			0
$575$		0			0
$576$	−1948.50	+	3374.90i	−0.140951	+	0.244133i
$577$	−1.00000	−	1.73205i	−7.21500e−5	−	0.000124967i	0.865989	−	0.500062i	$-0.166690\pi$
$577$	−1.00000	−	1.73205i	−7.21500e−5	−	0.000124967i	−0.866061	+	0.499938i	$0.833356\pi$
$578$	−4723.50	−	8181.34i	−0.339916	−	0.588753i
$579$	6051.00	−	10480.6i	0.434319	−	0.752263i
$580$	−1836.00			−0.131441
$581$		0			0
$582$	−2574.00			−0.183326
$583$	−8964.00	+	15526.1i	−0.636794	+	1.10296i
$584$	5271.00	+	9129.64i	0.373485	+	0.646896i
$585$	−2754.00	−	4770.07i	−0.194639	−	0.337125i
$586$	7677.00	−	13297.0i	0.541184	−	0.937359i
$587$	26364.0			1.85376			0.926881	−	0.375354i	$-0.122479\pi$
$587$	26364.0			1.85376			0.926881	+	0.375354i	$0.122479\pi$
$588$		0			0
$589$	19840.0			1.38793
$590$	3564.00	−	6173.03i	0.248691	−	0.430745i
$591$	−1971.00	−	3413.87i	−0.137185	−	0.237611i
$592$	14129.0	+	24472.1i	0.980909	+	1.69898i
$593$	−1149.00	+	1990.13i	−0.0795679	+	0.137816i	−0.903064	−	0.429507i	$-0.858687\pi$
$593$	−1149.00	+	1990.13i	−0.0795679	+	0.137816i	0.823496	+	0.567323i	$0.192021\pi$
$594$	−2916.00			−0.201422
$595$		0			0
$596$	−1746.00			−0.119998
$597$	7644.00	−	13239.8i	0.524034	−	0.907653i
$598$		0			0
$599$	−1536.00	−	2660.43i	−0.104773	−	0.181473i	0.808872	−	0.587984i	$-0.200078\pi$
$599$	−1536.00	−	2660.43i	−0.104773	−	0.181473i	−0.913646	+	0.406512i	$0.866745\pi$
$600$	6268.50	−	10857.4i	0.426517	−	0.738750i
$601$	24554.0			1.66652			0.833260	−	0.552881i	$-0.186472\pi$
$601$	24554.0			1.66652			0.833260	+	0.552881i	$0.186472\pi$
$602$		0			0
$603$	828.000			0.0559184
$604$	116.000	−	200.918i	0.00781452	−	0.0135352i
$605$	−315.000	−	545.596i	−0.0211679	−	0.0366639i
$606$	−1863.00	−	3226.81i	−0.124883	−	0.216304i
$607$	−8416.00	+	14576.9i	−0.562759	+	0.974728i	0.434495	+	0.900674i	$0.356927\pi$
$607$	−8416.00	+	14576.9i	−0.562759	+	0.974728i	−0.997254	+	0.0740535i	$0.976406\pi$
$608$	−5580.00			−0.372202
$609$		0			0
$610$	21492.0			1.42653
$611$	4080.00	−	7066.77i	0.270146	−	0.467906i
$612$	−189.000	−	327.358i	−0.0124835	−	0.0216220i
$613$	1241.00	+	2149.48i	0.0817676	+	0.141626i	0.904009	−	0.427513i	$-0.140610\pi$
$613$	1241.00	+	2149.48i	0.0817676	+	0.141626i	−0.822242	+	0.569139i	$0.807277\pi$
$614$	678.000	−	1174.33i	0.0445633	−	0.0771859i
$615$	−17172.0			−1.12592
$616$		0			0
$617$	−15798.0			−1.03080			−0.515400	−	0.856950i	$-0.672357\pi$
$617$	−15798.0			−1.03080			−0.515400	+	0.856950i	$0.672357\pi$
$618$	−252.000	+	436.477i	−0.0164028	+	0.0284105i
$619$	7730.00	+	13388.8i	0.501930	+	0.869369i	0.999998	+	0.00223050i	$0.000709990\pi$
$619$	7730.00	+	13388.8i	0.501930	+	0.869369i	−0.498067	+	0.867138i	$0.665957\pi$
$620$	−1440.00	−	2494.15i	−0.0932771	−	0.161561i
$621$		0			0
$622$	−15048.0			−0.970048
$623$		0			0
$624$	−7242.00			−0.464603
$625$	449.500	−	778.557i	0.0287680	−	0.0498276i
$626$	8103.00	+	14034.8i	0.517350	+	0.896076i
$627$	6696.00	+	11597.8i	0.426495	+	0.738711i
$628$	−847.000	+	1467.05i	−0.0538200	+	0.0932190i
$629$	16716.0			1.05964
$630$		0			0
$631$	−7720.00			−0.487050			−0.243525	−	0.969895i	$-0.578304\pi$
$631$	−7720.00			−0.487050			−0.243525	+	0.969895i	$0.578304\pi$
$632$	10752.0	−	18623.0i	0.676727	−	1.17213i
$633$	−4614.00	−	7991.68i	−0.289716	−	0.501802i
$634$	15129.0	+	26204.2i	0.947712	+	1.64149i
$635$	11520.0	−	19953.2i	0.719933	−	1.24696i
$636$	1494.00			0.0931462
$637$		0			0
$638$	11016.0			0.683586
$639$	3240.00	−	5611.84i	0.200583	−	0.347420i
$640$	−14931.0	−	25861.3i	−0.922187	−	1.59727i
$641$	8631.00	+	14949.3i	0.531832	+	0.921159i	0.999310	+	0.0371545i	$0.0118294\pi$
$641$	8631.00	+	14949.3i	0.531832	+	0.921159i	−0.467478	+	0.884005i	$0.654837\pi$
$642$	−54.0000	+	93.5307i	−0.00331964	+	0.00574979i
$643$	−12220.0			−0.749471			−0.374735	−	0.927132i	$-0.622266\pi$
$643$	−12220.0			−0.749471			−0.374735	+	0.927132i	$0.622266\pi$
$644$		0			0
$645$	−14472.0			−0.883464
$646$	−7812.00	+	13530.8i	−0.475788	+	0.824089i
$647$	−6780.00	−	11743.3i	−0.411977	−	0.713566i	0.583129	−	0.812380i	$-0.301828\pi$
$647$	−6780.00	−	11743.3i	−0.411977	−	0.713566i	−0.995106	+	0.0988143i	$0.968495\pi$
$648$	−850.500	−	1473.11i	−0.0515599	−	0.0893043i
$649$	−2376.00	+	4115.35i	−0.143707	+	0.248909i
$650$	20298.0			1.22485
$651$		0			0
$652$	−2932.00			−0.176113
$653$	−11547.0	+	20000.0i	−0.691989	+	1.19856i	0.279196	+	0.960234i	$0.409932\pi$
$653$	−11547.0	+	20000.0i	−0.691989	+	1.19856i	−0.971185	+	0.238326i	$0.923401\pi$
$654$	−6651.00	−	11519.9i	−0.397668	−	0.688781i
$655$	15876.0	+	27498.0i	0.947064	+	1.64036i
$656$	−11289.0	+	19553.1i	−0.671892	+	1.16375i
$657$	−4518.00			−0.268286
$658$		0			0
$659$	22548.0			1.33285			0.666423	−	0.745574i	$-0.267825\pi$
$659$	22548.0			1.33285			0.666423	+	0.745574i	$0.267825\pi$
$660$	972.000	−	1683.55i	0.0573258	−	0.0992913i
$661$	−8731.00	−	15122.5i	−0.513762	−	0.889862i	−0.999873	−	0.0159643i	$-0.994918\pi$
$661$	−8731.00	−	15122.5i	−0.513762	−	0.889862i	0.486111	−	0.873897i	$-0.338415\pi$
$662$	−12066.0	−	20898.9i	−0.708396	−	1.22698i
$663$	−2142.00	+	3710.05i	−0.125473	+	0.217325i
$664$	−4284.00			−0.250379
$665$		0			0
$666$	−10746.0			−0.625224
$667$		0			0
$668$	−588.000	−	1018.45i	−0.0340575	−	0.0589893i
$669$	−2832.00	−	4905.17i	−0.163664	−	0.283475i
$670$	−2484.00	+	4302.41i	−0.143232	+	0.248085i
$671$	−14328.0			−0.824331
$672$		0			0
$673$	−22462.0			−1.28655			−0.643274	−	0.765636i	$-0.722424\pi$
$673$	−22462.0			−1.28655			−0.643274	+	0.765636i	$0.722424\pi$
$674$	6267.00	−	10854.8i	0.358154	−	0.620341i
$675$	2686.50	+	4653.15i	0.153190	+	0.265333i
$676$	520.500	+	901.532i	0.0296142	+	0.0512934i
$677$	12777.0	−	22130.4i	0.725347	−	1.25634i	−0.233484	−	0.972361i	$-0.575013\pi$
$677$	12777.0	−	22130.4i	0.725347	−	1.25634i	0.958831	−	0.283977i	$-0.0916541\pi$
$678$	3618.00			0.204939
$679$		0			0
$680$	−15876.0			−0.895319
$681$	−7074.00	+	12252.5i	−0.398056	+	0.689454i
$682$	8640.00	+	14964.9i	0.485107	+	0.840229i
$683$	−4638.00	−	8033.25i	−0.259836	−	0.450050i	0.706362	−	0.707851i	$-0.250335\pi$
$683$	−4638.00	−	8033.25i	−0.259836	−	0.450050i	−0.966198	+	0.257802i	$0.917002\pi$
$684$	558.000	−	966.484i	0.0311925	−	0.0540270i
$685$	42444.0			2.36745
$686$		0			0
$687$	5070.00			0.281561
$688$	−9514.00	+	16478.7i	−0.527206	+	0.913148i
$689$	−8466.00	−	14663.5i	−0.468112	−	0.810793i
$690$		0			0
$691$	−13690.0	+	23711.8i	−0.753679	+	1.30541i	0.192349	+	0.981326i	$0.438389\pi$
$691$	−13690.0	+	23711.8i	−0.753679	+	1.30541i	−0.946028	+	0.324084i	$0.894944\pi$
$692$	870.000			0.0477925
$693$		0			0
$694$	−468.000			−0.0255980
$695$	−468.000	+	810.600i	−0.0255428	+	0.0442414i
$696$	3213.00	+	5565.08i	0.174983	+	0.303080i
$697$	6678.00	+	11566.6i	0.362909	+	0.628576i
$698$	−18627.0	+	32262.9i	−1.01009	+	1.74953i
$699$	−414.000			−0.0224019
$700$		0			0
$701$	25830.0			1.39171			0.695853	−	0.718184i	$-0.255027\pi$
$701$	25830.0			1.39171			0.695853	+	0.718184i	$0.255027\pi$
$702$	1377.00	−	2385.03i	0.0740335	−	0.128230i
$703$	24676.0	+	42740.1i	1.32386	+	2.29299i
$704$	7794.00	+	13499.6i	0.417255	+	0.722707i
$705$	−6480.00	+	11223.7i	−0.346172	+	0.599587i
$706$	23490.0			1.25221
$707$		0			0
$708$	396.000			0.0210206
$709$	3113.00	−	5391.87i	0.164896	−	0.285608i	−0.771722	−	0.635959i	$-0.780605\pi$
$709$	3113.00	−	5391.87i	0.164896	−	0.285608i	0.936618	+	0.350351i	$0.113938\pi$
$710$	19440.0	+	33671.1i	1.02756	+	1.77979i
$711$	4608.00	+	7981.29i	0.243057	+	0.420987i
$712$	−3717.00	+	6438.03i	−0.195647	+	0.338870i
$713$		0			0
$714$		0			0
$715$	−22032.0			−1.15238
$716$	1158.00	−	2005.71i	0.0604420	−	0.104689i
$717$	2844.00	+	4925.95i	0.148133	+	0.256573i
$718$	−13968.0	−	24193.3i	−0.726018	−	1.25750i
$719$	7536.00	−	13052.7i	0.390884	−	0.677030i	−0.601683	−	0.798735i	$-0.705503\pi$
$719$	7536.00	−	13052.7i	0.390884	−	0.677030i	0.992566	+	0.121705i	$0.0388361\pi$
$720$	11502.0			0.595353
$721$		0			0
$722$	−25551.0			−1.31705
$723$	−5397.00	+	9347.88i	−0.277616	+	0.480846i
$724$	53.0000	+	91.7987i	0.00272062	+	0.00471225i
$725$	−10149.0	−	17578.6i	−0.519896	−	0.900486i
$726$	157.500	−	272.798i	0.00805148	−	0.0139456i
$727$	−32920.0			−1.67942			−0.839708	−	0.543038i	$-0.817274\pi$
$727$	−32920.0			−1.67942			−0.839708	+	0.543038i	$0.817274\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	13554.0	−	23476.2i	0.687200	−	1.19027i
$731$	5628.00	+	9747.98i	0.284759	+	0.493218i
$732$	597.000	+	1034.03i	0.0301445	+	0.0522118i
$733$	3473.00	−	6015.41i	0.175004	−	0.303116i	−0.765158	−	0.643842i	$-0.777339\pi$
$733$	3473.00	−	6015.41i	0.175004	−	0.303116i	0.940163	+	0.340726i	$0.110673\pi$
$734$	11280.0			0.567238
$735$		0			0
$736$		0			0
$737$	1656.00	−	2868.28i	0.0827674	−	0.143357i
$738$	−4293.00	−	7435.69i	−0.214129	−	0.370883i
$739$	1178.00	+	2040.36i	0.0586379	+	0.101564i	0.893854	−	0.448358i	$-0.147991\pi$
$739$	1178.00	+	2040.36i	0.0586379	+	0.101564i	−0.835216	+	0.549922i	$0.814658\pi$
$740$	3582.00	−	6204.21i	0.177942	−	0.308204i
$741$	−12648.0			−0.627039
$742$		0			0
$743$	−23520.0			−1.16133			−0.580663	−	0.814144i	$-0.697207\pi$
$743$	−23520.0			−1.16133			−0.580663	+	0.814144i	$0.697207\pi$
$744$	−5040.00	+	8729.54i	−0.248354	+	0.430162i
$745$	−15714.0	−	27217.4i	−0.772774	−	1.33848i
$746$	8805.00	+	15250.7i	0.432137	+	0.748483i
$747$	918.000	−	1590.02i	0.0449637	−	0.0778794i
$748$	−1512.00			−0.0739094
$749$		0			0
$750$	−11988.0			−0.583653
$751$	−1504.00	+	2605.00i	−0.0730782	+	0.126575i	−0.900249	−	0.435376i	$-0.856616\pi$
$751$	−1504.00	+	2605.00i	−0.0730782	+	0.126575i	0.827171	+	0.561951i	$0.189949\pi$
$752$	8520.00	+	14757.1i	0.413155	+	0.715605i
$753$	−4590.00	−	7950.11i	−0.222137	−	0.384752i
$754$	−5202.00	+	9010.13i	−0.251254	+	0.435185i
$755$	4176.00			0.201298
$756$		0			0
$757$	−20770.0			−0.997224			−0.498612	−	0.866825i	$-0.666157\pi$
$757$	−20770.0			−0.997224			−0.498612	+	0.866825i	$0.666157\pi$
$758$	−2778.00	+	4811.64i	−0.133115	+	0.230563i
$759$		0			0
$760$	−23436.0	−	40592.3i	−1.11857	−	1.93742i
$761$	−5769.00	+	9992.20i	−0.274804	+	0.475975i	−0.970086	−	0.242763i	$-0.921946\pi$
$761$	−5769.00	+	9992.20i	−0.274804	+	0.475975i	0.695281	+	0.718738i	$0.255280\pi$
$762$	11520.0			0.547671
$763$		0			0
$764$	−1128.00			−0.0534157
$765$	3402.00	−	5892.44i	0.160784	−	0.278486i
$766$	3240.00	+	5611.84i	0.152828	+	0.264705i
$767$	−2244.00	−	3886.72i	−0.105640	−	0.182974i
$768$	2269.50	−	3930.89i	0.106632	−	0.184692i
$769$	8498.00			0.398499			0.199249	−	0.979949i	$-0.436150\pi$
$769$	8498.00			0.398499			0.199249	+	0.979949i	$0.436150\pi$
$770$		0			0
$771$	20466.0			0.955986
$772$	−2017.00	+	3493.55i	−0.0940329	+	0.162870i
$773$	16161.0	+	27991.7i	0.751967	+	1.30245i	0.946868	+	0.321623i	$0.104228\pi$
$773$	16161.0	+	27991.7i	0.751967	+	1.30245i	−0.194

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(9.00000 - 15.5885i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(9.00000 - 15.5885i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-27.0000 - 46.7654i) q^{10} +(18.0000 + 31.1769i) q^{11} +(1.50000 - 2.59808i) q^{12} -34.0000 q^{13} +54.0000 q^{15} +(35.5000 - 61.4878i) q^{16} +(-21.0000 - 36.3731i) q^{17} +(13.5000 + 23.3827i) q^{18} +(62.0000 - 107.387i) q^{19} -18.0000 q^{20} +108.000 q^{22} +(31.5000 + 54.5596i) q^{24} +(-99.5000 - 172.339i) q^{25} +(-51.0000 + 88.3346i) q^{26} -27.0000 q^{27} +102.000 q^{29} +(81.0000 - 140.296i) q^{30} +(80.0000 + 138.564i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(-54.0000 + 93.5307i) q^{33} -126.000 q^{34} +9.00000 q^{36} +(-199.000 + 344.678i) q^{37} +(-186.000 - 322.161i) q^{38} +(-51.0000 - 88.3346i) q^{39} +(189.000 - 327.358i) q^{40} -318.000 q^{41} -268.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(81.0000 + 140.296i) q^{45} +(-120.000 + 207.846i) q^{47} +213.000 q^{48} -597.000 q^{50} +(63.0000 - 109.119i) q^{51} +(17.0000 + 29.4449i) q^{52} +(249.000 + 431.281i) q^{53} +(-40.5000 + 70.1481i) q^{54} +648.000 q^{55} +372.000 q^{57} +(153.000 - 265.004i) q^{58} +(66.0000 + 114.315i) q^{59} +(-27.0000 - 46.7654i) q^{60} +(-199.000 + 344.678i) q^{61} +480.000 q^{62} +433.000 q^{64} +(-306.000 + 530.008i) q^{65} +(162.000 + 280.592i) q^{66} +(-46.0000 - 79.6743i) q^{67} +(-21.0000 + 36.3731i) q^{68} -720.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(251.000 + 434.745i) q^{73} +(597.000 + 1034.03i) q^{74} +(298.500 - 517.017i) q^{75} -124.000 q^{76} -306.000 q^{78} +(512.000 - 886.810i) q^{79} +(-639.000 - 1106.78i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-477.000 + 826.188i) q^{82} -204.000 q^{83} -756.000 q^{85} +(-402.000 + 696.284i) q^{86} +(153.000 + 265.004i) q^{87} +(378.000 + 654.715i) q^{88} +(-177.000 + 306.573i) q^{89} +486.000 q^{90} +(-240.000 + 415.692i) q^{93} +(360.000 + 623.538i) q^{94} +(-1116.00 - 1932.97i) q^{95} +(67.5000 - 116.913i) q^{96} -286.000 q^{97} -324.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} + 18 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 + 18 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} + 18 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9} - 54 q^{10} + 36 q^{11} + 3 q^{12} - 68 q^{13} + 108 q^{15} + 71 q^{16} - 42 q^{17} + 27 q^{18} + 124 q^{19} - 36 q^{20} + 216 q^{22} + 63 q^{24} - 199 q^{25} - 102 q^{26} - 54 q^{27} + 204 q^{29} + 162 q^{30} + 160 q^{31} - 45 q^{32} - 108 q^{33} - 252 q^{34} + 18 q^{36} - 398 q^{37} - 372 q^{38} - 102 q^{39} + 378 q^{40} - 636 q^{41} - 536 q^{43} + 36 q^{44} + 162 q^{45} - 240 q^{47} + 426 q^{48} - 1194 q^{50} + 126 q^{51} + 34 q^{52} + 498 q^{53} - 81 q^{54} + 1296 q^{55} + 744 q^{57} + 306 q^{58} + 132 q^{59} - 54 q^{60} - 398 q^{61} + 960 q^{62} + 866 q^{64} - 612 q^{65} + 324 q^{66} - 92 q^{67} - 42 q^{68} - 1440 q^{71} - 189 q^{72} + 502 q^{73} + 1194 q^{74} + 597 q^{75} - 248 q^{76} - 612 q^{78} + 1024 q^{79} - 1278 q^{80} - 81 q^{81} - 954 q^{82} - 408 q^{83} - 1512 q^{85} - 804 q^{86} + 306 q^{87} + 756 q^{88} - 354 q^{89} + 972 q^{90} - 480 q^{93} + 720 q^{94} - 2232 q^{95} + 135 q^{96} - 572 q^{97} - 648 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 + 18 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9 - 54 * q^10 + 36 * q^11 + 3 * q^12 - 68 * q^13 + 108 * q^15 + 71 * q^16 - 42 * q^17 + 27 * q^18 + 124 * q^19 - 36 * q^20 + 216 * q^22 + 63 * q^24 - 199 * q^25 - 102 * q^26 - 54 * q^27 + 204 * q^29 + 162 * q^30 + 160 * q^31 - 45 * q^32 - 108 * q^33 - 252 * q^34 + 18 * q^36 - 398 * q^37 - 372 * q^38 - 102 * q^39 + 378 * q^40 - 636 * q^41 - 536 * q^43 + 36 * q^44 + 162 * q^45 - 240 * q^47 + 426 * q^48 - 1194 * q^50 + 126 * q^51 + 34 * q^52 + 498 * q^53 - 81 * q^54 + 1296 * q^55 + 744 * q^57 + 306 * q^58 + 132 * q^59 - 54 * q^60 - 398 * q^61 + 960 * q^62 + 866 * q^64 - 612 * q^65 + 324 * q^66 - 92 * q^67 - 42 * q^68 - 1440 * q^71 - 189 * q^72 + 502 * q^73 + 1194 * q^74 + 597 * q^75 - 248 * q^76 - 612 * q^78 + 1024 * q^79 - 1278 * q^80 - 81 * q^81 - 954 * q^82 - 408 * q^83 - 1512 * q^85 - 804 * q^86 + 306 * q^87 + 756 * q^88 - 354 * q^89 + 972 * q^90 - 480 * q^93 + 720 * q^94 - 2232 * q^95 + 135 * q^96 - 572 * q^97 - 648 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more