LMFDB - Embedded newform 147.4.e.g.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.g.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	$0.464493\pi$
$5$	−9.00000	+	15.5885i	−0.804984	+	1.39427i	−0.916302	+	0.400489i	$0.868840\pi$
$6$	−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	$-0.381859\pi$
$13$	34.0000			0.725377			0.362689	+	0.931910i	$0.381859\pi$
$14$		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	0.976045	−	0.217568i	$-0.0698125\pi$
$17$	21.0000	+	36.3731i	0.299603	+	0.518927i	−0.676442	+	0.736496i	$0.736479\pi$
$18$	13.5000	+	23.3827i	0.176777	+	0.306186i
$19$	−62.0000	+	107.387i	−0.748620	+	1.29665i	0.199865	+	0.979824i	$0.435950\pi$
$19$	−62.0000	+	107.387i	−0.748620	+	1.29665i	−0.948484	+	0.316824i	$0.897384\pi$
$20$	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	0.535635	−	0.844450i	$-0.320072\pi$
$31$	−80.0000	−	138.564i	−0.463498	−	0.802801i	−0.999132	+	0.0416484i	$0.986739\pi$
$32$	−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	$-0.292913\pi$
$41$	318.000			1.21130			0.605649	+	0.795732i	$0.292913\pi$
$42$		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	−0.617516	−	0.786558i	$-0.711861\pi$
$47$	120.000	−	207.846i	0.372421	−	0.645053i	0.989937	+	0.141506i	$0.0451943\pi$
$48$	−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	0.783975	−	0.620793i	$-0.213189\pi$
$59$	−66.0000	−	114.315i	−0.145635	−	0.252247i	−0.929610	+	0.368546i	$0.879856\pi$
$60$	−27.0000	−	46.7654i	−0.0580948	−	0.100623i
$61$	199.000	−	344.678i	0.417694	−	0.723467i	−0.578013	−	0.816028i	$-0.696172\pi$
$61$	199.000	−	344.678i	0.417694	−	0.723467i	0.995707	+	0.0925602i	$0.0295051\pi$
$62$	−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	0.591589	−	0.806239i	$-0.298501\pi$
$73$	−251.000	−	434.745i	−0.402429	−	0.697028i	−0.994019	+	0.109212i	$0.965167\pi$
$74$	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	$-0.456932\pi$
$83$	204.000			0.269782			0.134891	+	0.990860i	$0.456932\pi$
$84$		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	−0.741159	−	0.671329i	$-0.765724\pi$
$89$	177.000	−	306.573i	0.210809	−	0.365131i	0.951968	+	0.306198i	$0.0990570\pi$
$90$	−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	$-0.452174\pi$
$97$	286.000			0.299370			0.149685	+	0.988734i	$0.452174\pi$
$98$		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	0.949792	−	0.312881i	$-0.101294\pi$
$101$	207.000	+	358.535i	0.203933	+	0.353223i	−0.745859	+	0.666104i	$0.767961\pi$
$102$	−189.000	−	327.358i	−0.183469	−	0.317777i
$103$	28.0000	−	48.4974i	0.0267857	−	0.0463941i	−0.852322	−	0.523018i	$-0.824806\pi$
$103$	28.0000	−	48.4974i	0.0267857	−	0.0463941i	0.879107	+	0.476624i	$0.158140\pi$
$104$	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	$-0.633151\pi$
$131$	882.000	−	1527.67i	0.588250	−	1.01888i	0.994462	−	0.105099i	$-0.0335161\pi$
$132$	−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	$-0.494950\pi$
$139$	52.0000			0.0317308			0.0158654	+	0.999874i	$0.494950\pi$
$140$		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	0.996922	−	0.0784048i	$-0.0249827\pi$
$157$	847.000	+	1467.05i	0.430560	+	0.745752i	−0.566361	+	0.824157i	$0.691649\pi$
$158$	−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	$-0.587837\pi$
$167$	−1176.00			−0.544920			−0.272460	+	0.962167i	$0.587837\pi$
$168$		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	−0.754468	−	0.656337i	$-0.772105\pi$
$173$	435.000	−	753.442i	0.191170	−	0.331116i	0.945638	+	0.325220i	$0.105438\pi$
$174$	−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	$-0.493071\pi$
$181$	106.000			0.0435299			0.0217650	+	0.999763i	$0.493071\pi$
$182$		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	$0.195461\pi$
$199$	2548.00	+	4413.27i	0.907653	+	1.57210i	0.0903369	+	0.995911i	$0.471206\pi$
$200$	−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	$-0.408513\pi$
$223$	1888.00			0.566950			0.283475	+	0.958980i	$0.408513\pi$
$224$		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	$-0.924517\pi$
$227$	−2358.00	−	4084.18i	−0.689454	−	1.19417i	0.282561	−	0.959249i	$-0.408816\pi$
$228$	−186.000	−	322.161i	−0.0540270	−	0.0935775i
$229$	−845.000	+	1463.58i	−0.243839	+	0.422342i	−0.961805	−	0.273737i	$-0.911740\pi$
$229$	−845.000	+	1463.58i	−0.243839	+	0.422342i	0.717965	+	0.696079i	$0.245074\pi$
$230$		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	0.518913	−	0.854827i	$-0.326337\pi$
$241$	−1799.00	−	3115.96i	−0.480846	−	0.832849i	−0.999758	+	0.0219782i	$0.993004\pi$
$242$	−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	$-0.374287\pi$
$251$	3060.00			0.769504			0.384752	+	0.923020i	$0.374287\pi$
$252$		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	$0.477136\pi$
$257$	−3411.00	+	5908.03i	−0.827908	+	1.43398i	−0.899676	+	0.436557i	$0.856198\pi$
$258$	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	$0.214296\pi$
$269$	4107.00	+	7113.53i	0.930886	+	1.61234i	0.149074	+	0.988826i	$0.452371\pi$
$270$	729.000	+	1262.67i	0.164317	+	0.284605i
$271$	−2672.00	+	4628.04i	−0.598939	+	1.03739i	0.394039	+	0.919094i	$0.371077\pi$
$271$	−2672.00	+	4628.04i	−0.598939	+	1.03739i	−0.992978	+	0.118299i	$0.962256\pi$
$272$	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	0.984874	−	0.173271i	$-0.0554338\pi$
$283$	1630.00	+	2823.24i	0.342380	+	0.593019i	−0.642494	+	0.766290i	$0.722100\pi$
$284$	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	$-0.670441\pi$
$293$	−5118.00			−1.02047			−0.510233	+	0.860036i	$0.670441\pi$
$294$		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	$-0.513378\pi$
$307$	−452.000			−0.0840293			−0.0420147	+	0.999117i	$0.513378\pi$
$308$		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	0.998816	−	0.0486397i	$-0.0154886\pi$
$311$	2508.00	+	4343.98i	0.457285	+	0.792041i	−0.541531	+	0.840681i	$0.682155\pi$
$312$	−1071.00	−	1855.03i	−0.194338	−	0.336603i
$313$	2701.00	−	4678.27i	0.487762	−	0.844829i	−0.512139	−	0.858903i	$-0.671147\pi$
$313$	2701.00	−	4678.27i	0.487762	−	0.844829i	0.999901	+	0.0140739i	$0.00448001\pi$
$314$	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	$-0.0986888\pi$
$349$	12418.0			1.90464			0.952321	+	0.305097i	$0.0986888\pi$
$350$		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	$-0.965678\pi$
$353$	−3915.00	−	6780.98i	−0.590296	−	1.02242i	0.403897	−	0.914805i	$-0.367656\pi$
$354$	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	0.700791	−	0.713367i	$-0.252831\pi$
$367$	−1880.00	−	3256.26i	−0.267398	−	0.463148i	−0.968189	+	0.250219i	$0.919497\pi$
$368$		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	−0.784945	−	0.619566i	$-0.787309\pi$
$383$	1080.00	−	1870.61i	0.144087	−	0.249566i	0.929032	+	0.369999i	$0.120642\pi$
$384$	−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	−0.995081	−	0.0990641i	$-0.968415\pi$
$397$	−3257.00	+	5641.29i	−0.411748	+	0.713169i	0.583333	+	0.812233i	$0.301748\pi$
$398$	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	0.655474	−	0.755218i	$-0.272469\pi$
$409$	−2699.00	−	4674.81i	−0.326301	−	0.565169i	−0.981775	+	0.190048i	$0.939136\pi$
$410$	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	$-0.776387\pi$
$419$	−13092.0			−1.52646			−0.763229	+	0.646128i	$0.776387\pi$
$420$		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	$-0.577095\pi$
$433$	−4322.00			−0.479681			−0.239841	+	0.970812i	$0.577095\pi$
$434$		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	−0.999935	−	0.0113909i	$-0.996374\pi$
$439$	−4508.00	+	7808.09i	−0.490103	+	0.848883i	0.509832	+	0.860274i	$0.329707\pi$
$440$	−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	$-0.412558\pi$
$461$	5370.00			0.542529			0.271264	+	0.962505i	$0.412558\pi$
$462$		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	−0.731090	−	0.682281i	$-0.760988\pi$
$467$	2274.00	−	3938.68i	0.225328	−	0.390280i	0.956418	+	0.292002i	$0.0943213\pi$
$468$	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	0.607108	−	0.794620i	$-0.292330\pi$
$479$	−4032.00	−	6983.63i	−0.384607	−	0.666159i	−0.991715	+	0.128461i	$0.958996\pi$
$480$	−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	$-0.406213\pi$
$503$	6552.00			0.580794			0.290397	+	0.956906i	$0.406213\pi$
$504$		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	−0.798873	−	0.601500i	$-0.794570\pi$
$509$	1395.00	−	2416.21i	0.121478	−	0.210406i	0.920351	+	0.391094i	$0.127903\pi$
$510$	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	$-0.951818\pi$
$521$	−7431.00	−	12870.9i	−0.624871	−	1.08231i	0.363694	−	0.931518i	$-0.381515\pi$
$522$	1377.00	+	2385.03i	0.115459	+	0.199981i
$523$	8830.00	−	15294.0i	0.738258	−	1.27870i	−0.215021	−	0.976609i	$-0.568982\pi$
$523$	8830.00	−	15294.0i	0.738258	−	1.27870i	0.953279	−	0.302091i	$-0.0976846\pi$
$524$	−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	$-0.935019\pi$
$563$	−8886.00	−	15391.0i	−0.665187	−	1.15214i	0.314048	−	0.949407i	$-0.398315\pi$
$564$	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	0.866061	−	0.499938i	$-0.166644\pi$
$577$	1.00000	+	1.73205i	7.21500e−5	+	0.000124967i	−0.865989	+	0.500062i	$0.833310\pi$
$578$	−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	$-0.877521\pi$
$587$	−26364.0			−1.85376			−0.926881	+	0.375354i	$0.877521\pi$
$588$		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	−0.823496	−	0.567323i	$-0.807979\pi$
$593$	1149.00	−	1990.13i	0.0795679	−	0.137816i	0.903064	+	0.429507i	$0.141313\pi$
$594$	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	$-0.813528\pi$
$601$	−24554.0			−1.66652			−0.833260	+	0.552881i	$0.813528\pi$
$602$		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	$-0.643073\pi$
$607$	8416.00	−	14576.9i	0.562759	−	0.974728i	0.997254	−	0.0740535i	$-0.0235935\pi$
$608$	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	$-0.999290\pi$
$619$	−7730.00	−	13388.8i	−0.501930	−	0.869369i	0.498067	−	0.867138i	$-0.334043\pi$
$620$	−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	$-0.377734\pi$
$643$	12220.0			0.749471			0.374735	+	0.927132i	$0.377734\pi$
$644$		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	0.995106	−	0.0988143i	$-0.0315050\pi$
$647$	6780.00	+	11743.3i	0.411977	+	0.713566i	−0.583129	+	0.812380i	$0.698172\pi$
$648$	−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	$0.00508182\pi$
$661$	8731.00	+	15122.5i	0.513762	+	0.889862i	−0.486111	+	0.873897i	$0.661585\pi$
$662$	−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	$0.424987\pi$
$677$	−12777.0	+	22130.4i	−0.725347	+	1.25634i	−0.958831	+	0.283977i	$0.908346\pi$
$678$	−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	$-0.561611\pi$
$691$	13690.0	−	23711.8i	0.753679	−	1.30541i	0.946028	−	0.324084i	$-0.105056\pi$
$692$	−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	−0.992566	−	0.121705i	$-0.961164\pi$
$719$	−7536.00	+	13052.7i	−0.390884	+	0.677030i	0.601683	+	0.798735i	$0.294497\pi$
$720$	−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	$-0.182726\pi$
$727$	32920.0			1.67942			0.839708	+	0.543038i	$0.182726\pi$
$728$		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	−0.940163	−	0.340726i	$-0.889327\pi$
$733$	−3473.00	+	6015.41i	−0.175004	+	0.303116i	0.765158	+	0.643842i	$0.222661\pi$
$734$	−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	−0.695281	−	0.718738i	$-0.744720\pi$
$761$	5769.00	−	9992.20i	0.274804	−	0.475975i	0.970086	+	0.242763i	$0.0780536\pi$
$762$	−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	$-0.563850\pi$
$769$	−8498.00			−0.398499			−0.199249	+	0.979949i	$0.563850\pi$
$770$		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	$-0.895772\pi$
$773$	−16161.0	−	27991.7i	−0.751967	−	1.30245i	0.194901	−	0.980823i	$-0.437562\pi$
$774$	−3618.00	−	6266.56i	−0.168019	−	0.291017i
$775$	−15920.0	+	27574.2i	−0.737888	+	1.27806i
$776$	6006.00			0.277839
$777$		0			0
$778$	20358.0			0.938136
$779$	−19716.0	+	34149.1i	−0.906802	+	1.57063i
$780$	−918.000	−	1590.02i	−0.0421406	−	0.0729897i
$781$	−12960.0	−	22447.4i	−0.593784	−	1.02846i
$782$		0			0
$783$	2754.00			0.125696
$784$		0			0
$785$	−30492.0			−1.38638
$786$	−7938.00	+	13749.0i	−0.360228	+	0.623933i
$787$	13114.0	+	22714.1i	0.593982	+	1.02881i	0.993690	+	0.112164i	$0.0357782\pi$
$787$	13114.0	+	22714.1i	0.593982	+	1.02881i	−0.399708	+	0.916643i	$0.630888\pi$
$788$	657.000	+	1137.96i	0.0297013	+	0.0514442i
$789$	−3888.00	+	6734.21i	−0.175433	+	0.303858i
$790$	55296.0			2.49031
$791$		0			0
$792$	−6804.00			−0.305265
$793$	6766.00	−	11719.1i	0.302986	−	0.524787i
$794$	9771.00	+	16923.9i	0.436725	+	0.756430i
$795$	13446.0	+	23289.2i	0.599850	+	1.03897i
$796$	2548.00	−	4413.27i	0.113457	−	0.196513i
$797$	43338.0			1.92611			0.963056	−	0.269302i	$-0.0867931\pi$
$797$	43338.0			1.92611			0.963056	+	0.269302i	$0.0867931\pi$
$798$		0			0
$799$	10080.0			0.446314
$800$	−4477.50	+	7755.26i	−0.197879	+	0.342737i
$801$	1593.00	+	2759.16i	0.0702695	+	0.121710i
$802$	4995.00	+	8651.59i	0.219925	+	0.380921i
$803$	9036.00	−	15650.8i	0.397103	−	0.687802i
$804$	276.000			0.0121067
$805$		0			0
$806$	−16320.0			−0.713210
$807$	12321.0	−	21340.6i	0.537447	−	0.930886i
$808$	4347.00	+	7529.22i	0.189266	+	0.327818i
$809$	14451.0	+	25029.9i	0.628022	+	1.08777i	0.987948	+	0.154786i	$0.0494687\pi$
$809$	14451.0	+	25029.9i	0.628022	+	1.08777i	−0.359926	+	0.932981i	$0.617198\pi$
$810$	2187.00	−	3788.00i	0.0948683	−	0.164317i
$811$	−27164.0			−1.17615			−0.588075	−	0.808807i	$-0.700114\pi$
$811$	−27164.0			−1.17615			−0.588075	+	0.808807i	$0.700114\pi$
$812$		0			0
$813$	16032.0			0.691595
$814$	−21492.0	+	37225.2i	−0.925423	+	1.60288i
$815$	26388.0	+	45705.4i	1.13415	+	1.96440i
$816$	−4473.00	−	7747.46i	−0.191895	−	0.332372i
$817$	16616.0	−	28779.8i	0.711530	−	1.23241i
$818$	−16194.0			−0.692188
$819$		0			0
$820$	5724.00			0.243769
$821$	8601.00	−	14897.4i	0.365624	−	0.633279i	−0.623252	−	0.782021i	$-0.714189\pi$
$821$	8601.00	−	14897.4i	0.365624	−	0.633279i	0.988876	+	0.148742i	$0.0475224\pi$
$822$	−10611.0	−	18378.8i	−0.450245	−	0.779847i
$823$	2996.00	+	5189.22i	0.126894	+	0.219787i	0.922472	−	0.386064i	$-0.126166\pi$
$823$	2996.00	+	5189.22i	0.126894	+	0.219787i	−0.795578	+	0.605852i	$0.792832\pi$
$824$	588.000	−	1018.45i	0.0248592	−	0.0430573i
$825$	−21492.0			−0.906976
$826$		0			0
$827$	25884.0			1.08836			0.544181	−	0.838968i	$-0.316841\pi$
$827$	25884.0			1.08836			0.544181	+	0.838968i	$0.316841\pi$
$828$		0			0
$829$	−737.000	−	1276.52i	−0.0308770	−	0.0534806i	0.850174	−	0.526502i	$-0.176497\pi$
$829$	−737.000	−	1276.52i	−0.0308770	−	0.0534806i	−0.881051	+	0.473021i	$0.843163\pi$
$830$	5508.00	+	9540.14i	0.230344	+	0.398967i
$831$	9771.00	−	16923.9i	0.407885	−	0.706477i
$832$	14722.0			0.613454
$833$		0			0
$834$	−468.000			−0.0194311
$835$	10584.0	−	18332.0i	0.438652	−	0.759768i
$836$	2232.00	+	3865.94i	0.0923389	+	0.159936i
$837$	−2160.00	−	3741.23i	−0.0892001	−	0.154499i
$838$	−19638.0	+	34014.0i	−0.809527	+	1.40214i
$839$	−33528.0			−1.37964			−0.689818	−	0.723983i	$-0.742310\pi$
$839$	−33528.0			−1.37964			−0.689818	+	0.723983i	$0.742310\pi$
$840$		0			0
$841$	−13985.0			−0.573414
$842$	−483.000	+	836.581i	−0.0197687	+	0.0342405i
$843$	−9927.00	−	17194.1i	−0.405580	−	0.702485i
$844$	1538.00	+	2663.89i	0.0627253	+	0.108643i
$845$	9369.00	−	16227.6i	0.381424	−	0.660646i
$846$	6480.00			0.263342
$847$		0			0
$848$	35358.0			1.43184
$849$	4890.00	−	8469.73i	0.197673	−	0.342380i
$850$	−12537.0	−	21714.7i	−0.505901	−	0.876246i
$851$		0			0
$852$	1080.00	−	1870.61i	0.0434275	−	0.0752186i
$853$	−1190.00			−0.0477665			−0.0238832	−	0.999715i	$-0.507603\pi$
$853$	−1190.00			−0.0477665			−0.0238832	+	0.999715i	$0.507603\pi$
$854$		0			0
$855$	20088.0			0.803503
$856$	−126.000	+	218.238i	−0.00503106	+	0.00871406i
$857$	17289.0	+	29945.4i	0.689126	+	1.19360i	0.972121	+	0.234480i	$0.0753387\pi$
$857$	17289.0	+	29945.4i	0.689126	+	1.19360i	−0.282995	+	0.959121i	$0.591328\pi$
$858$	−5508.00	−	9540.14i	−0.219161	−	0.379598i
$859$	−22202.0	+	38455.0i	−0.881865	+	1.52744i	−0.0326009	+	0.999468i	$0.510379\pi$
$859$	−22202.0	+	38455.0i	−0.881865	+	1.52744i	−0.849265	+	0.527967i	$0.822954\pi$
$860$	−4824.00			−0.191276
$861$		0			0
$862$	−7848.00			−0.310097
$863$	19164.0	−	33193.0i	0.755910	−	1.30927i	−0.189011	−	0.981975i	$-0.560528\pi$
$863$	19164.0	−	33193.0i	0.755910	−	1.30927i	0.944921	−	0.327299i	$-0.106138\pi$
$864$	−607.500	−	1052.22i	−0.0239208	−	0.0414320i
$865$	7830.00	+	13562.0i	0.307778	+	0.533087i
$866$	−6483.00	+	11228.9i	−0.254390	+	0.440616i
$867$	−9447.00			−0.370054
$868$		0			0
$869$	36864.0			1.43904
$870$	8262.00	−	14310.2i	0.321963	−	0.557657i
$871$	−1564.00	−	2708.93i	−0.0608428	−	0.105383i
$872$	−15519.0	−	26879.7i	−0.602683	−	1.04388i
$873$	−1287.00	+	2229.15i	−0.0498950	+	0.0864207i
$874$		0			0
$875$		0			0
$876$	1506.00			0.0580856
$877$	19421.0	−	33638.2i	0.747777	−	1.29519i	−0.201109	−	0.979569i	$-0.564454\pi$
$877$	19421.0	−	33638.2i	0.747777	−	1.29519i	0.948886	−	0.315619i	$-0.102212\pi$
$878$	13524.0	+	23424.3i	0.519832	+	0.900376i
$879$	7677.00	+	13297.0i	0.294583	+	0.510233i
$880$	−23004.0	+	39844.1i	−0.881210	+	1.52630i
$881$	35046.0			1.34022			0.670108	−	0.742264i	$-0.266248\pi$
$881$	35046.0			1.34022			0.670108	+	0.742264i	$0.266248\pi$
$882$		0			0
$883$	14204.0			0.541339			0.270670	−	0.962672i	$-0.412755\pi$
$883$	14204.0			0.541339			0.270670	+	0.962672i	$0.412755\pi$
$884$	714.000	−	1236.68i	0.0271656	−	0.0470523i
$885$	−3564.00	−	6173.03i	−0.135370	−	0.234468i
$886$	−7902.00	−	13686.7i	−0.299631	−	0.518976i
$887$	−13068.0	+	22634.4i	−0.494679	+	0.856810i	−0.999981	−	0.00613301i	$-0.998048\pi$
$887$	−13068.0	+	22634.4i	−0.494679	+	0.856810i	0.505302	+	0.862943i	$0.331381\pi$
$888$	25074.0			0.947554
$889$		0			0
$890$	19116.0			0.719966
$891$	1458.00	−	2525.33i	0.0548202	−	0.0949514i
$892$	−944.000	−	1635.06i	−0.0354344	−	0.0613741i
$893$	14880.0	+	25772.9i	0.557604	+	0.965798i
$894$	−7857.00	+	13608.7i	−0.293934	+	0.509109i
$895$	−41688.0			−1.55696
$896$		0			0
$897$		0			0
$898$	−7965.00	+	13795.8i	−0.295986	+	0.512663i
$899$	−8160.00	−	14133.5i	−0.302727	−	0.524338i
$900$	−895.500	−	1551.05i	−0.0331667	−	0.0574464i
$901$	−10458.0	+	18113.8i	−0.386689	+	0.669764i
$902$	34344.0			1.26777
$903$		0			0
$904$	8442.00			0.310594
$905$	−954.000	+	1652.38i	−0.0350409	+	0.0606927i
$906$	−1044.00	−	1808.26i	−0.0382832	−	0.0663084i
$907$	4526.00	+	7839.26i	0.165693	+	0.286988i	0.936901	−	0.349595i	$-0.113681\pi$
$907$	4526.00	+	7839.26i	0.165693	+	0.286988i	−0.771208	+	0.636583i	$0.780347\pi$
$908$	−2358.00	+	4084.18i	−0.0861817	+	0.149271i
$909$	−3726.00			−0.135956
$910$		0			0
$911$	5016.00			0.182423			0.0912116	−	0.995832i	$-0.470926\pi$
$911$	5016.00			0.182423			0.0912116	+	0.995832i	$0.470926\pi$
$912$	13206.0	−	22873.5i	0.479489	−	0.830500i
$913$	3672.00	+	6360.09i	0.133106	+	0.230546i
$914$	23655.0	+	40971.7i	0.856059	+	1.48274i
$915$	10746.0	−	18612.6i	0.388253	−	0.672475i
$916$	1690.00			0.0609598
$917$		0			0
$918$	3402.00			0.122312
$919$	−22276.0	+	38583.2i	−0.799584	+	1.38492i	0.120304	+	0.992737i	$0.461613\pi$
$919$	−22276.0	+	38583.2i	−0.799584	+	1.38492i	−0.919887	+	0.392182i	$0.871720\pi$
$920$		0			0
$921$	678.000	+	1174.33i	0.0242572	+	0.0420147i
$922$	8055.00	−	13951.7i	0.287719	−	0.498345i
$923$	−24480.0			−0.872989
$924$		0			0
$925$	79202.0			2.81529
$926$	−4992.00	+	8646.40i	−0.177157	+	0.306845i
$927$	252.000	+	436.477i	0.00892855	+	0.0154647i
$928$	−2295.00	−	3975.06i	−0.0811822	−	0.140612i
$929$	12117.0	−	20987.3i	0.427929	−	0.741194i	−0.568760	−	0.822503i	$-0.692577\pi$
$929$	12117.0	−	20987.3i	0.427929	−	0.741194i	0.996689	+	0.0813090i	$0.0259101\pi$
$930$	−25920.0			−0.913925
$931$		0			0
$932$	138.000			0.00485015
$933$	7524.00	−	13032.0i	0.264014	−	0.457285i
$934$	−6822.00	−	11816.1i	−0.238996	−	0.413954i
$935$	−13608.0	−	23569.7i	−0.475967	−	0.824399i
$936$	−3213.00	+	5565.08i	−0.112201	+	0.194338i
$937$	13894.0			0.484415			0.242208	−	0.970224i	$-0.422128\pi$
$937$	13894.0			0.484415			0.242208	+	0.970224i	$0.422128\pi$
$938$		0			0
$939$	−16206.0			−0.563219
$940$	2160.00	−	3741.23i	0.0749483	−	0.129814i
$941$	23379.0	+	40493.6i	0.809919	+	1.40282i	0.912920	+	0.408139i	$0.133822\pi$
$941$	23379.0	+	40493.6i	0.809919	+	1.40282i	−0.103001	+	0.994681i	$0.532844\pi$
$942$	−7623.00	−	13203.4i	−0.263663	−	0.456678i
$943$		0			0
$944$	−9372.00			−0.323128
$945$		0			0
$946$	−28944.0			−0.994768
$947$	−6906.00	+	11961.5i	−0.236974	+	0.410452i	−0.959845	−	0.280532i	$-0.909489\pi$
$947$	−6906.00	+	11961.5i	−0.236974	+	0.410452i	0.722870	+	0.690984i	$0.242822\pi$
$948$	1536.00	+	2660.43i	0.0526234	+	0.0911464i
$949$	−8534.00	−	14781.3i	−0.291913	−	0.505608i
$950$	37014.0	−	64110.1i	1.26410	−	2.18948i
$951$	30258.0			1.03174
$952$		0			0
$953$	−58518.0			−1.98907			−0.994535	−	0.104402i	$-0.966707\pi$
$953$	−58518.0			−1.98907			−0.994535	+	0.104402i	$0.966707\pi$
$954$	−6723.00	+	11644.6i	−0.228161	+	0.395186i
$955$	10152.0	+	17583.8i	0.343991	+	0.595809i
$956$	−948.000	−	1641.98i	−0.0320717	−	0.0555498i
$957$	5508.00	−	9540.14i	0.186048	−	0.322245i
$958$	−24192.0			−0.815875
$959$		0			0
$960$	23382.0			0.786095
$961$	2095.50	−	3629.51i	0.0703400	−	0.121833i
$962$	20298.0	+	35157.2i	0.680285	+	1.17829i
$963$	−54.0000	−	93.5307i	−0.00180698	−	0.00312979i
$964$	−1799.00	+	3115.96i	−0.0601057	+	0.104106i
$965$	72612.0			2.42224
$966$		0			0
$967$	19640.0			0.653133			0.326567	−	0.945174i	$-0.394108\pi$
$967$	19640.0			0.653133			0.326567	+	0.945174i	$0.394108\pi$
$968$	367.500	−	636.529i	0.0122024	−	0.0211351i
$969$	7812.00	+	13530.8i	0.258986	+	0.448577i
$970$	7722.00	+	13374.9i	0.255607	+	0.442724i
$971$	−29154.0	+	50496.2i	−0.963539	+	1.66890i	−0.250049	+	0.968233i	$0.580447\pi$
$971$	−29154.0	+	50496.2i	−0.963539	+	1.66890i	−0.713490	+	0.700665i	$0.752887\pi$
$972$	243.000			0.00801875
$973$		0			0
$974$	−49848.0			−1.63987
$975$	−10149.0	+	17578.6i	−0.333362	+	0.577400i
$976$	−14129.0	−	24472.1i	−0.463379	−	0.802597i
$977$	11775.0	+	20394.9i	0.385584	+	0.667851i	0.991850	−	0.127411i	$-0.0406666\pi$
$977$	11775.0	+	20394.9i	0.385584	+	0.667851i	−0.606266	+	0.795262i	$0.707333\pi$
$978$	−13194.0	+	22852.7i	−0.431388	+	0.747186i
$979$	12744.0			0.416037
$980$		0			0
$981$	13302.0			0.432926
$982$	−10710.0	+	18550.3i	−0.348034	+	0.602813i
$983$	7884.00	+	13655.5i	0.255809	+	0.443075i	0.965115	−	0.261826i	$-0.0843247\pi$
$983$	7884.00	+	13655.5i	0.255809	+	0.443075i	−0.709306	+	0.704901i	$0.750991\pi$
$984$	−10017.0	−	17350.0i	−0.324523	−	0.562090i
$985$	11826.0	−	20483.2i	0.382546	−	0.662589i
$986$	12852.0			0.415102
$987$		0			0
$988$	4216.00			0.135758
$989$		0			0
$990$	−8748.00	−	15152.0i	−0.280838	−	0.486426i
$991$	−17632.0	−	30539.5i	−0.565186	−	0.978930i	−0.997032	−	0.0769832i	$-0.975471\pi$
$991$	−17632.0	−	30539.5i	−0.565186	−	0.978930i	0.431847	−	0.901947i	$-0.357862\pi$
$992$	−3600.00	+	6235.38i	−0.115222	+	0.199570i
$993$	−24132.0			−0.771204
$994$		0			0
$995$	−91728.0			−2.92259
$996$	−306.000	+	530.008i	−0.00973492	+	0.0168614i
$997$	−14669.0	−	25407.5i	−0.465970	−	0.807083i	0.533275	−	0.845942i	$-0.320961\pi$
$997$	−14669.0	−	25407.5i	−0.465970	−	0.807083i	−0.999245	+	0.0388586i	$0.987628\pi$
$998$	−13686.0	−	23704.8i	−0.434091	−	0.751868i
$999$	−5373.00	+	9306.31i	−0.170164	+	0.294733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.g.79.1		2
3.2	odd	2		441.4.e.d.226.1		2
7.2	even	3		147.4.a.c.1.1		1
7.3	odd	6		147.4.e.i.67.1		2
7.4	even	3	inner	147.4.e.g.67.1		2
7.5	odd	6		21.4.a.a.1.1	✓	1
7.6	odd	2		147.4.e.i.79.1		2
21.2	odd	6		441.4.a.j.1.1		1
21.5	even	6		63.4.a.c.1.1		1
21.11	odd	6		441.4.e.d.361.1		2
21.17	even	6		441.4.e.b.361.1		2
21.20	even	2		441.4.e.b.226.1		2
28.19	even	6		336.4.a.f.1.1		1
28.23	odd	6		2352.4.a.r.1.1		1
35.12	even	12		525.4.d.c.274.1		2
35.19	odd	6		525.4.a.g.1.1		1
35.33	even	12		525.4.d.c.274.2		2
56.5	odd	6		1344.4.a.ba.1.1		1
56.19	even	6		1344.4.a.n.1.1		1
84.47	odd	6		1008.4.a.v.1.1		1
105.89	even	6		1575.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.a.1.1	✓	1	7.5	odd	6
63.4.a.c.1.1		1	21.5	even	6
147.4.a.c.1.1		1	7.2	even	3
147.4.e.g.67.1		2	7.4	even	3	inner
147.4.e.g.79.1		2	1.1	even	1	trivial
147.4.e.i.67.1		2	7.3	odd	6
147.4.e.i.79.1		2	7.6	odd	2
336.4.a.f.1.1		1	28.19	even	6
441.4.a.j.1.1		1	21.2	odd	6
441.4.e.b.226.1		2	21.20	even	2
441.4.e.b.361.1		2	21.17	even	6
441.4.e.d.226.1		2	3.2	odd	2
441.4.e.d.361.1		2	21.11	odd	6
525.4.a.g.1.1		1	35.19	odd	6
525.4.d.c.274.1		2	35.12	even	12
525.4.d.c.274.2		2	35.33	even	12
1008.4.a.v.1.1		1	84.47	odd	6
1344.4.a.n.1.1		1	56.19	even	6
1344.4.a.ba.1.1		1	56.5	odd	6
1575.4.a.b.1.1		1	105.89	even	6
2352.4.a.r.1.1		1	28.23	odd	6

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

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Varieties

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Database

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