LMFDB - Embedded newform 804.2.e.b.535.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.28
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.956986 + 1.04124i) q^{2} +1.00000 q^{3} +(-0.168355 + 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 + 1.04124i) q^{6} +1.56640 q^{7} +(-2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.956986 + 1.04124i) q^{2} +1.00000 q^{3} +(-0.168355 + 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 + 1.04124i) q^{6} +1.56640 q^{7} +(-2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +(1.41947 - 1.30461i) q^{10} +0.528628 q^{11} +(-0.168355 + 1.99290i) q^{12} +2.52074i q^{13} +(1.49903 + 1.63100i) q^{14} -1.36325i q^{15} +(-3.94331 - 0.671030i) q^{16} +5.97533 q^{17} +(0.956986 + 1.04124i) q^{18} +2.51124i q^{19} +(2.71682 + 0.229510i) q^{20} +1.56640 q^{21} +(0.505890 + 0.550428i) q^{22} +2.87303i q^{23} +(-2.23620 + 1.73188i) q^{24} +3.14155 q^{25} +(-2.62470 + 2.41232i) q^{26} +1.00000 q^{27} +(-0.263712 + 3.12169i) q^{28} -7.65326 q^{29} +(1.41947 - 1.30461i) q^{30} +8.15854 q^{31} +(-3.07499 - 4.74810i) q^{32} +0.528628 q^{33} +(5.71831 + 6.22174i) q^{34} -2.13540i q^{35} +(-0.168355 + 1.99290i) q^{36} -7.80230 q^{37} +(-2.61480 + 2.40322i) q^{38} +2.52074i q^{39} +(2.36098 + 3.04849i) q^{40} -11.2829i q^{41} +(1.49903 + 1.63100i) q^{42} +3.82695 q^{43} +(-0.0889972 + 1.05350i) q^{44} -1.36325i q^{45} +(-2.99151 + 2.74945i) q^{46} +3.73630i q^{47} +(-3.94331 - 0.671030i) q^{48} -4.54638 q^{49} +(3.00642 + 3.27111i) q^{50} +5.97533 q^{51} +(-5.02360 - 0.424380i) q^{52} -11.2351i q^{53} +(0.956986 + 1.04124i) q^{54} -0.720652i q^{55} +(-3.50279 + 2.71282i) q^{56} +2.51124i q^{57} +(-7.32406 - 7.96886i) q^{58} +8.44668i q^{59} +(2.71682 + 0.229510i) q^{60} +2.04476i q^{61} +(7.80761 + 8.49498i) q^{62} +1.56640 q^{63} +(2.00117 - 7.74566i) q^{64} +3.43640 q^{65} +(0.505890 + 0.550428i) q^{66} +(-7.97595 - 1.83962i) q^{67} +(-1.00598 + 11.9082i) q^{68} +2.87303i q^{69} +(2.22346 - 2.04354i) q^{70} -4.62331i q^{71} +(-2.23620 + 1.73188i) q^{72} -12.1580 q^{73} +(-7.46669 - 8.12405i) q^{74} +3.14155 q^{75} +(-5.00465 - 0.422780i) q^{76} +0.828045 q^{77} +(-2.62470 + 2.41232i) q^{78} -2.66595 q^{79} +(-0.914781 + 5.37572i) q^{80} +1.00000 q^{81} +(11.7481 - 10.7975i) q^{82} -11.3473i q^{83} +(-0.263712 + 3.12169i) q^{84} -8.14586i q^{85} +(3.66234 + 3.98477i) q^{86} -7.65326 q^{87} +(-1.18212 + 0.915522i) q^{88} +2.96297 q^{89} +(1.41947 - 1.30461i) q^{90} +3.94850i q^{91} +(-5.72567 - 0.483690i) q^{92} +8.15854 q^{93} +(-3.89038 + 3.57559i) q^{94} +3.42344 q^{95} +(-3.07499 - 4.74810i) q^{96} -13.7074i q^{97} +(-4.35083 - 4.73387i) q^{98} +0.528628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.956986	+	1.04124i	0.676691	+	0.736267i
$2$	0.956986	+	1.04124i	0.676691	+	0.736267i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.168355	+	1.99290i	−0.0841775	+	0.996451i
$5$		−	1.36325i		−	0.609663i	−0.952406	−	0.304832i	$-0.901400\pi$
$5$		−	1.36325i		−	0.609663i	0.952406	−	0.304832i	$-0.0986002\pi$
$6$	0.956986	+	1.04124i	0.390688	+	0.425084i
$7$	1.56640			0.592044			0.296022	−	0.955181i	$-0.404340\pi$
$7$	1.56640			0.592044			0.296022	+	0.955181i	$0.404340\pi$
$8$	−2.23620	+	1.73188i	−0.790616	+	0.612313i
$9$	1.00000			0.333333
$10$	1.41947	−	1.30461i	0.448875	−	0.412554i
$11$	0.528628			0.159387			0.0796937	−	0.996819i	$-0.474606\pi$
$11$	0.528628			0.159387			0.0796937	+	0.996819i	$0.474606\pi$
$12$	−0.168355	+	1.99290i	−0.0485999	+	0.575301i
$13$			2.52074i			0.699129i	0.936912	+	0.349564i	$0.113670\pi$
$13$			2.52074i			0.699129i	−0.936912	+	0.349564i	$0.886330\pi$
$14$	1.49903	+	1.63100i	0.400631	+	0.435903i
$15$		−	1.36325i		−	0.351989i
$16$	−3.94331	−	0.671030i	−0.985828	−	0.167757i
$17$	5.97533			1.44923			0.724615	−	0.689154i	$-0.242018\pi$
$17$	5.97533			1.44923			0.724615	+	0.689154i	$0.242018\pi$
$18$	0.956986	+	1.04124i	0.225564	+	0.245422i
$19$			2.51124i			0.576118i	0.957613	+	0.288059i	$0.0930099\pi$
$19$			2.51124i			0.576118i	−0.957613	+	0.288059i	$0.906990\pi$
$20$	2.71682	+	0.229510i	0.607499	+	0.0513199i
$21$	1.56640			0.341817
$22$	0.505890	+	0.550428i	0.107856	+	0.117352i
$23$			2.87303i			0.599069i	0.954085	+	0.299534i	$0.0968314\pi$
$23$			2.87303i			0.599069i	−0.954085	+	0.299534i	$0.903169\pi$
$24$	−2.23620	+	1.73188i	−0.456462	+	0.353519i
$25$	3.14155			0.628311
$26$	−2.62470	+	2.41232i	−0.514745	+	0.473094i
$27$	1.00000			0.192450
$28$	−0.263712	+	3.12169i	−0.0498368	+	0.589943i
$29$	−7.65326			−1.42117			−0.710587	−	0.703609i	$-0.751570\pi$
$29$	−7.65326			−1.42117			−0.710587	+	0.703609i	$0.751570\pi$
$30$	1.41947	−	1.30461i	0.259158	−	0.238188i
$31$	8.15854			1.46532			0.732658	−	0.680597i	$-0.238279\pi$
$31$	8.15854			1.46532			0.732658	+	0.680597i	$0.238279\pi$
$32$	−3.07499	−	4.74810i	−0.543587	−	0.839353i
$33$	0.528628			0.0920224
$34$	5.71831	+	6.22174i	0.980682	+	1.06702i
$35$		−	2.13540i		−	0.360948i
$36$	−0.168355	+	1.99290i	−0.0280592	+	0.332150i
$37$	−7.80230			−1.28269			−0.641345	−	0.767253i	$-0.721623\pi$
$37$	−7.80230			−1.28269			−0.641345	+	0.767253i	$0.721623\pi$
$38$	−2.61480	+	2.40322i	−0.424177	+	0.389854i
$39$			2.52074i			0.403642i
$40$	2.36098	+	3.04849i	0.373304	+	0.482009i
$41$		−	11.2829i		−	1.76209i	−0.473037	−	0.881043i	$-0.656842\pi$
$41$		−	11.2829i		−	1.76209i	0.473037	−	0.881043i	$-0.343158\pi$
$42$	1.49903	+	1.63100i	0.231305	+	0.251668i
$43$	3.82695			0.583605			0.291802	−	0.956479i	$-0.405745\pi$
$43$	3.82695			0.583605			0.291802	+	0.956479i	$0.405745\pi$
$44$	−0.0889972	+	1.05350i	−0.0134168	+	0.158822i
$45$		−	1.36325i		−	0.203221i
$46$	−2.99151	+	2.74945i	−0.441075	+	0.405385i
$47$			3.73630i			0.544995i	0.962156	+	0.272498i	$0.0878497\pi$
$47$			3.73630i			0.544995i	−0.962156	+	0.272498i	$0.912150\pi$
$48$	−3.94331	−	0.671030i	−0.569168	−	0.0968548i
$49$	−4.54638			−0.649483
$50$	3.00642	+	3.27111i	0.425172	+	0.462604i
$51$	5.97533			0.836713
$52$	−5.02360	−	0.424380i	−0.696647	−	0.0588509i
$53$		−	11.2351i		−	1.54326i	−0.636075	−	0.771628i	$-0.719443\pi$
$53$		−	11.2351i		−	1.54326i	0.636075	−	0.771628i	$-0.280557\pi$
$54$	0.956986	+	1.04124i	0.130229	+	0.141695i
$55$		−	0.720652i		−	0.0971727i
$56$	−3.50279	+	2.71282i	−0.468080	+	0.362516i
$57$			2.51124i			0.332622i
$58$	−7.32406	−	7.96886i	−0.961696	−	1.04636i
$59$			8.44668i			1.09966i	0.835275	+	0.549832i	$0.185308\pi$
$59$			8.44668i			1.09966i	−0.835275	+	0.549832i	$0.814692\pi$
$60$	2.71682	+	0.229510i	0.350740	+	0.0296296i
$61$			2.04476i			0.261805i	0.991395	+	0.130902i	$0.0417875\pi$
$61$			2.04476i			0.261805i	−0.991395	+	0.130902i	$0.958213\pi$
$62$	7.80761	+	8.49498i	0.991567	+	1.07886i
$63$	1.56640			0.197348
$64$	2.00117	−	7.74566i	0.250147	−	0.968208i
$65$	3.43640			0.426233
$66$	0.505890	+	0.550428i	0.0622707	+	0.0677530i
$67$	−7.97595	−	1.83962i	−0.974418	−	0.224745i
$67$	−7.97595	−	1.83962i	−0.974418	−	0.224745i
$68$	−1.00598	+	11.9082i	−0.121993	+	1.44409i
$69$			2.87303i			0.345873i
$70$	2.22346	−	2.04354i	0.265754	−	0.244250i
$71$		−	4.62331i		−	0.548686i	−0.961632	−	0.274343i	$-0.911540\pi$
$71$		−	4.62331i		−	0.548686i	0.961632	−	0.274343i	$-0.0884604\pi$
$72$	−2.23620	+	1.73188i	−0.263539	+	0.204104i
$73$	−12.1580			−1.42299			−0.711493	−	0.702694i	$-0.751981\pi$
$73$	−12.1580			−1.42299			−0.711493	+	0.702694i	$0.751981\pi$
$74$	−7.46669	−	8.12405i	−0.867985	−	0.944402i
$75$	3.14155			0.362755
$76$	−5.00465	−	0.422780i	−0.574073	−	0.0484962i
$77$	0.828045			0.0943644
$78$	−2.62470	+	2.41232i	−0.297188	+	0.273141i
$79$	−2.66595			−0.299942			−0.149971	−	0.988690i	$-0.547918\pi$
$79$	−2.66595			−0.299942			−0.149971	+	0.988690i	$0.547918\pi$
$80$	−0.914781	+	5.37572i	−0.102276	+	0.601023i
$81$	1.00000			0.111111
$82$	11.7481	−	10.7975i	1.29737	−	1.19239i
$83$		−	11.3473i		−	1.24553i	−0.782411	−	0.622763i	$-0.786010\pi$
$83$		−	11.3473i		−	1.24553i	0.782411	−	0.622763i	$-0.213990\pi$
$84$	−0.263712	+	3.12169i	−0.0287733	+	0.340604i
$85$		−	8.14586i		−	0.883542i
$86$	3.66234	+	3.98477i	0.394920	+	0.429689i
$87$	−7.65326			−0.820515
$88$	−1.18212	+	0.915522i	−0.126014	+	0.0975949i
$89$	2.96297			0.314075			0.157037	−	0.987593i	$-0.449806\pi$
$89$	2.96297			0.314075			0.157037	+	0.987593i	$0.449806\pi$
$90$	1.41947	−	1.30461i	0.149625	−	0.137518i
$91$			3.94850i			0.413915i
$92$	−5.72567	−	0.483690i	−0.596943	−	0.0504281i
$93$	8.15854			0.846001
$94$	−3.89038	+	3.57559i	−0.401262	+	0.368793i
$95$	3.42344			0.351238
$96$	−3.07499	−	4.74810i	−0.313840	−	0.484600i
$97$		−	13.7074i		−	1.39177i	−0.718152	−	0.695886i	$-0.755012\pi$
$97$		−	13.7074i		−	1.39177i	0.718152	−	0.695886i	$-0.244988\pi$
$98$	−4.35083	−	4.73387i	−0.439500	−	0.478193i
$99$	0.528628			0.0531291
$100$	−0.528896	+	6.26081i	−0.0528896	+	0.626081i
$101$		−	0.747709i		−	0.0743998i	−0.999308	−	0.0371999i	$-0.988156\pi$
$101$		−	0.747709i		−	0.0743998i	0.999308	−	0.0371999i	$-0.0118438\pi$
$102$	5.71831	+	6.22174i	0.566197	+	0.616044i
$103$			6.33839i			0.624540i	0.949993	+	0.312270i	$0.101089\pi$
$103$			6.33839i			0.624540i	−0.949993	+	0.312270i	$0.898911\pi$
$104$	−4.36563	−	5.63689i	−0.428085	−	0.552742i
$105$		−	2.13540i		−	0.208393i
$106$	11.6984	−	10.7518i	1.13625	−	1.04431i
$107$		−	3.47954i		−	0.336380i	−0.985755	−	0.168190i	$-0.946208\pi$
$107$		−	3.47954i		−	0.336380i	0.985755	−	0.168190i	$-0.0537923\pi$
$108$	−0.168355	+	1.99290i	−0.0162000	+	0.191767i
$109$			14.6802i			1.40611i	0.711135	+	0.703055i	$0.248181\pi$
$109$			14.6802i			1.40611i	−0.711135	+	0.703055i	$0.751819\pi$
$110$	0.750370	−	0.689654i	0.0715450	−	0.0657559i
$111$	−7.80230			−0.740562
$112$	−6.17681	−	1.05110i	−0.583654	−	0.0993199i
$113$		−	13.5436i		−	1.27407i	−0.770834	−	0.637036i	$-0.780160\pi$
$113$		−	13.5436i		−	1.27407i	0.770834	−	0.637036i	$-0.219840\pi$
$114$	−2.61480	+	2.40322i	−0.244898	+	0.225082i
$115$	3.91666			0.365230
$116$	1.28846	−	15.2522i	0.119631	−	1.41613i
$117$			2.52074i			0.233043i
$118$	−8.79501	+	8.08335i	−0.809646	+	0.744133i
$119$	9.35977			0.858009
$120$	2.36098	+	3.04849i	0.215527	+	0.278288i
$121$	−10.7206			−0.974596
$122$	−2.12909	+	1.95681i	−0.192758	+	0.177161i
$123$		−	11.2829i		−	1.01734i
$124$	−1.37353	+	16.2592i	−0.123347	+	1.46012i
$125$		−	11.0990i		−	0.992721i
$126$	1.49903	+	1.63100i	0.133544	+	0.145301i
$127$			11.8234i			1.04916i	0.851362	+	0.524578i	$0.175777\pi$
$127$			11.8234i			1.04916i	−0.851362	+	0.524578i	$0.824223\pi$
$128$	9.98018	−	5.32879i	0.882131	−	0.471003i
$129$	3.82695			0.336944
$130$	3.28859	+	3.57811i	0.288428	+	0.313821i
$131$			4.47623i			0.391090i	0.980695	+	0.195545i	$0.0626476\pi$
$131$			4.47623i			0.391090i	−0.980695	+	0.195545i	$0.937352\pi$
$132$	−0.0889972	+	1.05350i	−0.00774621	+	0.0916958i
$133$			3.93361i			0.341087i
$134$	−5.71739	−	10.0654i	−0.493908	−	0.869514i
$135$		−	1.36325i		−	0.117330i
$136$	−13.3620	+	10.3486i	−1.14578	+	0.887382i
$137$		−	3.72743i		−	0.318455i	−0.987242	−	0.159228i	$-0.949100\pi$
$137$		−	3.72743i		−	0.318455i	0.987242	−	0.159228i	$-0.0509004\pi$
$138$	−2.99151	+	2.74945i	−0.254655	+	0.234049i
$139$	9.91407			0.840900			0.420450	−	0.907316i	$-0.361872\pi$
$139$	9.91407			0.840900			0.420450	+	0.907316i	$0.361872\pi$
$140$	4.25563	+	0.359505i	0.359667	+	0.0303837i
$141$			3.73630i			0.314653i
$142$	4.81397	−	4.42445i	0.403979	−	0.371291i
$143$			1.33254i			0.111432i
$144$	−3.94331	−	0.671030i	−0.328609	−	0.0559192i
$145$			10.4333i			0.866437i
$146$	−11.6350	−	12.6594i	−0.962922	−	1.04770i
$147$	−4.54638			−0.374979
$148$	1.31356	−	15.5492i	0.107974	−	1.27814i
$149$	−3.92269			−0.321359			−0.160680	−	0.987007i	$-0.551369\pi$
$149$	−3.92269			−0.321359			−0.160680	+	0.987007i	$0.551369\pi$
$150$	3.00642	+	3.27111i	0.245473	+	0.267085i
$151$		−	23.1961i		−	1.88767i	−0.330412	−	0.943837i	$-0.607188\pi$
$151$		−	23.1961i		−	1.88767i	0.330412	−	0.943837i	$-0.392812\pi$
$152$	−4.34917	−	5.61563i	−0.352764	−	0.455488i
$153$	5.97533			0.483077
$154$	0.792427	+	0.862192i	0.0638556	+	0.0694774i
$155$		−	11.1221i		−	0.893349i
$156$	−5.02360	−	0.424380i	−0.402210	−	0.0339776i
$157$	−1.72814			−0.137921			−0.0689604	−	0.997619i	$-0.521968\pi$
$157$	−1.72814			−0.137921			−0.0689604	+	0.997619i	$0.521968\pi$
$158$	−2.55127	−	2.77589i	−0.202968	−	0.220838i
$159$		−	11.2351i		−	0.890999i
$160$	−6.47283	+	4.19198i	−0.511722	+	0.331405i
$161$			4.50033i			0.354675i
$162$	0.956986	+	1.04124i	0.0751879	+	0.0818074i
$163$			19.0214i			1.48987i	0.667136	+	0.744936i	$0.267520\pi$
$163$			19.0214i			1.48987i	−0.667136	+	0.744936i	$0.732480\pi$
$164$	22.4856	+	1.89952i	1.75583	+	0.148328i
$165$		−	0.720652i		−	0.0561027i
$166$	11.8152	−	10.8592i	0.917039	−	0.842836i
$167$		−	8.38078i		−	0.648524i	−0.945967	−	0.324262i	$-0.894884\pi$
$167$		−	8.38078i		−	0.648524i	0.945967	−	0.324262i	$-0.105116\pi$
$168$	−3.50279	+	2.71282i	−0.270246	+	0.209299i
$169$	6.64585			0.511219
$170$	8.48178	−	7.79547i	0.650523	−	0.597886i
$171$			2.51124i			0.192039i
$172$	−0.644287	+	7.62674i	−0.0491264	+	0.581534i
$173$	−4.16884			−0.316951			−0.158476	−	0.987363i	$-0.550658\pi$
$173$	−4.16884			−0.316951			−0.158476	+	0.987363i	$0.550658\pi$
$174$	−7.32406	−	7.96886i	−0.555235	−	0.604118i
$175$	4.92094			0.371988
$176$	−2.08455	−	0.354725i	−0.157129	−	0.0267384i
$177$			8.44668i			0.634891i
$178$	2.83553	+	3.08516i	0.212532	+	0.231243i
$179$	16.2271			1.21287			0.606436	−	0.795132i	$-0.292599\pi$
$179$	16.2271			1.21287			0.606436	+	0.795132i	$0.292599\pi$
$180$	2.71682	+	0.229510i	0.202500	+	0.0171066i
$181$	−5.93853			−0.441407			−0.220704	−	0.975341i	$-0.570835\pi$
$181$	−5.93853			−0.441407			−0.220704	+	0.975341i	$0.570835\pi$
$182$	−4.11133	+	3.77866i	−0.304752	+	0.280093i
$183$			2.04476i			0.151153i
$184$	−4.97575	−	6.42468i	−0.366817	−	0.473633i
$185$			10.6365i			0.782009i
$186$	7.80761	+	8.49498i	0.572481	+	0.622882i
$187$	3.15873			0.230989
$188$	−7.44607	−	0.629025i	−0.543061	−	0.0458763i
$189$	1.56640			0.113939
$190$	3.27619	+	3.56462i	0.237680	+	0.258605i
$191$	−14.8390			−1.07371			−0.536855	−	0.843675i	$-0.680388\pi$
$191$	−14.8390			−1.07371			−0.536855	+	0.843675i	$0.680388\pi$
$192$	2.00117	−	7.74566i	0.144422	−	0.558995i
$193$	11.3774			0.818967			0.409483	−	0.912318i	$-0.365709\pi$
$193$	11.3774			0.818967			0.409483	+	0.912318i	$0.365709\pi$
$194$	14.2726	−	13.1178i	1.02472	−	0.941800i
$195$	3.43640			0.246086
$196$	0.765407	−	9.06050i	0.0546719	−	0.647178i
$197$			14.0886i			1.00377i	0.864933	+	0.501887i	$0.167361\pi$
$197$			14.0886i			1.00377i	−0.864933	+	0.501887i	$0.832639\pi$
$198$	0.505890	+	0.550428i	0.0359520	+	0.0391172i
$199$		−	10.3476i		−	0.733523i	−0.930315	−	0.366762i	$-0.880466\pi$
$199$		−	10.3476i		−	0.733523i	0.930315	−	0.366762i	$-0.119534\pi$
$200$	−7.02514	+	5.44080i	−0.496752	+	0.384723i
$201$	−7.97595	−	1.83962i	−0.562580	−	0.129757i
$202$	0.778543	−	0.715547i	0.0547781	−	0.0503457i
$203$	−11.9881			−0.841398
$204$	−1.00598	+	11.9082i	−0.0704325	+	0.833744i
$205$	−15.3813			−1.07428
$206$	−6.59977	+	6.06575i	−0.459828	+	0.422621i
$207$			2.87303i			0.199690i
$208$	1.69150	−	9.94009i	0.117284	−	0.689221i
$209$			1.32751i			0.0918260i
$210$	2.22346	−	2.04354i	0.153433	−	0.141018i
$211$			11.9542i			0.822960i	0.911419	+	0.411480i	$0.134988\pi$
$211$			11.9542i			0.822960i	−0.911419	+	0.411480i	$0.865012\pi$
$212$	22.3904	+	1.89148i	1.53778	+	0.129907i
$213$		−	4.62331i		−	0.316784i
$214$	3.62304	−	3.32988i	0.247666	−	0.227626i
$215$		−	5.21709i		−	0.355802i
$216$	−2.23620	+	1.73188i	−0.152154	+	0.117840i
$217$	12.7795			0.867532
$218$	−15.2856	+	14.0488i	−1.03527	+	0.951503i
$219$	−12.1580			−0.821561
$220$	1.43619	+	0.121325i	0.0968278	+	0.00817975i
$221$			15.0623i			1.01320i
$222$	−7.46669	−	8.12405i	−0.501132	−	0.545251i
$223$			20.0207i			1.34069i	0.742052	+	0.670343i	$0.233853\pi$
$223$			20.0207i			1.34069i	−0.742052	+	0.670343i	$0.766147\pi$
$224$	−4.81668	−	7.43743i	−0.321828	−	0.496934i
$225$	3.14155			0.209437
$226$	14.1021	−	12.9610i	0.938057	−	0.862153i
$227$		−	26.1910i		−	1.73836i	−0.494496	−	0.869180i	$-0.664648\pi$
$227$		−	26.1910i		−	1.73836i	0.494496	−	0.869180i	$-0.335352\pi$
$228$	−5.00465	−	0.422780i	−0.331441	−	0.0279993i
$229$			2.35904i			0.155890i	0.996958	+	0.0779448i	$0.0248358\pi$
$229$			2.35904i			0.155890i	−0.996958	+	0.0779448i	$0.975164\pi$
$230$	3.74819	+	4.07818i	0.247148	+	0.268907i
$231$	0.828045			0.0544813
$232$	17.1142	−	13.2545i	1.12360	−	0.870203i
$233$		−	8.87262i		−	0.581264i	−0.956835	−	0.290632i	$-0.906134\pi$
$233$		−	8.87262i		−	0.581264i	0.956835	−	0.290632i	$-0.0938656\pi$
$234$	−2.62470	+	2.41232i	−0.171582	+	0.157698i
$235$	5.09350			0.332263
$236$	−16.8334	−	1.42204i	−1.09576	−	0.0925670i
$237$	−2.66595			−0.173172
$238$	8.95717	+	9.74575i	0.580607	+	0.631723i
$239$	1.14012			0.0737480			0.0368740	−	0.999320i	$-0.488260\pi$
$239$	1.14012			0.0737480			0.0368740	+	0.999320i	$0.488260\pi$
$240$	−0.914781	+	5.37572i	−0.0590488	+	0.347001i
$241$	−5.93089			−0.382042			−0.191021	−	0.981586i	$-0.561180\pi$
$241$	−5.93089			−0.382042			−0.191021	+	0.981586i	$0.561180\pi$
$242$	−10.2594	−	11.1627i	−0.659500	−	0.717562i
$243$	1.00000			0.0641500
$244$	−4.07501	−	0.344246i	−0.260876	−	0.0220381i
$245$			6.19785i			0.395966i
$246$	11.7481	−	10.7975i	0.749034	−	0.688426i
$247$	−6.33020			−0.402781
$248$	−18.2441	+	14.1296i	−1.15850	+	0.897232i
$249$		−	11.3473i		−	0.719104i
$250$	11.5567	−	10.6216i	0.730908	−	0.671766i
$251$	−10.4883			−0.662016			−0.331008	−	0.943628i	$-0.607389\pi$
$251$	−10.4883			−0.662016			−0.331008	+	0.943628i	$0.607389\pi$
$252$	−0.263712	+	3.12169i	−0.0166123	+	0.196648i
$253$			1.51877i			0.0954841i
$254$	−12.3110	+	11.3148i	−0.772459	+	0.709955i
$255$		−	8.14586i		−	0.510113i
$256$	15.0994	+	5.29216i	0.943715	+	0.330760i
$257$	31.3242			1.95395			0.976974	−	0.213357i	$-0.0684397\pi$
$257$	31.3242			1.95395			0.976974	+	0.213357i	$0.0684397\pi$
$258$	3.66234	+	3.98477i	0.228007	+	0.248081i
$259$	−12.2215			−0.759410
$260$	−0.578535	+	6.84841i	−0.0358792	+	0.424720i
$261$	−7.65326			−0.473725
$262$	−4.66083	+	4.28369i	−0.287947	+	0.264647i
$263$			6.28457i			0.387523i	0.981049	+	0.193762i	$0.0620689\pi$
$263$			6.28457i			0.387523i	−0.981049	+	0.193762i	$0.937931\pi$
$264$	−1.18212	+	0.915522i	−0.0727543	+	0.0563465i
$265$	−15.3162			−0.940866
$266$	−4.09583	+	3.76441i	−0.251131	+	0.230811i
$267$	2.96297			0.181331
$268$	5.00897	−	15.5856i	0.305972	−	0.952041i
$269$	−15.0340			−0.916638			−0.458319	−	0.888788i	$-0.651548\pi$
$269$	−15.0340			−0.916638			−0.458319	+	0.888788i	$0.651548\pi$
$270$	1.41947	−	1.30461i	0.0863860	−	0.0793960i
$271$	−18.8437			−1.14468			−0.572338	−	0.820018i	$-0.693963\pi$
$271$	−18.8437			−1.14468			−0.572338	+	0.820018i	$0.693963\pi$
$272$	−23.5626	−	4.00962i	−1.42869	−	0.243119i
$273$			3.94850i			0.238974i
$274$	3.88114	−	3.56709i	0.234468	−	0.215496i
$275$	1.66071			0.100145
$276$	−5.72567	−	0.483690i	−0.344645	−	0.0291147i
$277$	6.93613			0.416752			0.208376	−	0.978049i	$-0.433182\pi$
$277$	6.93613			0.416752			0.208376	+	0.978049i	$0.433182\pi$
$278$	9.48763	+	10.3229i	0.569030	+	0.619127i
$279$	8.15854			0.488439
$280$	3.69825	+	4.77517i	0.221013	+	0.285371i
$281$		−	14.3372i		−	0.855284i	−0.903948	−	0.427642i	$-0.859344\pi$
$281$		−	14.3372i		−	0.855284i	0.903948	−	0.427642i	$-0.140656\pi$
$282$	−3.89038	+	3.57559i	−0.231669	+	0.212923i
$283$			15.1828i			0.902524i	0.892392	+	0.451262i	$0.149026\pi$
$283$			15.1828i			0.902524i	−0.892392	+	0.451262i	$0.850974\pi$
$284$	9.21381	+	0.778358i	0.546739	+	0.0461870i
$285$	3.42344			0.202787
$286$	−1.38749	+	1.27522i	−0.0820439	+	0.0754053i
$287$		−	17.6735i		−	1.04323i
$288$	−3.07499	−	4.74810i	−0.181196	−	0.279784i
$289$	18.7046			1.10027
$290$	−10.8635	+	9.98451i	−0.637929	+	0.586311i
$291$		−	13.7074i		−	0.803540i
$292$	2.04686	−	24.2297i	0.119783	−	1.41793i
$293$	18.5571			1.08412			0.542060	−	0.840340i	$-0.317645\pi$
$293$	18.5571			1.08412			0.542060	+	0.840340i	$0.317645\pi$
$294$	−4.35083	−	4.73387i	−0.253745	−	0.276085i
$295$	11.5149			0.670425
$296$	17.4475	−	13.5127i	1.01412	−	0.785407i
$297$	0.528628			0.0306741
$298$	−3.75396	−	4.08445i	−0.217461	−	0.236606i
$299$	−7.24219			−0.418826
$300$	−0.528896	+	6.26081i	−0.0305358	+	0.361468i
$301$	5.99455			0.345520
$302$	24.1527	−	22.1984i	1.38983	−	1.27737i
$303$		−	0.747709i		−	0.0429547i
$304$	1.68512	−	9.90261i	0.0966481	−	0.567953i
$305$	2.78752			0.159613
$306$	5.71831	+	6.22174i	0.326894	+	0.355673i
$307$		−	9.16937i		−	0.523324i	−0.965160	−	0.261662i	$-0.915729\pi$
$307$		−	9.16937i		−	0.523324i	0.965160	−	0.261662i	$-0.0842705\pi$
$308$	−0.139405	+	1.65021i	−0.00794336	+	0.0940295i
$309$			6.33839i			0.360578i
$310$	11.5808	−	10.6437i	0.657744	−	0.604522i
$311$	0.305968			0.0173499			0.00867493	−	0.999962i	$-0.497239\pi$
$311$	0.305968			0.0173499			0.00867493	+	0.999962i	$0.497239\pi$
$312$	−4.36563	−	5.63689i	−0.247155	−	0.319126i
$313$		−	4.08597i		−	0.230952i	−0.993310	−	0.115476i	$-0.963161\pi$
$313$		−	4.08597i		−	0.230952i	0.993310	−	0.115476i	$-0.0368394\pi$
$314$	−1.65381	−	1.79941i	−0.0933298	−	0.101546i
$315$		−	2.13540i		−	0.120316i
$316$	0.448825	−	5.31297i	0.0252484	−	0.298878i
$317$	−12.1082			−0.680064			−0.340032	−	0.940414i	$-0.610438\pi$
$317$	−12.1082			−0.680064			−0.340032	+	0.940414i	$0.610438\pi$
$318$	11.6984	−	10.7518i	0.656013	−	0.602931i
$319$	−4.04573			−0.226517
$320$	−10.5593	−	2.72810i	−0.590281	−	0.152505i
$321$		−	3.47954i		−	0.194209i
$322$	−4.68591	+	4.30675i	−0.261136	+	0.240006i
$323$			15.0055i			0.834928i
$324$	−0.168355	+	1.99290i	−0.00935306	+	0.110717i
$325$			7.91906i			0.439270i
$326$	−19.8058	+	18.2032i	−1.09694	+	1.00818i
$327$			14.6802i			0.811818i
$328$	19.5406	+	25.2307i	1.07895	+	1.39313i
$329$			5.85255i			0.322661i
$330$	0.750370	−	0.689654i	0.0413065	−	0.0379642i
$331$	34.6082			1.90224			0.951120	−	0.308821i	$-0.0999345\pi$
$331$	34.6082			1.90224			0.951120	+	0.308821i	$0.0999345\pi$
$332$	22.6140	+	1.91037i	1.24110	+	0.104845i
$333$	−7.80230			−0.427563
$334$	8.72639	−	8.02029i	0.477487	−	0.438851i
$335$	−2.50786	+	10.8732i	−0.137019	+	0.594067i
$336$	−6.17681	−	1.05110i	−0.336973	−	0.0573424i
$337$			14.8377i			0.808261i	0.914701	+	0.404130i	$0.132426\pi$
$337$			14.8377i			0.808261i	−0.914701	+	0.404130i	$0.867574\pi$
$338$	6.35998	+	6.91991i	0.345937	+	0.376393i
$339$		−	13.5436i		−	0.735586i
$340$	16.2339	+	1.37140i	0.880407	+	0.0743744i
$341$	4.31283			0.233553
$342$	−2.61480	+	2.40322i	−0.141392	+	0.129951i
$343$	−18.0863			−0.976567
$344$	−8.55783	+	6.62783i	−0.461407	+	0.357349i
$345$	3.91666			0.210866
$346$	−3.98953	−	4.34076i	−0.214478	−	0.233361i
$347$	−20.5055			−1.10079			−0.550396	−	0.834904i	$-0.685523\pi$
$347$	−20.5055			−1.10079			−0.550396	+	0.834904i	$0.685523\pi$
$348$	1.28846	−	15.2522i	0.0690689	−	0.817603i
$349$	−13.8409			−0.740885			−0.370443	−	0.928855i	$-0.620794\pi$
$349$	−13.8409			−0.740885			−0.370443	+	0.928855i	$0.620794\pi$
$350$	4.70927	+	5.12387i	0.251721	+	0.273882i
$351$			2.52074i			0.134547i
$352$	−1.62553	−	2.50998i	−0.0866410	−	0.133782i
$353$			34.4969i			1.83608i	0.396483	+	0.918042i	$0.370231\pi$
$353$			34.4969i			1.83608i	−0.396483	+	0.918042i	$0.629769\pi$
$354$	−8.79501	+	8.08335i	−0.467449	+	0.429625i
$355$	−6.30272			−0.334514
$356$	−0.498832	+	5.90492i	−0.0264380	+	0.312960i
$357$	9.35977			0.495372
$358$	15.5291	+	16.8963i	0.820740	+	0.892998i
$359$			19.8390i			1.04706i	0.852007	+	0.523531i	$0.175386\pi$
$359$			19.8390i			1.04706i	−0.852007	+	0.523531i	$0.824614\pi$
$360$	2.36098	+	3.04849i	0.124435	+	0.160670i
$361$	12.6937			0.668088
$362$	−5.68309	−	6.18342i	−0.298696	−	0.324993i
$363$	−10.7206			−0.562683
$364$	−7.86897	−	0.664750i	−0.412446	−	0.0348424i
$365$			16.5744i			0.867542i
$366$	−2.12909	+	1.95681i	−0.111289	+	0.102284i
$367$	−30.4913			−1.59163			−0.795815	−	0.605540i	$-0.792957\pi$
$367$	−30.4913			−1.59163			−0.795815	+	0.605540i	$0.792957\pi$
$368$	1.92789	−	11.3293i	0.100498	−	0.590579i
$369$		−	11.2829i		−	0.587362i
$370$	−11.0751	+	10.1790i	−0.575767	+	0.529179i
$371$		−	17.5986i		−	0.913675i
$372$	−1.37353	+	16.2592i	−0.0712142	+	0.842998i
$373$		−	13.4697i		−	0.697436i	−0.937228	−	0.348718i	$-0.886617\pi$
$373$		−	13.4697i		−	0.697436i	0.937228	−	0.348718i	$-0.113383\pi$
$374$	3.02286	+	3.28899i	0.156308	+	0.170070i
$375$		−	11.0990i		−	0.573148i
$376$	−6.47083	−	8.35511i	−0.333707	−	0.430882i
$377$		−	19.2919i		−	0.993584i
$378$	1.49903	+	1.63100i	0.0771015	+	0.0838895i
$379$	0.700479			0.0359812			0.0179906	−	0.999838i	$-0.494273\pi$
$379$	0.700479			0.0359812			0.0179906	+	0.999838i	$0.494273\pi$
$380$	−0.576354	+	6.82259i	−0.0295663	+	0.349991i
$381$			11.8234i			0.605730i
$382$	−14.2007	−	15.4509i	−0.726570	−	0.790537i
$383$	−20.8295			−1.06434			−0.532170	−	0.846638i	$-0.678623\pi$
$383$	−20.8295			−1.06434			−0.532170	+	0.846638i	$0.678623\pi$
$384$	9.98018	−	5.32879i	0.509299	−	0.271934i
$385$		−	1.12883i		−	0.0575305i
$386$	10.8881	+	11.8466i	0.554188	+	0.602978i
$387$	3.82695			0.194535
$388$	27.3174	+	2.30770i	1.38683	+	0.117156i
$389$	−13.9967			−0.709661			−0.354830	−	0.934931i	$-0.615461\pi$
$389$	−13.9967			−0.709661			−0.354830	+	0.934931i	$0.615461\pi$
$390$	3.28859	+	3.57811i	0.166524	+	0.181185i
$391$			17.1673i			0.868189i
$392$	10.1666	−	7.87380i	0.513492	−	0.397687i
$393$			4.47623i			0.225796i
$394$	−14.6696	+	13.4826i	−0.739046	+	0.679245i
$395$			3.63435i			0.182864i
$396$	−0.0889972	+	1.05350i	−0.00447228	+	0.0529406i
$397$	−0.391387			−0.0196431			−0.00982157	−	0.999952i	$-0.503126\pi$
$397$	−0.391387			−0.0196431			−0.00982157	+	0.999952i	$0.503126\pi$
$398$	10.7743	−	9.90253i	0.540069	−	0.496369i
$399$			3.93361i			0.196927i
$400$	−12.3881	−	2.10808i	−0.619407	−	0.105404i
$401$			13.7484i			0.686561i	0.939233	+	0.343281i	$0.111538\pi$
$401$			13.7484i			0.686561i	−0.939233	+	0.343281i	$0.888462\pi$
$402$	−5.71739	−	10.0654i	−0.285158	−	0.502014i
$403$			20.5656i			1.02444i
$404$	1.49011	+	0.125881i	0.0741357	+	0.00626279i
$405$		−	1.36325i		−	0.0677404i
$406$	−11.4724	−	12.4824i	−0.569367	−	0.619493i
$407$	−4.12452			−0.204445
$408$	−13.3620	+	10.3486i	−0.661519	+	0.512330i
$409$			19.5659i			0.967469i	0.875215	+	0.483735i	$0.160720\pi$
$409$			19.5659i			0.967469i	−0.875215	+	0.483735i	$0.839280\pi$
$410$	−14.7197	−	16.0156i	−0.726955	−	0.790956i
$411$		−	3.72743i		−	0.183860i
$412$	−12.6318	−	1.06710i	−0.622323	−	0.0525722i
$413$			13.2309i			0.651050i
$414$	−2.99151	+	2.74945i	−0.147025	+	0.135128i
$415$	−15.4692			−0.759351
$416$	11.9687	−	7.75127i	0.586816	−	0.380038i
$417$	9.91407			0.485494
$418$	−1.38226	+	1.27041i	−0.0676084	+	0.0621378i
$419$			30.3583i			1.48310i	0.670896	+	0.741551i	$0.265910\pi$
$419$			30.3583i			1.48310i	−0.670896	+	0.741551i	$0.734090\pi$
$420$	4.25563	+	0.359505i	0.207654	+	0.0175420i
$421$	−8.09140			−0.394351			−0.197175	−	0.980368i	$-0.563177\pi$
$421$	−8.09140			−0.394351			−0.197175	+	0.980368i	$0.563177\pi$
$422$	−12.4472	+	11.4400i	−0.605918	+	0.556890i
$423$			3.73630i			0.181665i
$424$	19.4578	+	25.1238i	0.944954	+	1.22012i
$425$	18.7718			0.910567
$426$	4.81397	−	4.42445i	0.233238	−	0.214365i
$427$			3.20292i			0.155000i
$428$	6.93439	+	0.585799i	0.335186	+	0.0283156i
$429$			1.33254i			0.0643355i
$430$	5.43223	−	4.99268i	0.261965	−	0.240768i
$431$			21.3247i			1.02717i	0.858037	+	0.513587i	$0.171684\pi$
$431$			21.3247i			1.02717i	−0.858037	+	0.513587i	$0.828316\pi$
$432$	−3.94331	−	0.671030i	−0.189723	−	0.0322849i
$433$			10.3106i			0.495494i	0.968825	+	0.247747i	$0.0796901\pi$
$433$			10.3106i			0.495494i	−0.968825	+	0.247747i	$0.920310\pi$
$434$	12.2299	+	13.3066i	0.587052	+	0.638735i
$435$			10.4333i			0.500238i
$436$	−29.2562	−	2.47149i	−1.40112	−	0.118363i
$437$	−7.21488			−0.345134
$438$	−11.6350	−	12.6594i	−0.555943	−	0.604888i
$439$			35.7951i			1.70840i	0.519941	+	0.854202i	$0.325954\pi$
$439$			35.7951i			1.70840i	−0.519941	+	0.854202i	$0.674046\pi$
$440$	1.24808	+	1.61152i	0.0595000	+	0.0768262i
$441$	−4.54638			−0.216494
$442$	−15.6834	+	14.4144i	−0.745984	+	0.685623i
$443$	9.33817			0.443670			0.221835	−	0.975084i	$-0.428795\pi$
$443$	9.33817			0.443670			0.221835	+	0.975084i	$0.428795\pi$
$444$	1.31356	−	15.5492i	0.0623386	−	0.737933i
$445$		−	4.03927i		−	0.191480i
$446$	−20.8463	+	19.1595i	−0.987102	+	0.907230i
$447$	−3.92269			−0.185537
$448$	3.13464	−	12.1328i	0.148098	−	0.573222i
$449$	−6.33662			−0.299044			−0.149522	−	0.988758i	$-0.547773\pi$
$449$	−6.33662			−0.299044			−0.149522	+	0.988758i	$0.547773\pi$
$450$	3.00642	+	3.27111i	0.141724	+	0.154201i
$451$		−	5.96444i		−	0.280854i
$452$	26.9910	+	2.28013i	1.26955	+	0.107248i
$453$		−	23.1961i		−	1.08985i
$454$	27.2711	−	25.0644i	1.27990	−	1.17633i
$455$	5.38279			0.252349
$456$	−4.34917	−	5.61563i	−0.203669	−	0.262976i
$457$	2.11160			0.0987765			0.0493883	−	0.998780i	$-0.484273\pi$
$457$	2.11160			0.0987765			0.0493883	+	0.998780i	$0.484273\pi$
$458$	−2.45632	+	2.25757i	−0.114776	+	0.105489i
$459$	5.97533			0.278904
$460$	−0.659389	+	7.80552i	−0.0307442	+	0.363934i
$461$	16.4701			0.767087			0.383544	−	0.923523i	$-0.374704\pi$
$461$	16.4701			0.767087			0.383544	+	0.923523i	$0.374704\pi$
$462$	0.792427	+	0.862192i	0.0368670	+	0.0401128i
$463$	3.43056			0.159432			0.0797158	−	0.996818i	$-0.474599\pi$
$463$	3.43056			0.159432			0.0797158	+	0.996818i	$0.474599\pi$
$464$	30.1792	+	5.13556i	1.40103	+	0.238413i
$465$		−	11.1221i		−	0.515776i
$466$	9.23851	−	8.49097i	0.427966	−	0.393337i
$467$			3.69099i			0.170798i	0.996347	+	0.0853992i	$0.0272166\pi$
$467$			3.69099i			0.170798i	−0.996347	+	0.0853992i	$0.972783\pi$
$468$	−5.02360	−	0.424380i	−0.232216	−	0.0196170i
$469$	−12.4935	−	2.88158i	−0.576898	−	0.133059i
$470$	4.87441	+	5.30355i	0.224840	+	0.244635i
$471$	−1.72814			−0.0796286
$472$	−14.6286	−	18.8885i	−0.673338	−	0.869412i
$473$	2.02304			0.0930193
$474$	−2.55127	−	2.77589i	−0.117184	−	0.127501i
$475$			7.88920i			0.361981i
$476$	−1.57576	+	18.6531i	−0.0722250	+	0.854963i
$477$		−	11.2351i		−	0.514418i
$478$	1.09108	+	1.18713i	0.0499047	+	0.0542982i
$479$		−	21.8923i		−	1.00028i	−0.865943	−	0.500142i	$-0.833281\pi$
$479$		−	21.8923i		−	1.00028i	0.865943	−	0.500142i	$-0.166719\pi$
$480$	−6.47283	+	4.19198i	−0.295443	+	0.191337i
$481$		−	19.6676i		−	0.896766i
$482$	−5.67578	−	6.17547i	−0.258525	−	0.281285i
$483$			4.50033i			0.204772i
$484$	1.80486	−	21.3650i	0.0820390	−	0.971137i
$485$	−18.6865			−0.848512
$486$	0.956986	+	1.04124i	0.0434098	+	0.0472315i
$487$	11.7289			0.531488			0.265744	−	0.964044i	$-0.414382\pi$
$487$	11.7289			0.531488			0.265744	+	0.964044i	$0.414382\pi$
$488$	−3.54129	−	4.57250i	−0.160306	−	0.206987i
$489$			19.0214i			0.860178i
$490$	−6.45344	+	5.93126i	−0.291537	+	0.267947i
$491$			8.85707i			0.399714i	0.979825	+	0.199857i	$0.0640478\pi$
$491$			8.85707i			0.399714i	−0.979825	+	0.199857i	$0.935952\pi$
$492$	22.4856	+	1.89952i	1.01373	+	0.0856372i
$493$	−45.7307			−2.05961
$494$	−6.05791	−	6.59124i	−0.272558	−	0.296554i
$495$		−	0.720652i		−	0.0323909i
$496$	−32.1717	−	5.47462i	−1.44455	−	0.245818i
$497$		−	7.24197i		−	0.324847i
$498$	11.8152	−	10.8592i	0.529453	−	0.486612i
$499$	21.7924			0.975561			0.487781	−	0.872966i	$-0.337807\pi$
$499$	21.7924			0.975561			0.487781	+	0.872966i	$0.337807\pi$
$500$	22.1191	+	1.86857i	0.989198	+	0.0835648i
$501$		−	8.38078i		−	0.374426i
$502$	−10.0372	−	10.9208i	−0.447981	−	0.487421i
$503$	11.4232			0.509334			0.254667	−	0.967029i	$-0.418034\pi$
$503$	11.4232			0.509334			0.254667	+	0.967029i	$0.418034\pi$
$504$	−3.50279	+	2.71282i	−0.156027	+	0.120839i
$505$	−1.01931			−0.0453588
$506$	−1.58140	+	1.45344i	−0.0703017	+	0.0646132i
$507$	6.64585			0.295152
$508$	−23.5628	−	1.99053i	−1.04543	−	0.0883153i
$509$	−2.75233			−0.121995			−0.0609974	−	0.998138i	$-0.519428\pi$
$509$	−2.75233			−0.121995			−0.0609974	+	0.998138i	$0.519428\pi$
$510$	8.48178	−	7.79547i	0.375580	−	0.345189i
$511$	−19.0443			−0.842470
$512$	8.93955	+	20.7866i	0.395076	+	0.918648i
$513$			2.51124i			0.110874i
$514$	29.9768	+	32.6159i	1.32222	+	1.43863i
$515$	8.64079			0.380759
$516$	−0.644287	+	7.62674i	−0.0283631	+	0.335749i
$517$			1.97511i			0.0868654i
$518$	−11.6958	−	12.7255i	−0.513886	−	0.559128i
$519$	−4.16884			−0.182992
$520$	−7.68448	+	5.95144i	−0.336987	+	0.260988i
$521$			23.2054i			1.01665i	0.861166	+	0.508324i	$0.169735\pi$
$521$			23.2054i			1.01665i	−0.861166	+	0.508324i	$0.830265\pi$
$522$	−7.32406	−	7.96886i	−0.320565	−	0.348788i
$523$			3.30778i			0.144639i	0.997382	+	0.0723196i	$0.0230402\pi$
$523$			3.30778i			0.144639i	−0.997382	+	0.0723196i	$0.976960\pi$
$524$	−8.92069	−	0.753596i	−0.389702	−	0.0329210i
$525$	4.92094			0.214767
$526$	−6.54374	+	6.01425i	−0.285321	+	0.262234i
$527$	48.7499			2.12358
$528$	−2.08455	−	0.354725i	−0.0907183	−	0.0154374i
$529$	14.7457			0.641116
$530$	−14.6574	−	15.9478i	−0.636676	−	0.692728i
$531$			8.44668i			0.366555i
$532$	−7.83930	−	0.662243i	−0.339877	−	0.0287119i
$533$	28.4412			1.23192
$534$	2.83553	+	3.08516i	0.122705	+	0.133508i
$535$	−4.74348			−0.205079
$536$	21.0218	−	9.69965i	0.908004	−	0.418961i
$537$	16.2271			0.700252
$538$	−14.3873	−	15.6540i	−0.620281	−	0.674890i
$539$	−2.40335			−0.103519
$540$	2.71682	+	0.229510i	0.116913	+	0.00987653i
$541$		−	12.1689i		−	0.523183i	−0.965179	−	0.261592i	$-0.915753\pi$
$541$		−	12.1689i		−	0.523183i	0.965179	−	0.261592i	$-0.0842474\pi$
$542$	−18.0332	−	19.6208i	−0.774592	−	0.842787i
$543$	−5.93853			−0.254847
$544$	−18.3741	−	28.3714i	−0.787783	−	1.21642i
$545$	20.0128			0.857254
$546$	−4.11133	+	3.77866i	−0.175949	+	0.161712i
$547$	15.3448			0.656096			0.328048	−	0.944661i	$-0.393609\pi$
$547$	15.3448			0.656096			0.328048	+	0.944661i	$0.393609\pi$
$548$	7.42839	+	0.627531i	0.317325	+	0.0268068i
$549$			2.04476i			0.0872683i
$550$	1.58928	+	1.72920i	0.0677671	+	0.0737333i
$551$		−	19.2192i		−	0.818764i
$552$	−4.97575	−	6.42468i	−0.211782	−	0.273452i
$553$	−4.17594			−0.177579
$554$	6.63778	+	7.22216i	0.282012	+	0.306840i
$555$			10.6365i			0.451493i
$556$	−1.66908	+	19.7578i	−0.0707849	+	0.837916i
$557$	−22.2115			−0.941132			−0.470566	−	0.882365i	$-0.655950\pi$
$557$	−22.2115			−0.941132			−0.470566	+	0.882365i	$0.655950\pi$
$558$	7.80761	+	8.49498i	0.330522	+	0.359621i
$559$			9.64677i			0.408015i
$560$	−1.43291	+	8.42053i	−0.0605517	+	0.355832i
$561$	3.15873			0.133362
$562$	14.9284	−	13.7205i	0.629718	−	0.578764i
$563$	−46.6259			−1.96505			−0.982523	−	0.186143i	$-0.940401\pi$
$563$	−46.6259			−1.96505			−0.982523	+	0.186143i	$0.940401\pi$
$564$	−7.44607	−	0.629025i	−0.313536	−	0.0264867i
$565$	−18.4633			−0.776755
$566$	−15.8089	+	14.5297i	−0.664498	+	0.610730i
$567$	1.56640			0.0657827
$568$	8.00703	+	10.3386i	0.335967	+	0.433800i
$569$	13.3971			0.561637			0.280819	−	0.959761i	$-0.409394\pi$
$569$	13.3971			0.561637			0.280819	+	0.959761i	$0.409394\pi$
$570$	3.27619	+	3.56462i	0.137224	+	0.149306i
$571$		−	22.6544i		−	0.948059i	−0.880509	−	0.474029i	$-0.842799\pi$
$571$		−	22.6544i		−	0.948059i	0.880509	−	0.474029i	$-0.157201\pi$
$572$	−2.65562	−	0.224339i	−0.111037	−	0.00938010i
$573$	−14.8390			−0.619907
$574$	18.4023	−	16.9133i	0.768098	−	0.705947i
$575$			9.02579i			0.376401i
$576$	2.00117	−	7.74566i	0.0833822	−	0.322736i
$577$			28.6399i			1.19229i	0.802875	+	0.596147i	$0.203302\pi$
$577$			28.6399i			1.19229i	−0.802875	+	0.596147i	$0.796698\pi$
$578$	17.9000	+	19.4759i	0.744542	+	0.810091i
$579$	11.3774			0.472831
$580$	−20.7925	−	1.75650i	−0.863362	−	0.0729345i
$581$		−	17.7744i		−	0.737406i
$582$	14.2726	−	13.1178i	0.591620	−	0.543749i
$583$		−	5.93917i		−	0.245975i
$584$	27.1877	−	21.0562i	1.12503	−	0.871312i
$585$	3.43640			0.142078
$586$	17.7589	+	19.3224i	0.733614	+	0.798201i
$587$	−46.9051			−1.93598			−0.967990	−	0.250988i	$-0.919244\pi$
$587$	−46.9051			−1.93598			−0.967990	+	0.250988i	$0.919244\pi$
$588$	0.765407	−	9.06050i	0.0315648	−	0.373649i
$589$			20.4880i			0.844195i
$590$	11.0196	+	11.9898i	0.453671	+	0.493611i
$591$			14.0886i			0.579529i
$592$	30.7669	+	5.23558i	1.26451	+	0.215181i
$593$			32.0451i			1.31594i	0.753046	+	0.657968i	$0.228584\pi$
$593$			32.0451i			1.31594i	−0.753046	+	0.657968i	$0.771416\pi$
$594$	0.505890	+	0.550428i	0.0207569	+	0.0225843i
$595$		−	12.7597i		−	0.523096i
$596$	0.660404	−	7.81753i	0.0270512	−	0.320218i
$597$		−	10.3476i		−	0.423500i
$598$	−6.93067	−	7.54084i	−0.283416	−	0.308368i
$599$	30.2463			1.23583			0.617915	−	0.786245i	$-0.287978\pi$
$599$	30.2463			1.23583			0.617915	+	0.786245i	$0.287978\pi$
$600$	−7.02514	+	5.44080i	−0.286800	+	0.222120i
$601$	14.4069			0.587670			0.293835	−	0.955856i	$-0.405068\pi$
$601$	14.4069			0.587670			0.293835	+	0.955856i	$0.405068\pi$
$602$	5.73670	+	6.24175i	0.233810	+	0.254395i
$603$	−7.97595	−	1.83962i	−0.324806	−	0.0749151i
$604$	46.2276	+	3.90518i	1.88097	+	0.158900i
$605$			14.6148i			0.594175i
$606$	0.778543	−	0.715547i	0.0316262	−	0.0290671i
$607$		−	28.9051i		−	1.17322i	−0.809869	−	0.586611i	$-0.800462\pi$
$607$		−	28.9051i		−	1.17322i	0.809869	−	0.586611i	$-0.199538\pi$
$608$	11.9236	−	7.72205i	0.483566	−	0.313170i
$609$	−11.9881			−0.485781
$610$	2.66762	+	2.90247i	0.108009	+	0.117518i
$611$	−9.41825			−0.381022
$612$	−1.00598	+	11.9082i	−0.0406642	+	0.481362i
$613$	13.7771			0.556450			0.278225	−	0.960516i	$-0.410254\pi$
$613$	13.7771			0.556450			0.278225	+	0.960516i	$0.410254\pi$
$614$	9.54750	−	8.77496i	0.385306	−	0.354129i
$615$	−15.3813			−0.620235
$616$	−1.85167	+	1.43407i	−0.0746060	+	0.0577805i
$617$	27.5346			1.10850			0.554251	−	0.832349i	$-0.313005\pi$
$617$	27.5346			1.10850			0.554251	+	0.832349i	$0.313005\pi$
$618$	−6.59977	+	6.06575i	−0.265482	+	0.244000i
$619$		−	23.0359i		−	0.925891i	−0.886387	−	0.462945i	$-0.846793\pi$
$619$		−	23.0359i		−	0.925891i	0.886387	−	0.462945i	$-0.153207\pi$
$620$	22.1653	+	1.87246i	0.890179	+	0.0751999i
$621$			2.87303i			0.115291i
$622$	0.292807	+	0.318586i	0.0117405	+	0.0127741i
$623$	4.64121			0.185946
$624$	1.69150	−	9.94009i	0.0677140	−	0.397922i
$625$	0.577128			0.0230851
$626$	4.25447	−	3.91021i	0.170043	−	0.156284i
$627$			1.32751i			0.0530157i
$628$	0.290941	−	3.44402i	0.0116098	−	0.137431i
$629$	−46.6213			−1.85891
$630$	2.22346	−	2.04354i	0.0885846	−	0.0814167i
$631$	48.1322			1.91611			0.958055	−	0.286583i	$-0.0925193\pi$
$631$	48.1322			1.91611			0.958055	+	0.286583i	$0.0925193\pi$
$632$	5.96159	−	4.61710i	0.237139	−	0.183659i
$633$			11.9542i			0.475136i
$634$	−11.5874	−	12.6075i	−0.460193	−	0.500708i
$635$	16.1182			0.639632
$636$	22.3904	+	1.89148i	0.887836	+	0.0750020i
$637$		−	11.4603i		−	0.454073i
$638$	−3.87170	−	4.21257i	−0.153282	−	0.166777i
$639$		−	4.62331i		−	0.182895i
$640$	−7.26447	−	13.6055i	−0.287153	−	0.537803i
$641$		−	40.2935i		−	1.59150i	−0.605628	−	0.795748i	$-0.707078\pi$
$641$		−	40.2935i		−	1.59150i	0.605628	−	0.795748i	$-0.292922\pi$
$642$	3.62304	−	3.32988i	0.142990	−	0.131420i
$643$		−	0.501719i		−	0.0197859i	−0.999951	−	0.00989294i	$-0.996851\pi$
$643$		−	0.501719i		−	0.0197859i	0.999951	−	0.00989294i	$-0.00314907\pi$
$644$	−8.96871	−	0.757653i	−0.353417	−	0.0298557i
$645$		−	5.21709i		−	0.205423i
$646$	−15.6243	+	14.3600i	−0.614729	+	0.564988i
$647$	33.5887			1.32051			0.660253	−	0.751043i	$-0.270449\pi$
$647$	33.5887			1.32051			0.660253	+	0.751043i	$0.270449\pi$
$648$	−2.23620	+	1.73188i	−0.0878462	+	0.0680347i
$649$			4.46515i			0.175273i
$650$	−8.24562	+	7.57843i	−0.323420	+	0.297250i
$651$	12.7795			0.500870
$652$	−37.9078	−	3.20235i	−1.48458	−	0.125414i
$653$		−	16.6382i		−	0.651104i	−0.945524	−	0.325552i	$-0.894450\pi$
$653$		−	16.6382i		−	0.651104i	0.945524	−	0.325552i	$-0.105550\pi$
$654$	−15.2856	+	14.0488i	−0.597715	+	0.549350i
$655$	6.10222			0.238433
$656$	−7.57113	+	44.4918i	−0.295603	+	1.73711i
$657$	−12.1580			−0.474328
$658$	−6.09390	+	5.60080i	−0.237565	+	0.218342i
$659$			19.4030i			0.755835i	0.925839	+	0.377917i	$0.123360\pi$
$659$			19.4030i			0.755835i	−0.925839	+	0.377917i	$0.876640\pi$
$660$	1.43619	+	0.121325i	0.0559035	+	0.00472258i
$661$		−	12.7137i		−	0.494505i	−0.968951	−	0.247252i	$-0.920472\pi$
$661$		−	12.7137i		−	0.494505i	0.968951	−	0.247252i	$-0.0795277\pi$
$662$	33.1196	+	36.0354i	1.28723	+	1.40056i
$663$			15.0623i			0.584971i
$664$	19.6521	+	25.3748i	0.762651	+	0.984732i
$665$	5.36249			0.207948
$666$	−7.46669	−	8.12405i	−0.289328	−	0.314801i
$667$		−	21.9881i		−	0.851381i
$668$	16.7021	+	1.41095i	0.646223	+	0.0545912i
$669$			20.0207i			0.774045i
$670$	−13.7216	+	7.79423i	−0.530111	+	0.301117i
$671$			1.08092i			0.0417284i
$672$	−4.81668	−	7.43743i	−0.185807	−	0.286905i
$673$		−	49.2662i		−	1.89907i	−0.313660	−	0.949535i	$-0.601555\pi$
$673$		−	49.2662i		−	1.89907i	0.313660	−	0.949535i	$-0.398445\pi$
$674$	−15.4496	+	14.1995i	−0.595096	+	0.546943i
$675$	3.14155			0.120918
$676$	−1.11886	+	13.2445i	−0.0430331	+	0.509404i
$677$			5.46737i			0.210128i	0.994465	+	0.105064i	$0.0335048\pi$
$677$			5.46737i			0.210128i	−0.994465	+	0.105064i	$0.966495\pi$
$678$	14.1021	−	12.9610i	0.541587	−	0.497765i
$679$		−	21.4712i		−	0.823991i
$680$	14.1077	+	18.2158i	0.541004	+	0.698543i
$681$		−	26.1910i		−	1.00364i
$682$	4.12732	+	4.49069i	0.158043	+	0.171957i
$683$	27.5247			1.05320			0.526601	−	0.850112i	$-0.323466\pi$
$683$	27.5247			1.05320			0.526601	+	0.850112i	$0.323466\pi$
$684$	−5.00465	−	0.422780i	−0.191358	−	0.0161654i
$685$	−5.08141			−0.194151
$686$	−17.3083	−	18.8321i	−0.660835	−	0.719014i
$687$			2.35904i			0.0900029i
$688$	−15.0909	−	2.56800i	−0.575334	−	0.0979041i
$689$	28.3207			1.07893
$690$	3.74819	+	4.07818i	0.142691	+	0.155254i
$691$		−	42.9779i		−	1.63496i	−0.575960	−	0.817478i	$-0.695372\pi$
$691$		−	42.9779i		−	1.63496i	0.575960	−	0.817478i	$-0.304628\pi$
$692$	0.701846	−	8.30810i	0.0266802	−	0.315826i
$693$	0.828045			0.0314548
$694$	−19.6235	−	21.3511i	−0.744896	−	0.810476i
$695$		−	13.5153i		−	0.512666i
$696$	17.1142	−	13.2545i	0.648712	−	0.502412i
$697$		−	67.4188i		−	2.55367i
$698$	−13.2455	−	14.4117i	−0.501351	−	0.545489i
$699$		−	8.87262i		−	0.335593i
$700$	−0.828464	+	9.80694i	−0.0313130	+	0.370668i
$701$			21.8416i			0.824947i	0.910970	+	0.412473i	$0.135335\pi$
$701$			21.8416i			0.824947i	−0.910970	+	0.412473i	$0.864665\pi$
$702$	−2.62470	+	2.41232i	−0.0990628	+	0.0910471i
$703$		−	19.5934i		−	0.738981i
$704$	1.05788	−	4.09458i	0.0398702	−	0.154320i
$705$	5.09350			0.191832
$706$	−35.9195	+	33.0130i	−1.35185	+	1.24246i
$707$		−	1.17121i		−	0.0440480i
$708$	−16.8334	−	1.42204i	−0.632638	−	0.0534436i
$709$	25.6113			0.961854			0.480927	−	0.876761i	$-0.340300\pi$
$709$	25.6113			0.961854			0.480927	+	0.876761i	$0.340300\pi$
$710$	−6.03162	−	6.56264i	−0.226363	−	0.246291i
$711$	−2.66595			−0.0999808
$712$	−6.62580	+	5.13152i	−0.248312	+	0.192312i
$713$			23.4397i			0.877825i
$714$	8.95717	+	9.74575i	0.335214	+	0.364726i
$715$	1.81658			0.0679362
$716$	−2.73192	+	32.3391i	−0.102097	+	1.20857i
$717$	1.14012			0.0425785
$718$	−20.6571	+	18.9856i	−0.770917	+	0.708538i
$719$		−	22.2369i		−	0.829296i	−0.909982	−	0.414648i	$-0.863905\pi$
$719$		−	22.2369i		−	0.829296i	0.909982	−	0.414648i	$-0.136095\pi$
$720$	−0.914781	+	5.37572i	−0.0340919	+	0.200341i
$721$			9.92846i			0.369755i
$722$	12.1477	+	13.2171i	0.452089	+	0.491891i
$723$	−5.93089			−0.220572
$724$	0.999781	−	11.8349i	0.0371566	−	0.439841i
$725$	−24.0431			−0.892939
$726$	−10.2594	−	11.1627i	−0.380763	−	0.414285i
$727$	−44.1322			−1.63677			−0.818387	−	0.574668i	$-0.805131\pi$
$727$	−44.1322			−1.63677			−0.818387	+	0.574668i	$0.805131\pi$
$728$	−6.83833	−	8.82963i	−0.253446	−	0.327248i
$729$	1.00000			0.0370370
$730$	−17.2579	+	15.8614i	−0.638742	+	0.587058i
$731$	22.8673			0.845778
$732$	−4.07501	−	0.344246i	−0.150617	−	0.0127237i
$733$		−	25.1028i		−	0.927194i	−0.886046	−	0.463597i	$-0.846559\pi$
$733$		−	25.1028i		−	0.927194i	0.886046	−	0.463597i	$-0.153441\pi$
$734$	−29.1797	−	31.7487i	−1.07704	−	1.17186i
$735$			6.19785i			0.228611i
$736$	13.6414	−	8.83456i	0.502830	−	0.325646i
$737$	−4.21631	−	0.972474i	−0.155310	−	0.0358216i
$738$	11.7481	−	10.7975i	0.432455	−	0.397463i
$739$	−26.6506			−0.980358			−0.490179	−	0.871622i	$-0.663069\pi$
$739$	−26.6506			−0.980358			−0.490179	+	0.871622i	$0.663069\pi$
$740$	−21.1974	−	1.79070i	−0.779234	−	0.0658276i
$741$	−6.33020			−0.232546
$742$	18.3244	−	16.8416i	0.672709	−	0.618276i
$743$		−	24.2167i		−	0.888424i	−0.895922	−	0.444212i	$-0.853484\pi$
$743$		−	24.2167i		−	0.888424i	0.895922	−	0.444212i	$-0.146516\pi$
$744$	−18.2441	+	14.1296i	−0.668862	+	0.518017i
$745$			5.34760i			0.195921i
$746$	14.0252	−	12.8903i	0.513499	−	0.471949i
$747$		−	11.3473i		−	0.415175i
$748$	−0.531788	+	6.29503i	−0.0194441	+	0.230169i
$749$		−	5.45037i		−	0.199152i
$750$	11.5567	−	10.6216i	0.421990	−	0.387844i
$751$		−	51.6938i		−	1.88633i	−0.332321	−	0.943166i	$-0.607832\pi$
$751$		−	51.6938i		−	1.88633i	0.332321	−	0.943166i	$-0.392168\pi$
$752$	2.50717	−	14.7334i	0.0914270	−	0.537272i
$753$	−10.4883			−0.382215
$754$	20.0875	−	18.4621i	0.731543	−	0.672349i
$755$	−31.6221			−1.15085
$756$	−0.263712	+	3.12169i	−0.00959110	+	0.113535i
$757$			49.1422i			1.78610i	0.449953	+	0.893052i	$0.351441\pi$
$757$			49.1422i			1.78610i	−0.449953	+	0.893052i	$0.648559\pi$
$758$	0.670349	+	0.729366i	0.0243482	+	0.0264918i
$759$			1.51877i			0.0551277i
$760$	−7.65550	+	5.92900i	−0.277694	+	0.215067i
$761$	−42.2284			−1.53078			−0.765389	−	0.643567i	$-0.777454\pi$
$761$	−42.2284			−1.53078			−0.765389	+	0.643567i	$0.777454\pi$
$762$	−12.3110	+	11.3148i	−0.445979	+	0.409893i
$763$			22.9951i			0.832480i
$764$	2.49821	−	29.5726i	0.0903822	−	1.06990i
$765$		−	8.14586i		−	0.294514i
$766$	−19.9336	−	21.6885i	−0.720229	−	0.783638i
$767$	−21.2919			−0.768807
$768$	15.0994	+	5.29216i	0.544854	+	0.190964i
$769$		−	25.7365i		−	0.928081i	−0.885814	−	0.464040i	$-0.846399\pi$
$769$		−	25.7365i		−	0.928081i	0.885814	−	0.464040i	$-0.153601\pi$
$770$	1.17538	−	1.08028i	0.0423578	−	0.0389304i
$771$	31.3242			1.12811
$772$	−1.91545	+	22.6741i	−0.0689386	+	0.816060i
$773$	21.8098			0.784443			0.392221	−	0.919871i	$-0.371707\pi$
$773$	21.8098			0.784443			0.392221	+	0.919871i	$0.371707\pi$
$774$	3.66234	+	3.98477i	0.131640	+	0.143230i
$775$	25.6305			0.920674
$776$	23.7395	+	30.6524i	0.852200	+	1.10036i
$777$	−12.2215			−0.438445
$778$	−13.3946	−	14.5739i	−0.480221	−	0.522500i
$779$	28.3340			1.01517
$780$	−0.578535	+	6.84841i	−0.0207149	+	0.245212i
$781$		−	2.44401i		−	0.0874537i
$782$	−17.8753	+	16.4289i	−0.639219	+	0.587496i
$783$	−7.65326			−0.273505
$784$	17.9278	+	3.05076i	0.640279	+	0.108956i
$785$			2.35589i			0.0840852i
$786$	−4.66083	+	4.28369i	−0.166246	+	0.152794i
$787$	−14.5403			−0.518305			−0.259153	−	0.965836i	$-0.583443\pi$
$787$	−14.5403			−0.518305			−0.259153	+	0.965836i	$0.583443\pi$
$788$	−28.0773	−	2.37189i	−1.00021	−	0.0844952i
$789$			6.28457i			0.223737i
$790$	−3.78422	+	3.47802i	−0.134637	+	0.123742i
$791$		−	21.2147i		−	0.754307i
$792$	−1.18212	+	0.915522i	−0.0420047	+	0.0325316i
$793$	−5.15432			−0.183035
$794$	−0.374552	−	0.407527i	−0.0132923	−	0.0144626i
$795$	−15.3162			−0.543209
$796$	20.6218	+	1.74207i	0.730920	+	0.0617462i
$797$	22.2998			0.789899			0.394949	−	0.918703i	$-0.370762\pi$
$797$	22.2998			0.789899			0.394949	+	0.918703i	$0.370762\pi$
$798$	−4.09583	+	3.76441i	−0.144991	+	0.133259i
$799$			22.3256i			0.789823i
$800$	−9.66026	−	14.9164i	−0.341542	−	0.527374i
$801$	2.96297			0.104692
$802$	−14.3153	+	13.1570i	−0.505492	+	0.464590i
$803$	−6.42706			−0.226806
$804$	5.00897	−	15.5856i	0.176653	−	0.549661i
$805$	6.13506			0.216233
$806$	−21.4137	+	19.6810i	−0.754265	+	0.693233i
$807$	−15.0340			−0.529221
$808$	1.29494	+	1.67203i	0.0455559	+	0.0588217i
$809$		−	23.3384i		−	0.820536i	−0.911965	−	0.410268i	$-0.865435\pi$
$809$		−	23.3384i		−	0.820536i	0.911965	−	0.410268i	$-0.134565\pi$
$810$	1.41947	−	1.30461i	0.0498750	−	0.0458393i
$811$	7.29983			0.256332			0.128166	−	0.991753i	$-0.459091\pi$
$811$	7.29983			0.256332			0.128166	+	0.991753i	$0.459091\pi$
$812$	2.01825	−	23.8911i	0.0708268	−	0.838412i
$813$	−18.8437			−0.660879
$814$	−3.94711	−	4.29461i	−0.138346	−	0.150526i
$815$	25.9309			0.908320
$816$	−23.5626	−	4.00962i	−0.824856	−	0.140365i
$817$			9.61040i			0.336225i
$818$	−20.3727	+	18.7243i	−0.712315	+	0.654678i
$819$			3.94850i			0.137972i
$820$	2.58952	−	30.6535i	0.0904301	−	1.07047i
$821$	−35.0403			−1.22292			−0.611458	−	0.791277i	$-0.709417\pi$
$821$	−35.0403			−1.22292			−0.611458	+	0.791277i	$0.709417\pi$
$822$	3.88114	−	3.56709i	0.135370	−	0.124417i
$823$			10.4767i			0.365195i	0.983188	+	0.182597i	$0.0584505\pi$
$823$			10.4767i			0.365195i	−0.983188	+	0.182597i	$0.941550\pi$
$824$	−10.9773	−	14.1739i	−0.382413	−	0.493771i
$825$	1.66071			0.0578186
$826$	−13.7765	+	12.6618i	−0.479346	+	0.440560i
$827$			44.9087i			1.56163i	0.624764	+	0.780814i	$0.285195\pi$
$827$			44.9087i			1.56163i	−0.624764	+	0.780814i	$0.714805\pi$
$828$	−5.72567	−	0.483690i	−0.198981	−	0.0168094i
$829$	2.55939			0.0888911			0.0444456	−	0.999012i	$-0.485848\pi$
$829$	2.55939			0.0888911			0.0444456	+	0.999012i	$0.485848\pi$
$830$	−14.8038	−	16.1071i	−0.513846	−	0.559085i
$831$	6.93613			0.240612
$832$	19.5248	+	5.04445i	0.676902	+	0.174885i
$833$	−27.1661			−0.941251
$834$	9.48763	+	10.3229i	0.328530	+	0.357453i
$835$	−11.4251			−0.395381
$836$	−2.64560	−	0.223493i	−0.0915001	−	0.00772968i
$837$	8.15854			0.282000
$838$	−31.6103	+	29.0525i	−1.09196	+	1.00360i
$839$		−	25.4580i		−	0.878907i	−0.898265	−	0.439454i	$-0.855172\pi$
$839$		−	25.4580i		−	0.878907i	0.898265	−	0.439454i	$-0.144828\pi$
$840$	3.69825	+	4.77517i	0.127602	+	0.164759i
$841$	29.5723			1.01973
$842$	−7.74336	−	8.42508i	−0.266854	−	0.290347i
$843$		−	14.3372i		−	0.493799i
$844$	−23.8235	−	2.01255i	−0.820039	−	0.0692747i
$845$		−	9.05994i		−	0.311671i
$846$	−3.89038	+	3.57559i	−0.133754	+	0.122931i
$847$	−16.7927			−0.577004
$848$	−7.53907	+	44.3034i	−0.258893	+	1.52138i
$849$			15.1828i			0.521072i
$850$	17.9644	+	19.5459i	0.616173	+	0.670420i
$851$		−	22.4163i		−	0.768420i
$852$	9.21381	+	0.778358i	0.315660	+	0.0266661i
$853$	10.3963			0.355963			0.177981	−	0.984034i	$-0.443043\pi$
$853$	10.3963			0.355963			0.177981	+	0.984034i	$0.443043\pi$
$854$	−3.33500	+	3.06515i	−0.114121	+	0.104887i
$855$	3.42344			0.117079
$856$	6.02616	+	7.78095i	0.205970	+	0.265948i
$857$			11.9104i			0.406852i	0.979090	+	0.203426i	$0.0652077\pi$
$857$			11.9104i			0.406852i	−0.979090	+	0.203426i	$0.934792\pi$
$858$	−1.38749	+	1.27522i	−0.0473681	+	0.0435353i
$859$			11.2164i			0.382700i	0.981522	+	0.191350i	$0.0612865\pi$
$859$			11.2164i			0.382700i	−0.981522	+	0.191350i	$0.938713\pi$
$860$	10.3971	+	0.878323i	0.354540	+	0.0299506i
$861$		−	17.6735i		−	0.602311i
$862$	−22.2041	+	20.4074i	−0.756275	+	0.695080i
$863$			47.9119i			1.63094i	0.578799	+	0.815470i	$0.303522\pi$
$863$			47.9119i			1.63094i	−0.578799	+	0.815470i	$0.696478\pi$
$864$	−3.07499	−	4.74810i	−0.104613	−	0.161533i
$865$			5.68317i			0.193234i
$866$	−10.7357	+	9.86706i	−0.364816	+	0.335296i
$867$	18.7046			0.635240
$868$	−2.15150	+	25.4684i	−0.0730267	+	0.864453i
$869$	−1.40929			−0.0478070
$870$	−10.8635	+	9.98451i	−0.368309	+	0.338507i
$871$	4.63721	−	20.1053i	0.157126	−	0.681243i
$872$	−25.4244	−	32.8279i	−0.860979	−	1.11169i
$873$		−	13.7074i		−	0.463924i
$874$	−6.90454	−	7.51241i	−0.233549	−	0.254111i
$875$		−	17.3854i		−	0.587735i
$876$	2.04686	−	24.2297i	0.0691570	−	0.818645i
$877$	−27.5238			−0.929412			−0.464706	−	0.885465i	$-0.653840\pi$
$877$	−27.5238			−0.929412			−0.464706	+	0.885465i	$0.653840\pi$
$878$	−37.2712	+	34.2554i	−1.25784	+	1.15606i
$879$	18.5571			0.625917
$880$	−0.483579	+	2.84176i	−0.0163014	+	0.0957956i
$881$	28.1568			0.948626			0.474313	−	0.880356i	$-0.342697\pi$
$881$	28.1568			0.948626			0.474313	+	0.880356i	$0.342697\pi$
$882$	−4.35083	−	4.73387i	−0.146500	−	0.159398i
$883$	22.4001			0.753822			0.376911	−	0.926249i	$-0.376986\pi$
$883$	22.4001			0.753822			0.376911	+	0.926249i	$0.376986\pi$
$884$	−30.0176	−	2.53581i	−1.00960	−	0.0852885i
$885$	11.5149			0.387070
$886$	8.93650	+	9.72326i	0.300228	+	0.326659i
$887$			34.0814i			1.14434i	0.820134	+	0.572171i	$0.193899\pi$
$887$			34.0814i			1.14434i	−0.820134	+	0.572171i	$0.806101\pi$
$888$	17.4475	−	13.5127i	0.585500	−	0.453455i
$889$			18.5202i			0.621147i
$890$	4.20584	−	3.86553i	0.140980	−	0.129573i
$891$	0.528628			0.0177097
$892$	−39.8993	−	3.37059i	−1.33593	−	0.112856i
$893$	−9.38274			−0.313981
$894$	−3.75396	−	4.08445i	−0.125551	−	0.136605i
$895$		−	22.1216i		−	0.739444i
$896$	15.6330	−	8.34704i	0.522261	−	0.278855i
$897$	−7.24219			−0.241810
$898$	−6.06406	−	6.59793i	−0.202360	−	0.220176i
$899$	−62.4394			−2.08247
$900$	−0.528896	+	6.26081i	−0.0176299	+	0.208694i
$901$		−	67.1332i		−	2.23653i
$902$	6.21040	−	5.70788i	0.206784	−	0.190052i
$903$	5.99455			0.199486
$904$	23.4559	+	30.2861i	0.780130	+	1.00730i
$905$			8.09569i			0.269110i
$906$	24.1527	−	22.1984i	0.802420	−	0.737491i
$907$		−	35.6830i		−	1.18483i	−0.805632	−	0.592417i	$-0.798174\pi$
$907$		−	35.6830i		−	1.18483i	0.805632	−	0.592417i	$-0.201826\pi$
$908$	52.1961	+	4.40939i	1.73219	+	0.146331i
$909$		−	0.747709i		−	0.0247999i
$910$	5.15125	+	5.60476i	0.170762	+	0.185796i
$911$		−	22.3930i		−	0.741914i	−0.928650	−	0.370957i	$-0.879030\pi$
$911$		−	22.3930i		−	0.741914i	0.928650	−	0.370957i	$-0.120970\pi$
$912$	1.68512	−	9.90261i	0.0557998	−	0.327908i
$913$		−	5.99849i		−	0.198521i
$914$	2.02077	+	2.19868i	0.0668412	+	0.0727259i
$915$	2.78752			0.0921525
$916$	−4.70133	−	0.397156i	−0.155336	−	0.0131224i
$917$			7.01158i			0.231543i
$918$	5.71831	+	6.22174i	0.188732	+	0.205348i
$919$	−14.9161			−0.492036			−0.246018	−	0.969265i	$-0.579122\pi$
$919$	−14.9161			−0.492036			−0.246018	+	0.969265i	$0.579122\pi$
$920$	−8.75843	+	6.78319i	−0.288757	+	0.223635i
$921$		−	9.16937i		−	0.302141i
$922$	15.7616	+	17.1493i	0.519081	+	0.564781i
$923$	11.6542			0.383602
$924$	−0.139405	+	1.65021i	−0.00458610	+	0.0542880i
$925$	−24.5113			−0.805928
$926$	3.28300	+	3.57203i	0.107886	+	0.117384i
$927$			6.33839i			0.208180i
$928$	23.5337	+	36.3384i	0.772532	+	1.19287i
$929$		−	55.4132i		−	1.81805i	−0.416745	−	0.909023i	$-0.636829\pi$
$929$		−	55.4132i		−	1.81805i	0.416745	−	0.909023i	$-0.363171\pi$
$930$	11.5808	−	10.6437i	0.379748	−	0.349021i
$931$		−	11.4171i		−	0.374179i
$932$	17.6823	+	1.49375i	0.579201	+	0.0489294i
$933$	0.305968			0.0100169
$934$	−3.84320	+	3.53222i	−0.125753	+	0.115578i
$935$		−	4.30613i		−	0.140826i
$936$	−4.36563	−	5.63689i	−0.142695	−	0.184247i
$937$			32.0855i			1.04819i	0.851661	+	0.524094i	$0.175596\pi$
$937$			32.0855i			1.04819i	−0.851661	+	0.524094i	$0.824404\pi$
$938$	−8.95574	−	15.7664i	−0.292415	−	0.514791i
$939$		−	4.08597i		−	0.133340i
$940$	−0.857517	+	10.1508i	−0.0279691	+	0.331084i
$941$		−	50.7319i		−	1.65381i	−0.562339	−	0.826906i	$-0.690099\pi$
$941$		−	50.7319i		−	1.65381i	0.562339	−	0.826906i	$-0.309901\pi$
$942$	−1.65381	−	1.79941i	−0.0538840	−	0.0586279i
$943$	32.4160			1.05561
$944$	5.66797	−	33.3079i	0.184477	−	1.08408i
$945$		−	2.13540i		−	0.0694644i
$946$	1.93602	+	2.10646i	0.0629453	+	0.0684870i
$947$			21.3349i			0.693290i	0.937996	+	0.346645i	$0.112679\pi$
$947$			21.3349i			0.693290i	−0.937996	+	0.346645i	$0.887321\pi$
$948$	0.448825	−	5.31297i	0.0145772	−	0.172557i
$949$		−	30.6472i		−	0.994850i
$950$	−8.21453	+	7.54985i	−0.266515	+	0.244950i
$951$	−12.1082			−0.392635
$952$	−20.9303	+	16.2100i	−0.678355	+	0.525369i
$953$	−51.1663			−1.65744			−0.828720	−	0.559663i	$-0.810931\pi$
$953$	−51.1663			−1.65744			−0.828720	+	0.559663i	$0.810931\pi$
$954$	11.6984	−	10.7518i	0.378749	−	0.348102i
$955$			20.2292i			0.654601i
$956$	−0.191944	+	2.27214i	−0.00620793	+	0.0734863i
$957$	−4.04573			−0.130780
$958$	22.7951	−	20.9506i	0.736476	−	0.676884i
$959$		−	5.83865i		−	0.188540i
$960$	−10.5593	−	2.72810i	−0.340799	−	0.0880489i
$961$	35.5617			1.14715
$962$	20.4787	−	18.8216i	0.660259	−	0.606834i
$963$		−	3.47954i		−	0.112127i
$964$	0.998496	−	11.8197i	0.0321594	−	0.380687i
$965$		−	15.5103i		−	0.499294i
$966$	−4.68591	+	4.30675i	−0.150767	+	0.138567i
$967$		−	24.7300i		−	0.795264i	−0.917545	−	0.397632i	$-0.869832\pi$
$967$		−	24.7300i		−	0.795264i	0.917545	−	0.397632i	$-0.130168\pi$
$968$	23.9733	−	18.5667i	0.770531	−	0.596757i
$969$			15.0055i			0.482046i
$970$	−17.8828	−	19.4572i	−0.574181	−	0.624731i
$971$			21.2460i			0.681817i	0.940096	+	0.340908i	$0.110735\pi$
$971$			21.2460i			0.681817i	−0.940096	+	0.340908i	$0.889265\pi$
$972$	−0.168355	+	1.99290i	−0.00539999	+	0.0639223i
$973$	15.5294			0.497850
$974$	11.2244	+	12.2126i	0.359653	+	0.391317i
$975$			7.91906i			0.253613i
$976$	1.37210	−	8.06314i	0.0439197	−	0.258095i
$977$	12.6253			0.403919			0.201959	−	0.979394i	$-0.435269\pi$
$977$	12.6253			0.403919			0.201959	+	0.979394i	$0.435269\pi$
$978$	−19.8058	+	18.2032i	−0.633320	+	0.582075i
$979$	1.56631			0.0500596
$980$	−12.3517	−	1.04344i	−0.394561	−	0.0333314i
$981$			14.6802i			0.468703i
$982$	−9.22232	+	8.47610i	−0.294296	+	0.270483i
$983$	12.3440			0.393713			0.196856	−	0.980432i	$-0.436927\pi$
$983$	12.3440			0.393713			0.196856	+	0.980432i	$0.436927\pi$
$984$	19.5406	+	25.2307i	0.622930	+	0.804326i
$985$	19.2063			0.611964
$986$	−43.7637	−	47.6166i	−1.39372	−	1.51642i
$987$			5.85255i			0.186289i
$988$	1.06572	−	12.6155i	0.0339051	−	0.401351i
$989$			10.9950i			0.349620i
$990$	0.750370	−	0.689654i	0.0238483	−	0.0219186i
$991$	22.9311			0.728431			0.364215	−	0.931315i	$-0.381337\pi$
$991$	22.9311			0.728431			0.364215	+	0.931315i	$0.381337\pi$
$992$	−25.0874	−	38.7375i	−0.796527	−	1.22992i
$993$	34.6082			1.09826
$994$	7.54061	−	6.93046i	0.239174	−	0.219821i
$995$	−14.1064			−0.447202
$996$	22.6140	+	1.91037i	0.716552	+	0.0605324i
$997$	47.2660			1.49693			0.748464	−	0.663175i	$-0.230791\pi$
$997$	47.2660			1.49693			0.748464	+	0.663175i	$0.230791\pi$
$998$	20.8550	+	22.6911i	0.660154	+	0.718273i
$999$	−7.80230			−0.246854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.28	yes	34
4.3	odd	2		804.2.e.a.535.8	yes	34
67.66	odd	2		804.2.e.a.535.7	✓	34
268.267	even	2	inner	804.2.e.b.535.27	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.7	✓	34	67.66	odd	2
804.2.e.a.535.8	yes	34	4.3	odd	2
804.2.e.b.535.27	yes	34	268.267	even	2	inner
804.2.e.b.535.28	yes	34	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.956986 + 1.04124i) q^{2} +1.00000 q^{3} +(-0.168355 + 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 + 1.04124i) q^{6} +1.56640 q^{7} +(-2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.956986 + 1.04124i) q^{2} +1.00000 q^{3} +(-0.168355 + 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 + 1.04124i) q^{6} +1.56640 q^{7} +(-2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +(1.41947 - 1.30461i) q^{10} +0.528628 q^{11} +(-0.168355 + 1.99290i) q^{12} +2.52074i q^{13} +(1.49903 + 1.63100i) q^{14} -1.36325i q^{15} +(-3.94331 - 0.671030i) q^{16} +5.97533 q^{17} +(0.956986 + 1.04124i) q^{18} +2.51124i q^{19} +(2.71682 + 0.229510i) q^{20} +1.56640 q^{21} +(0.505890 + 0.550428i) q^{22} +2.87303i q^{23} +(-2.23620 + 1.73188i) q^{24} +3.14155 q^{25} +(-2.62470 + 2.41232i) q^{26} +1.00000 q^{27} +(-0.263712 + 3.12169i) q^{28} -7.65326 q^{29} +(1.41947 - 1.30461i) q^{30} +8.15854 q^{31} +(-3.07499 - 4.74810i) q^{32} +0.528628 q^{33} +(5.71831 + 6.22174i) q^{34} -2.13540i q^{35} +(-0.168355 + 1.99290i) q^{36} -7.80230 q^{37} +(-2.61480 + 2.40322i) q^{38} +2.52074i q^{39} +(2.36098 + 3.04849i) q^{40} -11.2829i q^{41} +(1.49903 + 1.63100i) q^{42} +3.82695 q^{43} +(-0.0889972 + 1.05350i) q^{44} -1.36325i q^{45} +(-2.99151 + 2.74945i) q^{46} +3.73630i q^{47} +(-3.94331 - 0.671030i) q^{48} -4.54638 q^{49} +(3.00642 + 3.27111i) q^{50} +5.97533 q^{51} +(-5.02360 - 0.424380i) q^{52} -11.2351i q^{53} +(0.956986 + 1.04124i) q^{54} -0.720652i q^{55} +(-3.50279 + 2.71282i) q^{56} +2.51124i q^{57} +(-7.32406 - 7.96886i) q^{58} +8.44668i q^{59} +(2.71682 + 0.229510i) q^{60} +2.04476i q^{61} +(7.80761 + 8.49498i) q^{62} +1.56640 q^{63} +(2.00117 - 7.74566i) q^{64} +3.43640 q^{65} +(0.505890 + 0.550428i) q^{66} +(-7.97595 - 1.83962i) q^{67} +(-1.00598 + 11.9082i) q^{68} +2.87303i q^{69} +(2.22346 - 2.04354i) q^{70} -4.62331i q^{71} +(-2.23620 + 1.73188i) q^{72} -12.1580 q^{73} +(-7.46669 - 8.12405i) q^{74} +3.14155 q^{75} +(-5.00465 - 0.422780i) q^{76} +0.828045 q^{77} +(-2.62470 + 2.41232i) q^{78} -2.66595 q^{79} +(-0.914781 + 5.37572i) q^{80} +1.00000 q^{81} +(11.7481 - 10.7975i) q^{82} -11.3473i q^{83} +(-0.263712 + 3.12169i) q^{84} -8.14586i q^{85} +(3.66234 + 3.98477i) q^{86} -7.65326 q^{87} +(-1.18212 + 0.915522i) q^{88} +2.96297 q^{89} +(1.41947 - 1.30461i) q^{90} +3.94850i q^{91} +(-5.72567 - 0.483690i) q^{92} +8.15854 q^{93} +(-3.89038 + 3.57559i) q^{94} +3.42344 q^{95} +(-3.07499 - 4.74810i) q^{96} -13.7074i q^{97} +(-4.35083 - 4.73387i) q^{98} +0.528628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Introduction

L-functions

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